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Date: Sat, 9 Jul 2016 03:43:53 0400
Subject: [PATCH] books/bookvolbib Axiom Citations in the Literature
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Goal: Axiom Literate Programming
\index{Mathews, J. }
\begin{chunk}{ignore}
@article{Math89,
author = "Mathews, J.",
title = "Symbolic computational algebra applied to Picard iteration",
journal = "Mathematics and computer education",
volume = "23",
number = "2",
pages = "117122",
year = "1989",
url =
"http://mathfaculty.fullerton.edu/mathews/articles/1989PicardIteration.pdf",
paper = "Math89.pdf",
keywords = "axiomref",
"The term ``Picard iteration'' occurs two places in undergraduate
mathematics. In numerical analysis it is used when discussing fixed
point iteration for finding a numerical approximation to the equation
$s=g(x)$. In differential equations, Picard iteration is a
constructive procedure for establishing the existence of a solution to
a differential equation $y^{\prime} = f(x,y)$.
The first type of Picard iteration uses computations to generate a
sequence of numbers which converges to a solution. We will not present
this application, but mention that it involves the traditional role of
the computer as a ``number cruncher.''
The second application of Picard iteration illustrates how to use a
computer to generate a sequence of functions which converges to a
solution. The purpose of this article is to show the step by step
process in translating mathematical theory into the symbolic
manipulation setting. Systems such as MACSYM, ALTRAN, REDUCE, SMP,
MAPLE, SCRATCHPAD and muMATH are being introduced in undergraduate
mathematics courses to assist in keeping trace of equations during
complicated manipulations."
}
\end{chunk}
\index{Ollivier, F.}
\begin{chunk}{axiom.bib}
@inproceedings{Olli89,
author = "Ollivier, F.",
title = "Inversibility of rational mappings and structural
identifiablility in automatics",
booktitle = "Proc. SIGSAM 1989",
series = "SIGSAM '89",
pages = "4354",
isbn = "0897913256",
year = "1989",
keywords = "axiomref",
paper = "Olli89.pdf",
abstract =
"We investigate different methods for testing whether a rational
mapping $f$ from $k^n$ to $k^m$ admits a rational inverse, or whether
a polynomial mapping admits a polynomial one. We give a new solution,
which seems much more efficient in practice than previously known ones
using ``tag'' variables and standard basis, and a majoration for the
degree of the standard basis calculations which is valid for both
methods in the case of a polynomial map which is birational. We
further show that a better bound can be given for our method, under
some assumptions on the form of $f$. Our method can also extend to
check whether a given polynomial belong to the subfield generated by a
finite set of fractions.
We then illustrate our algorithm, with a application to structural
identifiability. The implantation has been done in the IBM computer
algebra system Scratchpad II."
}
\end{chunk}
\index{Trevisan, Vilmar}
\index{Wang, Paul}
\begin{chunk}{axiom.bib}
@inproceedings{Trev91,
author = "Trevisan, Vilmar and Wang, Paul",
title = "Practical factorization of univariate polynomials over
finite fields",
booktitle = "Proc. ISSAC 1991",
series = "ISSAC '91",
publisher = "ACM",
isbn = "0897914376",
pages = "2231",
year = "1991",
url =
"http://lib.org/by/\_djvu\_Papers/Computer\_algebra/Algebraic\%20numbers",
paper = "Trev91.djvu",
abstract =
"Research presented here is part of an effort to establish
stateoftheart factoring routines for polynomials. The foundation of
such algorithms lies in the efficient factorization over a finite
field $GF(p^k)$. The CantorZassenhaus algorithm together with
innovative ideas suggested by others is compared with the Berlekamp
algorithm. The studies led us to design a hybrid algorithm that
combine the strengths of the different approaches. The algorithms are
also implemented and machine timings are obtained to measure the
performance of these algorithms."
}
\end{chunk}
\index{Bosma, Wieb}
\index{Cannon, John}
\index{Playoust, Catherine}
\begin{chunk}{axiom.bib}
@article{Bosm97,
author = "Bosma, Wieb and Cannon, John and Playoust, Catherine",
title = "The Magma Algebra System I: The User Language",
journal = "J. Symbolic Computation",
volume = "24",
pages = "235265",
year = "1997",
keywords = "axiomref",
url = "http://lib.org.by/_djvu/_Papers/Computer_algebra/CAS%20systems/",
paper = "Bosm97.djvu",
abstract =
"In the first of two papers on MAGMA, a new system for computational
algebra, we present the MAGMA language, outline the design principles
and theoretical background, and indicate its scope and use. Particular
attention is given to the constructors for structures, maps, and sets."
}
\end{chunk}
\index{Salvy, Bruno}
\begin{chunk}{axiom.bib}
@techreport{Salv89,
author = "Salvy, Bruno",
title = "Examples of automatic asymptotic expansions",
institution = "Inst. Nat. Recherche Inf. Autom.",
type = "technical report",
number = "114",
year = "1989",
paper = "Salv89.pdf",
comment = "SIGSAM Bulletin Vol 25 No 2 1991 pp417",
keywords = "axiomref",
abstract =
"We describe the current state of a Maple library, gdev, designed to
perform asymptotic expansions for a large class of expressions. Many
examples are provided, along with a short sketch of the underlying
principles. At the time when this report is written, a striking
feature of these examples is that none of them can be computed
directly with any of today's most widespread symbolic computation
systems (Macsyma, Mathematica, Maple or Scratchpad II)."
}
\end{chunk}
\index{Bronstein, Manuel}
\begin{chunk}{axiom.bib}
@inproceedings{Bron96b,
author = "Bronstein, Manuel",
title = "On the Factorization of Linear Ordinary Differential Operators",
booktitle = "Mathematics and Computers in Simulation",
volume = "42",
number = "46",
pages = "387389",
year = "1996",
paper = "Bro96b.pdf",
abstract =
"After reviewing the arithmetic of linear ordinary differential
operators, we describe the current status of the factorisation
algorithm, specially with respect to factoring over nonalgebraically
closed constant fields. We also describe recent results from Singer
and Ulmer that reduce determining the differential Galois group of an
operator to factoring."
}
\end{chunk}
\index{Diaz, Glauco Alfredo Lopez}
\begin{chunk}{axiom.bib}
@phdthesis{Diaz06,
author = "Diaz, Glauco Alfredo Lopez",
title = "Symbolic Methods for Factoring Linear Differential Operators",
school = "Johannes Kepler Universitat, Linz",
year = "2006",
month = "February",
paper = "Diaz06.pdf",
keywords = "axiomref",
abstract =
"A survey of symbolic methods for factoring linear differential
operators is given. Starting from basic notions – ring of operators,
differential Galois theory – methods for finding rational and
exponential solutions that can provide first order righthand factors
are considered. Subsequently several known algorithms for
factorization are presented. These include Singer’s eigenring
factorization algorithm, factorization via Newton polygons, van
Hoeij’s methods for local factorization, and an adapted version of
Pade approximation.
In addition a procedure based on pure algebraic methods for factoring
second order linear partial differential operators is
developed. Splitting an operator of this kind reduces to solving a
system of linear algebraic equations. Those solutions which satisfy a
certain different ial condition, immediately produce linear factors of
the operator. The method applies also to operators of third order,
thereby resulting in a more complicated system of equations. In
contrast to the second order case, differential equations must also be
solved, which, in particular cases, are simplified with the aid of
characteristic sets.
Finally, complete decomposition into linear factors of ordinary
differential operators of arbitrary order is discussed. A splitting
formula is developed, provided that a linear basis of solutions is
available. This theoretical representation is valuable in
understanding the nature of the classical Beke algorithm and its
variants like the algorithm LODEF by Schwarz and the BekeBronstein
algorithm."
}
\end{chunk}
\index{Schwarz, Fritz}
\begin{chunk}{axiom.bib}
@inproceedings{Schw89,
author = "Schwarz, Fritz",
title = "A factorization algorithm for linear ordinary
differential equations",
booktitle = "Proc. SYMSAC 1989",
series = "SYMSAC '89",
isbn = "0897913256",
year = "1989",
pages = "1725",
keywords = "axiomref",
abstract =
"The reducibility and factorization of linear homogeneous differential
equations are of great theoretical and practical importance in
mathematics. Although it has been known for a long time that
factorization is in principle a decision procedure, its use in an
automatic differential equation solver requires a more detailed
analysis of the various steps involved. Especially important are
certain auxiliary equations, the socalled associated equations. An
upper bound for the degree of its coefficients is derived. Another
important ingredient is the computation of optimal estimates for the
size of polynomial and rational solutions of certain differential
equations with rotational coefficients. Applying these results, the
design of the factorization algorithm LODEF and its implementation in
the Scratchpad II Computer Algebra System is described.",
}
\end{chunk}
\index{Schwarz, Fritz}
\begin{chunk}{axiom.bib}
@inproceedings{Schw89,
author = "Schwarz, Fritz",
title = "A factorization algorithm for linear ordinary
differential equations",
booktitle = "Proc. SYMSAC 1989",
series = "SYMSAC '89",
isbn = "0897913256",
year = "1989",
pages = "1725",
keywords = "axiomref",
paper = "Schw89.pdf",
abstract =
"The reducibility and factorization of linear homogeneous differential
equations are of great theoretical and practical importance in
mathematics. Although it has been known for a long time that
factorization is in principle a decision procedure, its use in an
automatic differential equation solver requires a more detailed
analysis of the various steps involved. Especially important are
certain auxiliary equations, the socalled associated equations. An
upper bound for the degree of its coefficients is derived. Another
important ingredient is the computation of optimal estimates for the
size of polynomial and rational solutions of certain differential
equations with rotational coefficients. Applying these results, the
design of the factorization algorithm LODEF and its implementation in
the Scratchpad II Computer Algebra System is described.",
}
\end{chunk}
\index{Fateman, Richard J.}
\index{Caspi, Eylon}
\begin{chunk}{axiom.bib}
@misc{Fate99a,
author = "Fateman, Richard J. and Caspi, Eylon",
title = "Parsing TeX into Mathematics",
year = "1999",
url = "http://lib.org.by/_djvu/_Papers/Computer_algebra/CAS%20systems/",
paper = "Fate99a.djvu",
keywords = "axiomref",
abstract =
"Communication, storage, transmission, and searching of complex
material has become increasingly important. Mathematical computing in
a distributed environment is also becoming more plausible as libraries
and computing facilities are connected with each other and with user
facilites. TeX is a wellknown mathematical typesetting language, and
from the display perspective it might seem that it could be used for
communication between computer systems as well as an intermediate form
for the results of OCR (optical character recognition) of mathematical
expressions. There are flaws in this reasoning, since exchanging
mathematical informaiton requires a system to parse and semantically
``understand'' the TeX, even if it is ``ambiguous'' notationally. A
program we developed can handle 43\% of 10,740 TeX formulas in a
wellknown table of integrals. We expect that a higher success rte can
be achieved easily."
}
\end{chunk}
\index{Sit, William Y.}
\begin{chunk}{axiom.bib}
@inproceedings{Sitx89,
author = "Sit, William Y.",
title = "On Goldman's algorithm for solving firstorder multinomial
autonomous systems",
booktitle = "Proc. Algebraic Algorithms and ErrorCorrecting Codes, AAECC6",
series = "Lecture Notes in Computer Science 357",
location = "Rome, Italy",
year = "1988",
isbn = "3540510834",
pages = "386395",
keywords = "axiomref",
abstract =
"In this article, a brief exposition of a method for finding first
integrals for first order multinomial autonomous systems (FOMAS) of
ordinary differential equations with constant coefficients will be
given. The method is a simplified as well as a redesigned version
based on a paper of Goldman (1987). We shall see how it can be applied
to FOMAS with parametric coefficients. The algorithm is currently
being implemented by the author, using the SCRATCHPAD II computer
algebra language and system at the IBM T.J. Watson Research Center.
FOMAS occur and are of interest in many disciplines and their first
integrals (or trajectories of motion) are generally difficult to
find. Examples of FOMAS are too numerous to list, some wellknown ones
are the Riccati equation, the LotkaVolterra equations for competing
populations, Selkov's model for chemical reactions, the Lorenz system
of the RayleighBernard problem, and Hamiltonian systems (where the
Hamiltonian is a sum of monomial terms with constant coefficients).
Let $Y=(y_1,\ldots,y_n)$ be $n$ functions depending on the variable
$\tau$. A monomial in $Y$ is a product of the form $y_1^{k_1}\cdots
y_n^{k_n}$, where $k_1,\ldots,k_n$ are constants. If
$K=(k_1,\ldots,k_n)$, we shall denote the monomial in $Y$ by $Y^K$,
and $K$ is called the exponent vector for the monomial. By convention,
exponent vectors are column vectors, but whenever convenient, we shall
write exponent vectors as row vectors. We say that $Y$ satisfies a
firstorder multinomial autonomous system (FOMAS) if for each $i$, $1
\le i \le n$, $y_i$ satisfies a first order differential equation of
the form:
\[y_i^{\prime} = f_i(Y)\quad\quad\quad(1)\]
where $f_i$ is a linear combination of monomials in $Y$ with coefficients
which may be either constants or parametric constants. For example, the
LotkaVolterra equations for three competing species considered by
Schwarz and Steeb (1984), form a FOMAS:
\[x_1^{\prime}=x_1(1+ax_2+bx_3)\]
\[x_2^{\prime}=x_2(1ax_1+bx_3)\]
\[x_3^{\prime}=x_3(1bx_1cx_2)\]
When the exponent vectors occuring in $f_i$ are all nonnegative integers,
as in the example above, a FOMAS reduces to a polynomial autonomous
system (FOPAS).
A computer program was developed by Schwarz (1986) to compute the
first integrals of FOPAS's which are themselves polynomials in
$y_1,\ldots,y_n$. Schwarz's algorithm literally takes a general
polynomial of a fixed degree $d$ in $n$ variables and substitutes it
into (1). This method does not work well on a FOMAS, because in a
FOMAS, the exponent vectors need not have integral components. Also,
it wll not find integrals with exponent vectors that involve
fractional or irrational numbers.
Goldman (1987) proved a theorem which gives necessary and sufficient
conditions for the existence of a multinomial first integral for
