From 94083eebc838536c17ffc4ea668a36ea026ecf8f Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Mon, 18 Jul 2016 00:12:39 0400
Subject: [PATCH] books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
\index{Corless, Robert M.}
\index{Jeffrey, David J.}
\begin{chunk}{axiom.bib}
@article{Corl98,
author = "Corless, Robert M. and Jeffrey, David J.",
title = "Graphing Elementary Riemann Surfaces",
journal = "SIGSAM Bulletin",
volume = "32",
number = "1",
pages = "1117",
year = "1998",
paper = "Corl98.djvu",
abstract =
"This paper discusses one of the prettiest pieces of elementary
mathematics or computer algebra, that we have ever had the pleasure
to learn. The tricks that we discuss here are certainly ``wellknown''
(that is, in the literature), but we didn't know them until recently,
and none of our immediate colleagues knew them either. Therefore we
believe that it is useful to publicize them further. We hope that
you find these ideas as pleasant and useful as we do."
}
\end{chunk}
\index{Corless, Robert M.}
\index{Jeffrey, David J.}
\index{Knuth, Donald E.}
\begin{chunk}{axiom.bib}
@misc{Corl97,
author = "Corless, Robert M. and Jeffrey, David J. and Knuth, Donald E.",
title = "A Sequence of Series for The Lambert W Function",
year = "1997",
paper = "Corl97.pdf",
abstract =
"We give a uniform treatment of several series expansions for the
Lambert $W$ function, leading to an infinite family of new series.
We also discuss standardization, complex branches, a family of
arbitraryorder iterative methods for computation of $W_i$, and
give a theorem showing how to correctly solve another simple and
frequently occurring nonlinear equation in terms of $W$ and the
unwinding number"
}
\end{chunk}
\index{Chow, Timothy Y.}
\begin{chunk}{axiom.bib}
@article{Chow99,
author = "Chow, Timothy Y.",
title = "What is a closedform number?",
journal = "The American Mathematical Monthly",
volume = "106",
number = "5",
pages = "440448",
paper = "Chowxx.pdf",
year = "1999"
}
\end{chunk}
\index{Hur, Namhyun}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@inproceedings{Hurx00,
author = "Hur, Namhyun and Davenport, James H.",
title = "An exact real algebraic arithmetic with equality determination",
booktitle = "Proc. ISSAC 2000",
series = "ISSAC '00",
pages = "169174",
year = "2000",
paper = "Hurx00.djvu",
abstract =
"We describe a new arithmetic model for real algebraic numbers with
an exact equality determination. The model represents a real algebraic
number as a pair of an arbitrary precision numerical value and a
symbolic expression. For the numerical part we currently (another
representation could be used) use the dyadic exact real number and
for the symbolic part we use a squarefree polynomial for the real
algebraic number. In this model we show that we can decide exactly
the equality of real algebraic numbers."
}
\end{chunk}
\index{Langley, Simon}
\index{Richardson, Daniel}
\begin{chunk}{axiom.bib}
@article{Lang02,
author = "Langley, Simon and Richardson, Daniel",
title = "What can we do with a Solution?",
journal = "Electronic Notes in Theoretical Computer Science",
volume = "66",
number = "1",
year = "2002",
url = "http://www.elsevier.nl/locate/entcs/volume66.html",
paper = "Lang02.pdf",
abstract =
"If $S=0$ is a system of $n$ equations and unknowns over $\mathbb{C}$
and $S(\alpha)=0$ to what extent can we compute with the point $\alpha$?
In particular, can we decide whether or not a polynomial expressions
in the components of $\alpha$ with integral coefficients is zero?
This question is considered for both algebraic and elementary systems
of equations."
}
\end{chunk}
\index{Wang, Paul S.}
\begin{chunk}{axiom.bib}
@article{Wang74,
author = "Wang, Paul S.",
title = "The Undecidability of the Existence of Zeros of Real Elementary
Functions",
journal = "J. ACM",
volume = "21",
number = "4",
pages = "586589",
year = "1974",
paper = "Wang74.djvu",
abstract =
"From Richardson's undecidability results, it is shown that the predicate
``there exists a real number $r$ such that $G(r)=0$'' is recursively
undecidable for $G(x)$ in a class of functions which involves polynomials
and the sine function. The deduction follows that the convergence of a
class of improper integrals is recursively undecidable."
}
\end{chunk}
\index{Daly, Timothy}
\begin{chunk}{axiom.bib}
@article{Daly02
author = "Daly, Timothy",
title = "Axiom as open source",
journal = "SIGSAM Bulletin",
volume = "36",
number = "1",
pages = "2828",
month = "March",
year = "2002",
keywords = "axiomref"
}
\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@article{Jenk92,
author = "Jenks, Richard D.",
title = "SCRATCHPAD",
volume = "??",
number = "24",
pages = "1617",
month = "October",
year = "1972",
keywords = "axiomref",
abstract =
"The following SCRATCHPAD solution of Problem \#2 was run on a 1280K
virtual machine under CP/CMS time sharing system on a System/360
model 67. The conversation below is a modification of a program
originally written by Yngve Sundblad, August 1972. The program uses
symmetrised formulae, saves certain intermediate results, but does not
eliminate numerical factors in denominators"
}
\end{chunk}
\index{Norman, Arthur C.}
\begin{chunk}{axiom.bib}
@article{Norm75a,
author = "Norman, Arthur C.",
title = "The SCRATCHPAD Power Series Package",
journal = "SIGSAM",
volume = "9",
number = "1",
pages = "1220",
year = "1975",
comment = "IBM T.J. Watson Research RC4998",
keywords = "axiomref"
}
\end{chunk}
\index{Griesmer, James H.}
\index{Jenks, Richard D.}
\index{Yun, David Y.Y.}
\begin{chunk}{axiom.bib}
@article{Grie75a,
author = "Griesmer, James H. and Jenks, Richard D. and Yun, David Y.Y."
title = "A SCRATCHPAD solution to problem \#7",
journal = "SIGSAM",
volume = "9",
number = "3",
pages = "1317",
year = "1975"
}
\end{chunk}
\index{Miller, Bruce R.}
\begin{chunk}{axiom.bib}
@misc{Mill95,
author = "Miller, Bruce R.",
title = "An expression formatter for MACSYMA",
keywords = "axiomref",
year = "1995",
paper = "Mill95.pdf",
abstract =
"A package for formatting algebraic expressions in MACSYA is described.
It provides facilities for userdirected hierarchical structuring of
expressions, as well as for directing simplifications to selected
subexpressions. It emphasizes a semantic rther than syntactic description
of the desired form. The package also provides utilities for obtaining
efficiently the coefficients of polynomials, trigonometric sums and
power series. Similar capabilities would be useful in other computer
algebra systems."
}
\end{chunk}
\index{Griesmer, James H.}
\index{Jenks, Richard D.}
\index{Yun, David Y.Y.}
\begin{chunk}{axiom.bib}
@article{Grie75b,
author = "Griesmer, James H. and Jenks, Richard D. and Yun, David Y.Y."
title = "A FORMAT statement in SCRATCHPAD",
journal = "SIGSAM",
volume = "9",
number = "3",
pages = "2425",
year = "1975",
keywords = "axiomref",
abstract =
"Algebraic manipulation covers branches of software, particularly list
processing, mathematics, notably logic and number theory, and
applications largely in physics. The lectures will deal with all of these
to a varying extent.
}
\end{chunk}
\index{Blair, Fred W.}
\index{Griesmer, James H.}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@inproceedings{Blai70,
author = "Blair, Fred W. and Griesmer, James H. and Jenks, Richard D.",
title = "An interactive facility for symbolic mathematics",
booktitle = "Proc. International Computing Symposium, Bonn, Germany",
year = "1970",
pages = "394419",
keywords = "axiomref",
abstract =
"The SCRATCHPAD/1 system is designed to provide an interactive symbolic
coputational facility for the mathematician user. The system features
a user language designed to capture the style and succinctness of
mathematical notation, together with a facility for conveniently
introducing new notations into the language. A comprehensive system
library incorporates symbolic capabilities provided by such systems as
SIN, MATHLAB, and REDUCE."
}
\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@article{Jenk79a,
author = "Jenks, Richard D.",
title = "SCRATCHPAD/360: reflections on a language design",
journal = "SIGSAM",
volume = "13",
number = "1",
pages = "1626",
year = "1979",
keywords = "axiomref",
comment = "IBM Research RC 7405",
abstract =
"The key concepts of the SCRATCHPAD language are described, assessed,
and illustrated by an example. The language was originally intended as
an interactive problem solving language for symbolic mathematics.
Nevertheless, as this paper intends to show, it can be used as a
programming language as well."
}
\end{chunk}
\index{Ng, Edward W.}
\begin{chunk}{axiom.bib}
@techreport{Ngxx80,
author = "Ng, Edward W.",
title = "SymbolicNumeric Interface: A Review",
type = "technical report",
number = "NASACR162690 HC A02/MF A01"
institution = "NASA Jet Propulsion Lab",
url = "http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19800008508.pdf",
paper = "Ngxx80.pdf",
keywords = "axiomref",
abstract =
"This is a survey of recent activities that either used or encouraged the
potential use of a combination of symbolic and numerical calculations.
Symbolic calculations here primarily refer to the computer processing of
procedures from classical algebra, analysis and calculus. Numerical
calculations refer to both numerical mathematics research and scientific
computation. This survey is inteded to point out a large number of problem
areas where a cooperation of symbolic and numeric methods is likely to
bear many fruits. These areas include such classical operations as
differentiation and integration, such diverse activities as function
approximations andqualitative analysis, and such contemporary topics as
finite element calculations and computational complexity. It is contended
that other less obvious topics such as the fast Fourier transform, linear
algebra, nonlinear analysis and error analysis would also benefti from a
synergistic approach advocated here."
