books/bookvol5 fix bug 7304: )show Type has duplicate output

20160616.02.tpd.patch books/bookvol10.3 add ++X documentation on Symbol

+20160619.01.tpd.patch +src/input/allfns.input test for algebra examples

diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 6ceeb40..986e6de 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -236,8 +236,8 @@ NUMERIC= dftrig.regress e1.regress ei.regress elemnum.regress en.regress \ fixed.regress gamma.regress numericgamma.regress REGRESSTESTS= ackermann.regress \ - algaggr.regress algbrbf.regress algfacob.regress alist.regress \ - allfact.regress antoine.regress \ + algaggr.regress algbrbf.regress algfacob.regress alist.regress \ + allfact.regress allfns.regress antoine.regress \ arith.regress array1.regress array2.regress \ arrows.regress asinatan.regress asinhatanh.regress \ assign.regress atansqrt.regress \ @@ -598,7 +598,8 @@ DOC=${MNT}/${SYS}/doc/src/input FILES= ${OUT}/ackermann.input \ ${OUT}/algaggr.input ${OUT}/algbrbf.input ${OUT}/algfacob.input \ - ${OUT}/alist.input ${OUT}/allfact.input ${OUT}/antoine.input \ + ${OUT}/alist.input ${OUT}/allfact.input ${OUT}/allfns.input \ + ${OUT}/antoine.input \ ${OUT}/array1.input ${OUT}/array2.input ${OUT}/arrows.input \ ${OUT}/asinatan.input ${OUT}/asinhatanh.input \ ${OUT}/assign.input ${OUT}/atansqrt.input ${OUT}/axiom.input \ @@ -923,7 +924,8 @@ DOCFILES= \ ${DOC}/ackermann.input.dvi \ ${DOC}/algaggr.input.dvi ${DOC}/algbrbf.input.dvi \ ${DOC}/algfacob.input.dvi ${DOC}/alist.input.dvi \ - ${DOC}/allfact.input.dvi ${DOC}/antoine.input.dvi \ + ${DOC}/allfact.input.dvi ${DOC}/allfns.input.dvi \ + ${DOC}/antoine.input.dvi \ ${DOC}/arith.input.dvi ${DOC}/array1.input.dvi \ ${DOC}/array2.input.dvi ${DOC}/arrows.input.dvi \ ${DOC}/asec.input.dvi ${DOC}/asinatan.input.dvi \ diff --git a/src/input/allfns.input.pamphlet b/src/input/allfns.input.pamphlet new file mode 100644 index 0000000..8ec84bc --- /dev/null +++ b/src/input/allfns.input.pamphlet @@ -0,0 +1,65495 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input allfns.input} +\author{Timothy Daly} +\maketitle +\begin{abstract} +This is a regression test file. It calls ')display' +on every Axiom function name to check whether the +result contains ++X examples for each function from +each spad file. Functions that are complete are marked +with a ``done'' comment on the --S line. +\end{abstract} +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f allfns.output +)spool allfns.output +)set message test on +)set message auto off +)clear all + +--S 1 of 3320 +)d op ^ +--R +--R +--RThere are 7 exposed functions called ^ : +--R [1] Boolean -> Boolean from Boolean +--R [2] D -> D from D if D has BTAGG +--R [3] (D,Integer) -> D from D if D has DIVRING +--R [4] (D,Integer) -> D from D if D has GROUP +--R [5] (D,NonNegativeInteger) -> D from D if D has MONOID +--R [6] (StochasticDifferential(D2),PositiveInteger) -> +--R StochasticDifferential(D2) +--R from StochasticDifferential(D2) +--R if D2 has Join(OrderedSet,IntegralDomain) +--R [7] (D,PositiveInteger) -> D from D if D has SGROUP +--R +--RExamples of ^ from Boolean +--R +--R +--RExamples of ^ from BitAggregate +--R +--R +--RExamples of ^ from DivisionRing +--R +--R +--RExamples of ^ from Group +--R +--R +--RExamples of ^ from Monoid +--R +--R +--RExamples of ^ from StochasticDifferential +--R +--R +--RExamples of ^ from SemiGroup +--R +--E 1 + +--S 2 of 3320 +)d op ~ +--R +--R +--RThere are 2 exposed functions called ~ : +--R [1] D -> D from D if D has LOGIC +--R [2] SingleInteger -> SingleInteger from SingleInteger +--R +--RExamples of ~ from Logic +--R +--R +--RExamples of ~ from SingleInteger +--R +--E 2 + +--S 3 of 3320 +)d op = +--R +--R +--RThere are 8 exposed functions called = : +--R [1] (ArrayStack(D2),ArrayStack(D2)) -> Boolean from ArrayStack(D2) +--R if D2 has SETCAT and D2 has SETCAT +--R [2] (D,D) -> Boolean from D if D has BASTYPE +--R [3] (Dequeue(D2),Dequeue(D2)) -> Boolean from Dequeue(D2) +--R if D2 has SETCAT and D2 has SETCAT +--R [4] (D1,D1) -> Equation(D1) from Equation(D1) if D1 has TYPE +--R [5] (FortranScalarType,FortranScalarType) -> Boolean from +--R FortranScalarType +--R [6] (Heap(D2),Heap(D2)) -> Boolean from Heap(D2) +--R if D2 has SETCAT and D2 has ORDSET +--R [7] (Queue(D2),Queue(D2)) -> Boolean from Queue(D2) +--R if D2 has SETCAT and D2 has SETCAT +--R [8] (Stack(D2),Stack(D2)) -> Boolean from Stack(D2) +--R if D2 has SETCAT and D2 has SETCAT +--R +--RThere are 2 unexposed functions called = : +--R [1] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R [2] (Reference(D2),Reference(D2)) -> Boolean from Reference(D2) if +--R D2 has TYPE +--R +--RExamples of = from ArrayStack +--R +--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] +--Rb:ArrayStack INT:= arrayStack [1,2,3,4,5] +--R(a=b)@Boolean +--R +--R +--RExamples of = from BasicType +--R +--R +--RExamples of = from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rb:Dequeue INT:= dequeue [1,2,3,4,5] +--R(a=b)@Boolean +--R +--R +--RExamples of = from Equation +--R +--R +--RExamples of = from FortranScalarType +--R +--R +--RExamples of = from Heap +--R +--Ra:Heap INT:= heap [1,2,3,4,5] +--Rb:Heap INT:= heap [1,2,3,4,5] +--R(a=b)@Boolean +--R +--R +--RExamples of = from OutputForm +--R +--R +--RExamples of = from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Rb:Queue INT:= queue [1,2,3,4,5] +--R(a=b)@Boolean +--R +--R +--RExamples of = from Reference +--R +--R +--RExamples of = from Stack +--R +--Ra:Stack INT:= stack [1,2,3,4,5] +--Rb:Stack INT:= stack [1,2,3,4,5] +--R(a=b)@Boolean +--R +--E 3 + +--S 4 of 3320 +)d op + +--R +--R +--RThere are 15 exposed functions called + : +--R [1] (D,D) -> D from D if D has ABELSG +--R [2] (Color,Color) -> Color from Color +--R [3] (Database(D1),Database(D1)) -> Database(D1) from Database(D1) +--R if D1 has OrderedSetwith +--R ?.? : (%,Symbol) -> String +--R display : % -> Void +--R fullDisplay : % -> Void +--R [4] (Equation(D1),D1) -> Equation(D1) from Equation(D1) +--R if D1 has ABELSG and D1 has TYPE +--R [5] (D1,Equation(D1)) -> Equation(D1) from Equation(D1) +--R if D1 has ABELSG and D1 has TYPE +--R [6] (D1,D) -> D from D if D has FAMONC(D1,D2) and D1 has SETCAT and +--R D2 has CABMON +--R [7] (D1,FullPartialFractionExpansion(D2,D1)) -> +--R FullPartialFractionExpansion(D2,D1) +--R from FullPartialFractionExpansion(D2,D1) +--R if D2 has Join(Field,CharacteristicZero) and D1 has UPOLYC +--R (D2) +--R [8] (D,D) -> D from D if D has GRMOD(D1,D2) and D1 has COMRING and +--R D2 has ABELMON +--R [9] (PolynomialIdeals(D1,D2,D3,D4),PolynomialIdeals(D1,D2,D3,D4)) +--R -> PolynomialIdeals(D1,D2,D3,D4) +--R from PolynomialIdeals(D1,D2,D3,D4) +--R if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4 +--R has POLYCAT(D1,D2,D3) +--R [10] ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2, +--R D3) +--R if D2 has SETCAT and D3 has RING +--R [11] (D,D) -> D from D +--R if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG +--R (D1) and D3 has FLAGG(D1) +--R [12] (D,Divisor(D)) -> Divisor(D) from D +--R if D has PLACESC(D2,D3) and D2 has FIELD and D3 has +--R LOCPOWC(D2) +--R [13] (Divisor(D),D) -> Divisor(D) from D +--R if D has PLACESC(D2,D3) and D2 has FIELD and D3 has +--R LOCPOWC(D2) +--R [14] (D,D) -> Divisor(D) from D +--R if D2 has FIELD and D3 has LOCPOWC(D2) and D has PLACESC( +--R D2,D3) +--R [15] (D,D) -> D from D if D has VECTCAT(D1) and D1 has TYPE and D1 +--R has ABELSG +--R +--RThere are 5 unexposed functions called + : +--R [1] (InputForm,InputForm) -> InputForm from InputForm +--R [2] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R [3] (Pattern(D1),Pattern(D1)) -> Pattern(D1) from Pattern(D1) if D1 +--R has SETCAT +--R [4] (Stream(D2),Stream(D2)) -> Stream(D2) +--R from StreamTaylorSeriesOperations(D2) if D2 has RING +--R [5] (Point(DoubleFloat),Point(DoubleFloat)) -> Point(DoubleFloat) +--R from TubePlotTools +--R +--RExamples of + from AbelianSemiGroup +--R +--R +--RExamples of + from Color +--R +--R +--RExamples of + from Database +--R +--R +--RExamples of + from Equation +--R +--R +--RExamples of + from FreeAbelianMonoidCategory +--R +--R +--RExamples of + from FullPartialFractionExpansion +--R +--R +--RExamples of + from GradedModule +--R +--R +--RExamples of + from PolynomialIdeals +--R +--R +--RExamples of + from InputForm +--R +--R +--RExamples of + from MappingPackage4 +--R +--Rf:=(x:INT):INT +-> 3*x +--Rg:=(x:INT):INT +-> 2*x+3 +--R(f+g)(4) +--R +--R +--RExamples of + from MatrixCategory +--R +--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] +--Rm+m +--R +--R +--RExamples of + from OutputForm +--R +--R +--RExamples of + from Pattern +--R +--R +--RExamples of + from PlacesCategory +--R +--R +--RExamples of + from StreamTaylorSeriesOperations +--R +--R +--RExamples of + from TubePlotTools +--R +--R +--RExamples of + from VectorCategory +--R +--E 4 + +--S 5 of 3320 +)d op - +--R +--R +--RThere are 17 exposed functions called - : +--R [1] (D,D) -> D from D if D has ABELGRP +--R [2] D -> D from D if D has ABELGRP +--R [3] (CardinalNumber,CardinalNumber) -> Union(CardinalNumber,"failed" +--R ) +--R from CardinalNumber +--R [4] (Database(D1),Database(D1)) -> Database(D1) from Database(D1) +--R if D1 has OrderedSetwith +--R ?.? : (%,Symbol) -> String +--R display : % -> Void +--R fullDisplay : % -> Void +--R [5] (Equation(D1),D1) -> Equation(D1) from Equation(D1) +--R if D1 has ABELGRP and D1 has TYPE +--R [6] (D1,Equation(D1)) -> Equation(D1) from Equation(D1) +--R if D1 has ABELGRP and D1 has TYPE +--R [7] (D,D) -> D from D if D has GRMOD(D1,D2) and D1 has COMRING and +--R D2 has ABELMON +--R [8] D -> D from D if D has GRMOD(D1,D2) and D1 has COMRING and D2 +--R has ABELMON +--R [9] ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2,D3 +--R ) +--R if D2 has SETCAT and D3 has RING +--R [10] D -> D from D +--R if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG +--R (D1) and D3 has FLAGG(D1) +--R [11] (D,D) -> D from D +--R if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG +--R (D1) and D3 has FLAGG(D1) +--R [12] D -> Divisor(D) from D +--R if D2 has FIELD and D3 has LOCPOWC(D2) and D has PLACESC( +--R D2,D3) +--R [13] (D,Divisor(D)) -> Divisor(D) from D +--R if D has PLACESC(D2,D3) and D2 has FIELD and D3 has +--R LOCPOWC(D2) +--R [14] (Divisor(D),D) -> Divisor(D) from D +--R if D has PLACESC(D2,D3) and D2 has FIELD and D3 has +--R LOCPOWC(D2) +--R [15] (D,D) -> Divisor(D) from D +--R if D2 has FIELD and D3 has LOCPOWC(D2) and D has PLACESC( +--R D2,D3) +--R [16] (D,D) -> D from D if D has VECTCAT(D1) and D1 has TYPE and D1 +--R has ABELGRP +--R [17] D -> D from D if D has VECTCAT(D1) and D1 has TYPE and D1 has +--R ABELGRP +--R +--RThere are 5 unexposed functions called - : +--R [1] OutputForm -> OutputForm from OutputForm +--R [2] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R [3] (Stream(D2),Stream(D2)) -> Stream(D2) +--R from StreamTaylorSeriesOperations(D2) if D2 has RING +--R [4] Stream(D2) -> Stream(D2) from StreamTaylorSeriesOperations(D2) +--R if D2 has RING +--R [5] (Point(DoubleFloat),Point(DoubleFloat)) -> Point(DoubleFloat) +--R from TubePlotTools +--R +--RExamples of - from AbelianGroup +--R +--R +--RExamples of - from CardinalNumber +--R +--Rc2:=2::CardinalNumber +--Rc2-c2 +--RA1:=Aleph 1 +--RA1-c2 +--R +--R +--RExamples of - from Database +--R +--R +--RExamples of - from Equation +--R +--R +--RExamples of - from GradedModule +--R +--R +--RExamples of - from MappingPackage4 +--R +--Rf:=(x:INT):INT +-> 3*x +--Rg:=(x:INT):INT +-> 2*x+3 +--R(f-g)(4) +--R +--R +--RExamples of - from MatrixCategory +--R +--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] +--R-m +--R +--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] +--Rm-m +--R +--R +--RExamples of - from OutputForm +--R +--R +--RExamples of - from PlacesCategory +--R +--R +--RExamples of - from StreamTaylorSeriesOperations +--R +--R +--RExamples of - from TubePlotTools +--R +--R +--RExamples of - from VectorCategory +--R +--E 5 + +--S 6 of 3320 +)d op * +--R +--R +--RThere are 39 exposed functions called * : +--R [1] (Integer,D) -> D from D if D has ABELGRP +--R [2] (NonNegativeInteger,D) -> D from D if D has ABELMON +--R [3] (PositiveInteger,D) -> D from D if D has ABELSG +--R [4] (CartesianTensor(D1,D2,D3),CartesianTensor(D1,D2,D3)) -> +--R CartesianTensor(D1,D2,D3) +--R from CartesianTensor(D1,D2,D3) if D1: INT and D2: NNI and +--R D3 has COMRING +--R [5] (DoubleFloat,Color) -> Color from Color +--R [6] (PositiveInteger,Color) -> Color from Color +--R [7] (DenavitHartenbergMatrix(D2),Point(D2)) -> Point(D2) +--R from DenavitHartenbergMatrix(D2) +--R if D2 has Join(Field,TranscendentalFunctionCategory) +--R [8] (D1,D) -> D from D if D has DIRPCAT(D2,D1) and D1 has TYPE and +--R D1 has MONOID +--R [9] (D,D1) -> D from D if D has DIRPCAT(D2,D1) and D1 has TYPE and +--R D1 has MONOID +--R [10] (D1,Equation(D1)) -> Equation(D1) from Equation(D1) +--R if D1 has SGROUP and D1 has TYPE +--R [11] (Equation(D1),D1) -> Equation(D1) from Equation(D1) +--R if D1 has SGROUP and D1 has TYPE +--R [12] (D1,D2) -> D from D if D has FAMONC(D2,D1) and D2 has SETCAT +--R and D1 has CABMON +--R [13] (D1,D2) -> D from D if D has FMCAT(D1,D2) and D1 has RING and +--R D2 has SETCAT +--R [14] (D,D1) -> D from D if D has GRMOD(D1,D2) and D1 has COMRING and +--R D2 has ABELMON +--R [15] (D1,D) -> D from D if D has GRMOD(D1,D2) and D1 has COMRING and +--R D2 has ABELMON +--R [16] (PolynomialIdeals(D1,D2,D3,D4),PolynomialIdeals(D1,D2,D3,D4)) +--R -> PolynomialIdeals(D1,D2,D3,D4) +--R from PolynomialIdeals(D1,D2,D3,D4) +--R if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4 +--R has POLYCAT(D1,D2,D3) +--R [17] (D1,D) -> D from D if D has LMODULE(D1) and D1 has RNG +--R [18] ((D5 -> D6),(D4 -> D5)) -> (D4 -> D6) from MappingPackage3(D4, +--R D5,D6) +--R if D4 has SETCAT and D5 has SETCAT and D6 has SETCAT +--R [19] ((D2 -> D3),(D2 -> D3)) -> (D2 -> D3) from MappingPackage4(D2, +--R D3) +--R if D2 has SETCAT and D3 has RING +--R [20] (D1,D) -> D1 from D +--R if D has MATCAT(D2,D1,D3) and D2 has RING and D1 has FLAGG +--R (D2) and D3 has FLAGG(D2) +--R [21] (D,D1) -> D1 from D +--R if D has MATCAT(D2,D3,D1) and D2 has RING and D3 has FLAGG +--R (D2) and D1 has FLAGG(D2) +--R [22] (Integer,D) -> D from D +--R if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG +--R (D2) and D4 has FLAGG(D2) +--R [23] (D,D1) -> D from D +--R if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG +--R (D1) and D3 has FLAGG(D1) +--R [24] (D1,D) -> D from D +--R if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG +--R (D1) and D3 has FLAGG(D1) +--R [25] (D,D) -> D from D +--R if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG +--R (D1) and D3 has FLAGG(D1) +--R [26] (D,D) -> D from D if D has MONAD +--R [27] (MyExpression(D1,D2),MyExpression(D1,D2)) -> MyExpression(D1,D2 +--R ) +--R from MyExpression(D1,D2) +--R if D1: SYMBOL and D2 has Join(Ring,OrderedSet, +--R IntegralDomain) +--R [28] (Integer,D) -> Divisor(D) from D +--R if D3 has FIELD and D4 has LOCPOWC(D3) and D has PLACESC( +--R D3,D4) +--R [29] (D,D1) -> D from D if D has RMODULE(D1) and D1 has RNG +--R [30] (Matrix(Fraction(D3)),SparseEchelonMatrix(D2,D3)) -> +--R SparseEchelonMatrix(D2,D3) +--R from SparseEchelonMatrix(D2,D3) +--R if D3 has INTDOM and D3 has RING and D2 has ORDSET +--R [31] (Matrix(D3),SparseEchelonMatrix(D2,D3)) -> SparseEchelonMatrix( +--R D2,D3) +--R from SparseEchelonMatrix(D2,D3) if D3 has RING and D2 has +--R ORDSET +--R [32] (D,D) -> D from D if D has SGROUP +--R [33] (D1,D) -> D1 from D +--R if D has SMATCAT(D2,D3,D1,D4) and D3 has RING and D1 has +--R DIRPCAT(D2,D3) and D4 has DIRPCAT(D2,D3) +--R [34] (D,D1) -> D1 from D +--R if D has SMATCAT(D2,D3,D4,D1) and D3 has RING and D4 has +--R DIRPCAT(D2,D3) and D1 has DIRPCAT(D2,D3) +--R [35] (D,D1) -> D from D if D has VECTCAT(D1) and D1 has TYPE and D1 +--R has MONOID +--R [36] (D1,D) -> D from D if D has VECTCAT(D1) and D1 has TYPE and D1 +--R has MONOID +--R [37] (Integer,D) -> D from D +--R if D has VECTCAT(D2) and D2 has TYPE and D2 has ABELGRP +--R +--R [38] (D1,D) -> D from D if D has XFALG(D1,D2) and D1 has ORDSET and +--R D2 has RING +--R [39] (D,D1) -> D from D if D has XFALG(D2,D1) and D2 has ORDSET and +--R D1 has RING +--R +--RThere are 23 unexposed functions called * : +--R [1] (FreeGroup(D1),D1) -> FreeGroup(D1) from FreeGroup(D1) if D1 +--R has SETCAT +--R [2] (D1,FreeGroup(D1)) -> FreeGroup(D1) from FreeGroup(D1) if D1 +--R has SETCAT +--R [3] (D1,D2) -> FreeModule1(D2,D1) from FreeModule1(D2,D1) +--R if D2 has RING and D1 has ORDSET +--R [4] (FreeMonoid(D1),D1) -> FreeMonoid(D1) from FreeMonoid(D1) if D1 +--R has SETCAT +--R [5] (D1,FreeMonoid(D1)) -> FreeMonoid(D1) from FreeMonoid(D1) if D1 +--R has SETCAT +--R [6] (D1,GeneralModulePolynomial(D2,D3,D4,D5,D6,D1)) -> +--R GeneralModulePolynomial(D2,D3,D4,D5,D6,D1) +--R from GeneralModulePolynomial(D2,D3,D4,D5,D6,D1) +--R if D2: LIST(SYMBOL) and D3 has COMRING and D5 has DIRPCAT( +--R #(D2),NNI) and D6: ((Record(index: D4,exponent: D5),Record( +--R index: D4,exponent: D5)) -> Boolean) and D4 has ORDSET and +--R D1 has POLYCAT(D3,D5,OVAR(D2)) +--R [7] (Vector(D2),Vector(D2)) -> Vector(D2) +--R from InnerNormalBasisFieldFunctions(D2) if D2 has FFIELDC +--R +--R [8] (InputForm,InputForm) -> InputForm from InputForm +--R [9] (InnerTaylorSeries(D2),Integer) -> InnerTaylorSeries(D2) +--R from InnerTaylorSeries(D2) if D2 has RING +--R [10] (InnerTaylorSeries(D1),D1) -> InnerTaylorSeries(D1) +--R from InnerTaylorSeries(D1) if D1 has RING +--R [11] (D1,InnerTaylorSeries(D1)) -> InnerTaylorSeries(D1) +--R from InnerTaylorSeries(D1) if D1 has RING +--R [12] (Magma(D1),Magma(D1)) -> Magma(D1) from Magma(D1) if D1 has +--R ORDSET +--R [13] (OrderedFreeMonoid(D1),D1) -> OrderedFreeMonoid(D1) +--R from OrderedFreeMonoid(D1) if D1 has ORDSET +--R [14] (D1,OrderedFreeMonoid(D1)) -> OrderedFreeMonoid(D1) +--R from OrderedFreeMonoid(D1) if D1 has ORDSET +--R [15] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R [16] (Pattern(D1),Pattern(D1)) -> Pattern(D1) from Pattern(D1) if D1 +--R has SETCAT +--R [17] (D2,Vector(D3)) -> Vector(D3) from PseudoRemainderSequence(D2, +--R D3) +--R if D3 has UPOLYC(D2) and D2 has INTDOM +--R [18] (D1,SparseMultivariateTaylorSeries(D2,D3,D1)) -> +--R SparseMultivariateTaylorSeries(D2,D3,D1) +--R from SparseMultivariateTaylorSeries(D2,D3,D1) +--R if D2 has RING and D3 has ORDSET and D1 has POLYCAT(D2, +--R INDE(D3),D3) +--R [19] (Stream(D2),Stream(D2)) -> Stream(D2) +--R from StreamTaylorSeriesOperations(D2) if D2 has RING +--R [20] (D2,Stream(D2)) -> Stream(D2) from StreamTaylorSeriesOperations +--R (D2) +--R if D2 has RING +--R [21] (Stream(D2),D2) -> Stream(D2) from StreamTaylorSeriesOperations +--R (D2) +--R if D2 has RING +--R [22] (DoubleFloat,Point(DoubleFloat)) -> Point(DoubleFloat) from +--R TubePlotTools +--R [23] (XPolynomialRing(D1,D2),D1) -> XPolynomialRing(D1,D2) +--R from XPolynomialRing(D1,D2) if D1 has RING and D2 has +--R ORDMON +--R +--RExamples of * from AbelianGroup +--R +--R +--RExamples of * from AbelianMonoid +--R +--R +--RExamples of * from AbelianSemiGroup +--R +--R +--RExamples of * from CartesianTensor +--R +--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] +--RTm:CartesianTensor(1,2,Integer):=m +--Rv:DirectProduct(2,Integer):=directProduct [3,4] +--RTv:CartesianTensor(1,2,Integer):=v +--RTm*Tv +--R +--R +--RExamples of * from Color +--R +--R +--RExamples of * from DenavitHartenbergMatrix +--R +--Rrotatex(30)*point([1,2,3]) +--R +--R +--RExamples of * from DirectProductCategory +--R +--R +--RExamples of * from Equation +--R +--R +--RExamples of * from FreeAbelianMonoidCategory +--R +--R +--RExamples of * from FreeGroup +--R +--R +--RExamples of * from FreeModule1 +--R +--R +--RExamples of * from FreeModuleCat +--R +--R +--RExamples of * from FreeMonoid +--R +--R +--RExamples of * from GeneralModulePolynomial +--R +--R +--RExamples of * from GradedModule +--R +--R +--RExamples of * from PolynomialIdeals +--R +--R +--RExamples of * from InnerNormalBasisFieldFunctions +--R +--R +--RExamples of * from InputForm +--R +--R +--RExamples of * from InnerTaylorSeries +--R +--R +--RExamples of * from LeftModule +--R +--R +--RExamples of * from Magma +--R +--R +--RExamples of * from MappingPackage3 +--R +--R +--RExamples of * from MappingPackage4 +--R +--Rf:=(x:INT):INT +-> 3*x +--Rg:=(x:INT):INT +-> 2*x+3 +--R(f*g)(4) +--R +--R +--RExamples of * from MatrixCategory +--R +--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] +--Rr:=transpose([1,2,3,4,5])@Matrix(INT) +--Rr*m +--R +--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] +--Rc:=coerce([1,2,3,4,5])@Matrix(INT) +--Rm*c +--R +--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] +--R3*m +--R +--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] +--Rm*1/3 +--R +--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] +--R1/3*m +--R +--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] +--Rm*m +--R +--R +--RExamples of * from Monad +--R +--R +--RExamples of * from MyExpression +--R +--R +--RExamples of * from OrderedFreeMonoid +--R +--Rm1:=(y**3)$OFMONOID(Symbol) +--Rm1*x +--R +--Rm1:=(x*y*y*z)$OFMONOID(Symbol) +--Rx*m1 +--R +--R +--RExamples of * from OutputForm +--R +--R +--RExamples of * from Pattern +--R +--R +--RExamples of * from PlacesCategory +--R +--R +--RExamples of * from PseudoRemainderSequence +--R +--R +--RExamples of * from RightModule +--R +--R +--RExamples of * from SparseEchelonMatrix +--R +--R +--RExamples of * from SemiGroup +--R +--R +--RExamples of * from SquareMatrixCategory +--R +--R +--RExamples of * from SparseMultivariateTaylorSeries +--R +--R +--RExamples of * from StreamTaylorSeriesOperations +--R +--R +--RExamples of * from TubePlotTools +--R +--R +--RExamples of * from VectorCategory +--R +--R +--RExamples of * from XFreeAlgebra +--R +--R +--RExamples of * from XPolynomialRing +--R +--E 6 + +--S 7 of 3320 +)d op / +--R +--R +--RThere are 15 exposed functions called / : +--R [1] (D,D1) -> D from D +--R if D has AMR(D1,D2) and D1 has RING and D2 has OAMON and +--R D1 has FIELD +--R [2] (DoubleFloat,Integer) -> DoubleFloat from DoubleFloat +--R [3] (D,D) -> D from D +--R if D = EQ(D1) and D1 has FIELD and D1 has TYPE or D = EQ( +--R D1) and D1 has GROUP and D1 has TYPE +--R [4] (D,D) -> D from D if D has FIELD +--R [5] (Float,Integer) -> Float from Float +--R [6] (SparseMultivariatePolynomial(D2,Kernel(D)), +--R SparseMultivariatePolynomial(D2,Kernel(D))) -> D +--R from D if D2 has INTDOM and D2 has ORDSET and D has FS(D2) +--R +--R [7] (D,D) -> D from D if D has GROUP +--R [8] (D,D1) -> D from D if D has LIECAT(D1) and D1 has COMRING and D1 +--R has FIELD +--R [9] ((D2 -> Expression(Integer)),(D2 -> Expression(Integer))) -> (D2 +--R -> Expression(Integer)) +--R from MappingPackage4(D2,D3) if D2 has SETCAT and D3 has +--R RING +--R [10] (D,D1) -> D from D +--R if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG +--R (D1) and D3 has FLAGG(D1) and D1 has FIELD +--R [11] (MyExpression(D1,D2),MyExpression(D1,D2)) -> MyExpression(D1,D2 +--R ) +--R from MyExpression(D1,D2) +--R if D1: SYMBOL and D2 has Join(Ring,OrderedSet, +--R IntegralDomain) +--R [12] (D1,D1) -> D from D if D has QFCAT(D1) and D1 has INTDOM +--R [13] (D,D1) -> D from D +--R if D has RMATCAT(D2,D3,D1,D4,D5) and D1 has RING and D4 +--R has DIRPCAT(D3,D1) and D5 has DIRPCAT(D2,D1) and D1 has +--R FIELD +--R [14] (StochasticDifferential(D2),Expression(D2)) -> +--R StochasticDifferential(D2) +--R from StochasticDifferential(D2) +--R if D2 has Join(OrderedSet,IntegralDomain) +--R [15] (D,D1) -> D from D if D has VSPACE(D1) and D1 has FIELD +--R +--RThere are 12 unexposed functions called / : +--R [1] (Vector(D2),Vector(D2)) -> Vector(D2) +--R from InnerNormalBasisFieldFunctions(D2) if D2 has FFIELDC +--R +--R [2] (InputForm,InputForm) -> InputForm from InputForm +--R [3] (D1,D2) -> LocalAlgebra(D1,D3,D2) from LocalAlgebra(D1,D3,D2) +--R if D3 has COMRING and D1 has ALGEBRA(D3) and D2 has +--R SubsetCategory(Monoid,D3) +--R [4] (LocalAlgebra(D2,D3,D1),D1) -> LocalAlgebra(D2,D3,D1) +--R from LocalAlgebra(D2,D3,D1) +--R if D3 has COMRING and D2 has ALGEBRA(D3) and D1 has +--R SubsetCategory(Monoid,D3) +--R [5] (D1,D2) -> Localize(D1,D3,D2) from Localize(D1,D3,D2) +--R if D3 has COMRING and D1 has MODULE(D3) and D2 has +--R SubsetCategory(Monoid,D3) +--R [6] (Localize(D2,D3,D1),D1) -> Localize(D2,D3,D1) from Localize(D2, +--R D3,D1) +--R if D3 has COMRING and D2 has MODULE(D3) and D1 has +--R SubsetCategory(Monoid,D3) +--R [7] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R [8] (OrdinaryWeightedPolynomials(D1,D2,D3,D4), +--R OrdinaryWeightedPolynomials(D1,D2,D3,D4)) -> Union( +--R OrdinaryWeightedPolynomials(D1,D2,D3,D4),"failed") +--R from OrdinaryWeightedPolynomials(D1,D2,D3,D4) +--R if D1 has FIELD and D1 has RING and D2: LIST(SYMBOL) and +--R D3: LIST(NNI) and D4: NNI +--R [9] (Pattern(D1),Pattern(D1)) -> Pattern(D1) from Pattern(D1) if D1 +--R has SETCAT +--R [10] (Stream(D2),Stream(D2)) -> Stream(D2) +--R from StreamTaylorSeriesOperations(D2) if D2 has RING +--R [11] (WeightedPolynomials(D1,D2,D3,D4,D5,D6,D7),WeightedPolynomials( +--R D1,D2,D3,D4,D5,D6,D7)) -> Union(WeightedPolynomials(D1,D2,D3,D4, +--R D5,D6,D7),"failed") +--R from WeightedPolynomials(D1,D2,D3,D4,D5,D6,D7) +--R if D1 has FIELD and D1 has RING and D2 has ORDSET and D3 +--R has OAMONS and D5: LIST(D2) and D4 has POLYCAT(D1,D3,D2) +--R and D6: LIST(NNI) and D7: NNI +--R [12] (XPolynomialRing(D1,D2),D1) -> XPolynomialRing(D1,D2) +--R from XPolynomialRing(D1,D2) +--R if D1 has FIELD and D1 has RING and D2 has ORDMON +--R +--RExamples of / from AbelianMonoidRing +--R +--R +--RExamples of / from DoubleFloat +--R +--R +--RExamples of / from Equation +--R +--R +--RExamples of / from Field +--R +--R +--RExamples of / from Float +--R +--R +--RExamples of / from FunctionSpace +--R +--R +--RExamples of / from Group +--R +--R +--RExamples of / from InnerNormalBasisFieldFunctions +--R +--R +--RExamples of / from InputForm +--R +--R +--RExamples of / from LocalAlgebra +--R +--R +--RExamples of / from LieAlgebra +--R +--R +--RExamples of / from Localize +--R +--R +--RExamples of / from MappingPackage4 +--R +--Rp:=(x:EXPR(INT)):EXPR(INT)+->3*x +--Rq:=(x:EXPR(INT)):EXPR(INT)+->2*x+3 +--R(p/q)(4) +--R(p/q)(x) +--R +--R +--RExamples of / from MatrixCategory +--R +--Rm:=matrix [[2**i for i in 2..4] for j in 1..5] +--Rm/4 +--R +--R +--RExamples of / from MyExpression +--R +--R +--RExamples of / from OutputForm +--R +--R +--RExamples of / from OrdinaryWeightedPolynomials +--R +--R +--RExamples of / from Pattern +--R +--R +--RExamples of / from QuotientFieldCategory +--R +--R +--RExamples of / from RectangularMatrixCategory +--R +--R +--RExamples of / from StochasticDifferential +--R +--R +--RExamples of / from StreamTaylorSeriesOperations +--R +--R +--RExamples of / from VectorSpace +--R +--R +--RExamples of / from WeightedPolynomials +--R +--R +--RExamples of / from XPolynomialRing +--R +--E 7 + +--S 8 of 3320 +)d op ** +--R +--R +--RThere are 22 exposed functions called ** : +--R [1] (CardinalNumber,CardinalNumber) -> CardinalNumber from +--R CardinalNumber +--R [2] (DoubleFloat,DoubleFloat) -> DoubleFloat from DoubleFloat +--R [3] (D,Integer) -> D from D if D has DIVRING +--R [4] (D,D) -> D from D if D has ELEMFUN +--R [5] (Float,Float) -> Float from Float +--R [6] (D,NonNegativeInteger) -> D from D +--R if D has FS(D2) and D2 has ORDSET and D2 has SGROUP +--R [7] (D,Integer) -> D from D if D has GROUP +--R [8] (PolynomialIdeals(D2,D3,D4,D5),NonNegativeInteger) -> +--R PolynomialIdeals(D2,D3,D4,D5) +--R from PolynomialIdeals(D2,D3,D4,D5) +--R if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D5 +--R has POLYCAT(D2,D3,D4) +--R [9] ((D3 -> D3),NonNegativeInteger) -> (D3 -> D3) from +--R MappingPackage1(D3) +--R if D3 has SETCAT +--R [10] (D,Integer) -> D from D +--R if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG +--R (D2) and D4 has FLAGG(D2) and D2 has FIELD +--R [11] (D,NonNegativeInteger) -> D from D +--R if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG +--R (D2) and D4 has FLAGG(D2) +--R [12] (ModuleOperator(D2,D3),Integer) -> ModuleOperator(D2,D3) +--R from ModuleOperator(D2,D3) if D2 has RING and D3 has +--R LMODULE(D2) +--R [13] (BasicOperator,Integer) -> ModuleOperator(D3,D4) +--R from ModuleOperator(D3,D4) if D3 has RING and D4 has +--R LMODULE(D3) +--R [14] (D,PositiveInteger) -> D from D if D has MONAD +--R [15] (D,NonNegativeInteger) -> D from D if D has MONADWU +--R [16] (D,NonNegativeInteger) -> D from D if D has MONOID +--R [17] (MyExpression(D1,D2),MyExpression(D1,D2)) -> MyExpression(D1,D2 +--R ) +--R from MyExpression(D1,D2) +--R if D1: SYMBOL and D2 has Join(Ring,OrderedSet, +--R IntegralDomain) +--R [18] (D,Fraction(Integer)) -> D from D if D has RADCAT +--R [19] (StochasticDifferential(D2),PositiveInteger) -> +--R StochasticDifferential(D2) +--R from StochasticDifferential(D2) +--R if D2 has Join(OrderedSet,IntegralDomain) +--R [20] (D,PositiveInteger) -> D from D if D has SGROUP +--R [21] (D,Integer) -> D from D +--R if D has SMATCAT(D2,D3,D4,D5) and D3 has RING and D4 has +--R DIRPCAT(D2,D3) and D5 has DIRPCAT(D2,D3) and D3 has FIELD +--R +--R [22] (D,D1) -> D from D if D has UTSCAT(D1) and D1 has RING and D1 +--R has FIELD +--R +--RThere are 18 unexposed functions called ** : +--R [1] (D1,Fraction(Integer)) -> D1 from AlgebraicFunction(D3,D1) +--R if D3 has RETRACT(INT) and D3 has Join(OrderedSet, +--R IntegralDomain) and D1 has FS(D3) +--R [2] (D1,D1) -> D1 from CombinatorialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R [3] (D1,Fraction(Integer)) -> D1 +--R from ElementaryFunctionsUnivariateLaurentSeries(D3,D4,D1) +--R if D3 has FIELD and D3 has ALGEBRA(FRAC(INT)) and D4 has +--R UTSCAT(D3) and D1 has ULSCCAT(D3,D4) +--R [4] (D1,Fraction(Integer)) -> D1 +--R from ElementaryFunctionsUnivariatePuiseuxSeries(D3,D4,D1, +--R D5) +--R if D3 has FIELD and D3 has ALGEBRA(FRAC(INT)) and D4 has +--R ULSCAT(D3) and D1 has UPXSCCA(D3,D4) and D5 has PTRANFN(D4) +--R +--R [5] (D1,Integer) -> FreeGroup(D1) from FreeGroup(D1) if D1 has +--R SETCAT +--R [6] (D1,NonNegativeInteger) -> FreeMonoid(D1) from FreeMonoid(D1) +--R if D1 has SETCAT +--R [7] (Vector(D3),Integer) -> Vector(D3) +--R from InnerNormalBasisFieldFunctions(D3) if D3 has FFIELDC +--R +--R [8] (InputForm,Integer) -> InputForm from InputForm +--R [9] (InputForm,NonNegativeInteger) -> InputForm from InputForm +--R [10] (Matrix(D3),NonNegativeInteger) -> Matrix(D3) +--R from StorageEfficientMatrixOperations(D3) if D3 has RING +--R +--R [11] (D1,NonNegativeInteger) -> OrderedFreeMonoid(D1) +--R from OrderedFreeMonoid(D1) if D1 has ORDSET +--R [12] (Operator(D2),Integer) -> Operator(D2) from Operator(D2) if D2 +--R has RING +--R [13] (BasicOperator,Integer) -> Operator(D3) from Operator(D3) if D3 +--R has RING +--R [14] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R [15] (Pattern(D1),Pattern(D1)) -> Pattern(D1) from Pattern(D1) if D1 +--R has SETCAT +--R [16] (Pattern(D2),NonNegativeInteger) -> Pattern(D2) from Pattern(D2 +--R ) +--R if D2 has SETCAT +--R [17] (Stream(D2),Stream(D2)) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [18] (Stream(D2),Stream(D2)) -> Stream(D2) +--R from StreamTranscendentalFunctions(D2) if D2 has ALGEBRA( +--R FRAC(INT)) +--R +--RExamples of ** from AlgebraicFunction +--R +--R +--RExamples of ** from CardinalNumber +--R +--Rc2:=2::CardinalNumber +--Rc2**c2 +--RA1:=Aleph 1 +--RA1**c2 +--RgeneralizedContinuumHypothesisAssumed true +--RA1**A1 +--R +--R +--RExamples of ** from CombinatorialFunction +--R +--R +--RExamples of ** from DoubleFloat +--R +--R +--RExamples of ** from DivisionRing +--R +--R +--RExamples of ** from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of ** from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of ** from ElementaryFunctionCategory +--R +--R +--RExamples of ** from FreeGroup +--R +--R +--RExamples of ** from Float +--R +--R +--RExamples of ** from FreeMonoid +--R +--R +--RExamples of ** from FunctionSpace +--R +--R +--RExamples of ** from Group +--R +--R +--RExamples of ** from PolynomialIdeals +--R +--R +--RExamples of ** from InnerNormalBasisFieldFunctions +--R +--R +--RExamples of ** from InputForm +--R +--R +--RExamples of ** from MappingPackage1 +--R +--R +--RExamples of ** from MatrixCategory +--R +--R(matrix [[j**i for i in 0..4] for j in 1..5]) ** 2 +--R +--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] +--Rm**3 +--R +--R +--RExamples of ** from StorageEfficientMatrixOperations +--R +--R +--RExamples of ** from ModuleOperator +--R +--R +--RExamples of ** from Monad +--R +--R +--RExamples of ** from MonadWithUnit +--R +--R +--RExamples of ** from Monoid +--R +--R +--RExamples of ** from MyExpression +--R +--R +--RExamples of ** from OrderedFreeMonoid +--R +--Rm1:=(y**3)$OFMONOID(Symbol) +--R +--R +--RExamples of ** from Operator +--R +--R +--RExamples of ** from OutputForm +--R +--R +--RExamples of ** from Pattern +--R +--R +--RExamples of ** from RadicalCategory +--R +--R +--RExamples of ** from StochasticDifferential +--R +--R +--RExamples of ** from SemiGroup +--R +--R +--RExamples of ** from SquareMatrixCategory +--R +--R +--RExamples of ** from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of ** from StreamTranscendentalFunctions +--R +--R +--RExamples of ** from UnivariateTaylorSeriesCategory +--R +--E 8 + +--S 9 of 3320 +)d op /\ +--R +--R +--RThere are 2 exposed functions called /\ : +--R [1] (D,D) -> D from D if D has LOGIC +--R [2] (SingleInteger,SingleInteger) -> SingleInteger from +--R SingleInteger +--R +--RExamples of /\ from Logic +--R +--R +--RExamples of /\ from SingleInteger +--R +--E 9 + +--S 10 of 3320 +)d op \/ +--R +--R +--RThere are 2 exposed functions called \/ : +--R [1] (D,D) -> D from D if D has LOGIC +--R [2] (SingleInteger,SingleInteger) -> SingleInteger from +--R SingleInteger +--R +--RExamples of \/ from Logic +--R +--R +--RExamples of \/ from SingleInteger +--R +--E 10 + +--S 11 of 3320 +)d op # +--R +--R +--RThere are 7 exposed functions called # : +--R [1] D -> NonNegativeInteger from D if D has finiteAggregate and D +--R has AGG +--R [2] ArrayStack(D2) -> NonNegativeInteger from ArrayStack(D2) +--R if $ has finiteAggregate and D2 has SETCAT +--R [3] Dequeue(D2) -> NonNegativeInteger from Dequeue(D2) +--R if $ has finiteAggregate and D2 has SETCAT +--R [4] Heap(D2) -> NonNegativeInteger from Heap(D2) +--R if $ has finiteAggregate and D2 has ORDSET +--R [5] Queue(D2) -> NonNegativeInteger from Queue(D2) +--R if $ has finiteAggregate and D2 has SETCAT +--R [6] D -> Integer from D +--R if D has SEXCAT(D2,D3,D4,D5,D6) and D2 has SETCAT and D3 +--R has SETCAT and D4 has SETCAT and D5 has SETCAT and D6 has +--R SETCAT +--R [7] Stack(D2) -> NonNegativeInteger from Stack(D2) +--R if $ has finiteAggregate and D2 has SETCAT +--R +--RThere is one unexposed function called # : +--R [1] XPolynomialRing(D2,D3) -> NonNegativeInteger from +--R XPolynomialRing(D2,D3) +--R if D2 has RING and D3 has ORDMON +--R +--RExamples of # from Aggregate +--R +--R +--RExamples of # from ArrayStack +--R +--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] +--R#a +--R +--R +--RExamples of # from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--R#a +--R +--R +--RExamples of # from Heap +--R +--Ra:Heap INT:= heap [1,2,3,4,5] +--R#a +--R +--R +--RExamples of # from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--R#a +--R +--R +--RExamples of # from SExpressionCategory +--R +--R +--RExamples of # from Stack +--R +--Ra:Stack INT:= stack [1,2,3,4,5] +--R#a +--R +--R +--RExamples of # from XPolynomialRing +--R +--E 11 + +--S 12 of 3320 +)d op ^= +--R +--R +--RThere is one unexposed function called ^= : +--R [1] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R +--RExamples of ^= from OutputForm +--R +--E 12 + +--S 13 of 3320 +)d op ^ +--R +--R +--RThere are 7 exposed functions called ^ : +--R [1] Boolean -> Boolean from Boolean +--R [2] D -> D from D if D has BTAGG +--R [3] (D,Integer) -> D from D if D has DIVRING +--R [4] (D,Integer) -> D from D if D has GROUP +--R [5] (D,NonNegativeInteger) -> D from D if D has MONOID +--R [6] (StochasticDifferential(D2),PositiveInteger) -> +--R StochasticDifferential(D2) +--R from StochasticDifferential(D2) +--R if D2 has Join(OrderedSet,IntegralDomain) +--R [7] (D,PositiveInteger) -> D from D if D has SGROUP +--R +--RExamples of ^ from Boolean +--R +--R +--RExamples of ^ from BitAggregate +--R +--R +--RExamples of ^ from DivisionRing +--R +--R +--RExamples of ^ from Group +--R +--R +--RExamples of ^ from Monoid +--R +--R +--RExamples of ^ from StochasticDifferential +--R +--R +--RExamples of ^ from SemiGroup +--R +--E 13 + +--S 14 of 3320 +)d op ~= +--R +--R +--RThere are 6 exposed functions called ~= : +--R [1] (ArrayStack(D2),ArrayStack(D2)) -> Boolean from ArrayStack(D2) +--R if D2 has SETCAT and D2 has SETCAT +--R [2] (D,D) -> Boolean from D if D has BASTYPE +--R [3] (Dequeue(D2),Dequeue(D2)) -> Boolean from Dequeue(D2) +--R if D2 has SETCAT and D2 has SETCAT +--R [4] (Heap(D2),Heap(D2)) -> Boolean from Heap(D2) +--R if D2 has SETCAT and D2 has ORDSET +--R [5] (Queue(D2),Queue(D2)) -> Boolean from Queue(D2) +--R if D2 has SETCAT and D2 has SETCAT +--R [6] (Stack(D2),Stack(D2)) -> Boolean from Stack(D2) +--R if D2 has SETCAT and D2 has SETCAT +--R +--RExamples of ~= from ArrayStack +--R +--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] +--Rb:=copy a +--R(a~=b) +--R +--R +--RExamples of ~= from BasicType +--R +--R +--RExamples of ~= from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rb:=copy a +--R(a~=b) +--R +--R +--RExamples of ~= from Heap +--R +--Ra:Heap INT:= heap [1,2,3,4,5] +--Rb:=copy a +--R(a~=b) +--R +--R +--RExamples of ~= from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Rb:=copy a +--R(a~=b) +--R +--R +--RExamples of ~= from Stack +--R +--Ra:Stack INT:= stack [1,2,3,4,5] +--Rb:=copy a +--R(a~=b) +--R +--E 14 + +--S 15 of 3320 +)d op <= +--R +--R +--RThere are 3 exposed functions called <= : +--R [1] (D,D) -> Boolean from D if D has DIVCAT(D2) and D2 has SETCAT +--R +--R [2] (D,D) -> Boolean from D if D has ORDSET +--R [3] (PermutationGroup(D2),PermutationGroup(D2)) -> Boolean +--R from PermutationGroup(D2) if D2 has SETCAT +--R +--RThere is one unexposed function called <= : +--R [1] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R +--RExamples of <= from DivisorCategory +--R +--R +--RExamples of <= from OrderedSet +--R +--R +--RExamples of <= from OutputForm +--R +--R +--RExamples of <= from PermutationGroup +--R +--E 15 + +--S 16 of 3320 +)d op < +--R +--R +--RThere are 4 exposed functions called < : +--R [1] (D,D) -> Boolean from D if D has ORDSET +--R [2] (D,D) -> Boolean from D if D has PERMCAT(D2) and D2 has SETCAT +--R +--R [3] (PermutationGroup(D2),PermutationGroup(D2)) -> Boolean +--R from PermutationGroup(D2) if D2 has SETCAT +--R [4] (D,D) -> Boolean from D if D has SETAGG(D2) and D2 has SETCAT +--R +--R +--RThere is one unexposed function called < : +--R [1] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R +--RExamples of < from OrderedSet +--R +--R +--RExamples of < from OutputForm +--R +--R +--RExamples of < from PermutationCategory +--R +--R +--RExamples of < from PermutationGroup +--R +--R +--RExamples of < from SetAggregate +--R +--E 16 + +--S 17 of 3320 +)d op >= +--R +--R +--RThere is one exposed function called >= : +--R [1] (D,D) -> Boolean from D if D has ORDSET +--R +--RThere is one unexposed function called >= : +--R [1] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R +--RExamples of >= from OrderedSet +--R +--R +--RExamples of >= from OutputForm +--R +--E 17 + +--S 18 of 3320 +)d op > +--R +--R +--RThere is one exposed function called > : +--R [1] (D,D) -> Boolean from D if D has ORDSET +--R +--RThere is one unexposed function called > : +--R [1] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R +--RExamples of > from OrderedSet +--R +--R +--RExamples of > from OutputForm +--R +--E 18 + +--S 19 of 3320 +--R--)d op 0 +--E 19 + +--S 20 of 3320 +--R--)d op 1 +--E 20 + +--S 21 of 3320 +)d op abelianGroup +--R +--R +--RThere is one exposed function called abelianGroup : +--R [1] List(PositiveInteger) -> PermutationGroup(Integer) +--R from PermutationGroupExamples +--R +--RExamples of abelianGroup from PermutationGroupExamples +--R +--E 21 + +--S 22 of 3320 +)d op abs +--R +--R +--RThere are 7 exposed functions called abs : +--R [1] D -> D from D if D has COMPCAT(D1) and D1 has COMRING and D1 +--R has RNS +--R [2] FortranExpression(D1,D2,D3) -> FortranExpression(D1,D2,D3) +--R from FortranExpression(D1,D2,D3) +--R if D1: LIST(SYMBOL) and D2: LIST(SYMBOL) and D3 has FMTC +--R +--R [3] D -> D1 from D if D has OC(D1) and D1 has COMRING and D1 has RNS +--R +--R [4] D -> D from D if D has ORDRING +--R [5] D -> D1 from D if D has QUATCAT(D1) and D1 has COMRING and D1 +--R has RNS +--R [6] D -> D from D if D has RNS +--R [7] D -> D from D if D has SPFCAT +--R +--RThere is one unexposed function called abs : +--R [1] D1 -> D1 from FunctionalSpecialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R +--RExamples of abs from ComplexCategory +--R +--R +--RExamples of abs from FortranExpression +--R +--R +--RExamples of abs from FunctionalSpecialFunction +--R +--R +--RExamples of abs from OctonionCategory +--R +--R +--RExamples of abs from OrderedRing +--R +--R +--RExamples of abs from QuaternionCategory +--R +--R +--RExamples of abs from RealNumberSystem +--R +--R +--RExamples of abs from SpecialFunctionCategory +--R +--E 22 + +--S 23 of 3320 done +)d op absolutelyIrreducible? +--R +--R +--RThere is one exposed function called absolutelyIrreducible? : +--R [1] -> Boolean from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC( +--R D2) and D4 has UPOLYC(FRAC(D3)) +--R +--RThere is one unexposed function called absolutelyIrreducible? : +--R [1] -> Boolean from FunctionFieldCategory&(D2,D3,D4,D5) +--R if D3 has UFD and D4 has UPOLYC(D3) and D5 has UPOLYC(FRAC +--R (D4)) and D2 has FFCAT(D3,D4,D5) +--R +--RExamples of absolutelyIrreducible? from FunctionFieldCategory& +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4) +--RabsolutelyIrreducible?()$R2 +--R +--R +--RExamples of absolutelyIrreducible? from FunctionFieldCategory +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4) +--RabsolutelyIrreducible?()$R2 +--R +--E 23 + +--S 24 of 3320 +)d op accuracyIF +--R +--R +--RThere is one exposed function called accuracyIF : +--R [1] Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector( +--R Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List( +--R DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat, +--R relerr: DoubleFloat) -> Float +--R from d02AgentsPackage +--R +--RExamples of accuracyIF from d02AgentsPackage +--R +--E 24 + +--S 25 of 3320 done +)d op aColumn +--R +--R +--RThere is one exposed function called aColumn : +--R [1] (D1,PositiveInteger) -> D1 from MatrixManipulation(D3,D4,D5,D1) +--R if D3 has FIELD and D4 has FLAGG(D3) and D5 has FLAGG(D3) +--R and D1 has MATCAT(D3,D4,D5) +--R +--RExamples of aColumn from MatrixManipulation +--R +--RM := matrix([[a,b,c],[d,e,f],[g,h,i]]) +--RaColumn(M, 2) +--R +--E 25 + +--S 26 of 3320 +)d op acos +--R +--R +--RThere are 2 exposed functions called acos : +--R [1] D -> D from D if D has ATRIG +--R [2] FortranExpression(D1,D2,D3) -> FortranExpression(D1,D2,D3) +--R from FortranExpression(D1,D2,D3) +--R if D1: LIST(SYMBOL) and D2: LIST(SYMBOL) and D3 has FMTC +--R +--R +--RThere are 5 unexposed functions called acos : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of acos from ArcTrigonometricFunctionCategory +--R +--R +--RExamples of acos from ElementaryFunction +--R +--R +--RExamples of acos from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of acos from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of acos from FortranExpression +--R +--R +--RExamples of acos from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of acos from StreamTranscendentalFunctions +--R +--E 26 + +--S 27 of 3320 +)d op acosh +--R +--R +--RThere is one exposed function called acosh : +--R [1] D -> D from D if D has AHYP +--R +--RThere are 5 unexposed functions called acosh : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of acosh from ArcHyperbolicFunctionCategory +--R +--R +--RExamples of acosh from ElementaryFunction +--R +--R +--RExamples of acosh from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of acosh from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of acosh from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of acosh from StreamTranscendentalFunctions +--R +--E 27 + +--S 28 of 3320 +)d op acoshIfCan +--R +--R +--RThere is one exposed function called acoshIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of acoshIfCan from PartialTranscendentalFunctions +--R +--E 28 + +--S 29 of 3320 +)d op acosIfCan +--R +--R +--RThere is one exposed function called acosIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of acosIfCan from PartialTranscendentalFunctions +--R +--E 29 + +--S 30 of 3320 +)d op acot +--R +--R +--RThere is one exposed function called acot : +--R [1] D -> D from D if D has ATRIG +--R +--RThere are 5 unexposed functions called acot : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of acot from ArcTrigonometricFunctionCategory +--R +--R +--RExamples of acot from ElementaryFunction +--R +--R +--RExamples of acot from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of acot from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of acot from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of acot from StreamTranscendentalFunctions +--R +--E 30 + +--S 31 of 3320 +)d op acoth +--R +--R +--RThere is one exposed function called acoth : +--R [1] D -> D from D if D has AHYP +--R +--RThere are 5 unexposed functions called acoth : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of acoth from ArcHyperbolicFunctionCategory +--R +--R +--RExamples of acoth from ElementaryFunction +--R +--R +--RExamples of acoth from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of acoth from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of acoth from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of acoth from StreamTranscendentalFunctions +--R +--E 31 + +--S 32 of 3320 +)d op acothIfCan +--R +--R +--RThere is one exposed function called acothIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of acothIfCan from PartialTranscendentalFunctions +--R +--E 32 + +--S 33 of 3320 +)d op acotIfCan +--R +--R +--RThere is one exposed function called acotIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of acotIfCan from PartialTranscendentalFunctions +--R +--E 33 + +--S 34 of 3320 +)d op acsc +--R +--R +--RThere is one exposed function called acsc : +--R [1] D -> D from D if D has ATRIG +--R +--RThere are 5 unexposed functions called acsc : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of acsc from ArcTrigonometricFunctionCategory +--R +--R +--RExamples of acsc from ElementaryFunction +--R +--R +--RExamples of acsc from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of acsc from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of acsc from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of acsc from StreamTranscendentalFunctions +--R +--E 34 + +--S 35 of 3320 +)d op acsch +--R +--R +--RThere is one exposed function called acsch : +--R [1] D -> D from D if D has AHYP +--R +--RThere are 5 unexposed functions called acsch : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of acsch from ArcHyperbolicFunctionCategory +--R +--R +--RExamples of acsch from ElementaryFunction +--R +--R +--RExamples of acsch from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of acsch from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of acsch from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of acsch from StreamTranscendentalFunctions +--R +--E 35 + +--S 36 of 3320 +)d op acsch +--R +--R +--RThere is one exposed function called acsch : +--R [1] D -> D from D if D has AHYP +--R +--RThere are 5 unexposed functions called acsch : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of acsch from ArcHyperbolicFunctionCategory +--R +--R +--RExamples of acsch from ElementaryFunction +--R +--R +--RExamples of acsch from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of acsch from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of acsch from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of acsch from StreamTranscendentalFunctions +--R +--E 36 + +--S 37 of 3320 +)d op acschIfCan +--R +--R +--RThere is one exposed function called acschIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of acschIfCan from PartialTranscendentalFunctions +--R +--E 37 + +--S 38 of 3320 +)d op acscIfCan +--R +--R +--RThere is one exposed function called acscIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of acscIfCan from PartialTranscendentalFunctions +--R +--E 38 + +--S 39 of 3320 +)d op actualExtensionV +--R +--R +--RThere is one exposed function called actualExtensionV : +--R [1] D -> D2 from D +--R if D has INFCLCT(D2,D3,D4,D5,D6,D7,D8,D9,D1) and D4 has +--R POLYCAT(D2,D5,OVAR(D3)) and D5 has DIRPCAT(#(D3),NNI) and +--R D6 has PRSPCAT(D2) and D7 has LOCPOWC(D2) and D8 has +--R PLACESC(D2,D7) and D1 has BLMETCT and D2 has FIELD +--R +--RExamples of actualExtensionV from InfinitlyClosePointCategory +--R +--E 39 + +--S 40 of 3320 +)d op aCubic +--R +--R +--RThere is one unexposed function called aCubic : +--R [1] (D2,D2,D2,D2) -> D2 from PolynomialSolveByFormulas(D3,D2) +--R if D2 has Fieldwith +--R D : (%,Fraction(Integer)) -> %and D3 has UPOLYC(D2) +--R +--R +--RExamples of aCubic from PolynomialSolveByFormulas +--R +--E 40 + +--S 41 of 3320 +)d op adaptive +--R +--R +--RThere are 3 exposed functions called adaptive : +--R [1] Boolean -> DrawOption from DrawOption +--R [2] -> Boolean from GraphicsDefaults +--R [3] Boolean -> Boolean from GraphicsDefaults +--R +--RThere is one unexposed function called adaptive : +--R [1] (List(DrawOption),Boolean) -> Boolean from DrawOptionFunctions0 +--R +--R +--RExamples of adaptive from DrawOptionFunctions0 +--R +--R +--RExamples of adaptive from DrawOption +--R +--R +--RExamples of adaptive from GraphicsDefaults +--R +--E 41 + +--S 42 of 3320 +)d op adaptive? +--R +--R +--RThere is one unexposed function called adaptive? : +--R [1] -> Boolean from Plot +--R +--RExamples of adaptive? from Plot +--R +--E 42 + +--S 43 of 3320 +)d op adaptive3D? +--R +--R +--RThere is one unexposed function called adaptive3D? : +--R [1] -> Boolean from Plot3D +--R +--RExamples of adaptive3D? from Plot3D +--R +--E 43 + +--S 44 of 3320 +)d op addBadValue +--R +--R +--RThere are 2 unexposed functions called addBadValue : +--R [1] (Pattern(D3),D2) -> Pattern(D3) from PatternFunctions1(D3,D2) +--R if D3 has SETCAT and D2 has TYPE +--R [2] (Pattern(D2),Any) -> Pattern(D2) from Pattern(D2) if D2 has +--R SETCAT +--R +--RExamples of addBadValue from PatternFunctions1 +--R +--R +--RExamples of addBadValue from Pattern +--R +--E 44 + +--S 45 of 3320 +)d op addiag +--R +--R +--RThere is one unexposed function called addiag : +--R [1] Stream(Stream(D3)) -> Stream(D3) from +--R StreamTaylorSeriesOperations(D3) +--R if D3 has RING +--R +--RExamples of addiag from StreamTaylorSeriesOperations +--R +--E 45 + +--S 46 of 3320 +)d op additive? +--R +--R +--RThere is one exposed function called additive? : +--R [1] (DirichletRing(D3),PositiveInteger) -> Boolean from +--R DirichletRing(D3) +--R if D3 has RING +--R +--RExamples of additive? from DirichletRing +--R +--E 46 + +--S 47 of 3320 +)d op addMatch +--R +--R +--RThere is one unexposed function called addMatch : +--R [1] (Pattern(D3),D2,PatternMatchResult(D3,D2)) -> PatternMatchResult +--R (D3,D2) +--R from PatternMatchResult(D3,D2) if D3 has SETCAT and D2 +--R has SETCAT +--R +--RExamples of addMatch from PatternMatchResult +--R +--E 47 + +--S 48 of 3320 +)d op addMatchRestricted +--R +--R +--RThere is one unexposed function called addMatchRestricted : +--R [1] (Pattern(D3),D2,PatternMatchResult(D3,D2),D2) -> +--R PatternMatchResult(D3,D2) +--R from PatternMatchResult(D3,D2) if D3 has SETCAT and D2 +--R has SETCAT +--R +--RExamples of addMatchRestricted from PatternMatchResult +--R +--E 48 + +--S 49 of 3320 +)d op addmod +--R +--R +--RThere is one exposed function called addmod : +--R [1] (D,D,D) -> D from D if D has INS +--R +--RExamples of addmod from IntegerNumberSystem +--R +--E 49 + +--S 50 of 3320 +)d op addPoint +--R +--R +--RThere are 3 unexposed functions called addPoint : +--R [1] (SubSpace(D3,D4),Point(D4)) -> NonNegativeInteger from SubSpace( +--R D3,D4) +--R if D4 has RING and D3: PI +--R [2] (SubSpace(D3,D4),List(NonNegativeInteger),NonNegativeInteger) +--R -> SubSpace(D3,D4) +--R from SubSpace(D3,D4) if D3: PI and D4 has RING +--R [3] (SubSpace(D3,D4),List(NonNegativeInteger),Point(D4)) -> SubSpace +--R (D3,D4) +--R from SubSpace(D3,D4) if D4 has RING and D3: PI +--R +--RExamples of addPoint from SubSpace +--R +--E 50 + +--S 51 of 3320 +)d op addPoint2 +--R +--R +--RThere is one unexposed function called addPoint2 : +--R [1] (SubSpace(D2,D3),Point(D3)) -> SubSpace(D2,D3) from SubSpace(D2, +--R D3) +--R if D3 has RING and D2: PI +--R +--RExamples of addPoint2 from SubSpace +--R +--E 51 + +--S 52 of 3320 +)d op addPointLast +--R +--R +--RThere is one unexposed function called addPointLast : +--R [1] (SubSpace(D3,D4),SubSpace(D3,D4),Point(D4),NonNegativeInteger) +--R -> SubSpace(D3,D4) +--R from SubSpace(D3,D4) if D4 has RING and D3: PI +--R +--RExamples of addPointLast from SubSpace +--R +--E 52 + +--S 53 of 3320 +)d op adjoint +--R +--R +--RThere are 4 exposed functions called adjoint : +--R [1] D -> D from D if D has LODOCAT(D1) and D1 has RING +--R [2] D2 -> Record(adjMat: D2,detMat: D3) +--R from MatrixLinearAlgebraFunctions(D3,D4,D5,D2) +--R if D3 has INTDOM and D3 has COMRING and D4 has FLAGG(D3) +--R and D5 has FLAGG(D3) and D2 has MATCAT(D3,D4,D5) +--R [3] (ModuleOperator(D1,D2),ModuleOperator(D1,D2)) -> ModuleOperator( +--R D1,D2) +--R from ModuleOperator(D1,D2) +--R if D1 has COMRING and D1 has RING and D2 has LMODULE(D1) +--R +--R [4] ModuleOperator(D1,D2) -> ModuleOperator(D1,D2) from +--R ModuleOperator(D1,D2) +--R if D1 has COMRING and D1 has RING and D2 has LMODULE(D1) +--R +--R +--RThere are 2 unexposed functions called adjoint : +--R [1] (Operator(D1),Operator(D1)) -> Operator(D1) from Operator(D1) +--R if D1 has COMRING and D1 has RING +--R [2] Operator(D1) -> Operator(D1) from Operator(D1) +--R if D1 has COMRING and D1 has RING +--R +--RExamples of adjoint from LinearOrdinaryDifferentialOperatorCategory +--R +--R +--RExamples of adjoint from MatrixLinearAlgebraFunctions +--R +--R +--RExamples of adjoint from ModuleOperator +--R +--R +--RExamples of adjoint from Operator +--R +--E 53 + +--S 54 of 3320 +)d op adjunctionDivisor +--R +--R +--RThere are 4 exposed functions called adjunctionDivisor : +--R [1] D5 -> D4 from DesingTreePackage(D6,D7,D8,D9,D10,D11,D1,D4,D2,D5, +--R D3) +--R if D6 has FIELD and D7: LIST(SYMBOL) and D8 has POLYCAT(D6 +--R ,D9,OVAR(D7)) and D9 has DIRPCAT(#(D7),NNI) and D10 has +--R PRSPCAT(D6) and D11 has LOCPOWC(D6) and D1 has PLACESC(D6, +--R D11) and D2 has INFCLCT(D6,D7,D8,D9,D10,D11,D1,D4,D3) and +--R D3 has BLMETCT and D4 has DIVCAT(D1) and D5 has DSTRCAT(D2) +--R +--R [2] -> D4 +--R from GeneralPackageForAlgebraicFunctionField(D5,D6,D7,D8, +--R D9,D10,D11,D4,D1,D2,D3) +--R if D5 has FIELD and D6: LIST(SYMBOL) and D7 has POLYCAT(D5 +--R ,D8,OVAR(D6)) and D8 has DIRPCAT(#(D6),NNI) and D9 has +--R PRSPCAT(D5) and D10 has LOCPOWC(D5) and D11 has PLACESC(D5, +--R D10) and D1 has INFCLCT(D5,D6,D7,D8,D9,D10,D11,D4,D3) and +--R D3 has BLMETCT and D4 has DIVCAT(D11) and D2 has DSTRCAT(D1 +--R ) +--R [3] -> Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(D2)) +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D2,D3 +--R ,D4) +--R if D2 has FFIELDC and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R [4] -> Divisor(Places(D2)) from PackageForAlgebraicFunctionField(D2 +--R ,D3,D4) +--R if D2 has FIELD and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R +--RExamples of adjunctionDivisor from DesingTreePackage +--R +--R +--RExamples of adjunctionDivisor from GeneralPackageForAlgebraicFunctionField +--R +--R +--RExamples of adjunctionDivisor from PackageForAlgebraicFunctionFieldOverFiniteField +--R +--R +--RExamples of adjunctionDivisor from PackageForAlgebraicFunctionField +--R +--E 54 + +--S 55 of 3320 +)d op affineAlgSet +--R +--R +--RThere are 2 exposed functions called affineAlgSet : +--R [1] List(D5) -> Union(List(D7),"failed",Infinite,Integer) +--R from AffineAlgebraicSetComputeWithGroebnerBasis(D3,D4,D5, +--R D6,D7) +--R if D5 has POLYCAT(D3,D6,OVAR(D4)) and D6 has DIRPCAT(#(D4) +--R ,NNI) and D3 has FIELD and D4: LIST(SYMBOL) and D7 has +--R PRSPCAT(D3) +--R [2] List(D5) -> Union(List(D7),"failed",Infinite,Integer) +--R from AffineAlgebraicSetComputeWithResultant(D3,D4,D5,D6,D7 +--R ) +--R if D5 has POLYCAT(D3,D6,OVAR(D4)) and D6 has DIRPCAT(#(D4) +--R ,NNI) and D3 has FIELD and D4: LIST(SYMBOL) and D7 has +--R PRSPCAT(D3) +--R +--RExamples of affineAlgSet from AffineAlgebraicSetComputeWithGroebnerBasis +--R +--R +--RExamples of affineAlgSet from AffineAlgebraicSetComputeWithResultant +--R +--E 55 + +--S 56 of 3320 +)d op affineAlgSetLocal +--R +--R +--RThere is one exposed function called affineAlgSetLocal : +--R [1] List(SparseUnivariatePolynomial(SparseUnivariatePolynomial(D3))) +--R -> Union(List(D7),"failed",Infinite,Integer) +--R from AffineAlgebraicSetComputeWithResultant(D3,D4,D5,D6,D7 +--R ) +--R if D3 has FIELD and D4: LIST(SYMBOL) and D6 has DIRPCAT(#( +--R D4),NNI) and D5 has POLYCAT(D3,D6,OVAR(D4)) and D7 has +--R PRSPCAT(D3) +--R +--RExamples of affineAlgSetLocal from AffineAlgebraicSetComputeWithResultant +--R +--E 56 + +--S 57 of 3320 +)d op affinePoint +--R +--R +--RThere is one exposed function called affinePoint : +--R [1] List(D2) -> D from D if D2 has FIELD and D has AFSPCAT(D2) +--R +--RExamples of affinePoint from AffineSpaceCategory +--R +--E 57 + +--S 58 of 3320 +)d op affineRationalPoints +--R +--R +--RThere are 2 exposed functions called affineRationalPoints : +--R [1] (D2,PositiveInteger) -> List(D7) +--R from AffineAlgebraicSetComputeWithGroebnerBasis(D4,D5,D2, +--R D6,D7) +--R if D4 has FIELD and D5: LIST(SYMBOL) and D6 has DIRPCAT(#( +--R D5),NNI) and D2 has POLYCAT(D4,D6,OVAR(D5)) and D7 has +--R PRSPCAT(D4) +--R [2] (D2,PositiveInteger) -> Union(List(D7),"failed",Infinite,Integer +--R ) +--R from AffineAlgebraicSetComputeWithResultant(D4,D5,D2,D6,D7 +--R ) +--R if D4 has FIELD and D5: LIST(SYMBOL) and D6 has DIRPCAT(#( +--R D5),NNI) and D2 has POLYCAT(D4,D6,OVAR(D5)) and D7 has +--R PRSPCAT(D4) +--R +--RExamples of affineRationalPoints from AffineAlgebraicSetComputeWithGroebnerBasis +--R +--R +--RExamples of affineRationalPoints from AffineAlgebraicSetComputeWithResultant +--R +--E 58 + +--S 59 of 3320 +)d op affineSingularPoints +--R +--R +--RThere are 3 exposed functions called affineSingularPoints : +--R [1] D2 -> Union(List(D6),"failed",Infinite,Integer) +--R from AffineAlgebraicSetComputeWithGroebnerBasis(D3,D4,D2, +--R D5,D6) +--R if D3 has FIELD and D4: LIST(SYMBOL) and D5 has DIRPCAT(#( +--R D4),NNI) and D2 has POLYCAT(D3,D5,OVAR(D4)) and D6 has +--R PRSPCAT(D3) +--R [2] D2 -> Union(List(D6),"failed",Infinite,Integer) +--R from AffineAlgebraicSetComputeWithResultant(D3,D4,D2,D5,D6 +--R ) +--R if D3 has FIELD and D4: LIST(SYMBOL) and D5 has DIRPCAT(#( +--R D4),NNI) and D2 has POLYCAT(D3,D5,OVAR(D4)) and D6 has +--R PRSPCAT(D3) +--R [3] SparseUnivariatePolynomial(SparseUnivariatePolynomial(D3)) -> +--R Union(List(D7),"failed",Infinite,Integer) +--R from AffineAlgebraicSetComputeWithResultant(D3,D4,D5,D6,D7 +--R ) +--R if D3 has FIELD and D4: LIST(SYMBOL) and D6 has DIRPCAT(#( +--R D4),NNI) and D5 has POLYCAT(D3,D6,OVAR(D4)) and D7 has +--R PRSPCAT(D3) +--R +--RExamples of affineSingularPoints from AffineAlgebraicSetComputeWithGroebnerBasis +--R +--R +--RExamples of affineSingularPoints from AffineAlgebraicSetComputeWithResultant +--R +--E 59 + +--S 60 of 3320 +)d op airyAi +--R +--R +--RThere are 3 exposed functions called airyAi : +--R [1] Complex(DoubleFloat) -> Complex(DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R [2] DoubleFloat -> DoubleFloat from DoubleFloatSpecialFunctions +--R [3] D -> D from D if D has SPFCAT +--R +--RThere is one unexposed function called airyAi : +--R [1] D1 -> D1 from FunctionalSpecialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R +--RExamples of airyAi from DoubleFloatSpecialFunctions +--R +--R +--RExamples of airyAi from FunctionalSpecialFunction +--R +--R +--RExamples of airyAi from SpecialFunctionCategory +--R +--E 60 + +--S 61 of 3320 +)d op airyBi +--R +--R +--RThere are 3 exposed functions called airyBi : +--R [1] DoubleFloat -> DoubleFloat from DoubleFloatSpecialFunctions +--R [2] Complex(DoubleFloat) -> Complex(DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R [3] D -> D from D if D has SPFCAT +--R +--RThere is one unexposed function called airyBi : +--R [1] D1 -> D1 from FunctionalSpecialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R +--RExamples of airyBi from DoubleFloatSpecialFunctions +--R +--R +--RExamples of airyBi from FunctionalSpecialFunction +--R +--R +--RExamples of airyBi from SpecialFunctionCategory +--R +--E 61 + +--S 62 of 3320 done +)d op Aleph +--R +--R +--RThere is one exposed function called Aleph : +--R [1] NonNegativeInteger -> CardinalNumber from CardinalNumber +--R +--RExamples of Aleph from CardinalNumber +--R +--RA0:=Aleph 0 +--R +--E 62 + +--S 63 of 3320 +)d op algDsolve +--R +--R +--RThere is one unexposed function called algDsolve : +--R [1] (LinearOrdinaryDifferentialOperator1(D3),D3) -> Record( +--R particular: Union(D3,"failed"),basis: List(D3)) +--R from PureAlgebraicLODE(D4,D5,D6,D3) +--R if D3 has FFCAT(D4,D5,D6) and D4 has Join(Field, +--R CharacteristicZero,RetractableTo(Integer),RetractableTo( +--R Fraction(Integer))) and D5 has UPOLYC(D4) and D6 has UPOLYC +--R (FRAC(D5)) +--R +--RExamples of algDsolve from PureAlgebraicLODE +--R +--E 63 + +--S 64 of 3320 +)d op algebraic? +--R +--R +--RThere are 2 exposed functions called algebraic? : +--R [1] (D2,D) -> Boolean from D +--R if D has TSETCAT(D3,D4,D2,D5) and D3 has INTDOM and D4 +--R has OAMONS and D2 has ORDSET and D5 has RPOLCAT(D3,D4,D2) +--R +--R [2] D -> Boolean from D if D has XF(D2) and D2 has FIELD +--R +--RExamples of algebraic? from TriangularSetCategory +--R +--R +--RExamples of algebraic? from ExtensionField +--R +--E 64 + +--S 65 of 3320 +)d op algebraicCoefficients? +--R +--R +--RThere is one exposed function called algebraicCoefficients? : +--R [1] (D2,D) -> Boolean from D +--R if D has RSETCAT(D3,D4,D5,D2) and D3 has GCDDOM and D4 +--R has OAMONS and D5 has ORDSET and D2 has RPOLCAT(D3,D4,D5) +--R +--R +--RExamples of algebraicCoefficients? from RegularTriangularSetCategory +--R +--E 65 + +--S 66 of 3320 +)d op algebraicDecompose +--R +--R +--RThere are 2 exposed functions called algebraicDecompose : +--R [1] (D2,D3,Boolean) -> Record(done: List(D3),todo: List(Record(val: +--R List(D2),tower: D3))) +--R from RegularSetDecompositionPackage(D5,D6,D7,D2,D3) +--R if D5 has GCDDOM and D6 has OAMONS and D7 has ORDSET and +--R D2 has RPOLCAT(D5,D6,D7) and D3 has RSETCAT(D5,D6,D7,D2) +--R +--R [2] (D2,D3) -> Record(done: List(D3),todo: List(Record(val: List(D2) +--R ,tower: D3))) +--R from SquareFreeRegularSetDecompositionPackage(D4,D5,D6,D2, +--R D3) +--R if D4 has GCDDOM and D5 has OAMONS and D6 has ORDSET and +--R D2 has RPOLCAT(D4,D5,D6) and D3 has SFRTCAT(D4,D5,D6,D2) +--R +--R +--RExamples of algebraicDecompose from RegularSetDecompositionPackage +--R +--R +--RExamples of algebraicDecompose from SquareFreeRegularSetDecompositionPackage +--R +--E 66 + +--S 67 of 3320 +)d op algebraicOf +--R +--R +--RThere is one exposed function called algebraicOf : +--R [1] (RightOpenIntervalRootCharacterization(RealClosure(D3), +--R SparseUnivariatePolynomial(RealClosure(D3))),OutputForm) -> +--R RealClosure(D3) +--R from RealClosure(D3) if D3 has Join(OrderedRing,Field, +--R RealConstant) +--R +--RExamples of algebraicOf from RealClosure +--R +--E 67 + +--S 68 of 3320 +)d op algebraicSet +--R +--R +--RThere is one exposed function called algebraicSet : +--R [1] List(D5) -> List(D7) from ProjectiveAlgebraicSetPackage(D3,D4,D5 +--R ,D6,D7) +--R if D5 has POLYCAT(D3,D6,OVAR(D4)) and D6 has DIRPCAT(#(D4) +--R ,NNI) and D3 has FIELD and D4: LIST(SYMBOL) and D7 has +--R PRSPCAT(D3) +--R +--RExamples of algebraicSet from ProjectiveAlgebraicSetPackage +--R +--E 68 + +--S 69 of 3320 +)d op algebraicSort +--R +--R +--RThere are 2 exposed functions called algebraicSort : +--R [1] List(D6) -> List(D6) from QuasiComponentPackage(D2,D3,D4,D5,D6) +--R if D6 has RSETCAT(D2,D3,D4,D5) and D2 has GCDDOM and D3 +--R has OAMONS and D4 has ORDSET and D5 has RPOLCAT(D2,D3,D4) +--R +--R [2] List(D6) -> List(D6) from SquareFreeQuasiComponentPackage(D2,D3, +--R D4,D5,D6) +--R if D6 has RSETCAT(D2,D3,D4,D5) and D2 has GCDDOM and D3 +--R has OAMONS and D4 has ORDSET and D5 has RPOLCAT(D2,D3,D4) +--R +--R +--RExamples of algebraicSort from QuasiComponentPackage +--R +--R +--RExamples of algebraicSort from SquareFreeQuasiComponentPackage +--R +--E 69 + +--S 70 of 3320 +)d op algebraicVariables +--R +--R +--RThere is one exposed function called algebraicVariables : +--R [1] D -> List(D4) from D +--R if D has TSETCAT(D2,D3,D4,D5) and D2 has INTDOM and D3 +--R has OAMONS and D4 has ORDSET and D5 has RPOLCAT(D2,D3,D4) +--R +--R +--RExamples of algebraicVariables from TriangularSetCategory +--R +--E 70 + +--S 71 of 3320 +)d op algint +--R +--R +--RThere is one unexposed function called algint : +--R [1] (D2,Kernel(D2),Kernel(D2),(SparseUnivariatePolynomial(D2) -> +--R SparseUnivariatePolynomial(D2))) -> IntegrationResult(D2) +--R from AlgebraicIntegration(D5,D2) +--R if D2 has Join(AlgebraicallyClosedField,FunctionSpace(D5)) +--R and D5 has Join(OrderedSet,IntegralDomain) +--R +--RExamples of algint from AlgebraicIntegration +--R +--E 71 + +--S 72 of 3320 +)d op algintegrate +--R +--R +--RThere is one unexposed function called algintegrate : +--R [1] (D2,(D6 -> D6)) -> IntegrationResult(D2) +--R from AlgebraicIntegrate(D4,D5,D6,D7,D2) +--R if D6 has UPOLYC(D5) and D5 has Join( +--R AlgebraicallyClosedField,FunctionSpace(D4)) and D4 has Join +--R (OrderedSet,IntegralDomain,RetractableTo(Integer)) and D7 +--R has UPOLYC(FRAC(D6)) and D2 has FFCAT(D5,D6,D7) +--R +--RExamples of algintegrate from AlgebraicIntegrate +--R +--E 72 + +--S 73 of 3320 +)d op algSplitSimple +--R +--R +--RThere is one exposed function called algSplitSimple : +--R [1] (D,(D4 -> D4)) -> Record(num: D,den: D4,derivden: D4,gd: D4) +--R from D +--R if D4 has UPOLYC(D3) and D3 has UFD and D5 has UPOLYC(FRAC +--R (D4)) and D has FFCAT(D3,D4,D5) +--R +--RExamples of algSplitSimple from FunctionFieldCategory +--R +--E 73 + +--S 74 of 3320 +)d op aLinear +--R +--R +--RThere is one unexposed function called aLinear : +--R [1] (D2,D2) -> D2 from PolynomialSolveByFormulas(D3,D2) +--R if D2 has Fieldwith +--R D : (%,Fraction(Integer)) -> %and D3 has UPOLYC(D2) +--R +--R +--RExamples of aLinear from PolynomialSolveByFormulas +--R +--E 74 + +--S 75 of 3320 +)d op allDegrees +--R +--R +--RThere is one exposed function called allDegrees : +--R [1] Boolean -> GuessOption from GuessOption +--R +--RThere is one unexposed function called allDegrees : +--R [1] List(GuessOption) -> Boolean from GuessOptionFunctions0 +--R +--RExamples of allDegrees from GuessOptionFunctions0 +--R +--R +--RExamples of allDegrees from GuessOption +--R +--E 75 + +--S 76 of 3320 +)d op allIndices +--R +--R +--RThere is one exposed function called allIndices : +--R [1] SparseEchelonMatrix(D2,D3) -> List(D2) from SparseEchelonMatrix( +--R D2,D3) +--R if D2 has ORDSET and D3 has RING +--R +--RExamples of allIndices from SparseEchelonMatrix +--R +--E 76 + +--S 77 of 3320 +)d op allPairsAmong +--R +--R +--RThere is one exposed function called allPairsAmong : +--R [1] List(SparseUnivariatePolynomial(SparseUnivariatePolynomial(D3))) +--R -> List(List(SparseUnivariatePolynomial( +--R SparseUnivariatePolynomial(D3)))) +--R from AffineAlgebraicSetComputeWithResultant(D3,D4,D5,D6,D7 +--R ) +--R if D3 has FIELD and D4: LIST(SYMBOL) and D6 has DIRPCAT(#( +--R D4),NNI) and D5 has POLYCAT(D3,D6,OVAR(D4)) and D7 has +--R PRSPCAT(D3) +--R +--RExamples of allPairsAmong from AffineAlgebraicSetComputeWithResultant +--R +--E 77 + +--S 78 of 3320 +)d op allRootsOf +--R +--R +--RThere are 7 exposed functions called allRootsOf : +--R [1] Polynomial(Integer) -> List(D) from D if D has RCFIELD +--R [2] Polynomial(Fraction(Integer)) -> List(D) from D if D has RCFIELD +--R +--R [3] Polynomial(D) -> List(D) from D if D has RCFIELD +--R [4] SparseUnivariatePolynomial(Integer) -> List(D) from D if D has +--R RCFIELD +--R [5] SparseUnivariatePolynomial(Fraction(Integer)) -> List(D) from D +--R if D has RCFIELD +--R [6] SparseUnivariatePolynomial(D) -> List(D) from D if D has RCFIELD +--R +--R [7] D2 -> List(D) from D +--R if D3 has Join(OrderedRing,Field) and D2 has UPOLYC(D3) +--R and D has RRCC(D3,D2) +--R +--RExamples of allRootsOf from RealClosedField +--R +--R +--RExamples of allRootsOf from RealRootCharacterizationCategory +--R +--E 78 + +--S 79 of 3320 +)d op allSimpleCells +--R +--R +--RThere are 2 exposed functions called allSimpleCells : +--R [1] (List(D5),Symbol) -> List(SimpleCell(D4,D5)) from SimpleCell(D4, +--R D5) +--R if D5 has UPOLYC(D4) and D4 has RCFIELD +--R [2] (D2,Symbol) -> List(SimpleCell(D4,D2)) from SimpleCell(D4,D2) +--R if D4 has RCFIELD and D2 has UPOLYC(D4) +--R +--RExamples of allSimpleCells from SimpleCell +--R +--E 79 + +--S 80 of 3320 +)d op alphabetic +--R +--R +--RThere is one exposed function called alphabetic : +--R [1] -> CharacterClass from CharacterClass +--R +--RExamples of alphabetic from CharacterClass +--R +--E 80 + +--S 81 of 3320 done +)d op alphabetic? +--R +--R +--RThere is one exposed function called alphabetic? : +--R [1] Character -> Boolean from Character +--R +--RExamples of alphabetic? from Character +--R +--Rchars := [char "a", char "A", char "X", char "8", char "+"] +--R[alphabetic? c for c in chars] +--R +--E 81 + +--S 82 of 3320 +)d op alphanumeric +--R +--R +--RThere is one exposed function called alphanumeric : +--R [1] -> CharacterClass from CharacterClass +--R +--RExamples of alphanumeric from CharacterClass +--R +--E 82 + +--S 83 of 3320 done +)d op alphanumeric? +--R +--R +--RThere is one exposed function called alphanumeric? : +--R [1] Character -> Boolean from Character +--R +--RExamples of alphanumeric? from Character +--R +--Rchars := [char "a", char "A", char "X", char "8", char "+"] +--R[alphanumeric? c for c in chars] +--R +--E 83 + +--S 84 of 3320 +)d op alterDrift! +--R +--R +--RThere is one exposed function called alterDrift! : +--R [1] (BasicStochasticDifferential,StochasticDifferential(D2)) -> +--R Union(StochasticDifferential(D2),"failed") +--R from StochasticDifferential(D2) +--R if D2 has Join(OrderedSet,IntegralDomain) +--R +--RExamples of alterDrift! from StochasticDifferential +--R +--E 84 + +--S 85 of 3320 +)d op alternating +--R +--R +--RThere is one exposed function called alternating : +--R [1] Integer -> SymmetricPolynomial(Fraction(Integer)) from +--R CycleIndicators +--R +--RExamples of alternating from CycleIndicators +--R +--E 85 + +--S 86 of 3320 +)d op alternatingGroup +--R +--R +--RThere are 2 exposed functions called alternatingGroup : +--R [1] PositiveInteger -> PermutationGroup(Integer) +--R from PermutationGroupExamples +--R [2] List(Integer) -> PermutationGroup(Integer) from +--R PermutationGroupExamples +--R +--RExamples of alternatingGroup from PermutationGroupExamples +--R +--E 86 + +--S 87 of 3320 +)d op alternative? +--R +--R +--RThere is one exposed function called alternative? : +--R [1] -> Boolean from D if D has FINAALG(D2) and D2 has COMRING +--R +--RThere is one unexposed function called alternative? : +--R [1] -> Boolean from FiniteRankNonAssociativeAlgebra&(D2,D3) +--R if D3 has COMRING and D2 has FINAALG(D3) +--R +--RExamples of alternative? from FiniteRankNonAssociativeAlgebra& +--R +--R +--RExamples of alternative? from FiniteRankNonAssociativeAlgebra +--R +--E 87 + +--S 88 of 3320 +)d op alterQuadVar! +--R +--R +--RThere is one exposed function called alterQuadVar! : +--R [1] (BasicStochasticDifferential,BasicStochasticDifferential, +--R StochasticDifferential(D2)) -> Union(StochasticDifferential(D2), +--R "failed") +--R from StochasticDifferential(D2) +--R if D2 has Join(OrderedSet,IntegralDomain) +--R +--RExamples of alterQuadVar! from StochasticDifferential +--R +--E 88 + +--S 89 of 3320 +)d op An +--R +--R +--RThere is one unexposed function called An : +--R [1] ModMonic(D2,D3) -> Vector(D2) from ModMonic(D2,D3) +--R if D2 has RING and D3 has UPOLYC(D2) +--R +--RExamples of An from ModMonic +--R +--E 89 + +--S 90 of 3320 +)d op and +--R +--R +--RThere are 2 exposed functions called and : +--R [1] (Boolean,Boolean) -> Boolean from Boolean +--R [2] (D,D) -> D from D if D has BTAGG +--R +--RThere is one unexposed function called and : +--R [1] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R +--RExamples of and from Boolean +--R +--R +--RExamples of and from BitAggregate +--R +--R +--RExamples of and from OutputForm +--R +--E 90 + +--S 91 of 3320 +)d op And +--R +--R +--RThere is one exposed function called And : +--R [1] (SingleInteger,SingleInteger) -> SingleInteger from +--R SingleInteger +--R +--RThere is one unexposed function called And : +--R [1] (IndexedBits(D1),IndexedBits(D1)) -> IndexedBits(D1) from +--R IndexedBits(D1) +--R if D1: INT +--R +--RExamples of And from IndexedBits +--R +--R +--RExamples of And from SingleInteger +--R +--E 91 + +--S 92 of 3320 +)d op AND +--R +--R +--RThere is one exposed function called AND : +--R [1] (Union(I: Expression(Integer),F: Expression(Float),CF: +--R Expression(Complex(Float)),switch: Switch),Union(I: Expression( +--R Integer),F: Expression(Float),CF: Expression(Complex(Float)), +--R switch: Switch)) -> Switch +--R from Switch +--R +--RExamples of AND from Switch +--R +--E 92 + +--S 93 of 3320 +)d op anfactor +--R +--R +--RThere is one unexposed function called anfactor : +--R [1] D2 -> Union(Factored(SparseUnivariatePolynomial(AlgebraicNumber) +--R ),"failed") +--R from FunctionSpaceUnivariatePolynomialFactor(D3,D4,D2) +--R if D4 has RETRACT(AN) and D3 has Join(IntegralDomain, +--R OrderedSet,RetractableTo(Integer)) and D4 has FS(D3) and D2 +--R has UPOLYC(D4) +--R +--RExamples of anfactor from FunctionSpaceUnivariatePolynomialFactor +--R +--E 93 + +--S 94 of 3320 +)d op antiAssociative? +--R +--R +--RThere is one exposed function called antiAssociative? : +--R [1] -> Boolean from D if D has FINAALG(D2) and D2 has COMRING +--R +--RThere is one unexposed function called antiAssociative? : +--R [1] -> Boolean from FiniteRankNonAssociativeAlgebra&(D2,D3) +--R if D3 has COMRING and D2 has FINAALG(D3) +--R +--RExamples of antiAssociative? from FiniteRankNonAssociativeAlgebra& +--R +--R +--RExamples of antiAssociative? from FiniteRankNonAssociativeAlgebra +--R +--E 94 + +--S 95 of 3320 +)d op antiCommutative? +--R +--R +--RThere is one exposed function called antiCommutative? : +--R [1] -> Boolean from D if D has FINAALG(D2) and D2 has COMRING +--R +--RThere is one unexposed function called antiCommutative? : +--R [1] -> Boolean from FiniteRankNonAssociativeAlgebra&(D2,D3) +--R if D3 has COMRING and D2 has FINAALG(D3) +--R +--RExamples of antiCommutative? from FiniteRankNonAssociativeAlgebra& +--R +--R +--RExamples of antiCommutative? from FiniteRankNonAssociativeAlgebra +--R +--E 95 + +--S 96 of 3320 +)d op antiCommutator +--R +--R +--RThere is one exposed function called antiCommutator : +--R [1] (D,D) -> D from D if D has NARNG +--R +--RExamples of antiCommutator from NonAssociativeRng +--R +--E 96 + +--S 97 of 3320 +)d op anticoord +--R +--R +--RThere is one unexposed function called anticoord : +--R [1] (List(D5),DistributedMultivariatePolynomial(D4,D5),List( +--R DistributedMultivariatePolynomial(D4,D5))) -> +--R DistributedMultivariatePolynomial(D4,D5) +--R from LinGroebnerPackage(D4,D5) if D5 has GCDDOM and D4: +--R LIST(SYMBOL) +--R +--RExamples of anticoord from LinGroebnerPackage +--R +--E 97 + +--S 98 of 3320 +)d op antisymmetric? +--R +--R +--RThere are 2 exposed functions called antisymmetric? : +--R [1] D -> Boolean from D +--R if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG +--R (D2) and D4 has FLAGG(D2) +--R [2] D -> Boolean from D +--R if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 +--R has DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4) +--R +--RExamples of antisymmetric? from MatrixCategory +--R +--Rantisymmetric? matrix [[j**i for i in 0..4] for j in 1..5] +--R +--R +--RExamples of antisymmetric? from RectangularMatrixCategory +--R +--E 98 + +--S 99 of 3320 +)d op antisymmetricTensors +--R +--R +--RThere are 2 exposed functions called antisymmetricTensors : +--R [1] (Matrix(D3),PositiveInteger) -> Matrix(D3) +--R from RepresentationPackage1(D3) if D3 has commutative(*) +--R and D3 has RING +--R [2] (List(Matrix(D3)),PositiveInteger) -> List(Matrix(D3)) +--R from RepresentationPackage1(D3) if D3 has commutative(*) +--R and D3 has RING +--R +--RExamples of antisymmetricTensors from RepresentationPackage1 +--R +--E 99 + +--S 100 of 3320 +)d op any +--R +--R +--RThere is one exposed function called any : +--R [1] (SExpression,None) -> Any from Any +--R +--RExamples of any from Any +--R +--E 100 + +--S 101 of 3320 +)d op any? +--R +--R +--RThere are 6 exposed functions called any? : +--R [1] ((D3 -> Boolean),ArrayStack(D3)) -> Boolean from ArrayStack(D3) +--R if $ has finiteAggregate and D3 has SETCAT +--R [2] ((D3 -> Boolean),Dequeue(D3)) -> Boolean from Dequeue(D3) +--R if $ has finiteAggregate and D3 has SETCAT +--R [3] ((D3 -> Boolean),Heap(D3)) -> Boolean from Heap(D3) +--R if $ has finiteAggregate and D3 has ORDSET +--R [4] ((D3 -> Boolean),D) -> Boolean from D +--R if D has finiteAggregate and D has HOAGG(D3) and D3 has +--R TYPE +--R [5] ((D3 -> Boolean),Queue(D3)) -> Boolean from Queue(D3) +--R if $ has finiteAggregate and D3 has SETCAT +--R [6] ((D3 -> Boolean),Stack(D3)) -> Boolean from Stack(D3) +--R if $ has finiteAggregate and D3 has SETCAT +--R +--RExamples of any? from ArrayStack +--R +--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] +--Rany?(x+->(x=4),a) +--R +--R +--RExamples of any? from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rany?(x+->(x=4),a) +--R +--R +--RExamples of any? from Heap +--R +--Ra:Heap INT:= heap [1,2,3,4,5] +--Rany?(x+->(x=4),a) +--R +--R +--RExamples of any? from HomogeneousAggregate +--R +--R +--RExamples of any? from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Rany?(x+->(x=4),a) +--R +--R +--RExamples of any? from Stack +--R +--Ra:Stack INT:= stack [1,2,3,4,5] +--Rany?(x+->(x=4),a) +--R +--E 101 + +--S 102 of 3320 +)d op append +--R +--R +--RThere is one exposed function called append : +--R [1] (List(D1),List(D1)) -> List(D1) from List(D1) if D1 has TYPE +--R +--RExamples of append from List +--R +--E 102 + +--S 103 of 3320 +)d op appendPoint +--R +--R +--RThere is one unexposed function called appendPoint : +--R [1] (GraphImage,Point(DoubleFloat)) -> Void from GraphImage +--R +--RExamples of appendPoint from GraphImage +--R +--E 103 + +--S 104 of 3320 +)d op appendRow! +--R +--R +--RThere is one exposed function called appendRow! : +--R [1] (SparseEchelonMatrix(D3,D4),Record(Indices: List(D3),Entries: +--R List(D4))) -> Void +--R from SparseEchelonMatrix(D3,D4) if D3 has ORDSET and D4 +--R has RING +--R +--RExamples of appendRow! from SparseEchelonMatrix +--R +--E 104 + +--S 105 of 3320 +)d op apply +--R +--R +--RThere are 2 exposed functions called apply : +--R [1] (Matrix(D2),D) -> D from D if D has FRNAALG(D2) and D2 has +--R COMRING +--R [2] (D,D1,D1) -> D1 from D if D has OREPCAT(D1) and D1 has RING +--R +--RThere are 2 unexposed functions called apply : +--R [1] (D2,(D1 -> D1),D1) -> D1 from ApplyUnivariateSkewPolynomial(D4, +--R D1,D2) +--R if D1 has LMODULE(D4) and D4 has RING and D2 has OREPCAT( +--R D4) +--R [2] (D2,D1,D1,Automorphism(D1),(D1 -> D1)) -> D1 +--R from UnivariateSkewPolynomialCategoryOps(D1,D2) +--R if D1 has RING and D2 has OREPCAT(D1) +--R +--RExamples of apply from ApplyUnivariateSkewPolynomial +--R +--R +--RExamples of apply from FramedNonAssociativeAlgebra +--R +--R +--RExamples of apply from UnivariateSkewPolynomialCategory +--R +--R +--RExamples of apply from UnivariateSkewPolynomialCategoryOps +--R +--E 105 + +--S 106 of 3320 +)d op applyQuote +--R +--R +--RThere are 5 exposed functions called applyQuote : +--R [1] (Symbol,List(D)) -> D from D if D has FS(D3) and D3 has ORDSET +--R +--R [2] (Symbol,D,D,D,D) -> D from D if D has FS(D2) and D2 has ORDSET +--R +--R [3] (Symbol,D,D,D) -> D from D if D has FS(D2) and D2 has ORDSET +--R [4] (Symbol,D,D) -> D from D if D has FS(D2) and D2 has ORDSET +--R [5] (Symbol,D) -> D from D if D has FS(D2) and D2 has ORDSET +--R +--RExamples of applyQuote from FunctionSpace +--R +--E 106 + +--S 107 of 3320 +)d op applyRules +--R +--R +--RThere are 2 unexposed functions called applyRules : +--R [1] (List(RewriteRule(D3,D4,D1)),D1) -> D1 from ApplyRules(D3,D4,D1) +--R if D3 has SETCAT and D4 has Join(Ring,PatternMatchable(D3) +--R ,OrderedSet,ConvertibleTo(Pattern(D3))) and D1 has Join( +--R FunctionSpace(D4),PatternMatchable(D3),ConvertibleTo( +--R Pattern(D3))) +--R [2] (List(RewriteRule(D4,D5,D1)),D1,PositiveInteger) -> D1 +--R from ApplyRules(D4,D5,D1) +--R if D4 has SETCAT and D5 has Join(Ring,PatternMatchable(D4) +--R ,OrderedSet,ConvertibleTo(Pattern(D4))) and D1 has Join( +--R FunctionSpace(D5),PatternMatchable(D4),ConvertibleTo( +--R Pattern(D4))) +--R +--RExamples of applyRules from ApplyRules +--R +--E 107 + +--S 108 of 3320 +)d op applyTransform +--R +--R +--RThere is one exposed function called applyTransform : +--R [1] (D1,D2) -> D1 from BlowUpPackage(D3,D4,D1,D5,D2) +--R if D3 has FIELD and D4: LIST(SYMBOL) and D5 has DIRPCAT(#( +--R D4),NNI) and D1 has FAMR(D3,D5) and D2 has BLMETCT +--R +--RExamples of applyTransform from BlowUpPackage +--R +--E 108 + +--S 109 of 3320 +)d op approximants +--R +--R +--RThere is one exposed function called approximants : +--R [1] ContinuedFraction(D2) -> Stream(Fraction(D2)) from +--R ContinuedFraction(D2) +--R if D2 has EUCDOM +--R +--RExamples of approximants from ContinuedFraction +--R +--E 109 + +--S 110 of 3320 +)d op approximate +--R +--R +--RThere are 4 exposed functions called approximate : +--R [1] (D,Integer) -> Integer from D if D has PADICCT(D2) +--R [2] (D,D) -> Fraction(Integer) from D if D has RCFIELD +--R [3] (D2,D,D1) -> D1 from D +--R if D has RRCC(D1,D2) and D1 has Join(OrderedRing,Field) +--R and D2 has UPOLYC(D1) +--R [4] (D1,D3) -> D2 from D1 +--R if D1 has UPSCAT(D2,D3) and D3 has OAMON and D2 has D: (D2 +--R ,D3) -> D2 and D2 has coerce: Symbol -> D2 and D2 has RING +--R +--R +--RThere are 3 unexposed functions called approximate : +--R [1] (BalancedPAdicRational(D3),Integer) -> Fraction(Integer) +--R from BalancedPAdicRational(D3) if D3: INT +--R [2] (PAdicRational(D3),Integer) -> Fraction(Integer) from +--R PAdicRational(D3) +--R if D3: INT +--R [3] (PAdicRationalConstructor(D3,D4),Integer) -> Fraction(Integer) +--R from PAdicRationalConstructor(D3,D4) if D3: INT and D4 +--R has PADICCT(D3) +--R +--RExamples of approximate from BalancedPAdicRational +--R +--R +--RExamples of approximate from PAdicIntegerCategory +--R +--R +--RExamples of approximate from PAdicRational +--R +--R +--RExamples of approximate from PAdicRationalConstructor +--R +--R +--RExamples of approximate from RealClosedField +--R +--R +--RExamples of approximate from RealRootCharacterizationCategory +--R +--R +--RExamples of approximate from UnivariatePowerSeriesCategory +--R +--E 110 + +--S 111 of 3320 +)d op approxNthRoot +--R +--R +--RThere is one exposed function called approxNthRoot : +--R [1] (D1,NonNegativeInteger) -> D1 from IntegerRoots(D1) if D1 has +--R INS +--R +--RExamples of approxNthRoot from IntegerRoots +--R +--E 111 + +--S 112 of 3320 +)d op approxSqrt +--R +--R +--RThere is one exposed function called approxSqrt : +--R [1] D1 -> D1 from IntegerRoots(D1) if D1 has INS +--R +--RExamples of approxSqrt from IntegerRoots +--R +--E 112 + +--S 113 of 3320 +)d op aQuadratic +--R +--R +--RThere is one unexposed function called aQuadratic : +--R [1] (D2,D2,D2) -> D2 from PolynomialSolveByFormulas(D3,D2) +--R if D2 has Fieldwith +--R D : (%,Fraction(Integer)) -> %and D3 has UPOLYC(D2) +--R +--R +--RExamples of aQuadratic from PolynomialSolveByFormulas +--R +--E 113 + +--S 114 of 3320 +)d op aQuartic +--R +--R +--RThere is one unexposed function called aQuartic : +--R [1] (D2,D2,D2,D2,D2) -> D2 from PolynomialSolveByFormulas(D3,D2) +--R if D2 has Fieldwith +--R D : (%,Fraction(Integer)) -> %and D3 has UPOLYC(D2) +--R +--R +--RExamples of aQuartic from PolynomialSolveByFormulas +--R +--E 114 + +--S 115 of 3320 +)d op areEquivalent? +--R +--R +--RThere are 3 exposed functions called areEquivalent? : +--R [1] (List(Matrix(D5)),List(Matrix(D5)),Boolean,Integer) -> Matrix(D5 +--R ) +--R from RepresentationPackage2(D5) if D5 has FIELD and D5 +--R has RING +--R [2] (List(Matrix(D3)),List(Matrix(D3))) -> Matrix(D3) +--R from RepresentationPackage2(D3) if D3 has FIELD and D3 +--R has RING +--R [3] (List(Matrix(D4)),List(Matrix(D4)),Integer) -> Matrix(D4) +--R from RepresentationPackage2(D4) if D4 has FIELD and D4 +--R has RING +--R +--RExamples of areEquivalent? from RepresentationPackage2 +--R +--E 115 + +--S 116 of 3320 +)d op arg1 +--R +--R +--RThere is one unexposed function called arg1 : +--R [1] (D1,D2) -> D1 from MappingPackageInternalHacks2(D1,D2) +--R if D1 has SETCAT and D2 has SETCAT +--R +--RExamples of arg1 from MappingPackageInternalHacks2 +--R +--E 116 + +--S 117 of 3320 +)d op arg2 +--R +--R +--RThere is one unexposed function called arg2 : +--R [1] (D2,D1) -> D1 from MappingPackageInternalHacks2(D2,D1) +--R if D2 has SETCAT and D1 has SETCAT +--R +--RExamples of arg2 from MappingPackageInternalHacks2 +--R +--E 117 + +--S 118 of 3320 done +)d op argscript +--R +--R +--RThere is one exposed function called argscript : +--R [1] (Symbol,List(OutputForm)) -> Symbol from Symbol +--R +--RExamples of argscript from Symbol +--R +--Rargscript(Big,[a,1]) +--R +--E 118 + +--S 119 of 3320 +)d op argument +--R +--R +--RThere is one exposed function called argument : +--R [1] D -> D1 from D if D has COMPCAT(D1) and D1 has COMRING and D1 +--R has TRANFUN +--R +--RThere are 2 unexposed functions called argument : +--R [1] FourierComponent(D1) -> D1 from FourierComponent(D1) if D1 has +--R ORDSET +--R [2] Kernel(D2) -> List(D2) from Kernel(D2) if D2 has ORDSET +--R +--RExamples of argument from ComplexCategory +--R +--R +--RExamples of argument from FourierComponent +--R +--R +--RExamples of argument from Kernel +--R +--E 119 + +--S 120 of 3320 +)d op argumentList! +--R +--R +--RThere are 3 exposed functions called argumentList! : +--R [1] List(Symbol) -> Void from TheSymbolTable +--R [2] (Symbol,List(Symbol)) -> Void from TheSymbolTable +--R [3] (Symbol,List(Symbol),TheSymbolTable) -> Void from TheSymbolTable +--R +--R +--RExamples of argumentList! from TheSymbolTable +--R +--E 120 + +--S 121 of 3320 +)d op argumentListOf +--R +--R +--RThere is one exposed function called argumentListOf : +--R [1] (Symbol,TheSymbolTable) -> List(Symbol) from TheSymbolTable +--R +--RExamples of argumentListOf from TheSymbolTable +--R +--E 121 + +--S 122 of 3320 +)d op arity +--R +--R +--RThere is one exposed function called arity : +--R [1] BasicOperator -> Union(NonNegativeInteger,"failed") from +--R BasicOperator +--R +--RExamples of arity from BasicOperator +--R +--E 122 + +--S 123 of 3320 +)d op aromberg +--R +--R +--RThere is one exposed function called aromberg : +--R [1] ((Float -> Float),Float,Float,Float,Float,Integer,Integer, +--R Integer) -> Record(value: Float,error: Float,totalpts: Integer, +--R success: Boolean) +--R from NumericalQuadrature +--R +--RExamples of aromberg from NumericalQuadrature +--R +--E 123 + +--S 124 of 3320 done +)d op aRow +--R +--R +--RThere is one exposed function called aRow : +--R [1] (D1,PositiveInteger) -> D1 from MatrixManipulation(D3,D4,D5,D1) +--R if D3 has FIELD and D4 has FLAGG(D3) and D5 has FLAGG(D3) +--R and D1 has MATCAT(D3,D4,D5) +--R +--RExamples of aRow from MatrixManipulation +--R +--RM := matrix([[a,b,c],[d,e,f],[g,h,i]]) +--RaRow(M, 1) +--RaRow(M, 2) +--R +--E 124 + +--S 125 of 3320 done +)d op arrayStack +--R +--R +--RThere is one exposed function called arrayStack : +--R [1] List(D2) -> ArrayStack(D2) from ArrayStack(D2) if D2 has SETCAT +--R +--R +--RExamples of arrayStack from ArrayStack +--R +--Rc:ArrayStack INT:= arrayStack [1,2,3,4,5] +--R +--E 125 + +--S 126 of 3320 +)d op asec +--R +--R +--RThere is one exposed function called asec : +--R [1] D -> D from D if D has ATRIG +--R +--RThere are 5 unexposed functions called asec : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of asec from ArcTrigonometricFunctionCategory +--R +--R +--RExamples of asec from ElementaryFunction +--R +--R +--RExamples of asec from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of asec from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of asec from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of asec from StreamTranscendentalFunctions +--R +--E 126 + +--S 127 of 3320 +)d op asech +--R +--R +--RThere is one exposed function called asech : +--R [1] D -> D from D if D has AHYP +--R +--RThere are 5 unexposed functions called asech : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of asech from ArcHyperbolicFunctionCategory +--R +--R +--RExamples of asech from ElementaryFunction +--R +--R +--RExamples of asech from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of asech from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of asech from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of asech from StreamTranscendentalFunctions +--R +--E 127 + +--S 128 of 3320 +)d op asechIfCan +--R +--R +--RThere is one exposed function called asechIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of asechIfCan from PartialTranscendentalFunctions +--R +--E 128 + +--S 129 of 3320 +)d op asecIfCan +--R +--R +--RThere is one exposed function called asecIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of asecIfCan from PartialTranscendentalFunctions +--R +--E 129 + +--S 130 of 3320 +)d op asimpson +--R +--R +--RThere is one exposed function called asimpson : +--R [1] ((Float -> Float),Float,Float,Float,Float,Integer,Integer, +--R Integer) -> Record(value: Float,error: Float,totalpts: Integer, +--R success: Boolean) +--R from NumericalQuadrature +--R +--RExamples of asimpson from NumericalQuadrature +--R +--E 130 + +--S 131 of 3320 +)d op asin +--R +--R +--RThere are 2 exposed functions called asin : +--R [1] D -> D from D if D has ATRIG +--R [2] FortranExpression(D1,D2,D3) -> FortranExpression(D1,D2,D3) +--R from FortranExpression(D1,D2,D3) +--R if D1: LIST(SYMBOL) and D2: LIST(SYMBOL) and D3 has FMTC +--R +--R +--RThere are 5 unexposed functions called asin : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of asin from ArcTrigonometricFunctionCategory +--R +--R +--RExamples of asin from ElementaryFunction +--R +--R +--RExamples of asin from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of asin from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of asin from FortranExpression +--R +--R +--RExamples of asin from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of asin from StreamTranscendentalFunctions +--R +--E 131 + +--S 132 of 3320 +)d op asinh +--R +--R +--RThere is one exposed function called asinh : +--R [1] D -> D from D if D has AHYP +--R +--RThere are 5 unexposed functions called asinh : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of asinh from ArcHyperbolicFunctionCategory +--R +--R +--RExamples of asinh from ElementaryFunction +--R +--R +--RExamples of asinh from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of asinh from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of asinh from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of asinh from StreamTranscendentalFunctions +--R +--E 132 + +--S 133 of 3320 +)d op asinhIfCan +--R +--R +--RThere is one exposed function called asinhIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of asinhIfCan from PartialTranscendentalFunctions +--R +--E 133 + +--S 134 of 3320 +)d op asinIfCan +--R +--R +--RThere is one exposed function called asinIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of asinIfCan from PartialTranscendentalFunctions +--R +--E 134 + +--S 135 of 3320 +)d op aspFilename +--R +--R +--RThere is one exposed function called aspFilename : +--R [1] String -> String from NAGLinkSupportPackage +--R +--RExamples of aspFilename from NAGLinkSupportPackage +--R +--E 135 + +--S 136 of 3320 +)d op assert +--R +--R +--RThere are 3 exposed functions called assert : +--R [1] (BasicOperator,String) -> BasicOperator from BasicOperator +--R [2] (D1,String) -> D1 from FunctionSpaceAssertions(D3,D1) +--R if D3 has ORDSET and D1 has FS(D3) +--R [3] (Symbol,String) -> Expression(Integer) from +--R PatternMatchAssertions +--R +--RExamples of assert from BasicOperator +--R +--R +--RExamples of assert from FunctionSpaceAssertions +--R +--R +--RExamples of assert from PatternMatchAssertions +--R +--E 136 + +--S 137 of 3320 +)d op assign +--R +--R +--RThere are 31 exposed functions called assign : +--R [1] (Symbol,List(Polynomial(Integer)),Expression(Complex(Float))) +--R -> FortranCode +--R from FortranCode +--R [2] (Symbol,List(Polynomial(Integer)),Expression(Float)) -> +--R FortranCode +--R from FortranCode +--R [3] (Symbol,List(Polynomial(Integer)),Expression(Integer)) -> +--R FortranCode +--R from FortranCode +--R [4] (Symbol,Vector(Expression(Complex(Float)))) -> FortranCode +--R from FortranCode +--R [5] (Symbol,Vector(Expression(Float))) -> FortranCode from +--R FortranCode +--R [6] (Symbol,Vector(Expression(Integer))) -> FortranCode from +--R FortranCode +--R [7] (Symbol,Matrix(Expression(Complex(Float)))) -> FortranCode +--R from FortranCode +--R [8] (Symbol,Matrix(Expression(Float))) -> FortranCode from +--R FortranCode +--R [9] (Symbol,Matrix(Expression(Integer))) -> FortranCode from +--R FortranCode +--R [10] (Symbol,Expression(Complex(Float))) -> FortranCode from +--R FortranCode +--R [11] (Symbol,Expression(Float)) -> FortranCode from FortranCode +--R [12] (Symbol,Expression(Integer)) -> FortranCode from FortranCode +--R +--R [13] (Symbol,List(Polynomial(Integer)),Expression(MachineComplex)) +--R -> FortranCode +--R from FortranCode +--R [14] (Symbol,List(Polynomial(Integer)),Expression(MachineFloat)) -> +--R FortranCode +--R from FortranCode +--R [15] (Symbol,List(Polynomial(Integer)),Expression(MachineInteger)) +--R -> FortranCode +--R from FortranCode +--R [16] (Symbol,Vector(Expression(MachineComplex))) -> FortranCode +--R from FortranCode +--R [17] (Symbol,Vector(Expression(MachineFloat))) -> FortranCode from +--R FortranCode +--R [18] (Symbol,Vector(Expression(MachineInteger))) -> FortranCode +--R from FortranCode +--R [19] (Symbol,Matrix(Expression(MachineComplex))) -> FortranCode +--R from FortranCode +--R [20] (Symbol,Matrix(Expression(MachineFloat))) -> FortranCode from +--R FortranCode +--R [21] (Symbol,Matrix(Expression(MachineInteger))) -> FortranCode +--R from FortranCode +--R [22] (Symbol,Vector(MachineComplex)) -> FortranCode from FortranCode +--R +--R [23] (Symbol,Vector(MachineFloat)) -> FortranCode from FortranCode +--R +--R [24] (Symbol,Vector(MachineInteger)) -> FortranCode from FortranCode +--R +--R [25] (Symbol,Matrix(MachineComplex)) -> FortranCode from FortranCode +--R +--R [26] (Symbol,Matrix(MachineFloat)) -> FortranCode from FortranCode +--R +--R [27] (Symbol,Matrix(MachineInteger)) -> FortranCode from FortranCode +--R +--R [28] (Symbol,Expression(MachineComplex)) -> FortranCode from +--R FortranCode +--R [29] (Symbol,Expression(MachineFloat)) -> FortranCode from +--R FortranCode +--R [30] (Symbol,Expression(MachineInteger)) -> FortranCode from +--R FortranCode +--R [31] (Symbol,String) -> FortranCode from FortranCode +--R +--RThere is one unexposed function called assign : +--R [1] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R +--RExamples of assign from FortranCode +--R +--R +--RExamples of assign from OutputForm +--R +--E 137 + +--S 138 of 3320 +)d op assoc +--R +--R +--RThere is one exposed function called assoc : +--R [1] (D2,D) -> Union(Record(key: D2,entry: D3),"failed") from D +--R if D has ALAGG(D2,D3) and D2 has SETCAT and D3 has SETCAT +--R +--R +--RExamples of assoc from AssociationListAggregate +--R +--E 138 + +--S 139 of 3320 +)d op associatedEquations +--R +--R +--RThere is one unexposed function called associatedEquations : +--R [1] (D2,PositiveInteger) -> Record(minor: List(PositiveInteger),eq: +--R D2,minors: List(List(PositiveInteger)),ops: List(D2)) +--R from AssociatedEquations(D4,D2) +--R if D4 has FIELD and D4 has INTDOM and D2 has LODOCAT(D4) +--R +--R +--RExamples of associatedEquations from AssociatedEquations +--R +--E 139 + +--S 140 of 3320 +)d op associatedSystem +--R +--R +--RThere is one unexposed function called associatedSystem : +--R [1] (D2,PositiveInteger) -> Record(mat: Matrix(D4),vec: Vector(List( +--R PositiveInteger))) +--R from AssociatedEquations(D4,D2) if D4 has INTDOM and D2 +--R has LODOCAT(D4) +--R +--RExamples of associatedSystem from AssociatedEquations +--R +--E 140 + +--S 141 of 3320 +)d op associates? +--R +--R +--RThere is one exposed function called associates? : +--R [1] (D,D) -> Boolean from D if D has INTDOM +--R +--RExamples of associates? from IntegralDomain +--R +--E 141 + +--S 142 of 3320 +)d op associative? +--R +--R +--RThere is one exposed function called associative? : +--R [1] -> Boolean from D if D has FINAALG(D2) and D2 has COMRING +--R +--RThere is one unexposed function called associative? : +--R [1] -> Boolean from FiniteRankNonAssociativeAlgebra&(D2,D3) +--R if D3 has COMRING and D2 has FINAALG(D3) +--R +--RExamples of associative? from FiniteRankNonAssociativeAlgebra& +--R +--R +--RExamples of associative? from FiniteRankNonAssociativeAlgebra +--R +--E 142 + +--S 143 of 3320 +)d op associator +--R +--R +--RThere is one exposed function called associator : +--R [1] (D,D,D) -> D from D if D has NARNG +--R +--RExamples of associator from NonAssociativeRng +--R +--E 143 + +--S 144 of 3320 +)d op associatorDependence +--R +--R +--RThere is one exposed function called associatorDependence : +--R [1] -> List(Vector(D2)) from D +--R if D has FINAALG(D2) and D2 has COMRING and D2 has INTDOM +--R +--R +--RThere is one unexposed function called associatorDependence : +--R [1] -> List(Vector(D3)) from FiniteRankNonAssociativeAlgebra&(D2,D3 +--R ) +--R if D3 has COMRING and D2 has FINAALG(D3) +--R +--RExamples of associatorDependence from FiniteRankNonAssociativeAlgebra& +--R +--R +--RExamples of associatorDependence from FiniteRankNonAssociativeAlgebra +--R +--E 144 + +--S 145 of 3320 +)d op atan +--R +--R +--RThere are 4 exposed functions called atan : +--R [1] D -> D from D if D has ATRIG +--R [2] (DoubleFloat,DoubleFloat) -> DoubleFloat from DoubleFloat +--R [3] FortranExpression(D1,D2,D3) -> FortranExpression(D1,D2,D3) +--R from FortranExpression(D1,D2,D3) +--R if D1: LIST(SYMBOL) and D2: LIST(SYMBOL) and D3 has FMTC +--R +--R [4] (Float,Float) -> Float from Float +--R +--RThere are 5 unexposed functions called atan : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of atan from ArcTrigonometricFunctionCategory +--R +--R +--RExamples of atan from DoubleFloat +--R +--R +--RExamples of atan from ElementaryFunction +--R +--R +--RExamples of atan from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of atan from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of atan from FortranExpression +--R +--R +--RExamples of atan from Float +--R +--R +--RExamples of atan from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of atan from StreamTranscendentalFunctions +--R +--E 145 + +--S 146 of 3320 +)d op atanh +--R +--R +--RThere is one exposed function called atanh : +--R [1] D -> D from D if D has AHYP +--R +--RThere are 5 unexposed functions called atanh : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of atanh from ArcHyperbolicFunctionCategory +--R +--R +--RExamples of atanh from ElementaryFunction +--R +--R +--RExamples of atanh from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of atanh from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of atanh from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of atanh from StreamTranscendentalFunctions +--R +--E 146 + +--S 147 of 3320 +)d op atanhIfCan +--R +--R +--RThere is one exposed function called atanhIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of atanhIfCan from PartialTranscendentalFunctions +--R +--E 147 + +--S 148 of 3320 +)d op atanIfCan +--R +--R +--RThere is one exposed function called atanIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of atanIfCan from PartialTranscendentalFunctions +--R +--E 148 + +--S 149 of 3320 +)d op atom? +--R +--R +--RThere is one exposed function called atom? : +--R [1] D -> Boolean from D +--R if D has SEXCAT(D2,D3,D4,D5,D6) and D2 has SETCAT and D3 +--R has SETCAT and D4 has SETCAT and D5 has SETCAT and D6 has +--R SETCAT +--R +--RExamples of atom? from SExpressionCategory +--R +--E 149 + +--S 150 of 3320 +)d op atoms +--R +--R +--RThere is one unexposed function called atoms : +--R [1] PatternMatchListResult(D2,D3,D4) -> PatternMatchResult(D2,D3) +--R from PatternMatchListResult(D2,D3,D4) +--R if D3 has SETCAT and D2 has SETCAT and D4 has LSAGG(D3) +--R +--R +--RExamples of atoms from PatternMatchListResult +--R +--E 150 + +--S 151 of 3320 +)d op atrapezoidal +--R +--R +--RThere is one exposed function called atrapezoidal : +--R [1] ((Float -> Float),Float,Float,Float,Float,Integer,Integer, +--R Integer) -> Record(value: Float,error: Float,totalpts: Integer, +--R success: Boolean) +--R from NumericalQuadrature +--R +--RExamples of atrapezoidal from NumericalQuadrature +--R +--E 151 + +--S 152 of 3320 +)d op att2Result +--R +--R +--RThere is one exposed function called att2Result : +--R [1] Record(endPointContinuity: Union(continuous: +--R Continuous at the end points,lowerSingular: +--R There is a singularity at the lower end point,upperSingular: +--R There is a singularity at the upper end point,bothSingular: +--R There are singularities at both end points,notEvaluated: +--R End point continuity not yet evaluated),singularitiesStream: +--R Union(str: Stream(DoubleFloat),notEvaluated: +--R Internal singularities not yet evaluated),range: Union(finite: +--R The range is finite,lowerInfinite: +--R The bottom of range is infinite,upperInfinite: +--R The top of range is infinite,bothInfinite: +--R Both top and bottom points are infinite,notEvaluated: +--R Range not yet evaluated)) -> Result +--R from ExpertSystemToolsPackage +--R +--RExamples of att2Result from ExpertSystemToolsPackage +--R +--E 152 + +--S 153 of 3320 +)d op augment +--R +--R +--RThere are 4 exposed functions called augment : +--R [1] (List(D6),List(D)) -> List(D) from D +--R if D has RSETCAT(D3,D4,D5,D6) and D3 has GCDDOM and D4 +--R has OAMONS and D5 has ORDSET and D6 has RPOLCAT(D3,D4,D5) +--R +--R [2] (List(D6),D) -> List(D) from D +--R if D6 has RPOLCAT(D3,D4,D5) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET and D has RSETCAT(D3,D4,D5,D6) +--R [3] (D2,List(D)) -> List(D) from D +--R if D has RSETCAT(D3,D4,D5,D2) and D3 has GCDDOM and D4 +--R has OAMONS and D5 has ORDSET and D2 has RPOLCAT(D3,D4,D5) +--R +--R [4] (D2,D) -> List(D) from D +--R if D3 has GCDDOM and D4 has OAMONS and D5 has ORDSET and +--R D2 has RPOLCAT(D3,D4,D5) and D has RSETCAT(D3,D4,D5,D2) +--R +--RExamples of augment from RegularTriangularSetCategory +--R +--E 153 + +--S 154 of 3320 +)d op autoReduced? +--R +--R +--RThere is one exposed function called autoReduced? : +--R [1] (D,((D6,List(D6)) -> Boolean)) -> Boolean from D +--R if D has TSETCAT(D3,D4,D5,D6) and D3 has INTDOM and D4 +--R has OAMONS and D5 has ORDSET and D6 has RPOLCAT(D3,D4,D5) +--R +--R +--RExamples of autoReduced? from TriangularSetCategory +--R +--E 154 + +--S 155 of 3320 +)d op axes +--R +--R +--RThere is one exposed function called axes : +--R [1] (ThreeDimensionalViewport,String) -> Void from +--R ThreeDimensionalViewport +--R +--RThere are 2 unexposed functions called axes : +--R [1] (TwoDimensionalViewport,PositiveInteger,Palette) -> Void +--R from TwoDimensionalViewport +--R [2] (TwoDimensionalViewport,PositiveInteger,String) -> Void +--R from TwoDimensionalViewport +--R +--RExamples of axes from TwoDimensionalViewport +--R +--R +--RExamples of axes from ThreeDimensionalViewport +--R +--E 155 + +--S 156 of 3320 +)d op axesColorDefault +--R +--R +--RThere are 2 exposed functions called axesColorDefault : +--R [1] -> Palette from ViewDefaultsPackage +--R [2] Palette -> Palette from ViewDefaultsPackage +--R +--RExamples of axesColorDefault from ViewDefaultsPackage +--R +--E 156 + +--S 157 of 3320 +)d op axServer +--R +--R +--RThere is one exposed function called axServer : +--R [1] (Integer,(SExpression -> Void)) -> Void from AxiomServer +--R +--RExamples of axServer from AxiomServer +--R +--E 157 + +--S 158 of 3320 +)d op B1solve +--R +--R +--RThere is one unexposed function called B1solve : +--R [1] Record(mat: Matrix(Fraction(Polynomial(D3))),vec: List(Fraction( +--R Polynomial(D3))),rank: NonNegativeInteger,rows: List(Integer), +--R cols: List(Integer)) -> Record(partsol: Vector(Fraction( +--R Polynomial(D3))),basis: List(Vector(Fraction(Polynomial(D3))))) +--R from ParametricLinearEquations(D3,D4,D5,D6) +--R if D3 has Join(EuclideanDomain,CharacteristicZero) and D4 +--R has Join(OrderedSet,ConvertibleTo(Symbol)) and D5 has +--R OAMONS and D6 has POLYCAT(D3,D5,D4) +--R +--RExamples of B1solve from ParametricLinearEquations +--R +--E 158 + +--S 159 of 3320 +)d op back +--R +--R +--RThere are 3 exposed functions called back : +--R [1] Dequeue(D1) -> D1 from Dequeue(D1) if D1 has SETCAT +--R [2] D -> D1 from D if D has QUAGG(D1) and D1 has TYPE +--R [3] Queue(D1) -> D1 from Queue(D1) if D1 has SETCAT +--R +--RExamples of back from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rback a +--R +--R +--RExamples of back from QueueAggregate +--R +--R +--RExamples of back from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Rback a +--R +--E 159 + +--S 160 of 3320 +)d op backOldPos +--R +--R +--RThere is one exposed function called backOldPos : +--R [1] Record(mval: Matrix(D2),invmval: Matrix(D2),genIdeal: +--R PolynomialIdeals(D2,D3,D4,D5)) -> PolynomialIdeals(D2,D3,D4,D5) +--R from PolynomialIdeals(D2,D3,D4,D5) +--R if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D5 +--R has POLYCAT(D2,D3,D4) +--R +--RExamples of backOldPos from PolynomialIdeals +--R +--E 160 + +--S 161 of 3320 +)d op badNum +--R +--R +--RThere are 2 unexposed functions called badNum : +--R [1] D2 -> Record(den: Integer,gcdnum: Integer) +--R from PointsOfFiniteOrderTools(D2,D3) +--R if D2 has UPOLYC(FRAC(INT)) and D3 has UPOLYC(FRAC(D2)) +--R +--R [2] D2 -> Integer from PointsOfFiniteOrderTools(D3,D2) +--R if D3 has UPOLYC(FRAC(INT)) and D2 has UPOLYC(FRAC(D3)) +--R +--R +--RExamples of badNum from PointsOfFiniteOrderTools +--R +--E 161 + +--S 162 of 3320 +)d op badValues +--R +--R +--RThere is one unexposed function called badValues : +--R [1] Pattern(D3) -> List(D4) from PatternFunctions1(D3,D4) +--R if D3 has SETCAT and D4 has TYPE +--R +--RExamples of badValues from PatternFunctions1 +--R +--E 162 + +--S 163 of 3320 +)d op bag +--R +--R +--RThere are 6 exposed functions called bag : +--R [1] List(D2) -> ArrayStack(D2) from ArrayStack(D2) if D2 has SETCAT +--R +--R [2] List(D2) -> D from D if D2 has TYPE and D has BGAGG(D2) +--R [3] List(D2) -> Dequeue(D2) from Dequeue(D2) if D2 has SETCAT +--R [4] List(D2) -> Heap(D2) from Heap(D2) if D2 has ORDSET +--R [5] List(D2) -> Queue(D2) from Queue(D2) if D2 has SETCAT +--R [6] List(D2) -> Stack(D2) from Stack(D2) if D2 has SETCAT +--R +--RExamples of bag from ArrayStack +--R +--Rbag([1,2,3,4,5])$ArrayStack(INT) +--R +--R +--RExamples of bag from BagAggregate +--R +--R +--RExamples of bag from Dequeue +--R +--Rbag([1,2,3,4,5])$Dequeue(INT) +--R +--R +--RExamples of bag from Heap +--R +--Rbag([1,2,3,4,5])$Heap(INT) +--R +--R +--RExamples of bag from Queue +--R +--Rbag([1,2,3,4,5])$Queue(INT) +--R +--R +--RExamples of bag from Stack +--R +--Rbag([1,2,3,4,5])$Stack(INT) +--R +--E 163 + +--S 164 of 3320 +)d op balancedBinaryTree +--R +--R +--RThere is one exposed function called balancedBinaryTree : +--R [1] (NonNegativeInteger,D2) -> BalancedBinaryTree(D2) +--R from BalancedBinaryTree(D2) if D2 has SETCAT +--R +--RExamples of balancedBinaryTree from BalancedBinaryTree +--R +--RbalancedBinaryTree(4, 0) +--R +--E 164 + +--S 165 of 3320 +)d op balancedFactorisation +--R +--R +--RThere are 2 unexposed functions called balancedFactorisation : +--R [1] (D2,D2) -> Factored(D2) from BalancedFactorisation(D3,D2) +--R if D3 has Join(GcdDomain,CharacteristicZero) and D2 has +--R UPOLYC(D3) +--R [2] (D2,List(D2)) -> Factored(D2) from BalancedFactorisation(D4,D2) +--R if D2 has UPOLYC(D4) and D4 has Join(GcdDomain, +--R CharacteristicZero) +--R +--RExamples of balancedFactorisation from BalancedFactorisation +--R +--E 165 + +--S 166 of 3320 +)d op bandedHessian +--R +--R +--RThere is one exposed function called bandedHessian : +--R [1] (D2,D3,NonNegativeInteger) -> Matrix(D2) +--R from MultiVariableCalculusFunctions(D5,D2,D6,D3) +--R if D5 has SETCAT and D2 has PDRING(D5) and D6 has FLAGG(D2 +--R ) and D3 has FiniteLinearAggregate(D5)with +--R finiteAggregate +--R +--RExamples of bandedHessian from MultiVariableCalculusFunctions +--R +--E 166 + +--S 167 of 3320 +)d op bandedJacobian +--R +--R +--RThere is one exposed function called bandedJacobian : +--R [1] (D2,D3,NonNegativeInteger,NonNegativeInteger) -> Matrix(D6) +--R from MultiVariableCalculusFunctions(D5,D6,D2,D3) +--R if D5 has SETCAT and D6 has PDRING(D5) and D2 has FLAGG(D6 +--R ) and D3 has FiniteLinearAggregate(D5)with +--R finiteAggregate +--R +--RExamples of bandedJacobian from MultiVariableCalculusFunctions +--R +--E 167 + +--S 168 of 3320 done +)d op bandMatrix +--R +--R +--RThere are 2 exposed functions called bandMatrix : +--R [1] (D1,List(Integer)) -> D1 from MatrixManipulation(D3,D4,D5,D1) +--R if D3 has FIELD and D4 has FLAGG(D3) and D5 has FLAGG(D3) +--R and D1 has MATCAT(D3,D4,D5) +--R [2] (D1,Segment(Integer)) -> D1 from MatrixManipulation(D3,D4,D5,D1) +--R if D3 has FIELD and D4 has FLAGG(D3) and D5 has FLAGG(D3) +--R and D1 has MATCAT(D3,D4,D5) +--R +--RExamples of bandMatrix from MatrixManipulation +--R +--RM := matrix([[a,b,c],[d,e,f],[g,h,i]]) +--RbandMatrix(M, -1..1) +--R +--RM := matrix([[a,b,c],[d,e,f],[g,h,i]]) +--RbandMatrix(M, [-1,1]) +--RbandMatrix(M, [-1,0,1]) +--R +--E 168 + +--S 169 of 3320 +)d op base +--R +--R +--RThere are 5 exposed functions called base : +--R [1] -> PositiveInteger from D if D has FPS +--R [2] -> D from D if D has INS +--R [3] PositiveInteger -> PositiveInteger from MachineFloat +--R [4] -> PositiveInteger from MachineFloat +--R [5] PermutationGroup(D2) -> List(D2) from PermutationGroup(D2) if D2 +--R has SETCAT +--R +--RExamples of base from FloatingPointSystem +--R +--R +--RExamples of base from IntegerNumberSystem +--R +--R +--RExamples of base from MachineFloat +--R +--R +--RExamples of base from PermutationGroup +--R +--E 169 + +--S 170 of 3320 +)d op baseRDE +--R +--R +--RThere is one unexposed function called baseRDE : +--R [1] (Fraction(D4),Fraction(D4)) -> Record(ans: Fraction(D4),nosol: +--R Boolean) +--R from TranscendentalRischDE(D3,D4) +--R if D3 has Join(Field,CharacteristicZero,RetractableTo( +--R Integer)) and D4 has UPOLYC(D3) +--R +--RExamples of baseRDE from TranscendentalRischDE +--R +--E 170 + +--S 171 of 3320 +)d op baseRDEsys +--R +--R +--RThere is one unexposed function called baseRDEsys : +--R [1] (Fraction(D4),Fraction(D4),Fraction(D4)) -> Union(List(Fraction( +--R D4)),"failed") +--R from TranscendentalRischDESystem(D3,D4) +--R if D3 has Join(Field,CharacteristicZero,RetractableTo( +--R Integer)) and D4 has UPOLYC(D3) +--R +--RExamples of baseRDEsys from TranscendentalRischDESystem +--R +--E 171 + +--S 172 of 3320 +)d op basicSet +--R +--R +--RThere are 2 exposed functions called basicSet : +--R [1] (List(D8),(D8 -> Boolean),((D8,D8) -> Boolean)) -> Union(Record( +--R bas: D,top: List(D8)),"failed") +--R from D +--R if D8 has RPOLCAT(D5,D6,D7) and