FOMAS. The proof also contained the outline of an algorithm for
finding such integrals. In Goldman's paper, he introduced the notion
of an integral array, which is a certain matrix satisfying some 10
conditions. He gave a few hints and several examples but did not
elaborate on how such an integral array can be found in general
(except in the case $q=2$). Assuming such an array is found, he can
compute the integral, in most cases, by solving systems of linear
equations, or at worse in certain cases, by solving a system of
algebraic equations. It was not clear when algebraic conditions are
necessary.
In this brief exposition, Goldman's method will be expanded to a
complete algorithm with a new simplified notation. The integral arrays
are replaced by addition schemes (which is equivalent to integral
arrays with some conditions removed). The generation of addition
schemes is a combinatorial problem unrelated, in a sense, to
FOMAS. When the first integral is a polynomial, the additioin scheme
is trivial to compute. We shall now begin by explaining some details
of this theory."
}
\end{chunk}
\index{Bronstein, Manuel}
\begin{chunk}{axiom.bib}
@misc{Bronxx,
author = "Bronstein, Manuel",
title = "Symbolic Integration in Computer Algebra",
url = "http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/26/042/26042580.pdf",
paper = "Bron90.pdf",
year = "1990",
keywords = "axiomref",
abstract =
"One major goal of symbolic integrators is to determine under what
circumstances the integral of the elementary functions of calculus can
themselves be expressed as elementary functions. While using tables
and the ad hoc tricks taught in calculus courses can have some limited
success, a decision procedure is necessary in all but the most trivial
cases. The first complete algorithm for solving this problem was
presented by Risch in 1969, but its complexity, specially when
algebraic functions are present in the integrand, has prevented it
from being fully implemented. Over the past 20 years, the Risch
integration algorithm has been completed, extended, and improved to
such a point that recent computer algebra systems can integrate
elementary functions without using any of the heuristics traditionally
taught in calculus courses and used by older systems. In this talk,
we give an overview and description of the algorithms used in the
Scratchpad symbolic integrator, and illustrate them with integrals
drawn from the physical sciences."
}
\end{chunk}
\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@article{Wang89,
author = "Wang, Dongming",
title = "A program for computing the Liapunov functions and Liapunov
constants in Scratchpad II",
journal = "SIGSAM Bulletin",
volume = "23",
number = "4",
pages = "2531",
year = "1989",
keywords = "axiomref",
abstract =
"This report describes the implementation and use of a program for
computing the Liapunov functions and Liapunov constants for a class
of differential systems in Scratchpad II"
}
\end{chunk}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@misc{Dave15,
author = "Davenport, James H.",
title = "SIAM AAG 15 and ICIAM 2015",
url = "http://people.bath.ac.uk/masjhd/Meetings/AAGICIAM15.pdf",
paper = "Dave15.pdf",
keywords = "axiomref"
}
\index{Watt, Stephen M.}
\begin{chunk}{axiom.bib}
@inproceedings{Watt89,
author = "Watt, Stephen M.",
title = "A fixed point method for power series computation",
booktitle = "Proc. ISSAC '88",
series = "Lecture Notes in Computer Science 358",
location = "Rome, Italy",
pages = "206217",
isbn = "3540510842",
year = "1988",
series = "AAECC6, ISSAC '88",
keywords = "axiomref",
abstract =
"This paper presents a novel technique for manipulating structures
which represents infinite power series.
When power series are implemented using lazy evaluation, many
operations can be written as simple recursive procedures. For example,
the programs to generate the series for the elementary transcendental
functions are almost transliterations of the defining integral
equations. However, a naive lazy algorithm provides an implementation
which may be orders of magnitude slower than a method which
manipulates the coefficients explicitly.
The technique described here allows a power series to be defined in a
very natural but computationally inefficient way and transforms it to
an equivalent, efficient form. This is achieved by using a fixed point
operator on the delayed part to remove redundant calculations.
This paper describes this fixed point method and the class of problems
to which it is applicable. It has been used in Scratchpad II to
improve the performance of a number of operations on infinite series,
including division, reversion, special functions and the solution of
linear and nonlinear ordinary differential equations.
A few examples are given of the method and of the speed up
obtained. To illustrate, the computation of the first $n$ terms of
exp($u$) for a dense, infinite series $u$ is reduced from $O(n^4)$ to
$O(n^2)$ coefficient operations, the same as required by the standard
online algorithms."
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@inproceedings{Fate90,
author = "Fateman, Richard J.",
title = "Advances and trends in the design and construction of algebraic
manipulation systems",
booktitle = "Proc. ISSAC 1990",
publisher = "ACM",
pages = "6067",
isbn = "0897914015",
year = "1990",
paper = "Fate90.pdf",
url = "http://people.eecs.berkeley.edu/~fateman/papers/advances.pdf",
keywords = "axiomref",
abstract =
"We compare and contrast several techniques for the implementation of
components of an algebraic manipulation system. On one hand is the
mathematicalalgebraic approach which chaaracterizes (for example)
IBM's Axiom. On the other hand is the more {\sl ad hoc} approach which
characterizes many other popular systems (for example, Macsyma,
Reduce, Maple, and Mathematica). While the algebraic approach has
generally positive results, careful examination suggests that there
are significant remaining problems, expecially in the representation
and manipulation of analytical, as opposed to algebraic,
mathematics. We describe some of these problems and some general
approaches for solutions."
}
\end{chunk}
\index{Fortenbacher, Albrecht}
\begin{chunk}{axiom.bib}
@inproceedings{Fort90,
author = "Fortenbacher, Albrecht",
title = "Efficient type inference and coercion in computer algebra",
booktitle = "Design and Implementation of Symbolic Computation Systems",
series = "Lecture Notes in Computer Science 429",
pages = "5660",
isbn = "0387525319",
year = "1990",
keywords = "axiomref",
abstract =
"Computer algebra systesm of the new generation, like SCRATCHPAD, are
characterized by a very rich type concept, which models the
relationship between mathematical domains of computation. To use these
systems interactively, however, the user should be freed of type
information. A type inference mechanism determines the appropriate
function to call. All known models which allow to define a semantics
for type inference cannot express the rich ``mathematical'' type
structure, so presently type inference is done heuristically. The
following paper defines a semantics for a subproblem therof, namely
coercion, which is based on rewrite rules. From this definition, an
efficient coercion algorithm for SCRATCHPAD is constructed using graph
techniques."
}
\end{chunk}
\index{Weber, Andreas}
\begin{chunk}{axiom.bib}
@inproceedings{Webe05,
author = "Weber, Andreas",
title = "A TypeCoercion Problem in Computer Algebra",
booktitle = "Artificial Intelligence and Symbolic Mathematical Computing",
series = "Lecture Notes in Computer Science 737",
year = "2005",
publisher = "Springer",
pages = "188194",
paper = "Webe05.pdf",
abstract =
"An important feature of modern computer algebra systems is the
support of a rich type system with the possibility of type inference.
Basic features of such a system are polymorphism and coercion between
types. Recently the use of ordersorted rewrite systems was proposed
as a general framework.
We will give a quite simple example of a family of types arising in
computer algebra whose coercion relations cannot be captured by a
finite set of firstorder rewrite rules."
}
\end{chunk}
\index{Fouche, Francois}
\begin{chunk}{axiom.bib}
@techreport{Fouc90,
author = "Fouche, Francois",
title = "Une implantation de l'algorithme de Kovacic en Scratchpad",
type = "technical report",
number = "ULPIRMA447P254",
year = "1990",
institution = {Institut de Recherche Math{\'{e}}matique Avanc{\'{e}}e''},
location = "Strasbourg, France",
keywords = "axiomref"
}
\end{chunk}
\index{Duval, Anne}
\index{LodayRichaud, Michele}
\begin{chunk}{axiom.bib}
@article{Duva92,
author = "Duval, Anne and LodayRichaud, Michele",
title = "Kovacic's Algorithm and Its Application to Some Families
of Special Functions",
journal = "Applicable Algebra in Engineering, Communication, and Computing",
series = "AAECC 3",
pages = "211246",
year = "1992",
publisher = "SpringerVerlag",
keywords = "axiomref",
abstract =
"We apply the Kovacic algorithm to some families of special functions,
mainly the hypergeometric one and that of Heun, in order to discuss
the existence of closedform solutions. We begin by giving a slightly
modified version of the kovacic algorithm and a sketch proof."
}
\end{chunk}
\index{Lewis, Robert H.}
\index{Wester, Michael}
\begin{chunk}{axiom.bib}
@article{Lewi99,
author = "Lewis, Robert H. and Wester, Michael",
title = "Comparison of polynomialorienged computer algebra systems",
journal = "SIGSAM Bulletin",
volume = "33",
number = "4",
pages = "513",
year = "1999",
url = "https://home.bway.net/lewis/cacomp.ps",
paper = "Lewi99.pdf",
keywords = "axiomref",
abstract =
"Exact symbolic computation with polynomials and matrices over
polynomial rings has wide applicability to many fields [Hereman96,
Lewis99]. By ``exact symbolic'', we mean computation with polynomials
whose coefficients are integers (of any size), rational numbers, or
from finite fields, as opposed to coefficients that are ``floats'' of a
certain precision. Such computation is part of most computer algebra
(CA) systems. Over the last dozen years, several large CA systems have
become widely available, such as Axiom, Derive, Macsyma, Maple,
Mathematica and Reduce. They tend to have great breadth, be produced
by profitmaking companies, and be relatively expensive, at least for
a full blown nonstudent version. However, most if not all of these
systems have difficulty computing with the polynomials and matrices
that arise in actual research. Real problems tend to produce large
polynomials and large matrices that the general CA systems cannot
handle [Lewis99].
In the last few years, several smaller CA systems focused on
polynomials have been produced at universities by individual
researchers or small teams. They run on Macs, PCs and workstations.
They are freeware or shareware. Several claim to be much more
efficient than the large systems at exact polynomial computations. The
list of these systems includes CoCoA, Fermat, MuPAD, PariGp and
Singular [CoCoA, Fermat, MuPAD, PariGp, Singular].
In this paper, we compare these small systems to each other and to two
of the large systems (Magma and Maple) on a set of problems involving
exact symbolic computation with polynomials and matrices. The problems
here involve:
\begin{itemize}
\item the ground rings $\mathbb{Z}$, $\mathbb{Q}$, $\mathbb{Z}/p$
and other finite fields
\item basic arithmetic of polynomials over the ground ring
\tem basic arithmetic of rational functions over the ground ring
\item polynomial evaluation (substitution)
\item matrix normal form
\item determinants and characteristic polynomial
\item GCDs of multivariate polynomial
\item resultants
\end{itemize}"
}
\end{chunk}
\index{Ganzha, Victor G.}
\index{Vorozhtsov, Evgenii V.}
\index{Wester, Michael}
\begin{chunk}{axiom.bib}
@book{Ganz00,
author = "Ganzha, Victor G. and Vorozhtsov, Evgenii V. and Wester, Michael",
title = "An Assessment of the Efficiency of Computer Algebra Systems in
the Solution of Scientific Computing Problems",
booktitle = "Computer Algebra in Scientific Computing",
year = "2000",
isbn = "9783540410409",
publisher = "Springer",
pages = "145166",
keywords = "axiomref",
abstract =
"Computer algebra systems (CASs) have become an important tool for the
solution of scientific computing problems. With the increasing number
of general purpose CASs, there is now a need for an assessment of the
efficiency of these systems. We discuss some peculiarities associated
with the analysis of CPU time efficiency in CASs, and then present
results from three specific systems (Maple Vr5, Mathematics 4.0 and
MuPAD 1.4) on a sample of intermediate size problems. These results
show that Maple Vr5 is generally the speediest on our
examples. Finally, we formulate some requirements for developing a
comprehensive suite for analyzing the efficiency of CASs."
}
\end{chunk}
\index{Zimmermann, Paul}
\begin{chunk}{axiom.bib}
@misc{Zimm96,
author = "Zimmermann, Paul",
title = "Wester's test suite in MuPAD 1.3",
year = "1996",
paper = "Zimm96.pdf",
keywords = "axiomref",
abstract =
"In December 1994, Michael Wester made a review of the mathematical
capabilities of different computer algebra systems, namely Axiom,
Derive, Macsyma, Maple, Mathematica and Reduce. This review, which is
available by anonymous ftp from math.unm.edu, file pub/cas/Paper.ps,
consists of 131 tests in different domains of mathematics (arithmetic,
algebraic equations, differential equations, integration, operator
computation, series expansions, limits).
We describe in this paper the problems that can be solved with MuPAD
1.3, and how to solve them. The problems marked as [New] are solved
using new functionalities of the version 1.3 with respect to 1.2.2"
}
\end{chunk}
\index{Zimmermann, Paul}
\begin{chunk}{axiom.bib}
@misc{Zimm95,
author = "Zimmermann, Paul",
title = "Wester's test suite in MuPAD 1.2.2",
year = "1995",
paper = "Zimm95.pdf",
keywords = "axiomref",
abstract =
"A few months ago, Michael Wester made a review of the mathematical
capabilities of different computer algebra systems, namely Axiom,
Derive, Macsyma, Maple, Mathematica and Reduce. This review, which is
available by anonymous ftp from math.unm.edu, file pub/cas/Paper.ps,
consists of 131 tests in different domains of mathematics (arithmetic,
algebraic equations, differential equations, integration, operator
computation, series expansions, limits).
We describe in this paper the problems that can be solved with MuPAD
1.2.2, and how to solve them. The problems marked as [New] are solved
using new functionalities of the version 1.2.2 with respect to 1.2.1"
}
\end{chunk}
\index{MartinezMoro, Edgar}
\index{Kotsireas, Ilias}
\begin{chunk}{axiom.bib}
@misc{ACA15,
authors = "MartinezMoro, Edgar Kotsireas, Ilias",
title = "21st Conference on Applications of Computer Algebra",
keywords = "axiomref",
conference = "Sessions of ACA2015",
location = "Kalamata, Greece",
year = "2015",
url = "http://www.singacom.uva.es/ACA2015/latex/ACAproc.pdf",
paper = "ACA15.pdf"
}
\end{chunk}

