From 242115e26c60902cc21a68ab44c7af5589812dc2 Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Fri, 8 Jul 2016 03:15:59 0400
Subject: [PATCH] books/bookvolbib Axiom Citations in the Literature
MIMEVersion: 1.0
ContentType: text/plain; charset=UTF8
ContentTransferEncoding: 8bit
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"
}
\end{chunk}
\index{Griesmer, James H.}
\index{Jenks, Richard D.}
\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",
keywords = "axiomref",
doi = "http://dx.doi.org/10.1145807019",
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."
}
\end{chunk}
\index{Jenks, Richard D.}
\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",
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."
}
\end{chunk}
\index{Norman, Arthur C.}
\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",
keywords = "axiomref",
doi = "10.1145/355656.355660"
}
\end{chunk}
\index{Jenks, Richard D.}
\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",
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."
}
\end{chunk}
\index{Lueken, E.}
\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"
}
\end{chunk}
\index{Kanigel, Robert}
\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"
}
\end{chunk}
\index{Andrews, George}
\index{Baxter, R.J.}
\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"
}
\end{chunk}
\index{Koepf, Wolfram}
\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",
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."
}
\end{chunk}
\index{Verstraete, Jacques}
\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"
}
\end{chunk}
\index{Lucks, Michael}
\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",
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."
}
\end{chunk}
\index{Purtilo, J.}
\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",
keywords = "axiomref",
doi = "http://dx.doi.org/10.1145/32439.32443"
}
\end{chunk}
\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)",
keywords = "axiomref",
year = "2016"
}
\end{chunk}
\index{Gebauer, R{\"u}diger}
\index{M{\"o}ller, H. Michael}
\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",
year = "1988",
paper = "GM88.pdf",
keywords = "axiomref",
abstract =
"Buchberger's algorithm calculates Groebner bases of polynomial
ideals. Its efficiency depends strongly on practical criteria for
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."
}
\end{chunk}
\index{Bronstein, Manuel}
\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",
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."
}
\end{chunk}
\index{Dicrescenzo, C.}
\index{Duval, Dominique}
\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",
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."
}
\end{chunk}
\index{Yun, David Y.Y}
\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",
}
\end{chunk}
\index{Gianni, Patrizia}
\index{Mora, T.}
\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."
}
\end{chunk}
\index{Sturmfels, Bernd}
\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",
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."
}
\end{chunk}
\index{Monagan, Michael B.}
\index{Gonnet, Gaston H.}
\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",
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."
}
\end{chunk}
\index{Kusche, K.}
\index{Kutzler, B.}
\index{Mayr, H.}
\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",
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."
}
\end{chunk}
\index{ElAlfy, Hazem Mohamed}
\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",
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.
The problem of implicitization is an active topic where research is
still taking place. Examples of further research points are included
in the conclusion"
}
\end{chunk}
\index{Chou, ShangChing}
\index{Gao, XiaoShan}
\index{Zhang, JingZhong}
\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"
}
\end{chunk}
\index{Chou, ShangChing}
\index{Gao, XiaoShan}
\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."
}
\end{chunk}

