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Date: Wed, 20 Jul 2016 22:15:33 0400
Subject: [PATCH] books/bookvolbib Axiom Citations in the Literature
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Goal: Axiom Literate Programming
\index{Sit, William Y.}
\begin{chunk}{axiom.bib}
@article{Sitx92,
author = "Sit, William Y.",
title = "An algorithm for solving parametric linear systems",
journal = "Journal of Symbolic Computations",
volume = "13",
number = "4",
pages = "353394",
year = "1992",
paper = "Sitx92.pdf",
keywords = "axiomref",
abstract =
"We present a theoretical foundation for studying parametric systesm of
linear equations and prove an efficient algorithm for identifying all
parametric values (including degnerate cases) for which the system is
consistent. The algorithm gives a small set of regimes where for each
regime, the solutions of the specialized systems may be given
uniformly. For homogeneous linear systems, or for systems were the
right hand side is arbitrary, this small set is irredunant. We discuss
in detail practical issues concerning implementations, with particular
emphasis on simplification of results. Examples are given based on a
close implementation of the algorithm in SCRATCHPAD II. We also give a
complexity analysis of the Gaussian elimination method and compare
that with our algorithm."
}
\end{chunk}
\index{Smedley, Trevor J.}
\begin{chunk}{axiom.bib}
@inproceedings{Smed92,
author = "Smedley, Trevor J.",
title = "Using pictorial and object oriented programming for computer
algebra",
booktitle = "Applied computing  technological challenges of the
1990's: proceedings of the 1992 ACM\slash SIGAPP
Symposium on Applied Computing, Kansas City Convention
Center, March 13, 1992",
publisher = "ACM Press",
pages = "12431247",
isbn = "089791502X",
keywords = "axiomref"
}
\end{chunk}
\index{Zenger, Christoph}
\begin{chunk}{axiom.bib}
@mastersthesis{Zeng92,
author = "Zenger, Christoph",
title = "Gr{\"o}bnerbasen f{\"u}r Differentialformen und ihre
Implementierung in AXIOM'",
type = "Diplomarbeit",
school = "Universit{\"a}t Karlsruhe",
address = "Karlsruhe, Germany",
year = "1992",
keywords = "axiomref"
}
\end{chunk}
\index{FullPartialFractionExpansion}
\index{Bronstein, Manuel}
\index{Salvy, Bruno}
\begin{chunk}{axiom.bib}
@inproceedings{Bron93,
author = "Bronstein, Manuel and Salvy, Bruno",
title = "Full partial fraction decomposition of rational functions",
booktitle = "Proc. ISSAC 1993",
year = "1993",
pages = "157160",
isbn = "0897916042",
url = "http://www.acm.org/pubs/citations/proceedings/issac/164081/",
paper = "Bron93.pdf",
algebra = "\newline\refto{domain FPARFRAC FullPartialFractionExpansion}",
abstract =
"We describe a rational algorithm that computes the full partial
fraction expansion of a rational function over the algebraic closure
of its field of definition. The algorithm uses only gcd operations
over the initial field but the resulting decomposition is expressed
with linear denominators. We give examples from its Axiom and Maple
implementations."
}
\end{chunk}
\index{TranscendentalRischDE}
\index{TranscendentalRischDESystem}
\index{Bronstein, Manuel}
\begin{chunk}{axiom.bib}
@article{Bron90,
author = "Bronstein, Manuel",
title = "The Transcendental Risch Differential Equation",
journal = "J. Symbolic Computation",
volume = "9",
pages = "4960",
year = "1990",
comment = "IBM Research Report RC13460 IBM Corp. Yorktown Heights, NY",
paper = "Bron90.pdf",
keywords = "axiomref",
algebra =
"\newline\refto{package RDETR TranscendentalRischDE}
\newline\refto{package RDETRS TranscendentalRischDESystem}",
abstract =
"We present a new rational algorithm for solving Risch differential
equations in towers of transcendental elementary extensions. In
contrast to a recent algorithm by Davenport we do not require a
progressive reduction of the denominators involved, but use weak
normality to obtain a formula for the denominator of a possible
solution. Implementation timings show this approach to be faster than
a Hermitelike reduction."
}
\end{chunk}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
\bibitem[Davenport 86]{Dav86} Davenport, J.H.
@article{Dave86,
author = "Davenport, James H.",
title = "The Risch Differential Equation Problem",
year = "1986",
journal = "SIAM J. COMPUT.",
volume = "15",
number = "4",
comment = "Technical Report 834, Dept. Comp. Sci, Univ. Delaware",
paper = "Dave86.pdf",
abstract = "
We propose a new algorithm, similar to Hermite's method for the
integration of rational functions, for the resolution of Risch
differential equations in closed form, or proving that they have no
resolution. By requiring more of the presentation of our differential
fields (in particular that the exponentials be weakly normalized), we
can avoid the introduction of arbitrary constants which have to be
solved for later.
We also define a class of fields known as exponentially reduced, and
show that solutions of Risch differential equations which arise from
integrating in these fields satisfy the ``natural'' degree constraints
in their main variables, and we conjecture (after Risch and Norman)
that this is true in all variables."
}
\end{chunk}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@book{Dave05,
author = "Davenport, James H.",
title = "Integration  What do we want from the theory?",
booktitle = "Computer Algebra",
publisher = "Springer",
series = "Lecture Notes in Computer Science 162",
pages = "211",
year = "2005",
abstract =
"The theory of integration has moved a long way in the last fourteen
years, thought not far enough to satisfy the demands placed on it by
its customers. This paper outlines what problems have yet to be solved,
and tries to explain why they are not trivial."
}
\end{chunk}
\index{Rothstein, Michael}
\begin{chunk}{ignore}
@phdthesis{Roth76,
author = "Rothstein, Michael",
title = "Aspects of symbolic integration and simplifcation of
exponential and primitive functions",
school = "University of WisconsinMadison",
year = "1976",
url = "http://www.cs.kent.edu/~rothstei/dis.pdf",
paper = "Ro76.pdf",
abstract =
"In this thesis we cover some aspects of the theory necessary to obtain
a canonical form for functions obtained by integration and
exponentiation from the set of rational functions.
These aspects include a new algorithm for symbolic integration of
functions involving logarithms and exponentials which avoids
factorization of polynomials in those cases where algebraic extension
of the constant field is not required, avoids partial fraction
decompositions, and only solves linear systems with a small number of
unknowns.
We have also found a theorem which states, roughly speaking, that if
integrals which can be represented as logarithms are represented as
such, the only algebraic dependence that a new exponential or
logarithm can satify is given by the law of exponents or the law of
logarithms."
}
\end{chunk}
\index{Bronstein, Manuel}
\begin{chunk}{axiom.bib}
@article{Bron92a,
author = "Bronstein, Manuel",
title = "Formulas for Series Computation",
journal = "Applied Algebra in Engineering, Communication and Computing",
volume = "2",
pages = "195206",
year = "1992",
abstract =
"We describe an algorithm that computes polynomials whose roots are
the coefficients of any specific order of the Laurent series of a
rational function. The algorithm uses only rational operations in the
coefficient field of the function. This allows us to compute with the
principal parts of the Laurent series, in particular with the residues
of the function, without factoring or splitting its denominator. As
applications, we get a generalisation of the residue formulas used in
symbolic integration algorithms to $n^{th}$order formulas. We also
get an algorithm that computes explicitly the principlal parts at all
the poles simultaneously, while computing in the field generated by
the coefficients of the series instead of the one generated by the
poles of the function. This yields an improved version of the
necessary conditions for the various cases of Kovacic's algorithm,
that expresses those conditions in the smallest possible extension
field."
}
\end{chunk}
\index{Goodloe, A.}
\index{Loustaunau, Philippe}
\begin{chunk}{axiom.bib}
@inproceedings{Good93,
author = "Goodloe, A. and Loustaunau, Philippe",
title = "An abstract data type development of graded rings",
booktitle = "Design and Implementation of Symbolic Computation Systems",
series = "Lecture Notes in Computer Science 721",
pages = "193202",
isbn = "0387572724 (New York), 3540572724 (Berlin)",
year = "1993",
keywords = "axiomref",
abstract =
"Recently new computer algebra systems such as Scratchpad and Weyl have
been developed with built in mechanisms for expressing abstract data types.
These systems are object oriented in that they incorporate multiple
inheritance and polymorphic types. Davenport and Trager have build much
of the framework for basic commutative algebra in Scratchpad II
utilizing its rich set of abstraction mechanisms. Davenport and Trager
concentrated on developing factorization algorithms on domains which
were abstract data types.
We are taking a similar approach to the development of algorithms for
computing in graded rings. The purpose of this paper is to develop the
tools required to compute with polynomials with coefficients in a graded
ring $R$. We focus on graded rings $R$ which are polynomial rings graded
by a monoid, and we allow partial orders on the monomials. The ideas
presented here can be applied to more general graded rings $R$, such as
associated graded rings to filtered rings, as long as certain computational
``requirements'' are satisfied"
}
\end{chunk}
\index{Beneke, T.}
\index{Schwippert, W.}
\begin{chunk}{axiom.bib}
@article{Bene94,
author = "Beneke, T. and Schwippert, W.",
title = "Doubletrack into the future: MathCAD will gain new users with
Standard and Plus versions",
journal = "Elektronik",
volume = "43",
number = "15",
pages = "107110",
year = "1994",
month = "July",
pages = "107110",
keywords = "axiomref",
abstract =
"MathCAD software is a type of `intelligent scratchpad with a pocket
calculator function'. Hitherto it has been suitable only to a limited
extent for engineering mathematics. The new Version 5.0 is now offered
in two implementations: as an inexpensive basic package and in a
considerably more costly Plus version. The authors question whether
MathCAD can catch up with the classical Maple and Mathematica products."
}
\end{chunk}
\index{Vakil, Ravi}
\begin{chunk}{axiom.bib}
@misc{Vaki98,
author = "Vakil, Ravi",
title = "A Beginner's Guide to Jet Bundles fromthe Point of View of
Algebraic Geometry",
url = "http://math.stanford.edu/~vakil/files/jets.pdf",
paper = "Vaki98.pdf",
year = "1998"
}
\index{Roesner, K. G.}
\begin{chunk}{axiom.bib}
@article{Roes95,
author = "Roesner, K. G.",
title = "Verified solutions for parameters of an exact solution for
nonNewtonian liquids using computer algebra",
journal = "Zeitschrift fur Angewandte Mathematik und Physik",
volume = "75",
number = "suppl. 2",
pages = "S435S438",
year = "1995",
keywords = "axiomref",
abstract =
"An exact solution of the time independent velocity field for the
TaylorCouette flow of a polymer solution is derived solving the
resulting first order ordinary differential equation of fifth degree
analytically. Intensive use is made of computer algebra systems AXIOM
and MACSYMA to find the exact solution. The coaxial cylinders in the
TaylorCouette flow problem are assumed to rotate at different
angular velocities. The geometrical and kinematic parameters can be
chosen arbitrarily. The model equation for the material law of the
viscoelastic liquid is based on the thermodynamic model for dilute
solutions due to Lhuillier and Ouibrahim (1980) which is an analogy to
the earlier paper of Frankel and Acrivos (1970). In the present
investigation the influence of the parameters of the viscoelastic
model on the velocity profile in the cylindrical gap is studied and
the range of validity of the constitutive equation is investigated."
}
\end{chunk}
\index{Benker, Hans}
\begin{chunk}{axiom.bib}
@book{Benk98,
author = "Benker, Hans",
title = "Engineering mathematics with computer algebra systems",
year = "1998",
keywords = "axiomref",
comment = "german"
}
\end{chunk}
\begin{chunk}{axiom.bib}
@misc{Linu15,
author = "Linux Links",
title = "Axiom",
url = "http://www.linuxlinks.com/article/20080810064748970/Axiom.html",
keywords = "axiomref",
year = "2015"
}
\end{chunk}
\index{Daly, Timothy}
\index{Barnes, Nick}
\begin{chunk}{axiom.bib}
@misc{Daly13a,
author = "Daly, Timothy and Barnes, Nick",
title = "Ten reasons you must publish your code",
year = "2013",
url =
"http://climatecode.org/blog/2013/07/tenreasonsyoumustpublishyourcode/",
keywords = "axiomref",
}
\end{chunk}
\index{Daly, Timothy}
\begin{chunk}{axiom.bib}
@misc{Daly05,
author = "Daly, Timothy",
title = "LispNYC Presentation at Trinity",
year = "2005",
month = "May",
day = "10",
keywords = "axiomref",
abstract =
"Timothy Daly presents Axiom
Timothy Daly, published author, academic researcher, open source
programmer and lead developer of Axiom will be presenting about his role
as the driving force behind Axiom. With over 70 developers and 200
researchers worldwide it can best be described as:
Axiom is a general purpose Computer Algebra system. It is useful
for research and development of mathematical algorithms providing
a very high level way to express abstract mathematical concepts.
The Axiom Library defines over 1,000 stronglytyped mathematical
domains and categories.
Axiom consists of an interpreter and compiler, a browser, a graphical
interface, and a new online wiki that allows users to create web pages
that inline computations.
Axiom is built upon Common Lisp."
}
\end{chunk}
\index{Daly, Timothy}
\begin{chunk}{axiom.bib}
@misc{Dalyxx,
author = "Daly, Timothy",
title = "Tim Daly on Lisp in Industry",
keywords = "axiomref",
url = "https://news.ycombinator.com/item?id=1580904"
}
\end{chunk}
\index{Harriss, Edmund}
\index{Daly, Timothy}
\begin{chunk}{axiom.bib}
@misc{Harr12,
author = "Harriss, Edmund and Daly, Timothy",
title = "Have we ever lost mathematics?",
url = "https://maxwelldemon.com/2012/05/09/haveweeverlostmathematics/",
keywords = "axiomref",
year = "2012"
}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate06a,
author = "Fateman, Richard J.",
title = "Comments on Extending Macsyma with New Data Types",
url = "http://www.cs.berkeley.edu/~/fateman/papers/addformat.pdf",
paper = "Fate06a.pdf",
abstract =
"Any design for a computer algebra system (CAS) naturally includes a
set of data layouts for symbolic or mathematical algebraic expressions
intended for use by builtin or userwritten programs. The CAS cannot
build in all plausible data designs, but supports those of most
interest to the programmers. In such a situation it is almost
inevitable that some new data encoding idea will come to mind and with
it an interest in adding additional data forms. The motivation may be
for compact representation, or efficient (fast) manipulation, or for
other reasons such as interchange with other programs. Most CAS
therefore include at least one way to extend the base set of
operations. We comment on the kinds of extensions possible, using
Macsyma as an example CAS. The particular interest in Macsyma and its
opensource soruceforge variant ``Maxima'' is that a substantial group
of verylosely coupled independent researchers are approaching this
problem and may benefit from some guidance. Some the observations
apply to other CAS, even though they are not opensource.",
keywords = "axiomref"
}
\end{chunk}
\index{Heckmann, Reinhold}
\index{Wilhelm, Reinhard}
\begin{chunk}{axiom.bib}
@article{Heck97,
author = "Heckmann, Reinhold and Wilhelm, Reinhard",
title = "A Functional Description of TeX's Formula Layout",
journal = "J. Functional Programming",
volume = "7",
number = "5",
pages = "451485",
year = "1997",
url = "http://http.cs.berkeley.edu/~fateman/temp/neuform.pdf",
comment = "ftp://ftp.cs.unisb.de/formulae/formulae.tar.gz",
abstract =
"While the quality of the results of TeX's mathematica formula layout
algorithm is convincing, its original description is hard to
understand since it is presented as an imperative program with complex
control flow and destructive manipulations of the data structures
representing formulae. In this paper, we present a reimplementation
of TeX's formula layout algorithm in the functional language SML,
thereby providing a more readable description of the algorithm,
extracted from the monolithical TeX system.",
paper = "Heck97.pdf"
}
\end{chunk}
\begin{chunk}{axiom.bib}
@misc{Unkn15,
author = "Unknown",
title = "Branches of Functions",
url = "http://scipp.ucsc.edu/~haber/ph116A/ComplexFunBranchTheory.pdf",
paper = "Unkn15.pdf"
}
\end{chunk}
\index{Phisanbut, Nalina}
\index{Bradford, Russell J.}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@article{Phis11,
author = "Phisanbut, Nalina and Bradford, Russell J. and
Davenport, James H.",
title = "Geometry of branch cuts",
journal = "ACM Communications in Computer Algebra",
volume = "44",
number = "34",
pages = "132135",
year = "2011",
abstract =
"'Simplification' is a key concept in Computer Algebra. But many
simplification rules, such as $\sqrt{x}\sqrt{y} \rightarrow \sqrt{xy}$
are not universally valid, due to the fact that many elementary
functions are multivalued. Hence a key question is ``Is this
simplification correct?'', which involves algorithmic analysis of the
branch cuts involved. In this paper, we look at variable ordering and
preconditioning as supporting technologies for this analysis.",
paper = "Phis11.pdf"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate97a,
author = "Fateman, Richard J.",
title = "The Fast Fourier Transform",
course = "Berkeley CS 292, Fall 1997, Handout 2",
year = "1997",
url = "http://www.cs.berkeley.edu/~/fateman/papers/fftnotes.pdf",
paper = "Fate97a.pdf"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate14,
author = "Fateman, Richard J.",
title = "Fun with Filon Quadrature  a Computer Algebra Perspective",
year = "2014",
url = "http://www.cs.berkeley.edu/~/fateman/papers/funfilon.pdf",
abstract =
"Filon quadrature, useful for oscillatory integrals, is easily
implemented in a computer algebra system (CAS) using exact or
approximate arithmetic. Although quadrature is almost always used in
the context of approximation, we see that various properties are
exhibited by running an exact algorithm on exact {\sl symbolic}
inputs. This experimental approach to the mathematics allows us to
prove the implementation of the algorithm has the expected
mathematical correctness properties, and is therefore more likely to
be, itself, a correct implementation."
paper = "Fate14.pdf"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate05a,
author = "Fateman, Richard J.",
title = "Haddock's eyes and computer algebra systems: Some essays",
url = "http://www.cs.berkeley.edu/~/fateman/papers/haddock.pdf",
year = "2005",
abstract =
"(From {\sl Through the Looking Glass} by Lewis Caroll)
\begin{verbatim}
The White Knight proposes to comfort Alice by singing her a song:
``Is it very long?'' Alice asked, for she had heard a good deal of
poetry that day.
``It's long,'' said the Knight, ``but it's very, very beautiful.
Everybody that hears me sing iteither it brings tears into the
eyes, or else 
``Or else what?'' said Alice, for the Knight had made a sudden pause.
``Or else it doesn't, you know. The name of the song is called
`Haddock's Eyes'.''
``Oh, that' the name of the song, is it?'' Alice said, trying to feel
interested.
``No, you don't understand,'' the Knight said, looking a little vexed.
``That's what the name is called. The name really is 'The Aged Aged Man'''
``Then I ought to have said 'That's what the song is called?'' Alice
corrected herself.
``No, you oughtn't: that's quite another thing! The song is called
`Ways and Means': but that's only what it's called, you know!''
``Well, what is the song, then?'' said Alice, who was by this time
completely bewildered.
``I was coming to that,'' the Knight said. ``The song really is
`Asitting on a Gate': and the tune's my own invention.''
\end{verbatim}",
paper = "Fate05a.pdf"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate15,
author = "Fateman, Richard J.",
title = "Interval Arithmetic, Extended Numbers and Computer Algebra
Systems",
url = "http://www.cs.berkeley.edu/~/fateman/papers/interval.pdf",
year = "2015",
abstract =
"Many ambitious computer algebra systems were initially designed in a
flush of enthusiasm, with the goal of automating any symbolic
mathematical manipulation “correctly.” Historically, this approach
resulted in programs that implicitly used certain identities to
simplify expressions. These identities, which very likely seemed
universally true to the programmers in the heat of writing the CAS,
(and often were true in wellknown abstract algebraic domains) later
needed reexamination when such systems were extended for dealing with
kinds of objects unanticipated in the original design. These new
objects are generally introduced to the CAS by extending “generically”
the arithmetic or other operations. For example, approximate floats
do not have the mathematical properties of exact integers or
rationals. Complex numbers may strain a system designed for
realvalued variables. In the situation examined here, we consider two
categories of “extended” numbers: ∞ or undefined, and real
intervals. We comment on issues raised by these two troublesome
notions, how their introduction into a computer algebra system may
require a (sometimes painful) reconsideration and redesign of parts of
the program, and how they are related. An alternative (followed most
notably by the Axiom system is to essentially envision a “meta” CAS
defined in terms of categories and inheritance with only the most
fundamental builtin concepts; from these one can build many variants
of specific CAS features. This approach is appealing but can fails to
accommodate extensions that violate some mathematical tenets in the
cause of practicality.",
paper = "Fate15.pdf"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@article{Fate91,
author = "Fateman, Richard J.",
title = "A Review of Macsyma",
year = "1991",
url = "http://people.eecs.berkeley.edu/~fateman/papers/mma.pdf",
abstract =
"The Mathematica computer system is reviewed from the perspective of
its contributions to symbolic and algebraic computation, as well as
its stated goals. Design and implementation issues are discussed.",
paper = "Fate91.pdf,
keywords = "axiomref"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate97b,
author = "Fateman, Richard J.",
title = "More Versatile Scientific Documents OverExtended Abstract,
working paper",
year = "1997",
url = "http://www.cs.berkeley.edu/~/fateman/papers/mvsd.ps",
abstract =
"The electronic representation of scientific documents: journals,
technical reports, program documentation, laboratory notebooks,
etc. present challenges in several distinct communities. We see five
distinct groups concerned with electronic versions of scientific
documents:
\begin{itemize}
\item Publishers of journals, texts, reference works, and their authors.
\item Software publishers for OCR/document analysis, document formatting
\item Software publishers whose products access ``contents semantics''
from documents, including library keyword search programs, natural language
search programs, database systems, visual presentation systems,
mathematical computation systems, etc.
\item Institutions maintain access to electronic libraries, which must
be broadly construed to include data and programs of all sorts.
\item Individuals and their programs acting as their agents who need to
use these libraries, to identify, locate, and retrieive relevant
documents
\end{itemize}
We need to have a convergence in design and standards for encoding new
or preexisting (typically paperbased) documents in order to most
efficiently meet the needs of all these groups. Various effort, some
loosely coordinated, but just as often competing, are trying to set
standards and build tools.
We approach this by first dividing the task into visual, syntactic,
and semantic components. These specifications can focus attention on
the addressing requirements of the different groups. Additionally,
these components rely on a structure for documents that incorporates
existing library models and extends them to new modes of operation.
Berkeley's MVD is one plausible structure which will allow prototype
development and explorations.",
paper = "Fate97b.pdf"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate97c,
author = "Fateman, Richard J.",
title = "Excerpts from a proposal to the National Science Foundation
on Programming Environments and Tools for Advanced Scientific
Computation",
year = "1997",
url = "http://www.cs.berkeley.edu/~/fateman/papers/newpse.pdf",
abstract =
"We propose to concentrate on investigations of technology in support
of advanced scientific computation, based on a higherlevel view of the
relationship of mathematical modeling to computation. This is based on
the following considerations:
\begin{enumerate}
\item Symbolic mathematical manipulation and computer algebra systems:
These are tools and techniques that support problem solving, code
development, comprehension, debugging and partial evaluation
(the principle behind many optimization techniques).
\item Data modeling: in particular, the use of IEEE floatingpoint
number representations and operations.
\item Closed form or exact solutions: For some subproblems of
scientific interest, numerical solutions are not the only paradigm.
The availability of exact solutions, or symbolicapproximation solutions
has advanced along with computing technology too.
\item The use of scripting languages: the linkage of highperformance
library routines to graphical interfaces for data analysis and model setup
can be enhanced by symbolic support and highlevel scripting languages.
\item Extending the use of remote computation. We are now using standard
network connections for the acquisition of complex data (in this case,
symbolic solution of definite integrals).
\end{enumerate}",
paper = "Fate97c.pdf",
keywords = "axiomref"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate00a,
author = "Fateman, Richard J.",
title = "Improving Exact Integral From Symbolic Algebra Systems",
year = "2000",
url = "http://www.cs.berkeley.edu/~/fateman/papers/nform2col.pdf",
abstract =
"Programs in symbolic algebraic manipulation systems can compute
certain classes of symbolic indefinite integrals in closed form. Although
these answers are ordinarily formally correct algebraic antiderivatives,
their form is often unsuitable for further numerical or even analytical
processing. In particular, we address cases in which such ``exact answers''
when numerically evaluated may give lessaccurate answers than numerical
approximations from first principles! The symbolic formulas may also
behave inappropriately near singularities. We discuss techniques, based
in part on the calculus of divided differences, for improving the form of
results of symbolic mathematics systems. In particular, computer alge
algebra systems must take explicit account of the possibility that they are
producing not “mathematics” but templates of programs consisting of se
sequences of arithmetic operations. In brief, mathematical correctness is
not enough. Forms produced by rational integration programs are used
for examples.",
paper = "Fate00a.pdf"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate08a,
author = "Fateman, Richard J.",
title = "Verbs, Nouns, and Computer Algebra, or What's Grammar Got
to do with Math?",
url = "http://www.cs.berkeley.edu/~/fateman/papers/nounverbmac.pdf",
year = "2008",
abstract =
"Computer algebra systems (CAS) are supposed to do mathematics.
Unfortunately, much of human mathematics presentation and
manipulation depends on humans to understand what is going on more
generally. This context is often not made available to the computer
system, and so it will sometimes fail to make the right guess at the
meaning of constructions, unless they are made unambiguous. Among many
issues, one that has been raised and resolved, is the need for
attributing properties to operators that distinguish between ``the name
of the operation'' and ``the operation itself''.
As a simple example, referential transparency requires that if $x = y$,
then any true statement $P(x)$ about $x$ must be true about $y$, namely
$P(y)$ is also true.
Consider now the wellknown equation $sin(0) = 0$, and the statement
$P(r) :=$ ``r = 0 is a rule to simplify the sin() function''. The
statement $P(sin(0))$ is clearly true. Therefore $P(0)$ should be true
as well. It is not, since $0 = 0$ is not a rule to simplify $sin()$.
The point here is that $sin(0)$ is not equal to 0 if sin is treated as
the name of an operation. Perhaps it is a character string, or a data
structure of some sort: a noun phrase. The corresponding expression
including the verb form of sin is one in which $sin(0)$ can be
simplified to something equivalent, but in some sense preferable. Here
it is reasonable to replace it by 0.",
paper = "Fate08a.pdf"
}
\end{chunk}
\index{OpenMath}
\index{Complex}
\index{DoubleFloat}
\index{Float}
\index{Fraction}
\index{Integer}
\index{List}
\index{SingleInteger}
\index{String}
\index{Symbol}
\index{ExpressionToOpenMath}
\index{OpenMathServerPackage}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate01a,
author = "Fateman, Richard J.",
title = "A Critique of OpenMath and Thoughts on Encoding Mathematics",
year = "2001",
url = "http://www.cs.berkeley.edu/~/fateman/papers/openmathcrit.pdf",
algebra =
"\newline\refto{category OM OpenMath}
\newline\refto{domain COMPLEX Complex}
\newline\refto{domain DFLOAT DoubleFloat}
\newline\refto{domain FLOAT Float}
\newline\refto{domain FRAC Fraction}
\newline\refto{domain INT Integer}
\newline\refto{domain LIST List}
\newline\refto{domain SINT SingleInteger}
\newline\refto{domain STRING String}
\newline\refto{domain SYMBOL Symbol}
\newline\refto{package OMEXPR ExpressionToOpenMath}
\newline\refto{package OMSERVER OpenMathServerPackage}",
abstract =
"The OpenMath project, as portrayed in the Special Issue of the SIGSAM
Bulletin (volume 34 no. 2), seems to have a number of problems to
face. One of them is the (apparently implicit) assumption that
OpenMath designers, through dint of mathematical thought and the
advice of the members of the Open Math Society, have solved, in their
domain, one of the most pressing problems of software engineering
today, namely software reuse. After six years there is insufficient
evidence on which to base any claims of success and it appears that
most substantive practical issues of mathematical representation and
communication have yet to be addressed. We also raise questions about
related computational mathematical goals and mathematical encodings.",
paper = "Fate01a.pdf"
}
\end{chunk}

books/bookvol10.2.pamphlet  3 +
books/bookvol10.3.pamphlet  34 +
books/bookvol10.4.pamphlet  14 +
books/bookvolbib.pamphlet  8568 ++++++++++++++++++++++++++++
changelog  5 +
patch  843 ++++
src/axiomwebsite/patches.html  2 +
7 files changed, 6968 insertions(+), 2501 deletions()
diff git a/books/bookvol10.2.pamphlet b/books/bookvol10.2.pamphlet
index 054a38b..5f457d0 100644
 a/books/bookvol10.2.pamphlet
+++ b/books/bookvol10.2.pamphlet
@@ 3374,7 +3374,7 @@ These are directly exported but not implemented:
OMwrite : (OpenMathDevice,%,Boolean) > Void
\end{verbatim}
See: Corless\cite{Corl00}
+See: Corless\cite{Corl00}, Fateman\cite{Fate01a}
\label{category OM OpenMath}
\begin{chunk}{category OM OpenMath}
)abbrev category OM OpenMath
@@ 3382,6 +3382,7 @@ See: Corless\cite{Corl00}
++ Basic Functions: OMwrite
++ References:
++ Corl00 According to Abramowitz and Stegun or arccoth needn't be Uncouth
+++ Fate01a A Critique of OpenMath and Thoughts on Encoding Mathematics
++ Description:
++ \spadtype{OpenMath} provides operations for exporting an object
++ in OpenMath format.
diff git a/books/bookvol10.3.pamphlet b/books/bookvol10.3.pamphlet
index 5a5fe3f..c73c31c 100644
 a/books/bookvol10.3.pamphlet
+++ b/books/bookvol10.3.pamphlet
@@ 31759,13 +31759,14 @@ o )show Complex
\cross{COMPLEX}{?rem?} &&
\end{tabular}
See: Corless\cite{Corl00}
+See: Corless\cite{Corl00}, Fateman\cite{Fate01a}
\label{domain COMPLEX Complex}
\begin{chunk}{domain COMPLEX Complex}
)abbrev domain COMPLEX Complex
++ Author: Mark Botch
++ References:
++ Corl00 According to Abramowitz and Stegun or arccoth needn't be Uncouth
+++ Fate01a A Critique of OpenMath and Thoughts on Encoding Mathematics
++ Description:
++ \spadtype{Complex(R)} creates the domain of elements of the form
++ \spad{a + b * i} where \spad{a} and b come from the ring R,
@@ 46430,7 +46431,7 @@ o )show DoubleFloat
\cross{DFLOAT}{?\~{}=?} &&
\end{tabular}
See: Corless\cite{Corl00}
+See: Corless\cite{Corl00}, Fateman\cite{Fate01a}
\label{domain DFLOAT DoubleFloat}
\begin{chunk}{domain DFLOAT DoubleFloat}
)abbrev domain DFLOAT DoubleFloat
@@ 46438,6 +46439,7 @@ See: Corless\cite{Corl00}
++ Date Created: January 1988
++ References:
++ Corl00 According to Abramowitz and Stegun or arccoth needn't be Uncouth
+++ Fate01a A Critique of OpenMath and Thoughts on Encoding Mathematics
++ Description:
++ \spadtype{DoubleFloat} is intended to make accessible
++ hardware floating point arithmetic in Axiom, either native double
@@ 69871,7 +69873,7 @@ o )show Float
\cross{FLOAT}{?rem?}
\end{tabular}
See: Corless\cite{Corl00}
+See: Corless\cite{Corl00}, Fateman\cite{Fate01a}
\label{domain FLOAT Float}
\begin{chunk}{domain FLOAT Float}
)abbrev domain FLOAT Float
@@ 69881,6 +69883,7 @@ See: Corless\cite{Corl00}
++ Change History: 19 Jun 1990
++ References:
++ Corl00 According to Abramowitz and Stegun or arccoth needn't be Uncouth
+++ Fate01a A Critique of OpenMath and Thoughts on Encoding Mathematics
++ Description:
++ \spadtype{Float} implements arbitrary precision floating point arithmetic.
++ The number of significant digits of each operation can be set
@@ 76291,7 +76294,7 @@ o )show Fraction
\cross{FRAC}{?rem?} &
\end{tabular}
See: Corless\cite{Corl00}
+See: Corless\cite{Corl00}, Fateman\cite{Fate01a}
\label{domain FRAC Fraction}
\begin{chunk}{domain FRAC Fraction}
)abbrev domain FRAC Fraction
@@ 76300,6 +76303,7 @@ See: Corless\cite{Corl00}
++ Basic Functions: Field, numer, denom
++ References:
++ Corl00 According to Abramowitz and Stegun or arccoth needn't be Uncouth
+++ Fate01a A Critique of OpenMath and Thoughts on Encoding Mathematics
++ Description:
++ Fraction takes an IntegralDomain S and produces
++ the domain of Fractions with numerators and denominators from S.
@@ 80337,14 +80341,15 @@ o )show FullPartialFractionExpansion
\cross{FPARFRAC}{?=?} &&
\end{tabular}
+See: Bronstein\cite{Bron93}
+\label{domain FPARFRAC FullPartialFractionExpansion}
\begin{chunk}{domain FPARFRAC FullPartialFractionExpansion}
)abbrev domain FPARFRAC FullPartialFractionExpansion
++ Author: Manuel Bronstein
++ Date Created: 9 December 1992
++ Date Last Updated: 6 October 1993
++ References: M.Bronstein & B.Salvy,
++ Full Partial Fraction Decomposition of Rational Functions,
++ in Proceedings of ISSAC'93, Kiev, ACM Press.
+++ References:
+++ Bron93 Full Partial Fraction Decomposition of Rational Functions
++ Description:
++ Full partial fraction expansion of rational functions
@@ 103763,13 +103768,14 @@ o )show Integer
\cross{INT}{writeOMInt}
\end{tabular}
See: Corless\cite{Corl00}
+See: Corless\cite{Corl00}, Fateman\cite{Fate01a}
\label{domain INT Integer}
\begin{chunk}{domain INT Integer}
)abbrev domain INT Integer
++ Author: Mark Botch
++ References:
++ Corl00 According to Abramowitz and Stegun or arccoth needn't be Uncouth
+++ Fate01a A Critique of OpenMath and Thoughts on Encoding Mathematics
++ Description:
++ \spadtype{Integer} provides the domain of arbitrary precision integers.
@@ 113564,7 +113570,7 @@ o )show List
\cross{LIST}{?.value} &
\end{tabular}
See: Corless\cite{Corl00}
+See: Corless\cite{Corl00}, Fateman\cite{Fate01a}
\label{domain LIST List}
\begin{chunk}{domain LIST List}
)abbrev domain LIST List
@@ 113572,6 +113578,7 @@ See: Corless\cite{Corl00}
++ Date Created: Sep 1987
++ References:
++ Corl00 According to Abramowitz and Stegun or arccoth needn't be Uncouth
+++ Fate01a A Critique of OpenMath and Thoughts on Encoding Mathematics
++ Description:
++ \spadtype{List} implements singlylinked lists that are
++ addressable by indices; the index of the first element
@@ 179359,7 +179366,7 @@ o )show SingleInteger
\cross{SINT}{?rem?}
\end{tabular}
See: Corless\cite{Corl00}
+See: Corless\cite{Corl00}, Fateman\cite{Fate01a}
\label{domain SINT SingleInteger}
\begin{chunk}{domain SINT SingleInteger}
)abbrev domain SINT SingleInteger
@@ 179374,6 +179381,7 @@ See: Corless\cite{Corl00}
++ Change History:
++ References:
++ Corl00 According to Abramowitz and Stegun or arccoth needn't be Uncouth
+++ Fate01a A Critique of OpenMath and Thoughts on Encoding Mathematics
++ Description:
++ SingleInteger is intended to support machine integer arithmetic.
@@ 196014,13 +196022,14 @@ o )show String
\cross{STRING}{?$>=$?} &&&
\end{tabular}
See: Corless\cite{Corl00}
+See: Corless\cite{Corl00}, Fateman\cite{Fate01a}
\label{domain STRING String}
\begin{chunk}{domain STRING String}
)abbrev domain STRING String
++ Author: Mark Botch
++ References:
++ Corl00 According to Abramowitz and Stegun or arccoth needn't be Uncouth
+++ Fate01a A Critique of OpenMath and Thoughts on Encoding Mathematics
++ Description:
++ This is the domain of character strings. Strings are 1 based.
@@ 198357,7 +198366,7 @@ o )show Symbol
\cross{SYMBOL}{?$>=$?} &&&
\end{tabular}
See: Corless\cite{Corl00}
+See: Corless\cite{Corl00}, Fateman\cite{Fate01a}
\label{domain SYMBOL Symbol}
\begin{chunk}{domain SYMBOL Symbol}
)abbrev domain SYMBOL Symbol
@@ 198366,6 +198375,7 @@ See: Corless\cite{Corl00}
++ Date Last Updated: 7 Mar 1991, 29 Apr. 1994 (FDLL)
++ References:
++ Corl00 According to Abramowitz and Stegun or arccoth needn't be Uncouth
+++ Fate01a A Critique of OpenMath and Thoughts on Encoding Mathematics
++ Description:
++ Basic and scripted symbols.
diff git a/books/bookvol10.4.pamphlet b/books/bookvol10.4.pamphlet
index 8aa366b..f09bf84 100644
 a/books/bookvol10.4.pamphlet
+++ b/books/bookvol10.4.pamphlet
@@ 44993,13 +44993,14 @@ o )show ExpressionToOpenMath
{\bf Exports:}\\
\cross{OMEXPR}{OMwrite}
See: Corless\cite{Corl00}
+See: Corless\cite{Corl00}, Fateman\cite{Fate01a}
\label{package OMEXPR ExpressionToOpenMath}
\begin{chunk}{package OMEXPR ExpressionToOpenMath}
)abbrev package OMEXPR ExpressionToOpenMath
++ Author: Mike Dewar & Vilya Harvey
++ References:
++ Corl00 According to Abramowitz and Stegun or arccoth needn't be Uncouth
+++ Fate01a A Critique of OpenMath and Thoughts on Encoding Mathematics
++ Description:
++ \spadtype{ExpressionToOpenMath} provides support for
++ converting objects of type \spadtype{Expression} into OpenMath.
@@ 191379,13 +191380,14 @@ o )show OpenMathServerPackage
\cross{OMSERVER}{OMserve}
\end{tabular}
See: Corless\cite{Corl00}
+See: Corless\cite{Corl00}, Fateman\cite{Fate01a}
\label{package OMSERVER OpenMathServerPackage}
\begin{chunk}{package OMSERVER OpenMathServerPackage}
)abbrev package OMSERVER OpenMathServerPackage
++ Author: Vilya Harvey
++ References:
++ Corl00 According to Abramowitz and Stegun or arccoth needn't be Uncouth
+++ Fate01a A Critique of OpenMath and Thoughts on Encoding Mathematics
++ Description:
++ \spadtype{OpenMathServerPackage} provides the necessary
++ operations to run AXIOM as an OpenMath server, reading/writing objects
@@ 250053,11 +250055,15 @@ o )show TranscendentalRischDE
\cross{RDETR}{polyRDE}
\end{tabular}
+See: Bronstein\cite{Bron90}
+\label{package RDETR TranscendentalRischDE}
\begin{chunk}{package RDETR TranscendentalRischDE}
)abbrev package RDETR TranscendentalRischDE
++ Author: Manuel Bronstein
++ Date Created: Jan 1988
++ Date Last Updated: 2 November 1995
+++ References:
+++ Bron90 The Transcendental Risch Differential Equation
++ Description:
++ Risch differential equation, transcendental case.
@@ 250413,11 +250419,15 @@ o )show TranscendentalRischDESystem
\cross{RDETRS}{monomRDEsys}
\end{tabular}
+See: Bronstein\cite{Bron90}
+\label{package RDETRS TranscendentalRischDESystem}
\begin{chunk}{package RDETRS TranscendentalRischDESystem}
)abbrev package RDETRS TranscendentalRischDESystem
++ Author: Manuel Bronstein
++ Date Created: 17 August 1992
++ Date Last Updated: 3 February 1994
+++ References
+++ Bron90 The Transcendental Risch Differential Equation
++ Description:
++ Risch differential equation system, transcendental case.
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 4be2556..32f40c3 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 28,18 +28,34 @@ paragraph for those unfamiliar with the terms.
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu00,
+@book{Book00,
author = "Axiom Authors",
title = "Volume 0: Axiom Jenks and Sutor",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol0.pdf",
 year = "2016"
+ year = "2016",
+ keywords = "axiomref",
+ beebe = "Jenks:2003:AVS"
+}
+
+\end{chunk}
+\begin{chunk}{Jenks:2003:AVS}
+@Book{Jenks:2003:AVS,
+ author = "Richard D. Jenks and Robert S. Sutor and Tim Daly",
+ title = "{Axiom} Volume 0: The Scientific Computation System",
+ pages = "xviii + 1187",
+ year = "2003",
+ LCCN = "????",
+ bibdate = "Tue Mar 30 08:43:19 2010",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.axiomdeveloper.org/axiomwebsite/bookvol0.pdf",
+ acknowledgement = acknhfb,
}
\end{chunk}
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu01,
+@book{Book01,
author = "Axiom Authors",
title = "Volume 1: Axiom Tutorial",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol1.pdf",
@@ 50,73 +66,169 @@ paragraph for those unfamiliar with the terms.
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu02,
+@book{Book02,
author = "Axiom Authors",
title = "Volume 2: Axiom Users Guide",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol2.pdf",
 year = "2016"
+ year = "2016",
+ keywords = "axiomref",
+ beebe = "Daly:2005:AVAb"
+}
+
+\end{chunk}
+\begin{chunk}{Daly:2005:AVAb}
+@Book{Daly:2005:AVAb,
+ author = "Tim Daly and Martin Dunstan",
+ title = "{Axiom} Volume 2: {Axiom} Users Guide",
+ pages = "iv + 7",
+ year = "2005",
+ LCCN = "????",
+ bibdate = "Tue Mar 30 08:43:19 2010",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.axiomdeveloper.org/axiomwebsite/bookvol2.pdf",
+ acknowledgement = acknhfb,
}
\end{chunk}
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu03,
+@book{Book03,
author = "Axiom Authors",
title = "Volume 3: Axiom Programmers Guide",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol3.pdf",
 year = "2016"
+ year = "2016",
+ keywords = "axiomref",
+ beebe = "Daly:2005:AVAc"
+}
+
+\end{chunk}
+\begin{chunk}{Daly:2005:AVAc}
+@Book{Daly:2005:AVAc,
+ author = "Tim Daly and Martin Dunstan",
+ title = "{Axiom} Volume 3: {Axiom} Programmers Guide",
+ pages = "iv + 3",
+ year = "2005",
+ LCCN = "????",
+ bibdate = "Tue Mar 30 08:43:19 2010",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.axiomdeveloper.org/axiomwebsite/bookvol3.pdf",
+ acknowledgement = acknhfb,
}
\end{chunk}
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu04,
+@book{Book04,
author = "Axiom Authors",
title = "Volume 4: Axiom Developers Guide",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol4.pdf",
 year = "2016"
+ year = "2016",
+ keywords = "axiomref",
+ beebe = "Daly:2005:AVAd"
+}
+
+\end{chunk}
+\begin{chunk}{Daly:2005:AVAd}
+@Book{Daly:2005:AVAd,
+ author = "Tim Daly and Martin Dunstan",
+ title = "{Axiom} Volume 4: {Axiom} Developers Guide",
+ pages = "v + 91",
+ year = "2005",
+ LCCN = "????",
+ bibdate = "Tue Mar 30 08:43:19 2010",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.axiomdeveloper.org/axiomwebsite/bookvol4.pdf",
+ acknowledgement = acknhfb,
}
\end{chunk}
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu05,
+@book{Book05,
author = "Axiom Authors",
title = "Volume 5: Axiom Interpreter",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol5.pdf",
 year = "2016"
+ year = "2016",
+ keywords = "axiomref",
+ beebe = "Daly:2003:AVA",
+}
+
+\end{chunk}
+\begin{chunk}{Daly:2003:AVA}
+@Book{Daly:2003:AVA,
+ author = "Tim Daly and Martin Dunstan",
+ title = "{Axiom} Volume 5: {Axiom} Interpreter",
+ pages = "xlvi + 1387",
+ year = "2003",
+ LCCN = "????",
+ bibdate = "Tue Mar 30 08:43:19 2010",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.axiomdeveloper.org/axiomwebsite/bookvol5.pdf",
+ acknowledgement = acknhfb,
}
\end{chunk}
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu06,
+@book{Book06,
author = "Axiom Authors",
title = "Volume 6: Axiom Command",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol6.pdf",
 year = "2016"
+ year = "2016",
+ keywords = "axiomref",
+ beebe = "Daly:2005:AVAe"
+}
+
+\end{chunk}
+\begin{chunk}{Daly:2005:AVAe}
+@Book{Daly:2005:AVAe,
+ author = "Tim Daly and Martin Dunstan",
+ title = "{Axiom} Volume 6: {Axiom} Command",
+ pages = "vi + 187",
+ year = "2005",
+ LCCN = "????",
+ bibdate = "Tue Mar 30 08:43:19 2010",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.axiomdeveloper.org/axiomwebsite/bookvol6.pdf",
+ acknowledgement = acknhfb,
}
\end{chunk}
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu07,
+@book{Book07,
author = "Axiom Authors",
title = "Volume 7: Axiom Hyperdoc",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol7.pdf",
 year = "2016"
+ year = "2016",
+ keywords = "axiomref",
+ beebe = "Daly:2005:AVAj"
+}
+
+\end{chunk}
+\begin{chunk}{Daly:2005:AVAj}
+@Book{Daly:2005:AVAj,
+ author = "Tim Daly and Martin Dunstan",
+ title = "{Axiom} Volume 7: {Axiom} Hyperdoc",
+ pages = "xvi + 632",
+ year = "2005",
+ LCCN = "????",
+ bibdate = "Tue Mar 30 08:43:19 2010",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.axiomdeveloper.org/axiomwebsite/bookvol7.pdf",
+ acknowledgement = acknhfb,
}
\end{chunk}
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu71,
+@book{Book71,
author = "Axiom Authors",
title = "Volume 7.1: Axiom Hyperdoc Pages",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol7.1.pdf",
@@ 127,18 +239,34 @@ paragraph for those unfamiliar with the terms.
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu08,
+@book{Book08,
author = "Axiom Authors",
title = "Volume 8: Axiom Graphics",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol8.pdf",
 year = "2016"
+ year = "2016",
+ keywords = "axiomref",
+ beebe = "Daly:2005:AVAf"
+}
+
+\end{chunk}
+\begin{chunk}{Daly:2005:AVAf}
+@Book{Daly:2005:AVAf,
+ author = "Tim Daly and Martin Dunstan",
+ title = "{Axiom} Volume 8: {Axiom} Graphics",
+ pages = "xi + 538",
+ year = "2005",
+ LCCN = "????",
+ bibdate = "Tue Mar 30 08:43:19 2010",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.axiomdeveloper.org/axiomwebsite/bookvol8.pdf",
+ acknowledgement = acknhfb,
}
\end{chunk}
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu81,
+@book{Book81,
author = "Axiom Authors",
title = "Volume 8.1: Axiom Gallery",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol8.1.pdf",
@@ 149,18 +277,34 @@ paragraph for those unfamiliar with the terms.
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu09,
+@book{Book09,
author = "Axiom Authors",
title = "Volume 9: Axiom Compiler",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol9.pdf",
 year = "2016"
+ year = "2016",
+ keywords = "axiomref",
+ beebe = "Daly:2005:AVAg"
+}
+
+\end{chunk}
+\begin{chunk}{Daly:2005:AVAg}
+@Book{Daly:2005:AVAg,
+ author = "Tim Daly and Martin Dunstan",
+ title = "{Axiom} Volume 9: {Axiom} Compiler",
+ pages = "iv + 30",
+ year = "2005",
+ LCCN = "????",
+ bibdate = "Tue Mar 30 08:43:19 2010",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.axiomdeveloper.org/axiomwebsite/bookvol9.pdf",
+ acknowledgement = acknhfb,
}
\end{chunk}
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu91,
+@book{Book91,
author = "Axiom Authors",
title = "Volume 9.1: Axiom Compiler Details",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol9.1.pdf",
@@ 171,18 +315,34 @@ paragraph for those unfamiliar with the terms.
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu10,
+@book{Book10,
author = "Axiom Authors",
title = "Volume 10: Axiom Algebra: Implementation",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol10.pdf",
 year = "2016"
+ year = "2016",
+ keywords = "axiomref",
+ beebe = "Daly:2005:AVAh"
+}
+
+\end{chunk}
+\begin{chunk}{Daly:2005:AVAh}
+@Book{Daly:2005:AVAh,
+ author = "Tim Daly and Martin Dunstan",
+ title = "{Axiom} Volume 10: {Axiom} Algebra: Implementation",
+ pages = "iv + 5",
+ year = "2005",
+ LCCN = "????",
+ bibdate = "Tue Mar 30 08:43:19 2010",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.axiomdeveloper.org/axiomwebsite/bookvol10.pdf",
+ acknowledgement = acknhfb,
}
\end{chunk}
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu101,
+@book{Book101,
author = "Axiom Authors",
title = "Volume 10.1: Axiom Algebra: Theory",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol10.1.pdf",
@@ 193,7 +353,7 @@ paragraph for those unfamiliar with the terms.
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu102,
+@book{Book102,
author = "Axiom Authors",
title = "Volume 10.2: Axiom Algebra: Categories",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol10.2.pdf",
@@ 204,7 +364,7 @@ paragraph for those unfamiliar with the terms.
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu103,
+@book{Book103,
author = "Axiom Authors",
title = "Volume 10.3: Axiom Algebra: Domains",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol10.3.pdf",
@@ 215,7 +375,7 @@ paragraph for those unfamiliar with the terms.
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu104,
+@book{Book104,
author = "Axiom Authors",
title = "Volume 10.4: Axiom Algebra: Packages",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol10.4.pdf",
@@ 226,7 +386,7 @@ paragraph for those unfamiliar with the terms.
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu105,
+@book{Book105,
author = "Axiom Authors",
title = "Volume 10.5: Axiom Algebra: Numerics",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol10.5.pdf",
@@ 237,29 +397,62 @@ paragraph for those unfamiliar with the terms.
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu11,
+@book{Book11,
author = "Axiom Authors",
title = "Volume 11: Axiom Browser",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol11.pdf",
 year = "2016"
+ year = "2016",
+ keywords = "axiomref",
+ beebe = "Portes:2007:AVA"
+}
+
+\end{chunk}
+\begin{chunk}{Portes:2007:AVA}
+@Book{Portes:2007:AVA,
+ author = "Alfredo Portes and Arthur Ralfs and Timothy Daly and
+ Martin Dunstan",
+ title = "{Axiom} Volume 11: {Axiom} Browser",
+ pages = "xix + 1193",
+ year = "2007",
+ LCCN = "????",
+ bibdate = "Tue Mar 30 08:43:19 2010",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.axiomdeveloper.org/axiomwebsite/bookvol11.pdf",
+ acknowledgement = acknhfb,
}
\end{chunk}
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu12,
+@book{Book12,
author = "Axiom Authors",
title = "Volume 12: Axiom Crystal",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol12.pdf",
 year = "2016"
+ year = "2016",
+ keywords = "axiomref",
+ beebe = "Daly:2005:AVAi"
+}
+
+\end{chunk}
+\begin{chunk}{Daly:2005:AVAi}
+@Book{Daly:2005:AVAi,
+ author = "Tim Daly and Martin Dunstan",
+ title = "{Axiom} Volume 12: {Axiom} Crystal",
+ pages = "iv + 9",
+ year = "2005",
+ LCCN = "????",
+ bibdate = "Tue Mar 30 08:43:19 2010",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.axiomdeveloper.org/axiomwebsite/bookvol12.pdf",
+ acknowledgement = acknhfb,
}
\end{chunk}
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu13,
+@book{Book13,
author = "Axiom Authors",
title = "Volume 13: Proving Axiom Correct",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol13.pdf",
@@ 270,7 +463,7 @@ paragraph for those unfamiliar with the terms.
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volu14,
+@book{Book14,
author = "Axiom Authors",
title = "Volume 14: Algorithms",
url = "http://axiomdeveloper.org/axiomwebsite/bookvol14.pdf",
@@ 281,7 +474,7 @@ paragraph for those unfamiliar with the terms.
\index{Axiom Authors}
\begin{chunk}{axiom.bib}
@book{Volubib,
+@book{Bookbib,
author = "Axiom Authors",
title = "Volume Bibliography: Axiom Literature Citations",
url = "http://axiomdeveloper.org/axiomwebsite/bookvolbib.pdf",
@@ 330,7 +523,6 @@ paragraph for those unfamiliar with the terms.
number = "2",
month = "April",
pages = "107130",
 paper = "Reed97.pdf",
algebra = "\newline\refto{domain ALGSC AlgebraGivenByStructuralConstants}",
url="http://www.ams.org/bull/19973402/S027309799700712X/S027309799700712X.pdf",
abstract =
@@ 352,7 +544,8 @@ paragraph for those unfamiliar with the terms.
survey article as another example of the breadth of mathematics that
has biological significance. The most comprehensive reference for the
mathematical research done in this area (through 1980) is
 WorzBusekros."
+ WorzBusekros.",
+ paper = "Reed97.pdf"
}
\end{chunk}
@@ 390,6 +583,25 @@ paragraph for those unfamiliar with the terms.
\section{Linear Algebra} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{matrix sparse}
+\index{matrix structured}
+\index{polynomial factoring}
+\index{Qmatrix}
+\index{Berlekamp algorithm}
+\index{algorithm!Berlekamp}
+\index{Wiedemann algorithm}
+\index{algorithm!Wiedemann}
+\index{TO!Wiedemann!Lanczos}
+\index{Lanczos algorithm}
+\index{algorithm!Lanczos}
+\index{Sparse diophantine linear problems}
+\index{Smith canonical form}
+\index{padic lifting}
+\index{finite field sparse matrix analysis}
+\index{Wiedemann preconditioners}
+\index{Wiedemann block projections}
+\index{Wiedemann Lanczos recurrences}
+\index{Wiedemann Kalman realizations}
\index{Kaltofen, Erich}
\begin{chunk}{axiom.bib}
@Unpublished{Kalt01,
@@ 398,7 +610,6 @@ paragraph for those unfamiliar with the terms.
over finite fields (Invited talk)",
year = "2001",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/01/Ka01_Fq6.pdf",
 paper = "Kalt01.pdf",
keywords = "survey",
abstract = "
Sparse and structured matrices over finite fields occur in many
@@ 415,31 +626,17 @@ paragraph for those unfamiliar with the terms.
ingredients are faster preconditioners, projections by an entire
block of random vectors, Lanczos recurrences, and a connection to
Kalman realizations of control theory. My talk surveys these
 developments and describe some major unresolved problems."
+ developments and describe some major unresolved problems.",
+ paper = "Kalt01.pdf"
}
\end{chunk}
\index{matrix sparse}
\index{matrix structured}
\index{polynomial factoring}
\index{Qmatrix}
\index{Berlekamp algorithm}
\index{algorithm!Berlekamp}
\index{Wiedemann algorithm}
\index{algorithm!Wiedemann}
\index{TO!Wiedemann!Lanczos}
\index{Lanczos algorithm}
\index{algorithm!Lanczos}
\index{Sparse diophantine linear problems}
\index{Smith canonical form}
\index{padic lifting}
\index{finite field sparse matrix analysis}
\index{Wiedemann preconditioners}
\index{Wiedemann block projections}
\index{Wiedemann Lanczos recurrences}
\index{Wiedemann Kalman realizations}

+\index{black box exact linear algebra}
+\index{minimum polynomials}
+\index{preconditioning}
+\index{condition number}
+\index{Toeplitz matrix}
\index{Chen, L.}
\index{Eberly, W.}
\index{Kaltofen, Erich}
@@ 456,7 +653,6 @@ paragraph for those unfamiliar with the terms.
volume = "343344",
pages = "119146",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/02/CEKSTV02.pdf",
 paper = "Chen02.pdf",
abstract = "
The main idea of the ``black box'' approach in exact linear algebra is
to reduce matrix problems to the computation of minimum polynomials.
@@ 473,16 +669,23 @@ paragraph for those unfamiliar with the terms.
linear algebra problems. Thus, improvements are offered for the
efficiency and applicability of preconditioners. The focus is on
linear algebra problems over finite fields, but most results are valid
 for entries from arbitrary fields."
+ for entries from arbitrary fields.",
+ paper = "Chen02.pdf"
}
\end{chunk}
\index{black box exact linear algebra}
\index{minimum polynomials}
\index{preconditioning}
\index{condition number}
\index{Toeplitz matrix}
+\index{exact linear algebra}
+\index{matrix rank}
+\index{matrix determinant}
+\index{matrix characteristic}
+\index{matrix minimal polynomial}
+\index{matrix rational canonical form}
+\index{matrix Frobenius normal form}
+\index{matrix Hermite normal form}
+\index{matrix Smith normal form}
+\index{matrix symmetric}
+\index{matrix definite}
\index{Kaltofen, Erich}
\index{Storjohann, Arne}
\begin{chunk}{axiom.bib}
@@ 493,7 +696,6 @@ paragraph for those unfamiliar with the terms.
crossref = "EACM",
year = "2011",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/11/KS11.pdf",
 paper = "Kalt11d.pdf",
abstract = "
Computational problems in exact linear algebra including computing an
exact solution of a system of linear equations with exact scalars,
@@ 504,22 +706,20 @@ paragraph for those unfamiliar with the terms.
polynomial, and rational canonical form (= Frobenius normal form). For
matrices with integer and polynomial entries one computes the Hermite
and Smith normal forms. If a rational matrix is symmetric, one
 determines if the matrix is definite."
+ determines if the matrix is definite.",
+ paper = "Kalt11d.pdf"
}
\end{chunk}
\index{exact linear algebra}
\index{matrix rank}
\index{matrix determinant}
\index{matrix characteristic}
\index{matrix minimal polynomial}
\index{matrix rational canonical form}
\index{matrix Frobenius normal form}
\index{matrix Hermite normal form}
\index{matrix Smith normal form}
\index{matrix symmetric}
\index{matrix definite}
+\index{matrix Hankel}
+\index{matrix Toeplitz}
+\index{matrix finite field}
+\index{matrix Berlekamp}
+\index{matrix Massey}
+\index{matrix singular}
+\index{matrix rank}
+\index{matrix blockHankel}
\index{Comer, Matthew T.}
\index{Kaltofen, Erich}
\begin{chunk}{axiom.bib}
@@ 534,7 +734,6 @@ paragraph for those unfamiliar with the terms.
number = "4",
pages = "480491",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/10/CoKa10.pdf",
 paper = "Come12.pdf",
abstract = "
We derive an explicit count for the number of singular $n\times n$
Hankel (Toeplitz) matrices whose entries range over a finite field
@@ 548,19 +747,19 @@ paragraph for those unfamiliar with the terms.
$r$ with generic rank profile, I.e., whose first $r$ leading principal
submatrices are nonsingular and the rest are singular, namely
$q^r(q1)^r$ in the case $r < n$ and $q^{r1}(q1)^r$ in the case
 $r=n$. This result generalizes to blockHankel matrices as well."
+ $r=n$. This result generalizes to blockHankel matrices as well.",
+ paper = "Come12.pdf"
}
\end{chunk}
\index{matrix Hankel}
\index{matrix Toeplitz}
\index{matrix finite field}
+
+\index{algorithm!Berlekamp/Massey}
+\index{Berlekamp/Massey algorithm}
\index{matrix Berlekamp}
\index{matrix Massey}
\index{matrix singular}
\index{matrix rank}
\index{matrix blockHankel}

+\index{matrix square}
+\index{matrix integral domain}
+\index{matrix integrability}
\index{Kaltofen, Erich}
\index{Yuhasz, George}
\begin{chunk}{axiom.bib}
@@ 574,7 +773,6 @@ paragraph for those unfamiliar with the terms.
month = "November",
pages = "25152526",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/08/KaYu08.pdf",
 paper = "Kalt13a.pdf",
abstract = "
We describe a fraction free version of the Matrix Berlekamp / Massey
algorithm. The algorithm computes a minimal matrix generator of
@@ 584,18 +782,22 @@ paragraph for those unfamiliar with the terms.
algorithm specializes to a more efficient algorithm than the algorithm
currently in the literature. The proof of integrality of the matrix
algorithm gives a new proof of integrality for the scalar
 specialization."
+ specialization.",
+ paper = "Kalt13a.pdf"
}
\end{chunk}
+
\index{algorithm!Berlekamp/Massey}
\index{Berlekamp/Massey algorithm}
\index{matrix Berlekamp}
\index{matrix Massey}
\index{matrix square}
\index{matrix integral domain}
\index{matrix integrability}

+\index{linear generators of scalar sequences}
+\index{TO!Massey!Rissanen}
+\index{TO!Berlekamp!Rissanen}
+\index{TO!Rissanen!Dickinson}
+\index{TO!Dickinson!Coppersmith}
+\index{matrix rank}
\index{Kaltofen, Erich}
\index{Yuhasz, George}
\begin{chunk}{axiom.bib}
@@ 608,7 +810,6 @@ paragraph for those unfamiliar with the terms.
month = "September",
journal = "ACM Trans. Algorithms",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/06/KaYu06.pdf",
 paper = "Kalt13.pdf",
abstract = "
We analyze the Matrix Berlekamp / Massey algorithm, which generalizes
the Berlekamp / Massey algorithm [Massey 1969] for computing linear
@@ 620,20 +821,11 @@ paragraph for those unfamiliar with the terms.
matrix sequence. We also give new proofs of correctness and complexity
for the algorithm, which is based on selfcontained loop invariants
and includes an explicit termination criterion for a given
 determinantal degree bound of the minimal matrix generator"
+ determinantal degree bound of the minimal matrix generator",
+ paper = "Kalt13.pdf"
}
\end{chunk}
\index{algorithm!Berlekamp/Massey}
\index{Berlekamp/Massey algorithm}
\index{matrix Berlekamp}
\index{matrix Massey}
\index{linear generators of scalar sequences}
\index{TO!Massey!Rissanen}
\index{TO!Berlekamp!Rissanen}
\index{TO!Rissanen!Dickinson}
\index{TO!Dickinson!Coppersmith}
\index{matrix rank}
\index{Kaltofen, Erich}
\begin{chunk}{axiom.bib}
@@ 646,11 +838,21 @@ paragraph for those unfamiliar with the terms.
pages = "138144",
year = "2002",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/02/Ka02.pdf",
 paper = "Kalt02a.pdf",
+ paper = "Kalt02a.pdf"
}
\end{chunk}
+\index{matrix determinant}
+\index{algorithm!Clarkson}
+\index{Clarson algorithm}
+\index{matrix condition}
+\index{algorithm!Chinese Remainder}
+\index{Chinese remainder algorithm}
+\index{Hensel lifting}
+\index{rational number recovery}
+\index{matrix determinant}
+\index{matrix largest invariant factor}
\index{Kaltofen, Erich}
\index{Villard, Gilles}
\begin{chunk}{axiom.bib}
@@ 664,7 +866,6 @@ paragraph for those unfamiliar with the terms.
isbn = "981024763X",
year = "2001",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/01/KaVi01.pdf",
 paper = "Kalt01a.pdf",
abstract = "
The computation of the determinant of an $n\times n$ matrix $A$ of
numbers or polynomials is a challenge for both numerical and symbolic
@@ 680,22 +881,30 @@ paragraph for those unfamiliar with the terms.
bit complexity in $n$, but the algorithm can only determine a factor
of the determinant, namely the largest invariant factor. If the matrix
is similar to a multiple of the identity matrix, the running time is
 again that of Chinese remaindering."
+ again that of Chinese remaindering.",
+ paper = "Kalt01a.pdf"
}
\end{chunk}
\index{matrix determinant}
\index{algorithm!Clarkson}
\index{Clarson algorithm}
\index{matrix condition}
\index{algorithm!Chinese Remainder}
\index{Chinese remainder algorithm}
\index{Hensel lifting}
\index{rational number recovery}
\index{matrix determinant}
\index{matrix largest invariant factor}

+\index{integer matrix}
+\index{matrix determinant}
+\index{characteristic polynomial}
+\index{Smith normal form}
+\index{Frebonius normal form}
+\index{bit complexity}
+\index{divisionfree complexity}
+\index{randomized algorithm}
+\index{multivariable control theory}
+\index{realization}
+\index{block Wiedemann algorithm}
+\index{algorithm!block Wiedemann}
+\index{block Lanczos algorithm}
+\index{algorithm!block Lanczos}
+\index{baby steps/giant steps algorithm}
+\index{algorithm!baby steps/giant steps}
+\index{Las Vegas}
+\index{matrix adjoint}
\index{Kaltofen, Erich}
\index{Villard, Gilles}
\begin{chunk}{axiom.bib}
@@ 709,7 +918,6 @@ paragraph for those unfamiliar with the terms.
pages = "91130",
url =
"http://www.math.ncsu.edu/~kaltofen/bibliography/04/KaVi04_2697263.pdf",
 paper = "Kalt04a.pdf",
abstract = "
We present new baby steps / giant steps algorithms of asymptotically
fast running time for dense matrix problems. Our algorithms compute
@@ 729,29 +937,22 @@ paragraph for those unfamiliar with the terms.
that is, when no divisions in the domain of entries are possible. We
present algorithms that deterministically compute the determinant,
characteristic polynomial and adjoint of $A$ with $n^{3.2+o(1)}$ and
 $O(n^{2.697263})$ ring additions, substractions, and multiplications."
+ $O(n^{2.697263})$ ring additions, substractions, and multiplications.",
+ paper = "Kalt04a.pdf"
}
\end{chunk}
\index{integer matrix}
\index{matrix determinant}
\index{characteristic polynomial}
\index{Smith normal form}
\index{Frebonius normal form}
\index{bit complexity}
\index{divisionfree complexity}
\index{randomized algorithm}
\index{multivariable control theory}
\index{realization}
\index{block Wiedemann algorithm}
\index{algorithm!block Wiedemann}
\index{block Lanczos algorithm}
\index{algorithm!block Lanczos}
\index{baby steps/giant steps algorithm}
\index{algorithm!baby steps/giant steps}
\index{Las Vegas}
\index{matrix adjoint}
+\index{Las Vegas algorithm}
+\index{algorithm!Las Vegas}
+\index{Lanczos algorithm}
+\index{algorithm!Lanczos}
+\index{randomized Lanczos algorithm}
+\index{algorithm!Lanczos randomized}
+\index{symmetric linear systems}
+\index{Wiedemann algorithm}
+\index{algorithm!Wiedemann}
+\index{matrix symmetric}
\index{Eberly, W.}
\index{Kaltofen, Erich}
\begin{chunk}{axiom.bib}
@@ 763,7 +964,6 @@ paragraph for those unfamiliar with the terms.
crossref = "ISSAC97",
pages = "176183",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/97/EbKa97.pdf",
 paper = "Kalt97b.pdf",
abstract = "
Las Vegas algorithms that are based on Lanczo's method for solving
symmetric linear systems are presented and analyzed. These are
@@ 772,20 +972,11 @@ paragraph for those unfamiliar with the terms.
Wiedemann. The analysis suggests that our Lanczos algorithms are
preferable to several versions of Wiedemann's method for computations
over large fields, expecially for certain symmetric matrix
 computations."
+ computations.",
+ paper = "Kalt97b.pdf"
}
\end{chunk}
\index{Las Vegas algorithm}
\index{algorithm!Las Vegas}
\index{Lanczos algorithm}
\index{algorithm!Lanczos}
\index{randomized Lanczos algorithm}
\index{algorithm!Lanczos randomized}
\index{symmetric linear systems}
\index{Wiedemann algorithm}
\index{algorithm!Wiedemann}
\index{matrix symmetric}
\index{explain!Sylvester matrix}
The Sylvester matrix is used to compute the {\bf resultant} of two
@@ 828,6 +1019,11 @@ The Axiom call of $resultant(t1,t2,x)$ is
In symbolic form the resultant can show the multiplicity of roots
when shown in factored form.
+\index{Toeplitz matrix}
+\index{matrix Toeplitz}
+\index{Sylvester matrix}
+\index{matrix Sylvester}
+\index{matrix displacement rank}
\index{Kaltofen, Erich}
\begin{chunk}{axiom.bib}
@InProceedings{Kalt94c,
@@ 839,7 +1035,6 @@ when shown in factored form.
crossref = "ISSAC94",
year = "1994",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/94/Ka94_issac.pdf",
 paper = "Kalt94c.pdf",
abstract = "
The Toeplitzlikeness of a matrix (Kailath et al. 1979) is the
generalization of the notion that a matrix is Toeplitz. Block matrices
@@ 853,16 +1048,17 @@ when shown in factored form.
implicitly represented by a sum of $\alpha$ matrices, each of which is
the product of a lower trainagular and an upper triangular Toeplitz
matrices. Such a $\sigmaLU$ representation can usually be obtained
 efficiently."
+ efficiently.",
+ paper = "Kalt94c.pdf"
}
\end{chunk}
\index{Toeplitz matrix}
\index{matrix Toeplitz}
\index{Sylvester matrix}
\index{matrix Sylvester}
\index{matrix displacement rank}
+\index{parallel homogeneous solutions}
+\index{homogeneous solutions of linear systems}
+\index{black box abstraction}
+\index{coefficient matrix}
+\index{matrix coefficient}
\index{Kaltofen, Erich}
\index{Lobo, A.}
\begin{chunk}{axiom.bib}
@@ 877,7 +1073,6 @@ when shown in factored form.
volume = "24",
number = "34",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/99/KaLo99.pdf",
 paper = "Kalt99.pdf",
abstract = "
We describe a coarsegrain parallel approach for the homogeneous
solution of linear systems. Our solutions are symbolic, i.e., exact
@@ 891,17 +1086,17 @@ when shown in factored form.
systems that arise in RSA challenge integer factoring efforts. For
example, we can solve a 252,222$\times$252,222 system with about 11.04
million nonzero entries over the Galois field with two elements using
 four processors of an SP2 multiprocessor, in about 26.5 hours CPU time."
+ four processors of an SP2 multiprocessor, in about 26.5 hours CPU time.",
+ paper = "Kalt99.pdf"
}
\end{chunk}
+
\index{parallel homogeneous solutions}
\index{homogeneous solutions of linear systems}
\index{black box abstraction}
\index{coefficient matrix}
\index{matrix coefficient}


\index{Kaltofen, Erich}
\index{Lobo, A.}
\begin{chunk}{axiom.bib}
@@ 917,7 +1112,6 @@ when shown in factored form.
publisher = "Simulation Councils, Inc.",
address = "San Diego, CA",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/96/KaLo96_hpc.pdf",
 paper = "Kalt96a.pdf",
abstract = "
We describe a coarsegrain parallel software system for the
homogeneous solution of linear systems. Our solutions are symbolic,
@@ 927,17 +1121,24 @@ when shown in factored form.
systems that arise in RSA challenge integer factoring efforts. For
example, we can solve a 252,222$\times$252,222 system with about 11.04
million nonzero entries over the Galois field with 2 elements using 4
 processors of an SP2 multiprocessor, in about 26.5 hours CPU time."
+ processors of an SP2 multiprocessor, in about 26.5 hours CPU time.",
+ paper = "Kalt96a.pdf"
}
\end{chunk}
\index{parallel homogeneous solutions}
\index{homogeneous solutions of linear systems}
\index{black box abstraction}
\index{coefficient matrix}
\index{matrix coefficient}

+\index{linear systems over finite fields}
+\index{matrix coefficient}
+\index{black box}
+\index{polynomial factoring, univariate}
+\index{polynomial factoring, finite field}
+\index{polynomial factoring, Berlekamp}
+\index{Berlekamp algorithm}
+\index{algorithm!Berlekamp}
+\index{Wiedemann algorithm}
+\index{algorithm!Wiedemann}
+\index{TO!Wiedemann!Coppersmith}
+\index{TO!Wiedemann!Kaltofen}
\index{Kaltofen, Erich}
\index{Lobo, A.}
\begin{chunk}{axiom.bib}
@@ 950,7 +1151,6 @@ when shown in factored form.
pages = "9098",
year = "1994",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/94/KaLo94.ps.gz",
 paper = "Kalt94a.ps",
abstract = "
Modern techniques for solving structured linear systems over finite
fields, which use the coefficient matrix as a black box and require an
@@ 960,23 +1160,19 @@ when shown in factored form.
aon a computer implementation of this idea that is based on the
parallel block Wiedemann linear system solver (Coppersmith 1994 and
Kaltofen 1993 and 1995). The program uses randomization and we also
 study the expected run time behavior of our method."
+ study the expected run time behavior of our method.",
+ paper = "Kalt94a.ps"
}
\end{chunk}
\index{linear systems over finite fields}
\index{matrix coefficient}
\index{black box}
\index{polynomial factoring, univariate}
\index{polynomial factoring, finite field}
\index{polynomial factoring, Berlekamp}
\index{Berlekamp algorithm}
\index{algorithm!Berlekamp}
\index{Wiedemann algorithm}
\index{algorithm!Wiedemann}
\index{TO!Wiedemann!Coppersmith}
\index{TO!Wiedemann!Kaltofen}
+\index{TO!Wiedemann!Coppersmith}
+\index{parallel}
+\index{Wiedemann coordinate recurrence algorithm}
+\index{algorithm!Wiedemann coordinate recurrence}
+\index{Krylov subspace}
+\index{singular block Toeplitz}
+\index{matrix singular block Toeplitz}
\index{Kaltofen, Erich}
\begin{chunk}{axiom.bib}
@Article{Kalt95,
@@ 989,7 +1185,6 @@ when shown in factored form.
number = "210",
pages = "777806",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/95/Ka95_mathcomp.pdf",
 paper = "Kalt95.pdf",
abstract = "
By using projections by a block of vectors in place of a single vector
it is possible to parallelize the outer loop of iterative methods for
@@ 1001,18 +1196,20 @@ when shown in factored form.
processors. Our analysis is valid for fields of entries that have
sufficiently large cardinality. Our analysis also deals with an
arising subproblem of solving a singular block Toeplitz system by use
 of the theory of Toeplitzlike matrices."
+ of the theory of Toeplitzlike matrices.",
+ paper = "Kalt95.pdf"
}
\end{chunk}
\index{TO!Wiedemann!Coppersmith}
\index{parallel}
\index{Wiedemann coordinate recurrence algorithm}
\index{algorithm!Wiedemann coordinate recurrence}
\index{Krylov subspace}
\index{singular block Toeplitz}
\index{matrix singular block Toeplitz}
+\index{parallel}
+\index{matrix normal forms}
+\index{matrix parallel normal form algorithms}
+\index{algorithm!matrix parallel normal form}
+\index{matrix Smith form}
+\index{Smith form matrix}
+\index{matrix Hermite form}
+\index{Hermite form matrix}
\index{Kaltofen, Erich}
\index{Krishnamoorthy, M.S.}
\index{Saunders, B. David}
@@ 1025,7 +1222,6 @@ when shown in factored form.
volume = "136",
pages = "189208",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/90/KKS90.pdf",
 paper = "Kalt90a.pdf",
abstract = "
Here we offer a new randomized parallel algorithm that determines the
Smith normal form of a matrix with entries being univariate
@@ 1041,19 +1237,17 @@ when shown in factored form.
form and testing similarity of matrices. Both the similarity and
nonsimilarity problems are in the complexity class RNC for the usual
coefficient fields, i.e., they can be probabilistically decided in
 polylogarithmic time using polynomially many processors."
+ polylogarithmic time using polynomially many processors.",
+ paper = "Kalt90a.pdf"
}
\end{chunk}
+
\index{parallel}
\index{matrix normal forms}
\index{matrix parallel normal form algorithms}
\index{algorithm!matrix parallel normal form}
\index{matrix Smith form}
\index{Smith form matrix}
\index{matrix Hermite form}
\index{Hermite form matrix}

\index{Kaltofen, Erich}
\index{Krishnamoorthy, M.S.}
\index{Saunders, B. David}
@@ 1067,7 +1261,6 @@ when shown in factored form.
volume = "8",
pages = "683690",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/87/KKS87.pdf",
 paper = "Kalt87.pdf",
abstract = "
Boolean circuits of polynomial size and polylogarithmic depth are
given for computing the Hermite and Smith normal forms of polynomial
@@ 1077,16 +1270,15 @@ when shown in factored form.
we give a polynomialtime deterministic sequential algorithm for the
Smith normal form over the rationals. The Smith normal form algorithms
are applied to the Rational canonical form of matrices over finite
 fields and the field of rational numbers."
+ fields and the field of rational numbers.",
+ paper = "Kalt87.pdf"
}
\end{chunk}
\index{parallel}
\index{matrix Smith form}
\index{Smith form matrix}
\index{matrix Hermite form}
\index{Hermite form matrix}
+\index{algorithm!parallel randomized}
+\index{parallel randomized algorithm}
+\index{matrix rank}
\index{Kaltofen, Erich}
\index{Pan, Victor}
\begin{chunk}{axiom.bib}
@@ 1100,7 +1292,6 @@ when shown in factored form.
publisher = "IEEE Computer Society Press",
address = "Los Alamitos, California",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/92/KaPa92.pdf",
 paper = "Kalt92.pdf",
abstract = "
We show that over any field, the solution set to a system of $n$
linear equations in $n$ unknowns can be computed in parallel with
@@ 1111,14 +1302,14 @@ when shown in factored form.
fast as those for nonsingular systems, due to our avoidance of binary
search in the matrix rank problem, except when the field has small
positive characteristic; in that case, binary search is avoided to a
 somewhat higher processor count measure."
+ somewhat higher processor count measure.",
+ paper = "Kalt92.pdf"
}
\end{chunk}
+
\index{algorithm!parallel randomized}
\index{parallel randomized algorithm}
\index{matrix rank}

\index{Kaltofen, Erich}
\index{Pan, Victor}
\begin{chunk}{axiom.bib}
@@ 1132,7 +1323,6 @@ when shown in factored form.
year = "1991",
address = "New York, N.Y.",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/91/KaPa91.pdf",
 paper = "Kalt91c.pdf",
abstract = "
Parallel randomized algorithms are presented that solve
$n$dimensional systems of linear equations and compute inverses of
@@ 1144,13 +1334,25 @@ when shown in factored form.
high probability provided the $O(n)$ random elements used are selected
uniformly from a sufficiently large set. For fields of small positive
characteristics, the processor count measures of our solutions are
 somewhat higher."
+ somewhat higher.",
+ paper = "Kalt91c.pdf"
}
\end{chunk}
\index{algorithm!parallel randomized}
\index{parallel randomized algorithm}
+\index{Wiedemann algorithm}
+\index{algorithm!Wiedemann}
+\index{sparse linear system solver}
+\index{Lanczos algorithm}
+\index{algorithm!Lanczos}
+\index{Krylov subspaces}
+\index{Berlekamp algorithm}
+\index{algorithm!Berlekamp}
+\index{Massey algorithm}
+\index{algorithm!Massey}
+\index{coordinate recurrences}
+\index{randomization}
+\index{black box}
\index{Kaltofen, Erich}
\index{Saunders, B. David}
\begin{chunk}{axiom.bib}
@@ 1165,7 +1367,6 @@ when shown in factored form.
publisher = "SpringerVerlag",
year = "1991",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/91/KaSa91.pdf",
 paper = "Kalt91.pdf",
abstract = "
Douglas Wiedemann's (1986) landmark approach to solving sparse linear
systems over finite fields provides the symbolic counterpart to
@@ 1188,24 +1389,20 @@ when shown in factored form.
log(x)$, otherwise one goes to a finite algebraic extension. The
complexity of the method is in the general singular case $O(n log
(n))$ calls to the black box for $A$ and an additional $O(n^2
 log(n)^2)$ field arithmetic operations."
+ log(n)^2)$ field arithmetic operations.",
+ paper = "Kalt91.pdf"
}
\end{chunk}
+
+\index{coordinate recurrence}
\index{Wiedemann algorithm}
\index{algorithm!Wiedemann}
\index{sparse linear system solver}
\index{Lanczos algorithm}
\index{algorithm!Lanczos}
\index{Krylov subspaces}
\index{Berlekamp algorithm}
\index{algorithm!Berlekamp}
\index{Massey algorithm}
\index{algorithm!Massey}
\index{coordinate recurrences}
\index{randomization}
\index{black box}

+\index{probablistic square matrix determinant}
+\index{matrix probablistic square determinant}
+\index{matrix minimum polynomial}
+\index{matrix rank}
+\index{Chinese remainder}
\index{Wiedemann, Douglas H.}
\begin{chunk}{axiom.bib}
@article{Wied86,
@@ 1218,7 +1415,6 @@ when shown in factored form.
pages = "5462",
url =
"http://www.csd.uwo.ca/~moreno/CS424/Ressources/WIEDEMANNIEE1986.pdf",
 paper = "Wied86.pdf",
abstract = "
A ``coordinate recurrence'' method for solving sparse systems of
linear equations over finite fields is described. The algorithms
@@ 1226,24 +1422,48 @@ when shown in factored form.
where $n_1$ is the maximum dimension of the coefficient matrix,
$\omega$ is approximately the number of field operations required to
apply the matrix to a test vector, and the value of $k$ depends on the
 algorithm. A probabilistic algorithm is shown to exist for finding the
 determinant of a square matrix. Also, probabilistic algorithms are
 shown to exist for finding the minimum polynomial and rank with some
 arbitrarily small possibility of error."
}

\end{chunk}
\index{coordinate recurrence}
\index{Wiedemann algorithm}
\index{algorithm!Wiedemann}
\index{probablistic square matrix determinant}
\index{matrix probablistic square determinant}
\index{matrix minimum polynomial}
\index{matrix rank}
\index{Chinese remainder}
+ algorithm. A probabilistic algorithm is shown to exist for finding the
+ determinant of a square matrix. Also, probabilistic algorithms are
+ shown to exist for finding the minimum polynomial and rank with some
+ arbitrarily small possibility of error.",
+ paper = "Wied86.pdf"
+}
+
+\end{chunk}
\section{Algebraic Algorithms} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{matrix computations}
+\index{polynomial zero approximation}
+\index{products of vectors}
+\index{products of matrices}
+\index{convolution of vectors}
+\index{matrix multiplication}
+\index{Gaussian elimination algorithm}
+\index{algorithm!Gaussian elimination}
+\index{singular linear systems of equations}
+\index{sparse linear systems}
+\index{banded linear systems}
+\index{direct sparse linear solution algorithm}
+\index{algorithm!direct sparse linear solution}
+\index{iterative sparse linear solution algorithm}
+\index{algorithm!iterative sparse linear solution}
+\index{matrix dense}
+\index{matrix structured}
+\index{matrix parallel computation}
+\index{matrix rational computation}
+\index{matrix computation in finite fields}
+\index{matrix computation in semirings}
+\index{matrix eigenvalues}
+\index{matrix singular values}
+\index{approximating polynomial zeros}
+\index{FFT and fast polynomial arithmetic}
+\index{resultant methods}
+\index{gr\"obner bases}
+\index{polynomial factoring over a finite field}
+\index{polynomial factoring over characteristic 0}
+\index{polynomial factoring in two variables}
+\index{polynomial factoring in many variables}
\index{Diaz, Angel}
\index{Kaltofen, Erich}
\index{Pan, Victor}
@@ 1260,7 +1480,6 @@ when shown in factored form.
chapter = "10",
keywords = "survey",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/97/DKP97.ps.gz",
 paper = "Diaz97.ps",
ref = "00965",
abstract = "
The title's subject is the algorithmic approach to algebra: arithmetic
@@ 1275,41 +1494,11 @@ when shown in factored form.
Mathematica systems, to name but two among many useful systems. This
chapter restricts itself to algorithms in four areas: linear matrix
algebra, root finding ov univariate polynomials, solution of systems
 of nonlinear algebraic equations, and polynomial factorization."
+ of nonlinear algebraic equations, and polynomial factorization.",
+ paper = "Diaz97.ps"
}
\end{chunk}
\index{matrix computations}
\index{polynomial zero approximation}
\index{products of vectors}
\index{products of matrices}
\index{convolution of vectors}
\index{matrix multiplication}
\index{Gaussian elimination algorithm}
\index{algorithm!Gaussian elimination}
\index{singular linear systems of equations}
\index{sparse linear systems}
\index{banded linear systems}
\index{direct sparse linear solution algorithm}
\index{algorithm!direct sparse linear solution}
\index{iterative sparse linear solution algorithm}
\index{algorithm!iterative sparse linear solution}
\index{matrix dense}
\index{matrix structured}
\index{matrix parallel computation}
\index{matrix rational computation}
\index{matrix computation in finite fields}
\index{matrix computation in semirings}
\index{matrix eigenvalues}
\index{matrix singular values}
\index{approximating polynomial zeros}
\index{FFT and fast polynomial arithmetic}
\index{resultant methods}
\index{gr\"obner bases}
\index{polynomial factoring over a finite field}
\index{polynomial factoring over characteristic 0}
\index{polynomial factoring in two variables}
\index{polynomial factoring in many variables}
\index{Diaz, Angel}
\index{Emiris, Ioannis Z.}
@@ 1328,7 +1517,6 @@ when shown in factored form.
isbn = "0849326494",
keywords = "survey",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/99/DEKP99.ps.gz",
 paper = "Diaz99.ps",
abstract = "
The title's subject is the algorithmic approach to algebra: arithmetic
with numbers, polynomials, matrices, differential polynomials, such as
@@ 1344,7 +1532,8 @@ when shown in factored form.
nonlinear algebraic equations, and polynomial factorization (see
section 5 on some pointers to the vast further material on algebraic
algorithms and section 2.2 and [Pan 1993] on further applications to
 the graph and combinatorial computations)."
+ the graph and combinatorial computations).",
+ paper = "Diaz99.ps"
}
\end{chunk}
@@ 1361,9 +1550,7 @@ when shown in factored form.
year = "1987",
volume = "2",
address = "Palo Alto, California",
 keywords = "survey,axiomref",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/87/Ka87_annrev.pdf",
 paper = "Kalt87a.pdf",
abstract = "
The origins of the discipline of computer algebra can be found in
Issac Newton's {\sl Universal Arithmetic} (1728) [130], where methods
@@ 1377,7 +1564,9 @@ when shown in factored form.
them {MACSYMA}, {MAPLE}, {muMATH}, {REDUCE}, {SAC/2}, {SCRATCHPAD/II},
and {SMP}. These systems carry out scientific computing tasks, whose
results are distinguished from numerical computing in two principle
 aspects."
+ aspects.",
+ paper = "Kalt87a.pdf",
+ keywords = "survey,axiomref"
}
\end{chunk}
@@ 1389,7 +1578,6 @@ when shown in factored form.
title = "Some NOtes on Algebraic Methods for Geometry Theorem Proving",
url = "http://wwwpolsys.lip6.fr/~wang/papers/GTPnote.ps.gz",
year = "1990",
 paper = "Wang90a.pdf",
abstract =
"A new geometry theorem prover which provides the first complete
implementation of Wu's method and includes several Groebner bases
@@ 1403,7 +1591,8 @@ when shown in factored form.
type reduction. Parallel variants of Wu's method are discussed; an
implementation of the parallelized version of his algorithm utilizing
workstation networks has also been included in our prover. Timing
 statistics for a set of typical examples is given."
+ statistics for a set of typical examples is given.",
+ paper = "Wang90a.pdf"
}
\end{chunk}
@@ 1418,7 +1607,6 @@ when shown in factored form.
pages = "138172",
institution = "Johannes Kepler University",
url = "http://wwwpolsys.lip6.fr/~wang/papers/Factor.ps.gz",
 paper = "Wang92.pdf",
year = "1992",
abstract =
"We present a method for factorizing multivariate polynomials over
@@ 1434,7 +1622,8 @@ when shown in factored form.
statistics in Maple 4.3 on 40 test examples which were partly taken
from the literature and partly randomly generated. For all those
examples to which Maple builtin algorithm is applicable, our
 algorithm is always faster."
+ algorithm is always faster.",
+ paper = "Wang92.pdf"
}
\end{chunk}
@@ 1456,7 +1645,6 @@ when shown in factored form.
keywords = "survey",
url =
"http://www.math.ncsu.edu/~kaltofen/bibliography/96/Ka96_stratagem.ps.gz",
 paper = "Kalt96b.ps",
abstract = "
The problem of solving a large sparse or structured system of linear
equations in the symbolic context, for instance when the coefficients
@@ 1473,7 +1661,8 @@ when shown in factored form.
matrices'' arise in the power series solution of algebraic or
differential equations by undetermined coefficients. The arising
linear systems for the coefficients usually have a distinct structure
 that allows a fast coefficient matrix times vector product."
+ that allows a fast coefficient matrix times vector product.",
+ paper = "Kalt96b.ps"
}
\end{chunk}
@@ 1495,7 +1684,6 @@ when shown in factored form.
year = "2004",
keywords = "survey",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/02/KaVi02.pdf",
 paper = "Kalt04.pdf",
abstract = "
Computation of the sign of the determinant of a matrix and the
determiant itself is a challenge for both numerical and exact
@@ 1504,12 +1692,12 @@ when shown in factored form.
entries. We study the bitcomplexities of the algorithms
asymptotically in $n$ and the norm $A$. Existing approaches rely on
numerical approximate computations, on exact computations, or on both
 types of arithmetic in combination."
+ types of arithmetic in combination.",
+ paper = "Kalt04.pdf"
}
\end{chunk}

\section{Open Problems} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Kaltofen, Erich}
@@ 1524,7 +1712,6 @@ when shown in factored form.
year = "2000",
keywords = "survey",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/2K/Ka2K.pdf",
 paper = "Kalt00.pdf",
abstract = "
The success of the symbolic mathematical computation discipline is
striking. The theoretical advances have been continuous and significant:
@@ 1549,7 +1736,8 @@ when shown in factored form.
to each of my problems and a clearcut test that evaluates whether a
proposed attack has solved one of my problems. An additional ninth
open problem by Rob Corless and David Jeffrey on complex function
 semantics is given in an appendix."
+ semantics is given in an appendix.",
+ paper = "Kalt00.pdf"
}
\end{chunk}
@@ 1570,7 +1758,6 @@ when shown in factored form.
keywords = "survey",
url =
"http://www.math.ncsu.edu/~kaltofen/bibliography/93/Ka93_synthesis.ps.gz",
 paper = "Kalt93a.ps",
abstract = "
One generic parallel evaluation scheme for algebraic objects, that of
evaluating algebraic computation trees or formulas, is presented by
@@ 1584,7 +1771,8 @@ when shown in factored form.
recomputed anew for each of these nodes. It is a small formal change
to allow node values to propagate to more than one node deeper level
of the computation. Thus we obtain the {\sl algebraic circuit model},
 which is equivalent to the {\sl straightline program model}."
+ which is equivalent to the {\sl straightline program model}.",
+ paper = "Kalt93a.ps"
}
\end{chunk}
@@ 1603,7 +1791,6 @@ when shown in factored form.
title = "On the Lambert W Function",
year = "1993",
url = "http://cs.uwaterloo.ca/research/tr/1993/03/W.pdf",
 paper = "Corl93.pdf",
abstract =
"The Lambert W function is defined to be the multivalued inverse of
the function $w \rightArrow we^w$. It has many applications in pure
@@ 1611,7 +1798,8 @@ when shown in factored form.
present a new discussion of the complex branches of $W$, an asymptotic
expansion valid for all branches, an efficient numerical procedure for
evaluating the function to arbitrary precision, and a method for the
 symbolic integration of expressions containing $W$."
+ symbolic integration of expressions containing $W$.",
+ paper = "Corl93.pdf"
}
\end{chunk}
@@ 1630,7 +1818,6 @@ when shown in factored form.
pages = "227234",
month = "July",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/10/HKZ10.pdf",
 paper = "Hutt10.pdf",
abstract = "
We give a stability criterion for real polynomial inequalities with
floating point or inexact scalars by estimating from below or
@@ 1657,7 +1844,8 @@ when shown in factored form.
coeffcients are numeric. They also offer a surprising alternative
sumofsquares proof for those polynomials that themselves cannot be
represented by a polynomial sumofsquares but that have a positive
 distance to the nearest indefinte polynomial."
+ distance to the nearest indefinte polynomial.",
+ paper = "Hutt10.pdf"
}
\end{chunk}
@@ 1673,7 +1861,6 @@ when shown in factored form.
crossref = "ISSAC06",
pages = "7",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/06/KaZhi06.pdf",
 paper = "Kalt06.pdf",
abstract = "
Several standard problems in symbolic computation, such as greatest
common divisors and factorization of polynomials, sparse
@@ 1700,7 +1887,8 @@ when shown in factored form.
numeriiical or symbolic methods alone.'' The focus of our tutorial is
on how to formulate several approximate symbolic computation problems
as numerical problems in linear algebra and optimization and on
 software that realizes their solutions."
+ software that realizes their solutions.",
+ paper = "Kalt06.pdf"
}
\end{chunk}
@@ 1718,7 +1906,6 @@ when shown in factored form.
crossref = "SNC09",
pages = "6569",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/09/KYZ09.pdf",
 paper = "Kalt09.pdf",
abstract = "
For a proof of the monotone column permanent (MCP) conjecture for
dimension 4 it is sufficient to show that 4 polynomials, which come
@@ 1727,7 +1914,8 @@ when shown in factored form.
variables of these polynomials are all 8. Here we apply a hybrid
symbolicnumerical algorithm for certifying that these polynomials can
be written as an exact fraction of two polynomial sumsofsquares
 (SOS) with rational coefficients."
+ (SOS) with rational coefficients.",
+ paper = "Kalt09.pdf"
}
\end{chunk}
@@ 1750,7 +1938,6 @@ when shown in factored form.
number = "1",
pages = "115",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/09/KLYZ09.pdf",
 paper = "Kalt12.pdf",
abstract = "
We present a hybrid symbolicnumeric algorithm for certifying a
polynomial or rational function with rational coefficients to be
@@ 1770,7 +1957,8 @@ when shown in factored form.
demenstrate our algorithm on 1. various exceptional SOS problems with
necessary polynomial denominators from the literature and on 2. very
large (thousands of variables) SOS lower bound certificates for Rump's
 model problem (up to $n=18$, factor degree $=17$)."
+ model problem (up to $n=18$, factor degree $=17$).",
+ paper = "Kalt12.pdf"
}
\end{chunk}
@@ 1790,7 +1978,6 @@ when shown in factored form.
crossref = "ISSAC08",
pages = "155163",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/08/KLYZ08.pdf",
 paper = "Kalt08b.pdf",
abstract = "
We generalize the technique by Peyrl and Parillo [Proc. SNC 2007] to
computing lower bound certificates for several wellknown
@@ 1810,7 +1997,8 @@ when shown in factored form.
refine the SOSes by rankpreserving Newton iteration. For smaller
problems the starting SOSes for Newton can be guessed without SDP
(``SDPfree SOS''), but for larger inputs we additionally appeal to
 sparsity techniques in our SDP formulation."
+ sparsity techniques in our SDP formulation.",
+ paper = "Kalt08b.pdf"
}
\end{chunk}
@@ 1828,7 +2016,6 @@ when shown in factored form.
crossref = "ISSAC06",
pages = "169176",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/06/KYZ06.pdf",
 paper = "Kalt06b.pdf",
abstract = "
We consider the problem of computing minimal real or complex
deformations to the coefficients in a list of relatively prime real or
@@ 1849,7 +2036,8 @@ when shown in factored form.
polynomials. Our algorithms can handle, via randomized
preconditioning, the difficult case when the nearest solution to a
list of real input polynomials actually has nonreal complex
 coefficients."
+ coefficients.",
+ paper = "Kalt06b.pdf"
}
\end{chunk}
@@ 1866,7 +2054,6 @@ when shown in factored form.
pages = "6983",
year = "2005",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/05/KYZ05.pdf",
 paper = "Kalt05.pdf",
abstract = "
The task of determining the approximate greatest common divisor (GCD)
of univariate polynomials with inexact coefficients can be formulated
@@ 1880,7 +2067,8 @@ when shown in factored form.
single iteration is carried out with a number of floating point
operations that is of cubic order in the input degrees. We also
demonstrate the practical performance of our algorithms on a diverse
 set of univariate pairs of polynomials."
+ set of univariate pairs of polynomials.",
+ paper = "Kalt05.pdf"
}
\end{chunk}
@@ 1896,7 +2084,6 @@ when shown in factored form.
crossref = "ISSAC03",
pages = "161168",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/03/KM03.pdf",
 paper = "Kalt03a.pdf",
abstract = "
We study the problem of bounding all factorizable polynomials away
from a polynomial that is absolutely irreducible. Such separation
@@ 1907,7 +2094,8 @@ when shown in factored form.
polynomials. We also use Ruppert's criterion to derive new, more
effective Noether forms for polynomials of arbitrarily many
variables. These forms lead to small separation bounds for polynomials
 of arbitrarily many variables."
+ of arbitrarily many variables.",
+ paper = "Kalt03a.pdf"
}
\end{chunk}
@@ 1928,7 +2116,6 @@ when shown in factored form.
crossref = "ISSAC04",
pages = "167174",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/04/GKMYZ04.pdf",
 paper = "Gao04a.pdf",
abstract = "
The input to our algorithm is a multivariate polynomial, whose complex
rational coefficient are considered imprecise with an unknown error
@@ 1944,7 +2131,8 @@ when shown in factored form.
data that our algorithm is practical and can find factorizable
polynomials within a distance that is about the same in relative
magnitude as the input error, even when the relative error in the
 input is substantial ($10^{3})."
+ input is substantial ($10^{3}).",
+ paper = "Gao04a.pdf"
}
\end{chunk}
@@ 1964,7 +2152,7 @@ when shown in factored form.
number = "5",
pages = "359376",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/07/KMYZ07.pdf",
 paper = "Kalt08.pdf",
+ paper = "Kalt08.pdf"
}
\end{chunk}
@@ 1982,7 +2170,7 @@ when shown in factored form.
pages = "205212",
year = "1999",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/99/HKL99.pdf",
 paper = "Hitz99.pdf",
+ paper = "Hitz99.pdf"
}
\end{chunk}
@@ 1999,7 +2187,7 @@ when shown in factored form.
year = "1998",
pages = "236243",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/98/HiKa98.pdf",
 paper = "Hitz98.pdf",
+ paper = "Hitz98.pdf"
}
\end{chunk}
@@ 2019,7 +2207,7 @@ when shown in factored form.
pages = "323332",
year = "1991",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/91/DKSV91.pdf",
 paper = "Diaz91.pdf",
+ paper = "Diaz91.pdf"
}
\end{chunk}
@@ 2039,7 +2227,7 @@ when shown in factored form.
series = "Proceedings of the Maple Summer Workshop and Symposium (MSWS'94)",
address = "Boston",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/94/CDK94.ps.gz",
 paper = "Chan94.ps",
+ paper = "Chan94.ps"
}
\end{chunk}
@@ 2065,7 +2253,7 @@ when shown in factored form.
pages = "4050",
year = "2002",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/02/Detal02.pdf",
 paper = "Duma02.pdf",
+ paper = "Duma02.pdf"
}
\end{chunk}
@@ 2082,7 +2270,7 @@ when shown in factored form.
crossref = "ISSAC05",
pages = "216223",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/05/KMY05.pdf",
 paper = "Kalt05a.pdf",
+ paper = "Kalt05a.pdf"
}
\end{chunk}
@@ 2100,7 +2288,6 @@ when shown in factored form.
year = "1998",
pages = "3037",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/98/DiKa98.pdf",
 paper = "Diaz98.pdf",
abstract =
"The FOXBOX system puts in practice the black box representation of
symbolic objects and provides algorithms for performing the symbolic
@@ 2124,7 +2311,8 @@ when shown in factored form.
used in the same computation. FOXBOX provides an MPI compliant
distribution mechanism that allows for parallel and distributed
execution of FOXBOX programs. Finally, FOXBOX plugs into a
 server/clientstyle Maple application interface."
+ server/clientstyle Maple application interface.",
+ paper = "Diaz98.pdf"
}
\end{chunk}
@@ 2146,7 +2334,7 @@ when shown in factored form.
volume = "722",
publisher = "SpringerVerlag",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/93/DHKLV93.pdf",
 paper = "Diaz93.pdf",
+ paper = "Diaz93.pdf"
}
\end{chunk}
@@ 2168,7 +2356,7 @@ when shown in factored form.
number = "13",
pages = "269282",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/95/DHKLV95.pdf",
 paper = "Diaz95a.pdf",
+ paper = "Diaz95a.pdf"
}
\end{chunk}
@@ 2189,7 +2377,7 @@ when shown in factored form.
number = "3",
pages = "218240",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/88/FIKY88.pdf",
 paper = "Free88.pdf",
+ paper = "Free88.pdf"
}
\end{chunk}
@@ 2208,7 +2396,7 @@ when shown in factored form.
year = "2010",
keywords = "survey",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/10/Ka10_7dwarfs.pdf",
 paper = "Kalt10a.pdf",
+ paper = "Kalt10a.pdf"
}
\end{chunk}
@@ 2248,7 +2436,6 @@ when shown in factored form.
volume = "60",
pages = "29832997",
year = "2010",
 paper = "Lixx10.pdf",
abstract =
"This paper presents algorithms for decomposing any zerodimensional
polynomial set into simple sets over an arbitrary finite field, with
@@ 2259,7 +2446,8 @@ when shown in factored form.
generalized squarefree decomposition approach, a method is proposed to
extract the $p$th root of any element in the field
product. Experiments with a preliminary implementation show the
 effectiveness of our algorithms."
+ effectiveness of our algorithms.",
+ paper = "Lixx10.pdf"
}
\end{chunk}
@@ 2278,7 +2466,6 @@ when shown in factored form.
month = "December",
type = "technical report",
number = "229",
 paper = "Ahre15.pdf",
url = "http://www.eecs.berkeley.edu/Pubs/TechRpts/2015/EECS2015229.pdf",
abstract =
"We define reproducibility to mean getting bitwise identical results
@@ 2305,7 +2492,8 @@ when shown in factored form.
performance results. For example, when computing the dot product of
4096 double precision floating point numbers, we get a $4x$ slowdown
compared to Intel Math Kernel Library (MKL) running on an Intel Core
 i72600 CPU operating at 3.4 GHz and 256 KB L2 Cache."
+ i72600 CPU operating at 3.4 GHz and 256 KB L2 Cache.",
+ paper = "Ahre15.pdf"
}
\end{chunk}
@@ 2332,7 +2520,6 @@ when shown in factored form.
school = "University of Minnesota",
year = "1995",
month = "February",
 paper = "Anda95.pdf",
abstract =
"A suite of {\sl selfscaling} fast circular plane rotation algorithms
is developed which obviates the monitoring and periodic rescaling
@@ 2371,8 +2558,8 @@ when shown in factored form.
and C90, of rotations both in and out of a matrix factorization
context are presented. Architectural features that can best exploit
the advantagous features of the new fast rotations are subsequently
 discussed."