books/bookvolbib.pamphlet  851 +++++++++++++++++++++++++
changelog  2 +
patch  1209 +++++++++++++++++++++
src/axiomwebsite/patches.html  2 +
4 files changed, 1384 insertions(+), 680 deletions()
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 4e74015..ad909e7 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 8,7 +8,8 @@
\chapter{The Axiom Bibliography}
This bibliography covers areas of computational mathematics.
Papers which mention Axiom have a ``keyword='' entry of ``axiomref''.
Papers we have on site have a ``paper='' entry.
+Papers we have on site have a ``paper='' entry. Papers which are
+referenced in the algebra have the ``algebra'' tag.
The authors are listed in the index. The topic keywords are listed in the
index. Algorithms are mentioned in the index.
@@ 3626,32 +3627,6 @@ Proc. IMACS Symposium, Lille, France, (1993)
\end{chunk}
\index{von zur Gathen, Joachim}
\index{Panario, Daniel}
\begin{chunk}{axiom.bib}
@article{Gath01,
 author = "von zur Gathen, Joachim and Panario, Daniel",
 title = "Factoring Polynomials Over Finite Fields: A Survey",
 journal = "J. Symbolic Computation",
 year = "2001",
 volume = "31",
 pages = "317",
 paper = "Gath01.pdf",
 url =
 "http://people.csail.mit.edu/dmoshdov/courses/codes/polyfactorization.pdf",
 keywords = "survey",
 abstract =
 "This survey reviews several algorithms for the factorization of
 univariate polynomials over finite fields. We emphasize the main ideas
 of the methods and provide and uptodate bibliography of the problem.
 This paper gives algorithms for {\sl squarefree factorization},
 {\sl distinctdegree factorization}, and {\sl equaldegree factorization}.
 The first and second algorithms are deterministic, the third is
 probabilistic."
}

\end{chunk}

\index{van Hoeij, Mark}
\index{Monagan, Michael}
\begin{chunk}{ignore}
@@ 5614,18 +5589,24 @@ Petkovsek, Marko
\end{chunk}
\index{Bronstein, Manuel}
\begin{chunk}{ignore}
\bibitem[Bronstein 96b]{Bro96b} Bronstein, Manuel
+\begin{chunk}{axiom.bib}
+@inproceedings{Bron96b,
+ author = "Bronstein, Manuel",
title = "On the Factorization of Linear Ordinary Differential Operators",
Mathematics and Computers in Simulation 42 pp 387389 (1996)
+ booktitle = "Mathematics and Computers in Simulation",
+ volume = "42",
+ number = "46",
+ pages = "387389",
+ year = "1996",
paper = "Bro96b.pdf",
 abstract = "
 After reviewing the arithmetic of linear ordinary differential
+ abstract =
+ "After reviewing the arithmetic of linear ordinary differential
operators, we describe the current status of the factorisation
algorithm, specially with respect to factoring over nonalgebraically
closed constant fields. We also describe recent results from Singer
and Ulmer that reduce determining the differential Galois group of an
operator to factoring."
+}
\end{chunk}
@@ 7920,6 +7901,49 @@ Proc ISSAC 97 pp172175 (1997)
\end{chunk}
+\index{Diaz, Angel}
+\index{Kaltofen, Erich}
+\begin{chunk}{axiom.bib}
+@InProceedings{Diaz95,
+ author = "Diaz, A. and Kaltofen, E.",
+ title = "On computing greatest common divisors with polynomials given by
+ black boxes for their evaluation",
+ booktitle = "Proc. 1995 Internat. Symp. Symbolic Algebraic Comput.",
+ crossref = "ISSAC95",
+ pages = "232239",
+ year = "1995",
+ url = "http://www.math.ncsu.edu/~kaltofen/bibliography/95/DiKa95.ps.gz",
+ paper = "Diaz95.ps",
+}
+
+\end{chunk}
+
+\index{von zur Gathen, Joachim}
+\index{Panario, Daniel}
+\begin{chunk}{axiom.bib}
+@article{Gath01,
+ author = "von zur Gathen, Joachim and Panario, Daniel",
+ title = "Factoring Polynomials Over Finite Fields: A Survey",
+ journal = "J. Symbolic Computation",
+ year = "2001",
+ volume = "31",
+ pages = "317",
+ paper = "Gath01.pdf",
+ url =
+ "http://people.csail.mit.edu/dmoshdov/courses/codes/polyfactorization.pdf",
+ keywords = "survey",
+ abstract =
+ "This survey reviews several algorithms for the factorization of
+ univariate polynomials over finite fields. We emphasize the main ideas
+ of the methods and provide and uptodate bibliography of the problem.
+ This paper gives algorithms for {\sl squarefree factorization},
+ {\sl distinctdegree factorization}, and {\sl equaldegree factorization}.
+ The first and second algorithms are deterministic, the third is
+ probabilistic."
+}
+
+\end{chunk}
+
\index{IdealDecompositionPackage}
\index{Gianni, Patrizia}
\index{Trager, Barry M.}
@@ 8117,30 +8141,6 @@ Proc ISSAC 97 pp172175 (1997)
\end{chunk}
\index{Diaz, Angel}
\index{Kaltofen, Erich}
\begin{chunk}{axiom.bib}
@InProceedings{Diaz95,
 author = "Diaz, A. and Kaltofen, E.",
 title = "On computing greatest common divisors with polynomials given by
 black boxes for their evaluation",
 booktitle = "Proc. 1995 Internat. Symp. Symbolic Algebraic Comput.",
 crossref = "ISSAC95",
 pages = "232239",
 year = "1995",
 url = "http://www.math.ncsu.edu/~kaltofen/bibliography/95/DiKa95.ps.gz",
 paper = "Diaz95.ps",
}

