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Subject: [PATCH] books/bookvolbib Axiom Citations in the Literature
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Goal: Axiom Literate Programming
\index{Bradford, Russell}
\begin{chunk}{axiom.bib}
@inproceedings{Brad92,
author = "Bradford, Russell",
title = "Algebraic Simplification of MultipleValued Functions",
booktitle = "Proc. DISCO 92",
series = "Lecture Notes in Computer Science 721",
year = "1992",
paper = "Brad92.pdf",
abstract =
"Many current algebra systems have a lax attitude to the
simplification of expressions involving functions like log and
$\sqrt{}$, leading the the ability to ``prove'' equalities like $1=1$
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."
}
\end{chunk}
\index{Schwarz, Fritz}
\begin{chunk}{axiom.bib}
@article{Schw91,
author = "Schwarz, Fritz",
title = "Monomial orderings and Groebner bases",
journal = "SIGSAM Bulletin",
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
monomial ordering} is considered. Is it possible to decide whether
these ordering relations are consistent and if so to extend them to an
{\sl admissible} ordering for all monomials? The answer is given in
terms of the algorithm {\sl MACOT} which constructs a matrix of so
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."
}
\end{chunk}
\index{Bradford, Russell}
\begin{chunk}{axiom.bib}
@inproceedings{Brad92,
author = "Bradford, Russell",
title = "Algebraic Simplification of MultipleValued Functions",
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
$\sqrt{}$, leading the the ability to ``prove'' equalities like $1=1$
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."
}
\end{chunk}
\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@article{Wang90,
author = "Wang, Dongming",
title = "A Class of Cubic Differential Systems with 6tuple Focus",
journal = "J. Differential Equations",
publisher = "Academic Press, Inc.",
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."
}
\end{chunk}
\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@article{Wang91,
author = "Wang, Dongming",
title = "Mechanical manipulation for a class of differential systems",
journal = "Journal of Symbolic Computation",
volume = "12",
number = "2",
pages = "233254",
year = "1991",
keywords = "axiomref",
abstract =
"The author describes a mechanical procedure for computing the
Liapunov functions and Liapunov constants for a class of differential
systems. These functions and constants are used for establishing the
stability criteria, the conditions for the existence of a center and
for the investigation of limit cycles. Some problems for handling the
computer constants, which are usually large polynomials in terms of
the coefficients of the differential system, and an approach towards
their solution by using computer algebraic methods are proposed. This
approach has been successfully applied to check some known results
mechanically. The author has implemented a system DEMS on an HP1000
and in Scratchpad II on an IBM4341 for computing and manipulating the
Liapunov functions and Liapunov constants. As examples, two particular
cubic systems are discussed in detail. The explicit algebraic
relations between the computed Liapunov constants and the conditions
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."
}
\end{chunk}
\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@misc{Wang95,
author = "Wang, Dongming",
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
well as their generalization for computing the characteristic set and
characteristic series of a set of multivariate polynomials are
presented. The characeristic set, which is of certain triangular form,
reflects in general the major part of zeros, and the characteristic
series, which is a sequence of polynomial sets of triangular form,
furnishes a complete zero decomposition of the given polynomial
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."
}
\end{chunk}
\index{Keady, G.}
\index{Richardson, M.G.}
\begin{chunk}{axiom.bib}
@inproceedings{Kead93a,
author = "Keady, G. and Richardson, M.G.",
title = "An application of IRENA to systems of nonlinear equations arising
in equilibrium flows in networks",
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
the NAG Fortran Library.
Here IRENA is tested on a problem closer to an engineering problem
than previously publised examples. We also illustrate the use of the
{\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."
}
\end{chunk}
\index{LeBlanc, S.E.}
\begin{chunk}{axiom.bib}
@inproceedings{LeBl91,
author = "LeBlanc, S.E.",
title = "The use of MathCAD and Theorist in the ChE classroom",
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
`electronic scratchpad' and it certainly lives up to its billing. It
is an extremely userfriendly collection of numerical routines that
eliminates the drudgery of solving many of the types of problems
encountered by undergraduate ChE's (and engineers in general). MathCAD
is available for both the Macintosh and IBM PC compatibles. The PC
version is available as a fullfunctioned student version for around
US\$40 (less than many textbooks). Theorist is a symbolic mathematical
package for the Macintosh. Many interesting and instructive things can
be done with it in the ChE curriculum. One of its many attractive
features includes the ability to generate high quality three
dimensional plots that can be very instructive in examining the
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."
}
\end{chunk}
\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@book{Wang01,
author = "Wang, Dongming",
title = "Elimination Methods",
publisher = "SpringerVerlag",
isbn = "9783709162026",
keywords = "axiomref",
year = "2001",
abstract =
"The development of polynomialelimination techniques from classical
theory to modern algorithms has undergone a tortuous and rugged
path. This can be observed L. van der Waerden's elimination of the
``elimination theory'' chapter from from B. his classic Modern Algebra
in later editions, A. Weil's hope to eliminate ``from algebraic
geometry the last traces of elimination theory,'' and S. Abhyankar's
suggestion to ``eliminate the eliminators of elimination theory.''
The renaissance and recognition of polynomial elimination owe much to
the advent and advance of modern computing technology, based on
which effective algorithms are implemented and applied to diverse
problems in science and engineering. In the last decade, both
theorists and practitioners have more and more realized the
significance and power of elimination methods and their underlying
theories. Active and extensive research has contributed a great deal
of new developments on algorithms and soft ware tools to the subject,
that have been widely acknowledged. Their applications have taken
place from pure and applied mathematics to geometric modeling and
robotics, and to artificial neural networks. This book provides a
systematic and uniform treatment of elimination algorithms that
compute various zero decompositions for systems of multivariate
polynomials. The central concepts are triangular sets and systems of
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."
}
\end{chunk}
\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@inproceedings{Wang92,
author = "Wang, Dongming",
title = "A Method for Factorizing Multivariate Polynomials over Successive
Algebraic Extension Fields",
booktitle = "Mathematics and MathematicsMechanization (2001)",
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
algebraic fields obtained from successive extensions of the rational
number field. The basic idea underlying this method is the reduction
of polynomial factorization over algebraic extension fields to the
factorization over the rational number vield via linear transformation
and the computation of characteristic sets with respect to a proper
variable ordering. The factors over the algebraic extension fields are
finally determined via GCD (greatest common divisor) computations. We
have implemented this method in the Maple system. Preliminary
experiments show that it is rather efficient. We give timing
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."
}
\end{chunk}
\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@misc{Wang90a,
author = "Wang, Dongming",
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
based methods is reported. This prover has been used to prove a number
of nontrivial geometry theorems including several {\sl large} ones
with less space and time cost than using the existing provers. The
author presents a new technique by introducing the notion of {\sl
normal ascending set}. This technique yields in some sense {\sl
simpler} nondegenerate conditions for Wu's method and allows one to
prove geometry theorems using characteristic sets but Groeber bases
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."
}
\end{chunk}
\index{Zhao, Ting}
\index{Wang, Dongming}
\index{Hong, Hoon}
\begin{chunk}{axiom.bib}
@article{Zhao11,
author = "Zhao, Ting and Wang, Dongming and Hong, Hoon",
title = "Solution formulats for cubic equations without or with constraints",
journal = "J. Symbolic Computation",
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."
}
\end{chunk}
\index{Li, Xiaoliang}
\index{Mou, Chenqi}
\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@article{Lixx10,
author = "Li, Xiaoliang and Mou, Chenqi and Wang, Dongming",
title = "Decomposing polynomial sets into simple sets over finite fields:
The zerodimensional case",
comment = "Provides clear polynomial algorithms",
journal = "Computers and Mathematics with Applications",
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
an associated ideal or zero decomposition. As a key ingredient of
these algorithms, we generalize the squarefree decomposition approach
for univariate polynomials over a finite field to that over the field
product determined by a simple set. As a subprocedure of the
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."
}
\end{chunk}
\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@article{Wang98,
author = "Wang, Dongming",