+ discussed.",
+ paper = "Anda95.pdf"
}
\end{chunk}
@@ 2386,7 +2573,6 @@ when shown in factored form.
url = "http://arxiv.org/pdf/1210.4539.pdf",
year = "2012",
month = "October",
 paper = "Baud12.pdf",
abstract =
"The most widely used algorithm for floating point complex division,
known as Smith's method, may fail more often than expected. This
@@ 2395,7 +2581,8 @@ when shown in factored form.
simulations show that this algorithm performs well in practice and is
significantly more robust than other known implementations. By
combining additional scaling methods with this first algorithm, we
 were able to create a second algorithm, which rarely fails."
+ were able to create a second algorithm, which rarely fails.",
+ paper = "Baud12.pdf"
}
\end{chunk}
@@ 2412,7 +2599,6 @@ when shown in factored form.
institution = "National Institute of Standards and Technology",
type = "Technical Report",
url = "http://math.nist.gov/MatrixMarket/reports/MMformat.ps",
 paper = "MMEF96.pdf",
abstract =
"We propose elementary ASCII exchange formats for matrices. Specific
instances of the format are defined for dense and sparse matrices with
@@ 2420,18 +2606,19 @@ when shown in factored form.
symmetric, skewsymmetric and Hermitian matrices. Sparse matrices are
represented in a coordinate storage format. The overall file structure
is designed to allow future definition of other specialized matrix
 formats, as well as for objects other than matrices."
+ formats, as well as for objects other than matrices.",
+ paper = "MMEF96.pdf"
}
\end{chunk}
\index{Bronstein, Manuel}
\begin{chunk}{ignore}
{Bro99,
+\begin{chunk}{axiom.bib}
+@misc{Bron99,
author = "Bronstein, Manuel",
title = "Fast Deterministic Computation of Determinants of Dense Matrices",
 url = "http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mb_papers.html",
 paper = "Bro99.pdf",
+ url =
+ "http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mb_papers.html",
abstract = "
In this paper we consider deterministic computation of the exact
determinant of a dense matrix $M$ of integers. We present a new
@@ 2444,7 +2631,8 @@ when shown in factored form.
assuming some plausible properties about the distribution of $M$.
We will also describe a practical version of the algorithm and include
timing data to compare this algorithm with existing ones. Our result
 does not depend on ``fast'' integer or matrix techniques."
+ does not depend on ``fast'' integer or matrix techniques.",
+ paper = "Bron99.pdf"
}
\end{chunk}
@@ 2471,7 +2659,6 @@ when shown in factored form.
title = "How To Write Fast Numerical Code: A Small Introduction",
year = "2006",
institution = "Carnegie Mellon University",
 paper = "Chel06.pdf",
url = "https://users.ece.cmu.edu/~franzf/papers/gttse07.pdf",
algebra = "\newline\refto{package BLAS1 BlasLevelOne}",
abstract =
@@ 2485,7 +2672,8 @@ when shown in factored form.
Further, program generators are discussed as a way to reduce the
implementation and optimization effort. Two running examples are
used to demonstrate these techniques: matrixmatrix multiplication
 and the discrete Fourier transform."
+ and the discrete Fourier transform.",
+ paper = "Chel06.pdf"
}
\end{chunk}
@@ 2501,7 +2689,6 @@ when shown in factored form.
institution = "New York University",
type = "Technical Report",
number = "326",
 paper = "Demm88.pdf",
abstract =
"Computing the singular values of a bidiagonal matrix is the final
phase of the standard algorithm for the singular value decomposition
@@ 2513,7 +2700,8 @@ when shown in factored form.
algorithm is comparable in speed to the standard algorithm, and
frequently faster. We also show how to accurately compute tiny
eigenvalues of some classes of symmetric trigiagonal matrices using
 the same technique."
+ the same technique.",
+ paper = "Demm88.pdf"
}
\end{chunk}
@@ 2533,7 +2721,6 @@ when shown in factored form.
institution = "Univerity of California, Berkeley",
type = "Technical Report",
number = "165",
 paper = "Demm05.pdf",
url = "http://www.netlib.org/lapack/lawnspdf/lawn165.pdf",
abstract =
"We present the design and testing of an algorithm for iterative
@@ 2560,7 +2747,8 @@ when shown in factored form.
$2max(10,\sqrt{n})\epsilon_w$, and indeed bounds the true error. Here,
$n$ is the matrix dimension and $\epsilon_w$ is a single precision
roundoff error. For worse conditioned problems, we get similarly small
 correct error bounds in over 89.4\% of cases."
+ correct error bounds in over 89.4\% of cases.",
+ paper = "Demm05.pdf"
}
\end{chunk}
@@ 2579,7 +2767,6 @@ when shown in factored form.
institution = "Univerity of California, Berkeley",
type = "Technical Report",
number = "203",
 paper = "Demm08.pdf",
url = "http://www.netlib.org/lapack/lawnspdf/lawn203.pdf",
abstract =
"The Householder reflections used in LAPACK's QR factorization leave
@@ 2593,7 +2780,9 @@ when shown in factored form.
matrices, those with nonzero entries mostly near the diagonal (e.g
band matrices), now requires far fewer operations. For example, QR
factorization of matrices with profile width $b$ that are stored
 densely in an $n \cross n$ matrix improves form $O(n^3)$ to $O(n^2+nb^2)$."
+ densely in an $n \cross n$ matrix improves form $O(n^3)$
+ to $O(n^2+nb^2)$.",
+ paper = "Demm08.pdf"
}
\end{chunk}
@@ 2610,7 +2799,6 @@ when shown in factored form.
year = "2011",
month = "November",
url = "http://yifanhu.net/PUB/matrices.pdf",
 paper = "Davi11.pdf",
abstract =
"We describe the Univerity of Florida Sparse Matrix Collection, a large
and actively growing set of sparse matrices that arise in real
@@ 2632,7 +2820,8 @@ when shown in factored form.
for accessing and managing the Collection, from MATLAB, Mathematica,
Fortran, and C, as well as an online search capability. Graph
visualization of the matrices is provided, and a new multilevel
 coarsening scheme is proposed to facilitate this task."
+ coarsening scheme is proposed to facilitate this task.",
+ paper = "Davi11.pdf"
}
\end{chunk}
@@ 2651,7 +2840,6 @@ when shown in factored form.
type = "Technical Report",
url =
"http://faculty.cse.tamu.edu/davis/publications_files/survey_tech_report.pdf",
 paper = "Davi16.pdf",
abstract =
"Wilkinson defined a sparse matrix as one with enough zeros that it
pays to take advantage of them. This informal yet practical definition
@@ 2668,7 +2856,8 @@ when shown in factored form.
systems and leastsquares problems, and to provide an overview of the
algorithms, data structures, and software available to solve these
problems, so that the reader can both understand the methods and know
 how best to use them."
+ how best to use them.",
+ paper = "Davi16.pdf"
}
\end{chunk}
@@ 2685,7 +2874,6 @@ when shown in factored form.
pages = "873912",
year = "1990",
url = "http://www.netlib.org/lapack/lawnspdf/lawn03.pdf",
 paper = "Demm90.pdf",
abstract =
"Computing the singular values of a bidiagonal matrix is the final
phase of the standard algorithm for the singular value decomposition
@@ 2695,8 +2883,8 @@ when shown in factored form.
for bidiagonal matrices may compute small singular values with no
relative accuracty at all. Numerical experiments show that the new
algorithm is comparable in speed to the standard algorithm, and
 frequently faster."

+ frequently faster.",
+ paper = "Demm90.pdf"
}
\end{chunk}
@@ 2712,7 +2900,6 @@ when shown in factored form.
number = "4",
pages = "12041245",
url = "http://www.netlib.org/lapack/lawnspdf/lawn15.pdf",
 paper = "Demm92.pdf",
abstract =
"We show that Jacobi's method (with a proper stopping criterion)
computes small eigenvalues of symmetric positive definite matrices
@@ 2728,7 +2915,8 @@ when shown in factored form.
Jacobi (modulo factors of dimensionality). We also show the
eigenvectors are computed more accurately by Jacobi than previously
thought possible. We prove similar results for using onesided Jacobi
 for the singular value decomposition of a general matrix."
+ for the singular value decomposition of a general matrix.",
+ paper = "Demm92.pdf"
}
\end{chunk}
@@ 2752,7 +2940,6 @@ when shown in factored form.
computational modifications are given and a comparison with the
wellknown GolubReinsch algorithm is made. Comparative experiments on
a CYBER 205 are reported."

}
\end{chunk}
@@ 2785,8 +2972,8 @@ when shown in factored form.
in this paper can be implemented as a reliable and highly accurate
procedure for computing the SVD of general real matrices whenever the
exact singular values do not exceed the underflow or overflow limits."

}
+
\end{chunk}
\index{Drmac, Zlatko}
@@ 2802,7 +2989,6 @@ when shown in factored form.
pages = "13221342",
comment = "LAPACK Working note 169",
url = "http://www.netlib.org/lapack/lawnspdf/lawn169.pdf",
 paper = "Drma08a.pdf",
abstract =
"This paper is the result of contrived efforts to break the barrier
between numerical accuracy and run time efficiency in computing the
@@ 2820,12 +3006,12 @@ when shown in factored form.
properties, and it outperforms not only the best implementations of
the onesided Jacobi algorithm but also the QR algorithm. Moreoever,
it seems that the potential of the new approach is yet to be fully
 exploited."
+ exploited.",
+ paper = "Drma08a.pdf"
}
\end{chunk}

\index{Drmac, Zlatko}
\index{Veselic, Kresimir}
\begin{chunk}{axiom.bib}
@@ 2839,7 +3025,6 @@ when shown in factored form.
pages = "13431362",
comment = "LAPACK Working note 170",
url = "http://www.netlib.org/lapack/lawnspdf/lawn170.pdf",
 paper = "Drma08b.pdf",
abstract =
"This paper presents new implementation of onesided Jacobi SVD for
triangular matrices and its use as the core routine in a new
@@ 2854,7 +3039,8 @@ when shown in factored form.
bidiagonalization based methods. The paper also discusses underflow
issues in floating point implementation, and shows how to use
perturbation theory to fix the imperfectness of machine arithmetic on
 some systems."
+ some systems.",
+ paper = "Drma08b.pdf"
}
\end{chunk}
@@ 2873,7 +3059,6 @@ when shown in factored form.
pages = "128",
comment = "LAPACK Working note 176",
url = "http://www.netlib.org/lapack/lawnspdf/lawn176.pdf",
 paper = "Drma08c.pdf",
abstract =
"This note reports an unexpected and rather erratic behavior of the
LAPACK software implementation of the QR factorization with
@@ 2882,13 +3067,12 @@ when shown in factored form.
catastrophically fail to produce triangular factor with the structure
characteristic to the BusingerGolub pivot strategy. The failure of
current {\sl state of the art} software, and a proposed alternative
 implementations are analyzed in detail."
+ implementations are analyzed in detail.",
+ paper = "Drma08c.pdf"
}
\end{chunk}


\index{Dhillon, Inderjit Singh}
\begin{chunk}{axiom.bib}
@phdthesis{Dhil97,
@@ 2898,7 +3082,6 @@ when shown in factored form.
school = "University of California, Berkeley",
year = "1997",
url = "http://www.eecs.berkeley.edu/Pubs/TechRpts/1997/CSD97971.pdf",
 paper = "Dhil97.pdf",
abstract =
"Computing the eigenvalues and orthogonal eigenvectors of an $n\times n$
symmetric tridiagonal matrix is an important task that arises while
@@ 2940,7 +3123,8 @@ when shown in factored form.
the modeling of a biphenyl molecule our method is about 10 times
faster than LAPACK's inverse iteration on a serial IBM RS/6000
processor and nearly 100 times faster on a 128 processor IBM SP2
 parallel machine."
+ parallel machine.",
+ paper = "Dhil97.pdf"
}
\end{chunk}
@@ 2958,7 +3142,6 @@ when shown in factored form.
pages = "128",
year = "2004",
month = "August",
 paper = "Dhil04a.pdf",
abstract =
"In this paper we present an $O(nk)$ procedure, Algorithm $MR^3$, for
computing $k$ eigenvectors of an $n\times n$ symmetric tridiagonal
@@ 2972,7 +3155,8 @@ when shown in factored form.
{\sl representation tree}. We present the tree and use it to show that if
each representation satisfies three prescribed conditions then the
computed eigenvectors are orthogonal to working accuracy and have
 small residual norms with respect to the original matrix $T$."
+ small residual norms with respect to the original matrix $T$.",
+ paper = "Dhil04a.pdf"
}
\end{chunk}
@@ 2986,7 +3170,6 @@ when shown in factored form.
journal = "SIAM Journal on Matrix Analysis and Applications",
volume = "25",
year = "2004",
 paper = "Dhil04.pdf",
abstract =
"Let $LDL^t$ be the triangular factorization of a real symmetric
$n\times n$ tridiagonal matrix so that $L$ is a unit lower bidiagonal
@@ 3006,7 +3189,8 @@ when shown in factored form.
GramSchmidt process.
The contents of this paper provide a highlevel description and
 theoretical justification for LAPACK (version 3.0) subroutine DLAR1V."
+ theoretical justification for LAPACK (version 3.0) subroutine DLAR1V.",
+ paper = "Dhil04.pdf"
}
\end{chunk}
@@ 3057,9 +3241,7 @@ when shown in factored form.
author = "Fateman, Richard J.",
title = "Interval Arithmetic, Extended Numbers and Computer Algebra Systems",
year = "2013",
 paper = "Fate13.pdf",
url = "http://www.cs.berkeley.edu/~fateman/papers/interval.pdf",
 keywords = "axiomref",
abstract =
"Many ambitious computer algebra systems were initially designed in a
flush of enthusiasm, with the goal of automating any symbolic
@@ 3085,8 +3267,9 @@ when shown in factored form.
only the most fundamental builtin concepts; from these one can build
many variants of specific CAS features. This approach is appealing but
can fail to accommodate extensions that violate some mathematical
 tenets in the cause of practicality."

+ tenets in the cause of practicality.",
+ paper = "Fate13.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 3101,7 +3284,6 @@ when shown in factored form.
institution = "University of California, Berkeley",
type = "Technical Report",
number = "PAM554",
 paper = "Fern92.pdf",
url = "http://www.dtic.mil/dtic/tr/fulltext/u2/a256582.pdf",
abstract =
"We have discovered a new implementaiton of the qd algorithm that has
@@ 3117,7 +3299,8 @@ when shown in factored form.
absolute accuracy with little or no degradation in efficiency when
compared with the LINPACK code. Our algorithm obtains maximal relative
accuracy for all the singluar values and runs at least four times
 faster than the LINPACK code."
+ faster than the LINPACK code.",
+ paper = "Fern92.pdf"
}
\end{chunk}
@@ 3160,7 +3343,6 @@ when shown in factored form.
number = "1",
year = "1986",
month = "January",
 paper = "High86.pdf",
abstract =
"Let $A$ be a tridiagonal matrix of order $n$. We show that it is
possible to compute $A^{1}_{\infty}$ and hence
@@ 3175,7 +3357,8 @@ when shown in factored form.
with the solution of a linear system $Ax=b$. In particular we describe
some simple modifications to the LINPACK routine SPTSL which enable
this routine to compute ${\rm cond}_1(A)$, efficiently, in addtion to
 solving $Ax=b$."
+ solving $Ax=b$.",
+ paper = "High86.pdf"
}
\end{chunk}
@@ 3245,7 +3428,6 @@ when shown in factored form.
year = "1993",
month = "December",
url = "http://www.netlib.org/lapack/lawnspdf/lawn75.pdf",
 paper = "Kags93.pdf",
comment = "LAPACK Working Note 75",
abstract =
"Level 3 algorithms for solving the generalized Sylvester equation
@@ 3265,8 +3447,8 @@ when shown in factored form.
algorithms for solving generalized Sylvester equations, and for
computing error bounds and Difestimators are presented. Computational
experiments that illustrate the accuracy, efficiency and reliability
 of our software are also described."

+ of our software are also described.",
+ paper = "Kags93.pdf"
}
\end{chunk}
@@ 3282,7 +3464,6 @@ when shown in factored form.
year = "1994",
month = "April",
url = "http://www.netlib.org/lapack/lawns/lawn87.ps",
 paper = "Kags94.pdf",
abstract =
"Theory, algorithms and LAPACK style software for computing a pair of
deflating subspaces with specified eigenvalues of a regular matrix
@@ 3312,7 +3493,8 @@ when shown in factored form.
for reordering eigenvalues, computing (left and right) deflating
subspaces with specified eigenvalues and condition number estimation
are presented. Computational experiments that illustrate the accuracy,
 efficiency and reliability of our software are also described."
+ efficiency and reliability of our software are also described.",
+ paper = "Kags94.pdf"
}
\end{chunk}
@@ 3361,7 +3543,6 @@ when shown in factored form.
institution = "Stanford University",
type = "Technical Report",
number = "CS41",
 paper = "Kaha66.pdf",
abstract =
"Having established tight bounds for the quotient of two different
lubnorms of the same tridiagonal matrix J, the author observes that
@@ 3372,7 +3553,8 @@ when shown in factored form.
using rounded floating point binary arithmetic, the biggest eigenvalue
of J can be computed easily to within 2.5 units in its last place, and
the smaller eigenvalues will suffer absolute errors which are no
 larger. These results are somewhat stronger than had been known before."
+ larger. These results are somewhat stronger than had been known before.",
+ paper = "Kaha66.pdf"
}
\end{chunk}
@@ 3383,7 +3565,6 @@ when shown in factored form.
author = "Kelsey, Tom",
title = "Exact Numerical Computation via Symbolic Computation",
url = "http://tom.host.cs.standrews.ac.uk/pub/ccapaper.pdf",
 paper = "Kel00.pdf",
abstract = "
We provide a method for converting any symbolic algebraic expression
that can be converted into a floating point number into an exact
@@ 3391,7 +3572,8 @@ when shown in factored form.
procedures for the representation of, and arithmetic over, exact real
numbers in the Maple computer algebra system. Exact reals are
represented by potentially infinite lists of binary digits, and
 interpreted as sums of negative powers of the golden ratio."
+ interpreted as sums of negative powers of the golden ratio.",
+ paper = "Kel00.pdf"
}
\end{chunk}
@@ 3406,7 +3588,6 @@ when shown in factored form.
year = "2014",
url = "http://slicot.org/objects/software/reports/SLWN2014_1.pdf",
note = "SLICOT Working Note 20141",
 paper = "Kohl14.pdf",
abstract =
"The solutions of Lyapunov and generalized Lyapunov equations are a
key player in many applications in systems and control theory. Their
@@ 3420,7 +3601,8 @@ when shown in factored form.
acyclic graphs describing the interdependence of single block
computations. Our contribution closes this gap by a transformation of
the aforementioned level2 variants to level3 versions and a
 comparison on a standard multicore machine."
+ comparison on a standard multicore machine.",
+ paper = "Kohl14.pdf"
}
\end{chunk}
@@ 3510,7 +3692,6 @@ when shown in factored form.
pages = "97120",
year = "2004",
month = "January",
 paper = "Livn04.pdf",
abstract =
"We present an interative algorithm (BIN) for scaling all the rows and
columns of a real symmetric matrix to unit 2norm. We study the
@@ 3519,7 +3700,8 @@ when shown in factored form.
matrixvector multiplications to obtain an adequate scaling, and in
many cases significantly reduces the condition number, more than other
scaling algorithms. We present generalizations to complex,
 nonsymmetric and rectangular matrices."
+ nonsymmetric and rectangular matrices.",
+ paper = "Livn04.pdf"
}
\end{chunk}
@@ 3534,13 +3716,13 @@ when shown in factored form.
year = "1972",
pages = "949951",
url = "http://www.dtic.mil/dtic/tr/fulltext/u2/727104.pdf",
 paper = "Malc72.pdf",
abstract =
"Two algorithms are presented in the form of Fortran subroutines. Each
subroutine computes the radix and number of digits of the floating
point numbers and whether rounding or chopping is done by the machine
on which it is run. The methods are shown to work on any ``reasonable''
 floatingpoint computer."
+ floatingpoint computer.",
+ paper = "Malc72.pdf"
}
\end{chunk}
@@ 3558,7 +3740,6 @@ when shown in factored form.
number = "5",
year = "2006",
url = "http://www.netlib.org/lapack/lawnspdf/lawn172.pdf",
 paper = "Marq06.pdf",
abstract =
"Bisection is one of the most common methods used to compute the
eigenvalues of symmetric tridiagonal matrices. Bisection relies on the
@@ 3599,7 +3780,8 @@ when shown in factored form.
The new Sturm count algorithms improve the speed of bisection by up to
2x on our test matrices. Furthermore, unlike the traditional
tinypivot substitutions, proper use of IEEE754 features provides a
 careful formulation that imposed no input range restrictions."
+ careful formulation that imposed no input range restrictions.",
+ paper = "Marq06.pdf"
}
\end{chunk}
@@ 3661,7 +3843,6 @@ when shown in factored form.
often, more intelligible results, approximate results guaranteed to
have requested error bounds, and recovery of exact results from
approximate ones."

}
\end{chunk}
@@ 3688,7 +3869,6 @@ when shown in factored form.
year = "2013",
month = "February",
url = "http://arxiv.org/pdf/0707.1838v3.pdf",
 paper = "Sutt13.pdf",
abstract =
"An algorithm is developed to compute the complete CS decomposition
(CSD) of a partitioned unitary matrix. Although the existence of the
@@ 3703,7 +3883,8 @@ when shown in factored form.
bidiagonal block form, as described by Sutton and Edelman. In the
second phase, the blocks are simultaneously diagonalized using
techniques from bidiagonal SVD algorithms of Golub, Kahan, and
 Demmel. The algorithm has a number of desirable numerical features."
+ Demmel. The algorithm has a number of desirable numerical features.",
+ paper = "Sutt13.pdf"
}
\end{chunk}
@@ 3717,7 +3898,7 @@ when shown in factored form.
using scheduled relation",
url =
"http://engineering.jhu.edu/fsag/wpcontent/uploads/sites/23/2013/10/JCP_revised_WebPost.pdf",
 paper = "Yang14.pdf",
+ paper = "Yang14.pdf"
}
\end{chunk}
@@ 3757,7 +3938,6 @@ when shown in factored form.
and Bradford, Russell and Davenport, James H.",
title = "Reasoning about the elementary functions of complex analysis",
url = "http://www.csd.uwo.ca/~watt/pub/reprints/2002amaireasoning.pdf",
 paper = "Corl05.pdf",
abstract = "
There are many problems with the simplification of elementary
functions, particularly over the complex plane. Systems tend to make
@@ 3767,7 +3947,8 @@ when shown in factored form.
though we have not yet reduced the simplification process to a
complete algorithm. The unsolved problems are probably more amenable
to the techniques of artificial intelligence and theorem proving than
 the original problem of complexvariable analysis."
+ the original problem of complexvariable analysis.",
+ paper = "Corl05.pdf"
}
\end{chunk}
@@ 3779,10 +3960,10 @@ when shown in factored form.
author = "Ng, Edward W. and Geller, Murray",
title = "A Table of Integrals of the Error functions",
url = "http://nvlpubs.nist.gov/nistpubs/jres/73B/jresv73Bn1p1_A1b.pdf",
 paper = "Ng68.pdf",
abstract = "
This is a compendium of indefinite and definite integrals of products
 of the Error functions with elementary and transcendental functions."
+ of the Error functions with elementary and transcendental functions.",
+ paper = "Ng68.pdf"
}
\end{chunk}
@@ 3796,10 +3977,10 @@ when shown in factored form.
author = "Geller, Murray and Ng, Edward W.",
title = "A Table of Integrals of the Exponential Integral",
url = "http://nvlpubs.nist.gov/nistpubs/jres/73B/jresv73Bn3p191_A1b.pdf",
 paper = "Gell69.pdf",
abstract = "
This is a compendium of indefinite and definite integrals of products
 of the Exponential Integral with elementary or transcendental functions."
+ of the Exponential Integral with elementary or transcendental functions.",
+ paper = "Gell69.pdf"
}
\end{chunk}
@@ 3815,7 +3996,6 @@ when shown in factored form.
Aberdeen Proving Ground, MD",
type = "Technical Report",
number = "ARLTR1758",
 paper = "Segl98.pdf",
algebra = "\newline\refto{package DFSFUN DoubleFloatSpecialFunctions}",
abstract = "
A fourparameter fit is developed for the class of integrals known as
@@ 3835,7 +4015,8 @@ when shown in factored form.
to smooth the value, slope, and higher derivatives in the transition
region between two piecewise domains. The general methodology employed
to develop this fit is outlined, since it may be used for other
 problems as well."
+ problems as well.",
+ paper = "Segl98.pdf"
}
\end{chunk}
@@ 3852,7 +4033,6 @@ when shown in factored form.
Aberdeen Proving Ground, MD",
year = "1998",
month = "September",
 paper = "Se09.pdf",
abstract = "
This is a writeup detailing the more accurate fits to $E_1(x)$,
relative to those presented in ARLTR1758. My actual fits are to
@@ 3863,7 +4043,8 @@ when shown in factored form.
isn't quite to 32bit floatingpoint accuracy. Nonetheless, the fit
is not a piecewise fit, but rather a single continuous function over
the domain of nonnegative x, which avoids some of the problems
 associated with piecewise domain splicing."
+ associated with piecewise domain splicing.",
+ paper = "Se09.pdf"
}
\end{chunk}
@@ 3881,21 +4062,26 @@ when shown in factored form.
year = "1999",
pages = "5966",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/99/KaMo99.pdf",
 paper = "Kalt99a.pdf",
+ paper = "Kalt99a.pdf"
}
\end{chunk}
\index{Knuth, Donald E.}
\begin{chunk}{ignore}
\bibitem[Knuth 71]{STPGCDKnu71}
+\begin{chunk}{axiom.bib}
+@book{Knut71,
author = "Knuth, Donald",
title = "The Art of Computer Programming Vol. 2 (Seminumerical Algorithms)",
 year = "1971,
 publisher = "AddisonWesley",
+ year = "1971",
+ publisher = "AddisonWesley"
+}
\end{chunk}
+\index{Euclidean algorithm}
+\index{algorithm!Euclidean}
+\index{greatest common divisor}
+\index{gcd over finite field}
\index{Ma, Keju}
\index{von zur Gathen, Joachim}
\begin{chunk}{axiom.bib}
@@ 3908,21 +4094,16 @@ when shown in factored form.
volume = "9",
pages = "429455",
url = "http://www.researchgate.net/publication/220161718_Analysis_of_Euclidean_Algorithms_for_Polynomials_over_Finite_Fields/file/60b7d52b326a1058e4.pdf",
 paper = "Ma90.pdf",
abstract = "
This paper analyzes the Euclidean algorithm and some variants of it
for computing the greatest common divisor of two univariate polynomials
over a finite field. The minimum, maximum, and average number of
arithmetic operations both on polynomials and in the ground field
 are derived."

+ are derived.",
+ paper = "Ma90.pdf"
}
\end{chunk}
\index{Euclidean algorithm}
\index{algorithm!Euclidean}
\index{greatest common divisor}
\index{gcd over finite field}
\index{Naylor, William A.}
\begin{chunk}{ignore}
@@ 3930,7 +4111,6 @@ when shown in factored form.
title = "Polynomial GCD Using Straight Line Program Representation",
PhD. Thesis, University of Bath, 2000
url = "http://www.sci.csd.uwo.ca/~bill/thesis.ps",
 paper = "N00.pdf",
abstract = "
This thesis is concerned with calculating polynomial greatest common
divisors using straight line program representation.
@@ 3960,7 +4140,8 @@ PhD. Thesis, University of Bath, 2000
program approach and possible extensions.
Finally we terminate with a number of appendices discussing side
 subjects encountered during the thesis."
+ subjects encountered during the thesis.",
+ paper = "N00.pdf"
\end{chunk}
@@ 3970,7 +4151,6 @@ PhD. Thesis, University of Bath, 2000
title = "Factoring Polynomials over Finite Fields: Asymptotic Complexity vs Reality*",
Proc. IMACS Symposium, Lille, France, (1993)
url = "http://www.shoup.net/papers/lille.pdf",
 paper = "STPGCDSh93.pdf",
abstract = "
This paper compares the algorithms by Berlekamp, Cantor and
Zassenhaus, and Gathen and Shoup to conclude that (a) if large
@@ 3978,7 +4158,8 @@ Proc. IMACS Symposium, Lille, France, (1993)
multiplication and division, (b) Gathen and Shoup should be used if
the number of irreducible factors of $f$ is small. (c) if nothing is
know about the degrees of the factors then Berlekamp's algorithm
 should be used."
+ should be used.",
+ paper = "STPGCDSh93.pdf"
\end{chunk}
@@ 3992,7 +4173,6 @@ Proc. IMACS Symposium, Lille, France, (1993)
booktitle = "Proc. ISSAC 04",
isbn = "158113827X",
url = "http://www.cecm.sfu.ca/personal/mmonagan/papers/AFGCD.pdf",
 paper = "Hoei04.pdf",
abstract =
"Let $L$ be an algebraic function field in $k \ge 0$ parameters
$t_1,\ldots,t)k$. Let $f_1$, $f_2$ be nonzero polynomials in
@@ 4003,7 +4183,8 @@ Proc. IMACS Symposium, Lille, France, (1993)
algorithm, is a modification of the Moreno Maza and Rioboo algorithm
for computing gcds over triangular sets. The modification reduces
coefficient grownth in $L$ to be linear. We give an empirical
 comparison of the two algorithms using implementations in Maple."
+ comparison of the two algorithms using implementations in Maple.",
+ paper = "Hoei04.pdf"
}
\end{chunk}
@@ 4014,7 +4195,6 @@ Proc. IMACS Symposium, Lille, France, (1993)
title = "An Improved Multivariate Polynomial Factoring Algorithm",
Mathematics of Computation, Vol 32, No 144 Oct 1978, pp12151231
url = "http://www.ams.org/journals/mcom/197832144/S00255718197805682843/S00255718197805682843.pdf",
 paper = "Wang78.pdf",
abstract = "
A new algorithm for factoring multivariate polynomials over the
integers based on an algorithm by Wang and Rothschild is described.
@@ 4026,7 +4206,8 @@ Mathematics of Computation, Vol 32, No 144 Oct 1978, pp12151231
described. Basically it is a linearly convergent variablebyvariable
parallel construction. The improved algorithm is generally faster and
requires less store than the original algorithm. Machine examples with
 comparative timing are included."
+ comparative timing are included.",
+ paper = "Wang78.pdf"
\end{chunk}
@@ 4045,7 +4226,6 @@ Mathematics of Computation, Vol 32, No 144 Oct 1978, pp12151231
\bibitem[Baez 09]{Baez09} Baez, John C.; Stay, Mike
title = "Physics, Topology, Logic and Computation: A Rosetta Stone",
url = "http://arxiv.org/pdf/0903.0340v3.pdf",
 paper = "Baez09.pdf",
abstract = "
In physics, Feynman diagrams are used to reason about quantum
processes. In the 1980s, it became clear that underlying these
@@ 4060,7 +4240,8 @@ Mathematics of Computation, Vol 32, No 144 Oct 1978, pp12151231
topology, logic and computation. In this expository paper, we make
some of these analogies precise using the concept of ``closed
symmetric monodial category''. We assume no prior knowledge of
 category theory, proof theory or computer science."
+ category theory, proof theory or computer science.",
+ paper = "Baez09.pdf"
\end{chunk}
@@ 4073,14 +4254,14 @@ Mathematics of Computation, Vol 32, No 144 Oct 1978, pp12151231
title = "Functional Programming with Bananas, Lenses, Envelopes and
Barbed Wire",
url = "http://eprints.eemcs.utwente.nl/7281/01/dbutwente40501F46.pdf",
 paper = "Meij91.pdf",
abstract = "
We develop a calculus for lazy functional programming based on
recursion operators associated with data type definitions. For these
operators we derive various algebraic laws that are useful in deriving
and manipulating programs. We shall show that all example functions in
Bird and Wadler's ``Introduction to Functional Programming'' can be
 expressed using these operators."
+ expressed using these operators.",
+ paper = "Meij91.pdf"
}
\end{chunk}
@@ 4093,13 +4274,13 @@ Mathematics of Computation, Vol 32, No 144 Oct 1978, pp12151231
year = "2004",
url =
"http://axiomwiki.newsynthesis.org/public/refs/YoussefProspectsForCategoryTheoryInAldor.pdf",
 paper = "Yous04.pdf",
abstract =
"Ways of encorporating category theory constructions and results into
the Aldor language are discussed. The main features of Aldor which
make this possible are identified, examples of categorical
constructions are provided and a suggestion is made for a foundation
 for rigorous results."
+ for rigorous results.",
+ paper = "Yous04.pdf"
}
\end{chunk}
@@ 4115,7 +4296,6 @@ Mathematics of Computation, Vol 32, No 144 Oct 1978, pp12151231
Martin, U.
title = "Automated theorem proving in support of computer algebra:
symbolic definite integration as a case study",
 paper = "Adam99.pdf",
abstract = "
We assess the current state of research in the application of computer
aided formal reasoning to computer algebra, and argue that embedded
@@ 4132,7 +4312,8 @@ Martin, U.
prototype is able to obtain correct answers in cases where computer
algebra systems [CAS] do not. We extend upon Fateman's webbased table
by including parametric limits of integration and queries with side
 conditions."
+ conditions.",
+ paper = "Adam99.pdf"
\end{chunk}
@@ 4153,8 +4334,6 @@ Martin, U.
year = "2001",
location = "Edinburgh, Scotland",
pages = "2742",
 keywords = "axiomref",
 paper = "Adam01.pdf",
abstract =
"We describe an interface between version 6 of the Maple computer
algebra system with the PVS automated theorem prover. The interface is
@@ 4163,7 +4342,9 @@ Martin, U.
of a library of proof strategies for use in real analysis. We
demonstrate examples using the interface and the real analysis
library. These examples provide proofs which are both illustrative and
 applicable to genuine symbolic computation problems."
+ applicable to genuine symbolic computation problems.",
+ paper = "Adam01.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 4177,7 +4358,6 @@ Martin, U.
Computer Algebra",
year = "1998",
url = http://www21.in.tum.de/~ballarin/publications/aisc98.pdf",
 paper = "Ball98.pdf",
abstract =
"The use of computer algebra is usually considered beneficial for
mechanised reasoning in mathematical domains. We present a case study,
@@ 4191,7 +4371,8 @@ Martin, U.
distinction is blurred in most computer algebra systems OUr
experimental interface therefore uses a computer algebra library. It
is based on theorem templates, which provide formal specifications for
 the algorithms."
+ the algorithms.",
+ paper = "Ball98.pdf"
}
\end{chunk}
@@ 4202,7 +4383,6 @@ Martin, U.
author = "Beeson, Michael",
title = "Automatic Generation of EpsilonDelta Proofs of Continuity",
url = "http://www.michaelbeeson.com/research/papers/aisc.pdf",
 paper = "Beesxx.pdf",
abstract =
"As part of a project on automatic generation of proofs involving both
logic and computation, we have automated the production of some proofs
@@ 4215,7 +4395,8 @@ Martin, U.
depend on certain variables. Control mechanisms have been developed
for intermixing logical deduction steps with computational steps and
with inequality reasoning. Problems discussed here as examples involve
 the continuity and uniform continuity of various specific functions."
+ the continuity and uniform continuity of various specific functions.",
+ paper = "Beesxx.pdf"
}
\end{chunk}
@@ 4261,12 +4442,12 @@ Martin, U.
journal = "ASIC 2004, LNAI 3249",
year = "2004",
pages = "171184",
 paper = "Bulo04.pdf",
abstract = "In this paper, we present the formal verification of a
Common Lisp implementation of Buchberger's algorithm for computing
Groebner bases of polynomial ideals. This work is carried out in the
ACL2 system and shows how verified Computer Algebra can be achieved
 in an executable logic."
+ in an executable logic.",
+ paper = "Bulo04.pdf"
}
\end{chunk}
@@ 4284,7 +4465,6 @@ Martin, U.
journal = "Journal of Symbolic Computation",
year = "2010",
pages = "96123",
 paper = "Bulo10.pdf",
abstract = "In this article, we present the formal verification of a
Common Lisp implementation of Buchberger's algorithm or computing
Groebner bases of polynomial ideals. This work is carried out in ACL2,
@@ 4295,7 +4475,8 @@ Martin, U.
directly executable within the ACL2 system or any compliant Common Lisp
system. We provide here snippets o real verified code, discuss the
formalization details in depth, and present quantitative data about
 the proof effort."
+ the proof effort.",
+ paper = "Bulo10.pdf"
}
\end{chunk}
@@ 4322,7 +4503,6 @@ Martin, U.
title = "Towards Integrated Systems for Symbolic Algebra and Formal
Constructive Mathematics",
url = "http://www.nuprl.org/documents/Constable/towardsintegrated.pdf",
 paper = "Cons98.pdf",
year = "1998",
abstract =
"The purpose of this paper is to report on our efforts to give e a
@@ 4330,7 +4510,8 @@ Martin, U.
(CAS). In particular, we look at the concepts used in the so called
3rd generation algebra systems, such as Axiom[4] and Weyl[9]. It is
our claim that the Nuprl proof development system is especially well
 suited to support this kind of mathematics."
+ suited to support this kind of mathematics.",
+ paper = "Cons98.pdf"
}
\end{chunk}
@@ 4346,8 +4527,6 @@ Martin, U.
title = "A Constructive Algebraic Hierarchy in Coq",
year = "2002",
journal = "Journal of Symbolic Computation",
 paper = "Geuv02.pdf",
 keywords = "axiomref",
abstract =
"We describe a framework of algebraic structures in the proof assistant
Coq. We have developed this framework as part of the FTA project in
@@ 4370,8 +4549,9 @@ Martin, U.
example, to use the structure $\mathcal{A} := \langle A, f, a \rangle$
as a synonym or the carrier set $A$, as is often done in mathematical
practice. Apart rom the inheritance and reuse of properties, the
 algebraic hierarchy has proven very useful for reusing notations."

+ algebraic hierarchy has proven very useful for reusing notations.",
+ paper = "Geuv02.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 4389,8 +4569,6 @@ Martin, U.
pages = "539567",
year = "2005",
url = "http://www.sciencedirect.com/science/article/pii/S0747717105000295",
 paper = "Gott05.pdf",
 keywords = "axiomref",
abstract =
"We present hidden verification as a means to make the power of
computational logic available to users of computer algebra systems
@@ 4402,7 +4580,9 @@ Martin, U.
able to support the analysis of differential equations in Maple by
direct calls to PVS for: result refinement and verification, discharge
of verification conditions, harnesses to ensure more reliable
 differential equation solvers, and verifiable lookup tables."
+ differential equation solvers, and verifiable lookup tables.",
+ paper = "Gott05.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 4416,8 +4596,6 @@ Martin, U.
school = "Cornell University",
year = "1995",
month = "1",
 paper = "Jack95.pdf",
 keyword = "axiomref",
abstract = "
This thesis describes substantial enhancements that were made to the
software tools in the Nuprl system that are used to interactively
@@ 4459,7 +4637,9 @@ Martin, U.
This work was all done in Nuprl's constructive type theory. The thesis
discusses the appropriateness of this foundation, and the extent to
 which the work relied on it."
+ which the work relied on it.",
+ paper = "Jack95.pdf",
+ keyword = "axiomref"
}
\end{chunk}
@@ 4472,12 +4652,12 @@ Martin, U.
title = "A Precise Description of the ACL2 Logic",
year = "1998",
url = "www.cs.utexas.edu/users/moore/publications/km97a.pdf",
 paper = "km97a.pdf",
abstract = "The ACL2 logic is a firstorder, essentially quantifierfree
logic of total recursive functions providing mathematical induction
and several extension principles, including symbol package definition
and recursive function definition. In this document we describe the
 logic more precisely."
+ logic more precisely.",
+ paper = "km97a.pdf"
}
\end{chunk}
@@ 4493,7 +4673,6 @@ Martin, U.
title = "Coq: The world's best macro assembler?",
year = "2013",
url = "http://research.microsoft.com/enus/um/people/nick/coqasm.pdf",
 paper = "Kenn13.pdf",
abstract =
"We describe a Coq formalization of a subset of the x86
architecture. One emphasis of the model is brevity: using dependent
@@ 4509,13 +4688,12 @@ Martin, U.
local variables and procedures with parameters. Assembly code can be
assembled within Coq, producing a sequence of hex bytes. The assembler
enjoys a correctness theorem relating machine code in memory to a
 separationlogic formula suitable for program verification."

+ separationlogic formula suitable for program verification.",
+ paper = "Kenn13.pdf"
}
\end{chunk}

\index{Krebbers, Robbert Jan}
\begin{chunk}{axiom.bib}
@phdthesis{Kreb15,
@@ 4525,7 +4703,6 @@ Martin, U.
year = "2015",
file = "Kreb15.pdf",
url = "http://robbertkrebbers.nl/thesis.html"

}
\end{chunk}
@@ 4574,8 +4751,6 @@ Martin, U.
year = "1998",
url =
"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.7.1457&rep=rep1&type=ps",
 paper = "Poll98.pdf",
 keywords = "axiomref",
abstract = "
This paper examines the proposal of using the type system of Axiom to
represent a logic, and thus to use the constructions of Axiom to
@@ 4598,7 +4773,9 @@ Martin, U.
Dependent product type (x:A,B(x)) Existential quantifier
Empty type Exit Contradictory proposition
One element type Triv True proposition
 \end{verbatim}"
+ \end{verbatim}",
+ paper = "Poll98.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 4610,8 +4787,6 @@ Martin, U.
author = "Poll, Erik and Thompson, Simon",
title = "Integrating Computer Algebra and Reasoning through the Type
System of Aldor",
 paper = "P0ll00.pdf",
 keywords = "axiomref",
year = "2000",
abstract =
"A number of combinations of reasoning and computer algebra systems
@@ 4622,7 +4797,9 @@ Martin, U.
system to model a logic, under the CurryHoward isomorphism. We give
a number of example applications of the logic we construct and explain
a prototype implementation of a modified typechecking system written
 in Haskell."
+ in Haskell.",
+ paper = "P0ll00.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 4655,8 +4832,6 @@ Martin, U.
volume = "29",
number = "34",
pages = "337363",
 keywords = "axiomref",
 paper = "Prev02.pdf",
abstract =
"In this paper, we present the FOC language, dedicated to the
development of certified computer algebra libraries (that is sets of
@@ 4665,7 +4840,9 @@ Martin, U.
of our language, we describe the static analyses, which reject
inconsistent programs. We then show how we translate FOC definitions
into OCAML and COQ, our target languages for the computational part
 and the proof checking, respectively."
+ and the proof checking, respectively.",
+ paper = "Prev02.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 4692,12 +4869,12 @@ Martin, U.
volume = "4130",
year = "2006",
pages = "438452",
 paper = "Mahb06.pdf",
abstract = "
We describe here a formal proof in the Coq system of the structure
theorem for subresultants which allows to prove formally the
correctness of our implementation of the subresultants algorithm.
 Up to our knowledge it is the first mechanized proof of this result."
+ Up to our knowledge it is the first mechanized proof of this result.",
+ paper = "Mahb06.pdf"
}
\end{chunk}
@@ 4788,7 +4965,6 @@ Martin, U.
linear narrative, plus a number of appendices covering additional
topics. All the core chapters are suitable for both upperlevel
undergraduate and graduate students."

}
\end{chunk}
@@ 4804,7 +4980,6 @@ Martin, U.
url = "http://arxiv.org/pdf/1507.04817v2.pdf",
year = "2016",
month = "February",
 paper = "Nguy16.pdf",
abstract =
"We present a new approach to automated reasoning about higherorder
programs by endowing symbolic execution with a notion of higherorder,
@@ 4845,7 +5020,8 @@ Martin, U.
tools  including type systems, flow analyzers, and model checkers 
on their own benchmarks. We have built a tool which analyzes programs
written in Racket, and report on its effectiveness in verifying and
 refuting contracts."
+ refuting contracts.",
+ paper = "Nguy16.pdf"
}
\end{chunk}
@@ 4863,9 +5039,7 @@ Martin, U.
number = "12",
pages = "143169",
year = "2001",
 keywords = "axiomref",
url = "https://inf.ug.edu.pl/~schwarzw/papers/jsc01.pdf",
 paper = "Rudn01.pdf",
abstract =
"We report on the development of algebra in the Mizar system. This
includes the construction of formal multivariate power series and
@@ 4877,7 +5051,9 @@ Martin, U.
number of such revisions. It seems that revising past developments
with an intent to generalize them is a necessity when building a
database of formalized mathematics. This poses a question: how much
 generalization is best?"
+ generalization is best?",
+ paper = "Rudn01.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 4889,8 +5065,6 @@ Martin, U.
title = "MIZAR verification of generic algebraic algorithms",
school = "University of Tubingen",
year = "1997",
 paper = "Schw97.pdf",
 keywords = "axiomref",
abstract =
"Although generic programming founds more and more attention –
nowadays generic programming languages as well as generic libraries
@@ 4914,7 +5088,9 @@ Martin, U.
To build a verification system using the MIZAR theorem prover, we also
implemented a generator which almost automatically computes for a
given algorithm a set of theorems that imply the correctness of this
 algorithm."
+ algorithm.",
+ paper = "Schw97.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 4928,11 +5104,11 @@ Martin, U.
volume = "26",
year = "2001",
pages = "107137",
 paper = "Ther01.pdf",
abstract = "We present an implementation of Buchberger's algorithm that
has been proved correct within the proof assistant Coq. The
implementation contains the basic algorithm plus two standard
 optimizations."
+ optimizations.",
+ paper = "Ther01.pdf"
}
\end{chunk}
@@ 4945,9 +5121,8 @@ Martin, U.
volume = "211",
year = "1999",
pages = "232252",
 paper = "Troe99.pdf",
abstract =
 {My field is mathematical logic, with a special interest in
+ "My field is mathematical logic, with a special interest in
constructivism, and I would not dare to call myself a computer
scientist. But some computer scientists regard my work as a
contribution to their field; and in this text I shall try to explain
@@ 4955,14 +5130,14 @@ Martin, U.
I want to describe how two interrelated ideas, connected with the
constructivistic trend in the foundations of mathematics, developed
 within mathematical logic and ultimatelyh diffused into computer
+ within mathematical logic and ultimately diffused into computer
science.
It will be seen that this development has not been a quite
straightforward one. In the history of ideas it often looks as if a
certain idea has to be discovered several times, by different people,
 before it really enters inthe the "consciousness" of science}

+ before it really enters inthe the ``consciousness'' of science",
+ paper = "Troe99.pdf"
}
\end{chunk}
@@ 4980,8 +5155,6 @@ Martin, U.
pages = "120",
year = "1999",
url = "http://www.cl.cam.ac.uk/~lp15/papers/Isabelle/coding.pdf",
 paper = "Ball99.pdf",
 keywords = "axiomref",
abstract = "
The use of computer algebra is usually considered beneficial for
mechanised reasoning in mathematical domains. We present a case study,
@@ 5000,7 +5173,9 @@ Martin, U.
We give details of the interface, the use of the computer algebra
system on the tacticlevel of Isabelle and its integration into proof
 procedures."
+ procedures.",
+ paper = "Ball99.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 5034,8 +5209,6 @@ Martin, U.
title = "Polymorphic Data Types, Objects, Modules and Functors,:
is it too much?",
url = "ftp://ftp.lip6.fr/lip6/reports/2000/lip6.2000.014.ps.gz",
 paper = "Boul00.pdf",
 keywords = "axiomref",
abstract = "
Abstraction is a powerful tool for developers and it is offered by
numerous features such as polymorphism, classes, modules, and
@@ 5048,7 +5221,9 @@ Martin, U.
specification. Then we show how to combine classes and modules to
produce code having very strong typing properties. Currently, this
library is made of one hundred units of functional code and behaves
 faster than analogous ones such as Axiom."
+ faster than analogous ones such as Axiom.",
+ paper = "Boul00.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 5068,8 +5243,6 @@ Martin, U.
publisher = "Elsevier",
location = "Trento, Italy",
pages = "1112",
 keywords = "axiomref",
 paper = "Boul99.pdf",
abstract =
"The FOC project aims at supporting, within a coherent software system,
the entire process of mathematical computation, starting with proved
@@ 5086,7 +5259,9 @@ Martin, U.
and how our concern for proving properties of programs has led us to
certain implementation choices in Ocaml. This way, the sources express
exactly the mathematical dependencies between different structures.
 This may ease the achievement of proofs."
+ This may ease the achievement of proofs.",
+ paper = "Boul99.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 5096,12 +5271,12 @@ Martin, U.
\bibitem[Daly 10]{Daly10} Daly, Timothy
title = "Intel Instruction Semantics Generator",
url = "http://daly.axiomdeveloper.org/TimothyDaly_files/publications/sei/intel/intel.pdf",
 paper = "Daly10.pdf",
abstract = "
Given an Intel x86 binary, extract the semantics of the instruction
stream as Conditional Concurrent Assignments (CCAs). These CCAs
represent the semantics of each individual instruction. They can be
 composed to represent higher level semantics."
+ composed to represent higher level semantics.",
+ paper = "Daly10.pdf"
\end{chunk}
@@ 5118,8 +5293,6 @@ Martin, U.
series = "POPL '06",
year = "2006",
location = "Charleston, South Carolina",
 keywords = "axiomref",
 paper = "Dani06.pdf",
abstract =
"Functional programmers often reason about programs as if they were
written in a total language, expecting the results to carry over to
@@ 5137,7 +5310,9 @@ Martin, U.
total language, then they have related semantics in the partial
language. It is also shown that the PER gives rise to a bicartesian
closed category which can be used to reason about values in the domain
 of the relation."
+ of the relation.",
+ paper = "Dani06.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 5152,7 +5327,6 @@ England, Matthew; Wilson, David
title = "Program Verification in the presence of complex numbers,
functions with branch cuts etc.",
url = "http://arxiv.org/pdf/1212.5417.pdf",
 paper = "Davenp12.pdf",
abstract = "
In considering the reliability of numerical programs, it is normal to
``limit our study to the semantics dealing with numerical precision''.
@@ 5171,7 +5345,8 @@ England, Matthew; Wilson, David
of being solved, and are {\sl practically} close to being solved, but
not yet solved, in several realworld examples. However, there is
still a long way to go before implementations match the theoretical
 possibilities."
+ possibilities.",
+ paper = "Davenp12.pdf"
\end{chunk}
@@ 5181,7 +5356,6 @@ England, Matthew; Wilson, David
\bibitem[Dolzmann 97]{Dolz97} Dolzmann, Andreas; Sturm, Thomas
title = "Guarded Expressions in Practice",
url = "http://redlog.dolzmann.de/papers/pdf/MIP9702.pdf",
 paper = "Dolz97.pdf",
abstract = "
Computer algebra systems typically drop some degenerate cases when
evaluating expressions, e.g. $x/x$ becomes 1 dropping the case
@@ 5195,7 +5369,8 @@ England, Matthew; Wilson, David
elimination. Our approach allows to simplify the expressions on the
basis of simplification knowledge on the logical side. The method
described in this paper is implemented in the REDUCE package GUARDIAN,
 which is freely available on the WWW."
+ which is freely available on the WWW.",
+ paper = "Dolz97.pdf"
\end{chunk}
@@ 5207,8 +5382,6 @@ England, Matthew; Wilson, David
title = "Retargeting OpenAxiom to Poly/ML: Towards an Integrated Proof Assistants and Computer Algebra System Framework",
Calculemus (2011) Springer
url = "http://paradise.caltech.edu/~yli/paper/oapolyml.pdf",
 keywords = "axiomref",
 paper = "DR11.pdf",
abstract = "
This paper presents an ongoing effort to integrate the Axiom family of
computer algebra systems with Poly/MLbased proof assistants in the
@@ 5217,7 +5390,9 @@ Calculemus (2011) Springer
assistants, and also to bring the power of mechanized formal
verification to a family of strongly typed computer algebra systems at
a modest cost. Our approach is based on retargeting the code generator
 of the OpenAxiom compiler to the Poly/ML abstract machine."
+ of the OpenAxiom compiler to the Poly/ML abstract machine.",
+ paper = "DR11.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 5225,7 +5400,6 @@ Calculemus (2011) Springer
\begin{chunk}{ignore}
\bibitem[Dunstan 00a]{Dun00a} Dunstan, Martin N.
title = "Adding Larch/Aldor Specifications to Aldor",
 paper = "Dunxx.pdf",
abstract = "
We describe a proposal to add Larchstyle annotations to the Aldor
programming language, based on our PhD research. The annotations
@@ 5233,7 +5407,8 @@ Calculemus (2011) Springer
of purposes ranging from compiler optimizations to verification
condition (VC) generation. In this report we highlight the options
available and describe the changes which would need to be made to
 the compiler to make use of this technology."
+ the compiler to make use of this technology.",
+ paper = "Dunxx.pdf"
\end{chunk}
@@ 5252,13 +5427,13 @@ Calculemus (2011) Springer
location = "Rostock, Germany",
pages = "8087",
url = "http://www.cs.standrews.ac.uk/~tom/pub/issac98.pdf",
 paper = "Duns98.pdf",
 keywords = "axiomref",
abstract =
"Demonstrates the use of formal methods tools to provide a semantics
for the type hierarchy of the Axiom computer algebra system, and a
methodology for Aldor program analysis and verification. There are
 examples of abstract specifications of Axiom primitives."
+ examples of abstract specifications of Axiom primitives.",
+ paper = "Duns98.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 5270,8 +5445,6 @@ Calculemus (2011) Springer
title = "Larch/Aldor  A Larch BISL for AXIOM and Aldor",
school = "University of St. Andrews",
year = "1999",
 paper = "Duns99a.pdf",
 keywords = "axiomref",
abstract = "
In this thesis we investigate the use of lightweight formal methods
and verification conditions (VCs) to help improve the reliability of
@@ 5282,7 +5455,9 @@ Calculemus (2011) Springer
language in its own right. We describe our idea of lightweight formal
methods, present a design for a lightweight verification condition
generator and review our implementation of a prototype verification
 condition generator for Larch/Aldor."
+ condition generator for Larch/Aldor.",
+ paper = "Duns99a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 5302,14 +5477,14 @@ Calculemus (2011) Springer
year = "1999",
pages = "17581777",
url = "http://tom.host.cs.standrews.ac.uk/pub/fm99.ps",
 paper = "Duns99.pdf",
 keywords = "axiomref",
abstract =
"We demonstrate the use of formal methods tools to provide a semantics
for the type hierarchy of the AXIOM computer algebra system, and a
methodology for Aldor program analysis and verification. We give a
case study of abstract specifications of AXIOM primitives, and provide
 an interface between these abstractions and Aldor code."
+ an interface between these abstractions and Aldor code.",
+ paper = "Duns99.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 5322,14 +5497,14 @@ Calculemus (2011) Springer
author = "Hardin, David S. and McClurg, Jedidiah R. and Davis, Jennifer A.",
title = "Creating Formally Verified Components for Layered Assurance with an LLVM to ACL2 Translator",
url = "http://www.jrmcclurg.com/papers/law_2013_paper.pdf",
 paper = "Hard13.pdf",
abstract = "
This paper describes an effort to create a library of formally
verified software component models from code that have been compiled
using the LowLevel Virtual Machine (LLVM) intermediate form. The idea
is to build a translator from LLVM to the applicative subset of Common
Lisp accepted by the ACL2 theorem prover. They perform verification of
 the component model using ACL2's automated reasoning capabilities."
+ the component model using ACL2's automated reasoning capabilities.",
+ paper = "Hard13.pdf"
}
\end{chunk}
@@ 5344,7 +5519,6 @@ Calculemus (2011) Springer
McClurg, Jedidiah R.",
title = "Development of a Translator from LLVM to ACL2",
url = "http://arxiv.org/pdf/1406.1566",
 paper = "Hard14.pdf",
abstract = "
In our current work a library of formally verified software components
is to be created, and assembled, using the LowLevel Virtual Machine
@@ 5363,7 +5537,8 @@ Calculemus (2011) Springer
computer. In this paper we overview the translation process and
illustrate the translator's capabilities by way of a concrete example,
including both a functional correctness theorem as well as a
 validation test for that example."
+ validation test for that example.",
+ paper = "Hard14.pdf"
}
\end{chunk}
@@ 5377,7 +5552,7 @@ Calculemus (2011) Springer
url = "http://research.microsoft.com/enus/um/people/lamport/tla/book020808.pdf",
publisher = "AddisonWesley",
isbn = "032114306X",
 paper = "Lamp02.pdf",
+ paper = "Lamp02.pdf"
}
\end{chunk}
@@ 5390,7 +5565,6 @@ Calculemus (2011) Springer
year = "2013",
url = "http://research.microsoft.com/enus/um/people/lamport/tla/errata1.pdf",
publisher = "Microsoft",
 paper = "Lamp13.pdf",
abstract = "
These are all the errors and omissions to the first printing (July
2002) of the book {\sl Specifying Systems} reported as of 29 October
@@ 5400,7 +5574,8 @@ Calculemus (2011) Springer
but all other lines are. Please report any additional errors to the
author, whose email address is posted on {\tt http://lamport.org}. The
first person to report an error will be acknowledged in any revised
 edition."
+ edition.",
+ paper = "Lamp13.pdf"
}
\end{chunk}
@@ 5413,12 +5588,12 @@ Calculemus (2011) Springer
year = "2014",
url = "http://research.microsoft.com/enus/um/people/lamport/pubs/paper.pdf",
publisher = "Microsoft",
 paper = "Lamp14.pdf",
abstract = "
A method of writing proofs is described that makes it harder to prove
things that are not true. The method, based on hierarchical
structuring, is simple and practical. The author's twenty years of
 experience writing such proofs is discussed."
+ experience writing such proofs is discussed.",
+ paper = "Lamp14.pdf"
}
\end{chunk}
@@ 5444,7 +5619,6 @@ Calculemus (2011) Springer
title = "Investigating some Embedded Verification Techniques for
Computer Algebra Systems",
url = "http://www.risc.jku.at/conferences/Theorema/papers/shand.ps.gz",
 paper = "Mart97.ps",
abstract = "
This paper reports some preliminary ideas on a collaborative project
between St. Andrews University in the UK and NAG Ltd. The project aims
@@ 5453,7 +5627,8 @@ Calculemus (2011) Springer
history of attempts to integrate computer algebra systems and
automated theorem provers and discuss possible advantages and
disadvantages of these approaches. We also discuss some possible case
 studies."
+ studies.",
+ paper = "Mart97.ps"
}
\end{chunk}
@@ 5524,11 +5699,11 @@ Munteanu, Bogdan; Brooker, Marc; Deardeuff, Michael
title = "The Type System of Axiom",
year = "1999",
url = "http://www.cs.ru.nl/E.Poll/talks/axiom.pdf",
 paper = "Poll99.pdf",
 keywords = "axiomref",
abstract =
"This is a slide deck from a talk on the correspondence between
 Axiom/Aldor types and Logic."
+ Axiom/Aldor types and Logic.",
+ paper = "Poll99.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 5540,13 +5715,13 @@ Munteanu, Bogdan; Brooker, Marc; Deardeuff, Michael
author = "Poll, Erik and Thompson, Simon",
title = "The Type System of Aldor",
url = "http://www.cs.kent.ac.uk/pubs/1999/874/content.ps",
 paper = "Poll99a.pdf",
 keywords = "axiomref",
abstract =
"This paper gives a formal description of  at least a part of 
the type system of Aldor, the extension language of the Axiom.
In the process of doing this a critique of the design of the system
 emerges."
+ emerges.",
+ paper = "Poll99a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 5573,7 +5748,6 @@ Munteanu, Bogdan; Brooker, Marc; Deardeuff, Michael
O'Donnell, Michael J.",
title = "Exact Real Arithmetic: A Case Study in Higher Order Programming",
url = "http://dev.acm.org/pubs/citations/proceedings/lfp/319838/p162boehm",
 paper = "Boeh86.pdf",
abstract =
"Two methods for implementing {\sl exact} real arithmetic are explored
One method is based on formulating real numbers as functions that map
@@ 5588,7 +5762,8 @@ Munteanu, Bogdan; Brooker, Marc; Deardeuff, Michael
theoretical problems involved m both methods, give algortthms for the
basic arithmetic operations, and give an empirical comparison of the
two techniques. We conclude wtth some general observations about the
 lazy evaluation paradigm and its implementation."
+ lazy evaluation paradigm and its implementation.",
+ paper = "Boeh86.pdf"
}
\end{chunk}
@@ 5598,7 +5773,7 @@ Munteanu, Bogdan; Brooker, Marc; Deardeuff, Michael
\bibitem[Briggs 04]{Bri04} Briggs, Keith
title = "Exact real arithmetic",
url = "http://keithbriggs.info/documents/xrkenttalkpp.pdf",
 paper = "Bri04.pdf",
+ paper = "Bri04.pdf"
\end{chunk}
@@ 5608,7 +5783,6 @@ Munteanu, Bogdan; Brooker, Marc; Deardeuff, Michael
\bibitem[Fateman 94]{Fat94} Fateman, Richard J.; Yan, Tak W.
title = "Computation with the Extended Rational Numbers and an Application to Interval Arithmetic",
url = "http://www.cs.berkeley.edu/~fateman/papers/extrat.pdf",
 paper = "Fat94.pdf",
abstract = "
Programming languages such as Common Lisp, and virtually every
computer algebra system (CAS), support exact arbitraryprecision
@@ 5617,7 +5791,8 @@ Munteanu, Bogdan; Brooker, Marc; Deardeuff, Michael
extended form indicated here. We explain why changes to the usual
rational number system to include infinity and ``notanumber'' may be
useful, especially to support robust interval computation. We describe
 techniques for implementing these changes."
+ techniques for implementing these changes.",
+ paper = "Fat94.pdf"
\end{chunk}
@@ 5627,7 +5802,6 @@ Munteanu, Bogdan; Brooker, Marc; Deardeuff, Michael
author = "Gustafson, John",
title = "A Radical Approach to Computation with Real Numbers",
url = "http://www.johngustafson.net/presentations/Multicore2016JLG.pdf",
 paper = "Gust16.pdf",
ppt = "Gust16.pptx",
abstract =
"If we are willing to give up compatibility with IEEE 754 floats and
@@ 5646,7 +5820,8 @@ Munteanu, Bogdan; Brooker, Marc; Deardeuff, Michael
is quickly solvable with absolute bounds. Also unlike interval
methods, it becomes possible to operate on arbitrary disconnected
subsets of the real number line with the same speed as operating on a
 simple bound."
+ simple bound.",
+ paper = "Gust16.pdf",
}
\end{chunk}
@@ 5686,7 +5861,6 @@ Munteanu, Bogdan; Brooker, Marc; Deardeuff, Michael
\bibitem[Atkinson 09]{Atk09} Atkinson, Kendall; Han, Welmin; Stewear, David
title = "Numerical Solution of Ordinary Differential Equations",
url = "http://homepage.math.uiowa.edu/~atkinson/papers/NAODE_Book.pdf",
 paper = "Atk09.pdf",
abstract = "
This book is an expanded version of supplementary notes that we used
for a course on ordinary differential equations for upperdivision
@@ 5700,7 +5874,8 @@ Munteanu, Bogdan; Brooker, Marc; Deardeuff, Michael
tied closely to theoretical behavior associated with the problem being
solved. For example, the criteria for the stability of a numerical
method is closely connected to the stability of the differential
 equation problem being solved."
+ equation problem being solved.",
+ paper = "Atk09.pdf"
\end{chunk}
@@ 5797,7 +5972,6 @@ in Lecture Notes in Computer Science, Springer ISBN 9783540855200
informal mathematics to fully formalised mathematics be divided into
smaller steps, each of which is a fully developed method in which
human input is minimal."

}
\end{chunk}
@@ 5807,7 +5981,6 @@ in Lecture Notes in Computer Science, Springer ISBN 9783540855200
@misc{Leeuxx,
author = {van Leeuwen, Andr\'e M.A.},
title = "Representation of mathematical object in interactive books",
 paper = "Leeuxx.pdf",
abstract = "
We present a model for the representation of mathematical objects in
structured electronic documents, in a way that allows for interaction
@@ 5821,7 +5994,8 @@ in Lecture Notes in Computer Science, Springer ISBN 9783540855200
application integration, e.g., parallel evaluation of subexpressions
(by different computer algebra systems), or a proof checker using a
computer algebra system to verify an equation involving a symbolic
 computation."
+ computation.",
+ paper = "Leeuxx.pdf"
}
\end{chunk}
@@ 5831,7 +6005,6 @@ in Lecture Notes in Computer Science, Springer ISBN 9783540855200
\bibitem[Soiffer 91]{Soif91} Soiffer, Neil Morrell
title = "The Design of a User Interface for Computer Algebra Systems",
url = "http://www.eecs.berkeley.edu/Pubs/TechRpts/1991/CSD91626.pdf",
 paper = "Soif91.pdf",
abstract = "
This thesis discusses the design and implementation of natural user
interfaces for Computer Algebra Systems. Such an interface must not
@@ 5840,7 +6013,8 @@ in Lecture Notes in Computer Science, Springer ISBN 9783540855200
and entry of expressions in that notation. The user interface should
also assist in understanding of large expressions that are generated
by Computer Algebra Systems and should be able to accommodate new
 notational forms."
+ notational forms.",
+ paper = "Soif91.pdf"
\end{chunk}
@@ 5881,7 +6055,7 @@ in Lecture Notes in Computer Science, Springer ISBN 9783540855200
crossref = "EUROSAM84",
year = "1984",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/84/Ka84_risch.ps.gz",
 paper = "Kalt84.ps",
+ paper = "Kalt84.ps"
}
\end{chunk}
@@ 5895,7 +6069,7 @@ Petkovsek, Marko
title = "On Polynomial Solutions of Linear Operator Equations",
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mb_papers.html",
 paper = "Abra95.pdf",
+ paper = "Abra95.pdf"
\end{chunk}
@@ 5920,7 +6094,6 @@ Petkovsek, Marko
year = "2001",
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mb_papers.html",
 paper = "Abra01.pdf",
algebra =
"\newline\refto{category OREPCAT UnivariateSkewPolynomialCategory}
\newline\refto{category LODOCAT LinearOrdinaryDifferentialOperatorCategory}
@@ 5943,7 +6116,8 @@ Petkovsek, Marko
the degress of the solutions with finite support. As a consequence, we
can boudn and compute the polynomial and rational solutions of very
general linear functional systems such as systems of differential or
 ($q$)difference equations."
+ ($q$)difference equations.",
+ paper = "Abra01.pdf"
}
\end{chunk}
@@ 5958,14 +6132,14 @@ Petkovsek, Marko
number = "46",
pages = "387389",
year = "1996",
 paper = "Bro96b.pdf",
abstract =
"After reviewing the arithmetic of linear ordinary differential
operators, we describe the current status of the factorisation
algorithm, specially with respect to factoring over nonalgebraically
closed constant fields. We also describe recent results from Singer
and Ulmer that reduce determining the differential Galois group of an
 operator to factoring."
+ operator to factoring.",
+ paper = "Bro96b.pdf"
}
\end{chunk}
@@ 5983,7 +6157,6 @@ Petkovsek, Marko
year = "1966",
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mb_papers.html",
 paper = "Bron96a.pdf",
algebra = "\newline\refto{category LORER LeftOreRing}",
abstract =
"Pseudolinear algebra is the study of common properties of linear
@@ 5992,7 +6165,8 @@ Petkovsek, Marko
operators) and describe several recent algorithms on them, which, when
applied in the differential and difference cases, yield algorithms for
uncoupling and solving systems of linear differential and difference
 equations in closed form."
+ equations in closed form.",
+ paper = "Bron96a.pdf"
}
\end{chunk}
@@ 6008,14 +6182,14 @@ Petkovsek, Marko
series = "Progress in Mathematics",
volume = "202",
pages = "105119",
 paper = "Bron01.pdf",
abstract = "
Galois theory has now produced algorithms for solving linear ordinary
differential and difference equations in closed form. In addition,
recent algorithmic advances have made those algorithms effective and
implementable in computer algebra systems. After introducing the
relevant parts of the theory, we describe the latest algorithms for
 solving such equations."
+ solving such equations.",
+ paper = "Bron01.pdf"
}
\end{chunk}
@@ 6046,7 +6220,6 @@ Petkovsek, Marko
title = "On Solutions of Linear Ordinary Differential Equations in their Coefficient Field",
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mb_papers.html",
 paper = "Bro90.pdf",
abstract = "
We describe a rational algorithm for finding the denominator of any
solution of a linear ordinary differential equation in its coefficient
@@ 6055,7 +6228,8 @@ Petkovsek, Marko
rational functions by finitely many algebraic and primitive
adjunctions. This also eliminates one of the computational bottlenecks
in algorithms that either factor or search for Liouvillian solutions
 of such equations with Liouvillian coefficients."
+ of such equations with Liouvillian coefficients.",
+ paper = "Bro90.pdf"
\end{chunk}
@@ 6066,7 +6240,6 @@ Petkovsek, Marko
"$\sum^{IT}$  A stronglytyped embeddable computer algebra library",
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mb_papers.html",
 paper = "Bro96.pdf",
abstract = "
We describe the new computer algebra library $\sum^{IT}$ and its
underlying design. The development of $\sum^{IT}$ is motivated by the
@@ 6076,7 +6249,8 @@ Petkovsek, Marko
the programming language or interactive system they use. As such,
$\sum^{IT}$ is not a computer algebra system per se, but a library (or
substrate) which is designed to be ``plugged'' with minimal efforts
 into different types of client applications."
+ into different types of client applications.",
+ paper = "Bro96.pdf"
\end{chunk}
@@ 6086,7 +6260,6 @@ Petkovsek, Marko
title = "Solving linear ordinary differential equations over $C(x,e^{\int{f(x)dx}})$",
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mb_papers.html",
 paper = "Bro99a.pdf",
abstract = "
We describe a new algorithm for computing the solutions in
\[F=C(x,e^{\int{f(x)dx}})\] of linear ordinary differential equations
@@ 6094,7 +6267,8 @@ Petkovsek, Marko
algorithm avoids the computation of exponential solutions of equations
with coefficients in $C(x)$, as well as the solving of linear
differential systems over $C(x)$. Our method is effective and has been
 implemented."
+ implemented.",
+ paper = "Bro99a.pdf"
\end{chunk}
@@ 6104,7 +6278,6 @@ Petkovsek, Marko
title = "On Solutions of Linear Ordinary Differential Equations in their Coefficient Field",
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mb_papers.html",
 paper = "Bro00.pdf",
abstract = "
We extend the notion of monomial extensions of differential fields,
i.e. simple transcendental extensions in which the polynomials are
@@ 6118,7 +6291,8 @@ Petkovsek, Marko
such equations in their coefficient fields to bounding their
degrees. In the base case, this yields in particular a new algorithm
for computing the rational solutions of $q$difference equations with
 polynomial coefficients."
+ polynomial coefficients.",
+ paper = "Bro00.pdf"
}
\end{chunk}
@@ 6137,7 +6311,6 @@ Petkovsek, Marko
isbn = "1581134843",
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/issac2002.pdf",
 paper = "Bron02.pdf",
url2 = "http://xena.hunter.cuny.edu/ksda/papers/bronstein2.pdf",
paper2 = "Bron02x.pdf",
abstract =
@@ 6153,7 +6326,8 @@ Petkovsek, Marko
special functions of mathematical physics, such as Airy, Bessel,
Kummer and Whittaker functions. It is also able to identify the values
of the parameters entering those special functions, and can be
 generalized to equations of higher order."
+ generalized to equations of higher order.",
+ paper = "Bron02.pdf"
}
\end{chunk}
@@ 6165,7 +6339,6 @@ Petkovsek, Marko
title = "A Reduction for Regular Differential Systems",
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mega2003.pdf",
 paper = "Bro03.pdf",
abstract = "
We propose a definition of regularity of a linear differential system
with coefficients in a monomial extension of a differential field, as
@@ 6174,7 +6347,8 @@ Petkovsek, Marko
into an equivalent one with simple finite poles. We then apply our
iteration to systems satisfied by bases of algebraic function fields,
obtaining algorithms for computing the number of irreducible
 components and the genus of algebraic curves."
+ components and the genus of algebraic curves.",
+ paper = "Bro03.pdf"
\end{chunk}
@@ 6185,13 +6359,13 @@ Petkovsek, Marko
title = "Linear recurrences with polynomial coefficients",
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mb_papers.html",
 paper = "Bro03a.pdf",
abstract = "
We relate sequences generated by recurrences with polynomial
coefficients to interleaving and multiplexing of sequences generated
by recurrences with constant coefficients. In the special case of
finite fields, we show that such sequences are periodic and provide
 linear complexity estimates for all three constructions."
+ linear complexity estimates for all three constructions.",
+ paper = "Bro03a.pdf"
\end{chunk}
@@ 6203,7 +6377,6 @@ Petkovsek, Marko
title = "PicardVessiot Extensions for Linear Functional Systems",
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/issac2005.pdf",
 paper = "Bro05.pdf",
abstract = "
PicardVessiot extensions for ordinary differential and difference
equations are well known and are at the core of the associated Galois
@@ 6211,17 +6384,22 @@ Petkovsek, Marko
PicardVessiot extensions for systems of linear partial functional
equations having finite linear dimension. We then use those extensions
to show that all the solutions of a factor of such a system can be
 completed to solutions of the original system."
+ completed to solutions of the original system.",
+ paper = "Bro05.pdf"
\end{chunk}
\index{Davenport, James H.}
\begin{chunk}{ignore}
+\begin{chunk}{axiom.bib}
\bibitem[Davenport 86]{Dav86} Davenport, J.H.
+@article{Dave86,
+ author = "Davenport, James H.",
title = "The Risch Differential Equation Problem",
year = "1986",
SIAM J. COMPUT. Vol 15, No. 4
 paper = "Dav86.pdf",
+ journal = "SIAM J. COMPUT.",
+ volume = "15",
+ number = "4",
+ comment = "Technical Report 834, Dept. Comp. Sci, Univ. Delaware",
abstract = "
We propose a new algorithm, similar to Hermite's method for the
integration of rational functions, for the resolution of Risch
@@ 6235,7 +6413,9 @@ SIAM J. COMPUT. Vol 15, No. 4
show that solutions of Risch differential equations which arise from
integrating in these fields satisfy the ``natural'' degree constraints
in their main variables, and we conjecture (after Risch and Norman)
 that this is true in all variables."
+ that this is true in all variables.",
+ paper = "Dave86.pdf"
+}
\end{chunk}
@@ 6246,7 +6426,6 @@ SIAM J. COMPUT. Vol 15, No. 4
J. Symbolic Computation V11 No 3 pp251273
year = "1991",
url = "http://www.sciencedirect.com/science/article/pii/S074771710880048X",
 paper = "Sing91.pdf",
abstract = "
Let $L(y)=b$ be a linear differential equation with coefficients in a
differential field $K$. We discuss the problem of deciding if such an
@@ 6256,7 +6435,8 @@ J. Symbolic Computation V11 No 3 pp251273
extension of the field of rational functions We show how one can use
this result to give a procedure to find a basis for the space of
solutions, liouvillian over $K$, of $L(y)=0$ where $K$ is such a field
 and $L(y)$ has coefficients in $K$."
+ and $L(y)$ has coefficients in $K$.",
+ paper = "Sing91.pdf"
\end{chunk}
@@ 6265,7 +6445,7 @@ J. Symbolic Computation V11 No 3 pp251273
\bibitem[Von Mohrenschildt 94]{Mohr94} {von Mohrenschildt}, Martin
title = "Symbolic Solutions of Discontinuous Differential Equations",
url = "http://ecollection.library.ethz.ch/eserv/eth:39463/eth3946301.pdf",
 paper = "Mohr94.pdf",
+ paper = "Mohr94.pdf"
\end{chunk}
@@ 6275,7 +6455,6 @@ J. Symbolic Computation V11 No 3 pp251273
title = "A Normal Form for Function Rings of Piecewise Functions",
J. Symbolic Computation (1998) Vol 26 pp607619
url = "http://www.cas.mcmaster.ca/~mohrens/JSC.pdf",
 paper = "Mohr98.pdf",
abstract = "
Computer algebra systems often have to deal with piecewise continuous
functions. These are, for example, the absolute value function,
@@ 6289,7 +6468,8 @@ J. Symbolic Computation (1998) Vol 26 pp607619
the function ring forms a lattice. Additionally, a method to solve
equalities and inequalities in this function ring is
presented. Finally, we give a ``user interface'' to the algebraic
 representation of the piecewise functions."
+ representation of the piecewise functions.",
+ paper = "Mohr98.pdf"
\end{chunk}
@@ 6299,7 +6479,6 @@ J. Symbolic Computation (1998) Vol 26 pp607619
title = "Quantifier Elimination on Real Closed Fields and Differential Equations",
url =
"http://cg.cs.unibonn.de/personalpages/weber/publications/pdf/WeberA/Weber2006a.pdf",
 paper = "Webe06.pdf",
keywords = "survey",
abstract = "
This paper surveys some recent applications of quantifier elimination
@@ 6312,7 +6491,8 @@ J. Symbolic Computation (1998) Vol 26 pp607619
theoretical interest, but due to recent advances on the algorithmic
side including algorithms for the simplification of quantifierfree
formulae the method has gained practical applications, e.g. in the
 context of computing threshold conditions in epidemic modeling."
+ context of computing threshold conditions in epidemic modeling.",
+ paper = "Webe06.pdf"
\end{chunk}
@@ 6323,7 +6503,6 @@ J. Symbolic Computation (1998) Vol 26 pp607619
J. Symbolic COmputations 36 pp 855889
year = "2003",
url = "http://www.sciencedirect.com/science/article/pii/S0747717103000658",
 paper = "Ulm03.pdf",
abstract = "
The Kovacic algorithm and its improvements give explicit formulae for
the Liouvillian solutions of second order linear differential
@@ 6337,7 +6516,8 @@ J. Symbolic COmputations 36 pp 855889
for the computation of the minimal polynomial for the remaining finite
set of finite groups (or any known finite group) by extracting
ramification information from the character table. Several examples
 have been constructed, illustrating the possibilities and limitations."
+ have been constructed, illustrating the possibilities and limitations.",
+ paper = "Ulm03.pdf"
\end{chunk}
@@ 6348,7 +6528,6 @@ J. Symbolic COmputations 36 pp 855889
\bibitem[Carette 04]{Car04} Carette, Jacques
title = "Understanding Expression Simplification",
url = "http://www.cas.mcmaster.ca/~carette/publications/simplification.pdf",
 paper = "Car04.pdf",
abstract = "
We give the first formal definition of the concept of {\sl
simplification} for general expressions in the context of Computer
@@ 6358,7 +6537,8 @@ J. Symbolic COmputations 36 pp 855889
Algorithmic Information Theory. In particular, we show how this theory
can justify the use of various ``magic constants'' for deciding
between some equivalent representations of an expression, as found in
 implementations of simplification routines."
+ implementations of simplification routines.",
+ paper = "Car04.pdf"
\end{chunk}
@@ 6387,7 +6567,7 @@ J. Symbolic COmputations 36 pp 855889
year = "1984",
url =
"http://www.math.ncsu.edu/~kaltofen/bibliography/84/Ka84_integration.pdf",
 paper = "Kalt84b.pdf",
+ paper = "Kalt84b.pdf"
}
\end{chunk}
@@ 6397,7 +6577,7 @@ J. Symbolic COmputations 36 pp 855889
\bibitem[Adamchik xx]{Adamxx} Adamchik, Victor
title = "Definite Integration",
url = "http://www.cs.cmu.edu/~adamchik/articles/integr/mj.pdf",
 paper = "Adamxx.pdf",
+ paper = "Adamxx.pdf"
\end{chunk}
@@ 6406,12 +6586,12 @@ J. Symbolic COmputations 36 pp 855889
\bibitem[Adamchik 97]{Adam97} Adamchik, Victor
title = "A Class of Logarithmic Integrals",
url = "http://www.cs.cmu.edu/~adamchik/articles/issac/issac97.pdf",
 paper = "Adam97.pdf",
abstract = "
A class of definite integrals involving cyclotomic polynomials and
nested logarithms is considered. The results are given in terms of
derivatives of the Hurwitz Zeta function. Some special cases for which
 such derivatives can be expressed in closed form are also considered."
+ such derivatives can be expressed in closed form are also considered.",
+ paper = "Adam97.pdf"
\end{chunk}
@@ 6421,7 +6601,6 @@ J. Symbolic COmputations 36 pp 855889
title =
"Definite Integration using the Generalized Hypergeometric Functions",
url = "http://dspace.mit.edu/handle/1721.1/16269",
 paper = "Avgo77.pdf",
abstract = "
A design for the definite integration of approximately fifty Special
Functions is described. The Generalized Hypergeometric Functions are
@@ 6434,7 +6613,8 @@ J. Symbolic COmputations 36 pp 855889
The result of an early implementation which involves Laplace
transforms are given and some actual examples with their corresponding
 timing are provided."
+ timing are provided.",
+ paper = "Avgo77.pdf"
\end{chunk}
@@ 6444,14 +6624,14 @@ J. Symbolic COmputations 36 pp 855889
title = "A Dilogarithmic Extension of Liouville's Theorem on Integration in
Finite Terms",
url = "http://www.dtic.mil/dtic/tr/fulltext/u2/a206681.pdf",
 paper = "Bad89.pdf",
abstract = "
The result obtained generalizes Liouville's Theorem by allowing, in
addition to the elementary functions, dilogarithms to appear in the
integral of an elementary function. The basic conclusion is that an
associated function to the dilogarihm, if dilogarithms appear in the
integral, appears linearly, with logarithms appearing in a nonlinear
 way."
+ way.",
+ paper = "Bad89.pdf"
\end{chunk}
@@ 6461,7 +6641,6 @@ J. Symbolic COmputations 36 pp 855889
title = "Integration in Finite Terms with Elementary Functions and
Dilogarithms",
url = "http://dspace.mit.edu/bitstream/handle/1721.1/26864/30757785.pdf",
 paper = "Bad94.pdf",
abstract = "
In this thesis, we report on a new theorem that generalizes
Liouville's theorem on integration in finite terms. The new theorem
@@ 6470,7 +6649,8 @@ J. Symbolic COmputations 36 pp 855889
that characterize all the possible algebraic relations among
dilogarithms of functions that are built up from the rational
functions by taking transcendental exponentials, dilogarithms, and
 logarithms."
+ logarithms.",
+ paper = "Bad94.pdf"
\end{chunk}
@@ 6480,7 +6660,6 @@ J. Symbolic COmputations 36 pp 855889
title = "A Note on Symbolic Integration with Polylogarithms",
year = "2011",
J. Math Vol 8 pp229241 (2011)
 paper = "Bad10.pdf",
abstract = "
We generalize partially Liouville's theorem on integration in finite
terms to allow polylogarithms of any order to occur in the integral in
@@ 6489,7 +6668,8 @@ J. Math Vol 8 pp229241 (2011)
dilogarithm. It is also a partial proof of a conjecture postulated by
the author in 1994. The basic conclusion is that an associated
function to the nth polylogarithm appears linearly with logarithms
 appearing possibly in a polynomial way with nonconstant coefficients."
+ appearing possibly in a polynomial way with nonconstant coefficients.",
+ paper = "Bad10.pdf"
\end{chunk}
@@ 6498,13 +6678,13 @@ J. Math Vol 8 pp229241 (2011)
\bibitem[Bajpai 70]{Bajp70} Bajpai, S.D.
title = "A contour integral involving legendre polynomial and Meijer's Gfunction",
url = "http://link.springer.com/article/10.1007/BF03049565",
 paper = "Bajp70.pdf",
abstract = "
In this paper a countour integral involving Legendre polynomial and
Meijer's Gfunction is evaluated. the integral is of general character
and it is a generalization of results recently given by Meijer,
MacRobert and others. An integral involving regular radial Coulomb
 wave function is also obtained as a particular case."
+ wave function is also obtained as a particular case.",
+ paper = "Bajp70.pdf"
\end{chunk}
@@ 6514,7 +6694,6 @@ J. Math Vol 8 pp229241 (2011)
title = "An Algorithm for the Integration of Elementary Functions",
Lecture Notes in Computer Science Vol 378 pp491497
year = "1989",
 paper = "Bro89a.pdf",
abstract = "
Trager (1984) recently gave a new algorithm for the indefinite
integration of algebraic functions. His approach was ``rational'' in
@@ 6523,7 +6702,8 @@ Lecture Notes in Computer Science Vol 378 pp491497
this approach that allows us to integrate mixed elementary
functions. Using only rational techniques, we are able to normalize
the integrand, and to check a necessary condition for elementary
 integrability."
+ integrability.",
+ paper = "Bro89a.pdf"
\end{chunk}
@@ 6536,7 +6716,6 @@ Lecture Notes in Computer Science Vol 378 pp491497
volume = "9",
pages = "117173",
year = "1990",
 paper = "Bro90a.pdf",
abstract =
"We extend a recent algorithm of Trager to a decision procedure for the
indefinite integration of elementary functions. We can express the
@@ 6557,7 +6736,8 @@ Lecture Notes in Computer Science Vol 378 pp491497
of the integrand at infinity and a generalization of the residues to
compute the integral. We also generalize a result of Rothstein that
gives us a necessary condition for elementary integrability, and
 provide examples of its use."
+ provide examples of its use.",
+ paper = "Bro90a.pdf"
}
\end{chunk}
@@ 6577,13 +6757,73 @@ Lecture Notes in Computer Science Vol 378 pp491497
\end{chunk}
+\index{FullPartialFractionExpansion}
\index{Bronstein, Manuel}
\index{Salvy, Bruno}
\begin{chunk}{ignore}
\bibitem[Bronstein 93]{REFBS93} Bronstein, Manuel; Salvy, Bruno
+\begin{chunk}{axiom.bib}
+@inproceedings{Bron93,
+ author = "Bronstein, Manuel and Salvy, Bruno",
title = "Full partial fraction decomposition of rational functions",
In Bronstein [Bro93] pp157160 ISBN 0897916042 LCCN QA76.95 I59 1993
+ booktitle = "Proc. ISSAC 1993",
+ year = "1993",
+ pages = "157160",
+ isbn = "0897916042",
url = "http://www.acm.org/pubs/citations/proceedings/issac/164081/",
+ algebra = "\newline\refto{domain FPARFRAC FullPartialFractionExpansion}",
+ abstract =
+ "We describe a rational algorithm that computes the full partial
+ fraction expansion of a rational function over the algebraic closure
+ of its field of definition. The algorithm uses only gcd operations
+ over the initial field but the resulting decomposition is expressed
+ with linear denominators. We give examples from its Axiom and Maple
+ implementations.",
+ paper = "Bron93.pdf",
+ keywords = "axiomref",
+ beebe = "Bronstein:1993:FPF"
+}
+
+\end{chunk}
+\begin{chunk}{Bronstein:1993:FPF}
+@InProceedings{Bronstein:1993:FPF,
+ author = "Manuel Bronstein and Bruno Salvy",
+ title = "Full Partial Fraction Decomposition of Rational
+ Functions",
+ crossref = "Bronstein:1993:IPI",
+ pages = "157160",
+ year = "1993",
+ bibdate = "Thu Mar 12 08:40:26 MST 1998",
+ bibsource = "http://www.acm.org/pubs/toc/;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/164081/p157bronstein/",
+ abstract = "We describe a rational algorithm that computes the
+ full partial fraction expansion of a rational function
+ over the algebraic closure of its field of definition.
+ The algorithm uses only gcd operations over the initial
+ field but the resulting decomposition is expressed with
+ linear denominators. We give examples from its Axiom
+ and Maple implementations.",
+ acknowledgement = acknhfb,
+ affiliation = "Wissenschaftliches Rechnen, Eidgenossische Tech.
+ Hochschule, Zurich, Switzerland",
+ classification = "B0290D (Functional analysis); B0290H (Linear
+ algebra); B0290M (Numerical integration and
+ differentiation); C4120 (Functional analysis); C4140
+ (Linear algebra); C4160 (Numerical integration and
+ differentiation); C7310 (Mathematics computing)",
+ keywords = "ACM; Algebraic closure; algebraic computation; Axiom;
+ Decomposition; Full partial fraction decomposition; Gcd
+ operations; Maple; Polynomial; Rational functions;
+ SIGSAM; symbolic computation; Symbolic integration,
+ ISSAC; theory; verification",
+ subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
+ ALGEBRAIC MANIPULATION, General. {\bf G.1.0}
+ Mathematics of Computing, NUMERICAL ANALYSIS, General.
+ {\bf I.1.2} Computing Methodologies, SYMBOLIC AND
+ ALGEBRAIC MANIPULATION, Algorithms.",
+ thesaurus = "Function evaluation; Integration; Matrix
+ decomposition; Polynomial matrices; Symbol
+ manipulation",
+}
\end{chunk}
@@ 6591,7 +6831,6 @@ In Bronstein [Bro93] pp157160 ISBN 0897916042 LCCN QA76.95 I59 1993
\begin{chunk}{ignore}
\bibitem[Bronstein 90]{Bro90b} Bronstein, Manuel
title = "A Unification of Liouvillian Extensions",
 paper = "Bro90b.pdf",
abstract = "
We generalize Liouville's theory of elementary functions to a larger
class of differential extensions. Elementary, Liouvillian and
@@ 6599,7 +6838,8 @@ In Bronstein [Bro93] pp157160 ISBN 0897916042 LCCN QA76.95 I59 1993
the transcendental case, we show how the rational techniques of
integration theory can be applied to our extensions, and we give a
unified presentation which does not require separate cases for
 different monomials."
+ different monomials.",
+ paper = "Bro90b.pdf"
\end{chunk}
@@ 6612,7 +6852,7 @@ In Bronstein [Bro93] pp157160 ISBN 0897916042 LCCN QA76.95 I59 1993
year = "1997",
isbn = "3540214933",
url = "http://evilwire.org/arrrXiv/Mathematics/Bronstein,_Symbolic_Integration_I,1997.pdf",
 paper = "Bron97.pdf",
+ paper = "Bron97.pdf"
}
\end{chunk}
@@ 6623,7 +6863,7 @@ In Bronstein [Bro93] pp157160 ISBN 0897916042 LCCN QA76.95 I59 1993
title = "The Poor Man's Integrator, a parallel integration heuristic",
url = "http://wwwsop.inria.fr/cafe/Manuel.Bronstein/pmint/pmint.txt",
url2 = "http://wwwsop.inria.fr/cafe/Manuel.Bronstein/pmint/examples",
 paper = "Bro05a.txt",
+ paper = "Bro05a.txt"
\end{chunk}
@@ 6641,7 +6881,6 @@ In Bronstein [Bro93] pp157160 ISBN 0897916042 LCCN QA76.95 I59 1993
url = "http://dx.doi.org/10.1134/S0361768806010075",
publisher = "Nauka/Interperiodica",
pages = "5960",
 paper = "Bron06.pdf",
abstract = "
Parallel integration is an alternative method for symbolic
integration. While also based on Liouville's theorem, it handles all
@@ 6650,7 +6889,8 @@ In Bronstein [Bro93] pp157160 ISBN 0897916042 LCCN QA76.95 I59 1993
one in a recursive fasion. Although it still contains heuristic
aspects, its ease of implementation, speed, high rate of success, and
ability to integrate functions that cannot be handled by the Risch
 algorithm make it an attractive alternative."
+ algorithm make it an attractive alternative.",
+ paper = "Bron06.pdf"
}
\end{chunk}
@@ 6666,7 +6906,6 @@ In Bronstein [Bro93] pp157160 ISBN 0897916042 LCCN QA76.95 I59 1993
pages = "757769",
year = "2007",
month = "July",
 paper = "Bron07.pdf",
abstract = "
We introduce structure theorems that refine Liouville's Theorem on
integration in closed form for general derivations on multivariate
@@ 6674,7 +6913,8 @@ In Bronstein [Bro93] pp157160 ISBN 0897916042 LCCN QA76.95 I59 1993
logarithms that an appear in integrals, as well as the denominator of
the rational part, those theorems provide theoretical backing for the
RischNorman integration method. They also generalize its applicability
 to nonmonomial extensions, for example the Lambert W function."
+ to nonmonomial extensions, for example the Lambert W function.",
+ paper = "Bron07.pdf"
}
\end{chunk}
@@ 6685,7 +6925,6 @@ In Bronstein [Bro93] pp157160 ISBN 0897916042 LCCN QA76.95 I59 1993
title = "Integration on Computer Algebra Systems",
The Electronic J of Math. and Tech. Vol 2, No 3, ISSN 19332823
url = "http://12000.org/my_notes/ten_hard_integrals/paper.pdf",
 paper = "Charl07.pdf",
abstract = "
In this article, we consider ten indefinite integrals and the ability
of three computer algebra systems (CAS) to evaluate them in
@@ 6695,7 +6934,8 @@ The Electronic J of Math. and Tech. Vol 2, No 3, ISSN 19332823
interesting to note that there are still indefinite integrals that
escape the capacity of these systems to provide antiderivatves. When
this occurs, we consider what a user may do to find a solution with
 the aid of a CAS."
+ the aid of a CAS.",
+ paper = "Charl07.pdf"
\end{chunk}
@@ 6704,12 +6944,12 @@ The Electronic J of Math. and Tech. Vol 2, No 3, ISSN 19332823
\bibitem[Charlwood 08]{Charl08} Charlwood, Kevin
title = "Symbolic Integration Problems",
url = "http://www.apmaths.uwo.ca/~arich/IndependentTestResults/CharlwoodIntegrationProblems.pdf",
 paper = "Charl08.pdf",
abstract = "
A list of the 50 example integration problems from Kevin Charlwood's 2008
article ``Integration on Computer Algebra Systems''. Each integral along
with its optimal antiderivative (that is, the best antiderivative found
 so far) is shown."
+ so far) is shown.",
+ paper = "Charl08.pdf"
\end{chunk}
@@ 6718,7 +6958,6 @@ The Electronic J of Math. and Tech. Vol 2, No 3, ISSN 19332823
\bibitem[Cherry 84]{Che84} Cherry, G.W.
title = "Integration in Finite Terms with Special Functions: The Error Function",
J. Symbolic Computation (1985) Vol 1 pp283302
 paper = "Che84.pdf",
abstract = "
A decision procedure for integrating a class of transcendental
elementary functions in terms of elementary functions and error
@@ 6730,7 +6969,8 @@ J. Symbolic Computation (1985) Vol 1 pp283302
Risch (1969) to solve it. The third case can be reduced to the
determination of what we have termed $\sum$decompositions. The resutl
presented here is the key procuedure to a more general algorithm which
 is described fully in Cherry (1983)."
+ is described fully in Cherry (1983).",
+ paper = "Che84.pdf"
\end{chunk}
@@ 6747,7 +6987,6 @@ SIAM J. Comput. Vol 15 pp121 February 1986
\bibitem[Cherry 89]{Che89} Cherry, G.W.
title = "An Analysis of the Rational Exponential Integral",
SIAM J. Computing Vol 18 pp 893905 (1989)
 paper = "Che89.pdf",
abstract = "
In this paper an algorithm is presented for integrating expressions of
the form $\int{ge^f~dx}$, where $f$ and $g$ are rational functions of
@@ 6764,7 +7003,8 @@ SIAM J. Computing Vol 18 pp 893905 (1989)
characteristic zero in which the basic field operations can be carried
out. (iii) This algorithm does not rely on Risch's solution of the
differential equation $y^\prime + fy = g$. Instead, a more direct
 method of undetermined coefficients is used."
+ method of undetermined coefficients is used.",
+ paper = "Che89.pdf"
\end{chunk}
@@ 6773,7 +7013,6 @@ SIAM J. Computing Vol 18 pp 893905 (1989)
\bibitem[Churchill 06]{Chur06} Churchill, R.C.
title = "Liouville's Theorem on Integration Terms of Elementary Functions",
url = "http://www.sci.ccny.cuny.edu/~ksda/PostedPapers/liouv06.pdf",
 paper = "Chur06.pdf",
abstract = "
This talk should be regarded as an elementary introduction to
differential algebra. It culminates in a purely algebraic proof, due
@@ 6788,7 +7027,8 @@ SIAM J. Computing Vol 18 pp 893905 (1989)
\item Differential Ring Extensions with No New Constants
\item Extending Derivations
\item Integration in Finite Terms
 \end{itemize}"
+ \end{itemize}",
+ paper = "Chur06.pdf"
\end{chunk}
@@ 6810,7 +7050,6 @@ SIAM J. Computing Vol 18 pp 893905 (1989)
\bibitem[Davenport 79c]{Dav79c} Davenport, J. H.
title = "Algorithms for the Integration of Algebraic Functions",
Lecture Notes in Computer Science V 72 pp415425 (1979)
 paper = "Dav79c.pdf",
abstract = "
The problem of finding elementary integrals of algebraic functions has
long been recognized as difficult, and has sometimes been thought
@@ 6821,7 +7060,8 @@ Lecture Notes in Computer Science V 72 pp415425 (1979)
the way of extending this algorithm, and outline some ways of solving
it. Using work of Manin we are able to solve the problem in all cases
where the algebraic expressions depend on a parameter as well as on
 the variable of integration."
+ the variable of integration.",
+ paper = "Dav79c.pdf"
\end{chunk}
@@ 6829,12 +7069,12 @@ Lecture Notes in Computer Science V 72 pp415425 (1979)
\begin{chunk}{ignore}
\bibitem[Davenport 82a]{Dav82a} Davenport, J.H.
title = "The Parallel Risch Algorithm (I)"
 paper = "Dav82a.pdf",
abstract = "
In this paper we review the socalled ``parallel Risch'' algorithm for
the integration of transcendental functions, and explain what the
problems with it are. We prove a positive result in the case of
 logarithmic integrands."
+ logarithmic integrands.",
+ paper = "Dav82a.pdf"
\end{chunk}
@@ 6851,11 +7091,11 @@ SIGSAM V16 no. 3 pp36 August 1982
\bibitem[Davenport 03]{Dav03} Davenport, James H.
title = "The Difficulties of Definite Integration",
url = "http://www.researchgate.net/publication/247837653_The_Diculties_of_Definite_Integration/file/72e7e52a9b1f06e196.pdf",
 paper = "Dav03.pdf",
abstract = "
Indefinite integration is the inverse operation to differentiation,
and, before we can understand what we mean by indefinite integration,
 we need to understand what we mean by differentiation."
+ we need to understand what we mean by differentiation.",
+ paper = "Dav03.pdf"
\end{chunk}
@@ 6864,7 +7104,7 @@ SIGSAM V16 no. 3 pp36 August 1982
\bibitem[Fateman 02]{Fat02} Fateman, Richard
title = "Symbolic Integration",
url = "http://inst.eecs.berkeley.edu/~cs282/sp02/lects/14.pdf",
 paper = "Fat02.pdf",
+ paper = "Fat02.pdf"
\end{chunk}
@@ 6888,7 +7128,6 @@ SIGSAM V16 no. 3 pp36 August 1982
acmid = "74567",
publisher = "ACM",
address = "New York, NY, USA",
 paper = "Gedd89.pdf",
abstract = "
Unlike the Recursive Risch Algorithm for the integration of
transcendental elementary functions, the RischNorman Method processes
@@ 6897,7 +7136,8 @@ SIGSAM V16 no. 3 pp36 August 1982
extentions in terms of tangents. Consequently, it allows trigonometric
functions to be treated without converting them to complex exponential
form. We review this method and describe its implementation in
 MAPLE. A heuristic enhancement to this method is also presented."
+ MAPLE. A heuristic enhancement to this method is also presented.",
+ paper = "Gedd89.pdf"
}
\end{chunk}
@@ 6909,7 +7149,7 @@ SIGSAM V16 no. 3 pp36 August 1982
\bibitem[Geddes 92a]{GCL92a} Geddes, K.O.; Czapor, S.R.; Labahn, G.
title = "The Risch Integration Algorithm",
Algorithms for Computer Algebra, Ch 12 pp511573 (1992)
 paper = "GCL92a.pdf",
+ paper = "GCL92a.pdf"
\end{chunk}
@@ 6927,7 +7167,6 @@ Cambridge Unversity Press, Cambridge, 1916
\bibitem[Harrington 78]{Harr87} Harrington, S.J.
title = "A new symbolic integration system in reduce",
url = "http://comjnl.oxfordjournals.or/content/22/2/127.full.pdf",
 paper = "Harr87.pdf",
abstract = "
A new integration system, employing both algorithmic and pattern match
integration schemes is presented. The organization of the system
@@ 6938,7 +7177,8 @@ Cambridge Unversity Press, Cambridge, 1916
collection of simplification and transformation rules. The facility
for user defined integrals and functions is also included. The program
is both fast and powerful, and can be easily modified to incorporate
 anticipated developments in symbolic integration."
+ anticipated developments in symbolic integration.",
+ paper = "Harr87.pdf"
\end{chunk}
@@ 6961,7 +7201,6 @@ Cambridge Unversity Press, Cambridge, 1916
title = "Algorithms for Partial Fraction Decomposition and Rational Function Integration",
SYMSAC '71 Proc. ACM Symp. on Symbolic and Algebraic Manipulation (1971)
pp441457
 paper = "Horo71.pdf",
ref = "00018",
abstract = "
Algorithms for symbolic partial fraction decomposition and indefinite
@@ 6974,7 +7213,8 @@ pp441457
is a number which is closely related to the size of the coefficients
which occur in A and B. The complete squarefree partical fraction
decomposition can then be directly obtained and it is shown that the
 computing time for this process is also bounded by $O(n^4(ln nf)^2)$."
+ computing time for this process is also bounded by $O(n^4(ln nf)^2)$.",
+ paper = "Horo71.pdf"
\end{chunk}
@@ 6984,7 +7224,6 @@ pp441457
\bibitem[Jeffrey 97]{Jeff97} Jeffrey, D.J.; Rich, A.D.
title = "Recursive integration of piecewisecontinuous functions",
url = "http://www.cybertester.com/data/recint.pdf",
 paper = "Jeff97.pdf",
abstract = "
An algorithm is given for the integration of a class of
piecewisecontinuous functions. The integration is with respect to a
@@ 6994,7 +7233,8 @@ pp441457
waves, triangular waves, and the floor function; it also includes the
signum function. The algorithm can be implemented recursively, and it
has the property of ensuring that integrals are continuous on domains
 of maximum extent."
+ of maximum extent.",
+ paper = "Jeff97.pdf"
\end{chunk}
@@ 7007,7 +7247,6 @@ pp441457
Rich, A.D.
title = "Integration of the signum, piecewise and related functions",
url = "http://cs.uwaterloo.ca/~glabahn/Papers/issac992.pdf",
 paper = "Jeff99.pdf",
abstract = "
When a computer algebra system has an assumption facility, it is
possible to distinguish between integration problems with respect to a
@@ 7015,7 +7254,8 @@ Rich, A.D.
class of integration problems is defined in which the integrand
consists of compositions of continuous functions and signum functions,
and integration is with respect to a real variable. Algorithms are
 given for evaluating such integrals."
+ given for evaluating such integrals.",
+ paper = "Jeff99.pdf"
\end{chunk}
@@ 7024,11 +7264,11 @@ Rich, A.D.
\begin{chunk}{ignore}
\bibitem[Kiymaz 04]{Kiym04} Kiymaz, Onur; Mirasyedioglu, Seref
title = "A new symbolic computation for formal integration with exact power series",
 paper = "Kiym04.pdf",
abstract = "
This paper describes a new symbolic algorithm for formal integration
of a class of functions in the context of exact power series by using
 generalized hypergeometric series and computer algebraic technique."
+ generalized hypergeometric series and computer algebraic technique.",
+ paper = "Kiym04.pdf"
\end{chunk}
@@ 7059,13 +7299,13 @@ Journal of Symbolic Computation Vol 16 pp227241 (1995)
pages = "6378",
year = "2009",
issn = "03617688",
 paper = "Krag09.pdf",
abstract = "
In this paper by means of computer experiment we study advantages and
disadvantages of the heuristical method of ``parallel integrator''. For
this purpose we describe and use implementation of the method in
Mathematica. In some cases we compare this implementation with the original
 one in Maple."
+ one in Maple.",
+ paper = "Krag09.pdf"
}
\end{chunk}
@@ 7084,13 +7324,13 @@ AddisonWesly, New York, 3rd edition 1993
\bibitem[Leerawat 02]{Leer02} Leerawat, Utsanee; Laohakosol, Vichian
title = "A Generalization of Liouville's Theorem on Integration in Finite Terms",
url = "http://www.mathnet.or.kr/mathnet/kms_tex/113666.pdf",
 paper = "Leer02.pdf",
abstract = "
A generalization of Liouville's theorem on integration in finite
terms, by enlarging the class of fields to an extension called
EiGamma extension is established. This extension includes the
$\mathcal{E}\mathcal{L}$elementary extensions of Singer, Saunders and
 Caviness and contains the Gamma function."
+ Caviness and contains the Gamma function.",
+ paper = "Leer02.pdf"
\end{chunk}
@@ 7099,7 +7339,7 @@ AddisonWesly, New York, 3rd edition 1993
\bibitem[Leslie 09]{Lesl09} Leslie, Martin
title = "Why you can't integrate exp($x^2$)",
url = "http://math.arizona.edu/~mleslie/files/integrationtalk.pdf",
 paper = "Lesl09.pdf",
+ paper = "Lesl09.pdf"
\end{chunk}
@@ 7109,7 +7349,6 @@ AddisonWesly, New York, 3rd edition 1993
title = "Symbolic definite (and indefinite) integration: methods and open issues",
ACM Comm. in Computer Algebra Issue 175, Vol 45, No.1 (2011)
url = "http://www.sigsam.org/bulletin/articles/175/issue175.pdf",
 paper = "Lich11.pdf",
abstract = "
The computation of definite integrals presents one with a variety of
choices. There are various methods such as NewtonLeibniz or Slater's
@@ 7118,7 +7357,9 @@ ACM Comm. in Computer Algebra Issue 175, Vol 45, No.1 (2011)
integration, when to issue conditional results, how to assess
(possibly conditional) convergence, and more. These various
considerations moreover interact with one another in a multitude of
 ways. Herein we discuss these various issues and illustrate with examples."
+ ways. Herein we discuss these various issues and illustrate
+ with examples.",
+ paper = "Lich11.pdf"
\end{chunk}
@@ 7183,7 +7424,7 @@ Vol 13(2) pp 93118, (1835)
title = "An Invitation to Integration in Finite Terms",
College Mathematics Journal Vol 25 No 4 (1994) pp295308
url = "http://www.rangevoting.org/MarchisottoZint.pdf",
 paper = "Marc94.pdf",
+ paper = "Marc94.pdf"
\end{chunk}
@@ 7192,14 +7433,14 @@ College Mathematics Journal Vol 25 No 4 (1994) pp295308
\bibitem[Marik 91]{Mari91} Marik, Jan
title = "A note on integration of rational functions",
url = "http://dml.cz/bitstream/handle/10338.dmlcz/126024/MathBohem_11619914_9.pdf",
 paper = "Mari91.pdf",
abstract = "
Let $P$ and $Q$ be polynomials in one variable with complex coefficients
and let $n$ be a natural number. Suppose that $Q$ is not constant and
has only simple roots. Then there is a rational function $\varphi$
with $\varphi^\prime=P/Q^{n+1}$ if and only if the Wronskian of the
functions $Q^\prime$, $(Q^2)^\prime,\ldots\,(Q^n)^\prime$,$P$ is
 divisible by $Q$."
+ divisible by $Q$.",
+ paper = "Mari91.pdf"
\end{chunk}
@@ 7208,7 +7449,6 @@ College Mathematics Journal Vol 25 No 4 (1994) pp295308
\bibitem[Moses 76]{Mos76} Moses, Joel
title = "An introduction to the Risch Integration Algorithm",
ACM Proc. 1976 annual conference pp425428
 paper = "Mos76.pdf",
ref = "00048",
abstract = "
Risch's decision procedure for determining the integrability in closed
@@ 7216,7 +7456,8 @@ ACM Proc. 1976 annual conference pp425428
examples. The exponential and logarithmic cases of the algorithsm had
been implemented for the MACSYMA system several years ago. The
implementation of the algebraic case of the algorithm is the subject
 of current research."
+ of current research.",
+ paper = "Mos76.pdf"
\end{chunk}
@@ 7226,7 +7467,6 @@ ACM Proc. 1976 annual conference pp425428
title = "Symbolic Integration: The Stormy Decade",
CACM Aug 1971 Vol 14 No 8 pp548560
url = "http://wwwinst.eecs.berkeley.edu/~cs282/sp02/readings/mosesint.pdf",
 paper = "Mos71a.pdf",
ref = "00017",
abstract = "
Three approaches to symbolic integration in the 1960's are
@@ 7239,7 +7479,8 @@ CACM Aug 1971 Vol 14 No 8 pp548560
for Risch's decision procedure for the elementary functions.
Generalizations of Risch's algorithm to a class of special
functions and programs for solving differential equations and for
 finding the definite integral are also described."
+ finding the definite integral are also described.",
+ paper = "Mos71a.pdf"
\end{chunk}
@@ 7248,7 +7489,6 @@ CACM Aug 1971 Vol 14 No 8 pp548560
\begin{chunk}{ignore}
\bibitem[Norman 79]{Nor79} Norman, A.C.; Davenport, J.H.
title = "Symbolic Integration  The Dust Settles?",
 paper = "Nor79.pdf",
abstract = "
By the end of the 1960s it had been shown that a computer could find
indefinite integrals with a competence exceeding that of typical
@@ 7259,7 +7499,8 @@ CACM Aug 1971 Vol 14 No 8 pp548560
barriers in the way of a complete system for automated analysis had
been breached. In this paper we survey the work that has grown out of
the abovementioned early results, showing where the development has
 been smooth and where it has spurred work in seemingly unrelated fields."
+ been smooth and where it has spurred work in seemingly unrelated fields.",
+ paper = "Nor79.pdf"
\end{chunk}
@@ 7277,7 +7518,6 @@ Comm. Math. Helv., Vol 18 pp 283308, (1946)
\bibitem[Raab 12]{Raab12} Raab, Clemens G.
title = "Definite Integration in Differential Fields",
url = "http://www.risc.jku.at/publications/download/risc_4583/PhD_CGR.pdf",
 paper = "Raab12.pdf",
abstract = "
The general goal of this thesis is to investigate and develop computer
algebra tools for the simplification resp. evaluation of definite
@@ 7326,7 +7566,8 @@ Comm. Math. Helv., Vol 18 pp 283308, (1946)
standard computer algebra systems like Mathematica or Maple do not
succeed. We also give examples of how parameter integrals coming from
the work of other researchers can be solved with the software, e.g.,
 an integral arising in analyzing the entropy of certain processes."
+ an integral arising in analyzing the entropy of certain processes.",
+ paper = "Raab12.pdf"
\end{chunk}
@@ 7335,7 +7576,6 @@ Comm. Math. Helv., Vol 18 pp 283308, (1946)
\bibitem[Raab 13]{Raab13} Raab, Clemens G.
title = "Generalization of Risch's Algorithm to Special Functions",
url = "http://arxiv.org/pdf/1305.1481.pdf",
 paper = "Raab13.pdf",
abstract = "
Symbolic integration deals with the evaluation of integrals in closed
form. We present an overview of Risch's algorithm including recent
@@ 7346,7 +7586,8 @@ Comm. Math. Helv., Vol 18 pp 283308, (1946)
to introduce the reader to some basic idea of differential algebra in
the context of integration and to raise awareness in the physics
community of computer algebra algorithms for indefinite and definite
 integration."
+ integration.",
+ paper = "Raab13.pdf"
\end{chunk}
@@ 7355,7 +7596,6 @@ Comm. Math. Helv., Vol 18 pp 283308, (1946)
\bibitem[Raab xx]{Raabxx} Raab, Clemens G.
title = "Integration in finite terms for Liouvillian functions",
url = "http://www.mmrc.iss.ac.cn/~dart4/posters/Raab.pdf",
 paper = "Raabxx.pdf",
abstract = "
Computing integrals is a common task in many areas of science,
antiderivatives are one way to accomplish this. The problem of
@@ 7376,7 +7616,8 @@ Comm. Math. Helv., Vol 18 pp 283308, (1946)
without the need to embed them into logexplicit extensions. For
example, this means that
\[\int{(zx)x^{z1}e^{x}dx} = x^ze^{x}\]
 can be computed without including log(x) in the differential field."
+ can be computed without including log(x) in the differential field.",
+ paper = "Raabxx.pdf"
\end{chunk}
@@ 7386,7 +7627,6 @@ Comm. Math. Helv., Vol 18 pp 283308, (1946)
\bibitem[Rich 09]{Rich09} Rich, A.D.; Jeffrey, D.J.
title = "A Knowledge Repository for Indefinite Integration Based on Transformation Rules",
url = "http://www.apmaths.uwo.ca/~arich/A%2520Rulebased%2520Knowedge%2520Repository.pdf",
 paper = "Rich09.pdf",
abstract = "
Taking the specific problem domain of indefinite integration, we
describe the ongoing development of a repository of mathematical
@@ 7397,7 +7637,8 @@ Comm. Math. Helv., Vol 18 pp 283308, (1946)
translated into other formats. The principles upon which the set of
rules is compiled is described. One important principle is
minimality. The benefits of the approach are illustrated with
 examples, and with the results of comparisons with other approaches."
+ examples, and with the results of comparisons with other approaches.",
+ paper = "Rich09.pdf"
\end{chunk}
@@ 7424,7 +7665,6 @@ Comm. Math. Helv., Vol 18 pp 283308, (1946)
number = "RC2042",
institution = "IBM Research, Yorktown Heights, NY, USA",
year = "1969"

