From ef0688e2271d18409b448529cb445a56642736a4 Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Mon, 4 Jul 2016 20:22:39 0400
Subject: [PATCH] books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
\index{Hearn, Anthony C.}
\index{Eberhard, Schrufer}
\begin{chunk}{axiom.bib}
@article{Hear95,
author = "Hearn, Anthony C. and Eberhard, Schrufer",
title = "A computer algebra system based on ordersorted algebra",
journal = "J. Symbolic Computing",
volume = "19",
number = "13",
pages = "6577",
year = "1995",
keywords = "axiomref",
paper = "Hear95.pdf",
abstract =
"This paper presents the prototype design of an algebraic computation
system that manipulates algebraic quantities as generic objects using
ordersorted algebra as the underlying model. The resulting programs
have a form that is closely related to the algorithmic description of
a problem, but with the security of full type checking in a compact,
natural style."
}
\end{chunk}
\index{Hoeppner, Sabine}
\begin{chunk}{axiom.bib}
@misc{Hoep95,
author = "Hoeppner, Sabine",
title = "Linear differential equations of second order in fields of
positive characteristic",
comment = "Essen: Univ. Essen, FB Math 71 S.",
year = "1995",
keywords = "axiomref",
abstract =
"Let be a differential field of characteristic $p>2$ of the type
$(\mathbb{F}_p(x),\frac{d}{dx})$. The equation studied is
$y^{\prime\prime}+ay^{\prime}+by=0$ with $a,b \in K$. The goal is to
produce a Liouvillian extension $L \supset K$ which contains two
independent solutions. This is done by solving the associated Riccati
equation $u^{\prime}+u^2+au+b=0$. Unlike the characteristic zero
situation, the Riccati equation has one or two solutions in an
algebraic extension of degree $\le 2$ of $K$. Full solutions are
given for the various cases that do occur. The paper ends with a
program in AXIOM which computes the solutions of the Riccati equation
and the Liouvillian extensions."
}
\end{chunk}
\index{Santas, Philip S.}
\begin{chunk}{axiom.bib}
@article{Sant95,
author = "Santas, Philip S.",
title = "A type system for computer algebra",
journal = "J. Symbolic Computation",
volume = "19",
number = "13",
pages = "79109",
year = "1995",
keywords = "axiomref",
paper = "Sant95.pdf",
abstract =
"This paper presents a type system for support of subtypes,
parameterized types with sharing and categories in a computer algebra
environment. By modeling representation of instances in terms of
existential types, we obtain a simplified model, and build a basis for
defining subtyping among algebraic domains. The inheritance at
category level has been formalized; this allows the automatic
inference of type classes. By means of type classes and existential
types we construct subtype relations without involving coercions. A
type sharing mechanism works in parallel and allows the consistent
extension and combination of domains. The expressiveness of the system
is further increased by viewing domain types as special case of
package types, forming weak and strong sums respectively. The
introduced system, although awkward at first sight, is simpler than
other proposed systems for computer algebra without including some of
their problems. The system can be further extended in other to support
more constructs and increase its flexibility."
}
\end{chunk}
\index{Dalmas, St\'ephane}
\begin{chunk}{axiom.bib}
author = "Dalmas, Stephane",
title = "A polymorphic functional language applied to symbolic computation",
year = "1992",
booktitle = "Proc. ISSAC 1992",
series = "ISSAC 1992",
pages = "369375",
isbn = "0897914899 (soft cover) 0897914902 (hard cover)",
keywords = "axiomref"
}
\end{chunk}
\index{Missura, Stephan A.}
\begin{chunk}{axiom.bib}
@InProceedings{Miss05,
author = "Missura, Stephan A.",
title = {Theories = Signatures + Propositions Used as Types},
keywords = "axiomref",
booktitle = "Integrating Symbolic Mathematics and Artificial Intelligence",
volume = "958",
pages = "144155",
year = "2005",
paper = "Miss05",
abstract =
"Languages that distinguish between types and structures use explicit
components for the carrier type(s) in structures. Examples are the
function language Standard ML and most algebraic specification
systems. Hence, they have to use general sum types or signatures to
give types to structures and be able to build, for instance, the
algebraic hierarchy."
}
\end{chunk}
\index{Fitch, John P.}
\begin{chunk}{axiom.bib}
@InProceedings{Fitc93,
author = "Fitch (ed), John P.",
title = "Design and Implementation of Symbolic Computation Systems",
year = "1992",
booktitle = "Int. Symp. DISCO '92 Proceedings",
series = "DISCO 92",
publisher = "SpringerVerlag, Berlin",
isbn = "0387572724",
keywords = "axiomref",
paper = "Fitc93.tex"
}
\end{chunk}
\index{Dupee, Brian J.}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@misc{Dupe95,
author = "Dupee, Brian J. and Davenport, James H.",
title = "Using Computer Algebra to Choose and Apply Numerical Routines",
year = "1995",
paper = "Dupe95.pdf",
keywords = "axiomref",
url =
"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.33.5645&rep=rep1&type=pdf",
algebra =
"\newline\refto{domain D01AJFA d01ajfAnnaType}
\newline\refto{domain D01AKFA d01akfAnnaType}
\newline\refto{domain D01ALFA d01alfAnnaType}
\newline\refto{domain D01AMFA d01amfAnnaType}
\newline\refto{domain D01ANFA d01anfAnnaType}
\newline\refto{domain D01APFA d01apfAnnaType}
\newline\refto{domain D01AQFA d01aqfAnnaType}
\newline\refto{domain D01ASFA d01asfAnnaType}
\newline\refto{domain D01FCFA d01fcfAnnaType}
\newline\refto{domain D01GBFA d01gbfAnnaType}
\newline\refto{domain D01TRNS d01TransformFunctionType}
\newline\refto{domain D02BBFA d02bbfAnnaType}
\newline\refto{domain D02BHFA d02bhfAnnaType}
\newline\refto{domain D02CJFA d02cjfAnnaType}
\newline\refto{domain D02EJFA d02ejfAnnaType}
\newline\refto{domain D03EEFA d03eefAnnaType}
\newline\refto{domain D03FAFA d03fafAnnaType}
\newline\refto{domain E04DGFA e04dgfAnnaType}
\newline\refto{domain E04FDFA e04fdfAnnaType}
\newline\refto{domain E04GCFA e04gcfAnnaType}
\newline\refto{domain E04JAFA e04jafAnnaType}
\newline\refto{domain E04MBFA e04mbfAnnaType}
\newline\refto{domain E04NAFA e04nafAnnaType}
\newline\refto{domain E04UCFA e04ucfAnnaType}
\newline\refto{domain NIPROB NumericalIntegrationProblem}
\newline\refto{domain ODEPROB NumericalODEProblem}
\newline\refto{domain OPTPROB NumericalOptimizationProblem}
\newline\refto{domain PDEPROB NumericalPDEProblem}",
abstract =
"In applied mathematics, electronic and chemical engineering, the
modelling process can produce a number of mathematical problems which
require numerical solutions for which symbolic methods are either not
possible or not obvious. With the plethora of numerical library
routines for the solution of these problems often the numerical
analyst has to answer the question {\sl Which routine to choose?} and
{\sl How do I use it?}. Some analysis needs to be carried out before
the appropriate routine can be identifed, i.e. {\sl How stiff is this
ODE?} and {\sl Is this function continuous?}. It may well be the case
that more than one routine is applicable to the problem. So the
question may become {\ls Which is likely to be the best?}. Such a
choice may be critical for both accuracy and efficiency.