books/bookvolbib.pamphlet  955 +++++++++++++++++++++++++++++
changelog  12 +
patch  1108 ++++++++++++++++++++++
src/axiomwebsite/patches.html  2 +
4 files changed, 1429 insertions(+), 648 deletions()
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index e49382b..4e74015 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 4,6 +4,7 @@
\mainmatter
\setcounter{chapter}{0} % Chapter 1
% See: http://www.swmath.org/software/63
+% See: http://www.netlib.org/bibnet/journals/axiom.ps.gz
\chapter{The Axiom Bibliography}
This bibliography covers areas of computational mathematics.
Papers which mention Axiom have a ``keyword='' entry of ``axiomref''.
@@ 1142,7 +1143,7 @@ when shown in factored form.
algorithm [6]. In that example, the matrix is not explicitly
constructed, but instead a fast algorithm for performing the matrix
times vector product is used. Further examples for such ``black box
 matrices'' arise in the power series solutoin of algebraic or
+ matrices'' arise in the power series solution of algebraic or
differential equations by undetermined coefficients. The arising
linear systems for the coefficients usually have a distinct structure
that allows a fast coefficient matrix times vector product."
@@ 4375,16 +4376,17 @@ Martin, U.
year = "2010",
month = "5",
file = "Mort10.pdf",
 note = {This thesis considers abstract algebra from a constructive point
+ abstract =
+ "This thesis considers abstract algebra from a constructive point
of view. The central concept of study is coherent rings  algebraic
structures in which it is possible to solve homogeneous systems of
linear equations. Three different algebraic theories are considered;
 B\'ezout domains, Pr\"ufer domains and polynomial rings. The first two
+ Bezout domains, Prufer domains and polynomial rings. The first two
of these are nonNoetherian analogues of classical notions. The
polynomial rings are presented from a constructive point of view with a
treatment of Groebner bases. The goal of the thesis is to study the
proofs that these theories are coherent and explore how the proofs can
 be implemented in functional programming and type theory.}
+ be implemented in functional programming and type theory."
}
\end{chunk}
@@ 10539,6 +10541,171 @@ J. Symbolic Computation 5, 237259 (1988)
\section{To Be Classified} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{Chou, ShangChing}
+\index{Gao, XiaoShan}
+\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."
+}
+
+\end{chunk}
+
+\index{Chou, ShangChing}
+\index{Gao, XiaoShan}
+\index{Zhang, JingZhong}
+\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"
+}
+
+\end{chunk}
+
+\index{Sturmfels, Bernd}
+\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",
+ 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."
+}
+
+\end{chunk}
+
+\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)",
+ keywords = "axiomref",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Verstraete, Jacques}
+\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"
+}
+
+\end{chunk}
+
+\index{Koepf, Wolfram}
+\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",
+ 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."
+}
+
+\end{chunk}
+
\index{Aslaksen, Helmer}
\begin{chunk}{axiom.bib}
@article{Asla96,
@@ 11624,6 +11791,42 @@ J. Symbolic Computation 5, 237259 (1988)
\end{chunk}
+\index{Andrews, George}
+\index{Baxter, R.J.}
+\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"
+}
+
+\end{chunk}
+
+\index{Andrews, George}
+\begin{chunk}{axiom.bib}
+@article{Andr09,
+ author = "Andrews, George",
+ title = "The Meaning of Ramanujan Now and for the Future",
+ journal = "Ramanujan Journal",
+ volume = "20",
+ pages = "257273",
+ year = "2009",
+ keywords = "axiomref",
+ url = "http://www.personal.psu.edu/gea1/pdf/274.pdf",
+ paper = "Andr09.pdf",
+ abstract =
+ "December 22, 2010 marks the 123th anniversary of Ramanujan's
+ birth. In this paper we pay homage to this towering figure whose
+ mathematical discoveries so affected mathematics throughout the
+ twentieth century and into the twentyfirst."
+}
+
+\end{chunk}
+
\index{Antoine, Xavier}
\begin{chunk}{axiom.bib}
@article{Anto01,
@@ 11767,8 +11970,9 @@ American Mathematical Society (1994)
author = "Andrews, George E.",
title = "Ramanujan and SCRATCHPAD",
booktitle = "Proc. of 1984 MACSYM Users' Conference, July 1984",
+ location = "General Electric, Schenectady, NY",
year = "1984",
 pages = "383??",
+ pages = "383408",
keywords = "axiomref"
}
@@ 11781,10 +11985,40 @@ American Mathematical Society (1994)
title = "Application of Scratchpad to problems in special functions and
combinatorics",
booktitle = "Trends in Computer Algebra",
+ publisher = "Springer",
+ series = "Lecture Notes in Comp. Sci. 296",
year = "1988",
isbn = "3540189289",
keywords = "axiomref",
 pages = "158??"
+ pages = "159166",
+ abstract =
+ "Within the last few years, there have been numerous applications of
+ computer algebra to special functions. G. Gasper (Northwestern
+ University) has studied classical hypergeometric functions, and
+ W. Gosper (Symbolics, Inc.) has developed a large variety of
+ spectacular transformation and summation techniques for MACSYMA. The
+ purpose of this note is to explore some of the interface between
+ computer algebra and special functions. In section 2 we examine an
+ application of MACSYMA which inadequately relied, in my opinion, on
+ what was readily available in the literature on hypergeometric
+ series. In Section 3 we consider classical observations on sums of
+ powers of binomial coefficients. In Section 4 we consdier a problem of
+ D.M. Jackson wherein SCRATCHPAD and classical hypergeometric series
+ interact nicely. We close with a problem inspired by work in
+ statistical mechanics which leads us to question about algorithsm that
+ would be useful in computer algebra applications.
+
+ In this brief survey, we have illustrated some of the uses of computer
+ algebra. It might be objected that our work could well be carried out
+ in almost any computer language; so why bother with SCRATCHPAD? The
+ answer, of course, lies in the naturalness and simplicity of computer
+ algebra approaches to these problems. Expressions like (2.2), (3.1)
+ and (4.1) can be coded in SCRATCHPAD in one line exactly as they are
+ written. They can then be studied with minimal thought about the
+ computer and maximal concentration on what is happening. Often
+ mathematical research consists of sifting low grade ore, and when such
+ sifting requires ingenious programming skills it is likely not to be
+ carried out."
}
\end{chunk}
@@ 12284,18 +12518,18 @@ Soc. for Industrial and Applied Mathematics, Philadelphia (1990)
\index{Boehm, HansJ.}
\begin{chunk}{axiom.bib}
@inproceedings{Boe89,
+@article{Boeh89,
author = "Boehm, HansJ.",
title = "Type Inference in the Presence of Type Abstraction",