D5 has INTDOM and D6 has +--R OAMONS and D7 has ORDSET and D has TSETCAT(D5,D6,D7,D8) +--R [2] (List(D7),((D7,D7) -> Boolean)) -> Union(Record(bas: D,top: List +--R (D7)),"failed") +--R from D +--R if D7 has RPOLCAT(D4,D5,D6) and D4 has INTDOM and D5 has +--R OAMONS and D6 has ORDSET and D has TSETCAT(D4,D5,D6,D7) +--R +--RExamples of basicSet from TriangularSetCategory +--R +--E 172 + +--S 173 of 3320 +)d op basis +--R +--R +--RThere are 5 exposed functions called basis : +--R [1] Vector(D3) -> Vector(D3) from AlgebraPackage(D2,D3) +--R if D3 has FRNAALG(D2) and D2 has EUCDOM and D2 has INTDOM +--R +--R [2] PositiveInteger -> Vector(D) from D if D3 has FIELD and D has +--R FAXF(D3) +--R [3] -> Vector(D) from D if D2 has FIELD and D has FAXF(D2) +--R [4] -> Vector(D) from D +--R if D2 has COMRING and D3 has UPOLYC(D2) and D has FRAMALG( +--R D2,D3) +--R [5] -> Vector(D) from D if D2 has COMRING and D has FRNAALG(D2) +--R +--RThere are 3 unexposed functions called basis : +--R [1] FractionalIdeal(D2,D3,D4,D5) -> Vector(D5) +--R from FractionalIdeal(D2,D3,D4,D5) +--R if D2 has EUCDOM and D3 has QFCAT(D2) and D4 has UPOLYC(D3 +--R ) and D5 has Join(FramedAlgebra(D3,D4),RetractableTo(D3)) +--R +--R [2] FramedModule(D2,D3,D4,D5,D6) -> Vector(D5) +--R from FramedModule(D2,D3,D4,D5,D6) +--R if D2 has EUCDOM and D3 has QFCAT(D2) and D4 has UPOLYC(D3 +--R ) and D5 has FRAMALG(D3,D4) and D6: VECTOR(D5) +--R [3] PositiveInteger -> Vector(Vector(D3)) +--R from InnerNormalBasisFieldFunctions(D3) if D3 has FFIELDC +--R +--R +--RExamples of basis from AlgebraPackage +--R +--R +--RExamples of basis from FiniteAlgebraicExtensionField +--R +--R +--RExamples of basis from FramedAlgebra +--R +--R +--RExamples of basis from FractionalIdeal +--R +--R +--RExamples of basis from FramedModule +--R +--R +--RExamples of basis from FramedNonAssociativeAlgebra +--R +--R +--RExamples of basis from InnerNormalBasisFieldFunctions +--R +--E 173 + +--S 174 of 3320 +)d op basisOfCenter +--R +--R +--RThere is one exposed function called basisOfCenter : +--R [1] -> List(D3) from AlgebraPackage(D2,D3) +--R if D2 has INTDOM and D3 has FRNAALG(D2) +--R +--RExamples of basisOfCenter from AlgebraPackage +--R +--E 174 + +--S 175 of 3320 +)d op basisOfCentroid +--R +--R +--RThere is one exposed function called basisOfCentroid : +--R [1] -> List(Matrix(D2)) from AlgebraPackage(D2,D3) +--R if D2 has INTDOM and D3 has FRNAALG(D2) +--R +--RExamples of basisOfCentroid from AlgebraPackage +--R +--E 175 + +--S 176 of 3320 +)d op basisOfCommutingElements +--R +--R +--RThere is one exposed function called basisOfCommutingElements : +--R [1] -> List(D3) from AlgebraPackage(D2,D3) +--R if D2 has INTDOM and D3 has FRNAALG(D2) +--R +--RExamples of basisOfCommutingElements from AlgebraPackage +--R +--E 176 + +--S 177 of 3320 +)d op basisOfLeftAnnihilator +--R +--R +--RThere is one exposed function called basisOfLeftAnnihilator : +--R [1] D2 -> List(D2) from AlgebraPackage(D3,D2) +--R if D3 has INTDOM and D2 has FRNAALG(D3) +--R +--RExamples of basisOfLeftAnnihilator from AlgebraPackage +--R +--E 177 + +--S 178 of 3320 +)d op basisOfLeftNucleus +--R +--R +--RThere is one exposed function called basisOfLeftNucleus : +--R [1] -> List(D3) from AlgebraPackage(D2,D3) +--R if D2 has INTDOM and D3 has FRNAALG(D2) +--R +--RExamples of basisOfLeftNucleus from AlgebraPackage +--R +--E 178 + +--S 179 of 3320 +)d op basisOfLeftNucloid +--R +--R +--RThere is one exposed function called basisOfLeftNucloid : +--R [1] -> List(Matrix(D2)) from AlgebraPackage(D2,D3) +--R if D2 has INTDOM and D3 has FRNAALG(D2) +--R +--RExamples of basisOfLeftNucloid from AlgebraPackage +--R +--E 179 + +--S 180 of 3320 +)d op basisOfMiddleNucleus +--R +--R +--RThere is one exposed function called basisOfMiddleNucleus : +--R [1] -> List(D3) from AlgebraPackage(D2,D3) +--R if D2 has INTDOM and D3 has FRNAALG(D2) +--R +--RExamples of basisOfMiddleNucleus from AlgebraPackage +--R +--E 180 + +--S 181 of 3320 +)d op basisOfNucleus +--R +--R +--RThere is one exposed function called basisOfNucleus : +--R [1] -> List(D3) from AlgebraPackage(D2,D3) +--R if D2 has INTDOM and D3 has FRNAALG(D2) +--R +--RExamples of basisOfNucleus from AlgebraPackage +--R +--E 181 + +--S 182 of 3320 +)d op basisOfRightAnnihilator +--R +--R +--RThere is one exposed function called basisOfRightAnnihilator : +--R [1] D2 -> List(D2) from AlgebraPackage(D3,D2) +--R if D3 has INTDOM and D2 has FRNAALG(D3) +--R +--RExamples of basisOfRightAnnihilator from AlgebraPackage +--R +--E 182 + +--S 183 of 3320 +)d op basisOfRightNucleus +--R +--R +--RThere is one exposed function called basisOfRightNucleus : +--R [1] -> List(D3) from AlgebraPackage(D2,D3) +--R if D2 has INTDOM and D3 has FRNAALG(D2) +--R +--RExamples of basisOfRightNucleus from AlgebraPackage +--R +--E 183 + +--S 184 of 3320 +)d op basisOfRightNucloid +--R +--R +--RThere is one exposed function called basisOfRightNucloid : +--R [1] -> List(Matrix(D2)) from AlgebraPackage(D2,D3) +--R if D2 has INTDOM and D3 has FRNAALG(D2) +--R +--RExamples of basisOfRightNucloid from AlgebraPackage +--R +--E 184 + +--S 185 of 3320 +)d op bat +--R +--R +--RThere is one unexposed function called bat : +--R [1] Tableau(List(D3)) -> List(List(D3)) from TableauxBumpers(D3) if +--R D3 has ORDSET +--R +--RExamples of bat from TableauxBumpers +--R +--E 185 + +--S 186 of 3320 +)d op bat1 +--R +--R +--RThere is one unexposed function called bat1 : +--R [1] List(List(List(D3))) -> List(List(D3)) from TableauxBumpers(D3) +--R if D3 has ORDSET +--R +--RExamples of bat1 from TableauxBumpers +--R +--E 186 + +--S 187 of 3320 +)d op beauzamyBound +--R +--R +--RThere is one unexposed function called beauzamyBound : +--R [1] D2 -> Integer from GaloisGroupFactorizationUtilities(D3,D2,D4) +--R if D3 has RING and D2 has UPOLYC(D3) and D4 has Join( +--R FloatingPointSystem,RetractableTo(D3),Field, +--R TranscendentalFunctionCategory,ElementaryFunctionCategory) +--R +--R +--RExamples of beauzamyBound from GaloisGroupFactorizationUtilities +--R +--E 187 + +--S 188 of 3320 +)d op belong? +--R +--R +--RThere is one exposed function called belong? : +--R [1] BasicOperator -> Boolean from D if D has ES +--R +--RThere are 7 unexposed functions called belong? : +--R [1] BasicOperator -> Boolean from AlgebraicFunction(D3,D4) +--R if D3 has Join(OrderedSet,IntegralDomain) and D4 has FS(D3 +--R ) +--R [2] BasicOperator -> Boolean from CombinatorialFunction(D3,D4) +--R if D3 has Join(OrderedSet,IntegralDomain) and D4 has FS(D3 +--R ) +--R [3] BasicOperator -> Boolean from ElementaryFunction(D3,D4) +--R if D3 has Join(OrderedSet,IntegralDomain) and D4 has Join( +--R FunctionSpace(D3),RadicalCategory) +--R [4] BasicOperator -> Boolean from ExpressionSpace&(D3) if D3 has ES +--R +--R [5] BasicOperator -> Boolean from FunctionSpace&(D3,D4) +--R if D4 has ORDSET and D3 has FS(D4) +--R [6] BasicOperator -> Boolean from FunctionalSpecialFunction(D3,D4) +--R if D3 has Join(OrderedSet,IntegralDomain) and D4 has FS(D3 +--R ) +--R [7] BasicOperator -> Boolean from LiouvillianFunction(D3,D4) +--R if D3 has Join(OrderedSet,IntegralDomain) and D4 has Join( +--R FunctionSpace(D3),RadicalCategory, +--R TranscendentalFunctionCategory) +--R +--RExamples of belong? from AlgebraicFunction +--R +--R +--RExamples of belong? from CombinatorialFunction +--R +--R +--RExamples of belong? from ElementaryFunction +--R +--R +--RExamples of belong? from ExpressionSpace& +--R +--R +--RExamples of belong? from ExpressionSpace +--R +--R +--RExamples of belong? from FunctionSpace& +--R +--R +--RExamples of belong? from FunctionalSpecialFunction +--R +--R +--RExamples of belong? from LiouvillianFunction +--R +--E 188 + +--S 189 of 3320 +)d op bernoulli +--R +--R +--RThere is one exposed function called bernoulli : +--R [1] Integer -> Fraction(Integer) from IntegerNumberTheoryFunctions +--R +--R +--RThere is one unexposed function called bernoulli : +--R [1] Integer -> SparseUnivariatePolynomial(Fraction(Integer)) +--R from PolynomialNumberTheoryFunctions +--R +--RExamples of bernoulli from IntegerNumberTheoryFunctions +--R +--R +--RExamples of bernoulli from PolynomialNumberTheoryFunctions +--R +--E 189 + +--S 190 of 3320 +)d op bernoulliB +--R +--R +--RThere is one exposed function called bernoulliB : +--R [1] (NonNegativeInteger,D1) -> D1 from +--R NumberTheoreticPolynomialFunctions(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has COMRING +--R +--RExamples of bernoulliB from NumberTheoreticPolynomialFunctions +--R +--E 190 + +--S 191 of 3320 +)d op besselI +--R +--R +--RThere are 3 exposed functions called besselI : +--R [1] (DoubleFloat,DoubleFloat) -> DoubleFloat from +--R DoubleFloatSpecialFunctions +--R [2] (Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex( +--R DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R [3] (D,D) -> D from D if D has SPFCAT +--R +--RThere is one unexposed function called besselI : +--R [1] (D1,D1) -> D1 from FunctionalSpecialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R +--RExamples of besselI from DoubleFloatSpecialFunctions +--R +--R +--RExamples of besselI from FunctionalSpecialFunction +--R +--R +--RExamples of besselI from SpecialFunctionCategory +--R +--E 191 + +--S 192 of 3320 +)d op besselJ +--R +--R +--RThere are 3 exposed functions called besselJ : +--R [1] (DoubleFloat,DoubleFloat) -> DoubleFloat from +--R DoubleFloatSpecialFunctions +--R [2] (Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex( +--R DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R [3] (D,D) -> D from D if D has SPFCAT +--R +--RThere is one unexposed function called besselJ : +--R [1] (D1,D1) -> D1 from FunctionalSpecialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R +--RExamples of besselJ from DoubleFloatSpecialFunctions +--R +--R +--RExamples of besselJ from FunctionalSpecialFunction +--R +--R +--RExamples of besselJ from SpecialFunctionCategory +--R +--E 192 + +--S 193 of 3320 +)d op besselK +--R +--R +--RThere are 3 exposed functions called besselK : +--R [1] (DoubleFloat,DoubleFloat) -> DoubleFloat from +--R DoubleFloatSpecialFunctions +--R [2] (Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex( +--R DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R [3] (D,D) -> D from D if D has SPFCAT +--R +--RThere is one unexposed function called besselK : +--R [1] (D1,D1) -> D1 from FunctionalSpecialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R +--RExamples of besselK from DoubleFloatSpecialFunctions +--R +--R +--RExamples of besselK from FunctionalSpecialFunction +--R +--R +--RExamples of besselK from SpecialFunctionCategory +--R +--E 193 + +--S 194 of 3320 +)d op besselY +--R +--R +--RThere are 3 exposed functions called besselY : +--R [1] (DoubleFloat,DoubleFloat) -> DoubleFloat from +--R DoubleFloatSpecialFunctions +--R [2] (Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex( +--R DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R [3] (D,D) -> D from D if D has SPFCAT +--R +--RThere is one unexposed function called besselY : +--R [1] (D1,D1) -> D1 from FunctionalSpecialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R +--RExamples of besselY from DoubleFloatSpecialFunctions +--R +--R +--RExamples of besselY from FunctionalSpecialFunction +--R +--R +--RExamples of besselY from SpecialFunctionCategory +--R +--E 194 + +--S 195 of 3320 +)d op Beta +--R +--R +--RThere are 4 exposed functions called Beta : +--R [1] (DoubleFloat,DoubleFloat) -> DoubleFloat from DoubleFloat +--R [2] (DoubleFloat,DoubleFloat) -> DoubleFloat from +--R DoubleFloatSpecialFunctions +--R [3] (Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex( +--R DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R [4] (D,D) -> D from D if D has SPFCAT +--R +--RThere are 2 unexposed functions called Beta : +--R [1] (D1,D1) -> D1 from FunctionalSpecialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R [2] (NonNegativeInteger,NonNegativeInteger) -> (() -> Float) +--R from RandomFloatDistributions +--R +--RExamples of Beta from DoubleFloat +--R +--R +--RExamples of Beta from DoubleFloatSpecialFunctions +--R +--R +--RExamples of Beta from FunctionalSpecialFunction +--R +--R +--RExamples of Beta from RandomFloatDistributions +--R +--R +--RExamples of Beta from SpecialFunctionCategory +--R +--E 195 + +--S 196 of 3320 +)d op bezoutDiscriminant +--R +--R +--RThere is one unexposed function called bezoutDiscriminant : +--R [1] D2 -> D1 from BezoutMatrix(D1,D2,D3,D4,D5) +--R if D1 has commutative(*) and D4 has FLAGG(D1) and D5 has +--R FLAGG(D1) and D1 has RING and D2 has UPOLYC(D1) and D3 has +--R MATCAT(D1,D4,D5) +--R +--RExamples of bezoutDiscriminant from BezoutMatrix +--R +--E 196 + +--S 197 of 3320 +)d op bezoutMatrix +--R +--R +--RThere is one unexposed function called bezoutMatrix : +--R [1] (D2,D2) -> D1 from BezoutMatrix(D3,D2,D1,D4,D5) +--R if D3 has RING and D1 has MATCAT(D3,D4,D5) and D2 has +--R UPOLYC(D3) and D4 has FLAGG(D3) and D5 has FLAGG(D3) +--R +--RExamples of bezoutMatrix from BezoutMatrix +--R +--E 197 + +--S 198 of 3320 +)d op bezoutResultant +--R +--R +--RThere is one unexposed function called bezoutResultant : +--R [1] (D2,D2) -> D1 from BezoutMatrix(D1,D2,D3,D4,D5) +--R if D1 has commutative(*) and D4 has FLAGG(D1) and D5 has +--R FLAGG(D1) and D1 has RING and D2 has UPOLYC(D1) and D3 has +--R MATCAT(D1,D4,D5) +--R +--RExamples of bezoutResultant from BezoutMatrix +--R +--E 198 + +--S 199 of 3320 +)d op bfEntry +--R +--R +--RThere is one exposed function called bfEntry : +--R [1] Symbol -> Record(zeros: Stream(DoubleFloat),ones: Stream( +--R DoubleFloat),singularities: Stream(DoubleFloat)) +--R from BasicFunctions +--R +--RExamples of bfEntry from BasicFunctions +--R +--E 199 + +--S 200 of 3320 +)d op bfKeys +--R +--R +--RThere is one exposed function called bfKeys : +--R [1] -> List(Symbol) from BasicFunctions +--R +--RExamples of bfKeys from BasicFunctions +--R +--E 200 + +--S 201 of 3320 done +)d op binary +--R +--R +--RThere is one exposed function called binary : +--R [1] Fraction(Integer) -> BinaryExpansion from BinaryExpansion +--R +--RThere is one unexposed function called binary : +--R [1] (InputForm,List(InputForm)) -> InputForm from InputForm +--R +--RExamples of binary from BinaryExpansion +--R +--Rbinary(22/7) +--R +--R +--RExamples of binary from InputForm +--R +--Ra:=[1,2,3]::List(InputForm) +--Rbinary(_+::InputForm,a) +--R +--E 201 + +--S 202 of 3320 +)d op binaryFunction +--R +--R +--RThere is one unexposed function called binaryFunction : +--R [1] Symbol -> ((D4,D5) -> D6) from MakeBinaryCompiledFunction(D3,D4, +--R D5,D6) +--R if D3 has KONVERT(INFORM) and D4 has TYPE and D5 has TYPE +--R and D6 has TYPE +--R +--RExamples of binaryFunction from MakeBinaryCompiledFunction +--R +--E 202 + +--S 203 of 3320 done +)d op binarySearchTree +--R +--R +--RThere is one exposed function called binarySearchTree : +--R [1] List(D2) -> BinarySearchTree(D2) from BinarySearchTree(D2) if D2 +--R has ORDSET +--R +--RExamples of binarySearchTree from BinarySearchTree +--R +--RbinarySearchTree [1,2,3,4] +--R +--E 203 + +--S 204 of 3320 done +)d op binaryTournament +--R +--R +--RThere is one exposed function called binaryTournament : +--R [1] List(D2) -> BinaryTournament(D2) from BinaryTournament(D2) if D2 +--R has ORDSET +--R +--RExamples of binaryTournament from BinaryTournament +--R +--RbinaryTournament [1,2,3,4] +--R +--E 204 + +--S 205 of 3320 done +)d op binaryTree +--R +--R +--RThere are 2 exposed functions called binaryTree : +--R [1] (BinaryTree(D1),D1,BinaryTree(D1)) -> BinaryTree(D1) from +--R BinaryTree(D1) +--R if D1 has SETCAT +--R [2] D1 -> BinaryTree(D1) from BinaryTree(D1) if D1 has SETCAT +--R +--RExamples of binaryTree from BinaryTree +--R +--Rt1:=binaryTree([1,2,3]) +--Rt2:=binaryTree([4,5,6]) +--RbinaryTree(t1,[7,8,9],t2) +--R +--Rt1:=binaryTree([1,2,3]) +--R +--E 205 + +--S 206 of 3320 +)d op binomial +--R +--R +--RThere are 2 exposed functions called binomial : +--R [1] (D,D) -> D from D if D has CFCAT +--R [2] (D1,D1) -> D1 from IntegerCombinatoricFunctions(D1) if D1 has +--R INS +--R +--RThere are 3 unexposed functions called binomial : +--R [1] (D1,D1) -> D1 from CombinatorialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R [2] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R [3] (Integer,RationalNumber) -> (() -> Integer) +--R from RandomIntegerDistributions +--R +--RExamples of binomial from CombinatorialFunctionCategory +--R +--R[binomial(5,i) for i in 0..5] +--R +--R +--RExamples of binomial from CombinatorialFunction +--R +--R[binomial(5,i) for i in 0..5] +--R +--R +--RExamples of binomial from IntegerCombinatoricFunctions +--R +--R[binomial(5,i) for i in 0..5] +--R +--R +--RExamples of binomial from OutputForm +--R +--R +--RExamples of binomial from RandomIntegerDistributions +--R +--E 206 + +--S 207 of 3320 +)d op binomThmExpt +--R +--R +--RThere is one exposed function called binomThmExpt : +--R [1] (D,D,NonNegativeInteger) -> D from D +--R if D has FAMR(D2,D3) and D2 has RING and D3 has OAMON and +--R D2 has COMRING +--R +--RExamples of binomThmExpt from FiniteAbelianMonoidRing +--R +--E 207 + +--S 208 of 3320 +)d op bipolar +--R +--R +--RThere is one exposed function called bipolar : +--R [1] D2 -> (Point(D2) -> Point(D2)) from CoordinateSystems(D2) +--R if D2 has Join(Field,TranscendentalFunctionCategory, +--R RadicalCategory) +--R +--RExamples of bipolar from CoordinateSystems +--R +--E 208 + +--S 209 of 3320 +)d op bipolarCylindrical +--R +--R +--RThere is one exposed function called bipolarCylindrical : +--R [1] D2 -> (Point(D2) -> Point(D2)) from CoordinateSystems(D2) +--R if D2 has Join(Field,TranscendentalFunctionCategory, +--R RadicalCategory) +--R +--RExamples of bipolarCylindrical from CoordinateSystems +--R +--E 209 + +--S 210 of 3320 +)d op biRank +--R +--R +--RThere is one exposed function called biRank : +--R [1] D2 -> NonNegativeInteger from AlgebraPackage(D3,D2) +--R if D3 has INTDOM and D2 has FRNAALG(D3) +--R +--RExamples of biRank from AlgebraPackage +--R +--E 210 + +--S 211 of 3320 +)d op biringToPolyRing +--R +--R +--RThere is one exposed function called biringToPolyRing : +--R [1] (DistributedMultivariatePolynomial([construct,QUOTEX,QUOTEY],D4) +--R ,D3) -> D1 +--R from BlowUpPackage(D4,D5,D1,D6,D3) +--R if D4 has FIELD and D5: LIST(SYMBOL) and D1 has FAMR(D4,D6 +--R ) and D6 has DIRPCAT(#(D5),NNI) and D3 has BLMETCT +--R +--RExamples of biringToPolyRing from BlowUpPackage +--R +--E 211 + +--S 212 of 3320 +)d op birth +--R +--R +--RThere is one unexposed function called birth : +--R [1] SubSpace(D1,D2) -> SubSpace(D1,D2) from SubSpace(D1,D2) +--R if D1: PI and D2 has RING +--R +--RExamples of birth from SubSpace +--R +--E 212 + +--S 213 of 3320 +)d op bit? +--R +--R +--RThere is one exposed function called bit? : +--R [1] (D,D) -> Boolean from D if D has INS +--R +--RExamples of bit? from IntegerNumberSystem +--R +--E 213 + +--S 214 of 3320 +)d op bitCoef +--R +--R +--RThere is one unexposed function called bitCoef : +--R [1] (Integer,Integer) -> Integer from IntegerBits +--R +--RExamples of bitCoef from IntegerBits +--R +--E 214 + +--S 215 of 3320 +)d op bitLength +--R +--R +--RThere is one unexposed function called bitLength : +--R [1] Integer -> Integer from IntegerBits +--R +--RExamples of bitLength from IntegerBits +--R +--E 215 + +--S 216 of 3320 +)d op bits +--R +--R +--RThere are 3 exposed functions called bits : +--R [1] (NonNegativeInteger,Boolean) -> Bits from Bits +--R [2] PositiveInteger -> PositiveInteger from D +--R if D has arbitraryPrecision and D has FPS +--R [3] -> PositiveInteger from D if D has FPS +--R +--RExamples of bits from Bits +--R +--R +--RExamples of bits from FloatingPointSystem +--R +--E 216 + +--S 217 of 3320 +)d op bitTruth +--R +--R +--RThere is one unexposed function called bitTruth : +--R [1] (Integer,Integer) -> Boolean from IntegerBits +--R +--RExamples of bitTruth from IntegerBits +--R +--E 217 + +--S 218 of 3320 +)d op bivariate? +--R +--R +--RThere is one unexposed function called bivariate? : +--R [1] D2 -> Boolean from PolynomialSetUtilitiesPackage(D3,D4,D5,D2) +--R if D3 has INTDOM and D4 has OAMONS and D5 has ORDSET and +--R D2 has RPOLCAT(D3,D4,D5) +--R +--RExamples of bivariate? from PolynomialSetUtilitiesPackage +--R +--E 218 + +--S 219 of 3320 +)d op bivariatePolynomials +--R +--R +--RThere is one unexposed function called bivariatePolynomials : +--R [1] List(D6) -> Record(goodPols: List(D6),badPols: List(D6)) +--R from PolynomialSetUtilitiesPackage(D3,D4,D5,D6) +--R if D3 has INTDOM and D4 has OAMONS and D5 has ORDSET and +--R D6 has RPOLCAT(D3,D4,D5) +--R +--RExamples of bivariatePolynomials from PolynomialSetUtilitiesPackage +--R +--E 219 + +--S 220 of 3320 +)d op bivariateSLPEBR +--R +--R +--RThere is one unexposed function called bivariateSLPEBR : +--R [1] (List(SparseUnivariatePolynomial(D6)),SparseUnivariatePolynomial +--R (D6),D3) -> Union(List(SparseUnivariatePolynomial(D6)),"failed") +--R from PolynomialFactorizationByRecursion(D4,D5,D3,D6) +--R if D6 has POLYCAT(D4,D5,D3) and D4 has PFECAT and D5 has +--R OAMONS and D3 has ORDSET +--R +--RExamples of bivariateSLPEBR from PolynomialFactorizationByRecursion +--R +--E 220 + +--S 221 of 3320 +)d op blankSeparate +--R +--R +--RThere is one unexposed function called blankSeparate : +--R [1] List(OutputForm) -> OutputForm from OutputForm +--R +--RExamples of blankSeparate from OutputForm +--R +--E 221 + +--S 222 of 3320 +)d op block +--R +--R +--RThere is one exposed function called block : +--R [1] List(FortranCode) -> FortranCode from FortranCode +--R +--RExamples of block from FortranCode +--R +--E 222 + +--S 223 of 3320 done +)d op blockConcat +--R +--R +--RThere is one exposed function called blockConcat : +--R [1] List(List(D1)) -> D1 from MatrixManipulation(D3,D4,D5,D1) +--R if D3 has FIELD and D1 has MATCAT(D3,D4,D5) and D4 has +--R FLAGG(D3) and D5 has FLAGG(D3) +--R +--RExamples of blockConcat from MatrixManipulation +--R +--RA := matrix([[a]]) +--RB := matrix([[b]]) +--RC := matrix([[c]]) +--RA11 := element(M, 3,3) +--RA12 := horizConcat([A,B,C]) +--RA21 := vertConcat([A,B,C]) +--RM := matrix([[a,b,c],[d,e,f],[g,h,i]]) +--RE := blockConcat([[A11,A12],[A21,M]]) +--Rt1 := blockSplit(E, 4, [2,2]) +--Rt2 := blockConcat t1 +--Rzero?(E-t2) +--Rt3 := blockSplit(E, [1,2,1], [2,2]) +--Rt4 := blockConcat t3 +--Rzero?(E-t4) +--R +--E 223 + +--S 224 of 3320 done +)d op blockSplit +--R +--R +--RThere are 4 exposed functions called blockSplit : +--R [1] (D2,PositiveInteger,PositiveInteger) -> List(List(D2)) +--R from MatrixManipulation(D4,D5,D6,D2) +--R if D4 has FIELD and D5 has FLAGG(D4) and D6 has FLAGG(D4) +--R and D2 has MATCAT(D4,D5,D6) +--R [2] (D2,List(PositiveInteger),PositiveInteger) -> List(List(D2)) +--R from MatrixManipulation(D5,D6,D7,D2) +--R if D5 has FIELD and D6 has FLAGG(D5) and D7 has FLAGG(D5) +--R and D2 has MATCAT(D5,D6,D7) +--R [3] (D2,PositiveInteger,List(PositiveInteger)) -> List(List(D2)) +--R from MatrixManipulation(D5,D6,D7,D2) +--R if D5 has FIELD and D6 has FLAGG(D5) and D7 has FLAGG(D5) +--R and D2 has MATCAT(D5,D6,D7) +--R [4] (D2,List(PositiveInteger),List(PositiveInteger)) -> List(List(D2 +--R )) +--R from MatrixManipulation(D4,D5,D6,D2) +--R if D4 has FIELD and D5 has FLAGG(D4) and D6 has FLAGG(D4) +--R and D2 has MATCAT(D4,D5,D6) +--R +--RExamples of blockSplit from MatrixManipulation +--R +--RE := matrix([[i,a,b,c],[a,a,b,c],[b,d,e,f],[c,g,h,i]]) +--Rt1:= blockSplit(E, [1,2,1], [2,2]) +--R +--RE := matrix([[i,a,b,c],[a,a,b,c],[b,d,e,f],[c,g,h,i]]) +--Rt1:= blockSplit(E, 4, [2,2]) +--R +--RE := matrix([[i,a,b,c],[a,a,b,c],[b,d,e,f],[c,g,h,i]]) +--Rt1:= blockSplit(E, [2,1,1], 2) +--R +--RE := matrix([[i,a,b,c],[a,a,b,c],[b,d,e,f],[c,g,h,i]]) +--Rt1:= blockSplit(E,2,2) +--R +--E 224 + +--S 225 of 3320 +)d op blowUp +--R +--R +--RThere is one exposed function called blowUp : +--R [1] D6 -> List(D6) +--R from DesingTreePackage(D7,D8,D9,D10,D11,D12,D1,D2,D6,D3,D4 +--R ) +--R if D7 has FIELD and D8: LIST(SYMBOL) and D9 has POLYCAT(D7 +--R ,D10,OVAR(D8)) and D10 has DIRPCAT(#(D8),NNI) and D11 has +--R PRSPCAT(D7) and D12 has LOCPOWC(D7) and D1 has PLACESC(D7, +--R D12) and D2 has DIVCAT(D1) and D6 has INFCLCT(D7,D8,D9,D10, +--R D11,D12,D1,D2,D4) and D4 has BLMETCT and D3 has DSTRCAT(D6) +--R +--R +--RExamples of blowUp from DesingTreePackage +--R +--E 225 + +--S 226 of 3320 +)d op blowUpWithExcpDiv +--R +--R +--RThere is one exposed function called blowUpWithExcpDiv : +--R [1] D6 -> Void from DesingTreePackage(D7,D8,D9,D10,D11,D12,D1,D2,D3, +--R D6,D4) +--R if D7 has FIELD and D8: LIST(SYMBOL) and D9 has POLYCAT(D7 +--R ,D10,OVAR(D8)) and D10 has DIRPCAT(#(D8),NNI) and D11 has +--R PRSPCAT(D7) and D12 has LOCPOWC(D7) and D1 has PLACESC(D7, +--R D12) and D2 has DIVCAT(D1) and D3 has INFCLCT(D7,D8,D9,D10, +--R D11,D12,D1,D2,D4) and D4 has BLMETCT and D6 has DSTRCAT(D3) +--R +--R +--RExamples of blowUpWithExcpDiv from DesingTreePackage +--R +--E 226 + +--S 227 of 3320 +)d op blue +--R +--R +--RThere is one exposed function called blue : +--R [1] -> Color from Color +--R +--RExamples of blue from Color +--R +--E 227 + +--S 228 of 3320 +)d op bombieriNorm +--R +--R +--RThere are 2 unexposed functions called bombieriNorm : +--R [1] D2 -> D1 from GaloisGroupFactorizationUtilities(D3,D2,D1) +--R if D3 has RING and D1 has Join(FloatingPointSystem, +--R RetractableTo(D3),Field,TranscendentalFunctionCategory, +--R ElementaryFunctionCategory) and D2 has UPOLYC(D3) +--R [2] (D2,PositiveInteger) -> D1 +--R from GaloisGroupFactorizationUtilities(D4,D2,D1) +--R if D4 has RING and D1 has Join(FloatingPointSystem, +--R RetractableTo(D4),Field,TranscendentalFunctionCategory, +--R ElementaryFunctionCategory) and D2 has UPOLYC(D4) +--R +--RExamples of bombieriNorm from GaloisGroupFactorizationUtilities +--R +--E 228 + +--S 229 of 3320 +)d op bottom! +--R +--R +--RThere are 2 exposed functions called bottom! : +--R [1] Dequeue(D1) -> D1 from Dequeue(D1) if D1 has SETCAT +--R [2] D -> D1 from D if D has DQAGG(D1) and D1 has TYPE +--R +--RExamples of bottom! from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rbottom! a +--Ra +--R +--R +--RExamples of bottom! from DequeueAggregate +--R +--E 229 + +--S 230 of 3320 +)d op BoundIntegerRoots +--R +--R BoundIntegerRoots is not a known function. Axiom will try to list +--R its functions which contain BoundIntegerRoots in their names. +--R This is the same output you would get by issuing +--R )what operations BoundIntegerRoots +--R +--R There are no operations containing those patterns +--R +--E 230 + +--S 231 of 3320 +)d op boundOfCauchy +--R +--R +--RThere is one exposed function called boundOfCauchy : +--R [1] D2 -> D1 from RealPolynomialUtilitiesPackage(D1,D2) +--R if D1 has FIELD and D1 has ORDRING and D2 has UPOLYC(D1) +--R +--R +--RExamples of boundOfCauchy from RealPolynomialUtilitiesPackage +--R +--E 231 + +--S 232 of 3320 +)d op box +--R +--R +--RThere are 2 exposed functions called box : +--R [1] List(D) -> D from D if D has ES +--R [2] D -> D from D if D has ES +--R +--RThere is one unexposed function called box : +--R [1] OutputForm -> OutputForm from OutputForm +--R +--RExamples of box from ExpressionSpace +--R +--R +--RExamples of box from OutputForm +--R +--E 232 + +--S 233 of 3320 +)d op brace +--R +--R +--RThere are 2 exposed functions called brace : +--R [1] List(D2) -> D from D if D2 has SETCAT and D has SETAGG(D2) +--R [2] -> D from D if D has SETAGG(D1) and D1 has SETCAT +--R +--RThere are 2 unexposed functions called brace : +--R [1] List(OutputForm) -> OutputForm from OutputForm +--R [2] OutputForm -> OutputForm from OutputForm +--R +--RExamples of brace from OutputForm +--R +--R +--RExamples of brace from SetAggregate +--R +--E 233 + +--S 234 of 3320 +)d op bracket +--R +--R +--RThere are 2 unexposed functions called bracket : +--R [1] List(OutputForm) -> OutputForm from OutputForm +--R [2] OutputForm -> OutputForm from OutputForm +--R +--RExamples of bracket from OutputForm +--R +--E 234 + +--S 235 of 3320 +)d op branchIfCan +--R +--R +--RThere are 2 exposed functions called branchIfCan : +--R [1] (List(D8),D3,List(D8),Boolean,Boolean,Boolean,Boolean,Boolean) +--R -> Union(Record(eq: List(D8),tower: D3,ineq: List(D8)),"failed") +--R from QuasiComponentPackage(D5,D6,D7,D8,D3) +--R if D5 has GCDDOM and D6 has OAMONS and D7 has ORDSET and +--R D8 has RPOLCAT(D5,D6,D7) and D3 has RSETCAT(D5,D6,D7,D8) +--R +--R [2] (List(D8),D3,List(D8),Boolean,Boolean,Boolean,Boolean,Boolean) +--R -> Union(Record(eq: List(D8),tower: D3,ineq: List(D8)),"failed") +--R from SquareFreeQuasiComponentPackage(D5,D6,D7,D8,D3) +--R if D5 has GCDDOM and D6 has OAMONS and D7 has ORDSET and +--R D8 has RPOLCAT(D5,D6,D7) and D3 has RSETCAT(D5,D6,D7,D8) +--R +--R +--RExamples of branchIfCan from QuasiComponentPackage +--R +--R +--RExamples of branchIfCan from SquareFreeQuasiComponentPackage +--R +--E 235 + +--S 236 of 3320 +)d op branchPoint? +--R +--R +--RThere are 2 exposed functions called branchPoint? : +--R [1] D2 -> Boolean from D +--R if D has FFCAT(D3,D2,D4) and D3 has UFD and D2 has UPOLYC( +--R D3) and D4 has UPOLYC(FRAC(D2)) +--R [2] D2 -> Boolean from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC( +--R D2) and D4 has UPOLYC(FRAC(D3)) +--R +--RExamples of branchPoint? from FunctionFieldCategory +--R +--E 236 + +--S 237 of 3320 done +)d op branchPointAtInfinity? +--R +--R +--RThere is one exposed function called branchPointAtInfinity? : +--R [1] -> Boolean from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC( +--R D2) and D4 has UPOLYC(FRAC(D3)) +--R +--RExamples of branchPointAtInfinity? from FunctionFieldCategory +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) +--RbranchPointAtInfinity?()$R +--RR2 := RadicalFunctionField(INT, P0, P1, 2 * x**2, 4) +--RbranchPointAtInfinity?()$R +--R +--E 237 + +--S 238 of 3320 +)d op bright +--R +--R +--RThere are 3 exposed functions called bright : +--R [1] String -> List(String) from DisplayPackage +--R [2] List(String) -> List(String) from DisplayPackage +--R [3] Color -> Palette from Palette +--R +--RExamples of bright from DisplayPackage +--R +--R +--RExamples of bright from Palette +--R +--E 238 + +--S 239 of 3320 +)d op brillhartIrreducible? +--R +--R +--RThere are 2 unexposed functions called brillhartIrreducible? : +--R [1] D2 -> Boolean from BrillhartTests(D2) if D2 has UPOLYC(INT) +--R [2] (D2,Boolean) -> Boolean from BrillhartTests(D2) if D2 has UPOLYC +--R (INT) +--R +--RExamples of brillhartIrreducible? from BrillhartTests +--R +--E 239 + +--S 240 of 3320 +)d op brillhartTrials +--R +--R +--RThere are 2 unexposed functions called brillhartTrials : +--R [1] -> NonNegativeInteger from BrillhartTests(D2) if D2 has UPOLYC( +--R INT) +--R [2] NonNegativeInteger -> NonNegativeInteger from BrillhartTests(D2) +--R if D2 has UPOLYC(INT) +--R +--RExamples of brillhartTrials from BrillhartTests +--R +--E 240 + +--S 241 of 3320 +)d op bringDown +--R +--R +--RThere are 2 unexposed functions called bringDown : +--R [1] D2 -> Fraction(Integer) from FunctionSpaceReduce(D3,D2) +--R if D3 has Join(OrderedSet,IntegralDomain,RetractableTo( +--R Integer)) and D2 has FS(D3) +--R [2] (D2,Kernel(D2)) -> SparseUnivariatePolynomial(Fraction(Integer)) +--R from FunctionSpaceReduce(D4,D2) +--R if D2 has FS(D4) and D4 has Join(OrderedSet,IntegralDomain +--R ,RetractableTo(Integer)) +--R +--RExamples of bringDown from FunctionSpaceReduce +--R +--E 241 + +--S 242 of 3320 +)d op bsolve +--R +--R +--RThere is one unexposed function called bsolve : +--R [1] (Matrix(D2),List(Fraction(Polynomial(D9))),NonNegativeInteger, +--R String,Integer) -> Record(rgl: List(Record(eqzro: List(D2),neqzro +--R : List(D2),wcond: List(Polynomial(D9)),bsoln: Record(partsol: +--R Vector(Fraction(Polynomial(D9))),basis: List(Vector(Fraction( +--R Polynomial(D9))))))),rgsz: Integer) +--R from ParametricLinearEquations(D9,D10,D1,D2) +--R if D9 has Join(EuclideanDomain,CharacteristicZero) and D2 +--R has POLYCAT(D9,D1,D10) and D10 has Join(OrderedSet, +--R ConvertibleTo(Symbol)) and D1 has OAMONS +--R +--RExamples of bsolve from ParametricLinearEquations +--R +--E 242 + +--S 243 of 3320 +)d op btwFact +--R +--R +--RThere is one unexposed function called btwFact : +--R [1] (D2,Boolean,Set(NonNegativeInteger),NonNegativeInteger) -> +--R Record(contp: Integer,factors: List(Record(irr: D2,pow: Integer)) +--R ) +--R from GaloisGroupFactorizer(D2) if D2 has UPOLYC(INT) +--R +--RExamples of btwFact from GaloisGroupFactorizer +--R +--E 243 + +--S 244 of 3320 +)d op bubbleSort! +--R +--R +--RThere are 2 unexposed functions called bubbleSort! : +--R [1] (D1,((D3,D3) -> Boolean)) -> D1 from SortPackage(D3,D1) +--R if D3 has TYPE and D1 has IndexedAggregate(Integer,D3)with +--R finiteAggregate +--R shallowlyMutable +--R [2] D1 -> D1 from SortPackage(D2,D1) +--R if D2 has ORDSET and D2 has TYPE and D1 has +--R IndexedAggregate(Integer,D2)with +--R finiteAggregate +--R shallowlyMutable +--R +--RExamples of bubbleSort! from SortPackage +--R +--E 244 + +--S 245 of 3320 +)d op build +--R +--R +--RThere is one unexposed function called build : +--R [1] (D1,D2,D3) -> GeneralModulePolynomial(D4,D1,D2,D3,D5,D6) +--R from GeneralModulePolynomial(D4,D1,D2,D3,D5,D6) +--R if D4: LIST(SYMBOL) and D1 has COMRING and D3 has DIRPCAT( +--R #(D4),NNI) and D5: ((Record(index: D2,exponent: D3),Record( +--R index: D2,exponent: D3)) -> Boolean) and D2 has ORDSET and +--R D6 has POLYCAT(D1,D3,OVAR(D4)) +--R +--RExamples of build from GeneralModulePolynomial +--R +--E 245 + +--S 246 of 3320 +)d op BumInSepFFE +--R +--R +--RThere is one unexposed function called BumInSepFFE : +--R [1] Record(flg: Union("nil","sqfr","irred","prime"),fctr: D3,xpnt: +--R Integer) -> Record(flg: Union("nil","sqfr","irred","prime"),fctr +--R : D3,xpnt: Integer) +--R from UnivariatePolynomialSquareFree(D2,D3) +--R if D3 has Join(UnivariatePolynomialCategory(D2), +--R IntegralDomain)with +--R gcd : (%,%) -> %and D2 has INTDOM +--R +--RExamples of BumInSepFFE from UnivariatePolynomialSquareFree +--R +--E 246 + +--S 247 of 3320 +)d op bumprow +--R +--R +--RThere is one unexposed function called bumprow : +--R [1] (((D5,D5) -> Boolean),List(D5),List(List(D5))) -> Record(fs: +--R Boolean,sd: List(D5),td: List(List(D5))) +--R from TableauxBumpers(D5) if D5 has ORDSET +--R +--RExamples of bumprow from TableauxBumpers +--R +--E 247 + +--S 248 of 3320 +)d op bumptab +--R +--R +--RThere is one unexposed function called bumptab : +--R [1] (((D4,D4) -> Boolean),List(D4),List(List(List(D4)))) -> List( +--R List(List(D4))) +--R from TableauxBumpers(D4) if D4 has ORDSET +--R +--RExamples of bumptab from TableauxBumpers +--R +--E 248 + +--S 249 of 3320 +)d op bumptab1 +--R +--R +--RThere is one unexposed function called bumptab1 : +--R [1] (List(D3),List(List(List(D3)))) -> List(List(List(D3))) +--R from TableauxBumpers(D3) if D3 has ORDSET +--R +--RExamples of bumptab1 from TableauxBumpers +--R +--E 249 + +--S 250 of 3320 +)d op BY +--R +--R +--RThere is one exposed function called BY : +--R [1] (D,Integer) -> D from D if D has SEGCAT(D2) and D2 has TYPE +--R +--RExamples of BY from SegmentCategory +--R +--E 250 + +--S 251 of 3320 +)d op c02aff +--R +--R +--RThere is one exposed function called c02aff : +--R [1] (Matrix(DoubleFloat),Integer,Boolean,Integer) -> Result +--R from NagPolynomialRootsPackage +--R +--RExamples of c02aff from NagPolynomialRootsPackage +--R +--E 251 + +--S 252 of 3320 +)d op c02agf +--R +--R +--RThere is one exposed function called c02agf : +--R [1] (Matrix(DoubleFloat),Integer,Boolean,Integer) -> Result +--R from NagPolynomialRootsPackage +--R +--RExamples of c02agf from NagPolynomialRootsPackage +--R +--E 252 + +--S 253 of 3320 +)d op c05adf +--R +--R +--RThere is one exposed function called c05adf : +--R [1] (DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Union( +--R fn: FileName,fp: Asp1(F))) -> Result +--R from NagRootFindingPackage +--R +--RExamples of c05adf from NagRootFindingPackage +--R +--E 253 + +--S 254 of 3320 +)d op c05nbf +--R +--R +--RThere is one exposed function called c05nbf : +--R [1] (Integer,Integer,Matrix(DoubleFloat),DoubleFloat,Integer,Union( +--R fn: FileName,fp: Asp6(FCN))) -> Result +--R from NagRootFindingPackage +--R +--RExamples of c05nbf from NagRootFindingPackage +--R +--E 254 + +--S 255 of 3320 +)d op c05pbf +--R +--R +--RThere is one exposed function called c05pbf : +--R [1] (Integer,Integer,Integer,Matrix(DoubleFloat),DoubleFloat,Integer +--R ,Union(fn: FileName,fp: Asp35(FCN))) -> Result +--R from NagRootFindingPackage +--R +--RExamples of c05pbf from NagRootFindingPackage +--R +--E 255 + +--S 256 of 3320 +)d op c06eaf +--R +--R +--RThere is one exposed function called c06eaf : +--R [1] (Integer,Matrix(DoubleFloat),Integer) -> Result +--R from NagSeriesSummationPackage +--R +--RExamples of c06eaf from NagSeriesSummationPackage +--R +--E 256 + +--S 257 of 3320 +)d op c06ebf +--R +--R +--RThere is one exposed function called c06ebf : +--R [1] (Integer,Matrix(DoubleFloat),Integer) -> Result +--R from NagSeriesSummationPackage +--R +--RExamples of c06ebf from NagSeriesSummationPackage +--R +--E 257 + +--S 258 of 3320 +)d op c06ecf +--R +--R +--RThere is one exposed function called c06ecf : +--R [1] (Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer) -> +--R Result +--R from NagSeriesSummationPackage +--R +--RExamples of c06ecf from NagSeriesSummationPackage +--R +--E 258 + +--S 259 of 3320 +)d op c06ekf +--R +--R +--RThere is one exposed function called c06ekf : +--R [1] (Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer +--R ) -> Result +--R from NagSeriesSummationPackage +--R +--RExamples of c06ekf from NagSeriesSummationPackage +--R +--E 259 + +--S 260 of 3320 +)d op c06fpf +--R +--R +--RThere is one exposed function called c06fpf : +--R [1] (Integer,Integer,String,Matrix(DoubleFloat),Matrix(DoubleFloat), +--R Integer) -> Result +--R from NagSeriesSummationPackage +--R +--RExamples of c06fpf from NagSeriesSummationPackage +--R +--E 260 + +--S 261 of 3320 +)d op c06fqf +--R +--R +--RThere is one exposed function called c06fqf : +--R [1] (Integer,Integer,String,Matrix(DoubleFloat),Matrix(DoubleFloat), +--R Integer) -> Result +--R from NagSeriesSummationPackage +--R +--RExamples of c06fqf from NagSeriesSummationPackage +--R +--E 261 + +--S 262 of 3320 +)d op c06frf +--R +--R +--RThere is one exposed function called c06frf : +--R [1] (Integer,Integer,String,Matrix(DoubleFloat),Matrix(DoubleFloat), +--R Matrix(DoubleFloat),Integer) -> Result +--R from NagSeriesSummationPackage +--R +--RExamples of c06frf from NagSeriesSummationPackage +--R +--E 262 + +--S 263 of 3320 +)d op c06fuf +--R +--R +--RThere is one exposed function called c06fuf : +--R [1] (Integer,Integer,String,Matrix(DoubleFloat),Matrix(DoubleFloat), +--R Matrix(DoubleFloat),Matrix(DoubleFloat),Integer) -> Result +--R from NagSeriesSummationPackage +--R +--RExamples of c06fuf from NagSeriesSummationPackage +--R +--E 263 + +--S 264 of 3320 +)d op c06gbf +--R +--R +--RThere is one exposed function called c06gbf : +--R [1] (Integer,Matrix(DoubleFloat),Integer) -> Result +--R from NagSeriesSummationPackage +--R +--RExamples of c06gbf from NagSeriesSummationPackage +--R +--E 264 + +--S 265 of 3320 +)d op c06gcf +--R +--R +--RThere is one exposed function called c06gcf : +--R [1] (Integer,Matrix(DoubleFloat),Integer) -> Result +--R from NagSeriesSummationPackage +--R +--RExamples of c06gcf from NagSeriesSummationPackage +--R +--E 265 + +--S 266 of 3320 +)d op c06gqf +--R +--R +--RThere is one exposed function called c06gqf : +--R [1] (Integer,Integer,Matrix(DoubleFloat),Integer) -> Result +--R from NagSeriesSummationPackage +--R +--RExamples of c06gqf from NagSeriesSummationPackage +--R +--E 266 + +--S 267 of 3320 +)d op c06gsf +--R +--R +--RThere is one exposed function called c06gsf : +--R [1] (Integer,Integer,Matrix(DoubleFloat),Integer) -> Result +--R from NagSeriesSummationPackage +--R +--RExamples of c06gsf from NagSeriesSummationPackage +--R +--E 267 + +--S 268 of 3320 +)d op cache +--R +--R +--RThere is one unexposed function called cache : +--R [1] -> List(D2) from SortedCache(D2) if D2 has CACHSET +--R +--RExamples of cache from SortedCache +--R +--E 268 + +--S 269 of 3320 +)d op cAcos +--R +--R +--RThere is one unexposed function called cAcos : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cAcos from InnerSparseUnivariatePowerSeries +--R +--E 269 + +--S 270 of 3320 +)d op cAcosh +--R +--R +--RThere is one unexposed function called cAcosh : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cAcosh from InnerSparseUnivariatePowerSeries +--R +--E 270 + +--S 271 of 3320 +)d op cAcot +--R +--R +--RThere is one unexposed function called cAcot : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cAcot from InnerSparseUnivariatePowerSeries +--R +--E 271 + +--S 272 of 3320 +)d op cAcoth +--R +--R +--RThere is one unexposed function called cAcoth : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cAcoth from InnerSparseUnivariatePowerSeries +--R +--E 272 + +--S 273 of 3320 +)d op cAcsc +--R +--R +--RThere is one unexposed function called cAcsc : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cAcsc from InnerSparseUnivariatePowerSeries +--R +--E 273 + +--S 274 of 3320 +)d op cAcsch +--R +--R +--RThere is one unexposed function called cAcsch : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cAcsch from InnerSparseUnivariatePowerSeries +--R +--E 274 + +--S 275 of 3320 +)d op calcRanges +--R +--R +--RThere is one unexposed function called calcRanges : +--R [1] List(List(Point(DoubleFloat))) -> List(Segment(DoubleFloat)) +--R from PlotTools +--R +--RExamples of calcRanges from PlotTools +--R +--E 275 + +--S 276 of 3320 +)d op call +--R +--R +--RThere is one exposed function called call : +--R [1] String -> FortranCode from FortranCode +--R +--RExamples of call from FortranCode +--R +--E 276 + +--S 277 of 3320 +)d op canonicalIfCan +--R +--R +--RThere is one exposed function called canonicalIfCan : +--R [1] (D1,D2) -> Union(D1,"failed") from D +--R if D has MAGCDOC(D1,D2) and D1 has TYPE and D2 has TYPE +--R +--R +--RExamples of canonicalIfCan from ModularAlgebraicGcdOperations +--R +--E 277 + +--S 278 of 3320 +)d op cap +--R +--R +--RThere is one exposed function called cap : +--R [1] (SymmetricPolynomial(Fraction(Integer)),SymmetricPolynomial( +--R Fraction(Integer))) -> Fraction(Integer) +--R from CycleIndicators +--R +--RExamples of cap from CycleIndicators +--R +--E 278 + +--S 279 of 3320 +)d op car +--R +--R +--RThere is one exposed function called car : +--R [1] D -> D from D +--R if D has SEXCAT(D1,D2,D3,D4,D5) and D1 has SETCAT and D2 +--R has SETCAT and D3 has SETCAT and D4 has SETCAT and D5 has +--R SETCAT +--R +--RExamples of car from SExpressionCategory +--R +--E 279 + +--S 280 of 3320 +)d op cardinality +--R +--R +--RThere is one exposed function called cardinality : +--R [1] D -> NonNegativeInteger from D if D has FSAGG(D2) and D2 has +--R SETCAT +--R +--RExamples of cardinality from FiniteSetAggregate +--R +--E 280 + +--S 281 of 3320 +)d op cartesian +--R +--R +--RThere is one exposed function called cartesian : +--R [1] Point(D2) -> Point(D2) from CoordinateSystems(D2) +--R if D2 has Join(Field,TranscendentalFunctionCategory, +--R RadicalCategory) +--R +--RExamples of cartesian from CoordinateSystems +--R +--E 281 + +--S 282 of 3320 +)d op cAsec +--R +--R +--RThere is one unexposed function called cAsec : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cAsec from InnerSparseUnivariatePowerSeries +--R +--E 282 + +--S 283 of 3320 +)d op cAsech +--R +--R +--RThere is one unexposed function called cAsech : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cAsech from InnerSparseUnivariatePowerSeries +--R +--E 283 + +--S 284 of 3320 +)d op cAsin +--R +--R +--RThere is one unexposed function called cAsin : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cAsin from InnerSparseUnivariatePowerSeries +--R +--E 284 + +--S 285 of 3320 +)d op cAsinh +--R +--R +--RThere is one unexposed function called cAsinh : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cAsinh from InnerSparseUnivariatePowerSeries +--R +--E 285 + +--S 286 of 3320 +)d op cAtan +--R +--R +--RThere is one unexposed function called cAtan : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cAtan from InnerSparseUnivariatePowerSeries +--R +--E 286 + +--S 287 of 3320 +)d op cAtanh +--R +--R +--RThere is one unexposed function called cAtanh : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cAtanh from InnerSparseUnivariatePowerSeries +--R +--E 287 + +--S 288 of 3320 +)d op cCos +--R +--R +--RThere is one unexposed function called cCos : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cCos from InnerSparseUnivariatePowerSeries +--R +--E 288 + +--S 289 of 3320 +)d op cCosh +--R +--R +--RThere is one unexposed function called cCosh : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cCosh from InnerSparseUnivariatePowerSeries +--R +--E 289 + +--S 290 of 3320 +)d op cCot +--R +--R +--RThere is one unexposed function called cCot : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cCot from InnerSparseUnivariatePowerSeries +--R +--E 290 + +--S 291 of 3320 +)d op cCoth +--R +--R +--RThere is one unexposed function called cCoth : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cCoth from InnerSparseUnivariatePowerSeries +--R +--E 291 + +--S 292 of 3320 +)d op cCsc +--R +--R +--RThere is one unexposed function called cCsc : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cCsc from InnerSparseUnivariatePowerSeries +--R +--E 292 + +--S 293 of 3320 +)d op cCsch +--R +--R +--RThere is one unexposed function called cCsch : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cCsch from InnerSparseUnivariatePowerSeries +--R +--E 293 + +--S 294 of 3320 +)d op cdr +--R +--R +--RThere is one exposed function called cdr : +--R [1] D -> D from D +--R if D has SEXCAT(D1,D2,D3,D4,D5) and D1 has SETCAT and D2 +--R has SETCAT and D3 has SETCAT and D4 has SETCAT and D5 has +--R SETCAT +--R +--RExamples of cdr from SExpressionCategory +--R +--E 294 + +--S 295 of 3320 +)d op ceiling +--R +--R +--RThere are 2 exposed functions called ceiling : +--R [1] D -> D1 from D if D has QFCAT(D1) and D1 has INTDOM and D1 has +--R INS +--R [2] D -> D from D if D has RNS +--R +--RExamples of ceiling from QuotientFieldCategory +--R +--R +--RExamples of ceiling from RealNumberSystem +--R +--E 295 + +--S 296 of 3320 +)d op center +--R +--R +--RThere are 3 exposed functions called center : +--R [1] (String,Integer,String) -> String from DisplayPackage +--R [2] (List(String),Integer,String) -> List(String) from +--R DisplayPackage +--R [3] D -> D1 from D if D has UPSCAT(D1,D2) and D2 has OAMON and D1 +--R has RING +--R +--RThere are 2 unexposed functions called center : +--R [1] OutputForm -> OutputForm from OutputForm +--R [2] (OutputForm,Integer) -> OutputForm from OutputForm +--R +--RExamples of center from DisplayPackage +--R +--R +--RExamples of center from OutputForm +--R +--R +--RExamples of center from UnivariatePowerSeriesCategory +--R +--E 296 + +--S 297 of 3320 +)d op central? +--R +--R +--RThere is one exposed function called central? : +--R [1] (DoubleFloat,DoubleFloat,List(Expression(DoubleFloat))) -> +--R Boolean +--R from d03AgentsPackage +--R +--RExamples of central? from d03AgentsPackage +--R +--E 297 + +--S 298 of 3320 +)d op certainlySubVariety? +--R +--R +--RThere is one unexposed function called certainlySubVariety? : +--R [1] (List(D6),List(D6)) -> Boolean +--R from PolynomialSetUtilitiesPackage(D3,D4,D5,D6) +--R if D6 has RPOLCAT(D3,D4,D5) and D3 has INTDOM and D4 has +--R OAMONS and D5 has ORDSET +--R +--RExamples of certainlySubVariety? from PolynomialSetUtilitiesPackage +--R +--E 298 + +--S 299 of 3320 +)d op cExp +--R +--R +--RThere is one unexposed function called cExp : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cExp from InnerSparseUnivariatePowerSeries +--R +--E 299 + +--S 300 of 3320 +)d op cfirst +--R +--R +--RThere is one unexposed function called cfirst : +--R [1] NonNegativeInteger -> (Stream(Polynomial(D3)) -> Stream( +--R Polynomial(D3))) +--R from WeierstrassPreparation(D3) if D3 has FIELD +--R +--RExamples of cfirst from WeierstrassPreparation +--R +--E 300 + +--S 301 of 3320 +)d op chainSubResultants +--R +--R +--RThere is one unexposed function called chainSubResultants : +--R [1] (D2,D2) -> List(D2) from PseudoRemainderSequence(D3,D2) +--R if D3 has INTDOM and D2 has UPOLYC(D3) +--R +--RExamples of chainSubResultants from PseudoRemainderSequence +--R +--E 301 + +--S 302 of 3320 +)d op changeBase +--R +--R +--RThere is one exposed function called changeBase : +--R [1] (Integer,Integer,PositiveInteger) -> MachineFloat from +--R MachineFloat +--R +--RThere is one unexposed function called changeBase : +--R [1] (Matrix(D4),Matrix(D4),Automorphism(D4),(D4 -> D4)) -> Matrix(D4 +--R ) +--R from PseudoLinearNormalForm(D4) if D4 has FIELD +--R +--RExamples of changeBase from MachineFloat +--R +--R +--RExamples of changeBase from PseudoLinearNormalForm +--R +--E 302 + +--S 303 of 3320 +)d op changeMeasure +--R +--R +--RThere is one exposed function called changeMeasure : +--R [1] (RoutinesTable,Symbol,Float) -> RoutinesTable from RoutinesTable +--R +--R +--RExamples of changeMeasure from RoutinesTable +--R +--E 303 + +--S 304 of 3320 +)d op changeName +--R +--R +--RThere is one exposed function called changeName : +--R [1] (Symbol,Symbol,Result) -> Result from d01AgentsPackage +--R +--RExamples of changeName from d01AgentsPackage +--R +--E 304 + +--S 305 of 3320 +)d op changeNameToObjf +--R +--R +--RThere is one exposed function called changeNameToObjf : +--R [1] (Symbol,Result) -> Result from e04AgentsPackage +--R +--RExamples of changeNameToObjf from e04AgentsPackage +--R +--E 305 + +--S 306 of 3320 +)d op changeThreshhold +--R +--R +--RThere is one exposed function called changeThreshhold : +--R [1] (RoutinesTable,Symbol,Float) -> RoutinesTable from RoutinesTable +--R +--R +--RExamples of changeThreshhold from RoutinesTable +--R +--E 306 + +--S 307 of 3320 +)d op changeVar +--R +--R +--RThere are 2 unexposed functions called changeVar : +--R [1] (D1,D2) -> D1 from PrimitiveRatRicDE(D3,D2,D1,D4) +--R if D3 has Join(Field,CharacteristicZero,RetractableTo( +--R Fraction(Integer))) and D2 has UPOLYC(D3) and D1 has +--R LODOCAT(D2) and D4 has LODOCAT(FRAC(D2)) +--R [2] (D1,Fraction(D4)) -> D1 from PrimitiveRatRicDE(D3,D4,D1,D5) +--R if D3 has Join(Field,CharacteristicZero,RetractableTo( +--R Fraction(Integer))) and D4 has UPOLYC(D3) and D1 has +--R LODOCAT(D4) and D5 has LODOCAT(FRAC(D4)) +--R +--RExamples of changeVar from PrimitiveRatRicDE +--R +--E 307 + +--S 308 of 3320 +)d op changeWeightLevel +--R +--R +--RThere are 2 unexposed functions called changeWeightLevel : +--R [1] NonNegativeInteger -> Void from OrdinaryWeightedPolynomials(D3, +--R D4,D5,D6) +--R if D3 has RING and D4: LIST(SYMBOL) and D5: LIST(NNI) and +--R D6: NNI +--R [2] NonNegativeInteger -> Void from WeightedPolynomials(D4,D5,D6,D7, +--R D8,D9,D1) +--R if D4 has RING and D5 has ORDSET and D6 has OAMONS and D8 +--R : LIST(D5) and D7 has POLYCAT(D4,D6,D5) and D9: LIST(NNI) +--R and D1: NNI +--R +--RExamples of changeWeightLevel from OrdinaryWeightedPolynomials +--R +--R +--RExamples of changeWeightLevel from WeightedPolynomials +--R +--E 308 + +--S 309 of 3320 done +)d op char +--R +--R +--RThere are 2 exposed functions called char : +--R [1] String -> Character from Character +--R [2] Integer -> Character from Character +--R +--RExamples of char from Character +--R +--R[char c for c in ["a","A","X","8","+"]] +--R +--R[char c for c in [97,65,88,56,43]] +--R +--E 309 + +--S 310 of 3320 +)d op character? +--R +--R +--RThere is one exposed function called character? : +--R [1] FortranScalarType -> Boolean from FortranScalarType +--R +--RExamples of character? from FortranScalarType +--R +--E 310 + +--S 311 of 3320 +)d op characteristic +--R +--R +--RThere are 2 exposed functions called characteristic : +--R [1] -> NonNegativeInteger from D if D has NASRING +--R [2] -> NonNegativeInteger from D if D has RING +--R +--RThere are 9 unexposed functions called characteristic : +--R [1] -> NonNegativeInteger from ComplexCategory&(D2,D3) +--R if D3 has COMRING and D2 has COMPCAT(D3) +--R [2] -> NonNegativeInteger from DirectProductCategory&(D2,D3,D4) +--R if D3: NNI and D4 has TYPE and D2 has DIRPCAT(D3,D4) +--R [3] -> NonNegativeInteger from FunctionSpace&(D2,D3) +--R if D3 has ORDSET and D2 has FS(D3) +--R [4] -> NonNegativeInteger from IntegerNumberSystem&(D2) if D2 has +--R INS +--R [5] -> NonNegativeInteger from OctonionCategory&(D2,D3) +--R if D3 has COMRING and D2 has OC(D3) +--R [6] -> NonNegativeInteger from QuotientFieldCategory&(D2,D3) +--R if D3 has INTDOM and D2 has QFCAT(D3) +--R [7] -> NonNegativeInteger from QuaternionCategory&(D2,D3) +--R if D3 has COMRING and D2 has QUATCAT(D3) +--R [8] -> NonNegativeInteger from RealClosedField&(D2) if D2 has +--R RCFIELD +--R [9] -> NonNegativeInteger from RealNumberSystem&(D2) if D2 has RNS +--R +--R +--RExamples of characteristic from ComplexCategory& +--R +--R +--RExamples of characteristic from DirectProductCategory& +--R +--R +--RExamples of characteristic from FunctionSpace& +--R +--R +--RExamples of characteristic from IntegerNumberSystem& +--R +--R +--RExamples of characteristic from NonAssociativeRing +--R +--R +--RExamples of characteristic from OctonionCategory& +--R +--R +--RExamples of characteristic from QuotientFieldCategory& +--R +--R +--RExamples of characteristic from QuaternionCategory& +--R +--R +--RExamples of characteristic from RealClosedField& +--R +--R +--RExamples of characteristic from Ring +--R +--R +--RExamples of characteristic from RealNumberSystem& +--R +--E 311 + +--S 312 of 3320 +)d op characteristicPolynomial +--R +--R +--RThere are 8 exposed functions called characteristicPolynomial : +--R [1] (Matrix(D1),D1) -> D1 from CharacteristicPolynomialPackage(D1) +--R if D1 has COMRING +--R [2] (Matrix(Fraction(Polynomial(D4))),Symbol) -> Polynomial(D4) +--R from EigenPackage(D4) if D4 has GCDDOM +--R [3] Matrix(Fraction(Polynomial(D3))) -> Polynomial(D3) from +--R EigenPackage(D3) +--R if D3 has GCDDOM +--R [4] D -> D1 from D +--R if D has FINRALG(D2,D1) and D2 has COMRING and D1 has +--R UPOLYC(D2) +--R [5] Matrix(Complex(Fraction(Integer))) -> Polynomial(Complex( +--R Fraction(Integer))) +--R from NumericComplexEigenPackage(D3) if D3 has Join(Field, +--R OrderedRing) +--R [6] (Matrix(Complex(Fraction(Integer))),Symbol) -> Polynomial( +--R Complex(Fraction(Integer))) +--R from NumericComplexEigenPackage(D4) if D4 has Join(Field, +--R OrderedRing) +--R [7] Matrix(Fraction(Integer)) -> Polynomial(Fraction(Integer)) +--R from NumericRealEigenPackage(D3) if D3 has Join(Field, +--R OrderedRing) +--R [8] (Matrix(Fraction(Integer)),Symbol) -> Polynomial(Fraction( +--R Integer)) +--R from NumericRealEigenPackage(D4) if D4 has Join(Field, +--R OrderedRing) +--R +--RThere is one unexposed function called characteristicPolynomial : +--R [1] D2 -> D1 from CharacteristicPolynomialInMonogenicalAlgebra(D3,D1 +--R ,D2) +--R if D3 has COMRING and D1 has UPOLYC(D3) and D2 has MONOGEN +--R (D3,D1) +--R +--RExamples of characteristicPolynomial from CharacteristicPolynomialPackage +--R +--R +--RExamples of characteristicPolynomial from CharacteristicPolynomialInMonogenicalAlgebra +--R +--R +--RExamples of characteristicPolynomial from EigenPackage +--R +--R +--RExamples of characteristicPolynomial from FiniteRankAlgebra +--R +--R +--RExamples of characteristicPolynomial from NumericComplexEigenPackage +--R +--R +--RExamples of characteristicPolynomial from NumericRealEigenPackage +--R +--E 312 + +--S 313 of 3320 +)d op characteristicSerie +--R +--R +--RThere are 2 exposed functions called characteristicSerie : +--R [1] List(D6) -> List(WuWenTsunTriangularSet(D3,D4,D5,D6)) +--R from WuWenTsunTriangularSet(D3,D4,D5,D6) +--R if D6 has RPOLCAT(D3,D4,D5) and D3 has INTDOM and D4 has +--R OAMONS and D5 has ORDSET +--R [2] (List(D8),((D8,D8) -> Boolean),((D8,D8) -> D8)) -> List( +--R WuWenTsunTriangularSet(D5,D6,D7,D8)) +--R from WuWenTsunTriangularSet(D5,D6,D7,D8) +--R if D8 has RPOLCAT(D5,D6,D7) and D5 has INTDOM and D6 has +--R OAMONS and D7 has ORDSET +--R +--RExamples of characteristicSerie from WuWenTsunTriangularSet +--R +--E 313 + +--S 314 of 3320 +)d op characteristicSet +--R +--R +--RThere are 2 exposed functions called characteristicSet : +--R [1] List(D5) -> Union(WuWenTsunTriangularSet(D2,D3,D4,D5),"failed") +--R from WuWenTsunTriangularSet(D2,D3,D4,D5) +--R if D5 has RPOLCAT(D2,D3,D4) and D2 has INTDOM and D3 has +--R OAMONS and D4 has ORDSET +--R [2] (List(D7),((D7,D7) -> Boolean),((D7,D7) -> D7)) -> Union( +--R WuWenTsunTriangularSet(D4,D5,D6,D7),"failed") +--R from WuWenTsunTriangularSet(D4,D5,D6,D7) +--R if D7 has RPOLCAT(D4,D5,D6) and D4 has INTDOM and D5 has +--R OAMONS and D6 has ORDSET +--R +--RExamples of characteristicSet from WuWenTsunTriangularSet +--R +--E 314 + +--S 315 of 3320 +)d op charClass +--R +--R +--RThere are 2 exposed functions called charClass : +--R [1] List(Character) -> CharacterClass from CharacterClass +--R [2] String -> CharacterClass from CharacterClass +--R +--RExamples of charClass from CharacterClass +--R +--E 315 + +--S 316 of 3320 +)d op charpol +--R +--R +--RThere is one unexposed function called charpol : +--R [1] Matrix(D3) -> SparseUnivariatePolynomial(D3) +--R from InnerNumericEigenPackage(D3,D4,D5) +--R if D3 has FIELD and D4 has FIELD and D5 has Join(Field, +--R OrderedRing) +--R +--RExamples of charpol from InnerNumericEigenPackage +--R +--E 316 + +--S 317 of 3320 +)d op chartCoord +--R +--R +--RThere is one exposed function called chartCoord : +--R [1] D -> Integer from D if D has BLMETCT +--R +--RExamples of chartCoord from BlowUpMethodCategory +--R +--E 317 + +--S 318 of 3320 +)d op charthRoot +--R +--R +--RThere are 3 exposed functions called charthRoot : +--R [1] D -> Union(D,"failed") from D if D has CHARNZ +--R [2] D -> D from D if D has FFIELDC +--R [3] D -> Union(D,"failed") from D if D has CHARNZ and D has PFECAT +--R +--R +--RExamples of charthRoot from FiniteFieldCategory +--R +--R +--RExamples of charthRoot from CharacteristicNonZero +--R +--E 318 + +--S 319 of 3320 +)d op chartV +--R +--R +--RThere is one exposed function called chartV : +--R [1] D -> D2 from D +--R if D has INFCLCT(D3,D4,D5,D6,D7,D8,D9,D1,D2) and D3 has +--R FIELD and D5 has POLYCAT(D3,D6,OVAR(D4)) and D6 has DIRPCAT +--R (#(D4),NNI) and D7 has PRSPCAT(D3) and D8 has LOCPOWC(D3) +--R and D9 has PLACESC(D3,D8) and D2 has BLMETCT +--R +--RExamples of chartV from InfinitlyClosePointCategory +--R +--E 319 + +--S 320 of 3320 +)d op chebyshevT +--R +--R +--RThere is one exposed function called chebyshevT : +--R [1] (NonNegativeInteger,D1) -> D1 from OrthogonalPolynomialFunctions +--R (D1) +--R if D1 has COMRING +--R +--RThere is one unexposed function called chebyshevT : +--R [1] Integer -> SparseUnivariatePolynomial(Integer) +--R from PolynomialNumberTheoryFunctions +--R +--RExamples of chebyshevT from OrthogonalPolynomialFunctions +--R +--R +--RExamples of chebyshevT from PolynomialNumberTheoryFunctions +--R +--E 320 + +--S 321 of 3320 +)d op chebyshevU +--R +--R +--RThere is one exposed function called chebyshevU : +--R [1] (NonNegativeInteger,D1) -> D1 from OrthogonalPolynomialFunctions +--R (D1) +--R if D1 has COMRING +--R +--RThere is one unexposed function called chebyshevU : +--R [1] Integer -> SparseUnivariatePolynomial(Integer) +--R from PolynomialNumberTheoryFunctions +--R +--RExamples of chebyshevU from OrthogonalPolynomialFunctions +--R +--R +--RExamples of chebyshevU from PolynomialNumberTheoryFunctions +--R +--E 321 + +--S 322 of 3320 +)d op check +--R +--R +--RThere are 2 exposed functions called check : +--R [1] Union(skip,MonteCarlo,deterministic) -> GuessOption from +--R GuessOption +--R [2] D -> D from D if D has SPACEC(D1) and D1 has RING +--R +--RThere are 2 unexposed functions called check : +--R [1] List(GuessOption) -> Union(skip,MonteCarlo,deterministic) +--R from GuessOptionFunctions0 +--R [2] (List(Record(factor: SparseUnivariatePolynomial(D5),exponent: +--R Integer)),List(Record(factor: SparseUnivariatePolynomial(D5), +--R exponent: Integer))) -> Boolean +--R from MultivariateSquareFree(D3,D4,D5,D6) +--R if D5 has EUCDOM and D3 has OAMONS and D4 has ORDSET and +--R D6 has POLYCAT(D5,D3,D4) +--R +--RExamples of check from GuessOptionFunctions0 +--R +--R +--RExamples of check from GuessOption +--R +--R +--RExamples of check from MultivariateSquareFree +--R +--R +--RExamples of check from ThreeSpaceCategory +--R +--E 322 + +--S 323 of 3320 +)d op checkExtraValues +--R +--R +--RThere is one exposed function called checkExtraValues : +--R [1] Boolean -> GuessOption from GuessOption +--R +--RThere is one unexposed function called checkExtraValues : +--R [1] List(GuessOption) -> Boolean from GuessOptionFunctions0 +--R +--RExamples of checkExtraValues from GuessOptionFunctions0 +--R +--R +--RExamples of checkExtraValues from GuessOption +--R +--E 323 + +--S 324 of 3320 +)d op checkForZero +--R +--R +--RThere are 2 unexposed functions called checkForZero : +--R [1] (Polynomial(D5),Symbol,OrderedCompletion(D6),OrderedCompletion( +--R D6),Boolean) -> Union(Boolean,"failed") +--R from DefiniteIntegrationTools(D5,D6) +--R if D5 has Join(GcdDomain,OrderedSet,RetractableTo(Integer) +--R ,LinearlyExplicitRingOver(Integer)) and D6 has Join( +--R TranscendentalFunctionCategory, +--R AlgebraicallyClosedFunctionSpace(D5)) +--R [2] (SparseUnivariatePolynomial(D5),OrderedCompletion(D5), +--R OrderedCompletion(D5),Boolean) -> Union(Boolean,"failed") +--R from DefiniteIntegrationTools(D4,D5) +--R if D5 has Join(TranscendentalFunctionCategory, +--R AlgebraicallyClosedFunctionSpace(D4)) and D4 has Join( +--R GcdDomain,OrderedSet,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R +--RExamples of checkForZero from DefiniteIntegrationTools +--R +--E 324 + +--S 325 of 3320 +)d op checkOptions +--R +--R +--RThere is one unexposed function called checkOptions : +--R [1] List(GuessOption) -> Void from GuessOptionFunctions0 +--R +--RExamples of checkOptions from GuessOptionFunctions0 +--R +--E 325 + +--S 326 of 3320 +)d op checkPrecision +--R +--R +--RThere is one exposed function called checkPrecision : +--R [1] -> Boolean from NAGLinkSupportPackage +--R +--RExamples of checkPrecision from NAGLinkSupportPackage +--R +--E 326 + +--S 327 of 3320 +)d op checkRur +--R +--R +--RThere is one unexposed function called checkRur : +--R [1] (D2,List(D2)) -> Boolean +--R from InternalRationalUnivariateRepresentationPackage(D4,D5 +--R ,D6,D7,D2) +--R if D2 has SFRTCAT(D4,D5,D6,D7) and D4 has Join( +--R EuclideanDomain,CharacteristicZero) and D5 has OAMONS and +--R D6 has ORDSET and D7 has RPOLCAT(D4,D5,D6) +--R +--RExamples of checkRur from InternalRationalUnivariateRepresentationPackage +--R +--E 327 + +--S 328 of 3320 +)d op child +--R +--R +--RThere is one unexposed function called child : +--R [1] (SubSpace(D2,D3),NonNegativeInteger) -> SubSpace(D2,D3) +--R from SubSpace(D2,D3) if D2: PI and D3 has RING +--R +--RExamples of child from SubSpace +--R +--E 328 + +--S 329 of 3320 +)d op child? +--R +--R +--RThere is one exposed function called child? : +--R [1] (D,D) -> Boolean from D if D has RCAGG(D2) and D2 has TYPE and +--R D2 has SETCAT +--R +--RExamples of child? from RecursiveAggregate +--R +--E 329 + +--S 330 of 3320 +)d op children +--R +--R +--RThere is one exposed function called children : +--R [1] D -> List(D) from D if D2 has TYPE and D has RCAGG(D2) +--R +--RThere is one unexposed function called children : +--R [1] SubSpace(D2,D3) -> List(SubSpace(D2,D3)) from SubSpace(D2,D3) +--R if D2: PI and D3 has RING +--R +--RExamples of children from RecursiveAggregate +--R +--R +--RExamples of children from SubSpace +--R +--E 330 + +--S 331 of 3320 +)d op chineseRemainder +--R +--R +--RThere are 3 exposed functions called chineseRemainder : +--R [1] (List(D1),List(D1)) -> D1 from CRApackage(D1) if D1 has EUCDOM +--R +--R [2] (List(List(D3)),List(D3)) -> List(D3) from CRApackage(D3) if D3 +--R has EUCDOM +--R [3] (Integer,Integer,Integer,Integer) -> Integer +--R from IntegerNumberTheoryFunctions +--R +--RThere is one unexposed function called chineseRemainder : +--R [1] (List(D7),List(Record(basis: Matrix(D6),basisDen: D6,basisInv: +--R Matrix(D6))),NonNegativeInteger) -> Record(basis: Matrix(D6), +--R basisDen: D6,basisInv: Matrix(D6)) +--R from ChineseRemainderToolsForIntegralBases(D5,D6,D7) +--R if D7 has UPOLYC(D6) and D6 has UPOLYC(D5) and D5 has +--R FFIELDC +--R +--RExamples of chineseRemainder from CRApackage +--R +--R +--RExamples of chineseRemainder from ChineseRemainderToolsForIntegralBases +--R +--R +--RExamples of chineseRemainder from IntegerNumberTheoryFunctions +--R +--E 331 + +--S 332 of 3320 +)d op chiSquare +--R +--R +--RThere is one unexposed function called chiSquare : +--R [1] NonNegativeInteger -> (() -> Float) from +--R RandomFloatDistributions +--R +--RExamples of chiSquare from RandomFloatDistributions +--R +--E 332 + +--S 333 of 3320 +)d op chiSquare1 +--R +--R +--RThere is one unexposed function called chiSquare1 : +--R [1] NonNegativeInteger -> Float from RandomFloatDistributions +--R +--RExamples of chiSquare1 from RandomFloatDistributions +--R +--E 333 + +--S 334 of 3320 +)d op choosemon +--R +--R +--RThere is one unexposed function called choosemon : +--R [1] (DistributedMultivariatePolynomial(D3,D4),List( +--R DistributedMultivariatePolynomial(D3,D4))) -> +--R DistributedMultivariatePolynomial(D3,D4) +--R from LinGroebnerPackage(D3,D4) if D3: LIST(SYMBOL) and D4 +--R has GCDDOM +--R +--RExamples of choosemon from LinGroebnerPackage +--R +--E 334 + +--S 335 of 3320 +)d op chvar +--R +--R +--RThere is one unexposed function called chvar : +--R [1] (D2,D2) -> Record(func: D2,poly: D2,c1: Fraction(D4),c2: +--R Fraction(D4),deg: NonNegativeInteger) +--R from ChangeOfVariable(D3,D4,D2) +--R if D3 has UFD and D4 has UPOLYC(D3) and D2 has UPOLYC(FRAC +--R (D4)) +--R +--RExamples of chvar from ChangeOfVariable +--R +--E 335 + +--S 336 of 3320 +)d op Ci +--R +--R +--RThere is one exposed function called Ci : +--R [1] D -> D from D if D has LFCAT +--R +--RThere is one unexposed function called Ci : +--R [1] D1 -> D1 from LiouvillianFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory, +--R TranscendentalFunctionCategory) +--R +--RExamples of Ci from LiouvillianFunctionCategory +--R +--R +--RExamples of Ci from LiouvillianFunction +--R +--E 336 + +--S 337 of 3320 +)d op classNumber +--R +--R +--RThere are 3 exposed functions called classNumber : +--R [1] -> Integer +--R from GeneralPackageForAlgebraicFunctionField(D6,D7,D8,D9, +--R D10,D11,D12,D1,D2,D3,D4) +--R if D6 has FINITE and D6 has FIELD and D7: LIST(SYMBOL) and +--R D8 has POLYCAT(D6,D9,OVAR(D7)) and D9 has DIRPCAT(#(D7),NNI +--R ) and D10 has PRSPCAT(D6) and D11 has LOCPOWC(D6) and D12 +--R has PLACESC(D6,D11) and D1 has DIVCAT(D12) and D2 has +--R INFCLCT(D6,D7,D8,D9,D10,D11,D12,D1,D4) and D4 has BLMETCT +--R and D3 has DSTRCAT(D2) +--R [2] -> Integer +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D2,D3 +--R ,D4) +--R if PseudoAlgebraicClosureOfFiniteField(D2) has FINITE and +--R D2 has FFIELDC and D3: LIST(SYMBOL) and D4 has BLMETCT +--R [3] -> Integer from PackageForAlgebraicFunctionField(D2,D3,D4) +--R if D2 has FINITE and D2 has FIELD and D3: LIST(SYMBOL) and +--R D4 has BLMETCT +--R +--RExamples of classNumber from GeneralPackageForAlgebraicFunctionField +--R +--R +--RExamples of classNumber from PackageForAlgebraicFunctionFieldOverFiniteField +--R +--R +--RExamples of classNumber from PackageForAlgebraicFunctionField +--R +--E 337 + +--S 338 of 3320 +)d op clearCache +--R +--R +--RThere is one unexposed function called clearCache : +--R [1] -> Void from SortedCache(D2) if D2 has CACHSET +--R +--RExamples of clearCache from SortedCache +--R +--E 338 + +--S 339 of 3320 +)d op clearDenominator +--R +--R +--RThere are 3 exposed functions called clearDenominator : +--R [1] D1 -> D1 from CommonDenominator(D2,D3,D1) +--R if D2 has INTDOM and D3 has QFCAT(D2) and D1 has FLAGG(D3) +--R +--R [2] Matrix(D4) -> Matrix(D3) from MatrixCommonDenominator(D3,D4) +--R if D4 has QFCAT(D3) and D3 has INTDOM +--R [3] D1 -> D1 from UnivariatePolynomialCommonDenominator(D2,D3,D1) +--R if D2 has INTDOM and D3 has QFCAT(D2) and D1 has UPOLYC(D3 +--R ) +--R +--RThere is one unexposed function called clearDenominator : +--R [1] D2 -> D1 from InnerCommonDenominator(D3,D4,D1,D2) +--R if D3 has INTDOM and D4 has QFCAT(D3) and D1 has FLAGG(D3) +--R and D2 has FLAGG(D4) +--R +--RExamples of clearDenominator from CommonDenominator +--R +--R +--RExamples of clearDenominator from InnerCommonDenominator +--R +--R +--RExamples of clearDenominator from MatrixCommonDenominator +--R +--R +--RExamples of clearDenominator from UnivariatePolynomialCommonDenominator +--R +--E 339 + +--S 340 of 3320 +)d op clearFortranOutputStack +--R +--R +--RThere is one exposed function called clearFortranOutputStack : +--R [1] -> Stack(String) from FortranOutputStackPackage +--R +--RExamples of clearFortranOutputStack from FortranOutputStackPackage +--R +--E 340 + +--S 341 of 3320 +)d op clearTable! +--R +--R +--RThere is one unexposed function called clearTable! : +--R [1] -> Void from TabulatedComputationPackage(D2,D3) +--R if D2 has SETCAT and D3 has SETCAT +--R +--RExamples of clearTable! from TabulatedComputationPackage +--R +--E 341 + +--S 342 of 3320 +)d op clearTheFTable +--R +--R +--RThere is one exposed function called clearTheFTable : +--R [1] -> Void from IntegrationFunctionsTable +--R +--RExamples of clearTheFTable from IntegrationFunctionsTable +--R +--E 342 + +--S 343 of 3320 +)d op clearTheIFTable +--R +--R +--RThere is one exposed function called clearTheIFTable : +--R [1] -> Void from ODEIntensityFunctionsTable +--R +--RExamples of clearTheIFTable from ODEIntensityFunctionsTable +--R +--E 343 + +--S 344 of 3320 +)d op clearTheSymbolTable +--R +--R +--RThere are 2 exposed functions called clearTheSymbolTable : +--R [1] Symbol -> Void from TheSymbolTable +--R [2] -> Void from TheSymbolTable +--R +--RExamples of clearTheSymbolTable from TheSymbolTable +--R +--E 344 + +--S 345 of 3320 +)d op clikeUniv +--R +--R +--RThere is one unexposed function called clikeUniv : +--R [1] Symbol -> (Polynomial(D3) -> SparseUnivariatePolynomial( +--R Polynomial(D3))) +--R from WeierstrassPreparation(D3) if D3 has FIELD +--R +--RExamples of clikeUniv from WeierstrassPreparation +--R +--E 345 + +--S 346 of 3320 +)d op clip +--R +--R +--RThere are 2 exposed functions called clip : +--R [1] List(Segment(Float)) -> DrawOption from DrawOption +--R [2] Boolean -> DrawOption from DrawOption +--R +--RThere are 4 unexposed functions called clip : +--R [1] Plot -> Record(brans: List(List(Point(DoubleFloat))),xValues: +--R Segment(DoubleFloat),yValues: Segment(DoubleFloat)) +--R from TwoDimensionalPlotClipping +--R [2] (Plot,Fraction(Integer),Fraction(Integer)) -> Record(brans: List +--R (List(Point(DoubleFloat))),xValues: Segment(DoubleFloat),yValues +--R : Segment(DoubleFloat)) +--R from TwoDimensionalPlotClipping +--R [3] List(Point(DoubleFloat)) -> Record(brans: List(List(Point( +--R DoubleFloat))),xValues: Segment(DoubleFloat),yValues: Segment( +--R DoubleFloat)) +--R from TwoDimensionalPlotClipping +--R [4] List(List(Point(DoubleFloat))) -> Record(brans: List(List(Point( +--R DoubleFloat))),xValues: Segment(DoubleFloat),yValues: Segment( +--R DoubleFloat)) +--R from TwoDimensionalPlotClipping +--R +--RExamples of clip from TwoDimensionalPlotClipping +--R +--R +--RExamples of clip from DrawOption +--R +--E 346 + +--S 347 of 3320 +)d op clipBoolean +--R +--R +--RThere is one unexposed function called clipBoolean : +--R [1] (List(DrawOption),Boolean) -> Boolean from DrawOptionFunctions0 +--R +--R +--RExamples of clipBoolean from DrawOptionFunctions0 +--R +--E 347 + +--S 348 of 3320 +)d op clipParametric +--R +--R +--RThere are 2 unexposed functions called clipParametric : +--R [1] Plot -> Record(brans: List(List(Point(DoubleFloat))),xValues: +--R Segment(DoubleFloat),yValues: Segment(DoubleFloat)) +--R from TwoDimensionalPlotClipping +--R [2] (Plot,Fraction(Integer),Fraction(Integer)) -> Record(brans: List +--R (List(Point(DoubleFloat))),xValues: Segment(DoubleFloat),yValues +--R : Segment(DoubleFloat)) +--R from TwoDimensionalPlotClipping +--R +--RExamples of clipParametric from TwoDimensionalPlotClipping +--R +--E 348 + +--S 349 of 3320 +)d op clipPointsDefault +--R +--R +--RThere are 2 exposed functions called clipPointsDefault : +--R [1] -> Boolean from GraphicsDefaults +--R [2] Boolean -> Boolean from GraphicsDefaults +--R +--RExamples of clipPointsDefault from GraphicsDefaults +--R +--E 349 + +--S 350 of 3320 +)d op clipSurface +--R +--R +--RThere is one exposed function called clipSurface : +--R [1] (ThreeDimensionalViewport,String) -> Void from +--R ThreeDimensionalViewport +--R +--RExamples of clipSurface from ThreeDimensionalViewport +--R +--E 350 + +--S 351 of 3320 +)d op clipWithRanges +--R +--R +--RThere is one unexposed function called clipWithRanges : +--R [1] (List(List(Point(DoubleFloat))),DoubleFloat,DoubleFloat, +--R DoubleFloat,DoubleFloat) -> Record(brans: List(List(Point( +--R DoubleFloat))),xValues: Segment(DoubleFloat),yValues: Segment( +--R DoubleFloat)) +--R from TwoDimensionalPlotClipping +--R +--RExamples of clipWithRanges from TwoDimensionalPlotClipping +--R +--E 351 + +--S 352 of 3320 +)d op cLog +--R +--R +--RThere is one unexposed function called cLog : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cLog from InnerSparseUnivariatePowerSeries +--R +--E 352 + +--S 353 of 3320 +)d op close +--R +--R +--RThere is one exposed function called close : +--R [1] ThreeDimensionalViewport -> Void from ThreeDimensionalViewport +--R +--R +--RThere are 2 unexposed functions called close : +--R [1] (SubSpaceComponentProperty,Boolean) -> Boolean +--R from SubSpaceComponentProperty +--R [2] TwoDimensionalViewport -> Void from TwoDimensionalViewport +--R +--RExamples of close from SubSpaceComponentProperty +--R +--R +--RExamples of close from TwoDimensionalViewport +--R +--R +--RExamples of close from ThreeDimensionalViewport +--R +--E 353 + +--S 354 of 3320 +)d op close! +--R +--R +--RThere are 2 exposed functions called close! : +--R [1] D -> D from D if D has FILECAT(D1,D2) and D1 has SETCAT and D2 +--R has SETCAT +--R [2] Library -> Library from Library +--R +--RExamples of close! from FileCategory +--R +--R +--RExamples of close! from Library +--R +--E 354 + +--S 355 of 3320 +)d op closeComponent +--R +--R +--RThere is one unexposed function called closeComponent : +--R [1] (SubSpace(D3,D4),List(NonNegativeInteger),Boolean) -> SubSpace( +--R D3,D4) +--R from SubSpace(D3,D4) if D3: PI and D4 has RING +--R +--RExamples of closeComponent from SubSpace +--R +--E 355 + +--S 356 of 3320 +)d op closed? +--R +--R +--RThere are 2 unexposed functions called closed? : +--R [1] SubSpaceComponentProperty -> Boolean from +--R SubSpaceComponentProperty +--R [2] TubePlot(D2) -> Boolean from TubePlot(D2) if D2 has PSCURVE +--R +--RExamples of closed? from SubSpaceComponentProperty +--R +--R +--RExamples of closed? from TubePlot +--R +--E 356 + +--S 357 of 3320 +)d op closedCurve +--R +--R +--RThere are 4 exposed functions called closedCurve : +--R [1] D -> List(Point(D2)) from D if D has SPACEC(D2) and D2 has RING +--R +--R [2] List(Point(D2)) -> D from D if D2 has RING and D has SPACEC(D2) +--R +--R [3] (D,List(List(D2))) -> D from D if D has SPACEC(D2) and D2 has +--R RING +--R [4] (D,List(Point(D2))) -> D from D if D has SPACEC(D2) and D2 has +--R RING +--R +--RExamples of closedCurve from ThreeSpaceCategory +--R +--E 357 + +--S 358 of 3320 +)d op closedCurve? +--R +--R +--RThere is one exposed function called closedCurve? : +--R [1] D -> Boolean from D if D has SPACEC(D2) and D2 has RING +--R +--RExamples of closedCurve? from ThreeSpaceCategory +--R +--E 358 + +--S 359 of 3320 +)d op cn +--R +--R +--RThere is one unexposed function called cn : +--R [1] (D1,D2) -> D1 from EllipticFunctionsUnivariateTaylorSeries(D2,D1 +--R ) +--R if D2 has FIELD and D1 has UTSCAT(D2) +--R +--RExamples of cn from EllipticFunctionsUnivariateTaylorSeries +--R +--E 359 + +--S 360 of 3320 +)d op code +--R +--R +--RThere is one exposed function called code : +--R [1] FortranCode -> Union(nullBranch: null,assignmentBranch: Record( +--R var: Symbol,arrayIndex: List(Polynomial(Integer)),rand: Record( +--R ints2Floats?: Boolean,expr: OutputForm)),arrayAssignmentBranch: +--R Record(var: Symbol,rand: OutputForm,ints2Floats?: Boolean), +--R conditionalBranch: Record(switch: Switch,thenClause: FortranCode, +--R elseClause: FortranCode),returnBranch: Record(empty?: Boolean, +--R value: Record(ints2Floats?: Boolean,expr: OutputForm)), +--R blockBranch: List(FortranCode),commentBranch: List(String), +--R callBranch: String,forBranch: Record(range: SegmentBinding( +--R Polynomial(Integer)),span: Polynomial(Integer),body: FortranCode) +--R ,labelBranch: SingleInteger,loopBranch: Record(switch: Switch, +--R body: FortranCode),commonBranch: Record(name: Symbol,contents: +--R List(Symbol)),printBranch: List(OutputForm)) +--R from FortranCode +--R +--RExamples of code from FortranCode +--R +--E 360 + +--S 361 of 3320 +)d op coef +--R +--R +--RThere are 3 exposed functions called coef : +--R [1] (XRecursivePolynomial(D3,D1),D) -> D1 from D +--R if D has FLALG(D3,D1) and D3 has ORDSET and D1 has COMRING +--R +--R [2] (D,D) -> D1 from D if D has XFALG(D2,D1) and D2 has ORDSET and +--R D1 has RING +--R [3] (D,OrderedFreeMonoid(D3)) -> D1 from D +--R if D has XFALG(D3,D1) and D3 has ORDSET and D1 has RING +--R +--R +--RThere is one unexposed function called coef : +--R [1] (XPolynomialRing(D1,D2),D2) -> D1 from XPolynomialRing(D1,D2) +--R if D1 has RING and D2 has ORDMON +--R +--RExamples of coef from FreeLieAlgebra +--R +--R +--RExamples of coef from XFreeAlgebra +--R +--R +--RExamples of coef from XPolynomialRing +--R +--E 361 + +--S 362 of 3320 +)d op coefChoose +--R +--R +--RThere is one unexposed function called coefChoose : +--R [1] (Integer,Factored(D1)) -> D1 from MultivariateSquareFree(D4,D5, +--R D6,D1) +--R if D1 has POLYCAT(D6,D4,D5) and D4 has OAMONS and D5 has +--R ORDSET and D6 has EUCDOM +--R +--RExamples of coefChoose from MultivariateSquareFree +--R +--E 362 + +--S 363 of 3320 +)d op coefficient +--R +--R +--RThere are 12 exposed functions called coefficient : +--R [1] (D,D2) -> D1 from D if D has AMR(D1,D2) and D2 has OAMON and D1 +--R has RING +--R [2] (CliffordAlgebra(D3,D1,D4),List(PositiveInteger)) -> D1 +--R from CliffordAlgebra(D3,D1,D4) +--R if D1 has FIELD and D3: PI and D4: QFORM(D3,D1) +--R [3] (D2,D) -> D1 from D if D has FAMONC(D2,D1) and D2 has SETCAT and +--R D1 has CABMON +--R [4] (D,D2) -> D1 from D if D has FMCAT(D1,D2) and D2 has SETCAT and +--R D1 has RING +--R [5] (D,NonNegativeInteger) -> D1 from D if D has MLO(D1) and D1 has +--R RING +--R [6] (D,List(D4),List(NonNegativeInteger)) -> D from D +--R if D has MTSCAT(D3,D4) and D3 has RING and D4 has ORDSET +--R +--R [7] (D,D1,NonNegativeInteger) -> D from D +--R if D has MTSCAT(D3,D1) and D3 has RING and D1 has ORDSET +--R +--R [8] (D,NonNegativeInteger) -> D1 from D if D has OREPCAT(D1) and D1 +--R has RING +--R [9] (D,List(D5),List(NonNegativeInteger)) -> D from D +--R if D has POLYCAT(D3,D4,D5) and D3 has RING and D4 has +--R OAMONS and D5 has ORDSET +--R [10] (D,D1,NonNegativeInteger) -> D from D +--R if D has POLYCAT(D3,D4,D1) and D3 has RING and D4 has +--R OAMONS and D1 has ORDSET +--R [11] (StochasticDifferential(D3),BasicStochasticDifferential) -> +--R Expression(D3) +--R from StochasticDifferential(D3) +--R if D3 has Join(OrderedSet,IntegralDomain) +--R [12] (TaylorSeries(D3),NonNegativeInteger) -> Polynomial(D3) +--R from TaylorSeries(D3) if D3 has RING +--R +--RThere are 5 unexposed functions called coefficient : +--R [1] (AntiSymm(D1,D2),AntiSymm(D1,D2)) -> D1 from AntiSymm(D1,D2) +--R if D1 has RING and D2: LIST(SYMBOL) +--R [2] (DeRhamComplex(D2,D3),DeRhamComplex(D2,D3)) -> Expression(D2) +--R from DeRhamComplex(D2,D3) +--R if D2 has Join(Ring,OrderedSet) and D3: LIST(SYMBOL) +--R [3] (LaurentPolynomial(D1,D3),Integer) -> D1 from LaurentPolynomial( +--R D1,D3) +--R if D1 has INTDOM and D3 has UPOLYC(D1) +--R [4] (MonoidRing(D1,D2),D2) -> D1 from MonoidRing(D1,D2) +--R if D1 has RING and D2 has MONOID +--R [5] (SparseMultivariateTaylorSeries(D3,D4,D1),NonNegativeInteger) +--R -> D1 +--R from SparseMultivariateTaylorSeries(D3,D4,D1) +--R if D1 has POLYCAT(D3,INDE(D4),D4) and D3 has RING and D4 +--R has ORDSET +--R +--RExamples of coefficient from AbelianMonoidRing +--R +--R +--RExamples of coefficient from AntiSymm +--R +--R +--RExamples of coefficient from CliffordAlgebra +--R +--R +--RExamples of coefficient from DeRhamComplex +--R +--Rder := DeRhamComplex(Integer,[x,y,z]) +--RR := Expression(Integer) +--R[dx,dy,dz] := [generator(i)$der for i in 1..3] +--Rf : R := x**2*y*z-5*x**3*y**2*z**5 +--Rg : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2 +--Rh : R :=x*y*z-2*x**3*y*z**2 +--Ralpha : der := f*dx + g*dy + h*dz +--Rbeta : der := cos(tan(x*y*z)+x*y*z)*dx + x*dy +--Rgamma := alpha * beta +--Rcoefficient(gamma, dx*dy) +--R +--R +--RExamples of coefficient from FreeAbelianMonoidCategory +--R +--R +--RExamples of coefficient from FreeModuleCat +--R +--R +--RExamples of coefficient from LaurentPolynomial +--R +--R +--RExamples of coefficient from MonogenicLinearOperator +--R +--R +--RExamples of coefficient from MonoidRing +--R +--R +--RExamples of coefficient from MultivariateTaylorSeriesCategory +--R +--R +--RExamples of coefficient from UnivariateSkewPolynomialCategory +--R +--R +--RExamples of coefficient from PolynomialCategory +--R +--R +--RExamples of coefficient from StochasticDifferential +--R +--R +--RExamples of coefficient from SparseMultivariateTaylorSeries +--R +--Rxts:=x::TaylorSeries Fraction Integer +--Rt1:=sin(xts) +--Rcoefficient(t1,3) +--R +--R +--RExamples of coefficient from TaylorSeries +--R +--E 363 + +--S 364 of 3320 +)d op coefficients +--R +--R +--RThere are 4 exposed functions called coefficients : +--R [1] D -> List(D2) from D if D has FAMR(D2,D3) and D2 has RING and D3 +--R has OAMON +--R [2] D -> List(D2) from D if D has FMCAT(D2,D3) and D2 has RING and +--R D3 has SETCAT +--R [3] D -> List(D2) from D if D has OREPCAT(D2) and D2 has RING +--R [4] D -> Stream(D2) from D if D has UTSCAT(D2) and D2 has RING +--R +--RThere are 3 unexposed functions called coefficients : +--R [1] InnerTaylorSeries(D2) -> Stream(D2) from InnerTaylorSeries(D2) +--R if D2 has RING +--R [2] MonoidRing(D2,D3) -> List(D2) from MonoidRing(D2,D3) +--R if D2 has RING and D3 has MONOID +--R [3] SparseMultivariateTaylorSeries(D2,D3,D4) -> Stream(D4) +--R from SparseMultivariateTaylorSeries(D2,D3,D4) +--R if D2 has RING and D3 has ORDSET and D4 has POLYCAT(D2, +--R INDE(D3),D3) +--R +--RExamples of coefficients from FiniteAbelianMonoidRing +--R +--R +--RExamples of coefficients from FreeModuleCat +--R +--R +--RExamples of coefficients from InnerTaylorSeries +--R +--R +--RExamples of coefficients from MonoidRing +--R +--R +--RExamples of coefficients from UnivariateSkewPolynomialCategory +--R +--R +--RExamples of coefficients from SparseMultivariateTaylorSeries +--R +--R +--RExamples of coefficients from UnivariateTaylorSeriesCategory +--R +--E 364 + +--S 365 of 3320 +)d op coefficientSet +--R +--R +--RThere is one exposed function called coefficientSet : +--R [1] SparseUnivariatePolynomial(Polynomial(D3)) -> List(Polynomial(D3 +--R )) +--R from CylindricalAlgebraicDecompositionPackage(D3) if D3 +--R has RCFIELD +--R +--RExamples of coefficientSet from CylindricalAlgebraicDecompositionPackage +--R +--E 365 + +--S 366 of 3320 +)d op coefOfFirstNonZeroTerm +--R +--R +--RThere is one exposed function called coefOfFirstNonZeroTerm : +--R [1] D -> D1 from D if D has LOCPOWC(D1) and D1 has FIELD +--R +--RExamples of coefOfFirstNonZeroTerm from LocalPowerSeriesCategory +--R +--E 366 + +--S 367 of 3320 +--R----------------------------------)d op coerce (System Error) +--E 367 + +--S 368 of 3320 +)d op coerceImages +--R +--R +--RThere is one exposed function called coerceImages : +--R [1] List(D2) -> Permutation(D2) from Permutation(D2) if D2 has +--R SETCAT +--R +--RExamples of coerceImages from Permutation +--R +--E 368 + +--S 369 of 3320 +)d op coerceL +--R +--R +--RThere are 2 exposed functions called coerceL : +--R [1] OutputForm -> String from HTMLFormat +--R [2] OutputForm -> String from MathMLFormat +--R +--RExamples of coerceL from HTMLFormat +--R +--RcoerceL(sqrt(3+x)::OutputForm)$HTMLFORM +--R +--R +--RExamples of coerceL from MathMLFormat +--R +--E 369 + +--S 370 of 3320 +)d op coerceListOfPairs +--R +--R +--RThere is one exposed function called coerceListOfPairs : +--R [1] List(List(D2)) -> Permutation(D2) from Permutation(D2) if D2 +--R has SETCAT +--R +--RExamples of coerceListOfPairs from Permutation +--R +--E 370 + +--S 371 of 3320 +)d op coerceP +--R +--R +--RThere is one unexposed function called coerceP : +--R [1] Vector(Matrix(D3)) -> Vector(Matrix(Polynomial(D3))) +--R from CoerceVectorMatrixPackage(D3) if D3 has COMRING +--R +--RExamples of coerceP from CoerceVectorMatrixPackage +--R +--E 371 + +--S 372 of 3320 done +)d op coercePreimagesImages +--R +--R +--RThere is one exposed function called coercePreimagesImages : +--R [1] List(List(D2)) -> Permutation(D2) from Permutation(D2) if D2 +--R has SETCAT +--R +--RExamples of coercePreimagesImages from Permutation +--R +--Rp := coercePreimagesImages([[1,2,3],[1,2,3]]) +--Rq := coercePreimagesImages([[0,1,2,3],[3,0,2,1]])$PERM ZMOD 4 +--R +--E 372 + +--S 373 of 3320 +)d op coerceS +--R +--R +--RThere are 2 exposed functions called coerceS : +--R [1] OutputForm -> String from HTMLFormat +--R [2] OutputForm -> String from MathMLFormat +--R +--RExamples of coerceS from HTMLFormat +--R +--RcoerceS(sqrt(3+x)::OutputForm)$HTMLFORM +--R +--R +--RExamples of coerceS from MathMLFormat +--R +--E 373 + +--S 374 of 3320 +)d op coHeight +--R +--R +--RThere is one exposed function called coHeight : +--R [1] D -> NonNegativeInteger from D +--R if D has TSETCAT(D2,D3,D4,D5) and D2 has INTDOM and D3 +--R has OAMONS and D4 has ORDSET and D5 has RPOLCAT(D2,D3,D4) +--R and D4 has FINITE +--R +--RExamples of coHeight from TriangularSetCategory +--R +--E 374 + +--S 375 of 3320 +)d op coleman +--R +--R +--RThere is one exposed function called coleman : +--R [1] (List(Integer),List(Integer),List(Integer)) -> Matrix(Integer) +--R from SymmetricGroupCombinatoricFunctions +--R +--RExamples of coleman from SymmetricGroupCombinatoricFunctions +--R +--E 375 + +--S 376 of 3320 +)d op collect +--R +--R +--RThere are 2 exposed functions called collect : +--R [1] D -> D from D if D has DIVCAT(D1) and D1 has SETCAT +--R [2] (D,D1) -> D from D +--R if D has PSETCAT(D2,D3,D1,D4) and D2 has RING and D3 has +--R OAMONS and D1 has ORDSET and D4 has RPOLCAT(D2,D3,D1) +--R +--RExamples of collect from DivisorCategory +--R +--R +--RExamples of collect from PolynomialSetCategory +--R +--E 376 + +--S 377 of 3320 +)d op collectQuasiMonic +--R +--R +--RThere is one exposed function called collectQuasiMonic : +--R [1] D -> D from D +--R if D has TSETCAT(D1,D2,D3,D4) and D1 has INTDOM and D2 +--R has OAMONS and D3 has ORDSET and D4 has RPOLCAT(D1,D2,D3) +--R +--R +--RExamples of collectQuasiMonic from TriangularSetCategory +--R +--E 377 + +--S 378 of 3320 +)d op collectUnder +--R +--R +--RThere is one exposed function called collectUnder : +--R [1] (D,D1) -> D from D +--R if D has PSETCAT(D2,D3,D1,D4) and D2 has RING and D3 has +--R OAMONS and D1 has ORDSET and D4 has RPOLCAT(D2,D3,D1) +--R +--RExamples of collectUnder from PolynomialSetCategory +--R +--E 378 + +--S 379 of 3320 +)d op collectUpper +--R +--R +--RThere is one exposed function called collectUpper : +--R [1] (D,D1) -> D from D +--R if D has PSETCAT(D2,D3,D1,D4) and D2 has RING and D3 has +--R OAMONS and D1 has ORDSET and D4 has RPOLCAT(D2,D3,D1) +--R +--RExamples of collectUpper from PolynomialSetCategory +--R +--E 379 + +--S 380 of 3320 +)d op color +--R +--R +--RThere is one exposed function called color : +--R [1] Integer -> Color from Color +--R +--RThere is one unexposed function called color : +--R [1] Point(D1) -> D1 from PointPackage(D1) if D1 has RING +--R +--RExamples of color from Color +--R +--R +--RExamples of color from PointPackage +--R +--E 380 + +--S 381 of 3320 +)d op colorDef +--R +--R +--RThere is one exposed function called colorDef : +--R [1] (ThreeDimensionalViewport,Color,Color) -> Void +--R from ThreeDimensionalViewport +--R +--RExamples of colorDef from ThreeDimensionalViewport +--R +--E 381 + +--S 382 of 3320 +)d op colorFunction +--R +--R +--RThere are 3 exposed functions called colorFunction : +--R [1] ((DoubleFloat,DoubleFloat,DoubleFloat) -> DoubleFloat) -> +--R DrawOption +--R from DrawOption +--R [2] ((DoubleFloat,DoubleFloat) -> DoubleFloat) -> DrawOption from +--R DrawOption +--R [3] (DoubleFloat -> DoubleFloat) -> DrawOption from DrawOption +--R +--RExamples of colorFunction from DrawOption +--R +--E 382 + +--S 383 of 3320 +)d op column +--R +--R +--RThere are 2 exposed functions called column : +--R [1] (D,Integer) -> D1 from D +--R if D has ARR2CAT(D3,D4,D1) and D3 has TYPE and D4 has +--R FLAGG(D3) and D1 has FLAGG(D3) +--R [2] (D,Integer) -> D1 from D +--R if D has RMATCAT(D3,D4,D5,D6,D1) and D5 has RING and D6 +--R has DIRPCAT(D4,D5) and D1 has DIRPCAT(D3,D5) +--R +--RExamples of column from TwoDimensionalArrayCategory +--R +--Rarr : ARRAY2 INT := new(5,4,10) +--Rcolumn(arr,1) +--R +--R +--RExamples of column from RectangularMatrixCategory +--R +--E 383 + +--S 384 of 3320 done +)d op columns +--R +--R +--RThere are 2 exposed functions called columns : +--R [1] (D1,List(PositiveInteger)) -> D1 from MatrixManipulation(D3,D4, +--R D5,D1) +--R if D3 has FIELD and D4 has FLAGG(D3) and D5 has FLAGG(D3) +--R and D1 has MATCAT(D3,D4,D5) +--R [2] (D1,Segment(PositiveInteger)) -> D1 from MatrixManipulation(D3, +--R D4,D5,D1) +--R if D3 has FIELD and D4 has FLAGG(D3) and D5 has FLAGG(D3) +--R and D1 has MATCAT(D3,D4,D5) +--R +--RExamples of columns from MatrixManipulation +--R +--RM := matrix([[a,b,c],[d,e,f],[g,h,i]]) +--Rcolumns(M, 1..2) +--R +--RM := matrix([[a,b,c],[d,e,f],[g,h,i]]) +--Rcolumns(M, [1,2]) +--Rcolumns(M, [3,2]) +--R +--E 384 + +--S 385 of 3320 done +)d op columnSpace +--R +--R +--RThere is one exposed function called columnSpace : +--R [1] D -> List(D4) from D +--R if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG +--R (D2) and D4 has FLAGG(D2) and D2 has EUCDOM +--R +--RExamples of columnSpace from MatrixCategory +--R +--RcolumnSpace matrix [[1,2,3],[4,5,6],[7,8,9],[1,1,1]] +--R +--E 385 + +--S 386 of 3320 +)d op combineFeatureCompatibility +--R +--R +--RThere are 2 exposed functions called combineFeatureCompatibility : +--R [1] (Float,Float) -> Float from d02AgentsPackage +--R [2] (Float,List(Float)) -> Float from d02AgentsPackage +--R +--RExamples of combineFeatureCompatibility from d02AgentsPackage +--R +--E 386 + +--S 387 of 3320 +)d op commaSeparate +--R +--R +--RThere is one exposed function called commaSeparate : +--R [1] List(String) -> String from d01AgentsPackage +--R +--RThere is one unexposed function called commaSeparate : +--R [1] List(OutputForm) -> OutputForm from OutputForm +--R +--RExamples of commaSeparate from d01AgentsPackage +--R +--R +--RExamples of commaSeparate from OutputForm +--R +--E 387 + +--S 388 of 3320 +)d op comment +--R +--R +--RThere are 2 exposed functions called comment : +--R [1] List(String) -> FortranCode from FortranCode +--R [2] String -> FortranCode from FortranCode +--R +--RExamples of comment from FortranCode +--R +--E 388 + +--S 389 of 3320 +)d op common +--R +--R +--RThere is one exposed function called common : +--R [1] (Symbol,List(Symbol)) -> FortranCode from FortranCode +--R +--RExamples of common from FortranCode +--R +--E 389 + +--S 390 of 3320 +)d op commonDenominator +--R +--R +--RThere are 3 exposed functions called commonDenominator : +--R [1] D2 -> D1 from CommonDenominator(D1,D3,D2) +--R if D3 has QFCAT(D1) and D1 has INTDOM and D2 has FLAGG(D3) +--R +--R [2] Matrix(D3) -> D1 from MatrixCommonDenominator(D1,D3) +--R if D3 has QFCAT(D1) and D1 has INTDOM +--R [3] D2 -> D1 from UnivariatePolynomialCommonDenominator(D1,D3,D2) +--R if D3 has QFCAT(D1) and D1 has INTDOM and D2 has UPOLYC(D3 +--R ) +--R +--RThere is one unexposed function called commonDenominator : +--R [1] D2 -> D1 from InnerCommonDenominator(D1,D3,D4,D2) +--R if D3 has QFCAT(D1) and D1 has INTDOM and D4 has FLAGG(D1) +--R and D2 has FLAGG(D3) +--R +--RExamples of commonDenominator from CommonDenominator +--R +--R +--RExamples of commonDenominator from InnerCommonDenominator +--R +--R +--RExamples of commonDenominator from MatrixCommonDenominator +--R +--R +--RExamples of commonDenominator from UnivariatePolynomialCommonDenominator +--R +--E 390 + +--S 391 of 3320 +)d op commutative? +--R +--R +--RThere is one exposed function called commutative? : +--R [1] -> Boolean from D if D has FINAALG(D2) and D2 has COMRING +--R +--RThere is one unexposed function called commutative? : +--R [1] -> Boolean from FiniteRankNonAssociativeAlgebra&(D2,D3) +--R if D3 has COMRING and D2 has FINAALG(D3) +--R +--RExamples of commutative? from FiniteRankNonAssociativeAlgebra& +--R +--R +--RExamples of commutative? from FiniteRankNonAssociativeAlgebra +--R +--E 391 + +--S 392 of 3320 +)d op commutativeEquality +--R +--R +--RThere is one unexposed function called commutativeEquality : +--R [1] (ListMonoidOps(D2,D3,D4),ListMonoidOps(D2,D3,D4)) -> Boolean +--R from ListMonoidOps(D2,D3,D4) +--R if D2 has SETCAT and D3 has ABELMON and D4: D3 +--R +--RExamples of commutativeEquality from ListMonoidOps +--R +--E 392 + +--S 393 of 3320 +)d op commutator +--R +--R +--RThere are 2 exposed functions called commutator : +--R [1] (D,D) -> D from D if D has GROUP +--R [2] (D,D) -> D from D if D has NARNG +--R +--RExamples of commutator from Group +--R +--R +--RExamples of commutator from NonAssociativeRng +--R +--E 393 + +--S 394 of 3320 +)d op comp +--R +--R +--RThere is one unexposed function called comp : +--R [1] ((D5 -> D1),(D4 -> D5),D4) -> D1 +--R from MappingPackageInternalHacks3(D4,D5,D1) +--R if D4 has SETCAT and D5 has SETCAT and D1 has SETCAT +--R +--RExamples of comp from MappingPackageInternalHacks3 +--R +--E 394 + +--S 395 of 3320 done +)d op compactFraction +--R +--R +--RThere is one exposed function called compactFraction : +--R [1] PartialFraction(D1) -> PartialFraction(D1) from PartialFraction( +--R D1) +--R if D1 has EUCDOM +--R +--RExamples of compactFraction from PartialFraction +--R +--Ra:=partialFraction(1,factorial 10) +--Rb:=padicFraction(a) +--RcompactFraction(b) +--R +--E 395 + +--S 396 of 3320 +)d op companionBlocks +--R +--R +--RThere is one unexposed function called companionBlocks : +--R [1] (Matrix(D4),Vector(D4)) -> List(Record(C: Matrix(D4),g: Vector( +--R D4))) +--R from PseudoLinearNormalForm(D4) if D4 has FIELD +--R +--RExamples of companionBlocks from PseudoLinearNormalForm +--R +--E 396 + +--S 397 of 3320 +)d op comparison +--R +--R +--RThere is one exposed function called comparison : +--R [1] (BasicOperator,((BasicOperator,BasicOperator) -> Boolean)) -> +--R BasicOperator +--R from BasicOperator +--R +--RExamples of comparison from BasicOperator +--R +--E 397 + +--S 398 of 3320 +)d op compBound +--R +--R +--RThere is one unexposed function called compBound : +--R [1] (D2,List(D2)) -> NonNegativeInteger from GenExEuclid(D4,D2) +--R if D2 has UPOLYC(D4) and D4 has EUCDOM +--R +--RExamples of compBound from GenExEuclid +--R +--E 398 + +--S 399 of 3320 +)d op compdegd +--R +--R +--RThere is one unexposed function called compdegd : +--R [1] List(Record(factor: SparseUnivariatePolynomial(D5),exponent: +--R Integer)) -> Integer +--R from MultivariateSquareFree(D3,D4,D5,D6) +--R if D5 has EUCDOM and D3 has OAMONS and D4 has ORDSET and +--R D6 has POLYCAT(D5,D3,D4) +--R +--RExamples of compdegd from MultivariateSquareFree +--R +--E 399 + +--S 400 of 3320 +)d op compile +--R +--R +--RThere is one unexposed function called compile : +--R [1] (Symbol,List(InputForm)) -> Symbol from InputForm +--R +--RExamples of compile from InputForm +--R +--E 400 + +--S 401 of 3320 done +)d op compiledFunction +--R +--R +--RThere are 2 unexposed functions called compiledFunction : +--R [1] (D2,Symbol,Symbol) -> ((D4,D5) -> D6) +--R from MakeBinaryCompiledFunction(D2,D4,D5,D6) +--R if D2 has KONVERT(INFORM) and D4 has TYPE and D5 has TYPE +--R and D6 has TYPE +--R [2] (D2,Symbol) -> (D4 -> D5) from MakeUnaryCompiledFunction(D2,D4, +--R D5) +--R if D2 has KONVERT(INFORM) and D4 has TYPE and D5 has TYPE +--R +--R +--RExamples of compiledFunction from MakeBinaryCompiledFunction +--R +--RMBCF:=MakeBinaryCompiledFunction(POLY(FRAC(INT)),FLOAT,FLOAT,FLOAT) +--Rf:=(x+3)*(y+4) +--Rg:=compiledFunction(f,x,y)$MBCF +--Rg(2.0,3.0) +--R +--R +--RExamples of compiledFunction from MakeUnaryCompiledFunction +--R +--RMUCF:=MakeUnaryCompiledFunction(POLY(FRAC(INT)),FLOAT,FLOAT) +--Rf:=(x+3)^2 +--Rg:=compiledFunction(f,x)$MUCF +--Rg(2.0) +--R +--E 401 + +--S 402 of 3320 +)d op complement +--R +--R +--RThere is one exposed function called complement : +--R [1] D -> D from D if D has FSAGG(D1) and D1 has SETCAT and D1 has +--R FINITE +--R +--RExamples of complement from FiniteSetAggregate +--R +--E 402 + +--S 403 of 3320 +)d op complementaryBasis +--R +--R +--RThere is one exposed function called complementaryBasis : +--R [1] Vector(D) -> Vector(D) from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC( +--R D2) and D4 has UPOLYC(FRAC(D3)) +--R +--RExamples of complementaryBasis from FunctionFieldCategory +--R +--E 403 + +--S 404 of 3320 +)d op complete +--R +--R +--RThere are 5 exposed functions called complete : +--R [1] ContinuedFraction(D1) -> ContinuedFraction(D1) from +--R ContinuedFraction(D1) +--R if D1 has EUCDOM +--R [2] Integer -> SymmetricPolynomial(Fraction(Integer)) from +--R CycleIndicators +--R [3] D -> D from D if D has LZSTAGG(D1) and D1 has TYPE +--R [4] D -> D from D if D has PADICCT(D1) +--R [5] D -> D from D +--R if D has PSCAT(D1,D2,D3) and D1 has RING and D2 has OAMON +--R and D3 has ORDSET +--R +--RExamples of complete from ContinuedFraction +--R +--R +--RExamples of complete from CycleIndicators +--R +--R +--RExamples of complete from LazyStreamAggregate +--R +--Rm:=[i for i in 1..] +--Rn:=filterUntil(i+->i>100,m) +--RnumberOfComputedEntries n +--Rcomplete n +--RnumberOfComputedEntries n +--R +--R +--RExamples of complete from PAdicIntegerCategory +--R +--R +--RExamples of complete from PowerSeriesCategory +--R +--E 404 + +--S 405 of 3320 +)d op completeEchelonBasis +--R +--R +--RThere is one exposed function called completeEchelonBasis : +--R [1] Vector(Vector(D3)) -> Matrix(D3) from RepresentationPackage2(D3) +--R if D3 has RING +--R +--RExamples of completeEchelonBasis from RepresentationPackage2 +--R +--E 405 + +--S 406 of 3320 +)d op completeEval +--R +--R +--RThere is one unexposed function called completeEval : +--R [1] (SparseUnivariatePolynomial(D8),List(D6),List(D7)) -> +--R SparseUnivariatePolynomial(D7) +--R from FactoringUtilities(D5,D6,D7,D8) +--R if D6 has ORDSET and D7 has RING and D8 has POLYCAT(D7,D5, +--R D6) and D5 has OAMONS +--R +--RExamples of completeEval from FactoringUtilities +--R +--E 406 + +--S 407 of 3320 +)d op completeHensel +--R +--R +--RThere is one unexposed function called completeHensel : +--R [1] (D2,List(D2),D3,PositiveInteger) -> List(D2) +--R from GeneralHenselPackage(D3,D2) if D2 has UPOLYC(D3) and +--R D3 has EUCDOM +--R +--RExamples of completeHensel from GeneralHenselPackage +--R +--E 407 + +--S 408 of 3320 +)d op completeHermite +--R +--R +--RThere is one exposed function called completeHermite : +--R [1] D2 -> Record(Hermite: D2,eqMat: D2) from SmithNormalForm(D3,D4, +--R D5,D2) +--R if D3 has EUCDOM and D4 has FLAGG(D3) and D5 has FLAGG(D3) +--R and D2 has MATCAT(D3,D4,D5) +--R +--RExamples of completeHermite from SmithNormalForm +--R +--E 408 + +--S 409 of 3320 +)d op completeSmith +--R +--R +--RThere is one exposed function called completeSmith : +--R [1] D2 -> Record(Smith: D2,leftEqMat: D2,rightEqMat: D2) +--R from SmithNormalForm(D3,D4,D5,D2) +--R if D3 has EUCDOM and D4 has FLAGG(D3) and D5 has FLAGG(D3) +--R and D2 has MATCAT(D3,D4,D5) +--R +--RExamples of completeSmith from SmithNormalForm +--R +--E 409 + +--S 410 of 3320 +)d op complex +--R +--R +--RThere is one exposed function called complex : +--R [1] (D1,D1) -> D from D if D has COMPCAT(D1) and D1 has COMRING +--R +--RExamples of complex from ComplexCategory +--R +--E 410 + +--S 411 of 3320 +)d op complex? +--R +--R +--RThere is one exposed function called complex? : +--R [1] FortranScalarType -> Boolean from FortranScalarType +--R +--RExamples of complex? from FortranScalarType +--R +--E 411 + +--S 412 of 3320 +)d op complexEigenvalues +--R +--R +--RThere is one exposed function called complexEigenvalues : +--R [1] (Matrix(Complex(Fraction(Integer))),D3) -> List(Complex(D3)) +--R from NumericComplexEigenPackage(D3) if D3 has Join(Field, +--R OrderedRing) +--R +--RExamples of complexEigenvalues from NumericComplexEigenPackage +--R +--E 412 + +--S 413 of 3320 +)d op complexEigenvectors +--R +--R +--RThere is one exposed function called complexEigenvectors : +--R [1] (Matrix(Complex(Fraction(Integer))),D3) -> List(Record(outval: +--R Complex(D3),outmult: Integer,outvect: List(Matrix(Complex(D3))))) +--R from NumericComplexEigenPackage(D3) if D3 has Join(Field, +--R OrderedRing) +--R +--RExamples of complexEigenvectors from NumericComplexEigenPackage +--R +--E 413 + +--S 414 of 3320 +)d op complexElementary +--R +--R +--RThere are 4 exposed functions called complexElementary : +--R [1] D1 -> D1 from ComplexTrigonometricManipulations(D2,D1) +--R if D2 has Join(IntegralDomain,OrderedSet,RetractableTo( +--R Integer)) and D1 has Join(AlgebraicallyClosedField, +--R TranscendentalFunctionCategory,FunctionSpace(Complex(D2))) +--R +--R [2] (D1,Symbol) -> D1 from ComplexTrigonometricManipulations(D3,D1) +--R if D3 has Join(IntegralDomain,OrderedSet,RetractableTo( +--R Integer)) and D1 has Join(AlgebraicallyClosedField, +--R TranscendentalFunctionCategory,FunctionSpace(Complex(D3))) +--R +--R [3] D1 -> D1 from TrigonometricManipulations(D2,D1) +--R if D2 has Join(GcdDomain,OrderedSet,RetractableTo(Integer) +--R ,LinearlyExplicitRingOver(Integer)) and D1 has Join( +--R AlgebraicallyClosedField,TranscendentalFunctionCategory, +--R FunctionSpace(D2)) +--R [4] (D1,Symbol) -> D1 from TrigonometricManipulations(D3,D1) +--R if D3 has Join(GcdDomain,OrderedSet,RetractableTo(Integer) +--R ,LinearlyExplicitRingOver(Integer)) and D1 has Join( +--R AlgebraicallyClosedField,TranscendentalFunctionCategory, +--R FunctionSpace(D3)) +--R +--RExamples of complexElementary from ComplexTrigonometricManipulations +--R +--R +--RExamples of complexElementary from TrigonometricManipulations +--R +--E 414 + +--S 415 of 3320 +)d op complexExpand +--R +--R +--RThere are 2 exposed functions called complexExpand : +--R [1] IntegrationResult(D1) -> D1 from IntegrationResultToFunction(D3, +--R D1) +--R if D1 has Join(AlgebraicallyClosedFunctionSpace(D3), +--R TranscendentalFunctionCategory) and D3 has Join(GcdDomain, +--R RetractableTo(Integer),OrderedSet,LinearlyExplicitRingOver( +--R Integer)) +--R [2] IntegrationResult(Fraction(Polynomial(D3))) -> Expression(D3) +--R from IntegrationResultRFToFunction(D3) +--R if D3 has Join(GcdDomain,RetractableTo(Integer),OrderedSet +--R ,LinearlyExplicitRingOver(Integer)) +--R +--RExamples of complexExpand from IntegrationResultToFunction +--R +--R +--RExamples of complexExpand from IntegrationResultRFToFunction +--R +--E 415 + +--S 416 of 3320 +)d op complexForm +--R +--R +--RThere are 2 exposed functions called complexForm : +--R [1] D2 -> Complex(Expression(D3)) +--R from ComplexTrigonometricManipulations(D3,D2) +--R if D3 has Join(IntegralDomain,OrderedSet,RetractableTo( +--R Integer)) and D2 has Join(AlgebraicallyClosedField, +--R TranscendentalFunctionCategory,FunctionSpace(Complex(D3))) +--R +--R [2] D2 -> Complex(D2) from TrigonometricManipulations(D3,D2) +--R if D3 has Join(GcdDomain,OrderedSet,RetractableTo(Integer) +--R ,LinearlyExplicitRingOver(Integer)) and D2 has Join( +--R AlgebraicallyClosedField,TranscendentalFunctionCategory, +--R FunctionSpace(D3)) +--R +--RExamples of complexForm from ComplexTrigonometricManipulations +--R +--R +--RExamples of complexForm from TrigonometricManipulations +--R +--E 416 + +--S 417 of 3320 +)d op complexIntegrate +--R +--R +--RThere are 2 exposed functions called complexIntegrate : +--R [1] (D1,Symbol) -> D1 from FunctionSpaceComplexIntegration(D3,D1) +--R if D3 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) and D1 has Join( +--R TranscendentalFunctionCategory, +--R AlgebraicallyClosedFunctionSpace(D3)) +--R [2] (Fraction(Polynomial(D4)),Symbol) -> Expression(D4) +--R from IntegrationResultRFToFunction(D4) +--R if D4 has CHARZ and D4 has Join(GcdDomain,RetractableTo( +--R Integer),OrderedSet,LinearlyExplicitRingOver(Integer)) +--R +--RExamples of complexIntegrate from FunctionSpaceComplexIntegration +--R +--R +--RExamples of complexIntegrate from IntegrationResultRFToFunction +--R +--E 417 + +--S 418 of 3320 +)d op complexLimit +--R +--R +--RThere are 3 exposed functions called complexLimit : +--R [1] (D2,Equation(OnePointCompletion(D2))) -> Union( +--R OnePointCompletion(D2),"failed") +--R from PowerSeriesLimitPackage(D4,D2) +--R if D4 has Join(GcdDomain,OrderedSet,RetractableTo(Integer) +--R ,LinearlyExplicitRingOver(Integer)) and D2 has Join( +--R AlgebraicallyClosedField,TranscendentalFunctionCategory, +--R FunctionSpace(D4)) +--R [2] (Fraction(Polynomial(D4)),Equation(OnePointCompletion(Polynomial +--R (D4)))) -> OnePointCompletion(Fraction(Polynomial(D4))) +--R from RationalFunctionLimitPackage(D4) if D4 has GCDDOM +--R [3] (Fraction(Polynomial(D4)),Equation(Fraction(Polynomial(D4)))) +--R -> OnePointCompletion(Fraction(Polynomial(D4))) +--R from RationalFunctionLimitPackage(D4) if D4 has GCDDOM +--R +--RExamples of complexLimit from PowerSeriesLimitPackage +--R +--R +--RExamples of complexLimit from RationalFunctionLimitPackage +--R +--E 418 + +--S 419 of 3320 +)d op complexNormalize +--R +--R +--RThere are 4 exposed functions called complexNormalize : +--R [1] D1 -> D1 from ComplexTrigonometricManipulations(D2,D1) +--R if D2 has Join(IntegralDomain,OrderedSet,RetractableTo( +--R Integer)) and D1 has Join(AlgebraicallyClosedField, +--R TranscendentalFunctionCategory,FunctionSpace(Complex(D2))) +--R +--R [2] (D1,Symbol) -> D1 from ComplexTrigonometricManipulations(D3,D1) +--R if D3 has Join(IntegralDomain,OrderedSet,RetractableTo( +--R Integer)) and D1 has Join(AlgebraicallyClosedField, +--R TranscendentalFunctionCategory,FunctionSpace(Complex(D3))) +--R +--R [3] D1 -> D1 from TrigonometricManipulations(D2,D1) +--R if D2 has Join(GcdDomain,OrderedSet,RetractableTo(Integer) +--R ,LinearlyExplicitRingOver(Integer)) and D1 has Join( +--R AlgebraicallyClosedField,TranscendentalFunctionCategory, +--R FunctionSpace(D2)) +--R [4] (D1,Symbol) -> D1 from TrigonometricManipulations(D3,D1) +--R if D3 has Join(GcdDomain,OrderedSet,RetractableTo(Integer) +--R ,LinearlyExplicitRingOver(Integer)) and D1 has Join( +--R AlgebraicallyClosedField,TranscendentalFunctionCategory, +--R FunctionSpace(D3)) +--R +--RExamples of complexNormalize from ComplexTrigonometricManipulations +--R +--R +--RExamples of complexNormalize from TrigonometricManipulations +--R +--E 419 + +--S 420 of 3320 +)d op complexNumeric +--R +--R +--RThere are 16 exposed functions called complexNumeric : +--R [1] D2 -> Complex(Float) from Numeric(D2) if D2 has KONVERT(FLOAT) +--R +--R [2] (D2,PositiveInteger) -> Complex(Float) from Numeric(D2) +--R if D2 has KONVERT(FLOAT) +--R [3] Complex(D3) -> Complex(Float) from Numeric(D3) +--R if D3 has COMRING and D3 has KONVERT(FLOAT) +--R [4] (Complex(D4),PositiveInteger) -> Complex(Float) from Numeric(D4) +--R if D4 has COMRING and D4 has KONVERT(FLOAT) +--R [5] Polynomial(Complex(D3)) -> Complex(Float) from Numeric(D3) +--R if D3 has COMRING and D3 has KONVERT(FLOAT) +--R [6] (Polynomial(Complex(D4)),PositiveInteger) -> Complex(Float) +--R from Numeric(D4) if D4 has COMRING and D4 has KONVERT( +--R FLOAT) +--R [7] Polynomial(D3) -> Complex(Float) from Numeric(D3) +--R if D3 has RING and D3 has KONVERT(FLOAT) +--R [8] (Polynomial(D4),PositiveInteger) -> Complex(Float) from Numeric( +--R D4) +--R if D4 has RING and D4 has KONVERT(FLOAT) +--R [9] Fraction(Polynomial(D3)) -> Complex(Float) from Numeric(D3) +--R if D3 has INTDOM and D3 has KONVERT(FLOAT) +--R [10] (Fraction(Polynomial(D4)),PositiveInteger) -> Complex(Float) +--R from Numeric(D4) if D4 has INTDOM and D4 has KONVERT(FLOAT +--R ) +--R [11] Fraction(Polynomial(Complex(D3))) -> Complex(Float) from +--R Numeric(D3) +--R if D3 has INTDOM and D3 has KONVERT(FLOAT) +--R [12] (Fraction(Polynomial(Complex(D4))),PositiveInteger) -> Complex( +--R Float) +--R from Numeric(D4) if D4 has INTDOM and D4 has KONVERT(FLOAT +--R ) +--R [13] Expression(D3) -> Complex(Float) from Numeric(D3) +--R if D3 has INTDOM and D3 has ORDSET and D3 has KONVERT( +--R FLOAT) +--R [14] (Expression(D4),PositiveInteger) -> Complex(Float) from Numeric +--R (D4) +--R if D4 has INTDOM and D4 has ORDSET and D4 has KONVERT( +--R FLOAT) +--R [15] Expression(Complex(D3)) -> Complex(Float) from Numeric(D3) +--R if D3 has INTDOM and D3 has ORDSET and D3 has KONVERT( +--R FLOAT) +--R [16] (Expression(Complex(D4)),PositiveInteger) -> Complex(Float) +--R from Numeric(D4) +--R if D4 has INTDOM and D4 has ORDSET and D4 has KONVERT( +--R FLOAT) +--R +--RExamples of complexNumeric from Numeric +--R +--E 420 + +--S 421 of 3320 +)d op complexNumericIfCan +--R +--R +--RThere are 12 exposed functions called complexNumericIfCan : +--R [1] Polynomial(Complex(D3)) -> Union(Complex(Float),"failed") +--R from Numeric(D3) if D3 has COMRING and D3 has KONVERT( +--R FLOAT) +--R [2] (Polynomial(Complex(D4)),PositiveInteger) -> Union(Complex(Float +--R ),"failed") +--R from Numeric(D4) if D4 has COMRING and D4 has KONVERT( +--R FLOAT) +--R [3] Polynomial(D3) -> Union(Complex(Float),"failed") from Numeric(D3 +--R ) +--R if D3 has RING and D3 has KONVERT(FLOAT) +--R [4] (Polynomial(D4),PositiveInteger) -> Union(Complex(Float), +--R "failed") +--R from Numeric(D4) if D4 has RING and D4 has KONVERT(FLOAT) +--R +--R [5] Fraction(Polynomial(D3)) -> Union(Complex(Float),"failed") +--R from Numeric(D3) if D3 has INTDOM and D3 has KONVERT(FLOAT +--R ) +--R [6] (Fraction(Polynomial(D4)),PositiveInteger) -> Union(Complex( +--R Float),"failed") +--R from Numeric(D4) if D4 has INTDOM and D4 has KONVERT(FLOAT +--R ) +--R [7] Fraction(Polynomial(Complex(D3))) -> Union(Complex(Float), +--R "failed") +--R from Numeric(D3) if D3 has INTDOM and D3 has KONVERT(FLOAT +--R ) +--R [8] (Fraction(Polynomial(Complex(D4))),PositiveInteger) -> Union( +--R Complex(Float),"failed") +--R from Numeric(D4) if D4 has INTDOM and D4 has KONVERT(FLOAT +--R ) +--R [9] Expression(D3) -> Union(Complex(Float),"failed") from Numeric(D3 +--R ) +--R if D3 has INTDOM and D3 has ORDSET and D3 has KONVERT( +--R FLOAT) +--R [10] (Expression(D4),PositiveInteger) -> Union(Complex(Float), +--R "failed") +--R from Numeric(D4) +--R if D4 has INTDOM and D4 has ORDSET and D4 has KONVERT( +--R FLOAT) +--R [11] Expression(Complex(D3)) -> Union(Complex(Float),"failed") +--R from Numeric(D3) +--R if D3 has INTDOM and D3 has ORDSET and D3 has KONVERT( +--R FLOAT) +--R [12] (Expression(Complex(D4)),PositiveInteger) -> Union(Complex( +--R Float),"failed") +--R from Numeric(D4) +--R if D4 has INTDOM and D4 has ORDSET and D4 has KONVERT( +--R FLOAT) +--R +--RExamples of complexNumericIfCan from Numeric +--R +--E 421 + +--S 422 of 3320 +)d op complexRoots +--R +--R +--RThere are 2 exposed functions called complexRoots : +--R [1] (Fraction(Polynomial(Complex(Integer))),D3) -> List(Complex(D3)) +--R from FloatingComplexPackage(D3) if D3 has Join(Field, +--R OrderedRing) +--R [2] (List(Fraction(Polynomial(Complex(Integer)))),List(Symbol),D4) +--R -> List(List(Complex(D4))) +--R from FloatingComplexPackage(D4) if D4 has Join(Field, +--R OrderedRing) +--R +--RExamples of complexRoots from FloatingComplexPackage +--R +--E 422 + +--S 423 of 3320 +)d op complexSolve +--R +--R +--RThere are 4 exposed functions called complexSolve : +--R [1] (List(Fraction(Polynomial(Complex(Integer)))),D3) -> List(List( +--R Equation(Polynomial(Complex(D3))))) +--R from FloatingComplexPackage(D3) if D3 has Join(Field, +--R OrderedRing) +--R [2] (List(Equation(Fraction(Polynomial(Complex(Integer))))),D3) -> +--R List(List(Equation(Polynomial(Complex(D3))))) +--R from FloatingComplexPackage(D3) if D3 has Join(Field, +--R OrderedRing) +--R [3] (Fraction(Polynomial(Complex(Integer))),D3) -> List(Equation( +--R Polynomial(Complex(D3)))) +--R from FloatingComplexPackage(D3) if D3 has Join(Field, +--R OrderedRing) +--R [4] (Equation(Fraction(Polynomial(Complex(Integer)))),D3) -> List( +--R Equation(Polynomial(Complex(D3)))) +--R from FloatingComplexPackage(D3) if D3 has Join(Field, +--R OrderedRing) +--R +--RExamples of complexSolve from FloatingComplexPackage +--R +--E 423 + +--S 424 of 3320 +)d op complexZeros +--R +--R +--RThere is one exposed function called complexZeros : +--R [1] (D2,D3) -> List(Complex(D3)) from ComplexRootPackage(D2,D3) +--R if D2 has UPOLYC(COMPLEX(INT)) and D3 has Join(Field, +--R OrderedRing) +--R +--RThere are 2 unexposed functions called complexZeros : +--R [1] D2 -> List(Complex(D3)) from ComplexRootFindingPackage(D3,D2) +--R if D3 has Join(Field,OrderedRing) and D2 has UPOLYC( +--R COMPLEX(D3)) +--R [2] (D2,D3) -> List(Complex(D3)) from ComplexRootFindingPackage(D3, +--R D2) +--R if D3 has Join(Field,OrderedRing) and D2 has UPOLYC( +--R COMPLEX(D3)) +--R +--RExamples of complexZeros from ComplexRootPackage +--R +--R +--RExamples of complexZeros from ComplexRootFindingPackage +--R +--E 424 + +--S 425 of 3320 +)d op component +--R +--R +--RThere are 3 unexposed functions called component : +--R [1] (GraphImage,Point(DoubleFloat),Palette,Palette,PositiveInteger) +--R -> Void +--R from GraphImage +--R [2] (GraphImage,Point(DoubleFloat)) -> Void from GraphImage +--R [3] (GraphImage,List(Point(DoubleFloat)),Palette,Palette, +--R PositiveInteger) -> Void +--R from GraphImage +--R +--RExamples of component from GraphImage +--R +--E 425 + +--S 426 of 3320 +)d op components +--R +--R +--RThere is one exposed function called components : +--R [1] D -> List(D) from D if D2 has RING and D has SPACEC(D2) +--R +--RExamples of components from ThreeSpaceCategory +--R +--E 426 + +--S 427 of 3320 +)d op compose +--R +--R +--RThere is one exposed function called compose : +--R [1] (D1,D1) -> D1 from PolynomialComposition(D1,D2) +--R if D2 has RING and D1 has UPOLYC(D2) +--R +--RThere is one unexposed function called compose : +--R [1] (Stream(D2),Stream(D2)) -> Stream(D2) +--R from StreamTaylorSeriesOperations(D2) if D2 has RING +--R +--RExamples of compose from PolynomialComposition +--R +--R +--RExamples of compose from StreamTaylorSeriesOperations +--R +--E 427 + +--S 428 of 3320 +)d op composite +--R +--R +--RThere are 3 exposed functions called composite : +--R [1] List(D) -> D from D if D has SPACEC(D2) and D2 has RING +--R [2] (Fraction(D),D) -> Union(Fraction(D),"failed") from D +--R if D has UPOLYC(D2) and D2 has RING and D2 has INTDOM +--R [3] (D,D) -> Union(D,"failed") from D +--R if D has UPOLYC(D1) and D1 has RING and D1 has INTDOM +--R +--RExamples of composite from ThreeSpaceCategory +--R +--R +--RExamples of composite from UnivariatePolynomialCategory +--R +--E 428 + +--S 429 of 3320 +)d op composites +--R +--R +--RThere is one exposed function called composites : +--R [1] D -> List(D) from D if D2 has RING and D has SPACEC(D2) +--R +--RExamples of composites from ThreeSpaceCategory +--R +--E 429 + +--S 430 of 3320 +)d op computeBasis +--R +--R +--RThere is one unexposed function called computeBasis : +--R [1] List(HomogeneousDistributedMultivariatePolynomial(D2,D3)) -> +--R List(HomogeneousDistributedMultivariatePolynomial(D2,D3)) +--R from LinGroebnerPackage(D2,D3) if D2: LIST(SYMBOL) and D3 +--R has GCDDOM +--R +--RExamples of computeBasis from LinGroebnerPackage +--R +--E 430 + +--S 431 of 3320 done +)d op computeCycleEntry +--R +--R +--RThere is one unexposed function called computeCycleEntry : +--R [1] (D1,D1) -> D1 from CyclicStreamTools(D2,D1) +--R if D2 has TYPE and D1 has LZSTAGG(D2) +--R +--RExamples of computeCycleEntry from CyclicStreamTools +--R +--Rp:=repeating([1,2,3]) +--Rq:=cons(4,p) +--RcomputeCycleEntry(q,cycleElt(q)) +--R +--E 431 + +--S 432 of 3320 done +)d op computeCycleLength +--R +--R +--RThere is one unexposed function called computeCycleLength : +--R [1] D2 -> NonNegativeInteger from CyclicStreamTools(D3,D2) +--R if D3 has TYPE and D2 has LZSTAGG(D3) +--R +--RExamples of computeCycleLength from CyclicStreamTools +--R +--Rp:=repeating([1,2,3]) +--Rq:=cons(4,p) +--RcomputeCycleLength(cycleElt(q)) +--R +--E 432 + +--S 433 of 3320 +)d op computeInt +--R +--R +--RThere is one unexposed function called computeInt : +--R [1] (Kernel(D3),D3,OrderedCompletion(D3),OrderedCompletion(D3), +--R Boolean) -> Union(OrderedCompletion(D3),"failed") +--R from DefiniteIntegrationTools(D5,D3) +--R if D3 has Join(TranscendentalFunctionCategory, +--R AlgebraicallyClosedFunctionSpace(D5)) and D5 has Join( +--R GcdDomain,OrderedSet,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R +--RExamples of computeInt from DefiniteIntegrationTools +--R +--E 433 + +--S 434 of 3320 +)d op computePowers +--R +--R +--RThere is one unexposed function called computePowers : +--R [1] -> PrimitiveArray(ModMonic(D2,D3)) from ModMonic(D2,D3) +--R if D2 has RING and D3 has UPOLYC(D2) +--R +--RExamples of computePowers from ModMonic +--R +--E 434 + +--S 435 of 3320 +)d op concat +--R +--R +--RThere are 11 exposed functions called concat : +--R [1] (D,D) -> D from D if D has DIVCAT(D1) and D1 has SETCAT +--R [2] (Result,Result) -> Result from ExpertSystemToolsPackage +--R [3] List(Result) -> Result from ExpertSystemToolsPackage +--R [4] List(D) -> D from D if D has LNAGG(D2) and D2 has TYPE +--R [5] (D,D) -> D from D if D has LNAGG(D1) and D1 has TYPE +--R [6] (D1,D) -> D from D if D has LNAGG(D1) and D1 has TYPE +--R [7] (D,D1) -> D from D if D has LNAGG(D1) and D1 has TYPE +--R [8] (RoutinesTable,RoutinesTable) -> RoutinesTable from +--R RoutinesTable +--R [9] Stream(Stream(D3)) -> Stream(D3) from StreamFunctions1(D3) if D3 +--R has TYPE +--R [10] (D1,D) -> D from D if D has URAGG(D1) and D1 has TYPE +--R [11] (D,D) -> D from D if D has URAGG(D1) and D1 has TYPE +--R +--RExamples of concat from DivisorCategory +--R +--R +--RExamples of concat from ExpertSystemToolsPackage +--R +--R +--RExamples of concat from LinearAggregate +--R +--R +--RExamples of concat from RoutinesTable +--R +--R +--RExamples of concat from StreamFunctions1 +--R +--Rm:=[i for i in 10..] +--Rn:=[j for j in 1.. | prime? j] +--Rp:=[m,n]::Stream(Stream(PositiveInteger)) +--Rconcat(p) +--R +--R +--RExamples of concat from UnaryRecursiveAggregate +--R +--Rt1:=[1,2,3] +--Rt2:=concat(4,t1) +--Rt1 +--Rt2 +--R +--Rt1:=[1,2,3] +--Rt2:=concat(t1,t1) +--Rt1 +--Rt2 +--R +--E 435 + +--S 436 of 3320 +)d op concat! +--R +--R +--RThere are 5 exposed functions called concat! : +--R [1] (D,D) -> D from D +--R if D has shallowlyMutable and D has DLAGG(D1) and D1 has +--R TYPE +--R [2] (D,D) -> D from D if D has ELAGG(D1) and D1 has TYPE +--R [3] (D,D1) -> D from D if D has ELAGG(D1) and D1 has TYPE +--R [4] (D,D1) -> D from D +--R if D has shallowlyMutable and D has URAGG(D1) and D1 has +--R TYPE +--R [5] (D,D) -> D from D +--R if D has shallowlyMutable and D has URAGG(D1) and D1 has +--R TYPE +--R +--RExamples of concat! from DoublyLinkedAggregate +--R +--R +--RExamples of concat! from ExtensibleLinearAggregate +--R +--R +--RExamples of concat! from UnaryRecursiveAggregate +--R +--Rt1:=[1,2,3] +--Rconcat!