An expert system is thus required to make this choice based on the
results of its own analysis of the problem, call the routine and act
on the outcome. This may be to put the answer in a relevant form or
react to an apparent failure of the chosen routine and thus choose and
call an alternative. It should also have sufficient explanation
mechanisms to inform on the choice of routine and the reasons for that
choice. Much of this work can be achieved using computer algebra and
symbolic algebra packages.
This paper describes an expert system currently in prototype in terms
of both its objectbased structure and its computational agents. Some
of these agents are described in detail, paying particular attention
to the practical aspects of their algorithms and the use of computer
algebra.
The {\bf axiom2} Symbolic Algebra System is used as a user interface
as well as the link to the NAG Foundation Library for the numerical
routines and the inference mechanisms for the expert system."
}
\end{chunk}
\index{Dewar, Michael C.}
\begin{chunk}{axiom.bib}
@InProceedings{Dewa92,
author = "Dewar, Michael C.",
title = "Using Computer Algebra to Select Numerical Algorithms",
booktitle = "Proc. ISSAC 1992",
series = "ISSAC 1992",
year = "1992",
location = "Berkeley, CA",
pages = "18",
paper = "Dewa92.pdf",
algebra =
"\newline\refto{domain D01AJFA d01ajfAnnaType}
\newline\refto{domain D01AKFA d01akfAnnaType}
\newline\refto{domain D01ALFA d01alfAnnaType}
\newline\refto{domain D01AMFA d01amfAnnaType}
\newline\refto{domain D01ANFA d01anfAnnaType}
\newline\refto{domain D01APFA d01apfAnnaType}
\newline\refto{domain D01AQFA d01aqfAnnaType}
\newline\refto{domain D01ASFA d01asfAnnaType}
\newline\refto{domain D01FCFA d01fcfAnnaType}
\newline\refto{domain D01GBFA d01gbfAnnaType}
\newline\refto{domain D01TRNS d01TransformFunctionType}
\newline\refto{domain D02BBFA d02bbfAnnaType}
\newline\refto{domain D02BHFA d02bhfAnnaType}
\newline\refto{domain D02CJFA d02cjfAnnaType}
\newline\refto{domain D02EJFA d02ejfAnnaType}
\newline\refto{domain D03EEFA d03eefAnnaType}
\newline\refto{domain D03FAFA d03fafAnnaType}
\newline\refto{domain E04DGFA e04dgfAnnaType}
\newline\refto{domain E04FDFA e04fdfAnnaType}
\newline\refto{domain E04GCFA e04gcfAnnaType}
\newline\refto{domain E04JAFA e04jafAnnaType}
\newline\refto{domain E04MBFA e04mbfAnnaType}
\newline\refto{domain E04NAFA e04nafAnnaType}
\newline\refto{domain E04UCFA e04ucfAnnaType}
\newline\refto{domain NIPROB NumericalIntegrationProblem}
\newline\refto{domain ODEPROB NumericalODEProblem}
\newline\refto{domain OPTPROB NumericalOptimizationProblem}
\newline\refto{domain PDEPROB NumericalPDEProblem}",
abstract =
"Many reallife problems require a compbination of both symbolic and
numerical methods for their solution. This has led to the development
of intgrated, interactive symbolic / numeric packages which use a
computer algebra system for the former and a standard subroutine
library for the latter. These systems may also be viewed as simplified
frontends to the numerical library. To use these packages, however, a
user must be able to select which of the many available routines is
the most appropriate for his or her problem, which contrsts with the
``blackbox'' style interfaces available in computer algebra
systems. This paper describes how a computer algebra system can be
used to make this decision, thus providing a muchsimplified and more
orthogonal interface."
}
\end{chunk}
\index{Brown, Christopher W.}
\begin{chunk}{axiom.bib}
@phdthesis{Brow99,
author = "Brown, Christopher W.",
title = "Solution Formula Construction for Truth Invariant CADs",
school = "University of Delaware",
year = "1999",
website = "http://www.usna.edu/CS/qepcadweb/B/impl/Implementation.html",
url = "http://www.usna.edu/Users/cs/wcbrown/research/thesis.ps.gz",
paper = "Brow99.pdf",
abstract =
"The CADbased quantifier elimination algorithm takes a formula from
the elementary theory of real closed fields as input, and constructs a
CAD of the space of the formula's unquantified variables. This
decomposition is truth invariant with respect to the input formula,
meaning that the formula is either identically true or identically
false in each cell of the decomposition. The method determines the
truth of the input formula for each cell of the CAD, and then uses the
CAD to construct a solution formula  a quantifier free formula that
is equivalent to the input formula. This final phase of the algorithm,
the solution formula construction phase, is the focus of this thesis.