}
\end{chunk}
@@ 7438,10 +7678,10 @@ Comm. Math. Helv., Vol 18 pp 283308, (1946)
volume = "139",
year = "1969",
pages = "167189",
 paper = "Ris69b.pdf",
abstract = "This paper deals with the problem of telling whether a
given elementary function, in the sense of analysis, has an elementary
 indefinite integral."
+ indefinite integral.",
+ paper = "Ris69b.pdf"
}
\end{chunk}
@@ 7457,7 +7697,6 @@ Comm. Math. Helv., Vol 18 pp 283308, (1946)
volume = "76",
number = "3",
pages = "605609",
 paper = "Risc70.pdf",
abstract = "
The problem of integration in finite terms asks for an algorithm for
deciding whether an elementary function has an elementary indefinite
@@ 7469,7 +7708,8 @@ Comm. Math. Helv., Vol 18 pp 283308, (1946)
writer has devised an algorithm which solves the classical problem of
Liouville. A complete account is planned for a future publication. The
present note is intended to indiciate some of the ideas and techniques
 involved."
+ involved.",
+ paper = "Risc70.pdf"
}
\end{chunk}
@@ 7502,7 +7742,6 @@ Columbia University Press, New York 1948
title = "Liouville's Theorem on Functions with Elementary Integrals",
Pacific Journal of Mathematics Vol 24 No 1 (1968)
url = "http://msp.org/pjm/1968/241/pjmv24n1p16p.pdf",
 paper = "Ro68.pdf",
ref = "00047",
abstract = "
Defining a function with one variable to be elemetary if it has an
@@ 7518,7 +7757,8 @@ Pacific Journal of Mathematics Vol 24 No 1 (1968)
algebraic nature of the problem, all proofs so far have been analytic.
This paper gives a self contained purely algebraic exposition of the
probelm, making a few new points in addition to the resulting
 simplicity and generalization."
+ simplicity and generalization.",
+ paper = "Ro68.pdf"
\end{chunk}
@@ 7531,21 +7771,22 @@ Pacific Journal of Mathematics Vol 24 No 1 (1968)
year = "1972",
volume = "79",
pages = "963972",
 paper = "Rose72.pdf",
+ paper = "Rose72.pdf"
}
\end{chunk}
\index{Rothstein, Michael}
\begin{chunk}{ignore}
\bibitem[Rothstein 76]{Ro76} Rothstein, Michael
 title = "Aspects of symbolic integration and simplifcation of exponential and primitive functions",
PhD thesis, University of WisconsinMadison (1976)
+@phdthesis{Roth76,
+ author = "Rothstein, Michael",
+ title = "Aspects of symbolic integration and simplifcation of
+ exponential and primitive functions",
+ school = "University of WisconsinMadison",
+ year = "1976",
url = "http://www.cs.kent.edu/~rothstei/dis.pdf",
 paper = "Ro76.pdf",
 ref = "00051",
 abstract = "
 In this thesis we cover some aspects of the theory necessary to obtain
+ abstract =
+ "In this thesis we cover some aspects of the theory necessary to obtain
a canonical form for functions obtained by integration and
exponentiation from the set of rational functions.
@@ 7560,7 +7801,9 @@ PhD thesis, University of WisconsinMadison (1976)
integrals which can be represented as logarithms are represented as
such, the only algebraic dependence that a new exponential or
logarithm can satify is given by the law of exponents or the law of
 logarithms."
+ logarithms.",
+ paper = "Ro76.pdf"
+}
\end{chunk}
@@ 7575,7 +7818,6 @@ PhD thesis, University of WisconsinMadison (1976)
volume = "10",
number = "4",
year = "1976",
 paper = "Ro76a.pdf",
abstract =
"In this paper a generalization of the Risch Structure Theorem is reported.
The generalization applies to fields $F(t_1,\ldots,t_n)$ where $F$
@@ 7585,7 +7827,8 @@ PhD thesis, University of WisconsinMadison (1976)
exponential of an element in $F_{i1}$, or is an integral of an element
in $F_{i1}$. If $t_i$ is an integral and can be expressed using
logarithms, it must be so expressed for the generalized structure
 theorem to apply."
+ theorem to apply.",
+ paper = "Ro76a.pdf"
}
\end{chunk}
@@ 7596,7 +7839,6 @@ PhD thesis, University of WisconsinMadison (1976)
\bibitem[Rothstein 76b]{Ro76b} Rothstein, Michael; Caviness, B.F.
title = "A structure theorem for exponential and primitive functions",
SIAM J. Computing Vol 8 No 3 (1979)
 paper = "Ro76b.pdf",
ref = "00104",
abstract = "
In this paper a new theorem is proved that generalizes a result of
@@ 7606,7 +7848,8 @@ SIAM J. Computing Vol 8 No 3 (1979)
functions so generated are called exponential and primitive functions.
From the theorem an algorithm for determining algebraic dependence
among a given set of exponential and primitive functions is derived.
 The algorithm is then applied to a problem in computer algebra."
+ The algorithm is then applied to a problem in computer algebra.",
+ paper = "Ro76b.pdf"
\end{chunk}
@@ 7652,7 +7895,6 @@ Proc. Amer. Math. Soc. Vol 23 pp689691 (1969)
pages = "965990",
year = "1985",
url = "http://www4.ncsu.edu/~singer/papers/singer_saunders_caviness.pdf",
 paper = "Sing85.pdf",
abstract =
"In Part 1 of this paper, we give an extension of Liouville's Theorem
and give a number of examples which show that integration with special
@@ 7666,7 +7908,8 @@ Proc. Amer. Math. Soc. Vol 23 pp689691 (1969)
appear, appear linearly. We give an algorithm which decides if an
elementary function, built up using only exponential functions and
rational operations has an integral which can be expressed in terms of
 elementary functions and error functions."
+ elementary functions and error functions.",
+ paper = "Sing85.pdf"
}
\end{chunk}
@@ 7688,7 +7931,6 @@ Ph.D Diss. MIT, May 1961; also Computers and Thought, Feigenbaum and Feldman.
school = "Royal Institute of Technology",
address = "Stockholm, Sweden",
year = "2009",
 paper = "Tere09.pdf",
abstract =
"Symbolic integration is the problem of expressing an indefinite integral
$\int{f}$ of a given function $f$ as a finite combination $g$ of elementary
@@ 7712,7 +7954,8 @@ Ph.D Diss. MIT, May 1961; also Computers and Thought, Feigenbaum and Feldman.
implementation of a computer algebra system and some of the
experiences it has given us. We also demonstrate an implementation of
the rulebased approach and how it can be used, not only to compute
 integrals, but also to generate readable derivations of the results."
+ integrals, but also to generate readable derivations of the results.",
+ paper = "Tere09.pdf"
}
\end{chunk}
@@ 7725,7 +7968,6 @@ Ph.D Diss. MIT, May 1961; also Computers and Thought, Feigenbaum and Feldman.
journal = "Proceedings of SYMSAC'76",
year = "1976",
pages = "219226",
 paper = "Trag76.pdf",
abstract = "
This paper presents a new, simple, and efficient algorithm for
factoring polynomials in several variables over an algebraic number
@@ 7735,7 +7977,8 @@ Ph.D Diss. MIT, May 1961; also Computers and Thought, Feigenbaum and Feldman.
problem of determining the transcendental part of the integral of a
rational function. In particular, a constructive procedure is given
for finding a least degree extension field in which the integral can
 be expressed."
+ be expressed.",
+ paper = "Trag76.pdf"
}
\end{chunk}
@@ 7746,7 +7989,6 @@ Ph.D Diss. MIT, May 1961; also Computers and Thought, Feigenbaum and Feldman.
title = "Algorithms for Manipulating Algebraic Functions",
MIT Master's Thesis.
url = "http://www.dm.unipi.it/pages/gianni/public_html/AlgComp/fattorizzazioneEA.pdf",
 paper = "Tr76a.pdf",
ref = "00050",
abstract = "
Given a base field $k$, of characteristic zero, with effective
@@ 7766,7 +8008,8 @@ MIT Master's Thesis.
field. The problem of algebraic function integration is also
examined, and a highly efficient procedure is presented for generating
the algebraic part of integrals whose function fields are defined by a
 single radical extension of the rational functions."
+ single radical extension of the rational functions.",
+ paper = "Tr76a.pdf"
\end{chunk}
@@ 7778,13 +8021,13 @@ MIT Master's Thesis.
school = "MIT",
year = "1984",
url = "http://www.dm.unipi.it/pages/gianni/public_html/AlgComp/thesis.pdf",
 paper = "Trag76.pdf",
abstract = "
We show how the ``rational'' approach for integrating algebraic
functions can be extended to handle elementary functions. The
resulting algorithm is a practical decision procedure for determining
whether a given elementary function has an elementary antiderivative,
 and for computing it if it exists."
+ and for computing it if it exists.",
+ paper = "Trag76.pdf"
}
\end{chunk}
@@ 7794,7 +8037,6 @@ MIT Master's Thesis.
\bibitem[W\"urfl 07]{Wurf07} W\"urfl, Andreas
title = "Basic Concepts of Differential Algebra",
url = "http://www14.in.tum.de/konferenzen/Jass07/courses/1/Wuerfl/wuerfl_paper.pdf",
 paper = "Wurf07.pdf",
abstract = "
Modern computer algebra systems symbolically integrate a vast variety
of functions. To reveal the underlying structure it is necessary to
@@ 7804,7 +8046,8 @@ MIT Master's Thesis.
used in modern algorithms. We present Hermite's method for integration
of rational functions as well as the Rothstein/Trager method for
rational and for elementary functions. Further applications of the
 mentioned algorithms in the field of ODE's conclude this paper."
+ mentioned algorithms in the field of ODE's conclude this paper.",
+ paper = "Wurf07.pdf"
\end{chunk}
@@ 7815,7 +8058,7 @@ MIT Master's Thesis.
\bibitem[Angell]{Angell} Angell, Tom
title = "Guidelines for Partial Fraction Decomposition",
url = "http://www.math.udel.edu/~angell/partfrac_I.pdf",
 paper = "Angell.pdf",
+ paper = "Angell.pdf"
\end{chunk}
@@ 7824,7 +8067,7 @@ MIT Master's Thesis.
\bibitem[Laval 08]{Lava08} Laval, Philippe B.
title = "Partial Fractions Decomposition",
url = "http://www.math.wisc.edu/~park/Fall2011/integration/Partial%20Fraction.pdf",
 paper = "Lava08.pdf",
+ paper = "Lava08.pdf"
\end{chunk}
@@ 7832,7 +8075,7 @@ MIT Master's Thesis.
\bibitem[Mudd 14]{Mudd14} Harvey Mudd College
title = "Partial Fractions",
url = "http://www.math.hmc.edu/calculus/tutorials/partial_fractions/partial_fractions.pdf",
 paper = "Mudd14.pdf",
+ paper = "Mudd14.pdf"
\end{chunk}
@@ 7841,7 +8084,7 @@ MIT Master's Thesis.
\bibitem[Rajasekaran 14]{Raja14} Rajasekaran, Raja
title = "Partial Fraction Expansion",
url = "http://www.utdallas.edu/~raja1/EE4361%20Spring%2014/Lecture%20Notes/Partial%20Fractions.pdf",
 paper = "Raja14.pdf",
+ paper = "Raja14.pdf"
\end{chunk}
@@ 7850,7 +8093,7 @@ MIT Master's Thesis.
\bibitem[Wootton 14]{Woot14} Wootton, Aaron
title = "Integration of Rational Functions by Partial Fractions",
url = "http://faculty.up.edu/wootton/calc2/section7.4.pdf",
 paper = "Woot14.pdf",
+ paper = "Woot14.pdf"
\end{chunk}
@@ 7865,11 +8108,11 @@ the least left common multiple (lcmCoef) function.
\bibitem[Abramov 97]{Abra97} Abramov, Sergei A.; van Hoeij, Mark
title = "A method for the Integration of Solutions of Ore Equations",
Proc ISSAC 97 pp172175 (1997)
 paper = "Abra97.pdf",
abstract = "
We introduce the notion of the adjoint Ore ring and give a definition
of adjoint polynomial, operator and equation. We apply this for
 integrating solutions of Ore equations."
+ integrating solutions of Ore equations.",
+ paper = "Abra97.pdf"
\end{chunk}
@@ 7881,7 +8124,6 @@ Proc ISSAC 97 pp172175 (1997)
author = "Delenclos, Jonathon and Leroy, Andr\'e",
title = "Noncommutative Symmetric functions and $W$polynomials",
url = "http://arxiv.org/pdf/math/0606614.pdf",
 paper = "Dele06.pdf",
algebra = "\newline\refto{category LORER LeftOreRing}",
abstract = "
Let $K$, $S$, $D$ be a division ring an endomorphism and a
@@ 7893,7 +8135,8 @@ Proc ISSAC 97 pp172175 (1997)
factorizations of $W$polynomials are analysed. Connections between
the existence of LLCM (least left common multiples) of monic linear
polynomials with coefficients in a ring and the left duo property are
 established at the end of the paper."
+ established at the end of the paper.",
+ paper = "Dele06.pdf"
}
\end{chunk}
@@ 7905,13 +8148,13 @@ Proc ISSAC 97 pp172175 (1997)
\bibitem[Abramov 05]{Abra05} Abramov, S.A.; Le, H.Q.; Li, Z.
``Univariate Ore Polynomial Rings in Computer Algebra''
url = "http://www.mmrc.iss.ac.cn/~zmli/papers/oretools.pdf",
 paper = "Abra05.pdf",
abstract = "
We present some algorithms related to rings of Ore polynomials (or,
briefly, Ore rings) and describe a computer algebra library for basic
operations in an arbitrary Ore ring. The library can be used as a
basis for various algorithms in Ore rings, in particular, in
 differential, shift, and $q$shift rings."
+ differential, shift, and $q$shift rings.",
+ paper = "Abra05.pdf"
\end{chunk}
@@ 7929,7 +8172,7 @@ Proc ISSAC 97 pp172175 (1997)
pages = "2633",
year = "1989",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/89/KVY89.pdf",
 paper = "Kalt89d.pdf",
+ paper = "Kalt89d.pdf"
}
\end{chunk}
@@ 7948,7 +8191,7 @@ Proc ISSAC 97 pp172175 (1997)
publisher = "SpringerVerlag",
year = "1991",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/91/KaYui91.pdf",
 paper = "Kalt91b.pdf",
+ paper = "Kalt91b.pdf"
}
\end{chunk}
@@ 7966,7 +8209,7 @@ Proc ISSAC 97 pp172175 (1997)
year = "1984",
url =
"http://www.math.ncsu.edu/~kaltofen/bibliography/84/KaYui84_eurosam.ps.gz",
 paper = "Kalt84a.ps",
+ paper = "Kalt84a.ps"
}
\end{chunk}
@@ 7978,7 +8221,6 @@ Proc ISSAC 97 pp172175 (1997)
title = "A Computational Introduction to Number Theory",
url = "http://shoup.net/ntb/ntbv2.pdf",
paper = "Sho08.pdf"

}
\end{chunk}
@@ 7998,7 +8240,7 @@ Proc ISSAC 97 pp172175 (1997)
crossref = "SNC07",
pages = "1117",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/07/KYZ07.pdf",
 paper = "Kalt07a.pdf",
+ paper = "Kalt07a.pdf"
}
\end{chunk}
@@ 8015,7 +8257,7 @@ Proc ISSAC 97 pp172175 (1997)
crossref = "ISSAC07",
pages = "203210",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/07/KaYa07.pdf",
 paper = "Kalt07b.pdf",
+ paper = "Kalt07b.pdf"
}
\end{chunk}
@@ 8034,7 +8276,7 @@ Proc ISSAC 97 pp172175 (1997)
number = "34",
pages = "401424",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/03/GKL03.pdf",
 paper = "Gies03.pdf",
+ paper = "Gies03.pdf"
}
\end{chunk}
@@ 8052,7 +8294,7 @@ Proc ISSAC 97 pp172175 (1997)
pages = "101108",
year = "2002",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/02/GKL02.pdf",
 paper = "Gies02.pdf",
+ paper = "Gies02.pdf"
}
\end{chunk}
@@ 8069,7 +8311,7 @@ Proc ISSAC 97 pp172175 (1997)
number = "34",
pages = "365400",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/03/KL03.pdf",
 paper = "Kalt03b.pdf",
+ paper = "Kalt03b.pdf"
}
\end{chunk}
@@ 8087,7 +8329,7 @@ Proc ISSAC 97 pp172175 (1997)
pages = "192201",
year = "2000",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/2K/KLL2K.pdf",
 paper = "Kalt00a.pdf",
+ paper = "Kalt00a.pdf"
}
\end{chunk}
@@ 8104,7 +8346,7 @@ Proc ISSAC 97 pp172175 (1997)
pages = "1017",
month = "July",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/10/Ka10_pasco.pdf",
 paper = "Kalt10b.pdf",
+ paper = "Kalt10b.pdf"
}
\end{chunk}
@@ 8122,7 +8364,7 @@ Proc ISSAC 97 pp172175 (1997)
publisher = "ACM Press",
year = "1990",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/90/KLW90.pdf",
 paper = "Kalt90.pdf",
+ paper = "Kalt90.pdf"
}
\end{chunk}
@@ 8138,7 +8380,7 @@ Proc ISSAC 97 pp172175 (1997)
pages = "467474",
year = "1988",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/88/KaLa88.pdf",
 paper = "Kalt88a.pdf",
+ paper = "Kalt88a.pdf"
}
\end{chunk}
@@ 8165,7 +8407,7 @@ Proc ISSAC 97 pp172175 (1997)
address = "Providence, Rhode Island, USA",
isbn = "9780821852286",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/10/GKKP10.pdf",
 paper = "Gren11.pdf",
+ paper = "Gren11.pdf"
}
\end{chunk}
@@ 8181,7 +8423,7 @@ Proc ISSAC 97 pp172175 (1997)
crossref = "ISSAC08",
pages = "141146",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/08/KaKoi08.pdf",
 paper = "Kalt08a.pdf",
+ paper = "Kalt08a.pdf"
}
\end{chunk}
@@ 8198,7 +8440,7 @@ Proc ISSAC 97 pp172175 (1997)
number = "8",
pages = "983989",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/95/HiKa95.pdf",
 paper = "Hitz95.pdf",
+ paper = "Hitz95.pdf"
}
\end{chunk}
@@ 8213,7 +8455,7 @@ Proc ISSAC 97 pp172175 (1997)
pages = "342349",
year = "1992",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/92/Ka92_issac.pdf",
 paper = "Kalt92a.pdf",
+ paper = "Kalt92a.pdf"
}
\end{chunk}
@@ 8230,7 +8472,7 @@ Proc ISSAC 97 pp172175 (1997)
number = "7",
pages = "693701",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/91/CaKa91.pdf",
 paper = "Cant91.pdf",
+ paper = "Cant91.pdf"
}
\end{chunk}
@@ 8247,7 +8489,7 @@ Proc ISSAC 97 pp172175 (1997)
number = "1",
pages = "231264",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/88/Ka88_jacm.pdf",
 paper = "Kalt88b.pdf",
+ paper = "Kalt88b.pdf"
}
\end{chunk}
@@ 8267,8 +8509,6 @@ Proc ISSAC 97 pp172175 (1997)
location = "Toulouse, France",
publisher = "Springer",
pages = "1528",
 keywords = "axiomref",
 paper = "Bern97a.pdf",
url = "http://www.cecm.sfu.ca/~monaganm/papers/AAECC.pdf",
abstract =
"We describe the Maple implementation of multivariate factorization
@@ 8282,7 +8522,9 @@ Proc ISSAC 97 pp172175 (1997)
because any multivariate factorization may depend on several bivariate
factorizations. The efficiency of our implementation is illustrated by
the ability to factor bivariate polynomials with over a million
 monomials over a small prime field."
+ monomials over a small prime field.",
+ paper = "Bern97a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 8299,7 +8541,7 @@ Proc ISSAC 97 pp172175 (1997)
pages = "232239",
year = "1995",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/95/DiKa95.ps.gz",
 paper = "Diaz95.ps",
+ paper = "Diaz95.ps"
}
\end{chunk}
@@ 8314,7 +8556,6 @@ Proc ISSAC 97 pp172175 (1997)
year = "2001",
volume = "31",
pages = "317",
 paper = "Gath01.pdf",
url =
"http://people.csail.mit.edu/dmoshdov/courses/codes/polyfactorization.pdf",
keywords = "survey",
@@ 8325,7 +8566,8 @@ Proc ISSAC 97 pp172175 (1997)
This paper gives algorithms for {\sl squarefree factorization},
{\sl distinctdegree factorization}, and {\sl equaldegree factorization}.
The first and second algorithms are deterministic, the third is
 probabilistic."
+ probabilistic.",
+ paper = "Gath01.pdf"
}
\end{chunk}
@@ 8343,8 +8585,8 @@ Proc ISSAC 97 pp172175 (1997)
pages = "149167",
year = "1988",
url = "http://www.sciencedirect.com/science/article/pii/S0747717188800403/pdf?md5=40c29b67947035884904fd4597ddf710&pid=1s2.0S0747717188800403main.pdf",
 paper = "Gian88.pdf",
 algebra = "\newline\refto{package IDECOMP IdealDecompositionPackage}"
+ algebra = "\newline\refto{package IDECOMP IdealDecompositionPackage}",
+ paper = "Gian88.pdf"
}
\end{chunk}
@@ 8360,7 +8602,6 @@ Proc ISSAC 97 pp172175 (1997)
volume = "7",
pages = "114",
year = "1996",

}
\end{chunk}
@@ 8376,7 +8617,7 @@ Proc ISSAC 97 pp172175 (1997)
year = "1982",
month = "December",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/82/Ka82_thesis.pdf",
 paper = "Kalt82.pdf",
+ paper = "Kalt82.pdf"
}
\end{chunk}
@@ 8393,7 +8634,7 @@ Proc ISSAC 97 pp172175 (1997)
pages = "265287",
url =
"http://www.math.ncsu.edu/~kaltofen/bibliography/85/GaKa85_mathcomp.ps.gz",
 paper = "Gath85.ps",
+ paper = "Gath85.ps"
}
\end{chunk}
@@ 8410,7 +8651,7 @@ Proc ISSAC 97 pp172175 (1997)
volume = "45",
pages = "251261",
url =
 "http://www.math.ncsu.edu/~kaltofen/bibliography/85/GaKa85_mathcomp.ps.gz",
+ "http://www.math.ncsu.edu/~kaltofen/bibliography/85/GaKa85\_mathcomp.ps.gz",
paper = "Gath85.ps",
abstract =
"We present a probabilistic algorithm that finds the irreducible
@@ 8436,7 +8677,7 @@ Proc ISSAC 97 pp172175 (1997)
pages = "382392",
year = "2011",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/11/KL11.pdf",
 paper = "Kalt11c.pdf",
+ paper = "Kalt11c.pdf"
}
\end{chunk}
@@ 8453,7 +8694,7 @@ Proc ISSAC 97 pp172175 (1997)
crossref = "ISSAC05",
pages = "208215",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/05/KaKoi05.pdf",
 paper = "Kalt05b.pdf",
+ paper = "Kalt05b.pdf"
}
\end{chunk}
@@ 8470,7 +8711,7 @@ Proc ISSAC 97 pp172175 (1997)
crossref = "ISSAC06",
pages = "162168",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/06/KaKoi06.pdf",
 paper = "Kalt06a.pdf",
+ paper = "Kalt06a.pdf"
}
\end{chunk}
@@ 8487,7 +8728,7 @@ Proc ISSAC 97 pp172175 (1997)
year = "1997",
pages = "184188",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/97/KaSh97.pdf",
 paper = "Kalt97a.pdf",
+ paper = "Kalt97a.pdf"
}
\end{chunk}
@@ 8505,7 +8746,7 @@ Proc ISSAC 97 pp172175 (1997)
number = "223",
pages = "11791197",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/98/KaSh98.pdf",
 paper = "Kalt98.pdf",
+ paper = "Kalt98.pdf"
}
\end{chunk}
@@ 8522,7 +8763,7 @@ Proc ISSAC 97 pp172175 (1997)
address = "New York, N.Y.",
pages = "398406",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/95/KaSh95.ps.gz",
 paper = "Kalt95a.ps",
+ paper = "Kalt95a.ps"
}
\end{chunk}
@@ 8540,7 +8781,7 @@ Proc ISSAC 97 pp172175 (1997)
year = "1988",
organization = "IEEE",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/88/focs88.ps.gz",
 paper = "Kalt88.ps",
+ paper = "Kalt88.ps"
}
\end{chunk}
@@ 8556,7 +8797,7 @@ Proc ISSAC 97 pp172175 (1997)
pages = "451458",
organization = "IEEE",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/85/Ka85_focs.ps.gz",
 paper = "Kalt85b.ps",
+ paper = "Kalt85b.ps"
}
\end{chunk}
@@ 8571,7 +8812,7 @@ Proc ISSAC 97 pp172175 (1997)
pages = "330337",
organization = "ACM",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/86/Ka86_stoc.pdf",
 paper = "Kalt86.pdf",
+ paper = "Kalt86.pdf"
}
\end{chunk}
@@ 8587,7 +8828,7 @@ Proc ISSAC 97 pp172175 (1997)
pages = "443452",
organization = "ACM",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/87/Ka87_stoc.pdf",
 paper = "Kalt87b.pdf",
+ paper = "Kalt87b.pdf"
}
\end{chunk}
@@ 8606,7 +8847,7 @@ Proc ISSAC 97 pp172175 (1997)
series = "Advances in Computing Research",
address = "Greenwhich, Connecticut",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/89/Ka89_slpfac.pdf",
 paper = "Kalt89.pdf",
+ paper = "Kalt89.pdf"
}
\end{chunk}
@@ 8625,7 +8866,7 @@ Proc ISSAC 97 pp172175 (1997)
number = "6",
pages = "14611470",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/01/GKL01.pdf",
 paper = "Gao04.pdf",
+ paper = "Gao04.pdf"
}
\end{chunk}
@@ 8641,7 +8882,7 @@ Proc ISSAC 97 pp172175 (1997)
volume = "4",
pages = "7782",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/87/Ka87_jsc.ps.gz",
 paper = "Kalt87c.ps",
+ paper = "Kalt87c.ps"
}
\end{chunk}
@@ 8657,7 +8898,7 @@ Proc ISSAC 97 pp172175 (1997)
number = "2",
pages = "274295",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/95/Ka95_jcss.pdf",
 paper = "Kalt95b.pdf",
+ paper = "Kalt95b.pdf"
}
\end{chunk}
@@ 8673,7 +8914,7 @@ Proc ISSAC 97 pp172175 (1997)
number = "1",
pages = "5767",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/85/Ka85_jsc.pdf",
 paper = "Kalt85a.pdf",
+ paper = "Kalt85a.pdf"
}
\end{chunk}
@@ 8690,7 +8931,7 @@ Proc ISSAC 97 pp172175 (1997)
pages = "251261",
url =
"http://www.math.ncsu.edu/~kaltofen/bibliography/85/GaKa85_mathcomp.ps.gz",
 paper = "Gath85a.ps",
+ paper = "Gath85a.ps"
}
\end{chunk}
@@ 8707,7 +8948,7 @@ Proc ISSAC 97 pp172175 (1997)
number = "2",
pages = "469489",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/85/Ka85_sicomp.pdf",
 paper = "Kalt85e.pdf",
+ paper = "Kalt85e.pdf"
}
\end{chunk}
@@ 8723,7 +8964,7 @@ Proc ISSAC 97 pp172175 (1997)
pages = "5764",
organization = "IEEE",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/82/Ka82_focs.pdf",
 paper = "Kalt82a.pdf",
+ paper = "Kalt82a.pdf"
}
\end{chunk}
@@ 8739,7 +8980,7 @@ Proc ISSAC 97 pp172175 (1997)
pages = "34",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/03/Ka03.pdf",
keywords = "survey",
 paper = "Kalt03.pdf",
+ paper = "Kalt03.pdf"
}
\end{chunk}
@@ 8758,7 +8999,7 @@ Proc ISSAC 97 pp172175 (1997)
year = "1992",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/92/Ka92_latin.pdf",
keywords = "survey",
 paper = "Kalt92b.pdf",
+ paper = "Kalt92b.pdf"
}
\end{chunk}
@@ 8778,7 +9019,7 @@ Proc ISSAC 97 pp172175 (1997)
address = "New York, N. Y.",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/90/Ka90_survey.ps.gz",
keywords = "survey",
 paper = "Kalt90c.ps",
+ paper = "Kalt90c.ps"
}
\end{chunk}
@@ 8796,7 +9037,7 @@ Proc ISSAC 97 pp172175 (1997)
year = "1982",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/82/Ka82_survey.ps.gz",
keywords = "survey",
 paper = "Kalt82b.ps",
+ paper = "Kalt82b.ps"
}
\end{chunk}
@@ 8809,7 +9050,6 @@ Proc ISSAC 97 pp172175 (1997)
over Finite Fields",
school = "Meron College",
year = "2004",
 paper = "Sale04.pdf",
url = "http://www.cs.aub.edu.lb/fa21/Dissertations/My\_thesis.pdf",
abstract =
"In this thesis we address algorithms for polynomial factorisation
@@ 8845,7 +9085,8 @@ Proc ISSAC 97 pp172175 (1997)
provide wider ranges of applicability. We achieve absolute
irreducibility testing of a bivariate and trivariate polynomial of
degree 30000, and of multivariate polynomials with up to 3000
 variables."
+ variables.",
+ paper = "Sale04.pdf"
}
\end{chunk}
@@ 8860,7 +9101,6 @@ Proc ISSAC 97 pp172175 (1997)
series = "ISSAC 1991",
year = "1991",
pages = "1421",
 paper = "Shou91.pdf",
url = "http://www.shoup.net/papers/quadfactor.pdf",
abstract =
"We present a new algorithm for factoring polynomials over finite
@@ 8868,7 +9108,8 @@ Proc ISSAC 97 pp172175 (1997)
``almost'' quadratic when the characteristic is a small fixed
prime. As such, our algorithm is asymptotically faster than previously
known deterministic algorithms for factoring polynomials over finite
 fields of small characteristic."
+ fields of small characteristic.",
+ paper = "Shou91.pdf"
}
\end{chunk}
@@ 8888,7 +9129,6 @@ Proc ISSAC 97 pp172175 (1997)
year = "1991",
url =
"http://lib.org/by/\_djvu\_Papers/Computer\_algebra/Algebraic\%20numbers",
 paper = "Trev91.djvu",
abstract =
"Research presented here is part of an effort to establish
stateoftheart factoring routines for polynomials. The foundation of
@@ 8898,7 +9138,8 @@ Proc ISSAC 97 pp172175 (1997)
algorithm. The studies led us to design a hybrid algorithm that
combine the strengths of the different approaches. The algorithms are
also implemented and machine timings are obtained to measure the
 performance of these algorithms."
+ performance of these algorithms.",
+ paper = "Trev91.djvu"
}
\end{chunk}
@@ 8916,7 +9157,6 @@ Proc ISSAC 97 pp172175 (1997)
series = "ISSAC'03",
year = "2003",
month = "August",
 paper = "Beau03.pdf",
abstract = "
In [5], we introduced an algorithm for deciding whether a proposed
simplification of elementary functions was correct in the presence of
@@ 8928,7 +9168,8 @@ Proc ISSAC 97 pp172175 (1997)
The purpose of the current paper is to investigate merging the two
techniques. In particular, we will show an explicit reduction to the
 constant problem [16]."
+ constant problem [16].",
+ paper = "Beau03.pdf"
}
\end{chunk}
@@ 8940,22 +9181,21 @@ Proc ISSAC 97 pp172175 (1997)
\index{Watt, Stephen M.}
\begin{chunk}{axiom.bib}
@article{Brad02,
 author="Bradford, Russell and Corless, Robert M. and Davenport, James H. and
 Jeffrey, David J. and Watt, Stephen M.",
 title="Reasoning about the Elementary Functions of Complex Analysis",
 journal="Annals of Mathematics and Artificial Intelligence",
 year="2002",
 issn="10122443",
 volume="36",
 number="3",
 doi="10.1023/A:1016007415899",
 url="http://dx.doi.org/10.1023/A%3A1016007415899",
 publisher="Kluwer Academic Publishers",
 keywords="elementary functions; branch cuts; complex identities",
 pages="303318",
 paper = "Brad02.pdf",
 abstract = "
 There are many problems with the simplification of elementary
+ author = "Bradford, Russell and Corless, Robert M. and Davenport, James H.
+ Jeffrey, David J. and Watt, Stephen M.",
+ title = "Reasoning about the Elementary Functions of Complex Analysis",
+ journal = "Annals of Mathematics and Artificial Intelligence",
+ year = "2002",
+ issn = "10122443",
+ volume = "36",
+ number = "3",
+ doi = "10.1023/A:1016007415899",
+ url = "http://dx.doi.org/10.1023/A%3A1016007415899",
+ publisher = "Kluwer Academic Publishers",
+ keywords = "elementary functions; branch cuts; complex identities",
+ pages = "303318",
+ abstract =
+ "There are many problems with the simplification of elementary
functions, particularly over the complex plane, though not
exclusively. Systems tend to make ``howlers'' or not to simplify
enough. In this paper we outline the ``unwinding number'' approach to
@@ 8964,7 +9204,8 @@ Proc ISSAC 97 pp172175 (1997)
the simplification process to a complete algorithm. The unsolved
problems are probably more amenable to the techniques of artificial
intelligence and theorem proving than the original problem of complex
 variable analysis."
+ variable analysis.",
+ paper = "Brad02.pdf"
}
\end{chunk}
@@ 8975,10 +9216,11 @@ Proc ISSAC 97 pp172175 (1997)
\index{Salvy, Bruno}
\begin{chunk}{axiom.bib}
@inproceedings{Chyz11,
 author = "Chyzak, Fr{\'e}d{\'e}ric and Davenport, James H. and
+ author = "Chyzak, Frederic and Davenport, James H. and
Koutschan, Christoph and Salvy, Bruno",
title = "On Kahan's Rules for Determining Branch Cuts",
 booktitle = "Proc. 13th Int. Symp. on Symbolic and Numeric Algorithms for Scientific Computing",
+ booktitle = "Proc. 13th Int. Symp. on Symbolic and Numeric Algorithms
+ for Scientific Computing",
year = "2011",
isbn = "9781467302074",
location = "Timisoara",
@@ 8986,16 +9228,17 @@ Proc ISSAC 97 pp172175 (1997)
doi = "10.1109/SYNASC.2011.51",
acmid = "258794",
publisher = "IEEE",
 paper = "Chyz11.pdf",
 abstract = "
 In computer algebra there are different ways of approaching the
+ abstract =
+ "In computer algebra there are different ways of approaching the
mathematical concept of functions, one of which is by defining them as
solutions of differential equations. We compare different such
appraoches and discuss the occurring problems. The main focus is on
the question of determining possible branch cuts. We explore the
extent to which the treatment of branch cuts can be rendered (more)
algorithmic, by adapting Kahan's rules to the differential equation
 setting."
+ setting.",
+ paper1 = "Chyz11a.pdf",
+ paper = "Chyz11.pdf"
}
\end{chunk}
@@ 9009,7 +9252,6 @@ Proc ISSAC 97 pp172175 (1997)
volume = "6167",
year = "2010",
pages = "112",
 paper = "Dave10.pdf",
abstract = "
Although, formally, mathematics is clear that a function is a
singlevalued object, mathematical practice is looser, particularly
@@ 9024,11 +9266,38 @@ Proc ISSAC 97 pp172175 (1997)
\end{itemize}
In particular we ask whether there might be a constant ``de Bruij factor''
[18] as we make these texts more formal, and conclude that the answer
 depends greatly on the interpretation being placed on the symbols."
+ depends greatly on the interpretation being placed on the symbols.",
+ paper = "Dave10.pdf"
}
\end{chunk}
+\index{Phisanbut, Nalina}
+\index{Bradford, Russell J.}
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@article{Phis11,
+ author = "Phisanbut, Nalina and Bradford, Russell J. and
+ Davenport, James H.",
+ title = "Geometry of branch cuts",
+ journal = "ACM Communications in Computer Algebra",
+ volume = "44",
+ number = "34",
+ pages = "132135",
+ year = "2011",
+ abstract =
+ "'Simplification' is a key concept in Computer Algebra. But many
+ simplification rules, such as $\sqrt{x}\sqrt{y} \rightarrow \sqrt{xy}$
+ are not universally valid, due to the fact that many elementary
+ functions are multivalued. Hence a key question is ``Is this
+ simplification correct?'', which involves algorithmic analysis of the
+ branch cuts involved. In this paper, we look at variable ordering and
+ preconditioning as supporting technologies for this analysis.",
+ paper = "Phis11.pdf"
+}
+
+\end{chunk}
+
\index{Davenport, James H.}
\index{Bradford, Russell}
\index{England, Matthew}
@@ 9045,7 +9314,6 @@ Proc ISSAC 97 pp172175 (1997)
series = "SYNASC'12",
pages = "8388",
publisher = "IEEE",
 paper = "Dave12.pdf",
abstract = "
In considering the reliability of numerical programs, it is normal to
``limit our study to the semantics dealing with numerical precision''.
@@ 9063,7 +9331,8 @@ Proc ISSAC 97 pp172175 (1997)
The good news is that these problems are theoretically capable of
being solved, and are practically close to being solved, but not yet
solved, in several realworld examples. However, there is still a long
 way to go before implementations match the theoretical possibilities."
+ way to go before implementations match the theoretical possibilities.",
+ paper = "Dave12.pdf"
}
\end{chunk}
@@ 9083,7 +9352,6 @@ Proc ISSAC 97 pp172175 (1997)
publisher = "Springer, Berlin",
pages = "136151",
isbn = "9783642393198",
 paper = "Engl13.pdf",
abstract = "
We assume some standard choices for the branch cuts of a group of
functions and consider the problem of then calculating the branch cuts
@@ 9099,7 +9367,8 @@ Proc ISSAC 97 pp172175 (1997)
classifying the different cuts produced. The techniques have been
gathered in the BranchCuts package, along with tools for visualising
the cuts. The package is included in Maple 17 as part of the
 FunctionAdvisor tool."
+ FunctionAdvisor tool.",
+ paper = "Engl13.pdf"
}
\end{chunk}
@@ 9125,7 +9394,6 @@ Proc ISSAC 97 pp172175 (1997)
acmid = "1040036",
publisher = "ACM",
address = "New York, NY, USA",
 paper = "Jeff04.pdf",
abstract = "
We discuss the multiple definitions of multivalued functions and their
suitability for computer algebra systems. We focus the discussion by
@@ 9136,7 +9404,8 @@ Proc ISSAC 97 pp172175 (1997)
these functions result in formulae that are correct only in the sense
that they give candidates for solutions; these candidates must then be
tested. Formulae that are based on singlevalued functions, in
 contract, are efficient and direct."
+ contract, are efficient and direct.",
+ paper = "Jeff04.pdf"
}
\end{chunk}
@@ 9150,7 +9419,9 @@ Proc ISSAC 97 pp172175 (1997)
year = "1986",
month = "April",
editor = "Powell, M.J.D and Iserles, A.",
 publisher = "Oxford University Press"
+ publisher = "Oxford University Press",
+ paper1 = "Kaha86a.pdf",
+ paper = "Kaha86.pdf"
}
\end{chunk}
@@ 9211,12 +9482,12 @@ Proc ISSAC 97 pp172175 (1997)
acmid = "235703",
publisher = "ACM",
address = "New York, NY, USA",
 paper = "Patt96.pdf",
abstract = "
Handling (possibly) multivalued functions is a problem in all current
computer algebra systems. The problem is not an issue of technology.
Its solution, however, is tied to a uniform handling of the issues by
 the mathematics community."
+ the mathematics community.",
+ paper = "Patt96.pdf"
}
\end{chunk}
@@ 9241,13 +9512,13 @@ Proc ISSAC 97 pp172175 (1997)
acmid = "123545",
publisher = "ACM",
address = "New York, NY, USA",
 paper = "Squi91.pdf",
abstract = "
This document provides the background on decisions that were made
during the development of the specification for Generic Complex
Elementary fuctions. It also rovides some information that was used to
develop error bounds, range, domain and definitions of complex
 elementary functions."
+ elementary functions.",
+ paper = "Squi91.pdf"
}
\end{chunk}
@@ 9280,6 +9551,18 @@ Proc ISSAC 97 pp172175 (1997)
\end{chunk}
+\begin{chunk}{axiom.bib}
+@misc{Unkn15,
+ author = "Unknown",
+ title = "Branches of Functions",
+ url = "http://scipp.ucsc.edu/~haber/ph116A/ComplexFunBranchTheory.pdf",
+ paper = "Unkn15.pdf"
+}
+
+\end{chunk}
+
+
+
\section{Squarefree Decomposition } %%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Bernardin, Laurent}
@@ 9294,8 +9577,6 @@ Proc ISSAC 97 pp172175 (1997)
year = "1997",
month = "November",
pages = "105116",
 keywords = "axiomref",
 paper = "Bern97.pdf",
abstract = "
In this paper we present a new deterministic algorithm for computing
the squarefree decomposition of multivariate polynomials with
@@ 9316,7 +9597,9 @@ Proc ISSAC 97 pp172175 (1997)
Maple (Char et al. 1991), where the new algorithm is used for Release
4 onwards, and Axiom (Jenks and Sutor, 1992) which is the only system
known to the author to use and implementation of Yun's modular
 algorithm mentioned above."
+ algorithm mentioned above.",
+ paper = "Bern97.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 9333,13 +9616,13 @@ Proc ISSAC 97 pp172175 (1997)
year = "2007",
month = "June",
pages = "380420",
 paper = "Chez07.pdf",
abstract = "
In the vein of recent algorithmic advances in polynomial factorization
based on lifting and recombination techniques, we present new faster
algorithms for computing the absolute factorization of a bivariate
polynomial. The running time of our probabilistic algorithm is less
 than quadratic in the dense size of the polynomial to be factored."
+ than quadratic in the dense size of the polynomial to be factored.",
+ paper = "Chez07.pdf"
}
\end{chunk}
@@ 9355,7 +9638,6 @@ Proc ISSAC 97 pp172175 (1997)
year = "2007",
month = "April",
pages = "477494",
 paper = "Lece07.pdf",
abstract = "
We present new deterministic and probabilistic algorithms that reduce
the factorization of dense polynomials from several variables to one
@@ 9363,7 +9645,9 @@ Proc ISSAC 97 pp172175 (1997)
the dense size of the input polynomial, and the probabilistic
algorithm is softly optimal when the number of variables is at least
three. We also investigate the reduction from several to two variables
 and improve the quantitative versions of Bertini's irreducibility theorem."
+ and improve the quantitative versions of Bertini's irreducibility
+ theorem.",
+ paper = "Lece07.pdf"
}
\end{chunk}
@@ 9379,7 +9663,6 @@ Proc ISSAC 97 pp172175 (1997)
year = "1977",
month = "May",
pages = "46",
 paper = "Wang77.pdf",
abstract = "
The concept of polynomial squarefree decomposition is an important one
in algebraic computation. The squarefree decomposition process has
@@ 9388,7 +9671,8 @@ Proc ISSAC 97 pp172175 (1997)
methods depend on computing the greated common divisor (gcd) of the
polynomial to be decomposed and its first derivative (with repect to
some variable). In the multivariate case, this gcd computation is
 nontrivial and dominates the cost for the squarefree decompostion."
+ nontrivial and dominates the cost for the squarefree decompostion.",
+ paper = "Wang77.pdf"
}
\end{chunk}
@@ 9406,7 +9690,6 @@ Proc ISSAC 97 pp172175 (1997)
year = "1979",
publisher = "Society for Industrial and Applied Mathematics",
issn = "00975397",
 paper = "Wang79.pdf",
abstract = "
Previously known algorithms for polynomial squarefree decomposition
rely on greatest common divisor (gcd) computations over the same
@@ 9423,7 +9706,8 @@ Proc ISSAC 97 pp172175 (1997)
factors there are, their multiplicities and their homomorphic
images. Since the multiplicities are known, only the squarefree
factors need to be constructed. Thus, these new algorithms are
 relatively insensitive to the multiplicities of the squarefree factors."
+ relatively insensitive to the multiplicities of the squarefree factors.",
+ paper = "Wang79.pdf"
}
\end{chunk}
@@ 9453,7 +9737,6 @@ Proc ISSAC 97 pp172175 (1997)
volume = "11",
number = "4",
pages = "324330",
 paper = "Abra71.pdf",
abstract = "
An algorithm is given for solving the following problem: let
$F(x_1,\ldots,x_n)$ be a rational function of the variables
@@ 9462,7 +9745,8 @@ Proc ISSAC 97 pp172175 (1997)
coefficients from the same field, such that
\[\sum_{x_1=v}^w{F(x_1,\ldots,x_n)} = G(v,w,x_2,\ldots,x_n)\]
for all integral values of $v \le w$. If $G$ exists, to obtain it.
 Realization of the algorithm in the LISP language is discussed."
+ Realization of the algorithm in the LISP language is discussed.",
+ paper = "Abra71.pdf"
}
\end{chunk}
@@ 9478,7 +9762,6 @@ Proc ISSAC 97 pp172175 (1997)
number = "1",
pages = "4042",
month = "January",
 paper = "Gosp78.pdf",
abstract = "
Given a summand $a_n$, we seek the ``indefinite sum'' $S(n)$
determined (within an additive constant) by
@@ 9509,7 +9792,8 @@ Proc ISSAC 97 pp172175 (1997)
\displaystyle\frac{2b}{ed}\frac{b(2m+3)+c+de}{b(m+1)^2+c(m+1)+e}
\right)
\displaystyle\prod_{j=1}^m{\frac{bj^2+cj+d}{bj^2+cj+e}}}
 {b^2c^2+d^2+e^2+2bd2de+2eb}}\]"
+ {b^2c^2+d^2+e^2+2bd2de+2eb}}\]",
+ paper = "Gosp78.pdf"
}
\end{chunk}
@@ 9528,7 +9812,6 @@ Proc ISSAC 97 pp172175 (1997)
pages = "305350",
url = "http://doi.acm.org/10.1145/322248.322255",
publisher = "ACM",
 paper = "Karr81",
abstract = "
Results which allow either the computation of symbolic solutions to
firstorder linear difference equations or the determination that
@@ 9539,7 +9822,8 @@ Proc ISSAC 97 pp172175 (1997)
fields that the difference equations may be posed and in which the
solutions are requested. The principal application of these results is
in finding formulas for a broad class of finite sums or in showing the
 nonexistence of such formula."
+ nonexistence of such formula.",
+ paper = "Karr81"
}
\end{chunk}
@@ 9553,14 +9837,14 @@ Proc ISSAC 97 pp172175 (1997)
publisher = "SpringerVerlag",
isbn = "321181776X",
pages = "7177",
 keywords = "axiomref,survey",
abstract = "
A survey on algorithms for summation in finite terms is given. After a
precise definition of the problem the cases of polynomial and rational
summands are treated. The main concern of this paper is a description
of Gosper's algorithm, which is applicable for a wide class of
summands. Karr's theory of extension difference fields and some
 heuristic techniques are touched on briefly."
+ heuristic techniques are touched on briefly.",
+ keywords = "axiomref,survey"
}
\end{chunk}
@@ 9575,15 +9859,15 @@ Proc ISSAC 97 pp172175 (1997)
volume = "25",
number = "5",
pages = "99102",
 paper = "Abra85.pdf",
 abstract = "
The problem of expanding a rational function of several variables into
terms with separable variables is formulated. An algorithm for solving
this problem is given. Programs which implement this algorithm can
occur in sets of algebraic alphabetical transformations on a computer
and can be used to reduce the multiplicity of sums and integrals of
rational functions for investigating differential equations with
rational righthand sides etc."
+ abstract =
+ "The problem of expanding a rational function of several variables into
+ terms with separable variables is formulated. An algorithm for solving
+ this problem is given. Programs which implement this algorithm can
+ occur in sets of algebraic alphabetical transformations on a computer
+ and can be used to reduce the multiplicity of sums and integrals of
+ rational functions for investigating differential equations with
+ rational righthand sides etc.",
+ paper = "Abra85.pdf"
}
\end{chunk}
@@ 9599,13 +9883,13 @@ rational righthand sides etc."
number = "3",
month = "September",
pages = "303315",
 paper = "Karr85.pdf",
abstract = "
This paper discusses some of the mathematical aspects of an algorithm
for finding formulas for finite sums. The results presented here
concern a property of difference fields which show that the algorithm
does not divide by zero, and an analogue to Liouville's theorem on
 elementary integrals."
+ elementary integrals.",
+ paper = "Karr85.pdf"
}
\end{chunk}
@@ 9618,7 +9902,6 @@ rational righthand sides etc."
publisher = "Springer",
year = "1998",
isbn = "9781447164647",
 paper = "Koep98.pdf",
abstract = "
Modern algorithmic techniques for summation, most of which were
introduced in the 1990s, are developed here and carefully implemented
@@ 9638,7 +9921,8 @@ rational righthand sides etc."
The materials covered are sutiable for an introductory course on
algorithmic summation and will appeal to students and researchers
 alike."
+ alike.",
+ paper = "Koep98.pdf"
}
\end{chunk}
@@ 9653,7 +9937,6 @@ rational righthand sides etc."
volume = "S43b",
pages = "110",
url = "",
 paper = "Schn00.pdf",
abstract = "
Implementations of the celebrated Gosper algorithm (1978) for
indefinite summation are available on almost any computer algebra
@@ 9666,8 +9949,8 @@ rational righthand sides etc."
addition we provide a feature to find automatically appropriate
difference field extensions in which a closed form for the summation
problem exists. These new aspects are illustrated by a variety of
 examples."

+ examples.",
+ paper = "Schn00.pdf"
}
\end{chunk}
@@ 9681,10 +9964,8 @@ rational righthand sides etc."
year = "2001",
url =
"http://www.risc.jku.at/publications/download/risc_3017/SymbSumTHESIS.pdf",
 paper = "Schn01.pdf",
 abstract = "

 There are implementations of the celebrated Gosper algorithm (1978) on
+ abstract =
+ "There are implementations of the celebrated Gosper algorithm (1978) on
almost any computer algebra platform. Within my PhD thesis work I
implemented Karr's Summation Algorithm (1981) based on difference
field theory in the Mathematica system. Karr's algorithm is, in a
@@ 9707,8 +9988,8 @@ rational righthand sides etc."
telescoping as a special case of sum extensions in an indefinite
summation problem. In particular we are able to determine sum
extensions, in case of existence, to reduce the order of a recurrence
 for a definite summation problem."

+ for a definite summation problem.",
+ paper = "Schn01.pdf"
}
\end{chunk}
@@ 9720,8 +10001,8 @@ rational righthand sides etc."
title = "Contributions to Symbolic Summation",
school = "Johannes Kepler University, RISC",
year = "1995",
 paper = "Scho95.pdf",
 url = "http://www.risc.jku.at/publications/download/risc_2246/diplom.pdf"
+ url = "http://www.risc.jku.at/publications/download/risc_2246/diplom.pdf",
+ paper = "Scho95.pdf"
}
\end{chunk}
@@ 9737,13 +10018,13 @@ rational righthand sides etc."
booktitle = "Proceedings of ISSAC'03",
year = "2003",
pages = "119126",
 paper = "Gerh03.pdf",
abstract = "
New algorithms are presented for computing the dispersion set of two
polynomials over {\bf Q} and for {\sl shiftless} factorization. Together
with a summability criterion by Abramov, these are applied to get a
polynomialtime algorithm for indefinite rational summation, using a
 sparse representation of the output."
+ sparse representation of the output.",
+ paper = "Gerh03.pdf"
}
\end{chunk}
@@ 9758,7 +10039,6 @@ rational righthand sides etc."
volume = "34",
number = "4",
pages = "740767",
 paper = "Schn05.pdf",
abstract = "
We present a general algorithmic framework that allows not only to
deal with summation problems over summands being rational expressions
@@ 9767,7 +10047,8 @@ rational righthand sides etc."
linear recurrence. This approach implies new computer algebra tools
implemented in Sigma to solve multisummation problems efficiently.
For instacne, the extended Sigma package has been applied successively
 to provide a computerassisted proof of Stembridge's TSPP Theorem."
+ to provide a computerassisted proof of Stembridge's TSPP Theorem.",
+ paper = "Schn05.pdf"
}
\end{chunk}
@@ 9783,14 +10064,14 @@ rational righthand sides etc."
volume = "306",
number = "17",
pages = "20732083",
 paper = "Kaue08a.pdf",
abstract = "
We provide a new algorithm for indefinite nested summation which is
applicable to summands involving unspecified sequences $x(n)$. More
than that, we show how to extend Karr's algorithm to a general
summation framework by which additional types of summand expressions
can be handled. Our treatment of unspecified sequences can be seen as
 a first illustrative application of this approach."
+ a first illustrative application of this approach.",
+ paper = "Kaue08a.pdf"
}
\end{chunk}
@@ 9806,16 +10087,16 @@ rational righthand sides etc."
number = "10",
month = "October",
pages = "948970",
 paper = "Kaue07.pdf",
 abstract = "
 We consider a class of sequences defined by triangular recurrence
+ abstract =
+ "We consider a class of sequences defined by triangular recurrence
equations. This class contains Stirling numbers and Eulerian numbers
of both kinds, and hypergeometric multiples of those. We give a
sufficient criterion for sums over such sequences to obey a recurrence
equation, and present algorithms for computing such recurrence
equations efficiently. Our algorithms can be used for verifying many
known summation identities on Stirling numbers instantly, and also for
 discovering new identities."
+ discovering new identities.",
+ paper = "Kaue07.pdf"
}
\end{chunk}
@@ 9830,12 +10111,12 @@ rational righthand sides etc."
volume = "56",
article = "B56b",
url = "",
 paper = "Schn07.pdf",
abstract = "
We present symbolic summation tools in the context of difference
fields that help scientists in practical problem solving. Throughout
this article we present multisum examples which are related to
 combinatorial problems."
+ combinatorial problems.",
+ paper = "Schn07.pdf"
}
\end{chunk}
@@ 9850,13 +10131,13 @@ rational righthand sides etc."
volume = "43",
number = "9",
pages = "611644",
 paper = "Schn08.pdf",
abstract = "
In this article we present a refined summation theory based on Karr's
difference field approach. The resulting algorithms find sum
representations with optimal nested depth. For instance, the
algorithms have been applied successively to evaluate Feynman
 integrals from Perturbative Quantum Field Theory"
+ integrals from Perturbative Quantum Field Theory",
+ paper = "Schn08.pdf"
}
\end{chunk}
@@ 9870,14 +10151,14 @@ rational righthand sides etc."
year = "2010",
volume = "21",
pages = "132",
 paper = "Schn09.pdf",
abstract = "
Starting with Karr's structural theorem for summation  the discrete
version of Liouville's structural theorem for integration  we work
out crucial properties of the underlying difference fields. This leads
to new and constructive structural theorems for symbolic summation.
E.g., these results can be applied for harmonic sums which arise
 frequently in particle physics."
+ frequently in particle physics.",
+ paper = "Schn09.pdf"
}
\end{chunk}
@@ 9896,7 +10177,6 @@ rational righthand sides etc."
pages = "190193",
url = "http://doi.acm.org/10.1145/1940475.1940517",
publisher = "ACM",
 paper = "Eroc10.pdf",
abstract = "
The summation analogue of the Risch integration algorithm developed by
Karr uses towers of difference fields to model nested indefinite sums
@@ 9913,7 +10193,8 @@ rational righthand sides etc."
structures involved while taking advantage of the state of the art
primitives provided by Sage. Even though these methods are used behind
the scenes in the summation package Sigma and they were previously
 implemented, this is the first open source implementation."
+ implemented, this is the first open source implementation.",
+ paper = "Eroc10.pdf"
}
\end{chunk}
@@ 9927,7 +10208,6 @@ rational righthand sides etc."
year = "2011",
url =
"http://www.risc.jku.at/publications/download/risc_4320/erocal_thesis.pdf",
 paper = "Eroc11.pdf",
abstract =
"The main result of this thesis is an effective method to extend Karr's
symbolic summation framework to algebraic extensions. These arise, for
@@ 9965,7 +10245,8 @@ rational righthand sides etc."
fields. We present a fast algorithm for matrices over $\mathbb{Q}(x)$
which uses fast arithmetic at the hardware level with calls to BLAS
subroutines after modular reduction. This part is joint work with Arne
 Storjohann."
+ Storjohann.",
+ paper = "Eroc11.pdf"
}
\end{chunk}
@@ 9982,7 +10263,6 @@ rational righthand sides etc."
volume = "37",
number = "6",
pages = "322325",
 paper = "Poly11.pdf",
abstract = "
A computer algebra algorithm for indefinite summation of rational
functions based on complete factorization of denominators is
@@ 9992,7 +10272,8 @@ rational righthand sides etc."
that additionally minimizes the degree of the denominator of
$g$. Computational complexity of the algorithms without regard to
denominator factorization is shown to be $O(m^2)$, where $m$ is the
 degree of the denominator of $f$."
+ degree of the denominator of $f$.",
+ paper = "Poly11.pdf"
}
\end{chunk}
@@ 10006,7 +10287,6 @@ rational righthand sides etc."
journal = "CoRR",
year = "2013",
volume = "abs/1307.7887",
 paper = "Schn13.pdf",
keywords = "survey",
abstract = "
Parameterized telescoping (including telescoping and creative
@@ 10017,7 +10297,8 @@ rational righthand sides etc."
covering as special cases, e.g., the (q)hypergeometric case and their
mixed versions. This survey article presents the available algorithms
in the framework of $\prod\sum$extensions and elaborates new results
 concerning efficiency."
+ concerning efficiency.",
+ paper = "Schn13.pdf"
}
\end{chunk}
@@ 10033,7 +10314,6 @@ rational righthand sides etc."
volume = "7",
number = "4",
pages = "455472",
 paper = "Zima13.pdf",
abstract = "
We present the history of indefinite summation starting with classics
(Newton, Montmort, Taylor, Stirling, Euler, Boole, Jordan) followed by
@@ 10042,7 +10322,8 @@ rational righthand sides etc."
we describe several ``acceleration techniques'' of algorithms for
indefinite summation which offer not only theoretical but also
practical improvements in running time. Implementations of these
 algorithms in Maple are compared to standard Maple summation tools"
+ algorithms in Maple are compared to standard Maple summation tools",
+ paper = "Zima13.pdf"
}
\end{chunk}
@@ 10053,7 +10334,6 @@ rational righthand sides etc."
author = "Schneider, Carsten",
title = "A Difference Ring Theory for Symbolic Summation",
year = "2014",
 paper = "Schn14.pdf",
abstract = "
A summation framework is developed that enhances Karr's difference
field approach. It covers not only indefinite nested sums and products
@@ 10068,7 +10348,8 @@ rational righthand sides etc."
summation paradigms of telescoping and Zeilberger's creative
telescoping. With this difference ring theory one obtains a rigorous
summation machinery that has been applied to numerous challenging
 problems coming, e.g., from combinatorics and particle physics."
+ problems coming, e.g., from combinatorics and particle physics.",
+ paper = "Schn14.pdf"
}
\end{chunk}
@@ 10080,7 +10361,6 @@ rational righthand sides etc."
title = "Symbolic Summation in Difference Fields",
year = "2014",
school = "CarnegieMellon University",
 paper = "Vazq14.pdf",
abstract = "
We seek to understand a general method for finding a closed form for a
given sum that acts as its antidifference in the same way that an
@@ 10102,7 +10382,8 @@ rational righthand sides etc."
examines the Homogeneous Group Membership Problem. Section 6 presents
some proofs for the denominator and polynomial bounds used in solving
difference equations, and Section 7 gives some directions for future
 work."
+ work.",
+ paper = "Vazq14.pdf"
}
\end{chunk}
@@ 10127,13 +10408,13 @@ rational righthand sides etc."
@misc{Temm14,
author = "Temme, N.M.",
title = "Bernoulli Polynomials Old and New",
 paper = "Temm14.pdf",
 abstract = "
 We consider two problems on generalized Bernoulli polynomials
+ abstract =
+ "We consider two problems on generalized Bernoulli polynomials
$B_n^u(z)$. One is connected with defining functions instead of
polynomials by making the degree $n$ of the polynomial a complex
variable. In the second problem we are concerned with the asymptotic
 behaviour of $B_n^u(z)$ when the degree $n$ tends to infinity."
+ behaviour of $B_n^u(z)$ when the degree $n$ tends to infinity.",
+ paper = "Temm14.pdf"
}
\end{chunk}
@@ 10298,7 +10579,6 @@ rational righthand sides etc."
title = "On Mechanical Quantifier Elimination for Elementary Algebra and Geometry",
J. Symbolic Computation 5, 237259 (1988)
url = "http://http://www.sciencedirect.com/science/article/pii/S0747717188800142/pdf?md5=62052077d84e6078cc024bc8e29c23c1&pid=1s2.0S0747717188800142main.pdf",
 paper = "Arno88.pdf",
abstract = "
We give solutions to two problems of elementary algebra and geometry:
(1) find conditions on real numbers $p$, $q$, and $r$ so that the
@@ 10312,7 +10592,8 @@ J. Symbolic Computation 5, 237259 (1988)
steps. We have found three equally simple but not obviously equivalent
solutions for the first problem, illustrating the difficulty of
obtaining unique ``simplest'' solutions to quantifier elimination
 problems of elementary algebra and geometry."
+ problems of elementary algebra and geometry.",
+ paper = "Arno88.pdf"
\end{chunk}
@@ 10332,7 +10613,6 @@ J. Symbolic Computation 5, 237259 (1988)
issn = "09381279",
publisher = "SpringerVerlag",
pages = "513543",
 paper = "Beau07.pdf",
abstract = "
One of the problems with manipulating function identities in computer
algebra systems is that they often involve functions which are
@@ 10354,7 +10634,8 @@ J. Symbolic Computation 5, 237259 (1988)
{\sl signed zeros} by W. Kahan, and develop this idea further in order to
allow us to cover previously untreatable cases. Finally, we discuss
other ways to improve upon our general methodology as well as topics
 for future research."
+ for future research.",
+ paper = "Beau07.pdf"
}
\end{chunk}
@@ 10372,7 +10653,6 @@ J. Symbolic Computation 5, 237259 (1988)
title = "Truth Table Invariant Cylindrical Algebraic Decomposition by
Regular Chains",
url = "https://arxiv.org/pdf/1401.6310.pdf",
 paper = "Brad14.pdf",
year = "2014",
abstract =
"A new algorithm to compute cylindrical algebraic decompositions
@@ 10385,7 +10665,8 @@ J. Symbolic Computation 5, 237259 (1988)
achieve the more sophisticated invariance criteria. Experimental
results on an implementation in the {\tt RegularChains} Library for Maple
verify that combining these advances gives an algorithm superior to
 its individual components and competitive with the state of the art."
+ its individual components and competitive with the state of the art.",
+ paper = "Brad14.pdf"
}
\end{chunk}
@@ 10401,7 +10682,6 @@ J. Symbolic Computation 5, 237259 (1988)
McCallum, Scott",
title = "Truth Table Invariant Cylindrical Algebraic Decomposition",
url = "https://arxiv.org/pdf/1401.0645.pdf",
 paper = "Brad15.pdf",
year = "2015",
abstract =
"When using cylindrical algebraic decomposition (CAD) to solve a
@@ 10421,7 +10701,8 @@ J. Symbolic Computation 5, 237259 (1988)
CAD algorithms, even in the context of a single equational constraint.
The algorithm is implemented fully in Maple and we present both
promising results from experimentation and a complexity analysis
 showing the benefits of our contributions."
+ showing the benefits of our contributions.",
+ paper = "Brad15.pdf"
}
\end{chunk}
@@ 10435,7 +10716,6 @@ J. Symbolic Computation 5, 237259 (1988)
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
@@ 10460,7 +10740,8 @@ J. Symbolic Computation 5, 237259 (1988)
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."
+ based on these implementations are discussed.",
+ paper = "Brow99.pdf"
}
\end{chunk}
@@ 10472,7 +10753,6 @@ J. Symbolic Computation 5, 237259 (1988)
title="The McCallum projection, lifting, and orderinvariance",
year="2001",
url="http://www.usna.edu/Users/cs/wcbrown/research/MOTS2001.1.ps.gz",
 paper = "Brow01.pdf",
abstract =
"The McCallum Projection for Cylindrical Algebraic Decomposition (CAD)
produces a smaller projection factor set than previous projections,
@@ 10504,7 +10784,8 @@ J. Symbolic Computation 5, 237259 (1988)
are printed when not needed. Neither McCallum's modified lifting
method nor our improvement of it have been implemented in QEPCAD. The
design of the system would make implementing such a feature quite
 difficult."
+ difficult.",
+ paper = "Brow01.pdf"
}
\end{chunk}
@@ 10515,7 +10796,6 @@ J. Symbolic Computation 5, 237259 (1988)
author = "Brown, Christopher W.",
title = "QEPCAD B  A program for computing with semialgebraic sets
using CADs",
 paper = "Brow02.pdf",
year = "2002",
abstract =
"This report introduces QEPCAD B, a program for computing with real
@@ 10528,7 +10808,8 @@ J. Symbolic Computation 5, 237259 (1988)
that go beyond quantifier elimination. The author is responsible for
most of the extended features of QEPCAD B, but improvements to the
basic CAD implementation and to the SACLIB library on which QEPCAD is
 based are the results of many people's work."
+ based are the results of many people's work.",
+ paper = "Brow02.pdf"
}
\end{chunk}
@@ 10546,7 +10827,6 @@ J. Symbolic Computation 5, 237259 (1988)
title = "Triangular Decomposition of Semialgebraic Systems",
year = "2010",
url = "https://arxiv.org/pdf/1002.4784.pdf",
 paper = "Chen10.pdf",
abstract =
"Regular chains and triangular decompositions are fundamental and
welldeveloped tools for describing the complex solutions of
@@ 10559,7 +10839,8 @@ J. Symbolic Computation 5, 237259 (1988)
assumptions, one type of decomposition can be computed in singly
exponential time w.r.t. the number of variables. We implement our
algorithms and the experimental results illustrate their
 effectiveness."
+ effectiveness.",
+ paper = "Chen10.pdf"
}
\end{chunk}
@@ 10572,7 +10853,6 @@ J. Symbolic Computation 5, 237259 (1988)
title = "An Incremental Algorithm for Computing Cylindrical Algebraic
Decompositions",
url = "https://arxiv.org/pdf/1210.5543.pdf",
 paper = "Chen12.pdf",
year = "2012",
abstract =
"In this paper, we propose an incremental algorithm for computing
@@ 10583,7 +10863,8 @@ J. Symbolic Computation 5, 237259 (1988)
is constructed by refining a previous complex cylindrical tree with a
polynomial constraint. We have implemented our algorithm in Maple. The
experimentation shows that the proposed algorithm outperforms existing
 ones for many examples taken from the literature"
+ ones for many examples taken from the literature",
+ paper = "Chen12.pdf"
}
\end{chunk}
@@ 10601,8 +10882,6 @@ J. Symbolic Computation 5, 237259 (1988)
isbn = "3540230254",
location = "Bergen, Norway",
pages = "652663",
 keywords = "axiomref",
 paper = "Emir04.pdf",
url = "http://wwwpolsys.lip6.fr/~elias/files//etesa04.pdf",
algebra = "\newline\refto{domain RECLOS RealClosure}",
abstract =
@@ 10626,7 +10905,9 @@ J. Symbolic Computation 5, 237259 (1988)
implementations: Rioboo’s approach on AXIOM, the package of
GuibasKaravelasRussel, and CORE v1.6, MAPLE v9, and SYNAPS
v2.0. Some existing limited tests had shown that it is faster than
 commercial library LEDA v4.5 for quadratic algebraic numbers."
+ commercial library LEDA v4.5 for quadratic algebraic numbers.",
+ paper = "Emir04.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 10642,7 +10923,6 @@ J. Symbolic Computation 5, 237259 (1988)
title = "Using the Regular Chains Library to build cylindrical algebraic
decompositions by projecting and lifting",
url = "https://arxiv.org/pdf/1405.6090.pdf",
 paper = "Engl14.pdf",
year = "2014",
abstract =
"Cylindrical algebraic decomposition (CAD) is an important tool, both
@@ 10657,7 +10937,8 @@ J. Symbolic Computation 5, 237259 (1988)
RegularChains Library to build CADs by projection and lifting. We
detail how the projection and lifting algorithms were modified to
allow this, discuss the motivation and survey the functionality of the
 package."
+ package.",
+ paper = "Engl14.pdf"
}
\end{chunk}
@@ 10673,7 +10954,6 @@ J. Symbolic Computation 5, 237259 (1988)
title = "Choosing a variable ordering for truthtable invariant cylindrical
algebraic decomposition by incremental triangular decomposition",
url = "https://arxiv.org/pdf/1405.6094.pdf",
 paper = "Engl14a.pdf",
year = "2014",
abstract =
"Cylindrical algebraic decomposition (CAD) is a key tool for solving
@@ 10687,7 +10967,8 @@ J. Symbolic Computation 5, 237259 (1988)
on the tractability of a problem. We evaluate existing heuristics to
help with the choice for this algorithm, suggest improvements and then
derive a new heuristic more closely aligned with the mechanics of the
 new algorithm."
+ new algorithm.",
+ paper = "Engl14a.pdf"
}
\end{chunk}
@@ 10705,7 +10986,6 @@ J. Symbolic Computation 5, 237259 (1988)
title = "Problem formulation for truthtable invariant cylindrical
algebraic decomposition by incremental triangular decomposition",
url = "https://arxiv.org/pdf/1404.6371.pdf",
 paper = "Engl14b.pdf",
year = "2014",
abstract =
"Cylindrical algebraic decompositions (CADs) are a key tool for
@@ 10721,7 +11001,8 @@ J. Symbolic Computation 5, 237259 (1988)
develop new heuristics to help make this choice and thus allow the
best use of the algorithm in practice. We also consider other choices
of problem formulation for CAD, as discussed in CICM 2013, revisiting
 these in the context of the new algorithm."
+ these in the context of the new algorithm.",
+ paper = "Engl14b.pdf"
}
\end{chunk}
@@ 10739,7 +11020,6 @@ J. Symbolic Computation 5, 237259 (1988)
series = "LNCS 7961",
publisher = "ACM",
url = "http://opus.bath.ac.uk/42451/",
 paper = "Engl15.pdf",
abstract = "
When building a cylindrical algebraic decomposition (CAD) savings can
be made in the presence of an equational constraint (EC): an equation
@@ 10750,7 +11030,8 @@ J. Symbolic Computation 5, 237259 (1988)
improve on the approach of McCallum in ISSAC 2001 by using the reduced
projection theory to make savings in the lifting phase (both to the
polynomials we lift with and the cells lifted over). We demonstrate
 the benefits with worked examples and a complexity analysis."
+ the benefits with worked examples and a complexity analysis.",
+ paper = "Engl15.pdf"
}
\end{chunk}
@@ 10777,14 +11058,14 @@ J. Symbolic Computation 5, 237259 (1988)
volume = "17",
year = "2007",
pages = "99127",
 paper = "Mahb07.pdf",
abstract = "The Coq system is a CurryHoward based proof assistant.
Therefore, it contains a full functional, strongly typed programming
language, which can be used to enhance the system with powerful
automation tools through the implementation of reflexive tactics.
We present the implementation of a cylindrical algebraic decomposition
algorithm within the Coq system, whose certification leads to a proof
 producing decision procedure for the firstorder theory of real numbers."
+ producing decision procedure for the firstorder theory of real numbers.",
+ paper = "Mahb07.pdf"
}
\end{chunk}
@@ 10795,7 +11076,6 @@ J. Symbolic Computation 5, 237259 (1988)
author = "Rioboo, Renaud",
title = "Cylindrical Algebraic Decomposition class notes",
url = "http://people.bath.ac.uk/masjhd/TRITA.pdf",
 paper = "Riobxx.pdf",
year = "2016",
abstract =
"This report describes techniques for resolving systems of polynomial
@@ 10805,7 +11085,8 @@ J. Symbolic Computation 5, 237259 (1988)
sign. Most of the report is spent describing the algebraic and
algorithmic prerequisites (resultants, algebraic numbers, Sturm
sequences, etc.), and then describing the method, first in two
 dimensions and then in an arbitrary number of dimensions"
+ dimensions and then in an arbitrary number of dimensions",
+ paper = "Riobxx.pdf"
}
\end{chunk}
@@ 10824,8 +11105,6 @@ J. Symbolic Computation 5, 237259 (1988)
location = "Berkeley, California",
pages = "206215",
isbn = "0897914899 (soft), 0897914902 (hard)",
 paper = "Riob92.pdf",
 keywords = "axiomref",
algebra = "\newline\refto{domain RECLOS RealClosure}",
abstract =
"Real algebraic numbers appear in many Computer Algebra problems. For
@@ 10835,7 +11114,43 @@ J. Symbolic Computation 5, 237259 (1988)
roots of a polynomial. This process is designed to be recursively
used, so the resulting domain of computation is the set of all real
algebraic numbers. An implementation for the real algebraic closure
 has been done in Axiom (previously called Scratchpad)."
+ has been done in Axiom (previously called Scratchpad).",
+ paper = "Riob92.pdf",
+ keywords = "axiomref",
+ beebe = "Rioboo:1992:RAC"
+}
+
+\end{chunk}
+\begin{chunk}{Rioboo:1992:RAC}
+@InProceedings{Rioboo:1992:RAC,
+ author = "Renaud Rioboo",
+ title = "Real algebraic closure of an ordered field,
+ implementation in {Axiom}",
+ crossref = "Wang:1992:ISS",
+ pages = "206215",
+ year = "1992",
+ bibdate = "Tue Sep 17 06:35:39 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "Real algebraic numbers appear in many computer algebra
+ problems. For instance the determination of a
+ cylindrical algebraic decomposition for an Euclidian
+ space requires computing with real algebraic numbers.
+ This paper describes an implementation for computations
+ with the real roots of a polynomial. This process is
+ designed to be recursively used, so the resulting
+ domain of computation is the set of all real algebraic
+ numbers. An implementation for the real algebraic
+ closure has been done in Axiom (previously called
+ Scratchpad).",
+ acknowledgement = acknhfb,
+ affiliation = "LITP, Univ. Pierre et Marie Curie, Paris, France",
+ classification = "C4130 (Interpolation and function approximation);
+ C6130 (Data handling techniques); C7310 (Mathematics)",
+ keywords = "Axiom; Computer algebra; Cylindrical algebraic
+ decomposition; Euclidian space; Ordered field;
+ Polynomial; Real algebraic closure",
+ language = "English",
+ thesaurus = "Polynomials; Symbol manipulation",
}
\end{chunk}
@@ 10850,7 +11165,6 @@ J. Symbolic Computation 5, 237259 (1988)
England, Matthew",
title = "Cylindrical Algebraic SubDecompositions",
url = "https://arxiv.org/pdf/1401.0647.pdf",
 paper = "Wils14.pdf",
year = "2014",
abstract =
"Cylindrical algebraic decompositions (CADs) are a key tool in real
@@ 10866,7 +11180,8 @@ J. Symbolic Computation 5, 237259 (1988)
each other and the recent theory of truthtable invariant CAD. We
give a complexity analysis showing that these techniques can offer
substantial theoretical savings, which is supported by experimentation
 using an implementation in Maple."
+ using an implementation in Maple.",
+ paper = "Wils14.pdf"
}
\end{chunk}
@@ 10882,13 +11197,13 @@ J. Symbolic Computation 5, 237259 (1988)
volume = "46",
pages = "904918",
year = "2011",
 paper = "Zhao11.pdf",
abstract =
"We present a convention (for square/cubic roots) which provides
correct interpretations of the Lagrange formula for all cubic
polynomial equations with real coefficients. Using this convention, we
also present a real solution formula for the general cubic equation
 with real coefficients under equality and inequality constraints."
+ with real coefficients under equality and inequality constraints.",
+ paper = "Zhao11.pdf"
}
\end{chunk}
@@ 10905,8 +11220,6 @@ J. Symbolic Computation 5, 237259 (1988)
number = "1",
pages = "920",
year = "1996",
 keywords = "axiomref",
 paper = "Bern96.pdf",
abstract =
"Solving equations and systems of equations symbolically is a key
feature of every Computer Algebra System. This review examines the
@@ 10922,7 +11235,9 @@ J. Symbolic Computation 5, 237259 (1988)
Maple V R4 [3], Mathematica 2.2 [10], MuPAD 1.2.9 [5] and Reduce 3.6
[6]. When available, we tried to use the latest shipping version of
each system. 2 The Problem Set The following table presents the set of
 80 problems that we used to evaluate the different solvers..."
+ 80 problems that we used to evaluate the different solvers...",
+ paper = "Bern96.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 10933,8 +11248,6 @@ J. Symbolic Computation 5, 237259 (1988)
author = "Wester, Michael J.",
title = "A Review of CAS Mathematical Capabilities",
year = "1995",
 keywords = "axiomref",
 paper = "West95.pdf",
url = "http://math.unm.edu/~wester/cas/Paper.ps",
abstract =
"Computer algebra systems (CASs) have become an important
@@ 10950,7 +11263,9 @@ J. Symbolic Computation 5, 237259 (1988)
difficult or possible to produce an answer and if an answer was
produced, whether it was correct. It is the author's hope that this
review will encourage the development of a comprehensive CAS test
 suite."
+ suite.",
+ paper = "West95.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 10963,8 +11278,6 @@ J. Symbolic Computation 5, 237259 (1988)
year = "1999",
url = "http://math.unm.edu/~wester/cas/book/Wester.pdf",
url2 = "http://math.unm.edu/~wester/cas_review.html",
 paper = "West99a.pdf",
 keywords = "axiomref",
abstract =
"Computer algebra systems (CASs) have become an essential computational
tool in the last decade. General purpose CASs, which are designed to
@@ 10972,13 +11285,394 @@ J. Symbolic Computation 5, 237259 (1988)
this chapter, the capabilities of seven major general purpose CASs
(Axiom, Derive, Macsyma, Maple, Mathmatica, MuPAD and Reduce) are
reviewed on 542 short problems covering a broad range of (primarily)
 symbolic mathematics."
+ symbolic mathematics.",
+ paper = "West99a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
\section{To Be Classified} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{OpenMath}
+\index{Complex}
+\index{DoubleFloat}
+\index{Float}
+\index{Fraction}
+\index{Integer}
+\index{List}
+\index{SingleInteger}
+\index{String}
+\index{Symbol}
+\index{ExpressionToOpenMath}
+\index{OpenMathServerPackage}
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate01a,
+ author = "Fateman, Richard J.",
+ title = "A Critique of OpenMath and Thoughts on Encoding Mathematics",
+ year = "2001",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/openmathcrit.pdf",
+ algebra =
+ "\newline\refto{category OM OpenMath}
+ \newline\refto{domain COMPLEX Complex}
+ \newline\refto{domain DFLOAT DoubleFloat}
+ \newline\refto{domain FLOAT Float}
+ \newline\refto{domain FRAC Fraction}
+ \newline\refto{domain INT Integer}
+ \newline\refto{domain LIST List}
+ \newline\refto{domain SINT SingleInteger}
+ \newline\refto{domain STRING String}
+ \newline\refto{domain SYMBOL Symbol}
+ \newline\refto{package OMEXPR ExpressionToOpenMath}
+ \newline\refto{package OMSERVER OpenMathServerPackage}",
+ abstract =
+ "The OpenMath project, as portrayed in the Special Issue of the SIGSAM
+ Bulletin (volume 34 no. 2), seems to have a number of problems to
+ face. One of them is the (apparently implicit) assumption that
+ OpenMath designers, through dint of mathematical thought and the
+ advice of the members of the Open Math Society, have solved, in their
+ domain, one of the most pressing problems of software engineering
+ today, namely software reuse. After six years there is insufficient
+ evidence on which to base any claims of success and it appears that
+ most substantive practical issues of mathematical representation and
+ communication have yet to be addressed. We also raise questions about
+ related computational mathematical goals and mathematical encodings.",
+ paper = "Fate01a.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate08a,
+ author = "Fateman, Richard J.",
+ title = "Verbs, Nouns, and Computer Algebra, or What's Grammar Got
+ to do with Math?",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/nounverbmac.pdf",
+ year = "2008",
+ abstract =
+ "Computer algebra systems (CAS) are supposed to do mathematics.
+ Unfortunately, much of human mathematics presentation and
+ manipulation depends on humans to understand what is going on more
+ generally. This context is often not made available to the computer
+ system, and so it will sometimes fail to make the right guess at the
+ meaning of constructions, unless they are made unambiguous. Among many
+ issues, one that has been raised and resolved, is the need for
+ attributing properties to operators that distinguish between ``the name
+ of the operation'' and ``the operation itself''.
+
+ As a simple example, referential transparency requires that if $x = y$,
+ then any true statement $P(x)$ about $x$ must be true about $y$, namely
+ $P(y)$ is also true.
+
+ Consider now the wellknown equation $sin(0) = 0$, and the statement
+ $P(r) :=$ ``r = 0 is a rule to simplify the sin() function''. The
+ statement $P(sin(0))$ is clearly true. Therefore $P(0)$ should be true
+ as well. It is not, since $0 = 0$ is not a rule to simplify $sin()$.
+
+ The point here is that $sin(0)$ is not equal to 0 if sin is treated as
+ the name of an operation. Perhaps it is a character string, or a data
+ structure of some sort: a noun phrase. The corresponding expression
+ including the verb form of sin is one in which $sin(0)$ can be
+ simplified to something equivalent, but in some sense preferable. Here
+ it is reasonable to replace it by 0.",
+ paper = "Fate08a.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate97c,
+ author = "Fateman, Richard J.",
+ title = "Excerpts from a proposal to the National Science Foundation
+ on Programming Environments and Tools for Advanced Scientific
+ Computation",
+ year = "1997",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/newpse.pdf",
+ abstract =
+ "We propose to concentrate on investigations of technology in support
+ of advanced scientific computation, based on a higherlevel view of the
+ relationship of mathematical modeling to computation. This is based on
+ the following considerations:
+ \begin{enumerate}
+ \item Symbolic mathematical manipulation and computer algebra systems:
+ These are tools and techniques that support problem solving, code
+ development, comprehension, debugging and partial evaluation
+ (the principle behind many optimization techniques).
+ \item Data modeling: in particular, the use of IEEE floatingpoint
+ number representations and operations.
+ \item Closed form or exact solutions: For some subproblems of
+ scientific interest, numerical solutions are not the only paradigm.
+ The availability of exact solutions, or symbolicapproximation solutions
+ has advanced along with computing technology too.
+ \item The use of scripting languages: the linkage of highperformance
+ library routines to graphical interfaces for data analysis and model setup
+ can be enhanced by symbolic support and highlevel scripting languages.
+ \item Extending the use of remote computation. We are now using standard
+ network connections for the acquisition of complex data (in this case,
+ symbolic solution of definite integrals).
+ \end{enumerate}",
+ paper = "Fate97c.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate98,
+ author = "Fateman, Richard J.",
+ title = "Open Problems in HumanComputer Interaction with Specific
+ Application to ComputerAided Mathematics",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/open4.ps",
+ year = "1998",
+ abstract =
+ "It is our intention, in this short paper, to indicate some of the
+ problems of humancomputer interactions at the boundaries of current
+ research is algebraic manipulation as we see the field now, some 35
+ years from the development of its first software systems (the
+ nowancient Macsyma was announced in 1971, and it had precurors.)
+
+ Because computers, algorithms, and software systems have advanced so
+ substantially, there is a tendency for computer scientists to think
+ that all of mathematics can be done by computer, or at least that we
+ are on track for the continued ``arithmetization of mathematics.''
+ Working mathematicians tend to disagree with the characterization that
+ we are at all close now, nor that we are headed toward any goal of
+ being able to do or understand mathematics.
+
+ Most of the problems which we indicate below are actually quite
+ general problems in computerhuman communication. For specificity (and
+ the possibility that one could qunatify a solution!) we will count our
+ discussion of in terms of applications in the area of algebraic
+ manipulation. If we cannot handle allegedly wellformed mathematical
+ issues, how can we expect to handle illformed ambigious
+ ``natural''communication?
+
+ Some of the problems are representative of strategic mathemaical
+ manipulation procedures which lack totally algorithmic approaches at
+ this time, and so are more of an interactive problemsolving protocol
+ than a fixed recipe.",
+ paper = "Fate98.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate00a,
+ author = "Fateman, Richard J.",
+ title = "Improving Exact Integral From Symbolic Algebra Systems",
+ year = "2000",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/nform2col.pdf",
+ abstract =
+ "Programs in symbolic algebraic manipulation systems can compute
+ certain classes of symbolic indefinite integrals in closed form. Although
+ these answers are ordinarily formally correct algebraic antiderivatives,
+ their form is often unsuitable for further numerical or even analytical
+ processing. In particular, we address cases in which such ``exact answers''
+ when numerically evaluated may give lessaccurate answers than numerical
+ approximations from first principles! The symbolic formulas may also
+ behave inappropriately near singularities. We discuss techniques, based
+ in part on the calculus of divided differences, for improving the form of
+ results of symbolic mathematics systems. In particular, computer alge
+ algebra systems must take explicit account of the possibility that they are
+ producing not “mathematics” but templates of programs consisting of se
+ sequences of arithmetic operations. In brief, mathematical correctness is
+ not enough. Forms produced by rational integration programs are used
+ for examples.",
+ paper = "Fate00a.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate03,
+ author = "Fateman, Richard J.",
+ title = "Continuity and Limits of Programs",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/limit.pdf",
+ year = "2003",
+ abstract =
+ "In demonstrations of proofs [3] of correctness for programs that are
+ designed to compute mathematical functions we attempted to show that
+ programs have the right properties, namely the same properties as the
+ mathematical functions they are alleged to compute. In the cited paper
+ we were forced to handwave (our excuse was the need for brevity) in
+ at least two places, trying to sidestep sticky issues. Here we try to
+ address these issues by clarifying two concepts: (a) computational
+ continuity and (b) equality in a domain where floatingpoint
+ computations can be done to variable (presumably high) precision. We
+ introduce notations prepresentable and pnegligible where p denotes
+ precision, and show how this helps in our applications.",
+ paper = "Fate03.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate15,
+ author = "Fateman, Richard J.",
+ title = "Interval Arithmetic, Extended Numbers and Computer Algebra
+ Systems",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/interval.pdf",
+ year = "2015",
+ abstract =
+ "Many ambitious computer algebra systems were initially designed in a
+ flush of enthusiasm, with the goal of automating any symbolic
+ mathematical manipulation “correctly.” Historically, this approach
+ resulted in programs that implicitly used certain identities to
+ simplify expressions. These identities, which very likely seemed
+ universally true to the programmers in the heat of writing the CAS,
+ (and often were true in wellknown abstract algebraic domains) later
+ needed reexamination when such systems were extended for dealing with
+ kinds of objects unanticipated in the original design. These new
+ objects are generally introduced to the CAS by extending “generically”
+ the arithmetic or other operations. For example, approximate floats
+ do not have the mathematical properties of exact integers or
+ rationals. Complex numbers may strain a system designed for
+ realvalued variables. In the situation examined here, we consider two
+ categories of “extended” numbers: ∞ or undefined, and real
+ intervals. We comment on issues raised by these two troublesome
+ notions, how their introduction into a computer algebra system may
+ require a (sometimes painful) reconsideration and redesign of parts of
+ the program, and how they are related. An alternative (followed most
+ notably by the Axiom system is to essentially envision a “meta” CAS
+ defined in terms of categories and inheritance with only the most
+ fundamental builtin concepts; from these one can build many variants
+ of specific CAS features. This approach is appealing but can fails to
+ accommodate extensions that violate some mathematical tenets in the
+ cause of practicality.",
+ paper = "Fate15.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate14,
+ author = "Fateman, Richard J.",
+ title = "Fun with Filon Quadrature  a Computer Algebra Perspective",
+ year = "2014",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/funfilon.pdf",
+ abstract =
+ "Filon quadrature, useful for oscillatory integrals, is easily
+ implemented in a computer algebra system (CAS) using exact or
+ approximate arithmetic. Although quadrature is almost always used in
+ the context of approximation, we see that various properties are
+ exhibited by running an exact algorithm on exact {\sl symbolic}
+ inputs. This experimental approach to the mathematics allows us to
+ prove the implementation of the algorithm has the expected
+ mathematical correctness properties, and is therefore more likely to
+ be, itself, a correct implementation.",
+ paper = "Fate14.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate97a,
+ author = "Fateman, Richard J.",
+ title = "The Fast Fourier Transform",
+ course = "Berkeley CS 292, Fall 1997, Handout 2",
+ year = "1997",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/fftnotes.pdf",
+ paper = "Fate97a.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate97b,
+ author = "Fateman, Richard J.",
+ title = "More Versatile Scientific Documents OverExtended Abstract,
+ working paper",
+ year = "1997",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/mvsd.ps",
+ abstract =
+ "The electronic representation of scientific documents: journals,
+ technical reports, program documentation, laboratory notebooks,
+ etc. present challenges in several distinct communities. We see five
+ distinct groups concerned with electronic versions of scientific
+ documents:
+ \begin{itemize}
+ \item Publishers of journals, texts, reference works, and their authors.
+ \item Software publishers for OCR/document analysis, document formatting
+ \item Software publishers whose products access ``contents semantics''
+ from documents, including library keyword search programs, natural language
+ search programs, database systems, visual presentation systems,
+ mathematical computation systems, etc.
+ \item Institutions maintain access to electronic libraries, which must
+ be broadly construed to include data and programs of all sorts.
+ \item Individuals and their programs acting as their agents who need to
+ use these libraries, to identify, locate, and retrieive relevant
+ documents
+ \end{itemize}
+
+ We need to have a convergence in design and standards for encoding new
+ or preexisting (typically paperbased) documents in order to most
+ efficiently meet the needs of all these groups. Various effort, some
+ loosely coordinated, but just as often competing, are trying to set
+ standards and build tools.
+
+ We approach this by first dividing the task into visual, syntactic,
+ and semantic components. These specifications can focus attention on
+ the addressing requirements of the different groups. Additionally,
+ these components rely on a structure for documents that incorporates
+ existing library models and extends them to new modes of operation.
+ Berkeley's MVD is one plausible structure which will allow prototype
+ development and explorations.",
+ paper = "Fate97b.pdf"
+}
+
+\end{chunk}
+
+\index{Heckmann, Reinhold}
+\index{Wilhelm, Reinhard}
+\begin{chunk}{axiom.bib}
+@article{Heck97,
+ author = "Heckmann, Reinhold and Wilhelm, Reinhard",
+ title = "A Functional Description of TeX's Formula Layout",
+ journal = "J. Functional Programming",
+ volume = "7",
+ number = "5",
+ pages = "451485",
+ year = "1997",
+ url = "http://http.cs.berkeley.edu/~fateman/temp/neuform.pdf",
+ comment = "ftp://ftp.cs.unisb.de/formulae/formulae.tar.gz",
+ abstract =
+ "While the quality of the results of TeX's mathematica formula layout
+ algorithm is convincing, its original description is hard to
+ understand since it is presented as an imperative program with complex
+ control flow and destructive manipulations of the data structures
+ representing formulae. In this paper, we present a reimplementation
+ of TeX's formula layout algorithm in the functional language SML,
+ thereby providing a more readable description of the algorithm,
+ extracted from the monolithical TeX system.",
+ paper = "Heck97.pdf"
+}
+
+\end{chunk}
+
+\index{Vakil, Ravi}
+\begin{chunk}{axiom.bib}
+@misc{Vaki98,
+ author = "Vakil, Ravi",
+ title = "A Beginner's Guide to Jet Bundles fromthe Point of View of
+ Algebraic Geometry",
+ url = "http://math.stanford.edu/~vakil/files/jets.pdf",
+ year = "1998",
+ paper = "Vaki98.pdf"
+}
+
+\end{chunk}
+
\index{Wang, Paul S.}
\begin{chunk}{axiom.bib}
@article{Wang74,
@@ 10990,13 +11684,13 @@ J. Symbolic Computation 5, 237259 (1988)
number = "4",
pages = "586589",
year = "1974",
 paper = "Wang74.djvu",
abstract =
"From Richardson's undecidability results, it is shown that the predicate
``there exists a real number $r$ such that $G(r)=0$'' is recursively
undecidable for $G(x)$ in a class of functions which involves polynomials
and the sine function. The deduction follows that the convergence of a
 class of improper integrals is recursively undecidable."
+ class of improper integrals is recursively undecidable.",
+ paper = "Wang74.djvu"
}
\end{chunk}
@@ 11012,14 +11706,14 @@ J. Symbolic Computation 5, 237259 (1988)
number = "1",
year = "2002",
url = "http://www.elsevier.nl/locate/entcs/volume66.html",
 paper = "Lang02.pdf",
abstract =
"If $S=0$ is a system of $n$ equations and unknowns over $\mathbb{C}$
and $S(\alpha)=0$ to what extent can we compute with the point $\alpha$?
In particular, can we decide whether or not a polynomial expressions
in the components of $\alpha$ with integral coefficients is zero?
This question is considered for both algebraic and elementary systems
 of equations."
+ of equations.",
+ paper = "Lang02.pdf"
}
\end{chunk}
@@ 11049,7 +11743,6 @@ J. Symbolic Computation 5, 237259 (1988)
number = "6",
year = "2007",
pages = "627645",
 paper = "Rich07.pdf",
abstract =
"An elementary point is a point in complex $n$ space, which is an
isolated, nonsingular solution of $n$ equations in $n$ variables,
@@ 11059,7 +11752,8 @@ J. Symbolic Computation 5, 237259 (1988)
this article a semialgorithm is given to decide whether or not a
given elementary number is zero. It is proved that this semialgorithm
is an algorithm, i.e. that it always terminates, unless it is given
 a problem containing a counter example to Schanuel's conjecture."
+ a problem containing a counter example to Schanuel's conjecture.",
+ paper = "Rich07.pdf"
}
\end{chunk}
@@ 11074,7 +11768,6 @@ J. Symbolic Computation 5, 237259 (1988)
series = "ISSAC '00",
pages = "169174",
year = "2000",
 paper = "Hurx00.djvu",
abstract =
"We describe a new arithmetic model for real algebraic numbers with
an exact equality determination. The model represents a real algebraic
@@ 11083,7 +11776,8 @@ J. Symbolic Computation 5, 237259 (1988)
representation could be used) use the dyadic exact real number and
for the symbolic part we use a squarefree polynomial for the real
algebraic number. In this model we show that we can decide exactly
 the equality of real algebraic numbers."
+ the equality of real algebraic numbers.",
+ paper = "Hurx00.djvu"
}
\end{chunk}
@@ 11097,8 +11791,8 @@ J. Symbolic Computation 5, 237259 (1988)
volume = "106",
number = "5",
pages = "440448",
 paper = "Chowxx.pdf",
 year = "1999"
+ year = "1999",
+ paper = "Chowxx.pdf"
}
\end{chunk}
@@ 11108,8 +11802,8 @@ J. Symbolic Computation 5, 237259 (1988)
@book{Yapx00,
author = "Yap, CheeKeng",
title = "Fundamental Problems in Algorithmic Algebra",
+ publisher = "John Wiley and Sons",
year = "2000",
 paper = "Yapx00.pdf",
url =
"http://www.csie.nuk.edu.tw/~cychen/gcd/Fundamental%20Problems%20in%20Algorithmic%20Algebra.pdf",
abstract =
@@ 11139,7 +11833,8 @@ J. Symbolic Computation 5, 237259 (1988)
&=&\displaystyle\frac{(aq+c,bq+d,ap,bp)}
{(a^{\prime}q+c^{\prime},b^{\prime}q+d^{\prime},a^{\prime}p,
b^{\prime}p)}{x^{\prime} \choose {y}}
 \end{array}\]"
+ \end{array}\]",
+ paper = "Yapx00.pdf"
}
\end{chunk}
@@ 11157,14 +11852,14 @@ J. Symbolic Computation 5, 237259 (1988)
volume = "27",
pages = "8799",
year = "2000",
 paper = "Burn00.pdf",
abstract =
"We consider arithmetic expressions over operators $+$, $$, $*$, $/$,
and $\sqrt[k]$, with integer operands. For an expression $E$ having
value $\eta$, a separation bound $sep(E)$ is a positive real number with
the property that $\eta \ne 0$ implies $\vert\eta\vert \ge sep(E)$. We
propose a new separation bound that is easy to compute and stronger
 than previous bounds."
+ than previous bounds.",
+ paper = "Burn00.pdf"
}
\end{chunk}
@@ 11180,7 +11875,6 @@ J. Symbolic Computation 5, 237259 (1988)
series = "ISSAC '97",
pages = "197204",
year = "1997",
 paper = "Corl97.pdf",
abstract =
"We give a uniform treatment of several series expansions for the
Lambert $W$ function, leading to an infinite family of new series.
@@ 11188,7 +11882,8 @@ J. Symbolic Computation 5, 237259 (1988)
arbitraryorder iterative methods for computation of $W_i$, and
give a theorem showing how to correctly solve another simple and
frequently occurring nonlinear equation in terms of $W$ and the
 unwinding number"
+ unwinding number",
+ paper = "Corl97.pdf"
}
\end{chunk}
@@ 11205,7 +11900,6 @@ J. Symbolic Computation 5, 237259 (1988)
issue = "115",
pages = "2835",
year = "1996",
 paper = "Corl96.pdf",
abstract =
"From the Oxford English Dictionary we find that {\sl to unwind}
can mean ``to become free from a convoluted state''. Further down
@@ 11213,7 +11907,8 @@ J. Symbolic Computation 5, 237259 (1988)
of all intricacies'', from H. Brooke (The Fool of Quality, 1809).
While we do not promise that the unwinding number, defined below,
will solve {\sl all} intricacies, we do show that it may help for
 quite a few problems."
+ quite a few problems.",
+ paper = "Corl96.pdf"
}
\end{chunk}
@@ 11229,7 +11924,6 @@ J. Symbolic Computation 5, 237259 (1988)
number = "1",
pages = "1117",
year = "1998",
 paper = "Corl98.pdf",
abstract =
"This paper discusses one of the prettiest pieces of elementary
mathematics or computer algebra, that we have ever had the pleasure
@@ 11237,7 +11931,8 @@ J. Symbolic Computation 5, 237259 (1988)
(that is, in the literature), but we didn't know them until recently,
and none of our immediate colleagues knew them either. Therefore we
believe that it is useful to publicize them further. We hope that
 you find these ideas as pleasant and useful as we do."
+ you find these ideas as pleasant and useful as we do.",
+ paper = "Corl98.pdf"
}
\end{chunk}
@@ 11252,7 +11947,6 @@ J. Symbolic Computation 5, 237259 (1988)
number = "2",
pages = "83114",
year = "1993",
 paper = "Wang93.pdf",
abstract =
"We present an elimination method for polynomial systems, in the form
of three main algorithms. For any given system [$\mathbb{P}$,$\mathbb{Q}$]
@@ 11275,7 +11969,8 @@ J. Symbolic Computation 5, 237259 (1988)
examples by a draft implementation of the method are provided, and show
that the efficiency of our method is comparable with that of some
wellknown methods. A few encouraging examples are given in detail for
 illustration."
+ illustration.",
+ paper = "Wang93.pdf"
}
\end{chunk}
@@ 11291,7 +11986,6 @@ J. Symbolic Computation 5, 237259 (1988)
number = "3",
pages = "249263",
year = "1994",
 paper = "Wang94.pdf",
abstract =
"In this paper we present some rules for the differentiation and
integration of expressions involving indefinite summations with
@@ 11302,7 +11996,8 @@ J. Symbolic Computation 5, 237259 (1988)
implementation issues and report our experiments with a set of typical
examples. The present work is motivated by our investigation in the
computeraided analysis and derivation of artificial neural systems.
 The application of our rules to this subject is briefly explained."
+ The application of our rules to this subject is briefly explained.",
+ paper = "Wang94.pdf"
}
\end{chunk}
@@ 11319,13 +12014,13 @@ J. Symbolic Computation 5, 237259 (1988)
pages = "658673",
year = "1995",
url = "http://www.jucs.org/jucs\_1\_9/a\_method\_for\_proving",
 paper = "Wang95a.pdf",
abstract =
"A zero decomposition algorithm is presented and used to devise a
method for proving theorems automatically in differential geometry and
mechanics. The method has been implemented and its practical
efficiency is demonstrated by several nontrivial examples including
 Bertrand s theorem, Schell s theorem and KeplerNewton s laws."
+ Bertrand s theorem, Schell s theorem and KeplerNewton s laws.",
+ paper = "Wang95a.pdf"
}
\end{chunk}
@@ 11339,7 +12034,6 @@ J. Symbolic Computation 5, 237259 (1988)
number = "3",
pages = "295314",
year = "1998",
 paper = "Wang98.pdf",
abstract =
"A simple system is a pair of multivariate polynomial sets (one set
for equations and the other for inequations) ordered in triangular
@@ 11348,7 +12042,8 @@ J. Symbolic Computation 5, 237259 (1988)
presents a method that decomposes any pair of polynomial sets into
finitely many simple systems with an associated zero decomposition.
The method employs topdown elimination with splitting and the
 formation of subresultant regular subchains as basic operation."
+ formation of subresultant regular subchains as basic operation.",
+ paper = "Wang98.pdf"
}
\end{chunk}
@@ 11363,7 +12058,6 @@ J. Symbolic Computation 5, 237259 (1988)
number = "12",
pages = "303315",
year = "1999",
 paper = "Wang99.pdf",
abstract =
"In this paper, combined elimination techniques are applied to
establish relations among center conditions for certain cubic
@@ 11374,7 +12068,8 @@ J. Symbolic Computation 5, 237259 (1988)
still open, are illustrated by interactive elimination. Some generated
polynomial systems that need be solved are made available
electronically for other developers to test elimination algorithms and
 their implementations."
+ their implementations.",
+ paper = "Wang99.pdf"
}
\end{chunk}
@@ 11389,7 +12084,6 @@ J. Symbolic Computation 5, 237259 (1988)
number = "2",
pages = "221236",
year = "2000",
 paper = "Wang00.pdf",
abstract =
"A previous algorithm of computing simple systems is modified and
extended to compute triangular systems and regular systems from any
@@ 11397,7 +12091,8 @@ J. Symbolic Computation 5, 237259 (1988)
computation of subresultant regular subchains, have a simple structure
and are efficient in practice. Preliminary experiments indicate that
they perform at least as well as some of the known algorithms. Several
 properties about regular systems are also proved."
+ properties about regular systems are also proved.",
+ paper = "Wang00.pdf"
}
\end{chunk}
@@ 11412,7 +12107,6 @@ J. Symbolic Computation 5, 237259 (1988)
number = "1",
pages = "899914",
year = "2004",
 paper = "Wang04.pdf",
abstract =
"This paper presents a simple method for converting rational
parametric equations of curves and surfaces into implicit
@@ 11428,7 +12122,8 @@ J. Symbolic Computation 5, 237259 (1988)
the same process, increasing the degree of $F$. Our experiments show
that this simple method is efficient. It performs particularly well in
the presence of base points and may detect the dependency of
 parameters incidentally."
+ parameters incidentally.",
+ paper = "Wang04.pdf"
}
\end{chunk}
@@ 11441,7 +12136,6 @@ J. Symbolic Computation 5, 237259 (1988)
booktitle = "Proc. DISCO 92",
series = "Lecture Notes in Computer Science 721",
year = "1992",
 paper = "Brad92.djvu",
abstract =
"Many current algebra systems have a lax attitude to the
simplification of expressions involving functions like log and
@@ 11449,7 +12143,8 @@ J. Symbolic Computation 5, 237259 (1988)
in such systems. In fact, only a little elementary arithmetic is
needed to devise what the correct simplification should be. We detail
some of these simplification rules, and outline a method for their
 incorporation into an algebra system."
+ incorporation into an algebra system.",
+ paper = "Brad92.djvu"
}
\end{chunk}
@@ 11477,7 +12172,6 @@ J. Symbolic Computation 5, 237259 (1988)
volume = "32",
number = "1",
year = "2001",
 paper = "Kalm01.pdf",
abstract =
"How do you solve the equation
\[1.6^x = 5054.4  122.35*x\]
@@ 11511,7 +12205,8 @@ J. Symbolic Computation 5, 237259 (1988)
dates to work of Lambert in 1758 and of Euler in 1777. Interesting
questions about glog arise at every turn, from symbolic integration,
to inequalities and estimation, to numerical computation. Elaborating
 these points is the goal of this paper."
+ these points is the goal of this paper.",
+ paper = "Kalm01.pdf"
}
\end{chunk}
@@ 11535,23 +12230,23 @@ J. Symbolic Computation 5, 237259 (1988)
title = "A Proposal for Automated Integral Tables (Work in Progress)",
year = "1992",
url = "http://people.eecs.berkeley.edu/~fateman/papers/intable.pdf",
 paper = "Fate92.pdf",
abstract =
"One of the longterm general goals of algebraic manipulation systems
has been the automation of difficult or tedious, yet common, symbolic
mathematical operations. Prominent amount these has been symbolic
integration. Although some effective algorithms have been devised for
integration expecially for those problems solvable in terms of
elementary functions and a few additional special functions, the vast
majority of entires in large tables of indefinite and definite
integrals remain out of reach of current machine algorithms. We
propose techniques for introducing the information in such tables to
computers, extending such tables, and measuring the success of such
automation.