+ journal = "ACM SIGPLAN Notices",
+ volume = "24",
+ number = "7",
+ month = "July",
year = "1989",
pages = "192206",
keywords = "axiomref",
url = "http://www.acm.org/pubs/citations/proceedings/pldi/73141/p192boehm",
 paper = "Boe89.pdf",
 booktitle = "ACM SIGPLAN Notices",
 volume = "24",
 number = "7",
 month = "July",
+ paper = "Boeh89.pdf",
abstract = "
A number of recent programming language designs incorporate a type
checking system based on the GirardReynolds polymorphic
@@ 12425,15 +12659,18 @@ in [Wit87], p18
\end{chunk}
\index{Bronstein, Manuel}
\begin{chunk}{ignore}
\bibitem[Bronstein 89]{Bro89}
 author= "Bronstein, M.",
+\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",
ACM [ACM89] pages LCCN QA76.95.I59 1989
keywords = "axiomref",
+ doi = "https://dx.doi.org/10.1145/74540.74566",
+ paper = "Bron88.djvu",
abstract = "
We describe an algorithm, based on Risch's real structure theorem, that
determines explicitly all the algebraic relations among a given set of
@@ 12780,14 +13017,30 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
\index{Burge, William H.}
\index{Watt, Stephen M.}
\begin{chunk}{axiom.bib}
@techreport{BW87,
 author = "Burge, W. and Watt, S.",
+@techreport{Burg87,
+ author = "Burge, William and Watt, Stephen",
title = "Infinite structures in SCRATCHPAD II",
year = "1987",
institution = "IBM Research",
type = "Technical Report",
 number = "RC 12794",
 keywords = "axiomref"
+ number = "RC 12794 (\#57573)",
+ keywords = "axiomref",
+ url = "http://www.csd.uwo.ca/~watt/pub/reprints/1987eurocalinfinite.pdf",
+ paper = "Burg87.pdf",
+ abstract =
+ "An {\sl infinite structure} is a data structure which cannot be fully
+ constructed in any fixed amount of space. Several varieties of
+ infinite structures are currently supported in Scratchpad II: infinite
+ sequences, radix expansions, power series and continued fractions. Two
+ basic methods are employed to represent infinite structures:
+ selfreferential data structures and lazy evaluation. These may be
+ employed separately or in conjunction.
+
+ This paper presents recently developed facilities in Scratchpad II for
+ manipulating infinite structures. General techniques for manipulating
+ infinite structures are covered, as well as the higher level
+ manipulations on the various types of mathematical objects represented
+ by infinite structures."
}
\end{chunk}
@@ 13860,7 +14113,7 @@ Mathematical Sciences Department, IBM Thomas Watson Research Center 1984
Sundaresan, Christine J. and Sutor, Robert S. and Trager, Barry",
title = "SCRATCHPAD System Programming Language Manual",
year = "1984",
 keywords = "axiomref",
+ keywords = "axiomref"
}
\end{chunk}
@@ 13891,7 +14144,7 @@ Mathematical Sciences Department, IBM Thomas Watson Research Center 1984
"Computer Algebra: Systems and Algorithms for Algebraic Computation",
publisher = "Academic Press",
year = "1988",
 isbn ="0122042329",
+ isbn ="0122042301",
url = "http://staff.bath.ac.uk/masjhd/masternew.pdf",
paper = "Dave88.pdf",
keywords = "axiomref",
@@ 14717,7 +14970,49 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
year = "1998",
pages = "440446",
isbn = "3540510842",
 keywords = "axiomref"
+ 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 algebraic 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."
}
\end{chunk}
@@ 15209,6 +15504,65 @@ CODEN ITATEC. ISSN 09265473
\subsection{E} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{ElAlfy, Hazem Mohamed}
+\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",
+ 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.
+
+ The problem of implicitization is an active topic where research is
+ still taking place. Examples of further research points are included
+ in the conclusion"
+}
+
+\end{chunk}
+
\begin{chunk}{axiom.bib}
@misc{Ency16,
author = "Unknown",
@@ 15772,29 +16126,37 @@ Strasbourg, France, 1990 31pp
\index{Gebauer, R{\"u}diger}
\index{M{\"o}ller, H. Michael}
\begin{chunk}{ignore}
\bibitem[Gebauer 86]{GM86} Gebauer, R{\"u}diger; M{\"o}ller, H. Michael
+\begin{chunk}{axiom.bib}
+@inproceedings{Gebu86,
+ author = "Gebauer, R{\"u}diger and M{\"o}ller, H. Michael",
title = "Buchberger's algorithm and staggered linear bases",
In Bruce W. Char, editor. Proceedings of the 1986
Symposium on Symbolic and Algebraic Computation: SYMSAC '86, July 2123, 1986
Waterloo, Ontario, pp218221 ACM Press, New York, NY 10036, USA, 1986.
ISBN 0897911997 LCCN QA155.7.E4 A281 1986 ACM order number 505860
+ booktitle = "Proc. 1986 Symposium on Symbolic and Algebraic Computation",
+ series = "SYMSAC '86",
+ year = "1986",
+ pages = "218221",
+ publisher = "ACM Press",
+ isbn = "0897911997",
keywords = "axiomref",
+ doi = "http://dx.doi.org/10.1145/32439.32482"
+}
\end{chunk}
\index{Gebauer, R{\"u}diger}
\index{M{\"o}ller, H. Michael}
\begin{chunk}{ignore}
\bibitem[Gebauer 88]{GM88} Gebauer, R.; M{\"o}ller, H. M.
+\begin{chunk}{axiom.bib}
+@article{Geba88,
+ author = "Gebauer, Rudiger and Moller, H. Michael",
title = "On an installation of Buchberger's algorithm",
Journal of Symbolic Computation, 6(23) pp275286 1988
CODEN JSYCEH ISSN 07477171
 url = "http://www.sciencedirect.com/science/article/pii/S0747717188800488/pdf?md5=f6ccf63002ef3bc58aaa92e12ef18980&pid=1s2.0S0747717188800488main.pdf",
+ journal = "Journal of Symbolic Computation",
+ volume = "6",
+ number = "23",
+ pages = "275286",
+ year = "1988",
paper = "GM88.pdf",
keywords = "axiomref",
 abstract = "
 Buchberger's algorithm calculates Groebner bases of polynomial
+ 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
@@ 15805,6 +16167,7 @@ CODEN JSYCEH ISSN 07477171
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."
+}
\end{chunk}
@@ 15935,11 +16298,86 @@ LCCN QA76.95.I57 1988 Conference held jointly with AAECC6
\index{Gianni, Patrizia}
\index{Mora, T.}
\begin{chunk}{ignore}
\bibitem[Gianni 89b]{GM89} Gianni, P.; Mora, T.
 title = "Algebraic solution of systems of polynomial equations using Gr{\"o}bner bases.",
In Huguet and Poli [HP89], pp247257 ISBN 3540510826 LCCN QA268.A35 1987
+\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."
+}
\end{chunk}
@@ 16235,8 +16673,9 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
series = "SYMSAC 71",
year = "1971",
pages = "4258",
+ doi = "http://dx.doi.org/10.1145806266",
url = "http://delivery.acm.org/10.1145/810000/806266/p42griesmer.pdf",
 paper = "GJ71.pdf",
+ paper = "Grie71.pdf",
keywords = "axiomref",
abstract = "
The SCRATCHPAD/1 system is designed to provide an interactive symbolic
@@ 16252,23 +16691,42 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
\index{Griesmer, James H.}
\index{Jenks, Richard D.}
\begin{chunk}{ignore}
\bibitem[Griesmer 72a]{GJ72a} Griesmer, J.; Jenks, R.
+\begin{chunk}{axiom.bib}
+@techreport{Grie72,
+ author = "Griesmer, James H. and Jenks, Richard D.",