title = "Decomposing Polynomial Systems into Simple Systems",
volume = "25",
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
form, in which every polynomial is squarefree and has nonvanishing
leading coefficient with respect to its leading variable. This paper
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."
}
\end{chunk}
\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@article{Wang94,
author = "Wang, Dongming",
title = "Differentiation and Integration of Indefinite Summations with
Respect to Indexed Variables  Some Rules and Applications",
journal = "J. Symbolic Computation",
volume = "18",
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
respect to indexed variables which have not yet been taken into
account of current computer algebra systems. These rules, together
with several others, have been implemented in MACSYMA and MAPLE as a
toolkit for manipulating indefinite summations. We discuss some
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."
}
\end{chunk}
\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@article{Wang95a,
author = "Wang, Dongming",
title = "A Method for Proving Theorems in Differential Geometry and
Mechanics",
journal = "J. Universal Computer Science",
volume = "1",
number = "9",
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."
}
\end{chunk}
\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@article{Wang93,
author = "Wang, Dongming",
title = "An Elimination Method for Polynomial Systems",
journal = "J. Symbolic Computation",
volume = "16",
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 [$\mathbb{P}$,$\mathbb{Q}$]
of two sets of multivariate polynomials, one of the algorithms computes a
sequence of triangular forms $\mathbb{T}_1,\ldots,\mathbb{T}_e$ and
polynomial sets $\mathbb{U}_1,\ldots,\mathbb{U}_e$ such that
Zero($\mathbb{P}$/$\mathbb{Q}$)
$= \cup_{i=1}^e {\rm\ Zero}(\mathbb{T}_i/\mathbb{U}_i)$,
where Zero($\mathbb{P}$/$\mathbb{Q}$) denotes the set of common zeros of
the polynomials in $\mathbb{P}$ which are not zeros of any polynomial in
$\mathbb{Q}$, and similarly for Zero($\mathbb{T}_i$/$\mathbb{U}_i$).
The two other algorithms compute the same zero decomposition but with nicer
properties such as Zero$(\mathbb{T}_i/\mathbb{U}_i) \ne 0$ for each $i$.
One of them, for which the computed triangular systems
[$\mathbb{T}_i$, $\mathbb{U}_i$] possess the projection property, provides
a quantifier elimination procedure for algebraically closed fields.
For the other, the computed triangular forms $\mathbb{T}_i$ are
irreducible. The relationship between our method and some existing
elimination methods is explained. Experimental data for a set of test
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."
}
\end{chunk}
\index{Houstis, E.N.}
\index{Gaffney, P.W.}
\begin{chunk}{axiom.bib}
@book{Hous92,
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 =
"Programming environments, as the name suggests, are intended to
provide a unified, extensive range of capabilities for a person
wishing to solve a problem using a computer. In this particular
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."
}
\end{chunk}
\index{Camion, Paul}
\index{Courteau, Bernard}
\index{Montpetit, Andre}
\begin{chunk}{axiom.bib}
@techreport{Cami92,
author = "Camion, Paul and Courteau, Bernard and Montpetit, Andre",
title = "A combinatorial problem in Hamming Graphs and its solution
in Scratchpad",
comment = {Un probl\`eme combinatoire dans les graphies de Hamming et sa
solution en Scratchpad},
year = "1992",
month = "January",
keywords = "axiomref",
paper = "Cami92.pdf",
url = "https://hal.inria.fr/inria00074974/document",
type = "Research report",
number = "1586",
institution = "Institut National de Recherche en Informatique et en
Automatique, Le Chesnay, France",
abstract =
"We present a combinatorial problem which arises in the determination
of the complete weight coset enumerators of errorcorrecting codes
[1]. In solving this problem by exponential power series with
coefficients in a ring of multivariate polynomials, we fall on a
system of differential equations with coefficients in a field of
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."
}
\end{chunk}
\index{Dalmas, St\'ephane}
\begin{chunk}{axiom.bib}
author = "Dalmas, Stephane",
title = "A polymorphic functional language applied to symbolic computation",
year = "1992",
booktitle = "Proc. ISSAC 1992",
series = "ISSAC 1992",
pages = "369375",
isbn = "0897914899 (soft cover) 0897914902 (hard cover)",
keywords = "axiomref",
"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
language. Although it was not designed as a specialized language, its
sophisticated type system can be successfully applied to describe
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."
}
\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{Corless, Robert M.}
\index{Jeffrey, David J.}
\index{Watt, Stephen M.}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@article{Corl00,
author = "Corless, Robert M. and Jeffrey, David J. and Watt, Stephen M. and
Davenport, James H.",
title = "``According to Abramowitz and Stegun'' or
arccoth needn't be Uncouth",
journal = "SIGSAM Bulletin  Special Issue on OpenMath",
volume = "34",
number = "2",
pages = "5865",
year = "2000",
paper = "Corl00.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 =
"This paper addresses the definitions in OpenMath of the elementary
functions. The original OpenMath definitions, like most other sources,
simply cite [2] as the definition. We show that this is not adequate,
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."
}
\end{chunk}
\index{Bronstein, Manuel}
\begin{chunk}{axiom.bib}
@article{Bron90a,
author = "Bronstein, Manuel",
title = "Integration of Elementary Functions",
journal = "J. Symbolic Computation",
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
integral as an elementary function or prove that it is not
elementary. We show that if the problem of integration in finite terms
is solvable on a given elementary function field $k$, then it is
solvable in any algebraic extension of $k(\theta)$, where $\theta$ is
a logarithm or exponential of an element of $k$. Our proof considers
an element of such an extension field to be an algebraic function of
one variable over $k$.
In his algorithm for the integration of algebraic functions, Trager
describes a Hermitetype reduction to reduce the problem to an
integrand with only simple finite poles on the associated Riemann
surface. We generalize that technique to curves over liouvillian
ground fields, and use it to simplify our integrands. Once the
multipe finite poles have been removed, we use the Puiseux expansions
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."
}
\end{chunk}
\index{Kauers, Manuel}
\begin{chunk}{axiom.bib}
@inproceedings{Kaue08,
author = "Kauers, Manuel",
title = "Integration of Algebraic Functions: A Simple Heuristic for
Finding the Logarithmic Part",
booktitle = "Proc ISSAC 2008",
series = "ISSAC '08",
year = "2008",
pages = "133140",
isbn = "978159593904",
url = "http://www.risc.jku.at/publications/download/risc_3427/Ka01.pdf",
paper = "Kau08.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."
}
\end{chunk}
\index{Lambe, Larry A.}
\begin{chunk}{axiom.bib}
@article{Lamb89,
author = "Lambe, Larry A.",
title = "Scratchpad II as a tool for mathematical research",
journal = "Notices of the AMS",
year = "1989",
pages = "143147",
keywords = "axiomref"
}
\end{chunk}
\index{H. Gollan}
\index{Grabmeier, Johannes}
\begin{chunk}{axiom.bib}
@article{Goll90,
author = "H. Gollan and Grabmeier, Johannes",
title = "Algorithms in Representation Theory and their Realization
in the Computer Algebra System Scratchpad",
journal = "Bayreuther Mathematische Schriften",
volume = "33",
year = "1990",
pages = "123"
}
\end{chunk}
\index{Bradford, Russell J.}
\index{Hearn, Anthony C.}
\index{Padget, Julian}
\index{Schr\"ufer, Eberhard}
\begin{chunk}{axiom.bib}
@inproceedings{Brad86,
author = "Bradford, Russell J. and Hearn, Anthony C. and Padget, Julian and
Schrufer, Eberhard",
title = "Enlarging the REDUCE domain of computation",
booktitle = "Proc SYMSAC 1986",
series = "SYMSAC '86",
publisher = "ACM",
year = "1986",
pages = "100106",
isbn = "0897911997",
abstract =
"We describe the methods available in the current REDUCE system for
introducing new mathematical domains, and illustrate these by discussing
several new domains that significantly increase the power of the overall
system."
}
\end{chunk}
\begin{chunk}{axiom.bib}
@misc{IBMx91,
author = "Computer Algebra Group",
title = "The AXIOM Users Guide",
publisher = "NAG Ltd., Oxford",
year = "1991"
}
\end{chunk}
\index{Hearn, Anthony}
\begin{chunk}{axiom.bib}
@misc{Hear87,
author = "Hearn, Anthony",
title = "REDUCE User's Manual",
version = "3.3",
institution = "Rand Corporation",
year = "1987"
}
\end{chunk}
\index{Fitch, John P.}
\begin{chunk}{axiom.bib}
@misc{Fitc74,
author = "Fitch, J.P.",
title = "CAMAL Users Manual",
institution = "University of Cambridge Computer Laboratory",
year = "1974"
}
\end{chunk}
\index{Barton, D.R.}
\index{Fitch, John P.}
\begin{chunk}{axiom.bib}
@article{Bart72,
author = "Barton, D.R. and Fitch, John P.",
title = "A Review of Algebraic Manipulative Programs and their Application",
journal = "The Computer Journal",
volume = "15",
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
is tutorial and severed typical problems are introduced which can be
solved using algebraic manipulative systems. Sample programs for the
solution of these problems using several algebra systems are then
presented. Next, two more difficult examples are used to introduce the
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."
}
\end{chunk}
\index{Duval, Dominique}
\index{Jung, F.}
\begin{chunk}{axiom.bib}
@inproceedings{Duva92,
author = "Duval, Dominique and Jung, F.",
title = "Examples of problem solving using computer algebra",
booktitle = "Programming environments for highlevel scientific problem
solving",
series = "IFIP Transactions",
editor = "Gaffney, Patrick W. and Houstis, Elias N.",
publisher = "NorthHolland",
pages = "133143",
year = "1992",
keywords = "axiomref"
}
\end{chunk}