An optimal solution formula construction algorithm would be {\sl
complete}  i.e. applicable to any truthinvariant CAD, would be {\sl
efficient}, and would produce {\sl simple} solution formulas. Prior to
this thesis, no method was available with even two of these three
properties. Several algorithms are presented, all addressing problems
related to solution formula construction. In combination, these
provide an efficient and complete method for constructing solution
formulas that are simple in a variety of ways.
Algorithms presented in this thesis have been implemented using the
SACLIB library, and integrated into QEPCAD, a SACLIBbased
implementation of quantifier elimination by CAD. Example computations
based on these implementations are discussed."
}
\end{chunk}

books/bookvolbib.pamphlet  346 ++++++++++++++++++++++++++++++++++
changelog  2 +
patch  310 +++++++++++++++++++++++++++++++++++
src/axiomwebsite/patches.html  4 +
4 files changed, 612 insertions(+), 50 deletions()
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 9b78dd2..7677e96 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 9898,6 +9898,45 @@ J. Symbolic Computation 5, 237259 (1988)
\index{Brown, Christopher W.}
\begin{chunk}{axiom.bib}
+@phdthesis{Brow99,
+ author = "Brown, Christopher W.",
+ title = "Solution Formula Construction for Truth Invariant CADs",
+ school = "University of Delaware",
+ year = "1999",
+ website = "http://www.usna.edu/CS/qepcadweb/B/impl/Implementation.html",
+ url = "http://www.usna.edu/Users/cs/wcbrown/research/thesis.ps.gz",
+ paper = "Brow99.pdf",
+ abstract =
+ "The CADbased quantifier elimination algorithm takes a formula from
+ the elementary theory of real closed fields as input, and constructs a
+ CAD of the space of the formula's unquantified variables. This
+ decomposition is truth invariant with respect to the input formula,
+ meaning that the formula is either identically true or identically
+ false in each cell of the decomposition. The method determines the
+ truth of the input formula for each cell of the CAD, and then uses the
+ CAD to construct a solution formula  a quantifier free formula that
+ is equivalent to the input formula. This final phase of the algorithm,
+ the solution formula construction phase, is the focus of this thesis.
+
+ An optimal solution formula construction algorithm would be {\sl
+ complete}  i.e. applicable to any truthinvariant CAD, would be {\sl
+ efficient}, and would produce {\sl simple} solution formulas. Prior to
+ this thesis, no method was available with even two of these three
+ properties. Several algorithms are presented, all addressing problems
+ related to solution formula construction. In combination, these
+ provide an efficient and complete method for constructing solution
+ formulas that are simple in a variety of ways.
+
+ Algorithms presented in this thesis have been implemented using the
+ SACLIB library, and integrated into QEPCAD, a SACLIBbased
+ implementation of quantifier elimination by CAD. Example computations
+ based on these implementations are discussed."
+}
+
+\end{chunk}
+
+\index{Brown, Christopher W.}
+\begin{chunk}{axiom.bib}
@article{Brow01,
author="Brown, Christopher W.",
title="The McCallum projection, lifting, and orderinvariance",
@@ 13072,12 +13111,16 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
\end{chunk}
\index{Dalmas, St\'ephane}
\begin{chunk}{ignore}
\bibitem[Dalmas 92]{Dal92} Dalmas, S.
+\begin{chunk}{axiom.bib}
+ author = "Dalmas, Stephane",
title = "A polymorphic functional language applied to symbolic computation",
In Wang [Wan92] pp369375 ISBN 0897914899 (soft cover) 0897914902
(hard cover) LCCN QA76.95.I59 1992
 keywords = "axiomref",
+ year = "1992",
+ booktitle = "Proc. ISSAC 1992",
+ series = "ISSAC 1992",
+ pages = "369375",
+ isbn = "0897914899 (soft cover) 0897914902 (hard cover)",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 13694,7 +13737,64 @@ May 1984
\end{chunk}
\index{Dewar, Mike C.}
+\index{Dewar, Michael C.}
+\begin{chunk}{axiom.bib}
+@InProceedings{Dewa92,
+ author = "Dewar, Michael C.",
+ title = "Using Computer Algebra to Select Numerical Algorithms",
+ booktitle = "Proc. ISSAC 1992",
+ series = "ISSAC 1992",
+ year = "1992",
+ location = "Berkeley, CA",
+ pages = "18",
+ paper = "Dewa92.pdf",
+ algebra =
+ "\newline\refto{domain D01AJFA d01ajfAnnaType}
+ \newline\refto{domain D01AKFA d01akfAnnaType}
+ \newline\refto{domain D01ALFA d01alfAnnaType}
+ \newline\refto{domain D01AMFA d01amfAnnaType}
+ \newline\refto{domain D01ANFA d01anfAnnaType}
+ \newline\refto{domain D01APFA d01apfAnnaType}
+ \newline\refto{domain D01AQFA d01aqfAnnaType}
+ \newline\refto{domain D01ASFA d01asfAnnaType}
+ \newline\refto{domain D01FCFA d01fcfAnnaType}
+ \newline\refto{domain D01GBFA d01gbfAnnaType}
+ \newline\refto{domain D01TRNS d01TransformFunctionType}
+ \newline\refto{domain D02BBFA d02bbfAnnaType}
+ \newline\refto{domain D02BHFA d02bhfAnnaType}
+ \newline\refto{domain D02CJFA d02cjfAnnaType}
+ \newline\refto{domain D02EJFA d02ejfAnnaType}
+ \newline\refto{domain D03EEFA d03eefAnnaType}
+ \newline\refto{domain D03FAFA d03fafAnnaType}
+ \newline\refto{domain E04DGFA e04dgfAnnaType}
+ \newline\refto{domain E04FDFA e04fdfAnnaType}
+ \newline\refto{domain E04GCFA e04gcfAnnaType}
+ \newline\refto{domain E04JAFA e04jafAnnaType}
+ \newline\refto{domain E04MBFA e04mbfAnnaType}
+ \newline\refto{domain E04NAFA e04nafAnnaType}
+ \newline\refto{domain E04UCFA e04ucfAnnaType}
+ \newline\refto{domain NIPROB NumericalIntegrationProblem}
+ \newline\refto{domain ODEPROB NumericalODEProblem}
+ \newline\refto{domain OPTPROB NumericalOptimizationProblem}
+ \newline\refto{domain PDEPROB NumericalPDEProblem}",
+ abstract =
+ "Many reallife problems require a compbination of both symbolic and
+ numerical methods for their solution. This has led to the development
+ of intgrated, interactive symbolic / numeric packages which use a
+ computer algebra system for the former and a standard subroutine
+ library for the latter. These systems may also be viewed as simplified
+ frontends to the numerical library. To use these packages, however, a
+ user must be able to select which of the many available routines is
+ the most appropriate for his or her problem, which contrsts with the
+ ``blackbox'' style interfaces available in computer algebra
+ systems. This paper describes how a computer algebra system can be
+ used to make this decision, thus providing a muchsimplified and more
+ orthogonal interface."