Similar tabular data concerning simplifications, summation identities,
and similar formulas could also be treated by some of the same
techniques."
+ "One of the longterm general goals of algebraic manipulation systems
+ has been the automation of difficult or tedious, yet common, symbolic
+ mathematical operations. Prominent amount these has been symbolic
+ integration. Although some effective algorithms have been devised for
+ integration expecially for those problems solvable in terms of
+ elementary functions and a few additional special functions, the vast
+ majority of entires in large tables of indefinite and definite
+ integrals remain out of reach of current machine algorithms. We
+ propose techniques for introducing the information in such tables to
+ computers, extending such tables, and measuring the success of such
+ automation.
+
+ Similar tabular data concerning simplifications, summation identities,
+ and similar formulas could also be treated by some of the same
+ techniques.",
+ paper = "Fate92.pdf"
}
\end{chunk}
@@ 11563,7 +12258,6 @@ techniques."
author = "Athale, Rahul Ramesh and Diaz, Glauco Alfredo Lopez",
title = "Explaining Schwarz's LODEF algorithm with examples",
url = "http://www.risc.jku.at/publications/download/risc\_1539/0311.ps.gz",
 paper = "Atha03.pdf",
year = "2003",
abstract =
"To every linear homogeneous ordinary differential equation
@@ 11578,7 +12272,8 @@ techniques."
of operators and composition as multiplication.
{\bf Problem}: Decompose $L$ as a product of operators of lower degree
 in $D$. We allow expressions algebraic over $K$."
+ in $D$. We allow expressions algebraic over $K$.",
+ paper = "Atha03.pdf"
}
\end{chunk}
@@ 11592,7 +12287,6 @@ techniques."
Mechanical Formula Derivation",
institution = "University of Texas, Austin",
url = "http://www.cs.utexas.edu/ftp/techreports/tr8922.pdf",
 paper = "Chou89.pdf",
type = "technical report",
number = "tr8922",
year = "1989",
@@ 11604,7 +12298,8 @@ techniques."
to our program and a collection of 120 examples. A typical example
consists of an informal description of the geometric problem, the
input to the program which is the exact specification of the problem,
 the result of the problem, and a diagram."
+ the result of the problem, and a diagram.",
+ paper = "Chou89.pdf"
}
\end{chunk}
@@ 11619,8 +12314,8 @@ techniques."
Proofs for Geometry Theorems",
publisher = "World Scientific",
url = "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.374.11778",
 paper = "Chou94.pdf",
 year = "1994"
+ year = "1994",
+ paper = "Chou94.pdf"
}
\end{chunk}
@@ 11631,7 +12326,6 @@ techniques."
author = "Sturmfels, Bernd",
title = "Solving Systems of Polynomial Equations",
url = "https://math.berkeley.edu/~bernd/cbms.pdf",
 paper = "Stur00.pdf",
year = "2000",
abstract =
"One of the most classical problems of mathematics is to solve systems
@@ 11673,7 +12367,8 @@ techniques."
will be particularly useful for readers with zero background in
algebraic geometry or commutative algebra. Within minutes, anyone can
learn how to type in polynomial equations and actually see some
 meaningful results on the computer screen."
+ meaningful results on the computer screen.",
+ paper = "Stur00.pdf"
}
\end{chunk}
@@ 11684,8 +12379,8 @@ techniques."
title = "Axiom (computer algebra system)",
url =
"http://ntcir11wmc.nii.ac.jp/index.php/Axiom\_(computer_algebra_system)",
 keywords = "axiomref",
 year = "2016"
+ year = "2016",
+ keywords = "axiomref"
}
\end{chunk}
@@ 11711,7 +12406,6 @@ techniques."
volume = "13",
pages = "581603",
year = "1992",
 paper = "Koep92.pdf",
abstract =
"Formal power series (FPS) of the form
$\sum_{k=0}^{\infty}{a_k(xx_0)^k}$ are important in calculus and
@@ 11743,7 +12437,8 @@ techniques."
Moreover, the same algorithm can sometimes be reversed to calculate a
function that corresponds to a given FPS, in those cases when a
 certain type of ordinary differential equation can be solved."
+ certain type of ordinary differential equation can be solved.",
+ paper = "Koep92.pdf"
}
\end{chunk}
@@ 11758,7 +12453,6 @@ techniques."
number = "2",
year = "1996",
pages = "1220",
 paper = "Asla96.pdf",
url = "http://www.math.nus.edu.sg/aslaksen/papers/cacas.pdf",
abstract =
"I recently taught a course on complex analysis. That forced me to
@@ 11782,7 +12476,8 @@ techniques."
comparative study of different computer algebra systems. My goal is
simply to make the readers aware of some of the problems, and to
encourage the readers to sit down and experiment with their favourite
 programs."
+ programs.",
+ paper = "Asla96.pdf"
}
\end{chunk}
@@ 11797,7 +12492,6 @@ techniques."
volume = "1",
number = "1",
issn = "19332823",
 paper = "Tonixx.pdf",
url = "https://php.radford.edu/~ejmt/deliveryBoy.php?paper=eJMT_v1n3p5",
abstract =
"In many cases when solving school algebra problems (e.g. simplifying
@@ 11807,7 +12501,8 @@ techniques."
systems and compares them with mathematically branchcomplete
solutions. It tries to identify possible reasons behind different
approaches and also indicate some ideas how such differences could be
 explained to the students."
+ explained to the students.",
+ paper = "Tonixx.pdf"
}
\end{chunk}
@@ 11860,14 +12555,14 @@ techniques."
author = "Apel, Joachim and Klaus, Uwe",
title = "Representing Polynomials in Computer Algebra Systems",
year = "1994",
 paper = "Apel94.pdf",
abstract =
"There are discussed implementational aspects of the specialpurpose
computer algebra system FELIX designed for computations in
constructive algebra. In particular, data types developed for the
representation of and computation with commutative and noncommuative
polynomials are described. Furthermore, comparison of time and memory
 requirements of different polynomial representations are reported."
+ requirements of different polynomial representations are reported.",
+ paper = "Apel94.pdf"
}
\end{chunk}
@@ 11896,7 +12591,7 @@ techniques."
pages = "236244",
publisher = "SpringerVerlag",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/83/Ka83_eurocal.pdf",
 paper = "Kalt83.pdf",
+ paper = "Kalt83.pdf"
}
\end{chunk}
@@ 11912,7 +12607,7 @@ techniques."
year = "1985",
url =
"http://www.math.ncsu.edu/~kaltofen/bibliography/85/Ka85_infcontr.ps.gz",
 paper = "Kalt85.ps",
+ paper = "Kalt85.ps"
}
\end{chunk}
@@ 11927,7 +12622,7 @@ techniques."
year = "1985",
number = "8512",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/85/Ka85_techrep.pdf",
 paper = "Kalt85c.pdf",
+ paper = "Kalt85c.pdf"
}
\end{chunk}
@@ 11942,7 +12637,7 @@ techniques."
pages = "417",
year = "1985",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/85/Ka85_eurocal.pdf",
 paper = "Kalt85d.pdf",
+ paper = "Kalt85d.pdf"
}
\end{chunk}
@@ 11961,7 +12656,7 @@ techniques."
number = "4",
pages = "687695",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/88/MRK88.pdf",
 paper = "Mill88.pdf",
+ paper = "Mill88.pdf"
}
\end{chunk}
@@ 11980,7 +12675,7 @@ techniques."
number = "2",
pages = "4149",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/88/GrKa88.pdf",
 paper = "Grey88.pdf",
+ paper = "Grey88.pdf"
}
\end{chunk}
@@ 11998,7 +12693,7 @@ techniques."
number = "188",
pages = "697720",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/89/KaRo89.pdf",
 paper = "Kalt89a.pdf",
+ paper = "Kalt89a.pdf"
}
\end{chunk}
@@ 12012,7 +12707,7 @@ techniques."
year = "1989",
month = "July",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/89/Ka89_gcd.ps.gz",
 paper = "Kalt89b.ps",
+ paper = "Kalt89b.ps"
}
\end{chunk}
@@ 12028,7 +12723,7 @@ techniques."
month = "July",
url =
"http://www.math.ncsu.edu/~kaltofen/bibliography/89/Ka89_parallel.ps.gz",
 paper = "Kalt89c.ps",
+ paper = "Kalt89c.ps"
}
\end{chunk}
@@ 12045,7 +12740,7 @@ techniques."
pages = "121128",
year = "1989",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/89/CKL89.pdf",
 paper = "Cann89.pdf",
+ paper = "Cann89.pdf"
}
\end{chunk}
@@ 12062,7 +12757,7 @@ techniques."
number = "2",
pages = "135148",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/90/Ka90_aaecc.pdf",
 paper = "Kalt90b.pdf",
+ paper = "Kalt90b.pdf"
}
\end{chunk}
@@ 12081,7 +12776,7 @@ techniques."
number = "3",
pages = "301320",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/90/KaTr90.pdf",
 paper = "Kalt90d.pdf",
+ paper = "Kalt90d.pdf"
}
\end{chunk}
@@ 12100,7 +12795,7 @@ techniques."
year = "1991",
address = "Singapore",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/91/KaSi91.pdf",
 paper = "Kalt91a.pdf",
+ paper = "Kalt91a.pdf"
}
\end{chunk}
@@ 12121,7 +12816,7 @@ techniques."
year = "1993",
pages = "2830",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/93/Ka93_diff.pdf",
 paper = "Kalt93.pdf",
+ paper = "Kalt93.pdf"
}
\end{chunk}
@@ 12138,7 +12833,7 @@ techniques."
pages = "2",
url =
"http://www.math.ncsu.edu/~kaltofen/bibliography/93/Ka93_sambull.ps.gz",
 paper = "Kalt93b.ps",
+ paper = "Kalt93b.ps"
}
\end{chunk}
@@ 12155,7 +12850,7 @@ techniques."
pages = "225233",
year = "1994",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/94/KaPa94.pdf",
 paper = "Kalt94.pdf",
+ paper = "Kalt94.pdf"
}
\end{chunk}
@@ 12169,7 +12864,6 @@ techniques."
volume = "abs/1305.1481",
year = "2013",
url = "http://arxiv.org/pdf/1305.1481v1.pdf",
 paper = "Raab13.pdf",
abstract =
"Symbolic integration deals with the evaluation of integrals in closed
form. We present an overview of Risch's algorithm including recent
@@ 12180,7 +12874,8 @@ techniques."
to introduce the reader to some basic ideas of differential algebra in
the context of integration and to raise awareness in the physics
community of computer algebra algorithms for indefinite and definite
 integration. "
+ integration. ",
+ paper = "Raab13.pdf"
}
\end{chunk}
@@ 12200,7 +12895,7 @@ techniques."
year = "1996",
url =
"http://www.math.ncsu.edu/~kaltofen/bibliography/95/SaKa95_poster.ps.gz",
 paper = "Sama95.ps",
+ paper = "Sama95.ps"
}
\end{chunk}
@@ 12217,7 +12912,7 @@ techniques."
year = "1996",
pages = "275282",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/96/EKM96.pdf",
 paper = "Erli96.pdf",
+ paper = "Erli96.pdf"
}
\end{chunk}
@@ 12233,7 +12928,7 @@ techniques."
year = "1996",
pages = "241249",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/96/KaLo96_issac.pdf",
 paper = "Kalt96.pdf",
+ paper = "Kalt96.pdf"
}
\end{chunk}
@@ 12250,15 +12945,15 @@ techniques."
year = "1997",
note = "Special issue on education, L. Lambe, editor.",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/97/Ka97_jsc.pdf",
 keywords = "axiomref,read",
 paper = "Kalt97.pdf",
abstract = "
We report on the contents and pedagogy of a course in abstract algebra
that was taught with the aid of educational software developed within
the Mathematica system. We describe the topics covered and the
didactical use of the corresponding Mathematica packages, as well as
draw conclusions for future such courses from the students' comments
 and our own experience."
+ and our own experience.",
+ paper = "Kalt97.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 12273,7 +12968,7 @@ techniques."
year = "1997",
month = "May",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/97/HiKa97_kharit.pdf",
 paper = "Hitz97.pdf",
+ paper = "Hitz97.pdf"
}
\end{chunk}
@@ 12290,7 +12985,7 @@ techniques."
year = "1999",
pages = "237244",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/99/BCK99.pdf",
 paper = "Bern99.pdf",
+ paper = "Bern99.pdf"
}
\end{chunk}
@@ 12308,7 +13003,7 @@ techniques."
publisher = "Waterloo Maple Inc.",
address = "Waterloo, Canada",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/02/KMN02.pdf",
 paper = "Kalt02.pdf",
+ paper = "Kalt02.pdf"
}
\end{chunk}
@@ 12336,8 +13031,35 @@ techniques."
\S4.2.17 FoxBox and other blackbox systems, pages 383385.",
isbn = "3540654666",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/01/symnum.pdf",
 keywords = "axiomref",
paper = "Grab03.pdf",
+ keywords = "axiomref",
+ beebe = "Grabmeier:2003:CAH"
+}
+
+\end{chunk}
+\begin{chunk}{Grabmeier:2003:CAH}
+@Book{Grabmeier:2003:CAH,
+ editor = "Johannes Grabmeier and Erich Kaltofen and Volker
+ Weispfenning",
+ title = "Computer algebra handbook: foundations, applications,
+ systems",
+ publisher = pubSV,
+ address = pubSV:adr,
+ pages = "xx + 637",
+ year = "2003",
+ ISBN = "3540654666",
+ ISBN13 = "9783540654667",
+ LCCN = "QA155.7.E4 C64954 2003",
+ MRclass = "68W30, 00B15, 6806",
+ bibdate = "Tue Nov 22 06:00:25 MST 2005",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib;
+ z3950.loc.gov:7090/Voyager",
+ note = "Includes CDROM.",
+ URL = "http://www.springer.com/sgw/cda/frontpage/0,11855,11022214778710,00.html",
+ acknowledgement = acknhfb,
+ keywords = "Aldor; AXIOM; Derive; exact arithmetic; Macsyma;
+ Magma; Maple Mathematica; MuPAD; REDUCE; TI92",
+ subject = "Algebra; Data processing",
}
\end{chunk}
@@ 12359,7 +13081,7 @@ techniques."
crossref = "SNC07",
pages = "203204",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/07/KLSYZ07.pdf",
 paper = "Kalt07.pdf",
+ paper = "Kalt07.pdf"
}
\end{chunk}
@@ 12378,7 +13100,7 @@ techniques."
pages = "118121",
month = "December",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/07/BKM07.pdf",
 paper = "Borw07.pdf",
+ paper = "Borw07.pdf"
}
\end{chunk}
@@ 12396,7 +13118,7 @@ techniques."
month = "September",
pages = "355366",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/09/KaLa09.pdf",
 paper = "Kalt10.pdf",
+ paper = "Kalt10.pdf"
}
\end{chunk}
@@ 12413,7 +13135,7 @@ techniques."
year = "2011",
pages = "177185",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/11/KaNe11.pdf",
 paper = "Kalt11.pdf",
+ paper = "Kalt11.pdf"
}
\end{chunk}
@@ 12433,7 +13155,7 @@ techniques."
pages = "543554",
year = "2011",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/11/GKKP11.pdf",
 paper = "Gren11a.pdf",
+ paper = "Gren11a.pdf"
}
\end{chunk}
@@ 12451,7 +13173,7 @@ techniques."
year = "2011",
pages = "171176",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/11/KNS11.pdf",
 paper = "Kalt11a.pdf",
+ paper = "Kalt11a.pdf"
}
\end{chunk}
@@ 12470,7 +13192,7 @@ techniques."
year = "2011",
pages = "130136",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/11/KLY11.pdf",
 paper = "Kalt11b.pdf",
+ paper = "Kalt11b.pdf"
}
\end{chunk}
@@ 12488,7 +13210,7 @@ techniques."
year = "2012",
pages = "195202",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/12/GKZ12.pdf",
 paper = "Guo12.pdf",
+ paper = "Guo12.pdf"
}
\end{chunk}
@@ 12507,7 +13229,7 @@ techniques."
year = "2012",
pages = "138145",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/12/CKP12.pdf",
 paper = "Come12a.pdf",
+ paper = "Come12a.pdf"
}
\end{chunk}
@@ 12525,7 +13247,7 @@ techniques."
year = "2013",
month = "October",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/13/BCK13.pdf",
 paper = "Boye13.pdf",
+ paper = "Boye13.pdf"
}
\end{chunk}
@@ 12542,7 +13264,7 @@ techniques."
crossref = "ISSAC13",
pages = "219226",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/13/KaYa13.pdf",
 paper = "Kalt13b.pdf",
+ paper = "Kalt13b.pdf"
}
\end{chunk}
@@ 12557,7 +13279,7 @@ techniques."
year = "2013",
month = "October",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/13/Ka13.pdf",
 paper = "Kalt13c.pdf",
+ paper = "Kalt13c.pdf"
}
\end{chunk}
@@ 12573,7 +13295,7 @@ techniques."
booktitle = "Internat. Symp. Symbolic Algebraic Comput. ISSAC'14",
crossref = "ISSAC14",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/14/KaYa14.pdf",
 paper = "Kalt14.pdf",
+ paper = "Kalt14.pdf"
}
\end{chunk}
@@ 12589,7 +13311,7 @@ techniques."
booktitle = "Internat. Symp. Symbolic Algebraic Comput. ISSAC'14",
crossref = "ISSAC14",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/14/KaPe14.pdf",
 paper = "Kalt14a.pdf",
+ paper = "Kalt14a.pdf"
}
\end{chunk}
@@ 12604,7 +13326,7 @@ techniques."
booktitle = "Internat. Symp. Symbolic Algebraic Comput. ISSAC'14",
crossref = "ISSAC14",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/14/DuKa14.pdf",
 paper = "Duma14.pdf",
+ paper = "Duma14.pdf"
}
\end{chunk}
@@ 12620,7 +13342,7 @@ techniques."
booktitle = "SNC'14 Proc. 2014 Int. Workshop on SymbolicNumeric Comput.",
crossref = "SNC14",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/14/BoKa14.pdf",
 paper = "Boye14.pdf",
+ paper = "Boye14.pdf"
}
\end{chunk}
@@ 12638,7 +13360,6 @@ techniques."
title = "Clifford algebras with numeric and symbolic computations",
publisher = "Birkhauser",
year = "1996",
 keyword = "axiomref",
abstract =
"The 20 articles of this volume will be reviewed individually. They
have been grouped into the following four sections: I) Verifying and
@@ 12653,7 +13374,8 @@ techniques."
These materials contain original packages, worksheets, notebooks,
computer programs, etc., that were used in deriving results presented
 in this book."
+ in this book.",
+ keyword = "axiomref"
}
\end{chunk}
@@ 12664,7 +13386,6 @@ techniques."
@misc{ACA00,
authors = "Kokolvoljc, Vlasta and Kutzler, Bernhard",
title = "Computer Algebra Meets Education",
 keywords = "axiomref",
conference = "Sessions of ACA2000",
year = "2000",
abstract =
@@ 12677,7 +13398,8 @@ techniques."
The goal of this session is to exchange ideas and experiences, to hear
about classroom experiments, and to discuss all issues related to the
use of computer algebra tools in the classroom (such as assessment,
 change of curricula, new support material, ...)"
+ change of curricula, new support material, ...)",
+ keywords = "axiomref"
}
\end{chunk}
@@ 12688,12 +13410,12 @@ techniques."
@misc{ACA15,
authors = "MartinezMoro, Edgar Kotsireas, Ilias",
title = "21st Conference on Applications of Computer Algebra",
 keywords = "axiomref",
conference = "Sessions of ACA2015",
location = "Kalamata, Greece",
year = "2015",
url = "http://www.singacom.uva.es/ACA2015/latex/ACAproc.pdf",
 paper = "ACA15.pdf"
+ paper = "ACA15.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 12705,13 +13427,13 @@ techniques."
Symposium on Symbolic and Algebraic Computation, ISSAC '89",
year = "1989",
isbn = "0897913256",
 keywords = "axiomref",
isbn = "0897913256",
url = "http://doi.acm.org/10.1145/74540.74567",
doi = "10.1145/74540.74567",
acmid = "74567",
publisher = "ACM Press",
 address = "New York, NY, USA"
+ address = "New York, NY, USA",
+ keywords = "axiomref"
}
\end{chunk}
@@ 12723,9 +13445,9 @@ techniques."
Symposium on Symbolic and Algebraic Computation, ISSAC '94",
year = "1994",
isbn = "0897916387",
 keywords = "axiomref",
publisher = "ACM Press",
 address = "New York, NY, USA"
+ address = "New York, NY, USA",
+ keywords = "axiomref"
}
\end{chunk}
@@ 12743,8 +13465,6 @@ techniques."
year = "1999",
location = "Trento, Italy",
pages = "112126",
 keywords = "axiomref",
 paper = "Adam99a.pdf",
url = "http://www.acubed.info/Publications/CADE99.pdf",
abstract =
"We present a verifiable symbolic definite integral table lookup: a
@@ 12759,7 +13479,9 @@ techniques."
for example, the prototype is able to obtain correct answers in cases
where computer algebra systems do not. We extend upon Fateman’s
webbased table by including parametric limits of integration and
 queries with side conditions."
+ queries with side conditions.",
+ paper = "Adam99a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 12778,7 +13500,6 @@ techniques."
number = "3",
pages = "195211",
year = "2008",
 keywords = "axiomref",
abstract =
"Computer Algebra System (CAS) is a software program that facilitates
symbolic mathematics. The core functionality of a typical CAS is
@@ 12792,7 +13513,8 @@ techniques."
platforms and highly scalable. The other key features include a very
simple and interactive user GUI support for a formula editor, making
it a self contained system, additionally the formula editor provides a
 realtime syntax checking for expressions."
+ realtime syntax checking for expressions.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 12811,8 +13533,6 @@ techniques."
number = "2",
pages = "171221",
year = "1999",
 keywords = "axiomref",
 paper = "Aitk99.pdf",
url = "http://www.nuprl.org/documents/Constable/MetalogicalFrameworksII.pdf",
abstract =
"Proving theorems is a creative act demanding new combinations of ideas
@@ 12835,7 +13555,9 @@ techniques."
a reflection rule to connect the procedure to the system. We also show
that using a rich underlying logic permits an abstract account of the
approach so that the results carry over to different implementations
 and other logics."
+ and other logics.",
+ paper = "Aitk99.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 12845,8 +13567,8 @@ techniques."
author = "america.pink",
title = "Axiom (computer algebra system)",
year = "2016",
 keywords = "axiomref",
 url = "http://america.pink/axiomcomputeralgebrasystem_526647.html"
+ url = "http://america.pink/axiomcomputeralgebrasystem_526647.html",
+ keywords = "axiomref"
}
\end{chunk}
@@ 12875,14 +13597,14 @@ techniques."
volume = "20",
pages = "257273",
year = "2009",
 keywords = "axiomref",
url = "http://www.personal.psu.edu/gea1/pdf/274.pdf",
 paper = "Andr09.pdf",
abstract =
"December 22, 2010 marks the 123th anniversary of Ramanujan's
birth. In this paper we pay homage to this towering figure whose
mathematical discoveries so affected mathematics throughout the
 twentieth century and into the twentyfirst."
+ twentieth century and into the twentyfirst.",
+ paper = "Andr09.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 12899,7 +13621,6 @@ techniques."
number = "6",
pages = "18771905",
year = "2001",
 keywords = "axiomref",
abstract =
"In [Commun. Pure Appl. Math. 28, 457478 (1975; Zbl 0332.35058)],
M. E. Taylor described a constructive diagonalization method to
@@ 12925,7 +13646,8 @@ techniques."
used as an onsurface radiation condition [G. A. Kriegsmann,
A. Taflove, and K. R. Umashankar, IEEE Trans. Antennas Propag. 35,
153161 (1987; Zbl 0947.78571)], it can give rise to an ultrafast
 numerical approximate solution of the scattered field."
+ numerical approximate solution of the scattered field.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 12940,10 +13662,8 @@ techniques."
number = "209",
pages = "355361",
year = "1995",
 keywords = "axiomref",
url =
"https://www.jointmathematicsmeetings.org/mcom/199564209/S00255718199512601242/S00255718199512601242.pdf",
 paper = "Arna95a.pdf",
abstract =
"The RabinMiller primality test is a probabilistic test which can be
found in several algebraic computing systems (such as Pari, Maple,
@@ 12955,7 +13675,9 @@ techniques."
ScratchPad implementation of the test, we obtain, by a method which
differs from a recent one by G. Jaeschke [ibid. 61, 915926 (1993; Zbl
0802.11001)], composite numbers which are found to be ``probably prime''
 by this test."
+ by this test.",
+ paper = "Arna95a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 12971,10 +13693,8 @@ techniques."
volume = "2",
pages = "385402",
year = "1995",
 keywords = "axiomref",
url =
"http://www.combinatorics.org/ojs/index.php/eljc/article/download/v2i1r24.pdf",
 paper = "Atki95.pdf",
abstract =
"A priority queue, a container data structure equipped with the
operations insert and deleteminimum, can reorder its input in
@@ 12987,7 +13707,9 @@ techniques."
determining the number of allowable pairs with a fixed input
component, or with a fixed output component. Finally, generating
functions are used to study the maximum number of output components
 with a fixed input component, and a symmetry result is derived."
+ with a fixed input component, and a symmetry result is derived.",
+ paper = "Atki95.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13004,8 +13726,6 @@ techniques."
year = "1991",
pages = "6573",
isbn = "0387543031",
 keywords = "axiomref",
 paper = "Augo91.pdf",
abstract =
"In this paper, we give a natural way of deciding whether a given
cyclic code contains a word of given weight. The method is based on
@@ 13028,11 +13748,14 @@ techniques."
minimum distance 253.
\item The cyclic codes of length $2^111$, $2^131$, $2^171$, with
generator polynomial $m_1(x)$ and $m_7(x)$ have minimum distance 4.
 \end{itemize}"
+ \end{itemize}",
+ paper = "Augo91.pdf",
+ keywords = "axiomref",
+ beebe = "Augot:1991:MDS"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Augot:1991:MDS}
@InProceedings{Augot:1991:MDS,
author = "D. Augot and P. Charpin and N. Sendrier",
title = "The minimum distance of some binary codes via the
@@ 13082,7 +13805,7 @@ techniques."
year = "1994",
American Mathematical Society (1994)
isbn = "0821838040",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 13099,7 +13822,7 @@ American Mathematical Society (1994)
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Andrews:1984:RS}
@InProceedings{Andrews:1984:RS,
author = "George E. Andrews",
title = "{Ramanujan} and {SCRATCHPAD}",
@@ 13123,7 +13846,6 @@ American Mathematical Society (1994)
series = "Lecture Notes in Comp. Sci. 296",
year = "1988",
isbn = "3540189289",
 keywords = "axiomref",
pages = "159166",
abstract =
"Within the last few years, there have been numerous applications of
@@ 13152,11 +13874,13 @@ American Mathematical Society (1994)
computer and maximal concentration on what is happening. Often
mathematical research consists of sifting low grade ore, and when such
sifting requires ingenious programming skills it is likely not to be
 carried out."
+ carried out.",
+ keywords = "axiomref",
+ beebe = "Andrews:1988:ASP"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Andrews:1988:ASP}
@InProceedings{Andrews:1988:ASP,
author = "G. E. Andrews",
title = "Application of {Scratchpad} to problems in special
@@ 13186,9 +13910,9 @@ American Mathematical Society (1994)
@book{Anon95,
author = "Anonymous",
title = "Zeitschrift fur Angewandte Mathematik und Physik, 75 (suppl. 2)",
 keywords = "axiomref",
year = "1995",
 issn = "00442267"
+ issn = "00442267",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13205,10 +13929,8 @@ American Mathematical Society (1994)
volume = "20",
number = "2",
pages = "151161",
 paper = "Arna95.pdf",
url =
"http://ac.elscdn.com/S0747717185710425/1s2.0S0747717185710425main.pdf",
 keywords = "axiomref",
algebra = "\newline\refto{package PRIMES IntegerPrimesPackage}",
abstract =
"We describe here a method of constructing Carmichael numbers which
@@ 13216,7 +13938,43 @@ American Mathematical Society (1994)
find composite numbers which are found to be prime by the RabinMiller
test of packages as Axiom or Maple. We also use a variation of this
method to construct strong Lucas pseudoprimes with respect to several
 pairs of parameters."
+ pairs of parameters.",
+ paper = "Arna95.pdf",
+ keywords = "axiomref",
+ beebe = "Arnault:1995:CCN"
+}
+
+\end{chunk}
+\begin{chunk}{Arnault:1995:CCN}
+@Article{Arnault:1995:CCN,
+ author = "Fran{\c{c}}ois Arnault",
+ title = "Constructing {Carmichael} Numbers Which are Strong
+ Pseudoprimes to Several Bases",
+ journal = jJSYMBOLICCOMP,
+ volume = "20",
+ number = "2",
+ pages = "151162 (or 151161??)",
+ month = aug,
+ year = "1995",
+ CODEN = "JSYCEH",
+ ISSN = "07477171 (print), 1095855X (electronic)",
+ ISSNL = "07477171",
+ MRclass = "11Y11 (11A51)",
+ MRnumber = "96k:11153",
+ MRreviewer = "Andrew Granville",
+ bibdate = "Sat May 10 15:54:09 MDT 1997",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib;
+ http://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
+ acknowledgement = acknhfb,
+ classcodes = "C7310 (Mathematics computing); C1160 (Combinatorial
+ mathematics)",
+ corpsource = "Fac. des Sci., Limoges Univ., France",
+ fjournal = "Journal of Symbolic Computation",
+ journalURL = "http://www.sciencedirect.com/science/journal/07477171",
+ keywords = "Axiom; Carmichael numbers; composite numbers; Lucas;
+ Maple; number theory; pseudoprimes; RabinMiller test;
+ symbol manipulation",
+ treatment = "T Theoretical or Mathematical",
}
\end{chunk}
@@ 13232,8 +13990,6 @@ American Mathematical Society (1994)
volume = "260",
pages = "6194",
year = "1997",
 keywords = "axiomref",
 paper = "Augo97.pdf",
abstract =
"Algorithms related to the computation of the minimal polynomial of an
$x\times n$ matrix over a field $K$ are introduced. The complexity of
@@ 13253,7 +14009,9 @@ American Mathematical Society (1994)
$O(n^3+n^2 log q)$.
Finally, the Frobenius form is obtained with asymptotic average
 complexity $O(n^3 log n)$."
+ complexity $O(n^3 log n)$.",
+ paper = "Augo97.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13263,10 +14021,10 @@ American Mathematical Society (1994)
author = "Numerical Algorithms Group",
title = "Axiom Press Release",
url = "http://www.dorn.org/uni/sls/kap05/e08\_01.htm",
 paper = "AxiomPressRelease.tgz"
year = "1996",
month = "July",
day = "24",
+ paper = "AxiomPressRelease.tgz"
keywords = "axiomref"
}
@@ 13282,7 +14040,6 @@ American Mathematical Society (1994)
journal = "unknown",
year = "2014",
url = "http://github.com/cahirwpz/phd",
 keywords = "axiomref",
abstract = "
The project aims to deliver a new type checker for SPAD language.
Several improvements over current type checker are planned.
@@ 13292,7 +14049,8 @@ American Mathematical Society (1994)
\item produce understandable diagnostic messages
\item eliminate well known bugs in the type system
\item find new type errors
 \end{itemize}"
+ \end{itemize}",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13302,9 +14060,9 @@ American Mathematical Society (1994)
@misc{Bake16,
author = "Baker, Martin",
title = "Axiom Maths Program",
 keywords = "axiomref",
year = "2016",
 url = "http://www.euclideanspace.com/prog/scratchpad/axiom/index.htm"
+ url = "http://www.euclideanspace.com/prog/scratchpad/axiom/index.htm",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13314,9 +14072,9 @@ American Mathematical Society (1994)
@misc{Bake16a,
author = "Baker, Martin",
title = "Axioms in Axiom",
 keywords = "axiomref",
year = "2016",
 url = "http://www.euclideanspace.com/prog/scratchpad/axiomsinAxiom"
+ url = "http://www.euclideanspace.com/prog/scratchpad/axiomsinAxiom",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13331,9 +14089,7 @@ American Mathematical Society (1994)
number = "2",
pages = "123153",
year = "2014",
 keywords = "axiomref",
url = "http://www21.in.tum.de/~ballarin/publications/jar2013.pdf",
 paper = "Ball14.pdf",
abstract =
"Locales are a module system for managing theory hierarchies in a
theorem prover through theory interpretation. They are available for
@@ 13350,7 +14106,9 @@ American Mathematical Society (1994)
provers, locales are made accessible to a wider audience beyond the
users of Isabelle. The discussed mechanisms include MLstyle functors,
type classes and mixins (the latter are found in modern
 objectoriented languages)."
+ objectoriented languages).",
+ paper = "Ball14.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13365,8 +14123,6 @@ American Mathematical Society (1994)
number = "4",
pages = "531",
year = "2002",
 keywords = "axiomref",
 paper = "Barn02.pdf",
url =
"https://notendur.hi.is/vae11/\%C3\%9Eekking/Systems\%20Biology/Biological\%20Algebra.PDF",
abstract =
@@ 13374,7 +14130,9 @@ American Mathematical Society (1994)
algebra (CA) to the life sciences, (2) cites literature that explains
the biological background of each application, (3) states the
mathematical methods that are used, (4) mentions the benefits of CA,
 and (5) suggests some topics for future work."
+ and (5) suggests some topics for future work.",
+ paper = "Barn02.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13398,8 +14156,39 @@ American Mathematical Society (1994)
author = "Benker, Hans",
title = "Engineering mathematics with computer algebra systems",
year = "1998",
 keywords = "axiomref",
 comment = "german"
+ comment = "german",
+ keywords = "axiomref",
+ beebe = "Benker:1998:ICS"
+}
+
+\end{chunk}
+\begin{chunk}{Benker:1998:ICS}
+@Book{Benker:1998:ICS,
+ author = "Hans Benker",
+ title = "{Ingenieurmathematik mit ComputeralgebraSystemen.
+ AXIOM, DERIVE, MACSYMA, MAPLE, MATHCAD, MATHEMATICA,
+ MATLAB und MuPAD in der Anwendung}. (German)
+ {Engineering mathematics with computer algebra systems.
+ The applications: AXIOM, DERIVE, MACSYMA, MAPLE,
+ MATHCAD, MATHEMATICA, MATLAB UND MuPAD.}",
+ publisher = pubVIEWEG,
+ address = pubVIEWEG:adr,
+ pages = "xiii + 439",
+ year = "1998",
+ MRclass = "68W30 (Symbolic computation and algebraic computation)
+ 6801 (Textbooks (computer science)) 00A06 (Mathematics
+ for nonmathematicians) 6804 (Machine computation,
+ programs (computer science)) 65D18 (Computer graphics
+ and computational geometry)",
+ bibdate = "Tue Mar 30 18:49:35 2010",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ ZMnumber = "0909.68109",
+ acknowledgement = acknhfb,
+ keywords = "calculus; differential equations; Fourier transform;
+ Laplace transform; linear algebra; optimization;
+ probability theory; statistics; textbook",
+ language = "German",
+ reviewer = "Helmut K{\"o}cher (Dresden)",
}
\end{chunk}
@@ 13410,8 +14199,8 @@ American Mathematical Society (1994)
author = "Bernard, Joey",
title = "Open Axiom",
url = "http://www.linuxjournal.com/content/openaxiom",
 keywords = "axiomref",
 year = "2014"
+ year = "2014",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13443,7 +14232,6 @@ American Mathematical Society (1994)
booktitle = "Proc. International Computing Symposium, Bonn, Germany",
year = "1970",
pages = "394419",
 keywords = "axiomref",
abstract =
"The SCRATCHPAD/1 system is designed to provide an interactive symbolic
coputational facility for the mathematician user. The system features
@@ 13451,7 +14239,8 @@ American Mathematical Society (1994)
mathematical notation, together with a facility for conveniently
introducing new notations into the language. A comprehensive system
library incorporates symbolic capabilities provided by such systems as
 SIN, MATHLAB, and REDUCE."
+ SIN, MATHLAB, and REDUCE.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13463,8 +14252,8 @@ American Mathematical Society (1994)
author = "Blair, Fred W. and Jenks, Richard D.",
title = "LPL: LISP programming language",
year = "1970",
 keywords = "axiomref",
IBM Research Report, RC3062 Sept
+IBM Research Report, RC3062 Sept ,
+ keywords = "axiomref"
\end{chunk}
@@ 13482,8 +14271,6 @@ IBM Research Report, RC3062 Sept
publisher = "ACM Press",
location = "Baltimore, MD",
pages = "5257",
 keywords = "axiomref",
 paper = "Bosm94.pdf",
url = "http://www.math.ru.nl/~bosma/pubs/ISSAC94.pdf",
abstract =
"MAGMA is a new software system for computational algebra, number
@@ 13496,7 +14283,9 @@ IBM Research Report, RC3062 Sept
objects in a mathematically rigorous manner. The conceptual and
implementation ideas behind MAGMA will be examined in this paper. This
conceptual base differs significantly from those underlying other
 computer algebra systems."
+ computer algebra systems.",
+ paper = "Bosm94.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13512,14 +14301,14 @@ IBM Research Report, RC3062 Sept
volume = "24",
pages = "235265",
year = "1997",
 keywords = "axiomref",
url = "http://lib.org.by/_djvu/_Papers/Computer_algebra/CAS%20systems/",
 paper = "Bosm97.djvu",
abstract =
"In the first of two papers on MAGMA, a new system for computational
algebra, we present the MAGMA language, outline the design principles
and theoretical background, and indicate its scope and use. Particular
 attention is given to the constructors for structures, maps, and sets."
+ attention is given to the constructors for structures, maps, and sets.",
+ paper = "Bosm97.djvu",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13555,8 +14344,6 @@ IBM Research Report, RC3062 Sept
pages = "7589",
isbn = "9783642026133",
url = "http://opus.bath.ac.uk/15188/1/RJBJHDCJSv2.pdf",
 paper = "Brad09.pdf",
 keywords = "axiomref",
abstract =
"How do we recognize when an answer is ``right''? This is a question
that has bedevilled the use of computer systems in mathematics (as
@@ 13567,7 +14354,9 @@ IBM Research Report, RC3062 Sept
pedagogically right. Here we explore the differences and show that,
despite the apparent distinction, it is possible to make many of the
differences amenable to formal treatment, by asking ``under which
 congruence is the pupil's answer equal to the teacher's?''."
+ congruence is the pupil's answer equal to the teacher's?''.",
+ paper = "Brad09.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13621,8 +14410,6 @@ IBM Research Report, RC3062 Sept
publisher = "ACM Press",
location = "Rostock, Germany",
pages = "1315",
 keywords = "axiomref",
 paper = "Breu98.pdf",
url = "http://www.gapsystem.org/Doc/Talks/paper.ps",
abstract =
"Version 4 of the GAP (Groups, Algorithms, Programming) system for
@@ 13639,7 +14426,9 @@ IBM Research Report, RC3062 Sept
the arguments is done in a uniform way by the method selection system,
making individual methods simpler and less prone to error. The methods
are combined automatically to produce a powerful and usable system for
 interactive use or programming."
+ interactive use or programming.",
+ paper = "Breu98.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13653,10 +14442,8 @@ IBM Research Report, RC3062 Sept
title = "On the Implementation of Dynamic Evaluation",
year = "1995",
pages = "7784",
 keywords = "axiomref",
isbn = "0897916999",
url = "http://pdf.aminer.org/000/449/014/on_the_implementation_of_dynamic_evaluation.pdf",
 paper = "Broa95.pdf",
abstract = "
Dynamic evaluation is a technique for producing multiple results
according to a decision tree which evolves with program execution.
@@ 13673,7 +14460,74 @@ IBM Research Report, RC3062 Sept
which avoid recomputing intermediate results. The first approach uses
Scheme ``continuations'' to record state for resuming program
execution. The second implementation uses the Unix ``fork'' operation
 to form new processes to explore alternative branches in parallel."
+ to form new processes to explore alternative branches in parallel.",
+ paper = "Broa95.pdf",
+ keywords = "axiomref",
+ beebe = "Broadbery:1995:IDE"
+}
+
+\end{chunk}
+\begin{chunk}{Broadbery:1995:IDE}
+@InProceedings{Broadbery:1995:IDE,
+ author = "P. A. Broadbery and T. G{\'o}mezD{\'\i}az and S. M.
+ Watt",
+ title = "On the Implementation of Dynamic Evaluation",
+ crossref = "Levelt:1995:IPI",
+ pages = "7784",
+ year = "1995",
+ bibdate = "Thu Mar 12 08:42:30 MST 1998",
+ bibsource = "http://www.acm.org/pubs/toc/;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/220346/p77broadbery/",
+ abstract = "Dynamic evaluation is a technique for producing
+ multiple results according to a decision tree which
+ evolves with program execution. Sometimes we need to
+ produce results for all possible branches in the
+ decision tree, while on other occasions it may be
+ sufficient to compute a single result which satisfies
+ certain properties. This technique finds use in
+ computer algebra where computing the correct result
+ depends on recognising and properly handling special
+ cases of parameters. In previous work, programs using
+ dynamic evaluation have explored all branches of
+ decision trees by repeating the computations prior to
+ decision points. The paper presents two new
+ implementations of dynamic evaluation which avoid
+ recomputing intermediate results. The first approach
+ uses Scheme `continuations' to record the state for
+ resuming program execution. The second implementation
+ uses the Unix `fork' operation to form new processes to
+ explore alternative branches in parallel. These
+ implementations are based on modifications to Lisp and
+ Cbased runtime systems for the Axiom Version 2
+ extension language (previously known as $ A^{\mbox
+ {Hash}} $ ). This allows the same highlevel source
+ code to be compared using the `reevaluation', the
+ `continuation', and the `fork' implementations.",
+ acknowledgement = acknhfb,
+ affiliation = "Numerical Algorithms Group Ltd., Oxford, UK",
+ classification = "C1140E (Game theory); C1160 (Combinatorial
+ mathematics); C6130 (Data handling techniques); C6150G
+ (Diagnostic, testing, debugging and evaluating
+ systems); C6150J (Operating systems)",
+ keywords = "algebraic computation, Dynamic evaluation; algorithms;
+ Axiom Version 2 extension language; Cbased runtime
+ systems; Computer algebra; Decision points; Decision
+ tree; Highlevel source code; ISSAC; languages;
+ Lispbased runtime systems; Multiple results; Program
+ execution; Reevaluation; Scheme continuations; State
+ recording; symbolic computation; Unix fork operation",
+ subject = "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
+ ALGEBRAIC MANIPULATION, Algorithms, Algebraic
+ algorithms. {\bf D.3.2} Software, PROGRAMMING
+ LANGUAGES, Language Classifications, SCHEME. {\bf
+ F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
+ AND PROBLEM COMPLEXITY, Numerical Algorithms and
+ Problems, Computations on polynomials. {\bf D.3.2}
+ Software, PROGRAMMING LANGUAGES, Language
+ Classifications, C.",
+ thesaurus = "Decision theory; Symbol manipulation; System
+ monitoring; Trees [mathematics]; Unix",
}
\end{chunk}
@@ 13684,9 +14538,7 @@ IBM Research Report, RC3062 Sept
author = "Bronstein, Manuel",
title = "Symbolic Integration in Computer Algebra",
url = "http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/26/042/26042580.pdf",
 paper = "Bron90.pdf",
year = "1990",
 keywords = "axiomref",
abstract =
"One major goal of symbolic integrators is to determine under what
circumstances the integral of the elementary functions of calculus can
@@ 13703,7 +14555,9 @@ IBM Research Report, RC3062 Sept
taught in calculus courses and used by older systems. In this talk,
we give an overview and description of the algorithms used in the
Scratchpad symbolic integrator, and illustrate them with integrals
 drawn from the physical sciences."
+ drawn from the physical sciences.",
+ paper = "Bron90.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13719,16 +14573,14 @@ IBM Research Report, RC3062 Sept
number = "1",
pages = "2240",
year = "2004",
 keywords = "axiomref",
 url =
 paper =
abstract =
"Procedures to manipulate pseudodifferential operators in MAPLE are
implemented in the program PSEUDO to perform calculations with
integrable models. We use lazy evaluation and streams to represent and
operate with pseudodifferential operators. No order of truncation is
needed since terms are produced on demand. We give a series of
 concrete examples."
+ concrete examples.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13744,9 +14596,7 @@ IBM Research Report, RC3062 Sept
month = "July",
year = "1989",
pages = "192206",
 keywords = "axiomref",
url = "http://www.acm.org/pubs/citations/proceedings/pldi/73141/p192boehm",
 paper = "Boeh89.pdf",
abstract = "
A number of recent programming language designs incorporate a type
checking system based on the GirardReynolds polymorphic
@@ 13761,11 +14611,14 @@ IBM Research Report, RC3062 Sept
Here we define a restricted version of the type inference problem and
present an efficient algorithm for its solution. We argue that the
 restriction is sufficiently weak to be unobtrusive in practice."
+ restriction is sufficiently weak to be unobtrusive in practice.",
+ paper = "Boeh89.pdf",
+ keywords = "axiomref",
+ beebe = "Boehm:1989:TIP"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Boehm:1989:TIP}
@Article{Boehm:1989:TIP,
author = "HansJ. Boehm",
title = "Type inference in the presence of type abstraction",
@@ 13837,7 +14690,6 @@ IBM Research Report, RC3062 Sept
year = "2004",
month = "April",
booktitle = "Proc 4th Int. Conf. on Integrated Formal Methods",
 keywords = "axiomref",
abstract = "
We introduce control engineering as a new domain of application for
formal methods. We discuss design verification, drawing attention to
@@ 13847,7 +14699,8 @@ IBM Research Report, RC3062 Sept
these criteria and provide symbolic, automated, and very general
alternatives to these standard numeric tests. We illustrate our work
with reference to a standard reference model drawn from military
 avionics."
+ avionics.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13860,9 +14713,9 @@ IBM Research Report, RC3062 Sept
year = "1991",
month = "September",
publisher = "Rapport de DEA Universite dl lille 1",
 keywords = "axiomref",