books/bookvolbib.pamphlet  1083 ++++++++++++++++++++++++++++++++
changelog  2 +
patch  792 +++++++++++++++++++++++++++++
src/axiomwebsite/patches.html  2 +
4 files changed, 1675 insertions(+), 204 deletions()
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 193daac..5e6b52b 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 1113,6 +1113,63 @@ when shown in factored form.
\end{chunk}
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@misc{Wang90a,
+ author = "Wang, Dongming",
+ 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
+ based methods is reported. This prover has been used to prove a number
+ of nontrivial geometry theorems including several {\sl large} ones
+ with less space and time cost than using the existing provers. The
+ author presents a new technique by introducing the notion of {\sl
+ normal ascending set}. This technique yields in some sense {\sl
+ simpler} nondegenerate conditions for Wu's method and allows one to
+ prove geometry theorems using characteristic sets but Groeber bases
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@inproceedings{Wang92,
+ author = "Wang, Dongming",
+ title = "A Method for Factorizing Multivariate Polynomials over Successive
+ Algebraic Extension Fields",
+ booktitle = "Mathematics and MathematicsMechanization (2001)",
+ 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
+ algebraic fields obtained from successive extensions of the rational
+ number field. The basic idea underlying this method is the reduction
+ of polynomial factorization over algebraic extension fields to the
+ factorization over the rational number vield via linear transformation
+ and the computation of characteristic sets with respect to a proper
+ variable ordering. The factors over the algebraic extension fields are
+ finally determined via GCD (greatest common divisor) computations. We
+ have implemented this method in the Maple system. Preliminary
+ experiments show that it is rather efficient. We give timing
+ 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."
+}
+
+\end{chunk}
+
\section{Sparse Linear Systems} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Kaltofen, Erich}
@@ 1909,6 +1966,35 @@ when shown in factored form.
\end{chunk}
+\index{Li, Xiaoliang}
+\index{Mou, Chenqi}
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Lixx10,
+ author = "Li, Xiaoliang and Mou, Chenqi and Wang, Dongming",
+ title = "Decomposing polynomial sets into simple sets over finite fields:
+ The zerodimensional case",
+ comment = "Provides clear polynomial algorithms",
+ journal = "Computers and Mathematics with Applications",
+ 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
+ an associated ideal or zero decomposition. As a key ingredient of
+ these algorithms, we generalize the squarefree decomposition approach
+ for univariate polynomials over a finite field to that over the field
+ product determined by a simple set. As a subprocedure of the
+ 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."
+}
+
+\end{chunk}
+
\section{Numerical Algorithms} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Ahrens, Peter}
@@ 6151,14 +6237,17 @@ Lecture Notes in Computer Science Vol 378 pp491497
\end{chunk}
\index{Bronstein, Manuel}
\begin{chunk}{ignore}
\bibitem[Bronstein 90a]{Bro90a} Bronstein, Manuel
+\begin{chunk}{axiom.bib}
+@article{Bron90a,
+ author = "Bronstein, Manuel",
title = "Integration of Elementary Functions",
J. Symbolic Computation 9, pp117173
+ journal = "J. Symbolic Computation",
+ volume = "9",
+ pages = "117173",
year = "1990",
paper = "Bro90a.pdf",
 abstract = "
 We extend a recent algorithm of Trager to a decision procedure for the
+ abstract =
+ "We extend a recent algorithm of Trager to a decision procedure for the
indefinite integration of elementary functions. We can express the
integral as an elementary function or prove that it is not
elementary. We show that if the problem of integration in finite terms
@@ 6178,6 +6267,7 @@ J. Symbolic Computation 9, pp117173
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."
+}
\end{chunk}
@@ 6413,13 +6503,13 @@ SIAM J. Computing Vol 18 pp 893905 (1989)
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@book{Dave79b,
+@book{Dave81,
author = "Davenport, James H.",
title = "On the Integration of Algebraic Functions",
publisher = "SpringerVerlag",
series = "Lecture Notes in Computer Science 102",
isbn = "0387102906",
 year = "1982"
+ year = "1981"
}
\end{chunk}
@@ 7388,7 +7478,7 @@ MIT Master's Thesis.
\begin{chunk}{axiom.bib}
@phdthesis{Trag84,
author = "Trager, Barry",
 title = "On the integration of algebraic functions",
+ title = "Integration of Algebraic Functions",
school = "MIT",
year = "1984",
url = "http://www.dm.unipi.it/pages/gianni/public_html/AlgComp/thesis.pdf",
@@ 9389,7 +9479,7 @@ rational righthand sides etc."
\index{Schneider, Carsten}
\index{Kauers, Manuel}
\begin{chunk}{axiom.bib}
@article{Kaue08,
+@article{Kaue08a,
author = "Kauers, Manuel and Schneider, Carsten",
title = "Indefinite summation with unspecified summands",
year = "2006",
@@ 9397,7 +9487,7 @@ rational righthand sides etc."
volume = "306",
number = "17",
pages = "20732083",
 paper = "Kaue80.pdf",
+ paper = "Kaue08a.pdf",
abstract = "
We provide a new algorithm for indefinite nested summation which is
applicable to summands involving unspecified sequences $x(n)$. More
@@ 10485,6 +10575,28 @@ J. Symbolic Computation 5, 237259 (1988)
\end{chunk}
+\index{Zhao, Ting}
+\index{Wang, Dongming}
+\index{Hong, Hoon}
+\begin{chunk}{axiom.bib}
+@article{Zhao11,
+ author = "Zhao, Ting and Wang, Dongming and Hong, Hoon",
+ title = "Solution formulats for cubic equations without or with constraints",
+ journal = "J. Symbolic Computation",
+ 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."
+}
+
+\end{chunk}
+
\section{Comparison of Computer Algebra System} %%%%%%%%%%%%%%%%%%%%%%
\index{Bernardin, Laurent}
@@ 10571,6 +10683,280 @@ J. Symbolic Computation 5, 237259 (1988)
\section{To Be Classified} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang93,
+ author = "Wang, Dongming",
+ title = "An Elimination Method for Polynomial Systems",
+ journal = "J. Symbolic Computation",
+ volume = "16",
+ 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 [$\mathbb{P}$,$\mathbb{Q}$]
+ of two sets of multivariate polynomials, one of the algorithms computes a
+ sequence of triangular forms $\mathbb{T}_1,\ldots,\mathbb{T}_e$ and
+ polynomial sets $\mathbb{U}_1,\ldots,\mathbb{U}_e$ such that
+ Zero($\mathbb{P}$/$\mathbb{Q}$)
+ $= \cup_{i=1}^e {\rm\ Zero}(\mathbb{T}_i/\mathbb{U}_i)$,
+ where Zero($\mathbb{P}$/$\mathbb{Q}$) denotes the set of common zeros of
+ the polynomials in $\mathbb{P}$ which are not zeros of any polynomial in
+ $\mathbb{Q}$, and similarly for Zero($\mathbb{T}_i$/$\mathbb{U}_i$).
+ The two other algorithms compute the same zero decomposition but with nicer
+ properties such as Zero$(\mathbb{T}_i/\mathbb{U}_i) \ne 0$ for each $i$.
+ One of them, for which the computed triangular systems
+ [$\mathbb{T}_i$, $\mathbb{U}_i$] possess the projection property, provides
+ a quantifier elimination procedure for algebraically closed fields.
+ For the other, the computed triangular forms $\mathbb{T}_i$ are
+ irreducible. The relationship between our method and some existing
+ elimination methods is explained. Experimental data for a set of test
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang94,
+ author = "Wang, Dongming",
+ title = "Differentiation and Integration of Indefinite Summations with
+ Respect to Indexed Variables  Some Rules and Applications",
+ journal = "J. Symbolic Computation",
+ volume = "18",
+ 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
+ respect to indexed variables which have not yet been taken into
+ account of current computer algebra systems. These rules, together
+ with several others, have been implemented in MACSYMA and MAPLE as a
+ toolkit for manipulating indefinite summations. We discuss some
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang95a,
+ author = "Wang, Dongming",
+ title = "A Method for Proving Theorems in Differential Geometry and
+ Mechanics",
+ journal = "J. Universal Computer Science",
+ volume = "1",
+ number = "9",
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang98,
+ author = "Wang, Dongming",
+ title = "Decomposing Polynomial Systems into Simple Systems",
+ volume = "25",
+ 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
+ form, in which every polynomial is squarefree and has nonvanishing
+ leading coefficient with respect to its leading variable. This paper
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang99,
+ author = "Wang, Dongming",
+ title = "Polynomial Systems from Certain Differential Equations",
+ journal = "J. Symbolic Computation",
+ volume = "28",
+ 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
+ differential systems initially investigated by Kukles in 1944. The
+ obtained relations clarify recent rediscoveries of some known
+ conditions of Cherkas. The computational difficulties of establishing
+ the complete center conditions for Kukles’ system, a problem that is
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang00,
+ author = "Wang, Dongming",
+ title = "Computing Triangular Systems and Regular Systems",
+ journal = "J. Symbolic Computation",
+ volume = "30",
+ 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
+ given polynomial system. The resulting algorithms, based on the
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang04,
+ author = "Wang, Dongming",
+ title = "A simple method for implicitizing rational curves and surfaces",
+ journal = "J. Symbolic Computation",
+ volume = "38",
+ 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
+ equations. The method proceeds via writing out the implicit polynomial
+ $F$ of estimated degree with indeterminate coefficients $u_i$,
+ substituting the rational expressions for the given parametric curve
+ or surface into $F$ to yield a rational expression $g/h$ in the
+ parameter $s$ (or $s$ and $t$), equating the coefficients of $g$ in
+ terms of $s$ (and $t$) to 0 to generate a sparse, partially triangular
+ system of linear equations in $u_i$ with constant coefficients, and
+ finally solving the linear system for ui. If a nontrivial solution is
+ found, then an implicit polynomial is obtained; otherwise, one repeats
+ 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."
+}
+
+\end{chunk}
+
+\index{Bradford, Russell}
+\begin{chunk}{axiom.bib}
+@inproceedings{Brad92,
+ author = "Bradford, Russell",
+ title = "Algebraic Simplification of MultipleValued Functions",
+ 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
+ $\sqrt{}$, leading the the ability to ``prove'' equalities like $1=1$
+ 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."
+}
+
+\end{chunk}
+
+\index{Kaisler, Stephen H.}
+\index{Madey, Gregory}
+\begin{chunk}{axiom.bib}
+@misc{Kais09,
+ author = "Kaisler, Stephen H. and Madey, Gregory",
+ title = "Complex Adaptive Systems: Emergence and SelfOrganization",
+ year = "2009",
+ institution = "University of Notre Dame",
+ comment = "source for Sweeney.eps",
+ url = "http://www3.nd.edu/~gmadey/Activities/CASBriefing.pdf"
+}
+
+\end{chunk}
+
+\index{Kalman, Dan}
+\begin{chunk}{axiom.bib}
+@article{Kalm01,
+ author = "Kalman, Dan",
+ title = "A Generalized Logarithm for ExponentialLinear Equations",
+ journal = "The College Mathematics Journal",
+ volume = "32",
+ number = "1",
+ year = "2001",
+ paper = "Kalm01.pdf",
+ abstract =
+ "How do you solve the equation
+ \[1.6^x = 5054.4  122.35*x\]
+ We will refer to equations of this type, with an exponential
+ expression on one side and a linear one on the other, as
+ {\sl exponentiallinear} equations. Numerical approaches such as Newton’s
+ method or bisection quickly lead to accurate approximate solutions of
+ exponentiallinear equations. But in terms of the elementary functions
+ of calculus and college algebra, there is no analytic solution.
+
+ One approach to remedying this situation is to introduce a special
+ function designed to solve exponentiallinear equations. Quadratic
+ equations, by way of analogy, are solvable in terms of the special
+ function $\sqrt{x}$ , which in turn is simply the inverse of a very
+ special and simple quadratic function. Similarly, exponential
+ equations are solvable in terms of the natural logarithm {\sl log},
+ and that too is the inverse of a very special function. So it is
+ reasonable to ask whether there is a special function in terms of
+ which exponentiallinear equations might be solved. Furthermore, an
+ obvious strategy for finding such a function is to invert some simple
+ function connected with exponentiallinear equations.
+
+ This line of thinking proves to be immediately successful, and leads
+ to a function I call {\sl glog} (pronounced {\sl geelog}) which is a
+ kind of generalized logarithm. As intended, glog can be used to solve
+ exponentiallinear equations. But that is by no means all it is good
+ for. For example, with glog you can write a closedform expression for
+ the iterated exponential ($x^{x^{x^.}}$), and solve $x + y = x^y$ for
+ $y$. The glog function is also closely related to another special
+ function, called the Lambert $W$ function in [3] and [6], whose study
+ 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."
+}
+
+\end{chunk}
+
\index{Dewar, Michael C.}
\begin{chunk}{axiom.bib}
@phdthesis{Dewa91,
@@ 12171,18 +12557,6 @@ American Mathematical Society (1994)
\end{chunk}
\begin{chunk}{axiom.bib}
@book{Anon92,
 author = "Anonymous",
 title = "Programming environments for highlevel scientific problem solving",
 year = "1992",
 keywords = "axiomref",
 publisher = "IFIP TC2",
 isbn = "9780444891761"
}