\end{chunk}

\index{von zur Gathen, J.}
\index{Kaltofen, Erich}
\begin{chunk}{axiom.bib}
@article{

\end{chunk}

\index{Kaltofen, Erich}
\index{Trager, Barry M.}
\begin{chunk}{axiom.bib}
@@ 8487,6 +8487,36 @@ Proc ISSAC 97 pp172175 (1997)
\end{chunk}
+\index{Trevisan, Vilmar}
+\index{Wang, Paul}
+\begin{chunk}{axiom.bib}
+@inproceedings{Trev91,
+ author = "Trevisan, Vilmar and Wang, Paul",
+ title = "Practical factorization of univariate polynomials over
+ finite fields",
+ booktitle = "Proc. ISSAC 1991",
+ series = "ISSAC '91",
+ publisher = "ACM",
+ isbn = "0897914376",
+ pages = "2231",
+ year = "1991",
+ url =
+ "http://lib.org/by/\_djvu\_Papers/Computer\_algebra/Algebraic\%20numbers",
+ paper = "Trev91.djvu",
+ abstract =
+ "Research presented here is part of an effort to establish
+ stateoftheart factoring routines for polynomials. The foundation of
+ such algorithms lies in the efficient factorization over a finite
+ field $GF(p^k)$. The CantorZassenhaus algorithm together with
+ innovative ideas suggested by others is compared with the Berlekamp
+ algorithm. The studies led us to design a hybrid algorithm that
+ combine the strengths of the different approaches. The algorithms are
+ also implemented and machine timings are obtained to measure the
+ performance of these algorithms."
+}
+
+\end{chunk}
+
\section{Branch Cuts} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Beaumont, James}
@@ 10526,6 +10556,7 @@ J. Symbolic Computation 5, 237259 (1988)
url = "http://math.unm.edu/~wester/cas/book/Wester.pdf",
url2 = "http://math.unm.edu/~wester/cas_review.html",
paper = "West99a.pdf",
+ keywords = "axiomref",
abstract =
"Computer algebra systems (CASs) have become an essential computational
tool in the last decade. General purpose CASs, which are designed to
@@ 10541,6 +10572,33 @@ J. Symbolic Computation 5, 237259 (1988)
\section{To Be Classified} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{Athale, Rahul Ramesh}
+\index{Diaz, Glauco Alfredo Lopez}
+\begin{chunk}{axiom.bib}
+@misc{Atha03,
+ author = "Athale, Rahul Ramesh and Diaz, Glauco Alfredo Lopez",
+ title = "Explaining Schwarz's LODEF algorithm with examples",
+ url = "http://www.risc.jku.at/publications/download/risc\_1539/0311.ps.gz",
+ paper = "Atha03.pdf",
+ year = "2003",
+ abstract =
+ "To every linear homogeneous ordinary differential equation
+ \[L(y)=y^{(n)}+a_1y^{(n1)}+\cdots+a_{n1}y^{\prime}+a_ny=0\]
+ one can associate the linear operator:
+ \[L(D)[y]=(D^n+a_1D^{n1}+\cdots+a_{n1}D+a_n)[y]\]
+ Here, $D^i$ is another notation for the $i$th derivative of $y$,
+ and the coefficients $a_i$ belong to a differential field $K$.
+ Such an operator is called a linear homogeneous differential operator
+ either over $K$, or with coefficients in $K$. Linear homogeneous
+ differential operators over $K$ form a ring under the usual addition
+ of operators and composition as multiplication.
+
+ {\bf Problem}: Decompose $L$ as a product of operators of lower degree
+ in $D$. We allow expressions algebraic over $K$."
+}
+
+\end{chunk}
+
\index{Chou, ShangChing}
\index{Gao, XiaoShan}
\begin{chunk}{axiom.bib}
@@ 11623,6 +11681,7 @@ J. Symbolic Computation 5, 237259 (1988)
title = "Computer Algebra Meets Education",
keywords = "axiomref",
conference = "Sessions of ACA2000",
+ year = "2000",
abstract =
"Education has become one of the fastest growing application areas for
computers in general and computer algebra in particular. Computer
@@ 11638,6 +11697,22 @@ J. Symbolic Computation 5, 237259 (1988)
\end{chunk}
+\index{MartinezMoro, Edgar}
+\index{Kotsireas, Ilias}
+\begin{chunk}{axiom.bib}
+@misc{ACA15,
+ authors = "MartinezMoro, Edgar Kotsireas, Ilias",
+ title = "21st Conference on Applications of Computer Algebra",
+ keywords = "axiomref",
+ conference = "Sessions of ACA2015",
+ location = "Kalamata, Greece",
+ year = "2015",
+ url = "http://www.singacom.uva.es/ACA2015/latex/ACAproc.pdf",
+ paper = "ACA15.pdf"
+}
+
+\end{chunk}
+
\begin{chunk}{axiom.bib}
@misc{ACM89,
author = "ACM",
@@ 12342,6 +12417,29 @@ IBM Research Report, RC3062 Sept
\end{chunk}
+\index{Bosma, Wieb}
+\index{Cannon, John}
+\index{Playoust, Catherine}
+\begin{chunk}{axiom.bib}
+@article{Bosm97,
+ author = "Bosma, Wieb and Cannon, John and Playoust, Catherine",
+ title = "The Magma Algebra System I: The User Language",
+ journal = "J. Symbolic Computation",
+ volume = "24",
+ pages = "235265",
+ year = "1997",
+ keywords = "axiomref",
+ url = "http://lib.org.by/_djvu/_Papers/Computer_algebra/CAS%20systems/",
+ paper = "Bosm97.djvu",
+ abstract =
+ "In the first of two papers on MAGMA, a new system for computational
+ algebra, we present the MAGMA language, outline the design principles
+ and theoretical background, and indicate its scope and use. Particular
+ attention is given to the constructors for structures, maps, and sets."
+}
+
+\end{chunk}
+
\index{Boyle, Ann}
\begin{chunk}{ignore}
\bibitem[Boyle 88]{Boyl88} Boyle, Ann
@@ 12491,6 +12589,36 @@ Soc. for Industrial and Applied Mathematics, Philadelphia (1990)
\end{chunk}
+\index{Bronstein, Manuel}
+\begin{chunk}{axiom.bib}
+@misc{Bronxx,
+ author = "Bronstein, Manuel",
+ title = "Symbolic Integration in Computer Algebra",
+ url = "http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/26/042/26042580.pdf",
+ paper = "Bron90.pdf",
+ year = "1990",
+ keywords = "axiomref",
+ abstract =
+ "One major goal of symbolic integrators is to determine under what
+ circumstances the integral of the elementary functions of calculus can
+ themselves be expressed as elementary functions. While using tables
+ and the ad hoc tricks taught in calculus courses can have some limited
+ success, a decision procedure is necessary in all but the most trivial
+ cases. The first complete algorithm for solving this problem was
+ presented by Risch in 1969, but its complexity, specially when
+ algebraic functions are present in the integrand, has prevented it
+ from being fully implemented. Over the past 20 years, the Risch
+ integration algorithm has been completed, extended, and improved to
+ such a point that recent computer algebra systems can integrate
+ elementary functions without using any of the heuristics traditionally
+ taught in calculus courses and used by older systems. In this talk,
+ we give an overview and description of the algorithms used in the
+ Scratchpad symbolic integrator, and illustrate them with integrals
+ drawn from the physical sciences."
+}
+
+\end{chunk}
+
\index{Brunelli, J.C.}
\begin{chunk}{axiom.bib}
\article{Brun04,
@@ 14427,6 +14555,7 @@ UK / etc., 1989 ISBN 3540515178 LCCN QA155.7.E4E86 1987
title = "Scratchpad's view of algebra I: Basic commutative algebra",
booktitle = "Design and Implementation of Symbolic Computation Systems",
year = "1990",
+ pages = "4054",
series = "DISCO '90",
location = "Capri, Italy",
publisher = "SpringerVerlag",
@@ 14656,6 +14785,16 @@ May 1984
\end{chunk}
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@misc{Dave15,
+ author = "Davenport, James H.",
+ title = "SIAM AAG 15 and ICIAM 2015",
+ url = "http://people.bath.ac.uk/masjhd/Meetings/AAGICIAM15.pdf",
+ paper = "Dave15.pdf",
+ keywords = "axiomref"
+}
+
\index{Decker, Wolfram}
\begin{chunk}{axiom.bib}
@misc{Deckxx,
@@ 14901,6 +15040,49 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
\end{chunk}
+\index{Diaz, Glauco Alfredo Lopez}
+\begin{chunk}{axiom.bib}
+@phdthesis{Diaz06,
+ author = "Diaz, Glauco Alfredo Lopez",
+ title = "Symbolic Methods for Factoring Linear Differential Operators",
+ school = "Johannes Kepler Universitat, Linz",
+ year = "2006",
+ month = "February",
+ paper = "Diaz06.pdf",
+ keywords = "axiomref",
+ abstract =
+ "A survey of symbolic methods for factoring linear differential
+ operators is given. Starting from basic notions – ring of operators,
+ differential Galois theory – methods for finding rational and
+ exponential solutions that can provide first order righthand factors
+ are considered. Subsequently several known algorithms for
+ factorization are presented. These include Singer’s eigenring
+ factorization algorithm, factorization via Newton polygons, van
+ Hoeij’s methods for local factorization, and an adapted version of
+ Pade approximation.
+
+ In addition a procedure based on pure algebraic methods for factoring
+ second order linear partial differential operators is
+ developed. Splitting an operator of this kind reduces to solving a
+ system of linear algebraic equations. Those solutions which satisfy a
+ certain different ial condition, immediately produce linear factors of
+ the operator. The method applies also to operators of third order,
+ thereby resulting in a more complicated system of equations. In
+ contrast to the second order case, differential equations must also be
+ solved, which, in particular cases, are simplified with the aid of
+ characteristic sets.
+
+ Finally, complete decomposition into linear factors of ordinary
+ differential operators of arbitrary order is discussed. A splitting
+ formula is developed, provided that a linear basis of solutions is
+ available. This theoretical representation is valuable in
+ understanding the nature of the classical Beke algorithm and its
+ variants like the algorithm LODEF by Schwarz and the BekeBronstein
+ algorithm."
+}
+
+\end{chunk}
+
\index{DiBlasio, Paolo}
\index{Temperini, Marco}
\begin{chunk}{axiom.bib}
@@ 15422,6 +15604,28 @@ TPHOLS 2001, Edinburgh
\end{chunk}
+\index{Duval, Anne}
+\index{LodayRichaud, Michele}
+\begin{chunk}{axiom.bib}
+@article{Duva92,
+ author = "Duval, Anne and LodayRichaud, Michele",
+ title = "Kovacic's Algorithm and Its Application to Some Families
+ of Special Functions",
+ journal = "Applicable Algebra in Engineering, Communication, and Computing",
+ series = "AAECC 3",
+ pages = "211246",
+ year = "1992",
+ publisher = "SpringerVerlag",
+ keywords = "axiomref",
+ abstract =
+ "We apply the Kovacic algorithm to some families of special functions,
+ mainly the hypergeometric one and that of Heun, in order to discuss
+ the existence of closedform solutions. We begin by giving a slightly
+ modified version of the kovacic algorithm and a sketch proof."
+}
+
+\end{chunk}
+
\index{Duval, Dominique}
\index{Jung, F.}
\begin{chunk}{ignore}
@@ 15685,11 +15889,32 @@ CODEN ITATEC. ISSN 09265473
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{ignore}
\bibitem[Fateman 90]{Fat90} Fateman, R. J.
 title = "Advances and trends in the design and construction of algebraic manipulation systems",
In Watanabe and Nagata [WN90], pp6067 ISBN 0897914015 LCCN QA76.95.I57 1990
+\begin{chunk}{axiom.bib}
+@inproceedings{Fate90,
+ author = "Fateman, Richard J.",
+ title = "Advances and trends in the design and construction of algebraic
+ manipulation systems",
+ booktitle = "Proc. ISSAC 1990",
+ publisher = "ACM",
+ pages = "6067",
+ isbn = "0897914015",
+ year = "1990",
+ paper = "Fate90.pdf",
+ url = "http://people.eecs.berkeley.edu/~fateman/papers/advances.pdf",
keywords = "axiomref",
+ abstract =
+ "We compare and contrast several techniques for the implementation of
+ components of an algebraic manipulation system. On one hand is the
+ mathematicalalgebraic approach which chaaracterizes (for example)
+ IBM's Axiom. On the other hand is the more {\sl ad hoc} approach which
+ characterizes many other popular systems (for example, Macsyma,
+ Reduce, Maple, and Mathematica). While the algebraic approach has
+ generally positive results, careful examination suggests that there
+ are significant remaining problems, expecially in the representation
+ and manipulation of analytical, as opposed to algebraic,
+ mathematics. We describe some of these problems and some general
+ approaches for solutions."
+}
\end{chunk}
@@ 15739,6 +15964,35 @@ In Watanabe and Nagata [WN90], pp6067 ISBN 0897914015 LCCN QA76.95.I57 1990
\end{chunk}
\index{Fateman, Richard J.}
+\index{Caspi, Eylon}
+\begin{chunk}{axiom.bib}
+@misc{Fate99a,
+ author = "Fateman, Richard J. and Caspi, Eylon",
+ title = "Parsing TeX into Mathematics",
+ year = "1999",
+ url = "http://lib.org.by/_djvu/_Papers/Computer_algebra/CAS%20systems/",
+ paper = "Fate99a.djvu",
+ keywords = "axiomref",
+ abstract =
+ "Communication, storage, transmission, and searching of complex
+ material has become increasingly important. Mathematical computing in
+ a distributed environment is also becoming more plausible as libraries
+ and computing facilities are connected with each other and with user
+ facilites. TeX is a wellknown mathematical typesetting language, and
+ from the display perspective it might seem that it could be used for
+ communication between computer systems as well as an intermediate form
+ for the results of OCR (optical character recognition) of mathematical
+ expressions. There are flaws in this reasoning, since exchanging
+ mathematical informaiton requires a system to parse and semantically
+ ``understand'' the TeX, even if it is ``ambiguous'' notationally. A
+ program we developed can handle 43\% of 10,740 TeX formulas in a
+ wellknown table of integrals. We expect that a higher success rte can
+ be achieved easily."
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@InProceedings{Fate00,
author = "Fateman, Richard J.",
@@ 15960,7 +16214,7 @@ LCCN QA155.7.E4 I57 1984
\end{chunk}
\index{Fortenbacher, A.}
+\index{Fortenbacher, Albrecht}
\index{Jenks, Richard}
\index{Lucks, Michael}
\index{Sutor, Robert}
@@ 15979,13 +16233,31 @@ LCCN QA155.7.E4 I57 1984
\end{chunk}
\index{Fortenbacher, A.}
\begin{chunk}{ignore}
\bibitem[Fortenbacher 90]{For90} Fortenbacher, A.
+\index{Fortenbacher, Albrecht}
+\begin{chunk}{axiom.bib}
+@inproceedings{Fort90,
+ author = "Fortenbacher, Albrecht",
title = "Efficient type inference and coercion in computer algebra",
In Miola [Mio90], pp5660. ISBN 0387525319 (New York), 3540525319
(Berlin). LCCN QA76.9.S88I576 1990
+ booktitle = "Design and Implementation of Symbolic Computation Systems",
+ series = "Lecture Notes in Computer Science 429",
+ pages = "5660",
+ isbn = "0387525319",
+ year = "1990",
keywords = "axiomref",
+ abstract =
+ "Computer algebra systesm of the new generation, like SCRATCHPAD, are
+ characterized by a very rich type concept, which models the
+ relationship between mathematical domains of computation. To use these
+ systems interactively, however, the user should be freed of type
+ information. A type inference mechanism determines the appropriate
+ function to call. All known models which allow to define a semantics
+ for type inference cannot express the rich ``mathematical'' type
+ structure, so presently type inference is done heuristically. The
+ following paper defines a semantics for a subproblem therof, namely
+ coercion, which is based on rewrite rules. From this definition, an
+ efficient coercion algorithm for SCRATCHPAD is constructed using graph
+ techniques."
+}
\end{chunk}
@@ 16021,12 +16293,17 @@ In Miola [Mio90], pp5660. ISBN 0387525319 (New York), 3540525319
\end{chunk}
\index{Fouche, Francois}
\begin{chunk}{ignore}
\bibitem[Fouche 90]{Fou90} Fouche, Francois
+\begin{chunk}{axiom.bib}
+@techreport{Fouc90,
+ author = "Fouche, Francois",
title = "Une implantation de l'algorithme de Kovacic en Scratchpad",
Technical report, Institut de Recherche Math{\'{e}}matique Avanc{\'{e}}e''
Strasbourg, France, 1990 31pp
 keywords = "axiomref",
+ type = "technical report",
+ number = "ULPIRMA447P254",
+ year = "1990",
+ institution = {Institut de Recherche Math{\'{e}}matique Avanc{\'{e}}e''},
+ location = "Strasbourg, France",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 16124,6 +16401,35 @@ Strasbourg, France, 1990 31pp
\end{chunk}
+\index{Ganzha, Victor G.}
+\index{Vorozhtsov, Evgenii V.}
+\index{Wester, Michael}
+\begin{chunk}{axiom.bib}
+@book{Ganz00,
+ author = "Ganzha, Victor G. and Vorozhtsov, Evgenii V. and Wester, Michael",
+ title = "An Assessment of the Efficiency of Computer Algebra Systems in
+ the Solution of Scientific Computing Problems",
+ booktitle = "Computer Algebra in Scientific Computing",
+ year = "2000",
+ isbn = "9783540410409",
+ publisher = "Springer",
+ pages = "145166",
+ keywords = "axiomref",
+ abstract =
+ "Computer algebra systems (CASs) have become an important tool for the
+ solution of scientific computing problems. With the increasing number
+ of general purpose CASs, there is now a need for an assessment of the
+ efficiency of these systems. We discuss some peculiarities associated
+ with the analysis of CPU time efficiency in CASs, and then present
+ results from three specific systems (Maple Vr5, Mathematics 4.0 and
+ MuPAD 1.4) on a sample of intermediate size problems. These results
+ show that Maple Vr5 is generally the speediest on our
+ examples. Finally, we formulate some requirements for developing a
+ comprehensive suite for analyzing the efficiency of CASs."
+}
+
+\end{chunk}
+
\index{Gebauer, R{\"u}diger}
\index{M{\"o}ller, H. Michael}
\begin{chunk}{axiom.bib}
@@ 19274,6 +19580,64 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
\end{chunk}
+\index{Lewis, Robert H.}
+\index{Wester, Michael}
+\begin{chunk}{axiom.bib}
+@article{Lewi99,
+ author = "Lewis, Robert H. and Wester, Michael",
+ title = "Comparison of polynomialorienged computer algebra systems",
+ journal = "SIGSAM Bulletin",
+ volume = "33",
+ number = "4",
+ pages = "513",
+ year = "1999",
+ url = "https://home.bway.net/lewis/cacomp.ps",
+ paper = "Lewi99.pdf",
+ keywords = "axiomref",
+ abstract =
+ "Exact symbolic computation with polynomials and matrices over
+ polynomial rings has wide applicability to many fields [Hereman96,
+ Lewis99]. By ``exact symbolic'', we mean computation with polynomials
+ whose coefficients are integers (of any size), rational numbers, or
+ from finite fields, as opposed to coefficients that are ``floats'' of a
+ certain precision. Such computation is part of most computer algebra
+ (CA) systems. Over the last dozen years, several large CA systems have
+ become widely available, such as Axiom, Derive, Macsyma, Maple,
+ Mathematica and Reduce. They tend to have great breadth, be produced
+ by profitmaking companies, and be relatively expensive, at least for
+ a full blown nonstudent version. However, most if not all of these
+ systems have difficulty computing with the polynomials and matrices
+ that arise in actual research. Real problems tend to produce large
+ polynomials and large matrices that the general CA systems cannot
+ handle [Lewis99].
+
+ In the last few years, several smaller CA systems focused on
+ polynomials have been produced at universities by individual
+ researchers or small teams. They run on Macs, PCs and workstations.
+ They are freeware or shareware. Several claim to be much more