(t1,7) +--Rt1 +--R +--Rt1:=[1,2,3] +--Rt2:=[4,5,6] +--Rconcat!(t1,t2) +--Rt1 +--Rt2 +--R +--E 436 + +--S 437 of 3320 +)d op cond +--R +--R +--RThere are 2 exposed functions called cond : +--R [1] (Switch,FortranCode,FortranCode) -> FortranCode from FortranCode +--R +--R [2] (Switch,FortranCode) -> FortranCode from FortranCode +--R +--RExamples of cond from FortranCode +--R +--E 437 + +--S 438 of 3320 +)d op condition +--R +--R +--RThere is one unexposed function called condition : +--R [1] SplittingNode(D2,D1) -> D1 from SplittingNode(D2,D1) +--R if D1 has Join(SetCategory,Aggregate) and D2 has Join( +--R SetCategory,Aggregate) +--R +--RExamples of condition from SplittingNode +--R +--E 438 + +--S 439 of 3320 +)d op conditionP +--R +--R +--RThere are 2 exposed functions called conditionP : +--R [1] Matrix(D) -> Union(Vector(D),"failed") from D if D has FFIELDC +--R +--R [2] Matrix(D) -> Union(Vector(D),"failed") from D if D has CHARNZ +--R and D has PFECAT +--R +--RExamples of conditionP from FiniteFieldCategory +--R +--R +--RExamples of conditionP from CharacteristicNonZero +--R +--E 439 + +--S 440 of 3320 +)d op conditions +--R +--R +--RThere is one unexposed function called conditions : +--R [1] SplittingTree(D2,D3) -> List(D3) from SplittingTree(D2,D3) +--R if D2 has Join(SetCategory,Aggregate) and D3 has Join( +--R SetCategory,Aggregate) +--R +--RExamples of conditions from SplittingTree +--R +--E 440 + +--S 441 of 3320 +--R--------------)d op conditionsForIdempotents (System Error) +--E 441 + +--S 442 of 3320 +)d op conical +--R +--R +--RThere is one exposed function called conical : +--R [1] (D2,D2) -> (Point(D2) -> Point(D2)) from CoordinateSystems(D2) +--R if D2 has Join(Field,TranscendentalFunctionCategory, +--R RadicalCategory) +--R +--RExamples of conical from CoordinateSystems +--R +--E 442 + +--S 443 of 3320 +)d op conjug +--R +--R +--RThere is one exposed function called conjug : +--R [1] D1 -> D1 from ModuleOperator(D1,D2) +--R if D1 has COMRING and D1 has RING and D2 has LMODULE(D1) +--R +--R +--RThere is one unexposed function called conjug : +--R [1] D1 -> D1 from Operator(D1) if D1 has COMRING and D1 has RING +--R +--RExamples of conjug from ModuleOperator +--R +--R +--RExamples of conjug from Operator +--R +--E 443 + +--S 444 of 3320 +)d op conjugate +--R +--R +--RThere are 10 exposed functions called conjugate : +--R [1] D -> D from D if D has AFSPCAT(D1) and D1 has FIELD +--R [2] (D,NonNegativeInteger) -> D from D if D has AFSPCAT(D2) and D2 +--R has FIELD +--R [3] D -> D from D if D has COMPCAT(D1) and D1 has COMRING +--R [4] (D,D) -> D from D if D has GROUP +--R [5] D -> D from D if D has OC(D1) and D1 has COMRING +--R [6] D -> D from D if D has PACPERC +--R [7] List(Integer) -> List(Integer) from PartitionsAndPermutations +--R +--R [8] D -> D from D if D has PRSPCAT(D1) and D1 has FIELD +--R [9] (D,NonNegativeInteger) -> D from D if D has PRSPCAT(D2) and D2 +--R has FIELD +--R [10] D -> D from D if D has QUATCAT(D1) and D1 has COMRING +--R +--RThere is one unexposed function called conjugate : +--R [1] Partition -> Partition from Partition +--R +--RExamples of conjugate from AffineSpaceCategory +--R +--R +--RExamples of conjugate from ComplexCategory +--R +--R +--RExamples of conjugate from Group +--R +--R +--RExamples of conjugate from OctonionCategory +--R +--R +--RExamples of conjugate from PseudoAlgebraicClosureOfPerfectFieldCategory +--R +--R +--RExamples of conjugate from PartitionsAndPermutations +--R +--R +--RExamples of conjugate from ProjectiveSpaceCategory +--R +--R +--RExamples of conjugate from Partition +--R +--R +--RExamples of conjugate from QuaternionCategory +--R +--E 444 + +--S 445 of 3320 +)d op conjugates +--R +--R +--RThere is one exposed function called conjugates : +--R [1] Stream(List(Integer)) -> Stream(List(Integer)) +--R from PartitionsAndPermutations +--R +--RExamples of conjugates from PartitionsAndPermutations +--R +--E 445 + +--S 446 of 3320 +)d op connect +--R +--R +--RThere is one unexposed function called connect : +--R [1] (TwoDimensionalViewport,PositiveInteger,String) -> Void +--R from TwoDimensionalViewport +--R +--RExamples of connect from TwoDimensionalViewport +--R +--E 446 + +--S 447 of 3320 +)d op cons +--R +--R +--RThere are 2 exposed functions called cons : +--R [1] (D1,List(D1)) -> List(D1) from List(D1) if D1 has TYPE +--R [2] (D1,Stream(D1)) -> Stream(D1) from Stream(D1) if D1 has TYPE +--R +--RExamples of cons from List +--R +--R +--RExamples of cons from Stream +--R +--Rm:=[1,2,3] +--Rn:=repeating(m) +--Rcons(4,n) +--R +--E 447 + +--S 448 of 3320 +)d op consnewpol +--R +--R +--RThere is one unexposed function called consnewpol : +--R [1] (SparseUnivariatePolynomial(D8),SparseUnivariatePolynomial(D7), +--R Integer) -> Record(pol: SparseUnivariatePolynomial(D8),polval: +--R SparseUnivariatePolynomial(D7)) +--R from MultivariateSquareFree(D5,D6,D7,D8) +--R if D5 has OAMONS and D6 has ORDSET and D7 has EUCDOM and +--R D8 has POLYCAT(D7,D5,D6) +--R +--RExamples of consnewpol from MultivariateSquareFree +--R +--E 448 + +--S 449 of 3320 +)d op consRow! +--R +--R +--RThere is one exposed function called consRow! : +--R [1] (SparseEchelonMatrix(D3,D4),Record(Indices: List(D3),Entries: +--R List(D4))) -> Void +--R from SparseEchelonMatrix(D3,D4) if D3 has ORDSET and D4 +--R has RING +--R +--RExamples of consRow! from SparseEchelonMatrix +--R +--E 449 + +--S 450 of 3320 +)d op const +--R +--R +--RThere is one exposed function called const : +--R [1] D2 -> (D3 -> D2) from MappingPackage2(D3,D2) +--R if D3 has SETCAT and D2 has SETCAT +--R +--RExamples of const from MappingPackage2 +--R +--E 450 + +--S 451 of 3320 +)d op constant +--R +--R +--RThere are 5 exposed functions called constant : +--R [1] (() -> D4) -> (D3 -> D4) from MappingPackage2(D3,D4) +--R if D4 has SETCAT and D3 has SETCAT +--R [2] D2 -> D1 from PackageForPoly(D1,D2,D3,D4) +--R if D3 has DIRPCAT(D4,NNI) and D4: NNI and D1 has RING and +--R D2 has FAMR(D1,D3) +--R [3] D1 -> D1 from FunctionSpaceAssertions(D2,D1) +--R if D2 has ORDSET and D1 has FS(D2) +--R [4] Symbol -> Expression(Integer) from PatternMatchAssertions +--R [5] D -> D1 from D if D has XFALG(D2,D1) and D2 has ORDSET and D1 +--R has RING +--R +--RThere is one unexposed function called constant : +--R [1] XPolynomialRing(D1,D2) -> D1 from XPolynomialRing(D1,D2) +--R if D1 has RING and D2 has ORDMON +--R +--RExamples of constant from MappingPackage2 +--R +--R +--RExamples of constant from PackageForPoly +--R +--R +--RExamples of constant from FunctionSpaceAssertions +--R +--R +--RExamples of constant from PatternMatchAssertions +--R +--R +--RExamples of constant from XFreeAlgebra +--R +--R +--RExamples of constant from XPolynomialRing +--R +--E 451 + +--S 452 of 3320 +)d op constant? +--R +--R +--RThere is one exposed function called constant? : +--R [1] D -> Boolean from D if D has XFALG(D2,D3) and D2 has ORDSET and +--R D3 has RING +--R +--RThere are 2 unexposed functions called constant? : +--R [1] Pattern(D2) -> Boolean from Pattern(D2) if D2 has SETCAT +--R [2] XPolynomialRing(D2,D3) -> Boolean from XPolynomialRing(D2,D3) +--R if D2 has RING and D3 has ORDMON +--R +--RExamples of constant? from Pattern +--R +--R +--RExamples of constant? from XFreeAlgebra +--R +--R +--RExamples of constant? from XPolynomialRing +--R +--E 452 + +--S 453 of 3320 +)d op constantCoefficientRicDE +--R +--R +--RThere is one unexposed function called constantCoefficientRicDE : +--R [1] (D2,(D5 -> List(D4))) -> List(Record(constant: D4,eq: D2)) +--R from PrimitiveRatRicDE(D4,D5,D2,D6) +--R if D4 has Join(Field,CharacteristicZero,RetractableTo( +--R Fraction(Integer))) and D5 has UPOLYC(D4) and D2 has +--R LODOCAT(D5) and D6 has LODOCAT(FRAC(D5)) +--R +--RExamples of constantCoefficientRicDE from PrimitiveRatRicDE +--R +--E 453 + +--S 454 of 3320 +)d op constantIfCan +--R +--R +--RThere is one exposed function called constantIfCan : +--R [1] Kernel(D3) -> Union(D1,"failed") from KernelFunctions2(D1,D3) +--R if D3 has ORDSET and D1 has ORDSET +--R +--RExamples of constantIfCan from KernelFunctions2 +--R +--E 454 + +--S 455 of 3320 +)d op constantKernel +--R +--R +--RThere is one exposed function called constantKernel : +--R [1] D2 -> Kernel(D3) from KernelFunctions2(D2,D3) +--R if D2 has ORDSET and D3 has ORDSET +--R +--RExamples of constantKernel from KernelFunctions2 +--R +--E 455 + +--S 456 of 3320 +)d op constantLeft +--R +--R +--RThere is one exposed function called constantLeft : +--R [1] (D4 -> D5) -> ((D3,D4) -> D5) from MappingPackage3(D3,D4,D5) +--R if D4 has SETCAT and D5 has SETCAT and D3 has SETCAT +--R +--RExamples of constantLeft from MappingPackage3 +--R +--E 456 + +--S 457 of 3320 +)d op constantOperator +--R +--R +--RThere is one exposed function called constantOperator : +--R [1] D2 -> BasicOperator from BasicOperatorFunctions1(D2) +--R if D2 has ORDSET and D2 has SETCAT +--R +--RExamples of constantOperator from BasicOperatorFunctions1 +--R +--E 457 + +--S 458 of 3320 +)d op constantOpIfCan +--R +--R +--RThere is one exposed function called constantOpIfCan : +--R [1] BasicOperator -> Union(D1,"failed") from BasicOperatorFunctions1 +--R (D1) +--R if D1 has SETCAT and D1 has ORDSET +--R +--RExamples of constantOpIfCan from BasicOperatorFunctions1 +--R +--E 458 + +--S 459 of 3320 +)d op constantRight +--R +--R +--RThere is one exposed function called constantRight : +--R [1] (D3 -> D5) -> ((D3,D4) -> D5) from MappingPackage3(D3,D4,D5) +--R if D3 has SETCAT and D5 has SETCAT and D4 has SETCAT +--R +--RExamples of constantRight from MappingPackage3 +--R +--E 459 + +--S 460 of 3320 +)d op constantToUnaryFunction +--R +--R +--RThere is one unexposed function called constantToUnaryFunction : +--R [1] DoubleFloat -> (DoubleFloat -> DoubleFloat) from +--R ExpressionTubePlot +--R +--RExamples of constantToUnaryFunction from ExpressionTubePlot +--R +--E 460 + +--S 461 of 3320 +)d op constDsolve +--R +--R +--RThere is one unexposed function called constDsolve : +--R [1] (D2,D3,Symbol) -> Record(particular: D3,basis: List(D3)) +--R from ConstantLODE(D5,D3,D2) +--R if D5 has Join(OrderedSet,EuclideanDomain,RetractableTo( +--R Integer),LinearlyExplicitRingOver(Integer), +--R CharacteristicZero) and D3 has Join( +--R AlgebraicallyClosedFunctionSpace(D5), +--R TranscendentalFunctionCategory,PrimitiveFunctionCategory) +--R and D2 has LODOCAT(D3) +--R +--RExamples of constDsolve from ConstantLODE +--R +--E 461 + +--S 462 of 3320 +)d op construct +--R +--R +--RThere are 7 exposed functions called construct : +--R [1] List(D2) -> D from D if D2 has TYPE and D has CLAGG(D2) +--R [2] List(Record(exponent: NonNegativeInteger,center: D3,num: D3)) +--R -> FullPartialFractionExpansion(D2,D3) +--R from FullPartialFractionExpansion(D2,D3) +--R if D3 has UPOLYC(D2) and D2 has Join(Field, +--R CharacteristicZero) +--R [3] (Union(fst: FortranScalarType,void: void),List(Polynomial( +--R Integer)),Boolean) -> FortranType +--R from FortranType +--R [4] (Union(fst: FortranScalarType,void: void),List(Symbol),Boolean) +--R -> FortranType +--R from FortranType +--R [5] InfiniteTuple(D2) -> Stream(D2) from InfiniteTuple(D2) if D2 +--R has TYPE +--R [6] (D,D) -> D from D if D has LIECAT(D1) and D1 has COMRING +--R [7] List(List(List(D2))) -> ThreeDimensionalMatrix(D2) +--R from ThreeDimensionalMatrix(D2) if D2 has SETCAT +--R +--RThere are 15 unexposed functions called construct : +--R [1] (LiePolynomial(D2,D3),LyndonWord(D2)) -> LiePolynomial(D2,D3) +--R from LiePolynomial(D2,D3) if D2 has ORDSET and D3 has +--R COMRING +--R [2] (LyndonWord(D2),LiePolynomial(D2,D3)) -> LiePolynomial(D2,D3) +--R from LiePolynomial(D2,D3) if D2 has ORDSET and D3 has +--R COMRING +--R [3] (LyndonWord(D2),LyndonWord(D2)) -> LiePolynomial(D2,D3) +--R from LiePolynomial(D2,D3) if D2 has ORDSET and D3 has +--R COMRING +--R [4] (D1,D2) -> ModuleMonomial(D1,D2,D3) from ModuleMonomial(D1,D2,D3 +--R ) +--R if D1 has ORDSET and D2 has SETCAT and D3: ((Record(index +--R : D1,exponent: D2),Record(index: D1,exponent: D2)) -> +--R Boolean) +--R [5] List(Record(key: Symbol,entry: D3)) -> PatternMatchResult(D2,D3) +--R from PatternMatchResult(D2,D3) if D3 has SETCAT and D2 +--R has SETCAT +--R [6] (D2,List(D4)) -> List(SplittingNode(D2,D4)) from SplittingNode( +--R D2,D4) +--R if D4 has Join(SetCategory,Aggregate) and D2 has Join( +--R SetCategory,Aggregate) +--R [7] List(Record(val: D3,tower: D4)) -> List(SplittingNode(D3,D4)) +--R from SplittingNode(D3,D4) +--R if D3 has Join(SetCategory,Aggregate) and D4 has Join( +--R SetCategory,Aggregate) +--R [8] Record(val: D2,tower: D3) -> SplittingNode(D2,D3) +--R from SplittingNode(D2,D3) +--R if D2 has Join(SetCategory,Aggregate) and D3 has Join( +--R SetCategory,Aggregate) +--R [9] (D1,D2) -> SplittingNode(D1,D2) from SplittingNode(D1,D2) +--R if D1 has Join(SetCategory,Aggregate) and D2 has Join( +--R SetCategory,Aggregate) +--R [10] (D1,D2,Boolean) -> SplittingNode(D1,D2) from SplittingNode(D1, +--R D2) +--R if D1 has Join(SetCategory,Aggregate) and D2 has Join( +--R SetCategory,Aggregate) +--R [11] (D1,D2,D1,List(D2)) -> SplittingTree(D1,D2) from SplittingTree( +--R D1,D2) +--R if D2 has Join(SetCategory,Aggregate) and D1 has Join( +--R SetCategory,Aggregate) +--R [12] (D1,D2,List(SplittingNode(D1,D2))) -> SplittingTree(D1,D2) +--R from SplittingTree(D1,D2) +--R if D1 has Join(SetCategory,Aggregate) and D2 has Join( +--R SetCategory,Aggregate) +--R [13] (D1,D2,List(SplittingTree(D1,D2))) -> SplittingTree(D1,D2) +--R from SplittingTree(D1,D2) +--R if D1 has Join(SetCategory,Aggregate) and D2 has Join( +--R SetCategory,Aggregate) +--R [14] SplittingNode(D2,D3) -> SplittingTree(D2,D3) from SplittingTree +--R (D2,D3) +--R if D2 has Join(SetCategory,Aggregate) and D3 has Join( +--R SetCategory,Aggregate) +--R [15] (D1,D2) -> SuchThat(D1,D2) from SuchThat(D1,D2) +--R if D1 has SETCAT and D2 has SETCAT +--R +--RExamples of construct from Collection +--R +--R +--RExamples of construct from FullPartialFractionExpansion +--R +--R +--RExamples of construct from FortranType +--R +--R +--RExamples of construct from InfiniteTuple +--R +--R +--RExamples of construct from LieAlgebra +--R +--R +--RExamples of construct from LiePolynomial +--R +--R +--RExamples of construct from ThreeDimensionalMatrix +--R +--R +--RExamples of construct from ModuleMonomial +--R +--R +--RExamples of construct from PatternMatchResult +--R +--R +--RExamples of construct from SplittingNode +--R +--R +--RExamples of construct from SplittingTree +--R +--R +--RExamples of construct from SuchThat +--R +--E 462 + +--S 463 of 3320 +)d op construct +--R +--R +--RThere are 7 exposed functions called construct : +--R [1] List(D2) -> D from D if D2 has TYPE and D has CLAGG(D2) +--R [2] List(Record(exponent: NonNegativeInteger,center: D3,num: D3)) +--R -> FullPartialFractionExpansion(D2,D3) +--R from FullPartialFractionExpansion(D2,D3) +--R if D3 has UPOLYC(D2) and D2 has Join(Field, +--R CharacteristicZero) +--R [3] (Union(fst: FortranScalarType,void: void),List(Polynomial( +--R Integer)),Boolean) -> FortranType +--R from FortranType +--R [4] (Union(fst: FortranScalarType,void: void),List(Symbol),Boolean) +--R -> FortranType +--R from FortranType +--R [5] InfiniteTuple(D2) -> Stream(D2) from InfiniteTuple(D2) if D2 +--R has TYPE +--R [6] (D,D) -> D from D if D has LIECAT(D1) and D1 has COMRING +--R [7] List(List(List(D2))) -> ThreeDimensionalMatrix(D2) +--R from ThreeDimensionalMatrix(D2) if D2 has SETCAT +--R +--RThere are 15 unexposed functions called construct : +--R [1] (LiePolynomial(D2,D3),LyndonWord(D2)) -> LiePolynomial(D2,D3) +--R from LiePolynomial(D2,D3) if D2 has ORDSET and D3 has +--R COMRING +--R [2] (LyndonWord(D2),LiePolynomial(D2,D3)) -> LiePolynomial(D2,D3) +--R from LiePolynomial(D2,D3) if D2 has ORDSET and D3 has +--R COMRING +--R [3] (LyndonWord(D2),LyndonWord(D2)) -> LiePolynomial(D2,D3) +--R from LiePolynomial(D2,D3) if D2 has ORDSET and D3 has +--R COMRING +--R [4] (D1,D2) -> ModuleMonomial(D1,D2,D3) from ModuleMonomial(D1,D2,D3 +--R ) +--R if D1 has ORDSET and D2 has SETCAT and D3: ((Record(index +--R : D1,exponent: D2),Record(index: D1,exponent: D2)) -> +--R Boolean) +--R [5] List(Record(key: Symbol,entry: D3)) -> PatternMatchResult(D2,D3) +--R from PatternMatchResult(D2,D3) if D3 has SETCAT and D2 +--R has SETCAT +--R [6] (D2,List(D4)) -> List(SplittingNode(D2,D4)) from SplittingNode( +--R D2,D4) +--R if D4 has Join(SetCategory,Aggregate) and D2 has Join( +--R SetCategory,Aggregate) +--R [7] List(Record(val: D3,tower: D4)) -> List(SplittingNode(D3,D4)) +--R from SplittingNode(D3,D4) +--R if D3 has Join(SetCategory,Aggregate) and D4 has Join( +--R SetCategory,Aggregate) +--R [8] Record(val: D2,tower: D3) -> SplittingNode(D2,D3) +--R from SplittingNode(D2,D3) +--R if D2 has Join(SetCategory,Aggregate) and D3 has Join( +--R SetCategory,Aggregate) +--R [9] (D1,D2) -> SplittingNode(D1,D2) from SplittingNode(D1,D2) +--R if D1 has Join(SetCategory,Aggregate) and D2 has Join( +--R SetCategory,Aggregate) +--R [10] (D1,D2,Boolean) -> SplittingNode(D1,D2) from SplittingNode(D1, +--R D2) +--R if D1 has Join(SetCategory,Aggregate) and D2 has Join( +--R SetCategory,Aggregate) +--R [11] (D1,D2,D1,List(D2)) -> SplittingTree(D1,D2) from SplittingTree( +--R D1,D2) +--R if D2 has Join(SetCategory,Aggregate) and D1 has Join( +--R SetCategory,Aggregate) +--R [12] (D1,D2,List(SplittingNode(D1,D2))) -> SplittingTree(D1,D2) +--R from SplittingTree(D1,D2) +--R if D1 has Join(SetCategory,Aggregate) and D2 has Join( +--R SetCategory,Aggregate) +--R [13] (D1,D2,List(SplittingTree(D1,D2))) -> SplittingTree(D1,D2) +--R from SplittingTree(D1,D2) +--R if D1 has Join(SetCategory,Aggregate) and D2 has Join( +--R SetCategory,Aggregate) +--R [14] SplittingNode(D2,D3) -> SplittingTree(D2,D3) from SplittingTree +--R (D2,D3) +--R if D2 has Join(SetCategory,Aggregate) and D3 has Join( +--R SetCategory,Aggregate) +--R [15] (D1,D2) -> SuchThat(D1,D2) from SuchThat(D1,D2) +--R if D1 has SETCAT and D2 has SETCAT +--R +--RExamples of construct from Collection +--R +--R +--RExamples of construct from FullPartialFractionExpansion +--R +--R +--RExamples of construct from FortranType +--R +--R +--RExamples of construct from InfiniteTuple +--R +--R +--RExamples of construct from LieAlgebra +--R +--R +--RExamples of construct from LiePolynomial +--R +--R +--RExamples of construct from ThreeDimensionalMatrix +--R +--R +--RExamples of construct from ModuleMonomial +--R +--R +--RExamples of construct from PatternMatchResult +--R +--R +--RExamples of construct from SplittingNode +--R +--R +--RExamples of construct from SplittingTree +--R +--R +--RExamples of construct from SuchThat +--R +--E 463 + +--S 464 of 3320 +)d op contains? +--R +--R +--RThere is one exposed function called contains? : +--R [1] (D,D2) -> Boolean from D +--R if D has INTCAT(D2) and D2 has Join(FloatingPointSystem, +--R TranscendentalFunctionCategory) +--R +--RExamples of contains? from IntervalCategory +--R +--E 464 + +--S 465 of 3320 +)d op content +--R +--R +--RThere are 3 exposed functions called content : +--R [1] D -> D1 from D +--R if D has FAMR(D1,D2) and D2 has OAMON and D1 has RING and +--R D1 has GCDDOM +--R [2] D -> D1 from D if D has OREPCAT(D1) and D1 has RING and D1 has +--R GCDDOM +--R [3] (D,D1) -> D from D +--R if D has POLYCAT(D2,D3,D1) and D2 has RING and D3 has +--R OAMONS and D1 has ORDSET and D2 has GCDDOM +--R +--RThere is one unexposed function called content : +--R [1] List(D3) -> List(Integer) from HeuGcd(D3) if D3 has UPOLYC(INT) +--R +--R +--RExamples of content from FiniteAbelianMonoidRing +--R +--R +--RExamples of content from HeuGcd +--R +--R +--RExamples of content from UnivariateSkewPolynomialCategory +--R +--R +--RExamples of content from PolynomialCategory +--R +--E 465 + +--S 466 of 3320 +)d op continue +--R +--R +--RThere is one exposed function called continue : +--R [1] SingleInteger -> FortranCode from FortranCode +--R +--RExamples of continue from FortranCode +--R +--E 466 + +--S 467 of 3320 +)d op continuedFraction +--R +--R +--RThere are 3 exposed functions called continuedFraction : +--R [1] (D1,Stream(D1),Stream(D1)) -> ContinuedFraction(D1) +--R from ContinuedFraction(D1) if D1 has EUCDOM +--R [2] Fraction(D2) -> ContinuedFraction(D2) from ContinuedFraction(D2) +--R if D2 has EUCDOM +--R [3] D2 -> ContinuedFraction(Integer) from NumericContinuedFraction( +--R D2) +--R if D2 has FPS +--R +--RThere are 3 unexposed functions called continuedFraction : +--R [1] BalancedPAdicRational(D2) -> ContinuedFraction(Fraction(Integer) +--R ) +--R from BalancedPAdicRational(D2) if D2: INT +--R [2] PAdicRational(D2) -> ContinuedFraction(Fraction(Integer)) +--R from PAdicRational(D2) if D2: INT +--R [3] PAdicRationalConstructor(D2,D3) -> ContinuedFraction(Fraction( +--R Integer)) +--R from PAdicRationalConstructor(D2,D3) if D2: INT and D3 +--R has PADICCT(D2) +--R +--RExamples of continuedFraction from BalancedPAdicRational +--R +--R +--RExamples of continuedFraction from ContinuedFraction +--R +--R +--RExamples of continuedFraction from NumericContinuedFraction +--R +--R +--RExamples of continuedFraction from PAdicRational +--R +--R +--RExamples of continuedFraction from PAdicRationalConstructor +--R +--E 467 + +--S 468 of 3320 +)d op contract +--R +--R +--RThere are 3 exposed functions called contract : +--R [1] (CartesianTensor(D2,D3,D4),Integer,Integer) -> CartesianTensor( +--R D2,D3,D4) +--R from CartesianTensor(D2,D3,D4) if D2: INT and D3: NNI and +--R D4 has COMRING +--R [2] (CartesianTensor(D2,D3,D4),Integer,CartesianTensor(D2,D3,D4), +--R Integer) -> CartesianTensor(D2,D3,D4) +--R from CartesianTensor(D2,D3,D4) if D2: INT and D3: NNI and +--R D4 has COMRING +--R [3] (PolynomialIdeals(Fraction(Integer),DirectProduct(D4, +--R NonNegativeInteger),OrderedVariableList(D3), +--R DistributedMultivariatePolynomial(D3,Fraction(Integer))),List( +--R OrderedVariableList(D3))) -> PolynomialIdeals(Fraction(Integer), +--R DirectProduct(D4,NonNegativeInteger),OrderedVariableList(D3), +--R DistributedMultivariatePolynomial(D3,Fraction(Integer))) +--R from IdealDecompositionPackage(D3,D4) if D3: LIST(SYMBOL) +--R and D4: NNI +--R +--RExamples of contract from CartesianTensor +--R +--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] +--RTm:CartesianTensor(1,2,Integer):=m +--Rv:DirectProduct(2,Integer):=directProduct [3,4] +--RTv:CartesianTensor(1,2,Integer):=v +--RTmv:=contract(Tm,2,1) +--R +--Rm:SquareMatrix(2,Integer):=matrix [[1,2],[4,5]] +--RTm:CartesianTensor(1,2,Integer):=m +--Rv:DirectProduct(2,Integer):=directProduct [3,4] +--RTv:CartesianTensor(1,2,Integer):=v +--RTmv:=contract(Tm,2,Tv,1) +--R +--R +--RExamples of contract from IdealDecompositionPackage +--R +--E 468 + +--S 469 of 3320 done +)d op contractSolve +--R +--R +--RThere are 2 exposed functions called contractSolve : +--R [1] (Equation(Fraction(Polynomial(D4))),Symbol) -> SuchThat(List( +--R Expression(D4)),List(Equation(Expression(D4)))) +--R from RadicalSolvePackage(D4) +--R if D4 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero) +--R [2] (Fraction(Polynomial(D4)),Symbol) -> SuchThat(List(Expression(D4 +--R )),List(Equation(Expression(D4)))) +--R from RadicalSolvePackage(D4) +--R if D4 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero) +--R +--RExamples of contractSolve from RadicalSolvePackage +--R +--Rb:Fraction(Polynomial(Integer)):=(3*x^3+7)/(5*x^2-13) +--RcontractSolve(b,x) +--R +--Rb:Fraction(Polynomial(Integer)):=(3*x^3+7)/(5*x^2-13) +--RcontractSolve(b=0,x) +--R +--E 469 + +--S 470 of 3320 +)d op controlPanel +--R +--R +--RThere is one exposed function called controlPanel : +--R [1] (ThreeDimensionalViewport,String) -> Void from +--R ThreeDimensionalViewport +--R +--RThere is one unexposed function called controlPanel : +--R [1] (TwoDimensionalViewport,String) -> Void from +--R TwoDimensionalViewport +--R +--RExamples of controlPanel from TwoDimensionalViewport +--R +--R +--RExamples of controlPanel from ThreeDimensionalViewport +--R +--E 470 + +--S 471 of 3320 +)d op convergents +--R +--R +--RThere is one exposed function called convergents : +--R [1] ContinuedFraction(D2) -> Stream(Fraction(D2)) from +--R ContinuedFraction(D2) +--R if D2 has EUCDOM +--R +--RExamples of convergents from ContinuedFraction +--R +--E 471 + +--S 472 of 3320 +)d op convert +--R +--R +--RThere are 32 exposed functions called convert : +--R [1] Symbol -> BasicStochasticDifferential from +--R BasicStochasticDifferential +--R [2] List(Segment(OrderedCompletion(Float))) -> List(Segment( +--R OrderedCompletion(DoubleFloat))) +--R from ExpertSystemToolsPackage +--R [3] DoubleFloat -> Float from Float +--R [4] (OutputForm,Integer) -> ScriptFormulaFormat from +--R ScriptFormulaFormat +--R [5] Vector(D2) -> D from D +--R if D2 has COMRING and D has FRAMALG(D2,D3) and D3 has +--R UPOLYC(D2) +--R [6] D -> Vector(D2) from D +--R if D has FRAMALG(D2,D3) and D2 has COMRING and D3 has +--R UPOLYC(D2) +--R [7] Vector(D2) -> D from D if D2 has COMRING and D has FRNAALG(D2) +--R +--R [8] D -> Vector(D2) from D if D has FRNAALG(D2) and D2 has COMRING +--R +--R [9] Factored(D) -> D from D if D has FS(D2) and D2 has INTDOM and D2 +--R has ORDSET +--R [10] D -> D1 from D if D has KONVERT(D1) and D1 has TYPE +--R [11] D1 -> D from D +--R if D2 has COMRING and D has MONOGEN(D2,D1) and D1 has +--R UPOLYC(D2) +--R [12] List(D2) -> D from D if D2 has RING and D has PTCAT(D2) +--R [13] Symbol -> RomanNumeral from RomanNumeral +--R [14] Polynomial(D2) -> D from D +--R if D2 has RING and D has RPOLCAT(D2,D3,D4) and D4 has +--R KONVERT(SYMBOL) and D3 has OAMONS and D4 has ORDSET +--R [15] D1 -> D from D +--R if D1 = POLY(INT) and D has RPOLCAT(D2,D3,D4) and not( +--R ofCategory(D2,Algebra(Fraction(Integer)))) and D2 has +--R ALGEBRA(INT) and D4 has KONVERT(SYMBOL) and D2 has RING and +--R D3 has OAMONS and D4 has ORDSET or D1 = POLY(INT) and D +--R has RPOLCAT(D2,D3,D4) and D2 has ALGEBRA(FRAC(INT)) and D4 +--R has KONVERT(SYMBOL) and D2 has RING and D3 has OAMONS and +--R D4 has ORDSET +--R [16] Polynomial(Fraction(Integer)) -> D from D +--R if D has RPOLCAT(D2,D3,D4) and D2 has ALGEBRA(FRAC(INT)) +--R and D4 has KONVERT(SYMBOL) and D2 has RING and D3 has +--R OAMONS and D4 has ORDSET +--R [17] Record(val: List(D6),tower: D7) -> String +--R from RegularSetDecompositionPackage(D3,D4,D5,D6,D7) +--R if D6 has RPOLCAT(D3,D4,D5) and D7 has RSETCAT(D3,D4,D5,D6 +--R ) and D3 has GCDDOM and D4 has OAMONS and D5 has ORDSET +--R [18] D1 -> D from D if D has SEGCAT(D1) and D1 has TYPE +--R [19] D1 -> D from D +--R if D has SEXCAT(D2,D3,D4,D5,D1) and D2 has SETCAT and D3 +--R has SETCAT and D4 has SETCAT and D5 has SETCAT and D1 has +--R SETCAT +--R [20] D1 -> D from D +--R if D has SEXCAT(D2,D3,D4,D1,D5) and D2 has SETCAT and D3 +--R has SETCAT and D4 has SETCAT and D1 has SETCAT and D5 has +--R SETCAT +--R [21] D1 -> D from D +--R if D has SEXCAT(D2,D3,D1,D4,D5) and D2 has SETCAT and D3 +--R has SETCAT and D1 has SETCAT and D4 has SETCAT and D5 has +--R SETCAT +--R [22] D1 -> D from D +--R if D has SEXCAT(D2,D1,D3,D4,D5) and D2 has SETCAT and D1 +--R has SETCAT and D3 has SETCAT and D4 has SETCAT and D5 has +--R SETCAT +--R [23] D1 -> D from D +--R if D has SEXCAT(D1,D2,D3,D4,D5) and D1 has SETCAT and D2 +--R has SETCAT and D3 has SETCAT and D4 has SETCAT and D5 has +--R SETCAT +--R [24] List(D) -> D from D +--R if D has SEXCAT(D2,D3,D4,D5,D6) and D2 has SETCAT and D3 +--R has SETCAT and D4 has SETCAT and D5 has SETCAT and D6 has +--R SETCAT +--R [25] Record(val: List(D6),tower: D7) -> String +--R from SquareFreeRegularSetDecompositionPackage(D3,D4,D5,D6, +--R D7) +--R if D6 has RPOLCAT(D3,D4,D5) and D7 has SFRTCAT(D3,D4,D5,D6 +--R ) and D3 has GCDDOM and D4 has OAMONS and D5 has ORDSET +--R [26] (OutputForm,Integer,OutputForm) -> TexFormat from TexFormat +--R [27] (OutputForm,Integer) -> TexFormat from TexFormat +--R [28] NewSparseMultivariatePolynomial(D3,OrderedVariableList(D4)) -> +--R NewSparseMultivariatePolynomial(D3,OrderedVariableList(D5)) +--R from ZeroDimensionalSolvePackage(D3,D4,D5) +--R if D3 has Join(OrderedRing,EuclideanDomain, +--R CharacteristicZero,RealConstant) and D4: LIST(SYMBOL) and +--R D5: LIST(SYMBOL) +--R [29] Polynomial(D3) -> Polynomial(RealClosure(Fraction(D3))) +--R from ZeroDimensionalSolvePackage(D3,D4,D5) +--R if D3 has Join(OrderedRing,EuclideanDomain, +--R CharacteristicZero,RealConstant) and D4: LIST(SYMBOL) and +--R D5: LIST(SYMBOL) +--R [30] NewSparseMultivariatePolynomial(D3,OrderedVariableList(D5)) -> +--R Polynomial(RealClosure(Fraction(D3))) +--R from ZeroDimensionalSolvePackage(D3,D4,D5) +--R if D3 has Join(OrderedRing,EuclideanDomain, +--R CharacteristicZero,RealConstant) and D5: LIST(SYMBOL) and +--R D4: LIST(SYMBOL) +--R [31] SparseUnivariatePolynomial(D3) -> SparseUnivariatePolynomial( +--R RealClosure(Fraction(D3))) +--R from ZeroDimensionalSolvePackage(D3,D4,D5) +--R if D3 has Join(OrderedRing,EuclideanDomain, +--R CharacteristicZero,RealConstant) and D4: LIST(SYMBOL) and +--R D5: LIST(SYMBOL) +--R [32] SquareFreeRegularTriangularSet(D3,IndexedExponents( +--R OrderedVariableList(D5)),OrderedVariableList(D5), +--R NewSparseMultivariatePolynomial(D3,OrderedVariableList(D5))) -> +--R List(NewSparseMultivariatePolynomial(D3,OrderedVariableList(D5))) +--R from ZeroDimensionalSolvePackage(D3,D4,D5) +--R if D3 has Join(OrderedRing,EuclideanDomain, +--R CharacteristicZero,RealConstant) and D5: LIST(SYMBOL) and +--R D4: LIST(SYMBOL) +--R +--RThere are 5 unexposed functions called convert : +--R [1] D2 -> Pattern(D3) from ComplexPattern(D3,D4,D2) +--R if D4 has Join(ConvertibleTo(Pattern(D3)),CommutativeRing) +--R and D3 has SETCAT and D2 has COMPCAT(D4) +--R [2] List(D5) -> GeneralPolynomialSet(D2,D3,D4,D5) +--R from GeneralPolynomialSet(D2,D3,D4,D5) +--R if D5 has RPOLCAT(D2,D3,D4) and D2 has RING and D3 has +--R OAMONS and D4 has ORDSET +--R [3] SExpression -> InputForm from InputForm +--R [4] List(Pattern(D2)) -> Pattern(D2) from Pattern(D2) if D2 has +--R SETCAT +--R [5] SingletonAsOrderedSet -> Symbol from SingletonAsOrderedSet +--R +--RExamples of convert from BasicStochasticDifferential +--R +--R +--RExamples of convert from ComplexPattern +--R +--R +--RExamples of convert from ExpertSystemToolsPackage +--R +--R +--RExamples of convert from Float +--R +--R +--RExamples of convert from ScriptFormulaFormat +--R +--R +--RExamples of convert from FramedAlgebra +--R +--R +--RExamples of convert from FramedNonAssociativeAlgebra +--R +--R +--RExamples of convert from FunctionSpace +--R +--R +--RExamples of convert from GeneralPolynomialSet +--R +--R +--RExamples of convert from InputForm +--R +--R +--RExamples of convert from ConvertibleTo +--R +--R +--RExamples of convert from MonogenicAlgebra +--R +--R +--RExamples of convert from Pattern +--R +--R +--RExamples of convert from PointCategory +--R +--R +--RExamples of convert from RomanNumeral +--R +--R +--RExamples of convert from RecursivePolynomialCategory +--R +--R +--RExamples of convert from RegularSetDecompositionPackage +--R +--R +--RExamples of convert from SingletonAsOrderedSet +--R +--R +--RExamples of convert from SegmentCategory +--R +--R +--RExamples of convert from SExpressionCategory +--R +--R +--RExamples of convert from SquareFreeRegularSetDecompositionPackage +--R +--R +--RExamples of convert from TexFormat +--R +--R +--RExamples of convert from ZeroDimensionalSolvePackage +--R +--E 472 + +--S 473 of 3320 +)d op convertIfCan +--R +--R +--RThere is one exposed function called convertIfCan : +--R [1] Symbol -> Union(BasicStochasticDifferential,"failed") +--R from BasicStochasticDifferential +--R +--RExamples of convertIfCan from BasicStochasticDifferential +--R +--E 473 + +--S 474 of 3320 +)d op coord +--R +--R +--RThere is one exposed function called coord : +--R [1] (Point(DoubleFloat) -> Point(DoubleFloat)) -> DrawOption from +--R DrawOption +--R +--RThere are 2 unexposed functions called coord : +--R [1] (List(DrawOption),(Point(DoubleFloat) -> Point(DoubleFloat))) +--R -> (Point(DoubleFloat) -> Point(DoubleFloat)) +--R from DrawOptionFunctions0 +--R [2] (HomogeneousDistributedMultivariatePolynomial(D4,D5),List( +--R HomogeneousDistributedMultivariatePolynomial(D4,D5))) -> Vector( +--R D5) +--R from LinGroebnerPackage(D4,D5) if D4: LIST(SYMBOL) and D5 +--R has GCDDOM +--R +--RExamples of coord from DrawOptionFunctions0 +--R +--R +--RExamples of coord from DrawOption +--R +--R +--RExamples of coord from LinGroebnerPackage +--R +--E 474 + +--S 475 of 3320 +)d op coordinate +--R +--R +--RThere are 3 exposed functions called coordinate : +--R [1] (ParametricPlaneCurve(D1),NonNegativeInteger) -> D1 +--R from ParametricPlaneCurve(D1) if D1 has TYPE +--R [2] (ParametricSpaceCurve(D1),NonNegativeInteger) -> D1 +--R from ParametricSpaceCurve(D1) if D1 has TYPE +--R [3] (ParametricSurface(D1),NonNegativeInteger) -> D1 +--R from ParametricSurface(D1) if D1 has TYPE +--R +--RExamples of coordinate from ParametricPlaneCurve +--R +--R +--RExamples of coordinate from ParametricSpaceCurve +--R +--R +--RExamples of coordinate from ParametricSurface +--R +--E 475 + +--S 476 of 3320 +)d op coordinates +--R +--R +--RThere are 12 exposed functions called coordinates : +--R [1] (Point(DoubleFloat) -> Point(DoubleFloat)) -> DrawOption from +--R DrawOption +--R [2] Vector(D) -> Matrix(D3) from D if D has FAXF(D3) and D3 has +--R FIELD +--R [3] D -> Vector(D2) from D if D has FAXF(D2) and D2 has FIELD +--R [4] (Vector(D),Vector(D)) -> Matrix(D3) from D +--R if D has FINAALG(D3) and D3 has COMRING +--R [5] (D,Vector(D)) -> Vector(D3) from D if D has FINAALG(D3) and D3 +--R has COMRING +--R [6] (Vector(D),Vector(D)) -> Matrix(D3) from D +--R if D has FINRALG(D3,D4) and D3 has COMRING and D4 has +--R UPOLYC(D3) +--R [7] (D,Vector(D)) -> Vector(D3) from D +--R if D has FINRALG(D3,D4) and D3 has COMRING and D4 has +--R UPOLYC(D3) +--R [8] Vector(D) -> Matrix(D3) from D +--R if D has FRAMALG(D3,D4) and D3 has COMRING and D4 has +--R UPOLYC(D3) +--R [9] D -> Vector(D2) from D +--R if D has FRAMALG(D2,D3) and D2 has COMRING and D3 has +--R UPOLYC(D2) +--R [10] Vector(D) -> Matrix(D3) from D if D has FRNAALG(D3) and D3 has +--R COMRING +--R [11] D -> Vector(D2) from D if D has FRNAALG(D2) and D2 has COMRING +--R +--R [12] (Matrix(D4),List(Matrix(D4))) -> Vector(D4) +--R from StructuralConstantsPackage(D4) if D4 has FIELD +--R +--RExamples of coordinates from DrawOption +--R +--R +--RExamples of coordinates from FiniteAlgebraicExtensionField +--R +--R +--RExamples of coordinates from FiniteRankNonAssociativeAlgebra +--R +--R +--RExamples of coordinates from FiniteRankAlgebra +--R +--R +--RExamples of coordinates from FramedAlgebra +--R +--R +--RExamples of coordinates from FramedNonAssociativeAlgebra +--R +--R +--RExamples of coordinates from StructuralConstantsPackage +--R +--E 476 + +--S 477 of 3320 +)d op copies +--R +--R +--RThere is one exposed function called copies : +--R [1] (Integer,String) -> String from DisplayPackage +--R +--RExamples of copies from DisplayPackage +--R +--E 477 + +--S 478 of 3320 +)d op copy +--R +--R +--RThere are 10 exposed functions called copy : +--R [1] D -> D from D if D has AGG +--R [2] ArrayStack(D1) -> ArrayStack(D1) from ArrayStack(D1) if D1 has +--R SETCAT +--R [3] BasicOperator -> BasicOperator from BasicOperator +--R [4] Dequeue(D1) -> Dequeue(D1) from Dequeue(D1) if D1 has SETCAT +--R [5] Heap(D1) -> Heap(D1) from Heap(D1) if D1 has ORDSET +--R [6] D -> D from D if D has INS +--R [7] Queue(D1) -> Queue(D1) from Queue(D1) if D1 has SETCAT +--R [8] SparseEchelonMatrix(D1,D2) -> SparseEchelonMatrix(D1,D2) +--R from SparseEchelonMatrix(D1,D2) if D1 has ORDSET and D2 +--R has RING +--R [9] D -> D from D if D has SPACEC(D1) and D1 has RING +--R [10] Stack(D1) -> Stack(D1) from Stack(D1) if D1 has SETCAT +--R +--RThere are 3 unexposed functions called copy : +--R [1] SubSpaceComponentProperty -> SubSpaceComponentProperty +--R from SubSpaceComponentProperty +--R [2] Pattern(D1) -> Pattern(D1) from Pattern(D1) if D1 has SETCAT +--R [3] SplittingNode(D1,D2) -> SplittingNode(D1,D2) from SplittingNode( +--R D1,D2) +--R if D1 has Join(SetCategory,Aggregate) and D2 has Join( +--R SetCategory,Aggregate) +--R +--RExamples of copy from Aggregate +--R +--R +--RExamples of copy from ArrayStack +--R +--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] +--Rcopy a +--R +--R +--RExamples of copy from BasicOperator +--R +--R +--RExamples of copy from SubSpaceComponentProperty +--R +--R +--RExamples of copy from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rcopy a +--R +--R +--RExamples of copy from Heap +--R +--Ra:Heap INT:= heap [1,2,3,4,5] +--Rcopy a +--R +--R +--RExamples of copy from IntegerNumberSystem +--R +--R +--RExamples of copy from Pattern +--R +--R +--RExamples of copy from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Rcopy a +--R +--R +--RExamples of copy from SparseEchelonMatrix +--R +--R +--RExamples of copy from ThreeSpaceCategory +--R +--R +--RExamples of copy from SplittingNode +--R +--R +--RExamples of copy from Stack +--R +--Ra:Stack INT:= stack [1,2,3,4,5] +--Rcopy a +--R +--E 478 + +--S 479 of 3320 +)d op copy! +--R +--R +--RThere is one unexposed function called copy! : +--R [1] (Matrix(D2),Matrix(D2)) -> Matrix(D2) +--R from StorageEfficientMatrixOperations(D2) if D2 has RING +--R +--R +--RExamples of copy! from StorageEfficientMatrixOperations +--R +--E 479 + +--S 480 of 3320 done +)d op copyBSD +--R +--R +--RThere is one exposed function called copyBSD : +--R [1] -> List(BasicStochasticDifferential) from +--R BasicStochasticDifferential +--R +--RExamples of copyBSD from BasicStochasticDifferential +--R +--Rintroduce!(t,dt) -- dt is a new stochastic differential +--RcopyBSD() +--R +--E 480 + +--S 481 of 3320 +)d op copyDrift +--R +--R +--RThere is one exposed function called copyDrift : +--R [1] -> Table(StochasticDifferential(D2),StochasticDifferential(D2)) +--R from StochasticDifferential(D2) +--R if D2 has Join(OrderedSet,IntegralDomain) +--R +--RExamples of copyDrift from StochasticDifferential +--R +--E 481 + +--S 482 of 3320 +)d op copy_first +--R +--R copy_first is not a known function. Axiom will try to list its +--R functions which contain copy_first in their names. This is the +--R same output you would get by issuing +--R )what operations copy_first +--R +--R There are no operations containing those patterns +--R +--E 482 + +--S 483 of 3320 +--R---------------------- )d op copyInto_! (fix this) +--E 483 + +--S 484 of 3320 done +)d op copyIto +--R +--R +--RThere is one exposed function called copyIto : +--R [1] -> Table(Symbol,BasicStochasticDifferential) +--R from BasicStochasticDifferential +--R +--RExamples of copyIto from BasicStochasticDifferential +--R +--Rintroduce!(t,dt) -- dt is a new stochastic differential +--RcopyIto() +--R +--E 484 + +--S 485 of 3320 +)d op copyQuadVar +--R +--R +--RThere is one exposed function called copyQuadVar : +--R [1] -> Table(StochasticDifferential(D2),StochasticDifferential(D2)) +--R from StochasticDifferential(D2) +--R if D2 has Join(OrderedSet,IntegralDomain) +--R +--RExamples of copyQuadVar from StochasticDifferential +--R +--E 485 + +--S 486 of 3320 +--R---------------------- )d op copy_slice (fix this) +--E 486 + +--S 487 of 3320 +)d op corrPoly +--R +--R +--RThere is one unexposed function called corrPoly : +--R [1] (SparseUnivariatePolynomial(D2),List(D1),List(D9),List( +--R NonNegativeInteger),List(SparseUnivariatePolynomial(D2)),Vector( +--R List(SparseUnivariatePolynomial(D9))),D9) -> Union(List( +--R SparseUnivariatePolynomial(D2)),"failed") +--R from MultivariateLifting(D10,D1,D9,D2) +--R if D1 has ORDSET and D9 has EUCDOM and D2 has POLYCAT(D9, +--R D10,D1) and D10 has OAMONS +--R +--RExamples of corrPoly from MultivariateLifting +--R +--E 487 + +--S 488 of 3320 +)d op cos +--R +--R +--RThere are 2 exposed functions called cos : +--R [1] FortranExpression(D1,D2,D3) -> FortranExpression(D1,D2,D3) +--R from FortranExpression(D1,D2,D3) +--R if D1: LIST(SYMBOL) and D2: LIST(SYMBOL) and D3 has FMTC +--R +--R [2] D -> D from D if D has TRIGCAT +--R +--RThere are 6 unexposed functions called cos : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] D1 -> FourierComponent(D1) from FourierComponent(D1) if D1 has +--R ORDSET +--R [5] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [6] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of cos from ElementaryFunction +--R +--R +--RExamples of cos from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of cos from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of cos from FourierComponent +--R +--R +--RExamples of cos from FortranExpression +--R +--R +--RExamples of cos from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of cos from StreamTranscendentalFunctions +--R +--R +--RExamples of cos from TrigonometricFunctionCategory +--R +--E 488 + +--S 489 of 3320 +)d op cos2sec +--R +--R +--RThere is one exposed function called cos2sec : +--R [1] D1 -> D1 from TranscendentalManipulations(D2,D1) +--R if D2 has Join(OrderedSet,GcdDomain) and D1 has Join( +--R FunctionSpace(D2),TranscendentalFunctionCategory) +--R +--RExamples of cos2sec from TranscendentalManipulations +--R +--E 489 + +--S 490 of 3320 +)d op cosh +--R +--R +--RThere are 2 exposed functions called cosh : +--R [1] FortranExpression(D1,D2,D3) -> FortranExpression(D1,D2,D3) +--R from FortranExpression(D1,D2,D3) +--R if D1: LIST(SYMBOL) and D2: LIST(SYMBOL) and D3 has FMTC +--R +--R [2] D -> D from D if D has HYPCAT +--R +--RThere are 5 unexposed functions called cosh : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of cosh from ElementaryFunction +--R +--R +--RExamples of cosh from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of cosh from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of cosh from FortranExpression +--R +--R +--RExamples of cosh from HyperbolicFunctionCategory +--R +--R +--RExamples of cosh from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of cosh from StreamTranscendentalFunctions +--R +--E 490 + +--S 491 of 3320 +)d op cosh +--R +--R +--RThere are 2 exposed functions called cosh : +--R [1] FortranExpression(D1,D2,D3) -> FortranExpression(D1,D2,D3) +--R from FortranExpression(D1,D2,D3) +--R if D1: LIST(SYMBOL) and D2: LIST(SYMBOL) and D3 has FMTC +--R +--R [2] D -> D from D if D has HYPCAT +--R +--RThere are 5 unexposed functions called cosh : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of cosh from ElementaryFunction +--R +--R +--RExamples of cosh from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of cosh from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of cosh from FortranExpression +--R +--R +--RExamples of cosh from HyperbolicFunctionCategory +--R +--R +--RExamples of cosh from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of cosh from StreamTranscendentalFunctions +--R +--E 491 + +--S 492 of 3320 +)d op cosh2sech +--R +--R +--RThere is one exposed function called cosh2sech : +--R [1] D1 -> D1 from TranscendentalManipulations(D2,D1) +--R if D2 has Join(OrderedSet,GcdDomain) and D1 has Join( +--R FunctionSpace(D2),TranscendentalFunctionCategory) +--R +--RExamples of cosh2sech from TranscendentalManipulations +--R +--E 492 + +--S 493 of 3320 +)d op coshIfCan +--R +--R +--RThere is one exposed function called coshIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of coshIfCan from PartialTranscendentalFunctions +--R +--E 493 + +--S 494 of 3320 +)d op cosIfCan +--R +--R +--RThere is one exposed function called cosIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of cosIfCan from PartialTranscendentalFunctions +--R +--E 494 + +--S 495 of 3320 +)d op cosSinInfo +--R +--R +--RThere is one unexposed function called cosSinInfo : +--R [1] Integer -> List(List(DoubleFloat)) from TubePlotTools +--R +--RExamples of cosSinInfo from TubePlotTools +--R +--E 495 + +--S 496 of 3320 +)d op cot +--R +--R +--RThere is one exposed function called cot : +--R [1] D -> D from D if D has TRIGCAT +--R +--RThere are 5 unexposed functions called cot : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of cot from ElementaryFunction +--R +--R +--RExamples of cot from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of cot from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of cot from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of cot from StreamTranscendentalFunctions +--R +--R +--RExamples of cot from TrigonometricFunctionCategory +--R +--E 496 + +--S 497 of 3320 +)d op cot2tan +--R +--R +--RThere is one exposed function called cot2tan : +--R [1] D1 -> D1 from TranscendentalManipulations(D2,D1) +--R if D2 has Join(OrderedSet,GcdDomain) and D1 has Join( +--R FunctionSpace(D2),TranscendentalFunctionCategory) +--R +--RExamples of cot2tan from TranscendentalManipulations +--R +--E 497 + +--S 498 of 3320 +)d op cot2trig +--R +--R +--RThere is one exposed function called cot2trig : +--R [1] D1 -> D1 from TranscendentalManipulations(D2,D1) +--R if D2 has Join(OrderedSet,GcdDomain) and D1 has Join( +--R FunctionSpace(D2),TranscendentalFunctionCategory) +--R +--RExamples of cot2trig from TranscendentalManipulations +--R +--E 498 + +--S 499 of 3320 +)d op coth +--R +--R +--RThere is one exposed function called coth : +--R [1] D -> D from D if D has HYPCAT +--R +--RThere are 5 unexposed functions called coth : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of coth from ElementaryFunction +--R +--R +--RExamples of coth from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of coth from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of coth from HyperbolicFunctionCategory +--R +--R +--RExamples of coth from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of coth from StreamTranscendentalFunctions +--R +--E 499 + +--S 500 of 3320 +)d op coth +--R +--R +--RThere is one exposed function called coth : +--R [1] D -> D from D if D has HYPCAT +--R +--RThere are 5 unexposed functions called coth : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of coth from ElementaryFunction +--R +--R +--RExamples of coth from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of coth from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of coth from HyperbolicFunctionCategory +--R +--R +--RExamples of coth from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of coth from StreamTranscendentalFunctions +--R +--E 500 + +--S 501 of 3320 +)d op coth2tanh +--R +--R +--RThere is one exposed function called coth2tanh : +--R [1] D1 -> D1 from TranscendentalManipulations(D2,D1) +--R if D2 has Join(OrderedSet,GcdDomain) and D1 has Join( +--R FunctionSpace(D2),TranscendentalFunctionCategory) +--R +--RExamples of coth2tanh from TranscendentalManipulations +--R +--E 501 + +--S 502 of 3320 +)d op coth2trigh +--R +--R +--RThere is one exposed function called coth2trigh : +--R [1] D1 -> D1 from TranscendentalManipulations(D2,D1) +--R if D2 has Join(OrderedSet,GcdDomain) and D1 has Join( +--R FunctionSpace(D2),TranscendentalFunctionCategory) +--R +--RExamples of coth2trigh from TranscendentalManipulations +--R +--E 502 + +--S 503 of 3320 +)d op cothIfCan +--R +--R +--RThere is one exposed function called cothIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of cothIfCan from PartialTranscendentalFunctions +--R +--E 503 + +--S 504 of 3320 +)d op cotIfCan +--R +--R +--RThere is one exposed function called cotIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of cotIfCan from PartialTranscendentalFunctions +--R +--E 504 + +--S 505 of 3320 +)d op count +--R +--R +--RThere are 12 exposed functions called count : +--R [1] (D2,ArrayStack(D2)) -> NonNegativeInteger from ArrayStack(D2) +--R if $ has finiteAggregate and D2 has SETCAT and D2 has +--R SETCAT +--R [2] ((D3 -> Boolean),ArrayStack(D3)) -> NonNegativeInteger +--R from ArrayStack(D3) if $ has finiteAggregate and D3 has +--R SETCAT +--R [3] (D2,Dequeue(D2)) -> NonNegativeInteger from Dequeue(D2) +--R if $ has finiteAggregate and D2 has SETCAT and D2 has +--R SETCAT +--R [4] ((D3 -> Boolean),Dequeue(D3)) -> NonNegativeInteger from Dequeue +--R (D3) +--R if $ has finiteAggregate and D3 has SETCAT +--R [5] (D2,Heap(D2)) -> NonNegativeInteger from Heap(D2) +--R if $ has finiteAggregate and D2 has SETCAT and D2 has +--R ORDSET +--R [6] ((D3 -> Boolean),Heap(D3)) -> NonNegativeInteger from Heap(D3) +--R if $ has finiteAggregate and D3 has ORDSET +--R [7] (D2,D) -> NonNegativeInteger from D +--R if D has finiteAggregate and D has HOAGG(D2) and D2 has +--R TYPE and D2 has SETCAT +--R [8] ((D3 -> Boolean),D) -> NonNegativeInteger from D +--R if D has finiteAggregate and D has HOAGG(D3) and D3 has +--R TYPE +--R [9] (D2,Queue(D2)) -> NonNegativeInteger from Queue(D2) +--R if $ has finiteAggregate and D2 has SETCAT and D2 has +--R SETCAT +--R [10] ((D3 -> Boolean),Queue(D3)) -> NonNegativeInteger from Queue(D3 +--R ) +--R if $ has finiteAggregate and D3 has SETCAT +--R [11] (D2,Stack(D2)) -> NonNegativeInteger from Stack(D2) +--R if $ has finiteAggregate and D2 has SETCAT and D2 has +--R SETCAT +--R [12] ((D3 -> Boolean),Stack(D3)) -> NonNegativeInteger from Stack(D3 +--R ) +--R if $ has finiteAggregate and D3 has SETCAT +--R +--RExamples of count from ArrayStack +--R +--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] +--Rcount(4,a) +--R +--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] +--Rcount(x+->(x>2),a) +--R +--R +--RExamples of count from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rcount(4,a) +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rcount(x+->(x>2),a) +--R +--R +--RExamples of count from Heap +--R +--Ra:Heap INT:= heap [1,2,3,4,5] +--Rcount(4,a) +--R +--Ra:Heap INT:= heap [1,2,3,4,5] +--Rcount(x+->(x>2),a) +--R +--R +--RExamples of count from HomogeneousAggregate +--R +--R +--RExamples of count from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Rcount(4,a) +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Rcount(x+->(x>2),a) +--R +--R +--RExamples of count from Stack +--R +--Ra:Stack INT:= stack [1,2,3,4,5] +--Rcount(4,a) +--R +--Ra:Stack INT:= stack [1,2,3,4,5] +--Rcount(x+->(x>2),a) +--R +--E 505 + +--S 506 of 3320 done +)d op countable? +--R +--R +--RThere is one exposed function called countable? : +--R [1] CardinalNumber -> Boolean from CardinalNumber +--R +--RExamples of countable? from CardinalNumber +--R +--Rc2:=2::CardinalNumber +--Rcountable? c2 +--RA0:=Aleph 0 +--Rcountable? A0 +--RA1:=Aleph 1 +--Rcountable? A1 +--R +--E 506 + +--S 507 of 3320 +)d op countRealRoots +--R +--R +--RThere is one exposed function called countRealRoots : +--R [1] UnivariatePolynomial(D4,D3) -> Integer from SturmHabichtPackage( +--R D3,D4) +--R if D3 has OINTDOM and D4: SYMBOL +--R +--RExamples of countRealRoots from SturmHabichtPackage +--R +--E 507 + +--S 508 of 3320 +)d op countRealRootsMultiple +--R +--R +--RThere is one exposed function called countRealRootsMultiple : +--R [1] UnivariatePolynomial(D4,D3) -> Integer from SturmHabichtPackage( +--R D3,D4) +--R if D3 has GCDDOM and D3 has OINTDOM and D4: SYMBOL +--R +--RExamples of countRealRootsMultiple from SturmHabichtPackage +--R +--E 508 + +--S 509 of 3320 +)d op cPower +--R +--R +--RThere is one unexposed function called cPower : +--R [1] (InnerSparseUnivariatePowerSeries(D1),D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cPower from InnerSparseUnivariatePowerSeries +--R +--E 509 + +--S 510 of 3320 +)d op cRationalPower +--R +--R +--RThere is one unexposed function called cRationalPower : +--R [1] (InnerSparseUnivariatePowerSeries(D2),Fraction(Integer)) -> +--R InnerSparseUnivariatePowerSeries(D2) +--R from InnerSparseUnivariatePowerSeries(D2) +--R if D2 has ALGEBRA(FRAC(INT)) and D2 has RING +--R +--RExamples of cRationalPower from InnerSparseUnivariatePowerSeries +--R +--E 510 + +--S 511 of 3320 +)d op create +--R +--R +--RThere are 4 exposed functions called create : +--R [1] (D2,D3) -> D from D +--R if D4 has FIELD and D6 has DIRPCAT(#(D5),NNI) and D7 has +--R LOCPOWC(D4) and D has INFCLCT(D4,D5,D3,D6,D2,D7,D8,D9,D1) +--R and D3 has POLYCAT(D4,D6,OVAR(D5)) and D2 has PRSPCAT(D4) +--R and D8 has PLACESC(D4,D7) and D1 has BLMETCT +--R [2] (D7,DistributedMultivariatePolynomial([construct,QUOTEX,QUOTEY], +--R D13),AffinePlane(D13),NonNegativeInteger,D11,NonNegativeInteger, +--R DIVISOR,D13,Symbol) -> D +--R from D +--R if D13 has FIELD and D3 has DIRPCAT(#(D1),NNI) and D4 has +--R LOCPOWC(D13) and D has INFCLCT(D13,D1,D2,D3,D7,D4,D5,D6,D11 +--R ) and D2 has POLYCAT(D13,D3,OVAR(D1)) and D7 has PRSPCAT( +--R D13) and D5 has PLACESC(D13,D4) and D11 has BLMETCT +--R [3] Symbol -> D from D +--R if D2 has FIELD and D has PLACESC(D2,D3) and D3 has +--R LOCPOWC(D2) +--R [4] List(D2) -> D from D +--R if D2 has FIELD and D has PLACESC(D2,D3) and D3 has +--R LOCPOWC(D2) +--R +--RThere is one unexposed function called create : +--R [1] -> SingletonAsOrderedSet from SingletonAsOrderedSet +--R +--RExamples of create from InfinitlyClosePointCategory +--R +--R +--RExamples of create from PlacesCategory +--R +--R +--RExamples of create from SingletonAsOrderedSet +--R +--E 511 + +--S 512 of 3320 +)d op create3Space +--R +--R +--RThere are 2 exposed functions called create3Space : +--R [1] SubSpace(3,D2) -> D from D if D2 has RING and D has SPACEC(D2) +--R +--R [2] -> D from D if D has SPACEC(D1) and D1 has RING +--R +--RExamples of create3Space from ThreeSpaceCategory +--R +--E 512 + +--S 513 of 3320 +)d op createGenericMatrix +--R +--R +--RThere is one exposed function called createGenericMatrix : +--R [1] NonNegativeInteger -> Matrix(Polynomial(D3)) +--R from RepresentationPackage1(D3) if D3 has RING +--R +--RExamples of createGenericMatrix from RepresentationPackage1 +--R +--E 513 + +--S 514 of 3320 +)d op createHN +--R +--R +--RThere is one exposed function called createHN : +--R [1] (Integer,Integer,Integer,Integer,Integer,Boolean,Union(left, +--R center,right,vertical,horizontal)) -> D +--R from D if D has BLMETCT +--R +--RExamples of createHN from BlowUpMethodCategory +--R +--E 514 + +--S 515 of 3320 +)d op createIrreduciblePoly +--R +--R +--RThere is one unexposed function called createIrreduciblePoly : +--R [1] PositiveInteger -> SparseUnivariatePolynomial(D3) +--R from FiniteFieldPolynomialPackage(D3) if D3 has FFIELDC +--R +--R +--RExamples of createIrreduciblePoly from FiniteFieldPolynomialPackage +--R +--E 515 + +--S 516 of 3320 +)d op createLowComplexityNormalBasis +--R +--R +--RThere is one unexposed function called createLowComplexityNormalBasis : +--R [1] PositiveInteger -> Union(SparseUnivariatePolynomial(D3),Vector( +--R List(Record(value: D3,index: SingleInteger)))) +--R from FiniteFieldFunctions(D3) if D3 has FFIELDC +--R +--RExamples of createLowComplexityNormalBasis from FiniteFieldFunctions +--R +--E 516 + +--S 517 of 3320 +)d op createLowComplexityTable +--R +--R +--RThere is one unexposed function called createLowComplexityTable : +--R [1] PositiveInteger -> Union(Vector(List(Record(value: D3,index: +--R SingleInteger))),"failed") +--R from FiniteFieldFunctions(D3) if D3 has FFIELDC +--R +--RExamples of createLowComplexityTable from FiniteFieldFunctions +--R +--E 517 + +--S 518 of 3320 +)d op createMultiplicationMatrix +--R +--R +--RThere is one unexposed function called createMultiplicationMatrix : +--R [1] Vector(List(Record(value: D3,index: SingleInteger))) -> Matrix( +--R D3) +--R from FiniteFieldFunctions(D3) if D3 has FFIELDC +--R +--RExamples of createMultiplicationMatrix from FiniteFieldFunctions +--R +--E 518 + +--S 519 of 3320 +)d op createMultiplicationTable +--R +--R +--RThere is one unexposed function called createMultiplicationTable : +--R [1] SparseUnivariatePolynomial(D3) -> Vector(List(Record(value: D3, +--R index: SingleInteger))) +--R from FiniteFieldFunctions(D3) if D3 has FFIELDC +--R +--RExamples of createMultiplicationTable from FiniteFieldFunctions +--R +--E 519 + +--S 520 of 3320 +)d op createNormalElement +--R +--R +--RThere is one exposed function called createNormalElement : +--R [1] -> D from D if D has FAXF(D1) and D1 has FINITE and D1 has +--R FIELD +--R +--RExamples of createNormalElement from FiniteAlgebraicExtensionField +--R +--E 520 + +--S 521 of 3320 +)d op createNormalPoly +--R +--R +--RThere is one unexposed function called createNormalPoly : +--R [1] PositiveInteger -> SparseUnivariatePolynomial(D3) +--R from FiniteFieldPolynomialPackage(D3) if D3 has FFIELDC +--R +--R +--RExamples of createNormalPoly from FiniteFieldPolynomialPackage +--R +--E 521 + +--S 522 of 3320 +)d op createNormalPrimitivePoly +--R +--R +--RThere is one unexposed function called createNormalPrimitivePoly : +--R [1] PositiveInteger -> SparseUnivariatePolynomial(D3) +--R from FiniteFieldPolynomialPackage(D3) if D3 has FFIELDC +--R +--R +--RExamples of createNormalPrimitivePoly from FiniteFieldPolynomialPackage +--R +--E 522 + +--S 523 of 3320 +)d op createPrimitiveElement +--R +--R +--RThere is one exposed function called createPrimitiveElement : +--R [1] -> D from D if D has FFIELDC +--R +--RExamples of createPrimitiveElement from FiniteFieldCategory +--R +--E 523 + +--S 524 of 3320 +)d op createPrimitiveNormalPoly +--R +--R +--RThere is one unexposed function called createPrimitiveNormalPoly : +--R [1] PositiveInteger -> SparseUnivariatePolynomial(D3) +--R from FiniteFieldPolynomialPackage(D3) if D3 has FFIELDC +--R +--R +--RExamples of createPrimitiveNormalPoly from FiniteFieldPolynomialPackage +--R +--E 524 + +--S 525 of 3320 +)d op createPrimitivePoly +--R +--R +--RThere is one unexposed function called createPrimitivePoly : +--R [1] PositiveInteger -> SparseUnivariatePolynomial(D3) +--R from FiniteFieldPolynomialPackage(D3) if D3 has FFIELDC +--R +--R +--RExamples of createPrimitivePoly from FiniteFieldPolynomialPackage +--R +--E 525 + +--S 526 of 3320 +)d op createRandomElement +--R +--R +--RThere is one exposed function called createRandomElement : +--R [1] (List(Matrix(D3)),Matrix(D3)) -> Matrix(D3) +--R from RepresentationPackage2(D3) if D3 has RING +--R +--RExamples of createRandomElement from RepresentationPackage2 +--R +--E 526 + +--S 527 of 3320 +)d op createThreeSpace +--R +--R +--RThere is one exposed function called createThreeSpace : +--R [1] -> ThreeSpace(DoubleFloat) from TopLevelThreeSpace +--R +--RExamples of createThreeSpace from TopLevelThreeSpace +--R +--E 527 + +--S 528 of 3320 +)d op createZechTable +--R +--R +--RThere is one unexposed function called createZechTable : +--R [1] SparseUnivariatePolynomial(D3) -> PrimitiveArray(SingleInteger) +--R from FiniteFieldFunctions(D3) if D3 has FFIELDC +--R +--RExamples of createZechTable from FiniteFieldFunctions +--R +--E 528 + +--S 529 of 3320 done +)d op credits +--R +--R +--RThere is one exposed function called credits : +--R [1] -> Void from ApplicationProgramInterface +--R +--RExamples of credits from ApplicationProgramInterface +--R +--Rcredits() +--R +--E 529 + +--S 530 of 3320 +)d op credPol +--R +--R +--RThere is one unexposed function called credPol : +--R [1] (D1,List(D1)) -> D1 from GroebnerInternalPackage(D3,D4,D5,D1) +--R if D1 has POLYCAT(D3,D4,D5) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET +--R +--RExamples of credPol from GroebnerInternalPackage +--R +--E 530 + +--S 531 of 3320 +)d op crest +--R +--R +--RThere is one unexposed function called crest : +--R [1] NonNegativeInteger -> (Stream(Polynomial(D3)) -> Stream( +--R Polynomial(D3))) +--R from WeierstrassPreparation(D3) if D3 has FIELD +--R +--RExamples of crest from WeierstrassPreparation +--R +--E 531 + +--S 532 of 3320 +)d op critB +--R +--R +--RThere is one unexposed function called critB : +--R [1] (D2,D2,D2,D2) -> Boolean from GroebnerInternalPackage(D3,D2,D4, +--R D5) +--R if D3 has GCDDOM and D2 has OAMONS and D4 has ORDSET and +--R D5 has POLYCAT(D3,D2,D4) +--R +--RExamples of critB from GroebnerInternalPackage +--R +--E 532 + +--S 533 of 3320 +)d op critBonD +--R +--R +--RThere is one unexposed function called critBonD : +--R [1] (D2,List(Record(lcmfij: D4,totdeg: NonNegativeInteger,poli: D2, +--R polj: D2))) -> List(Record(lcmfij: D4,totdeg: NonNegativeInteger, +--R poli: D2,polj: D2)) +--R from GroebnerInternalPackage(D3,D4,D5,D2) +--R if D4 has OAMONS and D2 has POLYCAT(D3,D4,D5) and D3 has +--R GCDDOM and D5 has ORDSET +--R +--RExamples of critBonD from GroebnerInternalPackage +--R +--E 533 + +--S 534 of 3320 +)d op critM +--R +--R +--RThere is one unexposed function called critM : +--R [1] (D2,D2) -> Boolean from GroebnerInternalPackage(D3,D2,D4,D5) +--R if D3 has GCDDOM and D2 has OAMONS and D4 has ORDSET and +--R D5 has POLYCAT(D3,D2,D4) +--R +--RExamples of critM from GroebnerInternalPackage +--R +--E 534 + +--S 535 of 3320 +)d op critMonD1 +--R +--R +--RThere is one unexposed function called critMonD1 : +--R [1] (D2,List(Record(lcmfij: D2,totdeg: NonNegativeInteger,poli: D5, +--R polj: D5))) -> List(Record(lcmfij: D2,totdeg: NonNegativeInteger, +--R poli: D5,polj: D5)) +--R from GroebnerInternalPackage(D3,D2,D4,D5) +--R if D2 has OAMONS and D5 has POLYCAT(D3,D2,D4) and D3 has +--R GCDDOM and D4 has ORDSET +--R +--RExamples of critMonD1 from GroebnerInternalPackage +--R +--E 535 + +--S 536 of 3320 +)d op critMTonD1 +--R +--R +--RThere is one unexposed function called critMTonD1 : +--R [1] List(Record(lcmfij: D3,totdeg: NonNegativeInteger,poli: D5,polj +--R : D5)) -> List(Record(lcmfij: D3,totdeg: NonNegativeInteger,poli +--R : D5,polj: D5)) +--R from GroebnerInternalPackage(D2,D3,D4,D5) +--R if D3 has OAMONS and D5 has POLYCAT(D2,D3,D4) and D2 has +--R GCDDOM and D4 has ORDSET +--R +--RExamples of critMTonD1 from GroebnerInternalPackage +--R +--E 536 + +--S 537 of 3320 +)d op critpOrder +--R +--R +--RThere is one unexposed function called critpOrder : +--R [1] (Record(lcmfij: D4,totdeg: NonNegativeInteger,poli: D6,polj: D6) +--R ,Record(lcmfij: D4,totdeg: NonNegativeInteger,poli: D6,polj: D6)) +--R -> Boolean +--R from GroebnerInternalPackage(D3,D4,D5,D6) +--R if D4 has OAMONS and D6 has POLYCAT(D3,D4,D5) and D3 has +--R GCDDOM and D5 has ORDSET +--R +--RExamples of critpOrder from GroebnerInternalPackage +--R +--E 537 + +--S 538 of 3320 +)d op critT +--R +--R +--RThere is one unexposed function called critT : +--R [1] Record(lcmfij: D4,totdeg: NonNegativeInteger,poli: D6,polj: D6) +--R -> Boolean +--R from GroebnerInternalPackage(D3,D4,D5,D6) +--R if D4 has OAMONS and D6 has POLYCAT(D3,D4,D5) and D3 has +--R GCDDOM and D5 has ORDSET +--R +--RExamples of critT from GroebnerInternalPackage +--R +--E 538 + +--S 539 of 3320 +)d op cross +--R +--R +--RThere are 2 exposed functions called cross : +--R [1] (D,D) -> D from D if D has PTCAT(D1) and D1 has RING +--R [2] (D,D) -> D from D if D has VECTCAT(D1) and D1 has TYPE and D1 +--R has RING +--R +--RThere is one unexposed function called cross : +--R [1] (Point(DoubleFloat),Point(DoubleFloat)) -> Point(DoubleFloat) +--R from TubePlotTools +--R +--RExamples of cross from PointCategory +--R +--R +--RExamples of cross from TubePlotTools +--R +--R +--RExamples of cross from VectorCategory +--R +--E 539 + +--S 540 of 3320 +)d op crushedSet +--R +--R +--RThere is one unexposed function called crushedSet : +--R [1] List(D5) -> List(D5) from PolynomialSetUtilitiesPackage(D2,D3,D4 +--R ,D5) +--R if D5 has RPOLCAT(D2,D3,D4) and D2 has INTDOM and D3 has +--R OAMONS and D4 has ORDSET +--R +--RExamples of crushedSet from PolynomialSetUtilitiesPackage +--R +--E 540 + +--S 541 of 3320 +)d op csc +--R +--R +--RThere is one exposed function called csc : +--R [1] D -> D from D if D has TRIGCAT +--R +--RThere are 5 unexposed functions called csc : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of csc from ElementaryFunction +--R +--R +--RExamples of csc from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of csc from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of csc from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of csc from StreamTranscendentalFunctions +--R +--R +--RExamples of csc from TrigonometricFunctionCategory +--R +--E 541 + +--S 542 of 3320 +)d op csc2sin +--R +--R +--RThere is one exposed function called csc2sin : +--R [1] D1 -> D1 from TranscendentalManipulations(D2,D1) +--R if D2 has Join(OrderedSet,GcdDomain) and D1 has Join( +--R FunctionSpace(D2),TranscendentalFunctionCategory) +--R +--RExamples of csc2sin from TranscendentalManipulations +--R +--E 542 + +--S 543 of 3320 +)d op csch +--R +--R +--RThere is one exposed function called csch : +--R [1] D -> D from D if D has HYPCAT +--R +--RThere are 5 unexposed functions called csch : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [2] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [4] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [5] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R +--RExamples of csch from ElementaryFunction +--R +--R +--RExamples of csch from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of csch from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of csch from HyperbolicFunctionCategory +--R +--R +--RExamples of csch from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of csch from StreamTranscendentalFunctions +--R +--E 543 + +--S 544 of 3320 +)d op csch2sinh +--R +--R +--RThere is one exposed function called csch2sinh : +--R [1] D1 -> D1 from TranscendentalManipulations(D2,D1) +--R if D2 has Join(OrderedSet,GcdDomain) and D1 has Join( +--R FunctionSpace(D2),TranscendentalFunctionCategory) +--R +--RExamples of csch2sinh from TranscendentalManipulations +--R +--E 544 + +--S 545 of 3320 +)d op cschIfCan +--R +--R +--RThere is one exposed function called cschIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of cschIfCan from PartialTranscendentalFunctions +--R +--E 545 + +--S 546 of 3320 +)d op cscIfCan +--R +--R +--RThere is one exposed function called cscIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of cscIfCan from PartialTranscendentalFunctions +--R +--E 546 + +--S 547 of 3320 +)d op cSec +--R +--R +--RThere is one unexposed function called cSec : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cSec from InnerSparseUnivariatePowerSeries +--R +--E 547 + +--S 548 of 3320 +)d op cSech +--R +--R +--RThere is one unexposed function called cSech : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cSech from InnerSparseUnivariatePowerSeries +--R +--E 548 + +--S 549 of 3320 +)d op cSin +--R +--R +--RThere is one unexposed function called cSin : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cSin from InnerSparseUnivariatePowerSeries +--R +--E 549 + +--S 550 of 3320 +)d op cSinh +--R +--R +--RThere is one unexposed function called cSinh : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cSinh from InnerSparseUnivariatePowerSeries +--R +--E 550 + +--S 551 of 3320 +)d op csubst +--R +--R +--RThere is one unexposed function called csubst : +--R [1] (List(D5),List(Stream(D6))) -> (D6 -> Stream(D6)) +--R from SparseMultivariateTaylorSeries(D4,D5,D6) +--R if D5 has ORDSET and D6 has POLYCAT(D4,INDE(D5),D5) and D4 +--R has RING +--R +--RExamples of csubst from SparseMultivariateTaylorSeries +--R +--E 551 + +--S 552 of 3320 +)d op cTan +--R +--R +--RThere is one unexposed function called cTan : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cTan from InnerSparseUnivariatePowerSeries +--R +--E 552 + +--S 553 of 3320 +)d op cTanh +--R +--R +--RThere is one unexposed function called cTanh : +--R [1] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R +--RExamples of cTanh from InnerSparseUnivariatePowerSeries +--R +--E 553 + +--S 554 of 3320 +)d op cubic +--R +--R +--RThere are 2 unexposed functions called cubic : +--R [1] D3 -> List(D4) from PolynomialSolveByFormulas(D3,D4) +--R if D4 has Fieldwith +--R D : (%,Fraction(Integer)) -> %and D3 has UPOLYC(D4) +--R +--R [2] (D3,D3,D3,D3) -> List(D3) from PolynomialSolveByFormulas(D4,D3) +--R if D3 has Fieldwith +--R D : (%,Fraction(Integer)) -> %and D4 has UPOLYC(D3) +--R +--R +--RExamples of cubic from PolynomialSolveByFormulas +--R +--E 554 + +--S 555 of 3320 done +)d op cubicBezier +--R +--R +--RThere is one exposed function called cubicBezier : +--R [1] (List(D3),List(D3),List(D3),List(D3)) -> (D3 -> List(D3)) from +--R Bezier(D3) +--R if D3 has RING +--R +--RExamples of cubicBezier from Bezier +--R +--Rn:=cubicBezier([2.0,2.0],[2.0,4.0],[6.0,4.0],[6.0,2.0]) +--R[n(t/10.0) for t in 0..10 by 1] +--R +--E 555 + +--S 556 of 3320 +)d op cup +--R +--R +--RThere is one exposed function called cup : +--R [1] (SymmetricPolynomial(Fraction(Integer)),SymmetricPolynomial( +--R Fraction(Integer))) -> SymmetricPolynomial(Fraction(Integer)) +--R from CycleIndicators +--R +--RExamples of cup from CycleIndicators +--R +--E 556 + +--S 557 of 3320 +)d op currentSubProgram +--R +--R +--RThere is one exposed function called currentSubProgram : +--R [1] -> Symbol from TheSymbolTable +--R +--RExamples of currentSubProgram from TheSymbolTable +--R +--E 557 + +--S 558 of 3320 +)d op curry +--R +--R +--RThere is one exposed function called curry : +--R [1] ((D3 -> D4),D3) -> (() -> D4) from MappingPackage2(D3,D4) +--R if D3 has SETCAT and D4 has SETCAT +--R +--RExamples of curry from MappingPackage2 +--R +--E 558 + +--S 559 of 3320 +)d op curryLeft +--R +--R +--RThere is one exposed function called curryLeft : +--R [1] (((D3,D4) -> D5),D3) -> (D4 -> D5) from MappingPackage3(D3,D4,D5 +--R ) +--R if D3 has SETCAT and D4 has SETCAT and D5 has SETCAT +--R +--RExamples of curryLeft from MappingPackage3 +--R +--E 559 + +--S 560 of 3320 +)d op curryRight +--R +--R +--RThere is one exposed function called curryRight : +--R [1] (((D4,D3) -> D5),D3) -> (D4 -> D5) from MappingPackage3(D4,D3,D5 +--R ) +--R if D4 has SETCAT and D3 has SETCAT and D5 has SETCAT +--R +--RExamples of curryRight from MappingPackage3 +--R +--E 560 + +--S 561 of 3320 +)d op curve +--R +--R +--RThere are 6 exposed functions called curve : +--R [1] (D1,D1) -> ParametricPlaneCurve(D1) from ParametricPlaneCurve(D1 +--R ) +--R if D1 has TYPE +--R [2] (D1,D1,D1) -> ParametricSpaceCurve(D1) from ParametricSpaceCurve +--R (D1) +--R if D1 has TYPE +--R [3] D -> List(Point(D2)) from D if D has SPACEC(D2) and D2 has RING +--R +--R [4] List(Point(D2)) -> D from D if D2 has RING and D has SPACEC(D2) +--R +--R [5] (D,List(List(D2))) -> D from D if D has SPACEC(D2) and D2 has +--R RING +--R [6] (D,List(Point(D2))) -> D from D if D has SPACEC(D2) and D2 has +--R RING +--R +--RExamples of curve from ParametricPlaneCurve +--R +--R +--RExamples of curve from ParametricSpaceCurve +--R +--R +--RExamples of curve from ThreeSpaceCategory +--R +--E 561 + +--S 562 of 3320 +)d op curve? +--R +--R +--RThere is one exposed function called curve? : +--R [1] D -> Boolean from D if D has SPACEC(D2) and D2 has RING +--R +--RExamples of curve? from ThreeSpaceCategory +--R +--E 562 + +--S 563 of 3320 +)d op curveColor +--R +--R +--RThere are 2 exposed functions called curveColor : +--R [1] Palette -> DrawOption from DrawOption +--R [2] Float -> DrawOption from DrawOption +--R +--RExamples of curveColor from DrawOption +--R +--E 563 + +--S 564 of 3320 +)d op curveColorPalette +--R +--R +--RThere is one unexposed function called curveColorPalette : +--R [1] (List(DrawOption),Palette) -> Palette from DrawOptionFunctions0 +--R +--R +--RExamples of curveColorPalette from DrawOptionFunctions0 +--R +--E 564 + +--S 565 of 3320 +)d op curveV +--R +--R +--RThere is one exposed function called curveV : +--R [1] D -> DistributedMultivariatePolynomial([construct,QUOTEX,QUOTEY] +--R ,D4) +--R from D +--R if D has INFCLCT(D4,D5,D6,D7,D8,D9,D10,D1,D2) and D4 has +--R FIELD and D6 has POLYCAT(D4,D7,OVAR(D5)) and D7 has DIRPCAT +--R (#(D5),NNI) and D8 has PRSPCAT(D4) and D9 has LOCPOWC(D4) +--R and D10 has PLACESC(D4,D9) and D2 has BLMETCT +--R +--RExamples of curveV from InfinitlyClosePointCategory +--R +--E 565 + +--S 566 of 3320 +)d op cycle +--R +--R +--RThere is one exposed function called cycle : +--R [1] List(D2) -> D from D if D2 has SETCAT and D has PERMCAT(D2) +--R +--RExamples of cycle from PermutationCategory +--R +--E 566 + +--S 567 of 3320 done +)d op cycleElt +--R +--R +--RThere is one unexposed function called cycleElt : +--R [1] D1 -> Union(D1,"failed") from CyclicStreamTools(D2,D1) +--R if D2 has TYPE and D1 has LZSTAGG(D2) +--R +--RExamples of cycleElt from CyclicStreamTools +--R +--Rp:=repeating([1,2,3]) +--Rq:=cons(4,p) +--RcycleElt q +--Rr:=[1,2,3]::Stream(Integer) +--RcycleElt r +--R +--E 567 + +--S 568 of 3320 done +)d op cycleEntry +--R +--R +--RThere is one exposed function called cycleEntry : +--R [1] D -> D from D if D has URAGG(D1) and D1 has TYPE +--R +--RExamples of cycleEntry from UnaryRecursiveAggregate +--R +--Rt1:=[1,2,3] +--Rt2:=concat!(t1,t1) +--RcycleEntry t2 +--R +--E 568 + +--S 569 of 3320 done +)d op cycleLength +--R +--R +--RThere is one exposed function called cycleLength : +--R [1] D -> NonNegativeInteger from D if D has URAGG(D2) and D2 has +--R TYPE +--R +--RExamples of cycleLength from UnaryRecursiveAggregate +--R +--Rt1:=[1,2,3] +--Rt2:=concat!(t1,t1) +--RcycleLength t2 +--R +--E 569 + +--S 570 of 3320 +)d op cyclePartition +--R +--R +--RThere is one exposed function called cyclePartition : +--R [1] Permutation(D2) -> Partition from Permutation(D2) if D2 has +--R SETCAT +--R +--RExamples of cyclePartition from Permutation +--R +--E 570 + +--S 571 of 3320 +)d op cycleRagits +--R +--R +--RThere is one exposed function called cycleRagits : +--R [1] RadixExpansion(D2) -> List(Integer) from RadixExpansion(D2) if +--R D2: INT +--R +--RExamples of cycleRagits from RadixExpansion +--R +--E 571 + +--S 572 of 3320 +)d op cycles +--R +--R +--RThere is one exposed function called cycles : +--R [1] List(List(D2)) -> D from D if D2 has SETCAT and D has PERMCAT(D2 +--R ) +--R +--RExamples of cycles from PermutationCategory +--R +--E 572 + +--S 573 of 3320 done +)d op cycleSplit! +--R +--R +--RThere is one exposed function called cycleSplit! : +--R [1] D -> D from D if D has shallowlyMutable and D has URAGG(D1) and +--R D1 has TYPE +--R +--RExamples of cycleSplit! from UnaryRecursiveAggregate +--R +--Rt1:=[1,2,3] +--Rt2:=concat!(t1,t1) +--Rt3:=[1,2,3] +--Rt4:=concat!(t3,t2) +--Rt5:=cycleSplit!(t4) +--Rt4 +--Rt5 +--R +--E 573 + +--S 574 of 3320 done +)d op cycleTail +--R +--R +--RThere is one exposed function called cycleTail : +--R [1] D -> D from D if D has URAGG(D1) and D1 has TYPE +--R +--RExamples of cycleTail from UnaryRecursiveAggregate +--R +--Rt1:=[1,2,3] +--Rt2:=concat!(t1,t1) +--RcycleTail t2 +--R +--E 574 + +--S 575 of 3320 +)d op cyclic +--R +--R +--RThere is one exposed function called cyclic : +--R [1] Integer -> SymmetricPolynomial(Fraction(Integer)) from +--R CycleIndicators +--R +--RExamples of cyclic from CycleIndicators +--R +--E 575 + +--S 576 of 3320 +)d op cyclic? +--R +--R +--RThere are 2 exposed functions called cyclic? : +--R [1] D -> Boolean from D if D has RCAGG(D2) and D2 has TYPE +--R [2] Tree(D2) -> Boolean from Tree(D2) if D2 has SETCAT +--R +--RExamples of cyclic? from RecursiveAggregate +--R +--R +--RExamples of cyclic? from Tree +--R +--Rt1:=tree [1,2,3,4] +--Rcyclic? t1 +--R +--E 576 + +--S 577 of 3320 done +)d op cyclicCopy +--R +--R +--RThere is one exposed function called cyclicCopy : +--R [1] Tree(D1) -> Tree(D1) from Tree(D1) if D1 has SETCAT +--R +--RExamples of cyclicCopy from Tree +--R +--Rt1:=tree [1,2,3,4] +--RcyclicCopy t1 +--R +--E 577 + +--S 578 of 3320 done +)d op cyclicEntries +--R +--R +--RThere is one exposed function called cyclicEntries : +--R [1] Tree(D2) -> List(Tree(D2)) from Tree(D2) if D2 has SETCAT +--R +--RExamples of cyclicEntries from Tree +--R +--Rt1:=tree [1,2,3,4] +--RcyclicEntries t1 +--R +--E 578 + +--S 579 of 3320 done +)d op cyclicEqual? +--R +--R +--RThere is one exposed function called cyclicEqual? : +--R [1] (Tree(D2),Tree(D2)) -> Boolean from Tree(D2) if D2 has SETCAT +--R +--R +--RExamples of cyclicEqual? from Tree +--R +--Rt1:=tree [1,2,3,4] +--Rt2:=tree [1,2,3,4] +--RcyclicEqual?(t1,t2) +--R +--E 579 + +--S 580 of 3320 +)d op cyclicGroup +--R +--R +--RThere are 2 exposed functions called cyclicGroup : +--R [1] PositiveInteger -> PermutationGroup(Integer) +--R from PermutationGroupExamples +--R [2] List(Integer) -> PermutationGroup(Integer) from +--R PermutationGroupExamples +--R +--RExamples of cyclicGroup from PermutationGroupExamples +--R +--E 580 + +--S 581 of 3320 done +)d op cyclicParents +--R +--R +--RThere is one exposed function called cyclicParents : +--R [1] Tree(D2) -> List(Tree(D2)) from Tree(D2) if D2 has SETCAT +--R +--RExamples of cyclicParents from Tree +--R +--Rt1:=tree [1,2,3,4] +--RcyclicParents t1 +--R +--E 581 + +--S 582 of 3320 +)d op cyclicSubmodule +--R +--R +--RThere is one exposed function called cyclicSubmodule : +--R [1] (List(Matrix(D4)),Vector(D4)) -> Vector(Vector(D4)) +--R from RepresentationPackage2(D4) if D4 has EUCDOM and D4 +--R has RING +--R +--RExamples of cyclicSubmodule from RepresentationPackage2 +--R +--E 582 + +--S 583 of 3320 +)d op cyclotomic +--R +--R +--RThere is one exposed function called cyclotomic : +--R [1] (NonNegativeInteger,D1) -> D1 from +--R NumberTheoreticPolynomialFunctions(D1) +--R if D1 has COMRING +--R +--RThere are 2 unexposed functions called cyclotomic : +--R [1] Integer -> SparseUnivariatePolynomial(Integer) +--R from CyclotomicPolynomialPackage +--R [2] Integer -> SparseUnivariatePolynomial(Integer) +--R from PolynomialNumberTheoryFunctions +--R +--RExamples of cyclotomic from CyclotomicPolynomialPackage +--R +--R +--RExamples of cyclotomic from NumberTheoreticPolynomialFunctions +--R +--R +--RExamples of cyclotomic from PolynomialNumberTheoryFunctions +--R +--E 583 + +--S 584 of 3320 +)d op cyclotomicDecomposition +--R +--R +--RThere is one unexposed function called cyclotomicDecomposition : +--R [1] Integer -> List(SparseUnivariatePolynomial(Integer)) +--R from CyclotomicPolynomialPackage +--R +--RExamples of cyclotomicDecomposition from CyclotomicPolynomialPackage +--R +--E 584 + +--S 585 of 3320 +)d op cyclotomicFactorization +--R +--R +--RThere is one unexposed function called cyclotomicFactorization : +--R [1] Integer -> Factored(SparseUnivariatePolynomial(Integer)) +--R from CyclotomicPolynomialPackage +--R +--RExamples of cyclotomicFactorization from CyclotomicPolynomialPackage +--R +--E 585 + +--S 586 of 3320 +)d op cylindrical +--R +--R +--RThere is one exposed function called cylindrical : +--R [1] Point(D2) -> Point(D2) from CoordinateSystems(D2) +--R if D2 has Join(Field,TranscendentalFunctionCategory, +--R RadicalCategory) +--R +--RExamples of cylindrical from CoordinateSystems +--R +--E 586 + +--S 587 of 3320 +)d op cylindricalDecomposition +--R +--R +--RThere are 2 exposed functions called cylindricalDecomposition : +--R [1] List(Polynomial(D3)) -> List(Cell(D3)) +--R from CylindricalAlgebraicDecompositionPackage(D3) if D3 +--R has RCFIELD +--R [2] (List(Polynomial(D4)),List(Symbol)) -> List(Cell(D4)) +--R from CylindricalAlgebraicDecompositionPackage(D4) if D4 +--R has RCFIELD +--R +--RExamples of cylindricalDecomposition from CylindricalAlgebraicDecompositionPackage +--R +--E 587 + +--S 588 of 3320 +)d op d +--R +--R +--RThere is one exposed function called d : +--R [1] Symbol -> Union(BasicStochasticDifferential,Integer) +--R from BasicStochasticDifferential +--R +--RExamples of d from BasicStochasticDifferential +--R +--E 588 + +--S 589 of 3320 +)d op D +--R +--R +--RThere are 11 exposed functions called D : +--R [1] (D,(D3 -> D3),NonNegativeInteger) -> D from D +--R if D has DIFEXT(D3) and D3 has RING +--R [2] (D,(D2 -> D2)) -> D from D if D has DIFEXT(D2) and D2 has RING +--R +--R [3] (D,NonNegativeInteger) -> D from D if D has DIFRING +--R [4] D -> D from D if D has DIFRING +--R [5] (FullPartialFractionExpansion(D2,D3),NonNegativeInteger) -> +--R FullPartialFractionExpansion(D2,D3) +--R from FullPartialFractionExpansion(D2,D3) +--R if D2 has Join(Field,CharacteristicZero) and D3 has UPOLYC +--R (D2) +--R [6] FullPartialFractionExpansion(D1,D2) -> +--R FullPartialFractionExpansion(D1,D2) +--R from FullPartialFractionExpansion(D1,D2) +--R if D1 has Join(Field,CharacteristicZero) and D2 has UPOLYC +--R (D1) +--R [7] -> D from D if D has LODOCAT(D1) and D1 has RING +--R [8] (D,List(D3),List(NonNegativeInteger)) -> D from D +--R if D has PDRING(D3) and D3 has SETCAT +--R [9] (D,D1,NonNegativeInteger) -> D from D if D has PDRING(D1) and D1 +--R has SETCAT +--R [10] (D,List(D2)) -> D from D if D has PDRING(D2) and D2 has SETCAT +--R +--R [11] (D,D1) -> D from D if D has PDRING(D1) and D1 has SETCAT +--R +--RExamples of D from DifferentialExtension +--R +--R +--RExamples of D from DifferentialRing +--R +--R +--RExamples of D from FullPartialFractionExpansion +--R +--R +--RExamples of D from LinearOrdinaryDifferentialOperatorCategory +--R +--R +--RExamples of D from PartialDifferentialRing +--R +--E 589 + +--S 590 of 3320 +)d op d01ajf +--R +--R +--RThere is one exposed function called d01ajf : +--R [1] (DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer +--R ,Integer,Union(fn: FileName,fp: Asp1(F))) -> Result +--R from NagIntegrationPackage +--R +--RExamples of d01ajf from NagIntegrationPackage +--R +--E 590 + +--S 591 of 3320 +)d op d01akf +--R +--R +--RThere is one exposed function called d01akf : +--R [1] (DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer +--R ,Integer,Union(fn: FileName,fp: Asp1(F))) -> Result +--R from NagIntegrationPackage +--R +--RExamples of d01akf from NagIntegrationPackage +--R +--E 591 + +--S 592 of 3320 +)d op d01alf +--R +--R +--RThere is one exposed function called d01alf : +--R [1] (DoubleFloat,DoubleFloat,Integer,Matrix(DoubleFloat),DoubleFloat +--R ,DoubleFloat,Integer,Integer,Integer,Union(fn: FileName,fp: Asp1( +--R F))) -> Result +--R from NagIntegrationPackage +--R +--RExamples of d01alf from NagIntegrationPackage +--R +--E 592 + +--S 593 of 3320 +)d op d01amf +--R +--R +--RThere is one exposed function called d01amf : +--R [1] (DoubleFloat,Integer,DoubleFloat,DoubleFloat,Integer,Integer, +--R Integer,Union(fn: FileName,fp: Asp1(F))) -> Result +--R from NagIntegrationPackage +--R +--RExamples of d01amf from NagIntegrationPackage +--R +--E 593 + +--S 594 of 3320 +)d op d01anf +--R +--R +--RThere is one exposed function called d01anf : +--R [1] (DoubleFloat,DoubleFloat,DoubleFloat,Integer,DoubleFloat, +--R DoubleFloat,Integer,Integer,Integer,Union(fn: FileName,fp: Asp1(G +--R ))) -> Result +--R from NagIntegrationPackage +--R +--RExamples of d01anf from NagIntegrationPackage +--R +--E 594 + +--S 595 of 3320 +)d op d01apf +--R +--R +--RThere is one exposed function called d01apf : +--R [1] (DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer, +--R DoubleFloat,DoubleFloat,Integer,Integer,Integer,Union(fn: +--R FileName,fp: Asp1(G))) -> Result +--R from NagIntegrationPackage +--R +--RExamples of d01apf from NagIntegrationPackage +--R +--E 595 + +--S 596 of 3320 +)d op d01aqf +--R +--R +--RThere is one exposed function called d01aqf : +--R [1] (DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat, +--R Integer,Integer,Integer,Union(fn: FileName,fp: Asp1(G))) -> +--R Result +--R from NagIntegrationPackage +--R +--RExamples of d01aqf from NagIntegrationPackage +--R +--E 596 + +--S 597 of 3320 +)d op d01asf +--R +--R +--RThere is one exposed function called d01asf : +--R [1] (DoubleFloat,DoubleFloat,Integer,DoubleFloat,Integer,Integer, +--R Integer,Integer,Union(fn: FileName,fp: Asp1(G))) -> Result +--R from NagIntegrationPackage +--R +--RExamples of d01asf from NagIntegrationPackage +--R +--E 597 + +--S 598 of 3320 +)d op d01bbf +--R +--R +--RThere is one exposed function called d01bbf : +--R [1] (DoubleFloat,DoubleFloat,Integer,Integer,Integer,Integer) -> +--R Result +--R from NagIntegrationPackage +--R +--RExamples of d01bbf from NagIntegrationPackage +--R +--E 598 + +--S 599 of 3320 +)d op d01fcf +--R +--R +--RThere is one exposed function called d01fcf : +--R [1] (Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer, +--R DoubleFloat,Integer,Integer,Integer,Union(fn: FileName,fp: Asp4( +--R FUNCTN))) -> Result +--R from NagIntegrationPackage +--R +--RExamples of d01fcf from NagIntegrationPackage +--R +--E 599 + +--S 600 of 3320 +)d op d01gaf +--R +--R +--RThere is one exposed function called d01gaf : +--R [1] (Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer) -> +--R Result +--R from NagIntegrationPackage +--R +--RExamples of d01gaf from NagIntegrationPackage +--R +--E 600 + +--S 601 of 3320 +)d op d01gbf +--R +--R +--RThere is one exposed function called d01gbf : +--R [1] (Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer, +--R DoubleFloat,Integer,Integer,Matrix(DoubleFloat),Integer,Union(fn +--R : FileName,fp: Asp4(FUNCTN))) -> Result +--R from NagIntegrationPackage +--R +--RExamples of d01gbf from NagIntegrationPackage +--R +--E 601 + +--S 602 of 3320 +)d op d02bbf +--R +--R +--RThere is one exposed function called d02bbf : +--R [1] (DoubleFloat,Integer,Integer,Integer,DoubleFloat,Matrix( +--R DoubleFloat),DoubleFloat,Integer,Union(fn: FileName,fp: Asp7(FCN) +--R ),Union(fn: FileName,fp: Asp8(OUTPUT))) -> Result +--R from NagOrdinaryDifferentialEquationsPackage +--R +--RExamples of d02bbf from NagOrdinaryDifferentialEquationsPackage +--R +--E 602 + +--S 603 of 3320 +)d op d02bhf +--R +--R +--RThere is one exposed function called d02bhf : +--R [1] (DoubleFloat,Integer,Integer,DoubleFloat,DoubleFloat,Matrix( +--R DoubleFloat),DoubleFloat,Integer,Union(fn: FileName,fp: Asp9(G)), +--R Union(fn: FileName,fp: Asp7(FCN))) -> Result +--R from NagOrdinaryDifferentialEquationsPackage +--R +--RExamples of d02bhf from NagOrdinaryDifferentialEquationsPackage +--R +--E 603 + +--S 604 of 3320 +)d op d02cjf +--R +--R +--RThere is one exposed function called d02cjf : +--R [1] (DoubleFloat,Integer,Integer,DoubleFloat,String,DoubleFloat, +--R Matrix(DoubleFloat),Integer,Union(fn: FileName,fp: Asp9(G)),Union +--R (fn: FileName,fp: Asp7(FCN)),Union(fn: FileName,fp: Asp8(OUTPUT)) +--R ) -> Result +--R from NagOrdinaryDifferentialEquationsPackage +--R +--RExamples of d02cjf from NagOrdinaryDifferentialEquationsPackage +--R +--E 604 + +--S 605 of 3320 +)d op d02ejf +--R +--R +--RThere is one exposed function called d02ejf : +--R [1] (DoubleFloat,Integer,Integer,String,Integer,DoubleFloat,Matrix( +--R DoubleFloat),DoubleFloat,Integer,Union(fn: FileName,fp: Asp9(G)), +--R Union(fn: FileName,fp: Asp7(FCN)),Union(fn: FileName,fp: Asp31( +--R PEDERV)),Union(fn: FileName,fp: Asp8(OUTPUT))) -> Result +--R from NagOrdinaryDifferentialEquationsPackage +--R +--RExamples of d02ejf from NagOrdinaryDifferentialEquationsPackage +--R +--E 605 + +--S 606 of 3320 +)d op d02gaf +--R +--R +--RThere is one exposed function called d02gaf : +--R [1] (Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,DoubleFloat, +--R DoubleFloat,DoubleFloat,Integer,Integer,Integer,Matrix( +--R DoubleFloat),Integer,Integer,Union(fn: FileName,fp: Asp7(FCN))) +--R -> Result +--R from NagOrdinaryDifferentialEquationsPackage +--R +--RExamples of d02gaf from NagOrdinaryDifferentialEquationsPackage +--R +--E 606 + +--S 607 of 3320 +)d op d02gbf +--R +--R +--RThere is one exposed function called d02gbf : +--R [1] (DoubleFloat,DoubleFloat,Integer,DoubleFloat,Integer,Integer, +--R Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Matrix(DoubleFloat),Integer,Integer,Union(fn: +--R FileName,fp: Asp77(FCNF)),Union(fn: FileName,fp: Asp78(FCNG))) +--R -> Result +--R from NagOrdinaryDifferentialEquationsPackage +--R +--RExamples of d02gbf from NagOrdinaryDifferentialEquationsPackage +--R +--E 607 + +--S 608 of 3320 +)d op d02kef +--R +--R +--RThere are 2 exposed functions called d02kef : +--R [1] (Matrix(DoubleFloat),Integer,Integer,DoubleFloat,Integer,Integer +--R ,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Integer,Integer, +--R Union(fn: FileName,fp: Asp10(COEFFN)),Union(fn: FileName,fp: +--R Asp80(BDYVAL))) -> Result +--R from NagOrdinaryDifferentialEquationsPackage +--R [2] (Matrix(DoubleFloat),Integer,Integer,DoubleFloat,Integer,Integer +--R ,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Integer,Integer, +--R Union(fn: FileName,fp: Asp10(COEFFN)),Union(fn: FileName,fp: +--R Asp80(BDYVAL)),FileName,FileName) -> Result +--R from NagOrdinaryDifferentialEquationsPackage +--R +--RExamples of d02kef from NagOrdinaryDifferentialEquationsPackage +--R +--E 608 + +--S 609 of 3320 +)d op d02raf +--R +--R +--RThere is one exposed function called d02raf : +--R [1] (Integer,Integer,Integer,Integer,DoubleFloat,Integer,Integer, +--R Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix( +--R DoubleFloat),DoubleFloat,Integer,Union(fn: FileName,fp: Asp41(FCN +--R ,JACOBF,JACEPS)),Union(fn: FileName,fp: Asp42(G,JACOBG,JACGEP))) +--R -> Result +--R from NagOrdinaryDifferentialEquationsPackage +--R +--RExamples of d02raf from NagOrdinaryDifferentialEquationsPackage +--R +--E 609 + +--S 610 of 3320 +)d op d03edf +--R +--R +--RThere is one exposed function called d03edf : +--R [1] (Integer,Integer,Integer,Integer,DoubleFloat,Integer,Matrix( +--R DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer) -> +--R Result +--R from NagPartialDifferentialEquationsPackage +--R +--RExamples of d03edf from NagPartialDifferentialEquationsPackage +--R +--E 610 + +--S 611 of 3320 +)d op d03eef +--R +--R +--RThere is one exposed function called d03eef : +--R [1] (DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Integer,Integer +--R ,Integer,String,Integer,Union(fn: FileName,fp: Asp73(PDEF)),Union +--R (fn: FileName,fp: Asp74(BNDY))) -> Result +--R from NagPartialDifferentialEquationsPackage +--R +--RExamples of d03eef from NagPartialDifferentialEquationsPackage +--R +--E 611 + +--S 612 of 3320 +)d op d03faf +--R +--R +--RThere is one exposed function called d03faf : +--R [1] (DoubleFloat,DoubleFloat,Integer,Integer,Matrix(DoubleFloat), +--R Matrix(DoubleFloat),DoubleFloat,DoubleFloat,Integer,Integer, +--R Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat,DoubleFloat, +--R Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat), +--R DoubleFloat,Integer,Integer,Integer,ThreeDimensionalMatrix( +--R DoubleFloat),Integer) -> Result +--R from NagPartialDifferentialEquationsPackage +--R +--RExamples of d03faf from NagPartialDifferentialEquationsPackage +--R +--E 612 + +--S 613 of 3320 +)d op dAndcExp +--R +--R +--RThere is one unexposed function called dAndcExp : +--R [1] (Vector(D4),NonNegativeInteger,SingleInteger) -> Vector(D4) +--R from InnerNormalBasisFieldFunctions(D4) if D4 has FFIELDC +--R +--R +--RExamples of dAndcExp from InnerNormalBasisFieldFunctions +--R +--E 613 + +--S 614 of 3320 +)d op dark +--R +--R +--RThere is one exposed function called dark : +--R [1] Color -> Palette from Palette +--R +--RExamples of dark from Palette +--R +--E 614 + +--S 615 of 3320 +)d op datalist +--R +--R +--RThere is one exposed function called datalist : +--R [1] List(D2) -> DataList(D2) from DataList(D2) if D2 has ORDSET +--R +--RExamples of datalist from DataList +--R +--E 615 + +--S 616 of 3320 +)d op ddFact +--R +--R +--RThere is one exposed function called ddFact : +--R [1] (D2,Integer) -> List(Record(factor: D2,degree: Integer)) +--R from ModularDistinctDegreeFactorizer(D2) if D2 has UPOLYC( +--R INT) +--R +--RExamples of ddFact from ModularDistinctDegreeFactorizer +--R +--E 616 + +--S 617 of 3320 +)d op debug +--R +--R +--RThere is one exposed function called debug : +--R [1] Boolean -> GuessOption from GuessOption +--R +--RThere are 2 unexposed functions called debug : +--R [1] List(GuessOption) -> Boolean from GuessOptionFunctions0 +--R [2] Boolean -> Boolean from Plot +--R +--RExamples of debug from GuessOptionFunctions0 +--R +--R +--RExamples of debug from GuessOption +--R +--R +--RExamples of debug from Plot +--R +--E 617 + +--S 618 of 3320 +)d op debug3D +--R +--R +--RThere is one unexposed function called debug3D : +--R [1] Boolean -> Boolean from Plot3D +--R +--RExamples of debug3D from Plot3D +--R +--E 618 + +--S 619 of 3320 +)d op dec +--R +--R +--RThere is one exposed function called dec : +--R [1] D -> D from D if D has INS +--R +--RExamples of dec from IntegerNumberSystem +--R +--E 619 + +--S 620 of 3320 +)d op decimal +--R +--R +--RThere is one exposed function called decimal : +--R [1] Fraction(Integer) -> DecimalExpansion from DecimalExpansion +--R +--RExamples of decimal from DecimalExpansion +--R +--E 620 + +--S 621 of 3320 +)d op declare +--R +--R +--RThere is one unexposed function called declare : +--R [1] List(InputForm) -> Symbol from InputForm +--R +--RExamples of declare from InputForm +--R +--E 621 + +--S 622 of 3320 +)d op declare! +--R +--R +--RThere are 6 exposed functions called declare! : +--R [1] (Symbol,FortranType,Symbol) -> FortranType from TheSymbolTable +--R +--R [2] (Symbol,FortranType) -> FortranType from TheSymbolTable +--R [3] (List(Symbol),FortranType,Symbol,TheSymbolTable) -> FortranType +--R from TheSymbolTable +--R [4] (Symbol,FortranType,Symbol,TheSymbolTable) -> FortranType +--R from TheSymbolTable +--R [5] (Symbol,FortranType,SymbolTable) -> FortranType from SymbolTable +--R +--R [6] (List(Symbol),FortranType,SymbolTable) -> FortranType from +--R SymbolTable +--R +--RExamples of declare! from TheSymbolTable +--R +--R +--RExamples of declare! from SymbolTable +--R +--E 622 + +--S 623 of 3320 +)d op decompose +--R +--R +--RThere are 7 exposed functions called decompose : +--R [1] D -> Record(id: FractionalIdeal(D3,Fraction(D3),D4,D5), +--R principalPart: D5) +--R from D +--R if D has FDIVCAT(D2,D3,D4,D5) and D2 has FIELD and D3 has +--R UPOLYC(D2) and D4 has UPOLYC(FRAC(D3)) and D5 has FFCAT(D2, +--R D3,D4) +--R [2] D2 -> List(D2) from PolynomialDecomposition(D2,D3) +--R if D3 has FIELD and D2 has UPOLYC(D3) +--R [3] (D2,NonNegativeInteger,NonNegativeInteger) -> Union(Record(left +--R : D2,right: D2),"failed") +--R from PolynomialDecomposition(D2,D4) +--R if D4 has FIELD and D2 has UPOLYC(D4) +--R [4] (List(D7),List(D8),Boolean,Boolean) -> List(D8) +--R from RegularSetDecompositionPackage(D4,D5,D6,D7,D8) +--R if D7 has RPOLCAT(D4,D5,D6) and D8 has RSETCAT(D4,D5,D6,D7 +--R ) and D4 has GCDDOM and D5 has OAMONS and D6 has ORDSET +--R [5] (List(D7),List(D8),Boolean,Boolean,Boolean,Boolean,Boolean) -> +--R List(D8) +--R from RegularSetDecompositionPackage(D4,D5,D6,D7,D8) +--R if D7 has RPOLCAT(D4,D5,D6) and D8 has RSETCAT(D4,D5,D6,D7 +--R ) and D4 has GCDDOM and D5 has OAMONS and D6 has ORDSET +--R [6] (List(D7),List(D8),Boolean,Boolean) -> List(D8) +--R from SquareFreeRegularSetDecompositionPackage(D4,D5,D6,D7, +--R D8) +--R if D7 has RPOLCAT(D4,D5,D6) and D8 has SFRTCAT(D4,D5,D6,D7 +--R ) and D4 has GCDDOM and D5 has OAMONS and D6 has ORDSET +--R [7] (List(D7),List(D8),Boolean,Boolean,Boolean,Boolean,Boolean) -> +--R List(D8) +--R from SquareFreeRegularSetDecompositionPackage(D4,D5,D6,D7, +--R D8) +--R if D7 has RPOLCAT(D4,D5,D6) and D8 has SFRTCAT(D4,D5,D6,D7 +--R ) and D4 has GCDDOM and D5 has OAMONS and D6 has ORDSET +--R +--RThere is one unexposed function called decompose : +--R [1] (Fraction(D5),(D5 -> D5)) -> Record(poly: D5,normal: Fraction(D5 +--R ),special: Fraction(D5)) +--R from MonomialExtensionTools(D4,D5) if D5 has UPOLYC(D4) +--R and D4 has FIELD +--R +--RExamples of decompose from FiniteDivisorCategory +--R +--R +--RExamples of decompose from MonomialExtensionTools +--R +--R +--RExamples of decompose from PolynomialDecomposition +--R +--R +--RExamples of decompose from RegularSetDecompositionPackage +--R +--R +--RExamples of decompose from SquareFreeRegularSetDecompositionPackage +--R +--E 623 + +--S 624 of 3320 +)d op decompose +--R +--R +--RThere are 7 exposed functions called decompose : +--R [1] D -> Record(id: FractionalIdeal(D3,Fraction(D3),D4,D5), +--R principalPart: D5) +--R from D +--R if D has FDIVCAT(D2,D3,D4,D5) and D2 has FIELD and D3 has +--R UPOLYC(D2) and D4 has UPOLYC(FRAC(D3)) and D5 has FFCAT(D2, +--R D3,D4) +--R [2] D2 -> List(D2) from PolynomialDecomposition(D2,D3) +--R if D3 has FIELD and D2 has UPOLYC(D3) +--R [3] (D2,NonNegativeInteger,NonNegativeInteger) -> Union(Record(left +--R : D2,right: D2),"failed") +--R from PolynomialDecomposition(D2,D4) +--R if D4 has FIELD and D2 has UPOLYC(D4) +--R [4] (List(D7),List(D8),Boolean,Boolean) -> List(D8) +--R from RegularSetDecompositionPackage(D4,D5,D6,D7,D8) +--R if D7 has RPOLCAT(D4,D5,D6) and D8 has RSETCAT(D4,D5,D6,D7 +--R ) and D4 has GCDDOM and D5 has OAMONS and D6 has ORDSET +--R [5] (List(D7),List(D8),Boolean,Boolean,Boolean,Boolean,Boolean) -> +--R List(D8) +--R from RegularSetDecompositionPackage(D4,D5,D6,D7,D8) +--R if D7 has RPOLCAT(D4,D5,D6) and D8 has RSETCAT(D4,D5,D6,D7 +--R ) and D4 has GCDDOM and D5 has OAMONS and D6 has ORDSET +--R [6] (List(D7),List(D8),Boolean,Boolean) -> List(D8) +--R from SquareFreeRegularSetDecompositionPackage(D4,D5,D6,D7, +--R D8) +--R if D7 has RPOLCAT(D4,D5,D6) and D8 has SFRTCAT(D4,D5,D6,D7 +--R ) and D4 has GCDDOM and D5 has OAMONS and D6 has ORDSET +--R [7] (List(D7),List(D8),Boolean,Boolean,Boolean,Boolean,Boolean) -> +--R List(D8) +--R from SquareFreeRegularSetDecompositionPackage(D4,D5,D6,D7, +--R D8) +--R if D7 has RPOLCAT(D4,D5,D6) and D8 has SFRTCAT(D4,D5,D6,D7 +--R ) and D4 has GCDDOM and D5 has OAMONS and D6 has ORDSET +--R +--RThere is one unexposed function called decompose : +--R [1] (Fraction(D5),(D5 -> D5)) -> Record(poly: D5,normal: Fraction(D5 +--R ),special: Fraction(D5)) +--R from MonomialExtensionTools(D4,D5) if D5 has UPOLYC(D4) +--R and D4 has FIELD +--R +--RExamples of decompose from FiniteDivisorCategory +--R +--R +--RExamples of decompose from MonomialExtensionTools +--R +--R +--RExamples of decompose from PolynomialDecomposition +--R +--R +--RExamples of decompose from RegularSetDecompositionPackage +--R +--R +--RExamples of decompose from SquareFreeRegularSetDecompositionPackage +--R +--E 624 + +--S 625 of 3320 +)d op decomposeFunc +--R +--R +--RThere is one unexposed function called decomposeFunc : +--R [1] (Fraction(SparseUnivariatePolynomial(Expression(D2))),Fraction( +--R SparseUnivariatePolynomial(Expression(D2))),Fraction( +--R SparseUnivariatePolynomial(Expression(D2)))) -> Fraction( +--R SparseUnivariatePolynomial(Expression(D2))) +--R from TransSolvePackageService(D2) +--R if D2 has Join(IntegralDomain,OrderedSet) +--R +--RExamples of decomposeFunc from TransSolvePackageService +--R +--E 625 + +--S 626 of 3320 +)d op decrease +--R +--R +--RThere are 2 exposed functions called decrease : +--R [1] String -> Float from AttributeButtons +--R [2] (String,String) -> Float from AttributeButtons +--R +--RExamples of decrease from AttributeButtons +--R +--E 626 + +--S 627 of 3320 +)d op decreasePrecision +--R +--R +--RThere is one exposed function called decreasePrecision : +--R [1] Integer -> PositiveInteger from D if D has arbitraryPrecision +--R and D has FPS +--R +--RExamples of decreasePrecision from FloatingPointSystem +--R +--E 627 + +--S 628 of 3320 +)d op deepCopy +--R +--R +--RThere is one unexposed function called deepCopy : +--R [1] SubSpace(D1,D2) -> SubSpace(D1,D2) from SubSpace(D1,D2) +--R if D1: PI and D2 has RING +--R +--RExamples of deepCopy from SubSpace +--R +--E 628 + +--S 629 of 3320 +)d op deepestInitial +--R +--R +--RThere is one exposed function called deepestInitial : +--R [1] D -> D from D +--R if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has +--R OAMONS and D3 has ORDSET +--R +--RExamples of deepestInitial from RecursivePolynomialCategory +--R +--E 629 + +--S 630 of 3320 +)d op deepestTail +--R +--R +--RThere is one exposed function called deepestTail : +--R [1] D -> D from D +--R if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has +--R OAMONS and D3 has ORDSET +--R +--RExamples of deepestTail from RecursivePolynomialCategory +--R +--E 630 + +--S 631 of 3320 +)d op deepExpand +--R +--R +--RThere is one exposed function called deepExpand : +--R [1] FreeNilpotentLie(D2,D3,D4) -> OutputForm from FreeNilpotentLie( +--R D2,D3,D4) +--R if D2: NNI and D3: NNI and D4 has COMRING +--R +--RExamples of deepExpand from FreeNilpotentLie +--R +--E 631 + +--S 632 of 3320 +)d op defineProperty +--R +--R +--RThere is one unexposed function called defineProperty : +--R [1] (SubSpace(D3,D4),List(NonNegativeInteger), +--R SubSpaceComponentProperty) -> SubSpace(D3,D4) +--R from SubSpace(D3,D4) if D3: PI and D4 has RING +--R +--RExamples of defineProperty from SubSpace +--R +--E 632 + +--S 633 of 3320 +)d op definingEquations +--R +--R +--RThere is one unexposed function called definingEquations : +--R [1] QuasiAlgebraicSet(D2,D3,D4,D5) -> List(D5) +--R from QuasiAlgebraicSet(D2,D3,D4,D5) +--R if D2 has GCDDOM and D3 has ORDSET and D4 has OAMONS and +--R D5 has POLYCAT(D2,D4,D3) +--R +--RExamples of definingEquations from QuasiAlgebraicSet +--R +--E 633 + +--S 634 of 3320 +)d op definingField +--R +--R +--RThere are 2 exposed functions called definingField : +--R [1] D -> D1 from D if D has AFSPCAT(D1) and D1 has FIELD +--R [2] D -> D1 from D if D has PRSPCAT(D1) and D1 has FIELD +--R +--RExamples of definingField from AffineSpaceCategory +--R +--R +--RExamples of definingField from ProjectiveSpaceCategory +--R +--E 634 + +--S 635 of 3320 +)d op definingInequation +--R +--R +--RThere is one unexposed function called definingInequation : +--R [1] QuasiAlgebraicSet(D2,D3,D4,D1) -> D1 from QuasiAlgebraicSet(D2, +--R D3,D4,D1) +--R if D1 has POLYCAT(D2,D4,D3) and D2 has GCDDOM and D3 has +--R ORDSET and D4 has OAMONS +--R +--RExamples of definingInequation from QuasiAlgebraicSet +--R +--E 635 + +--S 636 of 3320 +)d op definingPolynomial +--R +--R +--RThere are 6 exposed functions called definingPolynomial : +--R [1] D -> D from D if D has RING and D has ES +--R [2] -> SparseUnivariatePolynomial(D2) from D if D has FAXF(D2) and +--R D2 has FIELD +--R [3] -> D1 from D if D has MONOGEN(D2,D1) and D2 has COMRING and D1 +--R has UPOLYC(D2) +--R [4] D -> SparseUnivariatePolynomial(D) from D if D has PACPERC +--R [5] -> SparseUnivariatePolynomial(D) from D if D has PACPERC +--R [6] D -> D1 from D +--R if D has RRCC(D2,D1) and D2 has Join(OrderedRing,Field) +--R and D1 has UPOLYC(D2) +--R +--RThere are 2 unexposed functions called definingPolynomial : +--R [1] D1 -> D1 from AlgebraicFunction(D2,D1) +--R if D2 has RETRACT(INT) and D2 has Join(OrderedSet, +--R IntegralDomain) and D1 has FS(D2) +--R [2] -> SparseUnivariatePolynomial(D3) from ComplexCategory&(D2,D3) +--R if D3 has COMRING and D2 has COMPCAT(D3) +--R +--RExamples of definingPolynomial from AlgebraicFunction +--R +--R +--RExamples of definingPolynomial from ComplexCategory& +--R +--R +--RExamples of definingPolynomial from Ring +--R +--R +--RExamples of definingPolynomial from FiniteAlgebraicExtensionField +--R +--R +--RExamples of definingPolynomial from MonogenicAlgebra +--R +--R +--RExamples of definingPolynomial from PseudoAlgebraicClosureOfPerfectFieldCategory +--R +--R +--RExamples of definingPolynomial from RealRootCharacterizationCategory +--R +--E 636 + +--S 637 of 3320 +)d op degOneCoef +--R +--R +--RThere is one exposed function called degOneCoef : +--R [1] (D2,PositiveInteger) -> D1 from PackageForPoly(D1,D2,D4,D5) +--R if D4 has DIRPCAT(D5,NNI) and D5: NNI and D1 has RING and +--R D2 has FAMR(D1,D4) +--R +--RExamples of degOneCoef from PackageForPoly +--R +--E 637 + +--S 638 of 3320 +)d op degree +--R +--R +--RThere are 22 exposed functions called degree : +--R [1] D -> D1 from D if D has AMR(D2,D1) and D2 has RING and D1 has +--R OAMON +--R [2] D -> Integer from D if D has DIVCAT(D2) and D2 has SETCAT +--R [3] (D,D2) -> NonNegativeInteger from D +--R if D has DPOLCAT(D3,D2,D4,D5) and D3 has RING and D2 has +--R ORDSET and D4 has DVARCAT(D2) and D5 has OAMONS +--R [4] D -> PositiveInteger from D if D has FAXF(D2) and D2 has FIELD +--R +--R [5] D -> NonNegativeInteger from D +--R if D has FLALG(D2,D3) and D2 has ORDSET and D3 has COMRING +--R +--R [6] D -> D1 from D if D has GRMOD(D2,D1) and D2 has COMRING and D1 +--R has ABELMON +--R [7] D2 -> Integer from D if D has MAGCDOC(D2,D3) and D2 has TYPE and +--R D3 has TYPE +--R [8] D -> NonNegativeInteger from D if D has MLO(D2) and D2 has RING +--R +--R [9] D -> NonNegativeInteger from D if D has OREPCAT(D2) and D2 has +--R RING +--R [10] PermutationGroup(D2) -> NonNegativeInteger from +--R PermutationGroup(D2) +--R if D2 has SETCAT +--R [11] Permutation(D2) -> NonNegativeInteger from Permutation(D2) if +--R D2 has SETCAT +--R [12] (D2,Integer) -> NonNegativeInteger from PackageForPoly(D4,D2,D5 +--R ,D6) +--R if D4 has RING and D5 has DIRPCAT(D6,NNI) and D6: NNI and +--R D2 has FAMR(D4,D5) +--R [13] (D,List(D5)) -> List(NonNegativeInteger) from D +--R if D has POLYCAT(D3,D4,D5) and D3 has RING and D4 has +--R OAMONS and D5 has ORDSET +--R [14] (D,D2) -> NonNegativeInteger from D +--R if D has POLYCAT(D3,D4,D2) and D3 has RING and D4 has +--R OAMONS and D2 has ORDSET +--R [15] U32Vector -> Integer from U32VectorPolynomialOperations +--R [16] D -> D1 from D +--R if D has PSCAT(D2,D1,D3) and D2 has RING and D3 has ORDSET +--R and D1 has OAMON +--R [17] D -> PositiveInteger from D if D has SETCATD +--R [18] D -> NonNegativeInteger from D +--R if D has TSETCAT(D2,D3,D4,D5) and D2 has INTDOM and D3 +--R has OAMONS and D4 has ORDSET and D5 has RPOLCAT(D2,D3,D4) +--R +--R [19] D -> Integer from D +--R if D has ULSCCAT(D2,D3) and D2 has RING and D3 has UTSCAT( +--R D2) +--R [20] D -> Fraction(Integer) from D +--R if D has UPXSCCA(D2,D3) and D2 has RING and D3 has ULSCAT( +--R D2) +--R [21] D -> OnePointCompletion(PositiveInteger) from D +--R if D has XF(D2) and D2 has FIELD +--R [22] D -> NonNegativeInteger from D +--R if D has XPOLYC(D2,D3) and D2 has ORDSET and D3 has RING +--R +--R +--RThere are 5 unexposed functions called degree : +--R [1] AntiSymm(D2,D3) -> NonNegativeInteger from AntiSymm(D2,D3) +--R if D2 has RING and D3: LIST(SYMBOL) +--R [2] DeRhamComplex(D2,D3) -> NonNegativeInteger from DeRhamComplex(D2 +--R ,D3) +--R if D2 has Join(Ring,OrderedSet) and D3: LIST(SYMBOL) +--R [3] ExtAlgBasis -> NonNegativeInteger from ExtAlgBasis +--R [4] (SparseUnivariatePolynomial(D7),List(D5)) -> List( +--R NonNegativeInteger) +--R from FactoringUtilities(D4,D5,D6,D7) +--R if D5 has ORDSET and D7 has POLYCAT(D6,D4,D5) and D4 has +--R OAMONS and D6 has RING +--R [5] LaurentPolynomial(D2,D3) -> Integer from LaurentPolynomial(D2,D3 +--R ) +--R if D2 has INTDOM and D3 has UPOLYC(D2) +--R +--RExamples of degree from AbelianMonoidRing +--R +--R +--RExamples of degree from AntiSymm +--R +--R +--RExamples of degree from DeRhamComplex +--R +--Rder := DeRhamComplex(Integer,[x,y,z]) +--Rt1 := generator(1)$der +--Rf:BOP:=operator('f) +--Rg:BOP:=operator('g) +--Rh:BOP:=operator('h) +--Rsigma:der:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz +--Ra:BOP:=operator('a) +--Rb:BOP:=operator('b) +--Rc:BOP:=operator('c) +--Rtheta:der:=a(x,y,z)*dx*dy + b(x,y,z)*dx*dz + c(x,y,z)*dy*dz +--R[degree x for x in [sigma,theta,t1]] +--R +--R +--RExamples of degree from DivisorCategory +--R +--R +--RExamples of degree from DifferentialPolynomialCategory +--R +--R +--RExamples of degree from ExtAlgBasis +--R +--R +--RExamples of degree from FactoringUtilities +--R +--R +--RExamples of degree from FiniteAlgebraicExtensionField +--R +--R +--RExamples of degree from FreeLieAlgebra +--R +--R +--RExamples of degree from GradedModule +--R +--R +--RExamples of degree from LaurentPolynomial +--R +--R +--RExamples of degree from ModularAlgebraicGcdOperations +--R +--R +--RExamples of degree from MonogenicLinearOperator +--R +--R +--RExamples of degree from UnivariateSkewPolynomialCategory +--R +--R +--RExamples of degree from PermutationGroup +--R +--Ry : PERM INT := [[3,5,7,9]] +--Rz : PERM INT := [1,3,11] +--Rg : PERMGRP INT := [ y , z ] +--Rdegree g +--R +--R +--RExamples of degree from Permutation +--R +--R +--RExamples of degree from PackageForPoly +--R +--R +--RExamples of degree from PolynomialCategory +--R +--R +--RExamples of degree from U32VectorPolynomialOperations +--R +--R +--RExamples of degree from PowerSeriesCategory +--R +--R +--RExamples of degree from SetCategoryWithDegree +--R +--R +--RExamples of degree from TriangularSetCategory +--R +--R +--RExamples of degree from UnivariateLaurentSeriesConstructorCategory +--R +--R +--RExamples of degree from UnivariatePuiseuxSeriesConstructorCategory +--R +--R +--RExamples of degree from ExtensionField +--R +--R +--RExamples of degree from XPolynomialsCat +--R +--E 638 + +--S 639 of 3320 +)d op degreeOfMinimalForm +--R +--R +--RThere is one exposed function called degreeOfMinimalForm : +--R [1] D2 -> NonNegativeInteger from PackageForPoly(D3,D2,D4,D5) +--R if D3 has RING and D4 has DIRPCAT(D5,NNI) and D5: NNI and +--R D2 has FAMR(D3,D4) +--R +--RExamples of degreeOfMinimalForm from PackageForPoly +--R +--E 639 + +--S 640 of 3320 +)d op degreePartition +--R +--R +--RThere are 2 unexposed functions called degreePartition : +--R [1] List(Record(factor: D3,degree: Integer)) -> Multiset( +--R NonNegativeInteger) +--R from GaloisGroupFactorizer(D3) if D3 has UPOLYC(INT) +--R [2] Factored(D4) -> Multiset(NonNegativeInteger) +--R from GaloisGroupPolynomialUtilities(D3,D4) +--R if D4 has UPOLYC(D3) and D3 has RING +--R +--RExamples of degreePartition from GaloisGroupFactorizer +--R +--R +--RExamples of degreePartition from GaloisGroupPolynomialUtilities +--R +--E 640 + +--S 641 of 3320 +)d op degreeSubResultant +--R +--R +--RThere is one unexposed function called degreeSubResultant : +--R [1] (D1,D1,NonNegativeInteger) -> D1 from PseudoRemainderSequence(D3 +--R ,D1) +--R if D3 has INTDOM and D1 has UPOLYC(D3) +--R +--RExamples of degreeSubResultant from PseudoRemainderSequence +--R +--E 641 + +--S 642 of 3320 +)d op degreeSubResultantEuclidean +--R +--R +--RThere is one unexposed function called degreeSubResultantEuclidean : +--R [1] (D2,D2,NonNegativeInteger) -> Record(coef1: D2,coef2: D2, +--R subResultant: D2) +--R from PseudoRemainderSequence(D4,D2) +--R if D4 has INTDOM and D2 has UPOLYC(D4) +--R +--RExamples of degreeSubResultantEuclidean from PseudoRemainderSequence +--R +--E 642 + +--S 643 of 3320 +)d op delay +--R +--R +--RThere are 2 exposed functions called delay : +--R [1] (() -> D) -> D from D if D has LOCPOWC(D2) and D2 has FIELD +--R [2] (() -> Stream(D2)) -> Stream(D2) from Stream(D2) if D2 has TYPE +--R +--R +--RExamples of delay from LocalPowerSeriesCategory +--R +--R +--RExamples of delay from Stream +--R +--E 643 + +--S 644 of 3320 +)d op delete +--R +--R +--RThere are 2 exposed functions called delete : +--R [1] (D,UniversalSegment(Integer)) -> D from D if D has LNAGG(D2) and +--R D2 has TYPE +--R [2] (D,Integer) -> D from D if D has LNAGG(D2) and D2 has TYPE +--R +--RExamples of delete from LinearAggregate +--R +--E 644 + +--S 645 of 3320 done +)d op delete! +--R +--R +--RThere are 2 exposed functions called delete! : +--R [1] (D,UniversalSegment(Integer)) -> D from D if D has ELAGG(D2) and +--R D2 has TYPE +--R [2] (D,Integer) -> D from D if D has ELAGG(D2) and D2 has TYPE +--R +--RExamples of delete! from ExtensibleLinearAggregate +--R +--RData:=Record(age:Integer,gender:String) +--Ra1:AssociationList(String,Data):=table() +--Ra1."tim":=[55,"male"]$Data +--Rdelete!