\end{chunk}

\begin{chunk}{axiom.bib}
@book{Anon95,
author = "Anonymous",
title = "Zeitschrift fur Angewandte Mathematik und Physik, 75 (suppl. 2)",
@@ 13326,16 +13700,33 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
\index{Camion, Paul}
\index{Courteau, Bernard}
\index{Montpetit, Andre}
\begin{chunk}{ignore}
\bibitem[Camion 92]{CCM92}
+\begin{chunk}{axiom.bib}
+@techreport{Cami92,
author = "Camion, Paul and Courteau, Bernard and Montpetit, Andre",
title = "A combinatorial problem in Hamming Graphs and its solution
in Scratchpad",
+ comment = {Un probl\`eme combinatoire dans les graphies de Hamming et sa
+ solution en Scratchpad},
year = "1992",
month = "January",
keywords = "axiomref",
Rapports de recherche 1586, Institut National de Recherche en
Informatique et en Automatique, Le Chesnay, France, 12pp
+ paper = "Cami92.pdf",
+ url = "https://hal.inria.fr/inria00074974/document",
+ type = "Research report",
+ number = "1586",
+ institution = "Institut National de Recherche en Informatique et en
+ Automatique, Le Chesnay, France",
+ abstract =
+ "We present a combinatorial problem which arises in the determination
+ of the complete weight coset enumerators of errorcorrecting codes
+ [1]. In solving this problem by exponential power series with
+ coefficients in a ring of multivariate polynomials, we fall on a
+ system of differential equations with coefficients in a field of
+ 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."
+}
\end{chunk}
@@ 13970,6 +14361,59 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
\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{Corless, Robert M.}
+\index{Jeffrey, David J.}
+\index{Watt, Stephen M.}
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@article{Corl00,
+ author = "Corless, Robert M. and Jeffrey, David J. and Watt, Stephen M. and
+ Davenport, James H.",
+ title = "``According to Abramowitz and Stegun'' or
+ arccoth needn't be Uncouth",
+ journal = "SIGSAM Bulletin  Special Issue on OpenMath",
+ volume = "34",
+ number = "2",
+ pages = "5865",
+ year = "2000",
+ paper = "Corl00.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 =
+ "This paper addresses the definitions in OpenMath of the elementary
+ functions. The original OpenMath definitions, like most other sources,
+ simply cite [2] as the definition. We show that this is not adequate,
+ 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."
+}
+
+\end{chunk}
+
\index{GroebnerPackage}
\index{PseudoLinearNormalForm}
\index{PolyGroebner}
@@ 14124,7 +14568,16 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
series = "ISSAC 1992",
pages = "369375",
isbn = "0897914899 (soft cover) 0897914902 (hard cover)",
 keywords = "axiomref"
+ 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
+ language. Although it was not designed as a specialized language, its
+ sophisticated type system can be successfully applied to describe
+ 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."
}
\end{chunk}
@@ 14248,7 +14701,7 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
\index{Davenport, James H.}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@article{Dave81,
+@article{Dave81a,
author = "Davenport, James H. and Jenks, Richard D.",
title = "MODLISP",
year = "1981",
@@ 14355,133 +14808,7 @@ Mathematical Sciences Department, IBM Thomas Watson Research Center 1984
isbn ="0122042301",
url = "http://staff.bath.ac.uk/masjhd/masternew.pdf",
paper = "Dave88.pdf",
 keywords = "axiomref",
 abstract =
 "The need for a good general text on Computer Algebra has never been
 greater. From the very beginning, computers have been used for
 numerical calculation. It is not always realized however that their
 use for mathematical calculation of a symbolic nature has a history
 almost as long. It is only recently that improvement in algorithms,
 the development of small systems and the emergence of powerful
 workstations have combined to make Computer Algebra systems much more
 widely available and an increasingly important tool for almost all
 users of Mathematics. Part of the reason why Computer Algebra was for
 so long something of an esoteric discipline, has surely been the lack
 of textbooks on the subject. The arrival of the present volume on the
 scene has thus been particularly fortunate.

 The approach adopted by the authors is to begin by giving the reader
 an idea of the sort of calculations that Algebra Systems can
 perform. Next the questions of data representation are
 treated. Finally the bulk of the book is devoted to explaining the
 classical algorithms of the subject. The reader is thereby given both
 a feel for the problems, such as data representation and combinatorial
 explosion, that system designers need to face, and a general
 understanding of the underlying Mathematics. The book is not intended
 to provide encyclopedic coverage, nor is it meant to be serve as a
 manual for any particular system.

 One of the more difficult design decisions facing authors of such a
 book concerns the level of mathematical sophistication to be assumed
 on behalf of the reader. One wants the book to be accessible to as
 wide an audience as possible, but any understanding of the subject
 beyond the more superficial requires a reasonable grasp of the
 underlying Pure Mathematics. The compromise made in the present text
 is to fully explain the mathematical problems, to state the theorems
 and consequent algorithms, but not always to prove the theorems. Many
 of the more straightforward results are proved though. The decisions
 as to what to include and what to omit have been well thought out and
 the result is a considerable success. The book has a great deal to
 offer engineers and scientists and its early chapters in particular
 could most suitably serve as the basis for an undergraduate
 course. For the professional mathematician it provides a good quick
 allround introduction to a fascinating and rapidly evolving area.

 Of course in a book such as this, not everything that might fall under
 the umbrella of Computer Algebra can be covered. Thus some specialized
 topics, such as Computational Group Theory, are not mentioned, and the
 treatment of other areas is sometimes necessarily abbreviated. However
 the main stream of the subject is well represented, and the selection
 of material generally well judged. Typically, the main classical
 results are fully explained, some of the more interesting developments
 and variations are sketched, and the reader is referred to the
 standard literature of the subject for further details.

 The first chapter is entitled ``How to use a Computer Algebra
 System''. Here the reader is led through a session with the MACSYMA
 system obtaining a vicarious handson experience. Beginners would be
 well advised to follow the authors’ suggestion and duplicate the
 session on their local system as closely as possible. The examples
 chosen are interesting, though perhaps a little too ‘pure
 mathematical’ for some tastes. Overall the chapter gives a good idea
 of the capabilities of algebra systems.

 Chapter 2 is concerned with the representation of the various
 mathematical quantities which algebra systems handle. It might be
 thought that data repesentation is mainly a computerscience matter,
 but in fact some rather interesting mathematical problems concerning
 uniqueness arise. The chapter includes, among other things, discussion
 of the non modular methods for computing gcds (the subresultant
 algorithm for example), the handling of algebraic quantities the Risch
 Structure Theorem and the Bareiss Method of Gaussian elimination.

 The third chapter treats two major topics under the heading
 ``Polynomial Simplification''. Firstly there is a concise, but good,
 explanation of Buchberger’s Groebnerbasis methods for computations in
 polynomial rings. Secondly there is an equally good introduction to
 the use of cylindrical decomposition for obtaining approximations to
 real roots of polynomial equations.

 Chapter 4, which is headed ``Advanced Algorithms'', begins with a
 discussion of modular methods, in particular the modular gcd. A brisk
 treatment of the Berlekamp factorization method follows, together with
 both the linear and quadratic varieties of the Hensel Lemma. In
 addition there is a short section on the factorization of polynomials
 in several variables. In general the high standard of the book is
 maintained, but, unusually, the treatment of the modular gcd suffers a
 little from typos and the explanation of the Hensel Lemma could be
 clearer in places.

 The major part of the final chapter is devoted to symbolic integration
 and related topics concerning the formal solution of some ordinary
 differential equations. These form the ‘high point’ of the book. Here
 in particular the reader is led to the borders of current
 research. The final part of Chapter 5 is concerned with asymptotic
 expansions of solutions of differential equations. I found the
 treatment of this topic too brief to be entirely successful. Those
 already familiar with the theory of asymptotic expansion will no doubt
 be interested in the details of the implementation, but the beginner
 needs a fuller treatment, which this important topic surely deserves.