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@article{Fate01,
author = "Fateman, Richard J.",
title = "A Review of Macsyma",
journal = "IEEE Trans. Knowl. Eng.",
volume = "1",
number = "1",
year = "2001",
url = "http://people.eecs.berkeley.edu/~fateman/papers/mac82b.pdf",
paper = "Fate01.pdf",
keywords = "axiomref",
abstract =
"We review the successes and failures of the Macsyma algebraic
manipulation system from the point of view of one of the original
contributors. We provide a retrospective examination of some of the
controversial ideas that worked, and some that did not. We consider
input/output, language semantics, data types, pattern matching,
knowledgeadjunction, mathematical semantics, the user community,
and software engineering. We also comment on the porting of this
system to a variety of computing systems, and possible future
directions for algebraic manipulation systembuilding."
}
\end{chunk}
\index{Griesmer, James H.}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@article{Grie74,
author = "Griesmer, James H. and Jenks, Richard D.",
title = "A solution to problem \#4": the lie transform",
journal = "SIGSAM Bulletin",
volume = "8",
number = "4",
pages = "1213",
year = "1974",
keywords = "axiomref",
abstract =
"The following SCRATCHPAD conversation for carrying out the Lie
Transform computation represents a slight modification of one written
by Dr. David Barton, when he was a summer visitor during 1972 at the
Watson Research Center."
}
\end{chunk}
\begin{chunk}{axiom.bib}
@misc{SIGS16,
author = "SIGSAM, ACM",
title = "Axiom"
url = "http://www.sigsam.org/software/axiom.html",
year = "2016",
contact = "Infodir\_SIGSAM\@acm.org",
abstract =
"Axiom is a free, open source, generalpurpose computer algebra
system. It features a strongly typed language. The system has an
interactive interpreter and a compiler. It includes over 1100
supported categories, domains, and packages covering large areas of
Mathematics."
}
\end{chunk}
\index{Li, Yue}
\index{Dos Reis, Gabriel}
\begin{chunk}{axiom.bib}
@inproceedings{Lixx11,
author = "Li, Yue and Dos Reis, Gabriel",
title = "An Automatic Parallelization Framework for Algebraic
Computation Systems",
booktitle = "Proc. ISSAC 2011",
pages = "233240",
isbn = "9781450306751",
year = "2011",
url = "http://www.axiomatics.org/~gdr/concurrency/oaconcissac11.pdf",
paper = "Lixx11.pdf",
keywords = "axiomref",
abstract =
"This paper proposes a nonintrusive automatic parallelization
framework for typeful and propertyaware computer algebra systems.
Automatic parallelization remains a promising computer program
transformation for exploiting ubiquitous concurrency facilities
available in modern computers. The framework uses semanticsbased
static analysis to extract reductions in library components based on
algebraic properties. An early implementation shows up to 5 times
speedup for library functions and homotopybased polynomial system
solver. The general framework is applicable to algebraic computation
systems and programming languages with advanced type systems that
support userdefined axioms or annotation systems."
}
\end{chunk}
\index{Kendall, Wilfrid S.}
\begin{chunk}{axiom.bib}
@article{Kend01,
author = "Kendall, Wilfrid S.",
title = "Symbolic It\^o calculus in AXIOM: an ongoing story",
journal = "Statistics and Computing",
volume = "11",
pages = "2535",
year = "2001",
url = "http://www2.warwick.ac.uk/fac/sci/statistics/staff/academicresearch/kendall/personal/ppt/327.ps.gz",
paper = "Kend01.pdf",
keywords = "axiomref",
abstract =
"Symbolic It\^o calculus refers both to the implementation of the
It\^o calculus algebra package and to its application. This article
reports on progress in the implementation of It\^o calculus in the
powerful and innovative computer algebra package AXIOM, in the context
of a decade of previous implementations and applications. It is shown
how the elegant algebraic structure underylying the expressive and
effective formalism of It\^o calculus can be implemented directly in
AXIOM using the package's programmable facilities for ``strong
typing'' of computational objects. An application is given of the use
of the implementation to provide calculations for a new proof, based
on stochastic differentials, of the MardiaDryden distribution from
statistical shape theory."
}
\end{chunk}
\index{Senechaud, Pascale}
\index{Siebert, F.}
\begin{chunk}{axiom.bib}
@techreport{Sene87a,
author = "Senechaud, Pascale and Siebert, F.",
title = "Etude dl l'algorithme de Kovacic et son implantation sur
Scratchpad II",
type = "Technical Report",
number = "639",
institution = "Institut IMAG, Informatique et Mathematiques Appliquees
de Grenoble",
address = "Grenoble, France",
year = "1987",
keywords = "axiomref"
}
\end{chunk}
\index{Terelius, Bjorn}
\begin{chunk}{axiom.bib}
@mastersthesis{Tere09,
author = "Terelius, Bjorn",
title = "Symbolic Integration",
school = "Royal Institute of Technology",
address = "Stockholm, Sweden",
year = "2009",
paper = "Tere09.pdf",
abstract =
"Symbolic integration is the problem of expressing an indefinite integral
$\int{f}$ of a given function $f$ as a finite combination $g$ of elementary
functions, or more generally, to determine whether a certain class of
functions contains an element $g$ such that $g^\prime = f$."
In the first part of this thesis, we compare different algorithms for
symbolic integration. Specifically, we review the integration rules
taught in calculus courses and how they can be used systematically to
create a reasonable, but somewhat limited, integration method. Then we
present the differential algebra required to prove the transcendental
cases of Risch's algorithm. Risch's algorithm decides if the integral
of an elementary function is elementary and if so computes it. The
presentation is mostly selfcontained and, we hope, simpler than
previous descriptions of the algorithm. Finally, we describe
RischNorman's algorithm which, although it is not a decision
procedure, works well in practice and is considerably simpler than the
full Risch algorithm.
In the second part of this thesis, we briefly discuss an
implementation of a computer algebra system and some of the
experiences it has given us. We also demonstrate an implementation of
the rulebased approach and how it can be used, not only to compute
integrals, but also to generate readable derivations of the results."
}
\end{chunk}
\index{Kendall, Wilfrid S.}
\begin{chunk}{axiom.bib}
@article{Kend07,
author = "Kendall, Wilfrid S.",
title = "Coupling all the Levy Stochastic Areas of Multidimensional
Brownian Motion",
journal = "The Annals of Probability",
volume = "35",
number = "3",
pages = "935953",
year = "2007",
keywords = "axiomref",
comment = "Author used Axiom for computation but says missed citation",
url = "http://arxiv.org/pdf/math/0512336v2.pdf",
paper = "Kend07.pdf",
abstract =
"It is shown how to construct a successful coadapted coupling of two
copies of an $n$dimensional Brownian motion ($B_1,\ldots,B_n$) while
simultaneously coupling all corresponding copies of the L{\'e}vy
stochastic areas $\int B_idB_j$  \int B_j dB_i$. It is conjectured
that successful coadapted couplings still exist when the L{\'e}vy
stochastic areas are replaced by a finite set of multiply iterated
path and timeintegrals, subject to algebraic compatibility of the
initial conditions."
}
\end{chunk}
\index{Bronstein, Manuel}
\index{Lafaille, S\'ebastien}
\begin{chunk}{axiom.bib}
@inproceedings{Bron02,
author = "Bronstein, Manuel and Lafaille, S\'ebastien",
title = "Solutions of linear ordinary differential equations in terms
of special functions",
booktitle = "Proc. ISSAC '02",
publisher = "ACM Press",
pages = "2328",
year = "2002",
isbn = "1581134843",
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/issac2002.pdf",
paper = "Bron02.pdf",
url2 = "http://xena.hunter.cuny.edu/ksda/papers/bronstein2.pdf",
paper2 = "Bron02x.pdf",
abstract =
"We describe a new algorithm for computing special function solutions
of the form $y(x) = m(x)F(\eta(x))$ of second order linear ordinary
differential equations, where $m(x)$ is an arbitrary Liouvillian
function, $\eta(x)$ is an arbitrary rational function, and $F$
satisfies a given second order linear ordinary differential
equations. Our algorithm, which is base on finding an appropriate
point transformation between the equation defining $F$ and the one to
solve, is able to find all rational transformations for a large class
of functions $F$, in particular (but not only) the $_0F_1$ and $_1F_1$
special functions of mathematical physics, such as Airy, Bessel,
Kummer and Whittaker functions. It is also able to identify the values
of the parameters entering those special functions, and can be
generalized to equations of higher order."
}
\end{chunk}
\index{Chan, L.}
\index{ChebTerrab, E.S.}
\begin{chunk}{axiom.bib}
@inproceedings{Chan04,
author = "Chan, L. and ChebTerrab, E.S.",
title = "NonLiouvillian solutions for second order linear ODEs",
booktitle = "Proc. ISSAC 04",
pages = "8086",
isbn = "158113827X",
url = "http://www.cecm.sfu.ca/CAG/papers/edgardoIS04.pdf",
keywords = "axiomref",
paper = "Chan04.pdf",
abstract =
"There exist sound literature and algorithms for computing Liouvillian
solutions for the important problem of linear ODEs with rational
coefficients. Taking as sample the 363 second order equations of that
type found in Kamke's book, for instance, 51\% of them admit Liouvillian
solutions and so are solvable using Kovacic's algorithm. On the other
hand, special function solutions not admitting Liouvillian form appear
frequently in mathematical physics, but there are not so general
algorithms for computing them. In this paper we present an algorithm
for computing special function solutions which can be expressed using
the $_2F_1$, $_1F_1$ or $_0F_1$ hypergeometric functions. They algorithm
is easy to implement in the framework of a computer algebra system and
systematically solves 91\% of the 363 Kamke's linear ODE examples
mentioned."