+ efficient than the large systems at exact polynomial computations. The
+ list of these systems includes CoCoA, Fermat, MuPAD, PariGp and
+ Singular [CoCoA, Fermat, MuPAD, PariGp, Singular].
+
+ In this paper, we compare these small systems to each other and to two
+ of the large systems (Magma and Maple) on a set of problems involving
+ exact symbolic computation with polynomials and matrices. The problems
+ here involve:
+ \begin{itemize}
+ \item the ground rings $\mathbb{Z}$, $\mathbb{Q}$, $\mathbb{Z}/p$
+ and other finite fields
+ \item basic arithmetic of polynomials over the ground ring
+ \tem basic arithmetic of rational functions over the ground ring
+ \item polynomial evaluation (substitution)
+ \item matrix normal form
+ \item determinants and characteristic polynomial
+ \item GCDs of multivariate polynomial
+ \item resultants
+ \end{itemize}"
+}
+
+\end{chunk}
+
\index{Li, Xin}
\begin{chunk}{axiom.bib}
@phdthesis{Lixx05,
@@ 19657,11 +20021,39 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
\index{Mathews, J. }
\begin{chunk}{ignore}
\bibitem[Mathews 89]{Mat89} Mathews, J.
+@article{Math89,
+ author = "Mathews, J.",
title = "Symbolic computational algebra applied to Picard iteration",
Mathematics and computer education, 23(2) pp117122 Spring 1989 CODEN MCEDDA,
ISSN 07308639
 keywords = "axiomref",
+ journal = "Mathematics and computer education",
+ volume = "23",
+ number = "2",
+ pages = "117122",
+ year = "1989",
+ url =
+"http://mathfaculty.fullerton.edu/mathews/articles/1989PicardIteration.pdf",
+ paper = "Math89.pdf",
+ keywords = "axiomref",
+ "The term ``Picard iteration'' occurs two places in undergraduate
+ mathematics. In numerical analysis it is used when discussing fixed
+ point iteration for finding a numerical approximation to the equation
+ $s=g(x)$. In differential equations, Picard iteration is a
+ constructive procedure for establishing the existence of a solution to
+ a differential equation $y^{\prime} = f(x,y)$.
+
+ The first type of Picard iteration uses computations to generate a
+ sequence of numbers which converges to a solution. We will not present
+ this application, but mention that it involves the traditional role of
+ the computer as a ``number cruncher.''
+
+ The second application of Picard iteration illustrates how to use a
+ computer to generate a sequence of functions which converges to a
+ solution. The purpose of this article is to show the step by step
+ process in translating mathematical theory into the symbolic
+ manipulation setting. Systems such as MACSYM, ALTRAN, REDUCE, SMP,
+ MAPLE, SCRATCHPAD and muMATH are being introduced in undergraduate
+ mathematics courses to assist in keeping trace of equations during
+ complicated manipulations."
+}
\end{chunk}
@@ 20421,11 +20813,35 @@ IBM T.J. Watson Research RC4998
\end{chunk}
\index{Ollivier, F.}
\begin{chunk}{ignore}
\bibitem[Ollivier 89]{Oll89} Ollivier, F.
 title = "Inversibility of rational mappings and structural identifiablility in automatics",
In ACM [ACM89], pp4354 ISBN 0897913256 LCCN QA76.95.I59 1989
+\begin{chunk}{axiom.bib}
+@inproceedings{Olli89,
+ author = "Ollivier, F.",
+ title = "Inversibility of rational mappings and structural
+ identifiablility in automatics",
+ booktitle = "Proc. SIGSAM 1989",
+ series = "SIGSAM '89",
+ pages = "4354",
+ isbn = "0897913256",
+ year = "1989",
keywords = "axiomref",
+ paper = "Olli89.pdf",
+ abstract =
+ "We investigate different methods for testing whether a rational
+ mapping $f$ from $k^n$ to $k^m$ admits a rational inverse, or whether
+ a polynomial mapping admits a polynomial one. We give a new solution,
+ which seems much more efficient in practice than previously known ones
+ using ``tag'' variables and standard basis, and a majoration for the
+ degree of the standard basis calculations which is valid for both
+ methods in the case of a polynomial map which is birational. We
+ further show that a better bound can be given for our method, under
+ some assumptions on the form of $f$. Our method can also extend to
+ check whether a given polynomial belong to the subfield generated by a
+ finite set of fractions.
+
+ We then illustrate our algorithm, with a application to structural
+ identifiability. The implantation has been done in the IBM computer
+ algebra system Scratchpad II."
+}
\end{chunk}
@@ 20974,12 +21390,26 @@ Mathematik und Physik, 75 (suppl. 2):S435S438, 1995 ISSN 00442267
\end{chunk}
\index{Salvy, Bruno}
\begin{chunk}{ignore}
\bibitem[Salvy 89]{Sal89} Salvy, B.
+\begin{chunk}{axiom.bib}
+@techreport{Salv89,
+ author = "Salvy, Bruno",
title = "Examples of automatic asymptotic expansions",
Technical Report 114,
Inst. Nat. Recherche Inf. Autom., Le Chesnay, France, Dec. 1989 18pp
+ institution = "Inst. Nat. Recherche Inf. Autom.",
+ type = "technical report",
+ number = "114",
+ year = "1989",
+ paper = "Salv89.pdf",
+ comment = "SIGSAM Bulletin Vol 25 No 2 1991 pp417",
keywords = "axiomref",
+ abstract =
+ "We describe the current state of a Maple library, gdev, designed to
+ perform asymptotic expansions for a large class of expressions. Many
+ examples are provided, along with a short sketch of the underlying
+ principles. At the time when this report is written, a striking
+ feature of these examples is that none of them can be computed
+ directly with any of today's most widespread symbolic computation
+ systems (Macsyma, Mathematica, Maple or Scratchpad II)."
+}
\end{chunk}
@@ 21195,11 +21625,33 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
\end{chunk}
\index{Schwarz, Fritz}
\begin{chunk}{ignore}
\bibitem[Schwarz 89]{Sch89} Schwarz, F.
 title = "A factorization algorithm for linear ordinary differential equations",
In ACM [ACM89], pp1725 ISBN 0897913256 LCCN QA76.95.I59 1989
+\begin{chunk}{axiom.bib}
+@inproceedings{Schw89,
+ author = "Schwarz, Fritz",
+ title = "A factorization algorithm for linear ordinary
+ differential equations",
+ booktitle = "Proc. SYMSAC 1989",
+ series = "SYMSAC '89",
+ isbn = "0897913256",
+ year = "1989",
+ pages = "1725",
keywords = "axiomref",
+ paper = "Schw89.pdf",
+ abstract =
+ "The reducibility and factorization of linear homogeneous differential
+ equations are of great theoretical and practical importance in
+ mathematics. Although it has been known for a long time that
+ factorization is in principle a decision procedure, its use in an
+ automatic differential equation solver requires a more detailed
+ analysis of the various steps involved. Especially important are
+ certain auxiliary equations, the socalled associated equations. An
+ upper bound for the degree of its coefficients is derived. Another
+ important ingredient is the computation of optimal estimates for the
+ size of polynomial and rational solutions of certain differential
+ equations with rotational coefficients. Applying these results, the
+ design of the factorization algorithm LODEF and its implementation in
+ the Scratchpad II Computer Algebra System is described.",
+}
\end{chunk}
@@ 21543,12 +21995,89 @@ in Calmet [Cal94] pp103104
\end{chunk}
\index{Sit, William Y.}
\begin{chunk}{ignore}
\bibitem[Sit 89]{Sit89} Sit, W.Y.
 title = "On Goldman's algorithm for solving firstorder multinomial autonomous systems",
In Mora [Mor89], pp386395 ISBN 3540510834
LCCN QA268.A35 1998 Conference held jointly with ISSAC '88
+\begin{chunk}{axiom.bib}
+@inproceedings{Sitx89,
+ author = "Sit, William Y.",
+ title = "On Goldman's algorithm for solving firstorder multinomial
+ autonomous systems",
+ booktitle = "Proc. Algebraic Algorithms and ErrorCorrecting Codes, AAECC6",
+ series = "Lecture Notes in Computer Science 357",
+ location = "Rome, Italy",
+ year = "1988",
+ isbn = "3540510834",
+ pages = "386395",
keywords = "axiomref",
+ abstract =
+ "In this article, a brief exposition of a method for finding first
+ integrals for first order multinomial autonomous systems (FOMAS) of
+ ordinary differential equations with constant coefficients will be
+ given. The method is a simplified as well as a redesigned version
+ based on a paper of Goldman (1987). We shall see how it can be applied
+ to FOMAS with parametric coefficients. The algorithm is currently
+ being implemented by the author, using the SCRATCHPAD II computer
+ algebra language and system at the IBM T.J. Watson Research Center.
+
+ FOMAS occur and are of interest in many disciplines and their first
+ integrals (or trajectories of motion) are generally difficult to
+ find. Examples of FOMAS are too numerous to list, some wellknown ones
+ are the Riccati equation, the LotkaVolterra equations for competing
+ populations, Selkov's model for chemical reactions, the Lorenz system
+ of the RayleighBernard problem, and Hamiltonian systems (where the
+ Hamiltonian is a sum of monomial terms with constant coefficients).
+
+ Let $Y=(y_1,\ldots,y_n)$ be $n$ functions depending on the variable
+ $\tau$. A monomial in $Y$ is a product of the form $y_1^{k_1}\cdots
+ y_n^{k_n}$, where $k_1,\ldots,k_n$ are constants. If
+ $K=(k_1,\ldots,k_n)$, we shall denote the monomial in $Y$ by $Y^K$,
+ and $K$ is called the exponent vector for the monomial. By convention,
+ exponent vectors are column vectors, but whenever convenient, we shall
+ write exponent vectors as row vectors. We say that $Y$ satisfies a
+ firstorder multinomial autonomous system (FOMAS) if for each $i$, $1
+ \le i \le n$, $y_i$ satisfies a first order differential equation of
+ the form:
+ \[y_i^{\prime} = f_i(Y)\quad\quad\quad(1)\]
+ where $f_i$ is a linear combination of monomials in $Y$ with coefficients
+ which may be either constants or parametric constants. For example, the
+ LotkaVolterra equations for three competing species considered by
+ Schwarz and Steeb (1984), form a FOMAS:
+ \[x_1^{\prime}=x_1(1+ax_2+bx_3)\]
+ \[x_2^{\prime}=x_2(1ax_1+bx_3)\]
+ \[x_3^{\prime}=x_3(1bx_1cx_2)\]
+ When the exponent vectors occuring in $f_i$ are all nonnegative integers,
+ as in the example above, a FOMAS reduces to a polynomial autonomous
+ system (FOPAS).
+
+ A computer program was developed by Schwarz (1986) to compute the
+ first integrals of FOPAS's which are themselves polynomials in
+ $y_1,\ldots,y_n$. Schwarz's algorithm literally takes a general
+ polynomial of a fixed degree $d$ in $n$ variables and substitutes it
+ into (1). This method does not work well on a FOMAS, because in a
+ FOMAS, the exponent vectors need not have integral components. Also,
+ it wll not find integrals with exponent vectors that involve
+ fractional or irrational numbers.
+
+ Goldman (1987) proved a theorem which gives necessary and sufficient
+ conditions for the existence of a multinomial first integral for
+ FOMAS. The proof also contained the outline of an algorithm for
+ finding such integrals. In Goldman's paper, he introduced the notion
+ of an integral array, which is a certain matrix satisfying some 10
+ conditions. He gave a few hints and several examples but did not
+ elaborate on how such an integral array can be found in general
+ (except in the case $q=2$). Assuming such an array is found, he can
+ compute the integral, in most cases, by solving systems of linear
+ equations, or at worse in certain cases, by solving a system of
+ algebraic equations. It was not clear when algebraic conditions are
+ necessary.
+
+ In this brief exposition, Goldman's method will be expanded to a
+ complete algorithm with a new simplified notation. The integral arrays
+ are replaced by addition schemes (which is equivalent to integral
+ arrays with some conditions removed). The generation of addition
+ schemes is a combinatorial problem unrelated, in a sense, to
+ FOMAS. When the first integral is a polynomial, the additioin scheme
+ is trivial to compute. We shall now begin by explaining some details
+ of this theory."
+}
\end{chunk}
@@ 22194,13 +22723,22 @@ ISBN 3540213112
\subsection{W} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Wang, Dongming}
\begin{chunk}{ignore}
\bibitem[Wang 89]{Wan89} Wang, D.
 title = "A program for computing the Liapunov functions and Liapunov constants in Scratchpad II",
SIGSAM Bulletin (ACM Special Interest Group
on Symbolic and Algebraic Manipulation), 23(4) pp2531, Oct. 1989,
CODEN SIGSBZ ISSN 01635824
+\begin{chunk}{axiom.bib}
+@article{Wang89,
+ author = "Wang, Dongming",
+ title = "A program for computing the Liapunov functions and Liapunov
+ constants in Scratchpad II",
+ journal = "SIGSAM Bulletin",
+ volume = "23",
+ number = "4",
+ pages = "2531",
+ year = "1989",
keywords = "axiomref",
+ abstract =
+ "This report describes the implementation and use of a program for
+ computing the Liapunov functions and Liapunov constants for a class
+ of differential systems in Scratchpad II"
+}
\end{chunk}
@@ 22331,12 +22869,47 @@ in [Wit87], pp1317
\end{chunk}
\index{Watt, Stephen M.}
\begin{chunk}{ignore}
\bibitem[Watt 89]{Wat89} Watt, S. M.
+\begin{chunk}{axiom.bib}
+@inproceedings{Watt89,
+ author = "Watt, Stephen M.",
title = "A fixed point method for power series computation",
In Gianni [Gia89], pp206217 ISBN 3540510842 LCCN QA76.95.I57
1988 Conference held jointly with AAECC6
+ booktitle = "Proc. ISSAC '88",
+ series = "Lecture Notes in Computer Science 358",
+ location = "Rome, Italy",
+ pages = "206217",
+ isbn = "3540510842",
+ year = "1988",
+ series = "AAECC6, ISSAC '88",
keywords = "axiomref",
+ abstract =
+ "This paper presents a novel technique for manipulating structures
+ which represents infinite power series.
+
+ When power series are implemented using lazy evaluation, many
+ operations can be written as simple recursive procedures. For example,
+ the programs to generate the series for the elementary transcendental
+ functions are almost transliterations of the defining integral
+ equations. However, a naive lazy algorithm provides an implementation
+ which may be orders of magnitude slower than a method which
+ manipulates the coefficients explicitly.
+
+ The technique described here allows a power series to be defined in a
+ very natural but computationally inefficient way and transforms it to
+ an equivalent, efficient form. This is achieved by using a fixed point
+ operator on the delayed part to remove redundant calculations.
+
+ This paper describes this fixed point method and the class of problems
+ to which it is applicable. It has been used in Scratchpad II to
+ improve the performance of a number of operations on infinite series,
+ including division, reversion, special functions and the solution of
+ linear and nonlinear ordinary differential equations.
+
+ A few examples are given of the method and of the speed up
+ obtained. To illustrate, the computation of the first $n$ terms of
+ exp($u$) for a dense, infinite series $u$ is reduced from $O(n^4)$ to
+ $O(n^2)$ coefficient operations, the same as required by the standard
+ online algorithms."
+}
\end{chunk}
@@ 22616,6 +23189,32 @@ IBM T. J. Watson Research Center (2001)
\end{chunk}
\index{Weber, Andreas}
+\begin{chunk}{axiom.bib}
+@inproceedings{Webe05,
+ author = "Weber, Andreas",
+ title = "A TypeCoercion Problem in Computer Algebra",
+ booktitle = "Artificial Intelligence and Symbolic Mathematical Computing",
+ series = "Lecture Notes in Computer Science 737",
+ year = "2005",
+ publisher = "Springer",
+ pages = "188194",
+ paper = "Webe05.pdf",
+ abstract =
+ "An important feature of modern computer algebra systems is the
+ support of a rich type system with the possibility of type inference.
+
+ Basic features of such a system are polymorphism and coercion between
+ types. Recently the use of ordersorted rewrite systems was proposed
+ as a general framework.
+
+ We will give a quite simple example of a family of types arising in
+ computer algebra whose coercion relations cannot be captured by a
+ finite set of firstorder rewrite rules."
+}
+
+\end{chunk}
+
+\index{Weber, Andreas}
\begin{chunk}{ignore}
\bibitem[Weber 93b]{Webe93b} Weber, Andreas
title = "Type Systems for Computer Algebra",
@@ 23116,6 +23715,54 @@ Karlsruhe, Germany, 1992
\end{chunk}
+\index{Zimmermann, Paul}
+\begin{chunk}{axiom.bib}
+@misc{Zimm95,
+ author = "Zimmermann, Paul",
+ title = "Wester's test suite in MuPAD 1.2.2",
+ year = "1995",
+ paper = "Zimm95.pdf",
+ keywords = "axiomref",
+ abstract =
+ "A few months ago, Michael Wester made a review of the mathematical
+ capabilities of different computer algebra systems, namely Axiom,
+ Derive, Macsyma, Maple, Mathematica and Reduce. This review, which is
+ available by anonymous ftp from math.unm.edu, file pub/cas/Paper.ps,
+ consists of 131 tests in different domains of mathematics (arithmetic,
+ algebraic equations, differential equations, integration, operator
+ computation, series expansions, limits).
+
+ We describe in this paper the problems that can be solved with MuPAD
+ 1.2.2, and how to solve them. The problems marked as [New] are solved
+ using new functionalities of the version 1.2.2 with respect to 1.2.1"
+}
+
+\end{chunk}
+
+\index{Zimmermann, Paul}
+\begin{chunk}{axiom.bib}
+@misc{Zimm96,
+ author = "Zimmermann, Paul",
+ title = "Wester's test suite in MuPAD 1.3",
+ year = "1996",
+ paper = "Zimm96.pdf",
+ keywords = "axiomref",
+ abstract =
+ "In December 1994, Michael Wester made a review of the mathematical
+ capabilities of different computer algebra systems, namely Axiom,
+ Derive, Macsyma, Maple, Mathematica and Reduce. This review, which is
+ available by anonymous ftp from math.unm.edu, file pub/cas/Paper.ps,
+ consists of 131 tests in different domains of mathematics (arithmetic,
+ algebraic equations, differential equations, integration, operator
+ computation, series expansions, limits).
+
+ We describe in this paper the problems that can be solved with MuPAD
+ 1.3, and how to solve them. The problems marked as [New] are solved
+ using new functionalities of the version 1.3 with respect to 1.2.2"
+}
+
+\end{chunk}
+
\index{Zippel, Richard}
\begin{chunk}{ignore}
\bibitem[Zip92]{Zip92} Zippel, Richard
diff git a/changelog b/changelog
index 95daabd..6a3eee9 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,5 @@
+20160708 tpd src/axiomwebsite/patches.html 20160708.01.tpd.patch
+20160708 tpd books/bookvolbib Axiom Citations in the Literature
20160707 tpd src/axiomwebsite/patches.html 20160707.01.tpd.patch
20160707 tpd books/bookvolbib Axiom Citations in the Literature
20160706 tpd src/axiomwebsite/patches.html 20160706.02.tpd.patch
diff git a/patch b/patch
index e74e908..13e163a 100644
 a/patch
+++ b/patch
@@ 2,717 +2,770 @@ books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@techReport{Jenk71,
 author = "Jenks, Richard D.",
 title = "META/PLUS: The syntax extension facility for SCRATCHPAD",
 type = "Research Report",
 number = "RC 3259",
 institution = "IBM Research",
 year = "1971",
 keywords = "axiomref"
}