 The book also contains an appendix and an annex. The former is
 entitled ``Algebraic Background''. It is useful to refer to, but would
 not be sufficient for anyone whose background did not already include
 a fair familiarity with most of its contents. The annex contains a
 description of the REDUCE system. Here the reader is able to see how
 some of the algorithms described in the main part of the book are used
 in an actual system.

 The bibliography is excellent, though I do have two minor carps. One
 or two articles mentioned in the text do not appear in the
 bibliography, Also inclusion of one or two ‘standard’ mathematical
 works, and appropriate reference to them in the text, would make the
 book more accessible to people whose main speciality is not
 Mathematics.

 The few minor quibbles I have with this book are of little
 importance. It provides an excellent introduction to Computer
 Algebra. At the time of writing, it is still, to the best of my
 knowledge, the only general textbook on the subject and it is indeed
 fortunate that it is such a good one.

 The second edition incorporates many recent advances in theory and
 practice of computer algebra (a short proof of the convergence of
 Buchberger’s algorithm as well as recent releases of software
 described in the text). Further a description of the AXIOM system is
 included.

 This book definitely represents one of the best introductions to
 computer algebra accessible to beginners and researchers."
+ keywords = "axiomref"
}
\end{chunk}
@@ 14721,14 +15048,32 @@ Downer's Grove, IL, USA and Oxford, UK, December 1992
\end{chunk}
\index{Davenport, James H.}
\begin{chunk}{ignore}
\bibitem[Davenport 92a]{Dav92a} Davenport, J. H.
+\begin{chunk}{axiom.bib}
+@techreport{Dave92a,
+ author = "Davenport, James H.",
title = "The AXIOM system",
AXIOM Technical Report TR5/92 (ATR/3)
(NP2492) Numerical Algorithms Group, Inc., Downer's Grove, IL, USA and
Oxford, UK, December 1992
 url = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
+ type = "technical report",
+ 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
+ therefore in the possibilities it offers to its users. In these
+ lecture notes, we will
+ \begin{itemize}
+ \item outline the highlevel design of the AXIOM kernel and the AXIOM type
+ system,
+ \item explain some of the algebraic facilities implemented in AXIOM,
+ which may be more general than the reader is used to,
+ \item show how the type system and the information system interact,
+ \item give some references to the literature on particular aspects of
+ AXIOM and,
+ \item suggest the way forward.
+ \end{itemize}"
+}
\end{chunk}
@@ 15781,12 +16126,19 @@ TPHOLS 2001, Edinburgh
\index{Duval, Dominique}
\index{Jung, F.}
\begin{chunk}{ignore}
\bibitem[Duval 92]{DJ92} Duval, D.; Jung, F.
+\begin{chunk}{axiom.bib}
+@inproceedings{Duva92,
+ author = "Duval, Dominique and Jung, F.",
title = "Examples of problem solving using computer algebra",
IFIP Transactions. A. Computer Science and Technology, A2 pp133141, 143 1992
CODEN ITATEC. ISSN 09265473
 keywords = "axiomref",
+ booktitle = "Programming environments for highlevel scientific problem
+ solving",
+ series = "IFIP Transactions",
+ editor = "Gaffney, Patrick W. and Houstis, Elias N.",
+ publisher = "NorthHolland",
+ pages = "133143",
+ year = "1992",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 17330,6 +17682,33 @@ in [Wit87], pp58
\end{chunk}
+\index{Keady, G.}
+\index{Richardson, M.G.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Kead93a,
+ author = "Keady, G. and Richardson, M.G.",
+ title = "An application of IRENA to systems of nonlinear equations arising
+ in equilibrium flows in networks",
+ 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
+ the NAG Fortran Library.
+
+ Here IRENA is tested on a problem closer to an engineering problem
+ than previously publised examples. We also illustrate the use of the
+ {\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."
+}
+
+\end{chunk}
+
\index{Hawkes, Evatt}
\index{Keady, Grant}
\begin{chunk}{axiom.bib}
@@ 17963,6 +18342,28 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
\end{chunk}
+\index{Houstis, E.N.}
+\index{Gaffney, P.W.}
+\begin{chunk}{axiom.bib}
+@book{Hous92,
+ 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 =
+ "Programming environments, as the name suggests, are intended to
+ provide a unified, extensive range of capabilities for a person
+ wishing to solve a problem using a computer. In this particular
+ 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."
+}
+
+\end{chunk}
+
\index{Houstis, Elias N.}
\index{Rice, John R.}
\begin{chunk}{axiom.bib}
@@ 18888,38 +19289,45 @@ SIGSAM Communications in Computer Algebra, 157 2006
year = "1981",
abstract =
"Operators in functional languages such as APL and FFP are a useful
 programming concept. However, this concept cannot be ful ly
+ programming concept. However, this concept cannot be fully
exploited in these languages because of certain constraints. It is
 proposed that an operator should be associated with a structure hav
 ing the algebraic properties on which the operator's behavior depends.
+ proposed that an operator should be associated with a structure having
+ the algebraic properties on which the operator's behavior depends.
This is illustrated by introducing a language that provides mechanisms
for defining structures and operators on them. Using this language,
 it is possible to describe algorithms abstractly, thus empliasizing
+ it is possible to describe algorithms abstractly, thus emphasizing
the algebraic properties on which the algorithms depend. The role
that formal representation of mathematical knowledge can play in the
development of programs is illustrated through an example. An
 approach for associating complexity mea sures with a structure and
 operators is also suggested. This ap proach is useful in analyzing
+ 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."
}
\end{chunk}
\index{Kauers, Manuel}
\begin{chunk}{ignore}
\bibitem[Kauers 08]{Kau08} Kauers, Manuel
 title = "Integration of Algebraic Functions: A Simple Heuristic for Finding the Logarithmic Part",
ISSAC July 2008 ACM 978159593904 pp133140
+\begin{chunk}{axiom.bib}
+@inproceedings{Kaue08,
+ author = "Kauers, Manuel",
+ title = "Integration of Algebraic Functions: A Simple Heuristic for
+ Finding the Logarithmic Part",
+ booktitle = "Proc ISSAC 2008",
+ series = "ISSAC '08",
+ year = "2008",
+ pages = "133140",
+ isbn = "978159593904",
url = "http://www.risc.jku.at/publications/download/risc_3427/Ka01.pdf",
 paper = "Kau08.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 Gr{\"o}bner bases
+ 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."
+}
\end{chunk}
@@ 19601,7 +20009,7 @@ University of St Andrews, 6th April 2000
\end{chunk}
\index{Lambe, Larry A.}
\begin{chunk}{ignore}
+\begin{chunk}{axiom.bib}
@article{Lamb89,
author = "Lambe, Larry A.",
title = "Scratchpad II as a tool for mathematical research",
@@ 19911,11 +20319,33 @@ PhD thesis, Nov 2008 Florida State University
\end{chunk}
\index{LeBlanc, S.E.}
\begin{chunk}{ignore}
\bibitem[LeBlanc 91]{LeB91} LeBlanc, S.E.
+\begin{chunk}{axiom.bib}
+@inproceedings{LeBl91,
+ author = "LeBlanc, S.E.",
title = "The use of MathCAD and Theorist in the ChE classroom",
In Anonymous [Ano91], pp287299 (vol. 1) 2 vols.
+ 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
+ `electronic scratchpad' and it certainly lives up to its billing. It
+ is an extremely userfriendly collection of numerical routines that
+ eliminates the drudgery of solving many of the types of problems
+ encountered by undergraduate ChE's (and engineers in general). MathCAD
+ is available for both the Macintosh and IBM PC compatibles. The PC
+ version is available as a fullfunctioned student version for around
+ US\$40 (less than many textbooks). Theorist is a symbolic mathematical
+ package for the Macintosh. Many interesting and instructive things can
+ be done with it in the ChE curriculum. One of its many attractive
+ features includes the ability to generate high quality three
+ dimensional plots that can be very instructive in examining the
+ 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."
+}
\end{chunk}
@@ 20499,12 +20929,29 @@ June 2, 1997
\index{Lynch, R.}
\index{Mavromatis, H. A.}
\begin{chunk}{ignore}
\bibitem[Lynch 91]{LM91} Lynch, R.; Mavromatis, H. A.
 title = "New quantum mechanical perturbation technique using an 'electronic scratchpad' on an inexpensive computer",
American Journal of Pyhsics, 59(3) pp270273, March 1991.
CODEN AJPIAS ISSN 00029505
+\begin{chunk}{axiom.bib}
+@article{Lync91,
+ author = "Lynch, R. and Mavromatis, H. A.",
+ title = "New quantum mechanical perturbation technique using an
+ 'electronic scratchpad' on an inexpensive computer",
+ journal = "American Journal of Pyhsics",
+ volume = "59",
+ 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
+ Rayleigh–Schrödinger perturbation theory (division of the Hamiltonian
+ into an unperturbed Hamiltonian and a perturbing term, use of the
+ basis formed by the eigenfunctions of the unperturbed Hamiltonian)
+ while turning out to be a variational technique. Furthermore, it is
+ 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."
+}
\end{chunk}
@@ 22114,7 +22561,7 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
\end{chunk}
\index{Schwarz, Fritz}
\begin{chunk}{ignore}
+\begin{chunk}{axiom.bib}
@inproceedings{Schw88,
author = "Schwarz, Fritz",
title = "Programming with abstract data types: the symmetry package
@@ 22171,12 +22618,27 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
\end{chunk}
\index{Schwarz, Fritz}
\begin{chunk}{ignore}
\bibitem[Schwarz 91]{Sch91} Schwarz, F.
 title = "Monomial orderings and Gr{\"o}bner bases",
SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic
Manipulation) 2591) pp1023 Jan. 1991 CODEN SIGSBZ ISSN 01635824
+\begin{chunk}{axiom.bib}
+@article{Schw91,