}
\end{chunk}
\index{van Hoeij, Mark}
\index{Monagan, Michael}
\begin{chunk}{axiom.bib}
@inproceedings{Hoei04,
author = "van Hoeij, Mark and Monagan, Michael",
title = "Algorithms for Polynomial GCD Computation over Algebraic
Function Fields",
booktitle = "Proc. ISSAC 04",
isbn = "158113827X",
url = "http://www.cecm.sfu.ca/personal/mmonagan/papers/AFGCD.pdf",
paper = "Hoei04.pdf",
abstract =
"Let $L$ be an algebraic function field in $k \ge 0$ parameters
$t_1,\ldots,t)k$. Let $f_1$, $f_2$ be nonzero polynomials in
$L[x]$. We give two algorithms for computing their gcd. The first, a
modular GCD algorithm, is an extension of the modular GCD algorithm
for Brown for {\bf Z}$[x_1,\ldots,x_n]$ and Encarnacion for {\bf
Q}$(\alpha[x])$ to function fields. The second, a fractionfree
algorithm, is a modification of the Moreno Maza and Rioboo algorithm
for computing gcds over triangular sets. The modification reduces
coefficient grownth in $L$ to be linear. We give an empirical
comparison of the two algorithms using implementations in Maple."
}
\end{chunk}
\begin{chunk}{axiom.bib}
@misc{Maxi16a,
author = "Maxima",
title = "Symbolic Integration: The Algorithms",
url =
"http://maxima.sourceforge.net/docs/tutorial/en/gaertnertutorialrevision/Pages/SI001.htm"
}
\index{Gil, I.}
\begin{chunk}{axiom.bib}
@inproceedings{Gilx92,
author = "Gil, I.",
title = "Computation of the Jordan canonical form of a square matrix
(using the Axiom programming language)",
booktitle = "Proc ISSAC 1992",
series = "ISSAC '92",
publisher = "ACM",
pages = "138145",
isbn = "0897914899 (soft cover), 0897914902 (hard cover)",
keywords = "axiomref",
abstract =
"Presents an algorithm for computing: the Jordan form of a square
matrix with coefficients in a field K using the computer algebra
system Axiom. This system presents the advantage of allowing generic
programming. That is to say, the algorithm can first be implemented
for matrices with rational coefficients and then generalized to
matrices with coefficients in any field. Therefore the author
presents the general method which is essentially based on the use of
the Frobenius form of a matrix in order to compute its Jordan form;
and then restricts attention to matrices with rational
coefficients. On the one hand the author streamlines the algorithm
froben which computes the Frobenius form of a matrix, and on the other
she examines in some detail the transformation from the Frobenius form
to the Jordan form, and gives the so called algorithm Jordform. The
author studies in particular, the complexity of this algorithm and
proves that it is polynomial when the coefficients of the matrix are
rational. Finally the author gives some experiments and a conclusion."
}
\end{chunk}
\index{InnerNormalBasisFieldFunctions}
\index{Stinson, D.R.}
\begin{chunk}{axiom.bib}
@article{Stin90,
author = "Stinson, D.R.",
title = "Some observations on parallel Algorithms for fast exponentiation
in $GF(2^n)$",
journal = "Siam J. Comp.",
volume = "19",
number = "4",
pages = "711717",
year = "1990",
paper = "Stin90.pdf",
algebra = "\newline\refto{package INBFF InnerNormalBasisFieldFunctions}",
abstract =
"A normal basis represention in $GF(2^n)$ allows squaring to be
accomplished by a cyclic shift. Algorithms for multiplication in
$GF(2^n)$ using a normal basis have been studied by several
researchers. In this paper, algorithms for performing exponentiation
in $GF(2^n)$ using a normal basis, and how they can be speeded up by
using parallelization, are investigated."
}
\end{chunk}
\index{FiniteFieldPolynomialPackage}
\index{Lenstra, H. W.}
\index{Schoof, R. J.}
\begin{chunk}{axiom.bib}
@article{Lens87,
author = "Lenstra, H. W. and Schoof, R. J.",
title = "Primitive Normal Bases for Finite Fields",
journal = "Mathematics of Computation",
volume = "48",
number = "177",
year = "1987",
pages = "217231",
url = "http://www.math.leidenuniv.nl/~hwl/PUBLICATIONS/",
paper = "Lens87.pdf",
algebra = "\newline\refto{package FFPOLY FiniteFieldPolynomialPackage}",
abstract =
"It is proved that any finite extension of a finite field has a normal
basis consisting of primitive roots"
}
\end{chunk}
\index{CharacteristicNonZero}
\index{FieldOfPrimeCharacteristic}
\index{ExtensionField}
\index{FiniteFieldCategory}
\index{FiniteAlgebraicExtensionField}
\index{SimpleAlgebraicExtension}
\index{InnerPrimeField}
\index{PrimeField}
\index{FiniteFieldExtensionByPolynomial}
\index{FiniteFieldCyclicGroupExtensionByPolynomial}
\index{FiniteFieldNormalBasisExtensionByPolynomial}
\index{FiniteFieldExtension}
\index{FiniteFieldCyclicGroupExtension}
\index{FiniteFieldNormalBasisExtension}
\index{InnerFiniteField}
\index{FiniteField}
\index{FiniteFieldCyclicGroup}
\index{FiniteFieldNormalBasis}
\index{DiscreteLogarithmPackage}
\index{FiniteFieldFunctions}
\index{InnerNormalBasisFieldFunctions}
\index{FiniteFieldPolynomialPackage}
\index{FiniteFieldPolynomialPackage2}
\index{FiniteFieldHomomorphisms}
\index{FiniteFieldFactorizationWithSizeParseBySideEffect}
\index{Grabmeier, Johannes}
\index{Scheerhorn, Alfred}
\begin{chunk}{axiom.bib}
@techreport{Grab92,
author = "Grabmeier, Johannes and Scheerhorn, Alfred",
title = "Finite fields in Axiom",
type = "technical report",
number = "AXIOM Technical Report TR7/92 (ATR/5)(NP2522)",
institution = "Numerical Algorithms Group, Inc.",
address = "Downer's Grove, IL, USA and Oxford, UK",
year = "1992",
url = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
keywords = "axiomref",
paper = "Grab92.pdf",
algebra =
"\newline\refto{category CHARNZ CharacteristicNonZero}
\newline\refto{category FPC FieldOfPrimeCharacteristic}
\newline\refto{category XF ExtensionField}
\newline\refto{category FFIELDC FiniteFieldCategory}
\newline\refto{category FAXF FiniteAlgebraicExtensionField}
\newline\refto{domain SAE SimpleAlgebraicExtension}
\newline\refto{domain IPF InnerPrimeField}
\newline\refto{domain PF PrimeField}
\newline\refto{domain FFP FiniteFieldExtensionByPolynomial}
\newline\refto{domain FFCGP FiniteFieldCyclicGroupExtensionByPolynomial}
\newline\refto{domain FFNBP FiniteFieldNormalBasisExtensionByPolynomial}
\newline\refto{domain FFX FiniteFieldExtension}
\newline\refto{domain FFCGX FiniteFieldCyclicGroupExtension}
\newline\refto{domain FFNBX FiniteFieldNormalBasisExtension}
\newline\refto{domain IFF InnerFiniteField}
\newline\refto{domain FF FiniteField}
\newline\refto{domain FFCG FiniteFieldCyclicGroup}
\newline\refto{domain FFNB FiniteFieldNormalBasis}
\newline\refto{package DLP DiscreteLogarithmPackage}
\newline\refto{package FFF FiniteFieldFunctions}
\newline\refto{package INBFF InnerNormalBasisFieldFunctions}
\newline\refto{package FFPOLY FiniteFieldPolynomialPackage}
\newline\refto{package FFPOLY2 FiniteFieldPolynomialPackage2}
\newline\refto{package FFHOM FiniteFieldHomomorphisms}
\newline\refto
{package FFFACTSE FiniteFieldFactorizationWithSizeParseBySideEffect}",
abstract =
"Finite fields play an important role for many applications (e.g. coding
theory, cryptograpy). There are different ways to construct a finite
field for a given prime power. The paper describes the different
constructions implemented in AXIOM. These are {\sl polynomial basis
representation}, {\sl cyclic group representation}, and {\sl normal
basis representation}. Furthermore, the concept of the implementation,
the used algorithms and the various datatype coercions between these
representations are discussed."
}
\end{chunk}
\index{InnerNormalBasisFieldFunctions}
\index{Itoh, T.}
\index{Tsujii, S.}
\begin{chunk}{axiom.bib}
@article{Itoh88,
author = "Itoh, T. and Tsujii, S.",
title = "A fast algorithm for computing multiplicative inverses in
$GF(2^m)$ using normal bases",
journal = "Inf. and Comp.",
volume = "78",
pages = "171177",
year = "1988",
paper = "Itoh88.pdf",
algebra = "\newline\refto{package INBFF InnerNormalBasisFieldFunctions}",
abstract =
"This paper proposes a fast algorithm for computing multiplicative
inverses in $GF(2^m)$ using normal bases. Normal bases have the
following useful property: In the case that an element $x$ in
$GF(2^m)$ is represented by normal bases, $2^k$ power operation of an
element $x$ in $GF(2^m)$ can be carried out by $k$ times cyclic shift
of its vector representation. C.C. Wang et al. proposed an algorithm
for computing multiplicative inverses using normal bases, which
requires $(m2)$ multiplications in $GF(2^m)$ and $(m1)$ cyclic
shifts. The fast algorithm proposed in this paper also uses normal
bases, and computes multiplicative inverses iterating multiplications
in $GF(2^m)$. It requires at most $2[log_2(m1)]$ multiplications in
$GF(2^m)$ and $(m1)$ cyclic shifts, which are much less than those
required in Wang's method. The same idea of the proposed fast
algorithm is applicable to the general power operation in $GF(2^m)$
and the computation of multiplicative inverses in $GF(q^m)$
$(q=2^n)$."