+}
+
+\end{chunk}
+
+\index{Dewar, Michael C.}
\begin{chunk}{ignore}
\bibitem[Dewar 94]{Dew94} Dewar, M. C.
title = "Manipulating Fortran Code in AXIOM and the AXIOMNAG Link",
@@ 13704,7 +13804,7 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
\end{chunk}
\index{Dewar, Mike C.}
+\index{Dewar, Michael C.}
\begin{chunk}{axiom.bib}
@misc{Dewa95,
author = "Dewar, Mike C.",
@@ 14074,6 +14174,82 @@ Grant citation GR/L48256 Nov 1, 1997Feb 28, 2001
\end{chunk}
+\index{Dupee, Brian J.}
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@misc{Dupe95,
+ author = "Dupee, Brian J. and Davenport, James H.",
+ title = "Using Computer Algebra to Choose and Apply Numerical Routines",
+ year = "1995",
+ paper = "Dupe95.pdf",
+ keywords = "axiomref",
+ url =
+"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.33.5645&rep=rep1&type=pdf",
+ algebra =
+ "\newline\refto{domain D01AJFA d01ajfAnnaType}
+ \newline\refto{domain D01AKFA d01akfAnnaType}
+ \newline\refto{domain D01ALFA d01alfAnnaType}
+ \newline\refto{domain D01AMFA d01amfAnnaType}
+ \newline\refto{domain D01ANFA d01anfAnnaType}
+ \newline\refto{domain D01APFA d01apfAnnaType}
+ \newline\refto{domain D01AQFA d01aqfAnnaType}
+ \newline\refto{domain D01ASFA d01asfAnnaType}
+ \newline\refto{domain D01FCFA d01fcfAnnaType}
+ \newline\refto{domain D01GBFA d01gbfAnnaType}
+ \newline\refto{domain D01TRNS d01TransformFunctionType}
+ \newline\refto{domain D02BBFA d02bbfAnnaType}
+ \newline\refto{domain D02BHFA d02bhfAnnaType}
+ \newline\refto{domain D02CJFA d02cjfAnnaType}
+ \newline\refto{domain D02EJFA d02ejfAnnaType}
+ \newline\refto{domain D03EEFA d03eefAnnaType}
+ \newline\refto{domain D03FAFA d03fafAnnaType}
+ \newline\refto{domain E04DGFA e04dgfAnnaType}
+ \newline\refto{domain E04FDFA e04fdfAnnaType}
+ \newline\refto{domain E04GCFA e04gcfAnnaType}
+ \newline\refto{domain E04JAFA e04jafAnnaType}
+ \newline\refto{domain E04MBFA e04mbfAnnaType}
+ \newline\refto{domain E04NAFA e04nafAnnaType}
+ \newline\refto{domain E04UCFA e04ucfAnnaType}
+ \newline\refto{domain NIPROB NumericalIntegrationProblem}
+ \newline\refto{domain ODEPROB NumericalODEProblem}
+ \newline\refto{domain OPTPROB NumericalOptimizationProblem}
+ \newline\refto{domain PDEPROB NumericalPDEProblem}",
+ abstract =
+ "In applied mathematics, electronic and chemical engineering, the
+ modelling process can produce a number of mathematical problems which
+ require numerical solutions for which symbolic methods are either not
+ possible or not obvious. With the plethora of numerical library
+ routines for the solution of these problems often the numerical
+ analyst has to answer the question {\sl Which routine to choose?} and
+ {\sl How do I use it?}. Some analysis needs to be carried out before
+ the appropriate routine can be identifed, i.e. {\sl How stiff is this
+ ODE?} and {\sl Is this function continuous?}. It may well be the case
+ that more than one routine is applicable to the problem. So the
+ question may become {\sl Which is likely to be the best?}. Such a
+ choice may be critical for both accuracy and efficiency.
+
+ An expert system is thus required to make this choice based on the
+ results of its own analysis of the problem, call the routine and act
+ on the outcome. This may be to put the answer in a relevant form or
+ react to an apparent failure of the chosen routine and thus choose and
+ call an alternative. It should also have sufficient explanation
+ mechanisms to inform on the choice of routine and the reasons for that
+ choice. Much of this work can be achieved using computer algebra and
+ symbolic algebra packages.
+
+ This paper describes an expert system currently in prototype in terms
+ of both its objectbased structure and its computational agents. Some
+ of these agents are described in detail, paying particular attention
+ to the practical aspects of their algorithms and the use of computer
+ algebra.
+
+ The {\bf axiom2} Symbolic Algebra System is used as a user interface
+ as well as the link to the NAG Foundation Library for the numerical
+ routines and the inference mechanisms for the expert system."