+ keywords = "axiomref"
}
+
\end{chunk}
\index{Boulanger, JeanLouis}
@@ 13884,8 +14737,6 @@ IBM Research Report, RC3062 Sept
author = "Boulanger, JeanLouis",
title = "AXIOM, A Functional Language with Object Oriented Development",
year = "1993",
 paper = "Boul93b.pdf",
 keywords = "axiomref",
abstract =
"We present in this paper, a study about the computer algebra system
Axiom, which gives us many very interesting Software engineering
@@ 13894,7 +14745,9 @@ IBM Research Report, RC3062 Sept
mathematical world (Hierarchy) and provides a running with
mathematical sense. (All objects are functions). We present many
problems of running and development in Axiom. We can note that Aiom is
 the only system of this category."
+ the only system of this category.",
+ paper = "Boul93b.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13907,9 +14760,7 @@ IBM Research Report, RC3062 Sept
year = "1995",
month = "February",
pages = "3341",
 paper = "Boul95.pdf",
publisher = "ACM SIGPLAN Notices, 30(2) CODEN SINODQ ISSN 03621340",
 keywords = "axiomref",
abstract = "
Axiom is a very powerful computer algebra system which combines two
language paradigms (functional and OOP). Mathematical world is complex
@@ 13918,7 +14769,59 @@ IBM Research Report, RC3062 Sept
programming is based on several new tools for object oriented
development, it uses two levels of class and some operations such that
{\sl coerce}, {\sl retract}, or {\sl convert} which permit the type
 evolution. These notions introduce the concept of multiview."
+ evolution. These notions introduce the concept of multiview.",
+ paper = "Boul95.pdf",
+ keywords = "axiomref",
+ beebe = "Boulanger:1995:OOM"
+}
+
+\end{chunk}
+\begin{chunk}{Boulanger:1995:OOM}
+@Article{Boulanger:1995:OOM,
+ author = "J.L. Boulanger",
+ title = "Object oriented method for {Axiom}",
+ journal = jSIGPLAN,
+ volume = "30",
+ number = "2",
+ pages = "3341",
+ month = feb,
+ year = "1995",
+ CODEN = "SINODQ",
+ ISSN = "03621340 (print), 15232867 (print), 15581160
+ (electronic)",
+ ISSNL = "03621340",
+ bibdate = "Tue Sep 17 06:32:41 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "Axiom is a very powerful computer algebra system which
+ combines two language paradigms (functional and OOP).
+ The mathematical world is complex and mathematicians
+ use abstraction to design it. The paper presents some
+ aspects of object oriented development in Axiom. Axiom
+ programming is based on several new tools for object
+ oriented development, it uses two levels of class and
+ some operations such as coerce, retract or convert
+ which permit the type evolution. These notions
+ introduce the concept of multiview.",
+ acknowledgement = acknhfb,
+ affiliation = "Lab. d'Inf. Fondamentale de Lille, Lille I Univ.,
+ Villeneuve d'Ascq, France",
+ classification = "C4240 (Programming and algorithm theory); C6110J
+ (Objectoriented programming); C6120 (File
+ organisation); C6130 (Data handling techniques); C6140D
+ (High level languages); C7310 (Mathematics computing)",
+ fjournal = "ACM SIGPLAN Notices",
+ journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
+ keywords = "Abstraction; Axiom; Axiom programming; Class; Coerce;
+ Computer algebra system; Convert; Functional language;
+ Multiview concept; Object oriented development; Object
+ oriented method; Objectoriented language; Retract;
+ Tools; Type evolution",
+ language = "English",
+ pubcountry = "USA",
+ thesaurus = "Abstract data types; Functional languages; Functional
+ programming; Mathematics computing; Objectoriented
+ languages; Objectoriented programming; Symbol
+ manipulation; Type theory",
}
\end{chunk}
@@ 13930,7 +14833,7 @@ IBM Research Report, RC3062 Sept
title = "Integration of Algebraic and Mixed Functions",
year = "1987",
in [Wit87], p18
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 13944,19 +14847,20 @@ in [Wit87], p18
year = "1989",
pages = "207211",
isbn = "0897913256",
 keywords = "axiomref",
doi = "https://dx.doi.org/10.1145/74540.74566",
 paper = "Bron88.djvu",
abstract = "
We describe an algorithm, based on Risch's real structure theorem, that
determines explicitly all the algebraic relations among a given set of
real elementary functions. We also provide examples from its
implementation that illustrate the advantages over the use of complex
 logarithms and exponentials."
+ logarithms and exponentials.",
+ paper = "Bron88.djvu",
+ keywords = "axiomref",
+ beebe = "Bronstein:1989:SRE"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Bronstein:1989:SRE}
@InProceedings{Bronstein:1989:SRE,
author = "M. Bronstein",
title = "Simplification of real elementary functions",
@@ 13997,19 +14901,20 @@ in [Wit87], p18
pages = "241246",
isbn = "0897914376",
publisher = "ACM, NY",
 keywords = "axiomref",
 paper = "Bro91a.pdf",
abstract =
"We present a new rational algorithm for solving Risch differential
equations over algebraic curves. This algorithm can also be used to
solve $n^{th}$order linear ordinary differential equations with
coefficients in an algebraic extension of the rational functions. In
the general (``mixed function'') case, this algorithm finds the
 denominator of any solution of the equation."
+ denominator of any solution of the equation.",
+ paper = "Bro91a.pdf",
+ keywords = "axiomref",
+ beebe = "Bronstein:1991:RDE"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Bronstein:1991:RDE}
@InProceedings{Bronstein:1991:RDE,
author = "M. Bronstein",
title = "The {Risch} differential equation on an algebraic
@@ 14049,17 +14954,17 @@ in [Wit87], p18
author = "Bronstein, Manuel",
title = "Computer Algebra and Indefinite Integrals",
year = "1991",
 paper = "Bro91c.pdf",
in Computer Aided Proofs in Analysis, K.R. Meyers et al. (eds)
SpringerVerlag, NY (1991)
 keywords = "axiomref",
abstract = "
We give an overview, from an analytical point of view, of decision
procedures for determining whether an elementary function has an
elementary function has an elementary antiderivative. We give examples
of algebraic functions which are integrable and nonintegrable in
closed form, and mention the current implementation of various computer
 algebra systems."
+ algebra systems.",
+ paper = "Bro91c.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 14082,8 +14987,6 @@ SpringerVerlag, NY (1991)
year = "1992",
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/issac92.ps.gz",
 paper = "Bron92.pdf",
 keywords = "axiomref",
algebra =
"\newline\refto{package ODECONST ConstantLODE}
\newline\refto{package LODEEF ElementaryFunctionLODESolver}
@@ 14105,7 +15008,38 @@ SpringerVerlag, NY (1991)
singularities of the equation, and algebraic numbers are added only
when they appear in the potential solutions. Implementation of the
complete Singer algorithm for $n=2,3$ based on this building block is
 in progress."
+ in progress.",
+ paper = "Bron92.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Bronstein, Manuel}
+\begin{chunk}{axiom.bib}
+@article{Bron92a,
+ author = "Bronstein, Manuel",
+ title = "Formulas for Series Computation",
+ journal = "Applied Algebra in Engineering, Communication and Computing",
+ volume = "2",
+ pages = "195206",
+ year = "1992",
+ abstract =
+ "We describe an algorithm that computes polynomials whose roots are
+ the coefficients of any specific order of the Laurent series of a
+ rational function. The algorithm uses only rational operations in the
+ coefficient field of the function. This allows us to compute with the
+ principal parts of the Laurent series, in particular with the residues
+ of the function, without factoring or splitting its denominator. As
+ applications, we get a generalisation of the residue formulas used in
+ symbolic integration algorithms to $n^{th}$order formulas. We also
+ get an algorithm that computes explicitly the principlal parts at all
+ the poles simultaneously, while computing in the field generated by
+ the coefficients of the series instead of the one generated by the
+ poles of the function. This yields an improved version of the
+ necessary conditions for the various cases of Kovacic's algorithm,
+ that expresses those conditions in the smallest possible extension
+ field."
}
\end{chunk}
@@ 14121,7 +15055,7 @@ ISSAC'93: proceedings of the 1993 International Symposium on Symbolic
and Algebraic Computation, Kiev, Ukraine,
ACM Press New York, NY 10036, USA, ISBN
LCCN QA76.95 I59 1993 ACM order number 505930
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 14132,15 +15066,15 @@ LCCN QA76.95 I59 1993 ACM order number 505930
title = "Streams and Lazy Evaluation Applied to Integrable Models",
year = "2008",
url = "http://arxiv.org/PS_cache/nlin/pdf/0408/0408058v1.pdf",
 paper = "Brun08.pdf",
 keywords = "axiomref",
abstract = "
Computer algebra procedures to manipulate pseudodifferential
operators are implemented to perform calculations with integrable
models. We use lazy evaluation and streams to represent and operate
with pseudodifferential operators. No order of truncation is needed
since terms are produced on demand. We give a series of concrete
 examples using the computer algebra language MAPLE."
+ examples using the computer algebra language MAPLE.",
+ paper = "Brun08.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 14154,7 +15088,7 @@ LCCN QA76.95 I59 1993 ACM order number 505930
pages = "157160",
isbn = "0897916042",
In Bronstein [Bro93] LCCN QA76.95 I59 1993
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 14165,8 +15099,6 @@ In Bronstein [Bro93] LCCN QA76.95 I59 1993
title = "Integration and Differential Equations in Computer Algebra",
year = "1992",
url = "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.576",
 paper = "Bro92a.pdf",
 keywords = "axiomref",
abstract = "
We describe in this paper how the problems of computing indefinite
integrals and solving linear ordinary differential equations in closed
@@ 14174,23 +15106,71 @@ In Bronstein [Bro93] LCCN QA76.95 I59 1993
of the mathematical history of those problems, we outline the two
major algorithms for them (respectively the Risch and Singer
algorithms) and the recent improvements on those algorithms which has
 allowed them to be implemented."
+ allowed them to be implemented.",
+ paper = "Bro92a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
\index{Beneke, T.}
\index{Schwippert, W.}
\begin{chunk}{ignore}
\bibitem[Beneke 94]{BS94}
+\begin{chunk}{axiom.bib}
+@article{Bene94,
author = "Beneke, T. and Schwippert, W.",
title = "Doubletrack into the future: MathCAD will gain new users with
Standard and Plus versions",
+ journal = "Elektronik",
+ volume = "43",
+ number = "15",
+ pages = "107110",
year = "1994",
month = "July",
pages = "107110",
+ abstract =
+ "MathCAD software is a type of `intelligent scratchpad with a pocket
+ calculator function'. Hitherto it has been suitable only to a limited
+ extent for engineering mathematics. The new Version 5.0 is now offered
+ in two implementations: as an inexpensive basic package and in a
+ considerably more costly Plus version. The authors question whether
+ MathCAD can catch up with the classical Maple and Mathematica products.",
keywords = "axiomref",
Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
+ beebe = "Beneke:1994:DFM",
+}
+
+\end{chunk}
+\begin{chunk}{Beneke:1994:DFM}
+@Article{Beneke:1994:DFM,
+ author = "T. Beneke and W. Schwippert",
+ title = "Doubletrack into the future: {MathCAD} will gain new
+ users with {Standard} and {Plus} versions",
+ journal = jELECTRONIK,
+ volume = "43",
+ number = "15",
+ pages = "107110",
+ month = jul,
+ year = "1994",
+ CODEN = "EKRKAR",
+ ISSN = "00135658",
+ bibdate = "Tue Sep 17 06:35:39 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "MathCAD software is a type of `intelligent scratchpad
+ with a pocket calculator function'. Hitherto it has
+ been suitable only to a limited extent for engineering
+ mathematics. The new Version 5.0 is now offered in two
+ implementations: as an inexpensive basic package and in
+ a considerably more costly Plus version. The authors
+ question whether MathCAD can catch up with the
+ classical Maple and Mathematica products.",
+ acknowledgement = acknhfb,
+ classification = "C7310 (Mathematics computing)",
+ fjournal = "Elektronik",
+ keywords = "Engineering mathematics; Intelligent scratchpad;
+ MathCAD software",
+ language = "German",
+ pubcountry = "Germany",
+ thesaurus = "CAD; Mathematics computing; Software packages",
+}
\end{chunk}
@@ 14203,10 +15183,8 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
series = "ISSAC'97",
year = "1997",
pages = "156163",
 keywords = "axiomref",
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mb_papers.html",
 paper = "Bro97a.pdf",
publisher = "ACM, NY",
abstract = "
We present alternative algorithms for computing symmetric powers of
@@ 14216,7 +15194,9 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
sufficiently large order, or over sufficiently complicated coefficient
domains. The basic ideas are also applicable to other computations
involving cyclic vector techniques, such as exterior powers of
 differential or difference operators."
+ differential or difference operators.",
+ paper = "Bro97a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 14248,17 +15228,57 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
year = "1994",
month = "February",
misc = "CODEN JSYCEH ISSN 07477171",
 keywords = "axiomref",
 paper = "Brow94.pdf",
abstract =
 "Work on calculations with simplical and cubical groups in AXIOM was
+ "Work on calculations with simplicial and cubical groups in AXIOM was
carried out using loan equipment and software from IBM UK and guidance
from L. A. Lambe. We report on the results of this work, and present
the AXIOM code written by the second author during this period. This
includes an implementation of the monoids which model cubes and
simplices, together with a new AXIOM category of nearrings with which
to carry out nonabelian calculations. Examples of the use of this
 code in interactive AXIOM sessions are also given."
+ code in interactive AXIOM sessions are also given.",
+ paper = "Brow94.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+\begin{chunk}{Brown:1994:CSC}
+@Article{Brown:1994:CSC,
+ author = "R. Brown and A. Tonks",
+ title = "Calculations with simplicial and cubical groups in
+ {AXIOM}",
+ journal = jJSYMBOLICCOMP,
+ volume = "17",
+ number = "2",
+ pages = "159179",
+ month = feb,
+ year = "1994",
+ CODEN = "JSYCEH",
+ ISSN = "07477171 (print), 1095855X (electronic)",
+ ISSNL = "07477171",
+ bibdate = "Tue Sep 17 06:35:39 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "Work on calculations with simplicial and cubical
+ groups in AXIOM was carried out using loan equipment
+ and software from IBM UK and guidance from L. A. Lambe.
+ We report on the results of this work, and present the
+ AXIOM code written by the second author during this
+ period. This includes an implementation of the monoids
+ which model cubes and simplices, together with a new
+ AXIOM category of nearrings with which to carry out
+ nonabelian calculations. Examples of the use of this
+ code in interactive AXIOM sessions are also given.",
+ acknowledgement = acknhfb,
+ affiliation = "Sch. of Math., Univ. of Wales, Bangor, UK",
+ classification = "C6130 (Data handling techniques); C7310
+ (Mathematics)",
+ fjournal = "Journal of Symbolic Computation",
+ journalURL = "http://www.sciencedirect.com/science/journal/07477171",
+ keywords = "AXIOM; Cubical groups; Monoids; Nonabelian
+ calculations; Simplicial groups; Software",
+ language = "English",
+ pubcountry = "UK",
+ thesaurus = "Mathematics computing; Symbol manipulation",
}
\end{chunk}
@@ 14270,9 +15290,7 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
author = "Brown, Ronald and Dreckmann, Winfried",
title = "Domains of data and domains of terms in AXIOM",
year = "1995",
 keywords = "axiomref",
url = "http://axiomwiki.newsynthesis.org/public/refs/brownfreecg.pdf",
 paper = "Brow95.pdf",
abstract = "
The main new concept we wish to illustrate in this paper is a
distinction between ``domains of data'' and ``domains of terms'', and
@@ 14282,7 +15300,9 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
we believe that a formalisation of this is new, that standards and
conventions are necessary and will be useful in various other
contexts. We shall show how this concept may be used for the coding of
 free categories and groupoids on directed graphs."
+ free categories and groupoids on directed graphs.",
+ paper = "Brow95.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 14343,15 +15363,16 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
booktitle = "Proc. ISSAC 1991",
year = "1991",
pages = "189190",
 keywords = "axiomref",
 paper = "Burg91.pdf",
abstract =
"This note sketches the part played by Scratchpad in obtaining new
 proofs of Euler's theorem and the RogersRamanujan Identities."
+ proofs of Euler's theorem and the RogersRamanujan Identities.",
+ paper = "Burg91.pdf",
+ keywords = "axiomref",
+ beebe = "Burge:1991:SRI"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Burge:1991:SRI}
@InProceedings{Burge:1991:SRI,
author = "W. H. Burge",
title = "{Scratchpad} and the {RogersRamanujan} identities",
@@ 14388,9 +15409,7 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
institution = "IBM Research",
type = "Technical Report",
number = "RC 12794 (\#57573)",
 keywords = "axiomref",
url = "http://www.csd.uwo.ca/~watt/pub/reprints/1987eurocalinfinite.pdf",
 paper = "Burg87.pdf",
abstract =
"An {\sl infinite structure} is a data structure which cannot be fully
constructed in any fixed amount of space. Several varieties of
@@ 14404,11 +15423,13 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
manipulating infinite structures. General techniques for manipulating
infinite structures are covered, as well as the higher level
manipulations on the various types of mathematical objects represented
 by infinite structures."
+ by infinite structures.",
+ paper = "Burg87.pdf",
+ keywords = "axiomref"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Burge:1987:ISS}
@TechReport{Burge:1987:ISS,
author = "W. Burge and S. Watt",
title = "Infinite Structures in {SCRATCHPAD II}",
@@ 14432,8 +15453,8 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
title = "Streams and Power Series",
year = "1987",
pages = "912",
 keywords = "axiomref",
in [Wit87], pp912
+ keywords = "axiomref"
\end{chunk}
@@ 14448,7 +15469,6 @@ in [Wit87], pp912
year = "1987",
pages = "138148",
isbn = "3540515178",
 keywords = "axiomref",
abstract =
"An infinite structure is a data structure which cannot be fully
constructed in any fixed amount of space. Several varieties of
@@ 14461,12 +15481,14 @@ in [Wit87], pp912
infinite structures. General techniques for manipulating infinite
structures are covered, as well as the higher level manipulations on
the various types of mathematical objects represented by infinite
 structures."
+ structures.",
+ keywords = "axiomref",
+ beebe = "Burge:1989:ISS"
}
\end{chunk}
\begin{chunk}{beebe.bib}
@InProceedings{Burge:1989:ISS, DATE WRONG. SHOULD BE 87
+\begin{chunk}{Burge:1989:ISS}
+@InProceedings{Burge:1989:ISS,
author = "W. H. Burge and S. M. Watt",
title = "Infinite structures in {Scratchpad} {II}",
crossref = "Davenport:1989:EEC",
@@ 14514,7 +15536,7 @@ in [Wit87], pp912
\bibitem[Calmet 94]{Cal94} Calmet, J. (ed)
Rhine Workshop on Computer Algebra, Proceedings.
Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 14530,8 +15552,6 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
number = "34",
pages = "261277",
year = "1997",
 keywords = "axiomref",
 paper = "Calm97.pdf",
url =
"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.52.5425&rep=rep1&type=pdf",
abstract =
@@ 14544,7 +15564,9 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
into algebraic forms, exploitation of machine learning, qualitative
reasoning, and constraintbased programming. Knowledge representation,
for mathematical knowledge, is identified as a central focus for much
 of this work. Several promising topics for further research are stated."
+ of this work. Several promising topics for further research are stated.",
+ paper = "Calm97.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 14561,8 +15583,6 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
solution en Scratchpad},
year = "1992",
month = "January",
 keywords = "axiomref",
 paper = "Cami92.pdf",
url = "https://hal.inria.fr/inria00074974/document",
type = "Research report",
number = "1586",
@@ 14577,11 +15597,14 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
rational functions. Thanks to the abstraction capabilities of
Scratchpad this differential equation may be solved simply and
naturally, which seems not to be the case for the other computer
 algebra systems now available."
+ algebra systems now available.",
+ paper = "Cami92.pdf",
+ keywords = "axiomref",
+ beebe = "Camion:1992:PCG"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Camion:1992:PCG}
@TechReport{Camion:1992:PCG,
author = "Paul Camion and Bernard Courteau and Andre Montpetit",
title = "Un probl{\`e}me combinatoire dans les graphes de
@@ 14623,7 +15646,7 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
title = "Java Phrasebooks for Computer Algebra and Automated Deduction",
url = "http://www.sigsam.org/bulletin/articles/132/paper8.pdf",
paper = "CCR00.pdf",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 14653,8 +15676,8 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
pages = "5166",
publisher = "SpringerVerlag, Berlin, Germany",
url = "http://www.win.tue.nl/~hansc/lisbon.pdf",
 paper = "Capr99.pdf",
misc = "in Multimedia Tools for Communicating Mathematics",
+ paper = "Capr99.pdf",
keywords = "axiomref"
}
@@ 14671,9 +15694,7 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
number = "1",
pages = "324",
year = "2006",
 keywords = "axiomref",
url = "http://www.cas.mcmaster.ca/~carette/publications/ge.pdf",
 paper = "Care06.pdf",
abstract =
"The Gaussian Elimination algorithm is in fact an algorithm family –
common implementations contain at least six (mostly independent)
@@ 14683,7 +15704,9 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
produce a natural and typesafe implementation of Gaussian Elimination
which exposes its design choices at codegeneration time, so that
these choices can effectively be specialized away, and where the
 resulting code is quite efficient."
+ resulting code is quite efficient.",
+ paper = "Care06.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 14700,9 +15723,7 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
number = "5",
pages = "349375",
year = "2011",
 paper = "Care11.pdf",
url = "http://www.cas.mcmaster.ca/~carette/metamonads/metamonads.pdf",
 keywords = "axiomref",
abstract =
"We use multistage programming, monads and OCaml's advanced module
system to demonstrate how to eliminate all abstraction overhead from
@@ 14719,7 +15740,9 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
for temporaries, and ``interleaving'' of aspects. We also show how to
encode some domainspecific knowledge so that ``clearly wrong''
compositions can be rejected at or before generation time, rather than
 during the compilation or running of the generated code."
+ during the compilation or running of the generated code.",
+ paper = "Care11.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 14731,11 +15754,11 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
author = "Carpent, Quentin and Conil, Christophe",
title = "Utilisation de logiciels libres pour la r\'ealisation de TP MT26",
year = "2004",
 paper = "Carp04.pdf",
url = "http://axiomwiki.newsynthesis.org/public/refs/ac20.pdf",
 keywords = "axiomref",
comment = "french",
 abstract = "radicalSolve(x**3+x**27=0,x)"
+ abstract = "radicalSolve(x**3+x**27=0,x)",
+ paper = "Carp04.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 14746,8 +15769,6 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
author = "Caruso, Fabrizio",
title = "Factorization of NonCommutative Polynomials",
url = "https://arxiv.org/pdf/1002.3108.pdf",
 paper = "Caru10.pdf",
 keywords = "axiomref",
year = "2010",
abstract =
"We describe an algorithm for the factorization of noncommutative
@@ 14756,7 +15777,9 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
H. Davenport more than 20 years ago. This version of the algorithm
contains some improvements with respect to the original sketch. An
improved version of the algorithm has been fully implemented in the
 Axiom computer algebra system."
+ Axiom computer algebra system.",
+ paper = "Caru10.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 14770,8 +15793,6 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
title = "Dedicated to the Memory of Richard Dimick Jenks",
year = "2003",
url = "https://www.eecis.udel.edu/~caviness/jenks/issacded.pdf",
 keywords = "axiomref",
 paper = "Cavi03.pdf",
abstract =
"On December 30, 2003, Dick Jenks died at the age of 66, after an
extended and courageous battle with multiple system atrophy.
@@ 14845,7 +15866,36 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
Personally, Dick was warm, generous, and outgoing with many
friends. He will be missed for his technical accomplishments, his
artist talents, and most of all for his positive, gentle, charming
 spirit."
+ spirit.",
+ paper = "Cavi03.pdf",
+ keywords = "axiomref",
+ beebe = "Caviness:2004:MRD"
+}
+
+\end{chunk}
+\begin{chunk}{Caviness:2004:MRD}
+@Article{Caviness:2004:MRD,
+ author = "Bob Caviness and Barbara Gatje and James H. Griesmer
+ and Tony Hearn and Manual Bronstein and Erich
+ Kaltofen",
+ title = "In Memoriam: {Richard Dimick Jenks}: {Axiom} Developer
+ and Computer Algebra Pioneer",
+ journal = jSIGSAM,
+ volume = "38",
+ number = "1",
+ pages = "3030",
+ month = mar,
+ year = "2004",
+ CODEN = "SIGSBZ",
+ ISSN = "01635824 (print), 15579492 (electronic)",
+ ISSNL = "01635824",
+ bibdate = "Sat Apr 17 11:49:58 MDT 2004",
+ bibsource = "http://portal.acm.org/;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://savannah.nongnu.org/projects/axiom/",
+ acknowledgement = acknhfb,
+ fjournal = "SIGSAM Bulletin",
+ issue = "147",
}
\end{chunk}
@@ 14871,8 +15921,6 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
pages = "8086",
isbn = "158113827X",
url = "http://www.cecm.sfu.ca/CAG/papers/edgardoIS04.pdf",
 keywords = "axiomref",
 paper = "Chan04.pdf",
abstract =
"There exist sound literature and algorithms for computing Liouvillian
solutions for the important problem of linear ODEs with rational
@@ 14886,7 +15934,9 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
the $_2F_1$, $_1F_1$ or $_0F_1$ hypergeometric functions. They algorithm
is easy to implement in the framework of a computer algebra system and
systematically solves 91\% of the 363 Kamke's linear ODE examples
 mentioned."
+ mentioned.",
+ paper = "Chan04.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 14903,9 +15953,7 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
Scientific Computing",
series = "SYNASC 04",
location = "Imisoara, Romania",
 keywords = "axiomref",
year = "2004",
 paper = "Chic04.pdf",
url = "http://www.csd.uwo.ca/~watt/pub/reprints/2004synascppca.pdf",
abstract =
"This paper presents our experiments in providing mechanisms for
@@ 14915,7 +15963,9 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
an extension to CORBA IDL supporting generic types. We describe our
language bindings for C++, Java 1.5 and Aldor as well as aspects of
our implementation, consisting of a GIDL to IDL compiler and tools for
 generating interface code for the various language bindings."
+ generating interface code for the various language bindings.",
+ paper = "Chic04.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 14932,7 +15982,6 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
title = "Geometric Theorem Provers and Algebraic Equations Solvers",
comment = "Chapter 20",
url = "http://www.mmrc.iss.ac.cn/~xgao/papers/soft1.pdf",
 paper = "Chouxx.pdf",
abstract =
"The methods of mechanizing mathematics are realized by means of
compputer software for solving scientiØc and engineering problems via
@@ 14945,7 +15994,8 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
and mature geometric theorem provers of which some have already been
published as commercial software. On the other hand, building ef
fective equations solvers is still at the experimental stage and
 remains for further research and development."
+ remains for further research and development.",
+ paper = "Chouxx.pdf"
}
\end{chunk}
@@ 14972,7 +16022,7 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
title = "New Analytic Methods of Polynomial Root Finding",
year = "1987",
pages = "2",
 keywords = "axiomref",
+ keywords = "axiomref"
in [Wit87]
\end{chunk}
@@ 14986,8 +16036,8 @@ in [Wit87]
year = "1989",
month = "November",
pages = "81788182",
 keywords = "axiomref",
Proc. Natl. Acad. Sci. USA Vol 86
+Proc. Natl. Acad. Sci. USA Vol 86 ,
+ keywords = "axiomref"
\end{chunk}
@@ 15018,7 +16068,6 @@ Proc. Natl. Acad. Sci. USA Vol 86
publisher = "SpringerVerlag",
location = "Paris, France",
pages = "169182",
 keywords = "axiomref",
abstract =
"Let $k$ be a field and $f \in k[x]$ be a polynomial of degree $n$. The
permutation action of $G$ on the roots $\{\alpha_i\}_{i=1}^n$ of $f$
@@ 15059,7 +16108,8 @@ Proc. Natl. Acad. Sci. USA Vol 86
The paper closes with a short discussion of applicability. An
implementation using AXIOM and GAP is in process but has not yet been
 completed."
+ completed.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 15073,7 +16123,6 @@ Proc. Natl. Acad. Sci. USA Vol 86
volume = "117118",
pages = "195215",
year = "1997",
 keywords = "axiomref",
abstract =
"Let $(F)$ be a system of $p$ polynomial equations
$F_i({\bf X}) \in k[{\bf X}]$, where $k$ is a commutative field and
@@ 15137,7 +16186,8 @@ Proc. Natl. Acad. Sci. USA Vol 86
A slighly more general version of this theorem is also given. The
paper then presents an algorithm that applies the theory and has been
 implemented in AXIOM. It is followed by several examples."
+ implemented in AXIOM. It is followed by several examples.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 15183,8 +16233,8 @@ Proc. Natl. Acad. Sci. USA Vol 86
pages = "289306",
editor = "Joswig, M. and Takayma, N.",
publisher = "SpringerVerlag, Berlin, Germany",
 keywords = "axiomref",
 misc = "in Algebra, Geometry and Software Systems"
+ misc = "in Algebra, Geometry and Software Systems",
+ keywords = "axiomref"
}
\end{chunk}
@@ 15197,7 +16247,7 @@ EUROCODE '90 International Symposium on
Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
/ Heidelberg, Germany / London, UK / etc., 1991 ISBN 0387543031
(New York), 3540543031 (Berlin), LCCN QA268.E95 1990
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 15222,8 +16272,8 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
year = "2003",
publisher = "A. K. Peters",
isbn = "1568811594",
 keywords = "axiomref",
 paper = "Cohe03b.pdf"
+ paper = "Cohe03b.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 15237,9 +16287,7 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
author = "Conrad, Marc and French, Tim and Maple, Carsten and Pott, Sandra",
title = "Approaching Inheritance from a Natural Mathematical Perspective
and from a Java Driven Viewpoint: a Comparative Review",
 keywords = "axiomref",
url = "http://axiomwiki.newsynthesis.org/public/refs/McTfCmSpaxiom.pdf",
 paper = "Conrxxa.pdf",
abstract = "
It is wellknown that few objectoriented programming languages allow
objects to change their nature at runtime. There have been a number
@@ 15249,7 +16297,9 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
problems, particularly those arising in a mathematical context. It is
from this context that we present a framework that realistically
represents the dynamic and evolving characteristic of problems and
 algorithms."
+ algorithms.",
+ paper = "Conrxxa.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 15263,14 +16313,14 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
author = "Conrad, Marc and French, Tim and Maple, Carsten and Pott, Sandra",
title = "Mathematical Use Cases lead naturally to nonstandard Inheritance
Relationships: How to make them accessible in a mainstream language?",
 paper = "Conrxxb.pdf",
 keywords = "axiomref",
abstract = "
Conceptually there is a strong correspondence between Mathematical
Reasoning and ObjectOriented techniques. We investigate how the ideas
of Method Renaming, Dynamic Inheritance and Interclassing can be used
to strengthen this relationship. A discussion is initiated concerning
 the feasibility of each of these features."
+ the feasibility of each of these features.",
+ paper = "Conrxxb.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 15302,7 +16352,6 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
number = "2",
pages = "5865",
year = "2000",
 paper = "Corl00.pdf",
algebra =
"\newline\refto{category OM OpenMath}
\newline\refto{domain COMPLEX Complex}
@@ 15323,7 +16372,8 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
and propose precise definitions, and explore the relationships between
these definitions.In particular, we introduce the concept of a couth
pair of definitions, e.g. of arcsin and arcsinh, and show that the
 pair arccot and {\sl arccoth} can be couth."
+ pair arccot and {\sl arccoth} can be couth.",
+ paper = "Corl00.pdf"
}
\end{chunk}
@@ 15345,9 +16395,7 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
publisher = "Springer",
isbn = "9780387356501",
year = "2007",
 keywords = "axiomref",
url = "http://www.dm.unipi.it/~caboara/Misc/Cox,\%20Little,\%20O'Shea\%20\%20Ideals,\%20varieties\%20and%20algorithms.pdf",
 paper = "Coxx07.pdf",
algebra = "\newline\refto{package GB GroebnerPackage}
\newline\refto{package PSEUDLIN PseudoLinearNormalForm}
\newline\refto{package PGROEB PolyGroebner}
@@ 15397,7 +16445,9 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
typographical error as it was the case also with the first and second
edition. The reviewer is sure that it will be a excellent guide to
introduce further undergraduates in the algorithmic aspect of
 commutative algebra and algebraic geometry."
+ commutative algebra and algebraic geometry.",
+ paper = "Coxx07.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 15415,7 +16465,6 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
number = "4",
pages = "941960",
year = "1995",
 keywords = "axiomref",
abstract =
"The first two authors previously developed an algorithm for
constructing a parametrization of the observation space of a nonlinear
@@ 15428,7 +16477,8 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
approximating realizations are discussed. The final section of the
paper sketches the implementation of the algorithm using the symbolic
manipulation package AXIOM to find the realizations mentioned above in
 feasible cases."
+ feasible cases.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 15482,7 +16532,6 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
series = "ISSAC 1992",
pages = "369375",
isbn = "0897914899 (soft cover) 0897914902 (hard cover)",
 keywords = "axiomref",
"The programming language in which to describe mathematical objects
and algorithms is a fundamental issue in the design of a symbolic
computation system. XFun is a strongly typed functional programming
@@ 15491,11 +16540,13 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
mathematical objects and structures. After illustrating its main
features, the author sketches how it could be applied to symbolic
computation. A comparison with Scratchpad II is attempted. XFun seems
 to exhibit more flexibility simplicity and uniformity."
+ to exhibit more flexibility simplicity and uniformity.",
+ keywords = "axiomref",
+ beebe = "Dalmas:1992:PFL"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Dalmas:1992:PFL}
@InProceedings{Dalmas:1992:PFL,
author = "S. Dalmas",
title = "A polymorphic functional language applied to symbolic
@@ 15537,8 +16588,8 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
author = "Daly, Timothy",
title = "Axiom Computer Algebra System Information Sources",
video = "https://www.youtube.com/watch?v=CV8y3UrpadY",
 keywords = "axiomref",
 year = "2008"
+ year = "2008",
+ keywords = "axiomref"
}
\end{chunk}
@@ 15566,7 +16617,30 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
pages = "2828",
month = "March",
year = "2002",
 keywords = "axiomref"
+ keywords = "axiomref",
+ beebe = "Daly:2002:AOS"
+}
+
+\end{chunk}
+\begin{chunk}{Daly:2002:AOS}
+@Article{Daly:2002:AOS,
+ author = "T. Daly",
+ title = "{Axiom} as Open Source",
+ journal = jSIGSAM,
+ volume = "36",
+ number = "1",
+ pages = "28??",
+ month = mar,
+ year = "2002",
+ CODEN = "SIGSBZ",
+ ISSN = "01635824 (print), 15579492 (electronic)",
+ ISSNL = "01635824",
+ bibdate = "Mon Apr 29 07:16:09 MDT 2002",
+ bibsource = "http://portal.acm.org/;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ fjournal = "SIGSAM Bulletin",
+ issue = "139",
}
\end{chunk}
@@ 15581,6 +16655,49 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
\end{chunk}
\index{Daly, Timothy}
+\begin{chunk}{axiom.bib}
+@misc{Daly05,
+ author = "Daly, Timothy",
+ title = "LispNYC Presentation at Trinity",
+ year = "2005",
+ month = "May",
+ day = "10",
+ abstract =
+ "Timothy Daly presents Axiom
+
+ Timothy Daly, published author, academic researcher, open source
+ programmer and lead developer of Axiom will be presenting about his role
+ as the driving force behind Axiom. With over 70 developers and 200
+ researchers worldwide it can best be described as:
+
+ Axiom is a general purpose Computer Algebra system. It is useful
+ for research and development of mathematical algorithms providing
+ a very high level way to express abstract mathematical concepts.
+ The Axiom Library defines over 1,000 stronglytyped mathematical
+ domains and categories.
+
+ Axiom consists of an interpreter and compiler, a browser, a graphical
+ interface, and a new online wiki that allows users to create web pages
+ that inline computations.
+
+ Axiom is built upon Common Lisp.",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Daly, Timothy}
+\begin{chunk}{axiom.bib}
+@misc{Dalyxx,
+ author = "Daly, Timothy",
+ title = "Tim Daly on Lisp in Industry",
+ url = "https://news.ycombinator.com/item?id=1580904",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Daly, Timothy}
\begin{chunk}{ignore}
@book{Daly06,
author = "Daly, Timothy",
@@ 15590,7 +16707,29 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
year = "2006",
isbn = "141166597X",
url = "http://www.lulu.com/content/190827",
 keywords = "axiomref"
+ keywords = "axiomref",
+ beebe = "Daly:2006:AVA"
+}
+
+\end{chunk}
+\begin{chunk}{Daly:2006:AVA}
+@Book{Daly:2006:AVA,
+ author = "Timothy Daly",
+ title = "{Axiom} Volume 1: {Axiom} Tutorial",
+ publisher = "Lulu, Inc.",
+ address = "860 Aviation Parkway, Suite 300, Morrisville, NC
+ 27560, USA",
+ pages = "iv + 285",
+ year = "2006",
+ ISBN = "141166597X",
+ ISBN13 = "9781411665972",
+ LCCN = "????",
+ bibdate = "Thu Mar 23 05:24:19 2006",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ price = "US\$15.00",
+ URL = "http://www.axiomdeveloper.org/axiomwebsite/bookvol1.pdf;
+ http://www.lulu.com/content/190827",
+ acknowledgement = acknhfb,
}
\end{chunk}
@@ 15600,7 +16739,7 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
\bibitem[Daly 09]{Dal09} Daly, Timothy
title = "The Axiom Literate Documentation",
url = "http://axiomdeveloper.org/axiomwebsite/documentation.html",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 15612,7 +16751,40 @@ April 89, 2013 Portland Oregon
url = "http://conf.writethedocs.org",
url2 = "http://daly.axiomdeveloper.org",
video = "http://www.youtube.com/watch?v=Av0PQDVTP4A",
 keywords = "axiomref",
+ keywords = "axiomref"
+
+\end{chunk}
+
+\index{Daly, Timothy}
+\index{Barnes, Nick}
+\begin{chunk}{axiom.bib}
+@misc{Daly13a,
+ author = "Daly, Timothy and Barnes, Nick",
+ title = "Ten reasons you must publish your code",
+ year = "2013",
+ url =
+"http://climatecode.org/blog/2013/07/tenreasonsyoumustpublishyourcode/",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@book{Dave05,
+ author = "Davenport, James H.",
+ title = "Integration  What do we want from the theory?",
+ booktitle = "Computer Algebra",
+ publisher = "Springer",
+ series = "Lecture Notes in Computer Science 162",
+ pages = "211",
+ year = "2005",
+ abstract =
+ "The theory of integration has moved a long way in the last fourteen
+ years, thought not far enough to satisfy the demands placed on it by
+ its customers. This paper outlines what problems have yet to be solved,
+ and tries to explain why they are not trivial."
+}
\end{chunk}
@@ 15621,7 +16793,7 @@ April 89, 2013 Portland Oregon
\bibitem[Davenport 79a]{Dav79a} Davenport, J.H.
title = "What can SCRATCHPAD/370 do?",
VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 15650,8 +16822,8 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
type = "Research Report",
year = "1980",
number = "RC 8537 (\#37198)",
 keywords = "axiomref",
 comment = "http://www.computerhistory.org/collections/catalog/102719109"
+ comment = "http://www.computerhistory.org/collections/catalog/102719109",
+ keywords = "axiomref"
}
\end{chunk}
@@ 15668,7 +16840,6 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
issue = "1",
pages = "1120",
publisher = "ACM",
 keywords = "axiomref",
abstract =
"This paper discusses the design and implementation of MODLISP, a
LISPlike language enhanced with the idea of MODes. This extension
@@ 15678,7 +16849,8 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
functions of the same name, with arguments of different type
(e.g. PLUS could be declared for Integer arguments, or Rational, or
Real, or even Polynomial arguments) and the system will apply the
 correct function for the types of the arguments."
+ correct function for the types of the arguments.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 15700,12 +16872,13 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
title = "Scratchpad",
organization = "Mathematical Sciences Department",
address = "IBM Thomas Watson Research Center, Yorktown Heights, NY",
+ year = "1984",
keywords = "axiomref",
 year = "1984"
+ beebe = "Davenport:1984:S"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Davenport:1984:S}
@Manual{Davenport:1984:S,
author = "J. Davenport and P. Gianni and R. Jenks and V. Miller
and S. Morrison and M. Rothstein and C. Sundaresan and
@@ 15726,11 +16899,10 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
@misc{Dave84a,
author = "Davenport, James H.",
title = "A New Algebra System",
 paper = "Dave84a.pdf",
 keywords = "axiomref",
url = "http://axiomwiki.newsynthesis.org/public/refs/Davenport1984a\_new\_algebra\_system.pdf",
 abstract =
 "Seminal internal paper discussing Axiom design decisions."
+ abstract = "Seminal internal paper discussing Axiom design decisions.",
+ paper = "Dave84a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 15785,11 +16957,12 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
isbn ="0122042301",
url = "http://staff.bath.ac.uk/masjhd/masternew.pdf",
paper = "Dave88.pdf",
 keywords = "axiomref"
+ keywords = "axiomref",
+ beebe = "Davenport:1988:CA"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Davenport:1988:CA}
@Book{Davenport:1988:CA,
author = "J. H. Davenport and Y. Siret and E. Tournier",
title = "Computer Algebra: Systems and Algorithms for Algebraic
@@ 15834,7 +17007,6 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
institution = "University of Bath, School of Mathematical Sciences",
year = "1989",
type = "technical report",
 paper = "Dave89.pdf",
url =
"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.261.767\&rep=rep1&type=pdf",
abstract =
@@ 15846,7 +17018,8 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
this context, especially when, as is the case for the system under
investigation, the equations are highly structured. We conclude with
some examples of the polynomials that we factored in the course of
 this investigation."
+ this investigation.",
+ paper = "Dave89.pdf"
}
\end{chunk}
@@ 15872,7 +17045,6 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
year = "2000",
location = "Bratislava, Slovakia",
pages = "2135",
 keywords = "axiomref",
abstract =
"The theory of abstract data types was developed in the late 1970s and
the 1980s by several people, including the ``ADJ'' group, whose work
@@ 15884,7 +17056,8 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
this paper is to report on the practical applications of this theory
within computer algebra, and also to outline some of the theoretical
issues raised by this practical application. We also give a
 substantial bibliography."
+ substantial bibliography.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 15899,8 +17072,6 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
number = "4",
pages = "259270",
year = "2002",
 keywords = "axiomref",
 paper = "Dave02.pdf",
url = "http://www.calculemus.net/meetings/siena01/Papers/Davenport.pdf",
abstract =
"Equality is such a fundamental concept in mathematics that, in
@@ 15918,8 +17089,9 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
though they are equal as elements of $\mathbb{Q}(x)$. The aim of
this paper is to point out some of the problems, both with
mathematical equality and with data structure equality, and to
 explain how necessary it is to keep a clear distintion between the
 two."
+ explain how necessary it is to keep a clear distintion between the two.",
+ paper = "Dave02.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 15932,8 +17104,6 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
title = "Computer Algebra and the three 'E's: Efficiency, Elegance, and
Expressiveness",
url = "http://staff.bath.ac.uk/masjhd/Drafts/PLMMS2007",
 paper = "Dave07.pdf",
 keywords = "axiomref",
abstract =
"What author of a programming language would not claim that the 3 'E's
were the goals? Nevertheless, we claim that computer algebra does lead
@@ 15942,7 +17112,9 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
We restrict ``efficiency'' to mean machine efficiency, since the other
'E's cover programmer efficiency. For the sake of clarity, we describe
as ``expressiveness'', what can be expressed in the language, and
 ``elegance'' as how it can be expressed."
+ ``elegance'' as how it can be expressed.",
+ paper = "Dave07.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 15953,7 +17125,7 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
title = "Computer Algebra textbook",
url = "http://staff.bath.ac.uk/masjhd/JHDCA.pdf",
paper = "Dav14.pdf",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 15963,7 +17135,7 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
EUROCAL '87 European Conference on Computer Algebra Proceedings
SpringerVerlag, Berlin, Germany / Heidelberg, Germany / London,
UK / etc., 1989 ISBN 3540515178 LCCN QA155.7.E4E86 1987
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 15980,9 +17152,7 @@ UK / etc., 1989 ISBN 3540515178 LCCN QA155.7.E4E86 1987
location = "Capri, Italy",
publisher = "SpringerVerlag",
isbn = "0387525319",
 keywords = "axiomref",
url = "http://opus.bath.ac.uk/32336/1/Davenport\_DISCO\_1990.pdf",
 paper = "Dave90.pdf",
comment = "AXIOM Technical Report, ATR/1, NAG Ltd., Oxford, 1992",
keywords = "axiomref",
abstract =
@@ 15995,11 +17165,14 @@ UK / etc., 1989 ISBN 3540515178 LCCN QA155.7.E4E86 1987
algebra. Of necessity, such a theory is rather different from the
conventional, nonconstructive, theory. It is also somewhat different
from the theories of Seidenberg [1974] and his school, who are not
 particularly concerned with practical questions of efficiency."
+ particularly concerned with practical questions of efficiency.",
+ paper = "Dave90.pdf",
+ keywords = "axiomref",
+ beebe = "Davenport:1990:SVA"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Davenport:1990:SVA}
@InProceedings{Davenport:1990:SVA,
author = "J. H. Davenport and B. M. Trager",
title = "{Scratchpad}'s View of Algebra {I}: Basic Commutative
@@ 16064,8 +17237,6 @@ UK / etc., 1989 ISBN 3540515178 LCCN QA155.7.E4E86 1987
acmid = "120699",
publisher = "ACM",
address = "New York, NY, USA",
 keywords = "axiomref",
 paper = "Dave91.pdf",
abstract = "
This paper explains how Scratchpad solves the problem of presenting a
categorical view of factorization in unique factorization domains,
@@ 16086,11 +17257,14 @@ UK / etc., 1989 ISBN 3540515178 LCCN QA155.7.E4E86 1987
polyinmoals in $\overline{Z[\sqrt{5}]}[x]$ since the domain
$Z[\sqrt{5}]$ is not a unique factorization domain, even though
$\overline{Z[\sqrt{5}]}$ is, since it is a field. Of course, we can
 factor polynomials in $\overline{Z}[\sqrt{5}][x]$"
+ factor polynomials in $\overline{Z}[\sqrt{5}][x]$",
+ paper = "Dave91.pdf",
+ keywords = "axiomref",
+ beebe = "Davenport:1991:SVA"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Davenport:1991:SVA}
@InProceedings{Davenport:1991:SVA,
author = "J. H. Davenport and P. Gianni and B. M. Trager",
title = "{Scratchpad}'s view of algebra. {II}. {A} categorical
@@ 16146,8 +17320,6 @@ UK / etc., 1989 ISBN 3540515178 LCCN QA155.7.E4E86 1987
number = "TR3/92 (ATR/1) (NP2490)",
institution = "Numerical Algorithm Group (NAG) Ltd.",
year = "1992",
 keywords = "axiomref",
 paper = "Dave90.pdf",
abstract =
"While computer algebra systems have dealt with polynomials and
rational functions with integer coefficients for many years, dealing
@@ 16158,11 +17330,14 @@ UK / etc., 1989 ISBN 3540515178 LCCN QA155.7.E4E86 1987
algebra. Of necessity, such a theory is rather different from the
conventional, nonconstructive, theory. It is also somewhat different
from the theories of Seidenberg [1974] and his school, who are not
 particularly concerned with practical questions of efficiency."
+ particularly concerned with practical questions of efficiency.",
+ paper = "Dave90.pdf",
+ keywords = "axiomref",
+ beebe = "Davenport:1992:SVAa"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Davenport:1992:SVAa}
@TechReport{Davenport:1992:SVAa,
author = "J. H. Davenport and B. M. Trager",
title = "{Scratchpad}'s View of Algebra {I}: Basic Commutative
@@ 16195,8 +17370,6 @@ UK / etc., 1989 ISBN 3540515178 LCCN QA155.7.E4E86 1987
address = "Downer's Grove, IL, USA and Oxford, UK",
year = "1992",
url = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
 keywords = "axiomref",
 paper = "Dave91.pdf",
abstract = "
This paper explains how Scratchpad solves the problem of presenting a
categorical view of factorization in unique factorization domains,
@@ 16217,11 +17390,14 @@ UK / etc., 1989 ISBN 3540515178 LCCN QA155.7.E4E86 1987
polyinmoals in $\overline{Z[\sqrt{5}]}[x]$ since the domain
$Z[\sqrt{5}]$ is not a unique factorization domain, even though
$\overline{Z[\sqrt{5}]}$ is, since it is a field. Of course, we can
 factor polynomials in $\overline{Z}[\sqrt{5}][x]$"
+ factor polynomials in $\overline{Z}[\sqrt{5}][x]$",
+ paper = "Dave91.pdf",
+ keywords = "axiomref",
+ beebe = "Davenport:1992:SVAb"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Davenport:1992:SVAb}
@TechReport{Davenport:1992:SVAb,
author = "J. H. Davenport and P. Gianni and B. M. Trager",
title = "{Scratchpad}'s View of Algebra {II}: {A} Categorical
@@ 16249,8 +17425,6 @@ UK / etc., 1989 ISBN 3540515178 LCCN QA155.7.E4E86 1987
number = "TR5/92 (ATR/3) (NP2492)",
institution = "Numerical Algorithms Group, Inc.",
year = "1992",
 paper = "Dave92a.pdf",
 keywords = "axiomref",
abstract =
"AXIOM is a computer algebra system superficially like many others,
but fundamentally different in its internal construction, and
@@ 16265,11 +17439,14 @@ UK / etc., 1989 ISBN 3540515178 LCCN QA155.7.E4E86 1987
\item give some references to the literature on particular aspects of
AXIOM and,
\item suggest the way forward.
 \end{itemize}"
+ \end{itemize}",
+ paper = "Dave92a.pdf",
+ keywords = "axiomref",
+ beebe = "Davenport:1992:AS"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Davenport:1992:AS}
@TechReport{Davenport:1992:AS,
author = "J. H. Davenport",
title = "The {AXIOM} System",
@@ 16299,18 +17476,19 @@ UK / etc., 1989 ISBN 3540515178 LCCN QA155.7.E4E86 1987
type = "technical report",
number = "TR6/92 (ATR/4)(NP2493)",
url = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
 paper = "Dave92b.pdf",
 keywords = "axiomref",
abstract =
"Axiom is a computer algebra system superficially like many others, but
fundamentally different in its internal construction, and therefore in
the possibilities it offers to its users and programmers. In these
lecture notes, we will explain, by example, the methodology that the
 author uses for programming substantial bits of mathematics in Axiom."
+ author uses for programming substantial bits of mathematics in Axiom.",
+ paper = "Dave92b.pdf",
+ keywords = "axiomref",
+ beebe = "Davenport:1992:HDO"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Davenport:1992:HDO}
@TechReport{Davenport:1992:HDO,
author = "J. H. Davenport",
title = "How Does One Program in the {AXIOM} System?",
@@ 16340,7 +17518,7 @@ Technical Report TR3/92 (ATR/1)(NP2490), Numerical
Algorithms Group, Inc., Downer's Grove, IL, USA and Oxford, UK,
December 1992.
url = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 16356,15 +17534,38 @@ December 1992.
publisher = "ACM",
pages = "123129",
year = "1992",
 paper = "Dave92.pdf",
report = "Technical Report TR2/93 Numerical Algorithms Group, Inc",
 keywords = "axiomref",
algebra = "\newline\refto{package PRIMES IntegerPrimesPackage}",
abstract =
"Rabin's algorithm is commonly used in computer algebra systems and
elsewhere for primality testing. This paper presents an experience
with this in the Axiom computer algebra system. As a result of this
 experience, we suggest certain strengthenings of the algorithm."
+ experience, we suggest certain strengthenings of the algorithm.",
+ paper = "Dave92.pdf",
+ keywords = "axiomref",
+ beebe = "Davenport:1993:PTR"
+}
+
+\end{chunk}
+\begin{chunk}{Davenport:1993:PTR}
+@TechReport{Davenport:1993:PTR,
+ author = "J. H. Davenport",
+ title = "Primality Testing Revisited",
+ number = "TR2/93 (ATR/6) (NP2556)",
+ institution = instNAG,
+ address = instNAG:adr,
+ pages = "??",
+ month = aug,
+ year = "1993",
+ bibdate = "Fri Dec 29 16:31:49 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
+ abstract = "Rabin's algorithm is commonly used in computer algebra
+ systems and elsewhere for primality testing. This paper
+ presents an experience with this in the Axiom computer
+ algebra system. As a result of this experience, we
+ suggest certain strengthenings of the algorithm.",
+ acknowledgement = acknhfb,
}
\end{chunk}
@@ 16377,15 +17578,15 @@ December 1992.
title = "The Unknown in Computer Algebra",
url =
"http://axiomwiki.newsynthesis.org/public/refs/TheUnknownInComputerAlgebra.pdf",
 paper = "Davexx.pdf",
 keywords = "axiomref",
abstract = "
Computer algebra systems have to deal with the confusion between
``programming variables'' and ``mathematical symbols''. We claim that
they should also deal with ``unknowns'', i.e. elements whose values
are unknown, but whose type is known. For examples $x^p \ne x$ if $x$
is a symbol, but $x^p = x$ if $x \in GF(p)$. We show how we have
 extended Axiom to deal with this concept."
+ extended Axiom to deal with this concept.",
+ paper = "Davexx.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 16399,7 +17600,7 @@ James H. Davenport
May 1984
url = "http://xml.coverpages.org/openmath13.html",
paper = "Dav00.pdf",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 16411,10 +17612,10 @@ May 1984
journal = "Springer Lecture Notes in Artificial Intelligence 6824",
pages = "167",
url = "http://people.bath.ac.uk/masjhd/Meetings/CICM2011.pdf",
 keywords = "axiomref",
comment = "http://www.springerlink.com/conten/9783642226724",
year = "2011",
 paper = "Dave11.pdf"
+ paper = "Dave11.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 16426,10 +17627,10 @@ May 1984
title = "Computer Algebra or Computer Mathematics?",
year = "2012",
url = "http://people.bath.ac.uk/masjhd/Slides/CalculemusSchool2002.pdf",
 paper = "Dave12a.pdf",
abstract =
"Scope: ``polynomialtype'' systems: Axiom, Macsyma/Maxima, Maple,
 Mathematica, and Reduce."
+ Mathematica, and Reduce.",
+ paper = "Dave12a.pdf"
}
\index{Davenport, James H.}
@@ 16458,8 +17659,6 @@ May 1984
title = "Some Introductory Remarks on Computer Algebra",
url =
"https://www.math.unibielefeld.de/~rehmann/ECM/cdrom/3ecm/pdfs/pant3/decker.pdf",
 paper = "Deckxx.pdf",
 keywords = "axiomref",
abstract =
"Computer algebra is a relatively young but rapidly growing field. In
this introductory note to the minisymposium on computer algebra
@@ 16471,7 +17670,9 @@ May 1984
examples which underline the fact that computer algebra systems
provide easy access to powerful computing tools. And, I will quote
from and refer to a couple of survey papers, textbooks and webpages
 which I recommend for further reading."
+ which I recommend for further reading.",
+ paper = "Deckxx.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 16486,9 +17687,7 @@ May 1984
year = "2000",
type = "technical report",
number = "200016",
 paper = "Dell00.pdf",
url = "http://www.unilim.fr/laco/rapports/2000/R2000\_16.pdf",
 keywords = "axiomref",
abstract =
"Dynamic evaluation is a general method for computing with parameters
[6, 9]. In 1994, T. GomezDiaz implemented the dynamic constructible
@@ 16527,7 +17726,9 @@ May 1984
and D.M. Wang simple systems. In particular, this last section will
demonstrate well the importance of our $L$normalization
property. Indeed, we show that simple systems and squarefree
 $L$normalized constructible triangular systems are equivalent."
+ $L$normalized constructible triangular systems are equivalent.",
+ paper = "Dell00.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 16541,8 +17742,8 @@ May 1984
year = "2000",
type = "technical report",
number = "200017",
 paper = "Dell00a.pdf",
url = http://www.unilim.fr/laco/rapports/2000/R2000_17.pdf,
+ paper = "Dell00a.pdf",
keywords = "axiomref"
}
@@ 16559,7 +17760,6 @@ May 1984
number = "1",
pages = "4968",
year = "2001",
 keywords = "axiomref",
abstract =
"Two kinds of triangular systems are studied: normalized triangular
polynomial systems (a weaker form of Lazard’s triangular sets
@@ 16571,7 +17771,8 @@ May 1984
related. In particular, combining the two points of view
(constructible and polynomial) on the subject of squarefree
conditions, it allows us to effect dramatic improvements in the
 dynamic constructible closure programs."
+ dynamic constructible closure programs.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 16614,7 +17815,6 @@ May 1984
year = "1992",
location = "Berkeley, CA",
pages = "18",
 paper = "Dewa92.pdf",
algebra =
"\newline\refto{domain D01AJFA d01ajfAnnaType}
\newline\refto{domain D01AKFA d01akfAnnaType}
@@ 16656,7 +17856,8 @@ May 1984
``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."
+ orthogonal interface.",
+ paper = "Dewa92.pdf"
}
\end{chunk}
@@ 16676,10 +17877,10 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
@misc{Dewa95,
author = "Dewar, Mike C.",
title = "AXIOM and A\#: Current Status and Future Plans",
 paper = "Dewa95.pdf",
year = "1995",
 keywords = "axiomref",
 url = "ftp://ftp.inf.ethz.ch/org/cathode/workshops/jan95/abstracts/dewar.ps"
+ url = "ftp://ftp.inf.ethz.ch/org/cathode/workshops/jan95/abstracts/dewar.ps",
+ paper = "Dewa95.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 16704,8 +17905,6 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
school = "Johannes Kepler Universitat, Linz",
year = "2006",
month = "February",
 paper = "Diaz06.pdf",
 keywords = "axiomref",
abstract =
"A survey of symbolic methods for factoring linear differential
operators is given. Starting from basic notions – ring of operators,
@@ 16734,7 +17933,9 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
available. This theoretical representation is valuable in
understanding the nature of the classical Beke algorithm and its
variants like the algorithm LODEF by Schwarz and the BekeBronstein
 algorithm."
+ algorithm.",
+ paper = "Diaz06.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 16750,8 +17951,6 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
volume = "19",
pages = "3963",
year = "1995",
 paper = "DiBl95.pdf",
 keywords = "axiomref",
abstract =
"Application of objectoriented programming techniques to design and
implementation of symbolic computation is investigated. We show the
@@ 16770,7 +17969,9 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
specialization in a natural way. The {\sl ESI} mechanism verifies the
type correctness of language statements by means of type checking
rules and preserves their correctness at runtime by a suitable method
 lookup algorithm."
+ lookup algorithm.",
+ paper = "DiBl95.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 16786,13 +17987,13 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
year = "1997",
publisher = "Springer",
pages = "164178",
 keywords = "axiomref",
abstract =
"We want to define a strongly typed OOP language suitable as the
software development tool of a symbolic computation system, which
provides class structure to manage ADTs and supports multiple
inheritance to model specialization hierarchies. In this paper, we
 provide the theoretical background for such a task."
+ provide the theoretical background for such a task.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 16808,7 +18009,6 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
year = "1998",
pages = "440446",
isbn = "3540510842",
 keywords = "axiomref",
abstract =
"Many problems in computer algebra, as well as in highschool
exercises, are such that their statement only involves integers but
@@ 16850,12 +18050,14 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
The aim of this paper is to describe an implementation of an algebraic
closure domain constructor in the language Scratchpad II, simply
called Scratchpad below. In the first part we analyze the problem, and
 in the second part we describe a solution based on the D5 system."
+ in the second part we describe a solution based on the D5 system.",
+ keywords = "axiomref",
+ beebe = "Dicrescenzo:1989:AEA"
}
\end{chunk}
\begin{chunk}{beebe.bib}
@InProceedings{Dicrescenzo:1989:AEA, DATE WRONG, SHOULD BE 1988
+\begin{chunk}{Dicrescenzo:1989:AEA}
+@InProceedings{Dicrescenzo:1989:AEA,
author = "C. Dicrescenzo and D. Duval",
title = "Algebraic extensions and algebraic closure in
{Scratchpad} {II}",
@@ 16893,10 +18095,10 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
@misc{Dicr95,
author = "Dicrescenzo, C. and Jung, Francoise",
title = "COMPASS package",
 paper = "Dicr95.pdf",
year = "1995",
url =
"ftp://ftp.inf.ethz.ch/org/cathode/workshops/jan95/abstracts/bronstein.ps",
+ paper = "Dicr95.pdf",
keywords = "axiomref"
}
@@ 16913,7 +18115,7 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
year = "2005",
publisher = "Springer",
pages = "440446",
 keywords = "axiomref",
+ keywords = "axiomref"
}
\end{chunk}
@@ 16928,14 +18130,14 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
booktitle = "Proc. ISSAC 1994",
series = "ISSAC 94",
url = "http://www.cs.berkeley.edu/~fateman/papers/ding.ps",
 paper = "Ding94.pdf",
 keywords = "axiomref",
abstract =
"Many standard functions, such as the logarithms and square root
functions, cannot be defined continuously on the complex
plane. Mistaken assumptions about the properties of these functions
lead computer algebra systems into various conundrums. We discuss how
 they can manipulate such functions in a useful fashion."
+ they can manipulate such functions in a useful fashion.",
+ paper = "Ding94.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 16944,7 +18146,7 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
\bibitem[DLMF]{DLMF}.
title = "Digital Library of Mathematical Functions",
url = "http://dlmf.nist.gov/software/#T1",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 16960,7 +18162,6 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
publisher = "ACM Press",
location = "Rostock, Germany",
pages = "1315",
 keywords = "axiomref",
abstract =
"This paper presents a method for representing mathematical content
and presentation markup in interactive mathematical documents that
@@ 16978,7 +18179,8 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
for Linear Algebra. The issues involved in the implementation of the
interactive textbook also shed some light on the problems faced by the
MathML working group in representing both presentation and content for
 mathematics for interactive web documents."
+ mathematics for interactive web documents.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 16990,7 +18192,7 @@ ISSAC 99: July 2931, 1999, Simon Fraser University,
Vancouver, BC, Canada: proceedings of the 1999 International Symposium on
Symbolic and Algebraic Computation. ACM Press, New York, NY 10036, USA, 1999.
ISBN 1581130732 LCCN QA76.95.I57 1999
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 17005,10 +18207,8 @@ ISBN 1581130732 LCCN QA76.95.I57 1999
journal = "Intelligent computer mathematics (MKM 2011)",
year = "2011",
isbn = "9783642226724",
 paper = "Reis11.pdf",
url =
"https://www.semanticscholar.org/paper/RetargetingOpenAxiomtoPolyMLTowardsanReisMatthews/4ce5d85ea8424ced82d",
 keywords = "axiomref",
abstract =
"This paper presents an ongoing effort to integrate the AXIOM family
of computer algebra systems with Poly/MLbased proof assistants in the
@@ 17017,7 +18217,9 @@ ISBN 1581130732 LCCN QA76.95.I57 1999
assistants, and also to bring the power of mechanized formal
verification to a family of strongly typed computer algebra systems at
a modest cost. Our approach is based on retargeting the code generator
 of the OpenAxiom compiler to the Poly/ML abstract machine."
+ of the OpenAxiom compiler to the Poly/ML abstract machine.",
+ paper = "Reis11.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 17031,8 +18233,6 @@ ISBN 1581130732 LCCN QA76.95.I57 1999
publisher = "Springer",
year = "2012",
url = "http://www.axiomatics.org/~gdr/liz/cicm2012.pdf",
 paper = "Reis12.pdf",
 keywords = "axiomref",
abstract = "
We present the design and implementation of a system for axiomatic
programming, and its application to mathematical software
@@ 17041,7 +18241,9 @@ ISBN 1581130732 LCCN QA76.95.I57 1999
resolution based on equational theories and userdefined local
axioms. We illustrate uses of axioms, and their organization into
concepts, in structured generic programming as practiced in
 computational mathematical systems."
+ computational mathematical systems.",
+ paper = "Reis12.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 17053,8 +18255,6 @@ ISBN 1581130732 LCCN QA76.95.I57 1999
title = "Order Sorted Computer Algebra and Coercions",
school = "University of Bath",
year = "1997",
 keywords = "axiomref",
 paper = "Doye97.pdf",
abstract =
"Computer algebra systems are large collections of routines for solving
mathematical problems algorithmically, efficiently and above all,
@@ 17084,19 +18284,40 @@ ISBN 1581130732 LCCN QA76.95.I57 1999
type system which adheres to a set of assumptions. We shall prove that
this is an algorithm and that it always returns a coercion when one
exists. Finally, we present a demonstration implementation of this
 automated coerion algorithm in Axiom."
+ automated coerion algorithm in Axiom.",
+ paper = "Doye97.pdf",
+ keywords = "axiomref"
}
\end{chunk}
\index{Doye, Nicolas James}
\begin{chunk}{ignore}
\bibitem[Doye 99]{Doy99} Doye, Nicolas J.
+\begin{chunk}{axiom.bib}
+@inproceedings{Doye99,
+ author = "Doye, Nicolas James",
title = "Automated coercion for Axiom",
In Dooley [Doo99], pp229235
ISBN 1581130732 LCCN QA76.95.I57 1999 ACM Press
+ booktitle = "Proc. ISSAC 1999",
+ pages = "229235",
+ year = "1999",
+ isbn = "1581130732",
url = "http://www.acm.org/citation.cfm?id=309944",
keywords = "axiomref",
+ beebe = "Doye:1999:ACA"
+}
+
+\end{chunk}
+\begin{chunk}{Doye:1999:ACA}
+@InProceedings{Doye:1999:ACA,
+ author = "Nicolas J. Doye",
+ title = "Automated coercion for {Axiom}",
+ crossref = "Dooley:1999:IJS",
+ pages = "229235",
+ year = "1999",
+ bibdate = "Sat Mar 11 16:39:42 MST 2000",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.acm.org/pubs/contents/proceedings/issac/309831/",
+ acknowledgement = acknhfb,
+}
\end{chunk}
@@ 17109,8 +18330,6 @@ ISBN 1581130732 LCCN QA76.95.I57 1999 ACM Press
booktitle = "Proc. ISSAC 2001",
series = "ISSAC 2001",
year = "2001",
 keywords = "axiomref",
 paper = "Domi01.pdf",
abstract = "
In this paper the analysis of the data structures used in a symbolic
computation system, called Kenzo, is undertaken. We deal with the
@@ 17120,7 +18339,9 @@ ISBN 1581130732 LCCN QA76.95.I57 1999 ACM Press
simplicial sets and chain complexes, showing how the ordersorted
algebraic specifications formalisms can be adapted, through the
``inheritance as coercion'' metaphor, in order to model this Kenzo
 fragment."
+ fragment.",
+ paper = "Domi01.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 17136,9 +18357,7 @@ ISBN 1581130732 LCCN QA76.95.I57 1999 ACM Press
year = "2010",
location = "Tsakhadzor, Armenia",
pages = "7384",
 keywords = "axiomref",
url = "http://www.csd.uwo.ca/~watt/pub/reprints/2010cascspecdom.pdf",
 paper = "Drag10.pdf",
abstract =
"Computer algebra in scientific computation squarely faces the dilemma
of natural mathematical expression versus efficiency. While
@@ 17147,7 +18366,9 @@ ISBN 1581130732 LCCN QA76.95.I57 1999 ACM Press
abstractions, they can come at a considerable cost. We investigate how
deeply nested type constructions may be optimized to achieve
performance similar to that of handtuned code written in lowerlevel
 languages."
+ languages.",
+ paper = "Drag10.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 17161,7 +18382,7 @@ ISBN 1581130732 LCCN QA76.95.I57 1999 ACM Press
title = "Embedded Verification Techniques for Computer Algebra Systems",
Grant citation GR/L48256 Nov 1, 1997Feb 28, 2001
url = "http://www.cs.standrews.ac.uk/research/output/detail?output=ML97.php",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 17172,12 +18393,40 @@ Grant citation GR/L48256 Nov 1, 1997Feb 28, 2001
title = "An Introduction to Aldor and its Type System",
year = "1999",
url = "http://www.aldor.org/docs/reports/cfc99/aldorcfc99.pdf",
 paper = "Duns99b.pdf",
 comment = "slides"
+ comment = "slides",
+ paper = "Duns99b.pdf"
}
\end{chunk}
+\index{d01ajfAnnaType}
+\index{d01akfAnnaType}
+\index{d01alfAnnaType}
+\index{d01amfAnnaType}
+\index{d01anfAnnaType}
+\index{d01apfAnnaType}
+\index{d01aqfAnnaType}
+\index{d01asfAnnaType}
+\index{d01fcfAnnaType}
+\index{d01gbfAnnaType}
+\index{d01TransformFunctionType}
+\index{d02bbfAnnaType}
+\index{d02bhfAnnaType}
+\index{d02cjfAnnaType}
+\index{d02ejfAnnaType}
+\index{d03eefAnnaType}
+\index{d03fafAnnaType}
+\index{e04dgfAnnaType}
+\index{e04fdfAnnaType}
+\index{e04gcfAnnaType}
+\index{e04jafAnnaType}
+\index{e04mbfAnnaType}
+\index{e04nafAnnaType}
+\index{e04ucfAnnaType}
+\index{NumericalIntegrationProblem}
+\index{NumericalODEProblem}
+\index{NumericalOptimizationProblem}
+\index{NumericalPDEProblem}
\index{Dupee, Brian J.}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@@ 17185,8 +18434,6 @@ Grant citation GR/L48256 Nov 1, 1997Feb 28, 2001
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 =
@@ 17249,38 +18496,12 @@ Grant citation GR/L48256 Nov 1, 1997Feb 28, 2001
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."
+ routines and the inference mechanisms for the expert system.",
+ paper = "Dupe95.pdf",
+ keywords = "axiomref"
}
\end{chunk}
\index{d01ajfAnnaType}
\index{d01akfAnnaType}
\index{d01alfAnnaType}
\index{d01amfAnnaType}
\index{d01anfAnnaType}
\index{d01apfAnnaType}
\index{d01aqfAnnaType}
\index{d01asfAnnaType}
\index{d01fcfAnnaType}
\index{d01gbfAnnaType}
\index{d01TransformFunctionType}
\index{d02bbfAnnaType}
\index{d02bhfAnnaType}
\index{d02cjfAnnaType}
\index{d02ejfAnnaType}
\index{d03eefAnnaType}
\index{d03fafAnnaType}
\index{e04dgfAnnaType}
\index{e04fdfAnnaType}
\index{e04gcfAnnaType}
\index{e04jafAnnaType}
\index{e04mbfAnnaType}
\index{e04nafAnnaType}
\index{e04ucfAnnaType}
\index{NumericalIntegrationProblem}
\index{NumericalODEProblem}
\index{NumericalOptimizationProblem}
\index{NumericalPDEProblem}
\index{Dupee, Brian J.}
\index{Davenport, James H.}
@@ 17292,9 +18513,7 @@ Grant citation GR/L48256 Nov 1, 1997Feb 28, 2001
isbn = "9783540660477",
pages = "3750",
year = "1999",
 paper = "Dupe99.pdf",
url = "http://people.eecs.berkeley.edu/~fateman/papers/casc9934.pdf",
 keywords = "axiomref",
comment = "Contains FORTRAN Code of Taylor Series",
algebra = "\newline\refto{package EXPRODE ExpressionSpaceODESolver}",
abstract =
@@ 17314,7 +18533,9 @@ Grant citation GR/L48256 Nov 1, 1997Feb 28, 2001
Using current technology it has at last become possible to integrate
these two concepts and build an automatic adaptive symbolicnumeric
algorithm within a uniform framework which can hide the internal
 workings behind a modern interface."
+ workings behind a modern interface.",
+ paper = "Dupe99.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 17367,8 +18588,6 @@ Kelsey, Tom; Martin, Ursula; Owre, Sam
title = "Computer Algebra meets Automated Theorem Proving: Integrating Maple and PVS",
TPHOLS 2001, Edinburgh
url = "http://www.csl.sri.com/~owre/papers/tphols01/tphols01.pdf",
 paper = "DGKM01.pdf",
 keywords = "axiomref",
abstract = "
We describe an interface between version 6 of the Maple computer
algebra system with the PVS automated theorem prover. The interface is
@@ 17377,7 +18596,9 @@ TPHOLS 2001, Edinburgh
of a library of proof strategies for use in real analysis. We
demonstrate examples using the interface and the real analysis
library. These examples provide proofs which are both illustrative and
 applicable to genuine symbolic computation problems."
+ applicable to genuine symbolic computation problems.",
+ paper = "DGKM01.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 17393,12 +18614,12 @@ TPHOLS 2001, Edinburgh
pages = "211246",
year = "1992",
publisher = "SpringerVerlag",
 keywords = "axiomref",
abstract =
"We apply the Kovacic algorithm to some families of special functions,
mainly the hypergeometric one and that of Heun, in order to discuss
the existence of closedform solutions. We begin by giving a slightly
 modified version of the kovacic algorithm and a sketch proof."
+ modified version of the kovacic algorithm and a sketch proof.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 17416,11 +18637,12 @@ TPHOLS 2001, Edinburgh
publisher = "NorthHolland",
pages = "133143",
year = "1992",
 keywords = "axiomref"
+ keywords = "axiomref",
+ beebe = "Duval:1992:EPS"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Duval:1992:EPS}
@Article{Duval:1992:EPS,
author = "D. Duval and F. Jung",
title = "Examples of problem solving using computer algebra",
@@ 17495,7 +18717,6 @@ TPHOLS 2001, Edinburgh
number = "1",
pages = "117130",
year = "1994",
 keywords = "axiomref",
abstract =
"The paper deals with problems about conception and design of
highlevel computer algebra systems. Here we use a categorical
@@ 17506,7 +18727,8 @@ TPHOLS 2001, Edinburgh
A computer algebra system must allow the manipulation of algebraic
structures, in particular, the construction of new structures from
known ones. In the paper we give a definition, at the sketch level, of
 parametrization of a structure by another one."
+ parametrization of a structure by another one.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 17521,8 +18743,6 @@ TPHOLS 2001, Edinburgh
volume = "99",
year = "1995",
pages = "267295",
 keywords = "axiomref",
 paper = "Duva95.pdf",
abstract =
"Dynamic evaluation allows to compute with algebraic numbers without
factorizing polynomials. It also allows to manipulate parameters in a
@@ 17534,7 +18754,54 @@ TPHOLS 2001, Edinburgh
implements this, and give a user guide for it (only this last point
assumes some knowledge of Axiom) Dynamic evaluation is described here
without any reference to sketch theory, however our presentation, less
 rigourous, may be considered as more accessible."
+ rigourous, may be considered as more accessible.",
+ paper = "Duva95.pdf",
+ keywords = "axiomref",
+ beebe = "Duval:1995:DEA"
+}
+
+\end{chunk}
+\begin{chunk}{Duval:1995:DEA}
+@Article{Duval:1995:DEA,
+ author = "Dominique Duval",
+ title = "{{\'E}}valuation dynamique et cl{\^o}ture
+ alg{\'e}brique en {Axiom}. (French) {Dynamic evaluation
+ and algebraic closure in Axiom}",
+ journal = "J. Pure Appl. Algebra",
+ volume = "99",
+ number = "3",
+ pages = "267295",
+ year = "1995",
+ DOI = "http://dx.doi.org/10.1016/00224049(94)00053L",
+ ISSN = "00224049",
+ MRclass = "11Y40 (Algebraic number theory computations) 68W30
+ (Symbolic computation and algebraic computation) 68Q65
+ (Abstract data types; algebraic specification) 18C10
+ (Algebraic theories, etc.)",
+ bibdate = "Tue Mar 30 18:47:12 2010",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ ZMnumber = "0851.1107",
+ abstract = "Dynamic evaluation is a method of computing that
+ permits the computation to be refined into different
+ cases that are considered separately. A precise
+ description and mathematical foundation was given in
+ terms of sketch theory by {\it D. Duval} and {\it J.C.
+ Reynaud} [Math. Structures Comput. Sci. 4, 239271
+ (1994; Zbl 0822.68063)]. In the present paper, the
+ mechanism of dynamic evaluation is explained without
+ reference to sketch theory in order to make it
+ accessible to a wider audience. Next, it is shown how
+ dynamic evaluation can be employed to compute with
+ algebraic numbers without having to do explicit
+ factorization of polynomials. The essential step here
+ is to define the dynamic algebraic closure of a field.
+ Finally, a program for the Axiom system implementing
+ dynamic algebraic closure is presented.",
+ acknowledgement = acknhfb,
+ keywords = "algebraic numbers; Axiom; dynamic algebraic closure of
+ a field; dynamic evaluation; sketches",
+ language = "French",
+ reviewer = "A. Bijlsma (Eindhoven)",
}
\end{chunk}
@@ 17551,7 +18818,6 @@ TPHOLS 2001, Edinburgh
year = "2001",
url = "http://www.umiacs.umd.edu/~helalfy/pub/mscthesis01.pdf",
file = "ElAl01.pdf",
 keywords = "axiomref",
abstract =
"In the recent decades, it has been more and more realized that
computers are of enormous importance for numerical
@@ 17595,7 +18861,8 @@ TPHOLS 2001, Edinburgh
The problem of implicitization is an active topic where research is
still taking place. Examples of further research points are included
 in the conclusion"
+ in the conclusion",
+ keywords = "axiomref"
}
\end{chunk}
@@ 17617,15 +18884,15 @@ TPHOLS 2001, Edinburgh
\bibitem[Erocal 10]{ES10} Er\"ocal, Burcin; Stein, William
title = "The Sage Project",
url = "http://wstein.org/papers/icms/icms_2010.pdf",
 paper = "ES10.pdf",
 keywords = "axiomref",
abstract = "
Sage is a free, open source, selfcontained distribution of
mathematical software, including a large library that provides a
unified interface to the components of this distribution. This library
also builds on the components of Sage to implement novel algorithms
covering a broad range of mathematical functionality from algebraic
 combinatorics to number theory and arithmetic geometry."
+ combinatorics to number theory and arithmetic geometry.",
+ paper = "ES10.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 17642,8 +18909,6 @@ TPHOLS 2001, Edinburgh
number = "12",
pages = "2748",
year = "1997",
 paper = "Fakl97.pdf",
 keywords = "axiomref",
abstract =
"We determine all minimal polynomials for second order homogeneous
linear differential equations with algebraic solutions decomposed into
@@ 17657,7 +18922,9 @@ TPHOLS 2001, Edinburgh
we deduce an alternative method to the algorithms given in (loc. cit.)
for computing Liouvillian solutions. For irreducible second order
equations our method determines solutions by formulas in all but three
 cases."
+ cases.",
+ paper = "Fakl97.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 17673,8 +18940,6 @@ TPHOLS 2001, Edinburgh
number = "13",
pages = "165191",
year = "2003",
 keywords = "axiomref",
 paper = "Farm03.pdf",
url = "https://www.emis.de/proceedings/MKM2001/farmer.ps",
abstract =
"Mathematics is a process of creating, exploring, and connecting
@@ 17692,7 +18957,9 @@ TPHOLS 2001, Edinburgh
intended to be used with several background logics
simultaneously. Many of the ideas and mechanisms used in the framework
are inspired by the IMPS Interactive Mathematical Proof System and the
 Axiom computer algebra system."
+ Axiom computer algebra system.",
+ paper = "Farm03.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 17708,9 +18975,7 @@ TPHOLS 2001, Edinburgh
pages = "6067",
isbn = "0897914015",
year = "1990",
 paper = "Fate90.pdf",
url = "http://people.eecs.berkeley.edu/~fateman/papers/advances.pdf",
 keywords = "axiomref",
abstract =
"We compare and contrast several techniques for the implementation of
components of an algebraic manipulation system. On one hand is the
@@ 17722,11 +18987,14 @@ TPHOLS 2001, Edinburgh
are significant remaining problems, expecially in the representation
and manipulation of analytical, as opposed to algebraic,
mathematics. We describe some of these problems and some general
 approaches for solutions."
+ approaches for solutions.",
+ paper = "Fate90.pdf",
+ keywords = "axiomref",
+ beebe = "Fateman:1990:ATD"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Fateman:1990:ATD}
@InProceedings{Fateman:1990:ATD,
author = "R. J. Fateman",
title = "Advances and trends in the design and construction of
@@ 17769,9 +19037,7 @@ TPHOLS 2001, Edinburgh
@misc{Fate94,
author = "Fateman, Richard J.",
title = "On the Design and Construction of Algebraic Manipulation Systems",
 keywords = "axiomref",
url = "http://www.cs.berkeley.edu/~fateman/papers/asmerev94.ps",
 paper = "Fate94.pdf",
abstract =
"We compare and contrast several techniques for the implementation of
components of an algebraic manipulation system. On one hand is the
@@ 17783,7 +19049,9 @@ TPHOLS 2001, Edinburgh
are significant remaining problems, especially in the representation
and manipulation of analytical, as opposed to algebraic,
mathematics. We describe some of these problems and some general
 approaches for solutions."
+ approaches for solutions.",
+ paper = "Fate94.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 17797,8 +19065,6 @@ TPHOLS 2001, Edinburgh
series = "ISSAC 96",
year = "1996",
pages = "8694",
 keywords = "axiomref",
 paper = "Fate96.pdf",
url = "http://http.cs.berkeley.edu/~fateman/papers/eval.ps",
abstract =
"``Evaluation'' of expressions and programs in a computer algebra
@@ 17807,20 +19073,50 @@ TPHOLS 2001, Edinburgh
describe some solutions from current systems, and propose alternatives
that might be preferable sometimes. We give examples primarily from
Axiom, Macsyma, Maple, Mathematica, with passing metion of a few other
 systems."
+ systems.",
+ paper = "Fate96.pdf",
+ keywords = "axiomref"
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate99,
+@inproceedings{Fate97,
+ author = "Fateman, Richard J.",
+ title = "Network Servers for Symbolic Mathematics",
+ booktitle = "Proc. ISSAC 1997",
+ pages = "249256",
+ isbn = "0897918754",
+ url = "http://http.cs.berkeley.edu/~fateman/papers/casserve.ps",
+ abstract =
+ "We describe advantages to using network socket facilities for
+ communication and distributed computing from the perspective of
+ symbolic mathematics systems. For some applications, an easily
+ constructed Lisp server model provides a flexible portal between
+ computer algebra and other programs, and one need not use new
+ languages or new systems or write new standalone webspecific cgibin
+ applications. Such socket programs can use, if necessary, HTML as a
+ common transport encoding, but more efficient means are possible. We
+ show that, rather than distributing all information to each computer
+ algebra user's system, it makes sense to consider networking for
+ accessing tables of information maintained at one or a few
+ sites. Finally, we mention some consequences of the economic value of
+ computation.",
+ paper = "Fate97.pdf",
+ keywords = "axiomref"
+}
+
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Fate99,
author = "Fateman, Richard J.",
title = "Symbolic mathematics system evaluators",
+ booktitle = "Proc. ISSAC 1996",
+ pages = "8694",
year = "1999",
 keywords = "axiomref",
url = "http://people.eecs.berkeley.edu/~fateman/papers/evalnew.pdf",
 paper = "Fate99.pdf",
abstract =
"``Evaluation'' of expressions and programs in a computer algebra
system is central to every system, but inevitably fails to provide
@@ 17828,7 +19124,9 @@ TPHOLS 2001, Edinburgh
describe some solutions from current systems, and propose alternatives
that might be preferable sometimes. We give examples primarily from
Axiom, Macsyma, Maple, Mathematica, with passing metion of a few other
 systems."
+ systems.",
+ paper = "Fate99.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 17841,8 +19139,6 @@ TPHOLS 2001, Edinburgh
title = "Parsing TeX into Mathematics",
year = "1999",
url = "http://lib.org.by/\_djvu/\_Papers/Computer\_algebra/CAS%20systems/",
 paper = "Fate99a.djvu",
 keywords = "axiomref",
abstract =
"Communication, storage, transmission, and searching of complex
material has become increasingly important. Mathematical computing in
@@ 17857,7 +19153,9 @@ TPHOLS 2001, Edinburgh
``understand'' the TeX, even if it is ``ambiguous'' notationally. A
program we developed can handle 43\% of 10,740 TeX formulas in a
wellknown table of integrals. We expect that a higher success rte can
 be achieved easily."
+ be achieved easily.",
+ paper = "Fate99a.djvu",
+ keywords = "axiomref"
}
\end{chunk}
@@ 17871,8 +19169,6 @@ TPHOLS 2001, Edinburgh
publisher = "Kluwer Academic Publishers",
year = "2000",
pages = "91102",
 keywords = "axiomref",
 paper = "Fate00.pdf",
url = "http://people.eecs.berkeley.edu/~fateman/papers/psekluwer.pdf",
abstract =
"What role should be played by symbolic mathematical computation
@@ 17889,7 +19185,26 @@ TPHOLS 2001, Edinburgh
issues. In particular numerical, graphical, and other processing can
be viewed as special cases of symbolic manipulation with interactive
symbolic computing providing both an organizing backbone and the
 communication ``glue'' among otherwise dissimilar components"
+ communication ``glue'' among otherwise dissimilar components",
+ paper = "Fate00.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@article{Fate91,
+ author = "Fateman, Richard J.",
+ title = "A Review of Macsyma",
+ year = "1991",
+ url = "http://people.eecs.berkeley.edu/~fateman/papers/mma.pdf",
+ abstract =
+ "The Mathematica computer system is reviewed from the perspective of
+ its contributions to symbolic and algebraic computation, as well as
+ its stated goals. Design and implementation issues are discussed.",
+ paper = "Fate91.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 17904,8 +19219,6 @@ TPHOLS 2001, Edinburgh
number = "1",
year = "2001",
url = "http://people.eecs.berkeley.edu/~fateman/papers/mac82b.pdf",
 paper = "Fate01.pdf",
 keywords = "axiomref",
abstract =
"We review the successes and failures of the Macsyma algebraic
manipulation system from the point of view of one of the original
@@ 17915,7 +19228,22 @@ TPHOLS 2001, Edinburgh
knowledgeadjunction, mathematical semantics, the user community,
and software engineering. We also comment on the porting of this
system to a variety of computing systems, and possible future
 directions for algebraic manipulation systembuilding."
+ directions for algebraic manipulation systembuilding.",
+ paper = "Fate01.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate02,
+ author = "Fateman, Richard J.",
+ title = "Comparing the speed of programs for sparse polynomial
+ multiplication",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/fastmult.pdf",
+ paper = "Fate02.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 17939,12 +19267,48 @@ TPHOLS 2001, Edinburgh
\end{chunk}
\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate05a,
+ author = "Fateman, Richard J.",
+ title = "Haddock's eyes and computer algebra systems: Some essays",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/haddock.pdf",
+ year = "2005",
+ abstract =
+ "(From {\sl Through the Looking Glass} by Lewis Caroll)
+ \begin{verbatim}
+ The White Knight proposes to comfort Alice by singing her a song:
+
+ ``Is it very long?'' Alice asked, for she had heard a good deal of
+ poetry that day.
+ ``It's long,'' said the Knight, ``but it's very, very beautiful.
+ Everybody that hears me sing iteither it brings tears into the
+ eyes, or else 
+ ``Or else what?'' said Alice, for the Knight had made a sudden pause.
+ ``Or else it doesn't, you know. The name of the song is called
+ `Haddock's Eyes'.''
+ ``Oh, that' the name of the song, is it?'' Alice said, trying to feel
+ interested.
+ ``No, you don't understand,'' the Knight said, looking a little vexed.
+ ``That's what the name is called. The name really is 'The Aged Aged Man'''
+ ``Then I ought to have said 'That's what the song is called?'' Alice
+ corrected herself.
+ ``No, you oughtn't: that's quite another thing! The song is called
+ `Ways and Means': but that's only what it's called, you know!''
+ ``Well, what is the song, then?'' said Alice, who was by this time
+ completely bewildered.
+ ``I was coming to that,'' the Knight said. ``The song really is
+ `Asitting on a Gate': and the tune's my own invention.''
+ \end{verbatim}",
+ paper = "Fate05a.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
\begin{chunk}{ignore}
\bibitem[Fateman 06]{Fat06} Fateman, R. J.
title = "Building Algebra Systems by Overloading Lisp",
url = "http://www.cs.berkeley.edu/~fateman/generic/overloadsmall.pdf",
 paper = "Fat06.pdf",
 keywords = "axiomref",
abstract = "
Some of the earliest computer algebra systems (CAS) looked like
overloaded languages of the same era. FORMAC, PL/I FORMAC, Formula
@@ 17962,7 +19326,38 @@ TPHOLS 2001, Edinburgh
all goes so smoothly: we can view overloading as a case study and
perhaps an object lesson since it fails to solve a number of
fairlywell articulated and difficult design issues in CAS for which
 other approaches are preferable."
+ other approaches are preferable.",
+ paper = "Fat06.pdf",
+ keywords = "axiomref"
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate06a,
+ author = "Fateman, Richard J.",
+ title = "Comments on Extending Macsyma with New Data Types",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/addformat.pdf",
+ abstract =
+ "Any design for a computer algebra system (CAS) naturally includes a
+ set of data layouts for symbolic or mathematical algebraic expressions
+ intended for use by builtin or userwritten programs. The CAS cannot
+ build in all plausible data designs, but supports those of most
+ interest to the programmers. In such a situation it is almost
+ inevitable that some new data encoding idea will come to mind and with
+ it an interest in adding additional data forms. The motivation may be
+ for compact representation, or efficient (fast) manipulation, or for
+ other reasons such as interchange with other programs. Most CAS
+ therefore include at least one way to extend the base set of
+ operations. We comment on the kinds of extensions possible, using
+ Macsyma as an example CAS. The particular interest in Macsyma and its
+ opensource soruceforge variant ``Maxima'' is that a substantial group
+ of verylosely coupled independent researchers are approaching this
+ problem and may benefit from some guidance. Some the observations
+ apply to other CAS, even though they are not opensource.",
+ paper = "Fate06a.pdf",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 17983,8 +19378,6 @@ TPHOLS 2001, Edinburgh
year = "1984",
url = "http://wwwpolsys.lip6.fr/~jcf/Papers/FGLM.pdf",
publisher = "Academic Press Limited",
 keywords = "axiomref",
 paper = "Faug94.pdf",
abstract = "
We present an efficient algorithm for the transformation of a
Grobner basis of a zerodimensional ideal with respect to any given
@@ 17993,7 +19386,9 @@ TPHOLS 2001, Edinburgh
particular, the lexicographical Grobner basis can be obtained by
applying this algorithm after a total degree Grobner basis
computation: it is usually much faster to compute the basis this way
 than with a direct application of Buchberger's algorithm."
+ than with a direct application of Buchberger's algorithm.",
+ paper = "Faug94.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 18003,7 +19398,7 @@ TPHOLS 2001, Edinburgh
\begin{chunk}{ignore}
\bibitem[Faure 00a]{FDN00a} Faure, Christ\'ele; Davenport, James
title = "Parameters in Computer Algebra",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 18016,8 +19411,6 @@ Naciri, Hanane
ISSN 02496399 Institut National De Recherche en Informatique et en
Automatique Sept. 2000 No. 4001
url = "http://hal.inria.fr/inria00072643/PDF/RR4401.pdf",
 paper = "FDN00b.pdf",
 keywords = "axiomref",
abstract = "
One of the main strengths of computer algebra is being able to solve a
family of problems with one computation. In order to express not only
@@ 18039,7 +19432,9 @@ Automatique Sept. 2000 No. 4001
capture the situation in integration, where the form of the answer can
depend on whether certain quantities are positive, negative or
zero. We show that it is also necessary when solving modular linear
 equations or deducing congruence conditions from complex expressions."
+ equations or deducing congruence conditions from complex expressions.",
+ paper = "FDN00b.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 18051,7 +19446,7 @@ Algebraic Computation, Cambridge, England, July 911, 1984, volume 174 of
Lecture Notes in Computer Science. SpringerVerlag, Berlin, Germany /
Heildelberg, Germany / London, UK / etc., 1984 ISBN 038713350X
LCCN QA155.7.E4 I57 1984
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 18065,8 +19460,8 @@ LCCN QA155.7.E4 I57 1984
series = "DISCO 92",
publisher = "SpringerVerlag, Berlin",
isbn = "0387572724",
 keywords = "axiomref",
 paper = "Fitc93.tex"
+ paper = "Fitc93.tex",
+ keywords = "axiomref"
}
\end{chunk}
@@ 18106,7 +19501,7 @@ LCCN QA155.7.E4 I57 1984
\bibitem[Fogus 11]{Fog11} Fogus, Michael
title = "UnConj",
url = "http://clojure.com/blog/2011/11/22/unconj.html",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 18139,7 +19534,6 @@ LCCN QA155.7.E4 I57 1984
pages = "5660",
isbn = "0387525319",
year = "1990",
 keywords = "axiomref",
abstract =
"Computer algebra systesm of the new generation, like SCRATCHPAD, are
characterized by a very rich type concept, which models the
@@ 18152,11 +19546,13 @@ LCCN QA155.7.E4 I57 1984
following paper defines a semantics for a subproblem therof, namely
coercion, which is based on rewrite rules. From this definition, an
efficient coercion algorithm for SCRATCHPAD is constructed using graph
 techniques."
+ techniques.",
+ keywords = "axiomref",
+ beebe = "Fortenbacher:1990:ETI"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Fortenbacher:1990:ETI}
@InProceedings{Fortenbacher:1990:ETI,
author = "A. Fortenbacher",
title = "Efficient type inference and coercion in computer
@@ 18210,9 +19606,7 @@ LCCN QA155.7.E4 I57 1984
number = "5",
pages = "271292",
year = "2005",
 keywords = "axiomref",
url = "http://eprints.biblio.unitn.it/788/1/UTM671.pdf",
 paper = "Fort05.pdf",
abstract =
"The paper deals with the question of recognizing the mutual positions
of the connected components of a nonsingular real projective surface
@@ 18223,7 +19617,9 @@ LCCN QA155.7.E4 I57 1984
previous one returning as an output the topology of the surface,
computes a set of data invariant up to ambienthomeomorphism which,
though not sufficient to determine the pair $(\mathbb{R}\mathbb{P}^3,S)$,
 give information about the nature of the surface as an embedded object."
+ give information about the nature of the surface as an embedded object.",
+ paper = "Fort05.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 18239,10 +19635,11 @@ LCCN QA155.7.E4 I57 1984
institution = {Institut de Recherche Math{\'{e}}matique Avanc{\'{e}}e''},
location = "Strasbourg, France",
keywords = "axiomref",
+ beebe = "Fouche:1990:ILK"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Fouche:1990:ILK}
@TechReport{Fouche:1990:ILK,
author = "Francois Fouche",
title = "Une Implantation de l'algorithme de {Kovacic} en
@@ 18263,7 +19660,7 @@ LCCN QA155.7.E4 I57 1984
\bibitem[FSF 14]{FSF14} FSF
title = "Free Software Directory",
url = "http://directory.fsf.org/wiki/Axiom",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 18271,7 +19668,7 @@ LCCN QA155.7.E4 I57 1984
\bibitem[Frisco ]{Fris} Frisco
title = "Objectives and Results",
url = "http://www.nag.co.uk/projects/frisco/frisco/node3.htm",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 18289,8 +19686,6 @@ LCCN QA155.7.E4 I57 1984
number = "3",
pages = "241253",
year = "1994",
 keywords = "axiomref",
 paper = "Frit94.pdf",
abstract =
"Machine element analysis has a goal of describing function and other
aspects of machine elements in a theoretical form. This paper shows
@@ 18315,7 +19710,9 @@ LCCN QA155.7.E4 I57 1984
transformed int C++ code for efficient numerical solution. The reuse
of equations through inheritance reduced the size of the model by a
factor of two, compared to a direct representation of the model in the
 Mathematica computer algebra language."
+ Mathematica computer algebra language.",
+ paper = "Frit94.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 18334,10 +19731,8 @@ LCCN QA155.7.E4 I57 1984
year = "1992",
type = "technical report",
number = "CSDTR92032",
 paper = "Gall92.pdf",
url =
"http://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1953\&context=cstech",
 keywords = "axiomref",
abstract =
"During the early 19605 some were visualizing that computers could
provide a powerful problem solving environment (PSE) which would
@@ 18348,7 +19743,9 @@ LCCN QA155.7.E4 I57 1984
computational science. The dream of the 1960s can be the reality of
the 1990s; high performance computers combined with better
understanding of computing and computational science have put PSEs
 well within our reach."
+ well within our reach.",
+ paper = "Gall92.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 18366,7 +19763,6 @@ LCCN QA155.7.E4 I57 1984
isbn = "9783540410409",
publisher = "Springer",
pages = "145166",
 keywords = "axiomref",
abstract =
"Computer algebra systems (CASs) have become an important tool for the
solution of scientific computing problems. With the increasing number
@@ 18377,7 +19773,8 @@ LCCN QA155.7.E4 I57 1984
MuPAD 1.4) on a sample of intermediate size problems. These results
show that Maple Vr5 is generally the speediest on our
examples. Finally, we formulate some requirements for developing a
 comprehensive suite for analyzing the efficiency of CASs."
+ comprehensive suite for analyzing the efficiency of CASs.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 18394,12 +19791,13 @@ LCCN QA155.7.E4 I57 1984
pages = "218221",
publisher = "ACM Press",
isbn = "0897911997",
+ doi = "http://dx.doi.org/10.1145/32439.32482",
keywords = "axiomref",
 doi = "http://dx.doi.org/10.1145/32439.32482"
+ beebe = "Gebauer:1986:BAS"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Gebauer:1986:BAS}
@InProceedings{Gebauer:1986:BAS,
author = "R{\"u}diger Gebauer and H. Michael M{\"o}ller",
editor = "Bruce W. Char",
@@ 18435,8 +19833,6 @@ LCCN QA155.7.E4 I57 1984
number = "23",
pages = "275286",
year = "1988",
 paper = "GM88.pdf",
 keywords = "axiomref",
abstract =
"Buchberger's algorithm calculates Groebner bases of polynomial
ideals. Its efficiency depends strongly on practical criteria for
@@ 18448,11 +19844,14 @@ LCCN QA155.7.E4 I57 1984
syzygies and )superfluous reductions is incorporated now in our
installation of Buchberger's algorithm in SCRATCHPAD II and REDUCE
3.3. The paper concludes with statistics stressing the good
 computational properties of these installations."
+ computational properties of these installations.",
+ paper = "GM88.pdf",
+ keywords = "axiomref",
+ beebe = "Gebauer:1988:IBA"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Gebauer:1988:IBA}
@Article{Gebauer:1988:IBA,
author = "R. Gebauer and H. M. M{\"o}ller",
title = "On an installation of {Buchberger}'s algorithm",
@@ 18510,7 +19909,6 @@ LCCN QA155.7.E4 I57 1984
isbn = "0792392590",
month = "September",
year = "1992",
 keywords = "axiomref",
abstract =
"Computer Algebra (CA) is the name given to the discipline of
algebraic, rather than numerical, computation. There are a number of
@@ 18597,7 +19995,8 @@ LCCN QA155.7.E4 I57 1984
is too small, particularly for the relatively large line spacing used,
and it is much too expensive, particularly for a book that would
otherwise be an excellent student text. I recommend it highly to
 anyone who can afford it."
+ anyone who can afford it.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 18607,7 +20006,7 @@ LCCN QA155.7.E4 I57 1984
\bibitem[Gianni 87]{Gia87} Gianni, Patrizia
title = "Primary Decomposition of Ideals",
in [Wit87], pp1213
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 18619,7 +20018,7 @@ International Symposium ISSAC '88, Rome, Italy, July 48, 1988. Proceedings,
volume 358 of Lecture Notes in Computer Science. SpringerVerlag, Berlin,
Germany / Heildelberg, Germany / London, UK / etc., 1989. ISBN 3540510842
LCCN QA76.95.I57 1988 Conference held jointly with AAECC6
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 18636,8 +20035,6 @@ LCCN QA76.95.I57 1988 Conference held jointly with AAECC6
pages = "247257",
year = "1989",
isbn = "3540510826",
 keywords = "axiomref",
 paper = "Gian89.pdf",
abstract =
"One of the most important applications of Buchberger's algorithm for
Groebner basis computation is the solution of systems of polynomial
@@ 18703,11 +20100,14 @@ LCCN QA76.95.I57 1988 Conference held jointly with AAECC6
to obtain the Groebner basis w.r.t the lexicographical ordering from
the one w.r.t the totaldegree ordering; in Section 5, we present a
zerodimensional radical algorithm and show how to apply it to the
 present problem."
+ present problem.",
+ paper = "Gian89.pdf",
+ keywords = "axiomref",
+ beebe = "Gianni:1989:ASS"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Gianni:1989:ASS}
@InProceedings{Gianni:1989:ASS,
author = "P. Gianni and T. Mora",
title = "Algebraic solution of systems of polynomial equations
@@ 18773,7 +20173,6 @@ LCCN QA76.95.I57 1988 Conference held jointly with AAECC6
publisher = "ACM",
pages = "138145",
isbn = "0897914899 (soft cover), 0897914902 (hard cover)",
 keywords = "axiomref",
abstract =
"Presents an algorithm for computing: the Jordan form of a square
matrix with coefficients in a field K using the computer algebra
@@ 18790,11 +20189,13 @@ LCCN QA76.95.I57 1988 Conference held jointly with AAECC6
to the Jordan form, and gives the so called algorithm Jordform. The
author studies in particular, the complexity of this algorithm and
proves that it is polynomial when the coefficients of the matrix are
 rational. Finally the author gives some experiments and a conclusion."
+ rational. Finally the author gives some experiments and a conclusion.",
+ keywords = "axiomref",
+ beebe = "Gil:1992:CJC"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Gil:1992:CJC}
@InProceedings{Gil:1992:CJC,
author = "I. Gil",
title = "Computation of the {Jordan} canonical form of a square
@@ 18861,15 +20262,15 @@ LCCN QA76.95.I57 1988 Conference held jointly with AAECC6
\bibitem[GomezDiaz 93]{Gom93} G\'omezD\'iaz, Teresa
title = "Examples of using Dynamic Constructible Closure",
IMACS Symposium SC1993
 paper = "Gom93.pdf",
 keywords = "axiomref",
abstract = "
We present here some examples of using the ``Dynamic Constructible
Closure'' program, which performs automatic case distinction in
computations involving parameters over a base field $K$. This program
is an application of the ``Dynamic Evaluation'' principle, which
generalizes traditional evaluation and was first used to deal with
 algebraic numbers."
+ algebraic numbers.",
+ paper = "Gom93.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 18883,14 +20284,14 @@ IMACS Symposium SC1993
number = "46",
pages = "375383",
year = "1996",
 keywords = "axiomref",
abstract =
"We present here some examples of using the ``Dynamic Constructible
Closure'' program, which performs automatic case distinctions in
computations involving parameters over a base field ``K''. This
program is an application of the ``Dynamic Evaluation'' principle
which generalizes tradional evaluation and was first used to deal with
 algebraic numbers."
+ algebraic numbers.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 18906,18 +20307,19 @@ IMACS Symposium SC1993
comment = "Proc. 1991 Ann. Conf., Amer. Soc. for Engineering Education",
pages = "345349",
year = "1991",
 keywords = "axiomref",
abstract =
"We show how PCbased applications software, specifically MathCAD, is
used in the teaching of material and energy balance concepts. MathCAD
is a microcomputer software package which acts as a mathematical
scratchpad. It has proven to be a very useful instructional tool in
introductory chemical engineering courses. MathCAD solutions to
 typical course problems are presented."
+ typical course problems are presented.",
+ keywords = "axiomref",
+ beebe = "Goodwin:1991:UMT"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Goodwin:1991:UMT}
@InProceedings{Goodwin:1991:UMT,
author = "B. M. Goodwin and R. A. Buonopane and A. Lee",
title = "Using {MathCAD} in teaching material and energy
@@ 18958,7 +20360,7 @@ IMACS Symposium SC1993
Proceedings of the 1984 MACSYMA Users' Conference:
Schenectady, New York, July 2325, 1984, General Electric,
Schenectady, NY, USA, 1984
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 18967,18 +20369,81 @@ Schenectady, NY, USA, 1984
\bibitem[Gonnet 96]{Gon96} Gonnet, Gaston H.
title = "Official verion 1.0 of the Meta Content Dictionary",
url = "http://www.inf.ethz.ch/personal/gonnet/ContDict/Meta",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
\index{Goodloe, A.}
\index{Loustaunau, Philippe}
\begin{chunk}{ignore}
\bibitem[Goodloe 93]{GL93} Goodloe, A.; Loustaunau, P.
 title = "An abstract data type development of graded rings'",
In Fitch [Fit93], pp193202. ISBN 0387572724 (New York),
3540572724 (Berlin). LCCN QA76.9.S88I576 1992
 keywords = "axiomref",
+\begin{chunk}{axiom.bib}
+@inproceedings{Good93,
+ author = "Goodloe, A. and Loustaunau, Philippe",
+ title = "An abstract data type development of graded rings",
+ booktitle = "Design and Implementation of Symbolic Computation Systems",
+ series = "Lecture Notes in Computer Science 721",
+ pages = "193202",
+ isbn = "0387572724 (New York), 3540572724 (Berlin)",
+ year = "1993",
+ abstract =
+ "Recently new computer algebra systems such as Scratchpad and Weyl have
+ been developed with built in mechanisms for expressing abstract data types.
+ These systems are object oriented in that they incorporate multiple
+ inheritance and polymorphic types. Davenport and Trager have build much
+ of the framework for basic commutative algebra in Scratchpad II
+ utilizing its rich set of abstraction mechanisms. Davenport and Trager
+ concentrated on developing factorization algorithms on domains which
+ were abstract data types.
+
+ We are taking a similar approach to the development of algorithms for
+ computing in graded rings. The purpose of this paper is to develop the
+ tools required to compute with polynomials with coefficients in a graded
+ ring $R$. We focus on graded rings $R$ which are polynomial rings graded
+ by a monoid, and we allow partial orders on the monomials. The ideas
+ presented here can be applied to more general graded rings $R$, such as
+ associated graded rings to filtered rings, as long as certain computational
+ ``requirements'' are satisfied",
+ keywords = "axiomref",
+ beebe = "Goodloe:1993:ADT"
+}
+
+\end{chunk}
+\begin{chunk}{Goodloe:1993:ADT}
+@InProceedings{Goodloe:1993:ADT,
+ author = "A. Goodloe and P. Loustaunau",
+ title = "An abstract data type development of graded rings",
+ crossref = "Fitch:1993:DIS",
+ pages = "193202",
+ month = "",
+ year = "1993",
+ bibdate = "Tue Sep 17 06:37:45 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "Novel computer algebra systems such as Scratchpad and
+ Weyl have been developed with built in mechanisms for
+ expressing abstract data types. These systems are
+ object oriented in that they incorporate multiple
+ inheritance and polymorphic types. The authors are
+ taking a similar approach to the development of
+ algorithms for computing in graded rings. They develop
+ the tools required to compute with polynomials with
+ coefficients in a graded ring R. They focus on graded
+ rings R which are polynomial rings graded by a monoid,
+ and allow partial orders on the monomials. The ideas
+ presented can be applied to more general graded rings
+ R, such as associated graded rings to filtered rings,
+ as long as certain computational `requirements' are
+ satisfied.",
+ acknowledgement = acknhfb,
+ affiliation = "Dept. of Math., George Mason Univ., Fairfax, VA, USA",