title = "Experience with an online symbolic math system SCRATCHPAD",
in Online'72 [Onl72] ISBN 0903796023 LCCN QA76.55.O54 1972 Two volumes
 keywords = "axiomref",
+ year = "1972",
+ isbn = "0903796023",
+ keywords = "axiomref"
+}
\end{chunk}
\index{Griesmer, James H.}
\index{Jenks, Richard D.}
\begin{chunk}{ignore}
\bibitem[Griesmer 72b]{GJ72b} Griesmer, James H.; Jenks, Richard D.
+\begin{chunk}{axiom.bib}
+@article{Grie72,
+ author = "Griesmer, James H. and Jenks, Richard D.",
title = "SCRATCHPAD: A capsule view",
ACM SIGPLAN Notices, 7(10) pp93102, 1972. Proceedings of the symposium
on Twodimensional manmachine communications. Mark B. Wells and
James B. Morris (eds.).
+ journal = "ACM SIGPLAN Notices",
+ volume = "7",
+ number = "10",
+ pages = "93102",
+ year = "1972",
+ comment = "Proc. Symp. Twodimensional manmachine communications",
keywords = "axiomref",
+ doi = "http://dx.doi.org/10.1145807019",
+ abstract =
+ "SCRATCHPAD is an interactive system for algebraic manipulation
+ 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."
+}
\end{chunk}
@@ 17108,13 +17566,16 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{ignore}
\bibitem[Jenks 71]{Jen71} Jenks, R. D.
+\begin{chunk}{axiom.bib}
+@techReport{Jenk71,
+ author = "Jenks, Richard D.",
title = "META/PLUS: The syntax extension facility for SCRATCHPAD",
Research Report RC 3259, International Business Machines, Inc., Thomas J.
Watson Research Center, Yorktown Heights, NY, USA, 1971
% REF:00040
 keywords = "axiomref",
+ type = "Research Report",
+ number = "RC 3259",
+ institution = "IBM Research",
+ year = "1971",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 17129,21 +17590,44 @@ Watson Research Center, Yorktown Heights, NY, USA, 1971
number = "4",
pages = "101111",
year = "1974",
 keywords = "axiomref"
+ doi = "http://dx.doi.org/10.1145807051",
+ keywords = "axiomref",
+ abstract =
+ "SCRATCHPAD is an interactive system for symbolic mathematical
+ computation. Its user language, originally intended as a
+ 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."
}
\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{ignore}
\bibitem[Jen76]{Jen76} Jenks, Richard D.
+\begin{chunk}{axiom.bib}
+@inproceedings{Jenk76,
+ author = "Jenks, Richard D.",
title = "A pattern compiler",
In Richard D. Jenks, editor,
SYMSAC '76: proceedings of the 1976 ACM Symposium on Symbolic and Algebraic
Computation, August 1012, 1976, Yorktown Heights, New York, pp6065,
ACM Press, New York, NY 10036, USA, 1976. LCCN QA155.7.EA .A15 1976
QA9.58.A11 1976
+ booktitle = "Proc. 1976 ACM Symposium on Symbolic and Algebraic Computation",
+ series = "SYMSAC '76",
+ year = "1976",
+ publisher = "ACM Press",
keywords = "axiomref",
+ doi = "http://dx.doi.org/10.1145806324",
+ abstract =
+ "A pattern compiler for the SCRATCHPAD system provides an efficient
+ 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."
+}
\end{chunk}
@@ 17208,11 +17692,15 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{ignore}
\bibitem[Jenks 84a]{Jen84a} Jenks, Richard D.
 title = "The new SCRATCHPAD language and system for computer algebra",
In Golden and Hussain [GH84], pp409??
 keywords = "axiomref",
+\begin{chunk}{axiom.bib}
+@inproceedings{Jenk84a,
+ author = "Jenks, Richard D.",
+ title = "The New SCRATCHPAD Language and System for Computer Algebra",
+ booktitle = "Proc. 1984 MACSYMA Users Conference",
+ year = "1984",
+ pages = "409??",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 17355,13 +17843,18 @@ In Golden and Hussain [GH84], pp409??
\index{Jenks, Richard D.}
\index{Sutor, Robert S.}
\index{Watt, Stephen M.}
\begin{chunk}{ignore}
\bibitem[Jenks 87]{JWS87} Jenks, Richard D.; Sutor, Robert S.;
Watt, Stephen M.
 title = "Scratchpad II: an Abstract Datatype System for Mathematical Computation'",
Proceedings Trends in Computer Algebra, Bad Neuenahr, LNCS 296,
Springer Verlag, (1987)
 keywords = "axiomref",
+\begin{chunk}{axiom.bib}
+@inproceedings{Jenk87,
+ author = "Jenks, Richard D. and Sutor, Robert S. and Watt, Stephen M.",
+ title = "Scratchpad II: an Abstract Datatype System for
+ Mathematical Computation'",
+ booktitle = "Proceedings Trends in Computer Algebra",
+ series = "Lecture Notes in Computer Science 296",
+ publisher = "SpringerVerlag",
+ year = "1987",
+ comment = "IBM Research Report RC 12327 (\#55257) See Jenks86.pdf",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 17369,11 +17862,27 @@ Springer Verlag, (1987)
\index{Sutor, Robert S.}
\index{Watt, Stephen M.}
\begin{chunk}{ignore}
\bibitem[Jenks 88]{JSW88} Jenks, R. D.; Sutor, R. S.; Watt, S. M.
 title = "Scratchpad II: An abstract datatype system for mathematical computation",
In Jan{\ss}en [Jan88],
pp12?? ISBN 3540189289, 0387189289 LCCN QA155.7.E4T74 1988
+@inproceedings{Jenk88,
+ author = "Jenks, Richard D. and Sutor, Robert S. and Watt, Stephen M.",
+ title = "Scratchpad II: An Abstract Datatype System for Mathematical
+ Computation",
+ booktitle = "Mathematical Aspects of Scientific Software",
+ year = "1988",
+ pages = "157182",
+ publisher = "Springer",
+ isbn = "0387189289",
keywords = "axiomref",
+ abstract =
+ "Scratchpad II is an abstract datatype language and system that is
+ under development in the Computer Algebra Group, Mathematical Sciences
+ Department, at the IBM Thomas J. Watson Research Center. Many
+ different kinds of computational objects and data structures are
+ provided. Facilities for computation include symbolic integration,
+ differentation, factorization, solution of equations and linear
+ algebra. Code economy and modularity is achieved by having polymorphic
+ packages of functions that may create datatypes. The use of categories
+ makes these facilities as general as possible."
+}
\end{chunk}
@@ 17432,34 +17941,6 @@ Draft September 5, 1988
\index{Jenks, Richard D.}
\index{Sutor, Robert S.}
\index{Watt, Stephen M.}
\begin{chunk}{axiom.bib}
@book{Jenk88e,
 author = "Jenks, Richard D. and Sutor, Robert S. and Watt, Stephen M.",
 title = "Scratchpad II: An Abstract Datatype System for Mathematical
 Computation",
 booktitle = "Mathematical Aspects of Scientific Software",
 year = "1988",
 pages = "157182",
 publisher = "Springer",
 isbn = "0387189289",
 keywords = "axiomref",
 abstract =
 "Scratchpad II is an abstract datatype language and system that is
 under development in the Computer Algebra Group, Mathematical Sciences
 Department, at the IBM Thomas J. Watson Research Center. Many
 different kinds of computational objects and data structures are
 provided. Facilities for computation include symbolic integration,
 differentation, factorization, solution of equations and linear
 algebra. Code economy and modularity is achieved by having polymorphic
 packages of functions that may create datatypes. The use of categories
 makes these facilities as general as possible."
}