+}
+
+\end{chunk}
+
\index{Adams, Andrew A.}
\index{Dunstan, Martin}
\index{Gottlieben, Hanne}
@@ 14493,13 +14669,18 @@ LCCN QA155.7.E4 I57 1984
\end{chunk}
\index{Fitch, John P.}
\begin{chunk}{ignore}
\bibitem[Fitch 93]{Fit93} Fitch, J. (ed)
Design and Implementation of Symbolic Computation Systems
International Symposium DISCO '92 Proceedings. SpringerVerlag, Berlin,
Germany / Heildelberg, Germany / London, UK / etc., 1993. ISBN 0387572724
(New York), 3540572724 (Berlin). LCCN QA76.9.S88I576 1992
+\begin{chunk}{axiom.bib}
+@InProceedings{Fitc93,
+ author = "Fitch (ed), John P.",
+ title = "Design and Implementation of Symbolic Computation Systems",
+ year = "1992",
+ booktitle = "Int. Symp. DISCO '92 Proceedings",
+ series = "DISCO 92",
+ publisher = "SpringerVerlag, Berlin",
+ isbn = "0387572724",
keywords = "axiomref",
+ paper = "Fitc93.tex"
+}
\end{chunk}
@@ 15164,6 +15345,29 @@ in [Wit87], pp58
\end{chunk}
+\index{Hearn, Anthony C.}
+\index{Eberhard, Schrufer}
+\begin{chunk}{axiom.bib}
+@article{Hear95,
+ author = "Hearn, Anthony C. and Eberhard, Schrufer",
+ title = "A computer algebra system based on ordersorted algebra",
+ journal = "J. Symbolic Computing",
+ volume = "19",
+ number = "13",
+ pages = "6577",
+ year = "1995",
+ keywords = "axiomref",
+ abstract =
+ "This paper presents the prototype design of an algebraic computation
+ system that manipulates algebraic quantities as generic objects using
+ ordersorted algebra as the underlying model. The resulting programs
+ have a form that is closely related to the algorithmic description of
+ a problem, but with the security of full type checking in a compact,
+ natural style."
+}
+
+\end{chunk}
+
\index{Heck, Andrew}
\begin{chunk}{ignore}
\bibitem[Heck 01]{Hec01} Heck, A.
@@ 15546,6 +15750,31 @@ Vol. 8 No. 3 pp195210 (2001)
\end{chunk}
+\index{Hoeppner, Sabine}
+\begin{chunk}{axiom.bib}
+@misc{Hoep95,
+ author = "Hoeppner, Sabine",
+ title = "Linear differential equations of second order in fields of
+ positive characteristic",
+ comment = "Essen: Univ. Essen, FB Math 71 S.",
+ year = "1995",
+ keywords = "axiomref",
+ abstract =
+ "Let be a differential field of characteristic $p>2$ of the type
+ $(\mathbb{F}_p(x),\frac{d}{dx})$. The equation studied is
+ $y^{\prime\prime}+ay^{\prime}+by=0$ with $a,b \in K$. The goal is to
+ produce a Liouvillian extension $L \supset K$ which contains two
+ independent solutions. This is done by solving the associated Riccati
+ equation $u^{\prime}+u^2+au+b=0$. Unlike the characteristic zero
+ situation, the Riccati equation has one or two solutions in an
+ algebraic extension of degree $\le 2$ of $K$. Full solutions are
+ given for the various cases that do occur. The paper ends with a
+ program in AXIOM which computes the solutions of the Riccati equation
+ and the Liouvillian extensions."
+}
+
+\end{chunk}
+
\index{Hoeven, Joris van der}
\index{Lecerf, Gregoire}
\begin{chunk}{axiom.bib}
@@ 17637,6 +17866,28 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
\end{chunk}
\index{Missura, Stephan A.}
+\begin{chunk}{axiom.bib}
+@InProceedings{Miss05,
+ author = "Missura, Stephan A.",
+ title = {Theories = Signatures + Propositions Used as Types},
+ keywords = "axiomref",
+ booktitle = "Integrating Symbolic Mathematics and Artificial Intelligence",
+ volume = "958",
+ pages = "144155",
+ year = "2005",
+ paper = "Miss05",
+ abstract =
+ "Languages that distinguish between types and structures use explicit
+ components for the carrier type(s) in structures. Examples are the
+ function language Standard ML and most algebraic specification
+ systems. Hence, they have to use general sum types or signatures to
+ give types to structures and be able to build, for instance, the
+ algebraic hierarchy."
+}
+
+\end{chunk}
+
+\index{Missura, Stephan A.}
\index{Weber, Andreas}
\begin{chunk}{ignore}
\bibitem[Missura 94]{Miss94} Missura, Stephan A.; Weber, Andreas
@@ 18630,6 +18881,39 @@ April 1991 CODEN SIGSBZ ISSN 01635824
\end{chunk}
+\index{Santas, Philip S.}
+\begin{chunk}{axiom.bib}
+@article{Sant95,
+ author = "Santas, Philip S.",
+ title = "A type system for computer algebra",
+ journal = "J. Symbolic Computation",
+ volume = "19",
+ number = "13",
+ pages = "79109",
+ year = "1995",
+ keywords = "axiomref",
+ paper = "Sant95.pdf",
+ abstract =
+ "This paper presents a type system for support of subtypes,
+ parameterized types with sharing and categories in a computer algebra
+ environment. By modeling representation of instances in terms of
+ existential types, we obtain a simplified model, and build a basis for
+ defining subtyping among algebraic domains. The inheritance at
+ category level has been formalized; this allows the automatic
+ inference of type classes. By means of type classes and existential
+ types we construct subtype relations without involving coercions. A
+ type sharing mechanism works in parallel and allows the consistent
+ extension and combination of domains. The expressiveness of the system
+ is further increased by viewing domain types as special case of
+ package types, forming weak and strong sums respectively. The
+ introduced system, although awkward at first sight, is simpler than
+ other proposed systems for computer algebra without including some of
+ their problems. The system can be further extended in other to support
+ more constructs and increase its flexibility."