+ classification = "C4130 (Interpolation and function approximation);
+ C6120 (File organisation); C7310 (Mathematics)",
+ keywords = "Abstract data types; Computer algebra systems;
+ Filtered rings; Graded rings; Monoid; Multiple
+ inheritance; Object oriented; Partial orders;
+ Polymorphic types; Polynomial rings; Scratchpad; Weyl",
+ language = "English",
+ thesaurus = "Abstract data types; Polynomials; Symbol
+ manipulation",
+}
\end{chunk}
@@ 18988,17 +20453,17 @@ In Fitch [Fit93], pp193202. ISBN 0387572724 (New York),
author = "Grabe, HansGert",
title = "About the Polynomial System Solve Facility of Axiom, Macsyma,
Maple Mathematica, MuPAD, and Reduce",
 paper = "Grab98.pdf",
url =
"https://www.informatik.unileipzig.de/~graebe/ComputerAlgebra/Publications/WesterBook.pdf",
 keywords = "axiomref",
abstract =
"We report on some experiences with the general purpose Computer
Algebra Systems (CAS) Axiom, Macsyma, Maple, Mathematica, MuPAD, and
Reduce solving systems of polynomial equations and the way they
present their solutions. This snapshot (taken in the spring of 1996)
of the current power of the different systems in a special area
 concentrates on both CPUtimes and the quality of the output."
+ concentrates on both CPUtimes and the quality of the output.",
+ paper = "Grab98.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 19026,10 +20491,8 @@ In Fitch [Fit93], pp193202. ISBN 0387572724 (New York),
author = "Grabe, HansGert",
title = "The Groebner Factorizer and Polynomial System Solving",
year = "2006",
 keywords = "axiomref",
report = "Special Semester on Groebner Bases",
location = "Linz",
 paper = "Grab06.pdf",
url =
"https://www.ricam.oeaw.ac.at/specsem/srs/groeb/download/06\_02\_Solver.pdf",
abstract =
@@ 19085,7 +20548,9 @@ In Fitch [Fit93], pp193202. ISBN 0387572724 (New York),
be done by hand, but not really hard to require special efforts. It
should invoke a convenient interface to get the solutions in a form
that is (correct and) well suited for further analysis in the familiar
 environment of the given CAS as the personal mathematical assistant."
+ environment of the given CAS as the personal mathematical assistant.",
+ paper = "Grab06.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 19103,11 +20568,12 @@ In Fitch [Fit93], pp193202. ISBN 0387572724 (New York),
number = "TR 75.91.20",
location = "Heidelberg, Germany",
year = "1991",
 keywords = "axiomref"
+ keywords = "axiomref",
+ beebe = "Grabmeier:1991:CSA"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Grabmeier:1991:CSA}
@TechReport{Grabmeier:1991:CSA,
author = "J. Grabmeier and K. Huber and U. Krieger",
title = "{Das ComputeralgebraSystem AXIOM bei kryptologischen
@@ 19134,8 +20600,8 @@ In Fitch [Fit93], pp193202. ISBN 0387572724 (New York),
volume = "1",
number = "3",
pages = "1315",
 keywords = "axiomref",
paper = "Grab91b.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 19177,8 +20643,6 @@ In Fitch [Fit93], pp193202. ISBN 0387572724 (New York),
address = "Downer's Grove, IL, USA and Oxford, UK",
year = "1992",
url = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
 keywords = "axiomref",
 paper = "Grab92.pdf",
algebra =
"\newline\refto{category CHARNZ CharacteristicNonZero}
\newline\refto{category FPC FieldOfPrimeCharacteristic}
@@ 19214,7 +20678,29 @@ In Fitch [Fit93], pp193202. ISBN 0387572724 (New York),
representation}, {\sl cyclic group representation}, and {\sl normal
basis representation}. Furthermore, the concept of the implementation,
the used algorithms and the various datatype coercions between these
 representations are discussed."
+ representations are discussed.",
+ paper = "Grab92.pdf",
+ keywords = "axiomref",
+ beebe = "Grabmeier:1992:FFA"
+}
+
+\end{chunk}
+\begin{chunk}{Grabmeier:1992:FFA}
+@TechReport{Grabmeier:1992:FFA,
+ author = "J. Grabmeier and A. Scheerhorn",
+ title = "Finite Fields in {AXIOM}",
+ type = "AXIOM Technical Report",
+ number = "TR7/92 (ATR/5) (NP2522)",
+ institution = instNAG,
+ address = instNAG:adr,
+ pages = "??",
+ month = dec,
+ year = "1992",
+ bibdate = "Fri Dec 29 16:31:49 1995",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
+ acknowledgement = acknhfb,
}
\end{chunk}
@@ 19228,7 +20714,7 @@ Computer algebra handbook: foundations, applications, systems.
SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
2003. ISBN 3540654666 637pp Includes CDROM
url = "http://www.springer.com/sgw/cda/frontpage/0,11855,11022214778710,00.html",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 19243,7 +20729,6 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
volume = "232",
publisher = "American Mathematical Society",
year = "2001",
 keywords = "axiomref",
abstract =
"This volume contains papers related to the research conference,
``Symbolic Computation: Solving Equations in Algebra, Analysis, and
@@ 19255,7 +20740,8 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
develop the theoretical background and tools needed for this
purpose. Within this general framework, the conference focused on
several themes: systems of polynomials, systems of differential
 equations, noncommutative systems, and applications."
+ equations, noncommutative systems, and applications.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 19273,8 +20759,6 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
pages = "4258",
doi = "http://dx.doi.org/10.1145806266",
url = "http://delivery.acm.org/10.1145/810000/806266/p42griesmer.pdf",
 paper = "Grie71.pdf",
 keywords = "axiomref",
abstract = "
The SCRATCHPAD/1 system is designed to provide an interactive symbolic
computational facility for the mathematician user. The system features
@@ 19283,10 +20767,13 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
introducing new notations into the language. A comprehensive system
library incorporates symbolic capabilities provided by such systems as
SIN, MATHLAB, and REDUCE.",
+ paper = "Grie71.pdf",
+ keywords = "axiomref",
+ beebe = "Griesmer:1971:SIF"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Griesmer:1971:SIF}
@InProceedings{Griesmer:1971:SIF,
author = "J. H. Griesmer and R. D. Jenks",
title = "{SCRATCHPAD/1}  an interactive facility for
@@ 19311,11 +20798,12 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
title = "Experience with an online symbolic math system SCRATCHPAD",
year = "1972",
isbn = "0903796023",
 keywords = "axiomref"
+ keywords = "axiomref",
+ beebe = "Griesmer:1972:EOSb"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Griesmer:1972:EOSb}
@InProceedings{Griesmer:1972:EOSb,
author = "J. Griesmer and R. Jenks",
title = "Experience with an online symbolic math. system
@@ 19350,7 +20838,6 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
pages = "93102",
year = "1972",
comment = "Proc. Symp. Twodimensional manmachine communications",
 keywords = "axiomref",
doi = "http://dx.doi.org/10.1145807019",
abstract =
"SCRATCHPAD is an interactive system for algebraic manipulation
@@ 19361,11 +20848,13 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
other symbolic systems. Here we present a capsule view of SCRATCHPAD,
its language and its capabilities. This is followed by an example
which illustrates its use in an application involving the solution of
 an integral equation."
+ an integral equation.",
+ keywords = "axiomref",
+ beebe = "Griesmer:1972:SCV"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Griesmer:1972:SCV}
@Article{Griesmer:1972:SCV,
author = "James H. Griesmer and Richard D. Jenks",
title = "{SCRATCHPAD}: {A} capsule view",
@@ 19403,12 +20892,12 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
number = "4",
pages = "1213",
year = "1974",
 keywords = "axiomref",
abstract =
"The following SCRATCHPAD conversation for carrying out the Lie
Transform computation represents a slight modification of one written
by Dr. David Barton, when he was a summer visitor during 1972 at the
 Watson Research Center."
+ Watson Research Center.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 19456,12 +20945,12 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
number = "3",
pages = "2425",
year = "1975",
 keywords = "axiomref",
abstract =
"Algebraic manipulation covers branches of software, particularly list
processing, mathematics, notably logic and number theory, and
applications largely in physics. The lectures will deal with all of these
 to a varying extent."
+ to a varying extent.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 19473,7 +20962,7 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
\bibitem[Griesmer 76]{GJY76} Griesmer, J.H.; Jenks, R.D.; Yun, D.Y.Y
title = "A Set of SCRATCHPAD Examples",
April 1976 (private copy)
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 19494,12 +20983,67 @@ April 1976 (private copy)
\index{Gruntz, Dominik}
\index{Monagan, Michael B.}
\begin{chunk}{ignore}
\bibitem[Gruntz 94]{GM94} Gruntz, D.; Monagan, M.
+\begin{chunk}{axiom.bib}
+@article{Grun94,
+ author = "Gruntz, Dominik and Monagan, Michael B.",
title = "Introduction to Gauss",
SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic
Manipulation), 28(3) pp319 August 1994 CODEN SIGSBZ ISSN 01635824
+ journal = "SIGSAM Bulletin",
+ volume = "28",
+ number = "3",
+ pages = "319",
+ year = "1994",
+ url = "http://ftp.cecm.sfu.ca/personal/monaganm/papers/Gauss.pdf",
+ abstract =
+ "The Gauss package offers Maple users a new approach to programming
+ based on the idea of parameterized types (domains) which is central to
+ the AXIOM system. This approach to programming is now regarded by many
+ as the right way to go in computer algebra systems design. In this
+ article, we describe how Gauss is designed and show examples of usage.
+ We end with some comments about how Gauss is being used in Maple.",
+ paper = "Grun94.pdf",
keywords = "axiomref",
+ beebe = "Gruntz:1994:IG"
+}
+
+\end{chunk}
+\begin{chunk}{Gruntz:1994:IG}
+@Article{Gruntz:1994:IG,
+ author = "D. Gruntz and M. Monagan",
+ title = "Introduction to {Gauss}",
+ journal = jSIGSAM,
+ volume = "28",
+ number = "2",
+ pages = "319",
+ month = aug,
+ year = "1994",
+ CODEN = "SIGSBZ",
+ ISSN = "01635824 (print), 15579492 (electronic)",
+ ISSNL = "01635824",
+ bibdate = "Tue Dec 12 09:33:35 MST 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "The Gauss package offers Maple users a new approach to
+ programming based on the idea of parameterized types
+ (domains) which is central to the AXIOM system. This
+ approach to programming is now regarded by many as the
+ right way to go in computer algebra systems design. We
+ describe how Gauss is designed and show examples of
+ usage. We end with some comments about how Gauss is
+ being used in Maple.",
+ acknowledgement = acknhfb,
+ affiliation = "Inst. for Sci. Comput., Eidgenossische Tech.
+ Hochschule, Zurich, Switzerland",
+ classification = "C6110 (Systems analysis and programming); C6130
+ (Data handling techniques); C7310 (Mathematics
+ computing)",
+ fjournal = "SIGSAM Bulletin",
+ keywords = "AXIOM system; Computer algebra systems design; Gauss
+ package; Maple users; Parameterized types;
+ Programming",
+ language = "English",
+ pubcountry = "USA",
+ thesaurus = "Programming environments; Software packages; Symbol
+ manipulation; Systems analysis; Type theory",
+}
\end{chunk}
@@ 19510,9 +21054,7 @@ Manipulation), 28(3) pp319 August 1994 CODEN SIGSBZ ISSN 01635824
title = "On Computing Limits in a Symbolic Manipulation System",
school = "Swiss Federal Institute of Technology Zurich",
year = "1996",
 paper = "Grun96.pdf",
url = "http://www.cybertester.com/data/gruntz.pdf",
 keywords = "axiomref",
abstract = "
This thesis presents an algorithm for computing (onesided) limits
within a symbolic manipulation system. Computing limtis is an
@@ 19529,7 +21071,9 @@ Manipulation), 28(3) pp319 August 1994 CODEN SIGSBZ ISSN 01635824
have to be kept with each approximation in order to resolve the
cancellation problem, and this may lead to an intermediate expression
swell. Our algorithm avoids this problem and is thus suited to be
 implemented in a symbolic manipulation system."
+ implemented in a symbolic manipulation system.",
+ paper = "Grun96.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 19538,9 +21082,9 @@ Manipulation), 28(3) pp319 August 1994 CODEN SIGSBZ ISSN 01635824
@misc{Gute16,
author = "Gutenberg SelfPublishing Press",
title = "OpenAxiom",
 keywords = "axiomref",
url = "http://self.gutenberg.org/articles/openaxiom",
 year = "2016"
+ year = "2016",
+ keywords = "axiomref"
}
\end{chunk}
@@ 19558,8 +21102,6 @@ Manipulation), 28(3) pp319 August 1994 CODEN SIGSBZ ISSN 01635824
number = "3",
pages = "279294",
year = "1998",
 keywords = "axiomref",
 paper = "Harr98.pdf",
url = "http://www.cl.cam.ac.uk/~jrh13/papers/cas.ps.gz",
abstract =
"We contrast theorem provers and computer algebra systems, pointing
@@ 19572,11 +21114,24 @@ Manipulation), 28(3) pp319 August 1994 CODEN SIGSBZ ISSN 01635824
NP, and discuss different ways of exploiting a physical link between
systems. Finally, the method is illustrated by some concrete examples
of computer algebra results proved formally in the HOL theorem prover
 with the aid of Maple."
+ with the aid of Maple.",
+ paper = "Harr98.pdf",
+ keywords = "axiomref"
}
\end{chunk}
+\index{Harriss, Edmund}
+\index{Daly, Timothy}
+\begin{chunk}{axiom.bib}
+@misc{Harr12,
+ author = "Harriss, Edmund and Daly, Timothy",
+ title = "Have we ever lost mathematics?",
+ url = "https://maxwelldemon.com/2012/05/09/haveweeverlostmathematics/",
+ year = "2012",
+ keywords = "axiomref"
+}
+
\index{Hassner, Martin}
\index{Burge, William H.}
\index{Watt, Stephen M.}
@@ 19585,7 +21140,7 @@ Manipulation), 28(3) pp319 August 1994 CODEN SIGSBZ ISSN 01635824
Watt, Stephen M.
title = "Construction of Algebraic Error Control Codes (ECC) on the Elliptic Riemann Surface",
in [Wit87], pp58
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 19599,8 +21154,6 @@ in [Wit87], pp58
booktitle = "Proc. ISSAC 1993",
series = "ISSAC '93",
year = "1993",
 paper = "Kead93a.pdf",
 keywords = "axiomref",
abstract =
"IRENA  an $I$nterface from $RE$DUCE to $NA$G  runs under the REDUCE
Computer Algebra (CA) system and provides an interactive front end to
@@ 19611,11 +21164,42 @@ in [Wit87], pp58
{\tt codeonly} switch, which is relevant to larger scale problems. We
describe progress on an issue raised in the 'Future Developments'
section in our {\sl SIGSAM Bulletin} article [2]: the progress improves
 the practical effectiveness of IRENA."
+ the practical effectiveness of IRENA.",
+ paper = "Kead93a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
+\index{ASP1}
+\index{ASP10}
+\index{ASP12}
+\index{ASP19}
+\index{ASP20}
+\index{ASP24}
+\index{ASP27}
+\index{ASP28}
+\index{ASP29}
+\index{ASP30}
+\index{ASP31}
+\index{ASP33}
+\index{ASP34}
+\index{ASP35}
+\index{ASP4}
+\index{ASP41}
+\index{ASP42}
+\index{ASP49}
+\index{ASP50}
+\index{ASP55}
+\index{ASP6}
+\index{ASP7}
+\index{ASP73}
+\index{ASP74}
+\index{ASP77}
+\index{ASP78}
+\index{ASP8}
+\index{ASP80}
+\index{ASP9}
\index{Hawkes, Evatt}
\index{Keady, Grant}
\begin{chunk}{axiom.bib}
@@ 19625,8 +21209,6 @@ in [Wit87], pp58
booktitle = "IMACS Applied Computer Algebra Conference",
location = "University of New Mexico",
year = "1995",
 keywords = "axiomref",
 paper = "Hawk95.pdf",
algebra =
"\newline\refto{domain ASP1 Asp1}
\newline\refto{domain ASP10 Asp10}
@@ 19681,39 +21263,12 @@ in [Wit87], pp58
is not specific to the NAG library. Mike Dewar is an author both of
IRENA and the AXIOM2.0 link to the NAG library: see [D] foe discussion
of the differences between the IRENA project and the AXIOMNAG link
 project."
+ project.",
+ paper = "Hawk95.pdf",
+ keywords = "axiomref"
}
\end{chunk}
\index{ASP1}
\index{ASP10}
\index{ASP12}
\index{ASP19}
\index{ASP20}
\index{ASP24}
\index{ASP27}
\index{ASP28}
\index{ASP29}
\index{ASP30}
\index{ASP31}
\index{ASP33}
\index{ASP34}
\index{ASP35}
\index{ASP4}
\index{ASP41}
\index{ASP42}
\index{ASP49}
\index{ASP50}
\index{ASP55}
\index{ASP6}
\index{ASP7}
\index{ASP73}
\index{ASP74}
\index{ASP77}
\index{ASP78}
\index{ASP8}
\index{ASP80}
\index{ASP9}
\index{Hearn, Anthony C.}
\begin{chunk}{axiom.bib}
@@ 19723,7 +21278,6 @@ in [Wit87], pp58
booktitle = "Proc. 1980 CERN School of Computing",
pages = "390406",
year = "1980",
 paper = "Hear80.pdf",
url =
"http://www.iaea.org/inis/collection/NCLCollectionStore/\_Public/12/631/12631585.pdf",
abstract =
@@ 19742,7 +21296,8 @@ in [Wit87], pp58
is so fundamental to many of the calculational techniques used by high
energy physicists. Finally, we shall study the implications which the
current developments in hardware technology hold for scientific
 problem solving."
+ problem solving.",
+ paper = "Hear80.pdf"
}
\end{chunk}
@@ 19758,14 +21313,14 @@ in [Wit87], pp58
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."
+ natural style.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 19777,7 +21332,6 @@ in [Wit87], pp58
title = "Introduction to Maple",
year = "1993",
publisher = "SpringerVerlag",
 keywords = "axiomref",
abstract =
"This is an introductory book on one of the most powerful computer
algebra systems, viz, Maple: The primary emphasis in this book is on
@@ 19799,7 +21353,8 @@ in [Wit87], pp58
At the end of each chapter, a good number of excercises is given. A
list of relevant references is also given at the end of the book.
 This book is very useful to all users of Maple package."
+ This book is very useful to all users of Maple package.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 19810,7 +21365,7 @@ in [Wit87], pp58
title = "Variables in computer algebra, mathematics and science",
The International Journal of Computer Algebra in Mathematics Education
Vol. 8 No. 3 pp195210 (2001)
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 19851,7 +21406,6 @@ Vol. 8 No. 3 pp195210 (2001)
url = "http://axiomwiki.newsynthesis.org/WorkShopRISC2006",
year = "2006",
location = "Hagenberg, Austria",
 keywords = "axiomref",
abstract =
"Axiom is a computer algebra system with a long tradition. It recently
became free software.
@@ 19860,7 +21414,8 @@ Vol. 8 No. 3 pp195210 (2001)
of packages written for other Computer Algebra Systems or developers
of standalone packages. Furthermore, the workshop wants to make the
potential of Axiom and Aldor more widely known in order to attract new
 users and new developers."
+ users and new developers.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 19873,7 +21428,6 @@ Vol. 8 No. 3 pp195210 (2001)
url = "http://axiomwiki.newsynthesis.org/WorkShopRISC2007",
year = "2007",
location = "Hagenberg, Austria",
 keywords = "axiomref",
abstract =
"The workshop aims at a cooperation of Axiom developers with deelopers
of packages written for other Computer Algebra Systems, and
@@ 19882,7 +21436,8 @@ Vol. 8 No. 3 pp195210 (2001)
One goal of the workshop is to learn about the mathematical theory,
the design of packages written for other CAS and to make those
 functionalities available in Axiom."
+ functionalities available in Axiom." ,
+ keywords = "axiomref"
}
\end{chunk}
@@ 19895,8 +21450,6 @@ Vol. 8 No. 3 pp195210 (2001)
author = "Heras, Jonathan and MartinMateos, Franciso Jesus and
Pascual, Vico",
title = "A Hierarchy of Mathematical Structures in ACL2",
 keywords = "axiomref",
 paper = "Hera16.pdf",
url = "http://staff.computing.dundee.ac.uk/jheras/papers/ahomsia.pdf",
abstract =
"In this paper, we present a methodology which allows one to deal with
@@ 19913,7 +21466,9 @@ Vol. 8 No. 3 pp195210 (2001)
mathematical structures; for instance, the ones coming from Algebraic
Topology. The final aim of this work is the verification of Computer
Algebra systems, a field where our hierarchy fits better than the ones
 developed in other systems."
+ developed in other systems.",
+ paper = "Hera16.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 19931,7 +21486,6 @@ Vol. 8 No. 3 pp195210 (2001)
number = "3",
pages = "277303",
year = "2015",
 keywords = "axiomref",
abstract =
"In this paper, we present how algebraic structures and morphisms can
be modelled in the ACL2 theorem prover. Namely, we illustrate a
@@ 19945,7 +21499,8 @@ Vol. 8 No. 3 pp195210 (2001)
complex mathematical structures; for example, the structures employed
in Algebraic Topology. This work shows that ACL2 can be a suitable
tool for formalising algebraic concepts coming, for instance, from
 computer algebra systems."
+ computer algebra systems.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 19957,10 +21512,10 @@ Vol. 8 No. 3 pp195210 (2001)
title = "The Incredible World of Symbolic Mathematics
A Review of Computer Algebra Systems",
year = "1996",
 keywords = "axiomref",
url =
"https://inside.mines.edu/~whereman/papers/HeremanPhysicsWorld9March1996.pdf",
 paper = "Here96.pdf"
+ paper = "Here96.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 19975,8 +21530,6 @@ Vol. 8 No. 3 pp195210 (2001)
number = "8/9",
pages = "115132",
year = "1997",
 keywords = "axiomref",
 paper = "Here97.pdf",
abstract =
"Sophus Lie (18421899) pioneered the study of continuous
transformation groups that leave systems of differential equations
@@ 20042,7 +21595,9 @@ Vol. 8 No. 3 pp195210 (2001)
Lack of space forces us to give only a few key references for the Lie
symmetry packages. A comprehensive survey of the literature devoted
to theoretical as well as computational aspects of Lie symmetries,
 with over 300 references, can be found elsewhere [11]."
+ with over 300 references, can be found elsewhere [11].",
+ paper = "Here97.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 20058,9 +21613,7 @@ Vol. 8 No. 3 pp195210 (2001)
volume = "51",
number = "B51z",
year = "2004",
 keywords = "axiomref",
url = "http://www.emis.de/journals/SLC/wpapers/s51thiery.pdf",
 paper = "Hive04.pdf",
abstract =
"In this article we give an overview of the MuPADCombinat opensource
algebraic combinatorics package for the computer algebra system MuPAD
@@ 20071,7 +21624,9 @@ Vol. 8 No. 3 pp195210 (2001)
handbook; further details and references on the algorithms used can be
found there. The package and the handbook are available from the web
page, together with download and installation instructions, mailing
 lists, etc."
+ lists, etc.",
+ paper = "Hive04.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 20088,8 +21643,6 @@ Vol. 8 No. 3 pp195210 (2001)
number = "13",
pages = "217230",
year = "2000",
 keywords = "axiomref",
 paper = "Hoan00.pdf",
abstract =
"Generalized polylogarithms are defined as iterated integrals with
respect to the two differential forms $\omega_0=\frac{dz}{z}$ and
@@ 20098,7 +21651,9 @@ Vol. 8 No. 3 pp195210 (2001)
AXIOM, is based on the computation of the associator $\Phi_{KZ}$ of
Drinfel’d, in factorized form. The monodromy formulae involve special
constants, called multiple zeta values. We prove that the algebra of
 polylogarithms is isomorphic to a shuffle algebra."
+ polylogarithms is isomorphic to a shuffle algebra.",
+ paper = "Hoan00.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 20112,13 +21667,13 @@ Vol. 8 No. 3 pp195210 (2001)
year = "2008",
journal = "math.NA",
url = "http://arxiv.org/pdf/math/0611895.pdf",
 paper = "Hoar08.pdf",
 keywords = "axiomref",
abstract =
"A Mathematica based program has been elaborated in order to determine
the symmetry group of a finite difference equation. The package
provides functions which enabel use to solve the determining equations
 of the related Lie group."
+ of the related Lie group.",
+ paper = "Hoar08.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 20130,7 +21685,6 @@ Vol. 8 No. 3 pp195210 (2001)
title = "SymbolicNumeric Algorithms for Plane Algebraic Curves",
year = "2011",
school = "RISC Research Institute for Symbolic Computation",
 paper = "Hodo11.pdf",
abstract =
"In computer algebra, the problem of computing topological invariants
(i.e. deltainvariant, genus) of a plan complex algebraic curve is
@@ 20181,7 +21735,8 @@ Vol. 8 No. 3 pp195210 (2001)
compute the genus, the package {\sl Genom3ck} computes also other type
of information on a plane complex algebraic curve, such as the
singularities of the curve in the projective plane and the topological
 type of each singularity."
+ type of each singularity.",
+ paper = "Hodo11.pdf"
}
\end{chunk}
@@ 20194,7 +21749,6 @@ Vol. 8 No. 3 pp195210 (2001)
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
@@ 20206,7 +21760,8 @@ Vol. 8 No. 3 pp195210 (2001)
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."
+ and the Liouvillian extensions.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 20217,15 +21772,15 @@ Vol. 8 No. 3 pp195210 (2001)
@misc{Hoev13,
author = "Hoeven, Joris van der and Lecerf, Gregoire",
title = "Interfacing Mathemagix with C++",
 keywords = "axiomref",
url = "http://www.texmacs.org/joris/mmxcpp/mmxcpp.pdf",
 paper = "Hoev13.pdf",
abstract =
"In this paper, we give a detailed description of the interface
between the Mathemagix language and C++. In particular, we describe
the mechanism which allows us to import a C++ template library
(which only permits static instantiation) as a fully generic
 Mathemagix template library."
+ Mathemagix template library.",
+ paper = "Hoev13.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 20236,14 +21791,14 @@ Vol. 8 No. 3 pp195210 (2001)
@misc{Hoev15,
author = "Hoeven, Joris van der and Lecerf, Gregoire",
title = "Interfacing Mathemagix with C++",
 keywords = "axiomref",
url = "http://www.texmacs.org/joris/mmxcpp/mmxcpp.html",
abstract =
"In this paper, we give a detailed description of the interface
between the Mathemagix language and C++. In particular, we describe
the mechanism which allows us to import a C++ template library
(which only permits static instantiation) as a fully generic
 Mathemagix template library."
+ Mathemagix template library.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 20262,9 +21817,9 @@ Vol. 8 No. 3 pp195210 (2001)
publisher = "V.S Pless, W.C. Huffman and R.A. Brualdi (eds)",
volume = "I",
url = "http://www.win.tue.nl/~ruudp/paper/31.pdf",
 paper = "Hold11.pdf",
algebra = "\newline\refto{category PRSPCAT ProjectiveSpaceCategory}",
 isbn = "9780444814722"
+ isbn = "9780444814722",
+ paper = "Hold11.pdf"
}
\end{chunk}
@@ 20277,7 +21832,7 @@ Applied Algebra, Algebraic Algorithms and ErrorCorrecting Codes.
5th International Conference AAECC5 Proceedings.
SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
1989. ISBN 3540510826. LCCN QA268.A35 1987
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 20288,7 +21843,6 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
author = "Houstis, E.N. and Gaffney, P.W.",
title = "Programming environments for highlevel scientific problem solving",
year = "1992",
 keywords = "axiomref",
publisher = "Elsevier",
isbn = "9780444891761",
abstract =
@@ 20298,7 +21852,8 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
proceedings volume, the problem considered is a highlevel scientific
computation. In other words, a scientific problem whose solution
usually requires sophisticated computing techniques and a large
 allocation of computing resources."
+ allocation of computing resources.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 20314,7 +21869,6 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
number = "45",
pages = "243257",
year = "2000",
 keywords = "axiomref",
abstract =
"We review the current state of the Problem Solving Environment (PSE)
field and make projections for the future. First, we describe the
@@ 20322,7 +21876,8 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
stateoftheart is summarized along with the principal components and
paradigms for building PSEs. The discussion of the future is given in
three parts: future trends, scenarios for 2010/2025, and research
 issues to be addressed."
+ issues to be addressed.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 20337,7 +21892,7 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
Proceedings SC 93
International IMACS Symposium on Symbolic Computation. New Trends and
Developments. LIFL Univ. Lille, Lille France, 1993
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 20354,7 +21909,6 @@ Developments. LIFL Univ. Lille, Lille France, 1993
number = "1",
pages = "1953",
year = "1997",
 keywords = "axiomref",
comment = "french",
abstract =
"Drawing on the work of Mourtada, we show that a family of vector
@@ 20374,7 +21928,8 @@ Developments. LIFL Univ. Lille, Lille France, 1993
algebraic systems via the construction of Gröbner bases. The
calculations have been executed formally, that is to say without
making the least appeal to numerical approximation, in using the
 formal calculus system AXIOM."
+ formal calculus system AXIOM.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 20391,7 +21946,6 @@ Developments. LIFL Univ. Lille, Lille France, 1993
number = "1",
pages = "3155",
year = "2002",
 keywords = "axiomref",
abstract =
"The authors consider a problem coming from the theory of discrete
dynamical systems (iterations of diffeomorphisms in
@@ 20402,7 +21956,8 @@ Developments. LIFL Univ. Lille, Lille France, 1993
they apply Gröbner bases techniques and the theory of (formal) normal
forms in the space of the coefficients of the jets of the
mapping. They show that a language with typed objects like AXIOM is
 very convenient to solve such problems."
+ very convenient to solve such problems.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 20418,15 +21973,15 @@ Developments. LIFL Univ. Lille, Lille France, 1993
number = "204",
year = "1993",
pages = "915926",
 paper = "Jaes93.pdf",
 keywords = "axiomref",
algebra = "\newline\refto{package PRIMES IntegerPrimesPackage}",
abstract =
"With $\psi_k$ denoting the smallest strong pseudoprime to all of the
first $k$ primes taken as bases we determine the exact values for
$\psi_5$, $\psi_6$, $\psi_7$, $\psi_8$, and give upper bounds for
$\psi_9$, $\psi_{10}$, $\psi_{11}$. We discuss the methods and
 underlying facts for obtaining these results"
+ underlying facts for obtaining these results",
+ paper = "Jaes93.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 20440,9 +21995,7 @@ Developments. LIFL Univ. Lille, Lille France, 1993
journal = "J. Symbolic Computation",
volume = "22",
pages = "459468",
 paper = "Jage96.pdf",
url = "http://www.mate.tue.nl/mate/pdfs/1610.pdf",
 keywords = "axiomref",
abstract =
"An algorithm to generate solutions for members of a class of
completely integrable partial differential equations has been derived
@@ 20454,7 +22007,9 @@ Developments. LIFL Univ. Lille, Lille France, 1993
that actually can be solved are restricted in size and
complexity. Several examples, some derived from industrial practice,
are presented to illustrate the use of the algorithm and to
 demonstrate the advantages and shortcomings of the implementation."
+ demonstrate the advantages and shortcomings of the implementation.",
+ paper = "Jage96.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 20467,7 +22022,7 @@ Bad Neuenahr, May 1921, 1987, Proceedings, volume 296 of Lecture Notes in
Computer Science.
SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
1988 ISBN 3540189289, 0387189289 LCCN QA155.7.E4T74 1988
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 20477,7 +22032,7 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
title = "META/LISP: An interactive translator writing system",
Research Report International Business Machines, Inc., Thomas J.
Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 20490,11 +22045,12 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
number = "RC 3259",
institution = "IBM Research",
year = "1971",
 keywords = "axiomref"
+ keywords = "axiomref",
+ beebe = "Jenks:1971:MPS"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Jenks:1971:MPS}
@TechReport{Jenks:1971:MPS,
author = "R. D. Jenks",
title = "{META\slash PLUS}: The Syntax Extension Facility for
@@ 20524,14 +22080,14 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
pages = "1617",
month = "October",
year = "1972",
 keywords = "axiomref",
abstract =
"The following SCRATCHPAD solution of Problem \#2 was run on a 1280K
virtual machine under CP/CMS time sharing system on a System/360
model 67. The conversation below is a modification of a program
originally written by Yngve Sundblad, August 1972. The program uses
symmetrised formulae, saves certain intermediate results, but does not
 eliminate numerical factors in denominators"
+ eliminate numerical factors in denominators",
+ keywords = "axiomref"
}
\end{chunk}
@@ 20548,7 +22104,6 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
pages = "101111",
year = "1974",
doi = "http://dx.doi.org/10.1145807051",
 keywords = "axiomref",
abstract =
"SCRATCHPAD is an interactive system for symbolic mathematical
computation. Its user language, originally intended as a
@@ 20557,11 +22112,13 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
as a useful, effective tool for online problem solving. This paper
describes extensions to the language which enable it to serve also as
a highlevel programming language, both for the formal description of
 mathematical algorithms and their efficient implementation."
+ mathematical algorithms and their efficient implementation.",
+ keywords = "axiomref",
+ beebe = "Jenks:1974:SL"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Jenks:1974:SL}
@Article{Jenks:1974:SL,
author = "R. D. Jenks",
title = "The {SCRATCHPAD} language",
@@ 20627,7 +22184,6 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
series = "SYMSAC '76",
year = "1976",
publisher = "ACM Press",
 keywords = "axiomref",
doi = "http://dx.doi.org/10.1145806324",
abstract =
"A pattern compiler for the SCRATCHPAD system provides an efficient
@@ 20639,11 +22195,13 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
involves structural comparison of expression trees and evaluation of
predicates. Pattern recognizers are ``fully compiled''; if values of
match variables can be determined by solving equations at compile time.
 Recognition times for several pattern matchers are compared."
+ Recognition times for several pattern matchers are compared.",
+ keywords = "axiomref",
+ beebe = "Jenks:1976:PC"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Jenks:1976:PC}
@InProceedings{Jenks:1976:PC,
author = "Richard D. Jenks",
editor = "Richard D. Jenks",
@@ 20678,13 +22236,13 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
number = "1",
pages = "1619",
year = "1977",
 keywords = "axiomref",
abstract =
"This paper is a preliminary report on the design and implementation
of a modebased symbolic programming system and compiler which allows
programming with rewrite rules and LET and IS patternmatch constructs.
An important feature of this design is the provision for modevalued
 variables which allow algebraic domains to be runtime parameters."
+ variables which allow algebraic domains to be runtime parameters.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 20716,14 +22274,14 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
number = "1",
pages = "1626",
year = "1979",
 keywords = "axiomref",
comment = "IBM Research RC 7405",
abstract =
"The key concepts of the SCRATCHPAD language are described, assessed,
and illustrated by an example. The language was originally intended as
an interactive problem solving language for symbolic mathematics.
Nevertheless, as this paper intends to show, it can be used as a
 programming language as well."
+ programming language as well.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 20738,7 +22296,6 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
booktitle = "Proc. Symp. on Symbolic and Algebraic Manipulation",
series = "SYMSAC 1981",
location = "Snowbird, Utah",
 keywords = "axiomref",
comment = "IBM Research Report 8930",
abstract =
"This paper reports ongoing research at the IBM Research Center on the
@@ 20756,7 +22313,8 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
mechanism. Our notion of a category to group domains with common
properties appears novel among programming languages (cf. image
functor of RUSSELL) and leads to a very powerful notion of abstract
 algorithms missing from other work on data types known to the authors."
+ algorithms missing from other work on data types known to the authors.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 20767,7 +22325,7 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
\bibitem[Jenks 81a]{JT81a} Jenks, R.D.; Trager, B.M.
title = "A Language for Computational Algebra",
SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 20779,11 +22337,12 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
booktitle = "Proc. 1984 MACSYMA Users Conference",
year = "1984",
pages = "409??",
 keywords = "axiomref"
+ keywords = "axiomref",
+ beebe = "Jenks:1984:NSL"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Jenks:1984:NSL}
@InProceedings{Jenks:1984:NSL,
author = "Richard D. Jenks",
title = "The New {SCRATCHPAD} Language and System for Computer
@@ 20807,7 +22366,6 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
publisher = "SpringerVerlag",
pages = "123147",
isbn = "038713350X",
 keywords = "axiomref",
abstract =
"This paper is an abbreviated primer for the language of new
SCRATCHPAD, a new implementation of SCRATCHPAD which has been under
@@ 20849,11 +22407,13 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
This presentation of the language in this paper omits many details to
be covered in the SCRATCHPAD System Programming Manual [SCRA84] and an
expanded version of this paper will serve as a primer for SCRATCHPAD
 users [JESU84]."
+ users [JESU84].",
+ keywords = "axiomref",
+ beebe = "Jenks:1984:PKN"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Jenks:1984:PKN}
@InProceedings{Jenks:1984:PKN,
author = "Richard D. Jenks",
title = "A primer: 11 keys to {New Scratchpad}",
@@ 20928,8 +22488,6 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
type = "Research Report",
number = "RC 12327 (\#55257)",
url = "http://www.csd.uwo.ca/~watt/pub/reprints/1987imaspadadt.pdf",
 paper = "Jenk86.pdf",
 keywords = "axiomref",
abstract = "
Scratchpad II is an abstract datatype language and system that is
under development in the Computer Algebra Group, Mathematical Sciences
@@ 20940,11 +22498,14 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
differentiation, factorization, solution of equations and linear
algebra. Code economy and modularity is achieved by having
polymorphic packages of functions that may create datatypes. The use
 of categories makes these facilities as general as possible."
+ of categories makes these facilities as general as possible.",
+ paper = "Jenk86.pdf",
+ keywords = "axiomref",
+ beebe = "Jenks:1986:SIA"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Jenks:1986:SIA}
@TechReport{Jenks:1986:SIA,
author = "Richard D. Jenks and Robert S. Sutor and Stephen M.
Watt",
@@ 20981,7 +22542,6 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
isbn = "0387189289",
year = "1987",
comment = "IBM Research Report RC 12327 (\#55257) See Jenks86.pdf",
 keywords = "axiomref",
abstract =
"Scratchpad II is an abstract datatype language and system that is
under development in the Computer Algebra Group, Mathematical Sciences
@@ 20991,7 +22551,8 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
differentation, factorization, solution of equations and linear
algebra. Code economy and modularity is achieved by having polymorphic
packages of functions that may create datatypes. The use of categories
 makes these facilities as general as possible."
+ makes these facilities as general as possible.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 21009,7 +22570,6 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
pages = "157182",
publisher = "Springer",
isbn = "0387189289",
 keywords = "axiomref",
abstract =
"Scratchpad II is an abstract datatype language and system that is
under development in the Computer Algebra Group, Mathematical Sciences
@@ 21019,11 +22579,13 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
differentation, factorization, solution of equations and linear
algebra. Code economy and modularity is achieved by having polymorphic
packages of functions that may create datatypes. The use of categories
 makes these facilities as general as possible."
+ makes these facilities as general as possible.",
+ keywords = "axiomref",
+ beebe = "Jenks:1988:SIA"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Jenks:1988:SIA}
@InProceedings{Jenks:1988:SIA,
author = "R. D. Jenks and R. S. Sutor and S. M. Watt",
title = "{Scratchpad II}: An Abstract Datatype System for
@@ 21043,7 +22605,7 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
title = "A Guide to Programming in BOOT",
Computer Algebra Group, Mathematical Sciences Department, IBM Research
Draft September 5, 1988
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 21052,7 +22614,7 @@ Draft September 5, 1988
\bibitem[Jenks 88b]{Jen88b} Jenks, Richard
title = "The Scratchpad II Computer Algebra System Interactive Environment Users Guide",
Spring 1988
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 21066,7 +22628,6 @@ Draft September 5, 1988
volume = "83",
number = "S1",
pages = "S106",
 keywords = "axiomref",
abstract =
"The Scratchpad II system represents a new generation of systems for
doing symbolic mathematics, based on modern algebra and abstract data
@@ 21085,7 +22646,8 @@ Draft September 5, 1988
advanced user for the efficient implementation of
algorithms. Scratchpad II is built on Lisp/VM and runs on IBM/370
class mainframes. An implementation of the system on the RT/PC is
 expected soon."
+ expected soon.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 21099,7 +22661,26 @@ Draft September 5, 1988
publisher = "SpringerVerlag, Berlin, Germany",
year = "1992",
isbn = "0387978550",
 keywords = "axiomref"
+ keywords = "axiomref",
+ beebe = "Jenks:1992:ASC"
+}
+
+\end{chunk}
+\begin{chunk}{Jenks:1992:ASC}
+@Book{Jenks:1992:ASC,
+ author = "Richard D. Jenks and Robert S. Sutor",
+ title = "{AXIOM}: The Scientific Computation System",
+ publisher = pubSV,
+ address = pubSV:adr,
+ pages = "xxiv + 742",
+ year = "1992",
+ ISBN = "0387978550 (New York), 3540978550 (Berlin)",
+ ISBN13 = "9780387978550 (New York), 9783540978558
+ (Berlin)",
+ LCCN = "QA76.95.J46 1992",
+ bibdate = "Fri Dec 29 18:16:15 1995",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
}
\end{chunk}
@@ 21116,10 +22697,8 @@ Draft September 5, 1988
year = "1994",
pages = "3240",
isbn = "0897916387",
 keywords = "axiomref",
publisher = "ACM Press",
address = "New York, NY, USA",
 paper = "Jenk94.pdf",
abstract =
"Scratchpad [GrJe71] was a computer algebra system developed in the
early 1970s. Like M\&M (Maple [CGG91ab] and Mathematical [W01S92]) and
@@ 21155,7 +22734,68 @@ Draft September 5, 1988
current design for building libraries and interactive use. Section 5
describes a new interface design for AXIOM, its resulting paradigms,
and its underlying semantic model. Section 6 compares this work with
 others."
+ others.",
+ paper = "Jenk94.pdf",
+ keywords = "axiomref",
+ beebe = "Jenks:1994:HMA"
+}
+
+\end{chunk}
+\begin{chunk}{Jenks:1994:HMA}
+@InProceedings{Jenks:1994:HMA,
+ author = "Richard D. Jenks and Barry M. Trager",
+ title = "How to make {AXIOM} into a {Scratchpad}",
+ crossref = "ACM:1994:IPI",
+ pages = "3240",
+ year = "1994",
+ MRclass = "68W30 (Symbolic computation and algebraic
+ computation)",
+ bibdate = "Tue Sep 17 06:29:18 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ ZMnumber = "0945.68543",
+ abstract = "Scratchpad (Griesmer and Jenks, 1971) was a computer
+ algebra system that had one principal representation
+ for mathematical formulae based on expression trees.
+ Its user interface design was based on a
+ patternmatching paradigm with infinite rewrite rule
+ semantics, providing what we believe to be the most
+ natural paradigm for interactive symbolic problem
+ solving. Like M and M, however, user programs were
+ interpreted, often resulting in poor performance
+ relative to similar facilities coded in standard
+ programming languages such as FORTRAN and C. Scratchpad
+ development stopped in 1976 giving way to a new system
+ design that evolved into AXIOM. AXIOM has a
+ stronglytyped programming language for building a
+ library of parameterized types and algorithms, and a
+ typeinferencing interpreter that accesses the library
+ and can build any of an infinite number of types for
+ interactive use. We suggest that the addition of an
+ expression tree type to AXIOM can allow users to
+ operate with the same freedom and convenience of
+ untyped systems without giving up the expressive power
+ and runtime efficiency provided by the type system. We
+ also present a design that supports a multiplicity of
+ programming styles, from the Scratchpad
+ patternmatching paradigm to functional programming to
+ more conventional procedural programming.",
+ acknowledgement = acknhfb,
+ affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
+ NY, USA",
+ classification = "C6180 (User interfaces); C7310 (Mathematics
+ computing)",
+ keywords = "AXIOM; C; Computer algebra system; Expression trees;
+ FORTRAN; Functional programming; Infinite rewrite rule
+ semantics; Library; Mathematical formulae;
+ Patternmatching; Procedural programming; Runtime
+ efficiency; Scratchpad; Stronglytyped programming
+ language; Symbolic problem solving; Typeinferencing
+ interpreter; Untyped systems; User interface design;
+ User programs",
+ language = "English",
+ thesaurus = "Mathematics computing; Pattern matching; Program
+ interpreters; Programming; Symbol manipulation; User
+ interfaces",
}
\end{chunk}
@@ 21168,7 +22808,6 @@ Draft September 5, 1988
Precision",
school = "Johannes Kepler University, Linz, Austria RISC",
year = "2014",
 paper = "Joha14.pdf",
abstract =
"The problem of efficiently evaluating special functions to high
precision has been considered by numerous authors. Important tools
@@ 21198,7 +22837,8 @@ Draft September 5, 1988
than previous published software. The implementations are used for
record computations of the partition function, including the
tabulation of several billion Ramanujantype congruences, and of
 Taylor series associated with the Reimann zeta function."
+ Taylor series associated with the Reimann zeta function.",
+ paper = "Joha14.pdf"
}
\end{chunk}
@@ 21215,15 +22855,15 @@ Draft September 5, 1988
number = "2",
year = "2002",
pages = "315336",
 keywords = "axiomref",
 paper = "Joha02.pdf",
url = "http://projecteuclid.org/download/pdf\_1/euclid.hha/1139852468",
abstract =
"Let $k$ be a field, and $A$ be a polynomial algebra over $k$.
Let $I \subseteq A$ be an ideal. We present a novel method for
computing resolutions of $A/I$ over $A$. The method is a synthesis
of Groebner basis techniques and homological perturbation theory.
 The examples in this paper were computed using computer algebra."
+ The examples in this paper were computed using computer algebra.",
+ paper = "Joha02.pdf",
+ keywords = "axiomref"
}
\end {chunk}
@@ 21241,7 +22881,6 @@ Draft September 5, 1988
volume = "1",
pages = "124136",
year = "1994",
 keywords = "axiomref",
abstract =
"The connection between the motion of certain curves in $\mathbb{R}^3$
and $1+1$dimensional soliton equations is by now wellestablished. On the
@@ 21259,7 +22898,8 @@ Draft September 5, 1988
Bianchi type. The generalised Weingarten system incorporates an
integrable $2+1$dimensional sineGordon equation. The arbitrariness of the
solutions of the generalised Weingarten system is determined via a
 completion procedure."
+ completion procedure.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 21269,7 +22909,7 @@ Draft September 5, 1988
\bibitem[Rainer 14]{Rain14} Joswig, Rainer
title = "2014: 30+ Years Common Lisp the Language",
url = "http://lispm.de/30ycltl",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 21282,8 +22922,6 @@ Draft September 5, 1988
year = "2008",
url =
"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.124.7499&rep=rep1&type=pdf",
 paper = "Joyn08.pdf",
 keywords = "axiomref",
abstract =
"Open source software has had a profound effect on computing during
the last decade, especially on web servers (Apache), web browsers
@@ 21295,7 +22933,9 @@ Draft September 5, 1988
support of open source mathematical software de velopment. We argue
that careful funding of open source mathematical software may lead to
a lower total cost of ownership in the research and education
 community, and to more efficient and trustworthy mathematical software."
+ community, and to more efficient and trustworthy mathematical software.",
+ paper = "Joyn08.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 21305,8 +22945,8 @@ Draft September 5, 1988
@misc{Joyn16,
author = "Joyner, David",
title = "Links to some open source mathematical programs",
 keywords = "axiomref",
 url = "http://www.opensourcemath.org/opensource\_math.html"
+ url = "http://www.opensourcemath.org/opensource\_math.html",
+ keywords = "axiomref"
}
\end{chunk}
@@ 21321,7 +22961,6 @@ Draft September 5, 1988
number = "12",
pages = "3947",
year = "2008",
 keywords = "axiomref",
abstract =
"This survey will look at Axiom, a free and very powerful computer
algebra system available. It is a general purpose CAS useful for
@@ 21329,7 +22968,42 @@ Draft September 5, 1988
mathematical algorithms. Axiom is similar in some ways to Maxima,
covered in the survey, but different in many ways as well. Axiom,
Maxima, and SAGE, are the largest of the generalpurpose opensource
 CASs."
+ CASs.",
+ keywords = "axiomref",
+ beebe = "Joyner:2008:OSC"
+}
+
+\end{chunk}
+\begin{chunk}{Joyner:2008:OSC}
+@Article{Joyner:2008:OSC,
+ author = "David Joyner",
+ title = "Open source computer algebra systems: {Axiom}",
+ journal = jACMCOMMCOMPALGEBRA,
+ volume = "42",
+ number = "12",
+ pages = "3947",
+ month = mar # "/" # jun,
+ year = "2008",
+ CODEN = "????",
+ DOI = "http://doi.acm.org/10.1145/1394042.1394046",
+ ISSN = "19322232 (print), 19322240 (electronic)",
+ ISSNL = "19322232",
+ bibdate = "Tue Aug 12 17:30:40 MDT 2008",
+ bibsource = "http://portal.acm.org/;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "This survey will look at Axiom, a free and very
+ powerful computer algebra system available. It is a
+ general purpose CAS useful for symbolic computation,
+ research, and the development of new mathematical
+ algorithms. Axiom is similar in some ways to Maxima,
+ covered in the survey [J1], but different in many ways
+ as well. Axiom, Maxima, and SAGE [S], are the largest
+ of the generalpurpose opensource CAS's. If you want
+ to 'take a test drive,' Axiom can be tested without
+ installation via the web interface [AS] or the SAGE
+ online interface [S].",
+ acknowledgement = acknhfb,
+ fjournal = "ACM Communications in Computer Algebra",
}
\end{chunk}
@@ 21340,7 +23014,7 @@ Draft September 5, 1988
\bibitem[Joswig 03]{JT03} Joswig, Michael; Takayama, Nobuki
title = "Algebra, geometry, and software systems",
SpringerVerlag ISBN 3540002561 p291
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 21350,7 +23024,7 @@ SpringerVerlag ISBN 3540002561 p291
title = "OSCAS  Maxima",
SIGSAM Communications in Computer Algebra, 157 2006
url = "http://sage.math.washington.edu/home/wdj/sigsam/oscascca1.pdf",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 21359,7 +23033,7 @@ SIGSAM Communications in Computer Algebra, 157 2006
\bibitem[Joyner 14]{JO14} Joyner, David
title = "Links to some open source mathematical programs",
url = "http://www.opensourcemath.org/opensource_math.html",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 21376,8 +23050,6 @@ SIGSAM Communications in Computer Algebra, 157 2006
series = "ISSAC 1992",
pages = "376386",
isbn = "0897914899 (soft cover) 0897914902 (hard cover)",
 keywords = "axiomref",
 paper = "Kajl92.pdf",
abstract =
"CAS/$\pi$ is a Computer Algebra System graphic user interface
designed to be highly portable and extensible. It has been developed
@@ 21396,7 +23068,9 @@ SIGSAM Communications in Computer Algebra, 157 2006
intersystems communications, a toolkit to allow fast development of
custommade scientific software environments, or a very convenient
framework for experimenting with computer algebra systems protocols
 and manmachine interfaces."
+ and manmachine interfaces.",
+ paper = "Kajl92.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 21412,13 +23086,13 @@ SIGSAM Communications in Computer Algebra, 157 2006
number = "1",
pages = "1828",
year = "1994",
 keywords = "axiomref",
abstract =
"This paper addresses some of the current issues concerning the
improvement of user interfaces for computer algebra systems. Some
state of the art commercial software as well as research prototypes
are presented, followed by a description of present research
 directions."
+ directions.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 21445,8 +23119,8 @@ SIGSAM Communications in Computer Algebra, 157 2006
publisher = "Springer, Berlin, Germany",
year = "2005",
isbn = "3540213791",
 keywords = "axiomref",
 comment = "German Language"
+ comment = "German Language",
+ keywords = "axiomref"
}
\end{chunk}
@@ 21459,7 +23133,6 @@ SIGSAM Communications in Computer Algebra, 157 2006
author = "Kapur, D. and Musser, D.R. and Stepanov, A.A.",
title = "Operators and Algebraic Structures",
url = "http://www.stepanovpapers.com/p59kapur.pdf",
 paper = "Kapu81.pdf",
year = "1981",
abstract =
"Operators in functional languages such as APL and FFP are a useful
@@ 21475,7 +23148,8 @@ SIGSAM Communications in Computer Algebra, 157 2006
development of programs is illustrated through an example. An
approach for associating complexity measures with a structure and
operators is also suggested. This approach is useful in analyzing
 the complexity of algorithms in an abstract setting."
+ the complexity of algorithms in an abstract setting.",
+ paper = "Kapu81.pdf"
}
\end{chunk}
@@ 21492,19 +23166,48 @@ SIGSAM Communications in Computer Algebra, 157 2006
pages = "133140",
isbn = "978159593904",
url = "http://www.risc.jku.at/publications/download/risc_3427/Ka01.pdf",
 paper = "Kaue08.pdf",
 keywords = "axiomref",
abstract =
"A new method is proposed for finding the logarithmic part of an
integral over an algebraic function. The method uses Groebner bases
and is easy to implement. It does not have the feature of finding a
closed form of an integral whenever there is one. But it very often
does, as we will show by a comparison with the builtin integrators of
 some computer algebra systems."
+ some computer algebra systems.",
+ paper = "Kaue08.pdf",
+ keywords = "axiomref"
}
\end{chunk}
+\index{ASP1}
+\index{ASP10}
+\index{ASP12}
+\index{ASP19}
+\index{ASP20}
+\index{ASP24}
+\index{ASP27}
+\index{ASP28}
+\index{ASP29}
+\index{ASP30}
+\index{ASP31}
+\index{ASP33}
+\index{ASP34}
+\index{ASP35}
+\index{ASP4}
+\index{ASP41}
+\index{ASP42}
+\index{ASP49}
+\index{ASP50}
+\index{ASP55}
+\index{ASP6}
+\index{ASP7}
+\index{ASP73}
+\index{ASP74}
+\index{ASP77}
+\index{ASP78}
+\index{ASP8}
+\index{ASP80}
+\index{ASP9}
\index{Keady, G.}
\index{Nolan, G.}
\begin{chunk}{axiom.bib}
@@ 21518,8 +23221,6 @@ SIGSAM Communications in Computer Algebra, 157 2006
pages = "1332",
comment = "NAG Technical Report TR1/94",
url = "school.maths.uwa.edu.au/%7Ekeady/KeadyPapers/93Helsinki.ps",
 paper = "Kead93.pdf",
 keywords = "axiomref",
algebra =
"\newline\refto{domain ASP1 Asp1}
\newline\refto{domain ASP10 Asp10}
@@ 21556,46 +23257,37 @@ SIGSAM Communications in Computer Algebra, 157 2006
for generating Fortran. This paper is a sequel to [6]. Here we present
'examples' of some of the items discussed in [6]. We have attempted to
achieve some coherence by selecting our 'examples' from just the one
 application area  solving nonlinear systems."
+ application area  solving nonlinear systems.",
+ paper = "Kead93.pdf",
+ keywords = "axiomref",
+ beebe = "Keady:1994:PAS"
+}
+
+\end{chunk}
+\begin{chunk}{Keady:1994:PAS}
+@TechReport{Keady:1994:PAS,
+ author = "G. Keady and G. Nolan",
+ title = "Production of {Argument SubPrograms} in the {AXIOM}
+  {NAG} link: examples involving nonlinear systems",
+ number = "TR1/94 ATR/7 (NP2680)",
+ institution = instNAG,
+ address = instNAG:adr,
+ pages = "??",
+ year = "1994",
+ bibdate = "Thu Jan 04 18:40:00 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
+ acknowledgement = acknhfb,
}
\end{chunk}
\index{ASP1}
\index{ASP10}
\index{ASP12}
\index{ASP19}
\index{ASP20}
\index{ASP24}
\index{ASP27}
\index{ASP28}
\index{ASP29}
\index{ASP30}
\index{ASP31}
\index{ASP33}
\index{ASP34}
\index{ASP35}
\index{ASP4}
\index{ASP41}
\index{ASP42}
\index{ASP49}
\index{ASP50}
\index{ASP55}
\index{ASP6}
\index{ASP7}
\index{ASP73}
\index{ASP74}
\index{ASP77}
\index{ASP78}
\index{ASP8}
\index{ASP80}
\index{ASP9}
\index{Kelsey, Tom}
\begin{chunk}{ignore}
\bibitem[Kelsey 99]{Kel99} Kelsey, Tom
title = "Formal Methods and Computer Algebra: A Larch Specification of AXIOM Categories and Functors",
Ph.D. Thesis, University of St Andrews, 1999
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 21605,8 +23297,6 @@ Ph.D. Thesis, University of St Andrews, 1999
title = "Formal specification of computer algebra",
University of St Andrews, 6th April 2000
url = "http://www.cs.standrews.cs.uk/~tom/pub/fscbs.ps",
 paper = "Kel00a.pdf",
 keywords = "axiomref",
abstract = "
We investigate the use of formal methods languages and tools in the
design and development of computer algebra systems (henceforth CAS).
@@ 21614,7 +23304,9 @@ University of St Andrews, 6th April 2000
corrected by the use of (i) abstract specifications of types and
procedures, (ii) automated proofs of properties of the specifications,
and (iii) interface specifications which assist the verification of
 pre and post conditions of implemented code."
+ pre and post conditions of implemented code.",
+ paper = "Kel00a.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 21624,7 +23316,7 @@ University of St Andrews, 6th April 2000
title = "Formal specification of computer algebra",
(slides) University of St Andrews, Sept 21, 2000
url = "http://www.cs.standrews.cs.uk/~tom/pub/fscbstalk.ps",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 21633,7 +23325,7 @@ University of St Andrews, 6th April 2000
\bibitem[Kendall 99a]{Ken99a} Kendall, W.S.
title = "Itovsn3 in AXIOM: modules, algebras and stochastic differentials",
url = "http://www2.warwick.ac.uk/fac/sci/statistics/staff/academicresearch/kendall/personal/ppt/328.ps.gz",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 21647,8 +23339,6 @@ University of St Andrews, 6th April 2000
pages = "2535",
year = "2001",
url = "http://www2.warwick.ac.uk/fac/sci/statistics/staff/academicresearch/kendall/personal/ppt/327.ps.gz",
 paper = "Kend01.pdf",
 keywords = "axiomref",
abstract =
"Symbolic It\^o calculus refers both to the implementation of the
It\^o calculus algebra package and to its application. This article
@@ 21661,7 +23351,37 @@ University of St Andrews, 6th April 2000
typing'' of computational objects. An application is given of the use
of the implementation to provide calculations for a new proof, based
on stochastic differentials, of the MardiaDryden distribution from
 statistical shape theory."
+ statistical shape theory.",
+ paper = "Kend01.pdf",
+ keywords = "axiomref",
+ beebe = "Kendall:2001:SIC"
+}
+
+\end{chunk}
+\begin{chunk}{Kendall:2001:SIC}
+@Article{Kendall:2001:SIC,
+ author = "Wilfrid S. Kendall",
+ title = "Symbolic {It{\^o}} calculus in {AXIOM}: an ongoing
+ story",
+ journal = jSTATCOMP,
+ volume = "11",
+ number = "1",
+ pages = "2535",
+ year = "2001",
+ CODEN = "STACE3",
+ DOI = "http://dx.doi.org/10.1023/A:1026553731272",
+ ISSN = "09603174",
+ ISSNL = "09603174",
+ MRclass = "Database Expansion Item",
+ MRnumber = "MR1837142",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ fjournal = "Statistics and Computing",
+ keywords = "computer algebra; coupling of random processes; Dryden
+ density Mathematica; financial mathematics; Itovsn3;
+ It{\^o} calculus; It{\^o} formula; Macsyma; Maple;
+ Mardia; REDUCE; semimartingale; statistics of shape;
+ stochastic calculus; stochastic integral; symbolic
+ It{\^o} calculus; XIOM",
}
\end{chunk}
@@ 21677,10 +23397,8 @@ University of St Andrews, 6th April 2000
number = "3",
pages = "935953",
year = "2007",
 keywords = "axiomref",
comment = "Author used Axiom for computation but says missed citation",
url = "http://arxiv.org/pdf/math/0512336v2.pdf",
 paper = "Kend07.pdf",
abstract =
"It is shown how to construct a successful coadapted coupling of two
copies of an $n$dimensional Brownian motion ($B_1,\ldots,B_n$) while
@@ 21689,7 +23407,9 @@ University of St Andrews, 6th April 2000
that successful coadapted couplings still exist when the L{\'e}vy
stochastic areas are replaced by a finite set of multiply iterated
path and timeintegrals, subject to algebraic compatibility of the
 initial conditions."
+ initial conditions.",
+ paper = "Kend07.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 21705,8 +23425,6 @@ University of St Andrews, 6th April 2000
volume = "21",
number = "3",
pages = "327355",
 keywords = "axiomref",
 paper = "Kerb98.pdf",
url =
"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.40.3914&rep=rep1&type=pdf",
abstract =
@@ 21735,7 +23453,9 @@ University of St Andrews, 6th April 2000
the approach is well suited for producing a highlevel verbalized
explication as well as for a lowlevel, machinecheckable,
calculuslevel proof. We present an implementation of our ideas and
 exemplify them using an automatically solved example."
+ exemplify them using an automatically solved example.",
+ paper = "Kerb98.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 21751,8 +23471,6 @@ University of St Andrews, 6th April 2000
volume = "11",
pages = "116",
year = "1996",
 keywords = "axiomref",
 paper = "Kocb96.pdf",
abstract =
"Some large scale physical computations require algorithms performing
symbolic computations with a particular class of algebraic formulas in
@@ 21767,7 +23485,9 @@ University of St Andrews, 6th April 2000
calculation of matrix elements of Coulomb interaction and twocentre
exchange integrals needed in atomic collision codes, are
described. The method makes the developing and debugging of such
 algorithms easier and faster."
+ algorithms easier and faster.",
+ paper = "Kocb96.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 21782,7 +23502,6 @@ University of St Andrews, 6th April 2000
number = "1",
pages = "2126",
year = "1996",
 keywords = "axiomref",
abstract =
"Let $y$ be an algebraic function defined by a polynomial equation
$P(x,y)=0$ whose coefficients are polynomials in $x$ over a field $K$
@@ 21806,7 +23525,8 @@ University of St Andrews, 6th April 2000
coefficients may be calculated. He points out that on the other side
the complexity of the resulting recurrence equation may be extremely
high even for an algebraic function defined by a sparse polynomial of
 low degree."
+ low degree.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 21822,8 +23542,6 @@ University of St Andrews, 6th April 2000
publisher = "Kluwer Adademic Publishers",
location = "Newark, DE",
pages = "205234",
 keywords = "axiomref",
 paper = "Koep99.pdf",
abstract =
"Orthogonal polynomials have a long history, and are still important
objects of consideration in mathematical research as well as in
@@ 21860,7 +23578,9 @@ University of St Andrews, 6th April 2000
polynomials and other hypergeometric type special functions.
Implementations for this type of algorithms exist in Maple,
Mathematica and REDUCE, and maybe also in other computer algebra
 systems. Online demonstrations will be given using Maple V.5."
+ systems. Online demonstrations will be given using Maple V.5.",
+ paper = "Koep99.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 21874,13 +23594,13 @@ University of St Andrews, 6th April 2000
journal = "Electron. Trans. Numer. Anal.",
volume = "9",
year = "1999",
 keywords = "axiomref",
 paper = "Koep99a.pdf",
url = "http://arxiv.org/pdf/math/9809125v1.pdf",
abstract =
"An overview of the MAPLE routines that can be used for hypergeometric
and basic hypergeometric series with some discussion of how and why
 they work."
+ they work.",
+ paper = "Koep99a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 21894,10 +23614,10 @@ University of St Andrews, 6th April 2000
location = "Rutgers, NJ, USA",
url =
"http://www.mathematik.unikassel.de/~koepf/Vortrag/2014ZeilbergerVortrag.pdf",
 paper = "Koep14.pdf",
video1 = "https://vimeo.com/85573338",
video2 = "https://vimeo.com/85573712",
 website = "http://www.caop.org"
+ website = "http://www.caop.org",
+ paper = "Koep14.pdf"
}
\end{chunk}
@@ 21912,17 +23632,18 @@ University of St Andrews, 6th April 2000
number = "1",
pages = "241256",
year = "1991",
 keywords = "axiomref",
abstract =
"The author compares the efficiency of many methods which allow
calculations in Lie algebras. Many construction methods exist for the
base of free Lie algebras developed from finite sets. They use two
algorithms for calculation of several CampbellHausdorf formulas.
 Diverse implementations are realised in LISP on Scratchpad II"
+ Diverse implementations are realised in LISP on Scratchpad II",
+ keywords = "axiomref",
+ beebe = "Koseleff:1991:WGF"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Koseleff:1991:WGF}
@Article{Koseleff:1991:WGF,
author = "P.V. Koseleff",
title = "Word games in free {Lie} algebras: several bases and
@@ 21973,8 +23694,6 @@ University of St Andrews, 6th April 2000
year = "2008",
url =
"http://ac.elscdn.com/S0167642307001736/1s2.0S0167642307001736main.pdf",
 paper = "Kred08.pdf",
 keywords = "axiomref",
abstract =
"This paper considers Java as an implementation language for a
starting part of a computer algebra library. It describes a design of
@@ 21984,7 +23703,9 @@ University of St Andrews, 6th April 2000
design with Java's generic type parameters and threadsafe using
Java's concurrent programming facilities. We report on the performance
of the polynomial arithmetic and on applications built upon the core
 library."
+ library.",
+ paper = "Kred08.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22000,8 +23721,6 @@ University of St Andrews, 6th April 2000
isbn = "9783540878261",
location = "Singapore",
pages = "121138",
 keywords = "axiomref",
 paper = "Kred07.pdf",
url = "http://krum.rz.unimannheim.de/kredel/oocascasc2010slides.pdf",
abstract =
"This paper evaluates the suitability of Java as an implementation
@@ 22010,7 +23729,9 @@ University of St Andrews, 6th April 2000
have been presented. The library is typesafe due to its design with
Java's generic type parameters and threadsafe using Java's concurrent
programming facilities. We evaluate some key points of our library and
 differences to other computer algebra systems."
+ differences to other computer algebra systems.",
+ paper = "Kred07.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22027,8 +23748,6 @@ University of St Andrews, 6th April 2000
isbn = "9783642152733",
location = "Berlin",
pages = "162177",
 keywords = "axiomref",
 paper = "Kred10.pdf",
url = "http://krum.rz.unimannheim.de/kredel/oocascasc2010slides.pdf",
abstract =
"Advances in computer science, in particular object oriented
@@ 22043,7 +23762,9 @@ University of St Andrews, 6th April 2000
purpose, dynamic interactive expression interpreters (e.g. Python). To
illuatrate the workability of this approach, we have implemented and
studied computer algebra systems in Java and Scala. In this paper we
 report on the current state of this work by presenting new examples."
+ report on the current state of this work by presenting new examples.",
+ paper = "Kred10.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22057,7 +23778,6 @@ University of St Andrews, 6th April 2000
booktitle = "Automated deduction in geometry (ADG 2008)",
pages = "86115",
isbn = "9783642210457",
 keywords = "axiomref",
abstract =
"This paper describes the implementation of recursive algorithms in
unique factorization domains, namely multivariate polynomial greatest
@@ 22079,7 +23799,8 @@ University of St Andrews, 6th April 2000
rings. The new package provides factory methods for the selection of
one of the several implementations for non experts. Further we
introduce a parallel proxy for gcd implementations which runs
 different implementations concurrently."
+ different implementations concurrently.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22096,8 +23817,6 @@ University of St Andrews, 6th April 2000
isbn = "9783642235672",
location = "Berlin",
pages = "294308",
 keywords = "axiomref",
 paper = "Kred11a.pdf",
url = "http://krum.rz.unimannheim.de/kredel/tocascasc2011slides.pdf",
abstract =
"Following the research direction of strongly typed, generic, object
@@ 22110,7 +23829,9 @@ University of St Andrews, 6th April 2000
the delegation design concept has advantages over the modeling as
subtypes using subclass implementation. We further present a summary
of design problems, which we have encountered so far with our
 implementation in Java and present possbile solutions in Scala."
+ implementation in Java and present possbile solutions in Scala.",
+ paper = "Kred11a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22168,7 +23889,6 @@ University of St Andrews, 6th April 2000
number = "4647",
pages = "70037027",
year = "2000",
 keywords = "axiomref",
abstract =
"This article deals with the kinematic simulation of movable
structures that go through special configurations of kinematic
@@ 22185,7 +23905,8 @@ University of St Andrews, 6th April 2000
particular cases that are considered, it is found that the entire
process is inextensional, but a detailed study of the simulation
results shows that in more general cases, it is likely that stretching
 or wrinkling will occur."
+ or wrinkling will occur.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22203,7 +23924,6 @@ University of St Andrews, 6th April 2000
pages = "246257",
isbn = "3540515178",
year = "1987",
 keywords = "axiomref",
abstract =
"The problem of automatically proving geometric theorems has gained a
lot of attention in the last two years. Following the general approach
@@ 22219,11 +23939,13 @@ University of St Andrews, 6th April 2000
SCRATCHPAD II. We summarize the recent achievements in the area of
automated geometry theorem proving, shortly review the SCRATCHPAD II
system, describe the implementation of the geometry theorem proving
 package, and finally give a computing time statistics of 24 examples."
+ package, and finally give a computing time statistics of 24 examples.",
+ keywords = "axiomref",
+ beebe = "Kusche:1989:IGT"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Kusche:1989:IGT}
@InProceedings{Kusche:1989:IGT,
author = "K. Kusche and B. Kutzler and H. Mayr",
title = "Implementation of a geometry theorem proving package
@@ 22293,7 +24015,6 @@ University of St Andrews, 6th April 2000
volume = "14",
number = "3",
pages = "187215",
 keywords = "axiomref",
abstract =
"In a previous paper we characterized, in the category theory setting,
a class of implementations of abstract data types, which has been
@@ 22307,7 +24028,8 @@ University of St Andrews, 6th April 2000
formalisms, namely hidden specifications and the coalgebraic view. In
this paper, we explore these relations making explicit the implicit
objectoriented features of the EAT system and generalizing the data
 structure analysis we had previously done."
+ structure analysis we had previously done.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22335,8 +24057,6 @@ University of St Andrews, 6th April 2000
number = "1",
pages = "7187",
year = "1991",
 keywords = "axiomref",
 paper = "Lamb91.pdf",
abstract =
"The purpose of this paper is to review an algorithm for computing
``small'' resolutions in homological algebra, to provide examples of
@@ 22356,11 +24076,14 @@ University of St Andrews, 6th April 2000
are to be expected when trying to derive complexes smaller than
``standard complexes'' in other homological contexts. The complexes
produced are generally {\sl much} smaller than the bar construction, but
 larger than a {\sl minimal resolution}."
+ larger than a {\sl minimal resolution}.",
+ paper = "Lamb91.pdf",
+ keywords = "axiomref",
+ beebe = "Lambe:1991:RHP"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Lambe:1991:RHP}
@Article{Lambe:1991:RHP,
author = "L. A. Lambe",
title = "Resolutions via homological perturbation",
@@ 22420,9 +24143,7 @@ University of St Andrews, 6th April 2000
Scratchpad Concept: Applications to Research in Algebra",
publisher = "21st Nordic Congress of Mathematicians",
year = "1992",
 paper = "Lamb92.pdf",
url = "http://axiomwiki.newsynthesis.org/public/refs/axiom21cong.pdf",
 keywords = "axiomref",
algebra = "\newline\refto{category FMCAT FreeModuleCat}",
abstract =
"One way in which mathematicians deal with infinite amounts of data is
@@ 22444,7 +24165,78 @@ University of St Andrews, 6th April 2000
notions of domains and categories. By examining some aspects of the
Axiom system, the Scratchpad Concept will be illustrated. It will be
shown how some complex problems in homologicial algebra were solved
 through the use of this system."
+ through the use of this system.",
+ paper = "Lamb92.pdf",
+ keywords = "axiomref",
+ beebe = "Lambe:1994:NGC"
+}
+
+\end{chunk}
+\begin{chunk}{Lambe:1994:NGC}
+@InProceedings{Lambe:1994:NGC,
+ author = "Larry Lambe",
+ editor = "Mats Gyllenberg and Lars Erik Persson",
+ booktitle = "{Analysis, algebra, and computers in mathematical
+ research: proceedings of the Twentyfirst Nordic
+ Congress of Mathematicians, Lule{\aa} University of
+ Technology, Sweden, 1992}",
+ title = "Next generation computer algebra systems {AXIOM} and
+ the {Scratchpad} concept: Applications to research in
+ algebra",
+ volume = "156",
+ publisher = pubDEKKER,
+ address = pubDEKKER:adr,
+ pages = "201222",
+ year = "1994",
+ ISBN = "0824792173",
+ ISBN13 = "9780824792176",
+ LCCN = "QA299.6 .N67 1992",
+ MRclass = "1804 (Machine computation, programs (category
+ theory)) 68W30 (Symbolic computation and algebraic
+ computation) 2004 (Machine computation, programs
+ (group theory)) 18G15 (Ext and Tor, generalizations)
+ 18G35 (Chain complexes (homological algebra)) 55U15
+ (Chain complexes) 20J05 (Homological methods in group
+ theory) 16E40 (Homology and cohomology theories for
+ assoc. rings)",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ series = "Lecture Notes in Pure and Applied Mathematics",
+ URL = "http://www.loc.gov/catdir/enhancements/fy0647/94002464d.html",
+ ZMnumber = "0832.18001",
+ abstract = "One way in which mathematicians deal with infinite
+ amounts of data is symbolic representation. A simple
+ example is the quadratic equation $ x = { b \pm \sqrt
+ {b^2  4a} c \over 2a} $, a formula which uses symbolic
+ representation to describe the solutions to an infinite
+ class of equations. Most computer algebra systems can
+ deal with polynomials with symbolic coefficients, but
+ what if symbolic exponents are called for (e.g., $ 1 +
+ t^i) $ ? What if symbolic limits on summations are also
+ called for (e.g., $ 1 + t + \cdots + t^i = \sum_j t^j)
+ $ ? The ``Scratchpad concept'' is a theoretical ideal
+ which allows the implementation of objects at this
+ level of abstraction and beyond in a mathematically
+ consistent way. The AXIOM computer algebra system is an
+ implementation of a major part of the Scratchpad
+ concept. AXIOM (formerly called Scratchpad) is a
+ language with extensible parameterized types and
+ generic operators which is based on the notion of
+ domains and categories [{\it R. D. Jenks} and {\it R.
+ S. Sutor}, Axiom. The scientific computation system,
+ Springer, Berlin etc. (1992; Zbl 0758.68010)]. By
+ examining some aspects of the AXIOM system, the
+ Scratchpad concept will be illustrated. It will be
+ shown how some complex problems in homological algebra
+ [cf. the author, Contemp. Math. 134, 183218 (1992; Zbl
+ 0798.16028), J. Pure Appl. Algebra 84, No. 3, 311329
+ (1993; Zbl 0766.55015)] were solved through the use of
+ this system.",
+ bookpages = "ix + 408",
+ keywords = "AXIOM; bar construction; computer algebra; domains;
+ Ext; generic operators; parameterized types;
+ perturbation lemma; Scratchpad; symbolic exponents;
+ symbolic limits; Tor",
+ language = "English",
}
\end{chunk}
@@ 22454,7 +24246,7 @@ University of St Andrews, 6th April 2000
\bibitem[Lambe 93]{Lam93} Lambe, Larry
title = "On Using Axiom to Generate Code",
(preprint) 1993
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 22468,8 +24260,6 @@ University of St Andrews, 6th April 2000
journal = "3rd Int. Conf. on Expert Systems in Numerical Computing",
year = "1993",
url = "http://axiomwiki.newsynthesis.org/public/refs/axiomfem.pdf",
 paper = "Lamb93a.pdf",
 keywords = "axiomref",
abstract =
"The Axiom language is based on the notions of ``categories'',
``domains'', and ``packages''. These concepts are used to build an
@@ 22479,7 +24269,9 @@ University of St Andrews, 6th April 2000
symbolic computational environment are also included using the finite
element method. While the examples are elementary, we believe that
they point to very powerful methods for combining numeric and symbolic
 computational techniques."
+ computational techniques.",
+ paper = "Lamb93a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22494,15 +24286,15 @@ University of St Andrews, 6th April 2000
volume = "154",
pages = "228288",
year = "1993",
 keywords = "axiomref",
url = "pages.bangor.ac.uk/~mas019/papers/lamrad.pdf",
 paper = "Lamb93b.pdf",
abstract =
"In this paper we examine a variety of algebraic contexts in which the
quantum YangBaxter equation arises, and derive methods for generating
new solutions from given ones. The solutions we describe are encoded
in objects which have a module and a comodule structure over a
 bialgebra. Our work here is based in part on the ideas of [DR1,DR2]."
+ bialgebra. Our work here is based in part on the ideas of [DR1,DR2].",
+ paper = "Lamb93b.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22517,7 +24309,6 @@ University of St Andrews, 6th April 2000
booktitle = "Mathematics and its Applications",
publisher = "Kluwer Adademic Publishers",
year = "1997",
 keywords = "axiomref",
abstract =
"The quantum YangBaxter equation (QYBE) has roots in statistical
mechanics and the inverse scattering method and leads to a natural
@@ 22568,7 +24359,8 @@ University of St Andrews, 6th April 2000
purposes. Besides being a basic source book, the authors include some
new results and some novel approaches to earlier results. All this
makes this book a most welcome addition to the quantum group
 literature."
+ literature.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22585,8 +24377,6 @@ University of St Andrews, 6th April 2000
number = "4",
pages = "723774",
year = "2002",
 keywords = "axiomref",
 paper = "Lamb02.pdf",
url = "https://www.emis.de/journals/GMJ/vol9/v9n411.pdf",
abstract =
"Spencer cohomology is one of the classical tools in the study of
@@ 22597,7 +24387,9 @@ University of St Andrews, 6th April 2000
methods for its construction based on homological perturbation
theory. It also gives a detailed introduction to the subject, and
proposes a new algorithm of constructing the Spencer resolution by
 using symbolic computation systems."
+ using symbolic computation systems.",
+ paper = "Lamb02.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22614,8 +24406,6 @@ University of St Andrews, 6th April 2000
volume = "4",
year = "2003",
url = "http://pages.bangor.ac.uk.~mas019/papers/lln.pdf",
 paper = "Lamb03.pdf",
 keywords = "axiomref",
abstract =
"A new finite difference method for the Helmholtz equation is
presented. The method involves replacing the standard ``weights'' in the
@@ 22634,7 +24424,9 @@ University of St Andrews, 6th April 2000
While we do not want to make SC the focus of this work, we also do not
want to underestimate its value. Armed with robust and efficient SC
libraries, a researcher can {\sl comfortably} and {\sl conveniently}
 experiment with ideas that he or she might not examine otherwise."
+ experiment with ideas that he or she might not examine otherwise.",
+ paper = "Lamb03.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22650,14 +24442,14 @@ University of St Andrews, 6th April 2000
location = "Dagstuhl Castle, Germany",
publisher = "Kluwer Academic Publishers",
pages = "175181",
 keywords = "axiomref",
abstract =
"Different ways for representing rigid body motions (direct isometries)
by a computer are presented. It turns out that the choice between them
may have a dramatic effect on the difficulty of a computation or of a
proof. As an application, a computational proof is given of the fact
that the direct kinematic problem for the generalized Stewart platform
 has at most 40 complex solutions."
+ has at most 40 complex solutions.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22668,7 +24460,7 @@ University of St Andrews, 6th April 2000
title = "OpenMath Library for Computing on Riemann Surfaces",
PhD thesis, Nov 2008 Florida State University
url = "http://www.math.fsu.edu/~ylebedev/research/HyperbolicGeometry.html",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 22680,7 +24472,6 @@ PhD thesis, Nov 2008 Florida State University
booktitle = "Proc. ASEE Annual Meeting",
year = "1991",
pages = "287299",
 keywords = "axiomref",
abstract =
"MathCAD and Theorist are two powerful mathematical packages available
for instruction in the ChE classroom. MathCAD is advertised as an
@@ 22698,11 +24489,13 @@ PhD thesis, Nov 2008 Florida State University
behavior of an engineering system. The author discusses the
application and use of these packages in chemical engineering and give
example problems and their solutions for a number of courses including
 stoichiometry, unit operations, thermodynamics and design."
+ stoichiometry, unit operations, thermodynamics and design.",
+ keywords = "axiomref",
+ beebe = "LeBlanc:1991:UMT"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{LeBlanc:1991:UMT}
@InProceedings{LeBlanc:1991:UMT,
author = "S. E. LeBlanc",
title = "The use of {MathCAD} and {Theorist} in the {ChE}
@@ 22761,15 +24554,15 @@ PhD thesis, Nov 2008 Florida State University
number = "3",
pages = "247293",
year = "2002",
 keywords = "axiomref",
 paper = "Lece02.pdf",
abstract =
"The author proposes an efficient iterator with quadratic convergence
that generalizes Newton iterator for multiple roots. It is based on an
$m$adic topology where the ideal $m$ can be chosen generic
enough. Compared to the Newton iterator the proposed iterator
introduces a small overhead that grows with the square of the
 multiplicity of the root."
+ multiplicity of the root.",
+ paper = "Lece02.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22786,7 +24579,6 @@ PhD thesis, Nov 2008 Florida State University
isbn = "9783642155819",
location = "Berlin",
pages = "329332",
 keywords = "axiomref",
abstract =
"Coordinated by Joris van der Hoeven from the 90's, the Mathemagix
project aims at the design of a scientific programming language for
@@ 22799,7 +24591,8 @@ PhD thesis, Nov 2008 Florida State University
In my talk I will give an overview of the language, of the design and
the contents of the C++ libraries, and I will illustrate possibilities
 offered for certified numeric computations with balls and intervals."
+ offered for certified numeric computations with balls and intervals.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22822,7 +24615,7 @@ PhD thesis, Nov 2008 Florida State University
\bibitem[Lecerf 96a]{Le96a} Lecerf, Gr\'egoire
title = "The Dynamic Real Closure implemented in Axiom",
url = "http://lecerf.perso.math.cnrs.fr/software/drc/drc.ps",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 22835,14 +24628,14 @@ PhD thesis, Nov 2008 Florida State University
volume = "1",
number = "2",
year = "1994",
 keywords = "axiomref",
 paper = "Leeu94.pdf",
abstract =
"A description is given of LiE, a specialized computer algebra package
for computations concerning Lie groups and algebras, and their
representations. The functionality of the package is demonstrated by
sample computations, and the structure of the program and the
 algorithms implemented in it are discussed."
+ algorithms implemented in it are discussed.",
+ paper = "Leeu94.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22858,7 +24651,6 @@ PhD thesis, Nov 2008 Florida State University
number = "2",
pages = "283299",
year = "1997",
 keywords = "axiomref",
comment = "translated from Russian",
abstract =
"The algebraic programming system (APS) developed at the
@@ 22897,7 +24689,8 @@ PhD thesis, Nov 2008 Florida State University
provides tools for the objectoriented style of programming. This is
one of the possible ways of introducing types in APS. The
objectoriented technology also can be used to develop a hierarchical
 system of mathematical objects."
+ system of mathematical objects.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22909,7 +24702,7 @@ ISSAC '95: Proceedings of the 1995 International
Symposium on Symbolic and Algebraic Computation: July 1012, 1995, Montreal,
Canada ISSACPROCEEDINGS1995. ACM Press, New York, NY 10036, USA, 1995
ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 22925,8 +24718,6 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
pages = "513",
year = "1999",
url = "https://home.bway.net/lewis/cacomp.ps",
 paper = "Lewi99.pdf",
 keywords = "axiomref",
abstract =
"Exact symbolic computation with polynomials and matrices over
polynomial rings has wide applicability to many fields [Hereman96,
@@ 22966,7 +24757,9 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
\item determinants and characteristic polynomial
\item GCDs of multivariate polynomial
\item resultants
 \end{itemize}"
+ \end{itemize}",
+ paper = "Lewi99.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 22978,8 +24771,6 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
title = "Efficient Management of Symbolic Computation with Polynomials",
school = "University of Western Ontario",
year = "2005",
 paper = "Lixx05.pdf",
 keywords = "axiomref",
url =
"http://www.csd.uwo.ca/~moreno//Publications/XinLiMSThesis2005.pdf.gz",
abstract =
@@ 23001,7 +24792,9 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
our methods have great potential to improve the efficiency of exact
polynomial computations with the selected CASs. The performance of our
implementation is comparable to that of (often outperforming) the best
 available packages for polynomial computations."
+ available packages for polynomial computations.",
+ paper = "Lixx05.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 23019,8 +24812,6 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
isbn = "9783540380849",
location = "Spain",
pages = "1223",
 keywords = "axiomref",
 paper = "Lixx06.pdf",
url = "http://www.math.kobeu.ac.jp/icms2006/icms2006video/slides/046.pdf",
abstract =
"The purpose of this study is to investigate implementation techniques
@@ 23043,7 +24834,35 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
level, we combine the strengths of each language level and the
features of a specific machine architecture. Our experimentations show
that this allows us to improve performances of this operation in a
 significant manner."
+ significant manner.",
+ paper = "Lixx06.pdf",
+ keywords = "axiomref",
+ beebe = "Li:2006:EIP"
+}
+
+\end{chunk}
+\begin{chunk}{Li:2006:EIP}
+@Article{Li:2006:EIP,
+ author = "Xin Li and Moreno Maza",
+ title = "Efficient Implementation of Polynomial Arithmetic in a
+ MultipleLevel Programming Environment",
+ journal = jLECTNOTESCOMPSCI,
+ volume = "4151",
+ pages = "1223",
+ year = "2006",
+ CODEN = "LNCSD9",
+ ISBN = "3540380841",
+ ISBN13 = "9783540380849",
+ ISSN = "03029743 (print), 16113349 (electronic)",
+ ISSNL = "03029743",
+ bibdate = "Mon Apr 19 08:40:16 2010",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ note = "Proceedings of the International Congress of
+ Mathematical Software (ICMS 2006).",
+ URL = "http://www.csd.uwo.ca/~moreno//Publications/LiMorenoMazaICMS06.pdf",
+ acknowledgement = acknhfb,
+ fjournal = "Lecture Notes in Computer Science",
+ keywords = "Axiom symbolicalgebra system",
}
\end{chunk}
@@ 23061,7 +24880,6 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
pages = "251258",
year = "2007",
book = "Lixx07.pdf",
 keywords = "axiomref",
abstract =
"The purpose of this study is to measure the impact of C level code
polynomial arithmetic on the performances of Axiom highlevel algorithms,
@@ 23078,7 +24896,27 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
not rely much on the operations of U and implements its private univariate
polynomial operation, the P cannot benefit from our highly optimized C
level code. Consequently, code which is poorly generic reduces the
 speedup opportunities when applied to highly efficient and specialized."
+ speedup opportunities when applied to highly efficient and specialized.",
+ keywords = "axiomref",
+ beebe = "Li:2007:VGP"
+}
+
+\end{chunk}
+\begin{chunk}{Li:2007:VGP}
+@InProceedings{Li:2007:VGP,
+ author = "Xin Li and Marc Moreno Maza and {\'E}ric Schost",
+ title = "On the Virtues of Generic Programming for Symbolic
+ Computation",
+ crossref = "Shi:2007:CSIb",
+ pages = "251258",
+ year = "2007",
+ DOI = "http://dx.doi.org/10.1007/9783540725862_35",
+ bibdate = "Tue Aug 12 10:36:21 2014",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib;
+ http://www.math.utah.edu/pub/tex/bib/magma.bib;
+ http://www.math.utah.edu/pub/tex/bib/mapleextract.bib",
+ acknowledgement = acknhfb,
+ keywords = "Axiom; Magma; Maple",
}
\end{chunk}
@@ 23091,8 +24929,6 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
Triangluar Decompositions",
school = "University of Western Ontario",
year = "2009",
 paper = "Lixx09a.pdf",
 keywords = "axiomref",
url = "http://www.csd.uwo.ca/~moreno/Publications/XinLiPhDThesis2008.pdf",
abstract =
"This thesis is devoted to the design and implementation of polynomial
@@ 23121,7 +24957,9 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
routines and solving procedures written in the Maple computer algebra
system. The experimental result shows that our approaches are very
effective, since our code often outperforms preexisting solvers in a
 significant manner."
+ significant manner.",
+ paper = "Lixx09a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 23139,8 +24977,6 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
isbn = "9781595937438",
location = "Canada",
pages = "269276",
 keywords = "axiomref",
 paper = "Lixx09.pdf",
url =
"http://www.csd.uwo.ca/~moreno/Publications/LiMorenoSchostISSAC2007.pdf",
abstract =
@@ 23153,7 +24989,9 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
higherlevel algorithms, by interfacing our lowlevel implemention
with languages such as AXIOM or Maple. We show the potential for hugh
speedups, by comparing two AXIOM implementations of vanHoeij and
 Monagan's modular GCD algorithm."
+ Monagan's modular GCD algorithm.",
+ paper = "Lixx09.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 23170,10 +25008,8 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
number = "7",
pages = "891907",
year = "2009",
 keywords = "axiomref",
url =
"http://www.csd.uwo.ca/~moreno/Publications/LiMorenoSchostISSAC2007.pdf",
 paper = "Lixx09.pdf",
abstract =
"We study arithmetic operations for triangular families of
polynomials, concentrating on multiplication in dimension zero. By a
@@ 23184,7 +25020,9 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
higherlevel algorithms, by interfacing our lowlevel implemention
with languages such as AXIOM or Maple. We show the potential for hugh
speedups, by comparing two AXIOM implementations of vanHoeij and
 Monagan's modular GCD algorithm."
+ Monagan's modular GCD algorithm.",
+ paper = "Lixx09.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 23196,7 +25034,7 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
title = "A Quantitative Study of Reductions in Algebraic Libraries",
PASCO 2010
url = "http://www.axiomatics.org/~gdr/concurrency/quantpasco10.pdf",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 23212,8 +25050,6 @@ PASCO 2010
isbn = "9781450306751",
year = "2011",
url = "http://www.axiomatics.org/~gdr/concurrency/oaconcissac11.pdf",
 paper = "Lixx11.pdf",
 keywords = "axiomref",
abstract =
"This paper proposes a nonintrusive automatic parallelization
framework for typeful and propertyaware computer algebra systems.
@@ 23225,7 +25061,9 @@ PASCO 2010
speedup for library functions and homotopybased polynomial system
solver. The general framework is applicable to algebraic computation
systems and programming languages with advanced type systems that
 support userdefined axioms or annotation systems."
+ support userdefined axioms or annotation systems.",
+ paper = "Lixx11.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 23237,12 +25075,12 @@ PASCO 2010
Roy, Marie Francoise
title = "Generic computation of the real closure of an ordered field",
Math. and Computers in Simulation 42 pp 541549 (1996)
 paper = "Liga96.pdf",
 keywords = "axiomref",
abstract = "
This paper describes a generalization of the real closure computation
of an ordered field (Rioboo, 1991) enabling to use different technques
 to code a single real algebraic number."
+ to code a single real algebraic number.",
+ paper = "Liga96.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 23251,7 +25089,7 @@ Math. and Computers in Simulation 42 pp 541549 (1996)
\bibitem[Linton 93]{Lin93} Linton, Steve
title = "Vector Enumeration Programs, version 3.04",
url = "http://www.cs.standrews.ac.uk/~sal/nme/nme_toc.html#SEC1",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 23260,8 +25098,19 @@ Math. and Computers in Simulation 42 pp 541549 (1996)
@misc{Lint98,
author = "Linton, Stephen",
title = "The GAP 4 Type System Organising Algebraic Algorithms",
 paper = "Lint98.pdf",
url = "http://www.gapsystem.org/Doc/Talks/kobe.ps",
+ paper = "Lint98.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\begin{chunk}{axiom.bib}
+@misc{Linu15,
+ author = "Linux Links",
+ title = "Axiom",
+ url = "http://www.linuxlinks.com/article/20080810064748970/Axiom.html",
+ year = "2015",
keywords = "axiomref"
}
@@ 23279,7 +25128,7 @@ Sinor, Milan; Wester, Michael; Winkler, Franz
title = "Computer Algebra  algorithms, systems and applications",
June 2, 1997
url = "http://kfe.fjfi.cvut.cz/~liska/ca/all.html",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 23295,8 +25144,6 @@ June 2, 1997
isbn = "0821821407",
location = "Washington",
pages = "139202",
 keywords = "axiomref",
 paper = "Lomo02.pdf",
url = "https://arxiv.org/pdf/quantph/0201095v3.pdf",
abstract =
"The ultimate objective of this paper is to create a stepping stone to
@@ 23328,7 +25175,9 @@ June 2, 1997
of a very special random transversal $t_{\mu}:\widetilde{A}\rightarrow A$,
which we refer to as a Shor transversal. The algorithmic time
complexity of the first of these wandering Shor algorithms is found to
 be $O(n^2({rm lg\ } Q)^3 ({\rm lg\ }{\rm lg\ } Q)^{n+1})$."
+ be $O(n^2({rm lg\ } Q)^3 ({\rm lg\ }{\rm lg\ } Q)^{n+1})$.",
+ paper = "Lomo02.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 23345,7 +25194,6 @@ June 2, 1997
pages = "228232",
publisher = "ACM Press",
isbn = "0897911997",
 keywords = "axiomref",
doi = "http://dx.doi.org/10.1145/32439.32485",
abstract =
"A new package for factoring polynomials with integer coefficients is
@@ 23361,11 +25209,13 @@ June 2, 1997
approaches are discussed for the univariate case as well as for the
problem of finding good integer substitution values. The package has
been implemented both in Scratchpad II and in an experimental version
 of muMATH."
+ of muMATH.",
+ keywords = "axiomref",
+ beebe = "Lucks:1986:FIP"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Lucks:1986:FIP}
@InProceedings{Lucks:1986:FIP,
author = "Michael Lucks",
editor = "Bruce W. Char",
@@ 23398,11 +25248,12 @@ June 2, 1997
school = {Technischen Universit{\"{a}}t CaroloWilhelmina zu Braunschweig},
address = "Braunschweig, Germany",
year = "1977",
 keywords = "axiomref"
+ keywords = "axiomref",
+ beebe = "Lueken:1977:UIF"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Lueken:1977:UIF}
@MastersThesis{Lueken:1977:UIF,
author = "E. Lueken",
title = "{Ueberlegungen zur Implementierung eines
@@ 23433,7 +25284,6 @@ June 2, 1997
number = "3",
pages = "270273",
year = "1991",
 keywords = "axiomref",
abstract =
"The authors have developed a new method for doing numerical quantum
mechanical perturbation theory. It has the flavor of
@@ 23444,11 +25294,13 @@ June 2, 1997
easily implemented by means of the widely used ‘‘electronic
scratchpad,’’ MathCAD 2.0, using an inexpensive computer. As an
example of the method, the problem of a harmonic oscillator with a
 quartic perturbing term is examined."
+ quartic perturbing term is examined.",
+ keywords = "axiomref",
+ beebe = "Lynch:1991:NQM"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Lynch:1991:NQM}
@Article{Lynch:1991:NQM,
author = "R. Lynch and H. A. Mavromatis",
title = "New quantum mechanical perturbation technique using an
@@ 23509,7 +25361,7 @@ June 2, 1997
title = "Programming and certifying the CAD algorithm inside the coq system",
Mathematics, Algorithms, Proofs, volume 05021 of Dagstuhl
Seminar Proceedings, Schloss Dagstuhl (2005)
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 23525,8 +25377,6 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
year = "1989",
url =
"http://mathfaculty.fullerton.edu/mathews/articles/1989PicardIteration.pdf",
 paper = "Math89.pdf",
 keywords = "axiomref",
abstract =
"The term ``Picard iteration'' occurs two places in undergraduate
mathematics. In numerical analysis it is used when discussing fixed
@@ 23547,11 +25397,14 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
manipulation setting. Systems such as MACSYM, ALTRAN, REDUCE, SMP,
MAPLE, SCRATCHPAD and muMATH are being introduced in undergraduate
mathematics courses to assist in keeping trace of equations during
 complicated manipulations."
+ complicated manipulations.",
+ paper = "Math89.pdf",
+ keywords = "axiomref",
+ beebe = "Mathews:1989:SCA"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Mathews:1989:SCA}
@Article{Mathews:1989:SCA,
author = "J. Mathews",
title = "Symbolic computational algebra applied to {Picard}
@@ 23607,7 +25460,6 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
title = "Other Free Computer Algebra Systems",
url = "http://maxima.sourceforge.net/compalg.html",
year = "2016",
 keywords = "axiomref",
abstract =
"Axiom is a general purpose Computer Algebra system. It is useful for
doing mathematics by computer and for research and development of
@@ 23617,7 +25469,8 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
There is also an interesting Rosetta Stone which offers translations
of many basic operations for several computer algebra systems,
 including Maxima."
+ including Maxima.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 23637,9 +25490,7 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
month = "June",
type = "technical report",
number = "TR 4/99",
 paper = "Maza00.pdf",
url = "http://www.csd.uwo.ca/~moreno//Publications",
 keywords = "axiomref",
algebra =
"\newline\refto{category TSETCAT TriangularSetCategory}
\newline\refto{category RSETCAT RegularTriangularSetCategory}
@@ 23650,7 +25501,9 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
"Different kinds of triangular decompositions of algebraic varieties
are presented. The main result is an efficient method for obtaining
them. Our strategy is based on a lifting theorem for polynomial
 computations module regular chains."
+ computations module regular chains.",
+ paper = "Maza00.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 23665,8 +25518,6 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
number = "56",
pages = "509524",
year = "2010",
 keywords = "axiomref",
 paper = "Mcge10.pdf",
url = "https://arxiv.org/pdf/0911.1653v2.pdf",
abstract =
"We investigate the quantum versions of a onedimensional random walk,
@@ 23674,7 +25525,9 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
the walk having a memory of one previous step. We derive the
amplitudes and probabilities for these walks, and point out how they
differ from bot classical random walks, and quantum walks without
 memory."
+ memory.",
+ paper = "Mcge10.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 23684,7 +25537,7 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
\bibitem[McJones 11]{McJ11} McJones, Paul
title = "Software Presentation Group  Common Lisp family",
url = "http://www.softwarepreservation.org/projects/LISP/common_lisp_family",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 23699,7 +25552,6 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
number = "1",
pages = "7176",
year = "1990",
 keywords = "axiomref",
abstract =
"The case is presented for using mathematical scratchpad software,
such as MathCAD, in undergraduate and graduate engineering
@@ 23707,11 +25559,13 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
black box engineering software, are described. Several examples of
student written projects are presented. The projects solve problems in
operations research, control theory and statistical regression
 analysis."
+ analysis.",
+ keywords = "axiomref",
+ beebe = "Melachrinoudis:1990:TAT"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Melachrinoudis:1990:TAT}
@Article{Melachrinoudis:1990:TAT,
author = "E. Melachrinoudis and D. L. Rumpf",
title = "Teaching advantages of transparent computer software
@@ 23761,9 +25615,7 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
@misc{Mele88,
author = "Melenk, H. and Moller, H. M. and Neun, W.",
title = "On Groebner Bases Computation on a Supercomputer Using REDUCE",
 paper = "Mele88.pdf",
url = "https://opus4.kobv.de/opus4zib/files/10/SC8802.pdf",
 keywords = "axiomref",
abstract =
"Groebner bases are the main tool for solving systems of algebraic
equations and some other problems in connection with polynomial ideals
@@ 23771,7 +25623,9 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
Groebner bases in REDUCE 3.3 has been modified in order to solve more
complicated algebraic systems of equations by some general
improvements and by some tools based on the specific resources of the
 CRAY XMP. We present this modification and illustrate it by examples."
+ CRAY XMP. We present this modification and illustrate it by examples.",
+ paper = "Mele88.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 23787,9 +25641,7 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
number = "1",
pages = "75106",
year = "2001",
 keywords = "axiomref",
url = "https://www.jstage.jst.go.jp/article/kyushujm/55/1/55\_1\_75/\_pdf",
 paper = "Mich01.pdf",
abstract =
"Let $G$ be a finite group and $M$ a subgroup of $G$. Let the
permutation character of $G$ on the set of right cosets of $M$ be
@@ 23803,7 +25655,9 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
values of the multiplicityfree constituents of $(1_C)^{J_1}$, where
$J_1$ is the smallest Janko group of order 175560 and $C$ is the
centralizer of an involution in $J_1$. Using these, he then is able to
 compute the character table of $J_1$ which is already known."
+ compute the character table of $J_1$ which is already known.",
+ paper = "Mich01.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 23813,9 +25667,7 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
@misc{Mill95,
author = "Miller, Bruce R.",
title = "An expression formatter for MACSYMA",
 keywords = "axiomref",
year = "1995",
 paper = "Mill95.pdf",
abstract =
"A package for formatting algebraic expressions in MACSYA is described.
It provides facilities for userdirected hierarchical structuring of
@@ 23824,7 +25676,9 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
of the desired form. The package also provides utilities for obtaining
efficiently the coefficients of polynomials, trigonometric sums and
power series. Similar capabilities would be useful in other computer
 algebra systems."
+ algebra systems.",
+ paper = "Mill95.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 23839,7 +25693,6 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
lane departure avoidance",
booktitle = "Proc. 15 Med. Conf. on Control \& Automation",
year = "2007",
 keywords = "axiomref",
abstract =
"This paper presents a vehicle steering assistance designed to avoid
lane departure during driver inattention periods. Activated for a
@@ 23849,7 +25702,8 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
the centerline, the control law has been developed based on invariant
sets theory and on composite Lyapunov functions. The computation has
been performed using LMI methods, which allow in addition imposing a
 maximum bound for the control steering angle."
+ maximum bound for the control steering angle.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 23863,7 +25717,7 @@ volume 429 of Lecture Notes in Cmputer Science,
SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
1990 ISBN 0387525319 (New York), 3540525319 (Berlin) LCCN QA76.9.S88I576
1990
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 23875,7 +25729,7 @@ International Symposium DISCO '93 Gmunden, Austria, September 1517, 1993:
Proceedings.
SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
1993 ISBN 354057235X LCCN QA76.9.S88I576 1993
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 23887,7 +25741,6 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
publisher = "SpringerVerlag",
series = "Texts and Monographs in Computer Sciences",
year = "1993",
 keywords = "axiomref",
abstract =
"This book is based on a graduate course in computer science taught in
1987. The following topics are covered: computational ideal theory,
@@ 23904,7 +25757,8 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
size and the complexity issues are not considered.
The choice of topics is excellent, there are many exercises and
 examples. It is a very useful book."
+ examples. It is a very useful book.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 23914,19 +25768,19 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
@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."
+ algebraic hierarchy.",
+ paper = "Miss05",
+ keywords = "axiomref"
}
\end{chunk}
@@ 23937,8 +25791,6 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
\bibitem[Missura 94]{Miss94} Missura, Stephan A.; Weber, Andreas
title = "Using Commutativity Properties for Controlling Coercions",
url = "http://cg.cs.unibonn.de/personalpages/weber/publications/pdf/WeberA/MissuraWeber94a.pdf",
 paper = "Miss94.pdf",
 keywords = "axiomref",
abstract = "
This paper investigates some soundness conditions which have to be
fulfilled in systems with coercions and generic operators. A result of
@@ 23951,7 +25803,9 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
conditions  that allows distinguishing between cases of ambiguities
which can be resolved in a quite natural sense and those which
cannot. An algorithm is presented that detects such unresolvable
 ambiguities in expressions."
+ ambiguities in expressions.",
+ paper = "Miss94.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 23960,16 +25814,78 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
\bibitem[Monagan 87]{Mon87} Monagan, Michael B.
title = "Support for Data Structures in Scratchpad II",
in [Wit87], pp1718
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
\index{Monagan, Michael B.}
\begin{chunk}{ignore}
\bibitem[Monagan 93]{Mon93} Monagan, M. B.
 title = "Gauss: a parameterized domain of computation system with support for signature functions",
In Miola [Mio93], pp8194 ISBN 354057235X LCCN QA76.9.S88I576 1993
 keywords = "axiomref",
+\begin{chunk}{axiom.bib}
+@inproceedings{Mona93,
+ author = "Monagan, Michael B.",
+ title = "Gauss: a parameterized domain of computation system with
+ support for signature functions",
+ booktitle = "Design and Implementation of Symbolic Computation Systems",
+ series = "Lecture Notes in Computer Science 722",
+ pages = "8194",
+ isbn = "354057235X",
+ year = "1993",
+ url = "http://www.cecm.sfu.ca/~monaganm/papers/DISCO93.pdf",
+ abstract =
+ "The fastest known algorithms in classical algebra make use of signature
+ functions. That is, reducing computation with formulae to computing with
+ the integers module $p$, by substituting random numbers for variables,
+ and mapping constants module $p$. This isea is exploited in specific
+ algorithms in computer algebra systems, e.g. algorithms for polynomial
+ greatest common divisors. It is also used as a heuristic to speed up
+ other calculations. But none exploit it in a systematic manner. The
+ goal of this work was twofold. First, to design an AXIOM like system
+ in which these signature functions can be constructed automatically,
+ hence better exploited, and secondly, to exploit them in new ways. In
+ this paper we report on the design of such a system, Gauss.",
+ paper = "Mona93.pdf",
+ keywords = "axiomref",
+ beebe = "Monagan:1993:GPD"
+}
+
+\end{chunk}
+\begin{chunk}{Monagan:1993:GPD}
+@InProceedings{Monagan:1993:GPD,
+ author = "M. B. Monagan",
+ title = "{Gauss}: a parameterized domain of computation system
+ with support for signature functions",
+ crossref = "Miola:1993:DIS",