\end{chunk}

\index{Griesmer, James H.}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@techreport{Grie72,
 author = "Griesmer, James H. and Jenks, Richard D.",
 title = "Experience with an online symbolic math system SCRATCHPAD",
 year = "1972",
 isbn = "0903796023",
 keywords = "axiomref"
+\index{Mathews, J. }
+\begin{chunk}{ignore}
+@article{Math89,
+ author = "Mathews, J.",
+ title = "Symbolic computational algebra applied to Picard iteration",
+ journal = "Mathematics and computer education",
+ volume = "23",
+ number = "2",
+ pages = "117122",
+ year = "1989",
+ url =
+"http://mathfaculty.fullerton.edu/mathews/articles/1989PicardIteration.pdf",
+ paper = "Math89.pdf",
+ keywords = "axiomref",
+ "The term ``Picard iteration'' occurs two places in undergraduate
+ mathematics. In numerical analysis it is used when discussing fixed
+ point iteration for finding a numerical approximation to the equation
+ $s=g(x)$. In differential equations, Picard iteration is a
+ constructive procedure for establishing the existence of a solution to
+ a differential equation $y^{\prime} = f(x,y)$.
+
+ The first type of Picard iteration uses computations to generate a
+ sequence of numbers which converges to a solution. We will not present
+ this application, but mention that it involves the traditional role of
+ the computer as a ``number cruncher.''
+
+ The second application of Picard iteration illustrates how to use a
+ computer to generate a sequence of functions which converges to a
+ solution. The purpose of this article is to show the step by step
+ process in translating mathematical theory into the symbolic
+ manipulation setting. Systems such as MACSYM, ALTRAN, REDUCE, SMP,
+ MAPLE, SCRATCHPAD and muMATH are being introduced in undergraduate
+ mathematics courses to assist in keeping trace of equations during
+ complicated manipulations."
}
\end{chunk}
\index{Griesmer, James H.}
\index{Jenks, Richard D.}
+\index{Ollivier, F.}
\begin{chunk}{axiom.bib}
@article{Grie72,
 author = "Griesmer, James H. and Jenks, Richard D.",
 title = "SCRATCHPAD: A capsule view",
 journal = "ACM SIGPLAN Notices",
 volume = "7",
 number = "10",
 pages = "93102",
 year = "1972",
 comment = "Proc. Symp. Twodimensional manmachine communications",
+@inproceedings{Olli89,
+ author = "Ollivier, F.",
+ title = "Inversibility of rational mappings and structural
+ identifiablility in automatics",
+ booktitle = "Proc. SIGSAM 1989",
+ series = "SIGSAM '89",
+ pages = "4354",
+ isbn = "0897913256",
+ year = "1989",
keywords = "axiomref",
 doi = "http://dx.doi.org/10.1145807019",
+ paper = "Olli89.pdf",
abstract =
 "SCRATCHPAD is an interactive system for algebraic manipulation
 available under the CP/CMS timesharing system at Yorktown Heights. It
 features an extensible declarative language for the interactive
 formulation of symbolic computations. The system is a large and
 complex body of LISP programs incorporating significant portions of
 other symbolic systems. Here we present a capsule view of SCRATCHPAD,
 its language and its capabilities. This is followed by an example
 which illustrates its use in an application involving the solution of
 an integral equation."
+ "We investigate different methods for testing whether a rational
+ mapping $f$ from $k^n$ to $k^m$ admits a rational inverse, or whether
+ a polynomial mapping admits a polynomial one. We give a new solution,
+ which seems much more efficient in practice than previously known ones
+ using ``tag'' variables and standard basis, and a majoration for the
+ degree of the standard basis calculations which is valid for both
+ methods in the case of a polynomial map which is birational. We
+ further show that a better bound can be given for our method, under
+ some assumptions on the form of $f$. Our method can also extend to
+ check whether a given polynomial belong to the subfield generated by a
+ finite set of fractions.
+
+ We then illustrate our algorithm, with a application to structural
+ identifiability. The implantation has been done in the IBM computer
+ algebra system Scratchpad II."
}
\end{chunk}
\index{Jenks, Richard D.}
+\index{Trevisan, Vilmar}
+\index{Wang, Paul}
\begin{chunk}{axiom.bib}
@article{Jenk74,
 author = "Jenks, Richard D.",
 title = "The SCRATCHPAD language",
 journal = "ACM SIGPLAN Notices",
 comment = "reprinted in SIGSAM Bulletin, Vol 8, No. 2, May 1974",
 volume = "9",
 number = "4",
 pages = "101111",
 year = "1974",
 doi = "http://dx.doi.org/10.1145807051",
 keywords = "axiomref",
+@inproceedings{Trev91,
+ author = "Trevisan, Vilmar and Wang, Paul",
+ title = "Practical factorization of univariate polynomials over
+ finite fields",
+ booktitle = "Proc. ISSAC 1991",
+ series = "ISSAC '91",
+ publisher = "ACM",
+ isbn = "0897914376",
+ pages = "2231",
+ year = "1991",
+ url =
+ "http://lib.org/by/\_djvu\_Papers/Computer\_algebra/Algebraic\%20numbers",
+ paper = "Trev91.djvu",
abstract =
 "SCRATCHPAD is an interactive system for symbolic mathematical
 computation. Its user language, originally intended as a
 specialpurpose nonprocedural language, was designed to capture the
 style and succinctness of common mathematical notations, and to serve
 as a useful, effective tool for online problem solving. This paper
 describes extensions to the language which enable it to serve also as
 a highlevel programming language, both for the formal description of
 mathematical algorithms and their efficient implementation."
+ "Research presented here is part of an effort to establish
+ stateoftheart factoring routines for polynomials. The foundation of
+ such algorithms lies in the efficient factorization over a finite
+ field $GF(p^k)$. The CantorZassenhaus algorithm together with
+ innovative ideas suggested by others is compared with the Berlekamp
+ algorithm. The studies led us to design a hybrid algorithm that
+ combine the strengths of the different approaches. The algorithms are
+ also implemented and machine timings are obtained to measure the
+ performance of these algorithms."
}
\end{chunk}
\index{Norman, Arthur C.}
+\index{Bosma, Wieb}
+\index{Cannon, John}
+\index{Playoust, Catherine}
\begin{chunk}{axiom.bib}
@article{Norm75,
 author = "Norman, Arthur C.",
 title = "Computing with Formal Power Series",
 journal = "ACM Transactions on Mathematical Software",
 volume = "1",
 number = "4",
 pages = "346356",
 year = "1975",
+@article{Bosm97,
+ author = "Bosma, Wieb and Cannon, John and Playoust, Catherine",
+ title = "The Magma Algebra System I: The User Language",
+ journal = "J. Symbolic Computation",
+ volume = "24",
+ pages = "235265",
+ year = "1997",
keywords = "axiomref",
 doi = "10.1145/355656.355660"
+ url = "http://lib.org.by/_djvu/_Papers/Computer_algebra/CAS%20systems/",
+ paper = "Bosm97.djvu",
+ abstract =
+ "In the first of two papers on MAGMA, a new system for computational
+ algebra, we present the MAGMA language, outline the design principles
+ and theoretical background, and indicate its scope and use. Particular
+ attention is given to the constructors for structures, maps, and sets."
}
\end{chunk}
\index{Jenks, Richard D.}
+\index{Salvy, Bruno}
\begin{chunk}{axiom.bib}
@inproceedings{Jenk76,
 author = "Jenks, Richard D.",
 title = "A pattern compiler",
 booktitle = "Proc. 1976 ACM Symposium on Symbolic and Algebraic Computation",
 series = "SYMSAC '76",
 year = "1976",
 publisher = "ACM Press",
+@techreport{Salv89,
+ author = "Salvy, Bruno",
+ title = "Examples of automatic asymptotic expansions",
+ institution = "Inst. Nat. Recherche Inf. Autom.",
+ type = "technical report",
+ number = "114",
+ year = "1989",
+ paper = "Salv89.pdf",
+ comment = "SIGSAM Bulletin Vol 25 No 2 1991 pp417",
keywords = "axiomref",
 doi = "http://dx.doi.org/10.1145806324",
abstract =
 "A pattern compiler for the SCRATCHPAD system provides an efficient
 implementation of sets of userdefined patternreplacement rules for
 symbolic mathematical computation such as tables of integrals or
 summation identities. Rules are compiled together, with common search
 paths merged and factored out and with the resulting code optimized
 for efficient recognition over all patterns. Matching principally
 involves structural comparison of expression trees and evaluation of
 predicates. Pattern recognizers are ``fully compiled''; if values of
 match variables can be determined by solving equations at compile time.
 Recognition times for several pattern matchers are compared."
+ "We describe the current state of a Maple library, gdev, designed to
+ perform asymptotic expansions for a large class of expressions. Many
+ examples are provided, along with a short sketch of the underlying
+ principles. At the time when this report is written, a striking
+ feature of these examples is that none of them can be computed
+ directly with any of today's most widespread symbolic computation
+ systems (Macsyma, Mathematica, Maple or Scratchpad II)."
}
\end{chunk}
\index{Lueken, E.}
+\index{Bronstein, Manuel}
\begin{chunk}{axiom.bib}
@mastersthesis{Luek77,
 author = "Lueken, E.",
 title = "Ueberlegungen zur Implementierung eines Formelmanipulationssystems",
 school = {Technischen Universit{\"{a}}t CaroloWilhelmina zu Braunschweig},
 address = "Braunschweig, Germany",
 year = "1977",
 keywords = "axiomref"
+@inproceedings{Bron96b,
+ author = "Bronstein, Manuel",
+ title = "On the Factorization of Linear Ordinary Differential Operators",
+ booktitle = "Mathematics and Computers in Simulation",
+ volume = "42",
+ number = "46",
+ pages = "387389",
+ year = "1996",
+ paper = "Bro96b.pdf",
+ abstract =
+ "After reviewing the arithmetic of linear ordinary differential
+ operators, we describe the current status of the factorisation
+ algorithm, specially with respect to factoring over nonalgebraically
+ closed constant fields. We also describe recent results from Singer
+ and Ulmer that reduce determining the differential Galois group of an
+ operator to factoring."
}
\end{chunk}
\index{Kanigel, Robert}
+\index{Diaz, Glauco Alfredo Lopez}
\begin{chunk}{axiom.bib}
 author = "Kanigel, Robert",
 title = "OldQuotes",
 url = "http://www.oldquotes.com",
 year = "2016",
 abstract =
 "Sometimes in studying Ramanujan's work, George Andrews said at
 another time, ``I have wondered how much Ramanujan could have done if
 he had had MACSYMA or SCRATCHPAD or some other symbolic algebra package"
+@phdthesis{Diaz06,
+ author = "Diaz, Glauco Alfredo Lopez",
+ title = "Symbolic Methods for Factoring Linear Differential Operators",
+ school = "Johannes Kepler Universitat, Linz",
+ year = "2006",
+ month = "February",
+ paper = "Diaz06.pdf",
+ keywords = "axiomref",
+ abstract =
+ "A survey of symbolic methods for factoring linear differential
+ operators is given. Starting from basic notions – ring of operators,
+ differential Galois theory – methods for finding rational and
+ exponential solutions that can provide first order righthand factors
+ are considered. Subsequently several known algorithms for
+ factorization are presented. These include Singer’s eigenring
+ factorization algorithm, factorization via Newton polygons, van
+ Hoeij’s methods for local factorization, and an adapted version of
+ Pade approximation.
+
+ In addition a procedure based on pure algebraic methods for factoring
+ second order linear partial differential operators is
+ developed. Splitting an operator of this kind reduces to solving a
+ system of linear algebraic equations. Those solutions which satisfy a
+ certain different ial condition, immediately produce linear factors of
+ the operator. The method applies also to operators of third order,
+ thereby resulting in a more complicated system of equations. In
+ contrast to the second order case, differential equations must also be
+ solved, which, in particular cases, are simplified with the aid of
+ characteristic sets.
+
+ Finally, complete decomposition into linear factors of ordinary
+ differential operators of arbitrary order is discussed. A splitting
+ formula is developed, provided that a linear basis of solutions is
+ available. This theoretical representation is valuable in
+ understanding the nature of the classical Beke algorithm and its
+ variants like the algorithm LODEF by Schwarz and the BekeBronstein
+ algorithm."
}
\end{chunk}
\index{Andrews, George}
\index{Baxter, R.J.}
+\index{Schwarz, Fritz}
\begin{chunk}{axiom.bib}
@inproceedings{Andr90,
 author = "Andrews, George and Baxter, R.J.",
 title = "SCRATCHPAD explorations for elliptic theta functions",
 booktitle = "Computers in Mathematics",
 series = "Lecture Notes in Pure and Appl. Math 125",
 pages = "1733",
 year = "1990",
 keywords = "axiomref"
+@inproceedings{Schw89,
+ author = "Schwarz, Fritz",
+ title = "A factorization algorithm for linear ordinary
+ differential equations",
+ booktitle = "Proc. SYMSAC 1989",
+ series = "SYMSAC '89",
+ isbn = "0897913256",
+ year = "1989",
+ pages = "1725",
+ keywords = "axiomref",
+ abstract =
+ "The reducibility and factorization of linear homogeneous differential
+ equations are of great theoretical and practical importance in
+ mathematics. Although it has been known for a long time that
+ factorization is in principle a decision procedure, its use in an
+ automatic differential equation solver requires a more detailed
+ analysis of the various steps involved. Especially important are
+ certain auxiliary equations, the socalled associated equations. An
+ upper bound for the degree of its coefficients is derived. Another
+ important ingredient is the computation of optimal estimates for the
+ size of polynomial and rational solutions of certain differential
+ equations with rotational coefficients. Applying these results, the
+ design of the factorization algorithm LODEF and its implementation in
+ the Scratchpad II Computer Algebra System is described.",
}
\end{chunk}
\index{Koepf, Wolfram}
+\index{Schwarz, Fritz}
\begin{chunk}{axiom.bib}
@article{Koep92,
 author = "Koepf, Wolfram",
 title = "Power Series in Computer Algebra",
 journal = "J. Symbolic Computation",
 volume = "13",
 pages = "581603",
 year = "1992",
 paper = "Koep92.pdf",
+@inproceedings{Schw89,
+ author = "Schwarz, Fritz",
+ title = "A factorization algorithm for linear ordinary
+ differential equations",
+ booktitle = "Proc. SYMSAC 1989",
+ series = "SYMSAC '89",
+ isbn = "0897913256",
+ year = "1989",
+ pages = "1725",
+ keywords = "axiomref",
+ paper = "Schw89.pdf",
abstract =
 "Formal power series (FPS) of the form
 $\sum_{k=0}^{\infty}{a_k(xx_0)^k}$ are important in calculus and
 complex analysis. In some Computer Algebra Systems (CASs) it is
 possible to define an FPS by direct or recursive definition of its
 coefficients. Since some operations cannot be directly supported
 within the FPS domain, some systems generally convert FPS to finite
 truncated power series (TPS) for operations such as addition,
 multiplication, division, inversion and formal substitution. This
 results in a substantial loss of information. Since a goal of
 Computer Algebra is  in contrast to numerical programming  to work
 with formal objects and preserve such symbolic information, CAS should
 be able to use FPS when possible.

 There is a onetoone correspondence between FPS with positive radius
 of convergence and corresponding analytic functions. It should be
 possible to automate conversion between these forms. Among CASs
 only MACSYMA provides a procedure {\tt powerseries} to calculate FPS from
 analytic expressions in certain special cases, but this is rather
 limited.

 Here we give an algorithmic approach for computing an FPS for a
 function from a very rich family of functions including all of the
 most prominent ones that can be found in mathematical dictionaries
 except those where the general coefficient depends on the Bernoulli,
 Euler, or Eulerian numbers. The algorithm has been implemented by the
 author and A. Rennoch in the CAS MATHEMATICA, and by D. Gruntz in
 MAPLE.