\end{chunk}

\index{Jenks, Richard D.}
\index{Sutor, Robert S.}
\begin{chunk}{axiom.bib}
@book{Jenk92,
author = "Jenks, Richard D. and Sutor, Robert S.",
@@ 17559,7 +18040,7 @@ Draft September 5, 1988
Finally, we show that isolated values of the integer partition
function $p(n)$ can be computed rigorously with softly optimal
 complexity by means of the HardyRamanuganRademacher formula and
+ complexity by means of the HardyRamanujanRademacher formula and
careful numerical evaluation.
We provide open source implementations which run significantly faster
@@ 17766,6 +18247,20 @@ SIGSAM Communications in Computer Algebra, 157 2006
\end{chunk}
+\index{Kanigel, Robert}
+\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"
+}
+
+\end{chunk}
+
\index{Kaplan, Michael}
\begin{chunk}{axiom.bib}
@book{Kapl05,
@@ 18315,11 +18810,34 @@ ISSN 03043975
\index{Kusche, K.}
\index{Kutzler, B.}
\index{Mayr, H.}
\begin{chunk}{ignore}
\bibitem[Kusche 89]{KKM89} Kusche, K.; Kutzler, B.; Mayr, H.
 title = "Implementation of a geometry theorem proving package in SCRATCHPAD II",
In Davenport [Dav89] pp246257 ISBN 3540515178 LCCN QA155.7.E4E86 1987
+\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",
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."
+}
\end{chunk}
@@ 19069,24 +19587,48 @@ June 2, 1997
\end{chunk}
\index{Lucks, Michael}
\begin{chunk}{ignore}
\bibitem[Lucks 86]{Luc86} Lucks, Michael
+\begin{chunk}{axiom.bib}
+@inproceedings{Luck86,
+ author = "Lucks, Michael",
title = "A fast implementation of polynomial factorization",
In Bruce W. Char, editor, Proceedings of the 1986 Symposium on Symbolic
and Algebraic Computation: SYMSAC '86, July 2123, 1986, Waterloo, Ontario,
pp228232 ACM Press, New York, NY 10036, USA, 1986. ISBN 0897911997
LCCN QA155.7.E4 A281 1986 ACM order number 505860
+ booktitle = "Proc. 1986 Symposium on Symbolic and Algebraic Computation",
+ series = "SYMSAC '86",
+ year = "1986",
+ location = "Waterloo, Ontario",
+ pages = "228232",
+ publisher = "ACM Press",
+ isbn = "0897911997",
keywords = "axiomref",
+ doi = "http://dx.doi.org/10.1145/32439.32485",
+ abstract =
+ "A new package for factoring polynomials with integer coefficients is
+ 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."
+}
\end{chunk}
\index{Lueken, E. }
\begin{chunk}{ignore}
\bibitem[Lueken 77]{Lue77} Lueken, E.
+\index{Lueken, E.}
+\begin{chunk}{axiom.bib}
+@mastersthesis{Luek77,
+ author = "Lueken, E.",
title = "Ueberlegungen zur Implementierung eines Formelmanipulationssystems",
Master's thesis, Technischen Universit{\"{a}}t CaroloWilhelmina zu
Braunschweig. Braunschweig, Germany, 1977
 keywords = "axiomref",
+ school = {Technischen Universit{\"{a}}t CaroloWilhelmina zu Braunschweig},
+ address = "Braunschweig, Germany",
+ year = "1977",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 19418,6 +19960,36 @@ In Miola [Mio93], pp8194 ISBN 354057235X LCCN QA76.9.S88I576 1993
\end{chunk}
+\index{Monagan, Michael B.}
+\index{Gonnet, Gaston H.}
+\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",
+ 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."
+}
+
+\end{chunk}
+
\index{Monagan, Michael}
\index{Pearce, Roman}
\begin{chunk}{axiom.bib}
@@ 19658,12 +20230,18 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
\end{chunk}
\index{Norman, Arthur C.}
\begin{chunk}{ignore}
\bibitem[Norman 75]{Nor75} Norman, A. C.
 title = "Computing with formal power series",
ACM Transactions on Mathematical Software, 1(4) pp346356
Dec. 1975 CODEN ACMSCU ISSN 00983500
+\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",
keywords = "axiomref",
+ doi = "10.1145/355656.355660"
+}
\end{chunk}
@@ 20025,14 +20603,20 @@ Computers and Mathematics November 1993, Vol 40, Number 9 pp12031210
\end{chunk}
\index{Purtilo, J.}
\begin{chunk}{ignore}
\bibitem[Purtilo 86]{Pur86} Purtilo, J.
 title = "Applications of a software interconnection system in mathematical problem solving environments",
In Bruce W. Char, editor. Proceedings of the
1986 Symposium on Symbolic and Algebraic Computation: SYMSAC '86, July 2123,
ACM Press, New York, NY 10036, USA, 1986. ISBN 0897911997 LCCN QA155.7.E4
A281 1986 ACM order number 505860
+\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",
keywords = "axiomref",
+ doi = "http://dx.doi.org/10.1145/32439.32443"
+}
\end{chunk}
@@ 20586,11 +21170,27 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
\index{Schwarz, Fritz}
\begin{chunk}{ignore}
\bibitem[Schwarz 88]{Sch88} Schwarz, F.
 title = "Programming with abstract data types: the symmetry package SPDE in Scratchpad'",
In Jan{\ss}en [Jan88], pp167176, ISBN 3540189289,
0387189289 LCCN QA155.7.E4T74 1988
+@inproceedings{Schw88,
+ author = "Schwarz, Fritz",
+ title = "Programming with abstract data types: the symmetry package
+ SPDE in Scratchpad'",
+ booktitle = "Trends in Computer Algebra",
+ series = "Lecture Notes in Computer Science 296",
+ year = "1988",
+ pages = "167176",
+ isbn = "3540189289",
keywords = "axiomref",
+ abstract =
+ "The main problem which occurs in developing Computer Algebra packages
+ for special areas in mathematics is the complexity. The unique concept
+ which is advocated to cope with that problem is the introduction of
+ suitable abstract data types. The corresponding decomposition into
+ modules makes it much easier to develop, maintain and change the
+ program. After introducing the relevant concepts from software
+ engineering they are elaborated by means of the symmetry analysis of
+ differential equations and the Scratchpad package SPDE which
+ abbreviates Symmetries of Partial Differential Equations."
+}
\end{chunk}
@@ 20824,23 +21424,54 @@ in Calmet [Cal94] pp103104
\index{Senechaud, P.}
\index{Siebert, F.}
\index{Villard, Gilles}
\begin{chunk}{ignore}
\bibitem[SSV87]{SSV87} Senechaud, P.; Siebert, F.; Villard G.
 title =
 "Scratchpad II: Pr{\'e}sentation d'un nouveau langage de calcul formel",
Technical Report 640M, TIM 3 (IMAG), Grenoble, France, Feb 1987
 keywords = "axiomref",
+\begin{chunk}{axiom.bib}
+@techreport{Sene87,
+ author = "Senechaud, P. and Siebert, F. and Villard, Gilles",
+ title = "Scratchpad II: Pr{\'e}sentation d'un nouveau langage de
+ calcul formel",
+ type = "Technical Report",
+ number = "640M",
+ institution = "TIM 3 (IMAG)",
+ address = "Grenoble, France",
+ year = "1987",
+ keywords = "axiomref"
+}
\end{chunk}
\index{Shannon, D.}
\index{Sweedler, M.}
\begin{chunk}{ignore}
\bibitem[Shannon 88]{SS88} Shannon, D.; Sweedler, M.
 title = "Using Gr{\"o}bner bases to determine algebra membership, split surjective algebra homomorphisms determine birational equivalence",
Journal of Symbolic Computation 6(23) pp267273
Oct.Dec. 1988 CODEN JSYCEH ISSN 07477171
+\begin{chunk}{axiom.bib}
+@article{Shan88,
+ author = "Shannon, D. and Sweedler, M.",
+ title = "Using Gr{\"o}bner bases to determine algebra membership,
+ split surjective algebra homomorphisms determine birational
+ equivalence",
+ journal = "Journal of Symbolic Computation",
+ volume = "6",
+ number = "23",
+ pages = "267273",
+ year = "1988",
keywords = "axiomref",
+ abstract =
+ "This paper presents a simple algorithm, based on Groebner bases, to
+ test if a given polynomial $g$ of $k(X_1,\ldots,X_n)$ lies in
+ $k(f_1,\ldots,f_m)$ where $k$ is a field, $X_1,\ldots,X_n$ are
+ indeterminates over $k$ and $f_1,\ldots,f_m$ in $k(X_1,\ldots,X_n)$.
+ If so, the algorithm produces a polynomial $P$ of $m$ variables
+ where $g=P(f_1,\ldots,f_m)$. Say $\Omega(B)$ to $k(X_1,\ldots,X_n)$ is a
+ homomorphism where $\Omega(b_i)=f_i$, for algebra generators ($b_i$)
+ contained in / implied by $B$. If $\Omega$ is onto, the algorithm
+ gives a homomorphism $\lambda k(X_1,\ldots,X_n)$ to $B$, where the
+ composite $\Omega \lambda$ is the identity map. In particular, the
+ algorithm computes the inverse of algebra automorphisms of the
+ polynomial ring. A variation of the test if
+ $k(f_1,\ldots,f_m)=k(X_1,\ldots,X_n)$ tells if
+ $k(f_1,\ldots,f_m)=k(X_1,\ldots,X_n). Existing computer algebra
+ systems, such as IBM's SCRATCHPAD II, have Groebner basis packages
+ which allow the user to specify a term ordering sufficient to carry
+ out the algorithm."
+}
\end{chunk}
@@ 21256,13 +21887,13 @@ LCCN QA76.76.A65 S95 1992
title = "The type inference and coercion facilities in the Scratchpad II
interpreter",
journal = "SIGPLAN Notices",
 comment = "IBM Research Report RC 12595",
volume = "22",
number = "7",
pages = "5663",
year = "1987",
isbn = "0897912357",
paper = "Suto87.pdf",
+ comment = "IBM Research Report RC 12595 (\#56575)",
keywords = "axiomref",
abstract =
"The Scratchpad II system is an abstract datatype programming
@@ 22423,6 +23054,24 @@ Oxford University Press (2000) ISBN0195125169
\end{chunk}
\index{Yun, David Y.Y}
+\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",
+}
+
+\end{chunk}
+
+\index{Yun, David Y.Y}
\begin{chunk}{ignore}
\bibitem[Yun 83]{Yun83} Yun, David Y.Y.
title = "Computer Algebra and Complex Analysis",
diff git a/changelog b/changelog
index 627fd33..95daabd 100644
 a/changelog
+++ b/changelog
@@ 1,8 +1,10 @@
20160704 tpd src/axiomwebsite/patches.html 20160706.02.tpd.patch
20160705 tpd books/bookvolbib Axiom Citations in the Literature
20160704 tpd src/axiomwebsite/patches.html 20160706.01.tpd.patch
20160705 tpd books/bookvolbib Axiom Citations in the Literature
20160704 tpd src/axiomwebsite/patches.html 20160705.01.tpd.patch
+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
+20160706 tpd books/bookvolbib Axiom Citations in the Literature
+20160706 tpd src/axiomwebsite/patches.html 20160706.01.tpd.patch
+20160706 tpd books/bookvolbib Axiom Citations in the Literature
+20160705 tpd src/axiomwebsite/patches.html 20160705.01.tpd.patch
20160705 tpd books/bookvolbib Axiom Citations in the Literature
20160704 tpd src/axiomwebsite/patches.html 20160704.04.tpd.patch
20160704 tpd books/bookvolbib Axiom Citations in the Literature
diff git a/patch b/patch
index 663499d..e74e908 100644
 a/patch
+++ b/patch
@@ 2,589 +2,717 @@ books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
index{Caruso, Fabrizio}
+\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@misc{Caru10,
 author = "Caruso, Fabrizio",
 title = "Factorization of NonCommutative Polynomials",
 url = "https://arxiv.org/pdf/1002.3108.pdf",
 paper = "Caru10.pdf",
+@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"
+}
+
+\end{chunk}
+
+\index{Griesmer, James H.}
+\index{Jenks, Richard D.}
+\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",
keywords = "axiomref",
 year = "2010",
+ doi = "http://dx.doi.org/10.1145807019",
abstract =
 "We describe an algorithm for the factorization of noncommutative
 polynomials over a field. The first sketch of this algorithm appeared
 in an unpublished manuscript (literally hand written notes) by James
 H. Davenport more than 20 years ago. This version of the algorithm
 contains some improvements with respect to the original sketch. An
 improved version of the algorithm has been fully implemented in the
 Axiom computer algebra system."
+ "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."
}
\end{chunk}
\index{Chen, Changbo}
\index{Davenport, James H.}
\index{May, John P.}
\index{Maza, Marc Moreno}
\index{Xia, Bican}
\index{Xiao, Rong}
+\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@misc{Chen10,
 author = "Chen, Changbo and Davenport, James H. and May, John P. and
 Maza, Marc Moreno and Xia, Bican and Xiao, Rong",
 title = "Triangular Decomposition of Semialgebraic Systems",
 year = "2010",
 url = "https://arxiv.org/pdf/1002.4784.pdf",
 paper = "Chen10.pdf",
+@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",
abstract =
 "Regular chains and triangular decompositions are fundamental and
 welldeveloped tools for describing the complex solutions of
 polynomial systems. This paper proposes adaptations of these tools
 focusing on solutions of the real analogue: semialgebraic systems.