}
\end{chunk}

books/bookvol10.2.pamphlet  32 +
books/bookvol10.3.pamphlet  98 +
books/bookvol10.4.pamphlet  63 +
books/bookvolbib.pamphlet  3875 +++++++++++++++++++++++++++++++++++++
changelog  5 +
patch  818 +++++++++
src/axiomwebsite/patches.html  2 +
7 files changed, 4569 insertions(+), 324 deletions()
diff git a/books/bookvol10.2.pamphlet b/books/bookvol10.2.pamphlet
index 7c9a324..054a38b 100644
 a/books/bookvol10.2.pamphlet
+++ b/books/bookvol10.2.pamphlet
@@ 1,5 +1,5 @@
\documentclass[dvipdfm]{book}
\newcommand{\VolumeName}{Volume 10: Axiom Algebra: Categories}
+\newcommand{\VolumeName}{Volume 10.2: Axiom Algebra: Categories}
\input{bookheader.tex}
\mainmatter
\setcounter{chapter}{0} % Chapter 1
@@ 45946,8 +45946,12 @@ These exports come from \refto{Ring}():
?=? : (%,%) > Boolean
\end{verbatim}
+See: Grabmeier\cite{Grab92}
+\label{category CHARNZ CharacteristicNonZero}
\begin{chunk}{category CHARNZ CharacteristicNonZero}
)abbrev category CHARNZ CharacteristicNonZero
+++ References:
+++ Grab92 Finite Fields in Axiom
++ Description:
++ Rings of Characteristic Non Zero
@@ 72937,14 +72941,15 @@ These exports come from \refto{CharacteristicNonZero}():
charthRoot : % > Union(%,"failed")
\end{verbatim}
+See: Grabmeier\cite{Grab92}
+\label{category FPC FieldOfPrimeCharacteristic}
\begin{chunk}{category FPC FieldOfPrimeCharacteristic}
)abbrev category FPC FieldOfPrimeCharacteristic
++ Author: J. Grabmeier, A. Scheerhorn
++ Date Created: 10 March 1991
++ Date Last Updated: 31 March 1991
++ References:
++ J. Grabmeier, A. Scheerhorn: Finite Fields in AXIOM.
++ AXIOM Technical Report Series, ATR/5 NP2522.
+++ Grab92 Finite Fields in Axiom
++ Description:
++ FieldOfPrimeCharacteristic is the category of fields of prime
++ characteristic, for example, finite fields, algebraic closures of
@@ 85379,14 +85384,15 @@ These exports come from \refto{FieldOfPrimeCharacteristic}():
if F has CHARNZ or F has FINITE
\end{verbatim}
+See: Grabmeier\cite{Grab92}
+\label{category XF ExtensionField}
\begin{chunk}{category XF ExtensionField}
)abbrev category XF ExtensionField
++ Author: J. Grabmeier, A. Scheerhorn
++ Date Created: 10 March 1991
++ Date Last Updated: 31 March 1991
++ References:
++ J. Grabmeier, A. Scheerhorn: Finite Fields in AXIOM.
++ AXIOM Technical Report Series, ATR/5 NP2522.
+++ Grab92 Finite Fields in Axiom
++ Description:
++ ExtensionField F is the category of fields which extend the field F
@@ 85840,16 +85846,16 @@ These exports come from \refto{DifferentialRing}():
differentiate : (%,NonNegativeInteger) > %
\end{verbatim}
+See: Grabmeier\cite{Grab92}, Lipson\cite{Lips81}
+\label{category FFIELDC FiniteFieldCategory}
\begin{chunk}{category FFIELDC FiniteFieldCategory}
)abbrev category FFIELDC FiniteFieldCategory
++ Author: J. Grabmeier, A. Scheerhorn
++ Date Created: 11 March 1991
++ Date Last Updated: 31 March 1991
++ References:
++ D.Lipson, Elements of Algebra and Algebraic Computing, The
++ Benjamin/Cummings Publishing Company, Inc.Menlo Park, California, 1981.
++ J. Grabmeier, A. Scheerhorn: Finite Fields in AXIOM.
++ AXIOM Technical Report Series, ATR/5 NP2522.
+++ Grab92 Finite Fields in AXIOM.
+++ Lips81 Elements of Algebra and Algebraic Computing
++ Description:
++ FiniteFieldCategory is the category of finite fields
@@ 89636,16 +89642,16 @@ These exports come from \refto{FiniteFieldCategory}():
\end{verbatim}
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}
+\label{category FAXF FiniteAlgebraicExtensionField}
\begin{chunk}{category FAXF FiniteAlgebraicExtensionField}
)abbrev category FAXF FiniteAlgebraicExtensionField
++ Author: J. Grabmeier, A. Scheerhorn
++ Date Created: 11 March 1991
++ Date Last Updated: 31 March 1991
++ References:
++ R.Lidl, H.Niederreiter: Finite Field, Encycoldia of Mathematics and
++ Its Applications, Vol. 20, Cambridge Univ. Press, 1983,
++ ISBN 0 521 30240 4 J. Grabmeier, A. Scheerhorn: Finite Fields in AXIOM.
++ AXIOM Technical Report Series, ATR/5 NP2522.
+++ Grab92 Finite Fields in Axiom
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ FiniteAlgebraicExtensionField F is the category of fields
++ which are finite algebraic extensions of the field F.
diff git a/books/bookvol10.3.pamphlet b/books/bookvol10.3.pamphlet
index 55bc061..5a5fe3f 100644
 a/books/bookvol10.3.pamphlet
+++ b/books/bookvol10.3.pamphlet
@@ 1,5 +1,5 @@
\documentclass[dvipdfm]{book}
\newcommand{\VolumeName}{Volume 10: Axiom Algebra: Domains}
+\newcommand{\VolumeName}{Volume 10.3: Axiom Algebra: Domains}
\input{bookheader.tex}
\mainmatter
\setcounter{secnumdepth}{0} % override the one in bookheader.tex
@@ 64155,16 +64155,17 @@ o )show InnerFiniteField
\cross{FF}{?rem?} &&
\end{tabular}
+
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}
+\label{domain FF FiniteField}
\begin{chunk}{domain FF FiniteField}
)abbrev domain FF FiniteField
++ Author: Mark Botch
++ Date Created: ???
++ Date Last Updated: 29 May 1990
++ Reference:
++ R.Lidl, H.Niederreiter: Finite Field, Encyclopedia of Mathematics an
++ Its Applications, Vol. 20, Cambridge Univ. Press, 1983, ISBN 0 521 30240 4
++ J. Grabmeier, A. Scheerhorn: Finite Fields in AXIOM.
++ AXIOM Technical Report Series, ATR/5 NP2522.
+++ Grab92 Finite Fields in AXIOM.
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ FiniteField(p,n) implements finite fields with p**n elements.
++ This packages checks that p is prime.
@@ 64431,13 +64432,15 @@ o )show FiniteFieldCyclicGroup
\cross{FFCG}{?rem?} &
\end{tabular}
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}
+\label{domain FFCG FiniteFieldCyclicGroup}
\begin{chunk}{domain FFCG FiniteFieldCyclicGroup}
)abbrev domain FFCG FiniteFieldCyclicGroup
++ Authors: J.Grabmeier, A.Scheerhorn
++ Date Created: 04.04.1991
++ References:
++ R.Lidl, H.Niederreiter: Finite Field, Encycoldia of Mathematics and
++ Its Applications, Vol. 20, Cambridge Univ. Press, 1983, ISBN 0 521 30240 4
+++ Grab92 Finite Fields in Axiom
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ FiniteFieldCyclicGroup(p,n) implements a finite field extension of degee n
++ over the prime field with p elements. Its elements are represented by
@@ 64715,15 +64718,15 @@ o )show FiniteFieldCyclicGroupExtension
\cross{FFCGX}{?rem?} &
\end{tabular}
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}
+\label{domain FFCGX FiniteFieldCyclicGroupExtension}
\begin{chunk}{domain FFCGX FiniteFieldCyclicGroupExtension}
)abbrev domain FFCGX FiniteFieldCyclicGroupExtension
++ Authors: J.Grabmeier, A.Scheerhorn
++ Date Created: 04.04.1991
++ References:
++ R.Lidl, H.Niederreiter: Finite Field, Encycoldia of Mathematics and
++ Its Applications, Vol. 20, Cambridge Univ. Press, 1983, ISBN 0 521 30240 4
++ J. Grabmeier, A. Scheerhorn: Finite Fields in AXIOM.
++ AXIOM Technical Report Series, ATR/5 NP2522.
+++ Grab92 Finite Fields in Axiom
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ FiniteFieldCyclicGroupExtension(GF,n) implements a extension of degree n
++ over the ground field GF. Its elements are represented by powers of
@@ 64999,16 +65002,16 @@ o )show FiniteFieldCyclicGroupExtensionByPolynomial
\cross{FFCGP}{?rem?} &
\end{tabular}
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}
+\label{domain FFCGP FiniteFieldCyclicGroupExtensionByPolynomial}
\begin{chunk}{domain FFCGP FiniteFieldCyclicGroupExtensionByPolynomial}
)abbrev domain FFCGP FiniteFieldCyclicGroupExtensionByPolynomial
++ Authors: J.Grabmeier, A.Scheerhorn
++ Date Created: 26.03.1991
++ Date Last Updated: 31 March 1991
++ References:
++ R.Lidl, H.Niederreiter: Finite Field, Encycoldia of Mathematics and
++ Its Applications, Vol. 20, Cambridge Univ. Press, 1983, ISBN 0 521 30240 4
++ J. Grabmeier, A. Scheerhorn: Finite Fields in AXIOM.