(a1,1) +--R +--E 645 + +--S 646 of 3320 +)d op deleteProperty! +--R +--R +--RThere is one exposed function called deleteProperty! : +--R [1] (BasicOperator,String) -> BasicOperator from BasicOperator +--R +--RExamples of deleteProperty! from BasicOperator +--R +--E 646 + +--S 647 of 3320 +)d op deleteRoutine! +--R +--R +--RThere is one exposed function called deleteRoutine! : +--R [1] (RoutinesTable,Symbol) -> RoutinesTable from RoutinesTable +--R +--RExamples of deleteRoutine! from RoutinesTable +--R +--E 647 + +--S 648 of 3320 +)d op deleteRow! +--R +--R +--RThere is one exposed function called deleteRow! : +--R [1] (SparseEchelonMatrix(D3,D4),Integer) -> Void +--R from SparseEchelonMatrix(D3,D4) if D3 has ORDSET and D4 +--R has RING +--R +--RExamples of deleteRow! from SparseEchelonMatrix +--R +--E 648 + +--S 649 of 3320 +)d op delta +--R +--R +--RThere is one unexposed function called delta : +--R [1] (SetOfMIntegersInOneToN(D3,D4),PositiveInteger,PositiveInteger) +--R -> NonNegativeInteger +--R from SetOfMIntegersInOneToN(D3,D4) if D3: PI and D4: PI +--R +--R +--RExamples of delta from SetOfMIntegersInOneToN +--R +--E 649 + +--S 650 of 3320 +)d op denom +--R +--R +--RThere are 3 exposed functions called denom : +--R [1] AlgebraicNumber -> SparseMultivariatePolynomial(Integer,Kernel( +--R AlgebraicNumber)) +--R from AlgebraicNumber +--R [2] D -> SparseMultivariatePolynomial(D2,Kernel(D)) from D +--R if D2 has INTDOM and D2 has ORDSET and D has FS(D2) +--R [3] D -> D1 from D if D has QFCAT(D1) and D1 has INTDOM +--R +--RThere are 4 unexposed functions called denom : +--R [1] FractionalIdeal(D1,D2,D3,D4) -> D1 from FractionalIdeal(D1,D2,D3 +--R ,D4) +--R if D2 has QFCAT(D1) and D3 has UPOLYC(D2) and D1 has +--R EUCDOM and D4 has Join(FramedAlgebra(D2,D3),RetractableTo( +--R D2)) +--R [2] InnerAlgebraicNumber -> SparseMultivariatePolynomial(Integer, +--R Kernel(InnerAlgebraicNumber)) +--R from InnerAlgebraicNumber +--R [3] LocalAlgebra(D2,D3,D1) -> D1 from LocalAlgebra(D2,D3,D1) +--R if D3 has COMRING and D1 has SubsetCategory(Monoid,D3) and +--R D2 has ALGEBRA(D3) +--R [4] Localize(D2,D3,D1) -> D1 from Localize(D2,D3,D1) +--R if D3 has COMRING and D1 has SubsetCategory(Monoid,D3) and +--R D2 has MODULE(D3) +--R +--RExamples of denom from AlgebraicNumber +--R +--Rt1:=sqrt(3)/sqrt(5) +--Rdenom t1 +--R +--R +--RExamples of denom from FractionalIdeal +--R +--R +--RExamples of denom from FunctionSpace +--R +--R +--RExamples of denom from InnerAlgebraicNumber +--R +--R +--RExamples of denom from LocalAlgebra +--R +--R +--RExamples of denom from Localize +--R +--R +--RExamples of denom from QuotientFieldCategory +--R +--E 650 + +--S 651 of 3320 +)d op denominator +--R +--R +--RThere are 3 exposed functions called denominator : +--R [1] D -> D from D if D has FS(D1) and D1 has ORDSET and D1 has +--R INTDOM +--R [2] MyExpression(D1,D2) -> MyExpression(D1,D2) from MyExpression(D1, +--R D2) +--R if D1: SYMBOL and D2 has Join(Ring,OrderedSet, +--R IntegralDomain) +--R [3] D -> D from D if D has QFCAT(D1) and D1 has INTDOM +--R +--RExamples of denominator from FunctionSpace +--R +--R +--RExamples of denominator from MyExpression +--R +--R +--RExamples of denominator from QuotientFieldCategory +--R +--E 651 + +--S 652 of 3320 +)d op denominators +--R +--R +--RThere is one exposed function called denominators : +--R [1] ContinuedFraction(D2) -> Stream(D2) from ContinuedFraction(D2) +--R if D2 has EUCDOM +--R +--RExamples of denominators from ContinuedFraction +--R +--E 652 + +--S 653 of 3320 +)d op denomLODE +--R +--R +--RThere are 2 unexposed functions called denomLODE : +--R [1] (D2,Fraction(D1)) -> Union(D1,"failed") from PrimitiveRatDE(D4, +--R D1,D2,D5) +--R if D1 has UPOLYC(D4) and D4 has Join(Field, +--R CharacteristicZero,RetractableTo(Fraction(Integer))) and D2 +--R has LODOCAT(D1) and D5 has LODOCAT(FRAC(D1)) +--R [2] (D2,List(Fraction(D1))) -> D1 from PrimitiveRatDE(D4,D1,D2,D5) +--R if D1 has UPOLYC(D4) and D4 has Join(Field, +--R CharacteristicZero,RetractableTo(Fraction(Integer))) and D2 +--R has LODOCAT(D1) and D5 has LODOCAT(FRAC(D1)) +--R +--RExamples of denomLODE from PrimitiveRatDE +--R +--E 653 + +--S 654 of 3320 +)d op denomRicDE +--R +--R +--RThere is one unexposed function called denomRicDE : +--R [1] D2 -> D1 from PrimitiveRatRicDE(D3,D1,D2,D4) +--R if D1 has UPOLYC(D3) and D3 has Join(Field, +--R CharacteristicZero,RetractableTo(Fraction(Integer))) and D2 +--R has LODOCAT(D1) and D4 has LODOCAT(FRAC(D1)) +--R +--RExamples of denomRicDE from PrimitiveRatRicDE +--R +--E 654 + +--S 655 of 3320 +)d op depth +--R +--R +--RThere are 4 exposed functions called depth : +--R [1] ArrayStack(D2) -> NonNegativeInteger from ArrayStack(D2) if D2 +--R has SETCAT +--R [2] Dequeue(D2) -> NonNegativeInteger from Dequeue(D2) if D2 has +--R SETCAT +--R [3] D -> NonNegativeInteger from D if D has SKAGG(D2) and D2 has +--R TYPE +--R [4] Stack(D2) -> NonNegativeInteger from Stack(D2) if D2 has SETCAT +--R +--R +--RThere is one unexposed function called depth : +--R [1] Pattern(D2) -> NonNegativeInteger from Pattern(D2) if D2 has +--R SETCAT +--R +--RExamples of depth from ArrayStack +--R +--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] +--Rdepth a +--R +--R +--RExamples of depth from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rdepth a +--R +--R +--RExamples of depth from Pattern +--R +--R +--RExamples of depth from StackAggregate +--R +--Ra:Stack INT:= stack [1,2,3,4,5] +--Rdepth a +--R +--R +--RExamples of depth from Stack +--R +--Ra:Stack INT:= stack [1,2,3,4,5] +--Rdepth a +--R +--E 655 + +--S 656 of 3320 +)d op dequeue +--R +--R +--RThere are 4 exposed functions called dequeue : +--R [1] List(D2) -> Dequeue(D2) from Dequeue(D2) if D2 has SETCAT +--R [2] -> Dequeue(D1) from Dequeue(D1) if D1 has SETCAT +--R [3] List(D2) -> D from D if D2 has TYPE and D has DQAGG(D2) +--R [4] -> D from D if D has DQAGG(D1) and D1 has TYPE +--R +--RExamples of dequeue from Dequeue +--R +--Ra:Dequeue INT:= dequeue () +--R +--Rg:Dequeue INT:= dequeue [1,2,3,4,5] +--R +--R +--RExamples of dequeue from DequeueAggregate +--R +--E 656 + +--S 657 of 3320 +)d op dequeue! +--R +--R +--RThere are 3 exposed functions called dequeue! : +--R [1] Dequeue(D1) -> D1 from Dequeue(D1) if D1 has SETCAT +--R [2] D -> D1 from D if D has QUAGG(D1) and D1 has TYPE +--R [3] Queue(D1) -> D1 from Queue(D1) if D1 has SETCAT +--R +--RExamples of dequeue! from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rdequeue! a +--Ra +--R +--R +--RExamples of dequeue! from QueueAggregate +--R +--R +--RExamples of dequeue! from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Rdequeue! a +--Ra +--R +--E 657 + +--S 658 of 3320 +)d op deref +--R +--R +--RThere is one unexposed function called deref : +--R [1] Reference(D1) -> D1 from Reference(D1) if D1 has TYPE +--R +--RExamples of deref from Reference +--R +--E 658 + +--S 659 of 3320 +)d op deriv +--R +--R +--RThere is one unexposed function called deriv : +--R [1] Stream(D2) -> Stream(D2) from StreamTaylorSeriesOperations(D2) +--R if D2 has RING +--R +--RExamples of deriv from StreamTaylorSeriesOperations +--R +--E 659 + +--S 660 of 3320 +)d op derivationCoordinates +--R +--R +--RThere is one exposed function called derivationCoordinates : +--R [1] (Vector(D),(D4 -> D4)) -> Matrix(D4) from D +--R if D4 has FIELD and D has MONOGEN(D4,D5) and D4 has +--R COMRING and D5 has UPOLYC(D4) +--R +--RExamples of derivationCoordinates from MonogenicAlgebra +--R +--E 660 + +--S 661 of 3320 +)d op derivative +--R +--R +--RThere are 3 exposed functions called derivative : +--R [1] (BasicOperator,List((List(D3) -> D3))) -> BasicOperator +--R from BasicOperatorFunctions1(D3) if D3 has SETCAT +--R [2] (BasicOperator,(D3 -> D3)) -> BasicOperator +--R from BasicOperatorFunctions1(D3) if D3 has SETCAT +--R [3] BasicOperator -> Union(List((List(D3) -> D3)),"failed") +--R from BasicOperatorFunctions1(D3) if D3 has SETCAT +--R +--RExamples of derivative from BasicOperatorFunctions1 +--R +--E 661 + +--S 662 of 3320 +)d op desingTree +--R +--R +--RThere are 4 exposed functions called desingTree : +--R [1] D6 -> List(D3) +--R from DesingTreePackage(D7,D8,D6,D9,D10,D11,D12,D1,D2,D3,D4 +--R ) +--R if D7 has FIELD and D8: LIST(SYMBOL) and D6 has POLYCAT(D7 +--R ,D9,OVAR(D8)) and D9 has DIRPCAT(#(D8),NNI) and D10 has +--R PRSPCAT(D7) and D11 has LOCPOWC(D7) and D12 has PLACESC(D7, +--R D11) and D1 has DIVCAT(D12) and D2 has INFCLCT(D7,D8,D6,D9, +--R D10,D11,D12,D1,D4) and D4 has BLMETCT and D3 has DSTRCAT(D2 +--R ) +--R [2] -> List(D3) +--R from GeneralPackageForAlgebraicFunctionField(D6,D7,D8,D9, +--R D10,D11,D12,D1,D2,D3,D4) +--R if D6 has FIELD and D7: LIST(SYMBOL) and D8 has POLYCAT(D6 +--R ,D9,OVAR(D7)) and D9 has DIRPCAT(#(D7),NNI) and D10 has +--R PRSPCAT(D6) and D11 has LOCPOWC(D6) and D12 has PLACESC(D6, +--R D11) and D1 has DIVCAT(D12) and D2 has INFCLCT(D6,D7,D8,D9, +--R D10,D11,D12,D1,D4) and D4 has BLMETCT and D3 has DSTRCAT(D2 +--R ) +--R [3] -> List(DesingTree( +--R InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField(D2,D3, +--R D4))) +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D2,D3 +--R ,D4) +--R if D2 has FFIELDC and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R [4] -> List(DesingTree(InfClsPt(D2,D3,D4))) +--R from PackageForAlgebraicFunctionField(D2,D3,D4) +--R if D2 has FIELD and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R +--RExamples of desingTree from DesingTreePackage +--R +--R +--RExamples of desingTree from GeneralPackageForAlgebraicFunctionField +--R +--R +--RExamples of desingTree from PackageForAlgebraicFunctionFieldOverFiniteField +--R +--R +--RExamples of desingTree from PackageForAlgebraicFunctionField +--R +--E 662 + +--S 663 of 3320 +)d op desingTreeAtPoint +--R +--R +--RThere is one exposed function called desingTreeAtPoint : +--R [1] (D5,D6) -> D4 from DesingTreePackage(D7,D8,D6,D9,D5,D10,D11,D1, +--R D2,D4,D3) +--R if D7 has FIELD and D8: LIST(SYMBOL) and D6 has POLYCAT(D7 +--R ,D9,OVAR(D8)) and D9 has DIRPCAT(#(D8),NNI) and D5 has +--R PRSPCAT(D7) and D10 has LOCPOWC(D7) and D11 has PLACESC(D7, +--R D10) and D1 has DIVCAT(D11) and D3 has BLMETCT and D4 has +--R DSTRCAT(D2) and D2 has INFCLCT(D7,D8,D6,D9,D5,D10,D11,D1,D3 +--R ) +--R +--RExamples of desingTreeAtPoint from DesingTreePackage +--R +--E 663 + +--S 664 of 3320 +)d op desingTreeWoFullParam +--R +--R +--RThere are 3 exposed functions called desingTreeWoFullParam : +--R [1] -> List(D3) +--R from GeneralPackageForAlgebraicFunctionField(D6,D7,D8,D9, +--R D10,D11,D12,D1,D2,D3,D4) +--R if D6 has FIELD and D7: LIST(SYMBOL) and D8 has POLYCAT(D6 +--R ,D9,OVAR(D7)) and D9 has DIRPCAT(#(D7),NNI) and D10 has +--R PRSPCAT(D6) and D11 has LOCPOWC(D6) and D12 has PLACESC(D6, +--R D11) and D1 has DIVCAT(D12) and D2 has INFCLCT(D6,D7,D8,D9, +--R D10,D11,D12,D1,D4) and D4 has BLMETCT and D3 has DSTRCAT(D2 +--R ) +--R [2] -> List(DesingTree( +--R InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField(D2,D3, +--R D4))) +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D2,D3 +--R ,D4) +--R if D2 has FFIELDC and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R [3] -> List(DesingTree(InfClsPt(D2,D3,D4))) +--R from PackageForAlgebraicFunctionField(D2,D3,D4) +--R if D2 has FIELD and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R +--RExamples of desingTreeWoFullParam from GeneralPackageForAlgebraicFunctionField +--R +--R +--RExamples of desingTreeWoFullParam from PackageForAlgebraicFunctionFieldOverFiniteField +--R +--R +--RExamples of desingTreeWoFullParam from PackageForAlgebraicFunctionField +--R +--E 664 + +--S 665 of 3320 +)d op destruct +--R +--R +--RThere is one exposed function called destruct : +--R [1] D -> List(D) from D +--R if D2 has SETCAT and D3 has SETCAT and D4 has SETCAT and +--R D5 has SETCAT and D6 has SETCAT and D has SEXCAT(D2,D3,D4, +--R D5,D6) +--R +--RThere is one unexposed function called destruct : +--R [1] PatternMatchResult(D2,D3) -> List(Record(key: Symbol,entry: D3)) +--R from PatternMatchResult(D2,D3) if D2 has SETCAT and D3 +--R has SETCAT +--R +--RExamples of destruct from PatternMatchResult +--R +--R +--RExamples of destruct from SExpressionCategory +--R +--E 665 + +--S 666 of 3320 +)d op determinant +--R +--R +--RThere are 3 exposed functions called determinant : +--R [1] D -> D1 from D +--R if D has MATCAT(D1,D2,D3) and D2 has FLAGG(D1) and D3 has +--R FLAGG(D1) and D1 has commutative(*) and D1 has RING +--R [2] D2 -> D1 from MatrixLinearAlgebraFunctions(D1,D3,D4,D2) +--R if D3 has FLAGG(D1) and D4 has FLAGG(D1) and D1 has +--R COMRING and D2 has MATCAT(D1,D3,D4) +--R [3] D -> D1 from D +--R if D has SMATCAT(D2,D1,D3,D4) and D3 has DIRPCAT(D2,D1) +--R and D4 has DIRPCAT(D2,D1) and D1 has commutative(*) and D1 +--R has RING +--R +--RThere is one unexposed function called determinant : +--R [1] D2 -> D1 from InnerMatrixLinearAlgebraFunctions(D1,D3,D4,D2) +--R if D3 has FLAGG(D1) and D4 has FLAGG(D1) and D1 has FIELD +--R and D2 has MATCAT(D1,D3,D4) +--R +--RExamples of determinant from InnerMatrixLinearAlgebraFunctions +--R +--R +--RExamples of determinant from MatrixCategory +--R +--Rdeterminant matrix [[j**i for i in 0..4] for j in 1..5] +--R +--R +--RExamples of determinant from MatrixLinearAlgebraFunctions +--R +--R +--RExamples of determinant from SquareMatrixCategory +--R +--E 666 + +--S 667 of 3320 +)d op df2ef +--R +--R +--RThere is one exposed function called df2ef : +--R [1] DoubleFloat -> Expression(Float) from ExpertSystemToolsPackage +--R +--R +--RExamples of df2ef from ExpertSystemToolsPackage +--R +--E 667 + +--S 668 of 3320 +)d op df2fi +--R +--R +--RThere is one exposed function called df2fi : +--R [1] DoubleFloat -> Fraction(Integer) from ExpertSystemToolsPackage +--R +--R +--RExamples of df2fi from ExpertSystemToolsPackage +--R +--E 668 + +--S 669 of 3320 +)d op df2mf +--R +--R +--RThere is one exposed function called df2mf : +--R [1] DoubleFloat -> MachineFloat from ExpertSystemToolsPackage +--R +--RExamples of df2mf from ExpertSystemToolsPackage +--R +--E 669 + +--S 670 of 3320 +)d op df2st +--R +--R +--RThere are 3 exposed functions called df2st : +--R [1] DoubleFloat -> String from d01AgentsPackage +--R [2] DoubleFloat -> String from ExpertSystemContinuityPackage +--R [3] DoubleFloat -> String from ExpertSystemToolsPackage +--R +--RExamples of df2st from d01AgentsPackage +--R +--R +--RExamples of df2st from ExpertSystemContinuityPackage +--R +--R +--RExamples of df2st from ExpertSystemToolsPackage +--R +--E 670 + +--S 671 of 3320 +)d op dflist +--R +--R +--RThere is one exposed function called dflist : +--R [1] List(Record(left: Fraction(Integer),right: Fraction(Integer))) +--R -> List(DoubleFloat) +--R from ExpertSystemToolsPackage +--R +--RExamples of dflist from ExpertSystemToolsPackage +--R +--E 671 + +--S 672 of 3320 +)d op dfRange +--R +--R +--RThere is one exposed function called dfRange : +--R [1] Segment(OrderedCompletion(DoubleFloat)) -> Segment( +--R OrderedCompletion(DoubleFloat)) +--R from ExpertSystemToolsPackage +--R +--RExamples of dfRange from ExpertSystemToolsPackage +--R +--E 672 + +--S 673 of 3320 +)d op diag +--R +--R +--RThere is one exposed function called diag : +--R [1] ((D3,D3) -> D4) -> (D3 -> D4) from MappingPackage2(D3,D4) +--R if D3 has SETCAT and D4 has SETCAT +--R +--RExamples of diag from MappingPackage2 +--R +--E 673 + +--S 674 of 3320 +)d op diagonal +--R +--R +--RThere is one exposed function called diagonal : +--R [1] D -> D1 from D +--R if D has SMATCAT(D2,D3,D1,D4) and D3 has RING and D4 has +--R DIRPCAT(D2,D3) and D1 has DIRPCAT(D2,D3) +--R +--RExamples of diagonal from SquareMatrixCategory +--R +--E 674 + +--S 675 of 3320 +)d op diagonal? +--R +--R +--RThere are 2 exposed functions called diagonal? : +--R [1] D -> Boolean from D +--R if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG +--R (D2) and D4 has FLAGG(D2) +--R [2] D -> Boolean from D +--R if D has RMATCAT(D2,D3,D4,D5,D6) and D4 has RING and D5 +--R has DIRPCAT(D3,D4) and D6 has DIRPCAT(D2,D4) +--R +--RExamples of diagonal? from MatrixCategory +--R +--Rdiagonal? matrix [[j**i for i in 0..4] for j in 1..5] +--R +--R +--RExamples of diagonal? from RectangularMatrixCategory +--R +--E 675 + +--S 676 of 3320 +)d op diagonalMatrix +--R +--R +--RThere are 6 exposed functions called diagonalMatrix : +--R [1] (D1,Integer) -> D1 from MatrixManipulation(D3,D4,D5,D1) +--R if D3 has FIELD and D4 has FLAGG(D3) and D5 has FLAGG(D3) +--R and D1 has MATCAT(D3,D4,D5) +--R [2] D1 -> D1 from MatrixManipulation(D2,D3,D4,D1) +--R if D2 has FIELD and D3 has FLAGG(D2) and D4 has FLAGG(D2) +--R and D1 has MATCAT(D2,D3,D4) +--R [3] List(D) -> D from D +--R if D2 has RING and D has MATCAT(D2,D3,D4) and D3 has FLAGG +--R (D2) and D4 has FLAGG(D2) +--R [4] List(D2) -> D from D +--R if D2 has RING and D has MATCAT(D2,D3,D4) and D3 has FLAGG +--R (D2) and D4 has FLAGG(D2) +--R [5] Vector(D2) -> Matrix(D2) from Matrix(D2) if D2 has RING +--R [6] List(D3) -> D from D +--R if D3 has RING and D has SMATCAT(D2,D3,D4,D5) and D4 has +--R DIRPCAT(D2,D3) and D5 has DIRPCAT(D2,D3) +--R +--RExamples of diagonalMatrix from MatrixManipulation +--R +--RM := matrix([[a,b,c],[d,e,f],[g,h,i]]) +--RdiagonalMatrix(M) +--R +--RM := matrix([[a,b,c],[d,e,f],[g,h,i]]) +--RdiagonalMatrix(M, 1) +--RdiagonalMatrix(M, 2) +--RdiagonalMatrix(M, -1) +--R +--R +--RExamples of diagonalMatrix from MatrixCategory +--R +--RdiagonalMatrix [matrix [[1,2],[3,4]], matrix [[4,5],[6,7]]] +--R +--RdiagonalMatrix [1,2,3] +--R +--R +--RExamples of diagonalMatrix from Matrix +--R +--R +--RExamples of diagonalMatrix from SquareMatrixCategory +--R +--E 676 + +--S 677 of 3320 +)d op diagonalProduct +--R +--R +--RThere is one exposed function called diagonalProduct : +--R [1] D -> D1 from D +--R if D has SMATCAT(D2,D1,D3,D4) and D3 has DIRPCAT(D2,D1) +--R and D4 has DIRPCAT(D2,D1) and D1 has RING +--R +--RThere is one unexposed function called diagonalProduct : +--R [1] Matrix(D1) -> D1 from IntegralBasisTools(D1,D3,D4) +--R if D3 has UPOLYC(D1) and D1 has EuclideanDomainwith +--R squareFree : % -> Factored(%)and D4 has FRAMALG(D1, +--R D3) +--R +--RExamples of diagonalProduct from IntegralBasisTools +--R +--R +--RExamples of diagonalProduct from SquareMatrixCategory +--R +--E 677 + +--S 678 of 3320 +)d op diagonals +--R +--R +--RThere is one exposed function called diagonals : +--R [1] (ThreeDimensionalViewport,String) -> Void from +--R ThreeDimensionalViewport +--R +--RExamples of diagonals from ThreeDimensionalViewport +--R +--E 678 + +--S 679 of 3320 +)d op dictionary +--R +--R +--RThere are 2 exposed functions called dictionary : +--R [1] List(D2) -> D from D if D2 has SETCAT and D has DIOPS(D2) +--R [2] -> D from D if D has DIOPS(D1) and D1 has SETCAT +--R +--RExamples of dictionary from DictionaryOperations +--R +--E 679 + +--S 680 of 3320 +)d op diff +--R +--R +--RThere is one unexposed function called diff : +--R [1] Symbol -> (D4 -> D4) from ODEIntegration(D3,D4) +--R if D3 has Join(OrderedSet,EuclideanDomain,RetractableTo( +--R Integer),LinearlyExplicitRingOver(Integer), +--R CharacteristicZero) and D4 has Join( +--R AlgebraicallyClosedFunctionSpace(D3), +--R TranscendentalFunctionCategory,PrimitiveFunctionCategory) +--R +--R +--RExamples of diff from ODEIntegration +--R +--E 680 + +--S 681 of 3320 +)d op DiffAction +--R +--R +--RThere is one exposed function called DiffAction : +--R [1] (NonNegativeInteger,NonNegativeInteger,D3) -> D1 +--R from FractionFreeFastGaussian(D1,D3) +--R if D1 has Join(IntegralDomain,GcdDomain) and D3 has AMR(D1 +--R ,NNI) +--R +--RExamples of DiffAction from FractionFreeFastGaussian +--R +--E 681 + +--S 682 of 3320 +)d op DiffC +--R +--R +--RThere is one exposed function called DiffC : +--R [1] NonNegativeInteger -> List(D3) from FractionFreeFastGaussian(D3, +--R D4) +--R if D3 has Join(IntegralDomain,GcdDomain) and D4 has AMR(D3 +--R ,NNI) +--R +--RExamples of DiffC from FractionFreeFastGaussian +--R +--E 682 + +--S 683 of 3320 +)d op difference +--R +--R +--RThere are 2 exposed functions called difference : +--R [1] (D,D1) -> D from D if D has SETAGG(D1) and D1 has SETCAT +--R [2] (D,D) -> D from D if D has SETAGG(D1) and D1 has SETCAT +--R +--RExamples of difference from SetAggregate +--R +--E 683 + +--S 684 of 3320 +)d op differentialVariables +--R +--R +--RThere is one exposed function called differentialVariables : +--R [1] D -> List(D3) from D +--R if D has DPOLCAT(D2,D3,D4,D5) and D2 has RING and D3 has +--R ORDSET and D4 has DVARCAT(D3) and D5 has OAMONS +--R +--RExamples of differentialVariables from DifferentialPolynomialCategory +--R +--E 684 + +--S 685 of 3320 +)d op differentiate +--R +--R +--RThere are 19 exposed functions called differentiate : +--R [1] (D,(D3 -> D3),NonNegativeInteger) -> D from D +--R if D has DIFEXT(D3) and D3 has RING +--R [2] (D,(D2 -> D2)) -> D from D if D has DIFEXT(D2) and D2 has RING +--R +--R [3] (D,NonNegativeInteger) -> D from D if D has DIFRING +--R [4] D -> D from D if D has DIFRING +--R [5] (D,NonNegativeInteger) -> D from D if D has DVARCAT(D2) and D2 +--R has ORDSET +--R [6] D -> D from D if D has DVARCAT(D1) and D1 has ORDSET +--R [7] (D,(D3 -> D3)) -> D from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC( +--R D2) and D4 has UPOLYC(FRAC(D3)) +--R [8] (FullPartialFractionExpansion(D2,D3),NonNegativeInteger) -> +--R FullPartialFractionExpansion(D2,D3) +--R from FullPartialFractionExpansion(D2,D3) +--R if D2 has Join(Field,CharacteristicZero) and D3 has UPOLYC +--R (D2) +--R [9] FullPartialFractionExpansion(D1,D2) -> +--R FullPartialFractionExpansion(D1,D2) +--R from FullPartialFractionExpansion(D1,D2) +--R if D1 has Join(Field,CharacteristicZero) and D2 has UPOLYC +--R (D1) +--R [10] (GeneralUnivariatePowerSeries(D2,D3,D4),Variable(D3)) -> +--R GeneralUnivariatePowerSeries(D2,D3,D4) +--R from GeneralUnivariatePowerSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has RING and D4: D2 +--R [11] (D,List(D3),List(NonNegativeInteger)) -> D from D +--R if D has PDRING(D3) and D3 has SETCAT +--R [12] (D,D1,NonNegativeInteger) -> D from D if D has PDRING(D1) and +--R D1 has SETCAT +--R [13] (D,List(D2)) -> D from D if D has PDRING(D2) and D2 has SETCAT +--R +--R [14] (D,D1) -> D from D if D has PDRING(D1) and D1 has SETCAT +--R [15] (U32Vector,Integer) -> U32Vector from +--R U32VectorPolynomialOperations +--R [16] (U32Vector,NonNegativeInteger,Integer) -> U32Vector +--R from U32VectorPolynomialOperations +--R [17] (UnivariateFormalPowerSeries(D2),Variable(QUOTE(x))) -> +--R UnivariateFormalPowerSeries(D2) +--R from UnivariateFormalPowerSeries(D2) if D2 has RING +--R [18] (D,(D2 -> D2),D) -> D from D if D has UPOLYC(D2) and D2 has +--R RING +--R [19] (UnivariateTaylorSeriesCZero(D2,D3),Variable(D3)) -> +--R UnivariateTaylorSeriesCZero(D2,D3) +--R from UnivariateTaylorSeriesCZero(D2,D3) if D3: SYMBOL and +--R D2 has RING +--R +--RThere are 9 unexposed functions called differentiate : +--R [1] (IntegrationResult(D1),Symbol) -> D1 from IntegrationResult(D1) +--R if D1 has FIELD and D1 has PDRING(SYMBOL) +--R [2] (IntegrationResult(D1),(D1 -> D1)) -> D1 from IntegrationResult( +--R D1) +--R if D1 has FIELD +--R [3] (OutputForm,NonNegativeInteger) -> OutputForm from OutputForm +--R +--R [4] (SparseUnivariateLaurentSeries(D2,D3,D4),Variable(D3)) -> +--R SparseUnivariateLaurentSeries(D2,D3,D4) +--R from SparseUnivariateLaurentSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has RING and D4: D2 +--R [5] (SparseUnivariatePuiseuxSeries(D2,D3,D4),Variable(D3)) -> +--R SparseUnivariatePuiseuxSeries(D2,D3,D4) +--R from SparseUnivariatePuiseuxSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has RING and D4: D2 +--R [6] (SparseUnivariateTaylorSeries(D2,D3,D4),Variable(D3)) -> +--R SparseUnivariateTaylorSeries(D2,D3,D4) +--R from SparseUnivariateTaylorSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has RING and D4: D2 +--R [7] (UnivariateLaurentSeries(D2,D3,D4),Variable(D3)) -> +--R UnivariateLaurentSeries(D2,D3,D4) +--R from UnivariateLaurentSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has RING and D4: D2 +--R [8] (UnivariatePuiseuxSeries(D2,D3,D4),Variable(D3)) -> +--R UnivariatePuiseuxSeries(D2,D3,D4) +--R from UnivariatePuiseuxSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has RING and D4: D2 +--R [9] (UnivariateTaylorSeries(D2,D3,D4),Variable(D3)) -> +--R UnivariateTaylorSeries(D2,D3,D4) +--R from UnivariateTaylorSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has RING and D4: D2 +--R +--RExamples of differentiate from DifferentialExtension +--R +--R +--RExamples of differentiate from DifferentialRing +--R +--R +--RExamples of differentiate from DifferentialVariableCategory +--R +--R +--RExamples of differentiate from FunctionFieldCategory +--R +--R +--RExamples of differentiate from FullPartialFractionExpansion +--R +--R +--RExamples of differentiate from GeneralUnivariatePowerSeries +--R +--R +--RExamples of differentiate from IntegrationResult +--R +--R +--RExamples of differentiate from OutputForm +--R +--R +--RExamples of differentiate from PartialDifferentialRing +--R +--R +--RExamples of differentiate from U32VectorPolynomialOperations +--R +--R +--RExamples of differentiate from SparseUnivariateLaurentSeries +--R +--R +--RExamples of differentiate from SparseUnivariatePuiseuxSeries +--R +--R +--RExamples of differentiate from SparseUnivariateTaylorSeries +--R +--R +--RExamples of differentiate from UnivariateFormalPowerSeries +--R +--R +--RExamples of differentiate from UnivariateLaurentSeries +--R +--R +--RExamples of differentiate from UnivariatePolynomialCategory +--R +--R +--RExamples of differentiate from UnivariatePuiseuxSeries +--R +--R +--RExamples of differentiate from UnivariateTaylorSeries +--R +--R +--RExamples of differentiate from UnivariateTaylorSeriesCZero +--R +--E 685 + +--S 686 of 3320 +)d op diffHP +--R +--R +--RThere are 12 exposed functions called diffHP : +--R [1] List(GuessOption) -> Record(guessStream: ( +--R UnivariateFormalPowerSeries(AlgebraicNumber) -> Stream( +--R UnivariateFormalPowerSeries(AlgebraicNumber))),degreeStream: +--R Stream(NonNegativeInteger),testStream: ( +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial( +--R AlgebraicNumber)) -> Stream(UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(AlgebraicNumber)))),exprStream: (( +--R Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: (( +--R NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial( +--R AlgebraicNumber)) -> AlgebraicNumber),AF: ((NonNegativeInteger, +--R NonNegativeInteger,UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(AlgebraicNumber))) -> +--R SparseUnivariatePolynomial(AlgebraicNumber)),AX: (( +--R NonNegativeInteger,Symbol,Expression(Integer)) -> Expression( +--R Integer)),C: (NonNegativeInteger -> List(AlgebraicNumber))) +--R from GuessAlgebraicNumber +--R [2] Symbol -> (List(GuessOption) -> Record(guessStream: ( +--R UnivariateFormalPowerSeries(AlgebraicNumber) -> Stream( +--R UnivariateFormalPowerSeries(AlgebraicNumber))),degreeStream: +--R Stream(NonNegativeInteger),testStream: ( +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial( +--R AlgebraicNumber)) -> Stream(UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(AlgebraicNumber)))),exprStream: (( +--R Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: (( +--R NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial( +--R AlgebraicNumber)) -> AlgebraicNumber),AF: ((NonNegativeInteger, +--R NonNegativeInteger,UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(AlgebraicNumber))) -> +--R SparseUnivariatePolynomial(AlgebraicNumber)),AX: (( +--R NonNegativeInteger,Symbol,Expression(Integer)) -> Expression( +--R Integer)),C: (NonNegativeInteger -> List(AlgebraicNumber)))) +--R from GuessAlgebraicNumber if AlgebraicNumber has RETRACT( +--R SYMBOL) +--R [3] List(GuessOption) -> Record(guessStream: ( +--R UnivariateFormalPowerSeries(D3) -> Stream( +--R UnivariateFormalPowerSeries(D3))),degreeStream: Stream( +--R NonNegativeInteger),testStream: (UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(D3)) -> Stream( +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial(D3)))), +--R exprStream: ((Expression(Integer),Symbol) -> Stream(Expression( +--R Integer))),A: ((NonNegativeInteger,NonNegativeInteger, +--R SparseUnivariatePolynomial(D3)) -> D3),AF: ((NonNegativeInteger, +--R NonNegativeInteger,UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(D3))) -> SparseUnivariatePolynomial(D3 +--R )),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> +--R Expression(Integer)),C: (NonNegativeInteger -> List(D3))) +--R from GuessFinite(D3) +--R if D3 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [4] Symbol -> (List(GuessOption) -> Record(guessStream: ( +--R UnivariateFormalPowerSeries(D3) -> Stream( +--R UnivariateFormalPowerSeries(D3))),degreeStream: Stream( +--R NonNegativeInteger),testStream: (UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(D3)) -> Stream( +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial(D3)))), +--R exprStream: ((Expression(Integer),Symbol) -> Stream(Expression( +--R Integer))),A: ((NonNegativeInteger,NonNegativeInteger, +--R SparseUnivariatePolynomial(D3)) -> D3),AF: ((NonNegativeInteger, +--R NonNegativeInteger,UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(D3))) -> SparseUnivariatePolynomial(D3 +--R )),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> +--R Expression(Integer)),C: (NonNegativeInteger -> List(D3)))) +--R from GuessFinite(D3) +--R if D3 has RETRACT(SYMBOL) and D3 has Join( +--R FiniteFieldCategory,ConvertibleTo(Integer)) +--R [5] List(GuessOption) -> Record(guessStream: ( +--R UnivariateFormalPowerSeries(Fraction(Integer)) -> Stream( +--R UnivariateFormalPowerSeries(Fraction(Integer)))),degreeStream: +--R Stream(NonNegativeInteger),testStream: ( +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction( +--R Integer))) -> Stream(UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(Fraction(Integer))))),exprStream: (( +--R Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: (( +--R NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial( +--R Integer)) -> Integer),AF: ((NonNegativeInteger,NonNegativeInteger +--R ,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction( +--R Integer)))) -> SparseUnivariatePolynomial(Fraction(Integer))),AX +--R : ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression( +--R Integer)),C: (NonNegativeInteger -> List(Integer))) +--R from GuessInteger +--R [6] Symbol -> (List(GuessOption) -> Record(guessStream: ( +--R UnivariateFormalPowerSeries(Fraction(Integer)) -> Stream( +--R UnivariateFormalPowerSeries(Fraction(Integer)))),degreeStream: +--R Stream(NonNegativeInteger),testStream: ( +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction( +--R Integer))) -> Stream(UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(Fraction(Integer))))),exprStream: (( +--R Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: (( +--R NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial( +--R Integer)) -> Integer),AF: ((NonNegativeInteger,NonNegativeInteger +--R ,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction( +--R Integer)))) -> SparseUnivariatePolynomial(Fraction(Integer))),AX +--R : ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression( +--R Integer)),C: (NonNegativeInteger -> List(Integer)))) +--R from GuessInteger +--R if Fraction(Integer) has RETRACT(SYMBOL) and Integer has +--R RETRACT(SYMBOL) +--R [7] List(GuessOption) -> Record(guessStream: ( +--R UnivariateFormalPowerSeries(D4) -> Stream( +--R UnivariateFormalPowerSeries(D4))),degreeStream: Stream( +--R NonNegativeInteger),testStream: (UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(D4)) -> Stream( +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial(D4)))), +--R exprStream: ((D6,Symbol) -> Stream(D6)),A: ((NonNegativeInteger, +--R NonNegativeInteger,SparseUnivariatePolynomial(D5)) -> D5),AF: (( +--R NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries +--R (SparseUnivariatePolynomial(D4))) -> SparseUnivariatePolynomial( +--R D4)),AX: ((NonNegativeInteger,Symbol,D6) -> D6),C: ( +--R NonNegativeInteger -> List(D5))) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D7 has Join(OrderedSet,IntegralDomain) and D8: (D7 -> +--R D4) and D4 has FIELD and D5 has GCDDOM and D6 has Join( +--R FunctionSpace(Integer),IntegralDomain,RetractableTo(D7), +--R RetractableTo(Symbol),RetractableTo(Integer), +--R CombinatorialOpsCategory,PartialDifferentialRing(Symbol)) +--R with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Booleanand D9: (D4 -> D6) +--R [8] Symbol -> (List(GuessOption) -> Record(guessStream: ( +--R UnivariateFormalPowerSeries(D4) -> Stream( +--R UnivariateFormalPowerSeries(D4))),degreeStream: Stream( +--R NonNegativeInteger),testStream: (UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(D4)) -> Stream( +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial(D4)))), +--R exprStream: ((D6,Symbol) -> Stream(D6)),A: ((NonNegativeInteger, +--R NonNegativeInteger,SparseUnivariatePolynomial(D5)) -> D5),AF: (( +--R NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries +--R (SparseUnivariatePolynomial(D4))) -> SparseUnivariatePolynomial( +--R D4)),AX: ((NonNegativeInteger,Symbol,D6) -> D6),C: ( +--R NonNegativeInteger -> List(D5)))) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D7 has Join(OrderedSet,IntegralDomain) and D8: (D7 -> +--R D4) and D4 has RETRACT(SYMBOL) and D5 has RETRACT(SYMBOL) +--R and D4 has FIELD and D5 has GCDDOM and D6 has Join( +--R FunctionSpace(Integer),IntegralDomain,RetractableTo(D7), +--R RetractableTo(Symbol),RetractableTo(Integer), +--R CombinatorialOpsCategory,PartialDifferentialRing(Symbol)) +--R with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Booleanand D9: (D4 -> D6) +--R [9] List(GuessOption) -> Record(guessStream: ( +--R UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))) -> +--R Stream(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))) +--R )),degreeStream: Stream(NonNegativeInteger),testStream: ( +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction( +--R Polynomial(Integer)))) -> Stream(UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))), +--R exprStream: ((Expression(Integer),Symbol) -> Stream(Expression( +--R Integer))),A: ((NonNegativeInteger,NonNegativeInteger, +--R SparseUnivariatePolynomial(Polynomial(Integer))) -> Polynomial( +--R Integer)),AF: ((NonNegativeInteger,NonNegativeInteger, +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction( +--R Polynomial(Integer))))) -> SparseUnivariatePolynomial(Fraction( +--R Polynomial(Integer)))),AX: ((NonNegativeInteger,Symbol,Expression +--R (Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List +--R (Polynomial(Integer)))) +--R from GuessPolynomial +--R [10] Symbol -> (List(GuessOption) -> Record(guessStream: ( +--R UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))) -> +--R Stream(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))) +--R )),degreeStream: Stream(NonNegativeInteger),testStream: ( +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction( +--R Polynomial(Integer)))) -> Stream(UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))), +--R exprStream: ((Expression(Integer),Symbol) -> Stream(Expression( +--R Integer))),A: ((NonNegativeInteger,NonNegativeInteger, +--R SparseUnivariatePolynomial(Polynomial(Integer))) -> Polynomial( +--R Integer)),AF: ((NonNegativeInteger,NonNegativeInteger, +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction( +--R Polynomial(Integer))))) -> SparseUnivariatePolynomial(Fraction( +--R Polynomial(Integer)))),AX: ((NonNegativeInteger,Symbol,Expression +--R (Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List +--R (Polynomial(Integer))))) +--R from GuessPolynomial +--R if Fraction(Polynomial(Integer)) has RETRACT(SYMBOL) and +--R Polynomial(Integer) has RETRACT(SYMBOL) +--R [11] List(GuessOption) -> HPSPEC from GuessUnivariatePolynomial(D3) +--R if D3: SYMBOL +--R [12] Symbol -> (List(GuessOption) -> HPSPEC) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R +--RExamples of diffHP from GuessAlgebraicNumber +--R +--R +--RExamples of diffHP from GuessFinite +--R +--R +--RExamples of diffHP from GuessInteger +--R +--R +--RExamples of diffHP from Guess +--R +--R +--RExamples of diffHP from GuessPolynomial +--R +--R +--RExamples of diffHP from GuessUnivariatePolynomial +--R +--E 686 + +--S 687 of 3320 +)d op digamma +--R +--R +--RThere are 3 exposed functions called digamma : +--R [1] DoubleFloat -> DoubleFloat from DoubleFloatSpecialFunctions +--R [2] Complex(DoubleFloat) -> Complex(DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R [3] D -> D from D if D has SPFCAT +--R +--RThere is one unexposed function called digamma : +--R [1] D1 -> D1 from FunctionalSpecialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R +--RExamples of digamma from DoubleFloatSpecialFunctions +--R +--R +--RExamples of digamma from FunctionalSpecialFunction +--R +--R +--RExamples of digamma from SpecialFunctionCategory +--R +--E 687 + +--S 688 of 3320 +)d op digit +--R +--R +--RThere is one exposed function called digit : +--R [1] -> CharacterClass from CharacterClass +--R +--RExamples of digit from CharacterClass +--R +--E 688 + +--S 689 of 3320 done +)d op digit? +--R +--R +--RThere is one exposed function called digit? : +--R [1] Character -> Boolean from Character +--R +--RExamples of digit? from Character +--R +--Rchars := [char "a", char "A", char "X", char "8", char "+"] +--R[digit? c for c in chars] +--R +--E 689 + +--S 690 of 3320 +)d op digits +--R +--R +--RThere are 3 exposed functions called digits : +--R [1] PositiveInteger -> PositiveInteger from D +--R if D has arbitraryPrecision and D has FPS +--R [2] -> PositiveInteger from D if D has FPS +--R [3] D -> Stream(Integer) from D if D has PADICCT(D2) +--R +--RThere are 2 unexposed functions called digits : +--R [1] PositiveInteger -> PositiveInteger from FloatingPointSystem&(D2) +--R if D2 has FPS +--R [2] -> PositiveInteger from FloatingPointSystem&(D2) if D2 has FPS +--R +--R +--RExamples of digits from FloatingPointSystem& +--R +--R +--RExamples of digits from FloatingPointSystem +--R +--R +--RExamples of digits from PAdicIntegerCategory +--R +--E 690 + +--S 691 of 3320 +)d op dihedral +--R +--R +--RThere is one exposed function called dihedral : +--R [1] Integer -> SymmetricPolynomial(Fraction(Integer)) from +--R CycleIndicators +--R +--RExamples of dihedral from CycleIndicators +--R +--E 691 + +--S 692 of 3320 +)d op dihedralGroup +--R +--R +--RThere are 2 exposed functions called dihedralGroup : +--R [1] PositiveInteger -> PermutationGroup(Integer) +--R from PermutationGroupExamples +--R [2] List(Integer) -> PermutationGroup(Integer) from +--R PermutationGroupExamples +--R +--RExamples of dihedralGroup from PermutationGroupExamples +--R +--E 692 + +--S 693 of 3320 +)d op dilog +--R +--R +--RThere is one exposed function called dilog : +--R [1] D -> D from D if D has LFCAT +--R +--RThere is one unexposed function called dilog : +--R [1] D1 -> D1 from LiouvillianFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory, +--R TranscendentalFunctionCategory) +--R +--RExamples of dilog from LiouvillianFunctionCategory +--R +--R +--RExamples of dilog from LiouvillianFunction +--R +--E 693 + +--S 694 of 3320 +)d op dim +--R +--R +--RThere is one exposed function called dim : +--R [1] Color -> Palette from Palette +--R +--RThere is one unexposed function called dim : +--R [1] DeRhamComplex(D2,D3) -> NonNegativeInteger from DeRhamComplex(D2 +--R ,D3) +--R if D2 has Join(Ring,OrderedSet) and D3: LIST(SYMBOL) +--R +--RExamples of dim from DeRhamComplex +--R +--Rder := DeRhamComplex(Integer,[x,y,z]) +--Rf:BOP:=operator('f) +--Rg:BOP:=operator('g) +--Rh:BOP:=operator('h) +--Rsigma:der:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz +--Rdim sigma +--R +--R +--RExamples of dim from Palette +--R +--E 694 + +--S 695 of 3320 +)d op dimension +--R +--R +--RThere are 6 exposed functions called dimension : +--R [1] Cell(D2) -> NonNegativeInteger from Cell(D2) if D2 has RCFIELD +--R +--R [2] -> NonNegativeInteger from FreeNilpotentLie(D2,D3,D4) +--R if D2: NNI and D3: NNI and D4 has COMRING +--R [3] PolynomialIdeals(D2,D3,D4,D5) -> Integer +--R from PolynomialIdeals(D2,D3,D4,D5) +--R if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D5 +--R has POLYCAT(D2,D3,D4) +--R [4] (PolynomialIdeals(D3,D4,D5,D6),List(D5)) -> Integer +--R from PolynomialIdeals(D3,D4,D5,D6) +--R if D5 has ORDSET and D3 has FIELD and D4 has OAMONS and D6 +--R has POLYCAT(D3,D4,D5) +--R [5] D -> PositiveInteger from D if D has PTCAT(D2) and D2 has RING +--R +--R [6] -> CardinalNumber from D if D has VSPACE(D2) and D2 has FIELD +--R +--R +--RThere are 2 unexposed functions called dimension : +--R [1] -> CardinalNumber from DirectProductCategory&(D2,D3,D4) +--R if D3: NNI and D4 has TYPE and D2 has DIRPCAT(D3,D4) +--R [2] -> CardinalNumber from FiniteAlgebraicExtensionField&(D2,D3) +--R if D3 has FIELD and D2 has FAXF(D3) +--R +--RExamples of dimension from Cell +--R +--R +--RExamples of dimension from DirectProductCategory& +--R +--R +--RExamples of dimension from FiniteAlgebraicExtensionField& +--R +--R +--RExamples of dimension from FreeNilpotentLie +--R +--R +--RExamples of dimension from PolynomialIdeals +--R +--R +--RExamples of dimension from PointCategory +--R +--R +--RExamples of dimension from VectorSpace +--R +--E 695 + +--S 696 of 3320 +)d op dimensionOfIrreducibleRepresentation +--R +--R +--RThere is one exposed function called dimensionOfIrreducibleRepresentation : +--R [1] List(Integer) -> NonNegativeInteger from IrrRepSymNatPackage +--R +--RExamples of dimensionOfIrreducibleRepresentation from IrrRepSymNatPackage +--R +--E 696 + +--S 697 of 3320 +)d op dimensions +--R +--R +--RThere is one exposed function called dimensions : +--R [1] (ThreeDimensionalViewport,NonNegativeInteger,NonNegativeInteger, +--R PositiveInteger,PositiveInteger) -> Void +--R from ThreeDimensionalViewport +--R +--RThere is one unexposed function called dimensions : +--R [1] (TwoDimensionalViewport,NonNegativeInteger,NonNegativeInteger, +--R PositiveInteger,PositiveInteger) -> Void +--R from TwoDimensionalViewport +--R +--RExamples of dimensions from TwoDimensionalViewport +--R +--R +--RExamples of dimensions from ThreeDimensionalViewport +--R +--E 697 + +--S 698 of 3320 +)d op dimensionsOf +--R +--R +--RThere are 3 exposed functions called dimensionsOf : +--R [1] FortranType -> List(Polynomial(Integer)) from FortranType +--R [2] (Symbol,Matrix(DoubleFloat)) -> SExpression from +--R NAGLinkSupportPackage +--R [3] (Symbol,Matrix(Integer)) -> SExpression from +--R NAGLinkSupportPackage +--R +--RExamples of dimensionsOf from FortranType +--R +--R +--RExamples of dimensionsOf from NAGLinkSupportPackage +--R +--E 698 + +--S 699 of 3320 +)d op diophantineSystem +--R +--R +--RThere is one exposed function called diophantineSystem : +--R [1] (D2,D3) -> Record(particular: Union(D3,"failed"),basis: List(D3) +--R ) +--R from SmithNormalForm(D4,D5,D3,D2) +--R if D4 has EUCDOM and D5 has FLAGG(D4) and D3 has FLAGG(D4) +--R and D2 has MATCAT(D4,D5,D3) +--R +--RExamples of diophantineSystem from SmithNormalForm +--R +--E 699 + +--S 700 of 3320 +)d op dioSolve +--R +--R +--RThere is one exposed function called dioSolve : +--R [1] Equation(Polynomial(Integer)) -> Record(varOrder: List(Symbol), +--R inhom: Union(List(Vector(NonNegativeInteger)),"failed"),hom: List +--R (Vector(NonNegativeInteger))) +--R from DiophantineSolutionPackage +--R +--RExamples of dioSolve from DiophantineSolutionPackage +--R +--E 700 + +--S 701 of 3320 +)d op direction +--R +--R +--RThere is one unexposed function called direction : +--R [1] String -> Integer from ToolsForSign(D3) if D3 has RING +--R +--RExamples of direction from ToolsForSign +--R +--E 701 + +--S 702 of 3320 +)d op directory +--R +--R +--RThere is one exposed function called directory : +--R [1] D -> String from D if D has FNCAT +--R +--RExamples of directory from FileNameCategory +--R +--E 702 + +--S 703 of 3320 +)d op directProduct +--R +--R +--RThere is one exposed function called directProduct : +--R [1] Vector(D3) -> D from D if D3 has TYPE and D has DIRPCAT(D2,D3) +--R +--R +--RExamples of directProduct from DirectProductCategory +--R +--E 703 + +--S 704 of 3320 +)d op directSum +--R +--R +--RThere is one exposed function called directSum : +--R [1] (D,D) -> D from D if D has LODOCAT(D1) and D1 has RING and D1 +--R has FIELD +--R +--RThere is one unexposed function called directSum : +--R [1] (D1,D1,(D3 -> D3)) -> D1 +--R from LinearOrdinaryDifferentialOperatorsOps(D3,D1) +--R if D3 has FIELD and D1 has LODOCAT(D3) +--R +--RExamples of directSum from LinearOrdinaryDifferentialOperatorCategory +--R +--R +--RExamples of directSum from LinearOrdinaryDifferentialOperatorsOps +--R +--E 704 + +--S 705 of 3320 +)d op discreteLog +--R +--R +--RThere are 2 exposed functions called discreteLog : +--R [1] D -> NonNegativeInteger from D if D has FFIELDC +--R [2] (D,D) -> Union(NonNegativeInteger,"failed") from D if D has FPC +--R +--R +--RExamples of discreteLog from FiniteFieldCategory +--R +--R +--RExamples of discreteLog from FieldOfPrimeCharacteristic +--R +--E 705 + +--S 706 of 3320 +)d op discriminant +--R +--R +--RThere are 4 exposed functions called discriminant : +--R [1] Vector(D) -> D1 from D +--R if D has FINRALG(D1,D3) and D3 has UPOLYC(D1) and D1 has +--R COMRING +--R [2] -> D1 from D if D has FRAMALG(D1,D2) and D2 has UPOLYC(D1) and +--R D1 has COMRING +--R [3] (D,D1) -> D from D +--R if D has POLYCAT(D2,D3,D1) and D2 has RING and D3 has +--R OAMONS and D1 has ORDSET and D2 has COMRING +--R [4] D -> D1 from D if D has UPOLYC(D1) and D1 has RING and D1 has +--R COMRING +--R +--RThere are 4 unexposed functions called discriminant : +--R [1] -> D1 from ComplexCategory&(D2,D1) if D1 has COMRING and D2 +--R has COMPCAT(D1) +--R [2] -> D1 from FramedAlgebra&(D2,D1,D3) +--R if D3 has UPOLYC(D1) and D1 has COMRING and D2 has FRAMALG +--R (D1,D3) +--R [3] -> Integer from NumberFieldIntegralBasis(D2,D3) +--R if D2 has UPOLYC(INT) and D3 has FRAMALG(INT,D2) +--R [4] D2 -> D1 from PseudoRemainderSequence(D1,D2) +--R if D1 has INTDOM and D2 has UPOLYC(D1) +--R +--RExamples of discriminant from ComplexCategory& +--R +--R +--RExamples of discriminant from FiniteRankAlgebra +--R +--R +--RExamples of discriminant from FramedAlgebra& +--R +--R +--RExamples of discriminant from FramedAlgebra +--R +--R +--RExamples of discriminant from NumberFieldIntegralBasis +--R +--R +--RExamples of discriminant from PolynomialCategory +--R +--R +--RExamples of discriminant from PseudoRemainderSequence +--R +--R +--RExamples of discriminant from UnivariatePolynomialCategory +--R +--E 706 + +--S 707 of 3320 +)d op discriminantEuclidean +--R +--R +--RThere is one unexposed function called discriminantEuclidean : +--R [1] D2 -> Record(coef1: D2,coef2: D2,discriminant: D3) +--R from PseudoRemainderSequence(D3,D2) +--R if D3 has INTDOM and D2 has UPOLYC(D3) +--R +--RExamples of discriminantEuclidean from PseudoRemainderSequence +--R +--E 707 + +--S 708 of 3320 +)d op discriminantSet +--R +--R +--RThere is one exposed function called discriminantSet : +--R [1] List(SparseUnivariatePolynomial(Polynomial(D3))) -> List( +--R Polynomial(D3)) +--R from CylindricalAlgebraicDecompositionPackage(D3) if D3 +--R has RCFIELD +--R +--RExamples of discriminantSet from CylindricalAlgebraicDecompositionPackage +--R +--E 708 + +--S 709 of 3320 +)d op display +--R +--R +--RThere are 11 exposed functions called display : +--R [1] (BasicOperator,(OutputForm -> OutputForm)) -> BasicOperator +--R from BasicOperator +--R [2] (BasicOperator,(List(OutputForm) -> OutputForm)) -> +--R BasicOperator +--R from BasicOperator +--R [3] BasicOperator -> Union((List(OutputForm) -> OutputForm),"failed" +--R ) +--R from BasicOperator +--R [4] Database(D2) -> Void from Database(D2) +--R if D2 has OrderedSetwith +--R ?.? : (%,Symbol) -> String +--R display : % -> Void +--R fullDisplay : % -> Void +--R [5] ScriptFormulaFormat -> Void from ScriptFormulaFormat +--R [6] (ScriptFormulaFormat,Integer) -> Void from ScriptFormulaFormat +--R +--R [7] String -> Void from HTMLFormat +--R [8] IndexCard -> Void from IndexCard +--R [9] String -> Void from MathMLFormat +--R [10] TexFormat -> Void from TexFormat +--R [11] (TexFormat,Integer) -> Void from TexFormat +--R +--RExamples of display from BasicOperator +--R +--R +--RExamples of display from Database +--R +--R +--RExamples of display from ScriptFormulaFormat +--R +--R +--RExamples of display from HTMLFormat +--R +--Rdisplay(coerce(sqrt(3+x)::OutputForm)$HTMLFORM)$HTMLFORM +--R +--R +--RExamples of display from IndexCard +--R +--R +--RExamples of display from MathMLFormat +--R +--R +--RExamples of display from TexFormat +--R +--E 709 + +--S 710 of 3320 +)d op displayAsGF +--R +--R +--RThere is one unexposed function called displayAsGF : +--R [1] List(GuessOption) -> Boolean from GuessOptionFunctions0 +--R +--RExamples of displayAsGF from GuessOptionFunctions0 +--R +--E 710 + +--S 711 of 3320 +)d op displayKind +--R +--R +--RThere is one exposed function called displayKind : +--R [1] Symbol -> GuessOption from GuessOption +--R +--RExamples of displayKind from GuessOption +--R +--E 711 + +--S 712 of 3320 +)d op distance +--R +--R +--RThere is one exposed function called distance : +--R [1] (D,D) -> Integer from D if D has RCAGG(D2) and D2 has TYPE +--R +--RExamples of distance from RecursiveAggregate +--R +--E 712 + +--S 713 of 3320 +)d op distdfact +--R +--R +--RThere is one exposed function called distdfact : +--R [1] (D2,Boolean) -> Record(cont: D4,factors: List(Record(irr: D2,pow +--R : Integer))) +--R from DistinctDegreeFactorize(D4,D2) +--R if D4 has FFIELDC and D2 has UPOLYC(D4) +--R +--RExamples of distdfact from DistinctDegreeFactorize +--R +--E 713 + +--S 714 of 3320 +)d op distFact +--R +--R +--RThere is one unexposed function called distFact : +--R [1] (D3,List(SparseUnivariatePolynomial(D3)),Record(contp: D3, +--R factors: List(Record(irr: D1,pow: Integer))),List(D3),List(D8), +--R List(D3)) -> Union(Record(polfac: List(D1),correct: D3,corrfact: +--R List(SparseUnivariatePolynomial(D3))),"failed") +--R from LeadingCoefDetermination(D8,D9,D3,D1) +--R if D8 has ORDSET and D3 has EUCDOM and D1 has POLYCAT(D3, +--R D9,D8) and D9 has OAMONS +--R +--RExamples of distFact from LeadingCoefDetermination +--R +--E 714 + +--S 715 of 3320 +)d op distinguishedCommonRootsOf +--R +--R +--RThere is one exposed function called distinguishedCommonRootsOf : +--R [1] (List(SparseUnivariatePolynomial(D3)),D3) -> Record(zeros: List( +--R D3),extDegree: Integer) +--R from RootsFindingPackage(D3) if D3 has FIELD +--R +--RExamples of distinguishedCommonRootsOf from RootsFindingPackage +--R +--E 715 + +--S 716 of 3320 +)d op distinguishedRootsOf +--R +--R +--RThere are 2 exposed functions called distinguishedRootsOf : +--R [1] (SparseUnivariatePolynomial(D),D) -> List(D) from D if D has +--R PACPERC +--R [2] (SparseUnivariatePolynomial(D3),D3) -> Record(zeros: List(D3), +--R extDegree: Integer) +--R from RootsFindingPackage(D3) if D3 has FIELD +--R +--RExamples of distinguishedRootsOf from PseudoAlgebraicClosureOfPerfectFieldCategory +--R +--R +--RExamples of distinguishedRootsOf from RootsFindingPackage +--R +--E 716 + +--S 717 of 3320 +)d op distribute +--R +--R +--RThere are 2 exposed functions called distribute : +--R [1] (D,D) -> D from D if D has ES +--R [2] D -> D from D if D has ES +--R +--RExamples of distribute from ExpressionSpace +--R +--E 717 + +--S 718 of 3320 +)d op div +--R +--R +--RThere is one unexposed function called div : +--R [1] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R +--RExamples of div from OutputForm +--R +--E 718 + +--S 719 of 3320 +)d op divergence +--R +--R +--RThere is one exposed function called divergence : +--R [1] (D2,D3) -> D1 from MultiVariableCalculusFunctions(D4,D1,D2,D3) +--R if D4 has SETCAT and D1 has PDRING(D4) and D2 has FLAGG(D1 +--R ) and D3 has FiniteLinearAggregate(D4)with +--R finiteAggregate +--R +--RExamples of divergence from MultiVariableCalculusFunctions +--R +--E 719 + +--S 720 of 3320 +)d op divide +--R +--R +--RThere are 2 exposed functions called divide : +--R [1] (D,D) -> Record(quotient: D,remainder: D) from D if D has EUCDOM +--R +--R [2] (NonNegativeInteger,NonNegativeInteger) -> Record(quotient: +--R NonNegativeInteger,remainder: NonNegativeInteger) +--R from NonNegativeInteger +--R +--RThere are 3 unexposed functions called divide : +--R [1] (FreeMonoid(D2),FreeMonoid(D2)) -> Union(Record(lm: FreeMonoid( +--R D2),rm: FreeMonoid(D2)),"failed") +--R from FreeMonoid(D2) if D2 has SETCAT +--R [2] (OrderedFreeMonoid(D2),OrderedFreeMonoid(D2)) -> Union(Record(lm +--R : Union(OrderedFreeMonoid(D2),"failed"),rm: Union( +--R OrderedFreeMonoid(D2),"failed")),"failed") +--R from OrderedFreeMonoid(D2) if D2 has ORDSET +--R [3] (D2,D2) -> Record(quotient: D2,remainder: D2) +--R from PseudoRemainderSequence(D3,D2) +--R if D3 has INTDOM and D2 has UPOLYC(D3) +--R +--RExamples of divide from EuclideanDomain +--R +--R +--RExamples of divide from FreeMonoid +--R +--R +--RExamples of divide from NonNegativeInteger +--R +--R +--RExamples of divide from OrderedFreeMonoid +--R +--Rm1:=(x*y*y*z)$OFMONOID(Symbol) +--Rm2:=(x*y)$OFMONOID(Symbol) +--Rdivide(m1,m2) +--R +--R +--RExamples of divide from PseudoRemainderSequence +--R +--E 720 + +--S 721 of 3320 +)d op divide! +--R +--R +--RThere is one exposed function called divide! : +--R [1] (U32Vector,U32Vector,U32Vector,Integer) -> Void +--R from U32VectorPolynomialOperations +--R +--RExamples of divide! from U32VectorPolynomialOperations +--R +--E 721 + +--S 722 of 3320 +)d op divideExponents +--R +--R +--RThere is one exposed function called divideExponents : +--R [1] (D,NonNegativeInteger) -> Union(D,"failed") from D +--R if D has UPOLYC(D2) and D2 has RING +--R +--RExamples of divideExponents from UnivariatePolynomialCategory +--R +--E 722 + +--S 723 of 3320 +)d op divideIfCan +--R +--R +--RThere is one unexposed function called divideIfCan : +--R [1] (D2,D2) -> Union(Record(quotient: D2,remainder: D2),"failed") +--R from UnivariatePolynomialDivisionPackage(D3,D2) +--R if D3 has INTDOM and D2 has UPOLYC(D3) +--R +--RExamples of divideIfCan from UnivariatePolynomialDivisionPackage +--R +--E 723 + +--S 724 of 3320 +)d op divideIfCan_! +--R +--R divideIfCan_! is not a known function. Axiom will try to list its +--R functions which contain divideIfCan_! in their names. This is the +--R same output you would get by issuing +--R )what operations divideIfCan_! +--R +--R There are no operations containing those patterns +--R +--E 724 + +--S 725 of 3320 +)d op divisor +--R +--R +--RThere are 5 exposed functions called divisor : +--R [1] (D1,D2,D2,D2,D3) -> D from D +--R if D3 has FIELD and D2 has UPOLYC(D3) and D4 has UPOLYC( +--R FRAC(D2)) and D has FDIVCAT(D3,D2,D4,D1) and D1 has FFCAT( +--R D3,D2,D4) +--R [2] (D1,D1,Integer) -> D from D +--R if D1 has FIELD and D3 has UPOLYC(D1) and D4 has UPOLYC( +--R FRAC(D3)) and D has FDIVCAT(D1,D3,D4,D5) and D5 has FFCAT( +--R D1,D3,D4) +--R [3] (D1,D1) -> D from D +--R if D1 has FIELD and D2 has UPOLYC(D1) and D3 has UPOLYC( +--R FRAC(D2)) and D has FDIVCAT(D1,D2,D3,D4) and D4 has FFCAT( +--R D1,D2,D3) +--R [4] D1 -> D from D +--R if D2 has FIELD and D3 has UPOLYC(D2) and D4 has UPOLYC( +--R FRAC(D3)) and D has FDIVCAT(D2,D3,D4,D1) and D1 has FFCAT( +--R D2,D3,D4) +--R [5] FractionalIdeal(D3,Fraction(D3),D4,D5) -> D from D +--R if D3 has UPOLYC(D2) and D4 has UPOLYC(FRAC(D3)) and D5 +--R has FFCAT(D2,D3,D4) and D2 has FIELD and D has FDIVCAT(D2, +--R D3,D4,D5) +--R +--RExamples of divisor from FiniteDivisorCategory +--R +--E 725 + +--S 726 of 3320 +)d op divisorAtDesingTree +--R +--R +--RThere is one exposed function called divisorAtDesingTree : +--R [1] (D5,D6) -> D4 from DesingTreePackage(D7,D8,D5,D9,D10,D11,D1,D4, +--R D2,D6,D3) +--R if D7 has FIELD and D8: LIST(SYMBOL) and D5 has POLYCAT(D7 +--R ,D9,OVAR(D8)) and D9 has DIRPCAT(#(D8),NNI) and D10 has +--R PRSPCAT(D7) and D11 has LOCPOWC(D7) and D1 has PLACESC(D7, +--R D11) and D2 has INFCLCT(D7,D8,D5,D9,D10,D11,D1,D4,D3) and +--R D3 has BLMETCT and D4 has DIVCAT(D1) and D6 has DSTRCAT(D2) +--R +--R +--RExamples of divisorAtDesingTree from DesingTreePackage +--R +--E 726 + +--S 727 of 3320 +)d op divisorCascade +--R +--R +--RThere are 2 unexposed functions called divisorCascade : +--R [1] (D2,D2,Boolean) -> List(Record(factors: List(D2),error: D4)) +--R from ComplexRootFindingPackage(D4,D2) +--R if D4 has Join(Field,OrderedRing) and D2 has UPOLYC( +--R COMPLEX(D4)) +--R [2] (D2,D2) -> List(Record(factors: List(D2),error: D3)) +--R from ComplexRootFindingPackage(D3,D2) +--R if D3 has Join(Field,OrderedRing) and D2 has UPOLYC( +--R COMPLEX(D3)) +--R +--RExamples of divisorCascade from ComplexRootFindingPackage +--R +--E 727 + +--S 728 of 3320 +)d op divisors +--R +--R +--RThere is one exposed function called divisors : +--R [1] Integer -> List(Integer) from IntegerNumberTheoryFunctions +--R +--RExamples of divisors from IntegerNumberTheoryFunctions +--R +--E 728 + +--S 729 of 3320 +)d op divOfPole +--R +--R +--RThere is one exposed function called divOfPole : +--R [1] D -> D from D if D has DIVCAT(D1) and D1 has SETCAT +--R +--RExamples of divOfPole from DivisorCategory +--R +--E 729 + +--S 730 of 3320 +)d op divOfZero +--R +--R +--RThere is one exposed function called divOfZero : +--R [1] D -> D from D if D has DIVCAT(D1) and D1 has SETCAT +--R +--RExamples of divOfZero from DivisorCategory +--R +--E 730 + +--S 731 of 3320 +)d op dmp2rfi +--R +--R +--RThere are 3 unexposed functions called dmp2rfi : +--R [1] D2 -> Fraction(Polynomial(D3)) +--R from ParametricLinearEquations(D3,D4,D5,D2) +--R if D3 has Join(EuclideanDomain,CharacteristicZero) and D4 +--R has Join(OrderedSet,ConvertibleTo(Symbol)) and D5 has +--R OAMONS and D2 has POLYCAT(D3,D5,D4) +--R [2] Matrix(D6) -> Matrix(Fraction(Polynomial(D3))) +--R from ParametricLinearEquations(D3,D4,D5,D6) +--R if D6 has POLYCAT(D3,D5,D4) and D3 has Join( +--R EuclideanDomain,CharacteristicZero) and D4 has Join( +--R OrderedSet,ConvertibleTo(Symbol)) and D5 has OAMONS +--R [3] List(D6) -> List(Fraction(Polynomial(D3))) +--R from ParametricLinearEquations(D3,D4,D5,D6) +--R if D6 has POLYCAT(D3,D5,D4) and D3 has Join( +--R EuclideanDomain,CharacteristicZero) and D4 has Join( +--R OrderedSet,ConvertibleTo(Symbol)) and D5 has OAMONS +--R +--RExamples of dmp2rfi from ParametricLinearEquations +--R +--E 731 + +--S 732 of 3320 +)d op dmpToHdmp +--R +--R +--RThere is one unexposed function called dmpToHdmp : +--R [1] DistributedMultivariatePolynomial(D3,D4) -> +--R HomogeneousDistributedMultivariatePolynomial(D3,D4) +--R from PolToPol(D3,D4) if D3: LIST(SYMBOL) and D4 has RING +--R +--R +--RExamples of dmpToHdmp from PolToPol +--R +--E 732 + +--S 733 of 3320 +)d op dmpToP +--R +--R +--RThere is one unexposed function called dmpToP : +--R [1] DistributedMultivariatePolynomial(D3,D4) -> Polynomial(D4) +--R from PolToPol(D3,D4) if D3: LIST(SYMBOL) and D4 has RING +--R +--R +--RExamples of dmpToP from PolToPol +--R +--E 733 + +--S 734 of 3320 +)d op dn +--R +--R +--RThere is one unexposed function called dn : +--R [1] (D1,D2) -> D1 from EllipticFunctionsUnivariateTaylorSeries(D2,D1 +--R ) +--R if D2 has FIELD and D1 has UTSCAT(D2) +--R +--RExamples of dn from EllipticFunctionsUnivariateTaylorSeries +--R +--E 734 + +--S 735 of 3320 +)d op dom +--R +--R +--RThere is one exposed function called dom : +--R [1] Any -> SExpression from Any +--R +--RExamples of dom from Any +--R +--E 735 + +--S 736 of 3320 +)d op domainOf +--R +--R +--RThere is one exposed function called domainOf : +--R [1] Any -> OutputForm from Any +--R +--RExamples of domainOf from Any +--R +--E 736 + +--S 737 of 3320 +)d op dominantTerm +--R +--R +--RThere is one unexposed function called dominantTerm : +--R [1] UnivariatePuiseuxSeriesWithExponentialSingularity(D2,D3,D4,D5) +--R -> Union(Record(%term: Record(%coef: UnivariatePuiseuxSeries(D3, +--R D4,D5),%expon: ExponentialOfUnivariatePuiseuxSeries(D3,D4,D5), +--R %expTerms: List(Record(k: Fraction(Integer),c: D3))),%type: +--R String),"failed") +--R from UnivariatePuiseuxSeriesWithExponentialSingularity(D2, +--R D3,D4,D5) +--R if D2 has Join(OrderedSet,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer),GcdDomain) and D3 has +--R Join(AlgebraicallyClosedField, +--R TranscendentalFunctionCategory,FunctionSpace(D2)) and D4: +--R SYMBOL and D5: D3 +--R +--RExamples of dominantTerm from UnivariatePuiseuxSeriesWithExponentialSingularity +--R +--E 737 + +--S 738 of 3320 +)d op dot +--R +--R +--RThere are 2 exposed functions called dot : +--R [1] (D,D) -> D1 from D if D has DIRPCAT(D2,D1) and D1 has TYPE and +--R D1 has RING +--R [2] (D,D) -> D1 from D if D has VECTCAT(D1) and D1 has TYPE and D1 +--R has RING +--R +--RThere are 4 unexposed functions called dot : +--R [1] (DeRhamComplex(D3,D4),DeRhamComplex(D3,D4),SquareMatrix(#(D4), +--R Expression(D3))) -> Expression(D3) +--R from DeRhamComplex(D3,D4) +--R if D4: LIST(SYMBOL) and D3 has Join(Ring,OrderedSet) +--R [2] (OutputForm,NonNegativeInteger) -> OutputForm from OutputForm +--R +--R [3] OutputForm -> OutputForm from OutputForm +--R [4] (Point(DoubleFloat),Point(DoubleFloat)) -> DoubleFloat from +--R TubePlotTools +--R +--RExamples of dot from DeRhamComplex +--R +--Rder := DeRhamComplex(Integer,[x,y,z]) +--Rf:BOP:=operator('f) +--Rg:BOP:=operator('g) +--Rh:BOP:=operator('h) +--Rsigma:der:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz +--RG:SquareMatrix(3,Integer):=diagonalMatrix([1,1,1]) +--Rdot(sigma,sigma,G) +--R +--R +--RExamples of dot from DirectProductCategory +--R +--R +--RExamples of dot from OutputForm +--R +--R +--RExamples of dot from TubePlotTools +--R +--R +--RExamples of dot from VectorCategory +--R +--E 738 + +--S 739 of 3320 done +)d op dot2eps +--R +--R +--RThere is one exposed function called dot2eps : +--R [1] String -> Void from Graphviz +--R +--RExamples of dot2eps from Graphviz +--R +--Rdot2eps "NeuralNet" +--R +--E 739 + +--S 740 of 33 done20 +)d op dotview +--R +--R +--RThere is one exposed function called dotview : +--R [1] (String,String) -> Void from Graphviz +--R +--RExamples of dotview from Graphviz +--R +--Rdotview("evince","NeuralNet") -- on Linux +--Rdotview("gv","NeuralNet") -- on MAC +--Rdotview("firefox","NeuralNet") -- most places +--R +--E 740 + +--S 741 of 3320 +)d op double +--R +--R +--RThere is one unexposed function called double : +--R [1] (PositiveInteger,D1) -> D1 from RepeatedDoubling(D1) +--R if D1 has SetCategorywith +--R ?+? : (%,%) -> % +--R +--RExamples of double from RepeatedDoubling +--R +--E 741 + +--S 742 of 3320 +)d op double? +--R +--R +--RThere is one exposed function called double? : +--R [1] FortranScalarType -> Boolean from FortranScalarType +--R +--RExamples of double? from FortranScalarType +--R +--E 742 + +--S 743 of 3320 +)d op doubleComplex? +--R +--R +--RThere is one exposed function called doubleComplex? : +--R [1] FortranScalarType -> Boolean from FortranScalarType +--R +--RExamples of doubleComplex? from FortranScalarType +--R +--E 743 + +--S 744 of 3320 +)d op doubleDisc +--R +--R +--RThere is one unexposed function called doubleDisc : +--R [1] D2 -> Integer from PointsOfFiniteOrderTools(D3,D2) +--R if D3 has UPOLYC(FRAC(INT)) and D2 has UPOLYC(FRAC(D3)) +--R +--R +--RExamples of doubleDisc from PointsOfFiniteOrderTools +--R +--E 744 + +--S 745 of 3320 +)d op doubleFloatFormat +--R +--R +--RThere is one exposed function called doubleFloatFormat : +--R [1] String -> String from DoubleFloat +--R +--RExamples of doubleFloatFormat from DoubleFloat +--R +--E 745 + +--S 746 of 3320 +)d op doubleRank +--R +--R +--RThere is one exposed function called doubleRank : +--R [1] D2 -> NonNegativeInteger from AlgebraPackage(D3,D2) +--R if D3 has INTDOM and D2 has FRNAALG(D3) +--R +--RExamples of doubleRank from AlgebraPackage +--R +--E 746 + +--S 747 of 3320 +)d op doubleResultant +--R +--R +--RThere is one unexposed function called doubleResultant : +--R [1] (D2,(D1 -> D1)) -> D1 from DoubleResultantPackage(D4,D1,D5,D2) +--R if D4 has FIELD and D5 has UPOLYC(FRAC(D1)) and D1 has +--R UPOLYC(D4) and D2 has FFCAT(D4,D1,D5) +--R +--RExamples of doubleResultant from DoubleResultantPackage +--R +--E 747 + +--S 748 of 3320 +)d op doublyTransitive? +--R +--R +--RThere is one exposed function called doublyTransitive? : +--R [1] D2 -> Boolean from AlgFactor(D2) if D2 has UPOLYC(AN) +--R +--RExamples of doublyTransitive? from AlgFactor +--R +--E 748 + +--S 749 of 3320 +)d op draw +--R +--R +--RThere are 31 exposed functions called draw : +--R [1] ((DoubleFloat -> DoubleFloat),Segment(Float),List(DrawOption)) +--R -> TwoDimensionalViewport +--R from TopLevelDrawFunctionsForCompiledFunctions +--R [2] ((DoubleFloat -> DoubleFloat),Segment(Float)) -> +--R TwoDimensionalViewport +--R from TopLevelDrawFunctionsForCompiledFunctions +--R [3] (ParametricPlaneCurve((DoubleFloat -> DoubleFloat)),Segment( +--R Float),List(DrawOption)) -> TwoDimensionalViewport +--R from TopLevelDrawFunctionsForCompiledFunctions +--R [4] (ParametricPlaneCurve((DoubleFloat -> DoubleFloat)),Segment( +--R Float)) -> TwoDimensionalViewport +--R from TopLevelDrawFunctionsForCompiledFunctions +--R [5] (ParametricSpaceCurve((DoubleFloat -> DoubleFloat)),Segment( +--R Float),List(DrawOption)) -> ThreeDimensionalViewport +--R from TopLevelDrawFunctionsForCompiledFunctions +--R [6] (ParametricSpaceCurve((DoubleFloat -> DoubleFloat)),Segment( +--R Float)) -> ThreeDimensionalViewport +--R from TopLevelDrawFunctionsForCompiledFunctions +--R [7] ((DoubleFloat -> Point(DoubleFloat)),Segment(Float),List( +--R DrawOption)) -> ThreeDimensionalViewport +--R from TopLevelDrawFunctionsForCompiledFunctions +--R [8] ((DoubleFloat -> Point(DoubleFloat)),Segment(Float)) -> +--R ThreeDimensionalViewport +--R from TopLevelDrawFunctionsForCompiledFunctions +--R [9] (((DoubleFloat,DoubleFloat) -> DoubleFloat),Segment(Float), +--R Segment(Float),List(DrawOption)) -> ThreeDimensionalViewport +--R from TopLevelDrawFunctionsForCompiledFunctions +--R [10] (((DoubleFloat,DoubleFloat) -> DoubleFloat),Segment(Float), +--R Segment(Float)) -> ThreeDimensionalViewport +--R from TopLevelDrawFunctionsForCompiledFunctions +--R [11] (((DoubleFloat,DoubleFloat) -> Point(DoubleFloat)),Segment( +--R Float),Segment(Float),List(DrawOption)) -> +--R ThreeDimensionalViewport +--R from TopLevelDrawFunctionsForCompiledFunctions +--R [12] (((DoubleFloat,DoubleFloat) -> Point(DoubleFloat)),Segment( +--R Float),Segment(Float)) -> ThreeDimensionalViewport +--R from TopLevelDrawFunctionsForCompiledFunctions +--R [13] (ParametricSurface(((DoubleFloat,DoubleFloat) -> DoubleFloat)), +--R Segment(Float),Segment(Float),List(DrawOption)) -> +--R ThreeDimensionalViewport +--R from TopLevelDrawFunctionsForCompiledFunctions +--R [14] (ParametricSurface(((DoubleFloat,DoubleFloat) -> DoubleFloat)), +--R Segment(Float),Segment(Float)) -> ThreeDimensionalViewport +--R from TopLevelDrawFunctionsForCompiledFunctions +--R [15] (Equation(D6),Symbol,Symbol,List(DrawOption)) -> +--R TwoDimensionalViewport +--R from TopLevelDrawFunctionsForAlgebraicCurves(D5,D6) +--R if D6 has FS(D5) and D5 has Join(IntegralDomain,OrderedSet +--R ,RetractableTo(Integer)) +--R [16] (D2,SegmentBinding(Float),List(DrawOption)) -> +--R TwoDimensionalViewport +--R from TopLevelDrawFunctions(D2) +--R if D2 has Join(ConvertibleTo(InputForm),SetCategory) +--R [17] (D2,SegmentBinding(Float)) -> TwoDimensionalViewport +--R from TopLevelDrawFunctions(D2) +--R if D2 has Join(ConvertibleTo(InputForm),SetCategory) +--R [18] (ParametricPlaneCurve(D5),SegmentBinding(Float),List(DrawOption +--R )) -> TwoDimensionalViewport +--R from TopLevelDrawFunctions(D5) +--R if D5 has Join(ConvertibleTo(InputForm),SetCategory) +--R [19] (ParametricPlaneCurve(D4),SegmentBinding(Float)) -> +--R TwoDimensionalViewport +--R from TopLevelDrawFunctions(D4) +--R if D4 has Join(ConvertibleTo(InputForm),SetCategory) +--R [20] (ParametricSpaceCurve(D5),SegmentBinding(Float),List(DrawOption +--R )) -> ThreeDimensionalViewport +--R from TopLevelDrawFunctions(D5) +--R if D5 has Join(ConvertibleTo(InputForm),SetCategory) +--R [21] (ParametricSpaceCurve(D4),SegmentBinding(Float)) -> +--R ThreeDimensionalViewport +--R from TopLevelDrawFunctions(D4) +--R if D4 has Join(ConvertibleTo(InputForm),SetCategory) +--R [22] (D2,SegmentBinding(Float),SegmentBinding(Float),List(DrawOption +--R )) -> ThreeDimensionalViewport +--R from TopLevelDrawFunctions(D2) +--R if D2 has Join(ConvertibleTo(InputForm),SetCategory) +--R [23] (D2,SegmentBinding(Float),SegmentBinding(Float)) -> +--R ThreeDimensionalViewport +--R from TopLevelDrawFunctions(D2) +--R if D2 has Join(ConvertibleTo(InputForm),SetCategory) +--R [24] (ParametricSurface(D5),SegmentBinding(Float),SegmentBinding( +--R Float),List(DrawOption)) -> ThreeDimensionalViewport +--R from TopLevelDrawFunctions(D5) +--R if D5 has Join(ConvertibleTo(InputForm),SetCategory) +--R [25] (ParametricSurface(D4),SegmentBinding(Float),SegmentBinding( +--R Float)) -> ThreeDimensionalViewport +--R from TopLevelDrawFunctions(D4) +--R if D4 has Join(ConvertibleTo(InputForm),SetCategory) +--R [26] (List(DoubleFloat),List(DoubleFloat)) -> TwoDimensionalViewport +--R from TopLevelDrawFunctionsForPoints +--R [27] (List(DoubleFloat),List(DoubleFloat),List(DrawOption)) -> +--R TwoDimensionalViewport +--R from TopLevelDrawFunctionsForPoints +--R [28] List(Point(DoubleFloat)) -> TwoDimensionalViewport +--R from TopLevelDrawFunctionsForPoints +--R [29] (List(Point(DoubleFloat)),List(DrawOption)) -> +--R TwoDimensionalViewport +--R from TopLevelDrawFunctionsForPoints +--R [30] (List(DoubleFloat),List(DoubleFloat),List(DoubleFloat)) -> +--R ThreeDimensionalViewport +--R from TopLevelDrawFunctionsForPoints +--R [31] (List(DoubleFloat),List(DoubleFloat),List(DoubleFloat),List( +--R DrawOption)) -> ThreeDimensionalViewport +--R from TopLevelDrawFunctionsForPoints +--R +--RExamples of draw from TopLevelDrawFunctionsForCompiledFunctions +--R +--R +--RExamples of draw from TopLevelDrawFunctionsForAlgebraicCurves +--R +--R +--RExamples of draw from TopLevelDrawFunctions +--R +--R +--RExamples of draw from TopLevelDrawFunctionsForPoints +--R +--E 749 + +--S 750 of 3320 +)d op drawComplex +--R +--R +--RThere is one exposed function called drawComplex : +--R [1] ((Complex(DoubleFloat) -> Complex(DoubleFloat)),Segment( +--R DoubleFloat),Segment(DoubleFloat),Boolean) -> +--R ThreeDimensionalViewport +--R from DrawComplex +--R +--RExamples of drawComplex from DrawComplex +--R +--E 750 + +--S 751 of 3320 +)d op drawComplexVectorField +--R +--R +--RThere is one exposed function called drawComplexVectorField : +--R [1] ((Complex(DoubleFloat) -> Complex(DoubleFloat)),Segment( +--R DoubleFloat),Segment(DoubleFloat)) -> ThreeDimensionalViewport +--R from DrawComplex +--R +--RExamples of drawComplexVectorField from DrawComplex +--R +--E 751 + +--S 752 of 3320 +)d op drawCurves +--R +--R +--RThere are 2 unexposed functions called drawCurves : +--R [1] (List(List(Point(DoubleFloat))),Palette,Palette,PositiveInteger, +--R List(DrawOption)) -> TwoDimensionalViewport +--R from ViewportPackage +--R [2] (List(List(Point(DoubleFloat))),List(DrawOption)) -> +--R TwoDimensionalViewport +--R from ViewportPackage +--R +--RExamples of drawCurves from ViewportPackage +--R +--E 752 + +--S 753 of 3320 +)d op drawStyle +--R +--R +--RThere is one exposed function called drawStyle : +--R [1] (ThreeDimensionalViewport,String) -> Void from +--R ThreeDimensionalViewport +--R +--RExamples of drawStyle from ThreeDimensionalViewport +--R +--E 753 + +--S 754 of 3320 +)d op drawToScale +--R +--R +--RThere are 2 exposed functions called drawToScale : +--R [1] -> Boolean from GraphicsDefaults +--R [2] Boolean -> Boolean from GraphicsDefaults +--R +--RExamples of drawToScale from GraphicsDefaults +--R +--E 754 + +--S 755 of 3320 +)d op drift +--R +--R +--RThere is one exposed function called drift : +--R [1] StochasticDifferential(D1) -> StochasticDifferential(D1) +--R from StochasticDifferential(D1) +--R if D1 has Join(OrderedSet,IntegralDomain) +--R +--RExamples of drift from StochasticDifferential +--R +--E 755 + +--S 756 of 3320 +)d op droot +--R +--R +--RThere is one unexposed function called droot : +--R [1] List(D4) -> OutputForm from AlgebraicFunction(D3,D4) +--R if D4 has FS(D3) and D3 has Join(OrderedSet,IntegralDomain +--R ) +--R +--RExamples of droot from AlgebraicFunction +--R +--E 756 + +--S 757 of 3320 +)d op duplicates +--R +--R +--RThere is one exposed function called duplicates : +--R [1] D -> List(Record(entry: D2,count: NonNegativeInteger)) from D +--R if D has MDAGG(D2) and D2 has SETCAT +--R +--RExamples of duplicates from MultiDictionary +--R +--E 757 + +--S 758 of 3320 +)d op duplicates? +--R +--R +--RThere is one unexposed function called duplicates? : +--R [1] ListMultiDictionary(D2) -> Boolean from ListMultiDictionary(D2) +--R if D2 has SETCAT +--R +--RExamples of duplicates? from ListMultiDictionary +--R +--E 758 + +--S 759 of 3320 +)d op e +--R +--R +--RThere is one exposed function called e : +--R [1] PositiveInteger -> CliffordAlgebra(D2,D3,D4) +--R from CliffordAlgebra(D2,D3,D4) +--R if D2: PI and D3 has FIELD and D4: QFORM(D2,D3) +--R +--RExamples of e from CliffordAlgebra +--R +--E 759 + +--S 760 of 3320 +)d op e01baf +--R +--R +--RThere is one exposed function called e01baf : +--R [1] (Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer +--R ,Integer) -> Result +--R from NagInterpolationPackage +--R +--RExamples of e01baf from NagInterpolationPackage +--R +--E 760 + +--S 761 of 3320 +)d op e01bef +--R +--R +--RThere is one exposed function called e01bef : +--R [1] (Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer) -> +--R Result +--R from NagInterpolationPackage +--R +--RExamples of e01bef from NagInterpolationPackage +--R +--E 761 + +--S 762 of 3320 +)d op e01bff +--R +--R +--RThere is one exposed function called e01bff : +--R [1] (Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Integer,Matrix(DoubleFloat),Integer) -> Result +--R from NagInterpolationPackage +--R +--RExamples of e01bff from NagInterpolationPackage +--R +--E 762 + +--S 763 of 3320 +)d op e01bgf +--R +--R +--RThere is one exposed function called e01bgf : +--R [1] (Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Integer,Matrix(DoubleFloat),Integer) -> Result +--R from NagInterpolationPackage +--R +--RExamples of e01bgf from NagInterpolationPackage +--R +--E 763 + +--S 764 of 3320 +)d op e01bhf +--R +--R +--RThere is one exposed function called e01bhf : +--R [1] (Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),DoubleFloat,DoubleFloat,Integer) -> Result +--R from NagInterpolationPackage +--R +--RExamples of e01bhf from NagInterpolationPackage +--R +--E 764 + +--S 765 of 3320 +)d op e01daf +--R +--R +--RThere is one exposed function called e01daf : +--R [1] (Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Integer) -> Result +--R from NagInterpolationPackage +--R +--RExamples of e01daf from NagInterpolationPackage +--R +--E 765 + +--S 766 of 3320 +)d op e01saf +--R +--R +--RThere is one exposed function called e01saf : +--R [1] (Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Integer) -> Result +--R from NagInterpolationPackage +--R +--RExamples of e01saf from NagInterpolationPackage +--R +--E 766 + +--S 767 of 3320 +)d op e01sbf +--R +--R +--RThere is one exposed function called e01sbf : +--R [1] (Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Matrix(Integer),Matrix(DoubleFloat),DoubleFloat, +--R DoubleFloat,Integer) -> Result +--R from NagInterpolationPackage +--R +--RExamples of e01sbf from NagInterpolationPackage +--R +--E 767 + +--S 768 of 3320 +)d op e01sef +--R +--R +--RThere is one exposed function called e01sef : +--R [1] (Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Integer,Integer,DoubleFloat,DoubleFloat,Integer) -> +--R Result +--R from NagInterpolationPackage +--R +--RExamples of e01sef from NagInterpolationPackage +--R +--E 768 + +--S 769 of 3320 +)d op e01sff +--R +--R +--RThere is one exposed function called e01sff : +--R [1] (Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),DoubleFloat,Matrix(DoubleFloat),DoubleFloat, +--R DoubleFloat,Integer) -> Result +--R from NagInterpolationPackage +--R +--RExamples of e01sff from NagInterpolationPackage +--R +--E 769 + +--S 770 of 3320 +)d op e02adf +--R +--R +--RThere is one exposed function called e02adf : +--R [1] (Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat) +--R ,Matrix(DoubleFloat),Integer) -> Result +--R from NagFittingPackage +--R +--RExamples of e02adf from NagFittingPackage +--R +--E 770 + +--S 771 of 3320 +)d op e02aef +--R +--R +--RThere is one exposed function called e02aef : +--R [1] (Integer,Matrix(DoubleFloat),DoubleFloat,Integer) -> Result +--R from NagFittingPackage +--R +--RExamples of e02aef from NagFittingPackage +--R +--E 771 + +--S 772 of 3320 +)d op e02agf +--R +--R +--RThere is one exposed function called e02agf : +--R [1] (Integer,Integer,Integer,DoubleFloat,DoubleFloat,Matrix( +--R DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer, +--R Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Matrix(Integer), +--R Integer,Integer,Integer) -> Result +--R from NagFittingPackage +--R +--RExamples of e02agf from NagFittingPackage +--R +--E 772 + +--S 773 of 3320 +)d op e02ahf +--R +--R +--RThere is one exposed function called e02ahf : +--R [1] (Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Integer, +--R Integer,Integer,Integer,Integer) -> Result +--R from NagFittingPackage +--R +--RExamples of e02ahf from NagFittingPackage +--R +--E 773 + +--S 774 of 3320 +)d op e02ajf +--R +--R +--RThere is one exposed function called e02ajf : +--R [1] (Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Integer, +--R Integer,DoubleFloat,Integer,Integer,Integer) -> Result +--R from NagFittingPackage +--R +--RExamples of e02ajf from NagFittingPackage +--R +--E 774 + +--S 775 of 3320 +)d op e02akf +--R +--R +--RThere is one exposed function called e02akf : +--R [1] (Integer,DoubleFloat,DoubleFloat,Matrix(DoubleFloat),Integer, +--R Integer,DoubleFloat,Integer) -> Result +--R from NagFittingPackage +--R +--RExamples of e02akf from NagFittingPackage +--R +--E 775 + +--S 776 of 3320 +)d op e02baf +--R +--R +--RThere is one exposed function called e02baf : +--R [1] (Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Matrix(DoubleFloat),Integer) -> Result +--R from NagFittingPackage +--R +--RExamples of e02baf from NagFittingPackage +--R +--E 776 + +--S 777 of 3320 +)d op e02bbf +--R +--R +--RThere is one exposed function called e02bbf : +--R [1] (Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat, +--R Integer) -> Result +--R from NagFittingPackage +--R +--RExamples of e02bbf from NagFittingPackage +--R +--E 777 + +--S 778 of 3320 +)d op e02bcf +--R +--R +--RThere is one exposed function called e02bcf : +--R [1] (Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),DoubleFloat, +--R Integer,Integer) -> Result +--R from NagFittingPackage +--R +--RExamples of e02bcf from NagFittingPackage +--R +--E 778 + +--S 779 of 3320 +)d op e02bdf +--R +--R +--RThere is one exposed function called e02bdf : +--R [1] (Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer) -> +--R Result +--R from NagFittingPackage +--R +--RExamples of e02bdf from NagFittingPackage +--R +--E 779 + +--S 780 of 3320 +)d op e02bef +--R +--R +--RThere is one exposed function called e02bef : +--R [1] (String,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),DoubleFloat,Integer,Integer,Integer,Matrix( +--R DoubleFloat),Integer,Matrix(DoubleFloat),Matrix(Integer)) -> +--R Result +--R from NagFittingPackage +--R +--RExamples of e02bef from NagFittingPackage +--R +--E 780 + +--S 781 of 3320 +)d op e02daf +--R +--R +--RThere is one exposed function called e02daf : +--R [1] (Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat) +--R ,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat), +--R Matrix(Integer),Integer,Integer,Integer,DoubleFloat,Matrix( +--R DoubleFloat),Integer) -> Result +--R from NagFittingPackage +--R +--RExamples of e02daf from NagFittingPackage +--R +--E 781 + +--S 782 of 3320 +)d op e02dcf +--R +--R +--RThere is one exposed function called e02dcf : +--R [1] (String,Integer,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat), +--R Matrix(DoubleFloat),DoubleFloat,Integer,Integer,Integer,Integer, +--R Integer,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Matrix(Integer),Integer) -> Result +--R from NagFittingPackage +--R +--RExamples of e02dcf from NagFittingPackage +--R +--E 782 + +--S 783 of 3320 +)d op e02ddf +--R +--R +--RThere is one exposed function called e02ddf : +--R [1] (String,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Matrix(DoubleFloat),DoubleFloat,Integer,Integer, +--R Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Matrix( +--R DoubleFloat),Matrix(DoubleFloat),Integer) -> Result +--R from NagFittingPackage +--R +--RExamples of e02ddf from NagFittingPackage +--R +--E 783 + +--S 784 of 3320 +)d op e02def +--R +--R +--RThere is one exposed function called e02def : +--R [1] (Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat) +--R ,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat), +--R Integer) -> Result +--R from NagFittingPackage +--R +--RExamples of e02def from NagFittingPackage +--R +--E 784 + +--S 785 of 3320 +)d op e02dff +--R +--R +--RThere is one exposed function called e02dff : +--R [1] (Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Integer,Integer,Integer) -> Result +--R from NagFittingPackage +--R +--RExamples of e02dff from NagFittingPackage +--R +--E 785 + +--S 786 of 3320 +)d op e02gaf +--R +--R +--RThere is one exposed function called e02gaf : +--R [1] (Integer,Integer,Integer,DoubleFloat,Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Integer) -> Result +--R from NagFittingPackage +--R +--RExamples of e02gaf from NagFittingPackage +--R +--E 786 + +--S 787 of 3320 +)d op e02zaf +--R +--R +--RThere is one exposed function called e02zaf : +--R [1] (Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer +--R ,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer,Integer,Integer) +--R -> Result +--R from NagFittingPackage +--R +--RExamples of e02zaf from NagFittingPackage +--R +--E 787 + +--S 788 of 3320 +)d op e04dgf +--R +--R +--RThere is one exposed function called e04dgf : +--R [1] (Integer,DoubleFloat,DoubleFloat,Integer,DoubleFloat,Boolean, +--R DoubleFloat,DoubleFloat,Integer,Integer,Integer,Integer,Matrix( +--R DoubleFloat),Integer,Union(fn: FileName,fp: Asp49(OBJFUN))) -> +--R Result +--R from NagOptimisationPackage +--R +--RExamples of e04dgf from NagOptimisationPackage +--R +--E 788 + +--S 789 of 3320 +)d op e04fdf +--R +--R +--RThere is one exposed function called e04fdf : +--R [1] (Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Integer, +--R Union(fn: FileName,fp: Asp50(LSFUN1))) -> Result +--R from NagOptimisationPackage +--R +--RExamples of e04fdf from NagOptimisationPackage +--R +--E 789 + +--S 790 of 3320 +)d op e04gcf +--R +--R +--RThere is one exposed function called e04gcf : +--R [1] (Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Integer, +--R Union(fn: FileName,fp: Asp19(LSFUN2))) -> Result +--R from NagOptimisationPackage +--R +--RExamples of e04gcf from NagOptimisationPackage +--R +--E 790 + +--S 791 of 3320 +)d op e04jaf +--R +--R +--RThere is one exposed function called e04jaf : +--R [1] (Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Matrix(DoubleFloat),Integer,Union(fn: FileName,fp: +--R Asp24(FUNCT1))) -> Result +--R from NagOptimisationPackage +--R +--RExamples of e04jaf from NagOptimisationPackage +--R +--E 791 + +--S 792 of 3320 +)d op e04mbf +--R +--R +--RThere is one exposed function called e04mbf : +--R [1] (Integer,Integer,Integer,Integer,Integer,Integer,Matrix( +--R DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Boolean,Integer,Integer,Matrix(DoubleFloat),Integer) +--R -> Result +--R from NagOptimisationPackage +--R +--RExamples of e04mbf from NagOptimisationPackage +--R +--E 792 + +--S 793 of 3320 +)d op e04naf +--R +--R +--RThere is one exposed function called e04naf : +--R [1] (Integer,Integer,Integer,Integer,Integer,Integer,Integer,Integer +--R ,DoubleFloat,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Boolean,Boolean,Boolean,Integer,Integer,Matrix( +--R DoubleFloat),Matrix(Integer),Integer,Union(fn: FileName,fp: Asp20 +--R (QPHESS))) -> Result +--R from NagOptimisationPackage +--R +--RExamples of e04naf from NagOptimisationPackage +--R +--E 793 + +--S 794 of 3320 +)d op e04ucf +--R +--R +--RThere is one exposed function called e04ucf : +--R [1] (Integer,Integer,Integer,Integer,Integer,Integer,Matrix( +--R DoubleFloat),Matrix(DoubleFloat),Matrix(DoubleFloat),Integer, +--R Integer,Boolean,DoubleFloat,Integer,DoubleFloat,DoubleFloat, +--R Boolean,DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat,Boolean, +--R Integer,Integer,Integer,Integer,Integer,DoubleFloat,DoubleFloat, +--R DoubleFloat,Integer,Integer,Integer,Integer,Integer,Matrix( +--R Integer),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Matrix(DoubleFloat),Integer,Union(fn: FileName,fp: +--R Asp55(CONFUN)),Union(fn: FileName,fp: Asp49(OBJFUN))) -> Result +--R from NagOptimisationPackage +--R +--RExamples of e04ucf from NagOptimisationPackage +--R +--E 794 + +--S 795 of 3320 +)d op e04ycf +--R +--R +--RThere is one exposed function called e04ycf : +--R [1] (Integer,Integer,Integer,DoubleFloat,Matrix(DoubleFloat),Integer +--R ,Matrix(DoubleFloat),Integer) -> Result +--R from NagOptimisationPackage +--R +--RExamples of e04ycf from NagOptimisationPackage +--R +--E 795 + +--S 796 of 3320 +)d op E1 +--R +--R +--RThere is one exposed function called E1 : +--R [1] DoubleFloat -> OnePointCompletion(DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R +--RExamples of E1 from DoubleFloatSpecialFunctions +--R +--E 796 + +--S 797 of 3320 +)d op edf2df +--R +--R +--RThere is one exposed function called edf2df : +--R [1] Expression(DoubleFloat) -> DoubleFloat from +--R ExpertSystemToolsPackage +--R +--RExamples of edf2df from ExpertSystemToolsPackage +--R +--E 797 + +--S 798 of 3320 +)d op edf2ef +--R +--R +--RThere is one exposed function called edf2ef : +--R [1] Expression(DoubleFloat) -> Expression(Float) +--R from ExpertSystemToolsPackage +--R +--RExamples of edf2ef from ExpertSystemToolsPackage +--R +--E 798 + +--S 799 of 3320 +)d op edf2efi +--R +--R +--RThere is one exposed function called edf2efi : +--R [1] Expression(DoubleFloat) -> Expression(Fraction(Integer)) +--R from ExpertSystemToolsPackage +--R +--RExamples of edf2efi from ExpertSystemToolsPackage +--R +--E 799 + +--S 800 of 3320 +)d op edf2fi +--R +--R +--RThere is one exposed function called edf2fi : +--R [1] Expression(DoubleFloat) -> Fraction(Integer) +--R from ExpertSystemToolsPackage +--R +--RExamples of edf2fi from ExpertSystemToolsPackage +--R +--E 800 + +--S 801 of 3320 +)d op ef2edf +--R +--R +--RThere is one exposed function called ef2edf : +--R [1] Expression(Float) -> Expression(DoubleFloat) +--R from ExpertSystemToolsPackage +--R +--RExamples of ef2edf from ExpertSystemToolsPackage +--R +--E 801 + +--S 802 of 3320 +)d op effective? +--R +--R +--RThere is one exposed function called effective? : +--R [1] D -> Boolean from D if D has DIVCAT(D2) and D2 has SETCAT +--R +--RExamples of effective? from DivisorCategory +--R +--E 802 + +--S 803 of 3320 +)d op Ei +--R +--R +--RThere are 2 exposed functions called Ei : +--R [1] OnePointCompletion(DoubleFloat) -> OnePointCompletion( +--R DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R [2] D -> D from D if D has LFCAT +--R +--RThere is one unexposed function called Ei : +--R [1] D1 -> D1 from LiouvillianFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory, +--R TranscendentalFunctionCategory) +--R +--RExamples of Ei from DoubleFloatSpecialFunctions +--R +--R +--RExamples of Ei from LiouvillianFunctionCategory +--R +--R +--RExamples of Ei from LiouvillianFunction +--R +--E 803 + +--S 804 of 3320 +)d op Ei1 +--R +--R +--RThere is one exposed function called Ei1 : +--R [1] OnePointCompletion(DoubleFloat) -> OnePointCompletion( +--R DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R +--RExamples of Ei1 from DoubleFloatSpecialFunctions +--R +--E 804 + +--S 805 of 3320 +)d op Ei2 +--R +--R +--RThere is one exposed function called Ei2 : +--R [1] OnePointCompletion(DoubleFloat) -> OnePointCompletion( +--R DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R +--RExamples of Ei2 from DoubleFloatSpecialFunctions +--R +--E 805 + +--S 806 of 3320 +)d op Ei3 +--R +--R +--RThere is one exposed function called Ei3 : +--R [1] OnePointCompletion(DoubleFloat) -> OnePointCompletion( +--R DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R +--RExamples of Ei3 from DoubleFloatSpecialFunctions +--R +--E 806 + +--S 807 of 3320 +)d op Ei4 +--R +--R +--RThere is one exposed function called Ei4 : +--R [1] OnePointCompletion(DoubleFloat) -> OnePointCompletion( +--R DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R +--RExamples of Ei4 from DoubleFloatSpecialFunctions +--R +--E 807 + +--S 808 of 3320 +)d op Ei5 +--R +--R +--RThere is one exposed function called Ei5 : +--R [1] OnePointCompletion(DoubleFloat) -> OnePointCompletion( +--R DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R +--RExamples of Ei5 from DoubleFloatSpecialFunctions +--R +--E 808 + +--S 809 of 3320 +)d op Ei6 +--R +--R +--RThere is one exposed function called Ei6 : +--R [1] OnePointCompletion(DoubleFloat) -> OnePointCompletion( +--R DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R +--RExamples of Ei6 from DoubleFloatSpecialFunctions +--R +--E 809 + +--S 810 of 3320 +)d op eigenMatrix +--R +--R +--RThere is one exposed function called eigenMatrix : +--R [1] Matrix(Fraction(Polynomial(Integer))) -> Union(Matrix(Expression +--R (Integer)),"failed") +--R from RadicalEigenPackage +--R +--RExamples of eigenMatrix from RadicalEigenPackage +--R +--E 810 + +--S 811 of 3320 +)d op eigenvalues +--R +--R +--RThere is one exposed function called eigenvalues : +--R [1] Matrix(Fraction(Polynomial(D3))) -> List(Union(Fraction( +--R Polynomial(D3)),SuchThat(Symbol,Polynomial(D3)))) +--R from EigenPackage(D3) if D3 has GCDDOM +--R +--RExamples of eigenvalues from EigenPackage +--R +--E 811 + +--S 812 of 3320 +)d op eigenvector +--R +--R +--RThere is one exposed function called eigenvector : +--R [1] (Union(Fraction(Polynomial(D4)),SuchThat(Symbol,Polynomial(D4))) +--R ,Matrix(Fraction(Polynomial(D4)))) -> List(Matrix(Fraction( +--R Polynomial(D4)))) +--R from EigenPackage(D4) if D4 has GCDDOM +--R +--RExamples of eigenvector from EigenPackage +--R +--E 812 + +--S 813 of 3320 +)d op eigenvectors +--R +--R +--RThere is one exposed function called eigenvectors : +--R [1] Matrix(Fraction(Polynomial(D3))) -> List(Record(eigval: Union( +--R Fraction(Polynomial(D3)),SuchThat(Symbol,Polynomial(D3))),eigmult +--R : NonNegativeInteger,eigvec: List(Matrix(Fraction(Polynomial(D3)) +--R )))) +--R from EigenPackage(D3) if D3 has GCDDOM +--R +--RExamples of eigenvectors from EigenPackage +--R +--E 813 + +--S 814 of 3320 +)d op eisensteinIrreducible? +--R +--R +--RThere is one unexposed function called eisensteinIrreducible? : +--R [1] D2 -> Boolean from GaloisGroupFactorizer(D2) if D2 has UPOLYC( +--R INT) +--R +--RExamples of eisensteinIrreducible? from GaloisGroupFactorizer +--R +--E 814 + +--S 815 of 3320 +)d op elColumn2! +--R +--R +--RThere is one exposed function called elColumn2! : +--R [1] (D1,D2,Integer,Integer) -> D1 +--R from MatrixLinearAlgebraFunctions(D2,D4,D5,D1) +--R if D2 has COMRING and D4 has FLAGG(D2) and D5 has FLAGG(D2 +--R ) and D1 has MATCAT(D2,D4,D5) +--R +--RExamples of elColumn2! from MatrixLinearAlgebraFunctions +--R +--E 815 + +--S 816 of 3320 +)d op elem? +--R +--R +--RThere is one unexposed function called elem? : +--R [1] IntegrationResult(D2) -> Boolean from IntegrationResult(D2) if +--R D2 has FIELD +--R +--RExamples of elem? from IntegrationResult +--R +--E 816 + +--S 817 of 33 done20 +)d op element +--R +--R +--RThere is one exposed function called element : +--R [1] (D1,PositiveInteger,PositiveInteger) -> D1 +--R from MatrixManipulation(D3,D4,D5,D1) +--R if D3 has FIELD and D4 has FLAGG(D3) and D5 has FLAGG(D3) +--R and D1 has MATCAT(D3,D4,D5) +--R +--RExamples of element from MatrixManipulation +--R +--RM := matrix([[a,b,c],[d,e,f],[g,h,i]]) +--Relement(M,2,2) +--R +--E 817 + +--S 818 of 3320 +)d op element? +--R +--R +--RThere is one exposed function called element? : +--R [1] (D2,PolynomialIdeals(D3,D4,D5,D2)) -> Boolean +--R from PolynomialIdeals(D3,D4,D5,D2) +--R if D3 has FIELD and D4 has OAMONS and D5 has ORDSET and D2 +--R has POLYCAT(D3,D4,D5) +--R +--RExamples of element? from PolynomialIdeals +--R +--E 818 + +--S 819 of 3320 +)d op elementary +--R +--R +--RThere is one exposed function called elementary : +--R [1] Integer -> SymmetricPolynomial(Fraction(Integer)) from +--R CycleIndicators +--R +--RExamples of elementary from CycleIndicators +--R +--E 819 + +--S 820 of 3320 +)d op elements +--R +--R +--RThere is one unexposed function called elements : +--R [1] SetOfMIntegersInOneToN(D2,D3) -> List(PositiveInteger) +--R from SetOfMIntegersInOneToN(D2,D3) if D2: PI and D3: PI +--R +--R +--RExamples of elements from SetOfMIntegersInOneToN +--R +--E 820 + +--S 821 of 3320 +)d op elimZeroCols! +--R +--R +--RThere is one exposed function called elimZeroCols! : +--R [1] SparseEchelonMatrix(D2,D3) -> Void from SparseEchelonMatrix(D2, +--R D3) +--R if D2 has ORDSET and D3 has RING +--R +--RExamples of elimZeroCols! from SparseEchelonMatrix +--R +--E 821 + +--S 822 of 3320 +)d op elliptic +--R +--R +--RThere are 2 exposed functions called elliptic : +--R [1] D2 -> (Point(D2) -> Point(D2)) from CoordinateSystems(D2) +--R if D2 has Join(Field,TranscendentalFunctionCategory, +--R RadicalCategory) +--R [2] -> Union(D1,"failed") from D +--R if D has FFCAT(D2,D1,D3) and D2 has UFD and D3 has UPOLYC( +--R FRAC(D1)) and D1 has UPOLYC(D2) +--R +--RThere is one unexposed function called elliptic : +--R [1] -> Union(D1,"failed") from FunctionFieldCategory&(D2,D3,D1,D4) +--R if D3 has UFD and D4 has UPOLYC(FRAC(D1)) and D1 has +--R UPOLYC(D3) and D2 has FFCAT(D3,D1,D4) +--R +--RExamples of elliptic from CoordinateSystems +--R +--R +--RExamples of elliptic from FunctionFieldCategory& +--R +--R +--RExamples of elliptic from FunctionFieldCategory +--R +--E 822 + +--S 823 of 3320 +)d op elliptic? +--R +--R +--RThere is one exposed function called elliptic? : +--R [1] Record(pde: List(Expression(DoubleFloat)),constraints: List( +--R Record(start: DoubleFloat,finish: DoubleFloat,grid: +--R NonNegativeInteger,boundaryType: Integer,dStart: Matrix( +--R DoubleFloat),dFinish: Matrix(DoubleFloat))),f: List(List( +--R Expression(DoubleFloat))),st: String,tol: DoubleFloat) -> Boolean +--R from d03AgentsPackage +--R +--RExamples of elliptic? from d03AgentsPackage +--R +--E 823 + +--S 824 of 3320 +)d op ellipticCylindrical +--R +--R +--RThere is one exposed function called ellipticCylindrical : +--R [1] D2 -> (Point(D2) -> Point(D2)) from CoordinateSystems(D2) +--R if D2 has Join(Field,TranscendentalFunctionCategory, +--R RadicalCategory) +--R +--RExamples of ellipticCylindrical from CoordinateSystems +--R +--E 824 + +--S 825 of 3320 +)d op elRow1! +--R +--R +--RThere is one exposed function called elRow1! : +--R [1] (D1,Integer,Integer) -> D1 from MatrixLinearAlgebraFunctions(D3, +--R D4,D5,D1) +--R if D3 has COMRING and D4 has FLAGG(D3) and D5 has FLAGG(D3 +--R ) and D1 has MATCAT(D3,D4,D5) +--R +--RExamples of elRow1! from MatrixLinearAlgebraFunctions +--R +--E 825 + +--S 826 of 3320 +)d op elRow2! +--R +--R +--RThere is one exposed function called elRow2! : +--R [1] (D1,D2,Integer,Integer) -> D1 +--R from MatrixLinearAlgebraFunctions(D2,D4,D5,D1) +--R if D2 has COMRING and D4 has FLAGG(D2) and D5 has FLAGG(D2 +--R ) and D1 has MATCAT(D2,D4,D5) +--R +--RExamples of elRow2! from MatrixLinearAlgebraFunctions +--R +--E 826 + +--S 827 of 3320 +)d op elt +--R +--R +--RThere are 51 exposed functions called elt : +--R [1] (D,Integer) -> D1 from D if D has AFSPCAT(D1) and D1 has FIELD +--R +--R [2] (D,Integer,Integer,D1) -> D1 from D +--R if D has ARR2CAT(D1,D3,D4) and D1 has TYPE and D3 has +--R FLAGG(D1) and D4 has FLAGG(D1) +--R [3] (D,Integer,Integer) -> D1 from D +--R if D has ARR2CAT(D1,D3,D4) and D3 has FLAGG(D1) and D4 +--R has FLAGG(D1) and D1 has TYPE +--R [4] (D,right) -> D from D if D has BRAGG(D2) and D2 has TYPE +--R [5] (D,left) -> D from D if D has BRAGG(D2) and D2 has TYPE +--R [6] (CartesianTensor(D3,D4,D1),List(Integer)) -> D1 +--R from CartesianTensor(D3,D4,D1) if D1 has COMRING and D3: +--R INT and D4: NNI +--R [7] (CartesianTensor(D3,D4,D1),Integer,Integer,Integer,Integer) -> +--R D1 +--R from CartesianTensor(D3,D4,D1) if D1 has COMRING and D3: +--R INT and D4: NNI +--R [8] (CartesianTensor(D3,D4,D1),Integer,Integer,Integer) -> D1 +--R from CartesianTensor(D3,D4,D1) if D1 has COMRING and D3: +--R INT and D4: NNI +--R [9] (CartesianTensor(D3,D4,D1),Integer,Integer) -> D1 +--R from CartesianTensor(D3,D4,D1) if D1 has COMRING and D3: +--R INT and D4: NNI +--R [10] (CartesianTensor(D3,D4,D1),Integer) -> D1 from CartesianTensor( +--R D3,D4,D1) +--R if D1 has COMRING and D3: INT and D4: NNI +--R [11] CartesianTensor(D2,D3,D1) -> D1 from CartesianTensor(D2,D3,D1) +--R if D1 has COMRING and D2: INT and D3: NNI +--R [12] (Database(D3),Symbol) -> DataList(String) from Database(D3) +--R if D3 has OrderedSetwith +--R ?.? : (%,Symbol) -> String +--R display : % -> Void +--R fullDisplay : % -> Void +--R [13] (Database(D2),QueryEquation) -> Database(D2) from Database(D2) +--R if D2 has OrderedSetwith +--R ?.? : (%,Symbol) -> String +--R display : % -> Void +--R fullDisplay : % -> Void +--R [14] (DataList(D3),count) -> NonNegativeInteger from DataList(D3) +--R if D3 has ORDSET +--R [15] (DataList(D2),sort) -> DataList(D2) from DataList(D2) if D2 +--R has ORDSET +--R [16] (DataList(D2),unique) -> DataList(D2) from DataList(D2) if D2 +--R has ORDSET +--R [17] (D,D2) -> D1 from D if D has ELTAB(D2,D1) and D2 has SETCAT and +--R D1 has TYPE +--R [18] (D,D2,D1) -> D1 from D +--R if D has ELTAGG(D2,D1) and D2 has SETCAT and D1 has TYPE +--R +--R [19] (BasicOperator,List(D)) -> D from D if D has ES +--R [20] (BasicOperator,D,D,D,D) -> D from D if D has ES +--R [21] (BasicOperator,D,D,D) -> D from D if D has ES +--R [22] (BasicOperator,D,D) -> D from D if D has ES +--R [23] (BasicOperator,D) -> D from D if D has ES +--R [24] (D,D1,D1) -> D1 from D +--R if D has FFCAT(D1,D2,D3) and D1 has UFD and D2 has UPOLYC( +--R D1) and D3 has UPOLYC(FRAC(D2)) +--R [25] (D,Integer) -> D1 from D if D has FRNAALG(D1) and D1 has +--R COMRING +--R [26] (IndexCard,Symbol) -> String from IndexCard +--R [27] (Library,Symbol) -> Any from Library +--R [28] (D,UniversalSegment(Integer)) -> D from D if D has LNAGG(D2) +--R and D2 has TYPE +--R [29] (ThreeDimensionalMatrix(D1),NonNegativeInteger, +--R NonNegativeInteger,NonNegativeInteger) -> D1 +--R from ThreeDimensionalMatrix(D1) if D1 has SETCAT +--R [30] (D,List(Integer),List(Integer)) -> D from D +--R if D has MATCAT(D2,D3,D4) and D2 has RING and D3 has FLAGG +--R (D2) and D4 has FLAGG(D2) +--R [31] (D,D1) -> D1 from D if D has PERMCAT(D1) and D1 has SETCAT +--R [32] (PermutationGroup(D3),NonNegativeInteger) -> Permutation(D3) +--R from PermutationGroup(D3) if D3 has SETCAT +--R [33] (D,Integer) -> D1 from D +--R if D has PLACESC(D1,D3) and D3 has LOCPOWC(D1) and D1 has +--R FIELD +--R [34] (D,Integer) -> D1 from D if D has PRSPCAT(D1) and D1 has FIELD +--R +--R [35] (QuadraticForm(D3,D1),DirectProduct(D3,D1)) -> D1 +--R from QuadraticForm(D3,D1) if D3: PI and D1 has FIELD +--R [36] (D,value) -> D1 from D if D has RCAGG(D1) and D1 has TYPE +--R [37] (D,Integer,Integer,D1) -> D1 from D +--R if D has RMATCAT(D3,D4,D1,D5,D6) and D1 has RING and D5 +--R has DIRPCAT(D4,D1) and D6 has DIRPCAT(D3,D1) +--R [38] (D,Integer,Integer) -> D1 from D +--R if D has RMATCAT(D3,D4,D1,D5,D6) and D5 has DIRPCAT(D4,D1) +--R and D6 has DIRPCAT(D3,D1) and D1 has RING +--R [39] (RewriteRule(D3,D4,D1),D1,PositiveInteger) -> D1 +--R from RewriteRule(D3,D4,D1) +--R if D3 has SETCAT and D4 has Join(Ring,PatternMatchable(D3) +--R ,OrderedSet,ConvertibleTo(Pattern(D3))) and D1 has Join( +--R FunctionSpace(D4),PatternMatchable(D3),ConvertibleTo( +--R Pattern(D3))) +--R [40] (Ruleset(D3,D4,D1),D1,PositiveInteger) -> D1 from Ruleset(D3,D4 +--R ,D1) +--R if D3 has SETCAT and D4 has Join(Ring,PatternMatchable(D3) +--R ,OrderedSet,ConvertibleTo(Pattern(D3))) and D1 has Join( +--R FunctionSpace(D4),PatternMatchable(D3),ConvertibleTo( +--R Pattern(D3))) +--R [41] (SparseEchelonMatrix(D3,D1),Integer,D3) -> D1 +--R from SparseEchelonMatrix(D3,D1) if D1 has RING and D3 has +--R ORDSET +--R [42] (D,List(Integer)) -> D from D +--R if D has SEXCAT(D2,D3,D4,D5,D6) and D2 has SETCAT and D3 +--R has SETCAT and D4 has SETCAT and D5 has SETCAT and D6 has +--R SETCAT +--R [43] (D,Integer) -> D from D +--R if D has SEXCAT(D2,D3,D4,D5,D6) and D2 has SETCAT and D3 +--R has SETCAT and D4 has SETCAT and D5 has SETCAT and D6 has +--R SETCAT +--R [44] (D,D) -> D from D if D has SRAGG +--R [45] (Symbol,List(OutputForm)) -> Symbol from Symbol +--R [46] (Fraction(D),D1) -> D1 from D +--R if D has UPOLYC(D1) and D1 has RING and D1 has FIELD +--R [47] (Fraction(D),Fraction(D)) -> Fraction(D) from D +--R if D has UPOLYC(D2) and D2 has RING and D2 has INTDOM +--R [48] (D,D2) -> D1 from D if D has UPSCAT(D1,D2) and D2 has OAMON and +--R D1 has RING +--R [49] (D,last) -> D1 from D if D has URAGG(D1) and D1 has TYPE +--R [50] (D,rest) -> D from D if D has URAGG(D2) and D2 has TYPE +--R [51] (D,first) -> D1 from D if D has URAGG(D1) and D1 has TYPE +--R +--RThere are 4 unexposed functions called elt : +--R [1] (EuclideanModularRing(D2,D1,D3,D4,D5,D6),D1) -> D1 +--R from EuclideanModularRing(D2,D1,D3,D4,D5,D6) +--R if D2 has COMRING and D1 has UPOLYC(D2) and D3 has ABELMON +--R and D4: ((D1,D3) -> D1) and D5: ((D3,D3) -> Union(D3, +--R "failed")) and D6: ((D1,D1,D3) -> Union(D1,"failed")) +--R [2] (OutputForm,List(OutputForm)) -> OutputForm from OutputForm +--R [3] (BasicOperator,List(Pattern(D3))) -> Pattern(D3) from Pattern(D3 +--R ) +--R if D3 has SETCAT +--R [4] Reference(D1) -> D1 from Reference(D1) if D1 has TYPE +--R +--RExamples of elt from AffineSpaceCategory +--R +--R +--RExamples of elt from TwoDimensionalArrayCategory +--R +--Rarr : ARRAY2 INT := new(5,4,10) +--Relt(arr,1,1,6) +--Relt(arr,1,10,6) +--R +--Rarr : ARRAY2 INT := new(5,4,10) +--Relt(arr,1,1) +--R +--R +--RExamples of elt from BinaryRecursiveAggregate +--R +--R +--RExamples of elt from CartesianTensor +--R +--Rv:=[2,3] +--Rtv:CartesianTensor(1,2,Integer):=v +--Rtm:CartesianTensor(1,2,Integer):=[tv,tv] +--Rtn:CartesianTensor(1,2,Integer):=[tm,tm] +--Rtp:CartesianTensor(1,2,Integer):=[tn,tn] +--Rtq:CartesianTensor(1,2,Integer):=[tp,tp] +--Relt(tq,[2,2,2,2,2]) +--R +--Rv:=[2,3] +--Rtv:CartesianTensor(1,2,Integer):=v +--Rtm:CartesianTensor(1,2,Integer):=[tv,tv] +--Rtn:CartesianTensor(1,2,Integer):=[tm,tm] +--Rtp:CartesianTensor(1,2,Integer):=[tn,tn] +--Relt(tp,2,2,2,2) +--Rtp[2,2,2,2] +--R +--Rv:=[2,3] +--Rtv:CartesianTensor(1,2,Integer):=v +--Rtm:CartesianTensor(1,2,Integer):=[tv,tv] +--Rtn:CartesianTensor(1,2,Integer):=[tm,tm] +--Relt(tn,2,2,2) +--Rtn[2,2,2] +--R +--Rv:=[2,3] +--Rtv:CartesianTensor(1,2,Integer):=v +--Rtm:CartesianTensor(1,2,Integer):=[tv,tv] +--Relt(tm,2,2) +--Rtm[2,2] +--R +--Rv:=[2,3] +--Rtv:CartesianTensor(1,2,Integer):=v +--Relt(tv,2) +--Rtv[2] +--R +--Rtv:CartesianTensor(1,2,Integer):=8 +--Relt(tv) +--Rtv[] +--R +--R +--RExamples of elt from Database +--R +--R +--RExamples of elt from DataList +--R +--R +--RExamples of elt from Eltable +--R +--R +--RExamples of elt from EltableAggregate +--R +--R +--RExamples of elt from EuclideanModularRing +--R +--R +--RExamples of elt from ExpressionSpace +--R +--R +--RExamples of elt from FunctionFieldCategory +--R +--R +--RExamples of elt from FramedNonAssociativeAlgebra +--R +--R +--RExamples of elt from IndexCard +--R +--R +--RExamples of elt from Library +--R +--R +--RExamples of elt from LinearAggregate +--R +--R +--RExamples of elt from ThreeDimensionalMatrix +--R +--R +--RExamples of elt from MatrixCategory +--R +--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] +--Relt(m,3,3) +--R +--R +--RExamples of elt from OutputForm +--R +--R +--RExamples of elt from Pattern +--R +--R +--RExamples of elt from PermutationCategory +--R +--R +--RExamples of elt from PermutationGroup +--R +--R +--RExamples of elt from PlacesCategory +--R +--R +--RExamples of elt from ProjectiveSpaceCategory +--R +--R +--RExamples of elt from QuadraticForm +--R +--R +--RExamples of elt from RecursiveAggregate +--R +--R +--RExamples of elt from Reference +--R +--R +--RExamples of elt from RectangularMatrixCategory +--R +--R +--RExamples of elt from RewriteRule +--R +--R +--RExamples of elt from Ruleset +--R +--R +--RExamples of elt from SparseEchelonMatrix +--R +--R +--RExamples of elt from SExpressionCategory +--R +--R +--RExamples of elt from StringAggregate +--R +--R +--RExamples of elt from Symbol +--R +--Relt(S,[a1,a2]) +--Rs([a1,a2]) +--R +--R +--RExamples of elt from UnivariatePolynomialCategory +--R +--R +--RExamples of elt from UnivariatePowerSeriesCategory +--R +--R +--RExamples of elt from UnaryRecursiveAggregate +--R +--Rt1:=[1,2,3] +--Rt1.last +--R +--Rt1:=[1,2,3] +--Rt1.rest +--R +--Rt1:=[1,2,3] +--Rt1.first +--R +--E 827 + +--S 828 of 3320 +)d op empty +--R +--R +--RThere are 8 exposed functions called empty : +--R [1] -> D from D if D has AGG +--R [2] -> ArrayStack(D1) from ArrayStack(D1) if D1 has SETCAT +--R [3] -> Dequeue(D1) from Dequeue(D1) if D1 has SETCAT +--R [4] -> Heap(D1) from Heap(D1) if D1 has ORDSET +--R [5] -> Queue(D1) from Queue(D1) if D1 has SETCAT +--R [6] -> Stack(D1) from Stack(D1) if D1 has SETCAT +--R [7] -> TheSymbolTable from TheSymbolTable +--R [8] -> SymbolTable from SymbolTable +--R +--RThere are 3 unexposed functions called empty : +--R [1] -> OutputForm from OutputForm +--R [2] -> QuasiAlgebraicSet(D1,D2,D3,D4) from QuasiAlgebraicSet(D1,D2, +--R D3,D4) +--R if D1 has GCDDOM and D2 has ORDSET and D3 has OAMONS and +--R D4 has POLYCAT(D1,D3,D2) +--R [3] -> SplittingNode(D1,D2) from SplittingNode(D1,D2) +--R if D1 has Join(SetCategory,Aggregate) and D2 has Join( +--R SetCategory,Aggregate) +--R +--RExamples of empty from Aggregate +--R +--R +--RExamples of empty from ArrayStack +--R +--Rb:=empty()$(ArrayStack INT) +--R +--R +--RExamples of empty from Dequeue +--R +--Rb:=empty()$(Dequeue INT) +--R +--R +--RExamples of empty from Heap +--R +--Rb:=empty()$(Heap INT) +--R +--R +--RExamples of empty from OutputForm +--R +--R +--RExamples of empty from QuasiAlgebraicSet +--R +--R +--RExamples of empty from Queue +--R +--Rb:=empty()$(Queue INT) +--R +--R +--RExamples of empty from SplittingNode +--R +--R +--RExamples of empty from Stack +--R +--Rb:=empty()$(Stack INT) +--R +--R +--RExamples of empty from TheSymbolTable +--R +--R +--RExamples of empty from SymbolTable +--R +--E 828 + +--S 829 of 3320 +)d op empty? +--R +--R +--RThere are 6 exposed functions called empty? : +--R [1] D -> Boolean from D if D has AGG +--R [2] ArrayStack(D2) -> Boolean from ArrayStack(D2) if D2 has SETCAT +--R +--R [3] Dequeue(D2) -> Boolean from Dequeue(D2) if D2 has SETCAT +--R [4] Heap(D2) -> Boolean from Heap(D2) if D2 has ORDSET +--R [5] Queue(D2) -> Boolean from Queue(D2) if D2 has SETCAT +--R [6] Stack(D2) -> Boolean from Stack(D2) if D2 has SETCAT +--R +--RThere are 2 unexposed functions called empty? : +--R [1] QuasiAlgebraicSet(D2,D3,D4,D5) -> Boolean +--R from QuasiAlgebraicSet(D2,D3,D4,D5) +--R if D2 has GCDDOM and D3 has ORDSET and D4 has OAMONS and +--R D5 has POLYCAT(D2,D4,D3) +--R [2] SplittingNode(D2,D3) -> Boolean from SplittingNode(D2,D3) +--R if D2 has Join(SetCategory,Aggregate) and D3 has Join( +--R SetCategory,Aggregate) +--R +--RExamples of empty? from Aggregate +--R +--R +--RExamples of empty? from ArrayStack +--R +--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] +--Rempty? a +--R +--R +--RExamples of empty? from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rempty? a +--R +--R +--RExamples of empty? from Heap +--R +--Ra:Heap INT:= heap [1,2,3,4,5] +--Rempty? a +--R +--R +--RExamples of empty? from QuasiAlgebraicSet +--R +--R +--RExamples of empty? from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Rempty? a +--R +--R +--RExamples of empty? from SplittingNode +--R +--R +--RExamples of empty? from Stack +--R +--Ra:Stack INT:= stack [1,2,3,4,5] +--Rempty? a +--R +--E 829 + +--S 830 of 3320 +)d op En +--R +--R +--RThere is one exposed function called En : +--R [1] (Integer,DoubleFloat) -> OnePointCompletion(DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R +--RExamples of En from DoubleFloatSpecialFunctions +--R +--E 830 + +--S 831 of 3320 +)d op encode +--R +--R +--RThere is one exposed function called encode : +--R [1] DesingTree(D2) -> String from DesingTree(D2) if D2 has SETCAT +--R +--R +--RExamples of encode from DesingTree +--R +--E 831 + +--S 832 of 3320 +)d op endOfFile? +--R +--R +--RThere is one exposed function called endOfFile? : +--R [1] TextFile -> Boolean from TextFile +--R +--RExamples of endOfFile? from TextFile +--R +--E 832 + +--S 833 of 3320 +)d op endSubProgram +--R +--R +--RThere is one exposed function called endSubProgram : +--R [1] -> Symbol from TheSymbolTable +--R +--RExamples of endSubProgram from TheSymbolTable +--R +--E 833 + +--S 834 of 3320 +)d op enqueue! +--R +--R +--RThere are 3 exposed functions called enqueue! : +--R [1] (D1,Dequeue(D1)) -> D1 from Dequeue(D1) if D1 has SETCAT +--R [2] (D1,D) -> D1 from D if D has QUAGG(D1) and D1 has TYPE +--R [3] (D1,Queue(D1)) -> D1 from Queue(D1) if D1 has SETCAT +--R +--RExamples of enqueue! from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Renqueue! (9,a) +--Ra +--R +--R +--RExamples of enqueue! from QueueAggregate +--R +--R +--RExamples of enqueue! from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Renqueue! (9,a) +--Ra +--R +--E 834 + +--S 835 of 3320 +)d op enterInCache +--R +--R +--RThere are 2 unexposed functions called enterInCache : +--R [1] (D1,(D1 -> Boolean)) -> D1 from SortedCache(D1) if D1 has +--R CACHSET +--R [2] (D1,((D1,D1) -> Integer)) -> D1 from SortedCache(D1) if D1 has +--R CACHSET +--R +--RExamples of enterInCache from SortedCache +--R +--E 835 + +--S 836 of 3320 +)d op enterPointData +--R +--R +--RThere is one exposed function called enterPointData : +--R [1] (D,List(Point(D3))) -> NonNegativeInteger from D +--R if D has SPACEC(D3) and D3 has RING +--R +--RExamples of enterPointData from ThreeSpaceCategory +--R +--E 836 + +--S 837 of 3320 +)d op entries +--R +--R +--RThere are 2 exposed functions called entries : +--R [1] IntegrationFunctionsTable -> List(Record(key: Record(var: Symbol +--R ,fn: Expression(DoubleFloat),range: Segment(OrderedCompletion( +--R DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat),entry: +--R Record(endPointContinuity: Union(continuous: +--R Continuous at the end points,lowerSingular: +--R There is a singularity at the lower end point,upperSingular: +--R There is a singularity at the upper end point,bothSingular: +--R There are singularities at both end points,notEvaluated: +--R End point continuity not yet evaluated),singularitiesStream: +--R Union(str: Stream(DoubleFloat),notEvaluated: +--R Internal singularities not yet evaluated),range: Union(finite: +--R The range is finite,lowerInfinite: +--R The bottom of range is infinite,upperInfinite: +--R The top of range is infinite,bothInfinite: +--R Both top and bottom points are infinite,notEvaluated: +--R Range not yet evaluated)))) +--R from IntegrationFunctionsTable +--R [2] D -> List(D3) from D if D has IXAGG(D2,D3) and D2 has SETCAT and +--R D3 has TYPE +--R +--RExamples of entries from IntegrationFunctionsTable +--R +--R +--RExamples of entries from IndexedAggregate +--R +--E 837 + +--S 838 of 3320 +)d op entry +--R +--R +--RThere is one exposed function called entry : +--R [1] Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment( +--R OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: +--R DoubleFloat) -> Record(endPointContinuity: Union(continuous: +--R Continuous at the end points,lowerSingular: +--R There is a singularity at the lower end point,upperSingular: +--R There is a singularity at the upper end point,bothSingular: +--R There are singularities at both end points,notEvaluated: +--R End point continuity not yet evaluated),singularitiesStream: +--R Union(str: Stream(DoubleFloat),notEvaluated: +--R Internal singularities not yet evaluated),range: Union(finite: +--R The range is finite,lowerInfinite: +--R The bottom of range is infinite,upperInfinite: +--R The top of range is infinite,bothInfinite: +--R Both top and bottom points are infinite,notEvaluated: +--R Range not yet evaluated)) +--R from IntegrationFunctionsTable +--R +--RExamples of entry from IntegrationFunctionsTable +--R +--E 838 + +--S 839 of 3320 +)d op entry? +--R +--R +--RThere is one exposed function called entry? : +--R [1] (D2,D) -> Boolean from D +--R if D has finiteAggregate and D has IXAGG(D3,D2) and D3 +--R has SETCAT and D2 has TYPE and D2 has SETCAT +--R +--RExamples of entry? from IndexedAggregate +--R +--E 839 + +--S 840 of 3320 +)d op enumerate +--R +--R +--RThere is one exposed function called enumerate : +--R [1] -> List(D) from D if D has FINITE +--R +--RThere is one unexposed function called enumerate : +--R [1] -> Vector(SetOfMIntegersInOneToN(D2,D3)) +--R from SetOfMIntegersInOneToN(D2,D3) if D2: PI and D3: PI +--R +--R +--RExamples of enumerate from Finite +--R +--Renumerate()$OrderedVariableList([p,q]) +--R +--R +--RExamples of enumerate from SetOfMIntegersInOneToN +--R +--E 840 + +--S 841 of 3320 +)d op epilogue +--R +--R +--RThere are 2 exposed functions called epilogue : +--R [1] ScriptFormulaFormat -> List(String) from ScriptFormulaFormat +--R [2] TexFormat -> List(String) from TexFormat +--R +--RExamples of epilogue from ScriptFormulaFormat +--R +--R +--RExamples of epilogue from TexFormat +--R +--E 841 + +--S 842 of 3320 +)d op eq +--R +--R +--RThere is one exposed function called eq : +--R [1] (D,D) -> Boolean from D +--R if D has SEXCAT(D2,D3,D4,D5,D6) and D2 has SETCAT and D3 +--R has SETCAT and D4 has SETCAT and D5 has SETCAT and D6 has +--R SETCAT +--R +--RExamples of eq from SExpressionCategory +--R +--E 842 + +--S 843 of 3320 +)d op eq? +--R +--R +--RThere are 6 exposed functions called eq? : +--R [1] (D,D) -> Boolean from D if D has AGG +--R [2] (ArrayStack(D2),ArrayStack(D2)) -> Boolean from ArrayStack(D2) +--R if D2 has SETCAT +--R [3] (Dequeue(D2),Dequeue(D2)) -> Boolean from Dequeue(D2) if D2 has +--R SETCAT +--R [4] (Heap(D2),Heap(D2)) -> Boolean from Heap(D2) if D2 has ORDSET +--R +--R [5] (Queue(D2),Queue(D2)) -> Boolean from Queue(D2) if D2 has SETCAT +--R +--R [6] (Stack(D2),Stack(D2)) -> Boolean from Stack(D2) if D2 has SETCAT +--R +--R +--RExamples of eq? from Aggregate +--R +--R +--RExamples of eq? from ArrayStack +--R +--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] +--Rb:=copy a +--Req?