+ pages = "8194",
+ month = "",
+ year = "1993",
+ bibdate = "Fri Dec 29 12:46:02 MST 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "The fastest known algorithms in classical algebra make
+ use of signature functions. That is, reducing
+ computation with formulae to computing with the
+ integers modulo p, by substituting random numbers for
+ variables, and mapping constants modulo p. This idea is
+ exploited in specific algorithms in computer algebra
+ systems, e.g. algorithms for polynomial greatest common
+ divisors. It is also used as a heuristic to speed up
+ other calculations. But none exploit it in a systematic
+ manner. The author designs an AXIOM like system in
+ which these signature functions can be constructed
+ automatically, hence better exploited. He exploits them
+ in new ways. He reports on the design of such a system,
+ Gauss.",
+ acknowledgement = acknhfb,
+ affiliation = "Inst. fur Wissenschaftliches Rechnen, ETH, Zurich,
+ Switzerland",
+ classification = "C4130 (Interpolation and function approximation);
+ C7310 (Mathematics)",
+ keywords = "AXIOM like system; Classical algebra; Computation
+ system; Computer algebra systems; Gauss; Heuristic;
+ Integers modulo; Mapping constants modulo;
+ Parameterized domain; Polynomial greatest common
+ divisors; Random numbers; Signature functions",
+ language = "English",
+ thesaurus = "Polynomials; Symbol manipulation",
+}
\end{chunk}
@@ 23981,8 +25897,6 @@ In Miola [Mio93], pp8194 ISBN 354057235X LCCN QA76.9.S88I576 1993
title = "Signature Functions for Algebraic Numbers",
url =
"http://lib.org/by/\_djvu\_Papers/Computer\_algebra/Algebraic\%20numbers",
 paper = "Mona94.djvu",
 keywords = "axiomref",
abstract =
"In 1980 Schwartz gave a fast {\sl probabilistic} method which tests
if a matrix of polynomials of $\mathbb{Z}$ is singular or not. The
@@ 23998,7 +25912,9 @@ In Miola [Mio93], pp8194 ISBN 354057235X LCCN QA76.9.S88I576 1993
elementary functions and integer roots. In this paper we present and
compare methods for constructing signature functions for expressions
containing {\sl algebraic numbers}. Some experimental results are
 given."
+ given.",
+ paper = "Mona94.djvu",
+ keywords = "axiomref"
}
\end{chunk}
@@ 24016,8 +25932,6 @@ In Miola [Mio93], pp8194 ISBN 354057235X LCCN QA76.9.S88I576 1993
isbn = "9783540751861",
location = "Bonn",
pages = "295315",
 keywords = "axiomref",
 paper = "Mona07.pdf",
url = "http://www.cecm.sfu.ca/~rpearcea/sdmp/sdmp\_paper.pdf",
abstract =
"A common way of implementing multivariate polynomial multiplication
@@ 24042,7 +25956,9 @@ In Miola [Mio93], pp8194 ISBN 354057235X LCCN QA76.9.S88I576 1993
Maple. For comparison we have also implemented Yan’s ``geobuckets'' data
structure. Our timings demonstrate that heaps of pointers are
comparable in speed with geobuckets but use significantly less
 storage."
+ storage.",
+ paper = "Mona07.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 24054,8 +25970,6 @@ In Miola [Mio93], pp8194 ISBN 354057235X LCCN QA76.9.S88I576 1993
title = "On the canonical discussion of polynomial systems with parameters",
year = "2007",
url = "http://arxiv.org/pdf/math/0601674.pdf",
 paper = "Mont07.pdf",
 keywords = "axiomref",
abstract =
"Given a parametric polynomial ideal $I$, the algorithm DISPGB,
introduced by the author in 2002, builds up a binary tree describing a
@@ 24068,7 +25982,9 @@ In Miola [Mio93], pp8194 ISBN 354057235X LCCN QA76.9.S88I576 1993
difficulties and formulate a natural conjecture. If the conjecture is
true then such a canonical CGS will exist and can be computed. We also
give an algorithm to transform our original CGS in this direction and
 show its utility in applications."
+ show its utility in applications.",
+ paper = "Mont07.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 24082,7 +25998,7 @@ Proceedings, volume 357 of Lecture Notes in Computer Science
SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
1989 ISBN 3540510834, LCCN QA268.A35 1988 Conference held jointly with
ISSAC '88
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 24091,7 +26007,7 @@ ISSAC '88
\bibitem[Moses 71]{Mos71} Moses, Joel
title = "Algebraic Simplification: A Guide for the Perplexed",
CACM August 1971 Vol 14 No. 8 pp527537
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 24101,8 +26017,6 @@ CACM August 1971 Vol 14 No. 8 pp527537
title = "Macsyma: A Personal History",
Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
url = "http://esd.mit.edu/Faculty_Pages/moses/Macsyma.pdf",
 paper = "Mos08.pdf",
 keywords = "axiomref",
abstract = "
The Macsyma system arose out of research on mathematical software in
the AI group at MIT in the 1960's. Algorithm development in symbolic
@@ 24115,7 +26029,9 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
70's and the 80's to develop Macsyma systems that ran on popular
computer architectures. Finally, we discuss the impact of the
fundamental ideas in Macsyma on current research on large scale
 engineering systems."
+ engineering systems.",
+ paper = "Mos08.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 24136,11 +26052,9 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
@misc{Muld95,
author = "Mulders, Thom",
title = "Primitives: Orepoly and Lodo",
 paper = "Muld95.pdf",
year = "1995",
url =
"ftp://ftp.inf.ethz.ch/org/cathode/workshops/jan95/abstracts/mulders.ps",
 keywords = "axiomref",
algebra =
"\newline\refto{category OREPCAT UnivariateSkewPolynomialCategory}
\newline\refto{category LODOCAT LinearOrdinaryDifferentialOperatorCategory}
@@ 24153,7 +26067,9 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
\newline\refto{package APPLYORE ApplyUnivariateSkewPolynomial}
\newline\refto{package OREPCTO UnivariateSkewPolynomialCategoryOps}
\newline\refto{package LODOF LinearOrdinaryDifferentialOperatorFactorizer}
 \newline\refto{package LODOOPS LinearOrdinaryDifferentialOperatorsOps}"
+ \newline\refto{package LODOOPS LinearOrdinaryDifferentialOperatorsOps}",
+ paper = "Muld95.pdf",
+ keywords = "axiomref"
}
@@ 24168,12 +26084,10 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
author = "Naylor, William and Padget, Julian",
title = "From Untyped to Polymorphically Typed Objects in Mathematical
Web Services",
 paper = "NPxx.pdf",
series = "Lecture Notes in Computer Science",
volume = "4108",
pages = "222236",
year = "2006",
 keywords = "axiomref",
abstract =
"OpenMath is a widely recognized approach to the semantic markup of
mathematics that is often used for communication between OpenMath
@@ 24189,7 +26103,9 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
extention of this to the Parser category. In addition, the Aldor
service creation and invocation mechanism are explained. Thus we are
in a position to develop and deploy mathematical web services whose
 descriptions may be directly derived from Aldor's rich type language."
+ descriptions may be directly derived from Aldor's rich type language.",
+ paper = "NPxx.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 24199,8 +26115,6 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
\bibitem[Naylor 95]{N95} Naylor, Bill
title = "Symbolic Interface for an advanced hyperbolic PDE solver",
url = "http://www.sci.csd.uwo.ca/~bill/Papers/symbInterface2.ps",
 paper = "N95.pdf",
 keywords = "axiomref",
abstract = "
An Axiom front end is described, which is used to generate
mathematical objects needed by one of the latest NAG routines, to be
@@ 24213,7 +26127,9 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
the individual mathematical objects, considering the mathematical
theory which is relevant, and some of the problems which have been
encountered and solved during the FORTRAN generation necessary to
 realise the object. Finally we display some of our results."
+ realise the object. Finally we display some of our results.",
+ paper = "N95.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 24223,8 +26139,6 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
\bibitem[Naylor 00b]{ND00} Naylor, W.A.; Davenport, J.H.
title = "A MonteCarlo Extension to a CategoryBased Type System",
url = "http://www.sci.csd.uwo.ca/~bill/Papers/monteCarCat3.ps",
 paper = "ND00.pdf",
 keywords = "axiomref",
abstract = "
The normal claim for mathematics is that all calculations are 100\%
accurate and therefore one calculation can rely completely on the
@@ 24238,7 +26152,9 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
used in the Axiom computer algebra system may be extended to cover
probabilistic algorithms, which use MonteCarlo techniques. We follow
this with a specific example which uses Straight Line Program
 representation."
+ representation.",
+ paper = "ND00.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 24251,8 +26167,6 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
number = "NASACR162690 HC A02/MF A01",
institution = "NASA Jet Propulsion Lab",
url = "http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19800008508.pdf",
 paper = "Ngxx80.pdf",
 keywords = "axiomref",
abstract =
"This is a survey of recent activities that either used or encouraged the
potential use of a combination of symbolic and numerical calculations.
@@ 24267,7 +26181,9 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
finite element calculations and computational complexity. It is contended
that other less obvious topics such as the fast Fourier transform, linear
algebra, nonlinear analysis and error analysis would also benefti from a
 synergistic approach advocated here."
+ synergistic approach advocated here.",
+ paper = "Ngxx80.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 24282,12 +26198,13 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
number = "4",
pages = "346356",
year = "1975",
+ doi = "10.1145/355656.355660",
keywords = "axiomref",
 doi = "10.1145/355656.355660"
+ beebe = "Norman:1975:CFP"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Norman:1975:CFP}
@Article{Norman:1975:CFP,
author = "A. C. Norman",
title = "Computing with Formal Power Series",
@@ 24325,7 +26242,6 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
author = "Norman, Arthur C.",
title = "Notes 13: How to Compute a Groebner Basis",
url = "http://people.math.umass.edu/~norman/462\_11/notes/m462notes13.pdf",
 paper = "Normxx.pdf",
algebra =
"\newline\refto{package AFALGGRO AffineAlgebraicSetComputeWithGroebnerBasis}
\newline\refto{package GBEUCLID EuclideanGroebnerBasisPackage}
@@ 24335,7 +26251,8 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
\newline\refto{package GROEBSOL GroebnerSolve}
\newline\refto{package INTERGB InterfaceGroebnerPackage}
\newline\refto{package LGROBP LinGroebnerPackage}
 \newline\refto{package PGROEB PolyGroebner}"
+ \newline\refto{package PGROEB PolyGroebner}",
+ paper = "Normxx.pdf"
}
\end{chunk}
@@ 24378,16 +26295,16 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
publisher = "ACM Press",
location = "New York, NY",
pages = "113119",
 keywords = "axiomref",
url = "http://opus.bath.ac.uk/16452/1/NormanFitch96a.ps",
 paper = "Norm96.pdf",
abstract =
"We present a software tool which allows us to visualize details of the
use of memory during the execution of an algebra system. We apply this
to gain a better understanding of the behaviour of REDUCE, and hence
to make proposals for ways in which the execution can be improved. The
same tool will soon be used in the performance engineering of a
 version of axiom."
+ version of axiom.",
+ paper = "Norm96.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 24399,8 +26316,6 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
title = "Exploring Cryptography Using the Sage Computer Algebra System",
school = "Victoria University",
year = "2009",
 keywords = "axiomref",
 paper = "Nguy09.pdf",
abstract =
"Cryptography has become indispensable in areas such as ecommerce,
the legal safeguarding of medical records, and secure electronic
@@ 24416,7 +26331,9 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
the computer algebra system Sage. As Sage is free and open source,
students and educators of cryptology need not worry about paying
license fees in order to use Sage, but can instead concentrate on
 exploring cryptography using Sage’s builtin support for cryptography."
+ exploring cryptography using Sage’s builtin support for cryptography.",
+ paper = "Nguy09.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 24436,8 +26353,6 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
isbn = "1595930957",
location = "Beijing, China",
pages = "261268",
 keywords = "axiomref",
 paper = "Oanc05.pdf",
url = "http://www.csd.uwo.ca/~watt/pub/reprints/2005issacalma.pdf",
abstract =
"This paper describes a method to use compiled, strongly typed Aldor
@@ 24454,7 +26369,9 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
nontrivial semantic correspondence. Our solution allows Aldor
functions to run tightly coupled to the Maple environment, able to
directly and efficiently manipulate Maple data objects. We call the
 overall system Alma."
+ overall system Alma.",
+ paper = "Oanc05.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 24480,14 +26397,14 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
number = "12",
pages = "123138",
year = "1996",
 keywords = "axiomref",
abstract =
"A $k$arc in a projective space is a set of points, no three of which
are collinear. The author determines the $k$ arcs in $PG(n,q)$ which
are fixed by primitive groups isomorphic to $A_5$ or $A_6$. The best
known examples are $q+1$ arcs: in general these are normal rational
curves and are conics in $PG(2,q)$ and twisted cubics in $PG(3,q)$.
 The other cases turn out to be 6arcs or 10arcs."
+ The other cases turn out to be 6arcs or 10arcs.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 24503,8 +26420,6 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
pages = "4354",
isbn = "0897913256",
year = "1989",
 keywords = "axiomref",
 paper = "Olli89.pdf",
abstract =
"We investigate different methods for testing whether a rational
mapping $f$ from $k^n$ to $k^m$ admits a rational inverse, or whether
@@ 24520,11 +26435,14 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
We then illustrate our algorithm, with a application to structural
identifiability. The implantation has been done in the IBM computer
 algebra system Scratchpad II."
+ algebra system Scratchpad II.",
+ paper = "Olli89.pdf",
+ keywords = "axiomref",
+ beebe = "Ollivier:1989:IRM"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Ollivier:1989:IRM}
@InProceedings{Ollivier:1989:IRM,
author = "F. Ollivier",
title = "Inversibility of rational mappings and structural
@@ 24573,7 +26491,7 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
Online 72: conference proceedings ... international conference on online
interactive computing, Brunel University, Uxbridge, England, 47 September
1972 ISBN 0903796023 LCCN QA76.55.O54 1972 Two volumes.
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 24581,7 +26499,7 @@ interactive computing, Brunel University, Uxbridge, England, 47 September
\bibitem[OpenMath]{OpenMa}.
title = "OpenMath Technical Overview",
url = "http://www.openmath.org/overview/technical.html",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 24598,7 +26516,6 @@ interactive computing, Brunel University, Uxbridge, England, 47 September
volume = "41",
number = "3",
pages = "114",
 keywords = "axiomref",
abstract =
"Axiom has been in development since 1971. Originally called
Scratchpad II, it was developed by IBM under the direction of Richard
@@ 24621,7 +26538,60 @@ interactive computing, Brunel University, Uxbridge, England, 47 September
This exhibit includes a laptop computer running a recent version
of Axiom, Internet access (if available) to the Axiom Wiki website[4],
 and CDs containing Axiom software for free distribution[5]."
+ and CDs containing Axiom software for free distribution[5].",
+ keywords = "axiomref",
+ beebe = "Page:2007:AOS"
+}
+
+\end{chunk}
+\begin{chunk}{Page:2007:AOS}
+@Article{Page:2007:AOS,
+ author = "William S. Page",
+ title = "{Axiom}: open source computer algebra system",
+ journal = jACMCOMMCOMPALGEBRA,
+ volume = "41",
+ number = "3",
+ pages = "114114",
+ month = sep,
+ year = "2007",
+ CODEN = "????",
+ DOI = "http://doi.acm.org/10.1145/1358190.1358206",
+ ISSN = "19322232 (print), 19322240 (electronic)",
+ ISSNL = "19322232",
+ bibdate = "Wed Jun 18 09:23:01 MDT 2008",
+ bibsource = "http://portal.acm.org/;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "Axiom has been in development since 1971. Originally
+ called Scratchpad II, it was developed by IBM under the
+ direction of Richard Jenks[1]. The project evolved over
+ a period of 20 years as a research platform for
+ developing new ideas in computational mathematics.
+ ScratchPad also attracted the interest and
+ contributions of a large number of mathematicians and
+ computer scientists outside of IBM. In the 1990s, the
+ Scratchpad project was renamed to Axiom, and sold to
+ the Numerical Algorithms Group (NAG) in England who
+ marketed it as a commercial system. NAG withdrew Axiom
+ from the market in October 2001 and agreed to release
+ Axiom as free software, under an open source
+ license.\par
+
+ Tim Daly (a former ScratchPad developer at IBM) setup a
+ pubic open source Axiom project[2] in October 2002 with
+ a primary goal to improve the documentation of Axiom
+ through the extensive use of literate programming[3].
+ The first free open source version of Axiom was
+ released in 2003. Since that time the project has
+ attracted a small but very active group of developers
+ and a growing number of users.\par
+
+ This exhibit includes a laptop computer running a
+ recent version of Axiom, Internet access (if available)
+ to the Axiom Wiki website[4], and CDs containing Axiom
+ software for free distribution[5].",
+ acknowledgement = acknhfb,
+ fjournal = "ACM Communications in Computer Algebra",
+ issue = "161",
}
\end{chunk}
@@ 24649,8 +26619,8 @@ interactive computing, Brunel University, Uxbridge, England, 47 September
Schneider, Carsten and Winkler, Franz",
title = "Hot Topics in Symbolic Computation",
publisher = "Springer",
 paper = "Paulxx.pdf",
 url = "http://www.risc.jku.at/publications/download/risc_3845/chapter1.pdf"
+ url = "http://www.risc.jku.at/publications/download/risc_3845/chapter1.pdf",
+ paper = "Paulxx.pdf"
}
\end{chunk}
@@ 24665,8 +26635,6 @@ interactive computing, Brunel University, Uxbridge, England, 47 September
volume = "10",
number = "1",
year = "1999",
 keywords = "axiomref",
 paper = "Peti99.pdf",
url = "http://www.loria.fr/~petitjea/papers/jmiv99.pdf",
abstract =
"We review the different techniques known for doing exact computations
@@ 24677,7 +26645,9 @@ interactive computing, Brunel University, Uxbridge, England, 47 September
domain of artificial vision, where many constraints boil down to
polynomial systems, are presented. Emphasis is also put on very recent
methods for determining the number of (isolated) real and complex
 roots of such systems."
+ roots of such systems.",
+ paper = "Peti99.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 24687,16 +26657,56 @@ interactive computing, Brunel University, Uxbridge, England, 47 September
\bibitem[Petitot 90]{Pet90} Petitot, Michel
title = "Types r\'ecursifs en scratchpad, application aux polyn\^omes non commutatifs",
LIFL, 1990
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
\index{Petitot, Michel}
\begin{chunk}{ignore}
\bibitem[Petitot 93]{Pet93} Petitot, M.
+\begin{chunk}{axiom.bib}
+@inproceedings{Peti93,
+ author = "Petitot, Michel",
title = "Experience with Axiom",
In Jacob et al. [JOS93], page 240
+ booktitle = "Proc. Int. IMACS Symposium on Symbolic Computation",
+ pages = "240",
+ year = "1993",
keywords = "axiomref",
+ beebe = "Petitot:1993:EA"
+}
+
+\end{chunk}
+\begin{chunk}{Petitot:1993:EA}
+@InProceedings{Petitot:1993:EA,
+ author = "M. Petitot",
+ title = "Experience with {Axiom}",
+ crossref = "Jacob:1993:PSI",
+ pages = "240",
+ month = "",
+ year = "1993",
+ bibdate = "Tue Sep 17 06:35:39 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "The computer algebra system Axiom (formerly
+ Scratchpad) allows a strict typing of the manipulated
+ data. Using examples from noncommutative algebra
+ (polynomials in noncommutative variables, Lie
+ polynomials, Poincar{\'e}BirkoffWitt basis) the
+ authors show the interest and the limits of some
+ essential notions in Axiom: the genericity, the
+ inheritance, the distinction domain/category and the
+ type inference.",
+ acknowledgement = acknhfb,
+ affiliation = "LIFL, Lille I Univ., Villeneuve d'Ascq, France",
+ classification = "C1230 (Artificial intelligence); C4130
+ (Interpolation and function approximation); C7310
+ (Mathematics)",
+ keywords = "Category; Computer algebra system Axiom; Distinction
+ domain; Genericity; Inheritance; Lie polynomials;
+ Manipulated data; Noncommutative algebra;
+ Poincar{\'e}BirkoffWitt basis; Polynomials;
+ Scratchpad; Type inference",
+ language = "English",
+ thesaurus = "Inference mechanisms; Lie algebras; Mathematics
+ computing; Polynomials",
+}
\end{chunk}
@@ 24706,7 +26716,7 @@ In Jacob et al. [JOS93], page 240
Proceedings of the second symposium on Symbolic and
Algebraic Manipulation, March 2325, 1971, Los Angeles, California, ACM Press,
New York, NY 10036, USA, 1971. LCCN QA76.5.S94 1971
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 24716,7 +26726,7 @@ New York, NY 10036, USA, 1971. LCCN QA76.5.S94 1971
title = "Some Primality Testing Algorithms",
Devlin, Keith (ed.)
Computers and Mathematics November 1993, Vol 40, Number 9 pp12031210
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 24725,7 +26735,7 @@ Computers and Mathematics November 1993, Vol 40, Number 9 pp12031210
\bibitem[Poll (b)]{Polxx} Poll, Erik
title = "The type system of Axiom",
paper = "Polxx.pdf",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 24740,7 +26750,6 @@ Computers and Mathematics November 1993, Vol 40, Number 9 pp12031210
year = "2006",
pages = "283340",
isbn = "9783110193237",
 keywords = "axiomref",
abstract =
"This paper addresses polynomial implicit ODEs in an autonomous
context. These ODEs are defined by a system of the form
@@ 24759,7 +26768,8 @@ Computers and Mathematics November 1993, Vol 40, Number 9 pp12031210
together with the notions of the completion of a given ideal and the
algebraic index of the system, defined as the number of steps taken
by the process to stabilize. Over and underdetermined systems are
 also accommodated in their framework."
+ also accommodated in their framework.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 24776,12 +26786,13 @@ Computers and Mathematics November 1993, Vol 40, Number 9 pp12031210
year = "1986",
publisher = "ACM Press",
isbn = "0897911997",
+ doi = "http://dx.doi.org/10.1145/32439.32443",
keywords = "axiomref",
 doi = "http://dx.doi.org/10.1145/32439.32443"
+ beebe = "Purtilo:1986:ASI"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Purtilo:1986:ASI}
@InProceedings{Purtilo:1986:ASI,
author = "J. Purtilo",
editor = "Bruce W. Char",
@@ 24833,7 +26844,6 @@ Computers and Mathematics November 1993, Vol 40, Number 9 pp12031210
number = "6",
pages = "535538",
year = "1999",
 keywords = "axiomref",
abstract =
"For unsteady 2D diffusionconvection problems, we present two classes
of compact difference schemes of order 2 in time and 4 in space. These
@@ 24844,7 +26854,8 @@ Computers and Mathematics November 1993, Vol 40, Number 9 pp12031210
formulation of 2D schemes. Part II by M. Fournié [C. R. Acad. Sci.,
Paris, Sér. I, Math. 328, No. 6, 539542 (1999; reviewed below)]
focuses on the development and analysis of global schemes with the
 assistance of symbolic computation software (AXIOM)."
+ assistance of symbolic computation software (AXIOM).",
+ keywords = "axiomref"
}
\end{chunk}
@@ 24859,7 +26870,6 @@ Computers and Mathematics November 1993, Vol 40, Number 9 pp12031210
number = "34",
pages = "273296",
year = "2009",
 keywords = "axiomref",
abstract =
"We present a FoCaL formalization for quotient structures which are
common in mathematics. We first present a framework for stating
@@ 24872,7 +26882,8 @@ Computers and Mathematics November 1993, Vol 40, Number 9 pp12031210
arithmetic through the certification of quotient groups and quotient
rings which are involved in the model. We finally instantiate our
framework to provide a trusted replacement of the existing FoCaL
 library."
+ library.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 24884,7 +26895,7 @@ Computers and Mathematics November 1993, Vol 40, Number 9 pp12031210
Ph.D. Thesis, Laboratoire d'Informatique Th\'eorique et Programmationg
paper = "Riob03a.ps",
paper = "Riob03a.pdf",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 24893,8 +26904,6 @@ Ph.D. Thesis, Laboratoire d'Informatique Th\'eorique et Programmationg
\bibitem[Rioboo 03]{Riob03} Rioboo, Renaud
title = "Towards Faster Real Algebraic Numbers",
J. of Symbolic Computation 36 pp 513533 (2003)
 paper = "Riob03.pdf",
 keywords = "axiomref",
abstract = "
This paper presents a new encoding scheme for real algebraic number
manipulations which enhances current Axiom's real closure. Algebraic
@@ 24904,7 +26913,9 @@ J. of Symbolic Computation 36 pp 513533 (2003)
relations, to compute the roots and the signs of algebraic
numbers. This allows us to work in the ring of real algebraic integers
instead of the field of read algebraic numbers avoiding many
 denominators."
+ denominators.",
+ paper = "Riob03.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 24921,9 +26932,7 @@ J. of Symbolic Computation 36 pp 513533 (2003)
number = "910",
pages = "10051028",
year = "2003",
 keywords = "axiomref",
url = "ac.elscdn.com/S0895717703001158/1s2.0S0895717703001158main.pdf",
 paper = "Roan03.pdf",
abstract =
"Both Computer Algebra Systems (CASs) and dynamic geometry systems
(DGSs) have reached a high level of development. Some CASs (like Maple
@@ 24946,7 +26955,9 @@ J. of Symbolic Computation 36 pp 513533 (2003)
exploration. Nevertheless, its main interest is to provide a
convenient timesaving way to introduce data when dealing with rule
and compass geometry, which has a wider scope than only educational
 purposes."
+ purposes.",
+ paper = "Roan03.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 24964,9 +26975,7 @@ J. of Symbolic Computation 36 pp 513533 (2003)
number = "6",
pages = "11531176",
year = "2010",
 keywords = "axiomref",
url = "http://nvl.calques3d.org/publications/2010.MatCom.Connecting.pdf",
 paper = "Roan10.pdf",
abstract =
"Many (2D) Dynamic Geometry Systems (DGSs) are able to export numeric
coordinates and equations with numeric coefficients to Computer
@@ 24986,7 +26995,9 @@ J. of Symbolic Computation 36 pp 513533 (2003)
proving in geometry, geometry discovery (hypothesis completion),
geometric loci finding  As far as we know, there is no comparable
``symbolic'' link in the 3D case, except the prototype 3DLD
 (restricted to determining algebraic surfaces as geometric loci)."
+ (restricted to determining algebraic surfaces as geometric loci).",
+ paper = "Roan10.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 25002,7 +27013,6 @@ J. of Symbolic Computation 36 pp 513533 (2003)
number = "3",
pages = "815816",
year = "1999",
 keywords = "axiomref",
abstract =
"By an extensive use of the computer algebra system AXIOM, a power
series expansion with respect to the radial variable $r$ is used to
@@ 25010,8 +27020,8 @@ J. of Symbolic Computation 36 pp 513533 (2003)
the tip of slender conical bodies. The set of coupled nonlinear
differential equations for the coefficient functions, depending on
$\theta$ and $t$, is derived in closed form, and the first and second
 approximation of the coefficient functions are determined
 numerically."
+ approximation of the coefficient functions are determined numerically.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 25027,7 +27037,6 @@ J. of Symbolic Computation 36 pp 513533 (2003)
volume = "43",
number = "4",
pages = "13251336",
 keywords = "axiomref",
abstract =
"This paper deals with the variety of commutative algebras satsifying
the identity
@@ 25037,7 +27046,8 @@ J. of Symbolic Computation 36 pp 513533 (2003)
form. Moreover, if we assume the existence of degenerate trace form,
the $A$ satisfies the identity $((yx)x)x=y((xx)x)$, a generalization
of rightalternativity. Finally we prove that $Ass[A]$ and $N(A)$ are
 ideals in these algebras."
+ ideals in these algebras.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 25048,9 +27058,7 @@ J. of Symbolic Computation 36 pp 513533 (2003)
author = "Robidoux, Nicolas",
title = "Does Axiom Solve Systems of O.D.E's Like Mathematica?",
year = "1993",
 paper = "Robi93.pdf",
url = "http://axiomwiki.newsynthesis.org/public/refs/Robidoux.pdf",
 keywords = "axiomref",
abstract = "
If I were demonstrating Axiom and were asked this question, my reply
would be ``No, but I am not sure that this is a bad thing''. And I
@@ 25063,18 +27071,100 @@ J. of Symbolic Computation 36 pp 513533 (2003)
\frac{dx_2}{dt} & = & x_1  x_2
\end{array}
\]
 This is a very simple system: $x_1$ is actually uncoupled from $x_2$"
+ This is a very simple system: $x_1$ is actually uncoupled from $x_2$",
+ paper = "Robi93.pdf",
+ keywords = "axiomref"
}
\end{chunk}
\index{Roesner, K. G.}
\begin{chunk}{ignore}
\bibitem[Roesner 95]{Roe95} Roesner, K. G.
 title = "Verified solutions for parameters of an exact solution for nonNewtonian liquids using computer algebra",
Zeitschrift fur Angewandte
Mathematik und Physik, 75 (suppl. 2):S435S438, 1995 ISSN 00442267
 keywords = "axiomref",
+\begin{chunk}{axiom.bib}
+@article{Roes95,
+ author = "Roesner, K. G.",
+ title = "Verified solutions for parameters of an exact solution for
+ nonNewtonian liquids using computer algebra",
+ journal = "Zeitschrift fur Angewandte Mathematik und Physik",
+ volume = "75",
+ number = "suppl. 2",
+ pages = "S435S438",
+ year = "1995",
+ abstract =
+ "An exact solution of the time independent velocity field for the
+ TaylorCouette flow of a polymer solution is derived solving the
+ resulting first order ordinary differential equation of fifth degree
+ analytically. Intensive use is made of computer algebra systems AXIOM
+ and MACSYMA to find the exact solution. The coaxial cylinders in the
+ TaylorCouette flow problem are assumed to rotate at different
+ angular velocities. The geometrical and kinematic parameters can be
+ chosen arbitrarily. The model equation for the material law of the
+ viscoelastic liquid is based on the thermodynamic model for dilute
+ solutions due to Lhuillier and Ouibrahim (1980) which is an analogy to
+ the earlier paper of Frankel and Acrivos (1970). In the present
+ investigation the influence of the parameters of the viscoelastic
+ model on the velocity profile in the cylindrical gap is studied and
+ the range of validity of the constitutive equation is investigated.",
+ keywords = "axiomref",
+ beebe = "Roesner:1995:VSP"
+}
+
+\end{chunk}
+\begin{chunk}{Roesner:1995:VSP}
+@Article{Roesner:1995:VSP,
+ author = "K. G. Roesner",
+ title = "Verified solutions for parameters of an exact solution
+ for {nonNewtonian} liquids using computer algebra",
+ journal = jZEITANGEMATHPHYS,
+ volume = "75",
+ number = "suppl. 2",
+ pages = "S435S438",
+ month = "",
+ year = "1995",
+ ISSN = "00442267",
+ bibdate = "Fri Dec 29 12:46:02 MST 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "An exact solution of the time independent velocity
+ field for the TaylorCouette flow of a polymer
+ solution is derived solving the resulting first order
+ ordinary differential equation of fifth degree
+ analytically. Intensive use is made of computer algebra
+ systems AXIOM and MACSYMA to find the exact solution.
+ The coaxial cylinders in the TaylorCouette flow
+ problem are assumed to rotate at different angular
+ velocities. The geometrical and kinematic parameters
+ can be chosen arbitrarily. The model equation for the
+ material law of the viscoelastic liquid is based on the
+ thermodynamic model for dilute solutions due to
+ Lhuillier and Ouibrahim (1980) which is an analogy to
+ the earlier paper of Frankel and Acrivos (1970). In the
+ present investigation the influence of the parameters
+ of the viscoelastic model on the velocity profile in
+ the cylindrical gap is studied and the range of
+ validity of the constitutive equation is
+ investigated.",
+ acknowledgement = acknhfb,
+ affiliation = "Inst. fur Mech., Tech. Hochschule Darmstadt, Germany",
+ classification = "A0210 (Algebra, set theory, and graph theory); A0230
+ (Function theory, analysis); A0270 (Computational
+ techniques); A4710 (General fluid dynamics theory,
+ simulation and other computational methods); A4715
+ (Laminar flows); A4730 (Rotational flow, vortices,
+ buoyancy and other flows involving body forces); A4750
+ (NonNewtonian dynamics)",
+ keywords = "AXIOM; Coaxial cylinders; Computer algebra;
+ Constitutive equation; Cylindrical gap; Dilute
+ solutions; Exact solution; First order ordinary
+ differential equation; Geometrical parameters;
+ Kinematic parameters; MACSYMA; Material law;
+ NonNewtonian liquids; Polymer solution; TaylorCouette
+ flow; Thermodynamic model; Time independent velocity
+ field; Velocity profile; Viscoelastic liquid;
+ Viscoelastic model",
+ language = "English",
+ thesaurus = "Algebra; Couette flow; Differential equations; Flow
+ simulation; NonNewtonian fluids; Physics computing;
+ Polymer solutions; Rotational flow; Thermodynamics",
+}
\end{chunk}
@@ 25093,7 +27183,6 @@ Mathematik und Physik, 75 (suppl. 2):S435S438, 1995 ISSN 00442267
number = "2",
pages = "473495",
year = "2000",
 keywords = "axiomref",
abstract =
"Threecenter nuclear attraction and fourcenter twoelectron
Coulomb integrals over Slatertype orbitals are required for $ab$
@@ 25109,7 +27198,8 @@ Mathematik und Physik, 75 (suppl. 2):S435S438, 1995 ISSN 00442267
semiinfinite oscillatory integrals. The convergence properties of
the new methods are analyzed. The numerical results section shows
the high predetermined accuracy and the substantial gain in the
 calculation times obtained using the new methods."
+ calculation times obtained using the new methods.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 25126,14 +27216,14 @@ Mathematik und Physik, 75 (suppl. 2):S435S438, 1995 ISSN 00442267
number = "3",
pages = "213232",
year = "2001",
 keywords = "axiomref",
abstract =
"The $B$ function is a product of a spherical $K$ Bessel function and
a spherical harmonic. The integrals to be evaluated contain
complicated expressions of finite hypergeometric functions and
spherical $J$ Bessel functions. Sequence transformation techniques are
used for the numerical evaluation of the integrals. Numerical examples
 illustrate the accuracy and the efficiency of the method."
+ illustrate the accuracy and the efficiency of the method.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 25169,9 +27259,7 @@ Mathematik und Physik, 75 (suppl. 2):S435S438, 1995 ISSN 00442267
type = "technical report",
number = "114",
year = "1989",
 paper = "Salv89.pdf",
comment = "SIGSAM Bulletin Vol 25 No 2 1991 pp417",
 keywords = "axiomref",
abstract =
"We describe the current state of a Maple library, gdev, designed to
perform asymptotic expansions for a large class of expressions. Many
@@ 25179,11 +27267,14 @@ Mathematik und Physik, 75 (suppl. 2):S435S438, 1995 ISSN 00442267
principles. At the time when this report is written, a striking
feature of these examples is that none of them can be computed
directly with any of today's most widespread symbolic computation
 systems (Macsyma, Mathematica, Maple or Scratchpad II)."
+ systems (Macsyma, Mathematica, Maple or Scratchpad II).",
+ paper = "Salv89.pdf",
+ keywords = "axiomref",
+ beebe = "Salvy:1989:EAA"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Salvy:1989:EAA}
@TechReport{Salvy:1989:EAA,
author = "B. Salvy",
title = "Examples of automatic asymptotic expansions",
@@ 25217,13 +27308,63 @@ Mathematik und Physik, 75 (suppl. 2):S435S438, 1995 ISSN 00442267
\end{chunk}
\index{Salvy, Bruno}
\begin{chunk}{ignore}
\bibitem[Salvy 91]{Sal91} Salvy, B.
+\begin{chunk}{axiom.bib}
+@article{Salv91,
+ author = "Salvy, Bruno",
title = "Examples of automatic asymptotic expansions",
SIGSAM Bulletin (ACM Special Interest Group on Symbolic and
Algebraic Manipulation), 25(2) pp417
April 1991 CODEN SIGSBZ ISSN 01635824
+ journal = "SIGSAM Bulletin",
+ volume = "25",
+ number = "2",
+ pages = "417",
+ year = "1991",
+ abstract =
+ "We describe the current state of a Maple library, gdev, designed to
+ perform asymptotic expansions for a large class of expressions. Many
+ examples are provided, along with a short sketch of the underlying
+ principles. At the time when this report is written, a striking
+ feature of these examples is that none of them can be computed
+ directly with any of today's most widespread symbolic computation
+ systems (Macsyma, Mathematica, Maple or Scratchpad II).",
keywords = "axiomref",
+ beebe = "Salvy:1991:EAA"
+}
+
+\end{chunk}
+\begin{chunk}{Salvy:1991:EAA}
+@Article{Salvy:1991:EAA,
+ author = "B. Salvy",
+ title = "Examples of automatic asymptotic expansions",
+ journal = jSIGSAM,
+ volume = "25",
+ number = "2",
+ pages = "417",
+ month = apr,
+ year = "1991",
+ CODEN = "SIGSBZ",
+ ISSN = "01635824 (print), 15579492 (electronic)",
+ ISSNL = "01635824",
+ bibdate = "Tue Sep 17 06:44:07 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "Describes the current state of a Maple library, gdev,
+ designed to perform asymptotic expansions for a large
+ class of expressions. Many examples are provided, along
+ with a short sketch of the underlying principles. At
+ the time when this report is written, a striking
+ feature of these examples is that none of them can be
+ computed directly with any of today's most widespread
+ symbolic computation systems (Macsyma, Mathematica,
+ Maple or Scratchpad II).",
+ acknowledgement = acknhfb,
+ affiliation = "LIX, Ecole Polytech., Palaiseau, France",
+ classification = "C6130 (Data handling techniques); C7310
+ (Mathematics)",
+ fjournal = "SIGSAM Bulletin",
+ keywords = "Automatic asymptotic expansions; Expressions; Gdev;
+ Maple library; Symbolic computation systems",
+ language = "English",
+ pubcountry = "USA",
+ thesaurus = "Symbol manipulation",
+}
\end{chunk}
@@ 25237,8 +27378,6 @@ April 1991 CODEN SIGSBZ ISSN 01635824
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
@@ 25255,7 +27394,9 @@ April 1991 CODEN SIGSBZ ISSN 01635824
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."
+ more constructs and increase its flexibility.",
+ paper = "Sant95.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 25265,11 +27406,11 @@ April 1991 CODEN SIGSBZ ISSN 01635824
@inproceedings{Sant96,
author = "Santas, Philip S.",
title = "Conditional Categories and Domains",
 keywords = "axiomref",
booktitle = "Proc. DISCO 1996",
year = "1996",
pages = "112125",
 isbn = "3540616977"
+ isbn = "3540616977",
+ keywords = "axiomref"
}
\end{chunk}
@@ 25279,7 +27420,6 @@ April 1991 CODEN SIGSBZ ISSN 01635824
@book{Sant05,
author = "Santas, Philip S.",
title = "Conditional Categories and Domains",
 keywords = "axiomref",
booktitle = "Design and Implementation of Symbolic Computation Systems",
year = "2005",
series = "Lecture Notes in Computer Science",
@@ 25294,7 +27434,8 @@ April 1991 CODEN SIGSBZ ISSN 01635824
properties. Examples inspired by the Axiom library illustrate the
power of our apprach and its application in constructing algebraic
concepts. The full calculus has been implemented and tested with our
 LA compiler which generated executable files."
+ LA compiler which generated executable files.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 25318,8 +27459,8 @@ April 1991 CODEN SIGSBZ ISSN 01635824
acmid = "1089237",
publisher = "ACM",
address = "New York, NY, USA",
 keywords = "axiomref,survey",
paper = "Saun80.pdf",
+ keywords = "axiomref,survey"
}
\end{chunk}
@@ 25333,7 +27474,6 @@ April 1991 CODEN SIGSBZ ISSN 01635824
comment = "Darstellungen des algebraischen Abschlusses endlicher Korper
und spurkompatible Polynomfolgen",
year = "1993",
 keywords = "axiomref",
abstract =
"For numerical experiments concerning various problems in a finite
field $\mathbb{F}_q$ it is useful to have an explicit data
@@ 25373,7 +27513,8 @@ April 1991 CODEN SIGSBZ ISSN 01635824
tracecompatible polynomials of degree $n$, where $n \le 100$, and
$q=2,3,5,7,11,13$. For implementation, the computeralgebra system
AXIOM has been used. The details contained in this dissertation are
 not readily describable in a short review."
+ not readily describable in a short review.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 25384,7 +27525,7 @@ April 1991 CODEN SIGSBZ ISSN 01635824
title = "Implementing des CartanKuranishiTheorems in AXIOM",
Master's diploma thesis (in german), Institut f\"ur Algorithmen und
Kognitive Systeme, Universit\"t Karlsruhe 1992
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 25412,7 +27553,6 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
year = "1988",
pages = "167176",
isbn = "3540189289",
 keywords = "axiomref",
abstract =
"The main problem which occurs in developing Computer Algebra packages
for special areas in mathematics is the complexity. The unique concept
@@ 25422,11 +27562,13 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
program. After introducing the relevant concepts from software
engineering they are elaborated by means of the symmetry analysis of
differential equations and the Scratchpad package SPDE which
 abbreviates Symmetries of Partial Differential Equations."
+ abbreviates Symmetries of Partial Differential Equations.",
+ keywords = "axiomref",
+ beebe = "Schwarz:1988:PAD"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Schwarz:1988:PAD}
@InCollection{Schwarz:1988:PAD,
author = "F. Schwarz",
title = "Programming with abstract data types: the symmetry
@@ 25451,8 +27593,6 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
isbn = "0897913256",
year = "1989",
pages = "1725",
 keywords = "axiomref",
 paper = "Schw89.pdf",
abstract =
"The reducibility and factorization of linear homogeneous differential
equations are of great theoretical and practical importance in
@@ 25467,10 +27607,13 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
equations with rotational coefficients. Applying these results, the
design of the factorization algorithm LODEF and its implementation in
the Scratchpad II Computer Algebra System is described.",
+ paper = "Schw89.pdf",
+ keywords = "axiomref",
+ beebe = "Schwarz:1989:FAL"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Schwarz:1989:FAL}
@InProceedings{Schwarz:1989:FAL,
author = "F. Schwarz",
title = "A factorization algorithm for linear ordinary
@@ 25524,7 +27667,6 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
volume = "25",
number = "1",
pages = "1023",
 keywords = "axiomref",
abstract =
"Let there be given a set of monomials in n variables and some order
relations between them. The following {\sl fundamental problem of
@@ 25535,11 +27677,13 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
called {\sl cotes} which establishes the desired ordering
relations. The main area of application of this algorithm, i.e. the
construction of Groebner bases for different orderings and of
 universal Groebner bases is treated in the last section."
+ universal Groebner bases is treated in the last section.",
+ keywords = "axiomref",
+ beebe = "Schwarz:1991:MOG"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Schwarz:1991:MOG}
@Article{Schwarz:1991:MOG,
author = "F. Schwarz",
title = "Monomial orderings and {Gr{\"o}bner} bases",
@@ 25595,8 +27739,6 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
isbn = "9812380485",
location = "Beijing China",
pages = "486500",
 keywords = "axiomref",
 paper = "Schw02.pdf",
url =
"http://www.scai.fraunhofer.de/content/dam/scai/de/documents/MitarbeiterinnenundMitarbeiter/ICMS2002.pdf",
abstract =
@@ 25613,7 +27755,9 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
particularly supported due to a special portion of the language
dedicated to manipulating typed objects, i.e. for performing
userdefined or automatic type coercions. Type inquiries are also
 included in the language."
+ included in the language.",
+ paper = "Schw02.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 25628,7 +27772,6 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
publisher = "SpringerVerlag",
pages = "67117",
series = "CISM Courses Lecture 343",
 keywords = "axiomref",
abstract =
"The central subject of this article are two basic questions: How to
make the process of developing computer algebra software on a large
@@ 25642,7 +27785,8 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
additional abstraction level between the mathematics and the machine
in order to render it possible to develop (computer algebra) system
independent mathematical software. Basic constituents of this level
 are a type system and a highlevel language."
+ are a type system and a highlevel language.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 25653,8 +27797,6 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
title = "Analysis and Application of the Formal Theory of Partial Differential Equations",
PhD thesis, School of Physics and Materials, Lancaster University (1994)
url = "http://www.mathematik.unikassel.de/~seiler/Papers/Diss/diss.ps.gz",
 paper = "Sei94.pdf",
 keywords = "axiomref",
abstract = "
An introduction to the formal theory of partial differential equations
is given emphasizing the properties of involutive symbols and
@@ 25673,16 +27815,74 @@ PhD thesis, School of Physics and Materials, Lancaster University (1994)
geometric approaches to differential equations has been developed in
the computer algebra system Axiom. The appendices contain among others
brief introductions into CartenK{\"a}hler Theory and JanetRiquier
 Theory."
+ Theory.",
+ paper = "Sei94.pdf",
+ keywords = "axiomref"
\end{chunk}
\index{Seiler, Werner Markus}
\begin{chunk}{ignore}
\bibitem[Seiler 94a]{Sei94a} Seiler, W.M.
+\begin{chunk}{axiom.bib}
+@inproceedings{Seil94a,
+ author = "Seiler, Werner Markus",
title = "Completion to involution in AXIOM",
in Calmet [Cal94] pp103104
 keywords = "axiomref",
+ booktitle = "Proc. Rhine Workshop on Computer Algebra",
+ year = "1994",
+ pages = "103104",
+ abstract =
+ "We have implemented an algorithm to complete a given system of
+ partial differential equations to an involutive one in the computer
+ algebra system AXIOM. An earlier version of this program has been
+ described in Schu, Seiler, and Calmet (1992). The new version is much
+ more efficient due to better simplification and many new features. It
+ also provides procedures for the analysis of the arbitrariness of the
+ general solution. The goal of the implementation was not to transform
+ simply an algorithm into a program but to start with the construction
+ of an environment for symbolic computations within the geometric
+ theory of differential equations. The modular structure allows an easy
+ extension e.g. by a package for the symmetry analysis.",
+ keywords = "axiomref",
+ beebe = "Seiler:1994:CIA"
+}
+
+\end{chunk}
+\begin{chunk}{Seiler:1994:CIA}
+@InProceedings{Seiler:1994:CIA,
+ author = "W. M. Seiler",
+ title = "Completion to involution in {AXIOM}",
+ crossref = "Calmet:1994:RWC",
+ pages = "103104",
+ month = "",
+ year = "1994",
+ bibdate = "Tue Sep 17 06:32:41 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "We have implemented an algorithm to complete a given
+ system of partial differential equations to an
+ involutive one in the computer algebra system AXIOM. An
+ earlier version of this program has been described in
+ Schu, Seiler, and Calmet (1992). The new version is
+ much more efficient due to better simplification and
+ many new features. It also provides procedures for the
+ analysis of the arbitrariness of the general solution.
+ The goal of the implementation was not to transform
+ simply an algorithm into a program but to start with
+ the construction of an environment for symbolic
+ computations within the geometric theory of
+ differential equations. The modular structure allows an
+ easy extension e.g. by a package for the symmetry
+ analysis.",
+ acknowledgement = acknhfb,
+ affiliation = "Inst. fur Algorithmen und Kognitive Syst., Karlsruhe
+ Univ., Germany",
+ classification = "C4170 (Differential equations); C7310 (Mathematics
+ computing)",
+ keywords = "AXIOM; Computer algebra system; Involution; Partial
+ differential equations; Symbolic computations; Symmetry
+ analysis",
+ language = "English",
+ thesaurus = "Mathematics computing; Partial differential equations;
+ Symbol manipulation",
+}
\end{chunk}
@@ 25696,13 +27896,54 @@ in Calmet [Cal94] pp103104
number = "2",
pages = "329340",
year = "1994",
 paper = "Seil94b.pdf",
 keywords = "axiomref",
abstract =
"An implementation of the algebra of pseudo differential operators in
the computer algebra system Axiom is described. In several exmaples
the application of the package to typical computations in the theory
 of integrable systems is demonstrated."
+ of integrable systems is demonstrated.",
+ paper = "Seil94b.pdf",
+ keywords = "axiomref",
+ beebe = "Seiler:1994:PDO"
+}
+
+\end{chunk}
+\begin{chunk}{Seiler:1994:PDO}
+@Article{Seiler:1994:PDO,
+ author = "Werner M. Seiler",
+ title = "Pseudo differential operators and integrable systems
+ in {AXIOM}",
+ journal = jCOMPPHYSCOMM,
+ volume = "79",
+ number = "2",
+ pages = "329340",
+ month = apr,
+ year = "1994",
+ CODEN = "CPHCBZ",
+ DOI = "http://dx.doi.org/10.1016/00104655(94)900760",
+ ISSN = "00104655 (print), 18792944 (electronic)",
+ ISSNL = "00104655",
+ bibdate = "Mon Feb 13 21:29:43 MST 2012",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib;
+ http://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib",
+ URL = "http://www.sciencedirect.com/science/article/pii/0010465594900760",
+ abstract = "An implementation of the algebra of pseudo
+ differential operators in the computer algebra system
+ AXIOM is described. In several examples the application
+ of the package to typical computations in the theory of
+ integrable systems is demonstrated.",
+ acknowledgement = acknhfb,
+ affiliation = "Inst. fur Algorithmen und Kognitive Syst., Karlsruhe
+ Univ., Germany",
+ classification = "C4170 (Differential equations); C7310
+ (Mathematics)",
+ fjournal = "Computer Physics Communications",
+ journalURL = "http://www.sciencedirect.com/science/journal/00104655",
+ keywords = "AXIOM; Computer algebra; PDO; Pseudo differential
+ operators",
+ language = "English",
+ pubcountry = "Netherlands",
+ thesaurus = "Mathematics computing; Partial differential equations;
+ Symbol manipulation",
}
\end{chunk}
@@ 25717,8 +27958,6 @@ in Calmet [Cal94] pp103104
type = "Internal Report",
number = "9517",
url = "http://axiomwiki.newsynthesis.org/public/refs/Axiompdf.pdf",
 paper = "Seil95.pdf",
 keywords = "axiomref",
abstract =
"We present an Axiom environment called JET for geometric computations
with partial differential equations within the framework of the jet
@@ 25728,7 +27967,9 @@ in Calmet [Cal94] pp103104
for the generators of classical and nonclassical Lie
symmetries. Details of the implementations are described and
applications are given. An appendix contains tables of all exported
 functions."
+ functions.",
+ paper = "Seil95.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 25740,9 +27981,7 @@ in Calmet [Cal94] pp103104
author = "Seiler, Werner Markus and Calmet, J.",
title = "JET  An Axiom Environment for Geometric Computations with
Differential Equations",
 paper = "Seil95a.pdf",
url = "http://axiomwiki.newsynthesis.org/public/refs/axiomjet95.pdf",
 keywords = "axiomref",
abstract =
"JET is an environment within the computer algebra system Axiom to
perform such computations. The current implementation emphasises the
@@ 25750,7 +27989,9 @@ in Calmet [Cal94] pp103104
for the completion of a given system of differential equations to an
equivalent involutive one based on the CartanKuranishi theorem and
for setting up the determining equations for classical and
 nonclassical point symmetries."
+ nonclassical point symmetries.",
+ paper = "Seil95a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 25766,14 +28007,14 @@ in Calmet [Cal94] pp103104
year = "1997",
url =
"http://www.mathematik.unikassel.di/~seiler/Papers/Postscript/CADERep.ps.gz",
 keywords = "axiomref",
 paper = "Seil97.pdf",
abstract =
"We present an informal overview of a number of approaches to
differential equations which are popular in computer algebra. This
includes symmetry and completion theory, local analysis, differential
ideal and Galois theory, dynamical systems and numerical analysis. A
 large bibliography is provided."
+ large bibliography is provided.",
+ paper = "Seil97.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 25783,9 +28024,7 @@ in Calmet [Cal94] pp103104
@article{Seil99,
author = "Seiler, Werner Markus",
title = "DETools: A Library for Differential Equations",
 paper = "Seil99.pdf",
year = "1999",
 keywords = "axiomref",
abstract =
"This article tries to give at least a brief introduction. The MuPAD
library is extended on two levels. The first one consists of a new
@@ 25796,7 +28035,9 @@ in Calmet [Cal94] pp103104
routines for solving some classes of partial differential
equations. The use of this new library will be described in this
article. The second level is somewhat more advanced and requires a
 certain familiarity with the objectoriented domains."
+ certain familiarity with the objectoriented domains.",
+ paper = "Seil99.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 25814,11 +28055,12 @@ in Calmet [Cal94] pp103104
institution = "TIM 3 (IMAG)",
address = "Grenoble, France",
year = "1987",
 keywords = "axiomref"
+ keywords = "axiomref",
+ beebe = "Senechaud:1987:SIP"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Senechaud:1987:SIP}
@TechReport{Senechaud:1987:SIP,
author = "P. Senechaud and F. Siebert and G. Villard",
title = "Scratchpad {II}: Pr{\'e}sentation d'un nouveau langage
@@ 25866,7 +28108,6 @@ in Calmet [Cal94] pp103104
number = "23",
pages = "267273",
year = "1988",
 keywords = "axiomref",
abstract =
"This paper presents a simple algorithm, based on Groebner bases, to
test if a given polynomial $g$ of $k(X_1,\ldots,X_n)$ lies in
@@ 25884,11 +28125,13 @@ in Calmet [Cal94] pp103104
$k(f_1,\ldots,f_m)=k(X_1,\ldots,X_n). Existing computer algebra
systems, such as IBM's SCRATCHPAD II, have Groebner basis packages
which allow the user to specify a term ordering sufficient to carry
 out the algorithm."
+ out the algorithm.",
+ keywords = "axiomref",
+ beebe = "Shannon:1988:UGB"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Shannon:1988:UGB}
@Article{Shannon:1988:UGB,
author = "D. Shannon and M. Sweedler",
title = "Using {Gr{\"o}bner} bases to determine algebra
@@ 25976,8 +28219,6 @@ in Calmet [Cal94] pp103104
number = "1",
pages = "936",
year = "1993",
 keywords = "axiomref",
 paper = "Sing93.pdf",
abstract =
"The authors discuss the first problem of Galois theory of differential
equations. Let $F$ be an ordinary (for simplicity) differential field
@@ 25989,7 +28230,9 @@ in Calmet [Cal94] pp103104
to give simple necessary and sufficient conditions for a second order
linear differential equation to have Liouvillian solutions and for a
third order linear differential equation to have Liouvillian solutions
 or to be solvable in terms of second order equations."
+ or to be solvable in terms of second order equations.",
+ paper = "Sing93.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 26006,8 +28249,6 @@ in Calmet [Cal94] pp103104
number = "1",
pages = "3773",
year = "1993",
 paper = "Sing93a.pdf",
 keywords = "axiomref",
abstract =
"Let $F$ be an ordinary differential field of characteristic 0 and
$L \in F $ be a linear homogeneous polynomial. How can one find the
@@ 26026,7 +28267,9 @@ in Calmet [Cal94] pp103104
$L(y)$ is algebraic. They show that one can compute the minimal
polynomial $P(y) \in F[y]$ of $u$. We note that the authors
essentially used the tools of representation theory, invariant theory
 and computer algebra."
+ and computer algebra.",
+ paper = "Sing93a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 26043,7 +28286,6 @@ in Calmet [Cal94] pp103104
year = "1988",
isbn = "3540510834",
pages = "386395",
 keywords = "axiomref",
abstract =
"In this article, a brief exposition of a method for finding first
integrals for first order multinomial autonomous systems (FOMAS) of
@@ 26113,11 +28355,13 @@ in Calmet [Cal94] pp103104
schemes is a combinatorial problem unrelated, in a sense, to
FOMAS. When the first integral is a polynomial, the additioin scheme
is trivial to compute. We shall now begin by explaining some details
 of this theory."
+ of this theory.",
+ keywords = "axiomref",
+ beebe = "Sit:1989:GAS"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Sit:1989:GAS}
@InProceedings{Sit:1989:GAS,
author = "W. Y. Sit",
title = "On {Goldman}'s algorithm for solving firstorder
@@ 26155,16 +28399,17 @@ in Calmet [Cal94] pp103104
\end{chunk}
\index{Sit, William Y.}
\begin{chunk}{ignore}
\bibitem[Sit 92]{Sit92} Sit, W.Y.
+\begin{chunk}{axiom.bib}
+@article{Sitx92,
+ author = "Sit, William Y.",
title = "An algorithm for solving parametric linear systems",
Journal of Symbolic Computations, 13(4) pp353394, April 1992 CODEN JSYCEH
ISSN 07477171
 url = "http://www.sciencedirect.com/science/article/pii/S0747717108801046/pdf?md5=00aa65e18e6ea5c4a008c8dfdfcd4b83&pid=1s2.0S0747717108801046main.pdf",
 paper = "Sit92.pdf",
 keywords = "axiomref",
 abstract = "
 We present a theoretical foundation for studying parametric systesm of
+ journal = "Journal of Symbolic Computations",
+ volume = "13",
+ number = "4",
+ pages = "353394",
+ year = "1992",
+ abstract =
+ "We present a theoretical foundation for studying parametric systesm of
linear equations and prove an efficient algorithm for identifying all
parametric values (including degnerate cases) for which the system is
consistent. The algorithm gives a small set of regimes where for each
@@ 26175,7 +28420,59 @@ ISSN 07477171
emphasis on simplification of results. Examples are given based on a
close implementation of the algorithm in SCRATCHPAD II. We also give a
complexity analysis of the Gaussian elimination method and compare
 that with our algorithm."
+ that with our algorithm.",
+ paper = "Sitx92.pdf",
+ keywords = "axiomref",
+ beebe = "Sit:1992:ASP"
+}
+
+\end{chunk}
+\begin{chunk}{Sit:1992:ASP}
+@Article{Sit:1992:ASP,
+ author = "W. Y. Sit",
+ title = "An algorithm for solving parametric linear systems",
+ journal = jJSYMBOLICCOMP,
+ volume = "13",
+ number = "4",
+ pages = "353394",
+ month = apr,
+ year = "1992",
+ CODEN = "JSYCEH",
+ ISSN = "07477171 (print), 1095855X (electronic)",
+ ISSNL = "07477171",
+ bibdate = "Tue Sep 17 06:41:20 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "The author presents a theoretical foundation for
+ studying parametric systems of linear equations and
+ proves an efficient algorithm for identifying all
+ parametric values (including degenerate cases) for
+ which the system is consistent. The algorithm gives a
+ small set of regimes where for each regime, the
+ solutions of the specialized systems may be given
+ uniformly. For homogeneous linear systems, or for
+ systems where the right hand side is arbitrary, this
+ small set is irredundant. He discusses in detail
+ practical issues concerning implementations, with
+ particular emphasis on simplification of results.
+ Examples are given based on a close implementation of
+ the algorithm in SCRATCHPAD II. He also gives a
+ complexity analysis of the Gaussian elimination method
+ and compares that with the algorithm.",
+ acknowledgement = acknhfb,
+ affiliation = "Dept. of Math., City Coll. of New York, NY, USA",
+ classification = "B0290H (Linear algebra); C4140 (Linear algebra);
+ C4240 (Programming and algorithm theory); C7310
+ (Mathematics)",
+ fjournal = "Journal of Symbolic Computation",
+ journalURL = "http://www.sciencedirect.com/science/journal/07477171",
+ keywords = "Complexity analysis; Efficient algorithm; Gaussian
+ elimination method; Linear equations; Parametric linear
+ systems; SCRATCHPAD II",
+ language = "English",
+ pubcountry = "UK",
+ thesaurus = "Computational complexity; Matrix algebra; Symbol
+ manipulation",
+}
\end{chunk}
@@ 26184,20 +28481,52 @@ ISSN 07477171
\bibitem[Sit 06]{Sit06} Sit, Emil
title = "Tools for Repeatable Research",
url = "http://www.emilsit.net/blog/archives/toolsforrepeatableresearch",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
\index{Smedley, Trevor J.}
\begin{chunk}{ignore}
\bibitem[Smedley 92]{Sme92} Smedley, Trevor J.
 title = "Using pictorial and object oriented programming for computer algebra",
In Hal Berghel et al., editors. Applied computing 
technologicial challenges of the 199s: proceedings of the 1992 ACM/SIGAPP
Symposium on Applied Computing, Kansas City Convention Center, March 13, 1992
pp12431247. ACM Press, New York, NY 10036, USA, 1992. ISBN 089791502X
LCCN QA76.76.A65 S95 1992
+\begin{chunk}{axiom.bib}
+@inproceedings{Smed92,
+ author = "Smedley, Trevor J.",
+ title = "Using pictorial and object oriented programming for computer
+ algebra",
+ booktitle = "Applied computing  technological challenges of the
+ 1990's: proceedings of the 1992 ACM\slash SIGAPP
+ Symposium on Applied Computing, Kansas City Convention
+ Center, March 13, 1992",
+ publisher = "ACM Press",
+ pages = "12431247",
+ isbn = "089791502X",
keywords = "axiomref",
+ beebe = "Smedley:1992:UPO"
+}
+
+\end{chunk}
+\begin{chunk}{Smedley:1992:UPO}
+@InProceedings{Smedley:1992:UPO,
+ author = "Trevor J. Smedley",
+ editor = "Hal Berghel and others",
+ booktitle = "Applied computing  technological challenges of the
+ 1990's: proceedings of the 1992 ACM\slash SIGAPP
+ Symposium on Applied Computing, Kansas City Convention
+ Center, March 13, 1992",
+ title = "Using pictorial and object oriented programming for
+ computer algebra",
+ publisher = pubACM,
+ address = pubACM:adr,
+ pages = "12431247",
+ year = "1992",
+ DOI = "http://dx.doi.org/10.1145.130154",
+ ISBN = "089791502X",
+ ISBN13 = "9780897915021",
+ LCCN = "QA76.76.A65 S95 1992",
+ bibdate = "Thu Jul 26 09:02:03 2001",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ bookpages = "xiii + 1257 (2 volumes)",
+ keywords = "Scratchpad",
+}
\end{chunk}
@@ 26211,13 +28540,13 @@ LCCN QA76.76.A65 S95 1992
number = "2",
pages = "273280",
year = "1993",
 keywords = "axiomref",
abstract =
"There are a variety of theorems in group theory which admit of proofs
by machine. This talk illustrates these techniques in action. Examples
are given of this phenomenon, drawn from the theory of group
presentations, and from the theory of $p$groups. The systems involved
 include AXIOM, CAYLEY and QUOTPIC"
+ include AXIOM, CAYLEY and QUOTPIC",
+ keywords = "axiomref"
}
\end{chunk}
@@ 26233,9 +28562,7 @@ LCCN QA76.76.A65 S95 1992
series = "ISSAC 2007",
year = "2007",
pages = "347354",
 keywords = "axiomref",
isbn = "9781595937438",
 paper = "Smit07.pdf",
keywords = "axiomref",
abstract = "
This paper describes the design and implementation of an algorithmic
@@ 26249,7 +28576,43 @@ LCCN QA76.76.A65 S95 1992
the exact requirements for when a program can be algorithmically
differentiated. This leads to a general algorithmic differentiation
system, and is not confined to functions which compute with basic
 data types, such as floating point numbers."
+ data types, such as floating point numbers.",
+ paper = "Smit07.pdf",
+ keywords = "axiomref",
+ beebe = "Smith:2007:ADA"
+}
+
+\end{chunk}
+\begin{chunk}{Smith:2007:ADA}
+@InProceedings{Smith:2007:ADA,
+ author = "Jacob Smith and Gabriel {Dos Reis} and Jaakko
+ J{\"a}rvi",
+ title = "Algorithmic differentiation in {Axiom}",
+ crossref = "Brown:2007:PIS",
+ pages = "347354",
+ year = "2007",
+ DOI = "http://doi.acm.org/10.1145/1277548.1277595",
+ bibdate = "Fri Jun 20 08:46:50 MDT 2008",
+ bibsource = "http://portal.acm.org/;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "This paper describes the design and implementation of
+ an algorithmic differentiation framework in the Axiom
+ computer algebra system. Our implementation works by
+ transformations on Spad programs at the level of the
+ typed abstract syntax tree  Spad is the language for
+ extending Axiom with libraries. The framework
+ illustrates an algebraic theory of algorithmic
+ differentiation, here only for Spad programs, but we
+ suggest that the theory is general. In particular, if
+ it is possible to define a compositional semantics for
+ programs, we define the exact requirements for when a
+ program can be algorithmically differentiated. This
+ leads to a general algorithmic differentiation system,
+ and is not confined to functions which compute with
+ basic data types, such as floating point numbers.",
+ acknowledgement = acknhfb,
+ keywords = "algorithmic differentiation; axiom; program
+ transformation; symbolicnumeric computation",
}
\end{chunk}
@@ 26265,9 +28628,7 @@ LCCN QA76.76.A65 S95 1992
number = "4",
pages = "795825",
year = "2011",
 keywords = "axiomref",
url = "https://arxiv.org/pdf/1102.1323.pdf",
 paper = "Spit11.pdf",
abstract =
"The introduction of firstclass type classes in the Coq system calls
for a reexamination of the basic interfaces used for mathematical
@@ 26295,7 +28656,9 @@ LCCN QA76.76.A65 S95 1992
Algebra thrives on the interplay between syntax and semantics. The
Prologlike abilities of type class instance resolution allow us to
conveniently define a quote function, thus facilitating the use of
 reflective techniques."
+ reflective techniques.",
+ paper = "Spit11.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 26315,8 +28678,6 @@ LCCN QA76.76.A65 S95 1992
publisher = "Kluwer",
url =
"http://www.iks.kti.edu/fileadmin/User/calmet/papers/Acireale93.ps.gz",
 keywords = "axiomref",
 paper = "Schu92.pdf",
abstract =
"The authors recall the concepts of involutive nonlinear systems of
partial differential equations, the classical CartanRiquierJanet
@@ 26325,7 +28686,9 @@ LCCN QA76.76.A65 S95 1992
clearly outlined, the arising computational problems are discussed,
experience with implementation in the computer algebra system AXIOM
(1992) is described, and comparison with Maple and REDUCE algorithms
 is made."
+ is made.",
+ paper = "Schu92.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 26439,7 +28802,7 @@ LCCN QA76.76.A65 S95 1992
\bibitem[Steele]{Steele} Steele, Guy L.; Gabriel, Richard P.
title = "The Evolution of Lisp",
url = "http://www.dreamsongs.com/Files/HOPL2Uncut.pdf",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 26448,7 +28811,7 @@ LCCN QA76.76.A65 S95 1992
\bibitem[Sage 14]{Sage14} Stein, William
title = "Sage",
url = "http://www.sagemath.org/doc/reference/interfaces/sage/interfaces/axiom.html",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 26474,9 +28837,7 @@ LCCN QA76.76.A65 S95 1992
number = "3",
pages = "271284",
year = "1995",
 keywords = "axiomref",
url = "https://cage.ugent.be/~hvm/artikels/44.pdf",
 paper = "Stor95.pdf",
abstract =
"A $k$cap $K$ on $PG(n,q)$ is a set of $k$ points, no three of which
are collinear. $K$ is complete if it cannot be extended to a $k+1$
@@ 26494,7 +28855,9 @@ LCCN QA76.76.A65 S95 1992
that there exist cyclic $k$caps stabilized by a transitive cyclic
group $G$ fixed precisely one point and one plane of
$PG(3,q)$. Concrete examples of such caps, found using AXIOM and
 CAYLEY, are presented."
+ CAYLEY, are presented.",
+ paper = "Stor95.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 26508,7 +28871,6 @@ LCCN QA76.76.A65 S95 1992
mathematicians, engineers and econometricians",
year = "1999",
publisher = "Birkhauser",
 keywords = "axiomref",
abstract =
"During the past decade, the mathematical computer software packages
such as Mathematica, Maple, MATLAB (Axiom, Derive, Macsyma, MuPad are
@@ 26563,7 +28925,8 @@ LCCN QA76.76.A65 S95 1992
and it could probably be used along, without the bulky technical
documentation of the Maple language. Note that Maple has a
comprehensive online help program, which contains large parts of the
 original documentation."
+ original documentation.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 26579,11 +28942,12 @@ LCCN QA76.76.A65 S95 1992
pages = "3233",
year = "1985",
isbn = "0387159835 (vol. 1),0387159843 (vol. 2)",
 keywords = "axiomref"
+ keywords = "axiomref",
+ beebe = "Sutor:1985:SIC"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Sutor:1985:SIC}
@InProceedings{Sutor:1985:SIC,
author = "R. S. Sutor",
title = "The {Scratchpad II} Computer Algebra Language and
@@ 26610,9 +28974,7 @@ LCCN QA76.76.A65 S95 1992
pages = "5663",
year = "1987",
isbn = "0897912357",
 paper = "Suto87.pdf",
comment = "IBM Research Report RC 12595 (\#56575)",
 keywords = "axiomref",
abstract =
"The Scratchpad II system is an abstract datatype programming
language, a compiler for the language, a library of packages of
@@ 26623,11 +28985,14 @@ LCCN QA76.76.A65 S95 1992
programming language . This paper discusses aspects of the
implementation of the interpreter and how it attempts to provide a
user friendly and relatively weakly typed front end for the strongly
 typed programming language."
+ typed programming language.",
+ paper = "Suto87.pdf",
+ keywords = "axiomref",
+ beebe = "Sutor:1987:TICb"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Sutor:1987:TICb}
@InProceedings{Sutor:1987:TICb,
author = "R. S. Sutor and R. D. Jenks",
title = "The Type Inference and Coercion Facilities in the
@@ 26665,11 +29030,15 @@ LCCN QA76.76.A65 S95 1992
\end{chunk}
\index{Sutor, Robert S.}
\begin{chunk}{ignore}
\bibitem[Sutor 87b]{Su87} Sutor, Robert S.
 title = "The Scratchpad II Computer Algebra System. Using and Programming the Interpreter",
IBM Course presentation slide deck Spring 1987
 keywords = "axiomref",
+\begin{chunk}{axiom.bib}
+@misc{Suto87b,
+ author = "Sutor, Robert S.",
+ title = "The Scratchpad II Computer Algebra System.
+ Using and Programming the Interpreter",
+ type = "IBM Course presentation slide deck",
+ year = "1987",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 26685,8 +29054,6 @@ IBM Course presentation slide deck Spring 1987
institution = "Mathematical Sciences Department",
address = "IBM Thomas J. Watson Research Center, Yorktown Heights, NY",
year = "1987",
 paper = "Suto87c.pdf",
 keywords = "axiomref",
abstract =
"The Scratchpad II system is an abstract datatype programming language,
a compiler for the language, a library of packages of polymorphic
@@ 26697,11 +29064,14 @@ IBM Course presentation slide deck Spring 1987
programming language. This paper discusses aspects of the
implementation of the intepreter and how it attempts to provide a user
friendly and relatively weakly typed front end for the strongly typed
 programming language."
+ programming language.",
+ paper = "Suto87c.pdf",
+ keywords = "axiomref",
+ beebe = "Sutor:1987:TICa"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Sutor:1987:TICa}
@TechReport{Sutor:1987:TICa,
author = "Robert S. Sutor and Richard D. Jenks",
title = "The type inference and coercion facilities in the
@@ 26726,7 +29096,29 @@ IBM Course presentation slide deck Spring 1987
\bibitem[Sutor 88]{Su88} Sutor, Robert S.
title = "A guide to programming in the scratchpad 2 interpreter",
IBM Manual, March 1988
 keywords = "axiomref",
+ keywords = "axiomref"
+
+\end{chunk}
+
+\index{Sutor, Robert S.}
+\begin{chunk}{axiom.bib}
+ author = "R. D. Jenks R. S. Sutor and S. M. Watt",
+ title = ""Scratchpad II: An abstract Datatype system for
+ mathematical computation",
+ pages = "1237",
+ year = "1988"
+}
+\begin{chunk}{Sutor:1988:SIA}
+@InProceedings{Sutor:1988:SIA,
+ author = "R. D. Jenks R. S. Sutor and S. M. Watt",
+ title = "{Scratchpad II}: {An} abstract Datatype system for
+ mathematical computation",
+ crossref = "Janssen:1988:TCA",
+ pages = "12??",
+ year = "1988",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.1.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+}
\end{chunk}
@@ 26735,20 +29127,20 @@ IBM Manual, March 1988
author = "Unknown",
title = "Axiom",
url = "https://www.swmath.org/software/63",
 keywords = "axiomref",
abstract =
"Axiom is a general purpose Computer Algebra System (CAS). It is
useful for research and developement of mathematical algorithms.
It defines a strongly typed, mathematically correct type hierarchy.
 It has a programming language and a builtin compiler."
+ It has a programming language and a builtin compiler.",
+ keywords = "axiomref"
}
\end{chunk}
\begin{chunk}{axiom.bib}
@misc{Sympy,
 keywords = "axiomref",
 url = "https://github.com/sympy/sympy/wiki/SymPyvs.Axiom"
+ url = "https://github.com/sympy/sympy/wiki/SymPyvs.Axiom",
+ keywords = "axiomref"
}
\end{chunk}
@@ 26765,8 +29157,6 @@ IBM Manual, March 1988
year = "2001",
location = "St. Andrews, Scotland",
pages = "205233",
 keywords = "axiomref",
 paper = "Thom01.pdf",
url = "http://axiomwiki.newsynthesis.org/public/refs/aldorcalc2000.pdf",
abstract =
"We show how the Aldor type system can represent propositions of
@@ 26775,7 +29165,9 @@ IBM Manual, March 1988
pretend) but can be viewed as a prototype implementation of a modified
type system with {\sl type evaluation} reported elsewhere. The logic
is used to provide an axiomatisation of a number of familiar Aldor
 categories as well as a type of vectors."
+ categories as well as a type of vectors.",
+ paper = "Thom01.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 26786,8 +29178,6 @@ IBM Manual, March 1988
@misc{Thomxx,
author = "Thompson, Simon and Timochouk, Leonid",
title = "The Aldor\\ language",
 paper = "Thomxx.pdf",
 keywords = "axiomref",
abstract = "
This paper introduces the \verbAldor language, which is a
functional programming language with dependent types and a powerful,
@@ 26800,7 +29190,9 @@ IBM Manual, March 1988
of \verbAldor; a general discussion of overloading and how the
overloading in \verbAldor fits into the general scheme; examples
of logic within \verbAldor and notes on the implementation of the
 system."
+ system.",
+ paper = "Thomxx.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 26812,8 +29204,8 @@ IBM Manual, March 1988
title = {Etude du typage dans le syst\`eme de calcul scientifique Aldor},
comment = "Study of types in the Aldor scientific computation system",
year = "1998",
 paper = "Tour98.pdf",
url = "http://axiomwiki.newsynthesis.org/public/refs/AldorT1998_04.pdf",
+ paper = "Tour98.pdf",
keywords = "axiomref"
}
@@ 26824,10 +29216,10 @@ IBM Manual, March 1988
@misc{Tour95,
author = "Tournier, Evelyne",
title = "Summary of organisation, history and possible future",
 paper = "Tour95.pdf",
year = "1995",
url =
"ftp://ftp.inf.ethz.ch/org/cathode/workshops/jan95/abstracts/tournier.ps",
+ paper = "Tour95.pdf",
keywords = "axiomref"
}
@@ 26844,14 +29236,14 @@ IBM Manual, March 1988
number = "1",
pages = "158165",
year = "1996",
 keywords = "axiomref",
abstract =
"The paper is devoted to a problem which was of an interest in the
beginning of the theory of difference methods. The elementary
constructed explicit highorder approximations for the wave equation
(on the simplest cubic grid in space) assume that the solution is very
smooth and that no boundary conditions are given. Stability is also
 understood in the simplest way (in $L_2$)."
+ understood in the simplest way (in $L_2$).",
+ keywords = "axiomref"
}
\end{chunk}
@@ 26876,9 +29268,7 @@ IBM Manual, March 1988
title = "Overview of the Mathemagix type system",
journal = "ASCM 2102",
year = "2012",
 keywords = "axiomref",
url = "http://www.texmacs.org/joris/mmxtyping/mmxtyping.pdf",
 paper = "Hoev12.pdf",
abstract =
"The goal of the {\tt MATHEMAGIX} project is to develop a new and free
software for computer algebra and computer analysis, base on a
@@ 26888,7 +29278,9 @@ IBM Manual, March 1988
called ``categories''. The exposition is informal and aims at giving
the reader an overview of the main concepts, ideas and differences
with existing languages. In a forthcoming paer, we intend to describe
 the formal semantics of the type system in more detail."
+ the formal semantics of the type system in more detail.",
+ paper = "Hoev12.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 26898,7 +29290,7 @@ IBM Manual, March 1988
\bibitem[van der Hoeven 14]{JvdH14} van der Hoeven, Joris
title = "Computer algebra systems and TeXmacs",
url = "http://www.texmacs.org/tmweb/plugins/cas.en.html",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 26914,8 +29306,6 @@ IBM Manual, March 1988
year = "1994",
pages = "353363",
issn = "07477171",
 keywords = "axiomref",
 paper = "Hoei94.pdf",
abstract = "
Algorithms for computing integral bases of an algebraic function field
are implemented in some computer algebra systems. They are used e.g.
@@ 26934,7 +29324,61 @@ IBM Manual, March 1988
result 'intermediate expression swell' can be avoided.
The Puiseux expansions generally introduce algebraic extensions. These
 extensions will not appear in the resulting integral basis."
+ extensions will not appear in the resulting integral basis.",
+ paper = "Hoei94.pdf",
+ keywords = "axiomref",
+ beebe = "vanHoeij:1994:ACI"
+}
+
+\end{chunk}
+\begin{chunk}{vanHoeij:1994:ACI}
+@Article{vanHoeij:1994:ACI,
+ author = "M. van Hoeij",
+ title = "An algorithm for computing an integral basis in an
+ algebraic function field",
+ journal = jJSYMBOLICCOMP,
+ volume = "18",
+ number = "4",
+ pages = "353363",
+ month = oct,
+ year = "1994",
+ CODEN = "JSYCEH",
+ ISSN = "07477171 (print), 1095855X (electronic)",
+ ISSNL = "07477171",
+ bibdate = "Fri Dec 29 12:46:02 MST 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "Algorithms for computing integral bases of an
+ algebraic function field are implemented in some
+ computer algebra systems. They are used e.g. for the
+ integration of algebraic functions. The method used by
+ Maple 5.2 and AXIOM is given by B. M. Trager (1984). He
+ adapted an algorithm of Ford and Zassenhaus (1978),
+ that computes the ring of integers in an algebraic
+ number field, to the case of a function field. It turns
+ out that using algebraic geometry one can write a
+ faster algorithm. The method we give is based on
+ Puiseux expansions. One can see this as a variant on
+ the Coates' algorithm as it is described by Davenport
+ (1981). Some difficulties in computing with Puiseux
+ expansions can be avoided using a sharp bound for the
+ number of terms required which are given. We derive
+ which denominator is needed in the integral basis.
+ Using this result `intermediate expression swell' can
+ be avoided. The Puiseux expansions generally introduce
+ algebraic extensions.",
+ acknowledgement = acknhfb,
+ affiliation = "Dept. of Math., Nijmegen Univ., Netherlands",
+ classification = "C6130 (Data handling techniques); C7310 (Mathematics
+ computing)",
+ fjournal = "Journal of Symbolic Computation",
+ journalURL = "http://www.sciencedirect.com/science/journal/07477171",
+ keywords = "Algebraic function field; Algebraic number field;
+ AXIOM; Computer algebra systems; Integral basis;
+ Intermediate expression swell; Maple 5.2; Puiseux
+ expansions",
+ language = "English",
+ pubcountry = "UK",
+ thesaurus = "Mathematics computing; Symbol manipulation",
}
\end{chunk}
@@ 26948,14 +29392,14 @@ IBM Manual, March 1988
year = "2008",
month = "April",
url = "http://andy.novocin.com/pro/algext.pdf",
 paper = "Hoei08.pdf",
abstract = "
Computer algebra systesm often produce large expressions involving
complicated algebraic numbers. In this paper we study variations of
the {\tt polred} algorithm that can often be used to find better
representations for algebraic numbers. The main new algorithm
presented here is an algorithm that treats the same problem for the
 function field case."
+ function field case.",
+ paper = "Hoei08.pdf"
}
\end{chunk}
@@ 26966,7 +29410,7 @@ IBM Manual, March 1988
title = "Computational Methods in Commutative Algebra and Algebraic Geometry",
Springer, Algorithms and Computation in Mathematics, Vol 2 1999
ISBN 3540213112
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 26983,16 +29427,17 @@ ISBN 3540213112
number = "4",
pages = "2531",
year = "1989",
 keywords = "axiomref",
 paper = "Wang89.pdf",
abstract =
"This report describes the implementation and use of a program for
computing the Liapunov functions and Liapunov constants for a class
 of differential systems in Scratchpad II"
+ of differential systems in Scratchpad II",
+ paper = "Wang89.pdf",
+ keywords = "axiomref",
+ beebe = "Wang:1989:PCL"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Wang:1989:PCL}
@Article{Wang:1989:PCL,
author = "D. Wang",
title = "A program for computing the {Liapunov} functions and
@@ 27042,13 +29487,13 @@ ISBN 3540213112
volume = "87",
pages = "305315",
year = "1990",
 keywords = "axiomref",
 paper = "Wang90.pdf",
abstract =
"This paper presents a class of cubic differential systems with the
origin as a 6tuple focus from which 6 limit cycles may be
constructed. For this class of differential systems the stability of
 the origin is given."
+ the origin is given.",
+ paper = "Wang90.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 27063,8 +29508,6 @@ ISBN 3540213112
number = "2",
pages = "233254",
year = "1991",
 keywords = "axiomref",
 paper = "Wang91.pdf",
comment = "See Wang89 for the implementation code",
abstract =
"In this paper we describe a mechanical procedure for computing the
@@ 27084,11 +29527,14 @@ ISBN 3540213112
given by Saharnikov are established, which leads to a rediscovery of
the incompleteness of his conditions. A class of cubic systems with
6tuple focus is presented to demonstrate the feasibility of the
 approach for finding systems with higher multiple focus."
+ approach for finding systems with higher multiple focus.",
+ paper = "Wang91.pdf",
+ keywords = "axiomref",
+ beebe = "Wang:1991:MMC"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Wang:1991:MMC}
@Article{Wang:1991:MMC,
author = "Dongming Wang",
title = "Mechanical manipulation for a class of differential
@@ 27158,9 +29604,7 @@ ISBN 3540213112
title = "Characteristic Sets and Zero Structure of Polynomial Sets",
institution = "Johannes Kepler University",
comment = "Lecture Notes",
 paper = "Wang95.pdf",
url = "http://wwwpolsys.lip6.fr/~wang/papers/CharSet.ps.gz",
 keywords = "axiomref",
abtract =
"This paper provides a tutorial on the theory and method of
characteristic sets and some relevant topics. The basic algorithms as
@@ 27173,7 +29617,9 @@ ISBN 3540213112
set. Using this decomposition, a complete solution to the algebraic
decision problem and a method for decomposing any algebraic variety
into irreducible components are described. Some applications of the
 method are indicated."
+ method are indicated.",
+ paper = "Wang95.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 27185,7 +29631,6 @@ ISBN 3540213112
title = "Elimination Methods",
publisher = "SpringerVerlag",
isbn = "9783709162026",
 keywords = "axiomref",
year = "2001",
abstract =
"The development of polynomialelimination techniques from classical
@@ 27212,7 +29657,8 @@ ISBN 3540213112
different kinds, in terms of which the decompositions are
represented. The prerequisites for the concepts and algorithms are
results from basic algebra and some knowledge of algorithmic
 mathematics."
+ mathematics.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 27227,14 +29673,14 @@ ISBN 3540213112
year = "2002",
location = "Beijing China",
pages = "379389",
 keywords = "axiomref",
 paper = "Wang02.pdf",
url = "https://hal.inria.fr/inria00107607/file/A02R314.pdf",
abstract =
"This article presents a Maple library of functions for decomposing
systems of multivariate polynomials into triangular systems of
various kinds (regular, simple, or irreducible), with an application
 package for manipulating and proving geometric theorems."
+ package for manipulating and proving geometric theorems.",
+ paper = "Wang02.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 27246,7 +29692,7 @@ International System Symposium on Symbolic and
Algebraic Computation 92 ACM Press, New York, NY 10036, USA, 1992
ISBN 0897914899 (soft cover), 0897914902 (hard cover),
LCCN QA76.95.I59 1992
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 27257,7 +29703,7 @@ LCCN QA76.95.I59 1992
ISSAC '90 Proceedings of the
International Symposium on Symbolic and Algebraic Computation ACM Press,
New York, NY, 10036, USA. 1990 ISBN 0897914015 LCCN QA76.95.I57 1990
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 27267,7 +29713,7 @@ New York, NY, 10036, USA. 1990 ISBN 0897914015 LCCN QA76.95.I57 1990
title = "Bounded Parallelism in Computer Algebra",
PhD Thesis, University of Waterloo
url = "http://www.csd.uwo.ca/~watt/pub/reprints/1985smwphd.pdf",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 27291,7 +29737,7 @@ PhD Thesis, University of Waterloo
\bibitem[Watt 87]{Wat87} Watt, Stephen
title = "Domains and Subdomains in Scratchpad II",
in [Wit87], pp35
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 27301,7 +29747,7 @@ in [Wit87], pp35
\bibitem[Watt 87a]{WB87} Watt, Stephen M.; Burge, William H.
title = "Mapping as First Class Objects",
in [Wit87], pp1317
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 27312,10 +29758,8 @@ in [Wit87], pp1317
author = "Watt, Stephen M. and Jenks, Richard D.",
title = "Abstract Datatypes, Multiple Views and Multiple Inheritance in
Scratchpad II",
 keywords = "axiomref",
year = "1987",
url = "https://cs.uwaterloo.ca/~smatt/pub/reprints/1987itlspadviews.pdf",
 paper = "Watt87.pdf",
abstract =
"Scratchpad II is an abstract datatype language developed at Yorktown
Heights for the implementation of a new computer algebra system. It
@@ 27328,7 +29772,9 @@ in [Wit87], pp1317
parameters and to provide the mechanism for multiple inheritance. They
also allow the language to be statically type checked and the
generation of efficient code. This paper describes the role of
 categories in Scratchpad II."
+ categories in Scratchpad II.",
+ paper = "Watt87.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 27345,7 +29791,6 @@ in [Wit87], pp1317
isbn = "3540510842",
year = "1988",
series = "AAECC6, ISSAC '88",
 keywords = "axiomref",
abstract =
"This paper presents a novel technique for manipulating structures
which represents infinite power series.
@@ 27373,11 +29818,13 @@ in [Wit87], pp1317
obtained. To illustrate, the computation of the first $n$ terms of
exp($u$) for a dense, infinite series $u$ is reduced from $O(n^4)$ to
$O(n^2)$ coefficient operations, the same as required by the standard
 online algorithms."
+ online algorithms.",
+ keywords = "axiomref",
+ beebe = "Watt:1989:FPM"
}
\end{chunk}
\begin{chunk}{beebe.bib}
+\begin{chunk}{Watt:1989:FPM}
@InProceedings{Watt:1989:FPM,
author = "S. M. Watt",
title = "A fixed point method for power series computation",
@@ 27434,8 +29881,6 @@ in [Wit87], pp1317
publisher = "Academic Press",
url =
"https://cs.uwaterloo.ca/~smwatt/pub/reprints/1990miolaspadtypes.pdf",
 paper = "Watt90.pdf",
 keywords = "axiomref",
abstract =
"Scratchpad II is a language developed at Yorktown Heights for the
implementation of a new computer algebra system. The need to model the
@@ 27459,7 +29904,9 @@ in [Wit87], pp1317
Finally, the mechanisms of Scratchpad II are compared with those of
traditional abstract datatype and objectoriented programming
 languages."
+ languages.",
+ paper = "Watt90.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 27471,7 +29918,7 @@ Proceedings of the 1991 International Symposium on
Symbolic and Algebraic Computation, ISSAC'91, July 1517, 1991, Bonn, Germany,
ACM Press, New York, NY 10036, USA, 1991 ISBN 0897914376
LCCN QA76.95.I59 1991
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 27484,7 +29931,7 @@ LCCN QA76.95.I59 1991
Steinback, J.M.; Sutor, R.S.
title = "A\# User's Guide",
Version 1.0.0 O($\epsilon{}^1$) June 8, 1994
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 27504,9 +29951,7 @@ Version 1.0.0 O($\epsilon{}^1$) June 8, 1994
year = "1994",
type = "technical report",
number = "RC19529 (85075)",
 paper = "Watt94.pdf",
url = "http://www.aldor.org/docs/reports/i94acomp/i94acomp.pdf",
 keywords = "axiomref",
abstract =
"The $A^{#}$ compiler allows users of computer algebra to develop
programs in a context where multiple programming languages are
@@ 27529,7 +29974,9 @@ Version 1.0.0 O($\epsilon{}^1$) June 8, 1994
The original motivation for $A^{#}$ comes from the field of computer
algebra: to provide an improved extension language for the Axiom
 computer algebra system."
+ computer algebra system.",
+ paper = "Watt94.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 27539,7 +29986,7 @@ Version 1.0.0 O($\epsilon{}^1$) June 8, 1994
\bibitem[Watt 94c]{Wat94c} Watt, Stephen M.
title = "A\# Language Reference Version 0.35",
IBM Research Division Technical Report RC19530 May 1994
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 27555,7 +30002,7 @@ IBM Research Division Technical Report RC19530 May 1994
Steinbach, J.M.; Morrison, S.C.; Sutor, R.S.
title = "AXIOM Library Compiler Users Guide",
The Numerical Algorithms Group (NAG) Ltd, 1994
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 27564,9 +30011,9 @@ The Numerical Algorithms Group (NAG) Ltd, 1994
@misc{Watt95a,
author = "Watt, Stephen M.",
title = "The A\# Programming Language and Compiler",
 paper = "Watt95a.pdf",
year = "1995",
url = "ftp://ftp.inf.ethz.ch/org/cathode/workshops/march93/Watt.tex",
+ paper = "Watt95a.pdf",
keywords = "axiomref"
}
@@ 27594,8 +30041,8 @@ IBM T. J. Watson Research Center (2001)
year = "2000",
institution = "University of Western Ontario",
url = "http://www.aldor.org/docs/reports/sa2000/aldortalksa2000.pdf",
 keywords = "axiomref",
 paper = "Watt00.pdf"
+ paper = "Watt00.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 27608,8 +30055,8 @@ IBM T. J. Watson Research Center (2001)
year = "2000",
institution = "University of Western Ontario",
url = "http://www.aldor.org/docs/reports/ukqcd2000/intro1ukqcd00.pdf",
 keywords = "axiomref",
 paper = "Watt00a.pdf"
+ paper = "Watt00a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 27622,8 +30069,8 @@ IBM T. J. Watson Research Center (2001)
year = "2000",
institution = "University of Western Ontario",
url = "http://www.aldor.org/docs/reports/ukqcd2000/intro2ukqcd00.pdf",
 keywords = "axiomref",
 paper = "Watt00b.pdf"
+ paper = "Watt00b.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 27638,8 +30085,6 @@ IBM T. J. Watson Research Center (2001)
year = "2007",
location = "RISCLinz, Austria",
pages = "8190",
 keywords = "axiomref",
 paper = "Watt07.pdf",
url =
"http://www.csd.uwo.ca/~watt/pub/reprints/2007plmmswhat\_happened.pdf",
abstract =
@@ 27648,7 +30093,9 @@ IBM T. J. Watson Research Center (2001)
in programming language support for symbolic computation over the past
two decades. We summarize certain advances in programming languages
for computer algebra and propose a set of directions and challenges
 for programming languages for symbolic computation."
+ for programming languages for symbolic computation.",
+ paper = "Watt07.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 27660,8 +30107,6 @@ IBM T. J. Watson Research Center (2001)
title = "Type Systems for Computer Algebra",
school = "University of Tubingen",
year = "1993",
 paper = "Webe93b.pdf",
 keywords = "axiomref",
abstract =
"An important feature of modern computer algebra systems is the support
of a rich type system with the possibility of type inference. Basic
@@ 27669,7 +30114,9 @@ IBM T. J. Watson Research Center (2001)
types. Recently the use of ordersorted rewrite systems was proposed
as a general framework. We will give a quite simple example of a
family of types arising in computer algebra whose coercion relations
 cannot be captured by a finite set of firstorder rewrite rules."
+ cannot be captured by a finite set of firstorder rewrite rules.",
+ paper = "Webe93b.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 27679,8 +30126,6 @@ IBM T. J. Watson Research Center (2001)
\bibitem[Weber 92b]{Webe92b} Weber, Andreas
title = "Structuring the Type System of a Computer Algebra System",
url = "http://cg.cs.unibonn.de/personalpages/weber/publications/pdf/WeberA/Weber92a.pdf",
 paper = "Webe92b.pdf",
 keywords = "axiomref",
abstract = "
Most existing computer algebra systems are pure symbol manipulating
systems without language support for the occuring types. This is
@@ 27691,7 +30136,9 @@ IBM T. J. Watson Research Center (2001)
several problems for a type system of a symbolic computation system
can be solved by using results of this research. We will also provide
a variety of examples which will show some of the problems that remain
 and that will require further research."
+ and that will require further research.",
+ paper = "Webe92b.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 27705,7 +30152,6 @@ IBM T. J. Watson Research Center (2001)
year = "2005",
publisher = "Springer",
pages = "188194",
 paper = "Webe05.pdf",
abstract =
"An important feature of modern computer algebra systems is the
support of a rich type system with the possibility of type inference.
@@ 27716,7 +30162,8 @@ IBM T. J. Watson Research Center (2001)
We will give a quite simple example of a family of types arising in
computer algebra whose coercion relations cannot be captured by a
 finite set of firstorder rewrite rules."
+ finite set of firstorder rewrite rules.",
+ paper = "Webe05.pdf"
}
\end{chunk}
@@ 27726,8 +30173,6 @@ IBM T. J. Watson Research Center (2001)
\bibitem[Weber 93b]{Webe93b} Weber, Andreas
title = "Type Systems for Computer Algebra",
url = "http://cg.cs.unibonn.de/personalpages/weber/publications/pdf/WeberA/Weber93b.pdf",
 paper = "Webe93b.pdf",
 keywords = "axiomref",
abstract = "
We study type systems for computer algebra systems, which frequently
correspond to the ``pragmatically developed'' typing constructs used
@@ 27742,7 +30187,9 @@ IBM T. J. Watson Research Center (2001)
extensions of existing computer algebra systems: These typing concepts
can be used to implement category theoretic constructs and there are
many well known constructive interactions between category theory and
 algebra."
+ algebra.",
+ paper = "Webe93b.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 27755,8 +30202,6 @@ IBM T. J. Watson Research Center (2001)
series = "ISSAC 94",
pages = "324329",
year = "1994",
 keywords = "axiomref",
 paper = "Webe94.pdf",
abstract =
"This paper presents algorithms that perform a type inference for a
type system occurring in the context of computer algebra. The type
@@ 27768,7 +30213,9 @@ IBM T. J. Watson Research Center (2001)
Previously only algorithms for much more restricted cases of coercions
have been described or the frameworks used have been so general that
the corresponding type inference problems were known to be
 undecidable."
+ undecidable.",
+ paper = "Webe94.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 27785,8 +30232,6 @@ IBM T. J. Watson Research Center (2001)
year = "1995",
url =
"http://cg.cs.unibonn.de/personalpages/weber/publications/pdf/WeberA/Weber94e.pdf",
 paper = "Webe95.pdf",
 keywords = "axiomref",
abstract = "
Modern computer algebra systems (e.g. AXIOM) support a rich type
system including parameterized data types and the possibility of
@@ 27797,7 +30242,46 @@ IBM T. J. Watson Research Center (2001)
coherence}. We will prove a coherence theorem for a formal type system
having several possibilities of coercions covering many important
examples. Moreover, we will give some informal reasoning why the
 formally defined restrictions can be satisfied by an actual system."
+ formally defined restrictions can be satisfied by an actual system.",
+ paper = "Webe95.pdf",
+ keywords = "axiomref",
+ beebe = "Weber:1993:CCA"
+}
+
+\end{chunk}
+\begin{chunk}{Weber:1993:CCA}
+@InProceedings{Weber:1993:CCA,
+ author = "A. Weber",
+ title = "On coherence in computer algebra",
+ crossref = "Miola:1993:DIS",
+ pages = "95106",
+ month = "",
+ year = "1993",
+ bibdate = "Fri Dec 29 12:46:02 MST 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "Modern computer algebra systems (e.g. AXIOM) support a
+ rich type system including parameterized data types and
+ the possibility of implicit coercions between types. In
+ such a type system it will be frequently the case that
+ there are different ways of building coercions between
+ types. An important requirement is that all coercions
+ between two types coincide, a property which is called
+ coherence. The author proves a coherence theorem for a
+ formal type system having several possibilities of
+ coercions covering many important examples. Moreover,
+ he gives some informal reasoning why the formally
+ defined restrictions can be satisfied by an actual
+ system.",
+ acknowledgement = acknhfb,
+ affiliation = "WilhelmSchickardInst. fur Inf., Tubingen Univ.,
+ Germany",
+ classification = "C4210 (Formal logic); C4240 (Programming and
+ algorithm theory); C7310 (Mathematics)",
+ keywords = "AXIOM; Coherence; Coherence theorem; Computer algebra;
+ Formal type system; Informal reasoning; Parameterized
+ data types; Type system",
+ language = "English",
+ thesaurus = "Symbol manipulation; Theorem proving; Type theory",
}
\end{chunk}
@@ 27807,13 +30291,13 @@ IBM T. J. Watson Research Center (2001)
\bibitem[Weber 96]{Webe96} Weber, Andreas
title = "Computing Radical Expressions for Roots of Unity",
url = "http://cg.cs.unibonn.de/personalpages/weber/publications/pdf/WeberA/Weber96a.pdf",
 paper = "Webe96.pdf",
 keywords = "axiomref",
abstract = "
We present an improvement of an algorithm given by Gauss to compute a
radical expression for a $p$th root of unity. The time complexity of
the algorithm is $O(p^3m^6log p)$, where $m$ is the largest prime
 factor of $p1$."
+ factor of $p1$.",
+ paper = "Webe96.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 27822,8 +30306,6 @@ IBM T. J. Watson Research Center (2001)
\bibitem[Weber 99]{Webe99} Weber, Andreas
title = "Solving Cyclotomic Polynomials by Radical Expressions",
url = "http://cg.cs.unibonn.de/personalpages/weber/publications/pdf/WeberA/WeberKeckeisen99a.pdf",
 paper = "Webe99.pdf",
 keywords = "axiomref",
abstract = "
We describe a Maple package that allows the solution of cyclotomic
polynomials by radical expressions. We provide a function that is an
@@ 27831,7 +30313,9 @@ IBM T. J. Watson Research Center (2001)
ingredient of the package is an improvement of a method due to Gauss
which gives radical expressions for roots of unity. We will give a
summary for computations up to degree 100, which could be done within
 a few hours of cpu time on a standard workstation."
+ a few hours of cpu time on a standard workstation.",
+ paper = "Webe99.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 27840,7 +30324,7 @@ IBM T. J. Watson Research Center (2001)
\bibitem[WeiJiang 12]{WJ12} WeiJiang
title = "Top free algebra System",
url = "http://weijiang.com/it/software/topfreealgebrasystembyemathematicabyemaple",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 27849,9 +30333,7 @@ IBM T. J. Watson Research Center (2001)
@misc{Westxx,
author = "Wester, Michael J.",
title = "Computer Algebra Synonyms",
 keywords = "axiomref",
url = "http://math.unm.edu/~wester/cas/synonyms.pdf",
 paper = "Westxx.pdf",
abstract =
"The following is a collection of synonyms for various operations in
the seven general purpose computer algebra systems {\bf Axiom}, {\bf
@@ 27862,7 +30344,9 @@ IBM T. J. Watson Research Center (2001)
in many common situations. Note that for a blank entry means that
there is no exact translation of a particular operation for the
indicated system, but it may still be possible to work around this
 lack with a related functionality."
+ lack with a related functionality.",
+ paper = "Westxx.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 27875,7 +30359,6 @@ IBM T. J. Watson Research Center (2001)
year = "1999",
publisher = "Wiley",
isbn = "0471983535",
 keywords = "axiomref",
abstract =
"In this book some of the most popular general purpose computer
algebra systems (CAS), such as Mathematica, Maple, Derive, Axiom,
@@ 27901,7 +30384,8 @@ IBM T. J. Watson Research Center (2001)
(chapter 13), evaluation of expressions and programs in the embedded
computer algebra programming language (chapter 14), and computer
algebra in education (chapter 15). Chapter 16 covers the origin of CA,
 and, finally chapter 17 gives a list of most CAS available today."
+ and, finally chapter 17 gives a list of most CAS available today.",
+ keywords = "axiomref"
}
\end{chunk}
@@ 27913,7 +30397,7 @@ Proceedings of the SIGPLAN '87 Symposium on
Interpreter and Interpretive Techniques, St. Paul, Minnesota, June 2426, 1987
ACM Press, New York, NY 10036, USA, 1987 ISBN 0897912357
LCCN QA76.7.S54 v22:7 SIGPLAN Notices, vol 22, no 7 (July 1987)
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 27936,8 +30420,6 @@ LCCN QA76.7.S54 v22:7 SIGPLAN Notices, vol 22, no 7 (July 1987)
year = "1995",
location = "Halifax, Nova Scotia, Canada",
pages = "417431",
 keywords = "axiomref",
 paper = "Will95.pdf",
abstract =
"Let $K$ be a field of characteristic zero and assume
\[f(x)=x^ns_1x^{n1}+\cdots+s_n \in L[x]\]
@@ 27965,7 +30447,9 @@ LCCN QA76.7.S54 v22:7 SIGPLAN Notices, vol 22, no 7 (July 1987)
complete information about Galois groups etc., he can deduce e.g. that
if $s_1,\cdots,s_4$ are algebraically independent over $\mathbb{Q}$,
then $d_1,\cdots,d_4$ are not expressible in radicals over
 $\mathbb{Q}(s_1,\cdots,s_4)$. He mentions, however, a solvable subcase."
+ $\mathbb{Q}(s_1,\cdots,s_4)$. He mentions, however, a solvable subcase.",
+ paper = "Will95.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 27978,7 +30462,6 @@ LCCN QA76.7.S54 v22:7 SIGPLAN Notices, vol 22, no 7 (July 1987)
year = "1989",
publisher = "SpringerVerlag",
url = "http://www.risc.jku.at/publications/download/risc_3527/paper_47.pdf",
 paper = "Wink89.pdf",
abstract =
"Equational theorem proving is interesting both from a mathematical
and a computational point of view. Many mathematical structures like
@@ 28006,7 +30489,8 @@ LCCN QA76.7.S54 v22:7 SIGPLAN Notices, vol 22, no 7 (July 1987)
We show how rewrite systems can be used for proving theorems in
equational and inductive theories, and how an equational specification
 of a problem can be turned into a rewrite program."
+ of a problem can be turned into a rewrite program.",
+ paper = "Wink89.pdf"
}
\end{chunk}
@@ 28019,7 +30503,6 @@ LCCN QA76.7.S54 v22:7 SIGPLAN Notices, vol 22, no 7 (July 1987)
year = "1993",
journal = "IMACS Symposium SC1993",
url = "http://www.risc.jku.at/publications/download/risc_3777/paper_35.pdf",
 paper = "Wink93.pdf",
abstract =
"Computation with algebraic curves and surfaces are very well suited
for being treated with computer algebra. Many aspects of computer
@@ 28029,7 +30512,8 @@ LCCN QA76.7.S54 v22:7 SIGPLAN Notices, vol 22, no 7 (July 1987)
series approximations of branches. We will describe the application of
computer algebra to problems arising in algebraic geometry. The
program system CASA, which has been developed by the author and a
 group of students will be introduced."
+ group of students will be introduced.",
+ paper = "Wink93.pdf"
}
\end{chunk}
@@ 28121,7 +30605,7 @@ LCCN QA76.7.S54 v22:7 SIGPLAN Notices, vol 22, no 7 (July 1987)
\bibitem[WWW1]{WWW1}.
Software Preservation Group
url = "http://www.softwarepresentation.org/projects/LISP/common_lisp_family",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 28155,7 +30639,7 @@ Oxford University Press (2000) ISBN0195125169
\bibitem[Yapp 07]{Yapp07} Yapp, Clifford; Hebisch, Waldek; Kaminski, Kai
title = "Literate Programming Tools Implemented in ANSI Common Lisp",
url = "http://brlcad.org/~starseeker/clwebv0.8.lisp.pamphlet",
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 28169,10 +30653,10 @@ Oxford University Press (2000) ISBN0195125169
publisher = "ACM",
year = "1976",
pages = "248259",
 keywords = "axiomref",
 paper = "Yunx76.djvu",
url =
"http://lib.org/by/\_djvu\_Papers/Computer\_algebra/Algebraic\%20numbers",
+ paper = "Yunx76.djvu",
+ keywords = "axiomref"
}
\end{chunk}
@@ 28183,19 +30667,40 @@ Oxford University Press (2000) ISBN0195125169
title = "Computer Algebra and Complex Analysis",
Computational Aspects of Complex Analysis pp379393
D. Reidel Publishing Company H. Werner et. al. (eds.)
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
\subsection{Z} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Zenger, Christoph}
\begin{chunk}{ignore}
\bibitem[Zen92]{Zen92} Zenger, Ch.
 title = "Gr{\"o}bnerbasen f{\"u}r Differentialformen und ihre Implementierung in AXIOM'",
Diplomarbeit, Universit{\"a}t Karlsruhe,
Karlsruhe, Germany, 1992
+\begin{chunk}{axiom.bib}
+@mastersthesis{Zeng92,
+ author = "Zenger, Christoph",
+ title = "Gr{\"o}bnerbasen f{\"u}r Differentialformen und ihre
+ Implementierung in AXIOM'",
+ type = "Diplomarbeit",
+ school = "Universit{\"a}t Karlsruhe",
+ address = "Karlsruhe, Germany",
+ year = "1992",
keywords = "axiomref",
+ beebe = "Zenger:1992:GFD"
+}
+
+\end{chunk}
+\begin{chunk}{Zenger:1992:GFD}
+@MastersThesis{Zenger:1992:GFD,
+ author = "Ch. Zenger",
+ title = "{Gr{\"o}bnerbasen f{\"u}r Differentialformen und ihre
+ Implementierung in AXIOM}",
+ type = "Diplomarbeit",
+ school = "Universit{\"a}t Karlsruhe",
+ address = "Karlsruhe, Germany",
+ pages = "??",
+ year = "1992",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+}
\end{chunk}
@@ 28209,15 +30714,15 @@ Karlsruhe, Germany, 1992
numbers = "12",
pages = "147165",
year = "1997",
 keywords = "axiomref",
 paper = "Zeng97.pdf",
abstract =
"A new extension of the Hindley/Milner type system is proposed. The
type system has algebraic types, that have not only type parameters
but also value parameters (indices). This allows for example to
parameterize matrices and vectors by their size and to check size
compatibility statically. This is especially of interest in computer
 algebra."
+ algebra.",
+ paper = "Zeng97.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 28228,8 +30733,6 @@ Karlsruhe, Germany, 1992
author = "Zimmermann, Paul",
title = "Wester's test suite in MuPAD 1.2.2",
year = "1995",
 paper = "Zimm95.pdf",
 keywords = "axiomref",
abstract =
"A few months ago, Michael Wester made a review of the mathematical
capabilities of different computer algebra systems, namely Axiom,
@@ 28241,7 +30744,9 @@ Karlsruhe, Germany, 1992
We describe in this paper the problems that can be solved with MuPAD
1.2.2, and how to solve them. The problems marked as [New] are solved
 using new functionalities of the version 1.2.2 with respect to 1.2.1"
+ using new functionalities of the version 1.2.2 with respect to 1.2.1",
+ paper = "Zimm95.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 28252,8 +30757,6 @@ Karlsruhe, Germany, 1992
author = "Zimmermann, Paul",
title = "Wester's test suite in MuPAD 1.3",
year = "1996",
 paper = "Zimm96.pdf",
 keywords = "axiomref",
abstract =
"In December 1994, Michael Wester made a review of the mathematical
capabilities of different computer algebra systems, namely Axiom,
@@ 28265,7 +30768,9 @@ Karlsruhe, Germany, 1992
We describe in this paper the problems that can be solved with MuPAD
1.3, and how to solve them. The problems marked as [New] are solved
 using new functionalities of the version 1.3 with respect to 1.2.2"
+ using new functionalities of the version 1.3 with respect to 1.2.2",
+ paper = "Zimm96.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 28275,7 +30780,7 @@ Karlsruhe, Germany, 1992
\bibitem[Zip92]{Zip92} Zippel, Richard
title = "Algebraic Computation",
(unpublished) Cornell University Ithaca, NY Sept 1992
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 28284,11 +30789,11 @@ Karlsruhe, Germany, 1992
@misc{Zipp89,
author = "Zippel, Richard",
title = "The Weyl Computer Algebra Substrate",
 paper = "Zipp89.pdf",
 keywords = "axiomref",
year = "1989",
paper = "Zipp89.pdf",
 url = "https://ecommons.cornell.edu/bitstream/handle/1813/6917/901077.pdf"
+ url = "https://ecommons.cornell.edu/bitstream/handle/1813/6917/901077.pdf",
+ paper = "Zipp89.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 28298,12 +30803,12 @@ Karlsruhe, Germany, 1992
@misc{Zipp93,
author = "Zippel, Richard",
title = "The Weyl Computer Algebra Substrate",
 paper = "Zipp93.pdf",
 keywords = "axiomref",
booktitle = "Proc. of DISCO 1993",
series = "DISCO 93",
pages = "303=307",
 year = "1993"
+ year = "1993",
+ paper = "Zipp93.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 28313,7 +30818,7 @@ Karlsruhe, Germany, 1992
\bibitem[Zwi92]{Zwi92} Zwillinger, Daniel
title = "Handbook of Integration",
Jones and Bartlett, 1992, ISBN 0867202939
 keywords = "axiomref",
+ keywords = "axiomref"
\end{chunk}
@@ 28347,7 +30852,7 @@ Jones and Bartlett, 1992, ISBN 0867202939
pages = "5658",
publisher = "Pleiades Publishing Inc",
year = "2006",
 paper = "Abra06.pdf",
+ paper = "Abra06.pdf"
}
\end{chunk}
@@ 28464,20 +30969,20 @@ National Physical Laboratory. (1982)
a Comparison of Four Methods",
year = "1996",
url = "http://www.lip6.fr/lip6/reports/1997/lip6.1997.009.ps.gz",