++ AXIOM Technical Report Series, ATR/5 NP2522.
+++ Grab92 Finite Fields in Axiom
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ FiniteFieldCyclicGroupExtensionByPolynomial(GF,defpol) implements a
++ finite extension field of the ground field GF. Its elements are
@@ 65815,16 +65818,16 @@ o )show FiniteFieldExtension
\cross{FFX}{?rem?} &&
\end{tabular}
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}
+\label{domain FFX FiniteFieldExtension}
\begin{chunk}{domain FFX FiniteFieldExtension}
)abbrev domain FFX FiniteFieldExtension
++ Authors: R.Sutor, J. Grabmeier, A. Scheerhorn
++ Date Created:
++ Date Last Updated: 31 March 1991
++ Reference:
++ R.Lidl, H.Niederreiter: Finite Field, Encyclopedia of Mathematics an
++ Its Applications, Vol. 20, Cambridge Univ. Press, 1983, ISBN 0 521 30240 4
++ J. Grabmeier, A. Scheerhorn: Finite Fields in AXIOM.
++ AXIOM Technical Report Series, ATR/5 NP2522.
+++ Grab92 Finite Fields in Axiom
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ FiniteFieldExtensionByPolynomial(GF, n) implements an extension
++ of the finite field GF of degree n generated by the extension
@@ 66087,16 +66090,16 @@ o )show FiniteFieldExtensionByPolynomial
\cross{FFP}{?rem?} &
\end{tabular}
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}
+\label{domain FFP FiniteFieldExtensionByPolynomial}
\begin{chunk}{domain FFP FiniteFieldExtensionByPolynomial}
)abbrev domain FFP FiniteFieldExtensionByPolynomial
++ Authors: R.Sutor, J. Grabmeier, O. Gschnitzer, A. Scheerhorn
++ Date Created:
++ Date Last Updated: 31 March 1991
++ Reference:
++ R.Lidl, H.Niederreiter: Finite Field, Encyclopedia of Mathematics an
++ Its Applications, Vol. 20, Cambridge Univ. Press, 1983, ISBN 0 521 30240 4
++ J. Grabmeier, A. Scheerhorn: Finite Fields in AXIOM.
++ AXIOM Technical Report Series, ATR/5 NP2522.
+++ Grab92 Finite Fields in Axiom
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ FiniteFieldExtensionByPolynomial(GF, defpol) implements the extension
++ of the finite field GF generated by the extension polynomial
@@ 66803,15 +66806,15 @@ o )show FiniteFieldNormalBasis
\cross{FFNB}{?rem?} &&
\end{tabular}
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}
+\label{domain FFNB FiniteFieldNormalBasis}
\begin{chunk}{domain FFNB FiniteFieldNormalBasis}
)abbrev domain FFNB FiniteFieldNormalBasis
++ Authors: J.Grabmeier, A.Scheerhorn
++ Date Created: 26.03.1991
++ References:
++ R.Lidl, H.Niederreiter: Finite Field, Encyclopedia of Mathematics and
++ Its Applications, Vol. 20, Cambridge Univ. Press, 1983, ISBN 0 521 30240 4
++ J. Grabmeier, A. Scheerhorn: Finite Fields in AXIOM.
++ AXIOM Technical Report Series, ATR/5 NP2522.
+++ Grab92 Finite Fields in Axiom
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ FiniteFieldNormalBasis(p,n) implements a
++ finite extension field of degree n over the prime field with p elements.
@@ 67101,15 +67104,15 @@ o )show FiniteFieldNormalBasisExtension
\cross{FFNBX}{?rem?} &&
\end{tabular}
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}
+\label{domain FFNBX FiniteFieldNormalBasisExtension}
\begin{chunk}{domain FFNBX FiniteFieldNormalBasisExtension}
)abbrev domain FFNBX FiniteFieldNormalBasisExtension
++ Authors: J.Grabmeier, A.Scheerhorn
++ Date Created: 26.03.1991
++ References:
++ R.Lidl, H.Niederreiter: Finite Field, Encyclopedia of Mathematics and
++ Its Applications, Vol. 20, Cambridge Univ. Press, 1983, ISBN 0 521 30240 4
++ J. Grabmeier, A. Scheerhorn: Finite Fields in AXIOM.
++ AXIOM Technical Report Series, ATR/5 NP2522.
+++ Grab92 Finite Fields in Axiom
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ FiniteFieldNormalBasisExtensionByPolynomial(GF,n) implements a
++ finite extension field of degree n over the ground field GF.
@@ 67397,16 +67400,16 @@ o )show FiniteFieldNormalBasisExtensionByPolynomial
\cross{FFNBP}{?rem?} &&
\end{tabular}
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}
+\label{domain FFNBP FiniteFieldNormalBasisExtensionByPolynomial}
\begin{chunk}{domain FFNBP FiniteFieldNormalBasisExtensionByPolynomial}
)abbrev domain FFNBP FiniteFieldNormalBasisExtensionByPolynomial
++ Authors: J.Grabmeier, A.Scheerhorn
++ Date Created: 26.03.1991
++ Date Last Updated: 08 May 1991
++ References:
++ R.Lidl, H.Niederreiter: Finite Field, Encyclopedia of Mathematics and
++ Its Applications, Vol. 20, Cambridge Univ. Press, 1983, ISBN 0 521 30240 4
++ J. Grabmeier, A. Scheerhorn: Finite Fields in AXIOM .
++ AXIOM Technical Report Series, ATR/5 NP2522.
+++ Grab92 Finite Fields in Axiom
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ \spad{FiniteFieldNormalBasisExtensionByPolynomial(GF,uni)} implements a
++ finite extension of the ground field GF. The elements are
@@ 97721,15 +97724,15 @@ o )show FiniteField
\cross{IFF}{?rem?} &&
\end{tabular}
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}
+\label{domain IFF InnerFiniteField}
\begin{chunk}{domain IFF InnerFiniteField}
)abbrev domain IFF InnerFiniteField
++ Author: Mark Botch
++ Date Last Updated: 29 May 1990
++ Reference:
++ R.Lidl, H.Niederreiter: Finite Field, Encyclopedia of Mathematics an
++ Its Applications, Vol. 20, Cambridge Univ. Press, 1983, ISBN 0 521 30240 4
++ J. Grabmeier, A. Scheerhorn: Finite Fields in AXIOM.
++ AXIOM Technical Report Series, ATR/5 NP2522.
+++ Grab92 Finite Fields in Axiom
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ InnerFiniteField(p,n) implements finite fields with \spad{p**n} elements
++ where p is assumed prime but does not check.
@@ 99137,15 +99140,16 @@ o )show PrimeField
\cross{IPF}{?rem?} &
\end{tabular}
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}
+\label{domain IPF InnerPrimeField}
\begin{chunk}{domain IPF InnerPrimeField}
)abbrev domain IPF InnerPrimeField
++ Authors: N.N., J.Grabmeier, A.Scheerhorn
++ Date Created: ?, November 1990, 26.03.1991
++ Date Last Updated: 12 April 1991
++ References:
++ R.Lidl, H.Niederreiter: Finite Field, Encycoldia of Mathematics and
++ Its Applications, Vol. 20, Cambridge Univ. Press, 1983, ISBN 0 521 30240 4
++ AXIOM Technical Report Series, to appear.
+++ Grab92 Finite Fields in Axiom
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ InnerPrimeField(p) implements the field with p elements.
++ Note: argument p MUST be a prime (this domain does not check).
@@ 157752,14 +157756,16 @@ o )show PrimeField
\cross{PF}{?rem?} &&
\end{tabular}
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}
+\label{domain PF PrimeField}
\begin{chunk}{domain PF PrimeField}
)abbrev domain PF PrimeField
++ Authors: N.N.,
++ Date Created: November 1990, 26.03.1991
++ Date Last Updated: 31 March 1991
++ References:
++ R.Lidl, H.Niederreiter: Finite Field, Encycoldia of Mathematics and
++ Its Applications, Vol. 20, Cambridge Univ. Press, 1983, ISBN 0 521 30240 4
+++ Grab92 Finite Fields in Axiom
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ PrimeField(p) implements the field with p elements if p is a prime number.
++ Error: if p is not prime.
@@ 178113,11 +178119,15 @@ o )show SimpleAlgebraicExtension
\cross{SAE}{?rem?}
\end{tabular}
+See: Grabmeier\cite{Grab92}
+\label{domain SAE SimpleAlgebraicExtension}
\begin{chunk}{domain SAE SimpleAlgebraicExtension}
)abbrev domain SAE SimpleAlgebraicExtension
++ Author: Barry Trager, Manuel Bronstein, Clifton Williamson
++ Date Created: 1986
++ Date Last Updated: 9 May 1994
+++ References:
+++ Grab92 Finite Fields in Axiom
++ Description:
++ Algebraic extension of a ring by a single polynomial.