(a,b) +--R +--R +--RExamples of eq? from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rb:=copy a +--Req?(a,b) +--R +--R +--RExamples of eq? from Heap +--R +--Ra:Heap INT:= heap [1,2,3,4,5] +--Rb:=copy a +--Req?(a,b) +--R +--R +--RExamples of eq? from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Rb:=copy a +--Req?(a,b) +--R +--R +--RExamples of eq? from Stack +--R +--Ra:Stack INT:= stack [1,2,3,4,5] +--Rb:=copy a +--Req?(a,b) +--R +--E 843 + +--S 844 of 3320 +)d op EQ +--R +--R +--RThere is one exposed function called EQ : +--R [1] (Union(I: Expression(Integer),F: Expression(Float),CF: +--R Expression(Complex(Float)),switch: Switch),Union(I: Expression( +--R Integer),F: Expression(Float),CF: Expression(Complex(Float)), +--R switch: Switch)) -> Switch +--R from Switch +--R +--RExamples of EQ from Switch +--R +--E 844 + +--S 845 of 3320 +)d op equality +--R +--R +--RThere is one exposed function called equality : +--R [1] (BasicOperator,((BasicOperator,BasicOperator) -> Boolean)) -> +--R BasicOperator +--R from BasicOperator +--R +--RExamples of equality from BasicOperator +--R +--E 845 + +--S 846 of 3320 +)d op equation +--R +--R +--RThere are 5 exposed functions called equation : +--R [1] (D1,D1) -> Equation(D1) from Equation(D1) if D1 has TYPE +--R [2] (Symbol,String) -> QueryEquation from QueryEquation +--R [3] (D2,StochasticDifferential(D2)) -> Union(Equation( +--R StochasticDifferential(D2)),"failed") +--R from StochasticDifferential(D2) +--R if D2 has Join(OrderedSet,IntegralDomain) +--R [4] (StochasticDifferential(D2),D2) -> Union(Equation( +--R StochasticDifferential(D2)),"failed") +--R from StochasticDifferential(D2) +--R if D2 has Join(OrderedSet,IntegralDomain) +--R [5] (Symbol,Segment(D3)) -> SegmentBinding(D3) from SegmentBinding( +--R D3) +--R if D3 has TYPE +--R +--RExamples of equation from Equation +--R +--R +--RExamples of equation from QueryEquation +--R +--R +--RExamples of equation from StochasticDifferential +--R +--R +--RExamples of equation from SegmentBinding +--R +--E 846 + +--S 847 of 3320 +)d op erf +--R +--R +--RThere is one exposed function called erf : +--R [1] D -> D from D if D has LFCAT +--R +--RThere is one unexposed function called erf : +--R [1] D1 -> D1 from LiouvillianFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory, +--R TranscendentalFunctionCategory) +--R +--RExamples of erf from LiouvillianFunctionCategory +--R +--R +--RExamples of erf from LiouvillianFunction +--R +--E 847 + +--S 848 of 3320 +)d op error +--R +--R +--RThere are 4 exposed functions called error : +--R [1] String -> Exit from ErrorFunctions +--R [2] List(String) -> Exit from ErrorFunctions +--R [3] (String,String) -> Exit from ErrorFunctions +--R [4] (String,List(String)) -> Exit from ErrorFunctions +--R +--RExamples of error from ErrorFunctions +--R +--E 848 + +--S 849 of 3320 +)d op errorInfo +--R +--R +--RThere is one exposed function called errorInfo : +--R [1] OpenMathError -> List(Symbol) from OpenMathError +--R +--RExamples of errorInfo from OpenMathError +--R +--E 849 + +--S 850 of 3320 +)d op errorKind +--R +--R +--RThere is one exposed function called errorKind : +--R [1] OpenMathError -> OpenMathErrorKind from OpenMathError +--R +--RExamples of errorKind from OpenMathError +--R +--E 850 + +--S 851 of 33 done20 +)d op escape +--R +--R +--RThere is one exposed function called escape : +--R [1] -> Character from Character +--R +--RExamples of escape from Character +--R +--Rescape() +--R +--E 851 + +--S 852 of 3320 done +)d op euclideanGroebner +--R +--R +--RThere are 3 exposed functions called euclideanGroebner : +--R [1] List(D5) -> List(D5) from EuclideanGroebnerBasisPackage(D2,D3,D4 +--R ,D5) +--R if D5 has POLYCAT(D2,D3,D4) and D2 has EUCDOM and D3 has +--R OAMONS and D4 has ORDSET +--R [2] (List(D6),String) -> List(D6) +--R from EuclideanGroebnerBasisPackage(D3,D4,D5,D6) +--R if D6 has POLYCAT(D3,D4,D5) and D3 has EUCDOM and D4 has +--R OAMONS and D5 has ORDSET +--R [3] (List(D6),String,String) -> List(D6) +--R from EuclideanGroebnerBasisPackage(D3,D4,D5,D6) +--R if D6 has POLYCAT(D3,D4,D5) and D3 has EUCDOM and D4 has +--R OAMONS and D5 has ORDSET +--R +--RExamples of euclideanGroebner from EuclideanGroebnerBasisPackage +--R +--Ra1:DMP([y,x],INT):= (9*x**2 + 5*x - 3)+ y*(3*x**2 + 2*x + 1) +--Ra2:DMP([y,x],INT):= (6*x**3 - 2*x**2 - 3*x +3) + y*(2*x**3 - x - 1) +--Ra3:DMP([y,x],INT):= (3*x**3 + 2*x**2) + y*(x**3 + x**2) +--Ran:=[a1,a2,a3] +--ReuclideanGroebner(an,"info","redcrit") +--R +--Ra1:DMP([y,x],INT):= (9*x**2 + 5*x - 3)+ y*(3*x**2 + 2*x + 1) +--Ra2:DMP([y,x],INT):= (6*x**3 - 2*x**2 - 3*x +3) + y*(2*x**3 - x - 1) +--Ra3:DMP([y,x],INT):= (3*x**3 + 2*x**2) + y*(x**3 + x**2) +--Ran:=[a1,a2,a3] +--ReuclideanGroebner(an,"redcrit") +--ReuclideanGroebner(an,"info") +--R +--Ra1:DMP([y,x],INT):= (9*x**2 + 5*x - 3)+ y*(3*x**2 + 2*x + 1) +--Ra2:DMP([y,x],INT):= (6*x**3 - 2*x**2 - 3*x +3) + y*(2*x**3 - x - 1) +--Ra3:DMP([y,x],INT):= (3*x**3 + 2*x**2) + y*(x**3 + x**2) +--Ran:=[a1,a2,a3] +--ReuclideanGroebner(an) +--R +--E 852 + +--S 853 of 3320 +)d op euclideanNormalForm +--R +--R +--RThere is one exposed function called euclideanNormalForm : +--R [1] (D1,List(D1)) -> D1 from EuclideanGroebnerBasisPackage(D3,D4,D5, +--R D1) +--R if D1 has POLYCAT(D3,D4,D5) and D3 has EUCDOM and D4 has +--R OAMONS and D5 has ORDSET +--R +--RExamples of euclideanNormalForm from EuclideanGroebnerBasisPackage +--R +--E 853 + +--S 854 of 3320 +)d op euclideanSize +--R +--R +--RThere is one exposed function called euclideanSize : +--R [1] D -> NonNegativeInteger from D if D has EUCDOM +--R +--RExamples of euclideanSize from EuclideanDomain +--R +--E 854 + +--S 855 of 3320 +)d op euler +--R +--R +--RThere is one exposed function called euler : +--R [1] Integer -> Integer from IntegerNumberTheoryFunctions +--R +--RThere is one unexposed function called euler : +--R [1] Integer -> SparseUnivariatePolynomial(Fraction(Integer)) +--R from PolynomialNumberTheoryFunctions +--R +--RExamples of euler from IntegerNumberTheoryFunctions +--R +--R +--RExamples of euler from PolynomialNumberTheoryFunctions +--R +--E 855 + +--S 856 of 3320 +)d op eulerE +--R +--R +--RThere is one exposed function called eulerE : +--R [1] (NonNegativeInteger,D1) -> D1 from +--R NumberTheoreticPolynomialFunctions(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has COMRING +--R +--RExamples of eulerE from NumberTheoreticPolynomialFunctions +--R +--E 856 + +--S 857 of 3320 +)d op eulerPhi +--R +--R +--RThere is one exposed function called eulerPhi : +--R [1] Integer -> Integer from IntegerNumberTheoryFunctions +--R +--RExamples of eulerPhi from IntegerNumberTheoryFunctions +--R +--E 857 + +--S 858 of 3320 +)d op eval +--R +--R +--RThere are 43 exposed functions called eval : +--R [1] SymmetricPolynomial(Fraction(Integer)) -> Fraction(Integer) +--R from CycleIndicators +--R [2] (Matrix(Expression(DoubleFloat)),List(Symbol),Vector(Expression( +--R DoubleFloat))) -> Matrix(Expression(DoubleFloat)) +--R from d02AgentsPackage +--R [3] (Equation(D2),List(Equation(D2))) -> Equation(D2) from Equation( +--R D2) +--R if D2 has EVALAB(D2) and D2 has SETCAT and D2 has TYPE +--R [4] (Equation(D1),Equation(D1)) -> Equation(D1) from Equation(D1) +--R if D1 has EVALAB(D1) and D1 has SETCAT and D1 has TYPE +--R [5] (D,BasicOperator,(D -> D)) -> D from D if D has ES +--R [6] (D,BasicOperator,(List(D) -> D)) -> D from D if D has ES +--R [7] (D,List(BasicOperator),List((List(D) -> D))) -> D from D if D +--R has ES +--R [8] (D,List(BasicOperator),List((D -> D))) -> D from D if D has ES +--R +--R [9] (D,Symbol,(D -> D)) -> D from D if D has ES +--R [10] (D,Symbol,(List(D) -> D)) -> D from D if D has ES +--R [11] (D,List(Symbol),List((List(D) -> D))) -> D from D if D has ES +--R +--R [12] (D,List(Symbol),List((D -> D))) -> D from D if D has ES +--R [13] (D,List(Equation(D2))) -> D from D if D has EVALAB(D2) and D2 +--R has SETCAT +--R [14] (D,Equation(D2)) -> D from D if D has EVALAB(D2) and D2 has +--R SETCAT +--R [15] (D,List(D3),List(D)) -> D from D +--R if D has FLALG(D3,D4) and D3 has ORDSET and D4 has COMRING +--R +--R [16] (D,D1,D) -> D from D +--R if D has FLALG(D1,D2) and D1 has ORDSET and D2 has COMRING +--R +--R [17] (D,Symbol,NonNegativeInteger,(D -> D)) -> D from D +--R if D has FS(D4) and D4 has ORDSET and D4 has RING +--R [18] (D,Symbol,NonNegativeInteger,(List(D) -> D)) -> D from D +--R if D has FS(D4) and D4 has ORDSET and D4 has RING +--R [19] (D,List(Symbol),List(NonNegativeInteger),List((List(D) -> D))) +--R -> D +--R from D if D has FS(D4) and D4 has ORDSET and D4 has RING +--R +--R [20] (D,List(Symbol),List(NonNegativeInteger),List((D -> D))) -> D +--R from D +--R if D has FS(D4) and D4 has ORDSET and D4 has RING +--R [21] (D,List(BasicOperator),List(D),Symbol) -> D from D +--R if D has FS(D4) and D4 has ORDSET and D4 has KONVERT( +--R INFORM) +--R [22] (D,BasicOperator,D,Symbol) -> D from D +--R if D has FS(D3) and D3 has ORDSET and D3 has KONVERT( +--R INFORM) +--R [23] D -> D from D if D has FS(D1) and D1 has ORDSET and D1 has +--R KONVERT(INFORM) +--R [24] (D,List(Symbol)) -> D from D +--R if D has FS(D2) and D2 has ORDSET and D2 has KONVERT( +--R INFORM) +--R [25] (D,Symbol) -> D from D +--R if D has FS(D2) and D2 has ORDSET and D2 has KONVERT( +--R INFORM) +--R [26] (D5,D6) -> D4 +--R from GeneralPackageForAlgebraicFunctionField(D4,D7,D5,D8, +--R D9,D10,D6,D11,D1,D2,D3) +--R if D7: LIST(SYMBOL) and D5 has POLYCAT(D4,D8,OVAR(D7)) and +--R D8 has DIRPCAT(#(D7),NNI) and D9 has PRSPCAT(D4) and D10 +--R has LOCPOWC(D4) and D6 has PLACESC(D4,D10) and D11 has +--R DIVCAT(D6) and D1 has INFCLCT(D4,D7,D5,D8,D9,D10,D6,D11,D3) +--R and D3 has BLMETCT and D4 has FIELD and D2 has DSTRCAT(D1) +--R +--R [27] (D5,D5,D6) -> D4 +--R from GeneralPackageForAlgebraicFunctionField(D4,D7,D5,D8, +--R D9,D10,D6,D11,D1,D2,D3) +--R if D7: LIST(SYMBOL) and D5 has POLYCAT(D4,D8,OVAR(D7)) and +--R D8 has DIRPCAT(#(D7),NNI) and D9 has PRSPCAT(D4) and D10 +--R has LOCPOWC(D4) and D6 has PLACESC(D4,D10) and D11 has +--R DIVCAT(D6) and D1 has INFCLCT(D4,D7,D5,D8,D9,D10,D6,D11,D3) +--R and D3 has BLMETCT and D4 has FIELD and D2 has DSTRCAT(D1) +--R +--R [28] (Fraction(D9),D7) -> D5 +--R from GeneralPackageForAlgebraicFunctionField(D5,D8,D9,D10, +--R D11,D12,D7,D1,D2,D3,D4) +--R if D9 has POLYCAT(D5,D10,OVAR(D8)) and D10 has DIRPCAT(#( +--R D8),NNI) and D8: LIST(SYMBOL) and D11 has PRSPCAT(D5) and +--R D12 has LOCPOWC(D5) and D7 has PLACESC(D5,D12) and D1 has +--R DIVCAT(D7) and D2 has INFCLCT(D5,D8,D9,D10,D11,D12,D7,D1,D4 +--R ) and D4 has BLMETCT and D5 has FIELD and D3 has DSTRCAT(D2 +--R ) +--R [29] (D,D1,D2) -> D from D +--R if D has IEVALAB(D1,D2) and D1 has SETCAT and D2 has TYPE +--R +--R [30] (D,List(D3),List(D4)) -> D from D +--R if D has IEVALAB(D3,D4) and D3 has SETCAT and D4 has TYPE +--R +--R [31] (DistributedMultivariatePolynomial(D4,D1), +--R PlacesOverPseudoAlgebraicClosureOfFiniteField(D1)) -> D1 +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D1,D4 +--R ,D5) +--R if D4: LIST(SYMBOL) and D1 has FFIELDC and D5 has BLMETCT +--R +--R [32] (DistributedMultivariatePolynomial(D4,D1), +--R DistributedMultivariatePolynomial(D4,D1), +--R PlacesOverPseudoAlgebraicClosureOfFiniteField(D1)) -> D1 +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D1,D4 +--R ,D5) +--R if D4: LIST(SYMBOL) and D1 has FFIELDC and D5 has BLMETCT +--R +--R [33] (Fraction(DistributedMultivariatePolynomial(D4,D1)), +--R PlacesOverPseudoAlgebraicClosureOfFiniteField(D1)) -> D1 +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D1,D4 +--R ,D5) +--R if D4: LIST(SYMBOL) and D1 has FFIELDC and D5 has BLMETCT +--R +--R [34] (DistributedMultivariatePolynomial(D4,D1),Places(D1)) -> D1 +--R from PackageForAlgebraicFunctionField(D1,D4,D5) +--R if D4: LIST(SYMBOL) and D1 has FIELD and D5 has BLMETCT +--R +--R [35] (DistributedMultivariatePolynomial(D4,D1), +--R DistributedMultivariatePolynomial(D4,D1),Places(D1)) -> D1 +--R from PackageForAlgebraicFunctionField(D1,D4,D5) +--R if D4: LIST(SYMBOL) and D1 has FIELD and D5 has BLMETCT +--R +--R [36] (Fraction(DistributedMultivariatePolynomial(D4,D1)),Places(D1)) +--R -> D1 +--R from PackageForAlgebraicFunctionField(D1,D4,D5) +--R if D4: LIST(SYMBOL) and D1 has FIELD and D5 has BLMETCT +--R +--R [37] (D,D1) -> D1 from D if D has PERMCAT(D1) and D1 has SETCAT +--R [38] (D2,D3) -> D1 from PolynomialPackageForCurve(D1,D2,D4,D5,D3) +--R if D4 has DIRPCAT(D5,NNI) and D5: NNI and D1 has FIELD and +--R D2 has FAMR(D1,D4) and D3 has PRSPCAT(D1) +--R [39] (Fraction(Polynomial(D3)),Symbol,Fraction(Polynomial(D3))) -> +--R Fraction(Polynomial(D3)) +--R from RationalFunction(D3) if D3 has INTDOM +--R [40] (Fraction(Polynomial(D4)),List(Symbol),List(Fraction(Polynomial +--R (D4)))) -> Fraction(Polynomial(D4)) +--R from RationalFunction(D4) if D4 has INTDOM +--R [41] (Fraction(Polynomial(D3)),Equation(Fraction(Polynomial(D3)))) +--R -> Fraction(Polynomial(D3)) +--R from RationalFunction(D3) if D3 has INTDOM +--R [42] (Fraction(Polynomial(D3)),List(Equation(Fraction(Polynomial(D3) +--R )))) -> Fraction(Polynomial(D3)) +--R from RationalFunction(D3) if D3 has INTDOM +--R [43] (D1,D3) -> Stream(D3) from D1 +--R if D1 has UPSCAT(D3,D4) and D3 has RING and D4 has OAMON +--R and D3 has D: (D3,D4) -> D3 +--R +--RThere are 5 unexposed functions called eval : +--R [1] (D1,Fraction(D4),Fraction(D4)) -> D1 from ChangeOfVariable(D3,D4 +--R ,D1) +--R if D3 has UFD and D4 has UPOLYC(D3) and D1 has UPOLYC(FRAC +--R (D4)) +--R [2] ((Integer -> D1),SymmetricPolynomial(Fraction(Integer))) -> D1 +--R from EvaluateCycleIndicators(D1) if D1 has ALGEBRA(FRAC( +--R INT)) +--R [3] (MoebiusTransform(D2),OnePointCompletion(D2)) -> +--R OnePointCompletion(D2) +--R from MoebiusTransform(D2) if D2 has FIELD +--R [4] (MoebiusTransform(D1),D1) -> D1 from MoebiusTransform(D1) if D1 +--R has FIELD +--R [5] (Stream(D2),D2) -> Stream(D2) from StreamTaylorSeriesOperations( +--R D2) +--R if D2 has RING +--R +--RExamples of eval from ChangeOfVariable +--R +--R +--RExamples of eval from CycleIndicators +--R +--R +--RExamples of eval from d02AgentsPackage +--R +--R +--RExamples of eval from Equation +--R +--R +--RExamples of eval from ExpressionSpace +--R +--R +--RExamples of eval from Evalable +--R +--R +--RExamples of eval from EvaluateCycleIndicators +--R +--R +--RExamples of eval from FreeLieAlgebra +--R +--R +--RExamples of eval from FunctionSpace +--R +--R +--RExamples of eval from GeneralPackageForAlgebraicFunctionField +--R +--R +--RExamples of eval from InnerEvalable +--R +--R +--RExamples of eval from MoebiusTransform +--R +--R +--RExamples of eval from PackageForAlgebraicFunctionFieldOverFiniteField +--R +--R +--RExamples of eval from PackageForAlgebraicFunctionField +--R +--R +--RExamples of eval from PermutationCategory +--R +--R +--RExamples of eval from PolynomialPackageForCurve +--R +--R +--RExamples of eval from RationalFunction +--R +--R +--RExamples of eval from StreamTaylorSeriesOperations +--R +--R +--RExamples of eval from UnivariatePowerSeriesCategory +--R +--E 858 + +--S 859 of 3320 +)d op evalADE +--R +--R +--RThere is one exposed function called evalADE : +--R [1] (BasicOperator,Symbol,D1,D1,D1,List(D1)) -> D1 +--R from RecurrenceOperator(D5,D1) +--R if D1 has Join(FunctionSpace(D5),AbelianMonoid, +--R RetractableTo(Integer),RetractableTo(Symbol), +--R PartialDifferentialRing(Symbol),CombinatorialOpsCategory) +--R and D5 has Join(OrderedSet,IntegralDomain,ConvertibleTo( +--R InputForm)) +--R +--RExamples of evalADE from RecurrenceOperator +--R +--E 859 + +--S 860 of 3320 +--R--------------------------- )d op eval_at (fix this) +--E 860 + +--S 861 of 3320 +)d op evalIfCan +--R +--R +--RThere are 9 exposed functions called evalIfCan : +--R [1] (D5,D6) -> Union(D4,"failed") +--R from GeneralPackageForAlgebraicFunctionField(D4,D7,D5,D8, +--R D9,D10,D6,D11,D1,D2,D3) +--R if D7: LIST(SYMBOL) and D5 has POLYCAT(D4,D8,OVAR(D7)) and +--R D8 has DIRPCAT(#(D7),NNI) and D9 has PRSPCAT(D4) and D10 +--R has LOCPOWC(D4) and D6 has PLACESC(D4,D10) and D11 has +--R DIVCAT(D6) and D1 has INFCLCT(D4,D7,D5,D8,D9,D10,D6,D11,D3) +--R and D3 has BLMETCT and D4 has FIELD and D2 has DSTRCAT(D1) +--R +--R [2] (D5,D5,D6) -> Union(D4,"failed") +--R from GeneralPackageForAlgebraicFunctionField(D4,D7,D5,D8, +--R D9,D10,D6,D11,D1,D2,D3) +--R if D7: LIST(SYMBOL) and D5 has POLYCAT(D4,D8,OVAR(D7)) and +--R D8 has DIRPCAT(#(D7),NNI) and D9 has PRSPCAT(D4) and D10 +--R has LOCPOWC(D4) and D6 has PLACESC(D4,D10) and D11 has +--R DIVCAT(D6) and D1 has INFCLCT(D4,D7,D5,D8,D9,D10,D6,D11,D3) +--R and D3 has BLMETCT and D4 has FIELD and D2 has DSTRCAT(D1) +--R +--R [3] (Fraction(D9),D7) -> Union(D5,"failed") +--R from GeneralPackageForAlgebraicFunctionField(D5,D8,D9,D10, +--R D11,D12,D7,D1,D2,D3,D4) +--R if D9 has POLYCAT(D5,D10,OVAR(D8)) and D10 has DIRPCAT(#( +--R D8),NNI) and D8: LIST(SYMBOL) and D11 has PRSPCAT(D5) and +--R D12 has LOCPOWC(D5) and D7 has PLACESC(D5,D12) and D1 has +--R DIVCAT(D7) and D2 has INFCLCT(D5,D8,D9,D10,D11,D12,D7,D1,D4 +--R ) and D4 has BLMETCT and D5 has FIELD and D3 has DSTRCAT(D2 +--R ) +--R [4] (DistributedMultivariatePolynomial(D4,D1), +--R PlacesOverPseudoAlgebraicClosureOfFiniteField(D1)) -> Union(D1, +--R "failed") +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D1,D4 +--R ,D5) +--R if D4: LIST(SYMBOL) and D1 has FFIELDC and D5 has BLMETCT +--R +--R [5] (DistributedMultivariatePolynomial(D4,D1), +--R DistributedMultivariatePolynomial(D4,D1), +--R PlacesOverPseudoAlgebraicClosureOfFiniteField(D1)) -> Union(D1, +--R "failed") +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D1,D4 +--R ,D5) +--R if D4: LIST(SYMBOL) and D1 has FFIELDC and D5 has BLMETCT +--R +--R [6] (Fraction(DistributedMultivariatePolynomial(D4,D1)), +--R PlacesOverPseudoAlgebraicClosureOfFiniteField(D1)) -> Union(D1, +--R "failed") +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D1,D4 +--R ,D5) +--R if D4: LIST(SYMBOL) and D1 has FFIELDC and D5 has BLMETCT +--R +--R [7] (DistributedMultivariatePolynomial(D4,D1),Places(D1)) -> Union( +--R D1,"failed") +--R from PackageForAlgebraicFunctionField(D1,D4,D5) +--R if D4: LIST(SYMBOL) and D1 has FIELD and D5 has BLMETCT +--R +--R [8] (DistributedMultivariatePolynomial(D4,D1), +--R DistributedMultivariatePolynomial(D4,D1),Places(D1)) -> Union(D1, +--R "failed") +--R from PackageForAlgebraicFunctionField(D1,D4,D5) +--R if D4: LIST(SYMBOL) and D1 has FIELD and D5 has BLMETCT +--R +--R [9] (Fraction(DistributedMultivariatePolynomial(D4,D1)),Places(D1)) +--R -> Union(D1,"failed") +--R from PackageForAlgebraicFunctionField(D1,D4,D5) +--R if D4: LIST(SYMBOL) and D1 has FIELD and D5 has BLMETCT +--R +--R +--RExamples of evalIfCan from GeneralPackageForAlgebraicFunctionField +--R +--R +--RExamples of evalIfCan from PackageForAlgebraicFunctionFieldOverFiniteField +--R +--R +--RExamples of evalIfCan from PackageForAlgebraicFunctionField +--R +--E 861 + +--S 862 of 3320 +)d op evalRec +--R +--R +--RThere is one exposed function called evalRec : +--R [1] (BasicOperator,Symbol,D1,D1,D1,List(D1)) -> D1 +--R from RecurrenceOperator(D5,D1) +--R if D1 has Join(FunctionSpace(D5),AbelianMonoid, +--R RetractableTo(Integer),RetractableTo(Symbol), +--R PartialDifferentialRing(Symbol),CombinatorialOpsCategory) +--R and D5 has Join(OrderedSet,IntegralDomain,ConvertibleTo( +--R InputForm)) +--R +--RExamples of evalRec from RecurrenceOperator +--R +--E 862 + +--S 863 of 3320 +)d op evaluate +--R +--R +--RThere are 5 exposed functions called evaluate : +--R [1] (BasicOperator,List(D1)) -> Union(D1,"failed") +--R from BasicOperatorFunctions1(D1) if D1 has SETCAT +--R [2] (BasicOperator,(List(D3) -> D3)) -> BasicOperator +--R from BasicOperatorFunctions1(D3) if D3 has SETCAT +--R [3] (BasicOperator,(D3 -> D3)) -> BasicOperator +--R from BasicOperatorFunctions1(D3) if D3 has SETCAT +--R [4] BasicOperator -> Union((List(D3) -> D3),"failed") +--R from BasicOperatorFunctions1(D3) if D3 has SETCAT +--R [5] (ModuleOperator(D2,D3),(D3 -> D3)) -> ModuleOperator(D2,D3) +--R from ModuleOperator(D2,D3) if D3 has LMODULE(D2) and D2 +--R has RING +--R +--RThere is one unexposed function called evaluate : +--R [1] (Operator(D2),(D2 -> D2)) -> Operator(D2) from Operator(D2) if +--R D2 has RING +--R +--RExamples of evaluate from BasicOperatorFunctions1 +--R +--R +--RExamples of evaluate from ModuleOperator +--R +--R +--RExamples of evaluate from Operator +--R +--E 863 + +--S 864 of 3320 +)d op evaluateInverse +--R +--R +--RThere is one exposed function called evaluateInverse : +--R [1] (ModuleOperator(D2,D3),(D3 -> D3)) -> ModuleOperator(D2,D3) +--R from ModuleOperator(D2,D3) if D3 has LMODULE(D2) and D2 +--R has RING +--R +--RThere is one unexposed function called evaluateInverse : +--R [1] (Operator(D2),(D2 -> D2)) -> Operator(D2) from Operator(D2) if +--R D2 has RING +--R +--RExamples of evaluateInverse from ModuleOperator +--R +--R +--RExamples of evaluateInverse from Operator +--R +--E 864 + +--S 865 of 3320 +)d op even? +--R +--R +--RThere are 3 exposed functions called even? : +--R [1] D -> Boolean from D if D has RETRACT(INT) and D has ES +--R [2] D -> Boolean from D if D has INS +--R [3] Permutation(D2) -> Boolean from Permutation(D2) if D2 has SETCAT +--R +--R +--RExamples of even? from RetractableTo +--R +--R +--RExamples of even? from IntegerNumberSystem +--R +--R +--RExamples of even? from Permutation +--R +--Rp := coercePreimagesImages([[1,2,3],[1,2,3]]) +--Reven? p +--R +--E 865 + +--S 866 of 3320 +)d op evenInfiniteProduct +--R +--R +--RThere are 3 exposed functions called evenInfiniteProduct : +--R [1] D1 -> D1 from InfiniteProductCharacteristicZero(D2,D1) +--R if D2 has Join(IntegralDomain,CharacteristicZero) and D1 +--R has UTSCAT(D2) +--R [2] D1 -> D1 from InfiniteProductFiniteField(D2,D3,D4,D1) +--R if D2 has Join(Field,Finite,ConvertibleTo(Integer)) and D3 +--R has UPOLYC(D2) and D4 has MONOGEN(D2,D3) and D1 has UTSCAT +--R (D4) +--R [3] D1 -> D1 from InfiniteProductPrimeField(D2,D1) +--R if D2 has Join(Field,Finite,ConvertibleTo(Integer)) and D1 +--R has UTSCAT(D2) +--R +--RThere is one unexposed function called evenInfiniteProduct : +--R [1] Stream(D2) -> Stream(D2) from StreamInfiniteProduct(D2) +--R if D2 has Join(IntegralDomain,CharacteristicZero) +--R +--RExamples of evenInfiniteProduct from InfiniteProductCharacteristicZero +--R +--R +--RExamples of evenInfiniteProduct from InfiniteProductFiniteField +--R +--R +--RExamples of evenInfiniteProduct from InfiniteProductPrimeField +--R +--R +--RExamples of evenInfiniteProduct from StreamInfiniteProduct +--R +--E 866 + +--S 867 of 3320 +)d op evenlambert +--R +--R +--RThere are 2 exposed functions called evenlambert : +--R [1] UnivariateFormalPowerSeries(D1) -> UnivariateFormalPowerSeries( +--R D1) +--R from UnivariateFormalPowerSeries(D1) if D1 has RING +--R [2] UnivariateTaylorSeriesCZero(D1,D2) -> +--R UnivariateTaylorSeriesCZero(D1,D2) +--R from UnivariateTaylorSeriesCZero(D1,D2) if D1 has RING and +--R D2: SYMBOL +--R +--RThere are 2 unexposed functions called evenlambert : +--R [1] Stream(D2) -> Stream(D2) from StreamTaylorSeriesOperations(D2) +--R if D2 has RING +--R [2] UnivariateTaylorSeries(D1,D2,D3) -> UnivariateTaylorSeries(D1,D2 +--R ,D3) +--R from UnivariateTaylorSeries(D1,D2,D3) +--R if D1 has RING and D2: SYMBOL and D3: D1 +--R +--RExamples of evenlambert from StreamTaylorSeriesOperations +--R +--R +--RExamples of evenlambert from UnivariateFormalPowerSeries +--R +--R +--RExamples of evenlambert from UnivariateTaylorSeries +--R +--R +--RExamples of evenlambert from UnivariateTaylorSeriesCZero +--R +--E 867 + +--S 868 of 3320 +)d op every? +--R +--R +--RThere are 6 exposed functions called every? : +--R [1] ((D3 -> Boolean),ArrayStack(D3)) -> Boolean from ArrayStack(D3) +--R if $ has finiteAggregate and D3 has SETCAT +--R [2] ((D3 -> Boolean),Dequeue(D3)) -> Boolean from Dequeue(D3) +--R if $ has finiteAggregate and D3 has SETCAT +--R [3] ((D3 -> Boolean),Heap(D3)) -> Boolean from Heap(D3) +--R if $ has finiteAggregate and D3 has ORDSET +--R [4] ((D3 -> Boolean),D) -> Boolean from D +--R if D has finiteAggregate and D has HOAGG(D3) and D3 has +--R TYPE +--R [5] ((D3 -> Boolean),Queue(D3)) -> Boolean from Queue(D3) +--R if $ has finiteAggregate and D3 has SETCAT +--R [6] ((D3 -> Boolean),Stack(D3)) -> Boolean from Stack(D3) +--R if $ has finiteAggregate and D3 has SETCAT +--R +--RExamples of every? from ArrayStack +--R +--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] +--Revery?(x+->(x=4),a) +--R +--R +--RExamples of every? from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Revery?(x+->(x=4),a) +--R +--R +--RExamples of every? from Heap +--R +--Ra:Heap INT:= heap [1,2,3,4,5] +--Revery?(x+->(x=4),a) +--R +--R +--RExamples of every? from HomogeneousAggregate +--R +--R +--RExamples of every? from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Revery?(x+->(x=4),a) +--R +--R +--RExamples of every? from Stack +--R +--Ra:Stack INT:= stack [1,2,3,4,5] +--Revery?(x+->(x=4),a) +--R +--E 868 + +--S 869 of 3320 +)d op exactQuotient +--R +--R +--RThere are 2 exposed functions called exactQuotient : +--R [1] (D,D) -> D from D +--R if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has +--R OAMONS and D3 has ORDSET and D1 has INTDOM +--R [2] (D,D1) -> D from D +--R if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has +--R OAMONS and D3 has ORDSET and D1 has INTDOM +--R +--RExamples of exactQuotient from RecursivePolynomialCategory +--R +--E 869 + +--S 870 of 3320 +)d op exactQuotient! +--R +--R +--RThere are 2 exposed functions called exactQuotient! : +--R [1] (D,D) -> D from D +--R if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has +--R OAMONS and D3 has ORDSET and D1 has INTDOM +--R [2] (D,D1) -> D from D +--R if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has +--R OAMONS and D3 has ORDSET and D1 has INTDOM +--R +--RExamples of exactQuotient! from RecursivePolynomialCategory +--R +--E 870 + +--S 871 of 3320 +)d op excepCoord +--R +--R +--RThere is one exposed function called excepCoord : +--R [1] D -> Integer from D if D has BLMETCT +--R +--RExamples of excepCoord from BlowUpMethodCategory +--R +--E 871 + +--S 872 of 3320 +)d op excpDivV +--R +--R +--RThere is one exposed function called excpDivV : +--R [1] D -> DIVISOR from D +--R if D has INFCLCT(D4,D5,D6,D7,D8,D9,D10,D1,D2) and D4 has +--R FIELD and D6 has POLYCAT(D4,D7,OVAR(D5)) and D7 has DIRPCAT +--R (#(D5),NNI) and D8 has PRSPCAT(D4) and D9 has LOCPOWC(D4) +--R and D10 has PLACESC(D4,D9) and D2 has BLMETCT +--R +--RExamples of excpDivV from InfinitlyClosePointCategory +--R +--E 872 + +--S 873 of 3320 +)d op exists? +--R +--R +--RThere is one exposed function called exists? : +--R [1] D -> Boolean from D if D has FNCAT +--R +--RExamples of exists? from FileNameCategory +--R +--E 873 + +--S 874 of 3320 +)d op exp +--R +--R +--RThere are 2 exposed functions called exp : +--R [1] D -> D from D if D has ELEMFUN +--R [2] FortranExpression(D1,D2,D3) -> FortranExpression(D1,D2,D3) +--R from FortranExpression(D1,D2,D3) +--R if D1: LIST(SYMBOL) and D2: LIST(SYMBOL) and D3 has FMTC +--R +--R +--RThere are 9 unexposed functions called exp : +--R [1] List(Integer) -> AntiSymm(D2,D3) from AntiSymm(D2,D3) +--R if D2 has RING and D3: LIST(SYMBOL) +--R [2] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R [3] D1 -> D1 from ElementaryFunctionsUnivariateLaurentSeries(D2,D3, +--R D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has UTSCAT(D2) and D1 +--R has ULSCCAT(D2,D3) +--R [4] D1 -> D1 from ElementaryFunctionsUnivariatePuiseuxSeries(D2,D3, +--R D1,D4) +--R if D2 has ALGEBRA(FRAC(INT)) and D3 has ULSCAT(D2) and D1 +--R has UPXSCCA(D2,D3) and D4 has PTRANFN(D3) +--R [5] LiePolynomial(D2,D3) -> LieExponentials(D2,D3,D4) +--R from LieExponentials(D2,D3,D4) +--R if D2 has ORDSET and D3 has Join(CommutativeRing,Module( +--R Fraction(Integer))) and D4: PI +--R [6] Stream(D2) -> Stream(D2) +--R from StreamTranscendentalFunctionsNonCommutative(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [7] Stream(D2) -> Stream(D2) from StreamTranscendentalFunctions(D2) +--R if D2 has ALGEBRA(FRAC(INT)) +--R [8] (D1,NonNegativeInteger) -> D1 from XExponentialPackage(D3,D4,D1) +--R if D3 has Join(Ring,Module(Fraction(Integer))) and D4 has +--R ORDSET and D1 has XPOLYC(D4,D3) +--R [9] (XPBWPolynomial(D2,D3),NonNegativeInteger) -> XPBWPolynomial(D2, +--R D3) +--R from XPBWPolynomial(D2,D3) +--R if D3 has MODULE(FRAC(INT)) and D2 has ORDSET and D3 has +--R COMRING +--R +--RExamples of exp from AntiSymm +--R +--R +--RExamples of exp from ElementaryFunction +--R +--R +--RExamples of exp from ElementaryFunctionsUnivariateLaurentSeries +--R +--R +--RExamples of exp from ElementaryFunctionsUnivariatePuiseuxSeries +--R +--R +--RExamples of exp from ElementaryFunctionCategory +--R +--R +--RExamples of exp from FortranExpression +--R +--R +--RExamples of exp from LieExponentials +--R +--R +--RExamples of exp from StreamTranscendentalFunctionsNonCommutative +--R +--R +--RExamples of exp from StreamTranscendentalFunctions +--R +--R +--RExamples of exp from XExponentialPackage +--R +--R +--RExamples of exp from XPBWPolynomial +--R +--E 874 + +--S 875 of 3320 +)d op exp1 +--R +--R +--RThere are 2 exposed functions called exp1 : +--R [1] -> DoubleFloat from DoubleFloat +--R [2] -> Float from Float +--R +--RExamples of exp1 from DoubleFloat +--R +--R +--RExamples of exp1 from Float +--R +--E 875 + +--S 876 of 3320 +)d op expand +--R +--R +--RThere are 6 exposed functions called expand : +--R [1] Factored(D1) -> D1 from Factored(D1) if D1 has INTDOM +--R [2] IntegrationResult(D4) -> List(D4) from +--R IntegrationResultToFunction(D3,D4) +--R if D4 has Join(AlgebraicallyClosedFunctionSpace(D3), +--R TranscendentalFunctionCategory) and D3 has Join(GcdDomain, +--R RetractableTo(Integer),OrderedSet,LinearlyExplicitRingOver( +--R Integer)) +--R [3] IntegrationResult(Fraction(Polynomial(D3))) -> List(Expression( +--R D3)) +--R from IntegrationResultRFToFunction(D3) +--R if D3 has Join(GcdDomain,RetractableTo(Integer),OrderedSet +--R ,LinearlyExplicitRingOver(Integer)) +--R [4] D -> D1 from D if D has SEGXCAT(D2,D1) and D2 has ORDRING and D1 +--R has STAGG(D2) +--R [5] List(D) -> D1 from D +--R if D has SEGXCAT(D3,D1) and D3 has ORDRING and D1 has +--R STAGG(D3) +--R [6] D1 -> D1 from TranscendentalManipulations(D2,D1) +--R if D2 has Join(OrderedSet,GcdDomain) and D1 has Join( +--R FunctionSpace(D2),TranscendentalFunctionCategory) +--R +--RThere are 3 unexposed functions called expand : +--R [1] (Expression(D5),PositiveInteger) -> List(Expression(D5)) +--R from DegreeReductionPackage(D4,D5) +--R if D5 has Join(IntegralDomain,OrderedSet) and D4 has RING +--R +--R [2] XPolynomial(D2) -> XDistributedPolynomial(Symbol,D2) from +--R XPolynomial(D2) +--R if D2 has RING +--R [3] XRecursivePolynomial(D2,D3) -> XDistributedPolynomial(D2,D3) +--R from XRecursivePolynomial(D2,D3) if D2 has ORDSET and D3 +--R has RING +--R +--RExamples of expand from DegreeReductionPackage +--R +--R +--RExamples of expand from Factored +--R +--Rf:=nilFactor(y-x,3) +--Rexpand(f) +--R +--R +--RExamples of expand from IntegrationResultToFunction +--R +--R +--RExamples of expand from IntegrationResultRFToFunction +--R +--R +--RExamples of expand from SegmentExpansionCategory +--R +--R +--RExamples of expand from TranscendentalManipulations +--R +--R +--RExamples of expand from XPolynomial +--R +--R +--RExamples of expand from XRecursivePolynomial +--R +--E 876 + +--S 877 of 3320 +)d op expandLog +--R +--R +--RThere is one exposed function called expandLog : +--R [1] D1 -> D1 from TranscendentalManipulations(D2,D1) +--R if D2 has Join(OrderedSet,GcdDomain) and D1 has Join( +--R FunctionSpace(D2),TranscendentalFunctionCategory) +--R +--RExamples of expandLog from TranscendentalManipulations +--R +--E 877 + +--S 878 of 3320 +)d op expandPower +--R +--R +--RThere is one exposed function called expandPower : +--R [1] D1 -> D1 from TranscendentalManipulations(D2,D1) +--R if D2 has Join(OrderedSet,GcdDomain) and D1 has Join( +--R FunctionSpace(D2),TranscendentalFunctionCategory) +--R +--RExamples of expandPower from TranscendentalManipulations +--R +--E 878 + +--S 879 of 3320 +)d op expandTrigProducts +--R +--R +--RThere is one exposed function called expandTrigProducts : +--R [1] D1 -> D1 from TranscendentalManipulations(D2,D1) +--R if D2 has KONVERT(PATTERN(D2)) and D2 has PATMAB(D2) and +--R D2 has Join(OrderedSet,GcdDomain) and D1 has KONVERT( +--R PATTERN(D2)) and D1 has PATMAB(D2) and D1 has Join( +--R FunctionSpace(D2),TranscendentalFunctionCategory) +--R +--RExamples of expandTrigProducts from TranscendentalManipulations +--R +--E 879 + +--S 880 of 3320 +)d op expenseOfEvaluation +--R +--R +--RThere are 2 exposed functions called expenseOfEvaluation : +--R [1] Record(lfn: List(Expression(DoubleFloat)),init: List(DoubleFloat +--R )) -> Float +--R from e04AgentsPackage +--R [2] Vector(Expression(DoubleFloat)) -> Float from +--R ExpertSystemToolsPackage +--R +--RExamples of expenseOfEvaluation from e04AgentsPackage +--R +--R +--RExamples of expenseOfEvaluation from ExpertSystemToolsPackage +--R +--E 880 + +--S 881 of 3320 +)d op expenseOfEvaluationIF +--R +--R +--RThere is one exposed function called expenseOfEvaluationIF : +--R [1] Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector( +--R Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List( +--R DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat, +--R relerr: DoubleFloat) -> Float +--R from d02AgentsPackage +--R +--RExamples of expenseOfEvaluationIF from d02AgentsPackage +--R +--E 881 + +--S 882 of 3320 +)d op expextendedint +--R +--R +--RThere is one unexposed function called expextendedint : +--R [1] (Fraction(D6),(D6 -> D6),((Integer,D5) -> Record(ans: D5,right: +--R D5,sol?: Boolean)),Fraction(D6)) -> Union(Record(answer: Fraction +--R (D6),a0: D5),Record(ratpart: Fraction(D6),coeff: Fraction(D6)), +--R "failed") +--R from TranscendentalIntegration(D5,D6) +--R if D5 has FIELD and D6 has UPOLYC(D5) +--R +--RExamples of expextendedint from TranscendentalIntegration +--R +--E 882 + +--S 883 of 3320 +)d op expIfCan +--R +--R +--RThere is one exposed function called expIfCan : +--R [1] D1 -> Union(D1,"failed") from D if D has PTRANFN(D1) and D1 has +--R TRANFUN +--R +--RExamples of expIfCan from PartialTranscendentalFunctions +--R +--E 883 + +--S 884 of 3320 +)d op expint +--R +--R +--RThere is one unexposed function called expint : +--R [1] (D1,Symbol) -> D1 from ODEIntegration(D3,D1) +--R if D3 has Join(OrderedSet,EuclideanDomain,RetractableTo( +--R Integer),LinearlyExplicitRingOver(Integer), +--R CharacteristicZero) and D1 has Join( +--R AlgebraicallyClosedFunctionSpace(D3), +--R TranscendentalFunctionCategory,PrimitiveFunctionCategory) +--R +--R +--RExamples of expint from ODEIntegration +--R +--E 884 + +--S 885 of 3320 +)d op expintegrate +--R +--R +--RThere is one unexposed function called expintegrate : +--R [1] (Fraction(D6),(D6 -> D6),((Integer,D5) -> Record(ans: D5,right: +--R D5,sol?: Boolean))) -> Record(answer: IntegrationResult(Fraction( +--R D6)),a0: D5) +--R from TranscendentalIntegration(D5,D6) +--R if D5 has FIELD and D6 has UPOLYC(D5) +--R +--RExamples of expintegrate from TranscendentalIntegration +--R +--E 885 + +--S 886 of 3320 +)d op expintfldpoly +--R +--R +--RThere is one unexposed function called expintfldpoly : +--R [1] (LaurentPolynomial(D3,D4),((Integer,D3) -> Record(ans: D3,right +--R : D3,sol?: Boolean))) -> Union(LaurentPolynomial(D3,D4),"failed") +--R from TranscendentalIntegration(D3,D4) +--R if D3 has FIELD and D4 has UPOLYC(D3) +--R +--RExamples of expintfldpoly from TranscendentalIntegration +--R +--E 886 + +--S 887 of 3320 done +)d op explicitEntries? +--R +--R +--RThere is one exposed function called explicitEntries? : +--R [1] D -> Boolean from D if D has LZSTAGG(D2) and D2 has TYPE +--R +--RExamples of explicitEntries? from LazyStreamAggregate +--R +--Rm:=[i for i in 0..] +--RexplicitEntries? m +--R +--E 887 + +--S 888 of 3320 done +)d op explicitlyEmpty? +--R +--R +--RThere is one exposed function called explicitlyEmpty? : +--R [1] D -> Boolean from D if D has LZSTAGG(D2) and D2 has TYPE +--R +--RExamples of explicitlyEmpty? from LazyStreamAggregate +--R +--Rm:=[i for i in 0..] +--RexplicitlyEmpty? m +--R +--E 888 + +--S 889 of 3320 +)d op explicitlyFinite? +--R +--R +--RThere is one exposed function called explicitlyFinite? : +--R [1] D -> Boolean from D if D has STAGG(D2) and D2 has TYPE +--R +--RExamples of explicitlyFinite? from StreamAggregate +--R +--E 889 + +--S 890 of 3320 +)d op explimitedint +--R +--R +--RThere is one unexposed function called explimitedint : +--R [1] (Fraction(D7),(D7 -> D7),((Integer,D6) -> Record(ans: D6,right: +--R D6,sol?: Boolean)),List(Fraction(D7))) -> Union(Record(answer: +--R Record(mainpart: Fraction(D7),limitedlogs: List(Record(coeff: +--R Fraction(D7),logand: Fraction(D7)))),a0: D6),"failed") +--R from TranscendentalIntegration(D6,D7) +--R if D6 has FIELD and D7 has UPOLYC(D6) +--R +--RExamples of explimitedint from TranscendentalIntegration +--R +--E 890 + +--S 891 of 3320 +)d op explogs2trigs +--R +--R +--RThere is one unexposed function called explogs2trigs : +--R [1] D2 -> Complex(D4) from InnerTrigonometricManipulations(D3,D4,D2) +--R if D3 has Join(IntegralDomain,OrderedSet) and D4 has Join( +--R FunctionSpace(D3),RadicalCategory, +--R TranscendentalFunctionCategory) and D2 has Join( +--R FunctionSpace(Complex(D3)),RadicalCategory, +--R TranscendentalFunctionCategory) +--R +--RExamples of explogs2trigs from InnerTrigonometricManipulations +--R +--E 891 + +--S 892 of 3320 +)d op exponent +--R +--R +--RThere are 3 exposed functions called exponent : +--R [1] D -> Integer from D if D has FPS +--R [2] Factored(D2) -> Integer from Factored(D2) if D2 has INTDOM +--R [3] MachineFloat -> Integer from MachineFloat +--R +--RThere are 2 unexposed functions called exponent : +--R [1] ExponentialOfUnivariatePuiseuxSeries(D2,D3,D4) -> +--R UnivariatePuiseuxSeries(D2,D3,D4) +--R from ExponentialOfUnivariatePuiseuxSeries(D2,D3,D4) +--R if D2 has Join(Field,OrderedSet) and D3: SYMBOL and D4: D2 +--R +--R [2] ModuleMonomial(D2,D1,D3) -> D1 from ModuleMonomial(D2,D1,D3) +--R if D1 has SETCAT and D2 has ORDSET and D3: ((Record(index +--R : D2,exponent: D1),Record(index: D2,exponent: D1)) -> +--R Boolean) +--R +--RExamples of exponent from ExponentialOfUnivariatePuiseuxSeries +--R +--R +--RExamples of exponent from FloatingPointSystem +--R +--R +--RExamples of exponent from Factored +--R +--Rf:=nilFactor(y-x,3) +--Rexponent(f) +--R +--R +--RExamples of exponent from MachineFloat +--R +--R +--RExamples of exponent from ModuleMonomial +--R +--E 892 + +--S 893 of 3320 +)d op exponential +--R +--R +--RThere are 2 unexposed functions called exponential : +--R [1] UnivariatePuiseuxSeries(D2,D3,D4) -> +--R ExponentialOfUnivariatePuiseuxSeries(D2,D3,D4) +--R from ExponentialOfUnivariatePuiseuxSeries(D2,D3,D4) +--R if D2 has Join(Field,OrderedSet) and D3: SYMBOL and D4: D2 +--R +--R [2] Float -> (() -> Float) from RandomFloatDistributions +--R +--RExamples of exponential from ExponentialOfUnivariatePuiseuxSeries +--R +--R +--RExamples of exponential from RandomFloatDistributions +--R +--E 893 + +--S 894 of 3320 +)d op exponential1 +--R +--R +--RThere is one unexposed function called exponential1 : +--R [1] -> Float from RandomFloatDistributions +--R +--RExamples of exponential1 from RandomFloatDistributions +--R +--E 894 + +--S 895 of 3320 +)d op exponentialOrder +--R +--R +--RThere is one unexposed function called exponentialOrder : +--R [1] ExponentialOfUnivariatePuiseuxSeries(D2,D3,D4) -> Fraction( +--R Integer) +--R from ExponentialOfUnivariatePuiseuxSeries(D2,D3,D4) +--R if D2 has Join(Field,OrderedSet) and D3: SYMBOL and D4: D2 +--R +--R +--RExamples of exponentialOrder from ExponentialOfUnivariatePuiseuxSeries +--R +--E 895 + +--S 896 of 3320 +)d op exponents +--R +--R +--RThere is one unexposed function called exponents : +--R [1] ExtAlgBasis -> List(Integer) from ExtAlgBasis +--R +--RExamples of exponents from ExtAlgBasis +--R +--E 896 + +--S 897 of 3320 +)d op expPot +--R +--R +--RThere is one unexposed function called expPot : +--R [1] (Vector(D3),SingleInteger,SingleInteger) -> Vector(D3) +--R from InnerNormalBasisFieldFunctions(D3) if D3 has FFIELDC +--R +--R +--RExamples of expPot from InnerNormalBasisFieldFunctions +--R +--E 897 + +--S 898 of 3320 +)d op expr +--R +--R +--RThere is one exposed function called expr : +--R [1] D -> D1 from D +--R if D has SEXCAT(D2,D3,D4,D5,D1) and D2 has SETCAT and D3 +--R has SETCAT and D4 has SETCAT and D5 has SETCAT and D1 has +--R SETCAT +--R +--RExamples of expr from SExpressionCategory +--R +--E 898 + +--S 899 of 3320 +)d op expressIdealMember +--R +--R +--RThere is one exposed function called expressIdealMember : +--R [1] (List(D),D) -> Union(List(D),"failed") from D if D has PID +--R +--RExamples of expressIdealMember from PrincipalIdealDomain +--R +--E 899 + +--S 900 of 3320 +)d op exprex +--R +--R +--RThere are 2 exposed functions called exprex : +--R [1] OutputForm -> String from HTMLFormat +--R [2] OutputForm -> String from MathMLFormat +--R +--RExamples of exprex from HTMLFormat +--R +--Rexprex(sqrt(3+x)::OutputForm)$HTMLFORM +--R +--R +--RExamples of exprex from MathMLFormat +--R +--E 900 + +--S 901 of 3320 +)d op exprHasAlgebraicWeight +--R +--R +--RThere is one exposed function called exprHasAlgebraicWeight : +--R [1] Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment( +--R OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: +--R DoubleFloat) -> Union(List(DoubleFloat),"failed") +--R from d01WeightsPackage +--R +--RExamples of exprHasAlgebraicWeight from d01WeightsPackage +--R +--E 901 + +--S 902 of 3320 +)d op exprHasLogarithmicWeights +--R +--R +--RThere is one exposed function called exprHasLogarithmicWeights : +--R [1] Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment( +--R OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: +--R DoubleFloat) -> Integer +--R from d01WeightsPackage +--R +--RExamples of exprHasLogarithmicWeights from d01WeightsPackage +--R +--E 902 + +--S 903 of 3320 +)d op exprHasWeightCosWXorSinWX +--R +--R +--RThere is one exposed function called exprHasWeightCosWXorSinWX : +--R [1] Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment( +--R OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: +--R DoubleFloat) -> Union(Record(op: BasicOperator,w: DoubleFloat), +--R "failed") +--R from d01WeightsPackage +--R +--RExamples of exprHasWeightCosWXorSinWX from d01WeightsPackage +--R +--E 903 + +--S 904 of 3320 +)d op exprToGenUPS +--R +--R +--RThere is one unexposed function called exprToGenUPS : +--R [1] (D3,Boolean,String) -> Union(%series: D8,%problem: Record(func: +--R String,prob: String)) +--R from FunctionSpaceToUnivariatePowerSeries(D6,D3,D7,D8,D9, +--R D1) +--R if D6 has Join(GcdDomain,OrderedSet,RetractableTo(Integer) +--R ,LinearlyExplicitRingOver(Integer)) and D3 has Join( +--R AlgebraicallyClosedField,TranscendentalFunctionCategory, +--R FunctionSpace(D6))with +--R coerce : D7 -> %and D7 has ORDRING and D8 has Join( +--R UnivariatePowerSeriesCategory(D3,D7),Field, +--R TranscendentalFunctionCategory)with +--R differentiate : % -> % +--R integrate : % -> %and D9 has PTRANFN(D8) and D1: +--R SYMBOL +--R +--RExamples of exprToGenUPS from FunctionSpaceToUnivariatePowerSeries +--R +--E 904 + +--S 905 of 3320 +)d op exprToUPS +--R +--R +--RThere is one unexposed function called exprToUPS : +--R [1] (D3,Boolean,String) -> Union(%series: D8,%problem: Record(func: +--R String,prob: String)) +--R from FunctionSpaceToUnivariatePowerSeries(D6,D3,D7,D8,D9, +--R D1) +--R if D6 has Join(GcdDomain,OrderedSet,RetractableTo(Integer) +--R ,LinearlyExplicitRingOver(Integer)) and D3 has Join( +--R AlgebraicallyClosedField,TranscendentalFunctionCategory, +--R FunctionSpace(D6))with +--R coerce : D7 -> %and D7 has ORDRING and D8 has Join( +--R UnivariatePowerSeriesCategory(D3,D7),Field, +--R TranscendentalFunctionCategory)with +--R differentiate : % -> % +--R integrate : % -> %and D9 has PTRANFN(D8) and D1: +--R SYMBOL +--R +--RExamples of exprToUPS from FunctionSpaceToUnivariatePowerSeries +--R +--E 905 + +--S 906 of 3320 +)d op exprToXXP +--R +--R +--RThere is one unexposed function called exprToXXP : +--R [1] (D2,Boolean) -> Union(%expansion: ExponentialExpansion(D4,D2,D5, +--R D6),%problem: Record(func: String,prob: String)) +--R from FunctionSpaceToExponentialExpansion(D4,D2,D5,D6) +--R if D4 has Join(GcdDomain,OrderedSet,RetractableTo(Integer) +--R ,LinearlyExplicitRingOver(Integer)) and D2 has Join( +--R AlgebraicallyClosedField,TranscendentalFunctionCategory, +--R FunctionSpace(D4)) and D5: SYMBOL and D6: D2 +--R +--RExamples of exprToXXP from FunctionSpaceToExponentialExpansion +--R +--E 906 + +--S 907 of 3320 +)d op expt +--R +--R +--RThere is one unexposed function called expt : +--R [1] (D1,PositiveInteger) -> D1 from RepeatedSquaring(D1) +--R if D1 has SetCategorywith +--R ?*? : (%,%) -> % +--R +--RExamples of expt from RepeatedSquaring +--R +--E 907 + +--S 908 of 3320 +)d op exptMod +--R +--R +--RThere are 2 exposed functions called exptMod : +--R [1] (D1,NonNegativeInteger,D1) -> D1 from DistinctDegreeFactorize(D3 +--R ,D1) +--R if D3 has FFIELDC and D1 has UPOLYC(D3) +--R [2] (D1,Integer,D1,Integer) -> D1 from +--R ModularDistinctDegreeFactorizer(D1) +--R if D1 has UPOLYC(INT) +--R +--RExamples of exptMod from DistinctDegreeFactorize +--R +--R +--RExamples of exptMod from ModularDistinctDegreeFactorizer +--R +--E 908 + +--S 909 of 3320 +)d op exquo +--R +--R +--RThere are 7 exposed functions called exquo : +--R [1] (D,D1) -> Union(D,"failed") from D +--R if D has COMPCAT(D1) and D1 has COMRING and D1 has INTDOM +--R +--R [2] (D,D1) -> Union(D,"failed") from D +--R if D has FAMR(D1,D2) and D1 has RING and D2 has OAMON and +--R D1 has INTDOM +--R [3] (D,D) -> Union(D,"failed") from D if D has INTDOM +--R [4] (D,D1) -> Union(D,"failed") from D +--R if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG +--R (D1) and D3 has FLAGG(D1) and D1 has INTDOM +--R [5] (NonNegativeInteger,NonNegativeInteger) -> Union( +--R NonNegativeInteger,"failed") +--R from NonNegativeInteger +--R [6] (D,D1) -> Union(D,"failed") from D +--R if D has OREPCAT(D1) and D1 has RING and D1 has INTDOM +--R [7] (D,D1) -> Union(D,"failed") from D +--R if D has RMATCAT(D2,D3,D1,D4,D5) and D1 has RING and D4 +--R has DIRPCAT(D3,D1) and D5 has DIRPCAT(D2,D1) and D1 has +--R INTDOM +--R +--RThere are 3 unexposed functions called exquo : +--R [1] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R [2] (Vector(D3),D2) -> Vector(D3) from PseudoRemainderSequence(D2,D3 +--R ) +--R if D3 has UPOLYC(D2) and D2 has INTDOM +--R [3] (Stream(D2),Stream(D2)) -> Union(Stream(D2),"failed") +--R from StreamTaylorSeriesOperations(D2) if D2 has RING +--R +--RExamples of exquo from ComplexCategory +--R +--R +--RExamples of exquo from FiniteAbelianMonoidRing +--R +--R +--RExamples of exquo from IntegralDomain +--R +--R +--RExamples of exquo from MatrixCategory +--R +--Rm:=matrix [[2**i for i in 2..4] for j in 1..5] +--Rexquo(m,2) +--R +--R +--RExamples of exquo from NonNegativeInteger +--R +--R +--RExamples of exquo from UnivariateSkewPolynomialCategory +--R +--R +--RExamples of exquo from OutputForm +--R +--R +--RExamples of exquo from PseudoRemainderSequence +--R +--R +--RExamples of exquo from RectangularMatrixCategory +--R +--R +--RExamples of exquo from StreamTaylorSeriesOperations +--R +--E 909 + +--S 910 of 3320 +)d op exQuo +--R +--R +--RThere are 3 unexposed functions called exQuo : +--R [1] (EuclideanModularRing(D1,D2,D3,D4,D5,D6),EuclideanModularRing(D1 +--R ,D2,D3,D4,D5,D6)) -> Union(EuclideanModularRing(D1,D2,D3,D4,D5,D6 +--R ),"failed") +--R from EuclideanModularRing(D1,D2,D3,D4,D5,D6) +--R if D1 has COMRING and D2 has UPOLYC(D1) and D3 has ABELMON +--R and D4: ((D2,D3) -> D2) and D5: ((D3,D3) -> Union(D3, +--R "failed")) and D6: ((D2,D2,D3) -> Union(D2,"failed")) +--R [2] (ModularField(D1,D2,D3,D4,D5),ModularField(D1,D2,D3,D4,D5)) -> +--R Union(ModularField(D1,D2,D3,D4,D5),"failed") +--R from ModularField(D1,D2,D3,D4,D5) +--R if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> +--R D1) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1 +--R ,D2) -> Union(D1,"failed")) +--R [3] (ModularRing(D1,D2,D3,D4,D5),ModularRing(D1,D2,D3,D4,D5)) -> +--R Union(ModularRing(D1,D2,D3,D4,D5),"failed") +--R from ModularRing(D1,D2,D3,D4,D5) +--R if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> +--R D1) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1 +--R ,D2) -> Union(D1,"failed")) +--R +--RExamples of exQuo from EuclideanModularRing +--R +--R +--RExamples of exQuo from ModularField +--R +--R +--RExamples of exQuo from ModularRing +--R +--E 910 + +--S 911 of 3320 +)d op extDegree +--R +--R +--RThere is one exposed function called extDegree : +--R [1] D -> PositiveInteger from D if D has PACPERC +--R +--RExamples of extDegree from PseudoAlgebraicClosureOfPerfectFieldCategory +--R +--E 911 + +--S 912 of 3320 +)d op extend +--R +--R +--RThere are 11 exposed functions called extend : +--R [1] (ContinuedFraction(D2),Integer) -> ContinuedFraction(D2) +--R from ContinuedFraction(D2) if D2 has EUCDOM +--R [2] (D,Integer) -> D from D if D has LZSTAGG(D2) and D2 has TYPE +--R [3] (D,NonNegativeInteger) -> D from D +--R if D has MTSCAT(D2,D3) and D2 has RING and D3 has ORDSET +--R +--R [4] (D,Integer) -> D from D if D has PADICCT(D2) +--R [5] (D,List(D2)) -> D from D if D has PTCAT(D2) and D2 has RING +--R [6] (List(D6),List(D)) -> List(D) from D +--R if D has RSETCAT(D3,D4,D5,D6) and D3 has GCDDOM and D4 +--R has OAMONS and D5 has ORDSET and D6 has RPOLCAT(D3,D4,D5) +--R +--R [7] (List(D6),D) -> List(D) from D +--R if D6 has RPOLCAT(D3,D4,D5) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET and D has RSETCAT(D3,D4,D5,D6) +--R [8] (D2,List(D)) -> List(D) from D +--R if D has RSETCAT(D3,D4,D5,D2) and D3 has GCDDOM and D4 +--R has OAMONS and D5 has ORDSET and D2 has RPOLCAT(D3,D4,D5) +--R +--R [9] (D2,D) -> List(D) from D +--R if D3 has GCDDOM and D4 has OAMONS and D5 has ORDSET and +--R D2 has RPOLCAT(D3,D4,D5) and D has RSETCAT(D3,D4,D5,D2) +--R [10] (D,D1) -> D from D +--R if D has TSETCAT(D2,D3,D4,D1) and D2 has INTDOM and D3 +--R has OAMONS and D4 has ORDSET and D1 has RPOLCAT(D2,D3,D4) +--R +--R [11] (D,D1) -> D from D if D has UPSCAT(D2,D1) and D2 has RING and +--R D1 has OAMON +--R +--RExamples of extend from ContinuedFraction +--R +--R +--RExamples of extend from LazyStreamAggregate +--R +--Rm:=[i for i in 0..] +--RnumberOfComputedEntries m +--Rextend(m,20) +--RnumberOfComputedEntries m +--R +--R +--RExamples of extend from MultivariateTaylorSeriesCategory +--R +--R +--RExamples of extend from PAdicIntegerCategory +--R +--R +--RExamples of extend from PointCategory +--R +--R +--RExamples of extend from RegularTriangularSetCategory +--R +--R +--RExamples of extend from TriangularSetCategory +--R +--R +--RExamples of extend from UnivariatePowerSeriesCategory +--R +--E 912 + +--S 913 of 3320 +)d op extendedEuclidean +--R +--R +--RThere are 2 exposed functions called extendedEuclidean : +--R [1] (D,D,D) -> Union(Record(coef1: D,coef2: D),"failed") from D if D +--R has EUCDOM +--R [2] (D,D) -> Record(coef1: D,coef2: D,generator: D) from D if D has +--R EUCDOM +--R +--RExamples of extendedEuclidean from EuclideanDomain +--R +--E 913 + +--S 914 of 3320 +--R------------------- )d op extended_gcd (fix this) +--E 914 + +--S 915 of 3320 +)d op extendedint +--R +--R +--RThere is one unexposed function called extendedint : +--R [1] (Fraction(D4),Fraction(D4)) -> Union(Record(ratpart: Fraction(D4 +--R ),coeff: Fraction(D4)),"failed") +--R from RationalIntegration(D3,D4) +--R if D3 has Join(Field,CharacteristicZero,RetractableTo( +--R Integer)) and D4 has UPOLYC(D3) +--R +--RExamples of extendedint from RationalIntegration +--R +--E 915 + +--S 916 of 3320 +)d op extendedIntegrate +--R +--R +--RThere is one exposed function called extendedIntegrate : +--R [1] (Fraction(Polynomial(D4)),Symbol,Fraction(Polynomial(D4))) -> +--R Union(Record(ratpart: Fraction(Polynomial(D4)),coeff: Fraction( +--R Polynomial(D4))),"failed") +--R from RationalFunctionIntegration(D4) +--R if D4 has Join(IntegralDomain,RetractableTo(Integer), +--R CharacteristicZero) +--R +--RExamples of extendedIntegrate from RationalFunctionIntegration +--R +--E 916 + +--S 917 of 3320 +)d op extendedResultant +--R +--R +--RThere is one unexposed function called extendedResultant : +--R [1] (NewSparseUnivariatePolynomial(D2),NewSparseUnivariatePolynomial +--R (D2)) -> Record(resultant: D2,coef1: +--R NewSparseUnivariatePolynomial(D2),coef2: +--R NewSparseUnivariatePolynomial(D2)) +--R from NewSparseUnivariatePolynomial(D2) if D2 has INTDOM +--R and D2 has RING +--R +--RExamples of extendedResultant from NewSparseUnivariatePolynomial +--R +--E 917 + +--S 918 of 3320 +)d op extendedSubResultantGcd +--R +--R +--RThere is one exposed function called extendedSubResultantGcd : +--R [1] (D,D) -> Record(gcd: D,coef1: D,coef2: D) from D +--R if D2 has INTDOM and D2 has RING and D3 has OAMONS and D4 +--R has ORDSET and D has RPOLCAT(D2,D3,D4) +--R +--RThere is one unexposed function called extendedSubResultantGcd : +--R [1] (NewSparseUnivariatePolynomial(D2),NewSparseUnivariatePolynomial +--R (D2)) -> Record(gcd: NewSparseUnivariatePolynomial(D2),coef1: +--R NewSparseUnivariatePolynomial(D2),coef2: +--R NewSparseUnivariatePolynomial(D2)) +--R from NewSparseUnivariatePolynomial(D2) if D2 has INTDOM +--R and D2 has RING +--R +--RExamples of extendedSubResultantGcd from NewSparseUnivariatePolynomial +--R +--R +--RExamples of extendedSubResultantGcd from RecursivePolynomialCategory +--R +--E 918 + +--S 919 of 3320 +)d op extendIfCan +--R +--R +--RThere is one exposed function called extendIfCan : +--R [1] (D,D1) -> Union(D,"failed") from D +--R if D has TSETCAT(D2,D3,D4,D1) and D2 has INTDOM and D3 +--R has OAMONS and D4 has ORDSET and D1 has RPOLCAT(D2,D3,D4) +--R +--R +--RExamples of extendIfCan from TriangularSetCategory +--R +--E 919 + +--S 920 of 3320 +)d op extension +--R +--R +--RThere is one exposed function called extension : +--R [1] D -> String from D if D has FNCAT +--R +--RExamples of extension from FileNameCategory +--R +--E 920 + +--S 921 of 3320 +)d op extensionDegree +--R +--R +--RThere are 2 exposed functions called extensionDegree : +--R [1] -> PositiveInteger from D if D has FAXF(D2) and D2 has FIELD +--R +--R [2] -> OnePointCompletion(PositiveInteger) from D +--R if D has XF(D2) and D2 has FIELD +--R +--RThere are 2 unexposed functions called extensionDegree : +--R [1] -> PositiveInteger from FiniteAlgebraicExtensionField&(D2,D3) +--R if D3 has FIELD and D2 has FAXF(D3) +--R [2] -> OnePointCompletion(PositiveInteger) +--R from FiniteAlgebraicExtensionField&(D2,D3) +--R if D3 has FIELD and D2 has FAXF(D3) +--R +--RExamples of extensionDegree from FiniteAlgebraicExtensionField& +--R +--R +--RExamples of extensionDegree from FiniteAlgebraicExtensionField +--R +--R +--RExamples of extensionDegree from ExtensionField +--R +--E 921 + +--S 922 of 3320 done +)d op exteriorDifferential +--R +--R +--RThere is one unexposed function called exteriorDifferential : +--R [1] DeRhamComplex(D1,D2) -> DeRhamComplex(D1,D2) from DeRhamComplex( +--R D1,D2) +--R if D1 has Join(Ring,OrderedSet) and D2: LIST(SYMBOL) +--R +--RExamples of exteriorDifferential from DeRhamComplex +--R +--Rder := DeRhamComplex(Integer,[x,y,z]) +--RR := Expression(Integer) +--R[dx,dy,dz] := [generator(i)$der for i in 1..3] +--Rf : R := x**2*y*z-5*x**3*y**2*z**5 +--Rg : R := z**2*y*cos(z)-7*sin(x**3*y**2)*z**2 +--Rh : R :=x*y*z-2*x**3*y*z**2 +--Ralpha : der := f*dx + g*dy + h*dz +--RexteriorDifferential alpha +--R +--E 922 + +--S 923 of 3320 +)d op external? +--R +--R +--RThere is one exposed function called external? : +--R [1] FortranType -> Boolean from FortranType +--R +--RExamples of external? from FortranType +--R +--E 923 + +--S 924 of 3320 +)d op externalList +--R +--R +--RThere is one exposed function called externalList : +--R [1] SymbolTable -> List(Symbol) from SymbolTable +--R +--RExamples of externalList from SymbolTable +--R +--E 924 + +--S 925 of 3320 +)d op extract +--R +--R +--RThere is one exposed function called extract : +--R [1] (SparseEchelonMatrix(D2,D3),Integer,Integer) -> +--R SparseEchelonMatrix(D2,D3) +--R from SparseEchelonMatrix(D2,D3) if D2 has ORDSET and D3 +--R has RING +--R +--RExamples of extract from SparseEchelonMatrix +--R +--E 925 + +--S 926 of 3320 +)d op extract! +--R +--R +--RThere are 6 exposed functions called extract! : +--R [1] ArrayStack(D1) -> D1 from ArrayStack(D1) if D1 has SETCAT +--R [2] D -> D1 from D if D has BGAGG(D1) and D1 has TYPE +--R [3] Dequeue(D1) -> D1 from Dequeue(D1) if D1 has SETCAT +--R [4] Heap(D1) -> D1 from Heap(D1) if D1 has ORDSET +--R [5] Queue(D1) -> D1 from Queue(D1) if D1 has SETCAT +--R [6] Stack(D1) -> D1 from Stack(D1) if D1 has SETCAT +--R +--RExamples of extract! from ArrayStack +--R +--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] +--Rextract! a +--Ra +--R +--R +--RExamples of extract! from BagAggregate +--R +--R +--RExamples of extract! from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rextract! a +--Ra +--R +--R +--RExamples of extract! from Heap +--R +--Ra:Heap INT:= heap [1,2,3,4,5] +--Rextract! a +--Ra +--R +--R +--RExamples of extract! from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Rextract! a +--Ra +--R +--R +--RExamples of extract! from Stack +--R +--Ra:Stack INT:= stack [1,2,3,4,5] +--Rextract! a +--Ra +--R +--E 926 + +--S 927 of 3320 +)d op extractBottom! +--R +--R +--RThere are 2 exposed functions called extractBottom! : +--R [1] Dequeue(D1) -> D1 from Dequeue(D1) if D1 has SETCAT +--R [2] D -> D1 from D if D has DQAGG(D1) and D1 has TYPE +--R +--RExamples of extractBottom! from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--RextractBottom! a +--Ra +--R +--R +--RExamples of extractBottom! from DequeueAggregate +--R +--E 927 + +--S 928 of 3320 +)d op extractClosed +--R +--R +--RThere is one unexposed function called extractClosed : +--R [1] SubSpace(D2,D3) -> Boolean from SubSpace(D2,D3) if D2: PI and D3 +--R has RING +--R +--RExamples of extractClosed from SubSpace +--R +--E 928 + +--S 929 of 3320 +)d op extractIfCan +--R +--R +--RThere is one unexposed function called extractIfCan : +--R [1] D2 -> Union(D1,"failed") from TabulatedComputationPackage(D2,D1) +--R if D1 has SETCAT and D2 has SETCAT +--R +--RExamples of extractIfCan from TabulatedComputationPackage +--R +--E 929 + +--S 930 of 3320 +)d op extractIndex +--R +--R +--RThere is one unexposed function called extractIndex : +--R [1] SubSpace(D2,D3) -> NonNegativeInteger from SubSpace(D2,D3) +--R if D2: PI and D3 has RING +--R +--RExamples of extractIndex from SubSpace +--R +--E 930 + +--S 931 of 3320 +)d op extractPoint +--R +--R +--RThere is one unexposed function called extractPoint : +--R [1] SubSpace(D2,D3) -> Point(D3) from SubSpace(D2,D3) if D2: PI and +--R D3 has RING +--R +--RExamples of extractPoint from SubSpace +--R +--E 931 + +--S 932 of 3320 +)d op extractProperty +--R +--R +--RThere is one unexposed function called extractProperty : +--R [1] SubSpace(D2,D3) -> SubSpaceComponentProperty from SubSpace(D2,D3 +--R ) +--R if D2: PI and D3 has RING +--R +--RExamples of extractProperty from SubSpace +--R +--E 932 + +--S 933 of 3320 +)d op extractSplittingLeaf +--R +--R +--RThere is one unexposed function called extractSplittingLeaf : +--R [1] SplittingTree(D1,D2) -> Union(SplittingTree(D1,D2),"failed") +--R from SplittingTree(D1,D2) +--R if D1 has Join(SetCategory,Aggregate) and D2 has Join( +--R SetCategory,Aggregate) +--R +--RExamples of extractSplittingLeaf from SplittingTree +--R +--E 933 + +--S 934 of 3320 +)d op extractTop! +--R +--R +--RThere are 2 exposed functions called extractTop! : +--R [1] Dequeue(D1) -> D1 from Dequeue(D1) if D1 has SETCAT +--R [2] D -> D1 from D if D has DQAGG(D1) and D1 has TYPE +--R +--RExamples of extractTop! from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--RextractTop! a +--Ra +--R +--R +--RExamples of extractTop! from DequeueAggregate +--R +--E 934 + +--S 935 of 3320 +)d op eyeDistance +--R +--R +--RThere is one exposed function called eyeDistance : +--R [1] (ThreeDimensionalViewport,Float) -> Void from +--R ThreeDimensionalViewport +--R +--RExamples of eyeDistance from ThreeDimensionalViewport +--R +--E 935 + +--S 936 of 3320 +)d op F +--R +--R +--RThere is one unexposed function called F : +--R [1] (NonNegativeInteger,NonNegativeInteger) -> (() -> Float) +--R from RandomFloatDistributions +--R +--RExamples of F from RandomFloatDistributions +--R +--E 936 + +--S 937 of 3320 +)d op f01brf +--R +--R +--RThere is one exposed function called f01brf : +--R [1] (Integer,Integer,Integer,Integer,DoubleFloat,Boolean,Boolean, +--R List(Boolean),Matrix(DoubleFloat),Matrix(Integer),Matrix(Integer) +--R ,Integer) -> Result +--R from NagMatrixOperationsPackage +--R +--RExamples of f01brf from NagMatrixOperationsPackage +--R +--E 937 + +--S 938 of 3320 +)d op f01bsf +--R +--R +--RThere is one exposed function called f01bsf : +--R [1] (Integer,Integer,Integer,Matrix(Integer),Matrix(Integer),Matrix( +--R Integer),Matrix(Integer),Boolean,DoubleFloat,Boolean,Matrix( +--R Integer),Matrix(DoubleFloat),Integer) -> Result +--R from NagMatrixOperationsPackage +--R +--RExamples of f01bsf from NagMatrixOperationsPackage +--R +--E 938 + +--S 939 of 3320 +)d op f01maf +--R +--R +--RThere is one exposed function called f01maf : +--R [1] (Integer,Integer,Integer,Integer,List(Boolean),Matrix( +--R DoubleFloat),Matrix(Integer),Matrix(Integer),DoubleFloat, +--R DoubleFloat,Integer) -> Result +--R from NagMatrixOperationsPackage +--R +--RExamples of f01maf from NagMatrixOperationsPackage +--R +--E 939 + +--S 940 of 3320 +)d op f01mcf +--R +--R +--RThere is one exposed function called f01mcf : +--R [1] (Integer,Matrix(DoubleFloat),Integer,Matrix(Integer),Integer) +--R -> Result +--R from NagMatrixOperationsPackage +--R +--RExamples of f01mcf from NagMatrixOperationsPackage +--R +--E 940 + +--S 941 of 3320 +)d op f01qcf +--R +--R +--RThere is one exposed function called f01qcf : +--R [1] (Integer,Integer,Integer,Matrix(DoubleFloat),Integer) -> Result +--R from NagMatrixOperationsPackage +--R +--RExamples of f01qcf from NagMatrixOperationsPackage +--R +--E 941 + +--S 942 of 3320 +)d op f01qdf +--R +--R +--RThere is one exposed function called f01qdf : +--R [1] (String,String,Integer,Integer,Matrix(DoubleFloat),Integer, +--R Matrix(DoubleFloat),Integer,Integer,Matrix(DoubleFloat),Integer) +--R -> Result +--R from NagMatrixOperationsPackage +--R +--RExamples of f01qdf from NagMatrixOperationsPackage +--R +--E 942 + +--S 943 of 3320 +)d op f01qef +--R +--R +--RThere is one exposed function called f01qef : +--R [1] (String,Integer,Integer,Integer,Integer,Matrix(DoubleFloat), +--R Matrix(DoubleFloat),Integer) -> Result +--R from NagMatrixOperationsPackage +--R +--RExamples of f01qef from NagMatrixOperationsPackage +--R +--E 943 + +--S 944 of 3320 +)d op f01rcf +--R +--R +--RThere is one exposed function called f01rcf : +--R [1] (Integer,Integer,Integer,Matrix(Complex(DoubleFloat)),Integer) +--R -> Result +--R from NagMatrixOperationsPackage +--R +--RExamples of f01rcf from NagMatrixOperationsPackage +--R +--E 944 + +--S 945 of 3320 +)d op f01rdf +--R +--R +--RThere is one exposed function called f01rdf : +--R [1] (String,String,Integer,Integer,Matrix(Complex(DoubleFloat)), +--R Integer,Matrix(Complex(DoubleFloat)),Integer,Integer,Matrix( +--R Complex(DoubleFloat)),Integer) -> Result +--R from NagMatrixOperationsPackage +--R +--RExamples of f01rdf from NagMatrixOperationsPackage +--R +--E 945 + +--S 946 of 3320 +)d op f01ref +--R +--R +--RThere is one exposed function called f01ref : +--R [1] (String,Integer,Integer,Integer,Integer,Matrix(Complex( +--R DoubleFloat)),Matrix(Complex(DoubleFloat)),Integer) -> Result +--R from NagMatrixOperationsPackage +--R +--RExamples of f01ref from NagMatrixOperationsPackage +--R +--E 946 + +--S 947 of 3320 +)d op f02aaf +--R +--R +--RThere is one exposed function called f02aaf : +--R [1] (Integer,Integer,Matrix(DoubleFloat),Integer) -> Result +--R from NagEigenPackage +--R +--RExamples of f02aaf from NagEigenPackage +--R +--E 947 + +--S 948 of 3320 +)d op f02abf +--R +--R +--RThere is one exposed function called f02abf : +--R [1] (Matrix(DoubleFloat),Integer,Integer,Integer,Integer) -> Result +--R from NagEigenPackage +--R +--RExamples of f02abf from NagEigenPackage +--R +--E 948 + +--S 949 of 3320 +)d op f02adf +--R +--R +--RThere is one exposed function called f02adf : +--R [1] (Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat) +--R ,Integer) -> Result +--R from NagEigenPackage +--R +--RExamples of f02adf from NagEigenPackage +--R +--E 949 + +--S 950 of 3320 +)d op f02aef +--R +--R +--RThere is one exposed function called f02aef : +--R [1] (Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Integer) -> Result +--R from NagEigenPackage +--R +--RExamples of f02aef from NagEigenPackage +--R +--E 950 + +--S 951 of 3320 +)d op f02aff +--R +--R +--RThere is one exposed function called f02aff : +--R [1] (Integer,Integer,Matrix(DoubleFloat),Integer) -> Result +--R from NagEigenPackage +--R +--RExamples of f02aff from NagEigenPackage +--R +--E 951 + +--S 952 of 3320 +)d op f02agf +--R +--R +--RThere is one exposed function called f02agf : +--R [1] (Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Integer) +--R -> Result +--R from NagEigenPackage +--R +--RExamples of f02agf from NagEigenPackage +--R +--E 952 + +--S 953 of 3320 +)d op f02ajf +--R +--R +--RThere is one exposed function called f02ajf : +--R [1] (Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat) +--R ,Integer) -> Result +--R from NagEigenPackage +--R +--RExamples of f02ajf from NagEigenPackage +--R +--E 953 + +--S 954 of 3320 +)d op f02akf +--R +--R +--RThere is one exposed function called f02akf : +--R [1] (Integer,Integer,Integer,Integer,Integer,Matrix(DoubleFloat), +--R Matrix(DoubleFloat),Integer) -> Result +--R from NagEigenPackage +--R +--RExamples of f02akf from NagEigenPackage +--R +--E 954 + +--S 955 of 3320 +)d op f02awf +--R +--R +--RThere is one exposed function called f02awf : +--R [1] (Integer,Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat) +--R ,Integer) -> Result +--R from NagEigenPackage +--R +--RExamples of f02awf from NagEigenPackage +--R +--E 955 + +--S 956 of 3320 +)d op f02axf +--R +--R +--RThere is one exposed function called f02axf : +--R [1] (Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Integer,Integer +--R ,Integer,Integer,Integer) -> Result +--R from NagEigenPackage +--R +--RExamples of f02axf from NagEigenPackage +--R +--E 956 + +--S 957 of 3320 +)d op f02bbf +--R +--R +--RThere is one exposed function called f02bbf : +--R [1] (Integer,Integer,DoubleFloat,DoubleFloat,Integer,Integer,Matrix( +--R DoubleFloat),Integer) -> Result +--R from NagEigenPackage +--R +--RExamples of f02bbf from NagEigenPackage +--R +--E 957 + +--S 958 of 3320 +)d op f02bjf +--R +--R +--RThere is one exposed function called f02bjf : +--R [1] (Integer,Integer,Integer,DoubleFloat,Boolean,Integer,Matrix( +--R DoubleFloat),Matrix(DoubleFloat),Integer) -> Result +--R from NagEigenPackage +--R +--RExamples of f02bjf from NagEigenPackage +--R +--E 958 + +--S 959 of 3320 +)d op f02fjf +--R +--R +--RThere are 2 exposed functions called f02fjf : +--R [1] (Integer,Integer,DoubleFloat,Integer,Integer,Integer,Integer, +--R Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Union(fn: +--R FileName,fp: Asp27(DOT)),Union(fn: FileName,fp: Asp28(IMAGE))) +--R -> Result +--R from NagEigenPackage +--R [2] (Integer,Integer,DoubleFloat,Integer,Integer,Integer,Integer, +--R Integer,Integer,Integer,Matrix(DoubleFloat),Integer,Union(fn: +--R FileName,fp: Asp27(DOT)),Union(fn: FileName,fp: Asp28(IMAGE)), +--R FileName) -> Result +--R from NagEigenPackage +--R +--RExamples of f02fjf from NagEigenPackage +--R +--E 959 + +--S 960 of 3320 +)d op f02wef +--R +--R +--RThere is one exposed function called f02wef : +--R [1] (Integer,Integer,Integer,Integer,Integer,Boolean,Integer,Boolean +--R ,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Integer) -> +--R Result +--R from NagEigenPackage +--R +--RExamples of f02wef from NagEigenPackage +--R +--E 960 + +--S 961 of 3320 +)d op f02xef +--R +--R +--RThere is one exposed function called f02xef : +--R [1] (Integer,Integer,Integer,Integer,Integer,Boolean,Integer,Boolean +--R ,Integer,Matrix(Complex(DoubleFloat)),Matrix(Complex(DoubleFloat) +--R ),Integer) -> Result +--R from NagEigenPackage +--R +--RExamples of f02xef from NagEigenPackage +--R +--E 961 + +--S 962 of 3320 +)d op f04adf +--R +--R +--RThere is one exposed function called f04adf : +--R [1] (Integer,Matrix(Complex(DoubleFloat)),Integer,Integer,Integer, +--R Integer,Matrix(Complex(DoubleFloat)),Integer) -> Result +--R from NagLinearEquationSolvingPackage +--R +--RExamples of f04adf from NagLinearEquationSolvingPackage +--R +--E 962 + +--S 963 of 3320 +)d op f04arf +--R +--R +--RThere is one exposed function called f04arf : +--R [1] (Integer,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Integer +--R ) -> Result +--R from NagLinearEquationSolvingPackage +--R +--RExamples of f04arf from NagLinearEquationSolvingPackage +--R +--E 963 + +--S 964 of 3320 +)d op f04asf +--R +--R +--RThere is one exposed function called f04asf : +--R [1] (Integer,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Integer +--R ) -> Result +--R from NagLinearEquationSolvingPackage +--R +--RExamples of f04asf from NagLinearEquationSolvingPackage +--R +--E 964 + +--S 965 of 3320 +)d op f04atf +--R +--R +--RThere is one exposed function called f04atf : +--R [1] (Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Integer,Integer +--R ,Integer) -> Result +--R from NagLinearEquationSolvingPackage +--R +--RExamples of f04atf from NagLinearEquationSolvingPackage +--R +--E 965 + +--S 966 of 3320 +)d op f04axf +--R +--R +--RThere is one exposed function called f04axf : +--R [1] (Integer,Matrix(DoubleFloat),Integer,Matrix(Integer),Matrix( +--R Integer),Integer,Matrix(Integer),Matrix(DoubleFloat)) -> Result +--R from NagLinearEquationSolvingPackage +--R +--RExamples of f04axf from NagLinearEquationSolvingPackage +--R +--E 966 + +--S 967 of 3320 +)d op f04faf +--R +--R +--RThere is one exposed function called f04faf : +--R [1] (Integer,Integer,Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R DoubleFloat),Integer) -> Result +--R from NagLinearEquationSolvingPackage +--R +--RExamples of f04faf from NagLinearEquationSolvingPackage +--R +--E 967 + +--S 968 of 3320 +)d op f04jgf +--R +--R +--RThere is one exposed function called f04jgf : +--R [1] (Integer,Integer,Integer,DoubleFloat,Integer,Matrix(DoubleFloat) +--R ,Matrix(DoubleFloat),Integer) -> Result +--R from NagLinearEquationSolvingPackage +--R +--RExamples of f04jgf from NagLinearEquationSolvingPackage +--R +--E 968 + +--S 969 of 3320 +)d op f04maf +--R +--R +--RThere is one exposed function called f04maf : +--R [1] (Integer,Integer,Matrix(DoubleFloat),Integer,Matrix(Integer), +--R Integer,Matrix(Integer),Matrix(DoubleFloat),Matrix(Integer), +--R Matrix(Integer),Matrix(DoubleFloat),Matrix(DoubleFloat),Matrix( +--R Integer),Integer) -> Result +--R from NagLinearEquationSolvingPackage +--R +--RExamples of f04maf from NagLinearEquationSolvingPackage +--R +--E 969 + +--S 970 of 3320 +)d op f04mbf +--R +--R +--RThere is one exposed function called f04mbf : +--R [1] (Integer,Matrix(DoubleFloat),Boolean,DoubleFloat,Integer,Integer +--R ,Integer,Integer,DoubleFloat,Integer,Union(fn: FileName,fp: Asp28 +--R (APROD)),Union(fn: FileName,fp: Asp34(MSOLVE))) -> Result +--R from NagLinearEquationSolvingPackage +--R +--RExamples of f04mbf from NagLinearEquationSolvingPackage +--R +--E 970 + +--S 971 of 3320 +)d op f04mcf +--R +--R +--RThere is one exposed function called f04mcf : +--R [1] (Integer,Matrix(DoubleFloat),Integer,Matrix(DoubleFloat),Matrix( +--R Integer),Integer,Matrix(DoubleFloat),Integer,Integer,Integer, +--R Integer) -> Result +--R from NagLinearEquationSolvingPackage +--R +--RExamples of f04mcf from NagLinearEquationSolvingPackage +--R +--E 971 + +--S 972 of 3320 +)d op f04qaf +--R +--R +--RThere is one exposed function called f04qaf : +--R [1] (Integer,Integer,DoubleFloat,DoubleFloat,DoubleFloat,DoubleFloat +--R ,Integer,Integer,Integer,Integer,Matrix(DoubleFloat),Integer, +--R Union(fn: FileName,fp: Asp30(APROD))) -> Result +--R from NagLinearEquationSolvingPackage +--R +--RExamples of f04qaf from NagLinearEquationSolvingPackage +--R +--E 972 + +--S 973 of 3320 +)d op f07adf +--R +--R +--RThere is one exposed function called f07adf : +--R [1] (Integer,Integer,Integer,Matrix(DoubleFloat)) -> Result from +--R NagLapack +--R +--RExamples of f07adf from NagLapack +--R +--E 973 + +--S 974 of 3320 +)d op f07aef +--R +--R +--RThere is one exposed function called f07aef : +--R [1] (String,Integer,Integer,Matrix(DoubleFloat),Integer,Matrix( +--R Integer),Integer,Matrix(DoubleFloat)) -> Result +--R from NagLapack +--R +--RExamples of f07aef from NagLapack +--R +--E 974 + +--S 975 of 3320 +)d op f07fdf +--R +--R +--RThere is one exposed function called f07fdf : +--R [1] (String,Integer,Integer,Matrix(DoubleFloat)) -> Result from +--R NagLapack +--R +--RExamples of f07fdf from NagLapack +--R +--E 975 + +--S 976 of 3320 +)d op f07fef +--R +--R +--RThere is one exposed function called f07fef : +--R [1] (String,Integer,Integer,Matrix(DoubleFloat),Integer,Integer, +--R Matrix(DoubleFloat)) -> Result +--R from NagLapack +--R +--RExamples of f07fef from NagLapack +--R +--E 976 + +--S 977 of 3320 +)d op f2df +--R +--R +--RThere is one exposed function called f2df : +--R [1] Float -> DoubleFloat from ExpertSystemToolsPackage +--R +--RExamples of f2df from ExpertSystemToolsPackage +--R +--E 977 + +--S 978 of 3320 +)d op F2EXPRR +--R +--R +--RThere is one exposed function called F2EXPRR : +--R [1] D2 -> Expression(Integer) from GuessFiniteFunctions(D2) +--R if D2 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R +--RExamples of F2EXPRR from GuessFiniteFunctions +--R +--E 978 + +--S 979 of 3320 +)d op F2FG +--R +--R +--RThere is one unexposed function called F2FG : +--R [1] D2 -> D1 from InnerTrigonometricManipulations(D3,D2,D1) +--R if D3 has Join(IntegralDomain,OrderedSet) and D1 has Join( +--R FunctionSpace(Complex(D3)),RadicalCategory, +--R TranscendentalFunctionCategory) and D2 has Join( +--R FunctionSpace(D3),RadicalCategory, +--R TranscendentalFunctionCategory) +--R +--RExamples of F2FG from InnerTrigonometricManipulations +--R +--E 979 + +--S 980 of 3320 +)d op f2st +--R +--R +--RThere is one exposed function called f2st : +--R [1] Float -> String from ExpertSystemToolsPackage +--R +--RExamples of f2st from ExpertSystemToolsPackage +--R +--E 980 + +--S 981 of 3320 +)d op factor +--R +--R +--RThere are 21 exposed functions called factor : +--R [1] (D2,List(AlgebraicNumber)) -> Factored(D2) from AlgFactor(D2) +--R if D2 has UPOLYC(AN) +--R [2] D2 -> Factored(D2) from AlgFactor(D2) if D2 has UPOLYC(AN) +--R [3] (D2,List(AlgebraicNumber)) -> Factored(D2) +--R from AlgebraicMultFact(D4,D5,D2) +--R if D4 has ORDSET and D5 has OAMONS and D2 has POLYCAT(AN, +--R D5,D4) +--R [4] (SparseUnivariatePolynomial(D6),List(AlgebraicNumber)) -> +--R Factored(SparseUnivariatePolynomial(D6)) +--R from AlgebraicMultFact(D4,D5,D6) +--R if D4 has ORDSET and D5 has OAMONS and D6 has POLYCAT(AN, +--R D5,D4) +--R [5] D2 -> Factored(D2) from ComplexFactorization(D3,D2) +--R if D3 has EUCDOM and D2 has UPOLYC(COMPLEX(D3)) +--R [6] D2 -> Factored(D2) from DistinctDegreeFactorize(D3,D2) +--R if D3 has FFIELDC and D2 has UPOLYC(D3) +--R [7] (SparseUnivariatePolynomial(D3),D3) -> Factored( +--R SparseUnivariatePolynomial(D3)) +--R from +--R FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber +--R (D3) +--R if D3 has PACEXTC +--R [8] (SparseUnivariatePolynomial(D3),D3) -> Factored( +--R SparseUnivariatePolynomial(D3)) +--R from +--R FactorisationOverPseudoAlgebraicClosureOfRationalNumber(D3) +--R if D3 has PACRATC +--R [9] D2 -> Factored(D2) from FiniteFieldFactorization(D3,D2) +--R if D3 has FFIELDC and D2 has UPOLYC(D3) +--R [10] D2 -> Factored(D2) +--R from FiniteFieldFactorizationWithSizeParseBySideEffect(D3, +--R D2) +--R if D3 has FFIELDC and D2 has UPOLYC(D3) +--R [11] Complex(Integer) -> Factored(Complex(Integer)) +--R from GaussianFactorizationPackage +--R [12] (D2,Integer) -> List(D2) from ModularDistinctDegreeFactorizer( +--R D2) +--R if D2 has UPOLYC(INT) +--R [13] D2 -> Factored(D2) from MultFiniteFactorize(D3,D4,D5,D2) +--R if D3 has ORDSET and D4 has OAMONS and D5 has FFIELDC and +--R D2 has POLYCAT(D5,D4,D3) +--R [14] SparseUnivariatePolynomial(D6) -> Factored( +--R SparseUnivariatePolynomial(D6)) +--R from MultFiniteFactorize(D3,D4,D5,D6) +--R if D3 has ORDSET and D4 has OAMONS and D5 has FFIELDC and +--R D6 has POLYCAT(D5,D4,D3) +--R [15] D2 -> Factored(D2) from MPolyCatRationalFunctionFactorizer(D3, +--R D4,D5,D2) +--R if D3 has OAMONS and D4 has OrderedSetwith +--R convert : % -> Symboland D5 has INTDOM and D2 has +--R POLYCAT(FRAC(POLY(D5)),D3,D4) +--R [16] D2 -> Factored(D2) from MultivariateFactorize(D3,D4,D5,D2) +--R if D3 has ORDSET and D4 has OAMONS and D5 has Join( +--R EuclideanDomain,CharacteristicZero) and D2 has POLYCAT(D5, +--R D4,D3) +--R [17] SparseUnivariatePolynomial(D6) -> Factored( +--R SparseUnivariatePolynomial(D6)) +--R from MultivariateFactorize(D3,D4,D5,D6) +--R if D3 has ORDSET and D4 has OAMONS and D5 has Join( +--R EuclideanDomain,CharacteristicZero) and D6 has POLYCAT(D5, +--R D4,D3) +--R [18] D2 -> Factored(D2) from RationalFunctionFactor(D2) +--R if D2 has UPOLYC(FRAC(POLY(INT))) +--R [19] D2 -> Factored(D2) from SimpleAlgebraicExtensionAlgFactor(D3,D4 +--R ,D2) +--R if D3 has UPOLYC(FRAC(INT)) and D4 has Join(Field, +--R CharacteristicZero,MonogenicAlgebra(Fraction(Integer),D3)) +--R and D2 has UPOLYC(D4) +--R [20] D2 -> Factored(D2) from SAERationalFunctionAlgFactor(D3,D4,D2) +--R if D3 has UPOLYC(FRAC(POLY(INT))) and D4 has Join(Field, +--R CharacteristicZero,MonogenicAlgebra(Fraction(Polynomial( +--R Integer)),D3)) and D2 has UPOLYC(D4) +--R [21] D -> Factored(D) from D if D has UFD +--R +--RThere are 22 unexposed functions called factor : +--R [1] (D2,D3,Boolean) -> Factored(D2) from ComplexRootFindingPackage( +--R D3,D2) +--R if D3 has Join(Field,OrderedRing) and D2 has UPOLYC( +--R COMPLEX(D3)) +--R [2] (D2,D3) -> Factored(D2) from ComplexRootFindingPackage(D3,D2) +--R if D3 has Join(Field,OrderedRing) and D2 has UPOLYC( +--R COMPLEX(D3)) +--R [3] D2 -> Factored(D2) from ComplexRootFindingPackage(D3,D2) +--R if D3 has Join(Field,OrderedRing) and D2 has UPOLYC( +--R COMPLEX(D3)) +--R [4] D2 -> Factored(D2) from GaloisGroupFactorizer(D2) if D2 has +--R UPOLYC(INT) +--R [5] (D2,NonNegativeInteger) -> Factored(D2) from +--R GaloisGroupFactorizer(D2) +--R if D2 has UPOLYC(INT) +--R [6] (D2,List(NonNegativeInteger)) -> Factored(D2) +--R from GaloisGroupFactorizer(D2) if D2 has UPOLYC(INT) +--R [7] (D2,List(NonNegativeInteger),NonNegativeInteger) -> Factored(D2) +--R from GaloisGroupFactorizer(D2) if D2 has UPOLYC(INT) +--R [8] (D2,NonNegativeInteger,NonNegativeInteger) -> Factored(D2) +--R from GaloisGroupFactorizer(D2) if D2 has UPOLYC(INT) +--R [9] D2 -> Factored(D2) from GeneralizedMultivariateFactorize(D3,D4, +--R D5,D6,D2) +--R if D3 has OrderedSetwith +--R convert : % -> Symbol +--R variable : Symbol -> Union(%,"failed")and D4 has +--R OAMONS and D6 has INTDOM and D5 has INTDOM and D2 has +--R POLYCAT(D6,D4,D3) +--R [10] SparseUnivariatePolynomial(D3) -> Factored( +--R SparseUnivariatePolynomial(D3)) +--R from GenUFactorize(D3) if D3 has EUCDOM +--R [11] (D2,(D5 -> Factored(D5))) -> Factored(D2) +--R from InnerAlgFactor(D4,D5,D6,D2) +--R if D5 has UPOLYC(D4) and D4 has FIELD and D6 has Join( +--R Field,CharacteristicZero,MonogenicAlgebra(D4,D5)) and D2 +--R has UPOLYC(D6) +--R [12] (D2,(SparseUnivariatePolynomial(D6) -> Factored( +--R SparseUnivariatePolynomial(D6)))) -> Factored(D2) +--R from InnerMultFact(D4,D5,D6,D2) +--R if D6 has Join(EuclideanDomain,CharacteristicZero) and D4 +--R has ORDSET and D5 has OAMONS and D2 has POLYCAT(D6,D5,D4) +--R +--R [13] (SparseUnivariatePolynomial(D7),(SparseUnivariatePolynomial(D6) +--R -> Factored(SparseUnivariatePolynomial(D6)))) -> Factored( +--R SparseUnivariatePolynomial(D7)) +--R from InnerMultFact(D4,D5,D6,D7) +--R if D6 has Join(EuclideanDomain,CharacteristicZero) and D4 +--R has ORDSET and D5 has OAMONS and D7 has POLYCAT(D6,D5,D4) +--R +--R [14] D2 -> Factored(D2) from IntegerFactorizationPackage(D2) if D2 +--R has INS +--R [15] (LinearOrdinaryDifferentialOperator1(Fraction(D5)),(D5 -> List( +--R D4))) -> List(LinearOrdinaryDifferentialOperator1(Fraction(D5))) +--R from LinearOrdinaryDifferentialOperatorFactorizer(D4,D5) +--R if D4 has Join(Field,CharacteristicZero,RetractableTo( +--R Integer),RetractableTo(Fraction(Integer))) and D5 has +--R UPOLYC(D4) +--R [16] LinearOrdinaryDifferentialOperator1(Fraction(D4)) -> List( +--R LinearOrdinaryDifferentialOperator1(Fraction(D4))) +--R from LinearOrdinaryDifferentialOperatorFactorizer(D3,D4) +--R if D3 has ACF and D3 has Join(Field,CharacteristicZero, +--R RetractableTo(Integer),RetractableTo(Fraction(Integer))) +--R and D4 has UPOLYC(D3) +--R [17] OrderedFreeMonoid(D3) -> List(LyndonWord(D3)) from LyndonWord( +--R D3) +--R if D3 has ORDSET +--R [18] D2 -> Factored(D2) from MPolyCatPolyFactorizer(D3,D4,D5,D2) +--R if D3 has OAMONS and D4 has OrderedSetwith +--R convert : % -> Symbol +--R variable : Symbol -> Union(%,"failed")and D5 has +--R EUCDOM and D2 has POLYCAT(POLY(D5),D3,D4) +--R [19] D2 -> Factored(D2) from MRationalFactorize(D3,D4,D5,D2) +--R if D3 has OAMONS and D4 has ORDSET and D5 has Join( +--R EuclideanDomain,CharacteristicZero) and D2 has POLYCAT(FRAC +--R (D5),D3,D4) +--R [20] D2 -> Factored(D2) from RationalFactorize(D2) if D2 has UPOLYC( +--R FRAC(INT)) +--R [21] SparseUnivariatePolynomial(Fraction(D6)) -> Factored( +--R SparseUnivariatePolynomial(Fraction(D6))) +--R from SupFractionFactorizer(D3,D4,D5,D6) +--R if D3 has OAMONS and D4 has ORDSET and D5 has GCDDOM and +--R D6 has POLYCAT(D5,D3,D4) +--R [22] D2 -> Factored(D2) from UnivariateFactorize(D2) if D2 has +--R UPOLYC(INT) +--R +--RExamples of factor from AlgFactor +--R +--R +--RExamples of factor from AlgebraicMultFact +--R +--R +--RExamples of factor from ComplexFactorization +--R +--R +--RExamples of factor from ComplexRootFindingPackage +--R +--R +--RExamples of factor from DistinctDegreeFactorize +--R +--R +--RExamples of factor from FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber +--R +--R +--RExamples of factor from FactorisationOverPseudoAlgebraicClosureOfRationalNumber +--R +--R +--RExamples of factor from FiniteFieldFactorization +--R +--R +--RExamples of factor from FiniteFieldFactorizationWithSizeParseBySideEffect +--R +--R +--RExamples of factor from GaloisGroupFactorizer +--R +--R +--RExamples of factor from GaussianFactorizationPackage +--R +--R +--RExamples of factor from GeneralizedMultivariateFactorize +--R +--R +--RExamples of factor from GenUFactorize +--R +--R +--RExamples of factor from InnerAlgFactor +--R +--R +--RExamples of factor from InnerMultFact +--R +--R +--RExamples of factor from IntegerFactorizationPackage +--R +--R +--RExamples of factor from LinearOrdinaryDifferentialOperatorFactorizer +--R +--R +--RExamples of factor from LyndonWord +--R +--R +--RExamples of factor from ModularDistinctDegreeFactorizer +--R +--R +--RExamples of factor from MultFiniteFactorize +--R +--R +--RExamples of factor from MPolyCatPolyFactorizer +--R +--R +--RExamples of factor from MPolyCatRationalFunctionFactorizer +--R +--R +--RExamples of factor from MRationalFactorize +--R +--R +--RExamples of factor from MultivariateFactorize +--R +--R +--RExamples of factor from RationalFactorize +--R +--R +--RExamples of factor from RationalFunctionFactor +--R +--R +--RExamples of factor from SimpleAlgebraicExtensionAlgFactor +--R +--R +--RExamples of factor from SAERationalFunctionAlgFactor +--R +--R +--RExamples of factor from SupFractionFactorizer +--R +--R +--RExamples of factor from UniqueFactorizationDomain +--R +--R +--RExamples of factor from UnivariateFactorize +--R +--E 981 + +--S 982 of 3320 +)d op factor1 +--R +--R +--RThere is one unexposed function called factor1 : +--R [1] LinearOrdinaryDifferentialOperator1(Fraction(D4)) -> List( +--R LinearOrdinaryDifferentialOperator1(Fraction(D4))) +--R from LinearOrdinaryDifferentialOperatorFactorizer(D3,D4) +--R if D3 has ACF and D3 has Join(Field,CharacteristicZero, +--R RetractableTo(Integer),RetractableTo(Fraction(Integer))) +--R and D4 has UPOLYC(D3) +--R +--RExamples of factor1 from LinearOrdinaryDifferentialOperatorFactorizer +--R +--E 982 + +--S 983 of 3320 +)d op factorAndSplit +--R +--R +--RThere is one exposed function called factorAndSplit : +--R [1] Equation(D2) -> List(Equation(D2)) from Equation(D2) +--R if D2 has INTDOM and D2 has TYPE +--R +--RExamples of factorAndSplit from Equation +--R +--E 983 + +--S 984 of 3320 +)d op factorByRecursion +--R +--R +--RThere are 2 unexposed functions called factorByRecursion : +--R [1] SparseUnivariatePolynomial(D6) -> Factored( +--R SparseUnivariatePolynomial(D6)) +--R from PolynomialFactorizationByRecursion(D3,D4,D5,D6) +--R if D3 has PFECAT and D4 has OAMONS and D5 has ORDSET and +--R D6 has POLYCAT(D3,D4,D5) +--R [2] SparseUnivariatePolynomial(D4) -> Factored( +--R SparseUnivariatePolynomial(D4)) +--R from PolynomialFactorizationByRecursionUnivariate(D3,D4) +--R if D3 has PFECAT and D4 has UPOLYC(D3) +--R +--RExamples of factorByRecursion from PolynomialFactorizationByRecursion +--R +--R +--RExamples of factorByRecursion from PolynomialFactorizationByRecursionUnivariate +--R +--E 984 + +--S 985 of 3320 +)d op factorCantorZassenhaus +--R +--R +--RThere are 2 exposed functions called factorCantorZassenhaus : +--R [1] (D2,NonNegativeInteger) -> List(D2) from +--R FiniteFieldFactorization(D4,D2) +--R if D4 has FFIELDC and D2 has UPOLYC(D4) +--R [2] (D2,NonNegativeInteger) -> List(D2) +--R from FiniteFieldFactorizationWithSizeParseBySideEffect(D4, +--R D2) +--R if D4 has FFIELDC and D2 has UPOLYC(D4) +--R +--RExamples of factorCantorZassenhaus from FiniteFieldFactorization +--R +--R +--RExamples of factorCantorZassenhaus from FiniteFieldFactorizationWithSizeParseBySideEffect +--R +--E 985 + +--S 986 of 3320 +)d op factorFraction +--R +--R +--RThere is one exposed function called factorFraction : +--R [1] Fraction(Polynomial(D3)) -> Fraction(Factored(Polynomial(D3))) +--R from RationalFunctionFactorizer(D3) if D3 has EUCDOM +--R +--RExamples of factorFraction from RationalFunctionFactorizer +--R +--E 986 + +--S 987 of 3320 +)d op factorGroebnerBasis +--R +--R +--RThere are 2 exposed functions called factorGroebnerBasis : +--R [1] List(D6) -> List(List(D6)) from GroebnerFactorizationPackage(D3, +--R D4,D5,D6) +--R if D3 has Join(EuclideanDomain,CharacteristicZero) and D4 +--R has OAMONS and D5 has ORDSET and D6 has POLYCAT(D3,D4,D5) +--R +--R [2] (List(D7),Boolean) -> List(List(D7)) +--R from GroebnerFactorizationPackage(D4,D5,D6,D7) +--R if D4 has Join(EuclideanDomain,CharacteristicZero) and D5 +--R has OAMONS and D6 has ORDSET and D7 has POLYCAT(D4,D5,D6) +--R +--R +--RExamples of factorGroebnerBasis from GroebnerFactorizationPackage +--R +--E 987 + +--S 988 of 3320 +)d op factorial +--R +--R +--RThere are 2 exposed functions called factorial : +--R [1] D -> D from D if D has CFCAT +--R [2] D1 -> D1 from IntegerCombinatoricFunctions(D1) if D1 has INS +--R +--RThere is one unexposed function called factorial : +--R [1] D1 -> D1 from CombinatorialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R +--RExamples of factorial from CombinatorialFunctionCategory +--R +--R +--RExamples of factorial from CombinatorialFunction +--R +--R +--RExamples of factorial from IntegerCombinatoricFunctions +--R +--E 988 + +--S 989 of 3320 +)d op factorials +--R +--R +--RThere are 2 exposed functions called factorials : +--R [1] (D,Symbol) -> D from D if D has COMBOPC +--R [2] D -> D from D if D has COMBOPC +--R +--RThere are 2 unexposed functions called factorials : +--R [1] D1 -> D1 from CombinatorialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R [2] (D1,Symbol) -> D1 from CombinatorialFunction(D3,D1) +--R if D3 has Join(OrderedSet,IntegralDomain) and D1 has FS(D3 +--R ) +--R +--RExamples of factorials from CombinatorialFunction +--R +--R +--RExamples of factorials from CombinatorialOpsCategory +--R +--E 989 + +--S 990 of 3320 +)d op factorList +--R +--R +--RThere is one exposed function called factorList : +--R [1] Factored(D2) -> List(Record(flg: Union("nil","sqfr","irred", +--R "prime"),fctr: D2,xpnt: Integer)) +--R from Factored(D2) if D2 has INTDOM +--R +--RThere is one unexposed function called factorList : +--R [1] (D2,NonNegativeInteger,NonNegativeInteger,NonNegativeInteger) +--R -> List(SparseUnivariatePolynomial(D2)) +--R from ChineseRemainderToolsForIntegralBases(D2,D4,D5) +--R if D2 has FFIELDC and D4 has UPOLYC(D2) and D5 has UPOLYC( +--R D4) +--R +--RExamples of factorList from Factored +--R +--Rf:=nilFactor(x-y,3) +--RfactorList f +--R +--R +--RExamples of factorList from ChineseRemainderToolsForIntegralBases +--R +--E 990 + +--S 991 of 3320 +)d op factorOfDegree +--R +--R +--RThere are 6 unexposed functions called factorOfDegree : +--R [1] (PositiveInteger,D1) -> Union(D1,"failed") from +--R GaloisGroupFactorizer(D1) +--R if D1 has UPOLYC(INT) +--R [2] (PositiveInteger,D1,NonNegativeInteger) -> Union(D1,"failed") +--R from GaloisGroupFactorizer(D1) if D1 has UPOLYC(INT) +--R [3] (PositiveInteger,D1,List(NonNegativeInteger)) -> Union(D1, +--R "failed") +--R from GaloisGroupFactorizer(D1) if D1 has UPOLYC(INT) +--R [4] (PositiveInteger,D1,List(NonNegativeInteger),NonNegativeInteger) +--R -> Union(D1,"failed") +--R from GaloisGroupFactorizer(D1) if D1 has UPOLYC(INT) +--R [5] (PositiveInteger,D1,List(NonNegativeInteger),NonNegativeInteger, +--R Boolean) -> Union(D1,"failed") +--R from GaloisGroupFactorizer(D1) if D1 has UPOLYC(INT) +--R [6] (PositiveInteger,Factored(D1)) -> D1 +--R from GaloisGroupPolynomialUtilities(D4,D1) +--R if D1 has UPOLYC(D4) and D4 has RING +--R +--RExamples of factorOfDegree from GaloisGroupFactorizer +--R +--R +--RExamples of factorOfDegree from GaloisGroupPolynomialUtilities +--R +--E 991 + +--S 992 of 3320 +)d op factorPolynomial +--R +--R +--RThere are 2 exposed functions called factorPolynomial : +--R [1] SparseUnivariatePolynomial(Expression(D3)) -> Factored( +--R SparseUnivariatePolynomial(Expression(D3))) +--R from Expression(D3) if D3 has GCDDOM and D3 has INTDOM and +--R D3 has ORDSET +--R [2] SparseUnivariatePolynomial(D) -> Factored( +--R SparseUnivariatePolynomial(D)) +--R from D if D has PFECAT +--R +--RExamples of factorPolynomial from Expression +--R +--R +--RExamples of factorPolynomial from PolynomialFactorizationExplicit +--R +--E 992 + +--S 993 of 3320 +)d op factors +--R +--R +--RThere is one exposed function called factors : +--R [1] Factored(D2) -> List(Record(factor: D2,exponent: Integer)) +--R from Factored(D2) if D2 has INTDOM +--R +--RThere are 3 unexposed functions called factors : +--R [1] FreeGroup(D2) -> List(Record(gen: D2,exp: Integer)) from +--R FreeGroup(D2) +--R if D2 has SETCAT +--R [2] FreeMonoid(D2) -> List(Record(gen: D2,exp: NonNegativeInteger)) +--R from FreeMonoid(D2) if D2 has SETCAT +--R [3] OrderedFreeMonoid(D2) -> List(Record(gen: D2,exp: +--R NonNegativeInteger)) +--R from OrderedFreeMonoid(D2) if D2 has ORDSET +--R +--RExamples of factors from FreeGroup +--R +--R +--RExamples of factors from FreeMonoid +--R +--R +--RExamples of factors from Factored +--R +--Rf:=x*y^3-3*x^2*y^2+3*x^3*y-x^4 +--Rfactors f +--Rg:=makeFR(z,factorList f) +--Rfactors g +--R +--R +--RExamples of factors from OrderedFreeMonoid +--R +--Rm1:=(x*y*y*z)$OFMONOID(Symbol) +--Rfactors m1 +--R +--E 993 + +--S 994 of 3320 +)d op factorset +--R +--R +--RThere is one unexposed function called factorset : +--R [1] D2 -> List(D2) from ParametricLinearEquations(D3,D4,D5,D2) +--R if D3 has Join(EuclideanDomain,CharacteristicZero) and D4 +--R has Join(OrderedSet,ConvertibleTo(Symbol)) and D5 has +--R OAMONS and D2 has POLYCAT(D3,D5,D4) +--R +--RExamples of factorset from ParametricLinearEquations +--R +--E 994 + +--S 995 of 3320 +)d op factorSFBRlcUnit +--R +--R +--RThere are 2 unexposed functions called factorSFBRlcUnit : +--R [1] (List(D6),SparseUnivariatePolynomial(D7)) -> Factored( +--R SparseUnivariatePolynomial(D7)) +--R from PolynomialFactorizationByRecursion(D4,D5,D6,D7) +--R if D6 has ORDSET and D4 has PFECAT and D5 has OAMONS and +--R D7 has POLYCAT(D4,D5,D6) +--R [2] SparseUnivariatePolynomial(D4) -> Factored( +--R SparseUnivariatePolynomial(D4)) +--R from PolynomialFactorizationByRecursionUnivariate(D3,D4) +--R if D3 has PFECAT and D4 has UPOLYC(D3) +--R +--RExamples of factorSFBRlcUnit from PolynomialFactorizationByRecursion +--R +--R +--RExamples of factorSFBRlcUnit from PolynomialFactorizationByRecursionUnivariate +--R +--E 995 + +--S 996 of 3320 +)d op factorsOfCyclicGroupSize +--R +--R +--RThere is one exposed function called factorsOfCyclicGroupSize : +--R [1] -> List(Record(factor: Integer,exponent: Integer)) from D if D +--R has FFIELDC +--R +--RExamples of factorsOfCyclicGroupSize from FiniteFieldCategory +--R +--E 996 + +--S 997 of 3320 +)d op factorsOfDegree +--R +--R +--RThere is one unexposed function called factorsOfDegree : +--R [1] (PositiveInteger,Factored(D5)) -> List(D5) +--R from GaloisGroupPolynomialUtilities(D4,D5) +--R if D5 has UPOLYC(D4) and D4 has RING +--R +--RExamples of factorsOfDegree from GaloisGroupPolynomialUtilities +--R +--E 997 + +--S 998 of 3320 +)d op factorSqFree +--R +--R +--RThere are 2 exposed functions called factorSqFree : +--R [1] (SparseUnivariatePolynomial(D3),D3) -> Factored( +--R SparseUnivariatePolynomial(D3)) +--R from +--R FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber +--R (D3) +--R if D3 has PACEXTC +--R [2] (SparseUnivariatePolynomial(D3),D3) -> Factored( +--R SparseUnivariatePolynomial(D3)) +--R from +--R FactorisationOverPseudoAlgebraicClosureOfRationalNumber(D3) +--R if D3 has PACRATC +--R +--RExamples of factorSqFree from FactorisationOverPseudoAlgebraicClosureOfAlgExtOfRationalNumber +--R +--R +--RExamples of factorSqFree from FactorisationOverPseudoAlgebraicClosureOfRationalNumber +--R +--E 998 + +--S 999 of 3320 +)d op factorSquareFree +--R +--R +--RThere are 3 exposed functions called factorSquareFree : +--R [1] D2 -> Factored(D2) from DistinctDegreeFactorize(D3,D2) +--R if D3 has FFIELDC and D2 has UPOLYC(D3) +--R [2] D2 -> List(D2) from FiniteFieldFactorization(D3,D2) +--R if D3 has FFIELDC and D2 has UPOLYC(D3) +--R [3] D2 -> List(D2) +--R from FiniteFieldFactorizationWithSizeParseBySideEffect(D3, +--R D2) +--R if D3 has FFIELDC and D2 has UPOLYC(D3) +--R +--RThere are 7 unexposed functions called factorSquareFree : +--R [1] D2 -> Factored(D2) from GaloisGroupFactorizer(D2) if D2 has +--R UPOLYC(INT) +--R [2] (D2,NonNegativeInteger) -> Factored(D2) from +--R GaloisGroupFactorizer(D2) +--R if D2 has UPOLYC(INT) +--R [3] (D2,List(NonNegativeInteger)) -> Factored(D2) +--R from GaloisGroupFactorizer(D2) if D2 has UPOLYC(INT) +--R [4] (D2,List(NonNegativeInteger),NonNegativeInteger) -> Factored(D2) +--R from GaloisGroupFactorizer(D2) if D2 has UPOLYC(INT) +--R [5] (D2,NonNegativeInteger,NonNegativeInteger) -> Factored(D2) +--R from GaloisGroupFactorizer(D2) if D2 has UPOLYC(INT) +--R [6] D2 -> Factored(D2) from RationalFactorize(D2) if D2 has UPOLYC( +--R FRAC(INT)) +--R [7] D2 -> Factored(D2) from UnivariateFactorize(D2) if D2 has UPOLYC +--R (INT) +--R +--RExamples of factorSquareFree from DistinctDegreeFactorize +--R +--R +--RExamples of factorSquareFree from FiniteFieldFactorization +--R +--R +--RExamples of factorSquareFree from FiniteFieldFactorizationWithSizeParseBySideEffect +--R +--R +--RExamples of factorSquareFree from GaloisGroupFactorizer +--R +--R +--RExamples of factorSquareFree from RationalFactorize +--R +--R +--RExamples of factorSquareFree from UnivariateFactorize +--R +--E 999 + +--S 1000 of 3320 +)d op factorSquareFreeByRecursion +--R +--R +--RThere are 2 unexposed functions called factorSquareFreeByRecursion : +--R [1] SparseUnivariatePolynomial(D6) -> Factored( +--R SparseUnivariatePolynomial(D6)) +--R from PolynomialFactorizationByRecursion(D3,D4,D5,D6) +--R if D3 has PFECAT and D4 has OAMONS and D5 has ORDSET and +--R D6 has POLYCAT(D3,D4,D5) +--R [2] SparseUnivariatePolynomial(D4) -> Factored( +--R SparseUnivariatePolynomial(D4)) +--R from PolynomialFactorizationByRecursionUnivariate(D3,D4) +--R if D3 has PFECAT and D4 has UPOLYC(D3) +--R +--RExamples of factorSquareFreeByRecursion from PolynomialFactorizationByRecursion +--R +--R +--RExamples of factorSquareFreeByRecursion from PolynomialFactorizationByRecursionUnivariate +--R +--E 1000 + +--S 1001 of 3320 +)d op factorSquareFreePolynomial +--R +--R +--RThere is one exposed function called factorSquareFreePolynomial : +--R [1] SparseUnivariatePolynomial(D) -> Factored( +--R SparseUnivariatePolynomial(D)) +--R from D if D has PFECAT +--R +--RExamples of factorSquareFreePolynomial from PolynomialFactorizationExplicit +--R +--E 1001 + +--S 1002 of 3320 +)d op factorUsingMusser +--R +--R +--RThere are 2 exposed functions called factorUsingMusser : +--R [1] D2 -> Factored(D2) from FiniteFieldFactorization(D3,D2) +--R if D3 has FFIELDC and D2 has UPOLYC(D3) +--R [2] D2 -> Factored(D2) +--R from FiniteFieldFactorizationWithSizeParseBySideEffect(D3, +--R D2) +--R if D3 has FFIELDC and D2 has UPOLYC(D3) +--R +--RExamples of factorUsingMusser from FiniteFieldFactorization +--R +--R +--RExamples of factorUsingMusser from FiniteFieldFactorizationWithSizeParseBySideEffect +--R +--E 1002 + +--S 1003 of 3320 +)d op factorUsingYun +--R +--R +--RThere are 2 exposed functions called factorUsingYun : +--R [1] D2 -> Factored(D2) from FiniteFieldFactorization(D3,D2) +--R if D3 has FFIELDC and D2 has UPOLYC(D3) +--R [2] D2 -> Factored(D2) +--R from FiniteFieldFactorizationWithSizeParseBySideEffect(D3, +--R D2) +--R if D3 has FFIELDC and D2 has UPOLYC(D3) +--R +--RExamples of factorUsingYun from FiniteFieldFactorization +--R +--R +--RExamples of factorUsingYun from FiniteFieldFactorizationWithSizeParseBySideEffect +--R +--E 1003 + +--S 1004 of 3320 +)d op failed +--R +--R +--RThere are 2 unexposed functions called failed : +--R [1] -> PatternMatchListResult(D1,D2,D3) +--R from PatternMatchListResult(D1,D2,D3) +--R if D2 has SETCAT and D1 has SETCAT and D3 has LSAGG(D2) +--R +--R [2] -> PatternMatchResult(D1,D2) from PatternMatchResult(D1,D2) +--R if D1 has SETCAT and D2 has SETCAT +--R +--RExamples of failed from PatternMatchListResult +--R +--R +--RExamples of failed from PatternMatchResult +--R +--E 1004 + +--S 1005 of 3320 +)d op failed? +--R +--R +--RThere are 2 unexposed functions called failed? : +--R [1] PatternMatchListResult(D2,D3,D4) -> Boolean +--R from PatternMatchListResult(D2,D3,D4) +--R if D3 has SETCAT and D2 has SETCAT and D4 has LSAGG(D3) +--R +--R [2] PatternMatchResult(D2,D3) -> Boolean from PatternMatchResult(D2, +--R D3) +--R if D2 has SETCAT and D3 has SETCAT +--R +--RExamples of failed? from PatternMatchListResult +--R +--R +--RExamples of failed? from PatternMatchResult +--R +--E 1005 + +--S 1006 of 3320 +)d op false +--R +--R +--RThere is one exposed function called false : +--R [1] -> Boolean from Boolean +--R +--RExamples of false from Boolean +--R +--E 1006 + +--S 1007 of 3320 +)d op ffactor +--R +--R +--RThere is one unexposed function called ffactor : +--R [1] D2 -> Factored(D2) from FunctionSpaceUnivariatePolynomialFactor( +--R D3,D4,D2) +--R if D3 has Join(IntegralDomain,OrderedSet,RetractableTo( +--R Integer)) and D4 has FS(D3) and D2 has UPOLYC(D4) +--R +--RExamples of ffactor from FunctionSpaceUnivariatePolynomialFactor +--R +--E 1007 + +--S 1008 of 3320 +)d op fffg +--R +--R +--RThere is one exposed function called fffg : +--R [1] (List(D5),((NonNegativeInteger,Vector(SparseUnivariatePolynomial +--R (D5))) -> D5),List(NonNegativeInteger)) -> Matrix( +--R SparseUnivariatePolynomial(D5)) +--R from FractionFreeFastGaussian(D5,D6) +--R if D5 has Join(IntegralDomain,GcdDomain) and D6 has AMR(D5 +--R ,NNI) +--R +--RExamples of fffg from FractionFreeFastGaussian +--R +--E 1008 + +--S 1009 of 3320 +)d op FG2F +--R +--R +--RThere is one unexposed function called FG2F : +--R [1] D2 -> D1 from InnerTrigonometricManipulations(D3,D1,D2) +--R if D3 has Join(IntegralDomain,OrderedSet) and D1 has Join( +--R FunctionSpace(D3),RadicalCategory, +--R TranscendentalFunctionCategory) and D2 has Join( +--R FunctionSpace(Complex(D3)),RadicalCategory, +--R TranscendentalFunctionCategory) +--R +--RExamples of FG2F from InnerTrigonometricManipulations +--R +--E 1009 + +--S 1010 of 3320 +)d op fglmIfCan +--R +--R +--RThere are 2 unexposed functions called fglmIfCan : +--R [1] List(Polynomial(D2)) -> Union(List(Polynomial(D2)),"failed") +--R from FGLMIfCanPackage(D2,D3) if D2 has GCDDOM and D3: LIST +--R (SYMBOL) +--R [2] List(NewSparseMultivariatePolynomial(D2,OrderedVariableList(D3)) +--R ) -> Union(List(NewSparseMultivariatePolynomial(D2, +--R OrderedVariableList(D3))),"failed") +--R from LexTriangularPackage(D2,D3) if D2 has GCDDOM and D3: +--R LIST(SYMBOL) +--R +--RExamples of fglmIfCan from FGLMIfCanPackage +--R +--R +--RExamples of fglmIfCan from LexTriangularPackage +--R +--E 1010 + +--S 1011 of 3320 +)d op fi2df +--R +--R +--RThere is one exposed function called fi2df : +--R [1] Fraction(Integer) -> DoubleFloat from ExpertSystemToolsPackage +--R +--R +--RExamples of fi2df from ExpertSystemToolsPackage +--R +--E 1011 + +--S 1012 of 3320 +)d op fibonacci +--R +--R +--RThere is one exposed function called fibonacci : +--R [1] Integer -> Integer from IntegerNumberTheoryFunctions +--R +--RExamples of fibonacci from IntegerNumberTheoryFunctions +--R +--E 1012 + +--S 1013 of 3320 +)d op figureUnits +--R +--R +--RThere is one unexposed function called figureUnits : +--R [1] List(List(Point(DoubleFloat))) -> List(DoubleFloat) from +--R GraphImage +--R +--RExamples of figureUnits from GraphImage +--R +--E 1013 + +--S 1014 of 3320 +)d op filename +--R +--R +--RThere is one exposed function called filename : +--R [1] (String,String,String) -> D from D if D has FNCAT +--R +--RExamples of filename from FileNameCategory +--R +--E 1014 + +--S 1015 of 3320 +)d op fill! +--R +--R +--RThere are 2 exposed functions called fill! : +--R [1] (D,D1) -> D from D +--R if D has ARR2CAT(D1,D2,D3) and D1 has TYPE and D2 has +--R FLAGG(D1) and D3 has FLAGG(D1) +--R [2] (D,D1) -> D from D +--R if D has shallowlyMutable and D has IXAGG(D2,D1) and D2 +--R has SETCAT and D1 has TYPE +--R +--RExamples of fill! from TwoDimensionalArrayCategory +--R +--Rarr : ARRAY2 INT := new(5,4,0) +--Rfill!