+}
+
+\end{chunk}
+
\index{Saunders, B. David}
\begin{chunk}{axiom.bib}
@article{Saun80,
@@ 20763,41 +21047,6 @@ IBM Research Report RC13460 IBM Corp. Yorktown Heights, NY
\end{chunk}
\index{Brown, Christopher W.}
\begin{chunk}{ignore}
\bibitem[Brown 99]{Brow99} Brown, Christopher W.
 title = "Solution Formula Construction for Truth Invariant CADs",
Ph.D Thesis, Univ. Delaware (1999)
 url = "http://www.usna.edu/Users/cs/wcbrown/research/thesis.ps.gz",
 paper = "Brow99.pdf",
 abstract = "
 The CADbased quantifier elimination algorithm takes a formula from
 the elementary theory of real closed fields as input, and constructs a
 CAD of the space of the formula's unquantified variables. This
 decomposition is truth invariant with respect to the input formula,
 meaning that the formula is either identically true or identically
 false in each cell of the decomposition. The method determines the
 truth of the input formula for each cell of the CAD, and then uses the
 CAD to construct a solution formula  a quantifier free formula that
 is equivalent to the input formula. This final phase of the algorithm,
 the solution formula construction phase, is the focus of this thesis.

 An optimal solution formula construction algorithm would be {\sl
 complete}  i.e. applicable to any truthinvariant CAD, would be {\sl
 efficient}, and would produce {\sl simple} solution formulas. Prior to
 this thesis, no method was available with even two of these three
 properties. Several algorithms are presented, all addressing problems
 related to solution formula construction. In combination, these
 provide an efficient and complete method for constructing solution
 formulas that are simple in a variety of ways.

 Algorithms presented in this thesis have been implemented using the
 SACLIB library, and integrated into QEPCAD, a SACLIBbased
 implementation of quantifier elimination by CAD. Example computations
 based on these implementations are discussed."

\end{chunk}

\index{Burge, William H.}
\begin{chunk}{axiom.bib}
@article{Burg74,
@@ 22938,6 +23187,7 @@ Mathematical Surveys. 3 Am. Math. Soc., Providence, RI. (1966)
year = "1995",
journal = "Proceedings of AAECC11",
keywords = "axiomref",
+ paper = "Maza95.pdf",
algebra = "\newline\refto{category TSETCAT TriangularSetCategory}
\newline\refto{category RSETCAT RegularTriangularSetCategory}
\newline\refto{category NTSCAT NormalizedTriangularSetCategory}
diff git a/changelog b/changelog
index 46746ef..7ececb4 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,5 @@
+20160704 tpd src/axiomwebsite/patches.html 20160704.01.tpd.patch
+20160704 tpd books/bookvolbib Axiom Citations in the Literature
20160703 tpd src/axiomwebsite/patches.html 20160703.03.tpd.patch
20160703 tpd books/bookvol10.4 document PAFFFF and unit tests
20160703 tpd books/bookvol10 document PAFFFF
diff git a/patch b/patch
index 292af58..d4f43f1 100644
 a/patch
+++ b/patch
@@ 1,4 +1,312 @@
books/bookvol10.4, bookvol10 document PAFFFF and unit tests
+books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
+\index{Hearn, Anthony C.}
+\index{Eberhard, Schrufer}
+\begin{chunk}{axiom.bib}
+@article{Hear95,
+ author = "Hearn, Anthony C. and Eberhard, Schrufer",
+ title = "A computer algebra system based on ordersorted algebra",
+ journal = "J. Symbolic Computing",
+ volume = "19",
+ number = "13",
+ pages = "6577",
+ year = "1995",
+ keywords = "axiomref",
+ paper = "Hear95.pdf",
+ abstract =
+ "This paper presents the prototype design of an algebraic computation
+ system that manipulates algebraic quantities as generic objects using
+ ordersorted algebra as the underlying model. The resulting programs
+ have a form that is closely related to the algorithmic description of
+ a problem, but with the security of full type checking in a compact,
+ natural style."
+}
+
+\end{chunk}
+
+
+\index{Hoeppner, Sabine}
+\begin{chunk}{axiom.bib}
+@misc{Hoep95,
+ author = "Hoeppner, Sabine",
+ title = "Linear differential equations of second order in fields of
+ positive characteristic",
+ comment = "Essen: Univ. Essen, FB Math 71 S.",
+ year = "1995",
+ keywords = "axiomref",
+ abstract =
+ "Let be a differential field of characteristic $p>2$ of the type
+ $(\mathbb{F}_p(x),\frac{d}{dx})$. The equation studied is
+ $y^{\prime\prime}+ay^{\prime}+by=0$ with $a,b \in K$. The goal is to
+ produce a Liouvillian extension $L \supset K$ which contains two
+ independent solutions. This is done by solving the associated Riccati
+ equation $u^{\prime}+u^2+au+b=0$. Unlike the characteristic zero
+ situation, the Riccati equation has one or two solutions in an
+ algebraic extension of degree $\le 2$ of $K$. Full solutions are
+ given for the various cases that do occur. The paper ends with a
+ program in AXIOM which computes the solutions of the Riccati equation
+ and the Liouvillian extensions."
+}
+
+\end{chunk}
+
+\index{Santas, Philip S.}
+\begin{chunk}{axiom.bib}
+@article{Sant95,
+ author = "Santas, Philip S.",
+ title = "A type system for computer algebra",
+ journal = "J. Symbolic Computation",
+ volume = "19",
+ number = "13",
+ pages = "79109",
+ year = "1995",
+ keywords = "axiomref",
+ paper = "Sant95.pdf",
+ abstract =
+ "This paper presents a type system for support of subtypes,
+ parameterized types with sharing and categories in a computer algebra
+ environment. By modeling representation of instances in terms of
+ existential types, we obtain a simplified model, and build a basis for
+ defining subtyping among algebraic domains. The inheritance at
+ category level has been formalized; this allows the automatic
+ inference of type classes. By means of type classes and existential
+ types we construct subtype relations without involving coercions. A
+ type sharing mechanism works in parallel and allows the consistent
+ extension and combination of domains. The expressiveness of the system
+ is further increased by viewing domain types as special case of
+ package types, forming weak and strong sums respectively. The
+ introduced system, although awkward at first sight, is simpler than
+ other proposed systems for computer algebra without including some of
+ their problems. The system can be further extended in other to support
+ more constructs and increase its flexibility."