++ Domain which represents simple algebraic extensions of arbitrary
diff git a/books/bookvol10.4.pamphlet b/books/bookvol10.4.pamphlet
index b8a3da5..8aa366b 100644
 a/books/bookvol10.4.pamphlet
+++ b/books/bookvol10.4.pamphlet
@@ 1,5 +1,5 @@
\documentclass[dvipdfm]{book}
\newcommand{\VolumeName}{Volume 10: Axiom Algebra: Packages}
+\newcommand{\VolumeName}{Volume 10.4: Axiom Algebra: Packages}
\input{bookheader.tex}
\mainmatter
\setcounter{chapter}{0} % Chapter 1
@@ 21865,14 +21865,15 @@ o )show DiscreteLogarithmPackage
{\bf Exports:}\\
\cross{DLP}{shanksDiscLogAlgorithm}
+See: Grabmeier\cite{Grab92}
+\label{package DLP DiscreteLogarithmPackage}
\begin{chunk}{package DLP DiscreteLogarithmPackage}
)abbrev package DLP DiscreteLogarithmPackage
++ Author: J. Grabmeier, A. Scheerhorn
++ Date Created: 12 March 1991
++ Date Last Updated: 31 March 1991
++ References:
++ J. Grabmeier, A. Scheerhorn: Finite Fields in AXIOM.
++ AXIOM Technical Report Series, ATR/5 NP2522.
+++ Grab92 Finite Fields in Axiom
++ Description:
++ DiscreteLogarithmPackage implements help functions for discrete logarithms
++ in monoids using small cyclic groups.
@@ 49753,11 +49754,15 @@ o )show FiniteFieldFactorizationWithSizeParseBySideEffect
\end{tabular}
+See: Grabmeier\cite{Grab92}
+\label{package FFFACTSE FiniteFieldFactorizationWithSizeParseBySideEffect}
\begin{chunk}{package FFFACTSE FiniteFieldFactorizationWithSizeParseBySideEffect}
)abbrev package FFFACTSE FiniteFieldFactorizationWithSizeParseBySideEffect
++ Author: Patrice Naudin, Claude Quitte, Kaj Laursen
++ Date Created: September 1996
++ Date Last Updated: April 2010 by Tim Daly
+++ References:
+++ Grab92 Finite Fields in Axiom
++ Description:
++ Part of the package for Algebraic Function Fields in one variable (PAFF)
++ It has been modified (very slitely) so that each time the "factor"
@@ 50283,16 +50288,16 @@ o )show FiniteFieldFunctions
\cross{FFF}{sizeMultiplication}
\end{tabular}
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}
+\label{package FFF FiniteFieldFunctions}
\begin{chunk}{package FFF FiniteFieldFunctions}
)abbrev package FFF FiniteFieldFunctions
++ Author: J. Grabmeier, A. Scheerhorn
++ Date Created: 21 March 1991
++ Date Last Updated: 31 March 1991
++ References:
++ Lidl, R. & Niederreiter, H., "Finite Fields",
++ Encycl. of Math. 20, AddisonWesley, 1983
++ J. Grabmeier, A. Scheerhorn: Finite Fields in AXIOM.
++ AXIOM Technical Report Series, ATR/5 NP2522.
+++ Grab92 Finite Fields in Axiom
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ FiniteFieldFunctions(GF) is a package with functions
++ concerning finite extension fields of the finite ground field GF,
@@ 50755,15 +50760,15 @@ o )show FiniteFieldHomomorphisms
{\bf Exports:}\\
\cross{FFHOM}{coerce}
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}
+\label{package FFHOM FiniteFieldHomomorphisms}
\begin{chunk}{package FFHOM FiniteFieldHomomorphisms}
)abbrev package FFHOM FiniteFieldHomomorphisms
++ Authors: J.Grabmeier, A.Scheerhorn
++ Date Created: 26.03.1991
++ References:
++ R.Lidl, H.Niederreiter: Finite Field, Encycoldia of Mathematics and
++ Its Applications, Vol. 20, Cambridge Univ. Press, 1983, ISBN 0 521 30240 4
++ J. Grabmeier, A. Scheerhorn: Finite Fields in AXIOM.
++ AXIOM Technical Report Series, ATR/5 NP2522.
+++ Grab92 Finite Fields in Axiom
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ FiniteFieldHomomorphisms(F1,GF,F2) exports coercion functions of
++ elements between the fields F1 and F2, which both must be
@@ 51503,18 +51508,17 @@ o )show FiniteFieldPolynomialPackage
\cross{FFPOLY}{reducedQPowers}
\end{tabular}
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}, Lenstra\cite{Lens87}
+\label{package FFPOLY FiniteFieldPolynomialPackage}
\begin{chunk}{package FFPOLY FiniteFieldPolynomialPackage}
)abbrev package FFPOLY FiniteFieldPolynomialPackage
++ Author: A. Bouyer, J. Grabmeier, A. Scheerhorn, R. Sutor, B. Trager
++ Date Created: January 1991
++ Date Last Updated: 1 June 1994
++ References:
++ [LS] Lenstra, H. W. & Schoof, R. J., "Primitivive Normal Bases
++ for Finite Fields", Math. Comp. 48, 1987, pp. 217231
++ [LN] Lidl, R. & Niederreiter, H., "Finite Fields",
++ Encycl. of Math. 20, AddisonWesley, 1983
++ J. Grabmeier, A. Scheerhorn: Finite Fields in Axiom.
++ Axiom Technical Report Series, to appear.
+++ Grab92 Finite Fields in Axiom
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
+++ Lens87 Primitive Normal Bases for Finite Fields
++ Description:
++ This package provides a number of functions for generating, counting
++ and testing irreducible, normal, primitive, random polynomials
@@ 53299,14 +53303,15 @@ o )show FiniteFieldPolynomialPackage2
{\bf Exports:}\\
\cross{FFPOLY2}{rootOfIrreduciblePoly}
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}
+\label{package FFPOLY2 FiniteFieldPolynomialPackage2}
\begin{chunk}{package FFPOLY2 FiniteFieldPolynomialPackage2}
)abbrev package FFPOLY2 FiniteFieldPolynomialPackage2
++ Authors: J.Grabmeier, A.Scheerhorn
++ Date Created: 26.03.1991
++ References:
++ R.Lidl, H.Niederreiter: Finite Field, Encycoldia of Mathematics and
++ Its Applications, Vol. 20, Cambridge Univ. Press, 1983, ISBN 0 521 30240 4
++ AXIOM Technical Report Series, to appear.
+++ Grab92 Finite Fields in Axiom
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ FiniteFieldPolynomialPackage2(F,GF) exports some functions concerning
++ finite fields, which depend on a finite field GF and an
@@ 82726,21 +82731,21 @@ o )show InnerNormalBasisFieldFunctions
\cross{INBFF}{?/?}
\end{tabular}
+See: Grabmeier\cite{Grab92}, Lidl\cite{lidl83}, Stinson\cite{Stin90},
+Itoh\cite{Itoh88}
+\label{package INBFF InnerNormalBasisFieldFunctions}
\begin{chunk}{package INBFF InnerNormalBasisFieldFunctions}
)abbrev package INBFF InnerNormalBasisFieldFunctions
++ Authors: J.Grabmeier, A.Scheerhorn
++ Date Created: 26.03.1991
++ Date Last Updated: 31 March 1991
++ References:
++ R.Lidl, H.Niederreiter: Finite Field, Encyclopedia of Mathematics and
++ Its Applications, Vol. 20, Cambridge Univ. Press, 1983, ISBN 0 521 30240 4
++ D.R.Stinson: Some observations on parallel Algorithms for fast
++ exponentiation in GF(2^n), Siam J. Comp., Vol.19, No.4, pp.711717,
++ August 1990
++ T.Itoh, S.Tsujii: A fast algorithm for computing multiplicative inverses
++ in GF(2^m) using normal bases, Inf. and Comp. 78, pp.171177, 1988
++ J. Grabmeier, A. Scheerhorn: Finite Fields in AXIOM.
++ AXIOM Technical Report Series, ATR/5 NP2522.
+++ Grab92 Finite Fields in Axiom
+++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
+++ Stin90 Some observations on parallel Algorithms for fast exponentiation
+++ in GF(2^n)
+++ Itoh88 A fast algorithm for computing multiplicative inverses
+++ in GF(2^m) using normal bases
++ Description:
++ InnerNormalBasisFieldFunctions(GF) (unexposed):
++ This package has functions used by
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 5e6b52b..4be2556 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 6,6 +6,9 @@
% See: http://www.swmath.org/software/63
% See: http://www.netlib.org/bibnet/journals/axiom.ps.gz
\chapter{The Axiom Bibliography}
+This bibliography serves two purposes. It generates output for the
+ACM bibliography (beebe.bib) and Axiom (axiom.bib).
+
This bibliography covers areas of computational mathematics.
Papers which mention Axiom have a ``keyword='' entry of ``axiomref''.
Papers we have on site have a ``paper='' entry. Papers which are
@@ 21,6 +24,272 @@ named algorithm or author.
Introduction of special terms (e.g. Toeplitz matrix) may include a
paragraph for those unfamiliar with the terms.