+ author = "Schwarz, Fritz",
+ title = "Monomial orderings and Groebner bases",
+ journal = "SIGSAM Bulletin",
+ 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
+ monomial ordering} is considered. Is it possible to decide whether
+ these ordering relations are consistent and if so to extend them to an
+ {\sl admissible} ordering for all monomials? The answer is given in
+ terms of the algorithm {\sl MACOT} which constructs a matrix of so
+ 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."
+}
\end{chunk}
@@ 23361,12 +23823,124 @@ ISBN 3540213112
\end{chunk}
\index{Wang, Dongming}
\begin{chunk}{ignore}
\bibitem[Wang 91]{Wan91} Wang, Dongming
+\begin{chunk}{axiom.bib}
+@article{Wang90,
+ author = "Wang, Dongming",
+ title = "A Class of Cubic Differential Systems with 6tuple Focus",
+ journal = "J. Differential Equations",
+ publisher = "Academic Press, Inc.",
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang91,
+ author = "Wang, Dongming",
title = "Mechanical manipulation for a class of differential systems",
Journal of Symbolic Computation, 12(2) pp233254 Aug. 1991
CODEN JSYCEH ISSN 07477171
+ journal = "Journal of Symbolic Computation",
+ volume = "12",
+ number = "2",
+ pages = "233254",
+ year = "1991",
+ keywords = "axiomref",
+ paper = "Wang91.pdf",
+ abstract =
+ "In this paper we describe a mechanical procedure for computing the
+ Liapunov functions and Liapunov constants for a class of differential
+ systems. These functions and constants are used for establishing the
+ stability criteria, the conditions for the existence of a center and
+ for the investigation of limit cycles. Some problems for handling the
+ computer constants, which are usually large polynomials in terms of
+ the coefficients of the differential system, and an approach towards
+ their solution by using computer algebraic methods are proposed. This
+ approach has been successfully applied to check some known results
+ mechanically. The author has implemented a system DEMS on an HP1000
+ and in Scratchpad II on an IBM4341 for computing and manipulating the
+ Liapunov functions and Liapunov constants. As examples, two particular
+ cubic systems are discussed in detail. The explicit algebraic
+ relations between the computed Liapunov constants and the conditions
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@misc{Wang95,
+ author = "Wang, Dongming",
+ 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
+ well as their generalization for computing the characteristic set and
+ characteristic series of a set of multivariate polynomials are
+ presented. The characeristic set, which is of certain triangular form,
+ reflects in general the major part of zeros, and the characteristic
+ series, which is a sequence of polynomial sets of triangular form,
+ furnishes a complete zero decomposition of the given polynomial
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@book{Wang01,
+ author = "Wang, Dongming",
+ title = "Elimination Methods",
+ publisher = "SpringerVerlag",
+ isbn = "9783709162026",
keywords = "axiomref",
+ year = "2001",
+ abstract =
+ "The development of polynomialelimination techniques from classical
+ theory to modern algorithms has undergone a tortuous and rugged
+ path. This can be observed L. van der Waerden's elimination of the
+ ``elimination theory'' chapter from from B. his classic Modern Algebra
+ in later editions, A. Weil's hope to eliminate ``from algebraic
+ geometry the last traces of elimination theory,'' and S. Abhyankar's
+ suggestion to ``eliminate the eliminators of elimination theory.''
+ The renaissance and recognition of polynomial elimination owe much to
+ the advent and advance of modern computing technology, based on
+ which effective algorithms are implemented and applied to diverse
+ problems in science and engineering. In the last decade, both
+ theorists and practitioners have more and more realized the
+ significance and power of elimination methods and their underlying
+ theories. Active and extensive research has contributed a great deal
+ of new developments on algorithms and soft ware tools to the subject,
+ that have been widely acknowledged. Their applications have taken
+ place from pure and applied mathematics to geometric modeling and
+ robotics, and to artificial neural networks. This book provides a
+ systematic and uniform treatment of elimination algorithms that
+ compute various zero decompositions for systems of multivariate
+ polynomials. The central concepts are triangular sets and systems of
+ 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."
+}
\end{chunk}
@@ 24719,6 +25293,35 @@ Comm. ACM. 17, 6 319320. (1974)
\end{chunk}
+\index{Barton, D.R.}
+\index{Fitch, John P.}
+\begin{chunk}{axiom.bib}
+@article{Bart72,
+ author = "Barton, D.R. and Fitch, John P.",
+ title = "A Review of Algebraic Manipulative Programs and their Application",
+ journal = "The Computer Journal",
+ volume = "15",
+ 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
+ is tutorial and severed typical problems are introduced which can be
+ solved using algebraic manipulative systems. Sample programs for the
+ solution of these problems using several algebra systems are then
+ presented. Next, two more difficult examples are used to introduce the
+ 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."
+}
+
+\end{chunk}
+
\index{Batut, C.}
\index{Belabas, K.}
\index{Bernardi, D.}
@@ 24824,6 +25427,30 @@ J. Symbolic Computation (1993) 16, 131145
\end{chunk}
+\index{Bradford, Russell J.}
+\index{Hearn, Anthony C.}
+\index{Padget, Julian}
+\index{Schr\"ufer, Eberhard}
+\begin{chunk}{axiom.bib}
+@inproceedings{Brad86,
+ author = "Bradford, Russell J. and Hearn, Anthony C. and Padget, Julian and
+ Schrufer, Eberhard",
+ title = "Enlarging the REDUCE domain of computation",
+ booktitle = "Proc SYMSAC 1986",
+ series = "SYMSAC '86",
+ publisher = "ACM",
+ year = "1986",
+ pages = "100106",
+ isbn = "0897911997",
+ abstract =
+ "We describe the methods available in the current REDUCE system for
+ introducing new mathematical domains, and illustrate these by discussing
+ several new domains that significantly increase the power of the overall
+ system."
+}
+
+\end{chunk}
+
\index{Braman, K.}
\index{Byers, R.}
\index{Mathias, R.}
@@ 25709,6 +26336,17 @@ A.E.R.E. Report R.8730. HMSO. (1977)
\end{chunk}
+\index{Fitch, John P.}
+\begin{chunk}{axiom.bib}
+@misc{Fitc74,
+ author = "Fitch, J.P.",
+ title = "CAMAL Users Manual",
+ institution = "University of Cambridge Computer Laboratory",
+ year = "1974"
+}
+
+\end{chunk}
+
\index{Fletcher, John P.}
\begin{chunk}{axiom.bib}
@misc{Flet01,
@@ 26133,10 +26771,16 @@ J. of Pure and Applied Algebra, 45, 225240 (1987)
\index{H. Gollan}
\index{Grabmeier, Johannes}
\begin{chunk}{ignore}
\bibitem[Gollan 90]{GG90} H. Gollan; J. Grabmeier
 title = "Algorithms in Representation Theory and their Realization in the Computer Algebra System Scratchpad",
Bayreuther Mathematische Schriften, Heft 33, 1990, 123
+\begin{chunk}{axiom.bib}
+@article{Goll90,
+ author = "H. Gollan and Grabmeier, Johannes",
+ title = "Algorithms in Representation Theory and their Realization
+ in the Computer Algebra System Scratchpad",
+ journal = "Bayreuther Mathematische Schriften",
+ volume = "33",
+ year = "1990",
+ pages = "123"
+}
\end{chunk}
@@ 26159,6 +26803,17 @@ Johns Hopkins University Press ISBN 9780801854149 (1996)
\end{chunk}
\index{Grabmeier, Johannes}
+\begin{chunk}{axiom.bib}
+@misc{Grab91a,
+ author = "Grabmeier, Johannes",
+ title = "Groups, finite fields and algebras, constructions and calculations",
+ location = "IBM Europe Institute",
+ year = "1991"
+}
+
+\end{chunk}
+
+\index{Grabmeier, Johannes}
\begin{chunk}{ignore}
\bibitem[Grabmeier]{Grab} Grabmeier, J.
title = "On Plesken's root finding algorithm",
@@ 26380,6 +27035,18 @@ J. Inst. Math. Appl. 14 89103. (1974)
\end{chunk}
+\index{Hearn, Anthony}
+\begin{chunk}{axiom.bib}
+@misc{Hear87,
+ author = "Hearn, Anthony",
+ title = "REDUCE User's Manual",
+ version = "3.3",
+ institution = "Rand Corporation",
+ year = "1987"
+}
+
+\end{chunk}
+
\index{Guess}
\index{GuessAlgebraicNumber}
\index{GuessFinite}
@@ 26577,6 +27244,16 @@ IEEE Comput. Soc. Press, pp. 678687.
\subsection{I} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{chunk}{axiom.bib}
+@misc{IBMx91,
+ author = "Computer Algebra Group",
+ title = "The AXIOM Users Guide",
+ publisher = "NAG Ltd., Oxford",
+ year = "1991"
+}
+
+\end{chunk}
+
\begin{chunk}{ignore}
\bibitem[IBM]{IBM}.
SCRIPT Mathematical Formula Formatter User's Guide, SH206453,
diff git a/changelog b/changelog
index f3df496..b17d80c 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,5 @@
+20160714 tpd src/axiomwebsite/patches.html 20160714.04.tpd.patch
+20160714 tpd books/bookvolbib Axiom Citations in the Literature
20160714 tpd src/axiomwebsite/patches.html 20160714.03.tpd.patch
20160714 tpd books/bookheader.tex add books/appendix.sty for latex appendix
20160714 tpd src/axiomwebsite/patches.html 20160714.02.tpd.patch
diff git a/patch b/patch
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+++ b/patch
@@ 1,3 +1,793 @@
books/bookheader.tex add books/appendix.sty for latex appendix
+books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
+
+\index{Bradford, Russell}
+\begin{chunk}{axiom.bib}
+@inproceedings{Brad92,
+ author = "Bradford, Russell",
+ title = "Algebraic Simplification of MultipleValued Functions",
+ booktitle = "Proc. DISCO 92",
+ series = "Lecture Notes in Computer Science 721",
+ year = "1992",
+ paper = "Brad92.pdf",
+ abstract =
+ "Many current algebra systems have a lax attitude to the
+ simplification of expressions involving functions like log and
+ $\sqrt{}$, leading the the ability to ``prove'' equalities like $1=1$
+ 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."
+}
+
+\end{chunk}
+
+\index{Schwarz, Fritz}
+\begin{chunk}{axiom.bib}
+@article{Schw91,
+ author = "Schwarz, Fritz",