+}
+
+\end{chunk}
+
+\index{Dalmas, St\'ephane}
+\begin{chunk}{axiom.bib}
+ author = "Dalmas, Stephane",
+ title = "A polymorphic functional language applied to symbolic computation",
+ year = "1992",
+ booktitle = "Proc. ISSAC 1992",
+ series = "ISSAC 1992",
+ pages = "369375",
+ isbn = "0897914899 (soft cover) 0897914902 (hard cover)",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Missura, Stephan A.}
+\begin{chunk}{axiom.bib}
+@InProceedings{Miss05,
+ author = "Missura, Stephan A.",
+ title = {Theories = Signatures + Propositions Used as Types},
+ keywords = "axiomref",
+ booktitle = "Integrating Symbolic Mathematics and Artificial Intelligence",
+ volume = "958",
+ pages = "144155",
+ year = "2005",
+ paper = "Miss05",
+ abstract =
+ "Languages that distinguish between types and structures use explicit
+ components for the carrier type(s) in structures. Examples are the
+ function language Standard ML and most algebraic specification
+ systems. Hence, they have to use general sum types or signatures to
+ give types to structures and be able to build, for instance, the
+ algebraic hierarchy."
+}
+
+\end{chunk}
+
+\index{Fitch, John P.}
+\begin{chunk}{axiom.bib}
+@InProceedings{Fitc93,
+ author = "Fitch (ed), John P.",
+ title = "Design and Implementation of Symbolic Computation Systems",
+ year = "1992",
+ booktitle = "Int. Symp. DISCO '92 Proceedings",
+ series = "DISCO 92",
+ publisher = "SpringerVerlag, Berlin",
+ isbn = "0387572724",
+ keywords = "axiomref",
+ paper = "Fitc93.tex"
+}
+
+\end{chunk}
+
+\index{Dupee, Brian J.}
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@misc{Dupe95,
+ author = "Dupee, Brian J. and Davenport, James H.",
+ title = "Using Computer Algebra to Choose and Apply Numerical Routines",
+ year = "1995",
+ paper = "Dupe95.pdf",
+ keywords = "axiomref",
+ url =
+"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.33.5645&rep=rep1&type=pdf",
+ algebra =
+ "\newline\refto{domain D01AJFA d01ajfAnnaType}
+ \newline\refto{domain D01AKFA d01akfAnnaType}
+ \newline\refto{domain D01ALFA d01alfAnnaType}
+ \newline\refto{domain D01AMFA d01amfAnnaType}
+ \newline\refto{domain D01ANFA d01anfAnnaType}
+ \newline\refto{domain D01APFA d01apfAnnaType}
+ \newline\refto{domain D01AQFA d01aqfAnnaType}
+ \newline\refto{domain D01ASFA d01asfAnnaType}
+ \newline\refto{domain D01FCFA d01fcfAnnaType}
+ \newline\refto{domain D01GBFA d01gbfAnnaType}
+ \newline\refto{domain D01TRNS d01TransformFunctionType}
+ \newline\refto{domain D02BBFA d02bbfAnnaType}
+ \newline\refto{domain D02BHFA d02bhfAnnaType}
+ \newline\refto{domain D02CJFA d02cjfAnnaType}
+ \newline\refto{domain D02EJFA d02ejfAnnaType}
+ \newline\refto{domain D03EEFA d03eefAnnaType}
+ \newline\refto{domain D03FAFA d03fafAnnaType}
+ \newline\refto{domain E04DGFA e04dgfAnnaType}
+ \newline\refto{domain E04FDFA e04fdfAnnaType}
+ \newline\refto{domain E04GCFA e04gcfAnnaType}
+ \newline\refto{domain E04JAFA e04jafAnnaType}
+ \newline\refto{domain E04MBFA e04mbfAnnaType}
+ \newline\refto{domain E04NAFA e04nafAnnaType}
+ \newline\refto{domain E04UCFA e04ucfAnnaType}
+ \newline\refto{domain NIPROB NumericalIntegrationProblem}
+ \newline\refto{domain ODEPROB NumericalODEProblem}
+ \newline\refto{domain OPTPROB NumericalOptimizationProblem}
+ \newline\refto{domain PDEPROB NumericalPDEProblem}",
+ abstract =
+ "In applied mathematics, electronic and chemical engineering, the
+ modelling process can produce a number of mathematical problems which
+ require numerical solutions for which symbolic methods are either not
+ possible or not obvious. With the plethora of numerical library
+ routines for the solution of these problems often the numerical
+ analyst has to answer the question {\sl Which routine to choose?} and
+ {\sl How do I use it?}. Some analysis needs to be carried out before
+ the appropriate routine can be identifed, i.e. {\sl How stiff is this
+ ODE?} and {\sl Is this function continuous?}. It may well be the case
+ that more than one routine is applicable to the problem. So the
+ question may become {\ls Which is likely to be the best?}. Such a
+ choice may be critical for both accuracy and efficiency.
+
+ An expert system is thus required to make this choice based on the
+ results of its own analysis of the problem, call the routine and act
+ on the outcome. This may be to put the answer in a relevant form or
+ react to an apparent failure of the chosen routine and thus choose and
+ call an alternative. It should also have sufficient explanation
+ mechanisms to inform on the choice of routine and the reasons for that
+ choice. Much of this work can be achieved using computer algebra and
+ symbolic algebra packages.