(arr,10) +--R +--R +--RExamples of fill! from IndexedAggregate +--R +--E 1015 + +--S 1016 of 3320 +)d op fillPascalTriangle +--R +--R +--RThere is one unexposed function called fillPascalTriangle : +--R [1] -> Void from GaloisGroupUtilities(D2) if D2 has RING +--R +--RExamples of fillPascalTriangle from GaloisGroupUtilities +--R +--E 1016 + +--S 1017 of 3320 +)d op filterUntil +--R +--R +--RThere are 2 exposed functions called filterUntil : +--R [1] ((D2 -> Boolean),InfiniteTuple(D2)) -> InfiniteTuple(D2) +--R from InfiniteTuple(D2) if D2 has TYPE +--R [2] ((D2 -> Boolean),Stream(D2)) -> Stream(D2) from Stream(D2) if D2 +--R has TYPE +--R +--RExamples of filterUntil from InfiniteTuple +--R +--R +--RExamples of filterUntil from Stream +--R +--Rm:=[i for i in 1..] +--Rf(x:PositiveInteger):Boolean == x < 5 +--RfilterUntil(f,m) +--R +--E 1017 + +--S 1018 of 3320 +)d op filterUpTo +--R +--R +--RThere is one exposed function called filterUpTo : +--R [1] (D,Integer) -> D from D if D has LOCPOWC(D2) and D2 has FIELD +--R +--R +--RExamples of filterUpTo from LocalPowerSeriesCategory +--R +--E 1018 + +--S 1019 of 3320 +)d op filterWhile +--R +--R +--RThere are 2 exposed functions called filterWhile : +--R [1] ((D2 -> Boolean),InfiniteTuple(D2)) -> InfiniteTuple(D2) +--R from InfiniteTuple(D2) if D2 has TYPE +--R [2] ((D2 -> Boolean),Stream(D2)) -> Stream(D2) from Stream(D2) if D2 +--R has TYPE +--R +--RExamples of filterWhile from InfiniteTuple +--R +--R +--RExamples of filterWhile from Stream +--R +--Rm:=[i for i in 1..] +--Rf(x:PositiveInteger):Boolean == x < 5 +--RfilterWhile(f,m) +--R +--E 1019 + +--S 1020 of 3320 +)d op find +--R +--R +--RThere is one exposed function called find : +--R [1] ((D1 -> Boolean),D) -> Union(D1,"failed") from D +--R if D has CLAGG(D1) and D1 has TYPE +--R +--RExamples of find from Collection +--R +--E 1020 + +--S 1021 of 3320 +)d op findCoef +--R +--R +--RThere is one exposed function called findCoef : +--R [1] (D,Integer) -> D1 from D if D has LOCPOWC(D1) and D1 has FIELD +--R +--R +--RExamples of findCoef from LocalPowerSeriesCategory +--R +--E 1021 + +--S 1022 of 3320 done +)d op findCycle +--R +--R +--RThere is one exposed function called findCycle : +--R [1] (NonNegativeInteger,Stream(D3)) -> Record(cycle?: Boolean,prefix +--R : NonNegativeInteger,period: NonNegativeInteger) +--R from Stream(D3) if D3 has TYPE +--R +--RExamples of findCycle from Stream +--R +--Rm:=[1,2,3] +--Rn:=repeating(m) +--RfindCycle(3,n) +--RfindCycle(2,n) +--R +--E 1022 + +--S 1023 of 3320 +)d op findOrderOfDivisor +--R +--R +--RThere are 3 exposed functions called findOrderOfDivisor : +--R [1] (D7,Integer,Integer) -> Record(ord: Integer,num: D11,den: D11, +--R upTo: Integer) +--R from GeneralPackageForAlgebraicFunctionField(D9,D10,D11, +--R D12,D13,D1,D2,D7,D3,D4,D5) +--R if D9 has FIELD and D10: LIST(SYMBOL) and D11 has POLYCAT( +--R D9,D12,OVAR(D10)) and D12 has DIRPCAT(#(D10),NNI) and D13 +--R has PRSPCAT(D9) and D1 has LOCPOWC(D9) and D2 has PLACESC( +--R D9,D1) and D7 has DIVCAT(D2) and D3 has INFCLCT(D9,D10,D11, +--R D12,D13,D1,D2,D7,D5) and D5 has BLMETCT and D4 has DSTRCAT( +--R D3) +--R [2] (Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(D4)), +--R Integer,Integer) -> Record(ord: Integer,num: +--R DistributedMultivariatePolynomial(D5,D4),den: +--R DistributedMultivariatePolynomial(D5,D4),upTo: Integer) +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D4,D5 +--R ,D6) +--R if D4 has FFIELDC and D5: LIST(SYMBOL) and D6 has BLMETCT +--R +--R [3] (Divisor(Places(D4)),Integer,Integer) -> Record(ord: Integer,num +--R : DistributedMultivariatePolynomial(D5,D4),den: +--R DistributedMultivariatePolynomial(D5,D4),upTo: Integer) +--R from PackageForAlgebraicFunctionField(D4,D5,D6) +--R if D4 has FIELD and D5: LIST(SYMBOL) and D6 has BLMETCT +--R +--R +--RExamples of findOrderOfDivisor from GeneralPackageForAlgebraicFunctionField +--R +--R +--RExamples of findOrderOfDivisor from PackageForAlgebraicFunctionFieldOverFiniteField +--R +--R +--RExamples of findOrderOfDivisor from PackageForAlgebraicFunctionField +--R +--E 1023 + +--S 1024 of 3320 +)d op findTerm +--R +--R +--RThere is one exposed function called findTerm : +--R [1] (NeitherSparseOrDensePowerSeries(D3),Integer) -> Record(k: +--R Integer,c: D3) +--R from NeitherSparseOrDensePowerSeries(D3) if D3 has FIELD +--R +--R +--RExamples of findTerm from NeitherSparseOrDensePowerSeries +--R +--E 1024 + +--S 1025 of 3320 +)d op finite? +--R +--R +--RThere are 3 exposed functions called finite? : +--R [1] CardinalNumber -> Boolean from CardinalNumber +--R [2] OnePointCompletion(D2) -> Boolean from OnePointCompletion(D2) +--R if D2 has SETCAT +--R [3] OrderedCompletion(D2) -> Boolean from OrderedCompletion(D2) if +--R D2 has SETCAT +--R +--RExamples of finite? from CardinalNumber +--R +--Rc2:=2::CardinalNumber +--Rfinite? c2 +--RA0:=Aleph 0 +--Rfinite? A0 +--R +--R +--RExamples of finite? from OnePointCompletion +--R +--R +--RExamples of finite? from OrderedCompletion +--R +--E 1025 + +--S 1026 of 3320 +)d op finiteBasis +--R +--R +--RThere is one unexposed function called finiteBasis : +--R [1] FiniteDivisor(D2,D3,D4,D5) -> Vector(D5) from FiniteDivisor(D2, +--R D3,D4,D5) +--R if D2 has FIELD and D3 has UPOLYC(D2) and D4 has UPOLYC( +--R FRAC(D3)) and D5 has FFCAT(D2,D3,D4) +--R +--RExamples of finiteBasis from FiniteDivisor +--R +--E 1026 + +--S 1027 of 3320 +)d op finiteBound +--R +--R +--RThere is one exposed function called finiteBound : +--R [1] (List(OrderedCompletion(DoubleFloat)),DoubleFloat) -> List( +--R DoubleFloat) +--R from e04AgentsPackage +--R +--RExamples of finiteBound from e04AgentsPackage +--R +--E 1027 + +--S 1028 of 3320 +)d op finiteSeries2LinSys +--R +--R +--RThere is one exposed function called finiteSeries2LinSys : +--R [1] (List(D5),Integer) -> Matrix(D4) +--R from LinearSystemFromPowerSeriesPackage(D4,D5) +--R if D5 has LOCPOWC(D4) and D4 has FIELD +--R +--RExamples of finiteSeries2LinSys from LinearSystemFromPowerSeriesPackage +--R +--E 1028 + +--S 1029 of 3320 +)d op finiteSeries2LinSysWOVectorise +--R +--R +--RThere is one exposed function called finiteSeries2LinSysWOVectorise : +--R [1] (List(D5),Integer) -> Matrix(D4) +--R from LinearSystemFromPowerSeriesPackage(D4,D5) +--R if D5 has LOCPOWC(D4) and D4 has FIELD +--R +--RExamples of finiteSeries2LinSysWOVectorise from LinearSystemFromPowerSeriesPackage +--R +--E 1029 + +--S 1030 of 3320 +)d op finiteSeries2Vector +--R +--R +--RThere is one exposed function called finiteSeries2Vector : +--R [1] (D2,Integer) -> List(D4) from LinearSystemFromPowerSeriesPackage +--R (D4,D2) +--R if D4 has FIELD and D2 has LOCPOWC(D4) +--R +--RExamples of finiteSeries2Vector from LinearSystemFromPowerSeriesPackage +--R +--E 1030 + +--S 1031 of 3320 +)d op fintegrate +--R +--R +--RThere is one exposed function called fintegrate : +--R [1] ((() -> TaylorSeries(D3)),Symbol,D3) -> TaylorSeries(D3) +--R from TaylorSeries(D3) if D3 has ALGEBRA(FRAC(INT)) and D3 +--R has RING +--R +--RThere is one unexposed function called fintegrate : +--R [1] ((() -> SparseMultivariateTaylorSeries(D3,D2,D4)),D2,D3) -> +--R SparseMultivariateTaylorSeries(D3,D2,D4) +--R from SparseMultivariateTaylorSeries(D3,D2,D4) +--R if D3 has ALGEBRA(FRAC(INT)) and D3 has RING and D2 has +--R ORDSET and D4 has POLYCAT(D3,INDE(D2),D2) +--R +--RExamples of fintegrate from SparseMultivariateTaylorSeries +--R +--R +--RExamples of fintegrate from TaylorSeries +--R +--E 1031 + +--S 1032 of 3320 +)d op first +--R +--R +--RThere are 4 exposed functions called first : +--R [1] D -> D1 from D +--R if D has IXAGG(D2,D1) and D2 has SETCAT and D2 has ORDSET +--R and D1 has TYPE +--R [2] D -> Union(D1,"failed") from D +--R if D has TSETCAT(D2,D3,D4,D1) and D2 has INTDOM and D3 +--R has OAMONS and D4 has ORDSET and D1 has RPOLCAT(D2,D3,D4) +--R +--R [3] (D,NonNegativeInteger) -> D from D if D has URAGG(D2) and D2 +--R has TYPE +--R [4] D -> D1 from D if D has URAGG(D1) and D1 has TYPE +--R +--RThere are 3 unexposed functions called first : +--R [1] Magma(D1) -> D1 from Magma(D1) if D1 has ORDSET +--R [2] OrderedFreeMonoid(D1) -> D1 from OrderedFreeMonoid(D1) if D1 +--R has ORDSET +--R [3] PoincareBirkhoffWittLyndonBasis(D2) -> LyndonWord(D2) +--R from PoincareBirkhoffWittLyndonBasis(D2) if D2 has ORDSET +--R +--R +--RExamples of first from IndexedAggregate +--R +--R +--RExamples of first from Magma +--R +--R +--RExamples of first from OrderedFreeMonoid +--R +--Rm1:=(x*y*y*z)$OFMONOID(Symbol) +--Rfirst m1 +--R +--R +--RExamples of first from PoincareBirkhoffWittLyndonBasis +--R +--R +--RExamples of first from TriangularSetCategory +--R +--R +--RExamples of first from UnaryRecursiveAggregate +--R +--Rfirst [1,4,2,-6,0,3,5,4,2,3] +--R +--E 1032 + +--S 1033 of 3320 done +)d op firstDenom +--R +--R +--RThere is one exposed function called firstDenom : +--R [1] PartialFraction(D2) -> Factored(D2) from PartialFraction(D2) if +--R D2 has EUCDOM +--R +--RExamples of firstDenom from PartialFraction +--R +--Ra:=partialFraction(1,factorial 10) +--RfirstDenom(a) +--R +--E 1033 + +--S 1034 of 3320 +)d op firstExponent +--R +--R +--RThere is one exposed function called firstExponent : +--R [1] D2 -> D1 from PackageForPoly(D3,D2,D1,D4) +--R if D3 has RING and D1 has DIRPCAT(D4,NNI) and D2 has FAMR( +--R D3,D1) and D4: NNI +--R +--RExamples of firstExponent from PackageForPoly +--R +--E 1034 + +--S 1035 of 3320 done +)d op firstNumer +--R +--R +--RThere is one exposed function called firstNumer : +--R [1] PartialFraction(D1) -> D1 from PartialFraction(D1) if D1 has +--R EUCDOM +--R +--RExamples of firstNumer from PartialFraction +--R +--Ra:=partialFraction(1,factorial 10) +--RfirstNumer(a) +--R +--E 1035 + +--S 1036 of 3320 +)d op firstSubsetGray +--R +--R +--RThere is one unexposed function called firstSubsetGray : +--R [1] PositiveInteger -> Vector(Vector(Integer)) from GrayCode +--R +--RExamples of firstSubsetGray from GrayCode +--R +--E 1036 + +--S 1037 of 3320 +)d op firstUncouplingMatrix +--R +--R +--RThere is one unexposed function called firstUncouplingMatrix : +--R [1] (D2,PositiveInteger) -> Union(Matrix(D4),"failed") +--R from PrecomputedAssociatedEquations(D4,D2) +--R if D4 has INTDOM and D2 has LODOCAT(D4) +--R +--RExamples of firstUncouplingMatrix from PrecomputedAssociatedEquations +--R +--E 1037 + +--S 1038 of 3320 +)d op fixedDivisor +--R +--R +--RThere is one unexposed function called fixedDivisor : +--R [1] SparseUnivariatePolynomial(Integer) -> Integer +--R from PolynomialNumberTheoryFunctions +--R +--RExamples of fixedDivisor from PolynomialNumberTheoryFunctions +--R +--E 1038 + +--S 1039 of 3320 +)d op fixedPoint +--R +--R +--RThere are 2 exposed functions called fixedPoint : +--R [1] (D1 -> D1) -> D1 from MappingPackage1(D1) if D1 has SETCAT +--R [2] ((List(D4) -> List(D4)),Integer) -> List(D4) from +--R MappingPackage1(D4) +--R if D4 has SETCAT +--R +--RExamples of fixedPoint from MappingPackage1 +--R +--E 1039 + +--S 1040 of 3320 +)d op fixedPointExquo +--R +--R +--RThere is one unexposed function called fixedPointExquo : +--R [1] (D1,D1) -> D1 from UnivariateTaylorSeriesODESolver(D2,D1) +--R if D2 has ALGEBRA(FRAC(INT)) and D1 has UTSCAT(D2) +--R +--RExamples of fixedPointExquo from UnivariateTaylorSeriesODESolver +--R +--E 1040 + +--S 1041 of 3320 done +)d op fixedPoints +--R +--R +--RThere is one exposed function called fixedPoints : +--R [1] Permutation(D2) -> Set(D2) from Permutation(D2) +--R if D2 has FINITE and D2 has SETCAT +--R +--RExamples of fixedPoints from Permutation +--R +--Rp := coercePreimagesImages([[0,1,2,3],[3,0,2,1]])$PERM ZMOD 4 +--RfixedPoints p +--R +--E 1041 + +--S 1042 of 3320 +)d op fixPredicate +--R +--R +--RThere is one unexposed function called fixPredicate : +--R [1] (D5 -> Boolean) -> (D4 -> Boolean) from PatternMatchPushDown(D3, +--R D4,D5) +--R if D5 has Join(SetCategory,RetractableTo(D4)) and D4 has +--R PATMAB(D3) and D3 has SETCAT +--R +--RExamples of fixPredicate from PatternMatchPushDown +--R +--E 1042 + +--S 1043 of 3320 +)d op flagFactor +--R +--R +--RThere is one exposed function called flagFactor : +--R [1] (D1,Integer,Union("nil","sqfr","irred","prime")) -> Factored(D1) +--R from Factored(D1) if D1 has INTDOM +--R +--RExamples of flagFactor from Factored +--R +--E 1043 + +--S 1044 of 3320 +)d op flatten +--R +--R +--RThere is one unexposed function called flatten : +--R [1] InputForm -> InputForm from InputForm +--R +--RExamples of flatten from InputForm +--R +--E 1044 + +--S 1045 of 3320 +)d op flexible? +--R +--R +--RThere is one exposed function called flexible? : +--R [1] -> Boolean from D if D has FINAALG(D2) and D2 has COMRING +--R +--RThere is one unexposed function called flexible? : +--R [1] -> Boolean from FiniteRankNonAssociativeAlgebra&(D2,D3) +--R if D3 has COMRING and D2 has FINAALG(D3) +--R +--RExamples of flexible? from FiniteRankNonAssociativeAlgebra& +--R +--R +--RExamples of flexible? from FiniteRankNonAssociativeAlgebra +--R +--E 1045 + +--S 1046 of 3320 +)d op flexibleArray +--R +--R +--RThere is one exposed function called flexibleArray : +--R [1] List(D2) -> FlexibleArray(D2) from FlexibleArray(D2) if D2 has +--R TYPE +--R +--RThere is one unexposed function called flexibleArray : +--R [1] List(D2) -> IndexedFlexibleArray(D2,D3) from +--R IndexedFlexibleArray(D2,D3) +--R if D2 has TYPE and D3: INT +--R +--RExamples of flexibleArray from FlexibleArray +--R +--R +--RExamples of flexibleArray from IndexedFlexibleArray +--R +--RT1:=IndexedFlexibleArray(Integer,20) +--RflexibleArray([i for i in 1..10])$T1 +--R +--E 1046 + +--S 1047 of 3320 +)d op float +--R +--R +--RThere are 3 exposed functions called float : +--R [1] (Integer,Integer,PositiveInteger) -> D from D if D has FPS +--R [2] (Integer,Integer) -> D from D if D has FPS +--R [3] D -> D1 from D +--R if D has SEXCAT(D2,D3,D4,D1,D5) and D2 has SETCAT and D3 +--R has SETCAT and D4 has SETCAT and D5 has SETCAT and D1 has +--R SETCAT +--R +--RExamples of float from FloatingPointSystem +--R +--R +--RExamples of float from SExpressionCategory +--R +--E 1047 + +--S 1048 of 3320 +)d op float? +--R +--R +--RThere is one exposed function called float? : +--R [1] D -> Boolean from D +--R if D has SEXCAT(D2,D3,D4,D5,D6) and D2 has SETCAT and D3 +--R has SETCAT and D4 has SETCAT and D5 has SETCAT and D6 has +--R SETCAT +--R +--RExamples of float? from SExpressionCategory +--R +--E 1048 + +--S 1049 of 3320 +)d op floor +--R +--R +--RThere are 2 exposed functions called floor : +--R [1] D -> D1 from D if D has QFCAT(D1) and D1 has INTDOM and D1 has +--R INS +--R [2] D -> D from D if D has RNS +--R +--RExamples of floor from QuotientFieldCategory +--R +--R +--RExamples of floor from RealNumberSystem +--R +--E 1049 + +--S 1050 of 3320 +)d op flush +--R +--R +--RThere is one exposed function called flush : +--R [1] D -> Void from D if D has FILECAT(D2,D3) and D2 has SETCAT and +--R D3 has SETCAT +--R +--RExamples of flush from FileCategory +--R +--E 1050 + +--S 1051 of 3320 +)d op fmecg +--R +--R +--RThere are 2 exposed functions called fmecg : +--R [1] (MyUnivariatePolynomial(D3,D2),NonNegativeInteger,D2, +--R MyUnivariatePolynomial(D3,D2)) -> MyUnivariatePolynomial(D3,D2) +--R from MyUnivariatePolynomial(D3,D2) if D3: SYMBOL and D2 +--R has RING +--R [2] (UnivariatePolynomial(D3,D2),NonNegativeInteger,D2, +--R UnivariatePolynomial(D3,D2)) -> UnivariatePolynomial(D3,D2) +--R from UnivariatePolynomial(D3,D2) if D3: SYMBOL and D2 has +--R RING +--R +--RThere are 4 unexposed functions called fmecg : +--R [1] (NewSparseUnivariatePolynomial(D2),NonNegativeInteger,D2, +--R NewSparseUnivariatePolynomial(D2)) -> +--R NewSparseUnivariatePolynomial(D2) +--R from NewSparseUnivariatePolynomial(D2) if D2 has RING +--R [2] (PolynomialRing(D2,D1),D1,D2,PolynomialRing(D2,D1)) -> +--R PolynomialRing(D2,D1) +--R from PolynomialRing(D2,D1) +--R if D1 has CABMON and D2 has INTDOM and D2 has RING and D1 +--R has OAMON +--R [3] (SparseUnivariatePolynomial(D2),NonNegativeInteger,D2, +--R SparseUnivariatePolynomial(D2)) -> SparseUnivariatePolynomial(D2) +--R from SparseUnivariatePolynomial(D2) if D2 has RING +--R [4] (SymmetricPolynomial(D2),Partition,D2,SymmetricPolynomial(D2)) +--R -> SymmetricPolynomial(D2) +--R from SymmetricPolynomial(D2) +--R if Partition has CABMON and D2 has INTDOM and D2 has RING +--R +--R +--RExamples of fmecg from MyUnivariatePolynomial +--R +--R +--RExamples of fmecg from NewSparseUnivariatePolynomial +--R +--R +--RExamples of fmecg from PolynomialRing +--R +--R +--RExamples of fmecg from SparseUnivariatePolynomial +--R +--R +--RExamples of fmecg from SymmetricPolynomial +--R +--R +--RExamples of fmecg from UnivariatePolynomial +--R +--E 1051 + +--S 1052 of 3320 +)d op forLoop +--R +--R +--RThere are 2 exposed functions called forLoop : +--R [1] (SegmentBinding(Polynomial(Integer)),Polynomial(Integer), +--R FortranCode) -> FortranCode +--R from FortranCode +--R [2] (SegmentBinding(Polynomial(Integer)),FortranCode) -> FortranCode +--R from FortranCode +--R +--RExamples of forLoop from FortranCode +--R +--E 1052 + +--S 1053 of 3320 +)d op FormatArabic +--R +--R +--RThere is one unexposed function called FormatArabic : +--R [1] PositiveInteger -> String from NumberFormats +--R +--RExamples of FormatArabic from NumberFormats +--R +--E 1053 + +--S 1054 of 3320 +)d op FormatRoman +--R +--R +--RThere is one unexposed function called FormatRoman : +--R [1] PositiveInteger -> String from NumberFormats +--R +--RExamples of FormatRoman from NumberFormats +--R +--E 1054 + +--S 1055 of 3320 +)d op formula +--R +--R +--RThere is one exposed function called formula : +--R [1] ScriptFormulaFormat -> List(String) from ScriptFormulaFormat +--R +--RExamples of formula from ScriptFormulaFormat +--R +--E 1055 + +--S 1056 of 3320 +)d op fortran +--R +--R +--RThere is one exposed function called fortran : +--R [1] (Symbol,FortranScalarType,D3) -> SimpleFortranProgram(D4,D3) +--R from SimpleFortranProgram(D4,D3) if D4 has ORDSET and D3 +--R has FS(D4) +--R +--RExamples of fortran from SimpleFortranProgram +--R +--E 1056 + +--S 1057 of 3320 +)d op fortranCarriageReturn +--R +--R +--RThere is one exposed function called fortranCarriageReturn : +--R [1] -> Void from FortranTemplate +--R +--RExamples of fortranCarriageReturn from FortranTemplate +--R +--E 1057 + +--S 1058 of 3320 +)d op fortranCharacter +--R +--R +--RThere is one exposed function called fortranCharacter : +--R [1] -> FortranType from FortranType +--R +--RExamples of fortranCharacter from FortranType +--R +--E 1058 + +--S 1059 of 3320 +)d op fortranCompilerName +--R +--R +--RThere is one exposed function called fortranCompilerName : +--R [1] -> String from NAGLinkSupportPackage +--R +--RExamples of fortranCompilerName from NAGLinkSupportPackage +--R +--E 1059 + +--S 1060 of 3320 +)d op fortranComplex +--R +--R +--RThere is one exposed function called fortranComplex : +--R [1] -> FortranType from FortranType +--R +--RExamples of fortranComplex from FortranType +--R +--E 1060 + +--S 1061 of 3320 +)d op fortranDouble +--R +--R +--RThere is one exposed function called fortranDouble : +--R [1] -> FortranType from FortranType +--R +--RExamples of fortranDouble from FortranType +--R +--E 1061 + +--S 1062 of 3320 +)d op fortranDoubleComplex +--R +--R +--RThere is one exposed function called fortranDoubleComplex : +--R [1] -> FortranType from FortranType +--R +--RExamples of fortranDoubleComplex from FortranType +--R +--E 1062 + +--S 1063 of 3320 +)d op fortranInteger +--R +--R +--RThere is one exposed function called fortranInteger : +--R [1] -> FortranType from FortranType +--R +--RExamples of fortranInteger from FortranType +--R +--E 1063 + +--S 1064 of 3320 +)d op fortranLinkerArgs +--R +--R +--RThere is one exposed function called fortranLinkerArgs : +--R [1] -> String from NAGLinkSupportPackage +--R +--RExamples of fortranLinkerArgs from NAGLinkSupportPackage +--R +--E 1064 + +--S 1065 of 3320 +)d op fortranLiteral +--R +--R +--RThere is one exposed function called fortranLiteral : +--R [1] String -> Void from FortranTemplate +--R +--RExamples of fortranLiteral from FortranTemplate +--R +--E 1065 + +--S 1066 of 3320 +)d op fortranLiteralLine +--R +--R +--RThere is one exposed function called fortranLiteralLine : +--R [1] String -> Void from FortranTemplate +--R +--RExamples of fortranLiteralLine from FortranTemplate +--R +--E 1066 + +--S 1067 of 3320 +)d op fortranLogical +--R +--R +--RThere is one exposed function called fortranLogical : +--R [1] -> FortranType from FortranType +--R +--RExamples of fortranLogical from FortranType +--R +--E 1067 + +--S 1068 of 3320 +)d op fortranReal +--R +--R +--RThere is one exposed function called fortranReal : +--R [1] -> FortranType from FortranType +--R +--RExamples of fortranReal from FortranType +--R +--E 1068 + +--S 1069 of 3320 +)d op fortranTypeOf +--R +--R +--RThere is one exposed function called fortranTypeOf : +--R [1] (Symbol,SymbolTable) -> FortranType from SymbolTable +--R +--RExamples of fortranTypeOf from SymbolTable +--R +--E 1069 + +--S 1070 of 3320 +)d op foundPlaces +--R +--R +--RThere is one exposed function called foundPlaces : +--R [1] -> List(D) from D +--R if D2 has FIELD and D3 has LOCPOWC(D2) and D has PLACESC( +--R D2,D3) +--R +--RExamples of foundPlaces from PlacesCategory +--R +--E 1070 + +--S 1071 of 3320 +)d op foundZeroes +--R +--R +--RThere is one exposed function called foundZeroes : +--R [1] -> List(D2) from RootsFindingPackage(D2) if D2 has FIELD +--R +--RExamples of foundZeroes from RootsFindingPackage +--R +--E 1071 + +--S 1072 of 3320 +--R------------------------------)d op fp (what?) +--E 1072 + +--S 1073 of 3320 +--R------------------------------)d op fprindINFO (what?) +--E 1073 + +--S 1074 of 3320 +)d op fracPart +--R +--R +--RThere is one exposed function called fracPart : +--R [1] FullPartialFractionExpansion(D2,D3) -> List(Record(exponent: +--R NonNegativeInteger,center: D3,num: D3)) +--R from FullPartialFractionExpansion(D2,D3) +--R if D2 has Join(Field,CharacteristicZero) and D3 has UPOLYC +--R (D2) +--R +--RExamples of fracPart from FullPartialFractionExpansion +--R +--E 1074 + +--S 1075 of 3320 +)d op fractionFreeGauss! +--R +--R +--RThere is one exposed function called fractionFreeGauss! : +--R [1] D1 -> D1 from MatrixLinearAlgebraFunctions(D2,D3,D4,D1) +--R if D2 has INTDOM and D2 has COMRING and D3 has FLAGG(D2) +--R and D4 has FLAGG(D2) and D1 has MATCAT(D2,D3,D4) +--R +--RExamples of fractionFreeGauss! from MatrixLinearAlgebraFunctions +--R +--E 1075 + +--S 1076 of 3320 +)d op fractionPart +--R +--R +--RThere are 6 exposed functions called fractionPart : +--R [1] BinaryExpansion -> Fraction(Integer) from BinaryExpansion +--R [2] DecimalExpansion -> Fraction(Integer) from DecimalExpansion +--R [3] HexadecimalExpansion -> Fraction(Integer) from +--R HexadecimalExpansion +--R [4] D -> D from D if D has QFCAT(D1) and D1 has INTDOM and D1 has +--R EUCDOM +--R [5] RadixExpansion(D2) -> Fraction(Integer) from RadixExpansion(D2) +--R if D2: INT +--R [6] D -> D from D if D has RNS +--R +--RExamples of fractionPart from BinaryExpansion +--R +--R +--RExamples of fractionPart from DecimalExpansion +--R +--R +--RExamples of fractionPart from HexadecimalExpansion +--R +--R +--RExamples of fractionPart from QuotientFieldCategory +--R +--R +--RExamples of fractionPart from RadixExpansion +--R +--R +--RExamples of fractionPart from RealNumberSystem +--R +--E 1076 + +--S 1077 of 3320 +)d op fractRadix +--R +--R +--RThere is one exposed function called fractRadix : +--R [1] (List(Integer),List(Integer)) -> RadixExpansion(D2) +--R from RadixExpansion(D2) if D2: INT +--R +--RExamples of fractRadix from RadixExpansion +--R +--E 1077 + +--S 1078 of 3320 +)d op fractRagits +--R +--R +--RThere is one exposed function called fractRagits : +--R [1] RadixExpansion(D2) -> Stream(Integer) from RadixExpansion(D2) +--R if D2: INT +--R +--RExamples of fractRagits from RadixExpansion +--R +--E 1078 + +--S 1079 of 3320 +)d op freeOf? +--R +--R +--RThere are 3 exposed functions called freeOf? : +--R [1] (D,Symbol) -> Boolean from D if D has ES +--R [2] (D,D) -> Boolean from D if D has ES +--R [3] (StochasticDifferential(D3),BasicStochasticDifferential) -> +--R Boolean +--R from StochasticDifferential(D3) +--R if D3 has Join(OrderedSet,IntegralDomain) +--R +--RExamples of freeOf? from ExpressionSpace +--R +--R +--RExamples of freeOf? from StochasticDifferential +--R +--E 1079 + +--S 1080 of 3320 +)d op fresnelC +--R +--R +--RThere are 2 exposed functions called fresnelC : +--R [1] Float -> Float from DoubleFloatSpecialFunctions +--R [2] D -> D from D if D has LFCAT +--R +--RThere is one unexposed function called fresnelC : +--R [1] D1 -> D1 from LiouvillianFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory, +--R TranscendentalFunctionCategory) +--R +--RExamples of fresnelC from DoubleFloatSpecialFunctions +--R +--RfresnelC(1.5) +--R +--R +--RExamples of fresnelC from LiouvillianFunctionCategory +--R +--R +--RExamples of fresnelC from LiouvillianFunction +--R +--E 1080 + +--S 1081 of 3320 +)d op fresnelS +--R +--R +--RThere are 2 exposed functions called fresnelS : +--R [1] Float -> Float from DoubleFloatSpecialFunctions +--R [2] D -> D from D if D has LFCAT +--R +--RThere is one unexposed function called fresnelS : +--R [1] D1 -> D1 from LiouvillianFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory, +--R TranscendentalFunctionCategory) +--R +--RExamples of fresnelS from DoubleFloatSpecialFunctions +--R +--RfresnelS(1.5) +--R +--R +--RExamples of fresnelS from LiouvillianFunctionCategory +--R +--R +--RExamples of fresnelS from LiouvillianFunction +--R +--E 1081 + +--S 1082 of 3320 +)d op frobenius +--R +--R +--RThere is one unexposed function called frobenius : +--R [1] ModMonic(D1,D2) -> ModMonic(D1,D2) from ModMonic(D1,D2) +--R if D1 has FFIELDC and D1 has RING and D2 has UPOLYC(D1) +--R +--R +--RExamples of frobenius from ModMonic +--R +--E 1082 + +--S 1083 of 3320 +)d op Frobenius +--R +--R +--RThere are 2 exposed functions called Frobenius : +--R [1] (D,NonNegativeInteger) -> D from D +--R if D has XF(D2) and D2 has FIELD and D2 has FINITE +--R [2] D -> D from D if D has XF(D1) and D1 has FIELD and D1 has FINITE +--R +--R +--RThere is one unexposed function called Frobenius : +--R [1] D1 -> D1 from NormRetractPackage(D2,D3,D4,D1,D5) +--R if D2 has FFIELDC and D3 has FAXF(D2) and D4 has UPOLYC(D3 +--R ) and D1 has UPOLYC(D4) and D5: PI +--R +--RExamples of Frobenius from NormRetractPackage +--R +--R +--RExamples of Frobenius from ExtensionField +--R +--E 1083 + +--S 1084 of 3320 +)d op front +--R +--R +--RThere are 3 exposed functions called front : +--R [1] Dequeue(D1) -> D1 from Dequeue(D1) if D1 has SETCAT +--R [2] D -> D1 from D if D has QUAGG(D1) and D1 has TYPE +--R [3] Queue(D1) -> D1 from Queue(D1) if D1 has SETCAT +--R +--RExamples of front from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rfront a +--R +--R +--RExamples of front from QueueAggregate +--R +--R +--RExamples of front from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Rfront a +--R +--E 1084 + +--S 1085 of 3320 +)d op froot +--R +--R +--RThere is one unexposed function called froot : +--R [1] (D2,NonNegativeInteger) -> Record(exponent: NonNegativeInteger, +--R coef: D2,radicand: D2) +--R from PolynomialRoots(D4,D5,D6,D7,D2) +--R if D6 has GCDDOM and D4 has OAMONS and D5 has ORDSET and +--R D6 has INTDOM and D7 has POLYCAT(D6,D4,D5) and D2 has Field +--R with +--R numer : % -> D7 +--R denom : % -> D7 +--R coerce : D7 -> % +--R +--RExamples of froot from PolynomialRoots +--R +--E 1085 + +--S 1086 of 3320 done +)d op frst +--R +--R +--RThere is one exposed function called frst : +--R [1] D -> D1 from D if D has LZSTAGG(D1) and D1 has TYPE +--R +--RExamples of frst from LazyStreamAggregate +--R +--Rm:=[i for i in 0..] +--Rfrst m +--R +--E 1086 + +--S 1087 of 3320 +)d op fTable +--R +--R +--RThere is one exposed function called fTable : +--R [1] List(Record(key: Record(var: Symbol,fn: Expression(DoubleFloat), +--R range: Segment(OrderedCompletion(DoubleFloat)),abserr: +--R DoubleFloat,relerr: DoubleFloat),entry: Record(endPointContinuity +--R : Union(continuous: Continuous at the end points,lowerSingular: +--R There is a singularity at the lower end point,upperSingular: +--R There is a singularity at the upper end point,bothSingular: +--R There are singularities at both end points,notEvaluated: +--R End point continuity not yet evaluated),singularitiesStream: +--R Union(str: Stream(DoubleFloat),notEvaluated: +--R Internal singularities not yet evaluated),range: Union(finite: +--R The range is finite,lowerInfinite: +--R The bottom of range is infinite,upperInfinite: +--R The top of range is infinite,bothInfinite: +--R Both top and bottom points are infinite,notEvaluated: +--R Range not yet evaluated)))) -> IntegrationFunctionsTable +--R from IntegrationFunctionsTable +--R +--RExamples of fTable from IntegrationFunctionsTable +--R +--E 1087 + +--S 1088 of 3320 +)d op fullDesTree +--R +--R +--RThere are 2 exposed functions called fullDesTree : +--R [1] -> Void from PackageForAlgebraicFunctionFieldOverFiniteField(D2 +--R ,D3,D4) +--R if D2 has FFIELDC and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R [2] -> Void from PackageForAlgebraicFunctionField(D2,D3,D4) +--R if D2 has FIELD and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R +--RExamples of fullDesTree from PackageForAlgebraicFunctionFieldOverFiniteField +--R +--R +--RExamples of fullDesTree from PackageForAlgebraicFunctionField +--R +--E 1088 + +--S 1089 of 3320 +)d op fullDisplay +--R +--R +--RThere are 3 exposed functions called fullDisplay : +--R [1] (Database(D3),PositiveInteger,PositiveInteger) -> Void from +--R Database(D3) +--R if D3 has OrderedSetwith +--R ?.? : (%,Symbol) -> String +--R display : % -> Void +--R fullDisplay : % -> Void +--R [2] Database(D2) -> Void from Database(D2) +--R if D2 has OrderedSetwith +--R ?.? : (%,Symbol) -> String +--R display : % -> Void +--R fullDisplay : % -> Void +--R [3] IndexCard -> Void from IndexCard +--R +--RExamples of fullDisplay from Database +--R +--R +--RExamples of fullDisplay from IndexCard +--R +--E 1089 + +--S 1090 of 3320 +)d op fullInfClsPt +--R +--R +--RThere are 2 exposed functions called fullInfClsPt : +--R [1] -> Void from PackageForAlgebraicFunctionFieldOverFiniteField(D2 +--R ,D3,D4) +--R if D2 has FFIELDC and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R [2] -> Void from PackageForAlgebraicFunctionField(D2,D3,D4) +--R if D2 has FIELD and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R +--RExamples of fullInfClsPt from PackageForAlgebraicFunctionFieldOverFiniteField +--R +--R +--RExamples of fullInfClsPt from PackageForAlgebraicFunctionField +--R +--E 1090 + +--S 1091 of 3320 +)d op fullOut +--R +--R +--RThere are 4 exposed functions called fullOut : +--R [1] DesingTree(D2) -> OutputForm from DesingTree(D2) if D2 has +--R SETCAT +--R [2] InfClsPt(D2,D3,D4) -> OutputForm from InfClsPt(D2,D3,D4) +--R if D2 has FIELD and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R [3] InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField(D2,D3 +--R ,D4) -> OutputForm +--R from +--R InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField( +--R D2,D3,D4) +--R if D2 has FFIELDC and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R [4] InfinitlyClosePoint(D4,D5,D6,D7,D8,D9,D10,D1,D2) -> OutputForm +--R from InfinitlyClosePoint(D4,D5,D6,D7,D8,D9,D10,D1,D2) +--R if D4 has FIELD and D5: LIST(SYMBOL) and D7 has DIRPCAT(#( +--R D5),NNI) and D9 has LOCPOWC(D4) and D10 has PLACESC(D4,D9) +--R and D6 has POLYCAT(D4,D7,OVAR(D5)) and D8 has PRSPCAT(D4) +--R and D1 has DIVCAT(D10) and D2 has BLMETCT +--R +--RExamples of fullOut from DesingTree +--R +--R +--RExamples of fullOut from InfClsPt +--R +--R +--RExamples of fullOut from InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField +--R +--R +--RExamples of fullOut from InfinitlyClosePoint +--R +--E 1091 + +--S 1092 of 3320 +)d op fullOutput +--R +--R +--RThere are 12 exposed functions called fullOutput : +--R [1] -> Boolean from DesingTree(D2) if D2 has SETCAT +--R [2] Boolean -> Boolean from DesingTree(D2) if D2 has SETCAT +--R [3] -> Boolean from InfClsPt(D2,D3,D4) +--R if D2 has FIELD and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R [4] Boolean -> Boolean from InfClsPt(D2,D3,D4) +--R if D2 has FIELD and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R [5] -> Boolean +--R from +--R InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField( +--R D2,D3,D4) +--R if D2 has FFIELDC and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R [6] Boolean -> Boolean +--R from +--R InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField( +--R D2,D3,D4) +--R if D2 has FFIELDC and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R [7] -> Boolean from InfinitlyClosePoint(D4,D5,D6,D7,D8,D9,D10,D1,D2 +--R ) +--R if D4 has FIELD and D5: LIST(SYMBOL) and D7 has DIRPCAT(#( +--R D5),NNI) and D9 has LOCPOWC(D4) and D10 has PLACESC(D4,D9) +--R and D6 has POLYCAT(D4,D7,OVAR(D5)) and D8 has PRSPCAT(D4) +--R and D1 has DIVCAT(D10) and D2 has BLMETCT +--R [8] Boolean -> Boolean from InfinitlyClosePoint(D4,D5,D6,D7,D8,D9, +--R D10,D1,D2) +--R if D4 has FIELD and D5: LIST(SYMBOL) and D7 has DIRPCAT(#( +--R D5),NNI) and D9 has LOCPOWC(D4) and D10 has PLACESC(D4,D9) +--R and D6 has POLYCAT(D4,D7,OVAR(D5)) and D8 has PRSPCAT(D4) +--R and D1 has DIVCAT(D10) and D2 has BLMETCT +--R [9] PseudoAlgebraicClosureOfAlgExtOfRationalNumber(D2) -> OutputForm +--R from PseudoAlgebraicClosureOfAlgExtOfRationalNumber(D2) +--R if D2: PACRAT +--R [10] PseudoAlgebraicClosureOfFiniteField(D2) -> OutputForm +--R from PseudoAlgebraicClosureOfFiniteField(D2) if D2 has +--R FFIELDC +--R [11] D -> OutputForm from D if D has PACPERC +--R [12] PseudoAlgebraicClosureOfRationalNumber -> OutputForm +--R from PseudoAlgebraicClosureOfRationalNumber +--R +--RExamples of fullOutput from DesingTree +--R +--R +--RExamples of fullOutput from InfClsPt +--R +--R +--RExamples of fullOutput from InfinitlyClosePointOverPseudoAlgebraicClosureOfFiniteField +--R +--R +--RExamples of fullOutput from InfinitlyClosePoint +--R +--R +--RExamples of fullOutput from PseudoAlgebraicClosureOfAlgExtOfRationalNumber +--R +--R +--RExamples of fullOutput from PseudoAlgebraicClosureOfFiniteField +--R +--R +--RExamples of fullOutput from PseudoAlgebraicClosureOfPerfectFieldCategory +--R +--R +--RExamples of fullOutput from PseudoAlgebraicClosureOfRationalNumber +--R +--E 1092 + +--S 1093 of 3320 +)d op fullParamInit +--R +--R +--RThere is one exposed function called fullParamInit : +--R [1] D6 -> Void from DesingTreePackage(D7,D8,D9,D10,D11,D12,D1,D2,D3, +--R D6,D4) +--R if D7 has FIELD and D8: LIST(SYMBOL) and D9 has POLYCAT(D7 +--R ,D10,OVAR(D8)) and D10 has DIRPCAT(#(D8),NNI) and D11 has +--R PRSPCAT(D7) and D12 has LOCPOWC(D7) and D1 has PLACESC(D7, +--R D12) and D2 has DIVCAT(D1) and D3 has INFCLCT(D7,D8,D9,D10, +--R D11,D12,D1,D2,D4) and D4 has BLMETCT and D6 has DSTRCAT(D3) +--R +--R +--RExamples of fullParamInit from DesingTreePackage +--R +--E 1093 + +--S 1094 of 3320 +)d op fullPartialFraction +--R +--R +--RThere is one exposed function called fullPartialFraction : +--R [1] Fraction(D3) -> FullPartialFractionExpansion(D2,D3) +--R from FullPartialFractionExpansion(D2,D3) +--R if D3 has UPOLYC(D2) and D2 has Join(Field, +--R CharacteristicZero) +--R +--RExamples of fullPartialFraction from FullPartialFractionExpansion +--R +--E 1094 + +--S 1095 of 3320 +)d op function +--R +--R +--RThere are 4 exposed functions called function : +--R [1] (D2,Symbol) -> Symbol from MakeFunction(D2) if D2 has KONVERT( +--R INFORM) +--R [2] (D2,Symbol,Symbol) -> Symbol from MakeFunction(D2) if D2 has +--R KONVERT(INFORM) +--R [3] (D2,Symbol,Symbol,Symbol) -> Symbol from MakeFunction(D2) +--R if D2 has KONVERT(INFORM) +--R [4] (D2,Symbol,List(Symbol)) -> Symbol from MakeFunction(D2) +--R if D2 has KONVERT(INFORM) +--R +--RThere is one unexposed function called function : +--R [1] (InputForm,List(Symbol),Symbol) -> InputForm from InputForm +--R +--RExamples of function from InputForm +--R +--R +--RExamples of function from MakeFunction +--R +--E 1095 + +--S 1096 of 3320 +)d op functionIsContinuousAtEndPoints +--R +--R +--RThere is one exposed function called functionIsContinuousAtEndPoints : +--R [1] Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment( +--R OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: +--R DoubleFloat) -> Union(continuous: Continuous at the end points, +--R lowerSingular: There is a singularity at the lower end point, +--R upperSingular: There is a singularity at the upper end point, +--R bothSingular: There are singularities at both end points, +--R notEvaluated: End point continuity not yet evaluated) +--R from d01AgentsPackage +--R +--RExamples of functionIsContinuousAtEndPoints from d01AgentsPackage +--R +--E 1096 + +--S 1097 of 3320 +)d op functionIsFracPolynomial? +--R +--R +--RThere is one exposed function called functionIsFracPolynomial? : +--R [1] Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment( +--R OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: +--R DoubleFloat) -> Boolean +--R from ExpertSystemContinuityPackage +--R +--RExamples of functionIsFracPolynomial? from ExpertSystemContinuityPackage +--R +--E 1097 + +--S 1098 of 3320 +)d op functionIsOscillatory +--R +--R +--RThere is one exposed function called functionIsOscillatory : +--R [1] Record(var: Symbol,fn: Expression(DoubleFloat),range: Segment( +--R OrderedCompletion(DoubleFloat)),abserr: DoubleFloat,relerr: +--R DoubleFloat) -> Float +--R from d01AgentsPackage +--R +--RExamples of functionIsOscillatory from d01AgentsPackage +--R +--E 1098 + +--S 1099 of 3320 +)d op functionName +--R +--R +--RThere is one exposed function called functionName : +--R [1] Symbol -> GuessOption from GuessOption +--R +--RThere is one unexposed function called functionName : +--R [1] List(GuessOption) -> Symbol from GuessOptionFunctions0 +--R +--RExamples of functionName from GuessOptionFunctions0 +--R +--R +--RExamples of functionName from GuessOption +--R +--E 1099 + +--S 1100 of 3320 +)d op functionNames +--R +--R +--RThere is one exposed function called functionNames : +--R [1] List(Symbol) -> GuessOption from GuessOption +--R +--RExamples of functionNames from GuessOption +--R +--E 1100 + +--S 1101 of 3320 +)d op Gamma +--R +--R +--RThere are 7 exposed functions called Gamma : +--R [1] DoubleFloat -> DoubleFloat from DoubleFloat +--R [2] DoubleFloat -> DoubleFloat from DoubleFloatSpecialFunctions +--R [3] Complex(DoubleFloat) -> Complex(DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R [4] Float -> Float from FloatSpecialFunctions +--R [5] Complex(Float) -> Complex(Float) from FloatSpecialFunctions +--R [6] D -> D from D if D has SPFCAT +--R [7] (D,D) -> D from D if D has SPFCAT +--R +--RThere are 2 unexposed functions called Gamma : +--R [1] D1 -> D1 from FunctionalSpecialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R [2] (D1,D1) -> D1 from FunctionalSpecialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R +--RExamples of Gamma from DoubleFloat +--R +--R +--RExamples of Gamma from DoubleFloatSpecialFunctions +--R +--R +--RExamples of Gamma from FloatSpecialFunctions +--R +--Ra:Complex(Float):=3.5*%i +--RGamma(a) +--R +--RGamma(3.5) +--R +--R +--RExamples of Gamma from FunctionalSpecialFunction +--R +--R +--RExamples of Gamma from SpecialFunctionCategory +--R +--E 1101 + +--S 1102 of 3320 +)d op gbasis +--R +--R +--RThere is one unexposed function called gbasis : +--R [1] (List(D6),Integer,Integer) -> List(D6) +--R from GroebnerInternalPackage(D3,D4,D5,D6) +--R if D6 has POLYCAT(D3,D4,D5) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET +--R +--RExamples of gbasis from GroebnerInternalPackage +--R +--E 1102 + +--S 1103 of 3320 +)d op gcd +--R +--R +--RThere are 8 exposed functions called gcd : +--R [1] List(D) -> D from D if D has GCDDOM +--R [2] (D,D) -> D from D if D has GCDDOM +--R [3] (D1,D1,Integer) -> D1 from ModularDistinctDegreeFactorizer(D1) +--R if D1 has UPOLYC(INT) +--R [4] (NonNegativeInteger,NonNegativeInteger) -> NonNegativeInteger +--R from NonNegativeInteger +--R [5] (PositiveInteger,PositiveInteger) -> PositiveInteger from +--R PositiveInteger +--R [6] (U32Vector,U32Vector,Integer) -> U32Vector +--R from U32VectorPolynomialOperations +--R [7] (PrimitiveArray(U32Vector),Integer,Integer,Integer) -> U32Vector +--R from U32VectorPolynomialOperations +--R [8] (D1,D) -> D1 from D +--R if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has +--R OAMONS and D3 has ORDSET and D1 has GCDDOM +--R +--RThere are 6 unexposed functions called gcd : +--R [1] List(D1) -> D1 from HeuGcd(D1) if D1 has UPOLYC(INT) +--R [2] (D1,D1) -> D1 from PolynomialGcdPackage(D2,D3,D4,D1) +--R if D2 has OAMONS and D3 has ORDSET and D4 has EUCDOM and +--R D1 has POLYCAT(D4,D2,D3) +--R [3] List(D1) -> D1 from PolynomialGcdPackage(D3,D4,D5,D1) +--R if D1 has POLYCAT(D5,D3,D4) and D3 has OAMONS and D4 has +--R ORDSET and D5 has EUCDOM +--R [4] (SparseUnivariatePolynomial(D5),SparseUnivariatePolynomial(D5)) +--R -> SparseUnivariatePolynomial(D5) +--R from PolynomialGcdPackage(D2,D3,D4,D5) +--R if D5 has POLYCAT(D4,D2,D3) and D2 has OAMONS and D3 has +--R ORDSET and D4 has EUCDOM +--R [5] List(SparseUnivariatePolynomial(D6)) -> +--R SparseUnivariatePolynomial(D6) +--R from PolynomialGcdPackage(D3,D4,D5,D6) +--R if D3 has OAMONS and D4 has ORDSET and D5 has EUCDOM and +--R D6 has POLYCAT(D5,D3,D4) +--R [6] (D1,D1) -> D1 from PseudoRemainderSequence(D2,D1) +--R if D2 has GCDDOM and D2 has INTDOM and D1 has UPOLYC(D2) +--R +--R +--RExamples of gcd from GcdDomain +--R +--R +--RExamples of gcd from HeuGcd +--R +--Rgcd([671*671*x^2-1,671*671*x^2+2*671*x+1]) +--Rgcd([7*x^2+1,(7*x^2+1)^2]) +--R +--R +--RExamples of gcd from ModularDistinctDegreeFactorizer +--R +--R +--RExamples of gcd from NonNegativeInteger +--R +--R +--RExamples of gcd from PolynomialGcdPackage +--R +--Rp1:=(x+1)*(x+6) +--Rp2:=(x+1)*(x-6) +--Rgcd(p1,p2) +--R +--R +--RExamples of gcd from PositiveInteger +--R +--R +--RExamples of gcd from U32VectorPolynomialOperations +--R +--R +--RExamples of gcd from PseudoRemainderSequence +--R +--R +--RExamples of gcd from RecursivePolynomialCategory +--R +--E 1103 + +--S 1104 of 3320 +)d op gcdBasis +--R +--R +--RThere is one exposed function called gcdBasis : +--R [1] List(D3) -> List(D3) +--R from CylindricalAlgebraicDecompositionUtilities(D2,D3) +--R if D3 has UPOLYC(D2) and D2 has GCDDOM +--R +--RExamples of gcdBasis from CylindricalAlgebraicDecompositionUtilities +--R +--E 1104 + +--S 1105 of 3320 +)d op gcdBasisAdd +--R +--R +--RThere is one exposed function called gcdBasisAdd : +--R [1] (D2,List(D2)) -> List(D2) +--R from CylindricalAlgebraicDecompositionUtilities(D3,D2) +--R if D2 has UPOLYC(D3) and D3 has GCDDOM +--R +--RExamples of gcdBasisAdd from CylindricalAlgebraicDecompositionUtilities +--R +--E 1105 + +--S 1106 of 3320 +)d op gcdcofact +--R +--R +--RThere is one unexposed function called gcdcofact : +--R [1] List(D2) -> List(D2) from HeuGcd(D2) if D2 has UPOLYC(INT) +--R +--RExamples of gcdcofact from HeuGcd +--R +--E 1106 + +--S 1107 of 3320 +)d op gcdcofactprim +--R +--R +--RThere is one unexposed function called gcdcofactprim : +--R [1] List(D2) -> List(D2) from HeuGcd(D2) if D2 has UPOLYC(INT) +--R +--RExamples of gcdcofactprim from HeuGcd +--R +--E 1107 + +--S 1108 of 3320 +)d op gcdPolynomial +--R +--R +--RThere are 2 exposed functions called gcdPolynomial : +--R [1] (SparseUnivariatePolynomial(D),SparseUnivariatePolynomial(D)) +--R -> SparseUnivariatePolynomial(D) +--R from D if D has GCDDOM +--R [2] (SparseUnivariatePolynomial(D),SparseUnivariatePolynomial(D)) +--R -> SparseUnivariatePolynomial(D) +--R from D if D has PFECAT +--R +--RThere is one unexposed function called gcdPolynomial : +--R [1] (SparseUnivariatePolynomial(D5),SparseUnivariatePolynomial(D5)) +--R -> SparseUnivariatePolynomial(D5) +--R from GeneralPolynomialGcdPackage(D2,D3,D4,D5) +--R if D5 has POLYCAT(D4,D2,D3) and D2 has OAMONS and D3 has +--R ORDSET and D4 has PFECAT +--R +--RExamples of gcdPolynomial from GcdDomain +--R +--R +--RExamples of gcdPolynomial from GeneralPolynomialGcdPackage +--R +--R +--RExamples of gcdPolynomial from PolynomialFactorizationExplicit +--R +--E 1108 + +--S 1109 of 3320 +)d op gcdprim +--R +--R +--RThere is one unexposed function called gcdprim : +--R [1] List(D1) -> D1 from HeuGcd(D1) if D1 has UPOLYC(INT) +--R +--RExamples of gcdprim from HeuGcd +--R +--E 1109 + +--S 1110 of 3320 +)d op gcdPrimitive +--R +--R +--RThere are 3 unexposed functions called gcdPrimitive : +--R [1] (D1,D1) -> D1 from PolynomialGcdPackage(D2,D3,D4,D1) +--R if D2 has OAMONS and D3 has ORDSET and D4 has EUCDOM and +--R D1 has POLYCAT(D4,D2,D3) +--R [2] (SparseUnivariatePolynomial(D5),SparseUnivariatePolynomial(D5)) +--R -> SparseUnivariatePolynomial(D5) +--R from PolynomialGcdPackage(D2,D3,D4,D5) +--R if D5 has POLYCAT(D4,D2,D3) and D2 has OAMONS and D3 has +--R ORDSET and D4 has EUCDOM +--R [3] List(D1) -> D1 from PolynomialGcdPackage(D3,D4,D5,D1) +--R if D1 has POLYCAT(D5,D3,D4) and D3 has OAMONS and D4 has +--R ORDSET and D5 has EUCDOM +--R +--RExamples of gcdPrimitive from PolynomialGcdPackage +--R +--E 1110 + +--S 1111 of 3320 +)d op gderiv +--R +--R +--RThere is one unexposed function called gderiv : +--R [1] ((Integer -> D3),Stream(D3)) -> Stream(D3) +--R from StreamTaylorSeriesOperations(D3) if D3 has RING +--R +--RExamples of gderiv from StreamTaylorSeriesOperations +--R +--E 1111 + +--S 1112 of 3320 +)d op GE +--R +--R +--RThere is one exposed function called GE : +--R [1] (Union(I: Expression(Integer),F: Expression(Float),CF: +--R Expression(Complex(Float)),switch: Switch),Union(I: Expression( +--R Integer),F: Expression(Float),CF: Expression(Complex(Float)), +--R switch: Switch)) -> Switch +--R from Switch +--R +--RExamples of GE from Switch +--R +--E 1112 + +--S 1113 of 3320 +)d op generalCoefficient +--R +--R +--RThere is one exposed function called generalCoefficient : +--R [1] (((NonNegativeInteger,NonNegativeInteger,D6) -> D1),Vector(D6), +--R NonNegativeInteger,Vector(SparseUnivariatePolynomial(D1))) -> D1 +--R from FractionFreeFastGaussian(D1,D6) +--R if D6 has AMR(D1,NNI) and D1 has Join(IntegralDomain, +--R GcdDomain) +--R +--RExamples of generalCoefficient from FractionFreeFastGaussian +--R +--E 1113 + +--S 1114 of 3320 +)d op generalInfiniteProduct +--R +--R +--RThere are 3 exposed functions called generalInfiniteProduct : +--R [1] (D1,Integer,Integer) -> D1 from +--R InfiniteProductCharacteristicZero(D3,D1) +--R if D3 has Join(IntegralDomain,CharacteristicZero) and D1 +--R has UTSCAT(D3) +--R [2] (D1,Integer,Integer) -> D1 from InfiniteProductFiniteField(D3,D4 +--R ,D5,D1) +--R if D3 has Join(Field,Finite,ConvertibleTo(Integer)) and D4 +--R has UPOLYC(D3) and D5 has MONOGEN(D3,D4) and D1 has UTSCAT +--R (D5) +--R [3] (D1,Integer,Integer) -> D1 from InfiniteProductPrimeField(D3,D1) +--R if D3 has Join(Field,Finite,ConvertibleTo(Integer)) and D1 +--R has UTSCAT(D3) +--R +--RThere is one unexposed function called generalInfiniteProduct : +--R [1] (Stream(D3),Integer,Integer) -> Stream(D3) from +--R StreamInfiniteProduct(D3) +--R if D3 has Join(IntegralDomain,CharacteristicZero) +--R +--RExamples of generalInfiniteProduct from InfiniteProductCharacteristicZero +--R +--R +--RExamples of generalInfiniteProduct from InfiniteProductFiniteField +--R +--R +--RExamples of generalInfiniteProduct from InfiniteProductPrimeField +--R +--R +--RExamples of generalInfiniteProduct from StreamInfiniteProduct +--R +--E 1114 + +--S 1115 of 3320 +)d op generalInterpolation +--R +--R +--RThere are 4 exposed functions called generalInterpolation : +--R [1] (List(D6),((NonNegativeInteger,NonNegativeInteger,D7) -> D6), +--R Vector(D8),List(NonNegativeInteger)) -> Matrix( +--R SparseUnivariatePolynomial(D6)) +--R from FractionFreeFastGaussianFractions(D6,D7,D8) +--R if D6 has Join(IntegralDomain,GcdDomain) and D7 has FAMR( +--R D6,NNI) and D8 has FAMR(FRAC(D6),NNI) +--R [2] (List(D6),((NonNegativeInteger,NonNegativeInteger,D7) -> D6), +--R Vector(D8),NonNegativeInteger,NonNegativeInteger) -> Stream( +--R Matrix(SparseUnivariatePolynomial(D6))) +--R from FractionFreeFastGaussianFractions(D6,D7,D8) +--R if D6 has Join(IntegralDomain,GcdDomain) and D7 has FAMR( +--R D6,NNI) and D8 has FAMR(FRAC(D6),NNI) +--R [3] (List(D6),((NonNegativeInteger,NonNegativeInteger,D7) -> D6), +--R Vector(D7),List(NonNegativeInteger)) -> Matrix( +--R SparseUnivariatePolynomial(D6)) +--R from FractionFreeFastGaussian(D6,D7) +--R if D6 has Join(IntegralDomain,GcdDomain) and D7 has AMR(D6 +--R ,NNI) +--R [4] (List(D6),((NonNegativeInteger,NonNegativeInteger,D7) -> D6), +--R Vector(D7),NonNegativeInteger,NonNegativeInteger) -> Stream( +--R Matrix(SparseUnivariatePolynomial(D6))) +--R from FractionFreeFastGaussian(D6,D7) +--R if D6 has Join(IntegralDomain,GcdDomain) and D7 has AMR(D6 +--R ,NNI) +--R +--RExamples of generalInterpolation from FractionFreeFastGaussianFractions +--R +--R +--RExamples of generalInterpolation from FractionFreeFastGaussian +--R +--E 1115 + +--S 1116 of 3320 done +)d op generalizedContinuumHypothesisAssumed +--R +--R +--RThere is one exposed function called generalizedContinuumHypothesisAssumed : +--R [1] Boolean -> Boolean from CardinalNumber +--R +--RExamples of generalizedContinuumHypothesisAssumed from CardinalNumber +--R +--RgeneralizedContinuumHypothesisAssumed true +--Ra:=Aleph 0 +--Rc:=2**a +--Rf:=2**c +--R +--E 1116 + +--S 1117 of 3320 +)d op generalizedContinuumHypothesisAssumed? +--R +--R +--RThere is one exposed function called generalizedContinuumHypothesisAssumed? : +--R [1] -> Boolean from CardinalNumber +--R +--RExamples of generalizedContinuumHypothesisAssumed? from CardinalNumber +--R +--RgeneralizedContinuumHypothesisAssumed? +--R +--E 1117 + +--S 1118 of 3320 +)d op generalizedEigenvector +--R +--R +--RThere are 2 exposed functions called generalizedEigenvector : +--R [1] (Union(Fraction(Polynomial(D5)),SuchThat(Symbol,Polynomial(D5))) +--R ,Matrix(Fraction(Polynomial(D5))),NonNegativeInteger, +--R NonNegativeInteger) -> List(Matrix(Fraction(Polynomial(D5)))) +--R from EigenPackage(D5) if D5 has GCDDOM +--R [2] (Record(eigval: Union(Fraction(Polynomial(D4)),SuchThat(Symbol, +--R Polynomial(D4))),eigmult: NonNegativeInteger,eigvec: List(Matrix( +--R Fraction(Polynomial(D4))))),Matrix(Fraction(Polynomial(D4)))) -> +--R List(Matrix(Fraction(Polynomial(D4)))) +--R from EigenPackage(D4) if D4 has GCDDOM +--R +--RExamples of generalizedEigenvector from EigenPackage +--R +--E 1118 + +--S 1119 of 3320 +)d op generalizedEigenvectors +--R +--R +--RThere is one exposed function called generalizedEigenvectors : +--R [1] Matrix(Fraction(Polynomial(D3))) -> List(Record(eigval: Union( +--R Fraction(Polynomial(D3)),SuchThat(Symbol,Polynomial(D3))), +--R geneigvec: List(Matrix(Fraction(Polynomial(D3)))))) +--R from EigenPackage(D3) if D3 has GCDDOM +--R +--RExamples of generalizedEigenvectors from EigenPackage +--R +--E 1119 + +--S 1120 of 3320 +)d op generalizedInverse +--R +--R +--RThere is one unexposed function called generalizedInverse : +--R [1] D1 -> D1 from InnerMatrixLinearAlgebraFunctions(D2,D3,D4,D1) +--R if D2 has FIELD and D3 has FLAGG(D2) and D4 has FLAGG(D2) +--R and D1 has MATCAT(D2,D3,D4) +--R +--RExamples of generalizedInverse from InnerMatrixLinearAlgebraFunctions +--R +--E 1120 + +--S 1121 of 3320 +)d op generalLambert +--R +--R +--RThere are 2 exposed functions called generalLambert : +--R [1] (UnivariateFormalPowerSeries(D2),Integer,Integer) -> +--R UnivariateFormalPowerSeries(D2) +--R from UnivariateFormalPowerSeries(D2) if D2 has RING +--R [2] (UnivariateTaylorSeriesCZero(D2,D3),Integer,Integer) -> +--R UnivariateTaylorSeriesCZero(D2,D3) +--R from UnivariateTaylorSeriesCZero(D2,D3) if D2 has RING and +--R D3: SYMBOL +--R +--RThere are 2 unexposed functions called generalLambert : +--R [1] (Stream(D3),Integer,Integer) -> Stream(D3) +--R from StreamTaylorSeriesOperations(D3) if D3 has RING +--R [2] (UnivariateTaylorSeries(D2,D3,D4),Integer,Integer) -> +--R UnivariateTaylorSeries(D2,D3,D4) +--R from UnivariateTaylorSeries(D2,D3,D4) +--R if D2 has RING and D3: SYMBOL and D4: D2 +--R +--RExamples of generalLambert from StreamTaylorSeriesOperations +--R +--R +--RExamples of generalLambert from UnivariateFormalPowerSeries +--R +--R +--RExamples of generalLambert from UnivariateTaylorSeries +--R +--R +--RExamples of generalLambert from UnivariateTaylorSeriesCZero +--R +--E 1121 + +--S 1122 of 3320 +)d op generalPosition +--R +--R +--RThere is one exposed function called generalPosition : +--R [1] (PolynomialIdeals(D3,D4,D5,D6),List(D5)) -> Record(mval: Matrix( +--R D3),invmval: Matrix(D3),genIdeal: PolynomialIdeals(D3,D4,D5,D6)) +--R from PolynomialIdeals(D3,D4,D5,D6) +--R if D5 has ORDSET and D3 has FIELD and D4 has OAMONS and D6 +--R has POLYCAT(D3,D4,D5) +--R +--RExamples of generalPosition from PolynomialIdeals +--R +--E 1122 + +--S 1123 of 3320 +)d op generalSqFr +--R +--R +--RThere is one unexposed function called generalSqFr : +--R [1] SparseUnivariatePolynomial(SparseUnivariatePolynomial(D3)) -> +--R Factored(SparseUnivariatePolynomial(SparseUnivariatePolynomial(D3 +--R ))) +--R from TwoFactorize(D3) if D3 has FFIELDC +--R +--RExamples of generalSqFr from TwoFactorize +--R +--E 1123 + +--S 1124 of 3320 +)d op generalTwoFactor +--R +--R +--RThere is one unexposed function called generalTwoFactor : +--R [1] SparseUnivariatePolynomial(SparseUnivariatePolynomial(D3)) -> +--R Factored(SparseUnivariatePolynomial(SparseUnivariatePolynomial(D3 +--R ))) +--R from TwoFactorize(D3) if D3 has FFIELDC +--R +--RExamples of generalTwoFactor from TwoFactorize +--R +--E 1124 + +--S 1125 of 3320 +)d op generate +--R +--R +--RThere are 4 exposed functions called generate : +--R [1] (NonNegativeInteger,NonNegativeInteger) -> Vector(List(Integer)) +--R from HallBasis +--R [2] ((D2 -> D2),D2) -> InfiniteTuple(D2) from InfiniteTuple(D2) if +--R D2 has TYPE +--R [3] ((D2 -> D2),D2) -> Stream(D2) from Stream(D2) if D2 has TYPE +--R [4] (() -> D2) -> Stream(D2) from Stream(D2) if D2 has TYPE +--R +--RExamples of generate from HallBasis +--R +--R +--RExamples of generate from InfiniteTuple +--R +--R +--RExamples of generate from Stream +--R +--Rf(x:Integer):Integer == x+10 +--Rgenerate(f,10) +--R +--Rf():Integer == 1 +--Rgenerate(f) +--R +--E 1125 + +--S 1126 of 3320 +)d op generateIrredPoly +--R +--R +--RThere is one unexposed function called generateIrredPoly : +--R [1] PositiveInteger -> SparseUnivariatePolynomial(D3) +--R from IrredPolyOverFiniteField(D3) if D3 has FFIELDC +--R +--RExamples of generateIrredPoly from IrredPolyOverFiniteField +--R +--E 1126 + +--S 1127 of 3320 +)d op generator +--R +--R +--RThere are 4 exposed functions called generator : +--R [1] -> D from D if D has FAXF(D1) and D1 has FINITE and D1 has +--R FIELD +--R [2] D -> Union(D1,"failed") from D +--R if D has FDIVCAT(D2,D3,D4,D1) and D2 has FIELD and D3 has +--R UPOLYC(D2) and D4 has UPOLYC(FRAC(D3)) and D1 has FFCAT(D2, +--R D3,D4) +--R [3] NonNegativeInteger -> FreeNilpotentLie(D2,D3,D4) +--R from FreeNilpotentLie(D2,D3,D4) +--R if D2: NNI and D3: NNI and D4 has COMRING +--R [4] -> D from D if D1 has COMRING and D has MONOGEN(D1,D2) and D2 +--R has UPOLYC(D1) +--R +--RThere are 2 unexposed functions called generator : +--R [1] NonNegativeInteger -> AntiSymm(D2,D3) from AntiSymm(D2,D3) +--R if D2 has RING and D3: LIST(SYMBOL) +--R [2] NonNegativeInteger -> DeRhamComplex(D2,D3) from DeRhamComplex(D2 +--R ,D3) +--R if D2 has Join(Ring,OrderedSet) and D3: LIST(SYMBOL) +--R +--RExamples of generator from AntiSymm +--R +--RAS:=AntiSymm(Integer,[x,y,z]) +--R[dx,dy,dz]:=[generator(i)$AS for i in 1..3] +--R +--R +--RExamples of generator from DeRhamComplex +--R +--Rder := DeRhamComplex(Integer,[x,y,z]) +--R[dx,dy,dz] := [generator(i)$der for i in 1..3] +--R +--R +--RExamples of generator from FiniteAlgebraicExtensionField +--R +--R +--RExamples of generator from FiniteDivisorCategory +--R +--R +--RExamples of generator from FreeNilpotentLie +--R +--R +--RExamples of generator from MonogenicAlgebra +--R +--E 1127 + +--S 1128 of 3320 +)d op generators +--R +--R +--RThere are 2 exposed functions called generators : +--R [1] PolynomialIdeals(D2,D3,D4,D5) -> List(D5) +--R from PolynomialIdeals(D2,D3,D4,D5) +--R if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D5 +--R has POLYCAT(D2,D3,D4) +--R [2] PermutationGroup(D2) -> List(Permutation(D2)) from +--R PermutationGroup(D2) +--R if D2 has SETCAT +--R +--RExamples of generators from PolynomialIdeals +--R +--R +--RExamples of generators from PermutationGroup +--R +--E 1128 + +--S 1129 of 3320 +--R------------------------------)d op generic (System Error) +--E 1129 + +--S 1130 of 3320 +)d op generic? +--R +--R +--RThere is one unexposed function called generic? : +--R [1] Pattern(D2) -> Boolean from Pattern(D2) if D2 has SETCAT +--R +--RExamples of generic? from Pattern +--R +--E 1130 + +--S 1131 of 3320 +--R---------------------------)d op genericLeftDiscriminant (System Error) +--E 1131 + +--S 1132 of 3320 +--R---------------------------)d op genericLeftMinimalPolynomial (System Error) +--E 1132 + +--S 1133 of 3320 +--R---------------------------)d op genericLeftNorm (System Error) +--E 1133 + +--S 1134 of 3320 +--R---------------------------)d op genericLeftTrace (System Error) +--E 1134 + +--S 1135 of 3320 +--R---------------------------)d op genericLeftTraceForm (System Error) +--E 1135 + +--S 1136 of 3320 +)d op genericPosition +--R +--R +--RThere is one unexposed function called genericPosition : +--R [1] (List(DistributedMultivariatePolynomial(D4,D5)),List( +--R OrderedVariableList(D4))) -> Record(dpolys: List( +--R DistributedMultivariatePolynomial(D4,D5)),coords: List(Integer)) +--R from GroebnerSolve(D4,D5,D6) +--R if D4: LIST(SYMBOL) and D5 has GCDDOM and D6 has GCDDOM +--R +--R +--RExamples of genericPosition from GroebnerSolve +--R +--E 1136 + +--S 1137 of 3320 +--R---------------------------)d op genericRightDiscriminant (System Error) +--E 1137 + +--S 1138 of 3320 +--R------------------------)d op genericRightMinimalPolynomial (System Error) +--E 1138 + +--S 1139 of 3320 +--R------------------------)d op genericRightNorm (System Error) +--E 1139 + +--S 1140 of 3320 +--R------------------------)d op genericRightTrace (System Error) +--E 1140 + +--S 1141 of 3320 +--R------------------------)d op genericRightTraceForm (System Error) +--E 1141 + +--S 1142 of 3320 +)d op genus +--R +--R +--RThere are 5 exposed functions called genus : +--R [1] D6 -> NonNegativeInteger +--R from DesingTreePackage(D7,D8,D6,D9,D10,D11,D12,D1,D2,D3,D4 +--R ) +--R if D7 has FIELD and D8: LIST(SYMBOL) and D6 has POLYCAT(D7 +--R ,D9,OVAR(D8)) and D9 has DIRPCAT(#(D8),NNI) and D10 has +--R PRSPCAT(D7) and D11 has LOCPOWC(D7) and D12 has PLACESC(D7, +--R D11) and D1 has DIVCAT(D12) and D2 has INFCLCT(D7,D8,D6,D9, +--R D10,D11,D12,D1,D4) and D4 has BLMETCT and D3 has DSTRCAT(D2 +--R ) +--R [2] -> NonNegativeInteger from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC( +--R D2) and D4 has UPOLYC(FRAC(D3)) +--R [3] -> NonNegativeInteger +--R from GeneralPackageForAlgebraicFunctionField(D6,D7,D8,D9, +--R D10,D11,D12,D1,D2,D3,D4) +--R if D6 has FIELD and D7: LIST(SYMBOL) and D8 has POLYCAT(D6 +--R ,D9,OVAR(D7)) and D9 has DIRPCAT(#(D7),NNI) and D10 has +--R PRSPCAT(D6) and D11 has LOCPOWC(D6) and D12 has PLACESC(D6, +--R D11) and D1 has DIVCAT(D12) and D2 has INFCLCT(D6,D7,D8,D9, +--R D10,D11,D12,D1,D4) and D4 has BLMETCT and D3 has DSTRCAT(D2 +--R ) +--R [4] -> NonNegativeInteger +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D2,D3 +--R ,D4) +--R if D2 has FFIELDC and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R [5] -> NonNegativeInteger from PackageForAlgebraicFunctionField(D2, +--R D3,D4) +--R if D2 has FIELD and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R +--RThere is one unexposed function called genus : +--R [1] -> NonNegativeInteger from FunctionFieldCategory&(D2,D3,D4,D5) +--R if D3 has UFD and D4 has UPOLYC(D3) and D5 has UPOLYC(FRAC +--R (D4)) and D2 has FFCAT(D3,D4,D5) +--R +--RExamples of genus from DesingTreePackage +--R +--R +--RExamples of genus from FunctionFieldCategory& +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) +--Rgenus()$R +--R +--R +--RExamples of genus from FunctionFieldCategory +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) +--Rgenus()$R +--R +--R +--RExamples of genus from GeneralPackageForAlgebraicFunctionField +--R +--R +--RExamples of genus from PackageForAlgebraicFunctionFieldOverFiniteField +--R +--R +--RExamples of genus from PackageForAlgebraicFunctionField +--R +--E 1142 + +--S 1143 of 3320 +)d op genusNeg +--R +--R +--RThere are 4 exposed functions called genusNeg : +--R [1] D6 -> Integer from DesingTreePackage(D7,D8,D6,D9,D10,D11,D12,D1, +--R D2,D3,D4) +--R if D7 has FIELD and D8: LIST(SYMBOL) and D6 has POLYCAT(D7 +--R ,D9,OVAR(D8)) and D9 has DIRPCAT(#(D8),NNI) and D10 has +--R PRSPCAT(D7) and D11 has LOCPOWC(D7) and D12 has PLACESC(D7, +--R D11) and D1 has DIVCAT(D12) and D2 has INFCLCT(D7,D8,D6,D9, +--R D10,D11,D12,D1,D4) and D4 has BLMETCT and D3 has DSTRCAT(D2 +--R ) +--R [2] -> Integer +--R from GeneralPackageForAlgebraicFunctionField(D6,D7,D8,D9, +--R D10,D11,D12,D1,D2,D3,D4) +--R if D6 has FIELD and D7: LIST(SYMBOL) and D8 has POLYCAT(D6 +--R ,D9,OVAR(D7)) and D9 has DIRPCAT(#(D7),NNI) and D10 has +--R PRSPCAT(D6) and D11 has LOCPOWC(D6) and D12 has PLACESC(D6, +--R D11) and D1 has DIVCAT(D12) and D2 has INFCLCT(D6,D7,D8,D9, +--R D10,D11,D12,D1,D4) and D4 has BLMETCT and D3 has DSTRCAT(D2 +--R ) +--R [3] -> Integer +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D2,D3 +--R ,D4) +--R if D2 has FFIELDC and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R [4] -> Integer from PackageForAlgebraicFunctionField(D2,D3,D4) +--R if D2 has FIELD and D3: LIST(SYMBOL) and D4 has BLMETCT +--R +--R +--RExamples of genusNeg from DesingTreePackage +--R +--R +--RExamples of genusNeg from GeneralPackageForAlgebraicFunctionField +--R +--R +--RExamples of genusNeg from PackageForAlgebraicFunctionFieldOverFiniteField +--R +--R +--RExamples of genusNeg from PackageForAlgebraicFunctionField +--R +--E 1143 + +--S 1144 of 3320 +)d op genusTree +--R +--R +--RThere is one exposed function called genusTree : +--R [1] (NonNegativeInteger,List(D4)) -> NonNegativeInteger +--R from DesingTreePackage(D8,D9,D10,D11,D12,D13,D1,D2,D3,D4, +--R D5) +--R if D4 has DSTRCAT(D3) and D3 has INFCLCT(D8,D9,D10,D11,D12 +--R ,D13,D1,D2,D5) and D5 has BLMETCT and D8 has FIELD and D9: +--R LIST(SYMBOL) and D10 has POLYCAT(D8,D11,OVAR(D9)) and D11 +--R has DIRPCAT(#(D9),NNI) and D12 has PRSPCAT(D8) and D13 +--R has LOCPOWC(D8) and D1 has PLACESC(D8,D13) and D2 has +--R DIVCAT(D1) +--R +--RExamples of genusTree from DesingTreePackage +--R +--E 1144 + +--S 1145 of 3320 +)d op genusTreeNeg +--R +--R +--RThere is one exposed function called genusTreeNeg : +--R [1] (NonNegativeInteger,List(D5)) -> Integer +--R from DesingTreePackage(D10,D11,D12,D13,D14,D1,D2,D3,D4,D5, +--R D6) +--R if D5 has DSTRCAT(D4) and D4 has INFCLCT(D10,D11,D12,D13, +--R D14,D1,D2,D3,D6) and D6 has BLMETCT and D10 has FIELD and +--R D11: LIST(SYMBOL) and D12 has POLYCAT(D10,D13,OVAR(D11)) +--R and D13 has DIRPCAT(#(D11),NNI) and D14 has PRSPCAT(D10) +--R and D1 has LOCPOWC(D10) and D2 has PLACESC(D10,D1) and D3 +--R has DIVCAT(D2) +--R +--RExamples of genusTreeNeg from DesingTreePackage +--R +--E 1145 + +--S 1146 of 3320 +)d op geometric +--R +--R +--RThere is one unexposed function called geometric : +--R [1] RationalNumber -> (() -> Integer) from +--R RandomIntegerDistributions +--R +--RExamples of geometric from RandomIntegerDistributions +--R +--E 1146 + +--S 1147 of 3320 done +)d op getAncestors +--R +--R +--RThere is one exposed function called getAncestors : +--R [1] Symbol -> Set(Symbol) from ApplicationProgramInterface +--R +--RExamples of getAncestors from ApplicationProgramInterface +--R +--RgetAncestors 'IndexedAggregate +--R +--E 1147 + +--S 1148 of 3320 +)d op getBadValues +--R +--R +--RThere is one unexposed function called getBadValues : +--R [1] Pattern(D2) -> List(Any) from Pattern(D2) if D2 has SETCAT +--R +--RExamples of getBadValues from Pattern +--R +--E 1148 + +--S 1149 of 3320 +)d op getButtonValue +--R +--R +--RThere is one exposed function called getButtonValue : +--R [1] (String,String) -> Float from AttributeButtons +--R +--RExamples of getButtonValue from AttributeButtons +--R +--E 1149 + +--S 1150 of 3320 +)d op getCode +--R +--R +--RThere is one exposed function called getCode : +--R [1] FortranCode -> SExpression from FortranCode +--R +--RExamples of getCode from FortranCode +--R +--E 1150 + +--S 1151 of 3320 +)d op getCurve +--R +--R +--RThere is one unexposed function called getCurve : +--R [1] TubePlot(D1) -> D1 from TubePlot(D1) if D1 has PSCURVE +--R +--RExamples of getCurve from TubePlot +--R +--E 1151 + +--S 1152 of 3320 +)d op getDatabase +--R +--R +--RThere are 2 exposed functions called getDatabase : +--R [1] (String,String) -> String from AxiomServer +--R [2] String -> Database(IndexCard) from OperationsQuery +--R +--RExamples of getDatabase from AxiomServer +--R +--R +--RExamples of getDatabase from OperationsQuery +--R +--E 1152 + +--S 1153 of 3320 done +)d op getDomains +--R +--R +--RThere is one exposed function called getDomains : +--R [1] Symbol -> Set(Symbol) from ApplicationProgramInterface +--R +--RExamples of getDomains from ApplicationProgramInterface +--R +--RgetDomains 'IndexedAggregate +--R +--E 1153 + +--S 1154 of 3320 +)d op getEq +--R +--R +--RThere is one exposed function called getEq : +--R [1] D1 -> D1 from RecurrenceOperator(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain,ConvertibleTo( +--R InputForm)) and D1 has Join(FunctionSpace(D2),AbelianMonoid +--R ,RetractableTo(Integer),RetractableTo(Symbol), +--R PartialDifferentialRing(Symbol),CombinatorialOpsCategory) +--R +--R +--RExamples of getEq from RecurrenceOperator +--R +--E 1154 + +--S 1155 of 3320 +)d op getExplanations +--R +--R +--RThere is one exposed function called getExplanations : +--R [1] (RoutinesTable,String) -> List(String) from RoutinesTable +--R +--RExamples of getExplanations from RoutinesTable +--R +--E 1155 + +--S 1156 of 3320 +)d op getGoodPrime +--R +--R +--RThere is one unexposed function called getGoodPrime : +--R [1] Integer -> PositiveInteger from PointsOfFiniteOrderTools(D3,D4) +--R if D3 has UPOLYC(FRAC(INT)) and D4 has UPOLYC(FRAC(D3)) +--R +--R +--RExamples of getGoodPrime from PointsOfFiniteOrderTools +--R +--E 1156 + +--S 1157 of 3320 +)d op getGraph +--R +--R +--RThere is one unexposed function called getGraph : +--R [1] (TwoDimensionalViewport,PositiveInteger) -> GraphImage +--R from TwoDimensionalViewport +--R +--RExamples of getGraph from TwoDimensionalViewport +--R +--E 1157 + +--S 1158 of 3320 +)d op gethi +--R +--R +--RThere are 3 exposed functions called gethi : +--R [1] Segment(OrderedCompletion(DoubleFloat)) -> DoubleFloat +--R from d01AgentsPackage +--R [2] Segment(OrderedCompletion(DoubleFloat)) -> DoubleFloat +--R from ExpertSystemContinuityPackage +--R [3] Segment(OrderedCompletion(DoubleFloat)) -> DoubleFloat +--R from ExpertSystemToolsPackage +--R +--RExamples of gethi from d01AgentsPackage +--R +--R +--RExamples of gethi from ExpertSystemContinuityPackage +--R +--R +--RExamples of gethi from ExpertSystemToolsPackage +--R +--E 1158 + +--S 1159 of 3320 +)d op getlo +--R +--R +--RThere are 3 exposed functions called getlo : +--R [1] Segment(OrderedCompletion(DoubleFloat)) -> DoubleFloat +--R from d01AgentsPackage +--R [2] Segment(OrderedCompletion(DoubleFloat)) -> DoubleFloat +--R from ExpertSystemContinuityPackage +--R [3] Segment(OrderedCompletion(DoubleFloat)) -> DoubleFloat +--R from ExpertSystemToolsPackage +--R +--RExamples of getlo from d01AgentsPackage +--R +--R +--RExamples of getlo from ExpertSystemContinuityPackage +--R +--R +--RExamples of getlo from ExpertSystemToolsPackage +--R +--E 1159 + +--S 1160 of 3320 +)d op getMatch +--R +--R +--RThere is one unexposed function called getMatch : +--R [1] (Pattern(D3),PatternMatchResult(D3,D1)) -> Union(D1,"failed") +--R from PatternMatchResult(D3,D1) if D3 has SETCAT and D1 +--R has SETCAT +--R +--RExamples of getMatch from PatternMatchResult +--R +--E 1160 + +--S 1161 of 3320 +)d op getMeasure +--R +--R +--RThere is one exposed function called getMeasure : +--R [1] (RoutinesTable,Symbol) -> Float from RoutinesTable +--R +--RExamples of getMeasure from RoutinesTable +--R +--E 1161 + +--S 1162 of 3320 +)d op getMultiplicationMatrix +--R +--R +--RThere is one exposed function called getMultiplicationMatrix : +--R [1] -> Matrix(PrimeField(D2)) from FiniteFieldNormalBasis(D2,D3) +--R if D2: PI and D3: PI +--R +--RThere are 2 unexposed functions called getMultiplicationMatrix : +--R [1] -> Matrix(D2) from FiniteFieldNormalBasisExtensionByPolynomial( +--R D2,D3) +--R if D2 has FFIELDC and D3: Union(SUP(D2),VECTOR(LIST( +--R Record(value: D2,index: SingleInteger)))) +--R [2] -> Matrix(D2) from FiniteFieldNormalBasisExtension(D2,D3) +--R if D2 has FFIELDC and D3: PI +--R +--RExamples of getMultiplicationMatrix from FiniteFieldNormalBasis +--R +--R +--RExamples of getMultiplicationMatrix from FiniteFieldNormalBasisExtensionByPolynomial +--R +--R +--RExamples of getMultiplicationMatrix from FiniteFieldNormalBasisExtension +--R +--E 1162 + +--S 1163 of 3320 +)d op getMultiplicationTable +--R +--R +--RThere is one exposed function called getMultiplicationTable : +--R [1] -> Vector(List(Record(value: PrimeField(D2),index: +--R SingleInteger))) +--R from FiniteFieldNormalBasis(D2,D3) if D2: PI and D3: PI +--R +--R +--RThere are 2 unexposed functions called getMultiplicationTable : +--R [1] -> Vector(List(Record(value: D2,index: SingleInteger))) +--R from FiniteFieldNormalBasisExtensionByPolynomial(D2,D3) +--R if D2 has FFIELDC and D3: Union(SUP(D2),VECTOR(LIST( +--R Record(value: D2,index: SingleInteger)))) +--R [2] -> Vector(List(Record(value: D2,index: SingleInteger))) +--R from FiniteFieldNormalBasisExtension(D2,D3) if D2 has +--R FFIELDC and D3: PI +--R +--RExamples of getMultiplicationTable from FiniteFieldNormalBasis +--R +--R +--RExamples of getMultiplicationTable from FiniteFieldNormalBasisExtensionByPolynomial +--R +--R +--RExamples of getMultiplicationTable from FiniteFieldNormalBasisExtension +--R +--E 1163 + +--S 1164 of 3320 +)d op getOp +--R +--R +--RThere is one exposed function called getOp : +--R [1] D2 -> BasicOperator from RecurrenceOperator(D3,D2) +--R if D3 has Join(OrderedSet,IntegralDomain,ConvertibleTo( +--R InputForm)) and D2 has Join(FunctionSpace(D3),AbelianMonoid +--R ,RetractableTo(Integer),RetractableTo(Symbol), +--R PartialDifferentialRing(Symbol),CombinatorialOpsCategory) +--R +--R +--RExamples of getOp from RecurrenceOperator +--R +--E 1164 + +--S 1165 of 3320 +)d op getOrder +--R +--R +--RThere is one unexposed function called getOrder : +--R [1] -> Record(low: List(D2),high: List(D2)) +--R from UserDefinedPartialOrdering(D2) if D2 has SETCAT +--R +--RExamples of getOrder from UserDefinedPartialOrdering +--R +--E 1165 + +--S 1166 of 3320 +)d op getPickedPoints +--R +--R +--RThere is one unexposed function called getPickedPoints : +--R [1] TwoDimensionalViewport -> List(Point(DoubleFloat)) +--R from TwoDimensionalViewport +--R +--RExamples of getPickedPoints from TwoDimensionalViewport +--R +--E 1166 + +--S 1167 of 3320 +)d op getRef +--R +--R +--RThere is one unexposed function called getRef : +--R [1] InnerSparseUnivariatePowerSeries(D2) -> Reference( +--R OrderedCompletion(Integer)) +--R from InnerSparseUnivariatePowerSeries(D2) if D2 has RING +--R +--R +--RExamples of getRef from InnerSparseUnivariatePowerSeries +--R +--E 1167 + +--S 1168 of 3320 +)d op getShiftRec +--R +--R +--RThere is one exposed function called getShiftRec : +--R [1] (BasicOperator,Kernel(D6),Symbol) -> Union(Integer,"failed") +--R from RecurrenceOperator(D5,D6) +--R if D6 has Join(FunctionSpace(D5),AbelianMonoid, +--R RetractableTo(Integer),RetractableTo(Symbol), +--R PartialDifferentialRing(Symbol),CombinatorialOpsCategory) +--R and D5 has RING and D5 has Join(OrderedSet,IntegralDomain, +--R ConvertibleTo(InputForm)) +--R +--RExamples of getShiftRec from RecurrenceOperator +--R +--E 1168 + +--S 1169 of 3320 done +)d op getSmgl +--R +--R +--RThere is one exposed function called getSmgl : +--R [1] BasicStochasticDifferential -> Union(Symbol,"failed") +--R from BasicStochasticDifferential +--R +--RExamples of getSmgl from BasicStochasticDifferential +--R +--Rintroduce!(t,dt) -- dt is a new stochastic differential +--RgetSmgl(dt::BSD) +--R +--E 1169 + +--S 1170 of 3320 +)d op getStream +--R +--R +--RThere is one unexposed function called getStream : +--R [1] InnerSparseUnivariatePowerSeries(D2) -> Stream(Record(k: Integer +--R ,c: D2)) +--R from InnerSparseUnivariatePowerSeries(D2) if D2 has RING +--R +--R +--RExamples of getStream from InnerSparseUnivariatePowerSeries +--R +--E 1170 + +--S 1171 of 3320 +)d op getVariableOrder +--R +--R +--RThere is one exposed function called getVariableOrder : +--R [1] -> Record(high: List(Symbol),low: List(Symbol)) +--R from UserDefinedVariableOrdering +--R +--RExamples of getVariableOrder from UserDefinedVariableOrdering +--R +--E 1171 + +--S 1172 of 3320 +)d op getZechTable +--R +--R +--RThere is one exposed function called getZechTable : +--R [1] -> PrimitiveArray(SingleInteger) from FiniteFieldCyclicGroup(D2 +--R ,D3) +--R if D2: PI and D3: PI +--R +--RThere are 2 unexposed functions called getZechTable : +--R [1] -> PrimitiveArray(SingleInteger) +--R from FiniteFieldCyclicGroupExtensionByPolynomial(D2,D3) +--R if D2 has FFIELDC and D3: SUP(D2) +--R [2] -> PrimitiveArray(SingleInteger) +--R from FiniteFieldCyclicGroupExtension(D2,D3) if D2 has +--R FFIELDC and D3: PI +--R +--RExamples of getZechTable from FiniteFieldCyclicGroup +--R +--R +--RExamples of getZechTable from FiniteFieldCyclicGroupExtensionByPolynomial +--R +--R +--RExamples of getZechTable from FiniteFieldCyclicGroupExtension +--R +--E 1172 + +--S 1173 of 3320 +)d op GF2FG +--R +--R +--RThere is one unexposed function called GF2FG : +--R [1] Complex(D4) -> D1 from InnerTrigonometricManipulations(D3,D4,D1) +--R if D4 has Join(FunctionSpace(D3),RadicalCategory, +--R TranscendentalFunctionCategory) and D3 has Join( +--R IntegralDomain,OrderedSet) and D1 has Join(FunctionSpace( +--R Complex(D3)),RadicalCategory,TranscendentalFunctionCategory +--R ) +--R +--RExamples of GF2FG from InnerTrigonometricManipulations +--R +--E 1173 + +--S 1174 of 3320 done +)d op gnuDraw +--R +--R +--RThere are 4 exposed functions called gnuDraw : +--R [1] (Expression(Float),SegmentBinding(Float),String,List(DrawOption) +--R ) -> Void +--R from GnuDraw +--R [2] (Expression(Float),SegmentBinding(Float),String) -> Void from +--R GnuDraw +--R [3] (Expression(Float),SegmentBinding(Float),SegmentBinding(Float), +--R String,List(DrawOption)) -> Void +--R from GnuDraw +--R [4] (Expression(Float),SegmentBinding(Float),SegmentBinding(Float), +--R String) -> Void +--R from GnuDraw +--R +--RExamples of gnuDraw from GnuDraw +--R +--RgnuDraw(sin(x)*cos(y),x=-6..4,y=-4..6,"out3d.dat") +--R)sys gnuplot -persist out3d.dat +--R)sys evince out2d.dat.ps -- linux +--R)sys open out2d.dat.ps -- mac +--R)sys firefox out2d.dat.ps -- everywhere +--R +--RgnuDraw(sin(x)*cos(y),x=-6..4,y=-4..6,"out3d.dat",title=="out3d") +--R)sys gnuplot -persist out3d.dat +--R)sys evince out2d.dat.ps -- linux +--R)sys open out2d.dat.ps -- mac +--R)sys firefox out2d.dat.ps -- everywhere +--R +--RgnuDraw(D(cos(exp(z))/exp(z^2),z),z=-5..5,"out2d.dat") +--R)sys gnuplot -persist out2d.dat +--R)sys evince out2d.dat.ps -- linux +--R)sys open out2d.dat.ps -- mac +--R)sys firefox out2d.dat.ps -- everywhere +--R +--RgnuDraw(D(cos(exp(z))/exp(z^2),z),z=-5..5,"out2d.dat",title=="out2d") +--R)sys gnuplot -persist out2d.dat +--R)sys evince out2d.dat.ps -- linux +--R)sys open out2d.dat.ps -- mac +--R)sys firefox out2d.dat.ps -- everywhere +--R +--E 1174 + +--S 1175 of 3320 +)d op goodnessOfFit +--R +--R +--RThere are 2 exposed functions called goodnessOfFit : +--R [1] NumericalOptimizationProblem -> Result +--R from AnnaNumericalOptimizationPackage +--R [2] (List(Expression(Float)),List(Float)) -> Result +--R from AnnaNumericalOptimizationPackage +--R +--RExamples of goodnessOfFit from AnnaNumericalOptimizationPackage +--R +--E 1175 + +--S 1176 of 3320 +)d op goodPoint +--R +--R +--RThere is one unexposed function called goodPoint : +--R [1] (D2,D2) -> D1 from ChangeOfVariable(D1,D3,D2) +--R if D3 has UPOLYC(D1) and D1 has UFD and D2 has UPOLYC(FRAC +--R (D3)) +--R +--RExamples of goodPoint from ChangeOfVariable +--R +--E 1176 + +--S 1177 of 3320 +)d op goppaCode +--R +--R +--RThere are 4 exposed functions called goppaCode : +--R [1] (Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(D3)), +--R Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(D3))) -> +--R Matrix(D3) +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D3,D4 +--R ,D5) +--R if D3 has FFIELDC and D4: LIST(SYMBOL) and D5 has BLMETCT +--R +--R [2] (Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(D4)),List +--R (PlacesOverPseudoAlgebraicClosureOfFiniteField(D4))) -> Matrix(D4 +--R ) +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D4,D5 +--R ,D6) +--R if D4 has FFIELDC and D5: LIST(SYMBOL) and D6 has BLMETCT +--R +--R [3] (Divisor(Places(D3)),Divisor(Places(D3))) -> Matrix(D3) +--R from PackageForAlgebraicFunctionField(D3,D4,D5) +--R if D3 has FIELD and D4: LIST(SYMBOL) and D5 has BLMETCT +--R +--R [4] (Divisor(Places(D4)),List(Places(D4))) -> Matrix(D4) +--R from PackageForAlgebraicFunctionField(D4,D5,D6) +--R if D4 has FIELD and D5: LIST(SYMBOL) and D6 has BLMETCT +--R +--R +--RExamples of goppaCode from PackageForAlgebraicFunctionFieldOverFiniteField +--R +--R +--RExamples of goppaCode from PackageForAlgebraicFunctionField +--R +--E 1177 + +--S 1178 of 3320 +)d op GospersMethod +--R +--R +--RThere is one unexposed function called GospersMethod : +--R [1] (D1,D2,(() -> D2)) -> Union(D1,"failed") +--R from GosperSummationMethod(D4,D2,D5,D6,D1) +--R if D2 has ORDSET and D4 has OAMONS and D5 has INTDOM and +--R D6 has POLYCAT(D5,D4,D2) and D1 has Join(RetractableTo( +--R Fraction(Integer)),Field)with +--R coerce : D6 -> % +--R numer : % -> D6 +--R denom : % -> D6 +--R +--RExamples of GospersMethod from GosperSummationMethod +--R +--E 1178 + +--S 1179 of 3320 +)d op goto +--R +--R +--RThere is one exposed function called goto : +--R [1] SingleInteger -> FortranCode from FortranCode +--R +--RExamples of goto from FortranCode +--R +--E 1179 + +--S 1180 of 3320 +)d op gradient +--R +--R +--RThere is one exposed function called gradient : +--R [1] (D2,D3) -> Vector(D2) from MultiVariableCalculusFunctions(D4,D2, +--R D5,D3) +--R if D4 has SETCAT and D2 has PDRING(D4) and D5 has FLAGG(D2 +--R ) and D3 has FiniteLinearAggregate(D4)with +--R finiteAggregate +--R +--RExamples of gradient from MultiVariableCalculusFunctions +--R +--E 1180 + +--S 1181 of 3320 +)d op graeffe +--R +--R +--RThere is one unexposed function called graeffe : +--R [1] D1 -> D1 from ComplexRootFindingPackage(D2,D1) +--R if D2 has Join(Field,OrderedRing) and D1 has UPOLYC( +--R COMPLEX(D2)) +--R +--RExamples of graeffe from ComplexRootFindingPackage +--R +--E 1181 + +--S 1182 of 3320 +)d op gramschmidt +--R +--R +--RThere is one exposed function called gramschmidt : +--R [1] List(Matrix(Expression(Integer))) -> List(Matrix(Expression( +--R Integer))) +--R from RadicalEigenPackage +--R +--RExamples of gramschmidt from RadicalEigenPackage +--R +--E 1182 + +--S 1183 of 3320 +)d op graphCurves +--R +--R +--RThere are 3 unexposed functions called graphCurves : +--R [1] (List(List(Point(DoubleFloat))),Palette,Palette,PositiveInteger, +--R List(DrawOption)) -> GraphImage +--R from ViewportPackage +--R [2] List(List(Point(DoubleFloat))) -> GraphImage from +--R ViewportPackage +--R [3] (List(List(Point(DoubleFloat))),List(DrawOption)) -> GraphImage +--R from ViewportPackage +--R +--RExamples of graphCurves from ViewportPackage +--R +--E 1183 + +--S 1184 of 3320 +)d op graphImage +--R +--R +--RThere is one unexposed function called graphImage : +--R [1] -> GraphImage from GraphImage +--R +--RExamples of graphImage from GraphImage +--R +--E 1184 + +--S 1185 of 3320 +)d op graphs +--R +--R +--RThere is one exposed function called graphs : +--R [1] Integer -> SymmetricPolynomial(Fraction(Integer)) from +--R CycleIndicators +--R +--RThere is one unexposed function called graphs : +--R [1] TwoDimensionalViewport -> Vector(Union(GraphImage,undefined)) +--R from TwoDimensionalViewport +--R +--RExamples of graphs from CycleIndicators +--R +--R +--RExamples of graphs from TwoDimensionalViewport +--R +--E 1185 + +--S 1186 of 3320 +)d op graphState +--R +--R +--RThere is one unexposed function called graphState : +--R [1] (TwoDimensionalViewport,PositiveInteger,DoubleFloat,DoubleFloat, +--R DoubleFloat,DoubleFloat,Integer,Integer,Integer,Integer,Palette, +--R Integer,Palette,Integer) -> Void +--R from TwoDimensionalViewport +--R +--RExamples of graphState from TwoDimensionalViewport +--R +--E 1186 + +--S 1187 of 3320 +)d op graphStates +--R +--R +--RThere is one unexposed function called graphStates : +--R [1] TwoDimensionalViewport -> Vector(Record(scaleX: DoubleFloat, +--R scaleY: DoubleFloat,deltaX: DoubleFloat,deltaY: DoubleFloat, +--R points: Integer,connect: Integer,spline: Integer,axes: Integer, +--R axesColor: Palette,units: Integer,unitsColor: Palette,showing: +--R Integer)) +--R from TwoDimensionalViewport +--R +--RExamples of graphStates from TwoDimensionalViewport +--R +--E 1187 + +--S 1188 of 3320 +)d op green +--R +--R +--RThere is one exposed function called green : +--R [1] -> Color from Color +--R +--RExamples of green from Color +--R +--E 1188 + +--S 1189 of 3320 +)d op groebgen +--R +--R +--RThere is one unexposed function called groebgen : +--R [1] List(DistributedMultivariatePolynomial(D3,D4)) -> Record(glbase +--R : List(DistributedMultivariatePolynomial(D3,D4)),glval: List( +--R Integer)) +--R from LinGroebnerPackage(D3,D4) if D3: LIST(SYMBOL) and D4 +--R has GCDDOM +--R +--RExamples of groebgen from LinGroebnerPackage +--R +--E 1189 + +--S 1190 of 3320 +)d op groebner +--R +--R +--RThere are 5 exposed functions called groebner : +--R [1] List(D5) -> List(D5) from GroebnerPackage(D2,D3,D4,D5) +--R if D5 has POLYCAT(D2,D3,D4) and D2 has GCDDOM and D3 has +--R OAMONS and D4 has ORDSET +--R [2] (List(D6),String) -> List(D6) from GroebnerPackage(D3,D4,D5,D6) +--R if D6 has POLYCAT(D3,D4,D5) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET +--R [3] (List(D6),String,String) -> List(D6) from GroebnerPackage(D3,D4, +--R D5,D6) +--R if D6 has POLYCAT(D3,D4,D5) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET +--R [4] PolynomialIdeals(D1,D2,D3,D4) -> PolynomialIdeals(D1,D2,D3,D4) +--R from PolynomialIdeals(D1,D2,D3,D4) +--R if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4 +--R has POLYCAT(D1,D2,D3) +--R [5] List(D6) -> List(D6) from InterfaceGroebnerPackage(D2,D3,D4,D5, +--R D6) +--R if D6 has POLYCAT(D2,D4,D5) and D2 has FIELD and D4 has +--R OAMONS and D5 has ORDSET and D3: LIST(SYMBOL) +--R +--RThere are 2 unexposed functions called groebner : +--R [1] List(Polynomial(D2)) -> List(Polynomial(D2)) from +--R FGLMIfCanPackage(D2,D3) +--R if D2 has GCDDOM and D3: LIST(SYMBOL) +--R [2] List(NewSparseMultivariatePolynomial(D2,OrderedVariableList(D3)) +--R ) -> List(NewSparseMultivariatePolynomial(D2,OrderedVariableList( +--R D3))) +--R from LexTriangularPackage(D2,D3) if D2 has GCDDOM and D3: +--R LIST(SYMBOL) +--R +--RExamples of groebner from FGLMIfCanPackage +--R +--R +--RExamples of groebner from GroebnerPackage +--R +--Rs1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36 +--Rs2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s +--Rs3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2 +--Rs4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s +--Rs5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3 +--Rs6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 +--Rs7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000 +--Rsn7:=[s1,s2,s3,s4,s5,s6,s7] +--Rgroebner(sn7,"info","redcrit") +--R +--Rs1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36 +--Rs2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s +--Rs3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2 +--Rs4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s +--Rs5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3 +--Rs6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 +--Rs7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000 +--Rsn7:=[s1,s2,s3,s4,s5,s6,s7] +--Rgroebner(sn7,"info") +--Rgroebner(sn7,"redcrit") +--R +--Rs1:DMP([w,p,z,t,s,b],FRAC(INT)):= 45*p + 35*s - 165*b - 36 +--Rs2:DMP([w,p,z,t,s,b],FRAC(INT)):= 35*p + 40*z + 25*t - 27*s +--Rs3:DMP([w,p,z,t,s,b],FRAC(INT)):= 15*w + 25*p*s + 30*z - 18*t - 165*b**2 +--Rs4:DMP([w,p,z,t,s,b],FRAC(INT)):= -9*w + 15*p*t + 20*z*s +--Rs5:DMP([w,p,z,t,s,b],FRAC(INT)):= w*p + 2*z*t - 11*b**3 +--Rs6:DMP([w,p,z,t,s,b],FRAC(INT)):= 99*w - 11*b*s + 3*b**2 +--Rs7:DMP([w,p,z,t,s,b],FRAC(INT)):= b**2 + 33/50*b + 2673/10000 +--Rsn7:=[s1,s2,s3,s4,s5,s6,s7] +--Rgroebner(sn7) +--R +--R +--RExamples of groebner from PolynomialIdeals +--R +--R +--RExamples of groebner from InterfaceGroebnerPackage +--R +--R +--RExamples of groebner from LexTriangularPackage +--R +--E 1190 + +--S 1191 of 3320 +)d op groebner? +--R +--R +--RThere is one exposed function called groebner? : +--R [1] PolynomialIdeals(D2,D3,D4,D5) -> Boolean +--R from PolynomialIdeals(D2,D3,D4,D5) +--R if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D5 +--R has POLYCAT(D2,D3,D4) +--R +--RExamples of groebner? from PolynomialIdeals +--R +--E 1191 + +--S 1192 of 3320 done +)d op groebnerFactorize +--R +--R +--RThere are 4 exposed functions called groebnerFactorize : +--R [1] (List(D6),List(D6)) -> List(List(D6)) +--R from GroebnerFactorizationPackage(D3,D4,D5,D6) +--R if D3 has Join(EuclideanDomain,CharacteristicZero) and D4 +--R has OAMONS and D5 has ORDSET and D6 has POLYCAT(D3,D4,D5) +--R +--R [2] (List(D7),List(D7),Boolean) -> List(List(D7)) +--R from GroebnerFactorizationPackage(D4,D5,D6,D7) +--R if D4 has Join(EuclideanDomain,CharacteristicZero) and D5 +--R has OAMONS and D6 has ORDSET and D7 has POLYCAT(D4,D5,D6) +--R +--R [3] List(D6) -> List(List(D6)) from GroebnerFactorizationPackage(D3, +--R D4,D5,D6) +--R if D3 has Join(EuclideanDomain,CharacteristicZero) and D4 +--R has OAMONS and D5 has ORDSET and D6 has POLYCAT(D3,D4,D5) +--R +--R [4] (List(D7),Boolean) -> List(List(D7)) +--R from GroebnerFactorizationPackage(D4,D5,D6,D7) +--R if D4 has Join(EuclideanDomain,CharacteristicZero) and D5 +--R has OAMONS and D6 has ORDSET and D7 has POLYCAT(D4,D5,D6) +--R +--R +--RExamples of groebnerFactorize from GroebnerFactorizationPackage +--R +--Rmfzn : SQMATRIX(6,DMP([x,y,z],Fraction INT)) := +--R[ [0,1,1,1,1,1], [1,0,1,8/3,x,8/3], [1,1,0,1,8/3,y], +--R[1,8/3,1,0,1,8/3], [1,x,8/3,1,0,1], [1,8/3,y,8/3,1,0] ] +--Req := determinant mfzn +--RgroebnerFactorize +--R[eq,eval(eq, [x,y,z],[y,z,x]), eval(eq,[x,y,z],[z,x,y])] +--R +--E 1192 + +--S 1193 of 3320 +)d op groebnerIdeal +--R +--R +--RThere is one exposed function called groebnerIdeal : +--R [1] List(D5) -> PolynomialIdeals(D2,D3,D4,D5) +--R from PolynomialIdeals(D2,D3,D4,D5) +--R if D5 has POLYCAT(D2,D3,D4) and D2 has FIELD and D3 has +--R OAMONS and D4 has ORDSET +--R +--RExamples of groebnerIdeal from PolynomialIdeals +--R +--E 1193 + +--S 1194 of 3320 +)d op groebSolve +--R +--R +--RThere is one unexposed function called groebSolve : +--R [1] (List(DistributedMultivariatePolynomial(D4,D5)),List( +--R OrderedVariableList(D4))) -> List(List( +--R DistributedMultivariatePolynomial(D4,D5))) +--R from GroebnerSolve(D4,D5,D6) +--R if D4: LIST(SYMBOL) and D5 has GCDDOM and D6 has GCDDOM +--R +--R +--RExamples of groebSolve from GroebnerSolve +--R +--E 1194 + +--S 1195 of 3320 +)d op ground +--R +--R +--RThere are 2 exposed functions called ground : +--R [1] D -> D1 from D if D has FAMR(D1,D2) and D2 has OAMON and D1 has +--R RING +--R [2] D -> D1 from D if D has FS(D1) and D1 has ORDSET +--R +--RExamples of ground from FiniteAbelianMonoidRing +--R +--R +--RExamples of ground from FunctionSpace +--R +--E 1195 + +--S 1196 of 3320 +)d op ground? +--R +--R +--RThere are 4 exposed functions called ground? : +--R [1] D -> Boolean from D if D has FAMR(D2,D3) and D2 has RING and D3 +--R has OAMON +--R [2] D -> Boolean from D if D has FS(D2) and D2 has ORDSET +--R [3] MyExpression(D2,D3) -> Boolean from MyExpression(D2,D3) +--R if D2: SYMBOL and D3 has Join(Ring,OrderedSet, +--R IntegralDomain) +--R [4] D -> Boolean from D if D has PACPERC +--R +--RExamples of ground? from FiniteAbelianMonoidRing +--R +--R +--RExamples of ground? from FunctionSpace +--R +--R +--RExamples of ground? from MyExpression +--R +--R +--RExamples of ground? from PseudoAlgebraicClosureOfPerfectFieldCategory +--R +--E 1196 + +--S 1197 of 3320 +)d op GT +--R +--R +--RThere is one exposed function called GT : +--R [1] (Union(I: Expression(Integer),F: Expression(Float),CF: +--R Expression(Complex(Float)),switch: Switch),Union(I: Expression( +--R Integer),F: Expression(Float),CF: Expression(Complex(Float)), +--R switch: Switch)) -> Switch +--R from Switch +--R +--RExamples of GT from Switch +--R +--E 1197 + +--S 1198 of 3320 +)d op guess +--R +--R +--RThere are 24 exposed functions called guess : +--R [1] List(AlgebraicNumber) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [2] (List(AlgebraicNumber),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [3] (List(AlgebraicNumber),List(((List(AlgebraicNumber),List( +--R GuessOption)) -> List(Record(function: Expression(Integer),order +--R : NonNegativeInteger)))),List(Symbol)) -> List(Record(function: +--R Expression(Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [4] (List(AlgebraicNumber),List(((List(AlgebraicNumber),List( +--R GuessOption)) -> List(Record(function: Expression(Integer),order +--R : NonNegativeInteger)))),List(Symbol),List(GuessOption)) -> List( +--R Record(function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [5] List(D3) -> List(Record(function: Expression(Integer),order: +--R NonNegativeInteger)) +--R from GuessFinite(D3) +--R if D3 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [6] (List(D4),List(GuessOption)) -> List(Record(function: Expression +--R (Integer),order: NonNegativeInteger)) +--R from GuessFinite(D4) +--R if D4 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [7] (List(D5),List(((List(D5),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)))),List( +--R Symbol)) -> List(Record(function: Expression(Integer),order: +--R NonNegativeInteger)) +--R from GuessFinite(D5) +--R if D5 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [8] (List(D6),List(((List(D6),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)))),List( +--R Symbol),List(GuessOption)) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessFinite(D6) +--R if D6 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [9] List(Fraction(Integer)) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [10] (List(Fraction(Integer)),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [11] (List(Fraction(Integer)),List(((List(Fraction(Integer)),List( +--R GuessOption)) -> List(Record(function: Expression(Integer),order +--R : NonNegativeInteger)))),List(Symbol)) -> List(Record(function: +--R Expression(Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [12] (List(Fraction(Integer)),List(((List(Fraction(Integer)),List( +--R GuessOption)) -> List(Record(function: Expression(Integer),order +--R : NonNegativeInteger)))),List(Symbol),List(GuessOption)) -> List( +--R Record(function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [13] List(D4) -> List(Record(function: D6,order: NonNegativeInteger) +--R ) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D4 has FIELD and D9: (D4 -> D6) and D7 has Join( +--R OrderedSet,IntegralDomain) and D8: (D7 -> D4) and D5 has +--R GCDDOM and D6 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D7),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [14] (List(D6),List(GuessOption)) -> List(Record(function: D8,order +--R : NonNegativeInteger)) +--R from Guess(D6,D7,D8,D9,D10,D2) +--R if D6 has FIELD and D2: (D6 -> D8) and D9 has Join( +--R OrderedSet,IntegralDomain) and D10: (D9 -> D6) and D7 has +--R GCDDOM and D8 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D9),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [15] (List(D8),List(((List(D8),List(GuessOption)) -> List(Record( +--R function: D10,order: NonNegativeInteger)))),List(Symbol)) -> List +--R (Record(function: D10,order: NonNegativeInteger)) +--R from Guess(D8,D9,D10,D11,D2,D3) +--R if D8 has FIELD and D3: (D8 -> D10) and D11 has Join( +--R OrderedSet,IntegralDomain) and D2: (D11 -> D8) and D9 has +--R GCDDOM and D10 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D11),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [16] (List(D10),List(((List(D10),List(GuessOption)) -> List(Record( +--R function: D12,order: NonNegativeInteger)))),List(Symbol),List( +--R GuessOption)) -> List(Record(function: D12,order: +--R NonNegativeInteger)) +--R from Guess(D10,D11,D12,D2,D3,D4) +--R if D10 has FIELD and D4: (D10 -> D12) and D2 has Join( +--R OrderedSet,IntegralDomain) and D3: (D2 -> D10) and D11 has +--R GCDDOM and D12 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D2),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [17] List(Fraction(Polynomial(Integer))) -> List(Record(function: +--R Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [18] (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List +--R (Record(function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [19] (List(Fraction(Polynomial(Integer))),List(((List(Fraction( +--R Polynomial(Integer))),List(GuessOption)) -> List(Record(function +--R : Expression(Integer),order: NonNegativeInteger)))),List(Symbol)) +--R -> List(Record(function: Expression(Integer),order: +--R NonNegativeInteger)) +--R from GuessPolynomial +--R [20] (List(Fraction(Polynomial(Integer))),List(((List(Fraction( +--R Polynomial(Integer))),List(GuessOption)) -> List(Record(function +--R : Expression(Integer),order: NonNegativeInteger)))),List(Symbol), +--R List(GuessOption)) -> List(Record(function: Expression(Integer), +--R order: NonNegativeInteger)) +--R from GuessPolynomial +--R [21] List(Fraction(MyUnivariatePolynomial(D3,Integer))) -> List( +--R Record(function: MyExpression(D3,Integer),order: +--R NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R [22] (List(Fraction(MyUnivariatePolynomial(D4,Integer))),List( +--R GuessOption)) -> List(Record(function: MyExpression(D4,Integer), +--R order: NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D4) if D4: SYMBOL +--R [23] (List(Fraction(MyUnivariatePolynomial(D5,Integer))),List(((List +--R (Fraction(MyUnivariatePolynomial(D5,Integer))),List(GuessOption)) +--R -> List(Record(function: MyExpression(D5,Integer),order: +--R NonNegativeInteger)))),List(Symbol)) -> List(Record(function: +--R MyExpression(D5,Integer),order: NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D5) if D5: SYMBOL +--R [24] (List(Fraction(MyUnivariatePolynomial(D6,Integer))),List(((List +--R (Fraction(MyUnivariatePolynomial(D6,Integer))),List(GuessOption)) +--R -> List(Record(function: MyExpression(D6,Integer),order: +--R NonNegativeInteger)))),List(Symbol),List(GuessOption)) -> List( +--R Record(function: MyExpression(D6,Integer),order: +--R NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D6) if D6: SYMBOL +--R +--RExamples of guess from GuessAlgebraicNumber +--R +--R +--RExamples of guess from GuessFinite +--R +--R +--RExamples of guess from GuessInteger +--R +--R +--RExamples of guess from Guess +--R +--R +--RExamples of guess from GuessPolynomial +--R +--R +--RExamples of guess from GuessUnivariatePolynomial +--R +--E 1198 + +--S 1199 of 3320 +)d op guessADE +--R +--R +--RThere are 18 exposed functions called guessADE : +--R [1] List(AlgebraicNumber) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [2] (List(AlgebraicNumber),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [3] Symbol -> ((List(AlgebraicNumber),List(GuessOption)) -> List( +--R Record(function: Expression(Integer),order: NonNegativeInteger))) +--R from GuessAlgebraicNumber if AlgebraicNumber has RETRACT( +--R SYMBOL) +--R [4] List(D3) -> List(Record(function: Expression(Integer),order: +--R NonNegativeInteger)) +--R from GuessFinite(D3) +--R if D3 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [5] (List(D4),List(GuessOption)) -> List(Record(function: Expression +--R (Integer),order: NonNegativeInteger)) +--R from GuessFinite(D4) +--R if D4 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [6] Symbol -> ((List(D3),List(GuessOption)) -> List(Record(function +--R : Expression(Integer),order: NonNegativeInteger))) +--R from GuessFinite(D3) +--R if D3 has RETRACT(SYMBOL) and D3 has Join( +--R FiniteFieldCategory,ConvertibleTo(Integer)) +--R [7] List(Fraction(Integer)) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [8] (List(Fraction(Integer)),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [9] Symbol -> ((List(Fraction(Integer)),List(GuessOption)) -> List( +--R Record(function: Expression(Integer),order: NonNegativeInteger))) +--R from GuessInteger +--R if Fraction(Integer) has RETRACT(SYMBOL) and Integer has +--R RETRACT(SYMBOL) +--R [10] List(D4) -> List(Record(function: D6,order: NonNegativeInteger) +--R ) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D4 has FIELD and D9: (D4 -> D6) and D7 has Join( +--R OrderedSet,IntegralDomain) and D8: (D7 -> D4) and D5 has +--R GCDDOM and D6 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D7),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [11] (List(D6),List(GuessOption)) -> List(Record(function: D8,order +--R : NonNegativeInteger)) +--R from Guess(D6,D7,D8,D9,D10,D2) +--R if D6 has FIELD and D2: (D6 -> D8) and D9 has Join( +--R OrderedSet,IntegralDomain) and D10: (D9 -> D6) and D7 has +--R GCDDOM and D8 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D9),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [12] Symbol -> ((List(D4),List(GuessOption)) -> List(Record(function +--R : D6,order: NonNegativeInteger))) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D7 has Join(OrderedSet,IntegralDomain) and D8: (D7 -> +--R D4) and D4 has RETRACT(SYMBOL) and D5 has RETRACT(SYMBOL) +--R and D4 has FIELD and D5 has GCDDOM and D6 has Join( +--R FunctionSpace(Integer),IntegralDomain,RetractableTo(D7), +--R RetractableTo(Symbol),RetractableTo(Integer), +--R CombinatorialOpsCategory,PartialDifferentialRing(Symbol)) +--R with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Booleanand D9: (D4 -> D6) +--R [13] List(Fraction(Polynomial(Integer))) -> List(Record(function: +--R Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [14] (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List +--R (Record(function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [15] Symbol -> ((List(Fraction(Polynomial(Integer))),List( +--R GuessOption)) -> List(Record(function: Expression(Integer),order +--R : NonNegativeInteger))) +--R from GuessPolynomial +--R if Fraction(Polynomial(Integer)) has RETRACT(SYMBOL) and +--R Polynomial(Integer) has RETRACT(SYMBOL) +--R [16] List(Fraction(MyUnivariatePolynomial(D3,Integer))) -> List( +--R Record(function: MyExpression(D3,Integer),order: +--R NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R [17] (List(Fraction(MyUnivariatePolynomial(D4,Integer))),List( +--R GuessOption)) -> List(Record(function: MyExpression(D4,Integer), +--R order: NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D4) if D4: SYMBOL +--R [18] Symbol -> ((List(Fraction(MyUnivariatePolynomial(D3,Integer))), +--R List(GuessOption)) -> List(Record(function: MyExpression(D3, +--R Integer),order: NonNegativeInteger))) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R +--RExamples of guessADE from GuessAlgebraicNumber +--R +--R +--RExamples of guessADE from GuessFinite +--R +--R +--RExamples of guessADE from GuessInteger +--R +--R +--RExamples of guessADE from Guess +--R +--R +--RExamples of guessADE from GuessPolynomial +--R +--R +--RExamples of guessADE from GuessUnivariatePolynomial +--R +--E 1199 + +--S 1200 of 3320 +)d op guessAlg +--R +--R +--RThere are 12 exposed functions called guessAlg : +--R [1] List(AlgebraicNumber) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [2] (List(AlgebraicNumber),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [3] List(D3) -> List(Record(function: Expression(Integer),order: +--R NonNegativeInteger)) +--R from GuessFinite(D3) +--R if D3 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [4] (List(D4),List(GuessOption)) -> List(Record(function: Expression +--R (Integer),order: NonNegativeInteger)) +--R from GuessFinite(D4) +--R if D4 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [5] List(Fraction(Integer)) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [6] (List(Fraction(Integer)),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [7] List(D4) -> List(Record(function: D6,order: NonNegativeInteger)) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D4 has FIELD and D9: (D4 -> D6) and D7 has Join( +--R OrderedSet,IntegralDomain) and D8: (D7 -> D4) and D5 has +--R GCDDOM and D6 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D7),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [8] (List(D6),List(GuessOption)) -> List(Record(function: D8,order: +--R NonNegativeInteger)) +--R from Guess(D6,D7,D8,D9,D10,D2) +--R if D6 has FIELD and D2: (D6 -> D8) and D9 has Join( +--R OrderedSet,IntegralDomain) and D10: (D9 -> D6) and D7 has +--R GCDDOM and D8 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D9),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [9] List(Fraction(Polynomial(Integer))) -> List(Record(function: +--R Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [10] (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List +--R (Record(function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [11] List(Fraction(MyUnivariatePolynomial(D3,Integer))) -> List( +--R Record(function: MyExpression(D3,Integer),order: +--R NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R [12] (List(Fraction(MyUnivariatePolynomial(D4,Integer))),List( +--R GuessOption)) -> List(Record(function: MyExpression(D4,Integer), +--R order: NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D4) if D4: SYMBOL +--R +--RExamples of guessAlg from GuessAlgebraicNumber +--R +--R +--RExamples of guessAlg from GuessFinite +--R +--R +--RExamples of guessAlg from GuessInteger +--R +--R +--RExamples of guessAlg from Guess +--R +--R +--RExamples of guessAlg from GuessPolynomial +--R +--R +--RExamples of guessAlg from GuessUnivariatePolynomial +--R +--E 1200 + +--S 1201 of 3320 +)d op guessBinRat +--R +--R +--RThere are 18 exposed functions called guessBinRat : +--R [1] List(AlgebraicNumber) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [2] (List(AlgebraicNumber),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [3] Symbol -> ((List(AlgebraicNumber),List(GuessOption)) -> List( +--R Record(function: Expression(Integer),order: NonNegativeInteger))) +--R from GuessAlgebraicNumber if AlgebraicNumber has RETRACT( +--R SYMBOL) +--R [4] List(D3) -> List(Record(function: Expression(Integer),order: +--R NonNegativeInteger)) +--R from GuessFinite(D3) +--R if D3 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [5] (List(D4),List(GuessOption)) -> List(Record(function: Expression +--R (Integer),order: NonNegativeInteger)) +--R from GuessFinite(D4) +--R if D4 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [6] Symbol -> ((List(D3),List(GuessOption)) -> List(Record(function +--R : Expression(Integer),order: NonNegativeInteger))) +--R from GuessFinite(D3) +--R if D3 has RETRACT(SYMBOL) and D3 has Join( +--R FiniteFieldCategory,ConvertibleTo(Integer)) +--R [7] List(Fraction(Integer)) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [8] (List(Fraction(Integer)),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [9] Symbol -> ((List(Fraction(Integer)),List(GuessOption)) -> List( +--R Record(function: Expression(Integer),order: NonNegativeInteger))) +--R from GuessInteger +--R if Fraction(Integer) has RETRACT(SYMBOL) and Integer has +--R RETRACT(SYMBOL) +--R [10] List(D4) -> List(Record(function: D6,order: NonNegativeInteger) +--R ) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D4 has FIELD and D9: (D4 -> D6) and D7 has Join( +--R OrderedSet,IntegralDomain) and D8: (D7 -> D4) and D5 has +--R GCDDOM and D6 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D7),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [11] (List(D6),List(GuessOption)) -> List(Record(function: D8,order +--R : NonNegativeInteger)) +--R from Guess(D6,D7,D8,D9,D10,D2) +--R if D6 has FIELD and D2: (D6 -> D8) and D9 has Join( +--R OrderedSet,IntegralDomain) and D10: (D9 -> D6) and D7 has +--R GCDDOM and D8 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D9),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [12] Symbol -> ((List(D4),List(GuessOption)) -> List(Record(function +--R : D6,order: NonNegativeInteger))) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D7 has Join(OrderedSet,IntegralDomain) and D8: (D7 -> +--R D4) and D4 has RETRACT(SYMBOL) and D5 has RETRACT(SYMBOL) +--R and D4 has FIELD and D5 has GCDDOM and D6 has Join( +--R FunctionSpace(Integer),IntegralDomain,RetractableTo(D7), +--R RetractableTo(Symbol),RetractableTo(Integer), +--R CombinatorialOpsCategory,PartialDifferentialRing(Symbol)) +--R with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Booleanand D9: (D4 -> D6) +--R [13] List(Fraction(Polynomial(Integer))) -> List(Record(function: +--R Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [14] (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List +--R (Record(function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [15] Symbol -> ((List(Fraction(Polynomial(Integer))),List( +--R GuessOption)) -> List(Record(function: Expression(Integer),order +--R : NonNegativeInteger))) +--R from GuessPolynomial +--R if Fraction(Polynomial(Integer)) has RETRACT(SYMBOL) and +--R Polynomial(Integer) has RETRACT(SYMBOL) +--R [16] List(Fraction(MyUnivariatePolynomial(D3,Integer))) -> List( +--R Record(function: MyExpression(D3,Integer),order: +--R NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R [17] (List(Fraction(MyUnivariatePolynomial(D4,Integer))),List( +--R GuessOption)) -> List(Record(function: MyExpression(D4,Integer), +--R order: NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D4) if D4: SYMBOL +--R [18] Symbol -> ((List(Fraction(MyUnivariatePolynomial(D3,Integer))), +--R List(GuessOption)) -> List(Record(function: MyExpression(D3, +--R Integer),order: NonNegativeInteger))) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R +--RExamples of guessBinRat from GuessAlgebraicNumber +--R +--R +--RExamples of guessBinRat from GuessFinite +--R +--R +--RExamples of guessBinRat from GuessInteger +--R +--R +--RExamples of guessBinRat from Guess +--R +--R +--RExamples of guessBinRat from GuessPolynomial +--R +--R +--RExamples of guessBinRat from GuessUnivariatePolynomial +--R +--E 1201 + +--S 1202 of 3320 +)d op guessExpRat +--R +--R +--RThere are 18 exposed functions called guessExpRat : +--R [1] List(AlgebraicNumber) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [2] (List(AlgebraicNumber),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [3] Symbol -> ((List(AlgebraicNumber),List(GuessOption)) -> List( +--R Record(function: Expression(Integer),order: NonNegativeInteger))) +--R from GuessAlgebraicNumber if AlgebraicNumber has RETRACT( +--R SYMBOL) +--R [4] List(D3) -> List(Record(function: Expression(Integer),order: +--R NonNegativeInteger)) +--R from GuessFinite(D3) +--R if D3 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [5] (List(D4),List(GuessOption)) -> List(Record(function: Expression +--R (Integer),order: NonNegativeInteger)) +--R from GuessFinite(D4) +--R if D4 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [6] Symbol -> ((List(D3),List(GuessOption)) -> List(Record(function +--R : Expression(Integer),order: NonNegativeInteger))) +--R from GuessFinite(D3) +--R if D3 has RETRACT(SYMBOL) and D3 has Join( +--R FiniteFieldCategory,ConvertibleTo(Integer)) +--R [7] List(Fraction(Integer)) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [8] (List(Fraction(Integer)),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [9] Symbol -> ((List(Fraction(Integer)),List(GuessOption)) -> List( +--R Record(function: Expression(Integer),order: NonNegativeInteger))) +--R from GuessInteger +--R if Fraction(Integer) has RETRACT(SYMBOL) and Integer has +--R RETRACT(SYMBOL) +--R [10] List(D4) -> List(Record(function: D6,order: NonNegativeInteger) +--R ) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D4 has FIELD and D9: (D4 -> D6) and D7 has Join( +--R OrderedSet,IntegralDomain) and D8: (D7 -> D4) and D5 has +--R GCDDOM and D6 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D7),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [11] (List(D6),List(GuessOption)) -> List(Record(function: D8,order +--R : NonNegativeInteger)) +--R from Guess(D6,D7,D8,D9,D10,D2) +--R if D6 has FIELD and D2: (D6 -> D8) and D9 has Join( +--R OrderedSet,IntegralDomain) and D10: (D9 -> D6) and D7 has +--R GCDDOM and D8 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D9),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [12] Symbol -> ((List(D4),List(GuessOption)) -> List(Record(function +--R : D6,order: NonNegativeInteger))) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D7 has Join(OrderedSet,IntegralDomain) and D8: (D7 -> +--R D4) and D4 has RETRACT(SYMBOL) and D5 has RETRACT(SYMBOL) +--R and D4 has FIELD and D5 has GCDDOM and D6 has Join( +--R FunctionSpace(Integer),IntegralDomain,RetractableTo(D7), +--R RetractableTo(Symbol),RetractableTo(Integer), +--R CombinatorialOpsCategory,PartialDifferentialRing(Symbol)) +--R with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Booleanand D9: (D4 -> D6) +--R [13] List(Fraction(Polynomial(Integer))) -> List(Record(function: +--R Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [14] (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List +--R (Record(function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [15] Symbol -> ((List(Fraction(Polynomial(Integer))),List( +--R GuessOption)) -> List(Record(function: Expression(Integer),order +--R : NonNegativeInteger))) +--R from GuessPolynomial +--R if Fraction(Polynomial(Integer)) has RETRACT(SYMBOL) and +--R Polynomial(Integer) has RETRACT(SYMBOL) +--R [16] List(Fraction(MyUnivariatePolynomial(D3,Integer))) -> List( +--R Record(function: MyExpression(D3,Integer),order: +--R NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R [17] (List(Fraction(MyUnivariatePolynomial(D4,Integer))),List( +--R GuessOption)) -> List(Record(function: MyExpression(D4,Integer), +--R order: NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D4) if D4: SYMBOL +--R [18] Symbol -> ((List(Fraction(MyUnivariatePolynomial(D3,Integer))), +--R List(GuessOption)) -> List(Record(function: MyExpression(D3, +--R Integer),order: NonNegativeInteger))) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R +--RExamples of guessExpRat from GuessAlgebraicNumber +--R +--R +--RExamples of guessExpRat from GuessFinite +--R +--R +--RExamples of guessExpRat from GuessInteger +--R +--R +--RExamples of guessExpRat from Guess +--R +--R +--RExamples of guessExpRat from GuessPolynomial +--R +--R +--RExamples of guessExpRat from GuessUnivariatePolynomial +--R +--E 1202 + +--S 1203 of 3320 +)d op guessHolo +--R +--R +--RThere are 12 exposed functions called guessHolo : +--R [1] List(AlgebraicNumber) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [2] (List(AlgebraicNumber),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [3] List(D3) -> List(Record(function: Expression(Integer),order: +--R NonNegativeInteger)) +--R from GuessFinite(D3) +--R if D3 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [4] (List(D4),List(GuessOption)) -> List(Record(function: Expression +--R (Integer),order: NonNegativeInteger)) +--R from GuessFinite(D4) +--R if D4 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [5] List(Fraction(Integer)) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [6] (List(Fraction(Integer)),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [7] List(D4) -> List(Record(function: D6,order: NonNegativeInteger)) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D4 has FIELD and D9: (D4 -> D6) and D7 has Join( +--R OrderedSet,IntegralDomain) and D8: (D7 -> D4) and D5 has +--R GCDDOM and D6 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D7),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [8] (List(D6),List(GuessOption)) -> List(Record(function: D8,order: +--R NonNegativeInteger)) +--R from Guess(D6,D7,D8,D9,D10,D2) +--R if D6 has FIELD and D2: (D6 -> D8) and D9 has Join( +--R OrderedSet,IntegralDomain) and D10: (D9 -> D6) and D7 has +--R GCDDOM and D8 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D9),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [9] List(Fraction(Polynomial(Integer))) -> List(Record(function: +--R Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [10] (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List +--R (Record(function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [11] List(Fraction(MyUnivariatePolynomial(D3,Integer))) -> List( +--R Record(function: MyExpression(D3,Integer),order: +--R NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R [12] (List(Fraction(MyUnivariatePolynomial(D4,Integer))),List( +--R GuessOption)) -> List(Record(function: MyExpression(D4,Integer), +--R order: NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D4) if D4: SYMBOL +--R +--RExamples of guessHolo from GuessAlgebraicNumber +--R +--R +--RExamples of guessHolo from GuessFinite +--R +--R +--RExamples of guessHolo from GuessInteger +--R +--R +--RExamples of guessHolo from Guess +--R +--R +--RExamples of guessHolo from GuessPolynomial +--R +--R +--RExamples of guessHolo from GuessUnivariatePolynomial +--R +--E 1203 + +--S 1204 of 3320 +)d op guessHP +--R +--R +--RThere are 6 exposed functions called guessHP : +--R [1] (List(GuessOption) -> Record(guessStream: ( +--R UnivariateFormalPowerSeries(AlgebraicNumber) -> Stream( +--R