+ title = "Monomial orderings and Groebner bases",
+ journal = "SIGSAM Bulletin",
+ 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
+ monomial ordering} is considered. Is it possible to decide whether
+ these ordering relations are consistent and if so to extend them to an
+ {\sl admissible} ordering for all monomials? The answer is given in
+ terms of the algorithm {\sl MACOT} which constructs a matrix of so
+ 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."
+}
+
+\end{chunk}
+
+\index{Bradford, Russell}
+\begin{chunk}{axiom.bib}
+@inproceedings{Brad92,
+ author = "Bradford, Russell",
+ title = "Algebraic Simplification of MultipleValued Functions",
+ 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
+ $\sqrt{}$, leading the the ability to ``prove'' equalities like $1=1$
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang90,
+ author = "Wang, Dongming",
+ title = "A Class of Cubic Differential Systems with 6tuple Focus",
+ journal = "J. Differential Equations",
+ publisher = "Academic Press, Inc.",
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang91,
+ author = "Wang, Dongming",
+ title = "Mechanical manipulation for a class of differential systems",
+ journal = "Journal of Symbolic Computation",
+ volume = "12",
+ number = "2",
+ pages = "233254",
+ year = "1991",
+ keywords = "axiomref",
+ abstract =
+ "The author describes a mechanical procedure for computing the
+ Liapunov functions and Liapunov constants for a class of differential
+ systems. These functions and constants are used for establishing the
+ stability criteria, the conditions for the existence of a center and
+ for the investigation of limit cycles. Some problems for handling the
+ computer constants, which are usually large polynomials in terms of
+ the coefficients of the differential system, and an approach towards
+ their solution by using computer algebraic methods are proposed. This
+ approach has been successfully applied to check some known results
+ mechanically. The author has implemented a system DEMS on an HP1000
+ and in Scratchpad II on an IBM4341 for computing and manipulating the
+ Liapunov functions and Liapunov constants. As examples, two particular
+ cubic systems are discussed in detail. The explicit algebraic
+ relations between the computed Liapunov constants and the conditions
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@misc{Wang95,
+ author = "Wang, Dongming",
+ 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
+ well as their generalization for computing the characteristic set and
+ characteristic series of a set of multivariate polynomials are
+ presented. The characeristic set, which is of certain triangular form,
+ reflects in general the major part of zeros, and the characteristic
+ series, which is a sequence of polynomial sets of triangular form,
+ furnishes a complete zero decomposition of the given polynomial
+ 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."
+}
+
+\end{chunk}
+
+
+\index{Keady, G.}
+\index{Richardson, M.G.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Kead93a,
+ author = "Keady, G. and Richardson, M.G.",
+ title = "An application of IRENA to systems of nonlinear equations arising
+ in equilibrium flows in networks",
+ 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
+ the NAG Fortran Library.
+
+ Here IRENA is tested on a problem closer to an engineering problem
+ than previously publised examples. We also illustrate the use of the
+ {\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."
+}
+
+\end{chunk}
+
+\index{LeBlanc, S.E.}
+\begin{chunk}{axiom.bib}
+@inproceedings{LeBl91,
+ author = "LeBlanc, S.E.",
+ title = "The use of MathCAD and Theorist in the ChE classroom",
+ 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
+ `electronic scratchpad' and it certainly lives up to its billing. It
+ is an extremely userfriendly collection of numerical routines that
+ eliminates the drudgery of solving many of the types of problems
+ encountered by undergraduate ChE's (and engineers in general). MathCAD
+ is available for both the Macintosh and IBM PC compatibles. The PC
+ version is available as a fullfunctioned student version for around
+ US\$40 (less than many textbooks). Theorist is a symbolic mathematical
+ package for the Macintosh. Many interesting and instructive things can
+ be done with it in the ChE curriculum. One of its many attractive
+ features includes the ability to generate high quality three
+ dimensional plots that can be very instructive in examining the
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@book{Wang01,
+ author = "Wang, Dongming",
+ title = "Elimination Methods",
+ publisher = "SpringerVerlag",
+ isbn = "9783709162026",
+ keywords = "axiomref",
+ year = "2001",
+ abstract =
+ "The development of polynomialelimination techniques from classical
+ theory to modern algorithms has undergone a tortuous and rugged
+ path. This can be observed L. van der Waerden's elimination of the
+ ``elimination theory'' chapter from from B. his classic Modern Algebra
+ in later editions, A. Weil's hope to eliminate ``from algebraic
+ geometry the last traces of elimination theory,'' and S. Abhyankar's
+ suggestion to ``eliminate the eliminators of elimination theory.''
+ The renaissance and recognition of polynomial elimination owe much to
+ the advent and advance of modern computing technology, based on
+ which effective algorithms are implemented and applied to diverse
+ problems in science and engineering. In the last decade, both
+ theorists and practitioners have more and more realized the
+ significance and power of elimination methods and their underlying
+ theories. Active and extensive research has contributed a great deal
+ of new developments on algorithms and soft ware tools to the subject,
+ that have been widely acknowledged. Their applications have taken
+ place from pure and applied mathematics to geometric modeling and
+ robotics, and to artificial neural networks. This book provides a
+ systematic and uniform treatment of elimination algorithms that
+ compute various zero decompositions for systems of multivariate
+ polynomials. The central concepts are triangular sets and systems of
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@inproceedings{Wang92,
+ author = "Wang, Dongming",
+ title = "A Method for Factorizing Multivariate Polynomials over Successive
+ Algebraic Extension Fields",
+ booktitle = "Mathematics and MathematicsMechanization (2001)",
+ 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
+ algebraic fields obtained from successive extensions of the rational
+ number field. The basic idea underlying this method is the reduction
+ of polynomial factorization over algebraic extension fields to the
+ factorization over the rational number vield via linear transformation
+ and the computation of characteristic sets with respect to a proper
+ variable ordering. The factors over the algebraic extension fields are
+ finally determined via GCD (greatest common divisor) computations. We
+ have implemented this method in the Maple system. Preliminary
+ experiments show that it is rather efficient. We give timing
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@misc{Wang90a,
+ author = "Wang, Dongming",
+ 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
+ based methods is reported. This prover has been used to prove a number
+ of nontrivial geometry theorems including several {\sl large} ones
+ with less space and time cost than using the existing provers. The
+ author presents a new technique by introducing the notion of {\sl
+ normal ascending set}. This technique yields in some sense {\sl
+ simpler} nondegenerate conditions for Wu's method and allows one to
+ prove geometry theorems using characteristic sets but Groeber bases
+ 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."
+}
+
+\end{chunk}
+
+\index{Zhao, Ting}
+\index{Wang, Dongming}
+\index{Hong, Hoon}
+\begin{chunk}{axiom.bib}
+@article{Zhao11,
+ author = "Zhao, Ting and Wang, Dongming and Hong, Hoon",
+ title = "Solution formulats for cubic equations without or with constraints",
+ journal = "J. Symbolic Computation",
+ 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."
+}
+
+\end{chunk}
+
+\index{Li, Xiaoliang}
+\index{Mou, Chenqi}
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Lixx10,
+ author = "Li, Xiaoliang and Mou, Chenqi and Wang, Dongming",
+ title = "Decomposing polynomial sets into simple sets over finite fields:
+ The zerodimensional case",
+ comment = "Provides clear polynomial algorithms",
+ journal = "Computers and Mathematics with Applications",
+ 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
+ an associated ideal or zero decomposition. As a key ingredient of
+ these algorithms, we generalize the squarefree decomposition approach
+ for univariate polynomials over a finite field to that over the field
+ product determined by a simple set. As a subprocedure of the
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang98,
+ author = "Wang, Dongming",
+ title = "Decomposing Polynomial Systems into Simple Systems",
+ volume = "25",
+ 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
+ form, in which every polynomial is squarefree and has nonvanishing
+ leading coefficient with respect to its leading variable. This paper
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang94,
+ author = "Wang, Dongming",
+ title = "Differentiation and Integration of Indefinite Summations with
+ Respect to Indexed Variables  Some Rules and Applications",
+ journal = "J. Symbolic Computation",
+ volume = "18",
+ 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
+ respect to indexed variables which have not yet been taken into
+ account of current computer algebra systems. These rules, together
+ with several others, have been implemented in MACSYMA and MAPLE as a
+ toolkit for manipulating indefinite summations. We discuss some