+
+ This paper describes an expert system currently in prototype in terms
+ of both its objectbased structure and its computational agents. Some
+ of these agents are described in detail, paying particular attention
+ to the practical aspects of their algorithms and the use of computer
+ algebra.
+
+ The {\bf axiom2} Symbolic Algebra System is used as a user interface
+ as well as the link to the NAG Foundation Library for the numerical
+ routines and the inference mechanisms for the expert system."
+}
+
+\end{chunk}
+
+\index{Dewar, Michael C.}
+\begin{chunk}{axiom.bib}
+@InProceedings{Dewa92,
+ author = "Dewar, Michael C.",
+ title = "Using Computer Algebra to Select Numerical Algorithms",
+ booktitle = "Proc. ISSAC 1992",
+ series = "ISSAC 1992",
+ year = "1992",
+ location = "Berkeley, CA",
+ pages = "18",
+ paper = "Dewa92.pdf",
+ algebra =
+ "\newline\refto{domain D01AJFA d01ajfAnnaType}
+ \newline\refto{domain D01AKFA d01akfAnnaType}
+ \newline\refto{domain D01ALFA d01alfAnnaType}
+ \newline\refto{domain D01AMFA d01amfAnnaType}
+ \newline\refto{domain D01ANFA d01anfAnnaType}
+ \newline\refto{domain D01APFA d01apfAnnaType}
+ \newline\refto{domain D01AQFA d01aqfAnnaType}
+ \newline\refto{domain D01ASFA d01asfAnnaType}
+ \newline\refto{domain D01FCFA d01fcfAnnaType}
+ \newline\refto{domain D01GBFA d01gbfAnnaType}
+ \newline\refto{domain D01TRNS d01TransformFunctionType}
+ \newline\refto{domain D02BBFA d02bbfAnnaType}
+ \newline\refto{domain D02BHFA d02bhfAnnaType}
+ \newline\refto{domain D02CJFA d02cjfAnnaType}
+ \newline\refto{domain D02EJFA d02ejfAnnaType}
+ \newline\refto{domain D03EEFA d03eefAnnaType}
+ \newline\refto{domain D03FAFA d03fafAnnaType}
+ \newline\refto{domain E04DGFA e04dgfAnnaType}
+ \newline\refto{domain E04FDFA e04fdfAnnaType}
+ \newline\refto{domain E04GCFA e04gcfAnnaType}
+ \newline\refto{domain E04JAFA e04jafAnnaType}
+ \newline\refto{domain E04MBFA e04mbfAnnaType}
+ \newline\refto{domain E04NAFA e04nafAnnaType}
+ \newline\refto{domain E04UCFA e04ucfAnnaType}
+ \newline\refto{domain NIPROB NumericalIntegrationProblem}
+ \newline\refto{domain ODEPROB NumericalODEProblem}
+ \newline\refto{domain OPTPROB NumericalOptimizationProblem}
+ \newline\refto{domain PDEPROB NumericalPDEProblem}",
+ abstract =
+ "Many reallife problems require a compbination of both symbolic and
+ numerical methods for their solution. This has led to the development
+ of intgrated, interactive symbolic / numeric packages which use a
+ computer algebra system for the former and a standard subroutine
+ library for the latter. These systems may also be viewed as simplified
+ frontends to the numerical library. To use these packages, however, a
+ user must be able to select which of the many available routines is
+ the most appropriate for his or her problem, which contrsts with the
+ ``blackbox'' style interfaces available in computer algebra
+ systems. This paper describes how a computer algebra system can be
+ used to make this decision, thus providing a muchsimplified and more
+ orthogonal interface."
+}
+
+\end{chunk}
+
+
+\index{Brown, Christopher W.}
+\begin{chunk}{axiom.bib}
+@phdthesis{Brow99,
+ author = "Brown, Christopher W.",
+ title = "Solution Formula Construction for Truth Invariant CADs",
+ school = "University of Delaware",
+ year = "1999",
+ website = "http://www.usna.edu/CS/qepcadweb/B/impl/Implementation.html",
+ url = "http://www.usna.edu/Users/cs/wcbrown/research/thesis.ps.gz",
+ paper = "Brow99.pdf",
+ abstract =
+ "The CADbased quantifier elimination algorithm takes a formula from
+ the elementary theory of real closed fields as input, and constructs a
+ CAD of the space of the formula's unquantified variables. This
+ decomposition is truth invariant with respect to the input formula,
+ meaning that the formula is either identically true or identically
+ false in each cell of the decomposition. The method determines the
+ truth of the input formula for each cell of the CAD, and then uses the
+ CAD to construct a solution formula  a quantifier free formula that
+ is equivalent to the input formula. This final phase of the algorithm,
+ the solution formula construction phase, is the focus of this thesis.
+
+ An optimal solution formula construction algorithm would be {\sl
+ complete}  i.e. applicable to any truthinvariant CAD, would be {\sl
+ efficient}, and would produce {\sl simple} solution formulas. Prior to
+ this thesis, no method was available with even two of these three
+ properties. Several algorithms are presented, all addressing problems
+ related to solution formula construction. In combination, these
+ provide an efficient and complete method for constructing solution
+ formulas that are simple in a variety of ways.
+
+ Algorithms presented in this thesis have been implemented using the
+ SACLIB library, and integrated into QEPCAD, a SACLIBbased
+ implementation of quantifier elimination by CAD. Example computations
+ based on these implementations are discussed."
+}
+
+\end{chunk}
+
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index d997e6f..ffafb97 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5443,7 +5443,9 @@ books/bookvol10.4 Hache PAFF documentation and unit tests
20160703.02.tpd.patch
books/bookvol10.4 document algebra
20160703.03.tpd.patch
books/bookvol10.4, bookvol10 document PAFFFF and unit tests
+books/bookvol10.4, bookvol10 document PAFFFF and unit tests
+20160704.01.tpd.patch
+books/bookvolbib Axiom Citations in the Literature

1.7.5.4