 We show that any such system can be decomposed into finitely many
 regular semialgebraic systems. We propose two specifications of such
 a decomposition and present corresponding algorithms. Under some
 assumptions, one type of decomposition can be computed in singly
 exponential time w.r.t. the number of variables. We implement our
 algorithms and the experimental results illustrate their
 effectiveness."
+ "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."
}
\end{chunk}
\index{Certik, Ondrej}
+\index{Norman, Arthur C.}
\begin{chunk}{axiom.bib}
@misc{Cert16,
 author = "Certik, Ondrej",
 title = "SymPy vs. Axiom",
 url = "https://github.com/sympy/sympy/wiki/SymPyvs.Axiom",
 keywords = "axiomref"
+@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",
+ keywords = "axiomref",
+ doi = "10.1145/355656.355660"
}
\end{chunk}
\index{Baker, Martin}
+\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@misc{Bake16a,
 author = "Baker, Martin",
 title = "Axioms in Axiom",
+@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",
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."
+}
+
+\end{chunk}
+
+\index{Lueken, E.}
+\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"
+}
+
+\end{chunk}
+
+\index{Kanigel, Robert}
+\begin{chunk}{axiom.bib}
+ author = "Kanigel, Robert",
+ title = "OldQuotes",
+ url = "http://www.oldquotes.com",
year = "2016",
 url = "http://www.euclideanspace.com/prog/scratchpad/axiomsinAxiom"
+ 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"
+}
+
+\end{chunk}
+
+\index{Andrews, George}
+\index{Baxter, R.J.}
+\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"
+}
+
+\end{chunk}
+
+\index{Koepf, Wolfram}
+\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",
+ 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."
}
\end{chunk}
\index{Joyner, W. D.}
@misc{Joyn08,
 author = "Joyner, W. D.",
 title = "Open Source Mathematical Software: A White Paper",
 url = "http://wdjoyner.com/writing/research/oscasnsfwhitepaper12.tex",
 paper = "Joyn08.tex",
+\index{Verstraete, Jacques}
+\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"
+}
+
+\end{chunk}
+
+\index{Lucks, Michael}
+\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",
+ 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."
+}
+
+\end{chunk}
+
+\index{Purtilo, J.}
+\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",
keywords = "axiomref",
 year = "2008"
+ doi = "http://dx.doi.org/10.1145/32439.32443"
}
\index{Karpinski, Stefan}
+\end{chunk}
+
\begin{chunk}{axiom.bib}
@misc{Karp14,
 author = "Karpinski, Stefan",
 title = "Re: Symbolic Math: try a translation of Axiom to Julia?",
+@misc{NTCI16,
+ author = "NTCIR",
+ title = "Axiom (computer algebra system)",
url =
 "https://groups.google.com/forum/#!msg/juliadev/NTfS9fJuIcE/MINQuQuGfoUJ",
+ "http://ntcir11wmc.nii.ac.jp/index.php/Axiom\_(computer_algebra_system)",
keywords = "axiomref",
year = "2016"
}
\end{chunk}
+\index{Gebauer, R{\"u}diger}
+\index{M{\"o}ller, H. Michael}
\begin{chunk}{axiom.bib}
@misc{America,
 author = "america.pink",
 title = "Axiom (computer algebra system)",
 year = "2016",
+@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",
+ year = "1988",
+ paper = "GM88.pdf",
keywords = "axiomref",
 url = "http://america.pink/axiomcomputeralgebrasystem_526647.html"
+ 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."
}
\end{chunk}
\index{Davenport, James H.}
\index{Siret, Y.}
\index{Tournier, E.}
+\index{Bronstein, Manuel}
\begin{chunk}{axiom.bib}
@book{Dave88,
 author = "Davenport, James H. and Siret, Y. and Tournier, E.",
 title =
 "Computer Algebra: Systems and Algorithms for Algebraic Computation",
 publisher = "Academic Press",
 year = "1988",
 isbn ="0122042329",
 url = "http://staff.bath.ac.uk/masjhd/masternew.pdf",
 paper = "Dave88.pdf",
+@inproceedings{Bron89,
+ author = "Bronstein, Manuel",
+ title = "Simplification of real elementary functions",
+ booktitle = "Proc. ISSAC 1989",
+ series = "ISSAC 1989",
+ year = "1989",
+ pages = "207211",
+ isbn = "0897913256",
keywords = "axiomref",
 abstract =
 "The need for a good general text on Computer Algebra has never been
 greater. From the very beginning, computers have been used for
 numerical calculation. It is not always realized however that their
 use for mathematical calculation of a symbolic nature has a history
 almost as long. It is only recently that improvement in algorithms,
 the development of small systems and the emergence of powerful
 workstations have combined to make Computer Algebra systems much more
 widely available and an increasingly important tool for almost all
 users of Mathematics. Part of the reason why Computer Algebra was for
 so long something of an esoteric discipline, has surely been the lack
 of textbooks on the subject. The arrival of the present volume on the
 scene has thus been particularly fortunate.

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

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

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

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

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

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

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

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

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

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

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

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

 This book definitely represents one of the best introductions to
 computer algebra accessible to beginners and researchers."
+ 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."
}
\end{chunk}
\index{Heck, Andre}
+\index{Dicrescenzo, C.}
+\index{Duval, Dominique}
\begin{chunk}{axiom.bib}
@book{Heck93,
 author = "Heck, Andre",
 title = "Introduction to Maple",
 year = "1993",
 publisher = "SpringerVerlag",
+@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",
keywords = "axiomref",
abstract =
 "This is an introductory book on one of the most powerful computer
 algebra systems, viz, Maple: The primary emphasis in this book is on
 learning those things that can be done with Maple and how it can be
 used to solve mathematical problems. In this book usage of Maple as a
 programming language is not discussed at a higher level than that of
 defining simple procedures and using simple language constructs.
 However, the Maple data structures are discussed in detail.