UnivariateFormalPowerSeries(AlgebraicNumber))),degreeStream: +--R Stream(NonNegativeInteger),testStream: ( +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial( +--R AlgebraicNumber)) -> Stream(UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(AlgebraicNumber)))),exprStream: (( +--R Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: (( +--R NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial( +--R AlgebraicNumber)) -> AlgebraicNumber),AF: ((NonNegativeInteger, +--R NonNegativeInteger,UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(AlgebraicNumber))) -> +--R SparseUnivariatePolynomial(AlgebraicNumber)),AX: (( +--R NonNegativeInteger,Symbol,Expression(Integer)) -> Expression( +--R Integer)),C: (NonNegativeInteger -> List(AlgebraicNumber)))) -> ( +--R (List(AlgebraicNumber),List(GuessOption)) -> List(Record(function +--R : Expression(Integer),order: NonNegativeInteger))) +--R from GuessAlgebraicNumber +--R [2] (List(GuessOption) -> Record(guessStream: ( +--R UnivariateFormalPowerSeries(D3) -> Stream( +--R UnivariateFormalPowerSeries(D3))),degreeStream: Stream( +--R NonNegativeInteger),testStream: (UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(D3)) -> Stream( +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial(D3)))), +--R exprStream: ((Expression(Integer),Symbol) -> Stream(Expression( +--R Integer))),A: ((NonNegativeInteger,NonNegativeInteger, +--R SparseUnivariatePolynomial(D3)) -> D3),AF: ((NonNegativeInteger, +--R NonNegativeInteger,UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(D3))) -> SparseUnivariatePolynomial(D3 +--R )),AX: ((NonNegativeInteger,Symbol,Expression(Integer)) -> +--R Expression(Integer)),C: (NonNegativeInteger -> List(D3)))) -> (( +--R List(D3),List(GuessOption)) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger))) +--R from GuessFinite(D3) +--R if D3 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [3] (List(GuessOption) -> Record(guessStream: ( +--R UnivariateFormalPowerSeries(Fraction(Integer)) -> Stream( +--R UnivariateFormalPowerSeries(Fraction(Integer)))),degreeStream: +--R Stream(NonNegativeInteger),testStream: ( +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction( +--R Integer))) -> Stream(UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(Fraction(Integer))))),exprStream: (( +--R Expression(Integer),Symbol) -> Stream(Expression(Integer))),A: (( +--R NonNegativeInteger,NonNegativeInteger,SparseUnivariatePolynomial( +--R Integer)) -> Integer),AF: ((NonNegativeInteger,NonNegativeInteger +--R ,UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction( +--R Integer)))) -> SparseUnivariatePolynomial(Fraction(Integer))),AX +--R : ((NonNegativeInteger,Symbol,Expression(Integer)) -> Expression( +--R Integer)),C: (NonNegativeInteger -> List(Integer)))) -> ((List( +--R Fraction(Integer)),List(GuessOption)) -> List(Record(function: +--R Expression(Integer),order: NonNegativeInteger))) +--R from GuessInteger +--R [4] (List(GuessOption) -> Record(guessStream: ( +--R UnivariateFormalPowerSeries(D4) -> Stream( +--R UnivariateFormalPowerSeries(D4))),degreeStream: Stream( +--R NonNegativeInteger),testStream: (UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(D4)) -> Stream( +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial(D4)))), +--R exprStream: ((D6,Symbol) -> Stream(D6)),A: ((NonNegativeInteger, +--R NonNegativeInteger,SparseUnivariatePolynomial(D5)) -> D5),AF: (( +--R NonNegativeInteger,NonNegativeInteger,UnivariateFormalPowerSeries +--R (SparseUnivariatePolynomial(D4))) -> SparseUnivariatePolynomial( +--R D4)),AX: ((NonNegativeInteger,Symbol,D6) -> D6),C: ( +--R NonNegativeInteger -> List(D5)))) -> ((List(D4),List(GuessOption) +--R ) -> List(Record(function: D6,order: NonNegativeInteger))) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D4 has FIELD and D5 has GCDDOM and D6 has Join( +--R FunctionSpace(Integer),IntegralDomain,RetractableTo(D7), +--R RetractableTo(Symbol),RetractableTo(Integer), +--R CombinatorialOpsCategory,PartialDifferentialRing(Symbol)) +--R with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Booleanand D7 has Join(OrderedSet, +--R IntegralDomain) and D8: (D7 -> D4) and D9: (D4 -> D6) +--R +--R [5] (List(GuessOption) -> Record(guessStream: ( +--R UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))) -> +--R Stream(UnivariateFormalPowerSeries(Fraction(Polynomial(Integer))) +--R )),degreeStream: Stream(NonNegativeInteger),testStream: ( +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction( +--R Polynomial(Integer)))) -> Stream(UnivariateFormalPowerSeries( +--R SparseUnivariatePolynomial(Fraction(Polynomial(Integer)))))), +--R exprStream: ((Expression(Integer),Symbol) -> Stream(Expression( +--R Integer))),A: ((NonNegativeInteger,NonNegativeInteger, +--R SparseUnivariatePolynomial(Polynomial(Integer))) -> Polynomial( +--R Integer)),AF: ((NonNegativeInteger,NonNegativeInteger, +--R UnivariateFormalPowerSeries(SparseUnivariatePolynomial(Fraction( +--R Polynomial(Integer))))) -> SparseUnivariatePolynomial(Fraction( +--R Polynomial(Integer)))),AX: ((NonNegativeInteger,Symbol,Expression +--R (Integer)) -> Expression(Integer)),C: (NonNegativeInteger -> List +--R (Polynomial(Integer))))) -> ((List(Fraction(Polynomial(Integer))) +--R ,List(GuessOption)) -> List(Record(function: Expression(Integer), +--R order: NonNegativeInteger))) +--R from GuessPolynomial +--R [6] (List(GuessOption) -> HPSPEC) -> ((List(Fraction( +--R MyUnivariatePolynomial(D3,Integer))),List(GuessOption)) -> List( +--R Record(function: MyExpression(D3,Integer),order: +--R NonNegativeInteger))) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R +--RExamples of guessHP from GuessAlgebraicNumber +--R +--R +--RExamples of guessHP from GuessFinite +--R +--R +--RExamples of guessHP from GuessInteger +--R +--R +--RExamples of guessHP from Guess +--R +--R +--RExamples of guessHP from GuessPolynomial +--R +--R +--RExamples of guessHP from GuessUnivariatePolynomial +--R +--E 1204 + +--S 1205 of 3320 +)d op guessPade +--R +--R +--RThere are 12 exposed functions called guessPade : +--R [1] (List(AlgebraicNumber),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [2] List(AlgebraicNumber) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [3] (List(D4),List(GuessOption)) -> List(Record(function: Expression +--R (Integer),order: NonNegativeInteger)) +--R from GuessFinite(D4) +--R if D4 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [4] List(D3) -> List(Record(function: Expression(Integer),order: +--R NonNegativeInteger)) +--R from GuessFinite(D3) +--R if D3 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [5] (List(Fraction(Integer)),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [6] List(Fraction(Integer)) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [7] (List(D6),List(GuessOption)) -> List(Record(function: D8,order: +--R NonNegativeInteger)) +--R from Guess(D6,D7,D8,D9,D10,D2) +--R if D6 has FIELD and D2: (D6 -> D8) and D9 has Join( +--R OrderedSet,IntegralDomain) and D10: (D9 -> D6) and D7 has +--R GCDDOM and D8 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D9),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [8] List(D4) -> List(Record(function: D6,order: NonNegativeInteger)) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D4 has FIELD and D9: (D4 -> D6) and D7 has Join( +--R OrderedSet,IntegralDomain) and D8: (D7 -> D4) and D5 has +--R GCDDOM and D6 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D7),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [9] (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List( +--R Record(function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [10] List(Fraction(Polynomial(Integer))) -> List(Record(function: +--R Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [11] (List(Fraction(MyUnivariatePolynomial(D4,Integer))),List( +--R GuessOption)) -> List(Record(function: MyExpression(D4,Integer), +--R order: NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D4) if D4: SYMBOL +--R [12] List(Fraction(MyUnivariatePolynomial(D3,Integer))) -> List( +--R Record(function: MyExpression(D3,Integer),order: +--R NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R +--RExamples of guessPade from GuessAlgebraicNumber +--R +--R +--RExamples of guessPade from GuessFinite +--R +--R +--RExamples of guessPade from GuessInteger +--R +--R +--RExamples of guessPade from Guess +--R +--R +--RExamples of guessPade from GuessPolynomial +--R +--R +--RExamples of guessPade from GuessUnivariatePolynomial +--R +--E 1205 + +--S 1206 of 3320 +)d op guessPRec +--R +--R +--RThere are 18 exposed functions called guessPRec : +--R [1] (List(AlgebraicNumber),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [2] List(AlgebraicNumber) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [3] Symbol -> ((List(AlgebraicNumber),List(GuessOption)) -> List( +--R Record(function: Expression(Integer),order: NonNegativeInteger))) +--R from GuessAlgebraicNumber if AlgebraicNumber has RETRACT( +--R SYMBOL) +--R [4] (List(D4),List(GuessOption)) -> List(Record(function: Expression +--R (Integer),order: NonNegativeInteger)) +--R from GuessFinite(D4) +--R if D4 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [5] List(D3) -> List(Record(function: Expression(Integer),order: +--R NonNegativeInteger)) +--R from GuessFinite(D3) +--R if D3 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [6] Symbol -> ((List(D3),List(GuessOption)) -> List(Record(function +--R : Expression(Integer),order: NonNegativeInteger))) +--R from GuessFinite(D3) +--R if D3 has RETRACT(SYMBOL) and D3 has Join( +--R FiniteFieldCategory,ConvertibleTo(Integer)) +--R [7] (List(Fraction(Integer)),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [8] List(Fraction(Integer)) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [9] Symbol -> ((List(Fraction(Integer)),List(GuessOption)) -> List( +--R Record(function: Expression(Integer),order: NonNegativeInteger))) +--R from GuessInteger +--R if Fraction(Integer) has RETRACT(SYMBOL) and Integer has +--R RETRACT(SYMBOL) +--R [10] (List(D6),List(GuessOption)) -> List(Record(function: D8,order +--R : NonNegativeInteger)) +--R from Guess(D6,D7,D8,D9,D10,D2) +--R if D6 has FIELD and D2: (D6 -> D8) and D9 has Join( +--R OrderedSet,IntegralDomain) and D10: (D9 -> D6) and D7 has +--R GCDDOM and D8 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D9),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [11] List(D4) -> List(Record(function: D6,order: NonNegativeInteger) +--R ) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D4 has FIELD and D9: (D4 -> D6) and D7 has Join( +--R OrderedSet,IntegralDomain) and D8: (D7 -> D4) and D5 has +--R GCDDOM and D6 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D7),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [12] Symbol -> ((List(D4),List(GuessOption)) -> List(Record(function +--R : D6,order: NonNegativeInteger))) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D7 has Join(OrderedSet,IntegralDomain) and D8: (D7 -> +--R D4) and D4 has RETRACT(SYMBOL) and D5 has RETRACT(SYMBOL) +--R and D4 has FIELD and D5 has GCDDOM and D6 has Join( +--R FunctionSpace(Integer),IntegralDomain,RetractableTo(D7), +--R RetractableTo(Symbol),RetractableTo(Integer), +--R CombinatorialOpsCategory,PartialDifferentialRing(Symbol)) +--R with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Booleanand D9: (D4 -> D6) +--R [13] (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List +--R (Record(function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [14] List(Fraction(Polynomial(Integer))) -> List(Record(function: +--R Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [15] Symbol -> ((List(Fraction(Polynomial(Integer))),List( +--R GuessOption)) -> List(Record(function: Expression(Integer),order +--R : NonNegativeInteger))) +--R from GuessPolynomial +--R if Fraction(Polynomial(Integer)) has RETRACT(SYMBOL) and +--R Polynomial(Integer) has RETRACT(SYMBOL) +--R [16] (List(Fraction(MyUnivariatePolynomial(D4,Integer))),List( +--R GuessOption)) -> List(Record(function: MyExpression(D4,Integer), +--R order: NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D4) if D4: SYMBOL +--R [17] List(Fraction(MyUnivariatePolynomial(D3,Integer))) -> List( +--R Record(function: MyExpression(D3,Integer),order: +--R NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R [18] Symbol -> ((List(Fraction(MyUnivariatePolynomial(D3,Integer))), +--R List(GuessOption)) -> List(Record(function: MyExpression(D3, +--R Integer),order: NonNegativeInteger))) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R +--RExamples of guessPRec from GuessAlgebraicNumber +--R +--R +--RExamples of guessPRec from GuessFinite +--R +--R +--RExamples of guessPRec from GuessInteger +--R +--R +--RExamples of guessPRec from Guess +--R +--R +--RExamples of guessPRec from GuessPolynomial +--R +--R +--RExamples of guessPRec from GuessUnivariatePolynomial +--R +--E 1206 + +--S 1207 of 3320 +)d op guessRat +--R +--R +--RThere are 18 exposed functions called guessRat : +--R [1] (List(AlgebraicNumber),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [2] List(AlgebraicNumber) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [3] Symbol -> ((List(AlgebraicNumber),List(GuessOption)) -> List( +--R Record(function: Expression(Integer),order: NonNegativeInteger))) +--R from GuessAlgebraicNumber if AlgebraicNumber has RETRACT( +--R SYMBOL) +--R [4] (List(D4),List(GuessOption)) -> List(Record(function: Expression +--R (Integer),order: NonNegativeInteger)) +--R from GuessFinite(D4) +--R if D4 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [5] List(D3) -> List(Record(function: Expression(Integer),order: +--R NonNegativeInteger)) +--R from GuessFinite(D3) +--R if D3 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [6] Symbol -> ((List(D3),List(GuessOption)) -> List(Record(function +--R : Expression(Integer),order: NonNegativeInteger))) +--R from GuessFinite(D3) +--R if D3 has RETRACT(SYMBOL) and D3 has Join( +--R FiniteFieldCategory,ConvertibleTo(Integer)) +--R [7] (List(Fraction(Integer)),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [8] List(Fraction(Integer)) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [9] Symbol -> ((List(Fraction(Integer)),List(GuessOption)) -> List( +--R Record(function: Expression(Integer),order: NonNegativeInteger))) +--R from GuessInteger +--R if Fraction(Integer) has RETRACT(SYMBOL) and Integer has +--R RETRACT(SYMBOL) +--R [10] (List(D6),List(GuessOption)) -> List(Record(function: D8,order +--R : NonNegativeInteger)) +--R from Guess(D6,D7,D8,D9,D10,D2) +--R if D6 has FIELD and D2: (D6 -> D8) and D9 has Join( +--R OrderedSet,IntegralDomain) and D10: (D9 -> D6) and D7 has +--R GCDDOM and D8 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D9),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [11] List(D4) -> List(Record(function: D6,order: NonNegativeInteger) +--R ) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D4 has FIELD and D9: (D4 -> D6) and D7 has Join( +--R OrderedSet,IntegralDomain) and D8: (D7 -> D4) and D5 has +--R GCDDOM and D6 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D7),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [12] Symbol -> ((List(D4),List(GuessOption)) -> List(Record(function +--R : D6,order: NonNegativeInteger))) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D7 has Join(OrderedSet,IntegralDomain) and D8: (D7 -> +--R D4) and D4 has RETRACT(SYMBOL) and D5 has RETRACT(SYMBOL) +--R and D4 has FIELD and D5 has GCDDOM and D6 has Join( +--R FunctionSpace(Integer),IntegralDomain,RetractableTo(D7), +--R RetractableTo(Symbol),RetractableTo(Integer), +--R CombinatorialOpsCategory,PartialDifferentialRing(Symbol)) +--R with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Booleanand D9: (D4 -> D6) +--R [13] (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List +--R (Record(function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [14] List(Fraction(Polynomial(Integer))) -> List(Record(function: +--R Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [15] Symbol -> ((List(Fraction(Polynomial(Integer))),List( +--R GuessOption)) -> List(Record(function: Expression(Integer),order +--R : NonNegativeInteger))) +--R from GuessPolynomial +--R if Fraction(Polynomial(Integer)) has RETRACT(SYMBOL) and +--R Polynomial(Integer) has RETRACT(SYMBOL) +--R [16] (List(Fraction(MyUnivariatePolynomial(D4,Integer))),List( +--R GuessOption)) -> List(Record(function: MyExpression(D4,Integer), +--R order: NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D4) if D4: SYMBOL +--R [17] List(Fraction(MyUnivariatePolynomial(D3,Integer))) -> List( +--R Record(function: MyExpression(D3,Integer),order: +--R NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R [18] Symbol -> ((List(Fraction(MyUnivariatePolynomial(D3,Integer))), +--R List(GuessOption)) -> List(Record(function: MyExpression(D3, +--R Integer),order: NonNegativeInteger))) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R +--RExamples of guessRat from GuessAlgebraicNumber +--R +--R +--RExamples of guessRat from GuessFinite +--R +--R +--RExamples of guessRat from GuessInteger +--R +--R +--RExamples of guessRat from Guess +--R +--R +--RExamples of guessRat from GuessPolynomial +--R +--R +--RExamples of guessRat from GuessUnivariatePolynomial +--R +--E 1207 + +--S 1208 of 3320 +)d op guessRec +--R +--R +--RThere are 18 exposed functions called guessRec : +--R [1] List(AlgebraicNumber) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [2] (List(AlgebraicNumber),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessAlgebraicNumber +--R [3] Symbol -> ((List(AlgebraicNumber),List(GuessOption)) -> List( +--R Record(function: Expression(Integer),order: NonNegativeInteger))) +--R from GuessAlgebraicNumber if AlgebraicNumber has RETRACT( +--R SYMBOL) +--R [4] List(D3) -> List(Record(function: Expression(Integer),order: +--R NonNegativeInteger)) +--R from GuessFinite(D3) +--R if D3 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [5] (List(D4),List(GuessOption)) -> List(Record(function: Expression +--R (Integer),order: NonNegativeInteger)) +--R from GuessFinite(D4) +--R if D4 has Join(FiniteFieldCategory,ConvertibleTo(Integer)) +--R +--R [6] Symbol -> ((List(D3),List(GuessOption)) -> List(Record(function +--R : Expression(Integer),order: NonNegativeInteger))) +--R from GuessFinite(D3) +--R if D3 has RETRACT(SYMBOL) and D3 has Join( +--R FiniteFieldCategory,ConvertibleTo(Integer)) +--R [7] List(Fraction(Integer)) -> List(Record(function: Expression( +--R Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [8] (List(Fraction(Integer)),List(GuessOption)) -> List(Record( +--R function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessInteger +--R [9] Symbol -> ((List(Fraction(Integer)),List(GuessOption)) -> List( +--R Record(function: Expression(Integer),order: NonNegativeInteger))) +--R from GuessInteger +--R if Fraction(Integer) has RETRACT(SYMBOL) and Integer has +--R RETRACT(SYMBOL) +--R [10] List(D4) -> List(Record(function: D6,order: NonNegativeInteger) +--R ) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D4 has FIELD and D9: (D4 -> D6) and D7 has Join( +--R OrderedSet,IntegralDomain) and D8: (D7 -> D4) and D5 has +--R GCDDOM and D6 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D7),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [11] (List(D6),List(GuessOption)) -> List(Record(function: D8,order +--R : NonNegativeInteger)) +--R from Guess(D6,D7,D8,D9,D10,D2) +--R if D6 has FIELD and D2: (D6 -> D8) and D9 has Join( +--R OrderedSet,IntegralDomain) and D10: (D9 -> D6) and D7 has +--R GCDDOM and D8 has Join(FunctionSpace(Integer), +--R IntegralDomain,RetractableTo(D9),RetractableTo(Symbol), +--R RetractableTo(Integer),CombinatorialOpsCategory, +--R PartialDifferentialRing(Symbol))with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Boolean +--R [12] Symbol -> ((List(D4),List(GuessOption)) -> List(Record(function +--R : D6,order: NonNegativeInteger))) +--R from Guess(D4,D5,D6,D7,D8,D9) +--R if D7 has Join(OrderedSet,IntegralDomain) and D8: (D7 -> +--R D4) and D4 has RETRACT(SYMBOL) and D5 has RETRACT(SYMBOL) +--R and D4 has FIELD and D5 has GCDDOM and D6 has Join( +--R FunctionSpace(Integer),IntegralDomain,RetractableTo(D7), +--R RetractableTo(Symbol),RetractableTo(Integer), +--R CombinatorialOpsCategory,PartialDifferentialRing(Symbol)) +--R with +--R ?*? : (%,%) -> % +--R ?/? : (%,%) -> % +--R D : (%,%) -> % +--R numerator : % -> % +--R denominator : % -> % +--R ground? : % -> Booleanand D9: (D4 -> D6) +--R [13] List(Fraction(Polynomial(Integer))) -> List(Record(function: +--R Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [14] (List(Fraction(Polynomial(Integer))),List(GuessOption)) -> List +--R (Record(function: Expression(Integer),order: NonNegativeInteger)) +--R from GuessPolynomial +--R [15] Symbol -> ((List(Fraction(Polynomial(Integer))),List( +--R GuessOption)) -> List(Record(function: Expression(Integer),order +--R : NonNegativeInteger))) +--R from GuessPolynomial +--R if Fraction(Polynomial(Integer)) has RETRACT(SYMBOL) and +--R Polynomial(Integer) has RETRACT(SYMBOL) +--R [16] List(Fraction(MyUnivariatePolynomial(D3,Integer))) -> List( +--R Record(function: MyExpression(D3,Integer),order: +--R NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R [17] (List(Fraction(MyUnivariatePolynomial(D4,Integer))),List( +--R GuessOption)) -> List(Record(function: MyExpression(D4,Integer), +--R order: NonNegativeInteger)) +--R from GuessUnivariatePolynomial(D4) if D4: SYMBOL +--R [18] Symbol -> ((List(Fraction(MyUnivariatePolynomial(D3,Integer))), +--R List(GuessOption)) -> List(Record(function: MyExpression(D3, +--R Integer),order: NonNegativeInteger))) +--R from GuessUnivariatePolynomial(D3) if D3: SYMBOL +--R +--RExamples of guessRec from GuessAlgebraicNumber +--R +--R +--RExamples of guessRec from GuessFinite +--R +--R +--RExamples of guessRec from GuessInteger +--R +--R +--RExamples of guessRec from Guess +--R +--R +--RExamples of guessRec from GuessPolynomial +--R +--R +--RExamples of guessRec from GuessUnivariatePolynomial +--R +--E 1208 + +--S 1209 of 3320 +)d op halfExtendedResultant1 +--R +--R +--RThere is one unexposed function called halfExtendedResultant1 : +--R [1] (NewSparseUnivariatePolynomial(D2),NewSparseUnivariatePolynomial +--R (D2)) -> Record(resultant: D2,coef1: +--R NewSparseUnivariatePolynomial(D2)) +--R from NewSparseUnivariatePolynomial(D2) if D2 has INTDOM +--R and D2 has RING +--R +--RExamples of halfExtendedResultant1 from NewSparseUnivariatePolynomial +--R +--E 1209 + +--S 1210 of 3320 +)d op halfExtendedResultant2 +--R +--R +--RThere is one unexposed function called halfExtendedResultant2 : +--R [1] (NewSparseUnivariatePolynomial(D2),NewSparseUnivariatePolynomial +--R (D2)) -> Record(resultant: D2,coef2: +--R NewSparseUnivariatePolynomial(D2)) +--R from NewSparseUnivariatePolynomial(D2) if D2 has INTDOM +--R and D2 has RING +--R +--RExamples of halfExtendedResultant2 from NewSparseUnivariatePolynomial +--R +--E 1210 + +--S 1211 of 3320 +)d op halfExtendedSubResultantGcd1 +--R +--R +--RThere is one exposed function called halfExtendedSubResultantGcd1 : +--R [1] (D,D) -> Record(gcd: D,coef1: D) from D +--R if D2 has INTDOM and D2 has RING and D3 has OAMONS and D4 +--R has ORDSET and D has RPOLCAT(D2,D3,D4) +--R +--RThere is one unexposed function called halfExtendedSubResultantGcd1 : +--R [1] (NewSparseUnivariatePolynomial(D2),NewSparseUnivariatePolynomial +--R (D2)) -> Record(gcd: NewSparseUnivariatePolynomial(D2),coef1: +--R NewSparseUnivariatePolynomial(D2)) +--R from NewSparseUnivariatePolynomial(D2) if D2 has INTDOM +--R and D2 has RING +--R +--RExamples of halfExtendedSubResultantGcd1 from NewSparseUnivariatePolynomial +--R +--R +--RExamples of halfExtendedSubResultantGcd1 from RecursivePolynomialCategory +--R +--E 1211 + +--S 1212 of 3320 +)d op halfExtendedSubResultantGcd2 +--R +--R +--RThere is one exposed function called halfExtendedSubResultantGcd2 : +--R [1] (D,D) -> Record(gcd: D,coef2: D) from D +--R if D2 has INTDOM and D2 has RING and D3 has OAMONS and D4 +--R has ORDSET and D has RPOLCAT(D2,D3,D4) +--R +--RThere is one unexposed function called halfExtendedSubResultantGcd2 : +--R [1] (NewSparseUnivariatePolynomial(D2),NewSparseUnivariatePolynomial +--R (D2)) -> Record(gcd: NewSparseUnivariatePolynomial(D2),coef2: +--R NewSparseUnivariatePolynomial(D2)) +--R from NewSparseUnivariatePolynomial(D2) if D2 has INTDOM +--R and D2 has RING +--R +--RExamples of halfExtendedSubResultantGcd2 from NewSparseUnivariatePolynomial +--R +--R +--RExamples of halfExtendedSubResultantGcd2 from RecursivePolynomialCategory +--R +--E 1212 + +--S 1213 of 3320 +)d op harmonic +--R +--R +--RThere is one exposed function called harmonic : +--R [1] Integer -> Fraction(Integer) from IntegerNumberTheoryFunctions +--R +--R +--RExamples of harmonic from IntegerNumberTheoryFunctions +--R +--E 1213 + +--S 1214 of 3320 +)d op has? +--R +--R +--RThere is one exposed function called has? : +--R [1] (BasicOperator,String) -> Boolean from BasicOperator +--R +--RExamples of has? from BasicOperator +--R +--E 1214 + +--S 1215 of 3320 +)d op hasDimension? +--R +--R +--RThere are 2 exposed functions called hasDimension? : +--R [1] (Cell(D3),Symbol) -> Boolean from Cell(D3) if D3 has RCFIELD +--R [2] SimpleCell(D2,D3) -> Boolean from SimpleCell(D2,D3) +--R if D2 has RCFIELD and D3 has UPOLYC(D2) +--R +--RExamples of hasDimension? from Cell +--R +--R +--RExamples of hasDimension? from SimpleCell +--R +--E 1215 + +--S 1216 of 3320 +)d op hash +--R +--R +--RThere are 8 exposed functions called hash : +--R [1] ArrayStack(D2) -> SingleInteger from ArrayStack(D2) +--R if D2 has SETCAT and D2 has SETCAT +--R [2] Dequeue(D2) -> SingleInteger from Dequeue(D2) +--R if D2 has SETCAT and D2 has SETCAT +--R [3] DoubleFloat -> Integer from DoubleFloat +--R [4] Heap(D2) -> SingleInteger from Heap(D2) if D2 has SETCAT and D2 +--R has ORDSET +--R [5] D -> D from D if D has INS +--R [6] Queue(D2) -> SingleInteger from Queue(D2) if D2 has SETCAT and +--R D2 has SETCAT +--R [7] D -> SingleInteger from D if D has SETCAT +--R [8] Stack(D2) -> SingleInteger from Stack(D2) if D2 has SETCAT and +--R D2 has SETCAT +--R +--RThere is one unexposed function called hash : +--R [1] IndexedString(D2) -> Integer from IndexedString(D2) if D2: INT +--R +--R +--RExamples of hash from ArrayStack +--R +--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] +--Rhash a +--R +--R +--RExamples of hash from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rhash a +--R +--R +--RExamples of hash from DoubleFloat +--R +--R +--RExamples of hash from Heap +--R +--Ra:Heap INT:= heap [1,2,3,4,5] +--Rhash a +--R +--R +--RExamples of hash from IntegerNumberSystem +--R +--R +--RExamples of hash from IndexedString +--R +--R +--RExamples of hash from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Rhash a +--R +--R +--RExamples of hash from SetCategory +--R +--R +--RExamples of hash from Stack +--R +--Ra:Stack INT:= stack [1,2,3,4,5] +--Rhash a +--R +--E 1216 + +--S 1217 of 3320 +)d op hasHi +--R +--R +--RThere is one exposed function called hasHi : +--R [1] UniversalSegment(D2) -> Boolean from UniversalSegment(D2) if D2 +--R has TYPE +--R +--RExamples of hasHi from UniversalSegment +--R +--E 1217 + +--S 1218 of 3320 +)d op hasoln +--R +--R +--RThere is one unexposed function called hasoln : +--R [1] (List(D6),List(D6)) -> Record(sysok: Boolean,z0: List(D6),n0: +--R List(D6)) +--R from ParametricLinearEquations(D3,D4,D5,D6) +--R if D3 has Join(EuclideanDomain,CharacteristicZero) and D4 +--R has Join(OrderedSet,ConvertibleTo(Symbol)) and D5 has +--R OAMONS and D6 has POLYCAT(D3,D5,D4) +--R +--RExamples of hasoln from ParametricLinearEquations +--R +--E 1218 + +--S 1219 of 3320 +)d op hasPredicate? +--R +--R +--RThere is one unexposed function called hasPredicate? : +--R [1] Pattern(D2) -> Boolean from Pattern(D2) if D2 has SETCAT +--R +--RExamples of hasPredicate? from Pattern +--R +--E 1219 + +--S 1220 of 3320 +)d op hasSolution? +--R +--R +--RThere are 2 exposed functions called hasSolution? : +--R [1] (Matrix(D4),Vector(D4)) -> Boolean from +--R LinearSystemMatrixPackage1(D4) +--R if D4 has FIELD +--R [2] (D2,D3) -> Boolean from LinearSystemMatrixPackage(D4,D5,D3,D2) +--R if D4 has FIELD and D5 has FiniteLinearAggregate(D4)with +--R shallowlyMutableand D3 has FiniteLinearAggregate(D4) +--R with +--R shallowlyMutableand D2 has MATCAT(D4,D5,D3) +--R +--RExamples of hasSolution? from LinearSystemMatrixPackage1 +--R +--R +--RExamples of hasSolution? from LinearSystemMatrixPackage +--R +--E 1220 + +--S 1221 of 3320 +)d op hasTopPredicate? +--R +--R +--RThere is one unexposed function called hasTopPredicate? : +--R [1] Pattern(D2) -> Boolean from Pattern(D2) if D2 has SETCAT +--R +--RExamples of hasTopPredicate? from Pattern +--R +--E 1221 + +--S 1222 of 3320 +)d op Hausdorff +--R +--R +--RThere is one unexposed function called Hausdorff : +--R [1] (D1,D1,NonNegativeInteger) -> D1 from XExponentialPackage(D3,D4, +--R D1) +--R if D3 has Join(Ring,Module(Fraction(Integer))) and D4 has +--R ORDSET and D1 has XPOLYC(D4,D3) +--R +--RExamples of Hausdorff from XExponentialPackage +--R +--E 1222 + +--S 1223 of 3320 +)d op hclf +--R +--R +--RThere are 2 unexposed functions called hclf : +--R [1] (FreeMonoid(D1),FreeMonoid(D1)) -> FreeMonoid(D1) from +--R FreeMonoid(D1) +--R if D1 has SETCAT +--R [2] (OrderedFreeMonoid(D1),OrderedFreeMonoid(D1)) -> +--R OrderedFreeMonoid(D1) +--R from OrderedFreeMonoid(D1) if D1 has ORDSET +--R +--RExamples of hclf from FreeMonoid +--R +--R +--RExamples of hclf from OrderedFreeMonoid +--R +--Rm1:=(x*y*z)$OFMONOID(Symbol) +--Rm2:=(x*y)$OFMONOID(Symbol) +--Rhclf(m1,m2) +--R +--E 1223 + +--S 1224 of 3320 +)d op hconcat +--R +--R +--RThere are 2 unexposed functions called hconcat : +--R [1] List(OutputForm) -> OutputForm from OutputForm +--R [2] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R +--RExamples of hconcat from OutputForm +--R +--E 1224 + +--S 1225 of 3320 +)d op hcrf +--R +--R +--RThere are 2 unexposed functions called hcrf : +--R [1] (FreeMonoid(D1),FreeMonoid(D1)) -> FreeMonoid(D1) from +--R FreeMonoid(D1) +--R if D1 has SETCAT +--R [2] (OrderedFreeMonoid(D1),OrderedFreeMonoid(D1)) -> +--R OrderedFreeMonoid(D1) +--R from OrderedFreeMonoid(D1) if D1 has ORDSET +--R +--RExamples of hcrf from FreeMonoid +--R +--R +--RExamples of hcrf from OrderedFreeMonoid +--R +--Rm1:=(x*y*z)$OFMONOID(Symbol) +--Rm2:=(y*z)$OFMONOID(Symbol) +--Rhcrf(m1,m2) +--R +--E 1225 + +--S 1226 of 3320 +)d op hdmpToDmp +--R +--R +--RThere is one unexposed function called hdmpToDmp : +--R [1] HomogeneousDistributedMultivariatePolynomial(D3,D4) -> +--R DistributedMultivariatePolynomial(D3,D4) +--R from PolToPol(D3,D4) if D3: LIST(SYMBOL) and D4 has RING +--R +--R +--RExamples of hdmpToDmp from PolToPol +--R +--E 1226 + +--S 1227 of 3320 +)d op hdmpToP +--R +--R +--RThere is one unexposed function called hdmpToP : +--R [1] HomogeneousDistributedMultivariatePolynomial(D3,D4) -> +--R Polynomial(D4) +--R from PolToPol(D3,D4) if D3: LIST(SYMBOL) and D4 has RING +--R +--R +--RExamples of hdmpToP from PolToPol +--R +--E 1227 + +--S 1228 of 3320 +)d op head +--R +--R +--RThere are 3 exposed functions called head : +--R [1] Divisor(D2) -> Record(gen: D2,exp: Integer) from Divisor(D2) if +--R D2 has SETCATD +--R [2] D -> D from D if D has DLAGG(D1) and D1 has TYPE +--R [3] D -> D from D +--R if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has +--R OAMONS and D3 has ORDSET +--R +--RExamples of head from Divisor +--R +--R +--RExamples of head from DoublyLinkedAggregate +--R +--R +--RExamples of head from RecursivePolynomialCategory +--R +--E 1228 + +--S 1229 of 3320 +)d op headReduce +--R +--R +--RThere are 2 exposed functions called headReduce : +--R [1] (D,D) -> D from D +--R if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has +--R OAMONS and D3 has ORDSET +--R [2] (D1,D) -> D1 from D +--R if D has TSETCAT(D2,D3,D4,D1) and D2 has INTDOM and D3 +--R has OAMONS and D4 has ORDSET and D1 has RPOLCAT(D2,D3,D4) +--R +--R +--RExamples of headReduce from RecursivePolynomialCategory +--R +--R +--RExamples of headReduce from TriangularSetCategory +--R +--E 1229 + +--S 1230 of 3320 +)d op headReduced? +--R +--R +--RThere are 4 exposed functions called headReduced? : +--R [1] (D,List(D)) -> Boolean from D +--R if D has RPOLCAT(D3,D4,D5) and D3 has RING and D4 has +--R OAMONS and D5 has ORDSET +--R [2] (D,D) -> Boolean from D +--R if D has RPOLCAT(D2,D3,D4) and D2 has RING and D3 has +--R OAMONS and D4 has ORDSET +--R [3] D -> Boolean from D +--R if D has TSETCAT(D2,D3,D4,D5) and D2 has INTDOM and D3 +--R has OAMONS and D4 has ORDSET and D5 has RPOLCAT(D2,D3,D4) +--R +--R [4] (D2,D) -> Boolean from D +--R if D has TSETCAT(D3,D4,D5,D2) and D3 has INTDOM and D4 +--R has OAMONS and D5 has ORDSET and D2 has RPOLCAT(D3,D4,D5) +--R +--R +--RExamples of headReduced? from RecursivePolynomialCategory +--R +--R +--RExamples of headReduced? from TriangularSetCategory +--R +--E 1230 + +--S 1231 of 3320 +)d op headRemainder +--R +--R +--RThere is one exposed function called headRemainder : +--R [1] (D2,D) -> Record(num: D2,den: D3) from D +--R if D has PSETCAT(D3,D4,D5,D2) and D3 has RING and D4 has +--R OAMONS and D5 has ORDSET and D2 has RPOLCAT(D3,D4,D5) and +--R D3 has INTDOM +--R +--RExamples of headRemainder from PolynomialSetCategory +--R +--E 1231 + +--S 1232 of 3320 done +)d op heap +--R +--R +--RThere is one exposed function called heap : +--R [1] List(D2) -> Heap(D2) from Heap(D2) if D2 has ORDSET +--R +--RExamples of heap from Heap +--R +--Ri:Heap INT := heap [1,6,3,7,5,2,4] +--R +--E 1232 + +--S 1233 of 3320 +)d op heapSort +--R +--R +--RThere is one exposed function called heapSort : +--R [1] (((D3,D3) -> Boolean),D1) -> D1 from FiniteLinearAggregateSort( +--R D3,D1) +--R if D3 has TYPE and D1 has FiniteLinearAggregate(D3)with +--R shallowlyMutable +--R +--RExamples of heapSort from FiniteLinearAggregateSort +--R +--E 1233 + +--S 1234 of 3320 +)d op height +--R +--R +--RThere are 3 exposed functions called height : +--R [1] Dequeue(D2) -> NonNegativeInteger from Dequeue(D2) if D2 has +--R SETCAT +--R [2] D -> NonNegativeInteger from D if D has DQAGG(D2) and D2 has +--R TYPE +--R [3] D -> NonNegativeInteger from D if D has ES +--R +--RThere are 4 unexposed functions called height : +--R [1] D2 -> D1 from GaloisGroupFactorizationUtilities(D3,D2,D1) +--R if D3 has RING and D1 has Join(FloatingPointSystem, +--R RetractableTo(D3),Field,TranscendentalFunctionCategory, +--R ElementaryFunctionCategory) and D2 has UPOLYC(D3) +--R [2] Kernel(D2) -> NonNegativeInteger from Kernel(D2) if D2 has +--R ORDSET +--R [3] -> Integer from OutputForm +--R [4] OutputForm -> Integer from OutputForm +--R +--RExamples of height from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rheight a +--R +--R +--RExamples of height from DequeueAggregate +--R +--R +--RExamples of height from ExpressionSpace +--R +--R +--RExamples of height from GaloisGroupFactorizationUtilities +--R +--R +--RExamples of height from Kernel +--R +--R +--RExamples of height from OutputForm +--R +--E 1234 + +--S 1235 of 3320 +)d op henselFact +--R +--R +--RThere are 2 unexposed functions called henselFact : +--R [1] (D2,Boolean) -> Record(contp: Integer,factors: List(Record(irr: +--R D2,pow: Integer))) +--R from GaloisGroupFactorizer(D2) if D2 has UPOLYC(INT) +--R [2] (D2,Boolean) -> Record(contp: Integer,factors: List(Record(irr: +--R D2,pow: Integer))) +--R from UnivariateFactorize(D2) if D2 has UPOLYC(INT) +--R +--RExamples of henselFact from GaloisGroupFactorizer +--R +--R +--RExamples of henselFact from UnivariateFactorize +--R +--E 1235 + +--S 1236 of 3320 +)d op HenselLift +--R +--R +--RThere is one unexposed function called HenselLift : +--R [1] (D2,List(D2),D4,PositiveInteger) -> Record(plist: List(D2), +--R modulo: D4) +--R from GeneralHenselPackage(D4,D2) if D4 has EUCDOM and D2 +--R has UPOLYC(D4) +--R +--RExamples of HenselLift from GeneralHenselPackage +--R +--E 1236 + +--S 1237 of 3320 +)d op hermite +--R +--R +--RThere is one exposed function called hermite : +--R [1] D1 -> D1 from SmithNormalForm(D2,D3,D4,D1) +--R if D2 has EUCDOM and D3 has FLAGG(D2) and D4 has FLAGG(D2) +--R and D1 has MATCAT(D2,D3,D4) +--R +--RThere is one unexposed function called hermite : +--R [1] Integer -> SparseUnivariatePolynomial(Integer) +--R from PolynomialNumberTheoryFunctions +--R +--RExamples of hermite from PolynomialNumberTheoryFunctions +--R +--R +--RExamples of hermite from SmithNormalForm +--R +--E 1237 + +--S 1238 of 3320 +)d op hermiteH +--R +--R +--RThere is one exposed function called hermiteH : +--R [1] (NonNegativeInteger,D1) -> D1 from OrthogonalPolynomialFunctions +--R (D1) +--R if D1 has COMRING +--R +--RExamples of hermiteH from OrthogonalPolynomialFunctions +--R +--E 1238 + +--S 1239 of 3320 +)d op HermiteIntegrate +--R +--R +--RThere are 2 unexposed functions called HermiteIntegrate : +--R [1] (D2,(D5 -> D5)) -> Record(answer: D2,logpart: D2) +--R from AlgebraicHermiteIntegration(D4,D5,D6,D2) +--R if D5 has UPOLYC(D4) and D4 has FIELD and D6 has UPOLYC( +--R FRAC(D5)) and D2 has FFCAT(D4,D5,D6) +--R [2] (Fraction(D5),(D5 -> D5)) -> Record(answer: Fraction(D5),logpart +--R : Fraction(D5),specpart: Fraction(D5),polypart: D5) +--R from TranscendentalHermiteIntegration(D4,D5) +--R if D5 has UPOLYC(D4) and D4 has FIELD +--R +--RExamples of HermiteIntegrate from AlgebraicHermiteIntegration +--R +--R +--RExamples of HermiteIntegrate from TranscendentalHermiteIntegration +--R +--E 1239 + +--S 1240 of 3320 +)d op hessian +--R +--R +--RThere is one exposed function called hessian : +--R [1] (D2,D3) -> Matrix(D2) from MultiVariableCalculusFunctions(D4,D2, +--R D5,D3) +--R if D4 has SETCAT and D2 has PDRING(D4) and D5 has FLAGG(D2 +--R ) and D3 has FiniteLinearAggregate(D4)with +--R finiteAggregate +--R +--RExamples of hessian from MultiVariableCalculusFunctions +--R +--E 1240 + +--S 1241 of 3320 +)d op hex +--R +--R +--RThere is one exposed function called hex : +--R [1] Fraction(Integer) -> HexadecimalExpansion from +--R HexadecimalExpansion +--R +--RExamples of hex from HexadecimalExpansion +--R +--E 1241 + +--S 1242 of 3320 +)d op hexDigit +--R +--R +--RThere is one exposed function called hexDigit : +--R [1] -> CharacterClass from CharacterClass +--R +--RExamples of hexDigit from CharacterClass +--R +--E 1242 + +--S 1243 of 3320 done +)d op hexDigit? +--R +--R +--RThere is one exposed function called hexDigit? : +--R [1] Character -> Boolean from Character +--R +--RExamples of hexDigit? from Character +--R +--Rchars := [char "a", char "A", char "X", char "8", char "+"] +--R[hexDigit? c for c in chars] +--R +--E 1243 + +--S 1244 of 3320 +)d op hi +--R +--R +--RThere is one exposed function called hi : +--R [1] D -> D1 from D if D has SEGCAT(D1) and D1 has TYPE +--R +--RExamples of hi from SegmentCategory +--R +--E 1244 + +--S 1245 of 3320 +)d op high +--R +--R +--RThere is one exposed function called high : +--R [1] D -> D1 from D if D has SEGCAT(D1) and D1 has TYPE +--R +--RExamples of high from SegmentCategory +--R +--E 1245 + +--S 1246 of 3320 +)d op highCommonTerms +--R +--R +--RThere is one exposed function called highCommonTerms : +--R [1] (D,D) -> D from D +--R if D has FAMONC(D1,D2) and D1 has SETCAT and D2 has CABMON +--R and D2 has OAMON +--R +--RExamples of highCommonTerms from FreeAbelianMonoidCategory +--R +--E 1246 + +--S 1247 of 3320 +)d op hitherPlane +--R +--R +--RThere is one exposed function called hitherPlane : +--R [1] (ThreeDimensionalViewport,Float) -> Void from +--R ThreeDimensionalViewport +--R +--RExamples of hitherPlane from ThreeDimensionalViewport +--R +--E 1247 + +--S 1248 of 3320 +)d op hMonic +--R +--R +--RThere is one unexposed function called hMonic : +--R [1] D1 -> D1 from GroebnerInternalPackage(D2,D3,D4,D1) +--R if D2 has GCDDOM and D3 has OAMONS and D4 has ORDSET and +--R D1 has POLYCAT(D2,D3,D4) +--R +--RExamples of hMonic from GroebnerInternalPackage +--R +--E 1248 + +--S 1249 of 3320 done +)d op hodgeStar +--R +--R +--RThere is one unexposed function called hodgeStar : +--R [1] (DeRhamComplex(D2,D3),SquareMatrix(#(D3),Expression(D2))) -> +--R DeRhamComplex(D2,D3) +--R from DeRhamComplex(D2,D3) +--R if D2 has Join(Ring,OrderedSet) and D3: LIST(SYMBOL) +--R +--RExamples of hodgeStar from DeRhamComplex +--R +--Rder := DeRhamComplex(Integer,[x,y,z]) +--Rf:BOP:=operator('f) +--Rg:BOP:=operator('g) +--Rh:BOP:=operator('h) +--Rsigma:der:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz +--RG:SquareMatrix(3,Integer):=diagonalMatrix([1,1,1]) +--RhodgeStar(sigma,G) +--R +--E 1249 + +--S 1250 of 3320 +)d op homogeneous +--R +--R +--RThere is one exposed function called homogeneous : +--R [1] Union(PositiveInteger,Boolean) -> GuessOption from GuessOption +--R +--R +--RThere is one unexposed function called homogeneous : +--R [1] List(GuessOption) -> Union(PositiveInteger,Boolean) +--R from GuessOptionFunctions0 +--R +--RExamples of homogeneous from GuessOptionFunctions0 +--R +--R +--RExamples of homogeneous from GuessOption +--R +--E 1250 + +--S 1251 of 3320 +)d op homogeneous? +--R +--R +--RThere are 2 unexposed functions called homogeneous? : +--R [1] AntiSymm(D2,D3) -> Boolean from AntiSymm(D2,D3) +--R if D2 has RING and D3: LIST(SYMBOL) +--R [2] DeRhamComplex(D2,D3) -> Boolean from DeRhamComplex(D2,D3) +--R if D2 has Join(Ring,OrderedSet) and D3: LIST(SYMBOL) +--R +--RExamples of homogeneous? from AntiSymm +--R +--R +--RExamples of homogeneous? from DeRhamComplex +--R +--Rder:=DERHAM(Integer,[x,y,z]) +--R[dx,dy,dz]:=[generator(i)$der for i in 1..3] +--Rf:BOP:=operator('f) +--Rg:BOP:=operator('g) +--Rh:BOP:=operator('h) +--Rsigma:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz +--Rhomogeneous? sigma +--Ra:BOP:=operator('a) +--Rb:BOP:=operator('b) +--Rc:BOP:=operator('c) +--Rtheta:=a(x,y,z)*dx*dy + b(x,y,z)*dx*dz + c(x,y,z)*dy*dz +--Rhomogeneous? (sigma+theta) +--R +--E 1251 + +--S 1252 of 3320 +)d op homogenize +--R +--R +--RThere are 6 exposed functions called homogenize : +--R [1] (D5,Integer) -> D5 +--R from GeneralPackageForAlgebraicFunctionField(D7,D8,D5,D9, +--R D10,D11,D12,D1,D2,D3,D4) +--R if D7 has FIELD and D8: LIST(SYMBOL) and D5 has POLYCAT(D7 +--R ,D9,OVAR(D8)) and D9 has DIRPCAT(#(D8),NNI) and D10 has +--R PRSPCAT(D7) and D11 has LOCPOWC(D7) and D12 has PLACESC(D7, +--R D11) and D1 has DIVCAT(D12) and D2 has INFCLCT(D7,D8,D5,D9, +--R D10,D11,D12,D1,D4) and D4 has BLMETCT and D3 has DSTRCAT(D2 +--R ) +--R [2] (DistributedMultivariatePolynomial(D4,D3),Integer) -> +--R DistributedMultivariatePolynomial(D4,D3) +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D3,D4 +--R ,D5) +--R if D3 has FFIELDC and D4: LIST(SYMBOL) and D5 has BLMETCT +--R +--R [3] (DistributedMultivariatePolynomial(D4,D3),Integer) -> +--R DistributedMultivariatePolynomial(D4,D3) +--R from PackageForAlgebraicFunctionField(D3,D4,D5) +--R if D3 has FIELD and D4: LIST(SYMBOL) and D5 has BLMETCT +--R +--R [4] (D1,Integer) -> D1 from PackageForPoly(D3,D1,D4,D5) +--R if D3 has RING and D4 has DIRPCAT(D5,NNI) and D5: NNI and +--R D1 has FAMR(D3,D4) +--R [5] D -> D from D if D has PRSPCAT(D1) and D1 has FIELD +--R [6] (D,Integer) -> D from D if D has PRSPCAT(D2) and D2 has FIELD +--R +--R +--RExamples of homogenize from GeneralPackageForAlgebraicFunctionField +--R +--R +--RExamples of homogenize from PackageForAlgebraicFunctionFieldOverFiniteField +--R +--R +--RExamples of homogenize from PackageForAlgebraicFunctionField +--R +--R +--RExamples of homogenize from PackageForPoly +--R +--R +--RExamples of homogenize from ProjectiveSpaceCategory +--R +--E 1252 + +--S 1253 of 3320 done +)d op horizConcat +--R +--R +--RThere are 2 exposed functions called horizConcat : +--R [1] List(D1) -> D1 from MatrixManipulation(D3,D4,D5,D1) +--R if D3 has FIELD and D1 has MATCAT(D3,D4,D5) and D4 has +--R FLAGG(D3) and D5 has FLAGG(D3) +--R [2] (D,D) -> D from D +--R if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG +--R (D1) and D3 has FLAGG(D1) +--R +--RExamples of horizConcat from MatrixManipulation +--R +--RA := matrix([[a]]) +--RB := matrix([[b]]) +--RC := matrix([[c]]) +--RA12 := horizConcat([A,B,C]) +--R +--R +--RExamples of horizConcat from MatrixCategory +--R +--Rm:=matrix [[j**i for i in 0..4] for j in 1..5] +--RhorizConcat(m,m) +--R +--E 1253 + +--S 1254 of 3320 +)d op horizJoin +--R +--R +--RThere is one exposed function called horizJoin : +--R [1] (SparseEchelonMatrix(D1,D2),SparseEchelonMatrix(D1,D2)) -> +--R SparseEchelonMatrix(D1,D2) +--R from SparseEchelonMatrix(D1,D2) if D1 has ORDSET and D2 +--R has RING +--R +--RExamples of horizJoin from SparseEchelonMatrix +--R +--E 1254 + +--S 1255 of 3320 +)d op horizSplit +--R +--R +--RThere are 3 exposed functions called horizSplit : +--R [1] (D2,PositiveInteger) -> List(D2) from MatrixManipulation(D4,D5, +--R D6,D2) +--R if D4 has FIELD and D5 has FLAGG(D4) and D6 has FLAGG(D4) +--R and D2 has MATCAT(D4,D5,D6) +--R [2] (D2,List(PositiveInteger)) -> List(D2) +--R from MatrixManipulation(D4,D5,D6,D2) +--R if D4 has FIELD and D5 has FLAGG(D4) and D6 has FLAGG(D4) +--R and D2 has MATCAT(D4,D5,D6) +--R [3] (SparseEchelonMatrix(D2,D3),D2) -> Record(Left: +--R SparseEchelonMatrix(D2,D3),Right: SparseEchelonMatrix(D2,D3)) +--R from SparseEchelonMatrix(D2,D3) if D2 has ORDSET and D3 +--R has RING +--R +--RExamples of horizSplit from MatrixManipulation +--R +--RE := matrix([[i,a,b,c],[a,a,b,c],[b,d,e,f],[c,g,h,i]]) +--Rt1:= horizSplit(E, [2,2]) +--Rt2:= horizSplit(E, [1,2,1]) +--R +--RE := matrix([[i,a,b,c],[a,a,b,c],[b,d,e,f],[c,g,h,i]]) +--Rt1:= horizSplit(E, 2) +--R +--R +--RExamples of horizSplit from SparseEchelonMatrix +--R +--E 1255 + +--S 1256 of 3320 +)d op hspace +--R +--R +--RThere is one unexposed function called hspace : +--R [1] Integer -> OutputForm from OutputForm +--R +--RExamples of hspace from OutputForm +--R +--E 1256 + +--S 1257 of 3320 +)d op htrigs +--R +--R +--RThere is one exposed function called htrigs : +--R [1] D1 -> D1 from TranscendentalManipulations(D2,D1) +--R if D2 has Join(OrderedSet,GcdDomain) and D1 has Join( +--R FunctionSpace(D2),TranscendentalFunctionCategory) +--R +--RExamples of htrigs from TranscendentalManipulations +--R +--E 1257 + +--S 1258 of 3320 +)d op hue +--R +--R +--RThere are 2 exposed functions called hue : +--R [1] Color -> Integer from Color +--R [2] Palette -> Color from Palette +--R +--RThere is one unexposed function called hue : +--R [1] Point(D1) -> D1 from PointPackage(D1) if D1 has RING +--R +--RExamples of hue from Color +--R +--R +--RExamples of hue from Palette +--R +--R +--RExamples of hue from PointPackage +--R +--E 1258 + +--S 1259 of 3320 +)d op hyperelliptic +--R +--R +--RThere is one exposed function called hyperelliptic : +--R [1] -> Union(D1,"failed") from D +--R if D has FFCAT(D2,D1,D3) and D2 has UFD and D3 has UPOLYC( +--R FRAC(D1)) and D1 has UPOLYC(D2) +--R +--RThere is one unexposed function called hyperelliptic : +--R [1] -> Union(D1,"failed") from FunctionFieldCategory&(D2,D3,D1,D4) +--R if D3 has UFD and D4 has UPOLYC(FRAC(D1)) and D1 has +--R UPOLYC(D3) and D2 has FFCAT(D3,D1,D4) +--R +--RExamples of hyperelliptic from FunctionFieldCategory& +--R +--R +--RExamples of hyperelliptic from FunctionFieldCategory +--R +--E 1259 + +--S 1260 of 3320 +)d op hypergeometric0F1 +--R +--R +--RThere are 2 exposed functions called hypergeometric0F1 : +--R [1] (DoubleFloat,DoubleFloat) -> DoubleFloat from +--R DoubleFloatSpecialFunctions +--R [2] (Complex(DoubleFloat),Complex(DoubleFloat)) -> Complex( +--R DoubleFloat) +--R from DoubleFloatSpecialFunctions +--R +--RExamples of hypergeometric0F1 from DoubleFloatSpecialFunctions +--R +--E 1260 + +--S 1261 of 3320 +)d op iCompose +--R +--R +--RThere is one unexposed function called iCompose : +--R [1] (InnerSparseUnivariatePowerSeries(D1), +--R InnerSparseUnivariatePowerSeries(D1)) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) if D1 has RING +--R +--R +--RExamples of iCompose from InnerSparseUnivariatePowerSeries +--R +--E 1261 + +--S 1262 of 3320 +)d op id +--R +--R +--RThere is one exposed function called id : +--R [1] D1 -> D1 from MappingPackage1(D1) if D1 has SETCAT +--R +--RExamples of id from MappingPackage1 +--R +--E 1262 + +--S 1263 of 3320 +)d op ideal +--R +--R +--RThere are 2 exposed functions called ideal : +--R [1] D -> FractionalIdeal(D3,Fraction(D3),D4,D5) from D +--R if D has FDIVCAT(D2,D3,D4,D5) and D2 has FIELD and D3 has +--R UPOLYC(D2) and D4 has UPOLYC(FRAC(D3)) and D5 has FFCAT(D2, +--R D3,D4) +--R [2] List(D5) -> PolynomialIdeals(D2,D3,D4,D5) +--R from PolynomialIdeals(D2,D3,D4,D5) +--R if D5 has POLYCAT(D2,D3,D4) and D2 has FIELD and D3 has +--R OAMONS and D4 has ORDSET +--R +--RThere is one unexposed function called ideal : +--R [1] Vector(D5) -> FractionalIdeal(D2,D3,D4,D5) +--R from FractionalIdeal(D2,D3,D4,D5) +--R if D5 has Join(FramedAlgebra(D3,D4),RetractableTo(D3)) and +--R D3 has QFCAT(D2) and D4 has UPOLYC(D3) and D2 has EUCDOM +--R +--R +--RExamples of ideal from FiniteDivisorCategory +--R +--R +--RExamples of ideal from FractionalIdeal +--R +--R +--RExamples of ideal from PolynomialIdeals +--R +--E 1263 + +--S 1264 of 3320 +)d op idealiser +--R +--R +--RThere are 2 unexposed functions called idealiser : +--R [1] (Matrix(D2),Matrix(D2)) -> Matrix(D2) from IntegralBasisTools(D2 +--R ,D3,D4) +--R if D2 has EuclideanDomainwith +--R squareFree : % -> Factored(%)and D3 has UPOLYC(D2) +--R and D4 has FRAMALG(D2,D3) +--R [2] (Matrix(D2),Matrix(D2),D2) -> Matrix(D2) +--R from IntegralBasisTools(D2,D3,D4) +--R if D2 has EuclideanDomainwith +--R squareFree : % -> Factored(%)and D3 has UPOLYC(D2) +--R and D4 has FRAMALG(D2,D3) +--R +--RExamples of idealiser from IntegralBasisTools +--R +--E 1264 + +--S 1265 of 3320 +)d op idealiserMatrix +--R +--R +--RThere is one unexposed function called idealiserMatrix : +--R [1] (Matrix(D2),Matrix(D2)) -> Matrix(D2) from IntegralBasisTools(D2 +--R ,D3,D4) +--R if D2 has EuclideanDomainwith +--R squareFree : % -> Factored(%)and D3 has UPOLYC(D2) +--R and D4 has FRAMALG(D2,D3) +--R +--RExamples of idealiserMatrix from IntegralBasisTools +--R +--E 1265 + +--S 1266 of 3320 +)d op idealSimplify +--R +--R +--RThere is one unexposed function called idealSimplify : +--R [1] QuasiAlgebraicSet(D1,D2,D3,D4) -> QuasiAlgebraicSet(D1,D2,D3,D4) +--R from QuasiAlgebraicSet(D1,D2,D3,D4) +--R if D1 has GCDDOM and D2 has ORDSET and D3 has OAMONS and +--R D4 has POLYCAT(D1,D3,D2) +--R +--RExamples of idealSimplify from QuasiAlgebraicSet +--R +--E 1266 + +--S 1267 of 3320 +)d op identification +--R +--R +--RThere is one unexposed function called identification : +--R [1] (LieExponentials(D2,D3,D4),LieExponentials(D2,D3,D4)) -> List( +--R Equation(D3)) +--R from LieExponentials(D2,D3,D4) +--R if D2 has ORDSET and D3 has Join(CommutativeRing,Module( +--R Fraction(Integer))) and D4: PI +--R +--RExamples of identification from LieExponentials +--R +--E 1267 + +--S 1268 of 3320 +)d op identity +--R +--R +--RThere is one exposed function called identity : +--R [1] -> DenavitHartenbergMatrix(D1) from DenavitHartenbergMatrix(D1) +--R if D1 has Join(Field,TranscendentalFunctionCategory) +--R +--RExamples of identity from DenavitHartenbergMatrix +--R +--E 1268 + +--S 1269 of 3320 +)d op identityMatrix +--R +--R +--RThere is one exposed function called identityMatrix : +--R [1] NonNegativeInteger -> ThreeDimensionalMatrix(D2) +--R from ThreeDimensionalMatrix(D2) if D2 has RING and D2 has +--R SETCAT +--R +--RExamples of identityMatrix from ThreeDimensionalMatrix +--R +--E 1269 + +--S 1270 of 3320 +)d op identitySquareMatrix +--R +--R +--RThere is one exposed function called identitySquareMatrix : +--R [1] (Symbol,Polynomial(Integer)) -> FortranCode from +--R FortranCodePackage1 +--R +--RExamples of identitySquareMatrix from FortranCodePackage1 +--R +--E 1270 + +--S 1271 of 3320 +)d op iExquo +--R +--R +--RThere is one unexposed function called iExquo : +--R [1] (InnerSparseUnivariatePowerSeries(D2), +--R InnerSparseUnivariatePowerSeries(D2),Boolean) -> Union( +--R InnerSparseUnivariatePowerSeries(D2),"failed") +--R from InnerSparseUnivariatePowerSeries(D2) if D2 has RING +--R +--R +--RExamples of iExquo from InnerSparseUnivariatePowerSeries +--R +--E 1271 + +--S 1272 of 3320 +)d op iFTable +--R +--R +--RThere is one exposed function called iFTable : +--R [1] List(Record(key: Record(xinit: DoubleFloat,xend: DoubleFloat,fn +--R : Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat), +--R intvals: List(DoubleFloat),g: Expression(DoubleFloat),abserr: +--R DoubleFloat,relerr: DoubleFloat),entry: Record(stiffness: Float, +--R stability: Float,expense: Float,accuracy: Float, +--R intermediateResults: Float))) -> ODEIntensityFunctionsTable +--R from ODEIntensityFunctionsTable +--R +--RExamples of iFTable from ODEIntensityFunctionsTable +--R +--E 1272 + +--S 1273 of 3320 +)d op ignore? +--R +--R +--RThere is one unexposed function called ignore? : +--R [1] String -> Boolean from DefiniteIntegrationTools(D3,D4) +--R if D3 has Join(GcdDomain,OrderedSet,RetractableTo(Integer) +--R ,LinearlyExplicitRingOver(Integer)) and D4 has Join( +--R TranscendentalFunctionCategory, +--R AlgebraicallyClosedFunctionSpace(D3)) +--R +--RExamples of ignore? from DefiniteIntegrationTools +--R +--E 1273 + +--S 1274 of 3320 +)d op iiabs +--R +--R +--RThere is one unexposed function called iiabs : +--R [1] D1 -> D1 from FunctionalSpecialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R +--RExamples of iiabs from FunctionalSpecialFunction +--R +--E 1274 + +--S 1275 of 3320 +)d op iiacos +--R +--R +--RThere is one unexposed function called iiacos : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iiacos from ElementaryFunction +--R +--E 1275 + +--S 1276 of 3320 +)d op iiacosh +--R +--R +--RThere is one unexposed function called iiacosh : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iiacosh from ElementaryFunction +--R +--E 1276 + +--S 1277 of 3320 +)d op iiacot +--R +--R +--RThere is one unexposed function called iiacot : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iiacot from ElementaryFunction +--R +--E 1277 + +--S 1278 of 3320 +)d op iiacoth +--R +--R +--RThere is one unexposed function called iiacoth : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iiacoth from ElementaryFunction +--R +--E 1278 + +--S 1279 of 3320 +)d op iiacsc +--R +--R +--RThere is one unexposed function called iiacsc : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iiacsc from ElementaryFunction +--R +--E 1279 + +--S 1280 of 3320 +)d op iiacsch +--R +--R +--RThere is one unexposed function called iiacsch : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iiacsch from ElementaryFunction +--R +--E 1280 + +--S 1281 of 3320 +)d op iiAiryAi +--R +--R +--RThere is one unexposed function called iiAiryAi : +--R [1] D1 -> D1 from FunctionalSpecialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R +--RExamples of iiAiryAi from FunctionalSpecialFunction +--R +--E 1281 + +--S 1282 of 3320 +)d op iiAiryBi +--R +--R +--RThere is one unexposed function called iiAiryBi : +--R [1] D1 -> D1 from FunctionalSpecialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R +--RExamples of iiAiryBi from FunctionalSpecialFunction +--R +--E 1282 + +--S 1283 of 3320 +)d op iiasec +--R +--R +--RThere is one unexposed function called iiasec : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iiasec from ElementaryFunction +--R +--E 1283 + +--S 1284 of 3320 +)d op iiasech +--R +--R +--RThere is one unexposed function called iiasech : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iiasech from ElementaryFunction +--R +--E 1284 + +--S 1285 of 3320 +)d op iiasin +--R +--R +--RThere is one unexposed function called iiasin : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iiasin from ElementaryFunction +--R +--E 1285 + +--S 1286 of 3320 +)d op iiasinh +--R +--R +--RThere is one unexposed function called iiasinh : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iiasinh from ElementaryFunction +--R +--E 1286 + +--S 1287 of 3320 +)d op iiatan +--R +--R +--RThere is one unexposed function called iiatan : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iiatan from ElementaryFunction +--R +--E 1287 + +--S 1288 of 3320 +)d op iiatanh +--R +--R +--RThere is one unexposed function called iiatanh : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iiatanh from ElementaryFunction +--R +--E 1288 + +--S 1289 of 3320 +)d op iiBesselI +--R +--R +--RThere is one unexposed function called iiBesselI : +--R [1] List(D1) -> D1 from FunctionalSpecialFunction(D3,D1) +--R if D1 has FS(D3) and D3 has Join(OrderedSet,IntegralDomain +--R ) +--R +--RExamples of iiBesselI from FunctionalSpecialFunction +--R +--E 1289 + +--S 1290 of 3320 +)d op iiBesselJ +--R +--R +--RThere is one unexposed function called iiBesselJ : +--R [1] List(D1) -> D1 from FunctionalSpecialFunction(D3,D1) +--R if D1 has FS(D3) and D3 has Join(OrderedSet,IntegralDomain +--R ) +--R +--RExamples of iiBesselJ from FunctionalSpecialFunction +--R +--E 1290 + +--S 1291 of 3320 +)d op iiBesselK +--R +--R +--RThere is one unexposed function called iiBesselK : +--R [1] List(D1) -> D1 from FunctionalSpecialFunction(D3,D1) +--R if D1 has FS(D3) and D3 has Join(OrderedSet,IntegralDomain +--R ) +--R +--RExamples of iiBesselK from FunctionalSpecialFunction +--R +--E 1291 + +--S 1292 of 3320 +)d op iiBesselY +--R +--R +--RThere is one unexposed function called iiBesselY : +--R [1] List(D1) -> D1 from FunctionalSpecialFunction(D3,D1) +--R if D1 has FS(D3) and D3 has Join(OrderedSet,IntegralDomain +--R ) +--R +--RExamples of iiBesselY from FunctionalSpecialFunction +--R +--E 1292 + +--S 1293 of 3320 +)d op iiBeta +--R +--R +--RThere is one unexposed function called iiBeta : +--R [1] List(D1) -> D1 from FunctionalSpecialFunction(D3,D1) +--R if D1 has FS(D3) and D3 has Join(OrderedSet,IntegralDomain +--R ) +--R +--RExamples of iiBeta from FunctionalSpecialFunction +--R +--E 1293 + +--S 1294 of 3320 +)d op iibinom +--R +--R +--RThere is one unexposed function called iibinom : +--R [1] List(D1) -> D1 from CombinatorialFunction(D3,D1) +--R if D1 has FS(D3) and D3 has Join(OrderedSet,IntegralDomain +--R ) +--R +--RExamples of iibinom from CombinatorialFunction +--R +--E 1294 + +--S 1295 of 3320 +)d op iicos +--R +--R +--RThere is one unexposed function called iicos : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iicos from ElementaryFunction +--R +--E 1295 + +--S 1296 of 3320 +)d op iicosh +--R +--R +--RThere is one unexposed function called iicosh : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iicosh from ElementaryFunction +--R +--E 1296 + +--S 1297 of 3320 +)d op iicot +--R +--R +--RThere is one unexposed function called iicot : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iicot from ElementaryFunction +--R +--E 1297 + +--S 1298 of 3320 +)d op iicoth +--R +--R +--RThere is one unexposed function called iicoth : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iicoth from ElementaryFunction +--R +--E 1298 + +--S 1299 of 3320 +)d op iicsc +--R +--R +--RThere is one unexposed function called iicsc : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iicsc from ElementaryFunction +--R +--E 1299 + +--S 1300 of 3320 +)d op iicsch +--R +--R +--RThere is one unexposed function called iicsch : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iicsch from ElementaryFunction +--R +--E 1300 + +--S 1301 of 3320 +)d op iidigamma +--R +--R +--RThere is one unexposed function called iidigamma : +--R [1] D1 -> D1 from FunctionalSpecialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R +--RExamples of iidigamma from FunctionalSpecialFunction +--R +--E 1301 + +--S 1302 of 3320 +)d op iidprod +--R +--R +--RThere is one unexposed function called iidprod : +--R [1] List(D1) -> D1 from CombinatorialFunction(D3,D1) +--R if D1 has FS(D3) and D3 has Join(OrderedSet,IntegralDomain +--R ) +--R +--RExamples of iidprod from CombinatorialFunction +--R +--E 1302 + +--S 1303 of 3320 +)d op iidsum +--R +--R +--RThere is one unexposed function called iidsum : +--R [1] List(D1) -> D1 from CombinatorialFunction(D3,D1) +--R if D1 has FS(D3) and D3 has Join(OrderedSet,IntegralDomain +--R ) +--R +--RExamples of iidsum from CombinatorialFunction +--R +--E 1303 + +--S 1304 of 3320 +)d op iiexp +--R +--R +--RThere is one unexposed function called iiexp : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iiexp from ElementaryFunction +--R +--E 1304 + +--S 1305 of 3320 +)d op iifact +--R +--R +--RThere is one unexposed function called iifact : +--R [1] D1 -> D1 from CombinatorialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R +--RExamples of iifact from CombinatorialFunction +--R +--E 1305 + +--S 1306 of 3320 +)d op iiGamma +--R +--R +--RThere is one unexposed function called iiGamma : +--R [1] D1 -> D1 from FunctionalSpecialFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has FS(D2 +--R ) +--R +--RExamples of iiGamma from FunctionalSpecialFunction +--R +--E 1306 + +--S 1307 of 3320 +)d op iilog +--R +--R +--RThere is one unexposed function called iilog : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iilog from ElementaryFunction +--R +--E 1307 + +--S 1308 of 3320 +)d op iiperm +--R +--R +--RThere is one unexposed function called iiperm : +--R [1] List(D1) -> D1 from CombinatorialFunction(D3,D1) +--R if D1 has FS(D3) and D3 has Join(OrderedSet,IntegralDomain +--R ) +--R +--RExamples of iiperm from CombinatorialFunction +--R +--E 1308 + +--S 1309 of 3320 +)d op iipolygamma +--R +--R +--RThere is one unexposed function called iipolygamma : +--R [1] List(D1) -> D1 from FunctionalSpecialFunction(D3,D1) +--R if D1 has FS(D3) and D3 has Join(OrderedSet,IntegralDomain +--R ) +--R +--RExamples of iipolygamma from FunctionalSpecialFunction +--R +--E 1309 + +--S 1310 of 3320 +)d op iipow +--R +--R +--RThere is one unexposed function called iipow : +--R [1] List(D1) -> D1 from CombinatorialFunction(D3,D1) +--R if D1 has FS(D3) and D3 has Join(OrderedSet,IntegralDomain +--R ) +--R +--RExamples of iipow from CombinatorialFunction +--R +--E 1310 + +--S 1311 of 3320 +)d op iisec +--R +--R +--RThere is one unexposed function called iisec : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iisec from ElementaryFunction +--R +--E 1311 + +--S 1312 of 3320 +)d op iisech +--R +--R +--RThere is one unexposed function called iisech : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iisech from ElementaryFunction +--R +--E 1312 + +--S 1313 of 3320 +)d op iisin +--R +--R +--RThere is one unexposed function called iisin : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iisin from ElementaryFunction +--R +--E 1313 + +--S 1314 of 3320 +)d op iisinh +--R +--R +--RThere is one unexposed function called iisinh : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iisinh from ElementaryFunction +--R +--E 1314 + +--S 1315 of 3320 +)d op iisqrt2 +--R +--R +--RThere is one unexposed function called iisqrt2 : +--R [1] -> D1 from ElementaryFunction(D2,D1) +--R if D1 has Join(FunctionSpace(D2),RadicalCategory) and D2 +--R has Join(OrderedSet,IntegralDomain) +--R +--RExamples of iisqrt2 from ElementaryFunction +--R +--E 1315 + +--S 1316 of 3320 +)d op iisqrt3 +--R +--R +--RThere is one unexposed function called iisqrt3 : +--R [1] -> D1 from ElementaryFunction(D2,D1) +--R if D1 has Join(FunctionSpace(D2),RadicalCategory) and D2 +--R has Join(OrderedSet,IntegralDomain) +--R +--RExamples of iisqrt3 from ElementaryFunction +--R +--E 1316 + +--S 1317 of 3320 +)d op iitan +--R +--R +--RThere is one unexposed function called iitan : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iitan from ElementaryFunction +--R +--E 1317 + +--S 1318 of 3320 +)d op iitanh +--R +--R +--RThere is one unexposed function called iitanh : +--R [1] D1 -> D1 from ElementaryFunction(D2,D1) +--R if D2 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D2),RadicalCategory) +--R +--RExamples of iitanh from ElementaryFunction +--R +--E 1318 + +--S 1319 of 3320 +)d op imag +--R +--R +--RThere are 3 exposed functions called imag : +--R [1] D -> D1 from D if D has COMPCAT(D1) and D1 has COMRING +--R [2] D2 -> Expression(D3) from ComplexTrigonometricManipulations(D3, +--R D2) +--R if D3 has Join(IntegralDomain,OrderedSet,RetractableTo( +--R Integer)) and D2 has Join(AlgebraicallyClosedField, +--R TranscendentalFunctionCategory,FunctionSpace(Complex(D3))) +--R +--R [3] D1 -> D1 from TrigonometricManipulations(D2,D1) +--R if D2 has Join(GcdDomain,OrderedSet,RetractableTo(Integer) +--R ,LinearlyExplicitRingOver(Integer)) and D1 has Join( +--R AlgebraicallyClosedField,TranscendentalFunctionCategory, +--R FunctionSpace(D2)) +--R +--RExamples of imag from ComplexCategory +--R +--R +--RExamples of imag from ComplexTrigonometricManipulations +--R +--R +--RExamples of imag from TrigonometricManipulations +--R +--E 1319 + +--S 1320 of 3320 +)d op imagE +--R +--R +--RThere is one exposed function called imagE : +--R [1] D -> D1 from D if D has OC(D1) and D1 has COMRING +--R +--RExamples of imagE from OctonionCategory +--R +--E 1320 + +--S 1321 of 3320 +)d op imagi +--R +--R +--RThere is one exposed function called imagi : +--R [1] D -> D1 from D if D has OC(D1) and D1 has COMRING +--R +--RExamples of imagi from OctonionCategory +--R +--E 1321 + +--S 1322 of 3320 +)d op imagI +--R +--R +--RThere are 2 exposed functions called imagI : +--R [1] D -> D1 from D if D has OC(D1) and D1 has COMRING +--R [2] D -> D1 from D if D has QUATCAT(D1) and D1 has COMRING +--R +--RExamples of imagI from OctonionCategory +--R +--R +--RExamples of imagI from QuaternionCategory +--R +--E 1322 + +--S 1323 of 3320 +)d op imaginary +--R +--R +--RThere is one exposed function called imaginary : +--R [1] -> D from D if D has COMPCAT(D1) and D1 has COMRING +--R +--RExamples of imaginary from ComplexCategory +--R +--E 1323 + +--S 1324 of 3320 +)d op imagj +--R +--R +--RThere is one exposed function called imagj : +--R [1] D -> D1 from D if D has OC(D1) and D1 has COMRING +--R +--RExamples of imagj from OctonionCategory +--R +--E 1324 + +--S 1325 of 3320 +)d op imagJ +--R +--R +--RThere are 2 exposed functions called imagJ : +--R [1] D -> D1 from D if D has OC(D1) and D1 has COMRING +--R [2] D -> D1 from D if D has QUATCAT(D1) and D1 has COMRING +--R +--RExamples of imagJ from OctonionCategory +--R +--R +--RExamples of imagJ from QuaternionCategory +--R +--E 1325 + +--S 1326 of 3320 +)d op imagk +--R +--R +--RThere is one exposed function called imagk : +--R [1] D -> D1 from D if D has OC(D1) and D1 has COMRING +--R +--RExamples of imagk from OctonionCategory +--R +--E 1326 + +--S 1327 of 3320 +)d op imagK +--R +--R +--RThere are 2 exposed functions called imagK : +--R [1] D -> D1 from D if D has OC(D1) and D1 has COMRING +--R [2] D -> D1 from D if D has QUATCAT(D1) and D1 has COMRING +--R +--RExamples of imagK from OctonionCategory +--R +--R +--RExamples of imagK from QuaternionCategory +--R +--E 1327 + +--S 1328 of 3320 +)d op implies +--R +--R +--RThere is one exposed function called implies : +--R [1] (Boolean,Boolean) -> Boolean from Boolean +--R +--RExamples of implies from Boolean +--R +--E 1328 + +--S 1329 of 3320 +)d op in? +--R +--R +--RThere are 3 exposed functions called in? : +--R [1] DoubleFloat -> Boolean from ExpertSystemContinuityPackage1(D3,D4 +--R ) +--R if D3: DFLOAT and D4: DFLOAT +--R [2] (DoubleFloat,Segment(OrderedCompletion(DoubleFloat))) -> Boolean +--R from ExpertSystemToolsPackage +--R [3] (PolynomialIdeals(D2,D3,D4,D5),PolynomialIdeals(D2,D3,D4,D5)) +--R -> Boolean +--R from PolynomialIdeals(D2,D3,D4,D5) +--R if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D5 +--R has POLYCAT(D2,D3,D4) +--R +--RExamples of in? from ExpertSystemContinuityPackage1 +--R +--R +--RExamples of in? from ExpertSystemToolsPackage +--R +--R +--RExamples of in? from PolynomialIdeals +--R +--E 1329 + +--S 1330 of 3320 +)d op inBetweenExcpDiv +--R +--R +--RThere is one exposed function called inBetweenExcpDiv : +--R [1] D5 -> D4 from DesingTreePackage(D6,D7,D8,D9,D10,D11,D1,D4,D2,D5, +--R D3) +--R if D6 has FIELD and D7: LIST(SYMBOL) and D8 has POLYCAT(D6 +--R ,D9,OVAR(D7)) and D9 has DIRPCAT(#(D7),NNI) and D10 has +--R PRSPCAT(D6) and D11 has LOCPOWC(D6) and D1 has PLACESC(D6, +--R D11) and D2 has INFCLCT(D6,D7,D8,D9,D10,D11,D1,D4,D3) and +--R D3 has BLMETCT and D4 has DIVCAT(D1) and D5 has DSTRCAT(D2) +--R +--R +--RExamples of inBetweenExcpDiv from DesingTreePackage +--R +--E 1330 + +--S 1331 of 3320 +)d op inc +--R +--R +--RThere is one exposed function called inc : +--R [1] D -> D from D if D has INS +--R +--RExamples of inc from IntegerNumberSystem +--R +--E 1331 + +--S 1332 of 3320 +)d op inconsistent? +--R +--R +--RThere are 2 unexposed functions called inconsistent? : +--R [1] List(D6) -> Boolean from ParametricLinearEquations(D3,D4,D5,D6) +--R if D6 has POLYCAT(D3,D5,D4) and D3 has Join( +--R EuclideanDomain,CharacteristicZero) and D4 has Join( +--R OrderedSet,ConvertibleTo(Symbol)) and D5 has OAMONS +--R [2] List(Polynomial(D3)) -> Boolean +--R from ParametricLinearEquations(D3,D4,D5,D6) +--R if D3 has Join(EuclideanDomain,CharacteristicZero) and D4 +--R has Join(OrderedSet,ConvertibleTo(Symbol)) and D5 has +--R OAMONS and D6 has POLYCAT(D3,D5,D4) +--R +--RExamples of inconsistent? from ParametricLinearEquations +--R +--E 1332 + +--S 1333 of 3320 +)d op incr +--R +--R +--RThere are 2 exposed functions called incr : +--R [1] D -> D from D if D has DIVCAT(D1) and D1 has SETCAT +--R [2] D -> Integer from D if D has SEGCAT(D2) and D2 has TYPE +--R +--RExamples of incr from DivisorCategory +--R +--R +--RExamples of incr from SegmentCategory +--R +--E 1333 + +--S 1334 of 3320 +)d op increase +--R +--R +--RThere are 2 exposed functions called increase : +--R [1] String -> Float from AttributeButtons +--R [2] (String,String) -> Float from AttributeButtons +--R +--RExamples of increase from AttributeButtons +--R +--E 1334 + +--S 1335 of 3320 +)d op increasePrecision +--R +--R +--RThere is one exposed function called increasePrecision : +--R [1] Integer -> PositiveInteger from D if D has arbitraryPrecision +--R and D has FPS +--R +--RExamples of increasePrecision from FloatingPointSystem +--R +--E 1335 + +--S 1336 of 3320 +)d op increment +--R +--R +--RThere is one unexposed function called increment : +--R [1] -> (D2 -> D2) from IncrementingMaps(D2) +--R if D2 has Join(Monoid,AbelianSemiGroup) +--R +--RExamples of increment from IncrementingMaps +--R +--E 1336 + +--S 1337 of 3320 +)d op incrementBy +--R +--R +--RThere is one unexposed function called incrementBy : +--R [1] D2 -> (D2 -> D2) from IncrementingMaps(D2) +--R if D2 has Join(Monoid,AbelianSemiGroup) +--R +--RExamples of incrementBy from IncrementingMaps +--R +--E 1337 + +--S 1338 of 3320 +)d op incrementKthElement +--R +--R +--RThere is one unexposed function called incrementKthElement : +--R [1] (SetOfMIntegersInOneToN(D2,D3),PositiveInteger) -> Union( +--R SetOfMIntegersInOneToN(D2,D3),"failed") +--R from SetOfMIntegersInOneToN(D2,D3) if D2: PI and D3: PI +--R +--R +--RExamples of incrementKthElement from SetOfMIntegersInOneToN +--R +--E 1338 + +--S 1339 of 3320 +)d op index +--R +--R +--RThere is one exposed function called index : +--R [1] PositiveInteger -> D from D if D has FINITE +--R +--RThere are 2 unexposed functions called index : +--R [1] (PositiveInteger,PositiveInteger) -> Vector(D3) +--R from InnerNormalBasisFieldFunctions(D3) if D3 has FFIELDC +--R +--R [2] ModuleMonomial(D1,D2,D3) -> D1 from ModuleMonomial(D1,D2,D3) +--R if D1 has ORDSET and D2 has SETCAT and D3: ((Record(index +--R : D1,exponent: D2),Record(index: D1,exponent: D2)) -> +--R Boolean) +--R +--RExamples of index from Finite +--R +--R +--RExamples of index from InnerNormalBasisFieldFunctions +--R +--R +--RExamples of index from ModuleMonomial +--R +--E 1339 + +--S 1340 of 3320 +)d op index? +--R +--R +--RThere is one exposed function called index? : +--R [1] (D2,D) -> Boolean from D +--R if D has IXAGG(D2,D3) and D2 has SETCAT and D3 has TYPE +--R +--R +--RExamples of index? from IndexedAggregate +--R +--E 1340 + +--S 1341 of 3320 +)d op indexName +--R +--R +--RThere is one exposed function called indexName : +--R [1] Symbol -> GuessOption from GuessOption +--R +--RThere is one unexposed function called indexName : +--R [1] List(GuessOption) -> Symbol from GuessOptionFunctions0 +--R +--RExamples of indexName from GuessOptionFunctions0 +--R +--R +--RExamples of indexName from GuessOption +--R +--E 1341 + +--S 1342 of 3320 +)d op indices +--R +--R +--RThere is one exposed function called indices : +--R [1] D -> List(D2) from D if D has IXAGG(D2,D3) and D2 has SETCAT and +--R D3 has TYPE +--R +--RExamples of indices from IndexedAggregate +--R +--E 1342 + +--S 1343 of 3320 +)d op indiceSubResultant +--R +--R +--RThere is one unexposed function called indiceSubResultant : +--R [1] (D1,D1,NonNegativeInteger) -> D1 from PseudoRemainderSequence(D3 +--R ,D1) +--R if D3 has INTDOM and D1 has UPOLYC(D3) +--R +--RExamples of indiceSubResultant from PseudoRemainderSequence +--R +--E 1343 + +--S 1344 of 3320 +)d op indiceSubResultantEuclidean +--R +--R +--RThere is one unexposed function called indiceSubResultantEuclidean : +--R [1] (D2,D2,NonNegativeInteger) -> Record(coef1: D2,coef2: D2, +--R subResultant: D2) +--R from PseudoRemainderSequence(D4,D2) +--R if D4 has INTDOM and D2 has UPOLYC(D4) +--R +--RExamples of indiceSubResultantEuclidean from PseudoRemainderSequence +--R +--E 1344 + +--S 1345 of 3320 +)d op indicialEquation +--R +--R +--RThere are 2 unexposed functions called indicialEquation : +--R [1] (D2,D3) -> D1 from PrimitiveRatDE(D3,D1,D2,D4) +--R if D1 has UPOLYC(D3) and D3 has Join(Field, +--R CharacteristicZero,RetractableTo(Fraction(Integer))) and D2 +--R has LODOCAT(D1) and D4 has LODOCAT(FRAC(D1)) +--R [2] (D2,D3) -> D1 from PrimitiveRatDE(D3,D1,D4,D2) +--R if D1 has UPOLYC(D3) and D3 has Join(Field, +--R CharacteristicZero,RetractableTo(Fraction(Integer))) and D4 +--R has LODOCAT(D1) and D2 has LODOCAT(FRAC(D1)) +--R +--RExamples of indicialEquation from PrimitiveRatDE +--R +--E 1345 + +--S 1346 of 3320 +)d op indicialEquationAtInfinity +--R +--R +--RThere are 2 unexposed functions called indicialEquationAtInfinity : +--R [1] LinearOrdinaryDifferentialOperator1(Fraction(D1)) -> D1 +--R from RationalLODE(D3,D1) +--R if D1 has UPOLYC(D3) and D3 has Join(Field, +--R CharacteristicZero,RetractableTo(Integer),RetractableTo( +--R Fraction(Integer))) +--R [2] LinearOrdinaryDifferentialOperator2(D1,Fraction(D1)) -> D1 +--R from RationalLODE(D3,D1) +--R if D1 has UPOLYC(D3) and D3 has Join(Field, +--R CharacteristicZero,RetractableTo(Integer),RetractableTo( +--R Fraction(Integer))) +--R +--RExamples of indicialEquationAtInfinity from RationalLODE +--R +--E 1346 + +--S 1347 of 3320 +)d op indicialEquations +--R +--R +--RThere are 4 unexposed functions called indicialEquations : +--R [1] D2 -> List(Record(center: D4,equation: D4)) +--R from PrimitiveRatDE(D3,D4,D2,D5) +--R if D3 has Join(Field,CharacteristicZero,RetractableTo( +--R Fraction(Integer))) and D4 has UPOLYC(D3) and D2 has +--R LODOCAT(D4) and D5 has LODOCAT(FRAC(D4)) +--R [2] (D2,D3) -> List(Record(center: D3,equation: D3)) +--R from PrimitiveRatDE(D4,D3,D2,D5) +--R if D4 has Join(Field,CharacteristicZero,RetractableTo( +--R Fraction(Integer))) and D3 has UPOLYC(D4) and D2 has +--R LODOCAT(D3) and D5 has LODOCAT(FRAC(D3)) +--R [3] D2 -> List(Record(center: D4,equation: D4)) +--R from PrimitiveRatDE(D3,D4,D5,D2) +--R if D3 has Join(Field,CharacteristicZero,RetractableTo( +--R Fraction(Integer))) and D4 has UPOLYC(D3) and D5 has +--R LODOCAT(D4) and D2 has LODOCAT(FRAC(D4)) +--R [4] (D2,D3) -> List(Record(center: D3,equation: D3)) +--R from PrimitiveRatDE(D4,D3,D5,D2) +--R if D4 has Join(Field,CharacteristicZero,RetractableTo( +--R Fraction(Integer))) and D3 has UPOLYC(D4) and D5 has +--R LODOCAT(D3) and D2 has LODOCAT(FRAC(D3)) +--R +--RExamples of indicialEquations from PrimitiveRatDE +--R +--E 1347 + +--S 1348 of 3320 +)d op inf +--R +--R +--RThere is one exposed function called inf : +--R [1] D -> D1 from D +--R if D has INTCAT(D1) and D1 has Join(FloatingPointSystem, +--R TranscendentalFunctionCategory) +--R +--RExamples of inf from IntervalCategory +--R +--E 1348 + +--S 1349 of 3320 +)d op infClsPt? +--R +--R +--RThere is one exposed function called infClsPt? : +--R [1] D -> Boolean from D if D has BLMETCT +--R +--RExamples of infClsPt? from BlowUpMethodCategory +--R +--E 1349 + +--S 1350 of 3320 +)d op infieldint +--R +--R +--RThere is one unexposed function called infieldint : +--R [1] Fraction(D3) -> Union(Fraction(D3),"failed") +--R from RationalIntegration(D2,D3) +--R if D3 has UPOLYC(D2) and D2 has Join(Field, +--R CharacteristicZero,RetractableTo(Integer)) +--R +--RExamples of infieldint from RationalIntegration +--R +--E 1350 + +--S 1351 of 3320 +)d op infieldIntegrate +--R +--R +--RThere is one exposed function called infieldIntegrate : +--R [1] (Fraction(Polynomial(D3)),Symbol) -> Union(Fraction(Polynomial( +--R D3)),"failed") +--R from RationalFunctionIntegration(D3) +--R if D3 has Join(IntegralDomain,RetractableTo(Integer), +--R CharacteristicZero) +--R +--RExamples of infieldIntegrate from RationalFunctionIntegration +--R +--E 1351 + +--S 1352 of 3320 +)d op infinite? +--R +--R +--RThere are 2 exposed functions called infinite? : +--R [1] OnePointCompletion(D2) -> Boolean from OnePointCompletion(D2) +--R if D2 has SETCAT +--R [2] OrderedCompletion(D2) -> Boolean from OrderedCompletion(D2) if +--R D2 has SETCAT +--R +--RExamples of infinite? from OnePointCompletion +--R +--R +--RExamples of infinite? from OrderedCompletion +--R +--E 1352 + +--S 1353 of 3320 +)d op infiniteProduct +--R +--R +--RThere are 3 exposed functions called infiniteProduct : +--R [1] D1 -> D1 from InfiniteProductCharacteristicZero(D2,D1) +--R if D2 has Join(IntegralDomain,CharacteristicZero) and D1 +--R has UTSCAT(D2) +--R [2] D1 -> D1 from InfiniteProductFiniteField(D2,D3,D4,D1) +--R if D2 has Join(Field,Finite,ConvertibleTo(Integer)) and D3 +--R has UPOLYC(D2) and D4 has MONOGEN(D2,D3) and D1 has UTSCAT +--R (D4) +--R [3] D1 -> D1 from InfiniteProductPrimeField(D2,D1) +--R if D2 has Join(Field,Finite,ConvertibleTo(Integer)) and D1 +--R has UTSCAT(D2) +--R +--RThere is one unexposed function called infiniteProduct : +--R [1] Stream(D2) -> Stream(D2) from StreamInfiniteProduct(D2) +--R if D2 has Join(IntegralDomain,CharacteristicZero) +--R +--RExamples of infiniteProduct from InfiniteProductCharacteristicZero +--R +--R +--RExamples of infiniteProduct from InfiniteProductFiniteField +--R +--R +--RExamples of infiniteProduct from InfiniteProductPrimeField +--R +--R +--RExamples of infiniteProduct from StreamInfiniteProduct +--R +--E 1353 + +--S 1354 of 3320 +)d op infinity +--R +--R +--RThere are 2 exposed functions called infinity : +--R [1] -> OnePointCompletion(Integer) from Infinity +--R [2] -> OnePointCompletion(D1) from OnePointCompletion(D1) if D1 +--R has SETCAT +--R +--RExamples of infinity from Infinity +--R +--R +--RExamples of infinity from OnePointCompletion +--R +--E 1354 + +--S 1355 of 3320 +)d op infinityNorm +--R +--R +--RThere is one unexposed function called infinityNorm : +--R [1] D2 -> D1 from GaloisGroupFactorizationUtilities(D3,D2,D1) +--R if D3 has RING and D1 has Join(FloatingPointSystem, +--R RetractableTo(D3),Field,TranscendentalFunctionCategory, +--R ElementaryFunctionCategory) and D2 has UPOLYC(D3) +--R +--RExamples of infinityNorm from GaloisGroupFactorizationUtilities +--R +--E 1355 + +--S 1356 of 3320 +)d op infix +--R +--R +--RThere are 2 unexposed functions called infix : +--R [1] (OutputForm,OutputForm,OutputForm) -> OutputForm from OutputForm +--R +--R [2] (OutputForm,List(OutputForm)) -> OutputForm from OutputForm +--R +--RExamples of infix from OutputForm +--R +--E 1356 + +--S 1357 of 3320 +)d op infix? +--R +--R +--RThere is one unexposed function called infix? : +--R [1] OutputForm -> Boolean from OutputForm +--R +--RExamples of infix? from OutputForm +--R +--E 1357 + +--S 1358 of 3320 +)d op infLex? +--R +--R +--RThere is one unexposed function called infLex? : +--R [1] (SplittingNode(D4,D5),SplittingNode(D4,D5),((D4,D4) -> Boolean), +--R ((D5,D5) -> Boolean)) -> Boolean +--R from SplittingNode(D4,D5) +--R if D4 has Join(SetCategory,Aggregate) and D5 has Join( +--R SetCategory,Aggregate) +--R +--RExamples of infLex? from SplittingNode +--R +--E 1358 + +--S 1359 of 3320 +)d op infRittWu? +--R +--R +--RThere are 4 exposed functions called infRittWu? : +--R [1] (List(D6),List(D6)) -> Boolean from QuasiComponentPackage(D3,D4, +--R D5,D6,D7) +--R if D6 has RPOLCAT(D3,D4,D5) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET and D7 has RSETCAT(D3,D4,D5,D6) +--R +--R [2] (D,D) -> Boolean from D +--R if D has RPOLCAT(D2,D3,D4) and D2 has RING and D3 has +--R OAMONS and D4 has ORDSET +--R [3] (List(D6),List(D6)) -> Boolean +--R from SquareFreeQuasiComponentPackage(D3,D4,D5,D6,D7) +--R if D6 has RPOLCAT(D3,D4,D5) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET and D7 has RSETCAT(D3,D4,D5,D6) +--R +--R [4] (D,D) -> Boolean from D +--R if D has TSETCAT(D2,D3,D4,D5) and D2 has INTDOM and D3 +--R has OAMONS and D4 has ORDSET and D5 has RPOLCAT(D2,D3,D4) +--R +--R +--RExamples of infRittWu? from QuasiComponentPackage +--R +--R +--RExamples of infRittWu? from RecursivePolynomialCategory +--R +--R +--RExamples of infRittWu? from SquareFreeQuasiComponentPackage +--R +--R +--RExamples of infRittWu? from TriangularSetCategory +--R +--E 1359 + +--S 1360 of 3320 +)d op infRittWu? +--R +--R +--RThere are 4 exposed functions called infRittWu? : +--R [1] (List(D6),List(D6)) -> Boolean from QuasiComponentPackage(D3,D4, +--R D5,D6,D7) +--R if D6 has RPOLCAT(D3,D4,D5) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET and D7 has RSETCAT(D3,D4,D5,D6) +--R +--R [2] (D,D) -> Boolean from D +--R if D has RPOLCAT(D2,D3,D4) and D2 has RING and D3 has +--R OAMONS and D4 has ORDSET +--R [3] (List(D6),List(D6)) -> Boolean +--R from SquareFreeQuasiComponentPackage(D3,D4,D5,D6,D7) +--R if D6 has RPOLCAT(D3,D4,D5) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET and D7 has RSETCAT(D3,D4,D5,D6) +--R +--R [4] (D,D) -> Boolean from D +--R if D has TSETCAT(D2,D3,D4,D5) and D2 has INTDOM and D3 +--R has OAMONS and D4 has ORDSET and D5 has RPOLCAT(D2,D3,D4) +--R +--R +--RExamples of infRittWu? from QuasiComponentPackage +--R +--R +--RExamples of infRittWu? from RecursivePolynomialCategory +--R +--R +--RExamples of infRittWu? from SquareFreeQuasiComponentPackage +--R +--R +--RExamples of infRittWu? from TriangularSetCategory +--R +--E 1360 + +--S 1361 of 3320 +)d op inGroundField? +--R +--R +--RThere is one exposed function called inGroundField? : +--R [1] D -> Boolean from D if D has XF(D2) and D2 has FIELD +--R +--RExamples of inGroundField? from ExtensionField +--R +--E 1361 + +--S 1362 of 3320 +)d op inHallBasis? +--R +--R +--RThere is one exposed function called inHallBasis? : +--R [1] (Integer,Integer,Integer,Integer) -> Boolean from HallBasis +--R +--RExamples of inHallBasis? from HallBasis +--R +--E 1362 + +--S 1363 of 3320 +)d op init +--R +--R +--RThere are 2 exposed functions called init : +--R [1] D -> D from D +--R if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has +--R OAMONS and D3 has ORDSET +--R [2] -> D from D if D has STEP +--R +--RExamples of init from RecursivePolynomialCategory +--R +--R +--RExamples of init from StepThrough +--R +--E 1363 + +--S 1364 of 3320 +)d op initial +--R +--R +--RThere is one exposed function called initial : +--R [1] D -> D from D +--R if D has DPOLCAT(D1,D2,D3,D4) and D1 has RING and D2 has +--R ORDSET and D3 has DVARCAT(D2) and D4 has OAMONS +--R +--RExamples of initial from DifferentialPolynomialCategory +--R +--E 1364 + +--S 1365 of 3320 +)d op initializeGroupForWordProblem +--R +--R +--RThere are 2 exposed functions called initializeGroupForWordProblem : +--R [1] (PermutationGroup(D3),Integer,Integer) -> Void from +--R PermutationGroup(D3) +--R if D3 has SETCAT +--R [2] PermutationGroup(D2) -> Void from PermutationGroup(D2) if D2 +--R has SETCAT +--R +--RExamples of initializeGroupForWordProblem from PermutationGroup +--R +--E 1365 + +--S 1366 of 3320 +)d op initializeParamOfPlaces +--R +--R +--RThere are 2 exposed functions called initializeParamOfPlaces : +--R [1] D6 -> Void from DesingTreePackage(D7,D8,D9,D10,D11,D12,D1,D2,D3, +--R D6,D4) +--R if D7 has FIELD and D8: LIST(SYMBOL) and D9 has POLYCAT(D7 +--R ,D10,OVAR(D8)) and D10 has DIRPCAT(#(D8),NNI) and D11 has +--R PRSPCAT(D7) and D12 has LOCPOWC(D7) and D1 has PLACESC(D7, +--R D12) and D2 has DIVCAT(D1) and D3 has INFCLCT(D7,D8,D9,D10, +--R D11,D12,D1,D2,D4) and D4 has BLMETCT and D6 has DSTRCAT(D3) +--R +--R [2] (D7,List(D11)) -> Void +--R from DesingTreePackage(D9,D10,D11,D12,D13,D1,D2,D3,D4,D7, +--R D5) +--R if D11 has POLYCAT(D9,D12,OVAR(D10)) and D12 has DIRPCAT(# +--R (D10),NNI) and D9 has FIELD and D10: LIST(SYMBOL) and D13 +--R has PRSPCAT(D9) and D1 has LOCPOWC(D9) and D2 has PLACESC( +--R D9,D1) and D3 has DIVCAT(D2) and D4 has INFCLCT(D9,D10,D11, +--R D12,D13,D1,D2,D3,D5) and D5 has BLMETCT and D7 has DSTRCAT( +--R D4) +--R +--RExamples of initializeParamOfPlaces from DesingTreePackage +--R +--E 1366 + +--S 1367 of 3320 +)d op initiallyReduce +--R +--R +--RThere are 2 exposed functions called initiallyReduce : +--R [1] (D,D) -> D from D +--R if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has +--R OAMONS and D3 has ORDSET +--R [2] (D1,D) -> D1 from D +--R if D has TSETCAT(D2,D3,D4,D1) and D2 has INTDOM and D3 +--R has OAMONS and D4 has ORDSET and D1 has RPOLCAT(D2,D3,D4) +--R +--R +--RExamples of initiallyReduce from RecursivePolynomialCategory +--R +--R +--RExamples of initiallyReduce from TriangularSetCategory +--R +--E 1367 + +--S 1368 of 3320 +)d op initiallyReduced? +--R +--R +--RThere are 4 exposed functions called initiallyReduced? : +--R [1] (D,List(D)) -> Boolean from D +--R if D has RPOLCAT(D3,D4,D5) and D3 has RING and D4 has +--R OAMONS and D5 has ORDSET +--R [2] (D,D) -> Boolean from D +--R if D has RPOLCAT(D2,D3,D4) and D2 has RING and D3 has +--R OAMONS and D4 has ORDSET +--R [3] D -> Boolean from D +--R if D has TSETCAT(D2,D3,D4,D5) and D2 has INTDOM and D3 +--R has OAMONS and D4 has ORDSET and D5 has RPOLCAT(D2,D3,D4) +--R +--R [4] (D2,D) -> Boolean from D +--R if D has TSETCAT(D3,D4,D5,D2) and D3 has INTDOM and D4 +--R has OAMONS and D5 has ORDSET and D2 has RPOLCAT(D3,D4,D5) +--R +--R +--RExamples of initiallyReduced? from RecursivePolynomialCategory +--R +--R +--RExamples of initiallyReduced? from TriangularSetCategory +--R +--E 1368 + +--S 1369 of 3320 +)d op initiallyReduced? +--R +--R +--RThere are 4 exposed functions called initiallyReduced? : +--R [1] (D,List(D)) -> Boolean from D +--R if D has RPOLCAT(D3,D4,D5) and D3 has RING and D4 has +--R OAMONS and D5 has ORDSET +--R [2] (D,D) -> Boolean from D +--R if D has RPOLCAT(D2,D3,D4) and D2 has RING and D3 has +--R OAMONS and D4 has ORDSET +--R [3] D -> Boolean from D +--R if D has TSETCAT(D2,D3,D4,D5) and D2 has INTDOM and D3 +--R has OAMONS and D4 has ORDSET and D5 has RPOLCAT(D2,D3,D4) +--R +--R [4] (D2,D) -> Boolean from D +--R if D has TSETCAT(D3,D4,D5,D2) and D3 has INTDOM and D4 +--R has OAMONS and D5 has ORDSET and D2 has RPOLCAT(D3,D4,D5) +--R +--R +--RExamples of initiallyReduced? from RecursivePolynomialCategory +--R +--R +--RExamples of initiallyReduced? from TriangularSetCategory +--R +--E 1369 + +--S 1370 of 3320 +)d op initials +--R +--R +--RThere is one exposed function called initials : +--R [1] D -> List(D5) from D +--R if D has TSETCAT(D2,D3,D4,D5) and D2 has INTDOM and D3 +--R has OAMONS and D4 has ORDSET and D5 has RPOLCAT(D2,D3,D4) +--R +--R +--RExamples of initials from TriangularSetCategory +--R +--E 1370 + +--S 1371 of 3320 +)d op initParLocLeaves +--R +--R +--RThere is one exposed function called initParLocLeaves : +--R [1] D6 -> Void from DesingTreePackage(D7,D8,D9,D10,D11,D12,D1,D2,D3, +--R D6,D4) +--R if D7 has FIELD and D8: LIST(SYMBOL) and D9 has POLYCAT(D7 +--R ,D10,OVAR(D8)) and D10 has DIRPCAT(#(D8),NNI) and D11 has +--R PRSPCAT(D7) and D12 has LOCPOWC(D7) and D1 has PLACESC(D7, +--R D12) and D2 has DIVCAT(D1) and D3 has INFCLCT(D7,D8,D9,D10, +--R D11,D12,D1,D2,D4) and D4 has BLMETCT and D6 has DSTRCAT(D3) +--R +--R +--RExamples of initParLocLeaves from DesingTreePackage +--R +--E 1371 + +--S 1372 of 3320 +)d op initTable! +--R +--R +--RThere is one unexposed function called initTable! : +--R [1] -> Void from TabulatedComputationPackage(D2,D3) +--R if D2 has SETCAT and D3 has SETCAT +--R +--RExamples of initTable! from TabulatedComputationPackage +--R +--E 1372 + +--S 1373 of 3320 +)d op innerint +--R +--R +--RThere is one exposed function called innerint : +--R [1] (D2,Symbol,OrderedCompletion(D2),OrderedCompletion(D2),Boolean) +--R -> Union(f1: OrderedCompletion(D2),f2: List(OrderedCompletion(D2 +--R )),fail: failed,pole: potentialPole) +--R from ElementaryFunctionDefiniteIntegration(D6,D2) +--R if D6 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) and D2 has Join( +--R TranscendentalFunctionCategory,PrimitiveFunctionCategory, +--R AlgebraicallyClosedFunctionSpace(D6)) +--R +--RExamples of innerint from ElementaryFunctionDefiniteIntegration +--R +--E 1373 + +--S 1374 of 3320 +)d op input +--R +--R +--RThere are 2 exposed functions called input : +--R [1] BasicOperator -> Union((List(InputForm) -> InputForm),"failed") +--R from BasicOperator +--R [2] (BasicOperator,(List(InputForm) -> InputForm)) -> BasicOperator +--R from BasicOperator +--R +--RExamples of input from BasicOperator +--R +--E 1374 + +--S 1375 of 3320 +)d op inR? +--R +--R +--RThere is one unexposed function called inR? : +--R [1] Pattern(D2) -> Boolean from Pattern(D2) if D2 has SETCAT +--R +--RExamples of inR? from Pattern +--R +--E 1375 + +--S 1376 of 3320 +)d op inRadical? +--R +--R +--RThere is one exposed function called inRadical? : +--R [1] (D2,PolynomialIdeals(D3,D4,D5,D2)) -> Boolean +--R from PolynomialIdeals(D3,D4,D5,D2) +--R if D3 has FIELD and D4 has OAMONS and D5 has ORDSET and D2 +--R has POLYCAT(D3,D4,D5) +--R +--RExamples of inRadical? from PolynomialIdeals +--R +--E 1376 + +--S 1377 of 3320 +)d op inrootof +--R +--R +--RThere is one unexposed function called inrootof : +--R [1] (SparseUnivariatePolynomial(D1),D1) -> D1 from AlgebraicFunction +--R (D3,D1) +--R if D1 has FS(D3) and D3 has Join(OrderedSet,IntegralDomain +--R ) +--R +--RExamples of inrootof from AlgebraicFunction +--R +--E 1377 + +--S 1378 of 3320 +)d op insert +--R +--R +--RThere are 2 exposed functions called insert : +--R [1] (D,D,Integer) -> D from D if D has LNAGG(D2) and D2 has TYPE +--R [2] (D1,D,Integer) -> D from D if D has LNAGG(D1) and D1 has TYPE +--R +--R +--RExamples of insert from LinearAggregate +--R +--E 1378 + +--S 1379 of 3320 +)d op insert! +--R +--R +--RThere are 13 exposed functions called insert! : +--R [1] (D1,ArrayStack(D1)) -> ArrayStack(D1) from ArrayStack(D1) if D1 +--R has SETCAT +--R [2] (D1,D) -> D from D if D has BGAGG(D1) and D1 has TYPE +--R [3] (D1,BinarySearchTree(D1)) -> BinarySearchTree(D1) +--R from BinarySearchTree(D1) if D1 has ORDSET +--R [4] (D1,BinaryTournament(D1)) -> BinaryTournament(D1) +--R from BinaryTournament(D1) if D1 has ORDSET +--R [5] (D1,Dequeue(D1)) -> Dequeue(D1) from Dequeue(D1) if D1 has +--R SETCAT +--R [6] (D,D,Integer) -> D from D if D has ELAGG(D2) and D2 has TYPE +--R [7] (D1,D,Integer) -> D from D if D has ELAGG(D1) and D1 has TYPE +--R +--R [8] (D1,Heap(D1)) -> Heap(D1) from Heap(D1) if D1 has ORDSET +--R [9] Record(key: Record(var: Symbol,fn: Expression(DoubleFloat),range +--R : Segment(OrderedCompletion(DoubleFloat)),abserr: DoubleFloat, +--R relerr: DoubleFloat),entry: Record(endPointContinuity: Union( +--R continuous: Continuous at the end points,lowerSingular: +--R There is a singularity at the lower end point,upperSingular: +--R There is a singularity at the upper end point,bothSingular: +--R There are singularities at both end points,notEvaluated: +--R End point continuity not yet evaluated),singularitiesStream: +--R Union(str: Stream(DoubleFloat),notEvaluated: +--R Internal singularities not yet evaluated),range: Union(finite: +--R The range is finite,lowerInfinite: +--R The bottom of range is infinite,upperInfinite: +--R The top of range is infinite,bothInfinite: +--R Both top and bottom points are infinite,notEvaluated: +--R Range not yet evaluated))) -> IntegrationFunctionsTable +--R from IntegrationFunctionsTable +--R [10] (D1,D,NonNegativeInteger) -> D from D if D has MDAGG(D1) and D1 +--R has SETCAT +--R [11] Record(key: Record(xinit: DoubleFloat,xend: DoubleFloat,fn: +--R Vector(Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals +--R : List(DoubleFloat),g: Expression(DoubleFloat),abserr: +--R DoubleFloat,relerr: DoubleFloat),entry: Record(stiffness: Float, +--R stability: Float,expense: Float,accuracy: Float, +--R intermediateResults: Float)) -> ODEIntensityFunctionsTable +--R from ODEIntensityFunctionsTable +--R [12] (D1,Queue(D1)) -> Queue(D1) from Queue(D1) if D1 has SETCAT +--R [13] (D1,Stack(D1)) -> Stack(D1) from Stack(D1) if D1 has SETCAT +--R +--RThere is one unexposed function called insert! : +--R [1] (D2,D3) -> Void from TabulatedComputationPackage(D2,D3) +--R if D2 has SETCAT and D3 has SETCAT +--R +--RExamples of insert! from ArrayStack +--R +--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] +--Rinsert!(8,a) +--Ra +--R +--R +--RExamples of insert! from BagAggregate +--R +--R +--RExamples of insert! from BinarySearchTree +--R +--Rt1:=binarySearchTree [1,2,3,4] +--Rinsert!(5,t1) +--R +--R +--RExamples of insert! from BinaryTournament +--R +--Rt1:=binaryTournament [1,2,3,4] +--Rinsert!(5,t1) +--Rt1 +--R +--R +--RExamples of insert! from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rinsert! (8,a) +--Ra +--R +--R +--RExamples of insert! from ExtensibleLinearAggregate +--R +--R +--RExamples of insert! from Heap +--R +--Ra:Heap INT:= heap [1,2,3,4,5] +--Rinsert!(8,a) +--Ra +--R +--R +--RExamples of insert! from IntegrationFunctionsTable +--R +--R +--RExamples of insert! from MultiDictionary +--R +--R +--RExamples of insert! from ODEIntensityFunctionsTable +--R +--R +--RExamples of insert! from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Rinsert! (8,a) +--Ra +--R +--R +--RExamples of insert! from Stack +--R +--Ra:Stack INT:= stack [1,2,3,4,5] +--Rinsert!(8,a) +--Ra +--R +--R +--RExamples of insert! from TabulatedComputationPackage +--R +--E 1379 + +--S 1380 of 3320 +)d op insertBottom! +--R +--R +--RThere are 2 exposed functions called insertBottom! : +--R [1] (D1,Dequeue(D1)) -> D1 from Dequeue(D1) if D1 has SETCAT +--R [2] (D1,D) -> D1 from D if D has DQAGG(D1) and D1 has TYPE +--R +--RExamples of insertBottom! from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--RinsertBottom! a +--Ra +--R +--R +--RExamples of insertBottom! from DequeueAggregate +--R +--E 1380 + +--S 1381 of 3320 +)d op insertionSort! +--R +--R +--RThere are 2 unexposed functions called insertionSort! : +--R [1] (D1,((D3,D3) -> Boolean)) -> D1 from SortPackage(D3,D1) +--R if D3 has TYPE and D1 has IndexedAggregate(Integer,D3)with +--R finiteAggregate +--R shallowlyMutable +--R [2] D1 -> D1 from SortPackage(D2,D1) +--R if D2 has ORDSET and D2 has TYPE and D1 has +--R IndexedAggregate(Integer,D2)with +--R finiteAggregate +--R shallowlyMutable +--R +--RExamples of insertionSort! from SortPackage +--R +--E 1381 + +--S 1382 of 3320 +)d op insertMatch +--R +--R +--RThere is one unexposed function called insertMatch : +--R [1] (Pattern(D3),D2,PatternMatchResult(D3,D2)) -> PatternMatchResult +--R (D3,D2) +--R from PatternMatchResult(D3,D2) if D3 has SETCAT and D2 +--R has SETCAT +--R +--RExamples of insertMatch from PatternMatchResult +--R +--E 1382 + +--S 1383 of 3320 done +)d op insertRoot! +--R +--R +--RThere is one exposed function called insertRoot! : +--R [1] (D1,BinarySearchTree(D1)) -> BinarySearchTree(D1) +--R from BinarySearchTree(D1) if D1 has ORDSET +--R +--RExamples of insertRoot! from BinarySearchTree +--R +--Rt1:=binarySearchTree [1,2,3,4] +--RinsertRoot!