 paper = "Aubr96.pdf",
algebra =
"\newline\refto{category TSETCAT TriangularSetCategory}
\newline\refto{category RSETCAT RegularTriangularSetCategory}
\newline\refto{category NTSCAT NormalizedTriangularSetCategory}
\newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
\newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
 keywords = "axiomref",
abstract =
"Four methods for solving polynomial systems by means of triangular
sets are presented and implemented in a unified way. These methods are
those of Wu, Lazard, Kalkbrener, and Wang. They are compared on
various examples with emphasis on efficiency, conciseness and
 legibility of the outputs."
+ legibility of the outputs.",
+ paper = "Aubr96.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 28501,20 +31006,20 @@ National Physical Laboratory. (1982)
year = "1999",
url =
"http://www.csd.uwo.ca/~moreno/Publications/AubryMorenoMaza1999JSC.pdf",
 paper = "Aubr99a.pdf",
algebra =
"\newline\refto{category TSETCAT TriangularSetCategory}
\newline\refto{category RSETCAT RegularTriangularSetCategory}
\newline\refto{category NTSCAT NormalizedTriangularSetCategory}
\newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
\newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
 keywords = "axiomref",
abstract =
"Four methods for solving polynomial systems by means of triangular
sets are presented and implemented in a unified way. These methods are
those of Wu, Lazard, Kalkbrener, and Wang. They are compared on
various examples with emphasis on efficiency, conciseness and
 legibility of the outputs."
+ legibility of the outputs.",
+ paper = "Aubr99a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 28528,8 +31033,8 @@ National Physical Laboratory. (1982)
school = "l'Universite de Paris VI",
year = "1999",
month = "January",
 paper = "Aubr99b.pdf",
 comment = "French"
+ comment = "French",
+ paper = "Aubr99b.pdf"
}
\end{chunk}
@@ 28567,8 +31072,8 @@ Cambridge University Press, March 1996 ISBN 9870521450072
author = "Baker, Martin",
title = "Axiom Architecture",
year = "2014",
 keywords = "axiomref",
 url = "http://www.euclideanspace.com/prog/scratchpad/internals/ccode"
+ url = "http://www.euclideanspace.com/prog/scratchpad/internals/ccode",
+ keywords = "axiomref"
}
\end{chunk}
@@ 28619,9 +31124,7 @@ Comm. ACM. 17, 6 319320. (1974)
number = "4",
pages = "362381",
year = "1972",
 paper = "Bart72.pdf",
url = "http://comjnl.oxfordjournals.org/content/15/4/362.full.pdf+html",
 keywords = "axiomref",
abstract =
"This paper describes the applications area of computer programs that
carry out formal algebraic manipulation. The first part of the paper
@@ 28632,7 +31135,9 @@ Comm. ACM. 17, 6 319320. (1974)
reader to the true capabilities of an algebra program and these are
proposed as a means of comparison between rival algebra systems. A
brief review of the technical problems of algebraic manipulation is
 given in the final section."
+ given in the final section.",
+ paper = "Bart72.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 28659,7 +31164,7 @@ Comm. ACM. 17, 6 319320. (1974)
\bibitem[Beauzamy 92]{Bea92} Beauzamy, Bernard
title = "Products of polynomials and a priori estimates for coefficients in polynomial decompositions: a sharp result",
J. Symbolic Computation (1992) 13, 463472
 paper = "Bea92.pdf",
+ paper = "Bea92.pdf"
\end{chunk}
@@ 28671,7 +31176,7 @@ J. Symbolic Computation (1992) 13, 463472
Wang, Paul S.
title = "Polynomial Factorization: Sharp Bounds, Efficient Algorithms",
J. Symbolic Computation (1993) 15, 393413
 paper = "Bea93.pdf",
+ paper = "Bea93.pdf"
\end{chunk}
@@ 28729,7 +31234,7 @@ Ginn \& Co., Boston and New York. (1962)
\bibitem[Boyd9 3a]{Boyd93a} Boyd, David W.
title = "Bounds for the Height of a Factor of a Polynomial in Terms of Bombieri's Norms: I. The Largest Factor",
J. Symbolic Computation (1993) 16, 115130
 paper = "Boyd93a.pdf",
+ paper = "Boyd93a.pdf"
\end{chunk}
@@ 28738,7 +31243,7 @@ J. Symbolic Computation (1993) 16, 115130
\bibitem[Boyd 93b]{Boyd93b} Boyd, David W.
title = "Bounds for the Height of a Factor of a Polynomial in Terms of Bombieri's Norms: II. The Smallest Factor",
J. Symbolic Computation (1993) 16, 131145
 paper = "Boyd93b.pdf",
+ paper = "Boyd93b.pdf"
\end{chunk}
@@ 28881,7 +31386,6 @@ Mathematics of Computation, vol. 35, num. 35, Oct. 1980, 13791381
@misc{Bron95,
author = "Bronstein, Manuel",
title = "On radical solutions of linear ordinary differential equations",
 paper = "Bron95.pdf",
year = "1995",
url =
"ftp://ftp.inf.ethz.ch/org/cathode/workshops/jan95/abstracts/bronstein.ps",
@@ 28897,7 +31401,8 @@ Mathematics of Computation, vol. 35, num. 35, Oct. 1980, 13791381
\newline\refto{package APPLYORE ApplyUnivariateSkewPolynomial}
\newline\refto{package OREPCTO UnivariateSkewPolynomialCategoryOps}
\newline\refto{package LODOF LinearOrdinaryDifferentialOperatorFactorizer}
 \newline\refto{package LODOOPS LinearOrdinaryDifferentialOperatorsOps}"
+ \newline\refto{package LODOOPS LinearOrdinaryDifferentialOperatorsOps}",
+ paper = "Bron95.pdf"
}
\end{chunk}
@@ 28913,22 +31418,32 @@ ISBN 3764359013 (1998)
\end{chunk}
+\index{TranscendentalRischDE}
+\index{TranscendentalRischDESystem}
\index{Bronstein, Manuel}
\begin{chunk}{ignore}
\bibitem[Bronstein 88]{Bro88} Bronstein, Manual
+\begin{chunk}{axiom.bib}
+@article{Bron90,
+ author = "Bronstein, Manuel",
title = "The Transcendental Risch Differential Equation",
J. Symbolic Computation (1990) 9, pp4960 Feb 1988
IBM Research Report RC13460 IBM Corp. Yorktown Heights, NY
 url = "http://www.sciencedirect.com/science/article/pii/S0747717108800065",
 paper = "Bro88.pdf",
 abstract = "
 We present a new rational algorithm for solving Risch differential
+ journal = "J. Symbolic Computation",
+ volume = "9",
+ pages = "4960",
+ year = "1990",
+ comment = "IBM Research Report RC13460 IBM Corp. Yorktown Heights, NY",
+ algebra =
+ "\newline\refto{package RDETR TranscendentalRischDE}
+ \newline\refto{package RDETRS TranscendentalRischDESystem}",
+ abstract =
+ "We present a new rational algorithm for solving Risch differential
equations in towers of transcendental elementary extensions. In
contrast to a recent algorithm by Davenport we do not require a
progressive reduction of the denominators involved, but use weak
normality to obtain a formula for the denominator of a possible
solution. Implementation timings show this approach to be faster than
 a Hermitelike reduction."
+ a Hermitelike reduction.",
+ paper = "Bron90.pdf",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 28941,7 +31456,6 @@ IBM Research Report RC13460 IBM Corp. Yorktown Heights, NY
number = "RR3562",
year = "1998",
institution = "French Institute for Research in Computer Science",
 paper = "Bron98.pdf",
abstract = "
The Hermite reduction is a symbolic integration technique that reduces
algebraic functions to integrands having only simple affine
@@ 28952,7 +31466,8 @@ IBM Research Report RC13460 IBM Corp. Yorktown Heights, NY
ground fields. In this paper, we show that the Hermite reduction can
be performed without {\sl a priori} computation of either a primitive
element or integral basis, computing the smallest order necessary for
 a particular integrand along the way."
+ a particular integrand along the way.",
+ paper = "Bron98.pdf"
}
\end{chunk}
@@ 28967,7 +31482,7 @@ IBM Research Report RC13460 IBM Corp. Yorktown Heights, NY
address = "INRIA Sophia Antipolis",
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/issac98.pdf",
 paper = "Bro98b.pdf",
+ paper = "Bro98b.pdf"
}
\end{chunk}
@@ 29091,13 +31606,13 @@ GauthierVillars, Paris, 1891).
title = "Lifting and recombination techniques for absolute factorization",
Journal of Complexity, VOl 23 Issue 3 June 2007 pp 380420
url = "http://www.sciencedirect.com/science/article/pii/S0885064X07000465",
 paper = "Chez07.pdf",
abstract = "
In the vein of recent algorithmic advances in polynomial factorization
based on lifting and recombination techniques, we present new faster
algorithms for computing the absolute factorization of a bivariate
polynomial. The running time of our probabilistic algorithm is less
 than quadratic in the dense size of the polynomial to be factored."
+ than quadratic in the dense size of the polynomial to be factored.",
+ paper = "Chez07.pdf"
\end{chunk}
@@ 29480,8 +31995,8 @@ pp 1828
author = "Dongarra, Jack and et al.",
title = "Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard",
year = "2001",
 paper = "blas01.pdf",
url = "http://www.netlib.org/blas/blastforum/blasreport.pdf",
+ paper = "blas01.pdf"
}
\end{chunk}
@@ 29512,7 +32027,6 @@ A.E.R.E. Report R.8730. HMSO. (1977)
volume = "42",
pages = "551560",
year = "1996",
 paper = "Duva96a.pdf",
abstract = "
The aim of this paper is to present how the dynamic evaluation method
can be used to deal with the real closure of an ordered field. Two
@@ 29520,7 +32034,8 @@ A.E.R.E. Report R.8730. HMSO. (1977)
equality tests $(a=b?)$ and sign tests $(a > b?)$. Equality tests are
handled through splittings, exactly as in the algebraic closure of a
field. Sign tests are handled throug a structure called ``Tarski data
 type''."
+ type''.",
+ paper = "Duva96a.pdf"
}
\end{chunk}
@@ 29535,12 +32050,12 @@ A.E.R.E. Report R.8730. HMSO. (1977)
volume = "42",
pages = "363373",
year = "1996",
 paper = "Duva96.pdf",
abstract =
"The goal of this short paper is to describe one possible use of
sketches in computer algebra. We show that sketches are a powerful
tool for the description of mathematical structures and for the
 description of computations."
+ description of computations.",
+ paper = "Duva96.pdf"
}
\end{chunk}
@@ 29558,7 +32073,6 @@ A.E.R.E. Report R.8730. HMSO. (1977)
publisher = "Cambridge University Press",
year = "1994",
url = "http://journals.cambridge.org/abstract_S0960129500000438",
 paper = "Duva94a.pdf",
abstract =
"We define a categorical framework, based on the notion of {\sl
sketch}, for specification and evaluation in the sense of algebraic
@@ 29572,7 +32086,8 @@ A.E.R.E. Report R.8730. HMSO. (1977)
structures admit an initial model, but are not necessarily
equational. In Part II (Duval and Reynaud 1994), we study a more
general process, called {\sl dynamic evaluation}, for structures that
 may have no initial model."
+ may have no initial model.",
+ paper = "Duva94a.pdf"
}
\end{chunk}
@@ 29590,7 +32105,6 @@ A.E.R.E. Report R.8730. HMSO. (1977)
publisher = "Cambridge University Press",
year = "1994",
url = "http://journals.cambridge.org/abstract_S096012950000044X",
 paper = "Duva94b.pdf",
abstract =
"In the first part of this paper (Duval and Reynaud 1994), we defined a
categorical framework, based on the notion of {\sl sketch}, for
@@ 29602,7 +32116,8 @@ A.E.R.E. Report R.8730. HMSO. (1977)
has not been used in algebraic specification systems, but computer
algebra systems are beginning to use it as a basic tool. Finally, we
give some applications of dynamic evaluation to computation in field
 extensions."
+ extensions.",
+ paper = "Duva94b.pdf"
}
\end{chunk}
@@ 29617,14 +32132,14 @@ A.E.R.E. Report R.8730. HMSO. (1977)
pages = "429445",
year = "1994",
url = "http://www.sciencedirect.com/science/article/pii/S0747717106000551",
 paper = "Duva94c.pdf",
 keywords = "axiomref",
abstract = "
Dynamic evaluation is presented through examples: computations
involving algebraic numbers, automatic case discussion according to
the characteristic of a field. Implementation questions are addressed
too. Finally, branches are presented as ``dual'' to binary functions,
 according to the approach of sketch theory."
+ according to the approach of sketch theory.",
+ paper = "Duva94c.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 29632,11 +32147,12 @@ A.E.R.E. Report R.8730. HMSO. (1977)
\subsection{F} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Fateman, Richard J.}
\begin{chunk}{ignore}
\bibitem[Fateman 08]{Fat08} Fateman, Richard
 title = "Revisiting numeric/symbolic indefinite integration of rational functions, and extensions",
+\begin{chunk}{axiom.bib}
+@misc{Fate08,
+ author = "Fateman, Richard J,",
+ title = "Revisiting numeric/symbolic indefinite integration of rational
+ functions, and extensions",
url = "http://www.eecs.berkeley.edu/~fateman/papers/integ.pdf",
 paper = "Fat08.pdf",
abstract = "
We know we can solve this problem: Given any rational function
$f(x)=p(x)/q(x)$, where $p$ and $q$ are univariate polynomials over
@@ 29647,7 +32163,9 @@ A.E.R.E. Report R.8730. HMSO. (1977)
integration, or introduce additional parameters so that we can solve
multiple definite integrations. How can a computer algebra system
best answer the more useful questions? Finally, what if the integrand
 is not a ratio of polynomials, but something more challenging?"
+ is not a ratio of polynomials, but something more challenging?",
+ paper = "Fate08.pdf"
+}
\end{chunk}
@@ 29793,12 +32311,12 @@ AddisonWesley. 181187. (1965)
author = "Fulton, William",
title = "Algebraic Curves: An Introduction to Algebraic Geometry",
url = "http://www.math.lsa.umich.edu/~wfulton/CurveBook.pdf",
 paper = "Fult08.pdf",
year = "2008",
algebra =
"\newline\refto{package GPAFF GeneralPackageForAlgebraicFunctionField}
\newline\refto{package PAFFFF PackageForAlgebraicFunctionFieldOverFiniteField}
 \newline\refto{package PAFF PackageForAlgebraicFunctionField}"
+ \newline\refto{package PAFF PackageForAlgebraicFunctionField}",
+ paper = "Fult08.pdf"
}
\end{chunk}
@@ 29820,14 +32338,14 @@ Invent. Math., vol. 121, 1995, pp. 211222.
\bibitem[Gathen 90a]{Gat90a} {von zur Gathen}, Joachim; Giesbrecht, Mark
``Constructing Normal Bases in Finite Fields''
J. Symbolic Computation pp 547570 (1990)
 paper = "Gat90a.pdf",
abstract = "
An efficient probabilistic algorithm to find a normal basis in a
finite field is presented. It can, in fact, find an element of
arbitrary prescribed additive order. It is based on a density estimate
for normal elements. A similar estimate yields a probabilistic
polynomialtime reduction from finding primitive normal elements to
 finding primitive elements."
+ finding primitive elements.",
+ paper = "Gat90a.pdf"
\end{chunk}
@@ 30080,7 +32598,7 @@ Ann. Math. Studies, Princeton Univ. Press, 1940
title = "Integrals of multinomial systems of ordinary differential equations",
J. of Pure and Applied Algebra, 45, 225240 (1987)
url = "http://www.sciencedirect.com/science/article/pii/0022404987900727/pdf?md5=5a0c70643eab514ccf47d80e4fc6ec5a&verbpid=1s2.00022404987900727main.pdf",
 paper = "Gold87.pdf",
+ paper = "Gold87.pdf"
\end{chunk}
@@ 30163,7 +32681,7 @@ Grove, IL, USA and Oxford, UK, 1992
\bibitem[Granville 1911]{Gran1911} Granville, William Anthony
title = "Elements of the Differential and Integral Calculus",
url = "http://djm.cc/library/Elements_Differential_Integral_Calculus_Granville_edited_2.pdf",
 paper = "Gran1911.pdf",
+ paper = "Gran1911.pdf"
\end{chunk}
@@ 30172,7 +32690,6 @@ Grove, IL, USA and Oxford, UK, 1992
\bibitem[Gruntz 93]{Gru93} Gruntz, Dominik
title = "Limit computation in computer algebra",
url = "http://algo.inria.fr/seminars/sem9293/gruntz.pdf",
 paper = "Gru93.pdf",
abstract = "
The automatic computation of limits can be reduced to two main
subproblems. The first one is asymptotic comparison where one must
@@ 30191,7 +32708,8 @@ Grove, IL, USA and Oxford, UK, 1992
operations to one variable and the rational numbers. D. Gruntz and
G. Gonnet propose a slightly different algorithm for explog
functions. Extensions to larger classes of functions are also
 discussed."
+ discussed.",
+ paper = "Gru93.pdf"
\end{chunk}
@@ 30212,9 +32730,7 @@ Grove, IL, USA and Oxford, UK, 1992
month = "November",
year = "1995",
pages = "16151628",
 paper = "Hach95.pdf",
url = "https://hal.inria.fr/inria00074404/file/RR2267.pdf",
 keywords = "axiomref",
algebra =
"\newline\refto{package GPAFF GeneralPackageForAlgebraicFunctionField}
\newline\refto{package PAFFFF PackageForAlgebraicFunctionFieldOverFiniteField}
@@ 30229,7 +32745,9 @@ Grove, IL, USA and Oxford, UK, 1992
adjoint divisor of the curve. Finally we show how to use the algorithm
of BrillNoether to compute a basis of the vector space associated to
a divisor of the curve. Two examples of constructions of AGcodes are
 given at the end."
+ given at the end.",
+ paper = "Hach95.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 30320,7 +32838,7 @@ Methuen. (1967)
publisher = "IBM",
year = "2005",
url = "http://www.redbooks.ibm.com/redbooks/pdfs/sg246478.pdf",
 paper = "Haya05.pdf",
+ paper = "Haya05.pdf"
}
\end{chunk}
@@ 30378,7 +32896,6 @@ J. Inst. Math. Appl. 14 89103. (1974)
title = "Extended Rate, more GFUN",
year = "2010",
url = "https://arxiv.org/abs/math/0702086v2",
 paper = "Hebi10.pdf",
algebra =
"\newline\refto{package GUESS Guess}
\newline\refto{package GUESSAN GuessAlgebraicNumber}
@@ 30395,7 +32912,8 @@ J. Inst. Math. Appl. 14 89103. (1974)
efficient. Thus we extend and complement Christian Krattenthaler's
program Rate, the parts concerned with guessing of Bruno Salvy and
Paul Zimmermann's GFUN, the univariate case of Manuel Kauers' Guess.m
 and Manuel Kauers' and Christoph Koutschan's qGeneratingFunctions.m."
+ and Manuel Kauers' and Christoph Koutschan's qGeneratingFunctions.m.",
+ paper = "Hebi10.pdf"
}
\end{chunk}
@@ 30472,7 +32990,6 @@ IEEE Comput. Soc. Press, pp. 678687.
author = "Hubbard, John H. and Lundell, Benjamin",
title = "A First Look at Differential Algebra",
url = "http://www.math.cornell.edu/~hubbard/diffalg1.pdf",
 paper = "Hubb.pdf",
algebra = "\newline\refto{category DVARCAT DifferentialVariableCategory}",
abstract =
"The object of the paper is to prove that the differential equation
@@ 30495,7 +33012,8 @@ IEEE Comput. Soc. Press, pp. 678687.
polynomial equation
\[x^54x^22=0\]
has no solutions which can be written as radicals of solutions to
 lower degree polyomial equations."
+ lower degree polyomial equations.",
+ paper = "Hubb.pdf"
}
\end{chunk}
@@ 30510,8 +33028,6 @@ IEEE Comput. Soc. Press, pp. 678687.
series = "Lecture Notes in Computer Science 2630",
year = "2003",
pages = "139",
 keywords = "axiomref",
 paper = "Hube03.pdf",
url =
"http://wwwsop.inria.fr/members/Evelyne.Hubert/publications/sncsp.pdf",
abstract =
@@ 30524,7 +33040,9 @@ IEEE Comput. Soc. Press, pp. 678687.
independently of those. We also detail a selection of algorithms, one
for each task. We address here polynomial systems and some of the
material we develop here will be used in the second part, devoted to
 differential systems."
+ differential systems.",
+ paper = "Hube03.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 30539,8 +33057,6 @@ IEEE Comput. Soc. Press, pp. 678687.
series = "Lecture Notes in Computer Science 2630",
year = "2003",
pages = "4087",
 keywords = "axiomref",
 paper = "Hube03a.pdf",
url =
"http://wwwsop.inria.fr/members/Evelyne.Hubert/publications/sncsd.pdf",
abstract =
@@ 30553,7 +33069,9 @@ IEEE Comput. Soc. Press, pp. 678687.
independently of those. We also detail a selection of algorithms, one
for each task. The present article deals with differential systems. It
uses results presented in the first article on polynomial systems but
 can be read independently."
+ can be read independently.",
+ paper = "Hube03a.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 30606,7 +33124,6 @@ Dept. G68, P.O. Box 1900, Boulder, Colorado, USA 803019191.
volume = "78",
pages = "171177",
year = "1988",
 paper = "Itoh88.pdf",
algebra = "\newline\refto{package INBFF InnerNormalBasisFieldFunctions}",
abstract =
"This paper proposes a fast algorithm for computing multiplicative
@@ 30624,7 +33141,8 @@ Dept. G68, P.O. Box 1900, Boulder, Colorado, USA 803019191.
required in Wang's method. The same idea of the proposed fast
algorithm is applicable to the general power operation in $GF(2^m)$
and the computation of multiplicative inverses in $GF(q^m)$
 $(q=2^n)$."
+ $(q=2^n)$.",
+ paper = "Itoh88.pdf"
}
\end{chunk}
@@ 30658,8 +33176,8 @@ Dept. G68, P.O. Box 1900, Boulder, Colorado, USA 803019191.
year = "1951",
pages = "509530",
url = "http://www.math.uci.edu/~brusso/jacobson1951.pdf",
 paper = "Jaco51.pdf",
 algebra = "\newline\refto{category MONAD Monad}"
+ algebra = "\newline\refto{category MONAD Monad}",
+ paper = "Jaco51.pdf"
}
\end{chunk}
@@ 30724,9 +33242,9 @@ Comput. J. 9 281285. (1966)
author = "Joyner, W. D.",
title = "Open Source Mathematical Software: A White Paper",
url = "http://wdjoyner.com/writing/research/oscasnsfwhitepaper12.tex",
+ year = "2008",
paper = "Joyn08a.tex",
 keywords = "axiomref",
 year = "2008"
+ keywords = "axiomref"
}
\subsection{K} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ 30771,11 +33289,11 @@ Comput. J. 9 281285. (1966)
\newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
\newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
year = "1998",
 paper = "Kalk98.pdf",
abstract =
"In this paper we investigate how algorithms for computing heights,
radicals, unmixed and primary decompositions of ideals can be lifted
 from a Noetherian commutative ring $R$ to polynomial rings over $R$."
+ from a Noetherian commutative ring $R$ to polynomial rings over $R$.",
+ paper = "Kalk98.pdf"
}
\end{chunk}
@@ 30796,8 +33314,8 @@ Springer Verlag Heidelberg, 1989, ISBN 0387969802
title = "Re: Symbolic Math: try a translation of Axiom to Julia?",
url =
"https://groups.google.com/forum/#!msg/juliadev/NTfS9fJuIcE/MINQuQuGfoUJ",
 keywords = "axiomref",
 year = "2016"
+ year = "2016",
+ keywords = "axiomref"
}
\end{chunk}
@@ 30859,7 +33377,7 @@ AddisonWesley 1998
title = "On Radical ZeroDimensional Ideals",
J. Symbolic Computations 8, 545552 (1989)
url = "http://www.sciencedirect.com/science/article/pii/S0747717189800604/pdf?md5=f06dc6269514c90dcae57f0184bcbe65&pid=1s2.0S0747717189800604main.pdf",
 paper = "Koba88.pdf",
+ paper = "Koba88.pdf"
\end{chunk}
@@ 30875,8 +33393,8 @@ J. Symbolic Computations 8, 545552 (1989)
\begin{chunk}{ignore}
\bibitem[Koutschan 10]{Kou10} Koutschan, Christoph
title = "Axiom / FriCAS",
 keywords = "axiomref",
url = "http://www.risc.jku.at/education/courses/ws2010/cas/axiom.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 30961,7 +33479,6 @@ PrenticeHall. (1974)
year = "1979",
month = "September",
pages = "308325",
 paper = "Laws79.pdf",
abstract =
"A package of 38 low level subprograms for many of the basic
operations of numerical linear algebra is presented. The package is
@@ 30969,7 +33486,8 @@ PrenticeHall. (1974)
include dot product, elementary vector operations, Givens
transformations, vector copy and swap, vector norm, vector scaling,
and the determination of the index of the vector component of largest
 magnitude."
+ magnitude.",
+ paper = "Laws79.pdf"
}
\end{chunk}
@@ 30988,7 +33506,6 @@ PrenticeHall. (1974)
volume = "33",
year = "1991",
pages = "147160",
 paper = "Laza91.pdf",
algebra =
"\newline\refto{category TSETCAT TriangularSetCategory}
\newline\refto{category RSETCAT RegularTriangularSetCategory}
@@ 31002,7 +33519,8 @@ PrenticeHall. (1974)
details and proofs are omitted, for emphasising on the relation
between the algorithm design and a good representation of the
result. The algorithm is based on a new theorem of decomposition for
 algebraic varieties."
+ algebraic varieties.",
+ paper = "Laza91.pdf"
}
\end{chunk}
@@ 31028,15 +33546,15 @@ Journal of Symbolic Computation, 1992, 13, 117131
year = "1990",
month = "February",
pages = "113115",
 keywords = "axiomref",
 paper = "Laza90.pdf",
abstract = "
A new formula is given for the logarithmic part of the integral of a
rational function, one that strongly improves previous algorithms and
does not need any computation in an algebraic extension of the field
of constants, nor any factorisation since only polynomial arithmetic
and GCD computations are used. This formula was independently found
 and implemented in SCRATCHPAD by B.M. Trager."
+ and implemented in SCRATCHPAD by B.M. Trager.",
+ paper = "Laza90.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 31081,11 +33599,11 @@ Journal of Symbolic Computation, 1992, 13, 117131
year = "1987",
pages = "217231",
url = "http://www.math.leidenuniv.nl/~hwl/PUBLICATIONS/",
 paper = "Lens87.pdf",
algebra = "\newline\refto{package FFPOLY FiniteFieldPolynomialPackage}",
abstract =
"It is proved that any finite extension of a finite field has a normal
 basis consisting of primitive roots"
+ basis consisting of primitive roots",
+ paper = "Lens87.pdf"
}
\end{chunk}
@@ 31097,7 +33615,7 @@ Journal of Symbolic Computation, 1992, 13, 117131
title = "A quick introduction to Clifford Algebras",
publisher = "School of Mathematics, University of New South Wales",
year = "2003",
 paper = "Leop03.pdf",
+ paper = "Leop03.pdf"
}
\end{chunk}
@@ 31195,7 +33713,7 @@ AddisonWesley (March 1979) ISBN 0201144611
title = "Understanding the Dynamics of Complex Lisp Programs",
year = "2009",
url = "http://www.martinloetzsch.de/papers/loetzsch09understanding.pdf",
 paper = "Loet09.pdf",
+ paper = "Loet09.pdf"
}
\end{chunk}
@@ 31349,8 +33867,6 @@ Mathematical Surveys. 3 Am. Math. Soc., Providence, RI. (1966)
title = "Polynomial Gcd Computations over Towers of Algebraic Extensions",
year = "1995",
journal = "Proceedings of AAECC11",
 keywords = "axiomref",
 paper = "Maza95.pdf",
algebra =
"\newline\refto{category TSETCAT TriangularSetCategory}
\newline\refto{category RSETCAT RegularTriangularSetCategory}
@@ 31367,7 +33883,9 @@ Mathematical Surveys. 3 Am. Math. Soc., Providence, RI. (1966)
present here a new approach which takes permanently into account those
algebraic relations. It is based on a property of subresultant
remainder sequences and leads to a great increase of the speed of
 computations and thus the size of accessible systems."
+ computations and thus the size of accessible systems.",
+ paper = "Maza95.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 31385,8 +33903,6 @@ Mathematical Surveys. 3 Am. Math. Soc., Providence, RI. (1966)
resolution des systemes d'equations algebriques",
school = "Universite P.etM. Curie",
year = "1997",
 paper = "Maza97.pdf",
 keyword = "axiomref",
algebra =
"\newline\refto{category TSETCAT TriangularSetCategory}
\newline\refto{category RSETCAT RegularTriangularSetCategory}
@@ 31410,7 +33926,9 @@ Mathematical Surveys. 3 Am. Math. Soc., Providence, RI. (1966)
a theorecal and unified presentation, together with an experimental
comparison with similar methods due to Wu WenTsun, Dongming Wang and
Michael Kalkbrener were realized by Philippe Aubry and are reported in
 a third part of this document."
+ a third part of this document.",
+ paper = "Maza97.pdf",
+ keyword = "axiomref"
}
\end{chunk}
@@ 31480,12 +33998,12 @@ J. Res. Natl. Inst. Stand. Technol. (NIST) V105 No4 JulyAug 2000 pp589590
journal = "Interactive Systems for Experimental and Applied Mathematics",
publisher = "M. Klerer and J. Reinfelds, eds., Academic Press, New York",
pages = "7990",
 paper = "Mill68.pdf",
abstract = "
CHARYBDIS (from CHARactercomposed sYmBolic DISplay) is a LISP program
to display mathematical expressions on typewriterlike devices such as
line printers, teletypes, and scopes which display lines of characters,
 as well as typewriters."
+ as well as typewriters.",
+ paper = "Mill68.pdf"
}
\end{chunk}
@@ 31547,11 +34065,11 @@ SIAM J. Numer. Anal. 10 241256. 1973
number = "1",
month = "July",
pages = "4550",
 paper = "Muld97.pdf",
abstract = "
An ambiguity in a formula of Lazard, Rioboo and Trager, connecting
subresultants and rational function integration, is indicated and
 examples of incorrect interpretations are given."
+ examples of incorrect interpretations are given.",
+ paper = "Muld97.pdf"
}
\end{chunk}
@@ 31602,7 +34120,6 @@ Journal of the ACM, Vol. 25, No. 2, April 1978, pp. 271282
number = "12",
pages = "136",
year = "1998",
 paper = "Naud98.pdf",
abstract =
"This paper is a tutorial introduction to univariate polynomial
factorization over finite fields. The authors recall the classical
@@ 31611,7 +34128,8 @@ Journal of the ACM, Vol. 25, No. 2, April 1978, pp. 271282
to these methods. Explicit algorithms are presented in a form suitable
for almost immediate implementation. They give a detailed description
of an efficient implementation of the CantorZassenhaus algorithm used
 in the release 2 of the Axiom computer algebra system."
+ in the release 2 of the Axiom computer algebra system.",
+ paper = "Naud98.pdf"
}
\end{chunk}
@@ 31649,7 +34167,7 @@ ACM Trans. Math. Softw. 5 118125. (1979)
\bibitem[Ollagnier 94]{Olla94} Ollagnier, Jean Moulin
title = "Algorithms and methods in differential algebra",
url = "http://www.lix.polytechnique.fr/~moulin/papiers/atelier.pdf",
 paper = "Olla94.pdf",
+ paper = "Olla94.pdf"
\end{chunk}
@@ 31730,7 +34248,6 @@ ACM Trans. Math. Softw. 8 195209. (1982)
month = "February 6",
year = "2016",
url = "http://github.com/panicz/pamphlet/raw/master/pamphlet.pdf",
 paper = "Gode16.pdf",
abstract =
"R is a programming language that has been gaining popularity in the
domains such as machine learning and artificial intelligence over the
@@ 31745,7 +34262,8 @@ ACM Trans. Math. Softw. 8 195209. (1982)
This pamphlet explores and expresses various {\sl computational
intelligence methods} using {\sl Guile}, a very pleasant
 implementation of the {\sl Scheme} programming language."
+ implementation of the {\sl Scheme} programming language.",
+ paper = "Gode16.pdf"
}
@@ 31856,7 +34374,6 @@ J. Inst. Maths Applics. 8 1635. (1971)
school = "l'Universite de Paris 6",
year = "2002",
month = "December",
 paper = "Phil02.pdf",
abstract =
"Polynomial systems can be found in many industrial applications. They
are also in the heart of effective algebraic geometry. A fundamental
@@ 31878,7 +34395,8 @@ J. Inst. Maths Applics. 8 1635. (1971)
describe the sparse matrix elimination algorithm we used in or
program. Finally, we present some of the experiments we have done with
our program in domains like computer vision, algorithmic geometry,
 robotics, or pharmacology."
+ robotics, or pharmacology.",
+ paper = "Phil02.pdf"
}
\end{chunk}
@@ 31986,8 +34504,8 @@ Mathematical Programming: The State of the Art.
pages = "4151",
year = "1973",
url = "http://hall.org.ua/halls/wizzard/pdf/Vaughan.Pratt.TDOP.pdf",
 keywords = "axiomref",
paper = "Prat73.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 32171,7 +34689,7 @@ Oxford University Press, June 1993 ISBN 0198536798
\bibitem[Reznick 93]{Rezn93} Reznick, Bruce
title = "An Inequality for Products of Polynomials",
Proc. AMS Vol 117 No 4 April 1993
 paper = "Rezn93.pdf",
+ paper = "Rezn93.pdf"
\end{chunk}
@@ 32181,7 +34699,6 @@ Proc. AMS Vol 117 No 4 April 1993
\bibitem[Rich xx]{Rixx} Rich, A.D.; Jeffrey, D.J.
title = "Crafting a Repository of Knowledge Based on Transformation",
url = "http://www.apmaths.uwo.ca/~djeffrey/Offprints/IntegrationRules.pdf",
 paper = "Rixx.pdf",
abstract = "
We describe the development of a repository of mathematical knowledge
based on transformation rules. The specific mathematical problem is
@@ 32192,7 +34709,8 @@ Proc. AMS Vol 117 No 4 April 1993
formats. The principles upon which the set of rules is compiled is
described. One important principle is minimality. The benefits of the
approach are illustrated with examples, and with the results of
 comparisons with other approaches."
+ comparisons with other approaches.",
+ paper = "Rixx.pdf"
\end{chunk}
@@ 32251,8 +34769,8 @@ November 1996.
year = "1950",
volume = "33",
isbn = "9780821846384",
 paper = "Ritt50.pdf",
 algebra = "\newline\refto{category DVARCAT DifferentialVariableCategory}"
+ algebra = "\newline\refto{category DVARCAT DifferentialVariableCategory}",
+ paper = "Ritt50.pdf"
}
\end{chunk}
@@ 32284,7 +34802,6 @@ in Computational Discrete Mathematics ISBN 3540427759 pp119135
year = "2006",
location = "Nancy, France",
pages = "431434",
 paper = "Rube06.pdf",
url = "http://mathinfo06.iecn.unancy.fr/papers/dmAG431434.pdf",
algebra =
"\newline\refto{package GUESS Guess}
@@ 32299,7 +34816,8 @@ in Computational Discrete Mathematics ISBN 3540427759 pp119135
of, for example, rational numbers or rational functions, given the
first few terms. Thereby we extend and complement C. Krattenthaler's
program RATE [RATE: a Mathematics guessing machine] and the relevant
 parts of B. Salvy and P. Zimmermann's GFUN."
+ parts of B. Salvy and P. Zimmermann's GFUN.",
+ paper = "Rube06.pdf"
}
\end{chunk}
@@ 32353,7 +34871,6 @@ Num. Math. 16 205223. (1970)
year = "1961",
algebra = "\newline\refto{category NARNG NonAssociativeRng}",
url = "http://www.gutenberg.org/ebooks/25156",
 paper = "Scha61.pdf",
journal = "Advanced Subject Matter Institute",
abstract =
"These are notes for my lectures in July, 1961, at the Advanced
@@ 32368,7 +34885,8 @@ Num. Math. 16 205223. (1970)
article, bringing the statements there up to date and providing
detailed proofs of a selected group of theorems. The proofs illustrate
a number of important techniques used in the study of nonassociative
 algebras."
+ algebras.",
+ paper = "Scha61.pdf"
}
\end{chunk}
@@ 32453,8 +34971,8 @@ Software Practice and Experience. 6(1) (1976)
\begin{chunk}{ignore}
\bibitem[Seiler 95a]{Sei95a} Seiler, W.M.; Calmet, J.
title = "JET  An Axiom Environment for Geometric Computations with Differential Equations",
 keywords = "axiomref",
paper = "Sei95a.pdf",
+ keywords = "axiomref"
\end{chunk}
@@ 32472,7 +34990,6 @@ Princeton. 517523. 1968
\bibitem[Shirayanagi 96]{Shir96} Shirayanagi, Kiyoshi
title = "Floating point Gr\"obner bases",
Mathematics and Computers in Simulation 42 pp 509528 (1996)
 paper = "Shir96.pdf",
abstract = "
Bracket coefficients for polynomials are introduced. These are like
specific precision floating point numbers together with error
@@ 32486,7 +35003,8 @@ Mathematics and Computers in Simulation 42 pp 509528 (1996)
coefficientwise. Moreover, there is a precision $M$ such that if
$\mu \ge M$, then the sets of monomials with nonzero coefficients of
$G_\mu$ and $G$ are exactly the same. The practical usefulness of the
 algorithm is suggested by experimental results."
+ algorithm is suggested by experimental results.",
+ paper = "Shir96.pdf"
\end{chunk}
@@ 32509,14 +35027,14 @@ Mathematics and Computers in Simulation 42 pp 509528 (1996)
\bibitem[Singer 89]{Sing89} Singer, M.F.
``Formal Solutions of Differential Equations''
J. Symbolic COmputation 10, No.1 5994 (1990)
 paper = "Sing89.pdf",
 keywords = "survey",
abstract = "
We give a survey of some methods for finding formal solutions of
differential equations. These include methods for finding power series
solutions, elementary and liouvillian solutions, first integrals, Lie
theoretic methods, transform methods, asymptotic methods. A brief
 discussion of difference equations is also included."
+ discussion of difference equations is also included.",
+ paper = "Sing89.pdf",
+ keywords = "survey"
\end{chunk}
@@ 32563,8 +35081,8 @@ The University of Chicago Press. 1974
url = "http://daly.axiomdeveloper.org/clm.pdf",
publisher = "Digital Equipment Corporation",
isbn = "15555580416",
 paper = "Stee90.pdf",
 algebra = "\newline\refto{package DFSFUN DoubleFloatSpecialFunctions}"
+ algebra = "\newline\refto{package DFSFUN DoubleFloatSpecialFunctions}",
+ paper = "Stee90.pdf"
}
\end{chunk}
@@ 32592,7 +35110,6 @@ The University of Chicago Press. 1974
number = "4",
pages = "711717",
year = "1990",
 paper = "Stin90.pdf",
algebra = "\newline\refto{package INBFF InnerNormalBasisFieldFunctions}",
abstract =
"A normal basis represention in $GF(2^n)$ allows squaring to be
@@ 32600,7 +35117,8 @@ The University of Chicago Press. 1974
$GF(2^n)$ using a normal basis have been studied by several
researchers. In this paper, algorithms for performing exponentiation
in $GF(2^n)$ using a normal basis, and how they can be speeded up by
 using parallelization, are investigated."
+ using parallelization, are investigated.",
+ paper = "Stin90.pdf"
}
\end{chunk}
@@ 32698,7 +35216,7 @@ J. Comput. Phys. 52 340350. (1983)
month = "April",
year = "1994",
url = "http://www.ams.org/journals/bull/19943002/S027309791994005026/S027309791994005026.pdf",
 paper = "Thur94.pdf",
+ paper = "Thur94.pdf"
}
\end{chunk}
@@ 32723,8 +35241,6 @@ Chapter 8. NPL Notes on Applied Science (2nd Edition). 16 HMSO. 1961
year = "1999",
location = "Marktoberdorf, Germany",
pages = "301346",
 keywords = "axiomref",
 paper = "Mart99.pdf",
url =
"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.50.2061&rep=rep1&type=pdf",
abstract =
@@ 32756,7 +35272,9 @@ Chapter 8. NPL Notes on Applied Science (2nd Edition). 16 HMSO. 1961
computation have transformed mathematical logic, computation has made
constructive proof feasible, and effective notions of practice for
proofs about hardware and software are by no means well understood.
 However these matters fall outside the scope of this paper."
+ However these matters fall outside the scope of this paper.",
+ paper = "Mart99.pdf",
+ keywords = "axiomref"
}
\end{chunk}
@@ 33063,7 +35581,6 @@ Math. Tables Aids Comput. 10 9196. (1956)
\bibitem[Zakrajsek 02]{Zak02} Zakrajsek, Helena
title = "Applications of Hermite transform in computer algebra",
url = "http://www.imfm.si/preprinti/PDF/00835.pdf",
 paper = "Zak02.pdf",
abstract = "
let $L$ be a linear differential operator with polynomial
coefficients. We show that there is an isomorphism of differential
@@ 33073,7 +35590,8 @@ Math. Tables Aids Comput. 10 9196. (1956)
present an algorithm that computes the Hermite transform of a rational
function and use it to find $n+1$ linearly independent solutions of
${\bf L}y=0$ when $({\bf D_\alpha}{\bf L})f(x)=0$ has a rational
 solution with $n$ distinct finite poles."
+ solution with $n$ distinct finite poles.",
+ paper = "Zak02.pdf"
\end{chunk}
@@ 33095,7 +35613,6 @@ Math. Tables Aids Comput. 10 9196. (1956)
title = "Optimal Algorithm for Algebraic Factoring",
year = "1997",
url = "http://www.mmrc.iss.ac.cn/~lzhi/Publications/zopfac.pdf",
 paper = "Zhi97.pdf",
abstract = "
This paper presents an optimized method for factoring multivariate
polynomials over algebraic extension fields which defined by an
@@ 33105,7 +35622,8 @@ Math. Tables Aids Comput. 10 9196. (1956)
factorize the univariate polynomials over the algebraic number fields.
Finally, construct multivariate factors of the original polynomial by
Hensel lemma and TRUEFACTOR test. Some examples with timing are
 included."
+ included.",
+ paper = "Zhi97.pdf"
\end{chunk}
@@ 33127,10 +35645,10 @@ Math. Tables Aids Comput. 10 9196. (1956)
title = "Mathematics in the Age of the Turing Machine",
year = "2013",
url = "http://arxiv.org/pdf/1302.2898v1",
 paper = "Hale13.pdf",
abstract = "
This article gives a survey of mathematical proofs that rely on
 computer calculations and formal proofs"
+ computer calculations and formal proofs",
+ paper = "Hale13.pdf"
}
\end{chunk}
@@ 33142,7 +35660,6 @@ Math. Tables Aids Comput. 10 9196. (1956)
author = "Martin, W.A. and Fateman, R.J.",
title = "The Macsyma System",
url = "http://groups.csail.mit.edu/mac/classes/symbolic/spring13/readings/simplification/martinfatemanmacsyma.pdf",
 paper = "Martxx.pdf",
abstract = "
MACSYMA is a system for symbolic manipulation of algebraic expressions
which is being developed at Project MAC, M.I.T. This paper discusses
@@ 33164,7 +35681,8 @@ Math. Tables Aids Comput. 10 9196. (1956)
subsystem. The facilities derived from this are discussed in
considerable detail.
 An appendix briefly notes some highlights of the overall system."
+ An appendix briefly notes some highlights of the overall system.",
+ paper = "Martxx.pdf"
}
@@ 33181,7 +35699,6 @@ Math. Tables Aids Comput. 10 9196. (1956)
title = "Engel Expansions of qSeries by Computer Algebra",
year = "2000",
url = "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.32.207",
 paper = "Andr00.pdf",
abstract = "
The $q$Engle Expansion is an algorithm that leads to unique series
expansions of $q$series. Various examples related to classical
@@ 33193,7 +35710,8 @@ Math. Tables Aids Comput. 10 9196. (1956)
freely available via the web and should help to intensify research in
this new branch of $q$series theory. Among various illustrative
examples we present a new infinite RogersRamanujan type family that
 has been discovered by using the package."
+ has been discovered by using the package.",
+ paper = "Andr00.pdf"
}
@@ 33207,11 +35725,11 @@ Math. Tables Aids Comput. 10 9196. (1956)
title = "Integration of Solutions of Linear Functional Equations",
year = "1999",
url = "http://www.math.fsu.edu/~hoeij/papers/itsf99/ab_final.pdf",
 paper = "Abra99.pdf",
abstract = "
We introduce the notion of the adjoint Ore ring and give a definition
of adjoint polynomial, operator and equation. We apply this for
 integrating solutions of Ore equations."
+ integrating solutions of Ore equations.",
+ paper = "Abra99.pdf"
}
@@ 33226,7 +35744,6 @@ Math. Tables Aids Comput. 10 9196. (1956)
title = "On the Rapid Computation of Various Polylogarithmic Constants",
year = "1997",
url = "http://www.ams.org/journals/mcom/199766218/S0025571897008569/S0025571897008569.pdf",
 paper = "Bail97.pdf",
abstract = "
We give algorithms for the computation of the $d$th digit of certain
transcendental numbers in various bases. These algorithms can be
@@ 33248,7 +35765,8 @@ Math. Tables Aids Comput. 10 9196. (1956)
to be new, for example the critical identity for $\pi$:
\[\pi=\sum_{i=0}^\infty{\frac{1}{16^i}\left(
 \frac{4}{8i+1}\frac{2}{8i+4}\frac{1}{8i+5}\frac{1}{8i+6}\right)}\]"
+ \frac{4}{8i+1}\frac{2}{8i+4}\frac{1}{8i+5}\frac{1}{8i+6}\right)}\]",
+ paper = "Bail97.pdf"
}
@@ 33261,7 +35779,6 @@ Math. Tables Aids Comput. 10 9196. (1956)
title = "Open Digital Research Environment Toolkit for the Advancement of Mathematics",
year = "2015",
url = "http://opendreamkit.org",
 paper = "Thie15.pdf",
abstract =
"OpenDreamKit will deliver a flexible toolkit enabling research groups
to set up Virtual Research Environments, customised to meet the varied
@@ 33297,9 +35814,1092 @@ Math. Tables Aids Comput. 10 9196. (1956)
researchers, and software developers with a long track record of
delivering innovative open source software solutions for their
respective communities. All produced code and tools will be open
 source."
+ source.",
+ paper = "Thie15.pdf"
+}
+
+\end{chunk}
+
+\chapter{Beebe Bibliography}
+
+\begin{chunk}{beebe.bib}
+%%% *BibTeX*
+%%% ====================================================================
+%%% BibTeXfile{
+%%% author = "Nelson H. F. Beebe",
+%%% version = "1.18",
+%%% date = "15 August 2014",
+%%% time = "18:59:18 MDT",
+%%% filename = "axiom.bib",
+%%% address = "University of Utah
+%%% Department of Mathematics, 110 LCB
+%%% 155 S 1400 E RM 233
+%%% Salt Lake City, UT 841120090
+%%% USA",
+%%% telephone = "+1 801 581 5254",
+%%% FAX = "+1 801 581 4148",
+%%% URL = "http://www.math.utah.edu/~beebe",
+%%% checksum = "22023 4297 20558 200979",
+%%% email = "beebe at math.utah.edu, beebe at acm.org,
+%%% beebe at computer.org (Internet)",
+%%% codetable = "ISO/ASCII",
+%%% keywords = "bibliography; AXIOM;
+%%% Scratchpad; symbolic algebra",
+%%% license = "public domain",
+%%% supported = "yes",
+%%% docstring = "This file contains a bibliography of
+%%% publications about the AXIOM (formerly
+%%% known as Scratchpad) symbolic algebra
+%%% system. It also covers publications about
+%%% Scratchpad and a few about MathCAD.
+%%%
+%%% At version 1.18, the year coverage looked
+%%% like this:
+%%%
+%%% 1971 ( 3) 1984 ( 6) 1997 ( 0)
+%%% 1972 ( 3) 1985 ( 2) 1998 ( 1)
+%%% 1973 ( 0) 1986 ( 4) 1999 ( 2)
+%%% 1974 ( 1) 1987 ( 5) 2000 ( 0)
+%%% 1975 ( 1) 1988 ( 8) 2001 ( 1)
+%%% 1976 ( 1) 1989 ( 18) 2002 ( 1)
+%%% 1977 ( 1) 1990 ( 7) 2003 ( 3)
+%%% 1978 ( 0) 1991 ( 16) 2004 ( 1)
+%%% 1979 ( 0) 1992 ( 16) 2005 ( 9)
+%%% 1980 ( 0) 1993 ( 10) 2006 ( 2)
+%%% 1981 ( 0) 1994 ( 11) 2007 ( 6)
+%%% 1982 ( 0) 1995 ( 7) 2008 ( 1)
+%%%
+%%% Article: 34
+%%% Book: 17
+%%% InCollection: 1
+%%% InProceedings: 48
+%%% Manual: 1
+%%% MastersThesis: 2
+%%% Proceedings: 28
+%%% TechReport: 16
+%%%
+%%% Total entries: 147
+%%%
+%%% Scratchpad and AXIOM were developed at IBM
+%%% research laboratories over many years before
+%%% they were offered as supported products.
+%%% Today, AXIOM is marketed for several
+%%% platforms by the Numerical Algorithms Group,
+%%% Inc. (NAG) (Downer's Grove, IL, USA. and
+%%% Oxford, UK), and versions are available in
+%%% late 1995 for HewlettPackard 9000 (HPUX),
+%%% IBM RS/6000 (AIX), and Sun (SunOS) systems,
+%%% with ports to other systems under
+%%% development.
+%%%
+%%% Further information on AXIOM licensing
+%%% can be found at http://www.nag.com/ and
+%%% http://www.nag.co.uk/1h/symbolic/AX.html.
+%%%
+%%% NAG maintains an AXIOM code and documentation
+%%% repository at http://www.nag.co.uk/symbolic/
+%%% AX/Upload_Readme.html. All of the NAG
+%%% technical reports listed in this bibliography
+%%% can be found at that address.
+%%%
+%%% In 2006, AXIOM became free software, with a
+%%% Web site at
+%%%
+%%% http://www.axiomdeveloper.org
+%%%
+%%% This bibliography has been collected from the
+%%% author's personal bibliography files, from
+%%% the very large computer science bibliography
+%%% collection on ftp.ira.uka.de in
+%%% /pub/bibliography to which many people of
+%%% have contributed, and from several
+%%% Internetaccessible library catalogs, notably
+%%% those of the University of California,
+%%% Library of Congress, OCLC, plus the IEEE
+%%% INSPEC (19891995) database.
+%%%
+%%% This bibliography is sorted by year, and
+%%% within each year, by author and title key,
+%%% with ``bibsort byyear''. Crossreferenced
+%%% proceedings entries appear at the end,
+%%% because of a restriction in the current
+%%% BibTeX.
+%%%
+%%% The checksum field above contains a CRC16
+%%% checksum as the first value, followed by the
+%%% equivalent of the standard UNIX wc (word
+%%% count) utility output of lines, words, and
+%%% characters. This is produced by Robert
+%%% Solovay's checksum utility.",
+%%% }
+%%% ====================================================================
+
+%%% Acknowledgement abbreviations:
+
+@String{acknhfb = "Nelson H. F. Beebe,
+ University of Utah,
+ Department of Mathematics, 110 LCB,
+ 155 S 1400 E RM 233,
+ Salt Lake City, UT 841120090, USA,
+ Tel: +1 801 581 5254,
+ FAX: +1 801 581 4148,
+ email: \pathbeebe@math.utah.edu,
+ \pathbeebe@acm.org,
+ \pathbeebe@computer.org (Internet),
+ URL: \pathhttp://www.math.utah.edu/~beebe/"}
+
+%%% ====================================================================
+%%% Institution abbreviations:
+
+@String{instNAG = "Numerical Algorithms Group, Inc."}
+
+@String{instNAG:adr = "Downer's Grove, IL, USA and Oxford,
+ UK"}
+
+%%% ====================================================================
+%%% Journal abbreviations:
+
+@String{jACMCOMMCOMPALGEBRA = "ACM Communications in Computer Algebra"}
+
+@String{jAMERJPHYSICS = "American Journal of Physics"}
+
+@String{jCOED = "CoED"}
+
+@String{jCOMPPHYSCOMM = "Computer Physics Communications"}
+
+@String{jELECTRONIK = "Elektronik"}
+
+@String{jIFIPTRANSA = "IFIP Transactions. A. Computer Science and
+ Technology"}
+
+@String{jJSYMBOLICCOMP = "Journal of Symbolic Computation"}
+
+@String{jLECTNOTESCOMPSCI = "Lecture Notes in Computer Science"}
+
+@String{jMATHCOMPEDU = "Mathematics and computer education"}
+
+@String{jSIGPLAN = "ACM SIG{\}PLAN Notices"}
+
+@String{jSIGSAM = "SIGSAM Bulletin (ACM Special Interest
+ Group on Symbolic and Algebraic
+ Manipulation)"}
+
+@String{jSTATCOMP = "Statistics and Computing"}
+
+@String{jTHEORCOMPSCI = "Theoretical Computer Science"}
+
+@String{jTOMS = "ACM Transactions on Mathematical Software"}
+
+@String{jZEITANGEMATHPHYS = "Zeitschrift fur Angewandte Mathematik
+ und Physik"}
+
+%%% ====================================================================
+%%% Publisher abbreviations:
+
+@String{pubACM = "ACM Press"}
+
+@String{pubACM:adr = "New York, NY 10036, USA"}
+
+@String{pubAP = "Academic Press"}
+
+@String{pubAP:adr = "New York, NY, USA"}
+
+@String{pubDEKKER = "Marcel Dekker"}
+
+@String{pubDEKKER:adr = "New York, NY, USA"}
+
+@String{pubSV = "Spring{\}erVer{\}lag"}
+
+@String{pubSV:adr = "Berlin, Germany~/ Heidelberg,
+ Germany~/ London, UK~/ etc."}
+
+@String{pubVIEWEG = "Friedrich Vieweg und Sohn"}
+
+@String{pubVIEWEG:adr = "Braunschweig, Germany"}
+
+%%% ====================================================================
+%%% Series abbreviations:
+
+@String{serLNCS = "Lecture Notes in Computer Science"}
+
+%%% ====================================================================
+%%% Bibliography entries:
+
+\getchunk{Griesmer:1971:SIF}
+\getchunk{Jenks:1971:MPS}
+\getchunk{Griesmer:1972:EOSb}
+\getchunk{Griesmer:1972:SCV}
+\getchunk{Jenks:1974:SL}
+\getchunk{Norman:1975:CFP}
+\getchunk{Jenks:1976:PC}
+\getchunk{Lueken:1977:UIF}
+\getchunk{Andrews:1984:RS}
+\getchunk{Davenport:1984:S}
+\getchunk{Jenks:1984:NSL}
+\getchunk{Jenks:1984:PKN}
+\getchunk{Sutor:1985:SIC}
+\getchunk{Gebauer:1986:BAS}
+\getchunk{Jenks:1986:SIA}
+\getchunk{Lucks:1986:FIP}
+\getchunk{Purtilo:1986:ASI}
+\getchunk{Burge:1987:ISS}
+\getchunk{Senechaud:1987:SIP}
+\getchunk{Sutor:1987:TICa}
+\getchunk{Sutor:1987:TICb}
+\getchunk{Andrews:1988:ASP}
+\getchunk{Davenport:1988:CA}
+\getchunk{Gebauer:1988:IBA}
+\getchunk{Jenks:1988:SIA}
+\getchunk{Schwarz:1988:PAD}
+\getchunk{Shannon:1988:UGB}
+\getchunk{Sutor:1988:SIA}
+\getchunk{Boehm:1989:TIP}
+\getchunk{Bronstein:1989:SRE}
+\getchunk{Burge:1989:ISS}
+\getchunk{Dicrescenzo:1989:AEA}
+\getchunk{Gianni:1989:ASS}
+\getchunk{Kusche:1989:IGT}
+\getchunk{Mathews:1989:SCA}
+\getchunk{Ollivier:1989:IRM}
+\getchunk{Salvy:1989:EAA}
+\getchunk{Schwarz:1989:FAL}
+\getchunk{Sit:1989:GAS}
+\getchunk{Wang:1989:PCL}
+\getchunk{Watt:1989:FPM}
+\getchunk{Davenport:1990:SVA}
+\getchunk{Fateman:1990:ATD}
+\getchunk{Fortenbacher:1990:ETI}
+\getchunk{Fouche:1990:ILK}
+\getchunk{Melachrinoudis:1990:TAT}
+\getchunk{Augot:1991:MDS}
+\getchunk{Bronstein:1991:RDE}
+\getchunk{Burge:1991:SRI}
+\getchunk{Davenport:1991:SVA}
+\getchunk{Goodwin:1991:UMT}
+\getchunk{Grabmeier:1991:CSA}
+\getchunk{Koseleff:1991:WGF}
+\getchunk{Lambe:1991:RHP}
+\getchunk{LeBlanc:1991:UMT}
+\getchunk{Lynch:1991:NQM}
+\getchunk{Salvy:1991:EAA}
+\getchunk{Schwarz:1991:MOG}
+\getchunk{Wang:1991:MMC}
+\getchunk{Anonymous:1992:PEH}
+\getchunk{Camion:1992:PCG}
+\getchunk{Dalmas:1992:PFL}
+\getchunk{Davenport:1992:AS}
+\getchunk{Davenport:1992:HDO}
+\getchunk{Davenport:1992:SVAa}
+\getchunk{Davenport:1992:SVAb}
+\getchunk{Duval:1992:EPS}
+\getchunk{Gil:1992:CJC}
+\getchunk{Grabmeier:1992:FFA}
+\getchunk{Jenks:1992:ASC}
+\getchunk{Lambe:1994:NGC}
+\getchunk{Rioboo:1992:RAC}
+\getchunk{Sit:1992:ASP}
+\getchunk{Smedley:1992:UPO}
+\getchunk{Zenger:1992:GFD}
+\getchunk{Bronstein:1993:FPF}
+\getchunk{Davenport:1993:PTR}
+\getchunk{Goodloe:1993:ADT}
+\getchunk{Monagan:1993:GPD}
+\getchunk{Petitot:1993:EA}
+\getchunk{Weber:1993:CCA}
+\getchunk{Beneke:1994:DFM}
+\getchunk{Brown:1994:CSC}
+\getchunk{Gruntz:1994:IG}
+\getchunk{Jenks:1994:HMA}
+\getchunk{Keady:1994:PAS}
+\getchunk{Seiler:1994:CIA}
+\getchunk{Seiler:1994:PDO}
+\getchunk{vanHoeij:1994:ACI}
+\getchunk{Anonymous:1995:GAM}
+\getchunk{Arnault:1995:CCN}
+\getchunk{Boulanger:1995:OOM}
+\getchunk{Broadbery:1995:IDE}
+\getchunk{Duval:1995:DEA}
+\getchunk{Roesner:1995:VSP}
+\getchunk{Benker:1998:ICS}
+\getchunk{Doye:1999:ACA}
+\getchunk{Kendall:2001:SIC}
+\getchunk{Daly:2002:AOS}
+\getchunk{Daly:2003:AVA}
+\getchunk{Grabmeier:2003:CAH}
+\getchunk{Jenks:2003:AVS}
+\getchunk{Caviness:2004:MRD}
+\getchunk{Daly:2005:AVAb}
+\getchunk{Daly:2005:AVAc}
+\getchunk{Daly:2005:AVAd}
+\getchunk{Daly:2005:AVAe}
+\getchunk{Daly:2005:AVAf}
+\getchunk{Daly:2005:AVAg}
+\getchunk{Daly:2005:AVAh}
+\getchunk{Daly:2005:AVAi}
+\getchunk{Daly:2005:AVAj}
+\getchunk{Daly:2006:AVA}
+\getchunk{Li:2006:EIP}
+\getchunk{Li:2007:VGP}
+\getchunk{Portes:2007:AVA}
+\getchunk{Page:2007:AOS}
+\getchunk{Smith:2007:ADA}
+\getchunk{Joyner:2008:OSC}
+\getchunk{Petrick:1971:PSS}
+\getchunk{Online:1972:OCP}
+\getchunk{Golden:1984:PMU}
+\getchunk{Fitch:1984:E}
+\getchunk{Buchberger:1985:EEC}
+\getchunk{Wexelblat:1987:IIT}
+\getchunk{Janssen:1988:TCA}
+\getchunk{ACM:1989:PAI}
+\getchunk{Huguet:1989:AAA}
+\getchunk{Davenport:1989:EEC}
+\getchunk{Gianni:1989:SAC}
+\getchunk{Mora:1989:AAA}
+\getchunk{Watanabe:1990:IPI}
+\getchunk{Miola:1990:DIS}
+\getchunk{Cohen:1991:EIS}
+\getchunk{Watt:1991:PIS}
+\getchunk{Anonymous:1991:PAC}
+\getchunk{Wang:1992:ISS}
+\getchunk{Bronstein:1993:IPI}
+\getchunk{Fitch:1993:DIS}
+\getchunk{Jacob:1993:PSI}
+\getchunk{Miola:1993:DIS}
+\getchunk{ACM:1994:IPI}
+\getchunk{Calmet:1994:RWC}
+\getchunk{Levelt:1995:IPI}
+\getchunk{Dooley:1999:IJS}
+\getchunk{Brown:2007:PIS}
+\getchunk{Shi:2007:CSIb}
+\getchunk{Proceedings}
+\end{chunk}
+
+\begin{chunk}{Anonymous:1992:PEH}
+@Article{Anonymous:1992:PEH,
+ author = "Anonymous",
+ title = "Programming Environments for HighLevel Scientific
+ Problem Solving. {IFIP} {TC2}\slash {WG} 2.5 Working
+ Conference",
+ journal = jIFIPTRANSA,
+ volume = "A2",
+ pages = "????",
+ year = "1992",
+ CODEN = "ITATEC",
+ ISSN = "09265473",
+ bibdate = "Tue Sep 17 06:41:20 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ confdate = "2327 Sept. 1991",
+ conflocation = "Karlsruhe, Germany",
+ confsponsor = "IFIP",
+ fjournal = "IFIP Transactions. A. Computer Science and
+ Technology",
+ pubcountry = "Netherlands",
+}
+
+\end{chunk}
+
+\begin{chunk}{Anonymous:1995:GAM}
+@Article{Anonymous:1995:GAM,
+ author = "Anonymous",
+ title = "{GAMM} 94 Annual Meeting",
+ journal = jZEITANGEMATHPHYS,
+ volume = "75",
+ number = "suppl. 2",
+ pages = "",
+ year = "1995",
+ CODEN = "ZAMMAX",
+ ISSN = "00442267",
+ bibdate = "Fri Dec 29 12:46:02 MST 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ confdate = "48 April 1994",
+ conflocation = "Braunschweig, Germany",
+ pubcountry = "Germany",
+}
+
+\end{chunk}
+
+\begin{chunk}{Proceedings}
+%%% ====================================================================
+%%% Crossreferenced entries must come last:
+
+@Proceedings{Petrick:1971:PSS,
+ editor = "S. R. Petrick",
+ booktitle = "{Proceedings of the second symposium on Symbolic and
+ Algebraic Manipulation, March 2325, 1971, Los
+ Angeles, California}",
+ title = "{Proceedings of the second symposium on Symbolic and
+ Algebraic Manipulation, March 2325, 1971, Los
+ Angeles, California}",
+ publisher = pubACM,
+ address = pubACM:adr,
+ pages = "x + 464",
+ year = "1971",
+ LCCN = "QA76.5 .S94 1971",
+ bibdate = "Sat Dec 30 08:56:27 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ xxISBN = "none",
+}
+
+@Proceedings{Online:1972:OCP,
+ key = "Online'72",
+ booktitle = "{Online 72: conference proceedings \ldots{}
+ international conference on online interactive
+ computing, Brunel University, Uxbridge, England, 47
+ September 1972}",
+ title = "{Online 72: conference proceedings \ldots{}
+ international conference on online interactive
+ computing, Brunel University, Uxbridge, England, 47
+ September 1972}",
+ publisher = "Online Computer Systems Ltd",
+ address = "Uxbridge, England",
+ pages = "various",
+ month = sep,
+ year = "1972",
+ ISBN = "0903796023",
+ ISBN13 = "9780903796026",
+ LCCN = "QA76.55 .O54 1972",
+ bibdate = "Fri Dec 29 18:31:29 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ note = "Two volumes.",
+ acknowledgement = acknhfb,
+}
+
+@Proceedings{Golden:1984:PMU,
+ editor = "V. Ellen Golden and M. A. Hussain",
+ booktitle = "{Proceedings of the 1984 MACSYMA Users' Conference:
+ Schenectady, New York, July 2325, 1984}",
+ title = "{Proceedings of the 1984 MACSYMA Users' Conference:
+ Schenectady, New York, July 2325, 1984}",
+ publisher = "General Electric",
+ address = "Schenectady, NY, USA",
+ pages = "xv + 567",
+ year = "1984",
+ bibdate = "Sat Dec 30 09:01:01 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+}
+
+@Proceedings{Fitch:1984:E,
+ editor = "J. P. Fitch",
+ booktitle = "{EUROSAM '84: International Symposium on Symbolic and
+ Algebraic Computation, Cambridge, England, July 911,
+ 1984}",
+ title = "{EUROSAM '84: International Symposium on Symbolic and
+ Algebraic Computation, Cambridge, England, July 911,
+ 1984}",
+ volume = "174",
+ publisher = pubSV,
+ address = pubSV:adr,
+ pages = "xi + 396",
+ year = "1984",
+ ISBN = "038713350X",
+ ISBN13 = "9780387133508",
+ LCCN = "QA155.7.E4 I57 1984",
+ bibdate = "Fri Dec 29 18:17:16 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ series = "Lecture Notes In Computer Science",
+ acknowledgement = acknhfb,
+}
+
+@Proceedings{Buchberger:1985:EEC,
+ editor = "Bruno Buchberger and Bob F. Caviness",
+ booktitle = "{EUROCAL '85: European Conference on Computer Algebra,
+ Linz, Austria, April 13, 1985: proceedings}",
+ title = "{EUROCAL '85: European Conference on Computer Algebra,
+ Linz, Austria, April 13, 1985: proceedings}",
+ volume = "204",
+ publisher = pubSV,
+ address = pubSV:adr,
+ pages = "various",
+ year = "1985",
+ ISBN = "0387159835 (vol. 1), 0387159843 (vol. 2)",
+ ISBN13 = "9780387159836 (vol. 1), 9780387159843 (vol.
+ 2)",
+ LCCN = "QA155.7.E4 E86 1985",
+ bibdate = "Fri Dec 29 18:07:46 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ note = "Two volumes.",
+ series = "Lecture Notes in Computer Science",
+ acknowledgement = acknhfb,
+}
+
+@Proceedings{Wexelblat:1987:IIT,
+ editor = "Richard L. Wexelblat",
+ booktitle = "{Proceedings of the SIGPLAN '87 Symposium on
+ Interpreters and Interpretive Techniques, St. Paul,
+ Minnesota, June 2426, 1987}",
+ title = "{Proceedings of the SIGPLAN '87 Symposium on
+ Interpreters and Interpretive Techniques, St. Paul,
+ Minnesota, June 2426, 1987}",
+ publisher = pubACM,
+ address = pubACM:adr,
+ pages = "vii + 291",
+ year = "1987",
+ ISBN = "0897912357",
+ ISBN13 = "9780897912358",
+ LCCN = "QA76.7 .S54 v.22:7",
+ bibdate = "Thu Jan 04 18:40:07 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ note = "SIGPLAN Notices, vol. 22, no. 7 (July 1987).",
+ price = "US\$23.00",
+ acknowledgement = acknhfb,
+ keywords = "design; interpreters (computer programs) 
+ congresses; languages",
+ subject = "D.0 Software, GENERAL",
+}
+
+@Proceedings{Janssen:1988:TCA,
+ editor = "R. Jan{\ss}en",
+ booktitle = "{Trends in Computer Algebra, International Symposium
+ Bad Neuenahr, May 1921, 1987, Proceedings}",
+ title = "{Trends in Computer Algebra, International Symposium
+ Bad Neuenahr, May 1921, 1987, Proceedings}",
+ volume = "296",
+ publisher = pubSV,
+ address = pubSV:adr,
+ pages = "??",
+ year = "1988",
+ ISBN = "3540189289, 0387189289",
+ ISBN13 = "9783540189282, 9780387189284",
+ LCCN = "QA155.7.E4T74 1988",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ series = "Lecture Notes in Computer Science",
+ notes = "{\footnotesize Die Beitr{\"a}ge in diesem Band geben
+ einen guten {\"U}berblick {\"u}ber den aktuellen Stand
+ der Forschung in verschiedenen f{\"u}r die \CA\
+ wichtigen Teilgebieten, so z.B. Faktorisierung von
+ Polynomen, konstruktive Galois Theory,
+ Termersetzungssysteme und das System Scratchpad II.
+ \hfill F. Schwarz}",
+}
+
+@Proceedings{ACM:1989:PAI,
+ editor = "{ACM}",
+ booktitle = "{Proceedings of the ACMSIGSAM 1989 International
+ Symposium on Symbolic and Algebraic Computation, ISSAC
+ '89}",
+ title = "{Proceedings of the ACMSIGSAM 1989 International
+ Symposium on Symbolic and Algebraic Computation, ISSAC
+ '89}",
+ publisher = pubACM,
+ address = pubACM:adr,
+ pages = "399",
+ year = "1989",
+ ISBN = "0897913256",
+ ISBN13 = "9780897913256",
+ LCCN = "QA76.95.I59 1989",
+ bibdate = "Tue Sep 17 06:46:18 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ confdate = "1719 July 1989",
+ conflocation = "Portland, OR, USA",
+ confsponsor = "ACM",
+ pubcountry = "USA",
+}
+
+@Proceedings{Huguet:1989:AAA,
+ editor = "L. Huguet and A. Poli",
+ booktitle = "{Applied Algebra, Algebraic Algorithms and
+ ErrorCorrecting Codes. 5th International Conference,
+ AAECC5 Proceedings}",
+ title = "{Applied Algebra, Algebraic Algorithms and
+ ErrorCorrecting Codes. 5th International Conference,
+ AAECC5 Proceedings}",
+ publisher = pubSV,
+ address = pubSV:adr,
+ pages = "417",
+ year = "1989",
+ ISBN = "3540510826",
+ ISBN13 = "9783540510826",
+ LCCN = "QA268.A35 1987",
+ bibdate = "Tue Sep 17 06:46:18 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ confdate = "1519 June 1987",
+ conflocation = "Menorca, Spain",
+ pubcountry = "West Germany",
+}
+
+@Proceedings{Davenport:1989:EEC,
+ editor = "J. H. Davenport",
+ booktitle = "{EUROCAL '87. European Conference on Computer Algebra
+ Proceedings}",
+ title = "{EUROCAL '87. European Conference on Computer Algebra
+ Proceedings}",
+ publisher = pubSV,
+ address = pubSV:adr,
+ pages = "viii + 499",
+ year = "1989",
+ ISBN = "3540515178",
+ ISBN13 = "9783540515173",
+ LCCN = "QA155.7.E4E86 1987",
+ bibdate = "Tue Sep 17 06:46:18 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ confdate = "25 June 1987",
+ conflocation = "Leipzig, East Germany",
+ confsponsor = "Robotron; Rank Xerox",
+ pubcountry = "West Germany",
+}
+
+@Proceedings{Gianni:1989:SAC,
+ editor = "P. (Patrizia) Gianni",
+ booktitle = "{Symbolic and Algebraic Computation. International
+ Symposium ISSAC '88, Rome, Italy, July 48, 1988.
+ Proceedings}",
+ title = "{Symbolic and Algebraic Computation. International
+ Symposium ISSAC '88, Rome, Italy, July 48, 1988.
+ Proceedings}",
+ volume = "358",
+ publisher = pubSV,
+ address = pubSV:adr,
+ pages = "xi + 543",
+ year = "1989",
+ ISBN = "3540510842",
+ ISBN13 = "9783540510840",
+ LCCN = "QA76.95 .I57 1988",
+ bibdate = "Tue Sep 17 06:46:18 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ note = "Conference held jointly with AAECC6.",
+ series = "Lecture Notes In Computer Science",
+ acknowledgement = acknhfb,
+ confdate = "48 July 1988",
+ conflocation = "Rome, Italy",
+ pubcountry = "West Germany",
+}
+
+@Proceedings{Mora:1989:AAA,
+ editor = "T. Mora",
+ booktitle = "{Applied Algebra, Algebraic Algorithms and
+ ErrorCorrecting Codes. 6th International Conference,
+ AAECC6, Rome, Italy, July 48, 1988. Proceedings}",
+ title = "{Applied Algebra, Algebraic Algorithms and
+ ErrorCorrecting Codes. 6th International Conference,
+ AAECC6, Rome, Italy, July 48, 1988. Proceedings}",
+ volume = "357",
+ publisher = pubSV,
+ address = pubSV:adr,
+ pages = "ix + 480",
+ year = "1989",
+ ISBN = "3540510834",
+ ISBN13 = "9783540510833",
+ LCCN = "QA268 .A35 1988",
+ bibdate = "Tue Sep 17 06:46:18 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ note = "Conference held jointly with ISSAC '88.",
+ series = "Lecture Notes in Computer Science",
+ acknowledgement = acknhfb,
+ confdate = "48 July 1988",
+ conflocation = "Rome, Italy",
+ pubcountry = "West Germany",
+}
+
+@Proceedings{Watanabe:1990:IPI,
+ editor = "Shunro Watanabe and Morio Nagata",
+ booktitle = "{ISSAC '90. Proceedings of the International Symposium
+ on Symbolic and Algebraic Computation}",
+ title = "{ISSAC '90. Proceedings of the International Symposium
+ on Symbolic and Algebraic Computation}",
+ publisher = pubACM,
+ address = pubACM:adr,
+ pages = "ix + 307",
+ year = "1990",
+ ISBN = "0897914015",
+ ISBN13 = "9780897914017",
+ LCCN = "QA76.95 .I57 1990",
+ bibdate = "Tue Sep 17 06:44:07 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ confdate = "2024 Aug. 1990",
+ conflocation = "Tokyo, Japan",
+ confsponsor = "Inf. Processing Soc. Japan; Japan Soc. Software Sci.
+ Technol.; ACM",
+ pubcountry = "USA",
+}
+
+@Proceedings{Miola:1990:DIS,
+ editor = "A. Miola",
+ booktitle = "{Design and Implementation of Symbolic Computation
+ Systems, International Symposium DISCO '90, Capri,
+ Italy, April 1012, 1990, Proceedings}",
+ title = "{Design and Implementation of Symbolic Computation
+ Systems, International Symposium DISCO '90, Capri,
+ Italy, April 1012, 1990, Proceedings}",
+ volume = "429",
+ publisher = pubSV,
+ address = pubSV:adr,
+ pages = "xii + 283",
+ year = "1990",
+ ISBN = "0387525319 (New York), 3540525319 (Berlin)",
+ ISBN13 = "9780387525310 (New York), 9783540525318
+ (Berlin)",
+ LCCN = "QA76.9.S88I576 1990",
+ bibdate = "Tue Sep 17 06:44:07 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ series = "Lecture Notes in Computer Science",
+ acknowledgement = acknhfb,
+ confdate = "1012 April 1990",
+ conflocation = "Capri, Italy",
+ pubcountry = "West Germany",
+}
+
+@Proceedings{Cohen:1991:EIS,
+ editor = "G. Cohen and P. Charpin",
+ booktitle = "{EUROCODE '90. International Symposium on Coding
+ Theory and Applications Proceedings}",
+ title = "{EUROCODE '90. International Symposium on Coding
+ Theory and Applications Proceedings}",
+ publisher = pubSV,
+ address = pubSV:adr,
+ pages = "xi + 392",
+ year = "1991",
+ ISBN = "0387543031 (New York), 3540543031 (Berlin)",
+ ISBN13 = "9780387543031 (New York), 9783540543039
+ (Berlin)",
+ LCCN = "QA268.E95 1990",
+ bibdate = "Tue Sep 17 06:41:20 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ confdate = "59 Nov. 1990",
+ conflocation = "Udine, Italy",
+ pubcountry = "Germany",
+}
+
+@Proceedings{Watt:1991:PIS,
+ editor = "Stephen M. Watt",
+ booktitle = "{Proceedings of the 1991 International Symposium on
+ Symbolic and Algebraic Computation, ISSAC'91, July
+ 1517, 1991, Bonn, Germany}",
+ title = "{Proceedings of the 1991 International Symposium on
+ Symbolic and Algebraic Computation, ISSAC'91, July
+ 1517, 1991, Bonn, Germany}",
+ publisher = pubACM,
+ address = pubACM:adr,
+ pages = "xiii + 468",
+ year = "1991",
+ ISBN = "0897914376",
+ ISBN13 = "9780897914376",
+ LCCN = "QA76.95.I59 1991",
+ bibdate = "Fri Dec 29 18:17:57 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+}
+
+@Proceedings{Anonymous:1991:PAC,
+ editor = "Anonymous",
+ booktitle = "{Proceedings 1991 Annual Conference, American Society
+ for Engineering Education. Challenges of a Changing
+ World}",
+ title = "{Proceedings 1991 Annual Conference, American Society
+ for Engineering Education. Challenges of a Changing
+ World}",
+ publisher = "ASEE",
+ address = "Washington, DC, USA",
+ pages = "xxi + 2026",
+ year = "1991",
+ bibdate = "Tue Sep 17 06:37:45 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ note = "2 vol.",
+ acknowledgement = acknhfb,
+ confdate = "1619 June 1991",
+ conflocation = "New Orleans, LA, USA",
+ pubcountry = "USA",
+}
+
+@Proceedings{Wang:1992:ISS,
+ editor = "Paul S. Wang",
+ booktitle = "{International System Symposium on Symbolic and
+ Algebraic Computation 92}",
+ title = "{International System Symposium on Symbolic and
+ Algebraic Computation 92}",
+ publisher = pubACM,
+ address = pubACM:adr,
+ pages = "ix + 406",
+ year = "1992",
+ ISBN = "0897914899 (soft cover), 0897914902 (hard
+ cover)",
+ ISBN13 = "9780897914895 (soft cover), 9780897914901
+ (hard cover)",
+ LCCN = "QA76.95.I59 1992",
+ bibdate = "Tue Sep 17 06:35:39 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ confdate = "2729 July 1992",
+ conflocation = "Berkeley, CA, USA",
+ confsponsor = "ACM",
+ pubcountry = "USA",
+}
+
+@Proceedings{Bronstein:1993:IPI,
+ editor = "Manuel Bronstein",
+ booktitle = "{ISSAC'93: proceedings of the 1993 International
+ Symposium on Symbolic and Algebraic Computation, July
+ 68, 1993, Kiev, Ukraine}",
+ title = "{ISSAC'93: proceedings of the 1993 International
+ Symposium on Symbolic and Algebraic Computation, July
+ 68, 1993, Kiev, Ukraine}",
+ publisher = pubACM,
+ address = pubACM:adr,
+ pages = "viii + 321",
+ year = "1993",
+ ISBN = "0897916042",
+ ISBN13 = "9780897916042",
+ LCCN = "QA 76.95 I59 1993",
+ bibdate = "Thu Sep 26 05:45:15 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ note = "ACM order number: 505930.",
+ abstract = "The following topics were dealt with: algebraic
+ solutions of equations; computer algebra systems;
+ algorithm theory and complexity; automated theorem
+ proving; polynomials; and matrix algebra.",
+ acknowledgement = acknhfb,
+ classification = "C4210 (Formal logic); C4240 (Programming and
+ algorithm theory); C7310 (Mathematics computing)",
+ confdate = "68 July 1993",
+ conflocation = "Kiev, Ukraine",
+ confsponsor = "ACM",
+ keywords = "algebra  data processing  congresses; Algorithm
+ theory; Automated theorem proving; Complexity; Computer
+ algebra; mathematics  data processing 
+ congresses; Matrix algebra; Polynomials",
+ pubcountry = "USA",
+ source = "ISSAC '93",
+ sponsor = "Association for Computing Machinery.",
+ thesaurus = "Computational complexity; Mathematics computing;
+ Matrix algebra; Polynomials; Symbol manipulation;
+ Theorem proving",
+}
+
+@Proceedings{Fitch:1993:DIS,
+ editor = "J. Fitch",
+ booktitle = "{Design and Implementation of Symbolic Computation
+ Systems International Symposium, DISCO '92
+ Proceedings}",
+ title = "{Design and Implementation of Symbolic Computation
+ Systems International Symposium, DISCO '92
+ Proceedings}",
+ publisher = pubSV,
+ address = pubSV:adr,
+ pages = "214",
+ year = "1993",
+ ISBN = "0387572724 (New York), 3540572724 (Berlin)",
+ ISBN13 = "9780387572727 (New York), 9783540572725
+ (Berlin)",
+ LCCN = "QA76.9.S88I576 1992",
+ bibdate = "Tue Sep 17 06:37:45 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ confdate = "1315 April 1992",
+ conflocation = "Bath, UK",
+ pubcountry = "Germany",
+}
+
+@Proceedings{Jacob:1993:PSI,
+ editor = "G. Jacob and N. E. Oussous and S. Steinberg",
+ booktitle = "{Proceedings SC 93. International IMACS Symposium on
+ Symbolic Computation. New Trends and Developments}",
+ title = "{Proceedings SC 93. International IMACS Symposium on
+ Symbolic Computation. New Trends and Developments}",
+ publisher = "LIFL Univ. Lille",
+ address = "Lille, France",
+ pages = "vii + 239",
+ year = "1993",
+ bibdate = "Tue Sep 17 06:35:39 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ confdate = "1417 June 1993",
+ conflocation = "Lille, France",
+ confsponsor = "IMACSAICA",
+ pubcountry = "France",
+}
+
+@Proceedings{Miola:1993:DIS,
+ editor = "A. Miola",
+ booktitle = "{Design and Implementation of Symbolic Computation
+ Systems International Symposium. DISCO '93 Gmunden,
+ Austria, September 1517, 1993: Proceedings}",
+ title = "{Design and Implementation of Symbolic Computation
+ Systems International Symposium. DISCO '93 Gmunden,
+ Austria, September 1517, 1993: Proceedings}",
+ publisher = pubSV,
+ address = pubSV:adr,
+ pages = "xi + 383",
+ year = "1993",
+ ISBN = "354057235X",
+ ISBN13 = "9783540572350",
+ LCCN = "QA76.9.S88I576 1993",
+ bibdate = "Fri Dec 29 12:46:02 MST 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ confdate = "1517 Sept. 1993",
+ conflocation = "Gmunden, Austria",
+ pubcountry = "Germany",
+}
+
+@Proceedings{ACM:1994:IPI,
+ editor = "{ACM}",
+ booktitle = "{ISSAC'94. Proceedings of the International Symposium
+ on Symbolic and Algebraic Computation}",
+ title = "{ISSAC'94. Proceedings of the International Symposium
+ on Symbolic and Algebraic Computation}",
+ publisher = pubACM,
+ address = pubACM:adr,
+ pages = "ix + 359",
+ year = "1994",
+ ISBN = "0897916387",
+ ISBN13 = "9780897916387",
+ LCCN = "QA76.95.I59 1994",
+ bibdate = "Tue Sep 17 06:29:18 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ confdate = "2022 July 1994",
+ conflocation = "Oxford, UK",
+ confsponsor = "ACM",
+ pubcountry = "USA",
+}
+
+@Proceedings{Calmet:1994:RWC,
+ editor = "J. Calmet",
+ booktitle = "{Rhine Workshop on Computer Algebra. Proceedings}",
+ title = "{Rhine Workshop on Computer Algebra. Proceedings}",
+ publisher = "Universit{\"a}t Karlsruhe",
+ address = "Karlsruhe, Germany",
+ pages = "v + 224",
+ year = "1994",
+ bibdate = "Tue Sep 17 06:32:41 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ confdate = "2224 March 1994",
+ conflocation = "Karlsruhe, Germany",
+ confsponsor = "Universit{\"a}t Karlsruhe",
+ pubcountry = "Germany",
+}
+
+@Proceedings{Levelt:1995:IPI,
+ editor = "A. H. M. Levelt",
+ booktitle = "{ISSAC '95: Proceedings of the 1995 International
+ Symposium on Symbolic and Algebraic Computation: July
+ 1012, 1995, Montr{\'e}al, Canada}",
+ title = "{ISSAC '95: Proceedings of the 1995 International
+ Symposium on Symbolic and Algebraic Computation: July
+ 1012, 1995, Montr{\'e}al, Canada}",
+ publisher = pubACM,
+ address = pubACM:adr,
+ pages = "xviii + 314",
+ year = "1995",
+ ISBN = "0897916999",
+ ISBN13 = "9780897916998",
+ LCCN = "QA 76.95 I59 1995",
+ bibdate = "Thu Sep 26 05:34:21 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ note = "ACM order number: 505950",
+ series = "ISSAC PROCEEDINGS 1995",
+ abstract = "The following topics were dealt with: differential
+ equations; visualisation; algebraic numbers;
+ algorithms; systems; polynomial and differential
+ algebra; seminumerical methods; greatest common
+ divisors; and.",
+ acknowledgement = acknhfb,
+ classification = "C4100 (Numerical analysis); C4170 (Differential
+ equations); C7310 (Mathematics computing)",
+ confdate = "1012 July 1995",
+ conflocation = "Montr{\'e}al, Que., Canada",
+ confsponsor = "ACM",
+ keywords = "algebra  data processing  congresses; Algebraic
+ numbers; Algorithms; Differential algebra; Differential
+ equations; Greatest common divisors; mathematics 
+ data processing  congresses; Polynomial;
+ Seminumerical methods; Systems; Visualisation",
+ pubcountry = "USA",
+ source = "ISSAC '95",
+ thesaurus = "Data visualisation; Differential equations; Group
+ theory; Numerical analysis; Symbol manipulation",
+}
+
+@Proceedings{Dooley:1999:IJS,
+ editor = "Sam Dooley",
+ booktitle = "{ISSAC 99: July 2931, 1999, Simon Fraser University,
+ Vancouver, BC, Canada: proceedings of the 1999
+ International Symposium on Symbolic and Algebraic
+ Computation}",
+ title = "{ISSAC 99: July 2931, 1999, Simon Fraser University,
+ Vancouver, BC, Canada: proceedings of the 1999
+ International Symposium on Symbolic and Algebraic
+ Computation}",
+ publisher = pubACM,
+ address = pubACM:adr,
+ pages = "xxii + 311",
+ year = "1999",
+ ISBN = "1581130732",
+ ISBN13 = "9781581130737",
+ LCCN = "QA76.95 .I57 1999",
+ bibdate = "Sat Mar 11 16:51:59 2000",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+}
+
+@Proceedings{Brown:2007:PIS,
+ editor = "C. W. Brown",
+ booktitle = "{Proceedings of the 2007 International Symposium on
+ Symbolic and Algebraic Computation, July 29August 1,
+ 2007, University of Waterloo, Waterloo, Ontario,
+ Canada}",
+ title = "{Proceedings of the 2007 International Symposium on
+ Symbolic and Algebraic Computation, July 29August 1,
+ 2007, University of Waterloo, Waterloo, Ontario,
+ Canada}",
+ publisher = pubACM,
+ address = pubACM:adr,
+ pages = "????",
+ year = "2007",
+ ISBN = "1595937439 (print), 1595937420 (CDROM)",
+ ISBN13 = "9781595937438 (print), 9781595937421
+ (CDROM)",
+ LCCN = "QA76.5 S98 2007",
+ bibdate = "Fri Jun 20 08:53:37 2008",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib;
+ http://www.math.utah.edu/pub/tex/bib/issac.bib;
+ http://www.math.utah.edu/pub/tex/bib/mapleextract.bib",
+ note = "ACM order number 505070.",
+ acknowledgement = acknhfb,
}
+@Proceedings{Shi:2007:CSIb,
+ editor = "Yong Shi and Geert Dick van Albada and Jack Dongarra
+ and Peter M. A. Sloot",
+ booktitle = "{Computational Science  ICCS 2007: 7th
+ International Conference, Beijing, China, May 27 
+ 30, 2007, Proceedings, Part II}",
+ title = "{Computational Science  ICCS 2007: 7th
+ International Conference, Beijing, China, May 27 
+ 30, 2007, Proceedings, Part II}",
+ volume = "4488",
+ publisher = pubSV,
+ address = pubSV:adr,
+ pages = "153 (est.)",
+ year = "2007",
+ CODEN = "LNCSD9",
+ DOI = "http://dx.doi.org/10.1007/9783540725862",
+ ISBN = "3540725857 (print), 3540725865 (ebook)",
+ ISBN13 = "9783540725855 (print), 9783540725862
+ (ebook)",
+ ISSN = "03029743 (print), 16113349 (electronic)",
+ ISSNL = "03029743",
+ LCCN = "????",
+ bibdate = "Wed Dec 19 15:19:26 MST 2012",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib;
+ http://www.math.utah.edu/pub/tex/bib/lncs.bib;
+ http://www.math.utah.edu/pub/tex/bib/magma.bib;
+ http://www.math.utah.edu/pub/tex/bib/mapleextract.bib",
+ series = serLNCS,
+ URL = "http://www.springerlink.com/content/9783540725862",
+ acknowledgement = acknhfb,
+}
\end{chunk}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
diff git a/changelog b/changelog
index 49ebbc3..e11b573 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,8 @@
+20160720 tpd src/axiomwebsite/patches.html 20160720.01.tpd.patch
+20160720 tpd books/bookvol10.2 add citations to algebra
+20160720 tpd books/bookvol10.3 add citations to algebra
+20160720 tpd books/bookvol10.4 add citations to algebra
+20160720 tpd books/bookvolbib Axiom Citations in the Literature
20160718 tpd src/axiomwebsite/patches.html 20160718.01.tpd.patch
20160718 tpd src/input/Makefile add intalgorithm.input
20160718 tpd src/input/intalgorithm.input explain integration tests
diff git a/patch b/patch
index 1eb29ab..6a5cef2 100644
 a/patch
+++ b/patch
@@ 1,5 +1,844 @@
src/input/intalgorithm.input explain integration algorithms
+books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
Demonstrate 10 approaches to integration
+\index{Sit, William Y.}
+\begin{chunk}{axiom.bib}
+@article{Sitx92,
+ author = "Sit, William Y.",
+ title = "An algorithm for solving parametric linear systems",
+ journal = "Journal of Symbolic Computations",
+ volume = "13",
+ number = "4",
+ pages = "353394",
+ year = "1992",
+ paper = "Sitx92.pdf",
+ keywords = "axiomref",
+ abstract =
+ "We present a theoretical foundation for studying parametric systesm of
+ linear equations and prove an efficient algorithm for identifying all
+ parametric values (including degnerate cases) for which the system is
+ consistent. The algorithm gives a small set of regimes where for each
+ regime, the solutions of the specialized systems may be given
+ uniformly. For homogeneous linear systems, or for systems were the
+ right hand side is arbitrary, this small set is irredunant. We discuss
+ in detail practical issues concerning implementations, with particular
+ emphasis on simplification of results. Examples are given based on a
+ close implementation of the algorithm in SCRATCHPAD II. We also give a
+ complexity analysis of the Gaussian elimination method and compare
+ that with our algorithm."
+}
+
+\end{chunk}
+
+\index{Smedley, Trevor J.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Smed92,
+ author = "Smedley, Trevor J.",
+ title = "Using pictorial and object oriented programming for computer
+ algebra",
+ booktitle = "Applied computing  technological challenges of the
+ 1990's: proceedings of the 1992 ACM\slash SIGAPP
+ Symposium on Applied Computing, Kansas City Convention
+ Center, March 13, 1992",
+ publisher = "ACM Press",
+ pages = "12431247",
+ isbn = "089791502X",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Zenger, Christoph}
+\begin{chunk}{axiom.bib}
+@mastersthesis{Zeng92,
+ author = "Zenger, Christoph",
+ title = "Gr{\"o}bnerbasen f{\"u}r Differentialformen und ihre
+ Implementierung in AXIOM'",
+ type = "Diplomarbeit",
+ school = "Universit{\"a}t Karlsruhe",
+ address = "Karlsruhe, Germany",
+ year = "1992",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{FullPartialFractionExpansion}
+\index{Bronstein, Manuel}
+\index{Salvy, Bruno}
+\begin{chunk}{axiom.bib}
+@inproceedings{Bron93,
+ author = "Bronstein, Manuel and Salvy, Bruno",
+ title = "Full partial fraction decomposition of rational functions",
+ booktitle = "Proc. ISSAC 1993",
+ year = "1993",
+ pages = "157160",
+ isbn = "0897916042",
+ url = "http://www.acm.org/pubs/citations/proceedings/issac/164081/",
+ paper = "Bron93.pdf",
+ algebra = "\newline\refto{domain FPARFRAC FullPartialFractionExpansion}",
+ abstract =
+ "We describe a rational algorithm that computes the full partial
+ fraction expansion of a rational function over the algebraic closure
+ of its field of definition. The algorithm uses only gcd operations
+ over the initial field but the resulting decomposition is expressed
+ with linear denominators. We give examples from its Axiom and Maple
+ implementations."
+}
+
+\end{chunk}
+
+\index{TranscendentalRischDE}
+\index{TranscendentalRischDESystem}
+\index{Bronstein, Manuel}
+\begin{chunk}{axiom.bib}
+@article{Bron90,
+ author = "Bronstein, Manuel",
+ title = "The Transcendental Risch Differential Equation",
+ journal = "J. Symbolic Computation",
+ volume = "9",
+ pages = "4960",
+ year = "1990",
+ comment = "IBM Research Report RC13460 IBM Corp. Yorktown Heights, NY",
+ paper = "Bron90.pdf",
+ keywords = "axiomref",
+ algebra =
+ "\newline\refto{package RDETR TranscendentalRischDE}
+ \newline\refto{package RDETRS TranscendentalRischDESystem}",
+ abstract =
+ "We present a new rational algorithm for solving Risch differential
+ equations in towers of transcendental elementary extensions. In
+ contrast to a recent algorithm by Davenport we do not require a
+ progressive reduction of the denominators involved, but use weak
+ normality to obtain a formula for the denominator of a possible
+ solution. Implementation timings show this approach to be faster than
+ a Hermitelike reduction."
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+\bibitem[Davenport 86]{Dav86} Davenport, J.H.
+@article{Dave86,
+ author = "Davenport, James H.",
+ title = "The Risch Differential Equation Problem",
+ year = "1986",
+ journal = "SIAM J. COMPUT.",
+ volume = "15",
+ number = "4",
+ comment = "Technical Report 834, Dept. Comp. Sci, Univ. Delaware",
+ paper = "Dave86.pdf",
+ abstract = "
+ We propose a new algorithm, similar to Hermite's method for the
+ integration of rational functions, for the resolution of Risch
+ differential equations in closed form, or proving that they have no
+ resolution. By requiring more of the presentation of our differential
+ fields (in particular that the exponentials be weakly normalized), we
+ can avoid the introduction of arbitrary constants which have to be
+ solved for later.
+
+ We also define a class of fields known as exponentially reduced, and
+ show that solutions of Risch differential equations which arise from
+ integrating in these fields satisfy the ``natural'' degree constraints
+ in their main variables, and we conjecture (after Risch and Norman)
+ that this is true in all variables."
+}
+
+\end{chunk}
+
+
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@book{Dave05,
+ author = "Davenport, James H.",
+ title = "Integration  What do we want from the theory?",
+ booktitle = "Computer Algebra",
+ publisher = "Springer",
+ series = "Lecture Notes in Computer Science 162",
+ pages = "211",
+ year = "2005",
+ abstract =
+ "The theory of integration has moved a long way in the last fourteen
+ years, thought not far enough to satisfy the demands placed on it by
+ its customers. This paper outlines what problems have yet to be solved,
+ and tries to explain why they are not trivial."
+}
+
+\end{chunk}
+
+\index{Rothstein, Michael}
+\begin{chunk}{ignore}
+@phdthesis{Roth76,
+ author = "Rothstein, Michael",
+ title = "Aspects of symbolic integration and simplifcation of
+ exponential and primitive functions",
+ school = "University of WisconsinMadison",
+ year = "1976",
+ url = "http://www.cs.kent.edu/~rothstei/dis.pdf",
+ paper = "Ro76.pdf",
+ abstract =
+ "In this thesis we cover some aspects of the theory necessary to obtain
+ a canonical form for functions obtained by integration and
+ exponentiation from the set of rational functions.
+
+ These aspects include a new algorithm for symbolic integration of
+ functions involving logarithms and exponentials which avoids
+ factorization of polynomials in those cases where algebraic extension
+ of the constant field is not required, avoids partial fraction
+ decompositions, and only solves linear systems with a small number of
+ unknowns.
+
+ We have also found a theorem which states, roughly speaking, that if
+ integrals which can be represented as logarithms are represented as
+ such, the only algebraic dependence that a new exponential or
+ logarithm can satify is given by the law of exponents or the law of
+ logarithms."
+}
+
+\end{chunk}
+
+\index{Bronstein, Manuel}
+\begin{chunk}{axiom.bib}
+@article{Bron92a,
+ author = "Bronstein, Manuel",
+ title = "Formulas for Series Computation",
+ journal = "Applied Algebra in Engineering, Communication and Computing",
+ volume = "2",
+ pages = "195206",
+ year = "1992",
+ abstract =
+ "We describe an algorithm that computes polynomials whose roots are
+ the coefficients of any specific order of the Laurent series of a
+ rational function. The algorithm uses only rational operations in the
+ coefficient field of the function. This allows us to compute with the
+ principal parts of the Laurent series, in particular with the residues
+ of the function, without factoring or splitting its denominator. As
+ applications, we get a generalisation of the residue formulas used in
+ symbolic integration algorithms to $n^{th}$order formulas. We also
+ get an algorithm that computes explicitly the principlal parts at all
+ the poles simultaneously, while computing in the field generated by
+ the coefficients of the series instead of the one generated by the
+ poles of the function. This yields an improved version of the
+ necessary conditions for the various cases of Kovacic's algorithm,
+ that expresses those conditions in the smallest possible extension
+ field."
+}
+
+\end{chunk}
+
+\index{Goodloe, A.}
+\index{Loustaunau, Philippe}
+\begin{chunk}{axiom.bib}
+@inproceedings{Good93,
+ author = "Goodloe, A. and Loustaunau, Philippe",
+ title = "An abstract data type development of graded rings",
+ booktitle = "Design and Implementation of Symbolic Computation Systems",
+ series = "Lecture Notes in Computer Science 721",
+ pages = "193202",
+ isbn = "0387572724 (New York), 3540572724 (Berlin)",
+ year = "1993",
+ keywords = "axiomref",
+ abstract =
+ "Recently new computer algebra systems such as Scratchpad and Weyl have
+ been developed with built in mechanisms for expressing abstract data types.
+ These systems are object oriented in that they incorporate multiple
+ inheritance and polymorphic types. Davenport and Trager have build much
+ of the framework for basic commutative algebra in Scratchpad II
+ utilizing its rich set of abstraction mechanisms. Davenport and Trager
+ concentrated on developing factorization algorithms on domains which
+ were abstract data types.
+
+ We are taking a similar approach to the development of algorithms for
+ computing in graded rings. The purpose of this paper is to develop the
+ tools required to compute with polynomials with coefficients in a graded
+ ring $R$. We focus on graded rings $R$ which are polynomial rings graded
+ by a monoid, and we allow partial orders on the monomials. The ideas
+ presented here can be applied to more general graded rings $R$, such as
+ associated graded rings to filtered rings, as long as certain computational
+ ``requirements'' are satisfied"
+}
+
+\end{chunk}
+
+\index{Beneke, T.}
+\index{Schwippert, W.}
+\begin{chunk}{axiom.bib}
+@article{Bene94,
+ author = "Beneke, T. and Schwippert, W.",
+ title = "Doubletrack into the future: MathCAD will gain new users with
+ Standard and Plus versions",
+ journal = "Elektronik",
+ volume = "43",
+ number = "15",
+ pages = "107110",
+ year = "1994",
+ month = "July",
+ pages = "107110",
+ keywords = "axiomref",
+ abstract =
+ "MathCAD software is a type of `intelligent scratchpad with a pocket
+ calculator function'. Hitherto it has been suitable only to a limited
+ extent for engineering mathematics. The new Version 5.0 is now offered
+ in two implementations: as an inexpensive basic package and in a
+ considerably more costly Plus version. The authors question whether
+ MathCAD can catch up with the classical Maple and Mathematica products."
+}
+
+\end{chunk}
+
+\index{Vakil, Ravi}
+\begin{chunk}{axiom.bib}
+@misc{Vaki98,
+ author = "Vakil, Ravi",
+ title = "A Beginner's Guide to Jet Bundles fromthe Point of View of
+ Algebraic Geometry",
+ url = "http://math.stanford.edu/~vakil/files/jets.pdf",
+ paper = "Vaki98.pdf",
+ year = "1998"
+}
+
+\index{Roesner, K. G.}
+\begin{chunk}{axiom.bib}
+@article{Roes95,
+ author = "Roesner, K. G.",
+ title = "Verified solutions for parameters of an exact solution for
+ nonNewtonian liquids using computer algebra",
+ journal = "Zeitschrift fur Angewandte Mathematik und Physik",
+ volume = "75",
+ number = "suppl. 2",
+ pages = "S435S438",
+ year = "1995",
+ keywords = "axiomref",
+ abstract =
+ "An exact solution of the time independent velocity field for the
+ TaylorCouette flow of a polymer solution is derived solving the
+ resulting first order ordinary differential equation of fifth degree
+ analytically. Intensive use is made of computer algebra systems AXIOM
+ and MACSYMA to find the exact solution. The coaxial cylinders in the
+ TaylorCouette flow problem are assumed to rotate at different
+ angular velocities. The geometrical and kinematic parameters can be
+ chosen arbitrarily. The model equation for the material law of the
+ viscoelastic liquid is based on the thermodynamic model for dilute
+ solutions due to Lhuillier and Ouibrahim (1980) which is an analogy to
+ the earlier paper of Frankel and Acrivos (1970). In the present
+ investigation the influence of the parameters of the viscoelastic
+ model on the velocity profile in the cylindrical gap is studied and
+ the range of validity of the constitutive equation is investigated."
+}
+
+\end{chunk}
+
+\index{Benker, Hans}
+\begin{chunk}{axiom.bib}
+@book{Benk98,
+ author = "Benker, Hans",
+ title = "Engineering mathematics with computer algebra systems",
+ year = "1998",
+ keywords = "axiomref",
+ comment = "german"
+}
+
+\end{chunk}
+
+\begin{chunk}{axiom.bib}
+@misc{Linu15,
+ author = "Linux Links",
+ title = "Axiom",
+ url = "http://www.linuxlinks.com/article/20080810064748970/Axiom.html",
+ keywords = "axiomref",
+ year = "2015"
+}
+
+\end{chunk}
+
+\index{Daly, Timothy}
+\index{Barnes, Nick}
+\begin{chunk}{axiom.bib}
+@misc{Daly13a,
+ author = "Daly, Timothy and Barnes, Nick",
+ title = "Ten reasons you must publish your code",
+ year = "2013",
+ url =
+"http://climatecode.org/blog/2013/07/tenreasonsyoumustpublishyourcode/",
+ keywords = "axiomref",
+}
+
+\end{chunk}
+
+\index{Daly, Timothy}
+\begin{chunk}{axiom.bib}
+@misc{Daly05,
+ author = "Daly, Timothy",
+ title = "LispNYC Presentation at Trinity",
+ year = "2005",
+ month = "May",
+ day = "10",
+ keywords = "axiomref",
+ abstract =
+ "Timothy Daly presents Axiom
+
+ Timothy Daly, published author, academic researcher, open source
+ programmer and lead developer of Axiom will be presenting about his role
+ as the driving force behind Axiom. With over 70 developers and 200
+ researchers worldwide it can best be described as:
+
+ Axiom is a general purpose Computer Algebra system. It is useful
+ for research and development of mathematical algorithms providing
+ a very high level way to express abstract mathematical concepts.
+ The Axiom Library defines over 1,000 stronglytyped mathematical
+ domains and categories.
+
+ Axiom consists of an interpreter and compiler, a browser, a graphical
+ interface, and a new online wiki that allows users to create web pages
+ that inline computations.
+
+ Axiom is built upon Common Lisp."
+}
+
+\end{chunk}
+
+\index{Daly, Timothy}
+\begin{chunk}{axiom.bib}
+@misc{Dalyxx,
+ author = "Daly, Timothy",
+ title = "Tim Daly on Lisp in Industry",
+ keywords = "axiomref",
+ url = "https://news.ycombinator.com/item?id=1580904"
+}
+
+\end{chunk}
+
+\index{Harriss, Edmund}
+\index{Daly, Timothy}
+\begin{chunk}{axiom.bib}
+@misc{Harr12,
+ author = "Harriss, Edmund and Daly, Timothy",
+ title = "Have we ever lost mathematics?",
+ url = "https://maxwelldemon.com/2012/05/09/haveweeverlostmathematics/",
+ keywords = "axiomref",
+ year = "2012"
+}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate06a,
+ author = "Fateman, Richard J.",
+ title = "Comments on Extending Macsyma with New Data Types",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/addformat.pdf",
+ paper = "Fate06a.pdf",
+ abstract =
+ "Any design for a computer algebra system (CAS) naturally includes a
+ set of data layouts for symbolic or mathematical algebraic expressions
+ intended for use by builtin or userwritten programs. The CAS cannot
+ build in all plausible data designs, but supports those of most
+ interest to the programmers. In such a situation it is almost
+ inevitable that some new data encoding idea will come to mind and with
+ it an interest in adding additional data forms. The motivation may be
+ for compact representation, or efficient (fast) manipulation, or for
+ other reasons such as interchange with other programs. Most CAS
+ therefore include at least one way to extend the base set of
+ operations. We comment on the kinds of extensions possible, using
+ Macsyma as an example CAS. The particular interest in Macsyma and its
+ opensource soruceforge variant ``Maxima'' is that a substantial group
+ of verylosely coupled independent researchers are approaching this
+ problem and may benefit from some guidance. Some the observations
+ apply to other CAS, even though they are not opensource.",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Heckmann, Reinhold}
+\index{Wilhelm, Reinhard}
+\begin{chunk}{axiom.bib}
+@article{Heck97,
+ author = "Heckmann, Reinhold and Wilhelm, Reinhard",
+ title = "A Functional Description of TeX's Formula Layout",
+ journal = "J. Functional Programming",
+ volume = "7",
+ number = "5",
+ pages = "451485",
+ year = "1997",
+ url = "http://http.cs.berkeley.edu/~fateman/temp/neuform.pdf",
+ comment = "ftp://ftp.cs.unisb.de/formulae/formulae.tar.gz",
+ abstract =
+ "While the quality of the results of TeX's mathematica formula layout
+ algorithm is convincing, its original description is hard to
+ understand since it is presented as an imperative program with complex
+ control flow and destructive manipulations of the data structures
+ representing formulae. In this paper, we present a reimplementation
+ of TeX's formula layout algorithm in the functional language SML,
+ thereby providing a more readable description of the algorithm,
+ extracted from the monolithical TeX system.",
+ paper = "Heck97.pdf"
+}
+
+\end{chunk}
+
+\begin{chunk}{axiom.bib}
+@misc{Unkn15,
+ author = "Unknown",
+ title = "Branches of Functions",
+ url = "http://scipp.ucsc.edu/~haber/ph116A/ComplexFunBranchTheory.pdf",
+ paper = "Unkn15.pdf"
+}
+
+\end{chunk}
+
+\index{Phisanbut, Nalina}
+\index{Bradford, Russell J.}
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@article{Phis11,
+ author = "Phisanbut, Nalina and Bradford, Russell J. and
+ Davenport, James H.",
+ title = "Geometry of branch cuts",
+ journal = "ACM Communications in Computer Algebra",
+ volume = "44",
+ number = "34",
+ pages = "132135",
+ year = "2011",
+ abstract =
+ "'Simplification' is a key concept in Computer Algebra. But many
+ simplification rules, such as $\sqrt{x}\sqrt{y} \rightarrow \sqrt{xy}$
+ are not universally valid, due to the fact that many elementary
+ functions are multivalued. Hence a key question is ``Is this
+ simplification correct?'', which involves algorithmic analysis of the
+ branch cuts involved. In this paper, we look at variable ordering and
+ preconditioning as supporting technologies for this analysis.",
+ paper = "Phis11.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate97a,
+ author = "Fateman, Richard J.",
+ title = "The Fast Fourier Transform",
+ course = "Berkeley CS 292, Fall 1997, Handout 2",
+ year = "1997",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/fftnotes.pdf",
+ paper = "Fate97a.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate14,
+ author = "Fateman, Richard J.",
+ title = "Fun with Filon Quadrature  a Computer Algebra Perspective",
+ year = "2014",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/funfilon.pdf",
+ abstract =
+ "Filon quadrature, useful for oscillatory integrals, is easily
+ implemented in a computer algebra system (CAS) using exact or
+ approximate arithmetic. Although quadrature is almost always used in
+ the context of approximation, we see that various properties are
+ exhibited by running an exact algorithm on exact {\sl symbolic}
+ inputs. This experimental approach to the mathematics allows us to
+ prove the implementation of the algorithm has the expected
+ mathematical correctness properties, and is therefore more likely to
+ be, itself, a correct implementation."
+ paper = "Fate14.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate05a,
+ author = "Fateman, Richard J.",
+ title = "Haddock's eyes and computer algebra systems: Some essays",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/haddock.pdf",
+ year = "2005",
+ abstract =
+ "(From {\sl Through the Looking Glass} by Lewis Caroll)
+ \begin{verbatim}
+ The White Knight proposes to comfort Alice by singing her a song:
+
+ ``Is it very long?'' Alice asked, for she had heard a good deal of
+ poetry that day.
+ ``It's long,'' said the Knight, ``but it's very, very beautiful.
+ Everybody that hears me sing iteither it brings tears into the
+ eyes, or else 
+ ``Or else what?'' said Alice, for the Knight had made a sudden pause.
+ ``Or else it doesn't, you know. The name of the song is called
+ `Haddock's Eyes'.''
+ ``Oh, that' the name of the song, is it?'' Alice said, trying to feel
+ interested.
+ ``No, you don't understand,'' the Knight said, looking a little vexed.
+ ``That's what the name is called. The name really is 'The Aged Aged Man'''
+ ``Then I ought to have said 'That's what the song is called?'' Alice
+ corrected herself.
+ ``No, you oughtn't: that's quite another thing! The song is called
+ `Ways and Means': but that's only what it's called, you know!''
+ ``Well, what is the song, then?'' said Alice, who was by this time
+ completely bewildered.
+ ``I was coming to that,'' the Knight said. ``The song really is
+ `Asitting on a Gate': and the tune's my own invention.''
+ \end{verbatim}",
+ paper = "Fate05a.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate15,
+ author = "Fateman, Richard J.",
+ title = "Interval Arithmetic, Extended Numbers and Computer Algebra
+ Systems",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/interval.pdf",
+ year = "2015",
+ abstract =
+ "Many ambitious computer algebra systems were initially designed in a
+ flush of enthusiasm, with the goal of automating any symbolic
+ mathematical manipulation “correctly.” Historically, this approach
+ resulted in programs that implicitly used certain identities to
+ simplify expressions. These identities, which very likely seemed
+ universally true to the programmers in the heat of writing the CAS,
+ (and often were true in wellknown abstract algebraic domains) later
+ needed reexamination when such systems were extended for dealing with
+ kinds of objects unanticipated in the original design. These new
+ objects are generally introduced to the CAS by extending “generically”
+ the arithmetic or other operations. For example, approximate floats
+ do not have the mathematical properties of exact integers or
+ rationals. Complex numbers may strain a system designed for
+ realvalued variables. In the situation examined here, we consider two
+ categories of “extended” numbers: ∞ or undefined, and real
+ intervals. We comment on issues raised by these two troublesome
+ notions, how their introduction into a computer algebra system may
+ require a (sometimes painful) reconsideration and redesign of parts of
+ the program, and how they are related. An alternative (followed most
+ notably by the Axiom system is to essentially envision a “meta” CAS
+ defined in terms of categories and inheritance with only the most
+ fundamental builtin concepts; from these one can build many variants
+ of specific CAS features. This approach is appealing but can fails to
+ accommodate extensions that violate some mathematical tenets in the
+ cause of practicality.",
+ paper = "Fate15.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@article{Fate91,
+ author = "Fateman, Richard J.",
+ title = "A Review of Macsyma",
+ year = "1991",
+ url = "http://people.eecs.berkeley.edu/~fateman/papers/mma.pdf",
+ abstract =
+ "The Mathematica computer system is reviewed from the perspective of
+ its contributions to symbolic and algebraic computation, as well as
+ its stated goals. Design and implementation issues are discussed.",
+ paper = "Fate91.pdf,
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate97b,
+ author = "Fateman, Richard J.",
+ title = "More Versatile Scientific Documents OverExtended Abstract,
+ working paper",
+ year = "1997",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/mvsd.ps",
+ abstract =
+ "The electronic representation of scientific documents: journals,
+ technical reports, program documentation, laboratory notebooks,
+ etc. present challenges in several distinct communities. We see five
+ distinct groups concerned with electronic versions of scientific
+ documents:
+ \begin{itemize}
+ \item Publishers of journals, texts, reference works, and their authors.
+ \item Software publishers for OCR/document analysis, document formatting
+ \item Software publishers whose products access ``contents semantics''
+ from documents, including library keyword search programs, natural language
+ search programs, database systems, visual presentation systems,
+ mathematical computation systems, etc.
+ \item Institutions maintain access to electronic libraries, which must
+ be broadly construed to include data and programs of all sorts.
+ \item Individuals and their programs acting as their agents who need to
+ use these libraries, to identify, locate, and retrieive relevant
+ documents
+ \end{itemize}
+
+ We need to have a convergence in design and standards for encoding new
+ or preexisting (typically paperbased) documents in order to most
+ efficiently meet the needs of all these groups. Various effort, some
+ loosely coordinated, but just as often competing, are trying to set
+ standards and build tools.
+
+ We approach this by first dividing the task into visual, syntactic,
+ and semantic components. These specifications can focus attention on
+ the addressing requirements of the different groups. Additionally,
+ these components rely on a structure for documents that incorporates
+ existing library models and extends them to new modes of operation.
+ Berkeley's MVD is one plausible structure which will allow prototype
+ development and explorations.",
+ paper = "Fate97b.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate97c,
+ author = "Fateman, Richard J.",
+ title = "Excerpts from a proposal to the National Science Foundation
+ on Programming Environments and Tools for Advanced Scientific
+ Computation",
+ year = "1997",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/newpse.pdf",
+ abstract =
+ "We propose to concentrate on investigations of technology in support
+ of advanced scientific computation, based on a higherlevel view of the
+ relationship of mathematical modeling to computation. This is based on
+ the following considerations:
+ \begin{enumerate}
+ \item Symbolic mathematical manipulation and computer algebra systems:
+ These are tools and techniques that support problem solving, code
+ development, comprehension, debugging and partial evaluation
+ (the principle behind many optimization techniques).
+ \item Data modeling: in particular, the use of IEEE floatingpoint
+ number representations and operations.
+ \item Closed form or exact solutions: For some subproblems of
+ scientific interest, numerical solutions are not the only paradigm.
+ The availability of exact solutions, or symbolicapproximation solutions
+ has advanced along with computing technology too.
+ \item The use of scripting languages: the linkage of highperformance
+ library routines to graphical interfaces for data analysis and model setup
+ can be enhanced by symbolic support and highlevel scripting languages.
+ \item Extending the use of remote computation. We are now using standard
+ network connections for the acquisition of complex data (in this case,
+ symbolic solution of definite integrals).
+ \end{enumerate}",
+ paper = "Fate97c.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate00a,
+ author = "Fateman, Richard J.",
+ title = "Improving Exact Integral From Symbolic Algebra Systems",
+ year = "2000",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/nform2col.pdf",
+ abstract =
+ "Programs in symbolic algebraic manipulation systems can compute
+ certain classes of symbolic indefinite integrals in closed form. Although
+ these answers are ordinarily formally correct algebraic antiderivatives,
+ their form is often unsuitable for further numerical or even analytical
+ processing. In particular, we address cases in which such ``exact answers''
+ when numerically evaluated may give lessaccurate answers than numerical
+ approximations from first principles! The symbolic formulas may also
+ behave inappropriately near singularities. We discuss techniques, based
+ in part on the calculus of divided differences, for improving the form of
+ results of symbolic mathematics systems. In particular, computer alge
+ algebra systems must take explicit account of the possibility that they are
+ producing not “mathematics” but templates of programs consisting of se
+ sequences of arithmetic operations. In brief, mathematical correctness is
+ not enough. Forms produced by rational integration programs are used
+ for examples.",
+ paper = "Fate00a.pdf"
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate08a,
+ author = "Fateman, Richard J.",
+ title = "Verbs, Nouns, and Computer Algebra, or What's Grammar Got
+ to do with Math?",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/nounverbmac.pdf",
+ year = "2008",
+ abstract =
+ "Computer algebra systems (CAS) are supposed to do mathematics.
+ Unfortunately, much of human mathematics presentation and
+ manipulation depends on humans to understand what is going on more
+ generally. This context is often not made available to the computer
+ system, and so it will sometimes fail to make the right guess at the
+ meaning of constructions, unless they are made unambiguous. Among many
+ issues, one that has been raised and resolved, is the need for
+ attributing properties to operators that distinguish between ``the name
+ of the operation'' and ``the operation itself''.
+
+ As a simple example, referential transparency requires that if $x = y$,
+ then any true statement $P(x)$ about $x$ must be true about $y$, namely
+ $P(y)$ is also true.
+
+ Consider now the wellknown equation $sin(0) = 0$, and the statement
+ $P(r) :=$ ``r = 0 is a rule to simplify the sin() function''. The
+ statement $P(sin(0))$ is clearly true. Therefore $P(0)$ should be true
+ as well. It is not, since $0 = 0$ is not a rule to simplify $sin()$.
+
+ The point here is that $sin(0)$ is not equal to 0 if sin is treated as
+ the name of an operation. Perhaps it is a character string, or a data
+ structure of some sort: a noun phrase. The corresponding expression
+ including the verb form of sin is one in which $sin(0)$ can be
+ simplified to something equivalent, but in some sense preferable. Here
+ it is reasonable to replace it by 0.",
+ paper = "Fate08a.pdf"
+}
+
+\end{chunk}
+
+\index{OpenMath}
+\index{Complex}
+\index{DoubleFloat}
+\index{Float}
+\index{Fraction}
+\index{Integer}
+\index{List}
+\index{SingleInteger}
+\index{String}
+\index{Symbol}
+\index{ExpressionToOpenMath}
+\index{OpenMathServerPackage}
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate01a,
+ author = "Fateman, Richard J.",
+ title = "A Critique of OpenMath and Thoughts on Encoding Mathematics",
+ year = "2001",
+ url = "http://www.cs.berkeley.edu/~/fateman/papers/openmathcrit.pdf",
+ algebra =
+ "\newline\refto{category OM OpenMath}
+ \newline\refto{domain COMPLEX Complex}
+ \newline\refto{domain DFLOAT DoubleFloat}
+ \newline\refto{domain FLOAT Float}
+ \newline\refto{domain FRAC Fraction}
+ \newline\refto{domain INT Integer}
+ \newline\refto{domain LIST List}
+ \newline\refto{domain SINT SingleInteger}
+ \newline\refto{domain STRING String}
+ \newline\refto{domain SYMBOL Symbol}
+ \newline\refto{package OMEXPR ExpressionToOpenMath}
+ \newline\refto{package OMSERVER OpenMathServerPackage}",
+ abstract =
+ "The OpenMath project, as portrayed in the Special Issue of the SIGSAM
+ Bulletin (volume 34 no. 2), seems to have a number of problems to
+ face. One of them is the (apparently implicit) assumption that
+ OpenMath designers, through dint of mathematical thought and the
+ advice of the members of the Open Math Society, have solved, in their
+ domain, one of the most pressing problems of software engineering
+ today, namely software reuse. After six years there is insufficient
+ evidence on which to base any claims of success and it appears that
+ most substantive practical issues of mathematical representation and
+ communication have yet to be addressed. We also raise questions about
+ related computational mathematical goals and mathematical encodings.",
+ paper = "Fate01a.pdf"
+}
+
+\end{chunk}
+
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 0fa7e45..7edc353 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5490,6 +5490,8 @@ buglist add bug 7306: bad counter in )regress function
books/Makefile appendix.sty fix Appendix chapter handling
20160718.01.tpd.patch
src/input/Makefile add intalgorithm.input
+20160720.01.tpd.patch
+books/bookvolbib Axiom Citations in the Literature

1.7.5.4