 This book is divided into eighteen chapters spanning a variety of
 topics. Starting with an introduction to symbolic computation and
 other similar computer algebra systems, this book covers several
 topics like polynomials and rational functions, series,
 differentiation and integration, differential equations, linear
 algebra, 2D and 3D graphics, etc. The applications covered include
 kinematics of the Stanford manipulator, a 3component model for
 cadmium transfer through the human body, molecularorbital Hückel
 theory, prolate spheroidal coordinates and MoorePenrose inverses.

 At the end of each chapter, a good number of excercises is given. A
 list of relevant references is also given at the end of the book.
 This book is very useful to all users of Maple package."
+ "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."
}
\end{chunk}
\index{Lazard, Daniel}
+\index{Yun, David Y.Y}
\begin{chunk}{axiom.bib}
@InProceedings{Laza93,
 author = "Lazard, Daniel",
 title = "On the representation of rigidbody motions and its application
 to generalized platform manipulators",
 booktitle = "Proc. Workshop Computational Kinematics",
 year = "1993",
 location = "Dagstuhl Castle, Germany",
 publisher = "Kluwer Academic Publishers",
 pages = "175181",
+@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",
 abstract =
 "Different ways for representing rigid body motions (direct isometries)
 by a computer are presented. It turns out that the choice between them
 may have a dramatic effect on the difficulty of a computation or of a
 proof. As an application, a computational proof is given of the fact
 that the direct kinematic problem for the generalized Stewart platform
 has at most 40 complex solutions."
+ paper = "Yunx76.djvu",
+ url =
+ "http://lib.org/by/\_djvu\_Papers/Computer\_algebra/Algebraic\%20numbers",
}
\end{chunk}
\index{Mishra, Bhubaneswar}
+\index{Gianni, Patrizia}
+\index{Mora, T.}
\begin{chunk}{axiom.bib}
@book{Mish93,
 author = "Mishra, Bhubaneswar",
 title = "Algorithmic Algebra",
 publisher = "SpringerVerlag",
 series = "Texts and Monographs in Computer Sciences",
 year = "1993",
+@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 =
 "This book is based on a graduate course in computer science taught in
 1987. The following topics are covered: computational ideal theory,
 solving systems of polynomial equations, elimination theory, real
 algebra, as well as an introduction chapter and two chapters with the
 needed algebraic background. The book is selfcontained and the proofs
 are given with many details.

 It is clear that this book is only an introduction to the topic and
 does not cover the many improvements that appeared in the last 7 years
 about for example the computation of Groebner basis, polynomial
 solving, multivariate resultants and algorithms in real
 algebra. Choices had to be made to keep the content of a reasonable
 size and the complexity issues are not considered.

 The choice of topics is excellent, there are many exercises and
 examples. It is a very useful book."
+ "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."
}
\end{chunk}
\index{Scheerhorn, Alfred}
+\index{Sturmfels, Bernd}
\begin{chunk}{axiom.bib}
@misc{Sche93,
 author = "Scheerhorn, Alfred",
 title = "Presentation of the algebraic closure of finite fields and
 tracecompatible polynomial sequences",
 comment = "Darstellungen des algebraischen Abschlusses endlicher Korper
 und spurkompatible Polynomfolgen",
 year = "1993",
 keywords = "axiomref",
+@misc{Stur00,
+ author = "Sturmfels, Bernd",
+ title = "Solving Systems of Polynomial Equations",
+ url = "https://math.berkeley.edu/~bernd/cbms.pdf",
+ paper = "Stur00.pdf",
+ year = "2000",
abstract =
 "For numerical experiments concerning various problems in a finite
 field $\mathbb{F}_q$ it is useful to have an explicit data
 presentation $\mathbb{F}_{q^m}$ of for large $m$, and a method for the
 construction of towers
 \[\mathbb{F}_q \subset \mathbb{F}_{q^{d_1}} \subset \cdots \subset
 \mathbb{F}_{q^{d_k}} = \mathbb{F}_{q^m}\]
 In order to avoid the identification problem it is advantageous to
 have all fields in the tower presented by properly chosen normal bases,
 whereby the embedding
 $\mathbb{F}_{q^{d_i}} \subset \mathbb{F}_{q^{d_{i+1}}}$
 is given by the trace function.

 The following notion is introduced: A sequence of polynomials
 $\{f_n  n \ge 1\}$ with degree$(f_n)=n$ called tracecompatible over
 $\mathbb{F}_q$ if (1) $f_n$ is a normal polynomial over $\mathbb{F}_q$,
 (2) if $\alpha_n \in \mathbb{F}_{q^n}$ is a root of $f_n$, then for any
 proper divisor $d$ of $n$ the trace of $\alpha_n$ over $\mathbb{F}_{q^d}$
 is a root of $f_d$.

 The main goal of the dissertation is to give algorithms for
 construction of sequences of tracecompatible polynomials and to
 present explicit numerical data. An analogous notion of
 normcompatible sequences is also introduced and studied.

 The dissertation consists of four chapters and a supplement, as
 follows: (1) Basic notions (131). (2) Presentation of the algebraic
 closure of a finite field (3259). (3) Sequences of polynomials and
 sequences of elements (60115). (4) Implementations (118139). (5)
 Supplement (142171).

 In chapters (1)–(3) various known results and algorithms are
 collected, and new results are added and compared with those
 previously used.

 The numerical results in the supplement contain sequences of
 tracecompatible polynomials of degree $n$, where $n \le 100$, and
 $q=2,3,5,7,11,13$. For implementation, the computeralgebra system
 AXIOM has been used. The details contained in this dissertation are
 not readily describable in a short review."
+ "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."
}
\end{chunk}
\index{Singer, Michael F.}
\index{Ulmer, Felix}
+\index{Monagan, Michael B.}
+\index{Gonnet, Gaston H.}
\begin{chunk}{axiom.bib}
@article{Sing93,
 author = "Singer, Michael F. and Ulmer, Felix",
 title = "Galois groups of second and third order linear differential
 equations",
 journal = "J. Symb. Comput.",
 volume = "16",
 number = "1",
 pages = "936",
 year = "1993",
+@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",
keywords = "axiomref",
 paper = "Sing93.pdf",
abstract =
 "The authors discuss the first problem of Galois theory of differential
 equations. Let $F$ be an ordinary (for simplicity) differential field
 and $L(y)=0$ be an ordinary linear differential equation over $F$. How
 can one calculate the Galois group of $L$ over $F$? The authors
 suppose a new approach to the problem. They reduce it to the problem
 of finding solutions of linear differential equations in $F$ and to
 the factorization problem of such equations over $F$. These allow them
 to give simple necessary and sufficient conditions for a second order
 linear differential equation to have Liouvillian solutions and for a
 third order linear differential equation to have Liouvillian solutions
 or to be solvable in terms of second order equations."
}
+ "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."
+}
\end{chunk}
\index{Singer, Michael F.}
\index{Ulmer, Felix}
+\index{Kusche, K.}
+\index{Kutzler, B.}
+\index{Mayr, H.}
\begin{chunk}{axiom.bib}
@article{Sing93a,
 author = "Singer, Michael F. and Ulmer, Felix",
 title = "Liouvillian and algebraic solutions of second and third order
 linear differential equations",
 journal = "J. Symb. Comput.",
 volume = "16",
 number = "1",
 pages = "3773",
 year = "1993",
 paper = "Sing93a.pdf",
+@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",
keywords = "axiomref",
 abstract =
 "Let $F$ be an ordinary differential field of characteristic 0 and
 $L \in F $ be a linear homogeneous polynomial. How can one find the
 Liouvillian solutions of $L(y)=0$? In the paper this problem is
 reduced to the problems of (1) factorization and (2) finding $u$
 solutions such that $\frac{u^{\prime}}{y} \in F$ of $L$ and some
 polynomials associated with it (symmetric powers of $L$).