 Moreover, the same algorithm can sometimes be reversed to calculate a
 function that corresponds to a given FPS, in those cases when a
 certain type of ordinary differential equation can be solved."
+ "The reducibility and factorization of linear homogeneous differential
+ equations are of great theoretical and practical importance in
+ mathematics. Although it has been known for a long time that
+ factorization is in principle a decision procedure, its use in an
+ automatic differential equation solver requires a more detailed
+ analysis of the various steps involved. Especially important are
+ certain auxiliary equations, the socalled associated equations. An
+ upper bound for the degree of its coefficients is derived. Another
+ important ingredient is the computation of optimal estimates for the
+ size of polynomial and rational solutions of certain differential
+ equations with rotational coefficients. Applying these results, the
+ design of the factorization algorithm LODEF and its implementation in
+ the Scratchpad II Computer Algebra System is described.",
}
\end{chunk}
\index{Verstraete, Jacques}
+\index{Fateman, Richard J.}
+\index{Caspi, Eylon}
\begin{chunk}{axiom.bib}
@misc{Vers16,
 author = "Verstraete, Jacques",
 title = "Combinatorial Calculus of Formal Power Series",
 comment = "264A Lecture B",
 url = "http://www.math.ucsd.edu/~jverstra/264ALECTUREB.pdf",
 paper = "Vers16.pdf"
}
+@misc{Fate99a,
+ author = "Fateman, Richard J. and Caspi, Eylon",
+ title = "Parsing TeX into Mathematics",
+ year = "1999",
+ url = "http://lib.org.by/_djvu/_Papers/Computer_algebra/CAS%20systems/",
+ paper = "Fate99a.djvu",
+ keywords = "axiomref",
+ abstract =
+ "Communication, storage, transmission, and searching of complex
+ material has become increasingly important. Mathematical computing in
+ a distributed environment is also becoming more plausible as libraries
+ and computing facilities are connected with each other and with user
+ facilites. TeX is a wellknown mathematical typesetting language, and
+ from the display perspective it might seem that it could be used for
+ communication between computer systems as well as an intermediate form
+ for the results of OCR (optical character recognition) of mathematical
+ expressions. There are flaws in this reasoning, since exchanging
+ mathematical informaiton requires a system to parse and semantically
+ ``understand'' the TeX, even if it is ``ambiguous'' notationally. A
+ program we developed can handle 43\% of 10,740 TeX formulas in a
+ wellknown table of integrals. We expect that a higher success rte can
+ be achieved easily."
+}
\end{chunk}
\index{Lucks, Michael}
+\index{Sit, William Y.}
\begin{chunk}{axiom.bib}
@inproceedings{Luck86,
 author = "Lucks, Michael",
 title = "A fast implementation of polynomial factorization",
 booktitle = "Proc. 1986 Symposium on Symbolic and Algebraic Computation",
 series = "SYMSAC '86",
 year = "1986",
 location = "Waterloo, Ontario",
 pages = "228232",
 publisher = "ACM Press",
 isbn = "0897911997",
+@inproceedings{Sitx89,
+ author = "Sit, William Y.",
+ title = "On Goldman's algorithm for solving firstorder multinomial
+ autonomous systems",
+ booktitle = "Proc. Algebraic Algorithms and ErrorCorrecting Codes, AAECC6",
+ series = "Lecture Notes in Computer Science 357",
+ location = "Rome, Italy",
+ year = "1988",
+ isbn = "3540510834",
+ pages = "386395",
keywords = "axiomref",
abstract =
 "A new package for factoring polynomials with integer coefficients is
 described which yields significant improvements over previous
 implementations in both time and space requirements. For multivariate
 problems, the package features an inexpensive method for early
 detection and correction of spurious factors. This essentially solves
 the multivariate extraneous factor problem and eliminates the need to
 factor more than one univariate image, except in rare cases. Also
 included is an improved technique for coefficient prediction which is
 successful more frequently than prior versions at shortcircuiting the
 expensive multivariate Hensel lifting stage. In addition some new
 approaches are discussed for the univariate case as well as for the
 problem of finding good integer substitution values. The package has
 been implemented both in Scratchpad II and in an experimental version
 of muMATH."
+ "In this article, a brief exposition of a method for finding first
+ integrals for first order multinomial autonomous systems (FOMAS) of
+ ordinary differential equations with constant coefficients will be
+ given. The method is a simplified as well as a redesigned version
+ based on a paper of Goldman (1987). We shall see how it can be applied
+ to FOMAS with parametric coefficients. The algorithm is currently
+ being implemented by the author, using the SCRATCHPAD II computer
+ algebra language and system at the IBM T.J. Watson Research Center.
+
+ FOMAS occur and are of interest in many disciplines and their first
+ integrals (or trajectories of motion) are generally difficult to
+ find. Examples of FOMAS are too numerous to list, some wellknown ones
+ are the Riccati equation, the LotkaVolterra equations for competing
+ populations, Selkov's model for chemical reactions, the Lorenz system
+ of the RayleighBernard problem, and Hamiltonian systems (where the
+ Hamiltonian is a sum of monomial terms with constant coefficients).
+
+ Let $Y=(y_1,\ldots,y_n)$ be $n$ functions depending on the variable
+ $\tau$. A monomial in $Y$ is a product of the form $y_1^{k_1}\cdots
+ y_n^{k_n}$, where $k_1,\ldots,k_n$ are constants. If
+ $K=(k_1,\ldots,k_n)$, we shall denote the monomial in $Y$ by $Y^K$,
+ and $K$ is called the exponent vector for the monomial. By convention,
+ exponent vectors are column vectors, but whenever convenient, we shall
+ write exponent vectors as row vectors. We say that $Y$ satisfies a
+ firstorder multinomial autonomous system (FOMAS) if for each $i$, $1
+ \le i \le n$, $y_i$ satisfies a first order differential equation of
+ the form:
+ \[y_i^{\prime} = f_i(Y)\quad\quad\quad(1)\]
+ where $f_i$ is a linear combination of monomials in $Y$ with coefficients
+ which may be either constants or parametric constants. For example, the
+ LotkaVolterra equations for three competing species considered by
+ Schwarz and Steeb (1984), form a FOMAS:
+ \[x_1^{\prime}=x_1(1+ax_2+bx_3)\]
+ \[x_2^{\prime}=x_2(1ax_1+bx_3)\]
+ \[x_3^{\prime}=x_3(1bx_1cx_2)\]
+ When the exponent vectors occuring in $f_i$ are all nonnegative integers,
+ as in the example above, a FOMAS reduces to a polynomial autonomous
+ system (FOPAS).
+
+ A computer program was developed by Schwarz (1986) to compute the
+ first integrals of FOPAS's which are themselves polynomials in
+ $y_1,\ldots,y_n$. Schwarz's algorithm literally takes a general
+ polynomial of a fixed degree $d$ in $n$ variables and substitutes it
+ into (1). This method does not work well on a FOMAS, because in a
+ FOMAS, the exponent vectors need not have integral components. Also,
+ it wll not find integrals with exponent vectors that involve
+ fractional or irrational numbers.
+
+ Goldman (1987) proved a theorem which gives necessary and sufficient
+ conditions for the existence of a multinomial first integral for
+ FOMAS. The proof also contained the outline of an algorithm for
+ finding such integrals. In Goldman's paper, he introduced the notion
+ of an integral array, which is a certain matrix satisfying some 10
+ conditions. He gave a few hints and several examples but did not
+ elaborate on how such an integral array can be found in general
+ (except in the case $q=2$). Assuming such an array is found, he can
+ compute the integral, in most cases, by solving systems of linear
+ equations, or at worse in certain cases, by solving a system of
+ algebraic equations. It was not clear when algebraic conditions are
+ necessary.
+
+ In this brief exposition, Goldman's method will be expanded to a
+ complete algorithm with a new simplified notation. The integral arrays
+ are replaced by addition schemes (which is equivalent to integral
+ arrays with some conditions removed). The generation of addition
+ schemes is a combinatorial problem unrelated, in a sense, to
+ FOMAS. When the first integral is a polynomial, the additioin scheme
+ is trivial to compute. We shall now begin by explaining some details
+ of this theory."
}
\end{chunk}
\index{Purtilo, J.}
+\index{Bronstein, Manuel}
\begin{chunk}{axiom.bib}
@inproceedings{Purt86,
 author = "Purtilo, J.",
 title = "Applications of a software interconnection system in
 mathematical problem solving environments",
 booktitle = "Proc.1986 Symposium on Symbolic and Algebraic Computation",
 series = "SYMSAC '86",
 pages = "1623",
 year = "1986",
 publisher = "ACM Press",
 isbn = "0897911997",
+@misc{Bronxx,
+ author = "Bronstein, Manuel",
+ title = "Symbolic Integration in Computer Algebra",
+ url = "http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/26/042/26042580.pdf",
+ paper = "Bron90.pdf",
+ year = "1990",
keywords = "axiomref",
 doi = "http://dx.doi.org/10.1145/32439.32443"
+ abstract =
+ "One major goal of symbolic integrators is to determine under what
+ circumstances the integral of the elementary functions of calculus can
+ themselves be expressed as elementary functions. While using tables
+ and the ad hoc tricks taught in calculus courses can have some limited
+ success, a decision procedure is necessary in all but the most trivial
+ cases. The first complete algorithm for solving this problem was
+ presented by Risch in 1969, but its complexity, specially when
+ algebraic functions are present in the integrand, has prevented it
+ from being fully implemented. Over the past 20 years, the Risch
+ integration algorithm has been completed, extended, and improved to
+ such a point that recent computer algebra systems can integrate
+ elementary functions without using any of the heuristics traditionally
+ taught in calculus courses and used by older systems. In this talk,
+ we give an overview and description of the algorithms used in the
+ Scratchpad symbolic integrator, and illustrate them with integrals
+ drawn from the physical sciences."
}
\end{chunk}
+\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@misc{NTCI16,
 author = "NTCIR",
 title = "Axiom (computer algebra system)",
 url =
 "http://ntcir11wmc.nii.ac.jp/index.php/Axiom\_(computer_algebra_system)",
+@article{Wang89,
+ author = "Wang, Dongming",
+ title = "A program for computing the Liapunov functions and Liapunov
+ constants in Scratchpad II",
+ journal = "SIGSAM Bulletin",
+ volume = "23",
+ number = "4",
+ pages = "2531",
+ year = "1989",
keywords = "axiomref",
 year = "2016"
+ abstract =
+ "This report describes the implementation and use of a program for
+ computing the Liapunov functions and Liapunov constants for a class
+ of differential systems in Scratchpad II"
}
\end{chunk}
\index{Gebauer, R{\"u}diger}
\index{M{\"o}ller, H. Michael}
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@misc{Dave15,
+ author = "Davenport, James H.",
+ title = "SIAM AAG 15 and ICIAM 2015",
+ url = "http://people.bath.ac.uk/masjhd/Meetings/AAGICIAM15.pdf",
+ paper = "Dave15.pdf",
+ keywords = "axiomref"
+}
+
+\index{Watt, Stephen M.}
\begin{chunk}{axiom.bib}
@article{Geba88,
 author = "Gebauer, Rudiger and Moller, H. Michael",
 title = "On an installation of Buchberger's algorithm",
 journal = "Journal of Symbolic Computation",
 volume = "6",
 number = "23",
 pages = "275286",
+@inproceedings{Watt89,
+ author = "Watt, Stephen M.",
+ title = "A fixed point method for power series computation",
+ booktitle = "Proc. ISSAC '88",
+ series = "Lecture Notes in Computer Science 358",
+ location = "Rome, Italy",
+ pages = "206217",
+ isbn = "3540510842",
year = "1988",
 paper = "GM88.pdf",
+ series = "AAECC6, ISSAC '88",
keywords = "axiomref",
 abstract =
 "Buchberger's algorithm calculates Groebner bases of polynomial
 ideals. Its efficiency depends strongly on practical criteria for
 detecting superfluous reductions. Buchberger recommends two
 criteria. The more important one is interpreted in this paper as a
 criterion for detecting redundant elements in a basis of a module of
 syzygies. We present a method for obtaining a reduced, nearly minimal
 basis of that module. The simple procedure for detecting (redundant
 syzygies and )superfluous reductions is incorporated now in our
 installation of Buchberger's algorithm in SCRATCHPAD II and REDUCE
 3.3. The paper concludes with statistics stressing the good
 computational properties of these installations."
+ abstract =
+ "This paper presents a novel technique for manipulating structures
+ which represents infinite power series.
+
+ When power series are implemented using lazy evaluation, many
+ operations can be written as simple recursive procedures. For example,
+ the programs to generate the series for the elementary transcendental
+ functions are almost transliterations of the defining integral
+ equations. However, a naive lazy algorithm provides an implementation
+ which may be orders of magnitude slower than a method which
+ manipulates the coefficients explicitly.
+
+ The technique described here allows a power series to be defined in a
+ very natural but computationally inefficient way and transforms it to
+ an equivalent, efficient form. This is achieved by using a fixed point
+ operator on the delayed part to remove redundant calculations.
+
+ This paper describes this fixed point method and the class of problems
+ to which it is applicable. It has been used in Scratchpad II to
+ improve the performance of a number of operations on infinite series,
+ including division, reversion, special functions and the solution of
+ linear and nonlinear ordinary differential equations.
+
+ A few examples are given of the method and of the speed up
+ obtained. To illustrate, the computation of the first $n$ terms of
+ exp($u$) for a dense, infinite series $u$ is reduced from $O(n^4)$ to
+ $O(n^2)$ coefficient operations, the same as required by the standard
+ online algorithms."
}
\end{chunk}
\index{Bronstein, Manuel}
+\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@inproceedings{Bron89,
 author = "Bronstein, Manuel",
 title = "Simplification of real elementary functions",
 booktitle = "Proc. ISSAC 1989",
 series = "ISSAC 1989",
 year = "1989",
 pages = "207211",
 isbn = "0897913256",
+@inproceedings{Fate90,
+ author = "Fateman, Richard J.",
+ title = "Advances and trends in the design and construction of algebraic
+ manipulation systems",
+ booktitle = "Proc. ISSAC 1990",
+ publisher = "ACM",
+ pages = "6067",
+ isbn = "0897914015",
+ year = "1990",
+ paper = "Fate90.pdf",
+ url = "http://people.eecs.berkeley.edu/~fateman/papers/advances.pdf",
keywords = "axiomref",
 abstract = "
 We describe an algorithm, based on Risch's real structure theorem, that
 determines explicitly all the algebraic relations among a given set of
 real elementary functions. We also provide examples from its
 implementation that illustrate the advantages over the use of complex
 logarithms and exponentials."
+ abstract =
+ "We compare and contrast several techniques for the implementation of
+ components of an algebraic manipulation system. On one hand is the
+ mathematicalalgebraic approach which chaaracterizes (for example)
+ IBM's Axiom. On the other hand is the more {\sl ad hoc} approach which
+ characterizes many other popular systems (for example, Macsyma,
+ Reduce, Maple, and Mathematica). While the algebraic approach has
+ generally positive results, careful examination suggests that there
+ are significant remaining problems, expecially in the representation
+ and manipulation of analytical, as opposed to algebraic,
+ mathematics. We describe some of these problems and some general
+ approaches for solutions."
}
\end{chunk}
\index{Dicrescenzo, C.}
\index{Duval, Dominique}
+\index{Fortenbacher, Albrecht}
\begin{chunk}{axiom.bib}
@InProceedings{Dicr88,
 author = "Dicrescenzo, C. and Duval, D.",
 title = "Algebraic extensions and algebraic closure in Scratchpad II",
 booktitle = "Proc. ISSAC 1988",
 series = "ISSAC 1998",
 year = "1998",
 pages = "440446",
 isbn = "3540510842",
+@inproceedings{Fort90,
+ author = "Fortenbacher, Albrecht",
+ title = "Efficient type inference and coercion in computer algebra",
+ booktitle = "Design and Implementation of Symbolic Computation Systems",
+ series = "Lecture Notes in Computer Science 429",
+ pages = "5660",
+ isbn = "0387525319",
+ year = "1990",
keywords = "axiomref",
abstract =
 "Many problems in computer algebra, as well as in highschool
 exercises, are such that their statement only involves integers but
 their solution involves complex numbers. For example, the complex
 numbers $\sqrt{2}$ and $\sqrt{2}$ appear in the solutions of
 elementary problems in various domains.
 \begin{itemize}
 \item in {\bf integration}:
 \[\int{\frac{dx}{x^22}} = \frac{Log(x\sqrt{2})}{2\sqrt{2}}
 +\frac{Log(x(\sqrt{2}))}{2(\sqrt{2})}\]
 \item in {\bf linear algebra}: the eigenvalues of the matrix
 \[\left(\begin{array}{cc}
 1 & 1\\
 1 & 1
 \end{array}\right) = \sqrt{2} {\rm\ and\ }\sqrt{2}\]
 \item in {\bf geometry}: the line $y=x$ intersects the circle
 $y^2+x^2=1$ at the points
 \[(\sqrt{2},\sqrt{2}) {\rm\ and\ }(\sqrt{2},\sqrt{2})\]
 \end{itemize}
 Of course, more ``complicated'' complex numbers appear in more
 complicated examples.

 But two facts have to be emphasized:
 \begin{itemize}
 \item in general, if a problem is stated over the integers (or over
 the field $\mathbb{Q}$ of rational numbers), the complex numbers that
 appear are {\sl algebraic} complex numbers, which means that they are
 roots of some polynomial with rational coefficients, like $\sqrt{2}$
 and $\sqrt{2}$ are roots of $T^22$.
 \item Similar problems appear with base fields different from
 $mathbb{Q}$. For example finite fields, or fields of rational
 functions over $\mathbb{Q}$ or over a finite field. The general
 situation is that a given problem is stated over some ``small field''
 $K$, and its solution is expressed in an {\sl algebraci closure}
 $\overline{K}$ of $K$, which means that this solution involves numbers
 which are roots of polynomials with coefficients in $K$.
 \end{itemize}

 The aim of this paper is to describe an implementation of an algebraic
 closure domain constructor in the language Scratchpad II, simply
 called Scratchpad below. In the first part we analyze the problem, and
 in the second part we describe a solution based on the D5 system."
+ "Computer algebra systesm of the new generation, like SCRATCHPAD, are
+ characterized by a very rich type concept, which models the
+ relationship between mathematical domains of computation. To use these
+ systems interactively, however, the user should be freed of type
+ information. A type inference mechanism determines the appropriate
+ function to call. All known models which allow to define a semantics
+ for type inference cannot express the rich ``mathematical'' type
+ structure, so presently type inference is done heuristically. The
+ following paper defines a semantics for a subproblem therof, namely
+ coercion, which is based on rewrite rules. From this definition, an
+ efficient coercion algorithm for SCRATCHPAD is constructed using graph
+ techniques."
}
\end{chunk}
\index{Yun, David Y.Y}
+\index{Weber, Andreas}
\begin{chunk}{axiom.bib}
@inproceedings{Yunx76,
 author = "Yun, David Y.Y",
 title = "Algebraic Algorithms using padic Constructions",
 booktitle = "Proc. 1976 Symp. on Symbolic and Algebraic Computation",
 series = "SYMSAC '76",
 publisher = "ACM",
 year = "1976",
 pages = "248259",
 keywords = "axiomref",
 paper = "Yunx76.djvu",
 url =
 "http://lib.org/by/\_djvu\_Papers/Computer\_algebra/Algebraic\%20numbers",
+@inproceedings{Webe05,
+ author = "Weber, Andreas",
+ title = "A TypeCoercion Problem in Computer Algebra",
+ booktitle = "Artificial Intelligence and Symbolic Mathematical Computing",
+ series = "Lecture Notes in Computer Science 737",
+ year = "2005",
+ publisher = "Springer",
+ pages = "188194",
+ paper = "Webe05.pdf",
+ abstract =
+ "An important feature of modern computer algebra systems is the
+ support of a rich type system with the possibility of type inference.
+
+ Basic features of such a system are polymorphism and coercion between
+ types. Recently the use of ordersorted rewrite systems was proposed
+ as a general framework.
+
+ We will give a quite simple example of a family of types arising in
+ computer algebra whose coercion relations cannot be captured by a
+ finite set of firstorder rewrite rules."
}
\end{chunk}
\index{Gianni, Patrizia}
\index{Mora, T.}
+\index{Fouche, Francois}
\begin{chunk}{axiom.bib}
@inproceedings{Gian89,
 author = "Gianni, Patrizia and Mora, T.",
 title = "Algebraic solution of systems of polynomial equations
 using Groebner bases.",
 booktitle = "Applied Algebra, Algebraic Algorithms and ErrorCorrecting
 Codes",
 series = "AAECC5",
 pages = "247257",
 year = "1989",
 isbn = "3540510826",
 keywords = "axiomref",
 paper = "Gian89.pdf",
 abstract =
 "One of the most important applications of Buchberger's algorithm for
 Groebner basis computation is the solution of systems of polynomial
 equations (having finitely many roots), i.e. the computation of zeros
 of 0dimensional polynomial ideals. It is based on a relation between
 Groebner bases w.r.t. a lexicographical ordering and elimination
 ideals, which was discovered by Trinks.

 Packages for isolation of real roots of systems of polynomial
 equations using Groebner basis computation are currently available in
 different computer algebra systems, including SAC2, Reduce,
 Scratchpad II, Maple.

 In principle, BuchbergerTrinks algorithm should allow to compute
 solutions of such systems in the algebraic closure of the coefficient
 field $k$ (usually the rational numbers), in the sense that it is
 possible to represent explicitly a finite extension of $k$ containing
 all solutions and to express the roots in this field.

 However, this requires several factorisations of polynomials over a
 tower of algebraic extensions of $k$, which is usually very costly, so
 that the resulting algorithm is not very feasible and, as far as we
 know, no implementation is available.

 The results of [GT2] on primary decomposition of ideals include a
 thorough study on the structure of Groebner bases for 0dimensional
 ideals; in particular, the paper shows, that after a ``generic''
 linear change of coordinates, the roots of a system of polynomial
 equations can be expressed in a simple extension of $k$. Therefore, in
 this case, no factorisation of polynomials over towers of algebraic
 extensions is needed.

 However performing a change of coordinates has the undesirable effects
 of introducing dense polynomials and of increasing the size of
 coefficients.

 The problem then arises of producing strategies to compute Groebner
 bases for (0dimensional) ideals, which at least are able to control
 the influence of these sideeffects: two such strategies are presented
 in this paper, together with the application to the present problem of
 an algorithm by Gianni that computes the radical of a 0dimensional
 ideal after a ``generic'' change of coordinates.

 A different approach, based on her ``splitting algorithm'', to compute
 solutions of systems of polynomial equations without the need of
 polynomial factorisations has been proposed by D. Duval; also her
 algorithm should be simplified by a ``generic'' change of coordinates.

 The algorithms discussed in this paper are implemented in SCRATCHPAD II.

 In the first section we recall some wellknown properties of Groebner
 bases and properties on the structure of Groebner bases of
 zerodimensional ideals from [GT2]; in the second section we recall
 the Groebner basis algorithm for solving systems of algebraic
 equations.