(5,t1) +--R +--E 1383 + +--S 1384 of 3320 +)d op insertTop! +--R +--R +--RThere are 2 exposed functions called insertTop! : +--R [1] (D1,Dequeue(D1)) -> D1 from Dequeue(D1) if D1 has SETCAT +--R [2] (D1,D) -> D1 from D if D has DQAGG(D1) and D1 has TYPE +--R +--RExamples of insertTop! from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--RinsertTop! a +--Ra +--R +--R +--RExamples of insertTop! from DequeueAggregate +--R +--E 1384 + +--S 1385 of 3320 +)d op inspect +--R +--R +--RThere are 6 exposed functions called inspect : +--R [1] ArrayStack(D1) -> D1 from ArrayStack(D1) if D1 has SETCAT +--R [2] D -> D1 from D if D has BGAGG(D1) and D1 has TYPE +--R [3] Dequeue(D1) -> D1 from Dequeue(D1) if D1 has SETCAT +--R [4] Heap(D1) -> D1 from Heap(D1) if D1 has ORDSET +--R [5] Queue(D1) -> D1 from Queue(D1) if D1 has SETCAT +--R [6] Stack(D1) -> D1 from Stack(D1) if D1 has SETCAT +--R +--RExamples of inspect from ArrayStack +--R +--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] +--Rinspect a +--R +--R +--RExamples of inspect from BagAggregate +--R +--R +--RExamples of inspect from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rinspect a +--R +--R +--RExamples of inspect from Heap +--R +--Ra:Heap INT:= heap [1,2,3,4,5] +--Rinspect a +--R +--R +--RExamples of inspect from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Rinspect a +--R +--R +--RExamples of inspect from Stack +--R +--Ra:Stack INT:= stack [1,2,3,4,5] +--Rinspect a +--R +--E 1385 + +--S 1386 of 3320 +)d op int +--R +--R +--RThere are 5 unexposed functions called int : +--R [1] (D1,Symbol) -> D1 from ODEIntegration(D3,D1) +--R if D3 has Join(OrderedSet,EuclideanDomain,RetractableTo( +--R Integer),LinearlyExplicitRingOver(Integer), +--R CharacteristicZero) and D1 has Join( +--R AlgebraicallyClosedFunctionSpace(D3), +--R TranscendentalFunctionCategory,PrimitiveFunctionCategory) +--R +--R [2] (OutputForm,OutputForm,OutputForm) -> OutputForm from OutputForm +--R +--R [3] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R [4] OutputForm -> OutputForm from OutputForm +--R [5] D2 -> Stream(D2) from StreamTaylorSeriesOperations(D2) if D2 +--R has RING +--R +--RExamples of int from ODEIntegration +--R +--R +--RExamples of int from OutputForm +--R +--R +--RExamples of int from StreamTaylorSeriesOperations +--R +--E 1386 + +--S 1387 of 3320 +)d op intChoose +--R +--R +--RThere is one unexposed function called intChoose : +--R [1] (SparseUnivariatePolynomial(D8),List(D6),List(List(D7))) -> +--R Record(upol: SparseUnivariatePolynomial(D7),Lval: List(D7),Lfact +--R : List(Record(factor: SparseUnivariatePolynomial(D7),exponent: +--R Integer)),ctpol: D7) +--R from MultivariateSquareFree(D5,D6,D7,D8) +--R if D6 has ORDSET and D7 has EUCDOM and D8 has POLYCAT(D7, +--R D5,D6) and D5 has OAMONS +--R +--RExamples of intChoose from MultivariateSquareFree +--R +--E 1387 + +--S 1388 of 3320 +)d op intcompBasis +--R +--R +--RThere is one unexposed function called intcompBasis : +--R [1] (OrderedVariableList(D3),List( +--R HomogeneousDistributedMultivariatePolynomial(D3,D4)),List( +--R HomogeneousDistributedMultivariatePolynomial(D3,D4))) -> List( +--R HomogeneousDistributedMultivariatePolynomial(D3,D4)) +--R from LinGroebnerPackage(D3,D4) if D3: LIST(SYMBOL) and D4 +--R has GCDDOM +--R +--RExamples of intcompBasis from LinGroebnerPackage +--R +--E 1388 + +--S 1389 of 3320 +)d op integer +--R +--R +--RThere are 2 exposed functions called integer : +--R [1] D2 -> Integer from IntegerRetractions(D2) if D2 has RETRACT(INT) +--R +--R [2] D -> D1 from D +--R if D has SEXCAT(D2,D3,D1,D4,D5) and D2 has SETCAT and D3 +--R has SETCAT and D4 has SETCAT and D5 has SETCAT and D1 has +--R SETCAT +--R +--RExamples of integer from IntegerRetractions +--R +--R +--RExamples of integer from SExpressionCategory +--R +--E 1389 + +--S 1390 of 3320 +)d op integer? +--R +--R +--RThere are 3 exposed functions called integer? : +--R [1] FortranScalarType -> Boolean from FortranScalarType +--R [2] D2 -> Boolean from IntegerRetractions(D2) if D2 has RETRACT(INT) +--R +--R [3] D -> Boolean from D +--R if D has SEXCAT(D2,D3,D4,D5,D6) and D2 has SETCAT and D3 +--R has SETCAT and D4 has SETCAT and D5 has SETCAT and D6 has +--R SETCAT +--R +--RExamples of integer? from FortranScalarType +--R +--R +--RExamples of integer? from IntegerRetractions +--R +--R +--RExamples of integer? from SExpressionCategory +--R +--E 1390 + +--S 1391 of 3320 +)d op integers +--R +--R +--RThere is one unexposed function called integers : +--R [1] Integer -> Stream(Integer) from StreamTaylorSeriesOperations(D3) +--R if D3 has RING +--R +--RExamples of integers from StreamTaylorSeriesOperations +--R +--E 1391 + +--S 1392 of 3320 +)d op integral +--R +--R +--RThere are 2 exposed functions called integral : +--R [1] (D,Symbol) -> D from D if D has PRIMCAT +--R [2] (D,SegmentBinding(D)) -> D from D if D has PRIMCAT +--R +--RThere are 4 unexposed functions called integral : +--R [1] (D1,Symbol) -> IntegrationResult(D1) from IntegrationResult(D1) +--R if D1 has RETRACT(SYMBOL) and D1 has FIELD +--R [2] (D1,D1) -> IntegrationResult(D1) from IntegrationResult(D1) if +--R D1 has FIELD +--R [3] (D1,Symbol) -> D1 from LiouvillianFunction(D3,D1) +--R if D3 has Join(OrderedSet,IntegralDomain) and D1 has Join( +--R FunctionSpace(D3),RadicalCategory, +--R TranscendentalFunctionCategory) +--R [4] (D1,SegmentBinding(D1)) -> D1 from LiouvillianFunction(D3,D1) +--R if D1 has Join(FunctionSpace(D3),RadicalCategory, +--R TranscendentalFunctionCategory) and D3 has Join(OrderedSet, +--R IntegralDomain) +--R +--RExamples of integral from IntegrationResult +--R +--R +--RExamples of integral from LiouvillianFunction +--R +--R +--RExamples of integral from PrimitiveFunctionCategory +--R +--E 1392 + +--S 1393 of 3320 +)d op integral? +--R +--R +--RThere are 3 exposed functions called integral? : +--R [1] (D,D2) -> Boolean from D +--R if D has FFCAT(D3,D2,D4) and D3 has UFD and D2 has UPOLYC( +--R D3) and D4 has UPOLYC(FRAC(D2)) +--R [2] (D,D2) -> Boolean from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC( +--R D2) and D4 has UPOLYC(FRAC(D3)) +--R [3] D -> Boolean from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC( +--R D2) and D4 has UPOLYC(FRAC(D3)) +--R +--RExamples of integral? from FunctionFieldCategory +--R +--E 1393 + +--S 1394 of 3320 +)d op integralAtInfinity? +--R +--R +--RThere is one exposed function called integralAtInfinity? : +--R [1] D -> Boolean from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC( +--R D2) and D4 has UPOLYC(FRAC(D3)) +--R +--RExamples of integralAtInfinity? from FunctionFieldCategory +--R +--E 1394 + +--S 1395 of 3320 +)d op integralBasis +--R +--R +--RThere is one exposed function called integralBasis : +--R [1] -> Vector(D) from D +--R if D2 has UFD and D3 has UPOLYC(D2) and D4 has UPOLYC(FRAC +--R (D3)) and D has FFCAT(D2,D3,D4) +--R +--RThere are 4 unexposed functions called integralBasis : +--R [1] -> Record(basis: Matrix(D2),basisDen: D2,basisInv: Matrix(D2)) +--R from FunctionFieldIntegralBasis(D2,D3,D4) +--R if D2 has EuclideanDomainwith +--R squareFree : % -> Factored(%)and D3 has UPOLYC(D2) +--R and D4 has FRAMALG(D2,D3) +--R [2] -> Record(basis: Matrix(Integer),basisDen: Integer,basisInv: +--R Matrix(Integer)) +--R from NumberFieldIntegralBasis(D2,D3) +--R if D2 has UPOLYC(INT) and D3 has FRAMALG(INT,D2) +--R [3] -> Record(basis: Matrix(D3),basisDen: D3,basisInv: Matrix(D3)) +--R from PAdicWildFunctionFieldIntegralBasis(D2,D3,D4,D5) +--R if D2 has FFIELDC and D3 has UPOLYC(D2) and D4 has UPOLYC( +--R D3) and D5 has MONOGEN(D3,D4) +--R [4] -> Record(basis: Matrix(D3),basisDen: D3,basisInv: Matrix(D3)) +--R from WildFunctionFieldIntegralBasis(D2,D3,D4,D5) +--R if D2 has FFIELDC and D3 has UPOLYC(D2) and D4 has UPOLYC( +--R D3) and D5 has FRAMALG(D3,D4) +--R +--RExamples of integralBasis from FunctionFieldCategory +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) +--RintegralBasis()$R +--R +--R +--RExamples of integralBasis from FunctionFieldIntegralBasis +--R +--R +--RExamples of integralBasis from NumberFieldIntegralBasis +--R +--R +--RExamples of integralBasis from PAdicWildFunctionFieldIntegralBasis +--R +--R +--RExamples of integralBasis from WildFunctionFieldIntegralBasis +--R +--E 1395 + +--S 1396 of 3320 done +)d op integralBasisAtInfinity +--R +--R +--RThere is one exposed function called integralBasisAtInfinity : +--R [1] -> Vector(D) from D +--R if D2 has UFD and D3 has UPOLYC(D2) and D4 has UPOLYC(FRAC +--R (D3)) and D has FFCAT(D2,D3,D4) +--R +--RExamples of integralBasisAtInfinity from FunctionFieldCategory +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) +--RintegralBasisAtInfinity()$R +--R +--E 1396 + +--S 1397 of 3320 +)d op integralCoordinates +--R +--R +--RThere is one exposed function called integralCoordinates : +--R [1] D -> Record(num: Vector(D3),den: D3) from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC( +--R D2) and D4 has UPOLYC(FRAC(D3)) +--R +--RExamples of integralCoordinates from FunctionFieldCategory +--R +--E 1397 + +--S 1398 of 3320 +)d op integralDerivationMatrix +--R +--R +--RThere is one exposed function called integralDerivationMatrix : +--R [1] (D4 -> D4) -> Record(num: Matrix(D4),den: D4) from D +--R if D has FFCAT(D3,D4,D5) and D3 has UFD and D4 has UPOLYC( +--R D3) and D5 has UPOLYC(FRAC(D4)) +--R +--RExamples of integralDerivationMatrix from FunctionFieldCategory +--R +--E 1398 + +--S 1399 of 3320 +)d op integralLastSubResultant +--R +--R +--RThere is one exposed function called integralLastSubResultant : +--R [1] (D2,D2,D3) -> List(Record(val: D2,tower: D3)) +--R from RegularTriangularSetGcdPackage(D4,D5,D6,D2,D3) +--R if D4 has GCDDOM and D5 has OAMONS and D6 has ORDSET and +--R D2 has RPOLCAT(D4,D5,D6) and D3 has RSETCAT(D4,D5,D6,D2) +--R +--R +--RExamples of integralLastSubResultant from RegularTriangularSetGcdPackage +--R +--E 1399 + +--S 1400 of 3320 done +)d op integralMatrix +--R +--R +--RThere is one exposed function called integralMatrix : +--R [1] -> Matrix(Fraction(D3)) from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC( +--R D2) and D4 has UPOLYC(FRAC(D3)) +--R +--RExamples of integralMatrix from FunctionFieldCategory +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) +--RintegralMatrix()$R +--R +--E 1400 + +--S 1401 of 3320 done +)d op integralMatrixAtInfinity +--R +--R +--RThere is one exposed function called integralMatrixAtInfinity : +--R [1] -> Matrix(Fraction(D3)) from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC( +--R D2) and D4 has UPOLYC(FRAC(D3)) +--R +--RExamples of integralMatrixAtInfinity from FunctionFieldCategory +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) +--RintegralMatrixAtInfinity()$R +--R +--E 1401 + +--S 1402 of 3320 +)d op integralRepresents +--R +--R +--RThere is one exposed function called integralRepresents : +--R [1] (Vector(D2),D2) -> D from D +--R if D2 has UPOLYC(D3) and D3 has UFD and D has FFCAT(D3,D2, +--R D4) and D4 has UPOLYC(FRAC(D2)) +--R +--RExamples of integralRepresents from FunctionFieldCategory +--R +--E 1402 + +--S 1403 of 3320 +)d op integrate +--R +--R +--RThere are 32 exposed functions called integrate : +--R [1] (D2,SegmentBinding(OrderedCompletion(D2))) -> Union(f1: +--R OrderedCompletion(D2),f2: List(OrderedCompletion(D2)),fail: +--R failed,pole: potentialPole) +--R from ElementaryFunctionDefiniteIntegration(D4,D2) +--R if D2 has Join(TranscendentalFunctionCategory, +--R PrimitiveFunctionCategory,AlgebraicallyClosedFunctionSpace( +--R D4)) and D4 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R [2] (D2,SegmentBinding(OrderedCompletion(D2)),String) -> Union(f1: +--R OrderedCompletion(D2),f2: List(OrderedCompletion(D2)),fail: +--R failed,pole: potentialPole) +--R from ElementaryFunctionDefiniteIntegration(D5,D2) +--R if D2 has Join(TranscendentalFunctionCategory, +--R PrimitiveFunctionCategory,AlgebraicallyClosedFunctionSpace( +--R D5)) and D5 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R [3] (Fraction(Polynomial(D4)),SegmentBinding(OrderedCompletion( +--R Expression(D4)))) -> Union(f1: OrderedCompletion(Expression(D4)), +--R f2: List(OrderedCompletion(Expression(D4))),fail: failed,pole: +--R potentialPole) +--R from RationalFunctionDefiniteIntegration(D4) +--R if D4 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R [4] (Fraction(Polynomial(D5)),SegmentBinding(OrderedCompletion( +--R Expression(D5))),String) -> Union(f1: OrderedCompletion( +--R Expression(D5)),f2: List(OrderedCompletion(Expression(D5))),fail +--R : failed,pole: potentialPole) +--R from RationalFunctionDefiniteIntegration(D5) +--R if D5 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R [5] (Fraction(Polynomial(D4)),SegmentBinding(OrderedCompletion( +--R Fraction(Polynomial(D4))))) -> Union(f1: OrderedCompletion( +--R Expression(D4)),f2: List(OrderedCompletion(Expression(D4))),fail +--R : failed,pole: potentialPole) +--R from RationalFunctionDefiniteIntegration(D4) +--R if D4 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R [6] (Fraction(Polynomial(D5)),SegmentBinding(OrderedCompletion( +--R Fraction(Polynomial(D5)))),String) -> Union(f1: OrderedCompletion +--R (Expression(D5)),f2: List(OrderedCompletion(Expression(D5))),fail +--R : failed,pole: potentialPole) +--R from RationalFunctionDefiniteIntegration(D5) +--R if D5 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R [7] (D2,Symbol) -> Union(D2,List(D2)) from FunctionSpaceIntegration( +--R D4,D2) +--R if D4 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) and D2 has Join( +--R TranscendentalFunctionCategory,PrimitiveFunctionCategory, +--R AlgebraicallyClosedFunctionSpace(D4)) +--R [8] (GeneralUnivariatePowerSeries(D2,D3,D4),Variable(D3)) -> +--R GeneralUnivariatePowerSeries(D2,D3,D4) +--R from GeneralUnivariatePowerSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has ALGEBRA(FRAC(INT)) and D2 has +--R RING and D4: D2 +--R [9] (Expression(Float),Segment(OrderedCompletion(Float)),Float,Float +--R ,RoutinesTable) -> Result +--R from AnnaNumericalIntegrationPackage +--R [10] NumericalIntegrationProblem -> Result +--R from AnnaNumericalIntegrationPackage +--R [11] (Expression(Float),Segment(OrderedCompletion(Float)),Float, +--R Float) -> Result +--R from AnnaNumericalIntegrationPackage +--R [12] (Expression(Float),Segment(OrderedCompletion(Float)),Float) -> +--R Result +--R from AnnaNumericalIntegrationPackage +--R [13] (Expression(Float),Segment(OrderedCompletion(Float))) -> Result +--R from AnnaNumericalIntegrationPackage +--R [14] (Expression(Float),List(Segment(OrderedCompletion(Float)))) -> +--R Result +--R from AnnaNumericalIntegrationPackage +--R [15] (Expression(Float),List(Segment(OrderedCompletion(Float))), +--R Float) -> Result +--R from AnnaNumericalIntegrationPackage +--R [16] (Expression(Float),List(Segment(OrderedCompletion(Float))), +--R Float,Float) -> Result +--R from AnnaNumericalIntegrationPackage +--R [17] (Expression(Float),List(Segment(OrderedCompletion(Float))), +--R Float,Float,RoutinesTable) -> Result +--R from AnnaNumericalIntegrationPackage +--R [18] (Expression(Float),SegmentBinding(OrderedCompletion(Float)), +--R String) -> Union(Result,"failed") +--R from AnnaNumericalIntegrationPackage +--R [19] (Expression(Float),SegmentBinding(OrderedCompletion(Float)), +--R Symbol) -> Union(Result,"failed") +--R from AnnaNumericalIntegrationPackage +--R [20] (Fraction(Polynomial(D4)),Symbol) -> Union(Expression(D4),List( +--R Expression(D4))) +--R from IntegrationResultRFToFunction(D4) +--R if D4 has CHARZ and D4 has Join(GcdDomain,RetractableTo( +--R Integer),OrderedSet,LinearlyExplicitRingOver(Integer)) +--R [21] (D,D1) -> D from D +--R if D has MTSCAT(D2,D1) and D2 has RING and D1 has ORDSET +--R and D2 has ALGEBRA(FRAC(INT)) +--R [22] (Polynomial(D2),Symbol) -> Polynomial(D2) from Polynomial(D2) +--R if D2 has ALGEBRA(FRAC(INT)) and D2 has RING +--R [23] (TaylorSeries(D2),Symbol,D2) -> TaylorSeries(D2) from +--R TaylorSeries(D2) +--R if D2 has ALGEBRA(FRAC(INT)) and D2 has RING +--R [24] (UnivariateFormalPowerSeries(D2),Variable(QUOTE(x))) -> +--R UnivariateFormalPowerSeries(D2) +--R from UnivariateFormalPowerSeries(D2) +--R if D2 has ALGEBRA(FRAC(INT)) and D2 has RING +--R [25] (D,D1) -> D from D +--R if D1 = SYMBOL and D has ULSCAT(D2) and D2 has RING and D2 +--R has ACFS(INT) and D2 has PRIMCAT and D2 has TRANFUN and D2 +--R has ALGEBRA(FRAC(INT)) or D1 = SYMBOL and D has ULSCAT(D2) +--R and D2 has RING and D2 has variables: D2 -> List(D1) and D2 +--R has integrate: (D2,D1) -> D2 and D2 has ALGEBRA(FRAC(INT)) +--R +--R [26] D -> D from D +--R if D has ULSCAT(D1) and D1 has RING and D1 has ALGEBRA( +--R FRAC(INT)) +--R [27] D -> D from D +--R if D has UPOLYC(D1) and D1 has RING and D1 has ALGEBRA( +--R FRAC(INT)) +--R [28] (D,D1) -> D from D +--R if D1 = SYMBOL and D has UPXSCAT(D2) and D2 has RING and +--R D2 has ACFS(INT) and D2 has PRIMCAT and D2 has TRANFUN and +--R D2 has ALGEBRA(FRAC(INT)) or D1 = SYMBOL and D has UPXSCAT( +--R D2) and D2 has RING and D2 has variables: D2 -> List(D1) +--R and D2 has integrate: (D2,D1) -> D2 and D2 has ALGEBRA(FRAC +--R (INT)) +--R [29] D -> D from D +--R if D has UPXSCAT(D1) and D1 has RING and D1 has ALGEBRA( +--R FRAC(INT)) +--R [30] (D,D1) -> D from D +--R if D1 = SYMBOL and D has UTSCAT(D2) and D2 has RING and D2 +--R has ACFS(INT) and D2 has PRIMCAT and D2 has TRANFUN and D2 +--R has ALGEBRA(FRAC(INT)) or D1 = SYMBOL and D has UTSCAT(D2) +--R and D2 has RING and D2 has variables: D2 -> List(D1) and D2 +--R has integrate: (D2,D1) -> D2 and D2 has ALGEBRA(FRAC(INT)) +--R +--R [31] D -> D from D +--R if D has UTSCAT(D1) and D1 has RING and D1 has ALGEBRA( +--R FRAC(INT)) +--R [32] (UnivariateTaylorSeriesCZero(D2,D3),Variable(D3)) -> +--R UnivariateTaylorSeriesCZero(D2,D3) +--R from UnivariateTaylorSeriesCZero(D2,D3) +--R if D3: SYMBOL and D2 has ALGEBRA(FRAC(INT)) and D2 has +--R RING +--R +--RThere are 10 unexposed functions called integrate : +--R [1] Fraction(D4) -> IntegrationResult(Fraction(D4)) +--R from RationalIntegration(D3,D4) +--R if D3 has Join(Field,CharacteristicZero,RetractableTo( +--R Integer)) and D4 has UPOLYC(D3) +--R [2] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R [3] (SparseMultivariateTaylorSeries(D2,D1,D3),D1,D2) -> +--R SparseMultivariateTaylorSeries(D2,D1,D3) +--R from SparseMultivariateTaylorSeries(D2,D1,D3) +--R if D2 has ALGEBRA(FRAC(INT)) and D2 has RING and D1 has +--R ORDSET and D3 has POLYCAT(D2,INDE(D1),D1) +--R [4] (D2,Stream(D2)) -> Stream(D2) from StreamTaylorSeriesOperations( +--R D2) +--R if D2 has ALGEBRA(FRAC(INT)) and D2 has RING +--R [5] (SparseUnivariateLaurentSeries(D2,D3,D4),Variable(D3)) -> +--R SparseUnivariateLaurentSeries(D2,D3,D4) +--R from SparseUnivariateLaurentSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has ALGEBRA(FRAC(INT)) and D2 has +--R RING and D4: D2 +--R [6] (SparseUnivariatePuiseuxSeries(D2,D3,D4),Variable(D3)) -> +--R SparseUnivariatePuiseuxSeries(D2,D3,D4) +--R from SparseUnivariatePuiseuxSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has ALGEBRA(FRAC(INT)) and D2 has +--R RING and D4: D2 +--R [7] (SparseUnivariateTaylorSeries(D2,D3,D4),Variable(D3)) -> +--R SparseUnivariateTaylorSeries(D2,D3,D4) +--R from SparseUnivariateTaylorSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has ALGEBRA(FRAC(INT)) and D2 has +--R RING and D4: D2 +--R [8] (UnivariateLaurentSeries(D2,D3,D4),Variable(D3)) -> +--R UnivariateLaurentSeries(D2,D3,D4) +--R from UnivariateLaurentSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has ALGEBRA(FRAC(INT)) and D2 has +--R RING and D4: D2 +--R [9] (UnivariatePuiseuxSeries(D2,D3,D4),Variable(D3)) -> +--R UnivariatePuiseuxSeries(D2,D3,D4) +--R from UnivariatePuiseuxSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has ALGEBRA(FRAC(INT)) and D2 has +--R RING and D4: D2 +--R [10] (UnivariateTaylorSeries(D2,D3,D4),Variable(D3)) -> +--R UnivariateTaylorSeries(D2,D3,D4) +--R from UnivariateTaylorSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has ALGEBRA(FRAC(INT)) and D2 has +--R RING and D4: D2 +--R +--RExamples of integrate from ElementaryFunctionDefiniteIntegration +--R +--R +--RExamples of integrate from RationalFunctionDefiniteIntegration +--R +--R +--RExamples of integrate from FunctionSpaceIntegration +--R +--R +--RExamples of integrate from GeneralUnivariatePowerSeries +--R +--R +--RExamples of integrate from AnnaNumericalIntegrationPackage +--R +--R +--RExamples of integrate from RationalIntegration +--R +--R +--RExamples of integrate from IntegrationResultRFToFunction +--R +--R +--RExamples of integrate from InnerSparseUnivariatePowerSeries +--R +--R +--RExamples of integrate from MultivariateTaylorSeriesCategory +--R +--R +--RExamples of integrate from Polynomial +--R +--R +--RExamples of integrate from SparseMultivariateTaylorSeries +--R +--R +--RExamples of integrate from StreamTaylorSeriesOperations +--R +--R +--RExamples of integrate from SparseUnivariateLaurentSeries +--R +--R +--RExamples of integrate from SparseUnivariatePuiseuxSeries +--R +--R +--RExamples of integrate from SparseUnivariateTaylorSeries +--R +--R +--RExamples of integrate from TaylorSeries +--R +--R +--RExamples of integrate from UnivariateFormalPowerSeries +--R +--R +--RExamples of integrate from UnivariateLaurentSeriesCategory +--R +--R +--RExamples of integrate from UnivariateLaurentSeries +--R +--R +--RExamples of integrate from UnivariatePolynomialCategory +--R +--R +--RExamples of integrate from UnivariatePuiseuxSeriesCategory +--R +--R +--RExamples of integrate from UnivariatePuiseuxSeries +--R +--R +--RExamples of integrate from UnivariateTaylorSeriesCategory +--R +--R +--RExamples of integrate from UnivariateTaylorSeries +--R +--R +--RExamples of integrate from UnivariateTaylorSeriesCZero +--R +--E 1403 + +--S 1404 of 3320 +)d op integrate +--R +--R +--RThere are 32 exposed functions called integrate : +--R [1] (D2,SegmentBinding(OrderedCompletion(D2))) -> Union(f1: +--R OrderedCompletion(D2),f2: List(OrderedCompletion(D2)),fail: +--R failed,pole: potentialPole) +--R from ElementaryFunctionDefiniteIntegration(D4,D2) +--R if D2 has Join(TranscendentalFunctionCategory, +--R PrimitiveFunctionCategory,AlgebraicallyClosedFunctionSpace( +--R D4)) and D4 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R [2] (D2,SegmentBinding(OrderedCompletion(D2)),String) -> Union(f1: +--R OrderedCompletion(D2),f2: List(OrderedCompletion(D2)),fail: +--R failed,pole: potentialPole) +--R from ElementaryFunctionDefiniteIntegration(D5,D2) +--R if D2 has Join(TranscendentalFunctionCategory, +--R PrimitiveFunctionCategory,AlgebraicallyClosedFunctionSpace( +--R D5)) and D5 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R [3] (Fraction(Polynomial(D4)),SegmentBinding(OrderedCompletion( +--R Expression(D4)))) -> Union(f1: OrderedCompletion(Expression(D4)), +--R f2: List(OrderedCompletion(Expression(D4))),fail: failed,pole: +--R potentialPole) +--R from RationalFunctionDefiniteIntegration(D4) +--R if D4 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R [4] (Fraction(Polynomial(D5)),SegmentBinding(OrderedCompletion( +--R Expression(D5))),String) -> Union(f1: OrderedCompletion( +--R Expression(D5)),f2: List(OrderedCompletion(Expression(D5))),fail +--R : failed,pole: potentialPole) +--R from RationalFunctionDefiniteIntegration(D5) +--R if D5 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R [5] (Fraction(Polynomial(D4)),SegmentBinding(OrderedCompletion( +--R Fraction(Polynomial(D4))))) -> Union(f1: OrderedCompletion( +--R Expression(D4)),f2: List(OrderedCompletion(Expression(D4))),fail +--R : failed,pole: potentialPole) +--R from RationalFunctionDefiniteIntegration(D4) +--R if D4 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R [6] (Fraction(Polynomial(D5)),SegmentBinding(OrderedCompletion( +--R Fraction(Polynomial(D5)))),String) -> Union(f1: OrderedCompletion +--R (Expression(D5)),f2: List(OrderedCompletion(Expression(D5))),fail +--R : failed,pole: potentialPole) +--R from RationalFunctionDefiniteIntegration(D5) +--R if D5 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R [7] (D2,Symbol) -> Union(D2,List(D2)) from FunctionSpaceIntegration( +--R D4,D2) +--R if D4 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) and D2 has Join( +--R TranscendentalFunctionCategory,PrimitiveFunctionCategory, +--R AlgebraicallyClosedFunctionSpace(D4)) +--R [8] (GeneralUnivariatePowerSeries(D2,D3,D4),Variable(D3)) -> +--R GeneralUnivariatePowerSeries(D2,D3,D4) +--R from GeneralUnivariatePowerSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has ALGEBRA(FRAC(INT)) and D2 has +--R RING and D4: D2 +--R [9] (Expression(Float),Segment(OrderedCompletion(Float)),Float,Float +--R ,RoutinesTable) -> Result +--R from AnnaNumericalIntegrationPackage +--R [10] NumericalIntegrationProblem -> Result +--R from AnnaNumericalIntegrationPackage +--R [11] (Expression(Float),Segment(OrderedCompletion(Float)),Float, +--R Float) -> Result +--R from AnnaNumericalIntegrationPackage +--R [12] (Expression(Float),Segment(OrderedCompletion(Float)),Float) -> +--R Result +--R from AnnaNumericalIntegrationPackage +--R [13] (Expression(Float),Segment(OrderedCompletion(Float))) -> Result +--R from AnnaNumericalIntegrationPackage +--R [14] (Expression(Float),List(Segment(OrderedCompletion(Float)))) -> +--R Result +--R from AnnaNumericalIntegrationPackage +--R [15] (Expression(Float),List(Segment(OrderedCompletion(Float))), +--R Float) -> Result +--R from AnnaNumericalIntegrationPackage +--R [16] (Expression(Float),List(Segment(OrderedCompletion(Float))), +--R Float,Float) -> Result +--R from AnnaNumericalIntegrationPackage +--R [17] (Expression(Float),List(Segment(OrderedCompletion(Float))), +--R Float,Float,RoutinesTable) -> Result +--R from AnnaNumericalIntegrationPackage +--R [18] (Expression(Float),SegmentBinding(OrderedCompletion(Float)), +--R String) -> Union(Result,"failed") +--R from AnnaNumericalIntegrationPackage +--R [19] (Expression(Float),SegmentBinding(OrderedCompletion(Float)), +--R Symbol) -> Union(Result,"failed") +--R from AnnaNumericalIntegrationPackage +--R [20] (Fraction(Polynomial(D4)),Symbol) -> Union(Expression(D4),List( +--R Expression(D4))) +--R from IntegrationResultRFToFunction(D4) +--R if D4 has CHARZ and D4 has Join(GcdDomain,RetractableTo( +--R Integer),OrderedSet,LinearlyExplicitRingOver(Integer)) +--R [21] (D,D1) -> D from D +--R if D has MTSCAT(D2,D1) and D2 has RING and D1 has ORDSET +--R and D2 has ALGEBRA(FRAC(INT)) +--R [22] (Polynomial(D2),Symbol) -> Polynomial(D2) from Polynomial(D2) +--R if D2 has ALGEBRA(FRAC(INT)) and D2 has RING +--R [23] (TaylorSeries(D2),Symbol,D2) -> TaylorSeries(D2) from +--R TaylorSeries(D2) +--R if D2 has ALGEBRA(FRAC(INT)) and D2 has RING +--R [24] (UnivariateFormalPowerSeries(D2),Variable(QUOTE(x))) -> +--R UnivariateFormalPowerSeries(D2) +--R from UnivariateFormalPowerSeries(D2) +--R if D2 has ALGEBRA(FRAC(INT)) and D2 has RING +--R [25] (D,D1) -> D from D +--R if D1 = SYMBOL and D has ULSCAT(D2) and D2 has RING and D2 +--R has ACFS(INT) and D2 has PRIMCAT and D2 has TRANFUN and D2 +--R has ALGEBRA(FRAC(INT)) or D1 = SYMBOL and D has ULSCAT(D2) +--R and D2 has RING and D2 has variables: D2 -> List(D1) and D2 +--R has integrate: (D2,D1) -> D2 and D2 has ALGEBRA(FRAC(INT)) +--R +--R [26] D -> D from D +--R if D has ULSCAT(D1) and D1 has RING and D1 has ALGEBRA( +--R FRAC(INT)) +--R [27] D -> D from D +--R if D has UPOLYC(D1) and D1 has RING and D1 has ALGEBRA( +--R FRAC(INT)) +--R [28] (D,D1) -> D from D +--R if D1 = SYMBOL and D has UPXSCAT(D2) and D2 has RING and +--R D2 has ACFS(INT) and D2 has PRIMCAT and D2 has TRANFUN and +--R D2 has ALGEBRA(FRAC(INT)) or D1 = SYMBOL and D has UPXSCAT( +--R D2) and D2 has RING and D2 has variables: D2 -> List(D1) +--R and D2 has integrate: (D2,D1) -> D2 and D2 has ALGEBRA(FRAC +--R (INT)) +--R [29] D -> D from D +--R if D has UPXSCAT(D1) and D1 has RING and D1 has ALGEBRA( +--R FRAC(INT)) +--R [30] (D,D1) -> D from D +--R if D1 = SYMBOL and D has UTSCAT(D2) and D2 has RING and D2 +--R has ACFS(INT) and D2 has PRIMCAT and D2 has TRANFUN and D2 +--R has ALGEBRA(FRAC(INT)) or D1 = SYMBOL and D has UTSCAT(D2) +--R and D2 has RING and D2 has variables: D2 -> List(D1) and D2 +--R has integrate: (D2,D1) -> D2 and D2 has ALGEBRA(FRAC(INT)) +--R +--R [31] D -> D from D +--R if D has UTSCAT(D1) and D1 has RING and D1 has ALGEBRA( +--R FRAC(INT)) +--R [32] (UnivariateTaylorSeriesCZero(D2,D3),Variable(D3)) -> +--R UnivariateTaylorSeriesCZero(D2,D3) +--R from UnivariateTaylorSeriesCZero(D2,D3) +--R if D3: SYMBOL and D2 has ALGEBRA(FRAC(INT)) and D2 has +--R RING +--R +--RThere are 10 unexposed functions called integrate : +--R [1] Fraction(D4) -> IntegrationResult(Fraction(D4)) +--R from RationalIntegration(D3,D4) +--R if D3 has Join(Field,CharacteristicZero,RetractableTo( +--R Integer)) and D4 has UPOLYC(D3) +--R [2] InnerSparseUnivariatePowerSeries(D1) -> +--R InnerSparseUnivariatePowerSeries(D1) +--R from InnerSparseUnivariatePowerSeries(D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has RING +--R [3] (SparseMultivariateTaylorSeries(D2,D1,D3),D1,D2) -> +--R SparseMultivariateTaylorSeries(D2,D1,D3) +--R from SparseMultivariateTaylorSeries(D2,D1,D3) +--R if D2 has ALGEBRA(FRAC(INT)) and D2 has RING and D1 has +--R ORDSET and D3 has POLYCAT(D2,INDE(D1),D1) +--R [4] (D2,Stream(D2)) -> Stream(D2) from StreamTaylorSeriesOperations( +--R D2) +--R if D2 has ALGEBRA(FRAC(INT)) and D2 has RING +--R [5] (SparseUnivariateLaurentSeries(D2,D3,D4),Variable(D3)) -> +--R SparseUnivariateLaurentSeries(D2,D3,D4) +--R from SparseUnivariateLaurentSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has ALGEBRA(FRAC(INT)) and D2 has +--R RING and D4: D2 +--R [6] (SparseUnivariatePuiseuxSeries(D2,D3,D4),Variable(D3)) -> +--R SparseUnivariatePuiseuxSeries(D2,D3,D4) +--R from SparseUnivariatePuiseuxSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has ALGEBRA(FRAC(INT)) and D2 has +--R RING and D4: D2 +--R [7] (SparseUnivariateTaylorSeries(D2,D3,D4),Variable(D3)) -> +--R SparseUnivariateTaylorSeries(D2,D3,D4) +--R from SparseUnivariateTaylorSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has ALGEBRA(FRAC(INT)) and D2 has +--R RING and D4: D2 +--R [8] (UnivariateLaurentSeries(D2,D3,D4),Variable(D3)) -> +--R UnivariateLaurentSeries(D2,D3,D4) +--R from UnivariateLaurentSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has ALGEBRA(FRAC(INT)) and D2 has +--R RING and D4: D2 +--R [9] (UnivariatePuiseuxSeries(D2,D3,D4),Variable(D3)) -> +--R UnivariatePuiseuxSeries(D2,D3,D4) +--R from UnivariatePuiseuxSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has ALGEBRA(FRAC(INT)) and D2 has +--R RING and D4: D2 +--R [10] (UnivariateTaylorSeries(D2,D3,D4),Variable(D3)) -> +--R UnivariateTaylorSeries(D2,D3,D4) +--R from UnivariateTaylorSeries(D2,D3,D4) +--R if D3: SYMBOL and D2 has ALGEBRA(FRAC(INT)) and D2 has +--R RING and D4: D2 +--R +--RExamples of integrate from ElementaryFunctionDefiniteIntegration +--R +--R +--RExamples of integrate from RationalFunctionDefiniteIntegration +--R +--R +--RExamples of integrate from FunctionSpaceIntegration +--R +--R +--RExamples of integrate from GeneralUnivariatePowerSeries +--R +--R +--RExamples of integrate from AnnaNumericalIntegrationPackage +--R +--R +--RExamples of integrate from RationalIntegration +--R +--R +--RExamples of integrate from IntegrationResultRFToFunction +--R +--R +--RExamples of integrate from InnerSparseUnivariatePowerSeries +--R +--R +--RExamples of integrate from MultivariateTaylorSeriesCategory +--R +--R +--RExamples of integrate from Polynomial +--R +--R +--RExamples of integrate from SparseMultivariateTaylorSeries +--R +--R +--RExamples of integrate from StreamTaylorSeriesOperations +--R +--R +--RExamples of integrate from SparseUnivariateLaurentSeries +--R +--R +--RExamples of integrate from SparseUnivariatePuiseuxSeries +--R +--R +--RExamples of integrate from SparseUnivariateTaylorSeries +--R +--R +--RExamples of integrate from TaylorSeries +--R +--R +--RExamples of integrate from UnivariateFormalPowerSeries +--R +--R +--RExamples of integrate from UnivariateLaurentSeriesCategory +--R +--R +--RExamples of integrate from UnivariateLaurentSeries +--R +--R +--RExamples of integrate from UnivariatePolynomialCategory +--R +--R +--RExamples of integrate from UnivariatePuiseuxSeriesCategory +--R +--R +--RExamples of integrate from UnivariatePuiseuxSeries +--R +--R +--RExamples of integrate from UnivariateTaylorSeriesCategory +--R +--R +--RExamples of integrate from UnivariateTaylorSeries +--R +--R +--RExamples of integrate from UnivariateTaylorSeriesCZero +--R +--E 1404 + +--S 1405 of 3320 +)d op intensity +--R +--R +--RThere is one exposed function called intensity : +--R [1] (ThreeDimensionalViewport,Float) -> Void from +--R ThreeDimensionalViewport +--R +--RExamples of intensity from ThreeDimensionalViewport +--R +--E 1405 + +--S 1406 of 3320 done +)d op interiorProduct +--R +--R +--RThere is one unexposed function called interiorProduct : +--R [1] (Vector(Expression(D3)),DeRhamComplex(D3,D4),SquareMatrix(#(D4), +--R Expression(D3))) -> DeRhamComplex(D3,D4) +--R from DeRhamComplex(D3,D4) +--R if D3 has Join(Ring,OrderedSet) and D4: LIST(SYMBOL) +--R +--RExamples of interiorProduct from DeRhamComplex +--R +--R indented{1}{with the differential form a (w.r.t. metric g)} blankline +--RcoefRing := Integer +--RR3 : List Symbol := [x,y,z] +--RD := DERHAM(coefRing,R3) +--R[dx,dy,dz] := [generator(i)$D for i in 1..3] +--Rf : BOP := operator('f) +--Rg : BOP := operator('g) +--Rh : BOP := operator('h) +--Ra : BOP := operator('a) +--Rb : BOP := operator('b) +--Rc : BOP := operator('c) +--RU : BOP := operator('U) +--RV : BOP := operator('V) +--RW : BOP := operator('W) +--Rv := vector[U(x,y,z),V(x,y,z),W(x,y,z)] +--Rsigma := f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz +--Rtheta := a(x,y,z)*dx*dy + b(x,y,z)*dx*dz + c(x,y,z)*dy*dz +--RG := diagonalMatrix([1,1,1]) +--RinteriorProduct(v,sigma,G) +--RinteriorProduct(v,theta,G) +--R +--E 1406 + +--S 1407 of 3320 +)d op intermediateResultsIF +--R +--R +--RThere is one exposed function called intermediateResultsIF : +--R [1] Record(xinit: DoubleFloat,xend: DoubleFloat,fn: Vector( +--R Expression(DoubleFloat)),yinit: List(DoubleFloat),intvals: List( +--R DoubleFloat),g: Expression(DoubleFloat),abserr: DoubleFloat, +--R relerr: DoubleFloat) -> Float +--R from d02AgentsPackage +--R +--RExamples of intermediateResultsIF from d02AgentsPackage +--R +--E 1407 + +--S 1408 of 3320 +)d op internal? +--R +--R +--RThere is one unexposed function called internal? : +--R [1] SubSpace(D2,D3) -> Boolean from SubSpace(D2,D3) if D2: PI and D3 +--R has RING +--R +--RExamples of internal? from SubSpace +--R +--E 1408 + +--S 1409 of 3320 +)d op internalAugment +--R +--R +--RThere are 4 exposed functions called internalAugment : +--R [1] (D2,RegularTriangularSet(D4,D5,D6,D2),Boolean,Boolean,Boolean, +--R Boolean,Boolean) -> List(RegularTriangularSet(D4,D5,D6,D2)) +--R from RegularTriangularSet(D4,D5,D6,D2) +--R if D4 has GCDDOM and D5 has OAMONS and D6 has ORDSET and +--R D2 has RPOLCAT(D4,D5,D6) +--R [2] (List(D5),D) -> D from D +--R if D has RSETCAT(D2,D3,D4,D5) and D2 has GCDDOM and D3 +--R has OAMONS and D4 has ORDSET and D5 has RPOLCAT(D2,D3,D4) +--R +--R [3] (D1,D) -> D from D +--R if D has RSETCAT(D2,D3,D4,D1) and D2 has GCDDOM and D3 +--R has OAMONS and D4 has ORDSET and D1 has RPOLCAT(D2,D3,D4) +--R +--R [4] (D2,SquareFreeRegularTriangularSet(D4,D5,D6,D2),Boolean,Boolean, +--R Boolean,Boolean,Boolean) -> List(SquareFreeRegularTriangularSet( +--R D4,D5,D6,D2)) +--R from SquareFreeRegularTriangularSet(D4,D5,D6,D2) +--R if D4 has GCDDOM and D5 has OAMONS and D6 has ORDSET and +--R D2 has RPOLCAT(D4,D5,D6) +--R +--RExamples of internalAugment from RegularTriangularSet +--R +--R +--RExamples of internalAugment from RegularTriangularSetCategory +--R +--R +--RExamples of internalAugment from SquareFreeRegularTriangularSet +--R +--E 1409 + +--S 1410 of 3320 +)d op internalDecompose +--R +--R +--RThere are 6 exposed functions called internalDecompose : +--R [1] (D2,D3,NonNegativeInteger,Boolean) -> Record(done: List(D3),todo +--R : List(Record(val: List(D2),tower: D3))) +--R from RegularSetDecompositionPackage(D6,D7,D8,D2,D3) +--R if D6 has GCDDOM and D7 has OAMONS and D8 has ORDSET and +--R D2 has RPOLCAT(D6,D7,D8) and D3 has RSETCAT(D6,D7,D8,D2) +--R +--R [2] (D2,D3,NonNegativeInteger) -> Record(done: List(D3),todo: List( +--R Record(val: List(D2),tower: D3))) +--R from RegularSetDecompositionPackage(D5,D6,D7,D2,D3) +--R if D5 has GCDDOM and D6 has OAMONS and D7 has ORDSET and +--R D2 has RPOLCAT(D5,D6,D7) and D3 has RSETCAT(D5,D6,D7,D2) +--R +--R [3] (D2,D3) -> Record(done: List(D3),todo: List(Record(val: List(D2) +--R ,tower: D3))) +--R from RegularSetDecompositionPackage(D4,D5,D6,D2,D3) +--R if D4 has GCDDOM and D5 has OAMONS and D6 has ORDSET and +--R D2 has RPOLCAT(D4,D5,D6) and D3 has RSETCAT(D4,D5,D6,D2) +--R +--R [4] (D2,D3,NonNegativeInteger,Boolean) -> Record(done: List(D3),todo +--R : List(Record(val: List(D2),tower: D3))) +--R from SquareFreeRegularSetDecompositionPackage(D6,D7,D8,D2, +--R D3) +--R if D6 has GCDDOM and D7 has OAMONS and D8 has ORDSET and +--R D2 has RPOLCAT(D6,D7,D8) and D3 has SFRTCAT(D6,D7,D8,D2) +--R +--R [5] (D2,D3,NonNegativeInteger) -> Record(done: List(D3),todo: List( +--R Record(val: List(D2),tower: D3))) +--R from SquareFreeRegularSetDecompositionPackage(D5,D6,D7,D2, +--R D3) +--R if D5 has GCDDOM and D6 has OAMONS and D7 has ORDSET and +--R D2 has RPOLCAT(D5,D6,D7) and D3 has SFRTCAT(D5,D6,D7,D2) +--R +--R [6] (D2,D3) -> Record(done: List(D3),todo: List(Record(val: List(D2) +--R ,tower: D3))) +--R from SquareFreeRegularSetDecompositionPackage(D4,D5,D6,D2, +--R D3) +--R if D4 has GCDDOM and D5 has OAMONS and D6 has ORDSET and +--R D2 has RPOLCAT(D4,D5,D6) and D3 has SFRTCAT(D4,D5,D6,D2) +--R +--R +--RExamples of internalDecompose from RegularSetDecompositionPackage +--R +--R +--RExamples of internalDecompose from SquareFreeRegularSetDecompositionPackage +--R +--E 1410 + +--S 1411 of 3320 +)d op internalInfRittWu? +--R +--R +--RThere are 2 exposed functions called internalInfRittWu? : +--R [1] (List(D6),List(D6)) -> Boolean from QuasiComponentPackage(D3,D4, +--R D5,D6,D7) +--R if D6 has RPOLCAT(D3,D4,D5) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET and D7 has RSETCAT(D3,D4,D5,D6) +--R +--R [2] (List(D6),List(D6)) -> Boolean +--R from SquareFreeQuasiComponentPackage(D3,D4,D5,D6,D7) +--R if D6 has RPOLCAT(D3,D4,D5) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET and D7 has RSETCAT(D3,D4,D5,D6) +--R +--R +--RExamples of internalInfRittWu? from QuasiComponentPackage +--R +--R +--RExamples of internalInfRittWu? from SquareFreeQuasiComponentPackage +--R +--E 1411 + +--S 1412 of 3320 +)d op internalIntegrate +--R +--R +--RThere are 2 exposed functions called internalIntegrate : +--R [1] (D2,Symbol) -> IntegrationResult(D2) +--R from FunctionSpaceComplexIntegration(D4,D2) +--R if D4 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) and D2 has Join( +--R TranscendentalFunctionCategory, +--R AlgebraicallyClosedFunctionSpace(D4)) +--R [2] (Fraction(Polynomial(D4)),Symbol) -> IntegrationResult(Fraction( +--R Polynomial(D4))) +--R from RationalFunctionIntegration(D4) +--R if D4 has Join(IntegralDomain,RetractableTo(Integer), +--R CharacteristicZero) +--R +--RExamples of internalIntegrate from FunctionSpaceComplexIntegration +--R +--R +--RExamples of internalIntegrate from RationalFunctionIntegration +--R +--E 1412 + +--S 1413 of 3320 +)d op internalIntegrate0 +--R +--R +--RThere is one exposed function called internalIntegrate0 : +--R [1] (D2,Symbol) -> IntegrationResult(D2) +--R from FunctionSpaceComplexIntegration(D4,D2) +--R if D4 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) and D2 has Join( +--R TranscendentalFunctionCategory, +--R AlgebraicallyClosedFunctionSpace(D4)) +--R +--RExamples of internalIntegrate0 from FunctionSpaceComplexIntegration +--R +--E 1413 + +--S 1414 of 3320 +)d op internalLastSubResultant +--R +--R +--RThere are 2 exposed functions called internalLastSubResultant : +--R [1] (D2,D2,D3,Boolean,Boolean) -> List(Record(val: D2,tower: D3)) +--R from RegularTriangularSetGcdPackage(D5,D6,D7,D2,D3) +--R if D5 has GCDDOM and D6 has OAMONS and D7 has ORDSET and +--R D2 has RPOLCAT(D5,D6,D7) and D3 has RSETCAT(D5,D6,D7,D2) +--R +--R [2] (List(Record(val: List(D7),tower: D8)),D3,Boolean) -> List( +--R Record(val: D7,tower: D8)) +--R from RegularTriangularSetGcdPackage(D5,D6,D3,D7,D8) +--R if D7 has RPOLCAT(D5,D6,D3) and D8 has RSETCAT(D5,D6,D3,D7 +--R ) and D5 has GCDDOM and D6 has OAMONS and D3 has ORDSET +--R +--RExamples of internalLastSubResultant from RegularTriangularSetGcdPackage +--R +--E 1414 + +--S 1415 of 3320 +)d op internalSubPolSet? +--R +--R +--RThere are 2 exposed functions called internalSubPolSet? : +--R [1] (List(D6),List(D6)) -> Boolean from QuasiComponentPackage(D3,D4, +--R D5,D6,D7) +--R if D6 has RPOLCAT(D3,D4,D5) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET and D7 has RSETCAT(D3,D4,D5,D6) +--R +--R [2] (List(D6),List(D6)) -> Boolean +--R from SquareFreeQuasiComponentPackage(D3,D4,D5,D6,D7) +--R if D6 has RPOLCAT(D3,D4,D5) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET and D7 has RSETCAT(D3,D4,D5,D6) +--R +--R +--RExamples of internalSubPolSet? from QuasiComponentPackage +--R +--R +--RExamples of internalSubPolSet? from SquareFreeQuasiComponentPackage +--R +--E 1415 + +--S 1416 of 3320 +)d op internalSubQuasiComponent? +--R +--R +--RThere are 2 exposed functions called internalSubQuasiComponent? : +--R [1] (D2,D2) -> Union(Boolean,"failed") +--R from QuasiComponentPackage(D3,D4,D5,D6,D2) +--R if D3 has GCDDOM and D4 has OAMONS and D5 has ORDSET and +--R D6 has RPOLCAT(D3,D4,D5) and D2 has RSETCAT(D3,D4,D5,D6) +--R +--R [2] (D2,D2) -> Union(Boolean,"failed") +--R from SquareFreeQuasiComponentPackage(D3,D4,D5,D6,D2) +--R if D3 has GCDDOM and D4 has OAMONS and D5 has ORDSET and +--R D6 has RPOLCAT(D3,D4,D5) and D2 has RSETCAT(D3,D4,D5,D6) +--R +--R +--RExamples of internalSubQuasiComponent? from QuasiComponentPackage +--R +--R +--RExamples of internalSubQuasiComponent? from SquareFreeQuasiComponentPackage +--R +--E 1416 + +--S 1417 of 3320 +)d op internalZeroSetSplit +--R +--R +--RThere are 2 exposed functions called internalZeroSetSplit : +--R [1] (List(D7),Boolean,Boolean,Boolean) -> List(RegularTriangularSet( +--R D4,D5,D6,D7)) +--R from RegularTriangularSet(D4,D5,D6,D7) +--R if D7 has RPOLCAT(D4,D5,D6) and D4 has GCDDOM and D5 has +--R OAMONS and D6 has ORDSET +--R [2] (List(D7),Boolean,Boolean,Boolean) -> List( +--R SquareFreeRegularTriangularSet(D4,D5,D6,D7)) +--R from SquareFreeRegularTriangularSet(D4,D5,D6,D7) +--R if D7 has RPOLCAT(D4,D5,D6) and D4 has GCDDOM and D5 has +--R OAMONS and D6 has ORDSET +--R +--RExamples of internalZeroSetSplit from RegularTriangularSet +--R +--R +--RExamples of internalZeroSetSplit from SquareFreeRegularTriangularSet +--R +--E 1417 + +--S 1418 of 3320 +)d op interpolate +--R +--R +--RThere are 2 exposed functions called interpolate : +--R [1] (List(D4),List(D4),NonNegativeInteger) -> Fraction( +--R SparseUnivariatePolynomial(D4)) +--R from FractionFreeFastGaussian(D4,D5) +--R if D4 has Join(IntegralDomain,GcdDomain) and D5 has AMR(D4 +--R ,NNI) +--R [2] (List(Fraction(D4)),List(Fraction(D4)),NonNegativeInteger) -> +--R Fraction(SparseUnivariatePolynomial(D4)) +--R from FractionFreeFastGaussian(D4,D5) +--R if D4 has Join(IntegralDomain,GcdDomain) and D5 has AMR(D4 +--R ,NNI) +--R +--RThere are 3 unexposed functions called interpolate : +--R [1] (UnivariatePolynomial(D3,D4),List(D4),List(D4)) -> +--R UnivariatePolynomial(D3,D4) +--R from PolynomialInterpolation(D3,D4) if D3: SYMBOL and D4 +--R has FIELD +--R [2] (List(D4),List(D4)) -> SparseUnivariatePolynomial(D4) +--R from PolynomialInterpolation(D3,D4) if D4 has FIELD and D3 +--R : SYMBOL +--R [3] (List(D5),List(D5),NonNegativeInteger,NonNegativeInteger) -> +--R Fraction(Polynomial(D5)) +--R from RationalInterpolation(D4,D5) if D5 has FIELD and D4: +--R SYMBOL +--R +--RExamples of interpolate from FractionFreeFastGaussian +--R +--R +--RExamples of interpolate from PolynomialInterpolation +--R +--R +--RExamples of interpolate from RationalInterpolation +--R +--E 1418 + +--S 1419 of 3320 +)d op interpolateForms +--R +--R +--RThere are 4 exposed functions called interpolateForms : +--R [1] (D7,NonNegativeInteger) -> List(D11) +--R from GeneralPackageForAlgebraicFunctionField(D9,D10,D11, +--R D12,D13,D1,D2,D7,D3,D4,D5) +--R if D9 has FIELD and D10: LIST(SYMBOL) and D11 has POLYCAT( +--R D9,D12,OVAR(D10)) and D12 has DIRPCAT(#(D10),NNI) and D13 +--R has PRSPCAT(D9) and D1 has LOCPOWC(D9) and D2 has PLACESC( +--R D9,D1) and D7 has DIVCAT(D2) and D3 has INFCLCT(D9,D10,D11, +--R D12,D13,D1,D2,D7,D5) and D5 has BLMETCT and D4 has DSTRCAT( +--R D3) +--R [2] (D4,NonNegativeInteger,D6,List(D6)) -> List(D6) +--R from InterpolateFormsPackage(D7,D8,D6,D9,D10,D1,D2,D4) +--R if D6 has POLYCAT(D7,D9,OVAR(D8)) and D9 has DIRPCAT(#(D8) +--R ,NNI) and D7 has FIELD and D8: LIST(SYMBOL) and D1 has +--R LOCPOWC(D7) and D2 has PLACESC(D7,D1) and D10 has PRSPCAT( +--R D7) and D4 has DIVCAT(D2) +--R [3] (Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(D4)), +--R NonNegativeInteger) -> List(DistributedMultivariatePolynomial(D5, +--R D4)) +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D4,D5 +--R ,D6) +--R if D4 has FFIELDC and D5: LIST(SYMBOL) and D6 has BLMETCT +--R +--R [4] (Divisor(Places(D4)),NonNegativeInteger) -> List( +--R DistributedMultivariatePolynomial(D5,D4)) +--R from PackageForAlgebraicFunctionField(D4,D5,D6) +--R if D4 has FIELD and D5: LIST(SYMBOL) and D6 has BLMETCT +--R +--R +--RExamples of interpolateForms from GeneralPackageForAlgebraicFunctionField +--R +--R +--RExamples of interpolateForms from InterpolateFormsPackage +--R +--R +--RExamples of interpolateForms from PackageForAlgebraicFunctionFieldOverFiniteField +--R +--R +--RExamples of interpolateForms from PackageForAlgebraicFunctionField +--R +--E 1419 + +--S 1420 of 3320 +)d op interpolateFormsForFact +--R +--R +--RThere are 4 exposed functions called interpolateFormsForFact : +--R [1] (D6,List(D9)) -> List(D9) +--R from GeneralPackageForAlgebraicFunctionField(D7,D8,D9,D10, +--R D11,D12,D1,D6,D2,D3,D4) +--R if D9 has POLYCAT(D7,D10,OVAR(D8)) and D10 has DIRPCAT(#( +--R D8),NNI) and D7 has FIELD and D8: LIST(SYMBOL) and D11 has +--R PRSPCAT(D7) and D12 has LOCPOWC(D7) and D1 has PLACESC(D7, +--R D12) and D6 has DIVCAT(D1) and D2 has INFCLCT(D7,D8,D9,D10, +--R D11,D12,D1,D6,D4) and D4 has BLMETCT and D3 has DSTRCAT(D2) +--R +--R [2] (D3,List(D6)) -> List(D6) +--R from InterpolateFormsPackage(D4,D5,D6,D7,D8,D9,D1,D3) +--R if D6 has POLYCAT(D4,D7,OVAR(D5)) and D7 has DIRPCAT(#(D5) +--R ,NNI) and D4 has FIELD and D5: LIST(SYMBOL) and D9 has +--R LOCPOWC(D4) and D1 has PLACESC(D4,D9) and D8 has PRSPCAT(D4 +--R ) and D3 has DIVCAT(D1) +--R [3] (Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(D4)),List +--R (DistributedMultivariatePolynomial(D5,D4))) -> List( +--R DistributedMultivariatePolynomial(D5, +--R PseudoAlgebraicClosureOfFiniteField(D4))) +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D4,D5 +--R ,D6) +--R if D4 has FFIELDC and D5: LIST(SYMBOL) and D6 has BLMETCT +--R +--R [4] (Divisor(Places(D3)),List(DistributedMultivariatePolynomial(D4, +--R D3))) -> List(DistributedMultivariatePolynomial(D4,D3)) +--R from PackageForAlgebraicFunctionField(D3,D4,D5) +--R if D3 has FIELD and D4: LIST(SYMBOL) and D5 has BLMETCT +--R +--R +--RExamples of interpolateFormsForFact from GeneralPackageForAlgebraicFunctionField +--R +--R +--RExamples of interpolateFormsForFact from InterpolateFormsPackage +--R +--R +--RExamples of interpolateFormsForFact from PackageForAlgebraicFunctionFieldOverFiniteField +--R +--R +--RExamples of interpolateFormsForFact from PackageForAlgebraicFunctionField +--R +--E 1420 + +--S 1421 of 3320 +)d op interpret +--R +--R +--RThere are 2 unexposed functions called interpret : +--R [1] InputForm -> D1 from InputFormFunctions1(D1) if D1 has TYPE +--R [2] InputForm -> Any from InputForm +--R +--RExamples of interpret from InputFormFunctions1 +--R +--R +--RExamples of interpret from InputForm +--R +--E 1421 + +--S 1422 of 3320 +)d op interpretString +--R +--R +--RThere is one exposed function called interpretString : +--R [1] String -> Any from TemplateUtilities +--R +--RExamples of interpretString from TemplateUtilities +--R +--E 1422 + +--S 1423 of 3320 +)d op interReduce +--R +--R +--RThere is one unexposed function called interReduce : +--R [1] List(D5) -> List(D5) from PolynomialSetUtilitiesPackage(D2,D3,D4 +--R ,D5) +--R if D5 has RPOLCAT(D2,D3,D4) and D2 has INTDOM and D3 has +--R OAMONS and D4 has ORDSET +--R +--RExamples of interReduce from PolynomialSetUtilitiesPackage +--R +--E 1423 + +--S 1424 of 3320 +)d op intersect +--R +--R +--RThere are 7 exposed functions called intersect : +--R [1] List(PolynomialIdeals(D2,D3,D4,D5)) -> PolynomialIdeals(D2,D3,D4 +--R ,D5) +--R from PolynomialIdeals(D2,D3,D4,D5) +--R if D2 has FIELD and D3 has OAMONS and D4 has ORDSET and D5 +--R has POLYCAT(D2,D3,D4) +--R [2] (PolynomialIdeals(D1,D2,D3,D4),PolynomialIdeals(D1,D2,D3,D4)) +--R -> PolynomialIdeals(D1,D2,D3,D4) +--R from PolynomialIdeals(D1,D2,D3,D4) +--R if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4 +--R has POLYCAT(D1,D2,D3) +--R [3] (D2,List(D)) -> List(D) from D +--R if D has RSETCAT(D3,D4,D5,D2) and D3 has GCDDOM and D4 +--R has OAMONS and D5 has ORDSET and D2 has RPOLCAT(D3,D4,D5) +--R +--R [4] (List(D6),List(D)) -> List(D) from D +--R if D has RSETCAT(D3,D4,D5,D6) and D3 has GCDDOM and D4 +--R has OAMONS and D5 has ORDSET and D6 has RPOLCAT(D3,D4,D5) +--R +--R [5] (List(D6),D) -> List(D) from D +--R if D6 has RPOLCAT(D3,D4,D5) and D3 has GCDDOM and D4 has +--R OAMONS and D5 has ORDSET and D has RSETCAT(D3,D4,D5,D6) +--R [6] (D2,D) -> List(D) from D +--R if D3 has GCDDOM and D4 has OAMONS and D5 has ORDSET and +--R D2 has RPOLCAT(D3,D4,D5) and D has RSETCAT(D3,D4,D5,D2) +--R [7] (D,D) -> D from D if D has SETAGG(D1) and D1 has SETCAT +--R +--RExamples of intersect from PolynomialIdeals +--R +--R +--RExamples of intersect from RegularTriangularSetCategory +--R +--R +--RExamples of intersect from SetAggregate +--R +--E 1424 + +--S 1425 of 3320 +)d op intersectionDivisor +--R +--R +--RThere are 4 exposed functions called intersectionDivisor : +--R [1] D5 -> D4 +--R from GeneralPackageForAlgebraicFunctionField(D6,D7,D5,D8, +--R D9,D10,D11,D4,D1,D2,D3) +--R if D6 has FIELD and D7: LIST(SYMBOL) and D5 has POLYCAT(D6 +--R ,D8,OVAR(D7)) and D8 has DIRPCAT(#(D7),NNI) and D9 has +--R PRSPCAT(D6) and D10 has LOCPOWC(D6) and D11 has PLACESC(D6, +--R D10) and D1 has INFCLCT(D6,D7,D5,D8,D9,D10,D11,D4,D3) and +--R D3 has BLMETCT and D4 has DIVCAT(D11) and D2 has DSTRCAT(D1 +--R ) +--R [2] (D7,D7,List(D4),List(D13)) -> D6 +--R from IntersectionDivisorPackage(D10,D11,D7,D12,D13,D1,D2, +--R D6,D3,D4,D5) +--R if D13 has PRSPCAT(D10) and D4 has DSTRCAT(D3) and D10 +--R has FIELD and D3 has INFCLCT(D10,D11,D7,D12,D13,D1,D2,D6, +--R D5) and D5 has BLMETCT and D11: LIST(SYMBOL) and D7 has +--R POLYCAT(D10,D12,OVAR(D11)) and D12 has DIRPCAT(#(D11),NNI) +--R and D1 has LOCPOWC(D10) and D2 has PLACESC(D10,D1) and D6 +--R has DIVCAT(D2) +--R [3] DistributedMultivariatePolynomial(D4,D3) -> Divisor( +--R PlacesOverPseudoAlgebraicClosureOfFiniteField(D3)) +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D3,D4 +--R ,D5) +--R if D3 has FFIELDC and D4: LIST(SYMBOL) and D5 has BLMETCT +--R +--R [4] DistributedMultivariatePolynomial(D4,D3) -> Divisor(Places(D3)) +--R from PackageForAlgebraicFunctionField(D3,D4,D5) +--R if D3 has FIELD and D4: LIST(SYMBOL) and D5 has BLMETCT +--R +--R +--RExamples of intersectionDivisor from GeneralPackageForAlgebraicFunctionField +--R +--R +--RExamples of intersectionDivisor from IntersectionDivisorPackage +--R +--R +--RExamples of intersectionDivisor from PackageForAlgebraicFunctionFieldOverFiniteField +--R +--R +--RExamples of intersectionDivisor from PackageForAlgebraicFunctionField +--R +--E 1425 + +--S 1426 of 3320 +)d op interval +--R +--R +--RThere are 3 exposed functions called interval : +--R [1] Fraction(Integer) -> D from D +--R if D has INTCAT(D2) and D2 has Join(FloatingPointSystem, +--R TranscendentalFunctionCategory) +--R [2] D1 -> D from D +--R if D has INTCAT(D1) and D1 has Join(FloatingPointSystem, +--R TranscendentalFunctionCategory) +--R [3] (D1,D1) -> D from D +--R if D has INTCAT(D1) and D1 has Join(FloatingPointSystem, +--R TranscendentalFunctionCategory) +--R +--RExamples of interval from IntervalCategory +--R +--E 1426 + +--S 1427 of 3320 +)d op intPatternMatch +--R +--R +--RThere is one unexposed function called intPatternMatch : +--R [1] (D2,Symbol,((D2,Symbol) -> IntegrationResult(D2)),((D2,Symbol) +--R -> Union(Record(special: D2,integrand: D2),"failed"))) -> +--R IntegrationResult(D2) +--R from IntegrationTools(D6,D2) +--R if D2 has ELEMFUN and D2 has LFCAT and D2 has RETRACT( +--R SYMBOL) and D2 has FS(D6) and D6 has KONVERT(PATTERN(INT)) +--R and D6 has GCDDOM and D6 has PATMAB(INT) and D6 has ORDSET +--R +--R +--RExamples of intPatternMatch from IntegrationTools +--R +--E 1427 + +--S 1428 of 3320 done +)d op introduce! +--R +--R +--RThere is one exposed function called introduce! : +--R [1] (Symbol,Symbol) -> Union(BasicStochasticDifferential,"failed") +--R from BasicStochasticDifferential +--R +--RExamples of introduce! from BasicStochasticDifferential +--R +--Rintroduce!(t,dt) -- dt is a new stochastic differential +--RcopyBSD() +--R +--E 1428 + +--S 1429 of 3320 +)d op inv +--R +--R +--RThere are 4 exposed functions called inv : +--R [1] D -> D from D if D has DIVRING +--R [2] D -> D from D +--R if D = EQ(D1) and D1 has FIELD and D1 has TYPE or D = EQ( +--R D1) and D1 has GROUP and D1 has TYPE +--R [3] D -> D from D if D has GROUP +--R [4] D -> D from D if D has OC(D1) and D1 has COMRING and D1 has +--R FIELD +--R +--RThere are 3 unexposed functions called inv : +--R [1] EuclideanModularRing(D1,D2,D3,D4,D5,D6) -> EuclideanModularRing( +--R D1,D2,D3,D4,D5,D6) +--R from EuclideanModularRing(D1,D2,D3,D4,D5,D6) +--R if D1 has COMRING and D2 has UPOLYC(D1) and D3 has ABELMON +--R and D4: ((D2,D3) -> D2) and D5: ((D3,D3) -> Union(D3, +--R "failed")) and D6: ((D2,D2,D3) -> Union(D2,"failed")) +--R [2] Vector(D2) -> Vector(D2) from InnerNormalBasisFieldFunctions(D2) +--R if D2 has FFIELDC +--R [3] ModularRing(D1,D2,D3,D4,D5) -> ModularRing(D1,D2,D3,D4,D5) +--R from ModularRing(D1,D2,D3,D4,D5) +--R if D1 has COMRING and D2 has ABELMON and D3: ((D1,D2) -> +--R D1) and D4: ((D2,D2) -> Union(D2,"failed")) and D5: ((D1,D1 +--R ,D2) -> Union(D1,"failed")) +--R +--RExamples of inv from DivisionRing +--R +--R +--RExamples of inv from EuclideanModularRing +--R +--R +--RExamples of inv from Equation +--R +--R +--RExamples of inv from Group +--R +--R +--RExamples of inv from InnerNormalBasisFieldFunctions +--R +--R +--RExamples of inv from ModularRing +--R +--R +--RExamples of inv from OctonionCategory +--R +--E 1429 + +--S 1430 of 3320 +)d op inverse +--R +--R +--RThere are 4 exposed functions called inverse : +--R [1] D -> Union(D,"failed") from D +--R if D has MATCAT(D1,D2,D3) and D1 has RING and D2 has FLAGG +--R (D1) and D3 has FLAGG(D1) and D1 has FIELD +--R [2] D1 -> Union(D1,"failed") from MatrixLinearAlgebraFunctions(D2,D3 +--R ,D4,D1) +--R if D2 has FIELD and D2 has COMRING and D3 has FLAGG(D2) +--R and D4 has FLAGG(D2) and D1 has MATCAT(D2,D3,D4) +--R [3] Matrix(D1) -> Union(Matrix(D1),"failed") from Matrix(D1) +--R if D1 has FIELD and D1 has RING +--R [4] D -> Union(D,"failed") from D +--R if D has SMATCAT(D1,D2,D3,D4) and D2 has RING and D3 has +--R DIRPCAT(D1,D2) and D4 has DIRPCAT(D1,D2) and D2 has FIELD +--R +--R +--RThere are 3 unexposed functions called inverse : +--R [1] D1 -> Union(D1,"failed") +--R from InnerMatrixLinearAlgebraFunctions(D2,D3,D4,D1) +--R if D2 has FIELD and D3 has FLAGG(D2) and D4 has FLAGG(D2) +--R and D1 has MATCAT(D2,D3,D4) +--R [2] D2 -> Union(D1,"failed") +--R from InnerMatrixQuotientFieldFunctions(D3,D4,D5,D2,D6,D7, +--R D8,D1) +--R if D3 has INTDOM and D4 has FLAGG(D3) and D5 has FLAGG(D3) +--R and D6 has QFCAT(D3) and D1 has MATCAT(D6,D7,D8) and D2 +--R has MATCAT(D3,D4,D5) and D7 has FLAGG(D6) and D8 has FLAGG +--R (D6) +--R [3] List(D2) -> List(D2) from TableauxBumpers(D2) if D2 has ORDSET +--R +--R +--RExamples of inverse from InnerMatrixLinearAlgebraFunctions +--R +--R +--RExamples of inverse from InnerMatrixQuotientFieldFunctions +--R +--R +--RExamples of inverse from MatrixCategory +--R +--Rinverse matrix [[j**i for i in 0..4] for j in 1..5] +--R +--R +--RExamples of inverse from MatrixLinearAlgebraFunctions +--R +--R +--RExamples of inverse from Matrix +--R +--R +--RExamples of inverse from SquareMatrixCategory +--R +--R +--RExamples of inverse from TableauxBumpers +--R +--E 1430 + +--S 1431 of 3320 +)d op inverseColeman +--R +--R +--RThere is one exposed function called inverseColeman : +--R [1] (List(Integer),List(Integer),Matrix(Integer)) -> List(Integer) +--R from SymmetricGroupCombinatoricFunctions +--R +--RExamples of inverseColeman from SymmetricGroupCombinatoricFunctions +--R +--E 1431 + +--S 1432 of 3320 done +)d op inverseIntegralMatrix +--R +--R +--RThere is one exposed function called inverseIntegralMatrix : +--R [1] -> Matrix(Fraction(D3)) from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC( +--R D2) and D4 has UPOLYC(FRAC(D3)) +--R +--RExamples of inverseIntegralMatrix from FunctionFieldCategory +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) +--RinverseIntegralMatrix()$R +--R +--E 1432 + +--S 1433 of 3320 done +)d op inverseIntegralMatrixAtInfinity +--R +--R +--RThere is one exposed function called inverseIntegralMatrixAtInfinity : +--R [1] -> Matrix(Fraction(D3)) from D +--R if D has FFCAT(D2,D3,D4) and D2 has UFD and D3 has UPOLYC( +--R D2) and D4 has UPOLYC(FRAC(D3)) +--R +--RExamples of inverseIntegralMatrixAtInfinity from FunctionFieldCategory +--R +--RP0 := UnivariatePolynomial(x, Integer) +--RP1 := UnivariatePolynomial(y, Fraction P0) +--RR := RadicalFunctionField(INT, P0, P1, 1 - x**20, 20) +--RinverseIntegralMatrixAtInfinity()$R +--R +--E 1433 + +--S 1434 of 3320 +)d op inverseLaplace +--R +--R +--RThere is one exposed function called inverseLaplace : +--R [1] (D1,Symbol,Symbol) -> Union(D1,"failed") +--R from InverseLaplaceTransform(D3,D1) +--R if D3 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) and D1 has Join( +--R TranscendentalFunctionCategory,PrimitiveFunctionCategory, +--R SpecialFunctionCategory,AlgebraicallyClosedFunctionSpace(D3 +--R )) +--R +--RExamples of inverseLaplace from InverseLaplaceTransform +--R +--E 1434 + +--S 1435 of 3320 +)d op invertible? +--R +--R +--RThere are 2 exposed functions called invertible? : +--R [1] (D2,D) -> Boolean from D +--R if D has RSETCAT(D3,D4,D5,D2) and D3 has GCDDOM and D4 +--R has OAMONS and D5 has ORDSET and D2 has RPOLCAT(D3,D4,D5) +--R +--R [2] (D2,D) -> List(Record(val: Boolean,tower: D)) from D +--R if D3 has GCDDOM and D4 has OAMONS and D5 has ORDSET and +--R D2 has RPOLCAT(D3,D4,D5) and D has RSETCAT(D3,D4,D5,D2) +--R +--RExamples of invertible? from RegularTriangularSetCategory +--R +--E 1435 + +--S 1436 of 3320 +)d op invertibleElseSplit? +--R +--R +--RThere is one exposed function called invertibleElseSplit? : +--R [1] (D2,D) -> Union(Boolean,List(D)) from D +--R if D3 has GCDDOM and D4 has OAMONS and D5 has ORDSET and +--R D2 has RPOLCAT(D3,D4,D5) and D has RSETCAT(D3,D4,D5,D2) +--R +--RExamples of invertibleElseSplit? from RegularTriangularSetCategory +--R +--E 1436 + +--S 1437 of 3320 +)d op invertibleSet +--R +--R +--RThere is one exposed function called invertibleSet : +--R [1] (D2,D) -> List(D) from D +--R if D3 has GCDDOM and D4 has OAMONS and D5 has ORDSET and +--R D2 has RPOLCAT(D3,D4,D5) and D has RSETCAT(D3,D4,D5,D2) +--R +--RExamples of invertibleSet from RegularTriangularSetCategory +--R +--E 1437 + +--S 1438 of 3320 +)d op invertIfCan +--R +--R +--RThere is one exposed function called invertIfCan : +--R [1] D1 -> Union(D1,"failed") from MatrixLinearAlgebraFunctions(D2,D3 +--R ,D4,D1) +--R if D2 has INTDOM and D2 has COMRING and D3 has FLAGG(D2) +--R and D4 has FLAGG(D2) and D1 has MATCAT(D2,D3,D4) +--R +--RExamples of invertIfCan from MatrixLinearAlgebraFunctions +--R +--E 1438 + +--S 1439 of 3320 +)d op invmod +--R +--R +--RThere is one exposed function called invmod : +--R [1] (D,D) -> D from D if D has INS +--R +--RExamples of invmod from IntegerNumberSystem +--R +--E 1439 + +--S 1440 of 3320 +)d op invmultisect +--R +--R +--RThere are 2 exposed functions called invmultisect : +--R [1] (Integer,Integer,UnivariateFormalPowerSeries(D2)) -> +--R UnivariateFormalPowerSeries(D2) +--R from UnivariateFormalPowerSeries(D2) if D2 has RING +--R [2] (Integer,Integer,UnivariateTaylorSeriesCZero(D2,D3)) -> +--R UnivariateTaylorSeriesCZero(D2,D3) +--R from UnivariateTaylorSeriesCZero(D2,D3) if D2 has RING and +--R D3: SYMBOL +--R +--RThere are 2 unexposed functions called invmultisect : +--R [1] (Integer,Integer,Stream(D3)) -> Stream(D3) +--R from StreamTaylorSeriesOperations(D3) if D3 has RING +--R [2] (Integer,Integer,UnivariateTaylorSeries(D2,D3,D4)) -> +--R UnivariateTaylorSeries(D2,D3,D4) +--R from UnivariateTaylorSeries(D2,D3,D4) +--R if D2 has RING and D3: SYMBOL and D4: D2 +--R +--RExamples of invmultisect from StreamTaylorSeriesOperations +--R +--R +--RExamples of invmultisect from UnivariateFormalPowerSeries +--R +--R +--RExamples of invmultisect from UnivariateTaylorSeries +--R +--R +--RExamples of invmultisect from UnivariateTaylorSeriesCZero +--R +--E 1440 + +--S 1441 of 3320 +)d op iomode +--R +--R +--RThere is one exposed function called iomode : +--R [1] D -> String from D if D has FILECAT(D2,D3) and D2 has SETCAT and +--R D3 has SETCAT +--R +--RExamples of iomode from FileCategory +--R +--E 1441 + +--S 1442 of 3320 +)d op ipow +--R +--R +--RThere is one unexposed function called ipow : +--R [1] List(D1) -> D1 from CombinatorialFunction(D3,D1) +--R if D1 has FS(D3) and D3 has Join(OrderedSet,IntegralDomain +--R ) +--R +--RExamples of ipow from CombinatorialFunction +--R +--E 1442 + +--S 1443 of 3320 +)d op iprint +--R +--R +--RThere is one unexposed function called iprint : +--R [1] String -> Void from InternalPrintPackage +--R +--RExamples of iprint from InternalPrintPackage +--R +--E 1443 + +--S 1444 of 3320 +)d op iroot +--R +--R +--RThere is one unexposed function called iroot : +--R [1] (D2,Integer) -> D1 from AlgebraicFunction(D2,D1) +--R if D1 has FS(D2) and D2 has RETRACT(INT) and D2 has Join( +--R OrderedSet,IntegralDomain) +--R +--RExamples of iroot from AlgebraicFunction +--R +--E 1444 + +--S 1445 of 3320 +)d op irreducible? +--R +--R +--RThere are 3 exposed functions called irreducible? : +--R [1] D2 -> Boolean from DistinctDegreeFactorize(D3,D2) +--R if D3 has FFIELDC and D2 has UPOLYC(D3) +--R [2] D2 -> Boolean from FiniteFieldFactorization(D3,D2) +--R if D3 has FFIELDC and D2 has UPOLYC(D3) +--R [3] D2 -> Boolean +--R from FiniteFieldFactorizationWithSizeParseBySideEffect(D3, +--R D2) +--R if D3 has FFIELDC and D2 has UPOLYC(D3) +--R +--RExamples of irreducible? from DistinctDegreeFactorize +--R +--R +--RExamples of irreducible? from FiniteFieldFactorization +--R +--R +--RExamples of irreducible? from FiniteFieldFactorizationWithSizeParseBySideEffect +--R +--E 1445 + +--S 1446 of 3320 done +)d op irreducibleFactor +--R +--R +--RThere is one exposed function called irreducibleFactor : +--R [1] (D1,Integer) -> Factored(D1) from Factored(D1) if D1 has INTDOM +--R +--R +--RExamples of irreducibleFactor from Factored +--R +--Ra:=irreducibleFactor(3,1) +--RnthFlag(a,1) +--R +--E 1446 + +--S 1447 of 3320 +)d op irreducibleFactors +--R +--R +--RThere is one unexposed function called irreducibleFactors : +--R [1] List(D5) -> List(D5) from PolynomialSetUtilitiesPackage(D2,D3,D4 +--R ,D5) +--R if D5 has RPOLCAT(D2,D3,D4) and D2 has CHARZ and D2 has +--R EUCDOM and D2 has INTDOM and D3 has OAMONS and D4 has +--R ORDSET +--R +--RExamples of irreducibleFactors from PolynomialSetUtilitiesPackage +--R +--E 1447 + +--S 1448 of 3320 +)d op irreducibleRepresentation +--R +--R +--RThere are 3 exposed functions called irreducibleRepresentation : +--R [1] (List(Integer),Permutation(Integer)) -> Matrix(Integer) +--R from IrrRepSymNatPackage +--R [2] List(Integer) -> List(Matrix(Integer)) from IrrRepSymNatPackage +--R +--R [3] (List(Integer),List(Permutation(Integer))) -> List(Matrix( +--R Integer)) +--R from IrrRepSymNatPackage +--R +--RExamples of irreducibleRepresentation from IrrRepSymNatPackage +--R +--E 1448 + +--S 1449 of 3320 +)d op is? +--R +--R +--RThere are 5 exposed functions called is? : +--R [1] (BasicOperator,Symbol) -> Boolean from BasicOperator +--R [2] (D,Symbol) -> Boolean from D if D has ES +--R [3] (D,BasicOperator) -> Boolean from D if D has ES +--R [4] (D2,D3) -> Boolean from PatternMatch(D4,D2,D3) +--R if D4 has SETCAT and D2 has PATMAB(D4) and D3 has KONVERT( +--R PATTERN(D4)) +--R [5] (List(D5),D3) -> Boolean from PatternMatch(D4,D5,D3) +--R if D5 has PATMAB(D4) and D4 has SETCAT and D3 has KONVERT( +--R PATTERN(D4)) +--R +--RThere are 2 unexposed functions called is? : +--R [1] (Kernel(D3),Symbol) -> Boolean from Kernel(D3) if D3 has ORDSET +--R +--R [2] (Kernel(D3),BasicOperator) -> Boolean from Kernel(D3) if D3 has +--R ORDSET +--R +--RExamples of is? from BasicOperator +--R +--R +--RExamples of is? from ExpressionSpace +--R +--R +--RExamples of is? from Kernel +--R +--R +--RExamples of is? from PatternMatch +--R +--E 1449 + +--S 1450 of 3320 +)d op Is +--R +--R +--RThere are 4 exposed functions called Is : +--R [1] (List(D5),D3) -> PatternMatchListResult(D4,D5,List(D5)) +--R from PatternMatch(D4,D5,D3) +--R if D4 has SETCAT and D5 has PATMAB(D4) and D3 has KONVERT( +--R PATTERN(D4)) +--R [2] (D2,D3) -> List(Equation(D2)) from PatternMatch(D4,D2,D3) +--R if D4 has SETCAT and D2 has RETRACT(SYMBOL) and D2 has +--R PATMAB(D4) and D3 has KONVERT(PATTERN(D4)) +--R [3] (D2,D3) -> List(Equation(Polynomial(D2))) from PatternMatch(D4, +--R D2,D3) +--R if D4 has SETCAT and D2 has RING and not(ofCategory(D2, +--R RetractableTo(Symbol))) and D2 has PATMAB(D4) and D3 has +--R KONVERT(PATTERN(D4)) +--R [4] (D2,D3) -> PatternMatchResult(D4,D2) from PatternMatch(D4,D2,D3) +--R if D4 has SETCAT and not(ofCategory(D2,RetractableTo( +--R Symbol))) and not(ofCategory(D2,Ring)) and D2 has PATMAB(D4 +--R ) and D3 has KONVERT(PATTERN(D4)) +--R +--RExamples of Is from PatternMatch +--R +--E 1450 + +--S 1451 of 3320 +)d op isAbsolutelyIrreducible? +--R +--R +--RThere are 2 exposed functions called isAbsolutelyIrreducible? : +--R [1] (List(Matrix(D4)),Integer) -> Boolean from +--R RepresentationPackage2(D4) +--R if D4 has FIELD and D4 has RING +--R [2] List(Matrix(D3)) -> Boolean from RepresentationPackage2(D3) +--R if D3 has FIELD and D3 has RING +--R +--RExamples of isAbsolutelyIrreducible? from RepresentationPackage2 +--R +--E 1451 + +--S 1452 of 3320 +)d op isExpt +--R +--R +--RThere are 4 exposed functions called isExpt : +--R [1] (D,Symbol) -> Union(Record(var: Kernel(D),exponent: Integer), +--R "failed") +--R from D if D3 has RING and D3 has ORDSET and D has FS(D3) +--R +--R [2] (D,BasicOperator) -> Union(Record(var: Kernel(D),exponent: +--R Integer),"failed") +--R from D if D3 has RING and D3 has ORDSET and D has FS(D3) +--R +--R [3] D -> Union(Record(var: Kernel(D),exponent: Integer),"failed") +--R from D +--R if D2 has SGROUP and D2 has ORDSET and D has FS(D2) +--R [4] D -> Union(Record(var: D4,exponent: NonNegativeInteger),"failed" +--R ) from D +--R if D has POLYCAT(D2,D3,D4) and D2 has RING and D3 has +--R OAMONS and D4 has ORDSET +--R +--RThere are 2 unexposed functions called isExpt : +--R [1] Pattern(D2) -> Union(Record(val: Pattern(D2),exponent: +--R NonNegativeInteger),"failed") +--R from Pattern(D2) if D2 has SETCAT +--R [2] D2 -> Union(Record(var: D4,exponent: Integer),"failed") +--R from PolynomialCategoryQuotientFunctions(D3,D4,D5,D6,D2) +--R if D3 has OAMONS and D4 has ORDSET and D5 has RING and D6 +--R has POLYCAT(D5,D3,D4) and D2 has Fieldwith +--R coerce : D6 -> % +--R numer : % -> D6 +--R denom : % -> D6 +--R +--RExamples of isExpt from FunctionSpace +--R +--R +--RExamples of isExpt from Pattern +--R +--R +--RExamples of isExpt from PolynomialCategory +--R +--R +--RExamples of isExpt from PolynomialCategoryQuotientFunctions +--R +--E 1452 + +--S 1453 of 3320 +)d op isList +--R +--R +--RThere is one unexposed function called isList : +--R [1] Pattern(D2) -> Union(List(Pattern(D2)),"failed") from Pattern(D2 +--R ) +--R if D2 has SETCAT +--R +--RExamples of isList from Pattern +--R +--E 1453 + +--S 1454 of 3320 +)d op isMult +--R +--R +--RThere is one exposed function called isMult : +--R [1] D -> Union(Record(coef: Integer,var: Kernel(D)),"failed") from D +--R if D2 has ABELSG and D2 has ORDSET and D has FS(D2) +--R +--RExamples of isMult from FunctionSpace +--R +--E 1454 + +--S 1455 of 3320 +)d op isobaric? +--R +--R +--RThere is one exposed function called isobaric? : +--R [1] D -> Boolean from D +--R if D has DPOLCAT(D2,D3,D4,D5) and D2 has RING and D3 has +--R ORDSET and D4 has DVARCAT(D3) and D5 has OAMONS +--R +--RExamples of isobaric? from DifferentialPolynomialCategory +--R +--E 1455 + +--S 1456 of 3320 +)d op isOp +--R +--R +--RThere are 2 unexposed functions called isOp : +--R [1] Pattern(D2) -> Union(Record(op: BasicOperator,arg: List(Pattern( +--R D2))),"failed") +--R from Pattern(D2) if D2 has SETCAT +--R [2] (Pattern(D3),BasicOperator) -> Union(List(Pattern(D3)),"failed") +--R from Pattern(D3) if D3 has SETCAT +--R +--RExamples of isOp from Pattern +--R +--E 1456 + +--S 1457 of 3320 +)d op isPlus +--R +--R +--RThere are 2 exposed functions called isPlus : +--R [1] D -> Union(List(D),"failed") from D +--R if D2 has ABELSG and D2 has ORDSET and D has FS(D2) +--R [2] D -> Union(List(D),"failed") from D +--R if D2 has RING and D3 has OAMONS and D4 has ORDSET and D +--R has POLYCAT(D2,D3,D4) +--R +--RThere are 2 unexposed functions called isPlus : +--R [1] Pattern(D2) -> Union(List(Pattern(D2)),"failed") from Pattern(D2 +--R ) +--R if D2 has SETCAT +--R [2] D2 -> Union(List(D2),"failed") +--R from PolynomialCategoryQuotientFunctions(D3,D4,D5,D6,D2) +--R if D3 has OAMONS and D4 has ORDSET and D5 has RING and D6 +--R has POLYCAT(D5,D3,D4) and D2 has Fieldwith +--R coerce : D6 -> % +--R numer : % -> D6 +--R denom : % -> D6 +--R +--RExamples of isPlus from FunctionSpace +--R +--R +--RExamples of isPlus from Pattern +--R +--R +--RExamples of isPlus from PolynomialCategory +--R +--R +--RExamples of isPlus from PolynomialCategoryQuotientFunctions +--R +--E 1457 + +--S 1458 of 3320 +)d op isPower +--R +--R +--RThere is one exposed function called isPower : +--R [1] D -> Union(Record(val: D,exponent: Integer),"failed") from D +--R if D2 has RING and D2 has ORDSET and D has FS(D2) +--R +--RThere are 2 unexposed functions called isPower : +--R [1] Pattern(D2) -> Union(Record(val: Pattern(D2),exponent: Pattern( +--R D2)),"failed") +--R from Pattern(D2) if D2 has SETCAT +--R [2] D2 -> Union(Record(val: D2,exponent: Integer),"failed") +--R from PolynomialCategoryQuotientFunctions(D3,D4,D5,D6,D2) +--R if D3 has OAMONS and D4 has ORDSET and D5 has RING and D6 +--R has POLYCAT(D5,D3,D4) and D2 has Fieldwith +--R coerce : D6 -> % +--R numer : % -> D6 +--R denom : % -> D6 +--R +--RExamples of isPower from FunctionSpace +--R +--R +--RExamples of isPower from Pattern +--R +--R +--RExamples of isPower from PolynomialCategoryQuotientFunctions +--R +--E 1458 + +--S 1459 of 3320 +)d op isQuotient +--R +--R +--RThere is one exposed function called isQuotient : +--R [1] Expression(DoubleFloat) -> Union(Expression(DoubleFloat), +--R "failed") +--R from ExpertSystemToolsPackage +--R +--RThere is one unexposed function called isQuotient : +--R [1] Pattern(D2) -> Union(Record(num: Pattern(D2),den: Pattern(D2)), +--R "failed") +--R from Pattern(D2) if D2 has SETCAT +--R +--RExamples of isQuotient from ExpertSystemToolsPackage +--R +--R +--RExamples of isQuotient from Pattern +--R +--E 1459 + +--S 1460 of 3320 +)d op isTimes +--R +--R +--RThere are 2 exposed functions called isTimes : +--R [1] D -> Union(List(D),"failed") from D +--R if D2 has SGROUP and D2 has ORDSET and D has FS(D2) +--R [2] D -> Union(List(D),"failed") from D +--R if D2 has RING and D3 has OAMONS and D4 has ORDSET and D +--R has POLYCAT(D2,D3,D4) +--R +--RThere are 2 unexposed functions called isTimes : +--R [1] Pattern(D2) -> Union(List(Pattern(D2)),"failed") from Pattern(D2 +--R ) +--R if D2 has SETCAT +--R [2] D2 -> Union(List(D2),"failed") +--R from PolynomialCategoryQuotientFunctions(D3,D4,D5,D6,D2) +--R if D3 has OAMONS and D4 has ORDSET and D5 has RING and D6 +--R has POLYCAT(D5,D3,D4) and D2 has Fieldwith +--R coerce : D6 -> % +--R numer : % -> D6 +--R denom : % -> D6 +--R +--RExamples of isTimes from FunctionSpace +--R +--R +--RExamples of isTimes from Pattern +--R +--R +--RExamples of isTimes from PolynomialCategory +--R +--R +--RExamples of isTimes from PolynomialCategoryQuotientFunctions +--R +--E 1460 + +--S 1461 of 3320 +)d op iter +--R +--R +--RThere is one unexposed function called iter : +--R [1] ((D1 -> D1),NonNegativeInteger,D1) -> D1 +--R from MappingPackageInternalHacks1(D1) if D1 has SETCAT +--R +--RExamples of iter from MappingPackageInternalHacks1 +--R +--E 1461 + +--S 1462 of 3320 +)d op iteratedInitials +--R +--R +--RThere is one exposed function called iteratedInitials : +--R [1] D -> List(D) from D +--R if D2 has RING and D3 has OAMONS and D4 has ORDSET and D +--R has RPOLCAT(D2,D3,D4) +--R +--RExamples of iteratedInitials from RecursivePolynomialCategory +--R +--E 1462 + +--S 1463 of 3320 +)d op itsALeaf! +--R +--R +--RThere is one exposed function called itsALeaf! : +--R [1] D -> Void from D +--R if D has PLACESC(D2,D3) and D2 has FIELD and D3 has +--R LOCPOWC(D2) +--R +--RExamples of itsALeaf! from PlacesCategory +--R +--E 1463 + +--S 1464 of 3320 +)d op jacobi +--R +--R +--RThere is one exposed function called jacobi : +--R [1] (Integer,Integer) -> Integer from IntegerNumberTheoryFunctions +--R +--R +--RExamples of jacobi from IntegerNumberTheoryFunctions +--R +--E 1464 + +--S 1465 of 3320 +)d op jacobian +--R +--R +--RThere are 2 exposed functions called jacobian : +--R [1] (Vector(Expression(DoubleFloat)),List(Symbol)) -> Matrix( +--R Expression(DoubleFloat)) +--R from d02AgentsPackage +--R [2] (D2,D3) -> Matrix(D5) from MultiVariableCalculusFunctions(D4,D5, +--R D2,D3) +--R if D4 has SETCAT and D5 has PDRING(D4) and D2 has FLAGG(D5 +--R ) and D3 has FiniteLinearAggregate(D4)with +--R finiteAggregate +--R +--RExamples of jacobian from d02AgentsPackage +--R +--R +--RExamples of jacobian from MultiVariableCalculusFunctions +--R +--E 1465 + +--S 1466 of 3320 +)d op jacobiIdentity? +--R +--R +--RThere is one exposed function called jacobiIdentity? : +--R [1] -> Boolean from D if D has FINAALG(D2) and D2 has COMRING +--R +--RThere is one unexposed function called jacobiIdentity? : +--R [1] -> Boolean from FiniteRankNonAssociativeAlgebra&(D2,D3) +--R if D3 has COMRING and D2 has FINAALG(D3) +--R +--RExamples of jacobiIdentity? from FiniteRankNonAssociativeAlgebra& +--R +--R +--RExamples of jacobiIdentity? from FiniteRankNonAssociativeAlgebra +--R +--E 1466 + +--S 1467 of 3320 +)d op janko2 +--R +--R +--RThere are 2 exposed functions called janko2 : +--R [1] List(Integer) -> PermutationGroup(Integer) from +--R PermutationGroupExamples +--R [2] -> PermutationGroup(Integer) from PermutationGroupExamples +--R +--RExamples of janko2 from PermutationGroupExamples +--R +--E 1467 + +--S 1468 of 3320 +)d op join +--R +--R +--RThere is one exposed function called join : +--R [1] (SparseEchelonMatrix(D1,D2),SparseEchelonMatrix(D1,D2)) -> +--R SparseEchelonMatrix(D1,D2) +--R from SparseEchelonMatrix(D1,D2) if D1 has ORDSET and D2 +--R has RING +--R +--RExamples of join from SparseEchelonMatrix +--R +--E 1468 + +--S 1469 of 3320 +)d op jordanAdmissible? +--R +--R +--RThere is one exposed function called jordanAdmissible? : +--R [1] -> Boolean from D if D has FINAALG(D2) and D2 has COMRING +--R +--RThere is one unexposed function called jordanAdmissible? : +--R [1] -> Boolean from FiniteRankNonAssociativeAlgebra&(D2,D3) +--R if D3 has COMRING and D2 has FINAALG(D3) +--R +--RExamples of jordanAdmissible? from FiniteRankNonAssociativeAlgebra& +--R +--R +--RExamples of jordanAdmissible? from FiniteRankNonAssociativeAlgebra +--R +--E 1469 + +--S 1470 of 3320 +)d op jordanAlgebra? +--R +--R +--RThere is one exposed function called jordanAlgebra? : +--R [1] -> Boolean from D if D has FINAALG(D2) and D2 has COMRING +--R +--RThere is one unexposed function called jordanAlgebra? : +--R [1] -> Boolean from FiniteRankNonAssociativeAlgebra&(D2,D3) +--R if D3 has COMRING and D2 has FINAALG(D3) +--R +--RExamples of jordanAlgebra? from FiniteRankNonAssociativeAlgebra& +--R +--R +--RExamples of jordanAlgebra? from FiniteRankNonAssociativeAlgebra +--R +--E 1470 + +--S 1471 of 3320 +)d op karatsuba +--R +--R +--RThere is one exposed function called karatsuba : +--R [1] (D1,D1,NonNegativeInteger,NonNegativeInteger) -> D1 +--R from UnivariatePolynomialMultiplicationPackage(D3,D1) +--R if D3 has RING and D1 has UPOLYC(D3) +--R +--RExamples of karatsuba from UnivariatePolynomialMultiplicationPackage +--R +--E 1471 + +--S 1472 of 3320 +)d op karatsubaDivide +--R +--R +--RThere is one exposed function called karatsubaDivide : +--R [1] (D,NonNegativeInteger) -> Record(quotient: D,remainder: D) from +--R D +--R if D3 has RING and D has UPOLYC(D3) +--R +--RExamples of karatsubaDivide from UnivariatePolynomialCategory +--R +--E 1472 + +--S 1473 of 3320 +)d op karatsubaOnce +--R +--R +--RThere is one exposed function called karatsubaOnce : +--R [1] (D1,D1) -> D1 from UnivariatePolynomialMultiplicationPackage(D2, +--R D1) +--R if D2 has RING and D1 has UPOLYC(D2) +--R +--RExamples of karatsubaOnce from UnivariatePolynomialMultiplicationPackage +--R +--E 1473 + +--S 1474 of 3320 +)d op kernel +--R +--R +--RThere are 2 exposed functions called kernel : +--R [1] (BasicOperator,List(D)) -> D from D if D has ES +--R [2] (BasicOperator,D) -> D from D if D has ES +--R +--RThere are 2 unexposed functions called kernel : +--R [1] Symbol -> Kernel(D2) from Kernel(D2) if D2 has ORDSET +--R [2] (BasicOperator,List(D4),NonNegativeInteger) -> Kernel(D4) from +--R Kernel(D4) +--R if D4 has ORDSET +--R +--RExamples of kernel from ExpressionSpace +--R +--R +--RExamples of kernel from Kernel +--R +--E 1474 + +--S 1475 of 3320 +)d op kernels +--R +--R +--RThere is one exposed function called kernels : +--R [1] D -> List(Kernel(D)) from D if D has ES +--R +--RExamples of kernels from ExpressionSpace +--R +--E 1475 + +--S 1476 of 3320 +)d op key +--R +--R +--RThere is one exposed function called key : +--R [1] ThreeDimensionalViewport -> Integer from +--R ThreeDimensionalViewport +--R +--RThere are 2 unexposed functions called key : +--R [1] GraphImage -> Integer from GraphImage +--R [2] TwoDimensionalViewport -> Integer from TwoDimensionalViewport +--R +--R +--RExamples of key from GraphImage +--R +--R +--RExamples of key from TwoDimensionalViewport +--R +--R +--RExamples of key from ThreeDimensionalViewport +--R +--E 1476 + +--S 1477 of 3320 +)d op key? +--R +--R +--RThere is one exposed function called key? : +--R [1] (D2,D) -> Boolean from D +--R if D has KDAGG(D2,D3) and D2 has SETCAT and D3 has SETCAT +--R +--R +--RExamples of key? from KeyedDictionary +--R +--E 1477 + +--S 1478 of 3320 +)d op keys +--R +--R +--RThere are 3 exposed functions called keys : +--R [1] IntegrationFunctionsTable -> List(Record(var: Symbol,fn: +--R Expression(DoubleFloat),range: Segment(OrderedCompletion( +--R DoubleFloat)),abserr: DoubleFloat,relerr: DoubleFloat)) +--R from IntegrationFunctionsTable +--R [2] D -> List(D2) from D if D has KDAGG(D2,D3) and D2 has SETCAT and +--R D3 has SETCAT +--R [3] ODEIntensityFunctionsTable -> List(Record(xinit: DoubleFloat, +--R xend: DoubleFloat,fn: Vector(Expression(DoubleFloat)),yinit: List +--R (DoubleFloat),intvals: List(DoubleFloat),g: Expression( +--R DoubleFloat),abserr: DoubleFloat,relerr: DoubleFloat)) +--R from ODEIntensityFunctionsTable +--R +--RExamples of keys from IntegrationFunctionsTable +--R +--R +--RExamples of keys from KeyedDictionary +--R +--R +--RExamples of keys from ODEIntensityFunctionsTable +--R +--E 1478 + +--S 1479 of 3320 +)d op kmax +--R +--R +--RThere is one unexposed function called kmax : +--R [1] List(Kernel(D4)) -> Kernel(D4) from IntegrationTools(D3,D4) +--R if D3 has ORDSET and D4 has FS(D3) +--R +--RExamples of kmax from IntegrationTools +--R +--E 1479 + +--S 1480 of 3320 +)d op knownInfBasis +--R +--R +--RThere is one unexposed function called knownInfBasis : +--R [1] NonNegativeInteger -> Void from AlgebraicFunctionField(D3,D4,D5, +--R D6) +--R if D3 has FIELD and D4 has UPOLYC(D3) and D5 has UPOLYC( +--R FRAC(D4)) and D6: D5 +--R +--RExamples of knownInfBasis from AlgebraicFunctionField +--R +--E 1480 + +--S 1481 of 3320 +)d op kovacic +--R +--R +--RThere are 2 unexposed functions called kovacic : +--R [1] (Fraction(D4),Fraction(D4),Fraction(D4)) -> Union( +--R SparseUnivariatePolynomial(Fraction(D4)),"failed") +--R from Kovacic(D3,D4) +--R if D3 has Join(CharacteristicZero,AlgebraicallyClosedField +--R ,RetractableTo(Integer),RetractableTo(Fraction(Integer))) +--R and D4 has UPOLYC(D3) +--R [2] (Fraction(D5),Fraction(D5),Fraction(D5),(D5 -> Factored(D5))) +--R -> Union(SparseUnivariatePolynomial(Fraction(D5)),"failed") +--R from Kovacic(D4,D5) +--R if D5 has UPOLYC(D4) and D4 has Join(CharacteristicZero, +--R AlgebraicallyClosedField,RetractableTo(Integer), +--R RetractableTo(Fraction(Integer))) +--R +--RExamples of kovacic from Kovacic +--R +--E 1481 + +--S 1482 of 3320 done +)d op kroneckerDelta +--R +--R +--RThere is one exposed function called kroneckerDelta : +--R [1] -> CartesianTensor(D1,D2,D3) from CartesianTensor(D1,D2,D3) +--R if D1: INT and D2: NNI and D3 has COMRING +--R +--RExamples of kroneckerDelta from CartesianTensor +--R +--Rdelta:CartesianTensor(1,2,Integer):=kroneckerDelta() +--R +--E 1482 + +--S 1483 of 3320 +)d op KrullNumber +--R +--R +--RThere are 2 exposed functions called KrullNumber : +--R [1] (List(D7),List(D8)) -> NonNegativeInteger +--R from RegularSetDecompositionPackage(D4,D5,D6,D7,D8) +--R if D7 has RPOLCAT(D4,D5,D6) and D8 has RSETCAT(D4,D5,D6,D7 +--R ) and D4 has GCDDOM and D5 has OAMONS and D6 has ORDSET +--R [2] (List(D7),List(D8)) -> NonNegativeInteger +--R from SquareFreeRegularSetDecompositionPackage(D4,D5,D6,D7, +--R D8) +--R if D7 has RPOLCAT(D4,D5,D6) and D8 has SFRTCAT(D4,D5,D6,D7 +--R ) and D4 has GCDDOM and D5 has OAMONS and D6 has ORDSET +--R +--RExamples of KrullNumber from RegularSetDecompositionPackage +--R +--R +--RExamples of KrullNumber from SquareFreeRegularSetDecompositionPackage +--R +--E 1483 + +--S 1484 of 3320 +)d op ksec +--R +--R +--RThere is one unexposed function called ksec : +--R [1] (Kernel(D5),List(Kernel(D5)),Symbol) -> Kernel(D5) +--R from IntegrationTools(D4,D5) if D5 has FS(D4) and D4 has +--R ORDSET +--R +--RExamples of ksec from IntegrationTools +--R +--E 1484 + +--S 1485 of 3320 +)d op label +--R +--R +--RThere is one unexposed function called label : +--R [1] (OutputForm,OutputForm) -> OutputForm from OutputForm +--R +--RExamples of label from OutputForm +--R +--E 1485 + +--S 1486 of 3320 +)d op lagrange +--R +--R +--RThere are 2 exposed functions called lagrange : +--R [1] UnivariateFormalPowerSeries(D1) -> UnivariateFormalPowerSeries( +--R D1) +--R from UnivariateFormalPowerSeries(D1) if D1 has RING +--R [2] UnivariateTaylorSeriesCZero(D1,D2) -> +--R UnivariateTaylorSeriesCZero(D1,D2) +--R from UnivariateTaylorSeriesCZero(D1,D2) if D1 has RING and +--R D2: SYMBOL +--R +--RThere are 2 unexposed functions called lagrange : +--R [1] Stream(D2) -> Stream(D2) from StreamTaylorSeriesOperations(D2) +--R if D2 has RING +--R [2] UnivariateTaylorSeries(D1,D2,D3) -> UnivariateTaylorSeries(D1,D2 +--R ,D3) +--R from UnivariateTaylorSeries(D1,D2,D3) +--R if D1 has RING and D2: SYMBOL and D3: D1 +--R +--RExamples of lagrange from StreamTaylorSeriesOperations +--R +--R +--RExamples of lagrange from UnivariateFormalPowerSeries +--R +--R +--RExamples of lagrange from UnivariateTaylorSeries +--R +--R +--RExamples of lagrange from UnivariateTaylorSeriesCZero +--R +--E 1486 + +--S 1487 of 3320 +)d op LagrangeInterpolation +--R +--R +--RThere is one unexposed function called LagrangeInterpolation : +--R [1] (List(D3),List(D3)) -> D1 from PolynomialInterpolationAlgorithms +--R (D3,D1) +--R if D3 has FIELD and D1 has UPOLYC(D3) +--R +--RExamples of LagrangeInterpolation from PolynomialInterpolationAlgorithms +--R +--E 1487 + +--S 1488 of 3320 +)d op laguerre +--R +--R +--RThere is one unexposed function called laguerre : +--R [1] Integer -> SparseUnivariatePolynomial(Integer) +--R from PolynomialNumberTheoryFunctions +--R +--RExamples of laguerre from PolynomialNumberTheoryFunctions +--R +--E 1488 + +--S 1489 of 3320 +)d op laguerreL +--R +--R +--RThere are 2 exposed functions called laguerreL : +--R [1] (NonNegativeInteger,D1) -> D1 from OrthogonalPolynomialFunctions +--R (D1) +--R if D1 has COMRING +--R [2] (NonNegativeInteger,NonNegativeInteger,D1) -> D1 +--R from OrthogonalPolynomialFunctions(D1) if D1 has COMRING +--R +--R +--RExamples of laguerreL from OrthogonalPolynomialFunctions +--R +--E 1489 + +--S 1490 of 3320 +)d op lambda +--R +--R +--RThere is one unexposed function called lambda : +--R [1] (InputForm,List(Symbol)) -> InputForm from InputForm +--R +--RExamples of lambda from InputForm +--R +--E 1490 + +--S 1491 of 3320 +)d op lambert +--R +--R +--RThere are 2 exposed functions called lambert : +--R [1] UnivariateFormalPowerSeries(D1) -> UnivariateFormalPowerSeries( +--R D1) +--R from UnivariateFormalPowerSeries(D1) if D1 has RING +--R [2] UnivariateTaylorSeriesCZero(D1,D2) -> +--R UnivariateTaylorSeriesCZero(D1,D2) +--R from UnivariateTaylorSeriesCZero(D1,D2) if D1 has RING and +--R D2: SYMBOL +--R +--RThere are 2 unexposed functions called lambert : +--R [1] Stream(D2) -> Stream(D2) from StreamTaylorSeriesOperations(D2) +--R if D2 has RING +--R [2] UnivariateTaylorSeries(D1,D2,D3) -> UnivariateTaylorSeries(D1,D2 +--R ,D3) +--R from UnivariateTaylorSeries(D1,D2,D3) +--R if D1 has RING and D2: SYMBOL and D3: D1 +--R +--RExamples of lambert from StreamTaylorSeriesOperations +--R +--R +--RExamples of lambert from UnivariateFormalPowerSeries +--R +--R +--RExamples of lambert from UnivariateTaylorSeries +--R +--R +--RExamples of lambert from UnivariateTaylorSeriesCZero +--R +--E 1491 + +--S 1492 of 3320 +)d op laplace +--R +--R +--RThere is one exposed function called laplace : +--R [1] (D1,Symbol,Symbol) -> D1 from LaplaceTransform(D3,D1) +--R if D3 has Join(EuclideanDomain,OrderedSet, +--R CharacteristicZero,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) and D1 has Join( +--R TranscendentalFunctionCategory,PrimitiveFunctionCategory, +--R AlgebraicallyClosedFunctionSpace(D3)) +--R +--RExamples of laplace from LaplaceTransform +--R +--E 1492 + +--S 1493 of 3320 +)d op laplacian +--R +--R +--RThere is one exposed function called laplacian : +--R [1] (D1,D2) -> D1 from MultiVariableCalculusFunctions(D3,D1,D4,D2) +--R if D3 has SETCAT and D1 has PDRING(D3) and D4 has FLAGG(D1 +--R ) and D2 has FiniteLinearAggregate(D3)with +--R finiteAggregate +--R +--RExamples of laplacian from MultiVariableCalculusFunctions +--R +--E 1493 + +--S 1494 of 3320 +)d op largest +--R +--R +--RThere are 2 unexposed functions called largest : +--R [1] (List(D1),((D1,D1) -> Boolean)) -> D1 from +--R UserDefinedPartialOrdering(D1) +--R if D1 has SETCAT +--R [2] List(D1) -> D1 from UserDefinedPartialOrdering(D1) +--R if D1 has SETCAT and D1 has ORDSET +--R +--RExamples of largest from UserDefinedPartialOrdering +--R +--E 1494 + +--S 1495 of 3320 +)d op last +--R +--R +--RThere are 4 exposed functions called last : +--R [1] D -> D1 from D if D has DLAGG(D1) and D1 has TYPE +--R [2] D -> Union(D1,"failed") from D +--R if D has TSETCAT(D2,D3,D4,D1) and D2 has INTDOM and D3 +--R has OAMONS and D4 has ORDSET and D1 has RPOLCAT(D2,D3,D4) +--R +--R [3] (D,NonNegativeInteger) -> D from D if D has URAGG(D2) and D2 +--R has TYPE +--R [4] D -> D1 from D if D has URAGG(D1) and D1 has TYPE +--R +--RExamples of last from DoublyLinkedAggregate +--R +--R +--RExamples of last from TriangularSetCategory +--R +--R +--RExamples of last from UnaryRecursiveAggregate +--R +--Rlast([1,4,2,-6,0,3,5,4,2,3],3) +--R +--Rlast [1,4,2,-6,0,3,5,4,2,3] +--R +--E 1495 + +--S 1496 of 3320 +)d op lastNonNul +--R +--R +--RThere is one exposed function called lastNonNul : +--R [1] D -> Integer from D if D has PRSPCAT(D2) and D2 has FIELD +--R +--RExamples of lastNonNul from ProjectiveSpaceCategory +--R +--E 1496 + +--S 1497 of 3320 +)d op lastNonNull +--R +--R +--RThere is one exposed function called lastNonNull : +--R [1] D -> Integer from D if D has PRSPCAT(D2) and D2 has FIELD +--R +--RExamples of lastNonNull from ProjectiveSpaceCategory +--R +--E 1497 + +--S 1498 of 3320 +)d op lastSubResultant +--R +--R +--RThere are 2 exposed functions called lastSubResultant : +--R [1] (D,D) -> D from D +--R if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has +--R OAMONS and D3 has ORDSET and D1 has INTDOM +--R [2] (D2,D2,D) -> List(Record(val: D2,tower: D)) from D +--R if D3 has GCDDOM and D4 has OAMONS and D5 has ORDSET and +--R D2 has RPOLCAT(D3,D4,D5) and D has RSETCAT(D3,D4,D5,D2) +--R +--RThere are 2 unexposed functions called lastSubResultant : +--R [1] (NewSparseUnivariatePolynomial(D1),NewSparseUnivariatePolynomial +--R (D1)) -> NewSparseUnivariatePolynomial(D1) +--R from NewSparseUnivariatePolynomial(D1) if D1 has INTDOM +--R and D1 has RING +--R [2] (D1,D1) -> D1 from PseudoRemainderSequence(D2,D1) +--R if D2 has INTDOM and D1 has UPOLYC(D2) +--R +--RExamples of lastSubResultant from NewSparseUnivariatePolynomial +--R +--R +--RExamples of lastSubResultant from PseudoRemainderSequence +--R +--R +--RExamples of lastSubResultant from RecursivePolynomialCategory +--R +--R +--RExamples of lastSubResultant from RegularTriangularSetCategory +--R +--E 1498 + +--S 1499 of 3320 +)d op lastSubResultantElseSplit +--R +--R +--RThere is one exposed function called lastSubResultantElseSplit : +--R [1] (D2,D2,D) -> Union(D2,List(D)) from D +--R if D3 has GCDDOM and D4 has OAMONS and D5 has ORDSET and +--R D2 has RPOLCAT(D3,D4,D5) and D has RSETCAT(D3,D4,D5,D2) +--R +--RExamples of lastSubResultantElseSplit from RegularTriangularSetCategory +--R +--E 1499 + +--S 1500 of 3320 +)d op lastSubResultantEuclidean +--R +--R +--RThere is one unexposed function called lastSubResultantEuclidean : +--R [1] (D2,D2) -> Record(coef1: D2,coef2: D2,subResultant: D2) +--R from PseudoRemainderSequence(D3,D2) +--R if D3 has INTDOM and D2 has UPOLYC(D3) +--R +--RExamples of lastSubResultantEuclidean from PseudoRemainderSequence +--R +--E 1500 + +--S 1501 of 3320 +)d op latex +--R +--R +--RThere are 6 exposed functions called latex : +--R [1] ArrayStack(D2) -> String from ArrayStack(D2) +--R if D2 has SETCAT and D2 has SETCAT +--R [2] Dequeue(D2) -> String from Dequeue(D2) if D2 has SETCAT and D2 +--R has SETCAT +--R [3] Heap(D2) -> String from Heap(D2) if D2 has SETCAT and D2 has +--R ORDSET +--R [4] Queue(D2) -> String from Queue(D2) if D2 has SETCAT and D2 has +--R SETCAT +--R [5] D -> String from D if D has SETCAT +--R [6] Stack(D2) -> String from Stack(D2) if D2 has SETCAT and D2 has +--R SETCAT +--R +--RExamples of latex from ArrayStack +--R +--Ra:ArrayStack INT:= arrayStack [1,2,3,4,5] +--Rlatex a +--R +--R +--RExamples of latex from Dequeue +--R +--Ra:Dequeue INT:= dequeue [1,2,3,4,5] +--Rlatex a +--R +--R +--RExamples of latex from Heap +--R +--Ra:Heap INT:= heap [1,2,3,4,5] +--Rlatex a +--R +--R +--RExamples of latex from Queue +--R +--Ra:Queue INT:= queue [1,2,3,4,5] +--Rlatex a +--R +--R +--RExamples of latex from SetCategory +--R +--R +--RExamples of latex from Stack +--R +--Ra:Stack INT:= stack [1,2,3,4,5] +--Rlatex a +--R +--E 1501 + +--S 1502 of 3320 +)d op laurent +--R +--R +--RThere are 9 exposed functions called laurent : +--R [1] Symbol -> Any from ExpressionToUnivariatePowerSeries(D3,D4) +--R if D3 has Join(GcdDomain,OrderedSet,RetractableTo(Integer) +--R ,LinearlyExplicitRingOver(Integer)) and D4 has Join( +--R AlgebraicallyClosedField,TranscendentalFunctionCategory, +--R FunctionSpace(D3)) +--R [2] D2 -> Any from ExpressionToUnivariatePowerSeries(D3,D2) +--R if D3 has Join(GcdDomain,OrderedSet,RetractableTo(Integer) +--R ,LinearlyExplicitRingOver(Integer)) and D2 has Join( +--R AlgebraicallyClosedField,TranscendentalFunctionCategory, +--R FunctionSpace(D3)) +--R [3] (D2,Integer) -> Any from ExpressionToUnivariatePowerSeries(D4,D2 +--R ) +--R if D4 has Join(GcdDomain,OrderedSet,RetractableTo(Integer) +--R ,LinearlyExplicitRingOver(Integer)) and D2 has Join( +--R AlgebraicallyClosedField,TranscendentalFunctionCategory, +--R FunctionSpace(D4)) +--R [4] (D2,Equation(D2)) -> Any from ExpressionToUnivariatePowerSeries( +--R D4,D2) +--R if D2 has Join(AlgebraicallyClosedField, +--R TranscendentalFunctionCategory,FunctionSpace(D4)) and D4 +--R has Join(GcdDomain,OrderedSet,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R [5] (D2,Equation(D2),Integer) -> Any +--R from ExpressionToUnivariatePowerSeries(D5,D2) +--R if D2 has Join(AlgebraicallyClosedField, +--R TranscendentalFunctionCategory,FunctionSpace(D5)) and D5 +--R has Join(GcdDomain,OrderedSet,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R [6] ((Integer -> D6),Equation(D6),UniversalSegment(Integer)) -> Any +--R from GenerateUnivariatePowerSeries(D5,D6) +--R if D6 has Join(AlgebraicallyClosedField, +--R TranscendentalFunctionCategory,FunctionSpace(D5)) and D5 +--R has Join(IntegralDomain,OrderedSet,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R [7] (D2,Symbol,Equation(D2),UniversalSegment(Integer)) -> Any +--R from GenerateUnivariatePowerSeries(D6,D2) +--R if D2 has Join(AlgebraicallyClosedField, +--R TranscendentalFunctionCategory,FunctionSpace(D6)) and D6 +--R has Join(IntegralDomain,OrderedSet,RetractableTo(Integer), +--R LinearlyExplicitRingOver(Integer)) +--R [8] (Integer,D2) -> D from D +--R if D3 has RING and D has ULSCCAT(D3,D2) and D2 has UTSCAT( +--R D3) +--R [9] D -> D1 from D if D has UPXSCCA(D2,D1) and D2 has RING and D1 +--R has ULSCAT(D2) +--R +--RExamples of laurent from ExpressionToUnivariatePowerSeries +--R +--R +--RExamples of laurent from GenerateUnivariatePowerSeries +--R +--R +--RExamples of laurent from UnivariateLaurentSeriesConstructorCategory +--R +--R +--RExamples of laurent from UnivariatePuiseuxSeriesConstructorCategory +--R +--E 1502 + +--S 1503 of 3320 +)d op laurentIfCan +--R +--R +--RThere is one exposed function called laurentIfCan : +--R [1] D -> Union(D1,"failed") from D +--R if D has UPXSCCA(D2,D1) and D2 has RING and D1 has ULSCAT( +--R D2) +--R +--RExamples of laurentIfCan from UnivariatePuiseuxSeriesConstructorCategory +--R +--E 1503 + +--S 1504 of 3320 +)d op laurentRep +--R +--R +--RThere is one exposed function called laurentRep : +--R [1] D -> D1 from D if D has UPXSCCA(D2,D1) and D2 has RING and D1 +--R has ULSCAT(D2) +--R +--RExamples of laurentRep from UnivariatePuiseuxSeriesConstructorCategory +--R +--E 1504 + +--S 1505 of 3320 +)d op Lazard +--R +--R +--RThere is one unexposed function called Lazard : +--R [1] (D1,D1,NonNegativeInteger) -> D1 from PseudoRemainderSequence(D1 +--R ,D3) +--R if D1 has INTDOM and D3 has UPOLYC(D1) +--R +--RExamples of Lazard from PseudoRemainderSequence +--R +--E 1505 + +--S 1506 of 3320 +)d op Lazard2 +--R +--R +--RThere is one unexposed function called Lazard2 : +--R [1] (D1,D2,D2,NonNegativeInteger) -> D1 from PseudoRemainderSequence +--R (D2,D1) +--R if D2 has INTDOM and D1 has UPOLYC(D2) +--R +--RExamples of Lazard2 from PseudoRemainderSequence +--R +--E 1506 + +--S 1507 of 3320 +)d op LazardQuotient +--R +--R +--RThere is one exposed function called LazardQuotient : +--R [1] (D,D,NonNegativeInteger) -> D from D +--R if D has RPOLCAT(D2,D3,D4) and D2 has RING and D3 has +--R OAMONS and D4 has ORDSET and D2 has INTDOM +--R +--RExamples of LazardQuotient from RecursivePolynomialCategory +--R +--E 1507 + +--S 1508 of 3320 +)d op LazardQuotient2 +--R +--R +--RThere is one exposed function called LazardQuotient2 : +--R [1] (D,D,D,NonNegativeInteger) -> D from D +--R if D has RPOLCAT(D2,D3,D4) and D2 has RING and D3 has +--R OAMONS and D4 has ORDSET and D2 has INTDOM +--R +--RExamples of LazardQuotient2 from RecursivePolynomialCategory +--R +--E 1508 + +--S 1509 of 3320 done +)d op lazy? +--R +--R +--RThere is one exposed function called lazy? : +--R [1] D -> Boolean from D if D has LZSTAGG(D2) and D2 has TYPE +--R +--RExamples of lazy? from LazyStreamAggregate +--R +--Rm:=[i for i in 0..] +--Rlazy? m +--R +--E 1509 + +--S 1510 of 3320 +)d op lazyEvaluate +--R +--R +--RThere is one exposed function called lazyEvaluate : +--R [1] D -> D from D if D has LZSTAGG(D1) and D1 has TYPE +--R +--RExamples of lazyEvaluate from LazyStreamAggregate +--R +--E 1510 + +--S 1511 of 3320 +)d op lazyGintegrate +--R +--R +--RThere is one unexposed function called lazyGintegrate : +--R [1] ((Integer -> D3),D3,(() -> Stream(D3))) -> Stream(D3) +--R from StreamTaylorSeriesOperations(D3) if D3 has FIELD and +--R D3 has RING +--R +--RExamples of lazyGintegrate from StreamTaylorSeriesOperations +--R +--E 1511 + +--S 1512 of 3320 +)d op lazyIntegrate +--R +--R +--RThere is one unexposed function called lazyIntegrate : +--R [1] (D2,(() -> Stream(D2))) -> Stream(D2) +--R from StreamTaylorSeriesOperations(D2) +--R if D2 has ALGEBRA(FRAC(INT)) and D2 has RING +--R +--RExamples of lazyIntegrate from StreamTaylorSeriesOperations +--R +--E 1512 + +--S 1513 of 3320 +)d op lazyIrreducibleFactors +--R +--R +--RThere is one unexposed function called lazyIrreducibleFactors : +--R [1] List(D5) -> List(D5) from PolynomialSetUtilitiesPackage(D2,D3,D4 +--R ,D5) +--R if D5 has RPOLCAT(D2,D3,D4) and D2 has CHARZ and D2 has +--R EUCDOM and D2 has INTDOM and D3 has OAMONS and D4 has +--R ORDSET +--R +--RExamples of lazyIrreducibleFactors from PolynomialSetUtilitiesPackage +--R +--E 1513 + +--S 1514 of 3320 +)d op lazyPquo +--R +--R +--RThere are 2 exposed functions called lazyPquo : +--R [1] (D,D,D1) -> D from D +--R if D has RPOLCAT(D2,D3,D1) and D2 has RING and D3 has +--R OAMONS and D1 has ORDSET +--R [2] (D,D) -> D from D +--R if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has +--R OAMONS and D3 has ORDSET +--R +--RExamples of lazyPquo from RecursivePolynomialCategory +--R +--E 1514 + +--S 1515 of 3320 +)d op lazyPrem +--R +--R +--RThere are 2 exposed functions called lazyPrem : +--R [1] (D,D,D1) -> D from D +--R if D has RPOLCAT(D2,D3,D1) and D2 has RING and D3 has +--R OAMONS and D1 has ORDSET +--R [2] (D,D) -> D from D +--R if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has +--R OAMONS and D3 has ORDSET +--R +--RExamples of lazyPrem from RecursivePolynomialCategory +--R +--E 1515 + +--S 1516 of 3320 +)d op lazyPremWithDefault +--R +--R +--RThere are 2 exposed functions called lazyPremWithDefault : +--R [1] (D,D,D2) -> Record(coef: D,gap: NonNegativeInteger,remainder: D) +--R from D +--R if D3 has RING and D4 has OAMONS and D2 has ORDSET and D +--R has RPOLCAT(D3,D4,D2) +--R [2] (D,D) -> Record(coef: D,gap: NonNegativeInteger,remainder: D) +--R from D +--R if D2 has RING and D3 has OAMONS and D4 has ORDSET and D +--R has RPOLCAT(D2,D3,D4) +--R +--RExamples of lazyPremWithDefault from RecursivePolynomialCategory +--R +--E 1516 + +--S 1517 of 3320 +)d op lazyPseudoDivide +--R +--R +--RThere are 2 exposed functions called lazyPseudoDivide : +--R [1] (D,D,D2) -> Record(coef: D,gap: NonNegativeInteger,quotient: D, +--R remainder: D) +--R from D +--R if D3 has RING and D4 has OAMONS and D2 has ORDSET and D +--R has RPOLCAT(D3,D4,D2) +--R [2] (D,D) -> Record(coef: D,gap: NonNegativeInteger,quotient: D, +--R remainder: D) +--R from D +--R if D2 has RING and D3 has OAMONS and D4 has ORDSET and D +--R has RPOLCAT(D2,D3,D4) +--R +--RThere is one unexposed function called lazyPseudoDivide : +--R [1] (NewSparseUnivariatePolynomial(D2),NewSparseUnivariatePolynomial +--R (D2)) -> Record(coef: D2,gap: NonNegativeInteger,quotient: +--R NewSparseUnivariatePolynomial(D2),remainder: +--R NewSparseUnivariatePolynomial(D2)) +--R from NewSparseUnivariatePolynomial(D2) if D2 has RING +--R +--RExamples of lazyPseudoDivide from NewSparseUnivariatePolynomial +--R +--R +--RExamples of lazyPseudoDivide from RecursivePolynomialCategory +--R +--E 1517 + +--S 1518 of 3320 +)d op lazyPseudoQuotient +--R +--R +--RThere is one unexposed function called lazyPseudoQuotient : +--R [1] (NewSparseUnivariatePolynomial(D1),NewSparseUnivariatePolynomial +--R (D1)) -> NewSparseUnivariatePolynomial(D1) +--R from NewSparseUnivariatePolynomial(D1) if D1 has RING +--R +--RExamples of lazyPseudoQuotient from NewSparseUnivariatePolynomial +--R +--E 1518 + +--S 1519 of 3320 +)d op lazyPseudoRemainder +--R +--R +--RThere is one unexposed function called lazyPseudoRemainder : +--R [1] (NewSparseUnivariatePolynomial(D1),NewSparseUnivariatePolynomial +--R (D1)) -> NewSparseUnivariatePolynomial(D1) +--R from NewSparseUnivariatePolynomial(D1) if D1 has RING +--R +--RExamples of lazyPseudoRemainder from NewSparseUnivariatePolynomial +--R +--E 1519 + +--S 1520 of 3320 +)d op lazyResidueClass +--R +--R +--RThere is one exposed function called lazyResidueClass : +--R [1] (D,D) -> Record(polnum: D,polden: D,power: NonNegativeInteger) +--R from D +--R if D2 has RING and D3 has OAMONS and D4 has ORDSET and D +--R has RPOLCAT(D2,D3,D4) +--R +--RThere is one unexposed function called lazyResidueClass : +--R [1] (NewSparseUnivariatePolynomial(D2),NewSparseUnivariatePolynomial +--R (D2)) -> Record(polnum: NewSparseUnivariatePolynomial(D2),polden +--R : D2,power: NonNegativeInteger) +--R from NewSparseUnivariatePolynomial(D2) if D2 has RING +--R +--RExamples of lazyResidueClass from NewSparseUnivariatePolynomial +--R +--R +--RExamples of lazyResidueClass from RecursivePolynomialCategory +--R +--E 1520 + +--S 1521 of 3320 +)d op lazyVariations +--R +--R +--RThere is one exposed function called lazyVariations : +--R [1] (List(D4),Integer,Integer) -> NonNegativeInteger +--R from RealPolynomialUtilitiesPackage(D4,D5) +--R if D4 has ORDRING and D4 has FIELD and D5 has UPOLYC(D4) +--R +--R +--RExamples of lazyVariations from RealPolynomialUtilitiesPackage +--R +--E 1521 + +--S 1522 of 3320 +)d op lBasis +--R +--R +--RThere are 5 exposed functions called lBasis : +--R [1] D6 -> Record(num: List(D9),den: D9) +--R from GeneralPackageForAlgebraicFunctionField(D7,D8,D9,D10, +--R D11,D12,D1,D6,D2,D3,D4) +--R if D7 has FIELD and D8: LIST(SYMBOL) and D9 has POLYCAT(D7 +--R ,D10,OVAR(D8)) and D10 has DIRPCAT(#(D8),NNI) and D11 has +--R PRSPCAT(D7) and D12 has LOCPOWC(D7) and D1 has PLACESC(D7, +--R D12) and D6 has DIVCAT(D1) and D2 has INFCLCT(D7,D8,D9,D10, +--R D11,D12,D1,D6,D4) and D4 has BLMETCT and D3 has DSTRCAT(D2) +--R +--R [2] (Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(D4)), +--R NonNegativeInteger) -> List(Fraction( +--R DistributedMultivariatePolynomial(D5,D4))) +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D4,D5 +--R ,D6) +--R if D4 has FFIELDC and D5: LIST(SYMBOL) and D6 has BLMETCT +--R +--R [3] Divisor(PlacesOverPseudoAlgebraicClosureOfFiniteField(D3)) -> +--R Record(num: List(DistributedMultivariatePolynomial(D4,D3)),den: +--R DistributedMultivariatePolynomial(D4,D3)) +--R from PackageForAlgebraicFunctionFieldOverFiniteField(D3,D4 +--R ,D5) +--R if D3 has FFIELDC and D4: LIST(SYMBOL) and D5 has BLMETCT +--R +--R [4] (Divisor(Places(D4)),NonNegativeInteger) -> List(Fraction( +--R DistributedMultivariatePolynomial(D5,D4))) +--R from PackageForAlgebraicFunctionField(D4,D5,D6) +--R if D4 has FIELD and D5: LIST(SYMBOL) and D6 has BLMETCT +--R +--R [5] Divisor(Places(D3)) -> Record(num: List( +--R DistributedMultivariatePolynomial(D4,D3)),den: +--R DistributedMultivariatePolynomial(D4,D3)) +--R from PackageForAlgebraicFunctionField(D3,D4,D5) +--R if D3 has FIELD and D4: LIST(SYMBOL) and D5 has BLMETCT +--R +--R +--RExamples of lBasis from GeneralPackageForAlgebraicFunctionField +--R +--R +--RExamples of lBasis from PackageForAlgebraicFunctionFieldOverFiniteField +--R +--R +--RExamples of lBasis from PackageForAlgebraicFunctionField +--R +--E 1522 + +--S 1523 of 3320 +)d op lcm +--R +--R +--RThere are 3 exposed functions called lcm : +--R [1] List(D) -> D from D if D has GCDDOM +--R [2] (D,D) -> D from D if D has GCDDOM +--R [3] (PrimitiveArray(U32Vector),Integer,Integer,Integer) -> U32Vector +--R from U32VectorPolynomialOperations +--R +--RExamples of lcm from GcdDomain +--R +--R +--RExamples of lcm from U32VectorPolynomialOperations +--R +--E 1523 + +--S 1524 of 3320 +)d op lcmCoef +--R +--R +--RThere is one exposed function called lcmCoef : +--R [1] (D,D) -> Record(llcmres: D,coeff1: D,coeff2: D) from D if D has +--R LORER +--R +--RExamples of lcmCoef from LeftOreRing +--R +--E 1524 + +--S 1525 of 3320 +)d op ldf2lst +--R +--R +--RThere are 3 exposed functions called ldf2lst : +--R [1] List(DoubleFloat) -> List(String) from d01AgentsPackage +--R [2] List(DoubleFloat) -> List(String) from +--R ExpertSystemContinuityPackage +--R [3] List(DoubleFloat) -> List(String) from ExpertSystemToolsPackage +--R +--R +--RExamples of ldf2lst from d01AgentsPackage +--R +--R +--RExamples of ldf2lst from ExpertSystemContinuityPackage +--R +--R +--RExamples of ldf2lst from ExpertSystemToolsPackage +--R +--E 1525 + +--S 1526 of 3320 +)d op ldf2vmf +--R +--R +--RThere is one exposed function called ldf2vmf : +--R [1] List(DoubleFloat) -> Vector(MachineFloat) from +--R ExpertSystemToolsPackage +--R +--RExamples of ldf2vmf from ExpertSystemToolsPackage +--R +--E 1526 + +--S 1527 of 3320 +)d op LE +--R +--R +--RThere is one exposed function called LE : +--R [1] (Union(I: Expression(Integer),F: Expression(Float),CF: +--R Expression(Complex(Float)),switch: Switch),Union(I: Expression( +--R Integer),F: Expression(Float),CF: Expression(Complex(Float)), +--R switch: Switch)) -> Switch +--R from Switch +--R +--RExamples of LE from Switch +--R +--E 1527 + +--S 1528 of 3320 +)d op leader +--R +--R +--RThere is one exposed function called leader : +--R [1] D -> D1 from D +--R if D has DPOLCAT(D2,D3,D1,D4) and D2 has RING and D3 has +--R ORDSET and D4 has OAMONS and D1 has DVARCAT(D3) +--R +--RExamples of leader from DifferentialPolynomialCategory +--R +--E 1528 + +--S 1529 of 3320 +)d op leadingBasisTerm +--R +--R +--RThere are 2 unexposed functions called leadingBasisTerm : +--R [1] AntiSymm(D1,D2) -> AntiSymm(D1,D2) from AntiSymm(D1,D2) +--R if D1 has RING and D2: LIST(SYMBOL) +--R [2] DeRhamComplex(D1,D2) -> DeRhamComplex(D1,D2) from DeRhamComplex( +--R D1,D2) +--R if D1 has Join(Ring,OrderedSet) and D2: LIST(SYMBOL) +--R +--RExamples of leadingBasisTerm from AntiSymm +--R +--R +--RExamples of leadingBasisTerm from DeRhamComplex +--R +--Rder:=DERHAM(Integer,[x,y,z]) +--R[dx,dy,dz]:=[generator(i)$der for i in 1..3] +--Rf:BOP:=operator('f) +--Rg:BOP:=operator('g) +--Rh:BOP:=operator('h) +--Rsigma:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz +--RleadingBasisTerm sigma +--R +--E 1529 + +--S 1530 of 3320 +)d op leadingCoefficient +--R +--R +--RThere are 7 exposed functions called leadingCoefficient : +--R [1] D -> D1 from D if D has AMR(D1,D2) and D2 has OAMON and D1 has +--R RING +--R [2] D -> D1 from D if D has FMCAT(D1,D2) and D2 has SETCAT and D1 +--R has RING +--R [3] D -> D1 from D if D has IDPC(D1,D2) and D2 has ORDSET and D1 +--R has SETCAT +--R [4] D -> D1 from D if D has MLO(D1) and D1 has RING +--R [5] D -> D1 from D if D has OREPCAT(D1) and D1 has RING +--R [6] D -> D1 from D +--R if D has PSCAT(D1,D2,D3) and D2 has OAMON and D3 has +--R ORDSET and D1 has RING +--R [7] (D,D1) -> D from D +--R if D has RPOLCAT(D2,D3,D1) and D2 has RING and D3 has +--R OAMONS and D1 has ORDSET +--R +--RThere are 5 unexposed functions called leadingCoefficient : +--R [1] AntiSymm(D1,D2) -> D1 from AntiSymm(D1,D2) if D1 has RING and D2 +--R : LIST(SYMBOL) +--R [2] DeRhamComplex(D2,D3) -> Expression(D2) from DeRhamComplex(D2,D3) +--R if D2 has Join(Ring,OrderedSet) and D3: LIST(SYMBOL) +--R [3] GeneralModulePolynomial(D2,D1,D3,D4,D5,D6) -> D1 +--R from GeneralModulePolynomial(D2,D1,D3,D4,D5,D6) +--R if D2: LIST(SYMBOL) and D4 has DIRPCAT(#(D2),NNI) and D5: +--R ((Record(index: D3,exponent: D4),Record(index: D3,exponent +--R : D4)) -> Boolean) and D1 has COMRING and D3 has ORDSET and +--R D6 has POLYCAT(D1,D4,OVAR(D2)) +--R [4] LaurentPolynomial(D1,D2) -> D1 from LaurentPolynomial(D1,D2) +--R if D1 has INTDOM and D2 has UPOLYC(D1) +--R [5] MonoidRing(D1,D2) -> D1 from MonoidRing(D1,D2) +--R if D1 has RING and D2 has ORDSET and D2 has MONOID +--R +--RExamples of leadingCoefficient from AbelianMonoidRing +--R +--R +--RExamples of leadingCoefficient from AntiSymm +--R +--R +--RExamples of leadingCoefficient from DeRhamComplex +--R +--Rder:=DERHAM(Integer,[x,y,z]) +--R[dx,dy,dz]:=[generator(i)$der for i in 1..3] +--Rf:BOP:=operator('f) +--Rg:BOP:=operator('g) +--Rh:BOP:=operator('h) +--Rsigma:=f(x,y,z)*dx + g(x,y,z)*dy + h(x,y,z)*dz +--RleadingCoefficient sigma +--R +--R +--RExamples of leadingCoefficient from FreeModuleCat +--R +--R +--RExamples of leadingCoefficient from GeneralModulePolynomial +--R +--R +--RExamples of leadingCoefficient from IndexedDirectProductCategory +--R +--R +--RExamples of leadingCoefficient from LaurentPolynomial +--R +--R +--RExamples of leadingCoefficient from MonogenicLinearOperator +--R +--R +--RExamples of leadingCoefficient from MonoidRing +--R +--R +--RExamples of leadingCoefficient from UnivariateSkewPolynomialCategory +--R +--R +--RExamples of leadingCoefficient from PowerSeriesCategory +--R +--R +--RExamples of leadingCoefficient from RecursivePolynomialCategory +--R +--E 1530 + +--S 1531 of 3320 +)d op leadingCoefficientRicDE +--R +--R +--RThere is one unexposed function called leadingCoefficientRicDE : +--R [1] D2 -> List(Record(deg: NonNegativeInteger,eq: D4)) +--R from PrimitiveRatRicDE(D3,D4,D2,D5) +--R if D3 has Join(Field,CharacteristicZero,RetractableTo( +--R Fraction(Integer))) and D4 has UPOLYC(D3) and D2 has +--R LODOCAT(D4) and D5 has LODOCAT(FRAC(D4)) +--R +--RExamples of leadingCoefficientRicDE from PrimitiveRatRicDE +--R +--E 1531 + +--S 1532 of 3320 +)d op leadingExponent +--R +--R +--RThere is one unexposed function called leadingExponent : +--R [1] GeneralModulePolynomial(D2,D3,D4,D1,D5,D6) -> D1 +--R from GeneralModulePolynomial(D2,D3,D4,D1,D5,D6) +--R if D2: LIST(SYMBOL) and D3 has COMRING and D5: ((Record( +--R index: D4,exponent: D1),Record(index: D4,exponent: D1)) -> +--R Boolean) and D1 has DIRPCAT(#(D2),NNI) and D4 has ORDSET +--R and D6 has POLYCAT(D3,D1,OVAR(D2)) +--R +--RExamples of leadingExponent from GeneralModulePolynomial +--R +--E 1532 + +--S 1533 of 3320 +)d op leadingIdeal +--R +--R +--RThere is one exposed function called leadingIdeal : +--R [1] PolynomialIdeals(D1,D2,D3,D4) -> PolynomialIdeals(D1,D2,D3,D4) +--R from PolynomialIdeals(D1,D2,D3,D4) +--R if D1 has FIELD and D2 has OAMONS and D3 has ORDSET and D4 +--R has POLYCAT(D1,D2,D3) +--R +--RExamples of leadingIdeal from PolynomialIdeals +--R +--E 1533 + +--S 1534 of 3320 +)d op leadingIndex +--R +--R +--RThere is one unexposed function called leadingIndex : +--R [1] GeneralModulePolynomial(D2,D3,D1,D4,D5,D6) -> D1 +--R from GeneralModulePolynomial(D2,D3,D1,D4,D5,D6) +--R if D2: LIST(SYMBOL) and D3 has COMRING and D4 has DIRPCAT( +--R #(D2),NNI) and D5: ((Record(index: D1,exponent: D4),Record( +--R index: D1,exponent: D4)) -> Boolean) and D1 has ORDSET and +--R D6 has POLYCAT(D3,D4,OVAR(D2)) +--R +--RExamples of leadingIndex from GeneralModulePolynomial +--R +--E 1534 + +--S 1535 of 3320 +)d op leadingMonomial +--R +--R +--RThere are 3 exposed functions called leadingMonomial : +--R [1] D -> D from D if D has AMR(D1,D2) and D1 has RING and D2 has +--R OAMON +--R [2] D -> D1 from D if D has FMCAT(D2,D1) and D2 has RING and D1 has +--R SETCAT +--R [3] D -> D from D +--R if D has PSCAT(D1,D2,D3) and D1 has RING and D2 has OAMON +--R and D3 has ORDSET +--R +--RThere are 2 unexposed functions called leadingMonomial : +--R [1] GeneralModulePolynomial(D2,D3,D4,D5,D6,D7) -> ModuleMonomial(D4, +--R D5,D6) +--R from GeneralModulePolynomial(D2,D3,D4,D5,D6,D7) +--R if D2: LIST(SYMBOL) and D3 has COMRING and D5 has DIRPCAT( +--R #(D2),NNI) and D6: ((Record(index: D4,exponent: D5),Record( +--R index: D4,exponent: D5)) -> Boolean) and D4 has ORDSET and +--R D7 has POLYCAT(D3,D5,OVAR(D2)) +--R [2] MonoidRing(D2,D1) -> D1 from MonoidRing(D2,D1) +--R if D1 has MONOID and D1 has ORDSET and D2 has RING +--R +--RExamples of leadingMonomial from AbelianMonoidRing +--R +--R +--RExamples of leadingMonomial from FreeModuleCat +--R +--R +--RExamples of leadingMonomial from GeneralModulePolynomial +--R +--R +--RExamples of leadingMonomial from MonoidRing +--R +--R +--RExamples of leadingMonomial from PowerSeriesCategory +--R +--E 1535 + +--S 1536 of 3320 +)d op leadingSupport +--R +--R +--RThere is one exposed function called leadingSupport : +--R [1] D -> D1 from D if D has IDPC(D2,D1) and D2 has SETCAT and D1 +--R has ORDSET +--R +--RExamples of leadingSupport from IndexedDirectProductCategory +--R +--E 1536 + +--S 1537 of 3320 +)d op leadingTerm +--R +--R +--RThere is one exposed function called leadingTerm : +--R [1] D -> Record(k: D3,c: D2) from D +--R if D has FMCAT(D2,D3) and D2 has RING and D3 has SETCAT +--R +--R +--RExamples of leadingTerm from FreeModuleCat +--R +--E 1537 + +--S 1538 of 3320 +)d op leaf? +--R +--R +--RThere are 2 exposed functions called leaf? : +--R [1] D -> Boolean from D +--R if D has PLACESC(D2,D3) and D2 has FIELD and D3 has +--R LOCPOWC(D2) +--R [2] D -> Boolean from D if D has RCAGG(D2) and D2 has TYPE +--R +--RThere is one unexposed function called leaf? : +--R [1] SubSpace(D2,D3) -> Boolean from SubSpace(D2,D3) if D2: PI and D3 +--R has RING +--R +--RExamples of leaf? from PlacesCategory +--R +--R +--RExamples of leaf? from RecursiveAggregate +--R +--R +--RExamples of leaf? from SubSpace +--R +--E 1538 + +--S 1539 of 3320 +)d op leastAffineMultiple +--R +--R +--RThere is one unexposed function called leastAffineMultiple : +--R [1] SparseUnivariatePolynomial(D2) -> SparseUnivariatePolynomial(D2) +--R from FiniteFieldPolynomialPackage(D2) if D2 has FFIELDC +--R +--R +--RExamples of leastAffineMultiple from FiniteFieldPolynomialPackage +--R +--E 1539 + +--S 1540 of 3320 +)d op leastMonomial +--R +--R +--RThere is one exposed function called leastMonomial : +--R [1] D -> D from D +--R if D has RPOLCAT(D1,D2,D3) and D1 has RING and D2 has +--R OAMONS and D3 has ORDSET +--R +--RExamples of leastMonomial from RecursivePolynomialCategory +--R +--E 1540 + +--S 1541 of 3320 +)d op leastPower +--R +--R +--RThere is one unexposed function called leastPower : +--R [1] (NonNegativeInteger,NonNegativeInteger) -> NonNegativeInteger +--R from IntegralBasisTools(D2,D3,D4) +--R if D2 has EuclideanDomainwith +--R squareFree : % -> Factored(%)and D3 has UPOLYC(D2) +--R and D4 has FRAMALG(D2,D3) +--R +--RExamples of leastPower from IntegralBasisTools +--R +--E 1541 + +--S 1542 of 3320 +)d op leaves +--R +--R +--RThere is one exposed function called leaves : +--R [1] D -> List(D2) from D if D has RCAGG(D2) and D2 has TYPE +--R +--RExamples of leaves from RecursiveAggregate +--R +--E 1542 + +--S 1543 of 3320 +)d op left +--R +--R +--RThere are 2 exposed functions called left : +--R [1] D -> D from D if D has BRAGG(D1) and D1 has TYPE +--R [2] RightOpenIntervalRootCharacterization(D1,D2) -> D1 +--R from RightOpenIntervalRootCharacterization(D1,D2) +--R if D1 has Join(OrderedRing,Field) and D2 has UPOLYC(D1) +--R +--R +--RThere are 4 unexposed functions called left : +--R [1] LyndonWord(D1) -> LyndonWord(D1) from LyndonWord(D1) if D1 has +--R ORDSET +--R [2] Magma(D1) -> Magma(D1) from Magma(D1) if D1 has ORDSET +--R [3] OutputForm -> OutputForm from OutputForm +--R [4] (OutputForm,Integer) -> OutputForm from OutputForm +--R +--RExamples of left from BinaryRecursiveAggregate +--R +--R +--RExamples of left from LyndonWord +--R +--R +--RExamples of left from Magma +--R +--R +--RExamples of left from OutputForm +--R +--R +--RExamples of left from RightOpenIntervalRootCharacterization +--R +--E 1543 + +--S 1544 of 3320 +)d op leftAlternative? +--R +--R +--RThere is one exposed function called leftAlternative? : +--R [1] -> Boolean from D if D has FINAALG(D2) and D2 has COMRING +--R +--RThere is one unexposed function called leftAlternative? : +--R [1] -> Boolean from FiniteRankNonAssociativeAlgebra&(D2,D3) +--R if D3 has COMRING and D2 has FINAALG(D3) +--R +--RExamples of leftAlternative? from FiniteRankNonAssociativeAlgebra& +--R +--R +--RExamples of leftAlternative? from FiniteRankNonAssociativeAlgebra +--R +--E 1544 + +--S 1545 of 3320 +)d op leftCharacteristicPolynomial +--R +--R +--RThere is one exposed function called leftCharacteristicPolynomial : +--R [1] D -> SparseUnivariatePolynomial(D2) from D +--R if D has FINAALG(D2) and D2 has COMRING +--R +--RExamples of leftCharacteristicPolynomial from FiniteRankNonAssociativeAlgebra +--R +--E 1545 + +--S 1546 of 3320 +)d op leftDiscriminant +--R +--R +--RThere are 2 exposed functions called leftDiscriminant : +--R [1] Vector(D) -> D1 from D if D has FINAALG(D1) and D1 has COMRING +--R +--R [2] -> D1 from D if D has FRNAALG(D1) and D1 has COMRING +--R +--RThere is one unexposed function called leftDiscriminant : +--R [1] -> D1 from FramedNonAssociativeAlgebra&(D2,D1) +--R if D1 has COMRING and D2 has FRNAALG(D1) +--R +--RExamples of leftDiscriminant from FiniteRankNonAssociativeAlgebra +--R +--R +--RExamples of leftDiscriminant from FramedNonAssociativeAlgebra& +--R +--R +--RExamples of leftDiscriminant from FramedNonAssociativeAlgebra +--R +--E 1546 + +--S 1547 of 3320 +)d op leftDivide +--R +--R +--RThere is one exposed function called leftDivide : +--R [1] (D,D) -> Record(quotient: D,remainder: D) from D +--R if D2 has FIELD and D2 has RING and D has OREPCAT(D2) +--R +--RThere are 2 unexposed functions called leftDivide : +--R [1] (D2,D2) -> Record(quotient: D2,remainder: D2) +--R from NonCommutativeOperatorDivision(D2,D3) +--R if D3 has FIELD and D2 has MLO(D3) +--R [2] (D2,D2,Automorphism(D4)) -> Record(quotient: D2,remainder: D2) +--R from UnivariateSkewPolynomialCategoryOps(D4,D2) +--R if D4 has FIELD and D4 has RING and D2 has OREPCAT(D4) +--R +--RExamples of leftDivide from NonCommutativeOperatorDivision +--R +--R +--RExamples of leftDivide from UnivariateSkewPolynomialCategory +--R +--R +--RExamples of leftDivide from UnivariateSkewPolynomialCategoryOps +--R +--E 1547 + +--S 1548 of 3320 +)d op leftExactQuotient +--R +--R +--RThere is one exposed function called leftExactQuotient : +--R [1] (D,D) -> Union(D,"failed") from D +--R if D has OREPCAT(D1) and D1 has RING and D1 has FIELD +--R +--RThere is one unexposed function called leftExactQuotient : +--R [1] (D1,D1) -> Union(D1,"failed") from +--R NonCommutativeOperatorDivision(D1,D2) +--R if D2 has FIELD and D1 has MLO(D2) +--R +--RExamples of leftExactQuotient from NonCommutativeOperatorDivision +--R +--R +--RExamples of leftExactQuotient from UnivariateSkewPolynomialCategory +--R +--E 1548 + +--S 1549 of 3320 +)d op leftExtendedGcd +--R +--R +--RThere is one exposed function called leftExtendedGcd : +--R [1] (D,D) -> Record(coef1: D,coef2: D,generator: D) from D +--R if D2 has FIELD and D2 has RING and D has OREPCAT(D2) +--R +--RExamples of leftExtendedGcd from UnivariateSkewPolynomialCategory +--R +--E 1549 + +--S 1550 of 3320 +)d op leftFactor +--R +--R +--RThere is one exposed function called leftFactor : +--R [1] (D1,D1) -> Union(D1,"failed") from PolynomialDecomposition(D1,D2 +--R ) +--R if D2 has FIELD and D1 has UPOLYC(D2) +--R +--RExamples of leftFactor from PolynomialDecomposition +--R +--E 1550 + +--S 1551 of 3320 +)d op leftFactorIfCan +--R +--R +--RThere is one unexposed function called leftFactorIfCan : +--R [1] (D1,D1) -> Union(D1,"failed") +--R from UnivariatePolynomialDecompositionPackage(D2,D1) +--R if D2 has Join(IntegralDomain,CharacteristicZero) and D1 +--R has UPOLYC(D2) +--R +--RExamples of leftFactorIfCan from UnivariatePolynomialDecompositionPackage +--R +--E 1551 + +--S 1552 of 3320 +)d op leftGcd +--R +--R +--RThere is one exposed function called leftGcd : +--R [1] (D,D) -> D from D if D has OREPCAT(D1) and D1 has RING and D1 +--R has FIELD +--R +--RThere is one unexposed function called leftGcd : +--R [1] (D1,D1) -> D1 from NonCommutativeOperatorDivision(D1,D2) +--R if D2 has FIELD and D1 has MLO(D2) +--R +--RExamples of leftGcd from NonCommutativeOperatorDivision +--R +--R +--RExamples of leftGcd from UnivariateSkewPolynomialCategory +--R +--E 1552 + +--S 1553 of 3320 +)d op leftLcm +--R +--R +--RThere is one exposed function called leftLcm : +--R [1] (D,D) -> D from D if D has OREPCAT(D1) and D1 has RING and D1 +--R has FIELD +--R +--RThere is one unexposed function called leftLcm : +--R [1] (D1,D1) -> D1 from NonCommutativeOperatorDivision(D1,D2) +--R if D2 has FIELD and D1 has MLO(D2) +--R +--RExamples of leftLcm from NonCommutativeOperatorDivision +--R +--R +--RExamples of leftLcm from UnivariateSkewPolynomialCategory +--R +--E 1553 + +--S 1554 of 3320 +)d op leftMinimalPolynomial +--R +--R +--RThere is one exposed function called leftMinimalPolynomial : +--R [1] D -> SparseUnivariatePolynomial(D2) from D +--R if D has FINAALG(D2) and D2 has COMRING and D2 has INTDOM +--R +--R +--RExamples of leftMinimalPolynomial from FiniteRankNonAssociativeAlgebra +--R +--E 1554 + +--S 1555 of 3320 +)d op leftMult +--R +--R +--RThere is one unexposed function called leftMult : +--R [1] (D1,ListMonoidOps(D1,D2,D3)) -> ListMonoidOps(D1,D2,D3) +--R from ListMonoidOps(D1,D2,D3) +--R if D1 has SETCAT and D2 has ABELMON and D3: D2 +--R +--RExamples of leftMult from ListMonoidOps +--R +--E 1555 + +--S 1556 of 3320 +)d op leftNorm +--R +--R +--RThere is one exposed function called leftNorm : +--R [1] D -> D1 from D if D has FINAALG(D1) and D1 has COMRING +--R +--RExamples of leftNorm from FiniteRankNonAssociativeAlgebra +--R +--E 1556 + +--S 1557 of 3320 +)d op leftOne +--R +--R +--RThere is one exposed function called leftOne : +--R [1] Equation(D1) -> Union(Equation(D1),"failed") from Equation(D1) +--R if D1 has MONOID and D1 has TYPE +--R +--RExamples of leftOne from Equation +--R +--E 1557 + +--S 1558 of 3320 +)d op leftPower +--R +--R +--RThere are 2 exposed functions called leftPower : +--R [1] (D,PositiveInteger) -> D from D if D has MONAD +--R [2] (D,NonNegativeInteger) -> D from D if D has MONADWU +--R +--RExamples of leftPower from Monad +--R +--R +--RExamples of leftPower from MonadWithUnit +--R +--E 1558 + +--S 1559 of 3320 +)d op leftQuotient +--R +--R +--RThere is one exposed function called leftQuotient : +--R [1] (D,D) -> D from D if D has OREPCAT(D1) and D1 has RING and D1 +--R has FIELD +--R +--RThere is one unexposed function called leftQuotient : +--R [1] (D1,D1) -> D1 from NonCommutativeOperatorDivision(D1,D2) +--R if D2 has FIELD and D1 has MLO(D2) +--R +--RExamples of leftQuotient from NonCommutativeOperatorDivision +--R +--R +--RExamples of leftQuotient from UnivariateSkewPolynomialCategory +--R +--E 1559 + +--S 1560 of 3320 +)d op leftRank +--R +--R +--RThere is one exposed function called leftRank : +--R [1] D2 -> NonNegativeInteger from AlgebraPackage(D3,D2) +--R if D3 has INTDOM and D2 has FRNAALG(D3) +--R +--RExamples of leftRank from AlgebraPackage +--R +--E 1560 + +--S 1561 of 3320 +--R--------------------------)d op leftRankPolynomial (System Error) +--E 1561 + +--S 1562 of 3320 +)d op leftRecip +--R +--R +--RThere are 2 exposed functions called leftRecip : +--R [1] D -> Union(D,"failed") from D +--R if D has FINAALG(D1) and D1 has COMRING and D1 has INTDOM +--R +--R [2] D -> Union(D,"failed") from D if D has MONADWU +--R +--RExamples of leftRecip from FiniteRankNonAssociativeAlgebra +--R +--R +--RExamples of leftRecip from MonadWithUnit +--R +--E 1562 + +--S 1563 of 3320 +)d op leftRegularRepresentation +--R +--R +--RThere are 2 exposed functions called leftRegularRepresentation : +--R [1] (D,Vector(D)) -> Matrix(D3) from D if D has FINAALG(D3) and D3 +--R has COMRING +--R [2] D -> Matrix(D2) from D if D has FRNAALG(D2) and D2 has COMRING +--R +--R +--RExamples of leftRegularRepresentation from FiniteRankNonAssociativeAlgebra +--R +--R +--RExamples of leftRegularRepresentation from FramedNonAssociativeAlgebra +--R +--E 1563 + +--S 1564 of 3320 +)d op leftRemainder +--R +--R +--RThere is one exposed function called leftRemainder : +--R [1] (D,D) -> D from D if D has OREPCAT(D1) and D1 has RING and D1 +--R has FIELD +--R +--RThere is one unexposed function called leftRemainder : +--R [1] (D1,D1) -> D1 from NonCommutativeOperatorDivision(D1,D2) +--R if D2 has FIELD and D1 has MLO(D2) +--R +--RExamples of leftRemainder from NonCommutativeOperatorDivision +--R +--R +--RExamples of leftRemainder from UnivariateSkewPolynomialCategory +--R +--E 1564 + +--S 1565 of 3320 +)d op leftScalarTimes! +--R +--R +--RThere is one unexposed function called leftScalarTimes! : +--R [1] (Matrix(D2),D2,Matrix(D2)) -> Matrix(D2) +--R from StorageEfficientMatrixOperations(D2) if D2 has RING +--R +--R +--RExamples of leftScalarTimes! from StorageEfficientMatrixOperations +--R +--E 1565 + +--S 1566 of 3320 +)d op leftTrace +--R +--R +--RThere is one exposed function called leftTrace : +--R [1] D -> D1 from D if D has FINAALG(D1) and D1 has COMRING +--R +--RExamples of leftTrace from FiniteRankNonAssociativeAlgebra +--R +--E 1566 + +--S 1567 of 3320 +)d op leftTraceMatrix +--R +--R +--RThere are 2 exposed functions called leftTraceMatrix : +--R [1] Vector(D) -> Matrix(D3) from D if D has FINAALG(D3) and D3 has +--R COMRING +--R [2] -> Matrix(D2) from D if D has FRNAALG(D2) and D2 has COMRING +--R +--R +--RThere is one unexposed function called leftTraceMatrix : +--R [1] -> Matrix(D3) from FramedNonAssociativeAlgebra&(D2,D3) +--R if D3 has COMRING and D2 has FRNAALG(D3) +--R +--RExamples of leftTraceMatrix from FiniteRankNonAssociativeAlgebra +--R +--R +--RExamples of leftTraceMatrix from FramedNonAssociativeAlgebra& +--R +--R +--RExamples of leftTraceMatrix from FramedNonAssociativeAlgebra +--R +--E 1567 + +--S 1568 of 3320 +)d op leftTrim +--R +--R +--RThere are 2 exposed functions called leftTrim : +--R [1] (D,CharacterClass) -> D from D if D has SRAGG +--R [2] (D,Character) -> D from D if D has SRAGG +--R +--RExamples of leftTrim from StringAggregate +--R +--E 1568 + +--S 1569 of 3320 +)d op leftUnit +--R +--R +--RThere is one exposed function called leftUnit : +--R [1] -> Union(D,"failed") from D +--R if D has FINAALG(D1) and D1 has INTDOM and D1 has COMRING +--R +--R +--RExamples of leftUnit from FiniteRankNonAssociativeAlgebra +--R +--E 1569 + +--S 1570 of 3320 +--R-------------------------)d op leftUnits (System Error) +--E 1570 + +--S 1571 of 3320 +)d op leftZero +--R +--R +--RThere is one exposed function called leftZero : +--R [1] Equation(D1) -> Equation(D1) from Equation(D1) +--R if D1 has ABELGRP and D1 has TYPE +--R +--RExamples of leftZero from Equation +--R +--E 1571 + +--S 1572 of 3320 +)d op legendre +--R +--R +--RThere is one exposed function called legendre : +--R [1] (Integer,Integer) -> Integer from IntegerNumberTheoryFunctions +--R +--R +--RThere is one unexposed function called legendre : +--R [1] Integer -> SparseUnivariatePolynomial(Fraction(Integer)) +--R from PolynomialNumberTheoryFunctions +--R +--RExamples of legendre from IntegerNumberTheoryFunctions +--R +--R +--RExamples of legendre from PolynomialNumberTheoryFunctions +--R +--E 1572 + +--S 1573 of 3320 +)d op legendreP +--R +--R +--RThere is one exposed function called legendreP : +--R [1] (NonNegativeInteger,D1) -> D1 from OrthogonalPolynomialFunctions +--R (D1) +--R if D1 has ALGEBRA(FRAC(INT)) and D1 has COMRING +--R +--RExamples of legendreP from OrthogonalPolynomialFunctions +--R +--E 1573 + +--S 1574 of 3320 +)d op length +--R +--R +--RThere are 5 exposed functions called length : +--R [1] Dequeue(D2) -> NonNegativeInteger from Dequeue(D2) if D2 has +--R SETCAT +--R [2] D -> D from D if D has INS +--R [3] D -> NonNegativeInteger from D if D has QUAGG(D2) and D2 has +--R TYPE +--R [4] Queue(D2) -> NonNegativeInteger from Queue(D2) if D2 has SETCAT +--R +--R [5] D -> D1 from D +--R if D has VECTCAT(D1) and D1 has TYPE and D1 has RADCAT and +--R D1 has RING +--R +--RThere are 6 unexposed functions called length : +--R [1] D2 -> D1 from GaloisGroupFactorizationUtilities(D3,D2,D1) +--R if D3 has RING and D1 has Join(FloatingPointSystem, +--R RetractableTo(D3),Field,TranscendentalFunctionCategory, +--R ElementaryFunctionCategory) and D2 has UPOLYC(D3) +--R [2] LyndonWord(D2) -> PositiveInteger from LyndonWord(D2) if D2 has +--R ORDSET +--R [3] Magma(D2) -> PositiveInteger from Magma(D2) if D2 has ORDSET +--R [4] OrderedFreeMonoid(D2) -> NonNegativeInteger from +--R OrderedFreeMonoid(D2) +--R if D2 has ORDSET +--R [5] PoincareBirkhoffWittLyndonBasis(D2) -> NonNegativeInteger +--R from PoincareBirkhoffWittLyndonBasis(D2) if D2 has ORDSET +--R +--R [6] Tuple(D2) -> NonNegativeInteger from Tuple(D2) if D2 has TYPE +--R +--R +-