 Now there are the algorithms for the solution of the last problems for
 $F=\mathbb{Q}(x)$ [see D. Yu. Grigor’ev, J. Symb. Comput. 10, 737
 (1990; Zbl 0728.68067) and M. F. Singer, Am. J. Math. 103, 661682
 (1981; Zbl 0477.12026)].

 For polynomials $L$ of the second and third order the authors provide
 full investigation of the most difficult case when the solution $u$ of
 $L(y)$ is algebraic. They show that one can compute the minimal
 polynomial $P(y) \in F[y]$ of $u$. We note that the authors
 essentially used the tools of representation theory, invariant theory
 and computer algebra."
+ 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."
}
\end{chunk}
\index{Smith, Geoff C.}
+\index{ElAlfy, Hazem Mohamed}
\begin{chunk}{axiom.bib}
@article{Smit93,
 author = "Smith, Geoff C.",
 title = "Group theory results with machine generated proofs",
 journal = "An. Univ. Timis., Ser. Mat.Inform.",
 volume = "31",
 number = "2",
 pages = "273280",
 year = "1993",
+@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",
keywords = "axiomref",
 abstract =
 "There are a variety of theorems in group theory which admit of proofs
 by machine. This talk illustrates these techniques in action. Examples
 are given of this phenomenon, drawn from the theory of group
 presentations, and from the theory of $p$groups. The systems involved
 include AXIOM, CAYLEY and QUOTPIC"
+ 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.
+
+ The problem of implicitization is an active topic where research is
+ still taking place. Examples of further research points are included
+ in the conclusion"
}
\end{chunk}
\index{Geddes, K. O.}
\index{Czapor, S.R.}
\index{Labahn, George}
+\index{Chou, ShangChing}
+\index{Gao, XiaoShan}
+\index{Zhang, JingZhong}
\begin{chunk}{axiom.bib}
@book{Gedd92,
 author = "Geddes, Keith and Czapor, O. and Stephen R. and Labahn, George",
 title = "Algorithms For Computer Algebra",
 year = "1992",
 publisher = "Kluwer Academic Publishers",
 isbn = "0792392590",
 month = "September",
 year = "1992",
 keywords = "axiomref",
 abstract =
 "Computer Algebra (CA) is the name given to the discipline of
 algebraic, rather than numerical, computation. There are a number of
 computer programs – Computer Algebra Systems (CASs) – available for
 doing this. The most widely used generalpurpose systems that are
 currently available commercially are Axiom, Derive, Macsyma, Maple,
 Mathematica and REDUCE. The discipline of computer algebra began in
 the early 1960s and the first version of REDUCE appeared in 1968.

 A large class of mathematical problems can be solved by using a CAS
 purely interactively, guided only by the user documentation. However,
 sophisticated use requires an understanding of the considerable amount
 of theory behind computer algebra, which in itself is an interesting
 area of constructive mathematics. For example, most systems provide
 some kind of programming language that allows the user to expand or
 modify the capabilities of the system.

 This book is probably the most general introduction to the theory of
 computer algebra that is written as a textbook that develops the
 subject through a smooth progression of topics. It describes not only
 the algorithms but also the mathematics that underlies them. The book
 provides an excellent starting point for the reader new to the
 subject, and would make an excellent text for a postgraduate or
 advanced undergraduate course. It is probably desirable for the reader
 to have some background in abstract algebra, algorithms and
 programming at about secondyear undergraduate level.

 The book introduces the necessary mathematical background as it is
 required for the algorithms. The authors have avoided the temptation
 to pursue mathematics for its own sake, and it is all sharply focused
 on the task of performing algebraic computation. The algorithms are
 presented in a pseudolanguage that resembles a cross between Maple
 and C. They provide a good basis for actual implementations although
 quite a lot of work would still be required in most cases. There are
 no code examples in any actual programming language except in the
 introduction.

 The authors are all associated with the group that began the
 development of Maple. Hence, the book reflects the approach taken by
 Maple, but the majority of the discussion is completely independent of
 any actual system. The authors’ experience in implementing a practical
 CAS comes across clearly.

 The book focuses on the core of computer algebra. The first chapter
 introduces the general concept and provides a very nice historical
 survey. The next three chapters discuss the fundamental topics – data
 structures, representations and the basic arithmetic of integers,
 rational numbers, multivariate polynomials and rational functions – on
 which the rest of the book is built.

 A major technique in CA involves projection onto one or more
 homomorphic images, for which the ground ring is usually chosen to be
 a finite field. The image solution is lifted back to the original
 problem domain by means of the Chinese Remainder Theorem in the case
 of multiple homomorphic images, or the Hensel (adic or idealadic)
 construction in the case of a single image. The next two chapters are
 devoted to these techniques in a fairly general setting. The two
 subsequent chapters specialise them to GCD computation and
 factorisation for multivariate polynomials; the first of these
 chapters also discusses the important but difficult topic of
 subresultants.

 The next two chapters describe the use of fractionfree Gaussian
 elimination, resultants and Gröbner Bases for manipulation and exact
 solution of linear and nonlinear polynomial equations. The two final
 chapters describe ``classical'' algorithms and the more recent Risch
 algorithm for symbolic indefinite integration, and provide an
 introduction to differential algebra.

 The book does not consider more specialised problem areas such as
 symbolic summation, definite integration, differential equations,
 group theory or number theory. Nor does it consider more applied
 problem areas such as vectors, tensors, differential forms, special
 functions, geometry or statistics, even though Maple and other CASs
 provide facilities in all or many of these areas. It does not consider
 questions of CA programming language design, nor any of the important
 but nonalgebraic facilities provided by current CASs such as their
 user interfaces, numerical and graphical facilities.

 This is a long book (nearly 600 pages); it is generally very well
 presented and the three authors have merged their contributions
 seamlessly. I noticed very few typographical errors, and none of any
 consequence. I have only two complaints about the book. The typeface
 is too small, particularly for the relatively large line spacing used,
 and it is much too expensive, particularly for a book that would
 otherwise be an excellent student text. I recommend it highly to
 anyone who can afford it."
}
+@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"
+}
+
+\end{chunk}
+
+\index{Chou, ShangChing}
+\index{Gao, XiaoShan}
+\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."
+}
\end{chunk}
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index e3c6295..273b3ec 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5458,6 +5458,8 @@ books/bookvolbib Axiom Citations in the Literature
books/bookvolbib Axiom Citations in the Literature
20160706.02.tpd.patch
books/bookvolbib Axiom Citations in the Literature
+20160707.01.tpd.patch
+books/bookvolbib Axiom Citations in the Literature

1.7.5.4