 The original results are contained in Sections 3 to 5; in Section 3 we
 take advantage of the obvious fact that density can be controlled by
 performing ``small'' changes of coordinates: we show that such
 approach is possible during a Groebner basis computation, in such a
 way that computations done before a change of coordinates are valid
 also after it; in Section 4 we propose a ``linear algebra'' approach
 to obtain the Groebner basis w.r.t the lexicographical ordering from
 the one w.r.t the totaldegree ordering; in Section 5, we present a
 zerodimensional radical algorithm and show how to apply it to the
 present problem."
+@techreport{Fouc90,
+ author = "Fouche, Francois",
+ title = "Une implantation de l'algorithme de Kovacic en Scratchpad",
+ type = "technical report",
+ number = "ULPIRMA447P254",
+ year = "1990",
+ institution = {Institut de Recherche Math{\'{e}}matique Avanc{\'{e}}e''},
+ location = "Strasbourg, France",
+ keywords = "axiomref"
}
\end{chunk}
\index{Sturmfels, Bernd}
+\index{Duval, Anne}
+\index{LodayRichaud, Michele}
\begin{chunk}{axiom.bib}
@misc{Stur00,
 author = "Sturmfels, Bernd",
 title = "Solving Systems of Polynomial Equations",
 url = "https://math.berkeley.edu/~bernd/cbms.pdf",
 paper = "Stur00.pdf",
 year = "2000",
+@article{Duva92,
+ author = "Duval, Anne and LodayRichaud, Michele",
+ title = "Kovacic's Algorithm and Its Application to Some Families
+ of Special Functions",
+ journal = "Applicable Algebra in Engineering, Communication, and Computing",
+ series = "AAECC 3",
+ pages = "211246",
+ year = "1992",
+ publisher = "SpringerVerlag",
+ keywords = "axiomref",
abstract =
 "One of the most classical problems of mathematics is to solve systems
 of polynomial equations in several unknowns. Today, polynomial
 models are ubiquitous and widely applied across the sciences. They
 arise in robotics, coding theory, optimization, mathematical
 biology, computer vision, game theory, statistics, machine learning,
 control theory, and numerous other areas. The set of solutions to a
 system of polynomial equations is an algebraic variety, the basic
 object of algebraic geometry. The algorithmic study of algebraic
 varieties is the central theme of computational algebraic
 geometry. Exciting recent developments in symbolic algebra and
 numerical software for geometric calculations have revolutionized
 the field, making formerly inaccessible problems tractable, and
 providing fertile ground for experimentation and conjecture.

 The first half of this book furnishes an introduction and represents a
 snapshot of the state of the art regarding systems of polynomial
 equations. Afficionados of the wellknown text books by Cox, Little,
 and O’Shea will find familiar themes in the first five chapters:
 polynomials in one variable, Groebner bases of zerodimensional
 ideals, Newton polytopes and Bernstein’s Theorem, multidimensional
 resultants, and primary decomposition.

 The second half of this book explores polynomial equations from a
 variety of novel and perhaps unexpected angles. Interdisciplinary
 connections are introduced, highlights of current research are
 discussed, and the author’s hopes for future algorithms are
 outlined. The topics in these chapters include computation of Nash
 equilibria in game theory, semidefinite programming and the real
 Nullstellensatz, the algebraic geometry of statistical models, the
 piecewiselinear geometry of valuations and amoebas, and the
 EhrenpreisPalamodov theorem on linear partial differential equations
 with constant coefficients.

 Throughout the text, there are many handson examples and exercises,
 including short but complete sessions in the software systems maple,
 matlab, Macaulay 2, Singular, PHC, and SOStools . These examples
 will be particularly useful for readers with zero background in
 algebraic geometry or commutative algebra. Within minutes, anyone can
 learn how to type in polynomial equations and actually see some
 meaningful results on the computer screen."
+ "We apply the Kovacic algorithm to some families of special functions,
+ mainly the hypergeometric one and that of Heun, in order to discuss
+ the existence of closedform solutions. We begin by giving a slightly
+ modified version of the kovacic algorithm and a sketch proof."
}
\end{chunk}
\index{Monagan, Michael B.}
\index{Gonnet, Gaston H.}
+\index{Lewis, Robert H.}
+\index{Wester, Michael}
\begin{chunk}{axiom.bib}
@misc{Mona94,
 author = "Monagan, Michael B. and Gonnet, Gaston H.",
 title = "Signature Functions for Algebraic Numbers",
 url =
 "http://lib.org/by/\_djvu\_Papers/Computer\_algebra/Algebraic\%20numbers",
 paper = "Mona94.djvu",
+@article{Lewi99,
+ author = "Lewis, Robert H. and Wester, Michael",
+ title = "Comparison of polynomialorienged computer algebra systems",
+ journal = "SIGSAM Bulletin",
+ volume = "33",
+ number = "4",
+ pages = "513",
+ year = "1999",
+ url = "https://home.bway.net/lewis/cacomp.ps",
+ paper = "Lewi99.pdf",
keywords = "axiomref",
 abstract =
 "In 1980 Schwartz gave a fast {\sl probabilistic} method which tests
 if a matrix of polynomials of $\mathbb{Z}$ is singular or not. The
 method is based on the idea of {\sl signature functions} which are
 mappings of mathematical expressions into finite rings. In Schwartz's
 paper, they were polynomials over $\mathbb{Z}$ into GF($p$). Because
 computation in GF($p$) is very fast compared with computing with
 polynomials, Schwartz's method yields an enormous speedup both in
 theory and in practice. Therefore it is desirable to extend the class
 of expressions for which we can find effective signature functions. In
 the mid 80's Gonnet extended the class of expressions, for which
 signature functions can be found, to include a restricted class of
 elementary functions and integer roots. In this paper we present and
 compare methods for constructing signature functions for expressions
 containing {\sl algebraic numbers}. Some experimental results are
 given."
}
+ abstract =
+ "Exact symbolic computation with polynomials and matrices over
+ polynomial rings has wide applicability to many fields [Hereman96,
+ Lewis99]. By ``exact symbolic'', we mean computation with polynomials
+ whose coefficients are integers (of any size), rational numbers, or
+ from finite fields, as opposed to coefficients that are ``floats'' of a
+ certain precision. Such computation is part of most computer algebra
+ (CA) systems. Over the last dozen years, several large CA systems have
+ become widely available, such as Axiom, Derive, Macsyma, Maple,
+ Mathematica and Reduce. They tend to have great breadth, be produced
+ by profitmaking companies, and be relatively expensive, at least for
+ a full blown nonstudent version. However, most if not all of these
+ systems have difficulty computing with the polynomials and matrices
+ that arise in actual research. Real problems tend to produce large
+ polynomials and large matrices that the general CA systems cannot
+ handle [Lewis99].
+
+ In the last few years, several smaller CA systems focused on
+ polynomials have been produced at universities by individual
+ researchers or small teams. They run on Macs, PCs and workstations.
+ They are freeware or shareware. Several claim to be much more
+ efficient than the large systems at exact polynomial computations. The
+ list of these systems includes CoCoA, Fermat, MuPAD, PariGp and
+ Singular [CoCoA, Fermat, MuPAD, PariGp, Singular].
+
+ In this paper, we compare these small systems to each other and to two
+ of the large systems (Magma and Maple) on a set of problems involving
+ exact symbolic computation with polynomials and matrices. The problems
+ here involve:
+ \begin{itemize}
+ \item the ground rings $\mathbb{Z}$, $\mathbb{Q}$, $\mathbb{Z}/p$
+ and other finite fields
+ \item basic arithmetic of polynomials over the ground ring
+ \tem basic arithmetic of rational functions over the ground ring
+ \item polynomial evaluation (substitution)
+ \item matrix normal form
+ \item determinants and characteristic polynomial
+ \item GCDs of multivariate polynomial
+ \item resultants
+ \end{itemize}"
+}
\end{chunk}
\index{Kusche, K.}
\index{Kutzler, B.}
\index{Mayr, H.}
+\index{Ganzha, Victor G.}
+\index{Vorozhtsov, Evgenii V.}
+\index{Wester, Michael}
\begin{chunk}{axiom.bib}
@inproceedings{Kusc89,
 author = "Kusche, K. and Kutzler, B. and Mayr, H.",
 title = "Implementation of a geometry theorem proving package
 in SCRATCHPAD II",
 booktitle = "Proc. of Eurocal '87",
 series = "Lecture Notes in Computer Science 378",
 pages = "246257",
 isbn = "3540515178",
 year = "1987",
+@book{Ganz00,
+ author = "Ganzha, Victor G. and Vorozhtsov, Evgenii V. and Wester, Michael",
+ title = "An Assessment of the Efficiency of Computer Algebra Systems in
+ the Solution of Scientific Computing Problems",
+ booktitle = "Computer Algebra in Scientific Computing",
+ year = "2000",
+ isbn = "9783540410409",
+ publisher = "Springer",
+ pages = "145166",
keywords = "axiomref",
 abstract =
 "The problem of automatically proving geometric theorems has gained a
 lot of attention in the last two years. Following the general approach
 of translating a given geometric theorem into an algebraic one,
 various powerful provers based on characteristic sets and Groebner
 bases have been implemented by groups at Academia Sinica Bejing
 (China), U. Texas at Austin (USA), General Electric Schenectady (USA),
 and Research Institute for Symbolic Computation Linz (Austria). So ar,
 fair comparisons of the various provers were not possible, because the
 underlying hardware and the underlying algebra systems differed
 greatly. This paper reports on the first uniform implementation of all
 of these provers in the computer algebra system and language
 SCRATCHPAD II. We summarize the recent achievements in the area of
 automated geometry theorem proving, shortly review the SCRATCHPAD II
 system, describe the implementation of the geometry theorem proving
 package, and finally give a computing time statistics of 24 examples."
+ abstract =
+ "Computer algebra systems (CASs) have become an important tool for the
+ solution of scientific computing problems. With the increasing number
+ of general purpose CASs, there is now a need for an assessment of the
+ efficiency of these systems. We discuss some peculiarities associated
+ with the analysis of CPU time efficiency in CASs, and then present
+ results from three specific systems (Maple Vr5, Mathematics 4.0 and
+ MuPAD 1.4) on a sample of intermediate size problems. These results
+ show that Maple Vr5 is generally the speediest on our
+ examples. Finally, we formulate some requirements for developing a
+ comprehensive suite for analyzing the efficiency of CASs."
}
\end{chunk}
\index{ElAlfy, Hazem Mohamed}
+\index{Zimmermann, Paul}
\begin{chunk}{axiom.bib}
@mastersthesis{ElAl01,
 author = "ElAlfy, Hazem Mohamed",
 title = "Computer Algebra and its Applications",
 school = "Alexandria University, Department of Engineering, Mathematics,
 and Physics",
 year = "2001",
 url = "http://www.umiacs.umd.edu/~helalfy/pub/mscthesis01.pdf",
 file = "ElAl01.pdf",
+@misc{Zimm96,
+ author = "Zimmermann, Paul",
+ title = "Wester's test suite in MuPAD 1.3",
+ year = "1996",
+ paper = "Zimm96.pdf",
keywords = "axiomref",
 abstract =
 "In the recent decades, it has been more and more realized that
 computers are of enormous importance for numerical
 computations. However, these powerful generalpurpose machines can
 also be used for transforming, combining and computing symbolic
 algebraic expressions. In other words, computers can not only deal
 with numbers, but also with abstract symbols representing mathematical
 formulas. This fact has been realized much later and is only now
 gaining acceptance among mathematicians and engineers. [Franz Winkler,
 1996].

 Computer Algebra is that field of computer science and mathematics,
 where computation is performed on symbols representing mathematical
 objects rather than their numeric values.

 This thesis attempts to present a definition of computer algebra by
 means of a survey of its main topics, together with its major
 application areas. The survey includes necessary algebraic basics and
 fundamental algorithms, essential in most computer algebra problems,
 together with some problems that rely heavily on these algorithms. The
 set of applications, presented from a range of fields of engineering
 and science, although very short, indicates the applied nature of
 computer algebra systems.

 A recent research area, central in most computer algebra software
 packages and in geometric modeling, is the implicitization
 problem. Curves and surfaces are naturally reperesented either
 parametrically or implicitly. Both forms are important and have their
 uses, but many design systems start from parametric
 representations. Implicitization is the process of converting curevs
 and surfaces from parametric form into implicit form.

 We have surveyed the problem of implicitization and investigated its
 currently available methods. Algorithms for such methods have been
 devised, implemented and tested for practical examples. In addition, a
 new method has been devised for curves for which a direct method is
 not available. The new method has been called {\sl near implicitization}
 since it relies on an approximation of the input problem. Several
 variants of the method try to compromise between accuracy and
 complexity of the designed algorithms.
+ abstract =
+ "In December 1994, Michael Wester made a review of the mathematical
+ capabilities of different computer algebra systems, namely Axiom,
+ Derive, Macsyma, Maple, Mathematica and Reduce. This review, which is
+ available by anonymous ftp from math.unm.edu, file pub/cas/Paper.ps,
+ consists of 131 tests in different domains of mathematics (arithmetic,
+ algebraic equations, differential equations, integration, operator
+ computation, series expansions, limits).
 The problem of implicitization is an active topic where research is
 still taking place. Examples of further research points are included
 in the conclusion"
+ We describe in this paper the problems that can be solved with MuPAD
+ 1.3, and how to solve them. The problems marked as [New] are solved
+ using new functionalities of the version 1.3 with respect to 1.2.2"
}
\end{chunk}
\index{Chou, ShangChing}
\index{Gao, XiaoShan}
\index{Zhang, JingZhong}
+\index{Zimmermann, Paul}
\begin{chunk}{axiom.bib}
@book{Chou94,
 author = "Chou, ShangChing and Gao, XiaoShan and Zhang, JingZhong",
 title = "Machine Proofs in Geometry: Automated Production of Readable
 Proofs for Geometry Theorems",
 publisher = "World Scientific",
 url = "http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.374.11778",
 paper = "Chou94.pdf",
 year = "1994"
}
+@misc{Zimm95,
+ author = "Zimmermann, Paul",
+ title = "Wester's test suite in MuPAD 1.2.2",
+ year = "1995",
+ paper = "Zimm95.pdf",
+ keywords = "axiomref",
+ abstract =
+ "A few months ago, Michael Wester made a review of the mathematical
+ capabilities of different computer algebra systems, namely Axiom,
+ Derive, Macsyma, Maple, Mathematica and Reduce. This review, which is
+ available by anonymous ftp from math.unm.edu, file pub/cas/Paper.ps,
+ consists of 131 tests in different domains of mathematics (arithmetic,
+ algebraic equations, differential equations, integration, operator
+ computation, series expansions, limits).
+
+ We describe in this paper the problems that can be solved with MuPAD
+ 1.2.2, and how to solve them. The problems marked as [New] are solved
+ using new functionalities of the version 1.2.2 with respect to 1.2.1"
+}
\end{chunk}
\index{Chou, ShangChing}
\index{Gao, XiaoShan}
+\index{MartinezMoro, Edgar}
+\index{Kotsireas, Ilias}
\begin{chunk}{axiom.bib}
@techreport{Chou89,
 author = "Chou, ShangChing and Gao, XiaoShan",
 title = "A Collection of 120 Computer Solved Geometry Problems in
 Mechanical Formula Derivation",
 institution = "University of Texas, Austin",
 url = "http://www.cs.utexas.edu/ftp/techreports/tr8922.pdf",
 paper = "Chou89.pdf",
 type = "technical report",
 number = "tr8922",
 year = "1989"
 abstract =
 "This is a collection of 120 geometric problems mechanically solved by
 a program based on the methods introduced by us. Researchers can use
 this collection to experiment with their methods/programs similar to
 ours. It consists of two parts: the exact specification of the input
 to our program and a collection of 120 examples. A typical example
 consists of an informal description of the geometric problem, the
 input to the program which is the exact specification of the problem,
 the result of the problem, and a diagram."
}
+@misc{ACA15,
+ authors = "MartinezMoro, Edgar Kotsireas, Ilias",
+ title = "21st Conference on Applications of Computer Algebra",
+ keywords = "axiomref",
+ conference = "Sessions of ACA2015",
+ location = "Kalamata, Greece",
+ year = "2015",
+ url = "http://www.singacom.uva.es/ACA2015/latex/ACAproc.pdf",
+ paper = "ACA15.pdf"
+}
\end{chunk}
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 273b3ec..831a35b 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5460,6 +5460,8 @@ books/bookvolbib Axiom Citations in the Literature
books/bookvolbib Axiom Citations in the Literature
20160707.01.tpd.patch
books/bookvolbib Axiom Citations in the Literature
+20160708.01.tpd.patch
+books/bookvolbib Axiom Citations in the Literature

1.7.5.4