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang95a,
+ author = "Wang, Dongming",
+ title = "A Method for Proving Theorems in Differential Geometry and
+ Mechanics",
+ journal = "J. Universal Computer Science",
+ volume = "1",
+ number = "9",
+ 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."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang93,
+ author = "Wang, Dongming",
+ title = "An Elimination Method for Polynomial Systems",
+ journal = "J. Symbolic Computation",
+ volume = "16",
+ 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 [$\mathbb{P}$,$\mathbb{Q}$]
+ of two sets of multivariate polynomials, one of the algorithms computes a
+ sequence of triangular forms $\mathbb{T}_1,\ldots,\mathbb{T}_e$ and
+ polynomial sets $\mathbb{U}_1,\ldots,\mathbb{U}_e$ such that
+ Zero($\mathbb{P}$/$\mathbb{Q}$)
+ $= \cup_{i=1}^e {\rm\ Zero}(\mathbb{T}_i/\mathbb{U}_i)$,
+ where Zero($\mathbb{P}$/$\mathbb{Q}$) denotes the set of common zeros of
+ the polynomials in $\mathbb{P}$ which are not zeros of any polynomial in
+ $\mathbb{Q}$, and similarly for Zero($\mathbb{T}_i$/$\mathbb{U}_i$).
+ The two other algorithms compute the same zero decomposition but with nicer
+ properties such as Zero$(\mathbb{T}_i/\mathbb{U}_i) \ne 0$ for each $i$.
+ One of them, for which the computed triangular systems
+ [$\mathbb{T}_i$, $\mathbb{U}_i$] possess the projection property, provides
+ a quantifier elimination procedure for algebraically closed fields.
+ For the other, the computed triangular forms $\mathbb{T}_i$ are
+ irreducible. The relationship between our method and some existing
+ elimination methods is explained. Experimental data for a set of test
+ 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."
+}
+
+\end{chunk}
+
+\index{Houstis, E.N.}
+\index{Gaffney, P.W.}
+\begin{chunk}{axiom.bib}
+@book{Hous92,
+ 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 =
+ "Programming environments, as the name suggests, are intended to
+ provide a unified, extensive range of capabilities for a person
+ wishing to solve a problem using a computer. In this particular
+ 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."
+}
+
+\end{chunk}
+
+\index{Camion, Paul}
+\index{Courteau, Bernard}
+\index{Montpetit, Andre}
+\begin{chunk}{axiom.bib}
+@techreport{Cami92,
+ author = "Camion, Paul and Courteau, Bernard and Montpetit, Andre",
+ title = "A combinatorial problem in Hamming Graphs and its solution
+ in Scratchpad",
+ comment = {Un probl\`eme combinatoire dans les graphies de Hamming et sa
+ solution en Scratchpad},
+ year = "1992",
+ month = "January",
+ keywords = "axiomref",
+ paper = "Cami92.pdf",
+ url = "https://hal.inria.fr/inria00074974/document",
+ type = "Research report",
+ number = "1586",
+ institution = "Institut National de Recherche en Informatique et en
+ Automatique, Le Chesnay, France",
+ abstract =
+ "We present a combinatorial problem which arises in the determination
+ of the complete weight coset enumerators of errorcorrecting codes
+ [1]. In solving this problem by exponential power series with
+ coefficients in a ring of multivariate polynomials, we fall on a
+ system of differential equations with coefficients in a field of
+ 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."
+}
+
+\end{chunk}
+
+\index{Dalmas, St\'ephane}
+\begin{chunk}{axiom.bib}
+ author = "Dalmas, Stephane",
+ title = "A polymorphic functional language applied to symbolic computation",
+ year = "1992",
+ booktitle = "Proc. ISSAC 1992",
+ series = "ISSAC 1992",
+ pages = "369375",
+ isbn = "0897914899 (soft cover) 0897914902 (hard cover)",
+ keywords = "axiomref",
+ "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
+ language. Although it was not designed as a specialized language, its
+ sophisticated type system can be successfully applied to describe
+ 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."
+}
+
+\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{Corless, Robert M.}
+\index{Jeffrey, David J.}
+\index{Watt, Stephen M.}
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@article{Corl00,
+ author = "Corless, Robert M. and Jeffrey, David J. and Watt, Stephen M. and
+ Davenport, James H.",
+ title = "``According to Abramowitz and Stegun'' or
+ arccoth needn't be Uncouth",
+ journal = "SIGSAM Bulletin  Special Issue on OpenMath",
+ volume = "34",
+ number = "2",
+ pages = "5865",
+ year = "2000",
+ paper = "Corl00.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 =
+ "This paper addresses the definitions in OpenMath of the elementary
+ functions. The original OpenMath definitions, like most other sources,
+ simply cite [2] as the definition. We show that this is not adequate,
+ 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."
+}
+
+\end{chunk}
+
+\index{Bronstein, Manuel}
+\begin{chunk}{axiom.bib}
+@article{Bron90a,
+ author = "Bronstein, Manuel",
+ title = "Integration of Elementary Functions",
+ journal = "J. Symbolic Computation",
+ 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
+ integral as an elementary function or prove that it is not
+ elementary. We show that if the problem of integration in finite terms
+ is solvable on a given elementary function field $k$, then it is
+ solvable in any algebraic extension of $k(\theta)$, where $\theta$ is
+ a logarithm or exponential of an element of $k$. Our proof considers
+ an element of such an extension field to be an algebraic function of
+ one variable over $k$.
+
+ In his algorithm for the integration of algebraic functions, Trager
+ describes a Hermitetype reduction to reduce the problem to an
+ integrand with only simple finite poles on the associated Riemann
+ surface. We generalize that technique to curves over liouvillian
+ ground fields, and use it to simplify our integrands. Once the
+ multipe finite poles have been removed, we use the Puiseux expansions
+ 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."
+}
+
+\end{chunk}
+
+\index{Kauers, Manuel}
+\begin{chunk}{axiom.bib}
+@inproceedings{Kaue08,
+ author = "Kauers, Manuel",
+ title = "Integration of Algebraic Functions: A Simple Heuristic for
+ Finding the Logarithmic Part",
+ booktitle = "Proc ISSAC 2008",
+ series = "ISSAC '08",
+ year = "2008",
+ pages = "133140",
+ isbn = "978159593904",
+ url = "http://www.risc.jku.at/publications/download/risc_3427/Ka01.pdf",
+ paper = "Kau08.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."
+}
+
+\end{chunk}
+
+\index{Lambe, Larry A.}
+\begin{chunk}{axiom.bib}
+@article{Lamb89,
+ author = "Lambe, Larry A.",
+ title = "Scratchpad II as a tool for mathematical research",
+ journal = "Notices of the AMS",
+ year = "1989",
+ pages = "143147",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{H. Gollan}
+\index{Grabmeier, Johannes}
+\begin{chunk}{axiom.bib}
+@article{Goll90,
+ author = "H. Gollan and Grabmeier, Johannes",
+ title = "Algorithms in Representation Theory and their Realization
+ in the Computer Algebra System Scratchpad",
+ journal = "Bayreuther Mathematische Schriften",
+ volume = "33",
+ year = "1990",
+ pages = "123"
+}
+
+\end{chunk}
+
+\index{Bradford, Russell J.}
+\index{Hearn, Anthony C.}
+\index{Padget, Julian}
+\index{Schr\"ufer, Eberhard}
+\begin{chunk}{axiom.bib}
+@inproceedings{Brad86,
+ author = "Bradford, Russell J. and Hearn, Anthony C. and Padget, Julian and
+ Schrufer, Eberhard",
+ title = "Enlarging the REDUCE domain of computation",
+ booktitle = "Proc SYMSAC 1986",
+ series = "SYMSAC '86",
+ publisher = "ACM",
+ year = "1986",
+ pages = "100106",
+ isbn = "0897911997",
+ abstract =
+ "We describe the methods available in the current REDUCE system for
+ introducing new mathematical domains, and illustrate these by discussing
+ several new domains that significantly increase the power of the overall
+ system."
+}
+
+\end{chunk}
+
+\begin{chunk}{axiom.bib}
+@misc{IBMx91,
+ author = "Computer Algebra Group",
+ title = "The AXIOM Users Guide",
+ publisher = "NAG Ltd., Oxford",
+ year = "1991"
+}
+
+\end{chunk}
+
+\index{Hearn, Anthony}
+\begin{chunk}{axiom.bib}
+@misc{Hear87,
+ author = "Hearn, Anthony",
+ title = "REDUCE User's Manual",
+ version = "3.3",
+ institution = "Rand Corporation",
+ year = "1987"
+}
+
+\end{chunk}
+
+\index{Fitch, John P.}
+\begin{chunk}{axiom.bib}
+@misc{Fitc74,
+ author = "Fitch, J.P.",
+ title = "CAMAL Users Manual",
+ institution = "University of Cambridge Computer Laboratory",
+ year = "1974"
+}
+
+\end{chunk}
+
+\index{Barton, D.R.}
+\index{Fitch, John P.}
+\begin{chunk}{axiom.bib}
+@article{Bart72,
+ author = "Barton, D.R. and Fitch, John P.",
+ title = "A Review of Algebraic Manipulative Programs and their Application",
+ journal = "The Computer Journal",
+ volume = "15",
+ 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
+ is tutorial and severed typical problems are introduced which can be
+ solved using algebraic manipulative systems. Sample programs for the
+ solution of these problems using several algebra systems are then
+ presented. Next, two more difficult examples are used to introduce the
+ 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."
+}
+
+\end{chunk}
+
+\index{Duval, Dominique}
+\index{Jung, F.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Duva92,
+ author = "Duval, Dominique and Jung, F.",
+ title = "Examples of problem solving using computer algebra",
+ booktitle = "Programming environments for highlevel scientific problem
+ solving",
+ series = "IFIP Transactions",
+ editor = "Gaffney, Patrick W. and Houstis, Elias N.",
+ publisher = "NorthHolland",
+ pages = "133143",
+ year = "1992",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 3cc03fb..9b38d29 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5474,6 +5474,8 @@ books/axiom.sty add \pct for resizing the % character
books/ps/sweeney.eps added
20160714.03.tpd.patch
books/bookheader.tex add books/appendix.sty for latex appendix
+20160714.04.tpd.patch
+books/bookvolbib Axiom Citations in the Literature

1.7.5.4