+\section{Axiom Literate Sources}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu00,
+ author = "Axiom Authors",
+ title = "Volume 0: Axiom Jenks and Sutor",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol0.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu01,
+ author = "Axiom Authors",
+ title = "Volume 1: Axiom Tutorial",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol1.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu02,
+ author = "Axiom Authors",
+ title = "Volume 2: Axiom Users Guide",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol2.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu03,
+ author = "Axiom Authors",
+ title = "Volume 3: Axiom Programmers Guide",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol3.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu04,
+ author = "Axiom Authors",
+ title = "Volume 4: Axiom Developers Guide",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol4.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu05,
+ author = "Axiom Authors",
+ title = "Volume 5: Axiom Interpreter",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol5.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu06,
+ author = "Axiom Authors",
+ title = "Volume 6: Axiom Command",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol6.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu07,
+ author = "Axiom Authors",
+ title = "Volume 7: Axiom Hyperdoc",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol7.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu71,
+ author = "Axiom Authors",
+ title = "Volume 7.1: Axiom Hyperdoc Pages",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol7.1.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu08,
+ author = "Axiom Authors",
+ title = "Volume 8: Axiom Graphics",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol8.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu81,
+ author = "Axiom Authors",
+ title = "Volume 8.1: Axiom Gallery",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol8.1.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu09,
+ author = "Axiom Authors",
+ title = "Volume 9: Axiom Compiler",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol9.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu91,
+ author = "Axiom Authors",
+ title = "Volume 9.1: Axiom Compiler Details",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol9.1.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu10,
+ author = "Axiom Authors",
+ title = "Volume 10: Axiom Algebra: Implementation",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol10.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu101,
+ author = "Axiom Authors",
+ title = "Volume 10.1: Axiom Algebra: Theory",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol10.1.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu102,
+ author = "Axiom Authors",
+ title = "Volume 10.2: Axiom Algebra: Categories",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol10.2.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu103,
+ author = "Axiom Authors",
+ title = "Volume 10.3: Axiom Algebra: Domains",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol10.3.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu104,
+ author = "Axiom Authors",
+ title = "Volume 10.4: Axiom Algebra: Packages",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol10.4.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu105,
+ author = "Axiom Authors",
+ title = "Volume 10.5: Axiom Algebra: Numerics",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol10.5.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu11,
+ author = "Axiom Authors",
+ title = "Volume 11: Axiom Browser",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol11.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu12,
+ author = "Axiom Authors",
+ title = "Volume 12: Axiom Crystal",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol12.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu13,
+ author = "Axiom Authors",
+ title = "Volume 13: Proving Axiom Correct",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol13.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volu14,
+ author = "Axiom Authors",
+ title = "Volume 14: Algorithms",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvol14.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Axiom Authors}
+\begin{chunk}{axiom.bib}
+@book{Volubib,
+ author = "Axiom Authors",
+ title = "Volume Bibliography: Axiom Literature Citations",
+ url = "http://axiomdeveloper.org/axiomwebsite/bookvolbib.pdf",
+ year = "2016"
+}
+
+\end{chunk}
+
\section{Algebra Documentation References}
\index{Gonshor, H.}
@@ 3483,7 +3752,7 @@ when shown in factored form.
\index{Bradford, Russell}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@misc{Corl0,
+@misc{Corl05,
author = "Corless, Robert M. and Jeffrey, David J. and Watt, Stephen M.
and Bradford, Russell and Davenport, James H.",
title = "Reasoning about the elementary functions of complex analysis",
@@ 3715,13 +3984,17 @@ Proc. IMACS Symposium, Lille, France, (1993)
\index{van Hoeij, Mark}
\index{Monagan, Michael}
\begin{chunk}{ignore}
\bibitem[van Hoeij]{Hoeij04} {van Hoeij}, Mark; Monagan, Michael
 title = "Algorithms for Polynomial GCD Computation over Algebraic Function Fields",
+\begin{chunk}{axiom.bib}
+@inproceedings{Hoei04,
+ author = "van Hoeij, Mark and Monagan, Michael",
+ title = "Algorithms for Polynomial GCD Computation over Algebraic
+ Function Fields",
+ booktitle = "Proc. ISSAC 04",
+ isbn = "158113827X",
url = "http://www.cecm.sfu.ca/personal/mmonagan/papers/AFGCD.pdf",
 paper = "Hoeij04.pdf",
 abstract = "
 Let $L$ be an algebraic function field in $k \ge 0$ parameters
+ paper = "Hoei04.pdf",
+ abstract =
+ "Let $L$ be an algebraic function field in $k \ge 0$ parameters
$t_1,\ldots,t)k$. Let $f_1$, $f_2$ be nonzero polynomials in
$L[x]$. We give two algorithms for computing their gcd. The first, a
modular GCD algorithm, is an extension of the modular GCD algorithm
@@ 3731,6 +4004,7 @@ Proc. IMACS Symposium, Lille, France, (1993)
for computing gcds over triangular sets. The modification reduces
coefficient grownth in $L$ to be linear. We give an empirical
comparison of the two algorithms using implementations in Maple."
+}
\end{chunk}
@@ 5724,11 +5998,17 @@ Petkovsek, Marko
\end{chunk}
\index{Bronstein, Manuel}
\begin{chunk}{ignore}
\bibitem[Bronstein xb]{Broxb} Bronstein, Manuel
 title = "Computer Algebra Algorithms for Linear Ordinary Differential and Difference equations",
+\begin{chunk}{axiom.bib}
+@inproceedings{Bron01,
+ author = "Bronstein, Manuel",
+ title = "Computer Algebra Algorithms for Linear Ordinary Differential
+ and Difference equations",
url = "http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/ecm3.pdf",
 paper = "Broxb.pdf",
+ booktitle = "European Congress of Mathematics",
+ series = "Progress in Mathematics",
+ volume = "202",
+ pages = "105119",
+ paper = "Bron01.pdf",
abstract = "
Galois theory has now produced algorithms for solving linear ordinary
differential and difference equations in closed form. In addition,
@@ 5736,6 +6016,7 @@ Petkovsek, Marko
implementable in computer algebra systems. After introducing the
relevant parts of the theory, we describe the latest algorithms for
solving such equations."
+}
\end{chunk}
@@ 5838,19 +6119,29 @@ Petkovsek, Marko
degrees. In the base case, this yields in particular a new algorithm
for computing the rational solutions of $q$difference equations with
polynomial coefficients."
+}
\end{chunk}
\index{Bronstein, Manuel}
\index{Lafaille, S\'ebastien}
\begin{chunk}{ignore}
\bibitem[Bronstein 02]{Bro02} Bronstein, Manuel; Lafaille, S\'ebastien
 title = "Solutions of linear ordinary differential equations in terms of special functions",
+\begin{chunk}{axiom.bib}
+@inproceedings{Bron02,
+ author = "Bronstein, Manuel and Lafaille, S\'ebastien",
+ title = "Solutions of linear ordinary differential equations in terms
+ of special functions",
+ booktitle = "Proc. ISSAC '02",
+ publisher = "ACM Press",
+ pages = "2328",
+ year = "2002",
+ isbn = "1581134843",
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/issac2002.pdf",
 paper = "Bro02.pdf",
 abstract = "
 We describe a new algorithm for computing special function solutions
+ paper = "Bron02.pdf",
+ url2 = "http://xena.hunter.cuny.edu/ksda/papers/bronstein2.pdf",
+ paper2 = "Bron02x.pdf",
+ abstract =
+ "We describe a new algorithm for computing special function solutions
of the form $y(x) = m(x)F(\eta(x))$ of second order linear ordinary
differential equations, where $m(x)$ is an arbitrary Liouvillian
function, $\eta(x)$ is an arbitrary rational function, and $F$
@@ 5863,7 +6154,7 @@ Petkovsek, Marko
Kummer and Whittaker functions. It is also able to identify the values
of the parameters entering those special functions, and can be
generalized to equations of higher order."

+}
\end{chunk}
@@ 7390,12 +7681,16 @@ Ph.D Diss. MIT, May 1961; also Computers and Thought, Feigenbaum and Feldman.
\end{chunk}
\index{Terelius, Bjorn}
\begin{chunk}{ignore}
\bibitem[Terelius 09]{Tere09} Terelius, Bjorn
+\begin{chunk}{axiom.bib}
+@mastersthesis{Tere09,
+ author = "Terelius, Bjorn",
title = "Symbolic Integration",
+ school = "Royal Institute of Technology",
+ address = "Stockholm, Sweden",
+ year = "2009",
paper = "Tere09.pdf",
 abstract = "
 Symbolic integration is the problem of expressing an indefinite integral
+ abstract =
+ "Symbolic integration is the problem of expressing an indefinite integral
$\int{f}$ of a given function $f$ as a finite combination $g$ of elementary
functions, or more generally, to determine whether a certain class of
functions contains an element $g$ such that $g^\prime = f$.
@@ 7418,6 +7713,7 @@ Ph.D Diss. MIT, May 1961; also Computers and Thought, Feigenbaum and Feldman.
experiences it has given us. We also demonstrate an implementation of
the rulebased approach and how it can be used, not only to compute
integrals, but also to generate readable derivations of the results."
+}
\end{chunk}
@@ 10683,95 +10979,358 @@ J. Symbolic Computation 5, 237259 (1988)
\section{To Be Classified} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Wang, Dongming}
+\index{Wang, Paul S.}
\begin{chunk}{axiom.bib}
@article{Wang93,
 author = "Wang, Dongming",
 title = "An Elimination Method for Polynomial Systems",
 journal = "J. Symbolic Computation",
 volume = "16",
 number = "2",
 pages = "83114",
 year = "1993",
 paper = "Wang93.pdf",
+@article{Wang74,
+ author = "Wang, Paul S.",
+ title = "The Undecidability of the Existence of Zeros of Real Elementary
+ Functions",
+ journal = "J. ACM",
+ volume = "21",
+ number = "4",
+ pages = "586589",
+ year = "1974",
+ paper = "Wang74.djvu",
abstract =
 "We present an elimination method for polynomial systems, in the form
 of three main algorithms. For any given system [$\mathbb{P}$,$\mathbb{Q}$]
 of two sets of multivariate polynomials, one of the algorithms computes a
 sequence of triangular forms $\mathbb{T}_1,\ldots,\mathbb{T}_e$ and
 polynomial sets $\mathbb{U}_1,\ldots,\mathbb{U}_e$ such that
 Zero($\mathbb{P}$/$\mathbb{Q}$)
 $= \cup_{i=1}^e {\rm\ Zero}(\mathbb{T}_i/\mathbb{U}_i)$,
 where Zero($\mathbb{P}$/$\mathbb{Q}$) denotes the set of common zeros of
 the polynomials in $\mathbb{P}$ which are not zeros of any polynomial in
 $\mathbb{Q}$, and similarly for Zero($\mathbb{T}_i$/$\mathbb{U}_i$).
 The two other algorithms compute the same zero decomposition but with nicer
 properties such as Zero$(\mathbb{T}_i/\mathbb{U}_i) \ne 0$ for each $i$.
 One of them, for which the computed triangular systems
 [$\mathbb{T}_i$, $\mathbb{U}_i$] possess the projection property, provides
 a quantifier elimination procedure for algebraically closed fields.
 For the other, the computed triangular forms $\mathbb{T}_i$ are
 irreducible. The relationship between our method and some existing
 elimination methods is explained. Experimental data for a set of test
 examples by a draft implementation of the method are provided, and show
 that the efficiency of our method is comparable with that of some
 wellknown methods. A few encouraging examples are given in detail for
 illustration."
+ "From Richardson's undecidability results, it is shown that the predicate
+ ``there exists a real number $r$ such that $G(r)=0$'' is recursively
+ undecidable for $G(x)$ in a class of functions which involves polynomials
+ and the sine function. The deduction follows that the convergence of a
+ class of improper integrals is recursively undecidable."
}
\end{chunk}
\index{Wang, Dongming}
+\index{Langley, Simon}
+\index{Richardson, Daniel}
\begin{chunk}{axiom.bib}
@article{Wang94,
 author = "Wang, Dongming",
 title = "Differentiation and Integration of Indefinite Summations with
 Respect to Indexed Variables  Some Rules and Applications",
 journal = "J. Symbolic Computation",
 volume = "18",
 number = "3",
 pages = "249263",
 year = "1994",
 paper = "Wang94.pdf",
 abstract =
 "In this paper we present some rules for the differentiation and
 integration of expressions involving indefinite summations with
 respect to indexed variables which have not yet been taken into
 account of current computer algebra systems. These rules, together
 with several others, have been implemented in MACSYMA and MAPLE as a
 toolkit for manipulating indefinite summations. We discuss some
 implementation issues and report our experiments with a set of typical
 examples. The present work is motivated by our investigation in the
 computeraided analysis and derivation of artificial neural systems.
 The application of our rules to this subject is briefly explained."
+@article{Lang02,
+ author = "Langley, Simon and Richardson, Daniel",
+ title = "What can we do with a Solution?",
+ journal = "Electronic Notes in Theoretical Computer Science",
+ volume = "66",
+ number = "1",
+ year = "2002",
+ url = "http://www.elsevier.nl/locate/entcs/volume66.html",
+ paper = "Lang02.pdf",
+ abstract =
+ "If $S=0$ is a system of $n$ equations and unknowns over $\mathbb{C}$
+ and $S(\alpha)=0$ to what extent can we compute with the point $\alpha$?
+ In particular, can we decide whether or not a polynomial expressions
+ in the components of $\alpha$ with integral coefficients is zero?
+ This question is considered for both algebraic and elementary systems
+ of equations."
}
\end{chunk}
\index{Wang, Dongming}
+\index{Johnson, S.C.}
\begin{chunk}{axiom.bib}
@article{Wang95a,
 author = "Wang, Dongming",
 title = "A Method for Proving Theorems in Differential Geometry and
 Mechanics",
 journal = "J. Universal Computer Science",
 volume = "1",
 number = "9",
 pages = "658673",
 year = "1995",
 url = "http://www.jucs.org/jucs\_1\_9/a\_method\_for\_proving",
 paper = "Wang95a.pdf",
 abstract =
 "A zero decomposition algorithm is presented and used to devise a
 method for proving theorems automatically in differential geometry and
 mechanics. The method has been implemented and its practical
 efficiency is demonstrated by several nontrivial examples including
 Bertrand s theorem, Schell s theorem and KeplerNewton s laws."
+@article{John71,
+ author = "Johnson, S.C.",
+ title = "On the Problem of Recognizing Zero",
+ journal = "J. ACM",
+ volume = "18",
+ number = "4",
+ year = "1971",
+ pages = "559565",
+ paper = "John71.djvu"
}
\end{chunk}
\index{Wang, Dongming}
+\index{Richardson, Daniel}
+\begin{chunk}{axiom.bib}
+@article{Rich07,
+ author = "Richardson, Daniel",
+ title = "How to Recognize Zero",
+ journal = "J. Symbolic Computation",
+ volume = "24",
+ number = "6",
+ year = "2007",
+ pages = "627645",
+ paper = "Rich07.pdf",
+ abstract =
+ "An elementary point is a point in complex $n$ space, which is an
+ isolated, nonsingular solution of $n$ equations in $n$ variables,
+ each equation being either or the form $p=0$, where $p$ is a polynomial
+ in $\mathbb{Q}[x_1,\ldots,x_n]$, or of the form $x_j=e^{x_i}=0$. An
+ elementary number is the polynomial image of an elementary point. In
+ this article a semialgorithm is given to decide whether or not a
+ given elementary number is zero. It is proved that this semialgorithm
+ is an algorithm, i.e. that it always terminates, unless it is given
+ a problem containing a counter example to Schanuel's conjecture."
+}
+
+\end{chunk}
+
+\index{Hur, Namhyun}
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Hurx00,
+ author = "Hur, Namhyun and Davenport, James H.",
+ title = "An exact real algebraic arithmetic with equality determination",
+ booktitle = "Proc. ISSAC 2000",
+ series = "ISSAC '00",
+ pages = "169174",
+ year = "2000",
+ paper = "Hurx00.djvu",
+ abstract =
+ "We describe a new arithmetic model for real algebraic numbers with
+ an exact equality determination. The model represents a real algebraic
+ number as a pair of an arbitrary precision numerical value and a
+ symbolic expression. For the numerical part we currently (another
+ representation could be used) use the dyadic exact real number and
+ for the symbolic part we use a squarefree polynomial for the real
+ algebraic number. In this model we show that we can decide exactly
+ the equality of real algebraic numbers."
+}
+
+\end{chunk}
+
+\index{Chow, Timothy Y.}
+\begin{chunk}{axiom.bib}
+@article{Chow99,
+ author = "Chow, Timothy Y.",
+ title = "What is a closedform number?",
+ journal = "The American Mathematical Monthly",
+ volume = "106",
+ number = "5",
+ pages = "440448",
+ paper = "Chowxx.pdf",
+ year = "1999"
+}
+
+\end{chunk}
+
+\index{Yap, CheeKeng}
+\begin{chunk}{axiom.bib}
+@book{Yapx00,
+ author = "Yap, CheeKeng",
+ title = "Fundamental Problems in Algorithmic Algebra",
+ year = "2000",
+ paper = "Yapx00.pdf",
+ url =
+"http://www.csie.nuk.edu.tw/~cychen/gcd/Fundamental%20Problems%20in%20Algorithmic%20Algebra.pdf",
+ abstract =
+ "The author shows an interesting way to write arithmetic operations.
+ Given
+ \[z(x,y)=\frac{axy+bx+cy+d}
+ {a^{\prime}xy+b^{\prime}x+c^{\prime}y+d^{\prime}}\]
+ we call the numerical constants $a,b,\ldots,c^{\prime},d^{\prime}$
+ {\sl state variables} and use the compact notation
+ \[z(x,y)=\frac{(a,b,c,d)}{(a^{\prime},b^{\prime},c^{\prime},d^{\prime})}
+ {x \choose y}\]
+ The arithmetic operations can be recovered by suitable choices for
+ the state variables:
+ \[x+y=\frac{(0,1,1,0)}{(0,0,0,1)}{x \choose y}\]
+ \[xy=\frac{(0,1,1,0)}{(0,0,0,1)}{x \choose y}\]
+ \[xy=\frac{(1,0,0,0)}{(0,0,0,1)}{x \choose y}\]
+ \[x/y=\frac{(0,1,0,0)}{(0,0,1,0)}{x \choose y}\]
+ \[\frac{ax+b}{cx+d}=\frac{(0,a,0,b)}{(0,c,0,d)}{x \choose y}\]
+ and if
+ \[x=q+\frac{p}{x^{\prime}}\]
+ then
+ \[\begin{array}{ccc}
+ z(x,y)&=&\displaystyle\frac{a(q+p/x^{\prime})y+b(q+p/x^{\prime})+cy+d}
+ {a^{\prime}(q+p/x^{\prime})y+
+ b^{\prime}(q+p/x^{\prime})+
+ c^{\prime}y+d^{\prime}}\\
+ &=&\displaystyle\frac{(aq+c,bq+d,ap,bp)}
+ {(a^{\prime}q+c^{\prime},b^{\prime}q+d^{\prime},a^{\prime}p,
+ b^{\prime}p)}{x^{\prime} \choose {y}}
+ \end{array}\]"
+}
+
+\end{chunk}
+
+\index{Burnikel, C.}
+\index{Fleischer, R.}
+\index{Mehlhom, K.}
+\index{Schirra, S.}
+\begin{chunk}{axiom.bib}
+@article{Burn00,
+ author = "Burnikel, C. and Fleischer, R. and Mehlhom, K. and Schirra, S.",
+ title = "A Strong and Easily Computable Separation Bound for Arithmetic
+ Expressions Involving Radicals",
+ journal = "Algorithmica",
+ volume = "27",
+ pages = "8799",
+ year = "2000",
+ paper = "Burn00.pdf",
+ abstract =
+ "We consider arithmetic expressions over operators $+$, $$, $*$, $/$,
+ and $\sqrt[k]$, with integer operands. For an expression $E$ having
+ value $\eta$, a separation bound $sep(E)$ is a positive real number with
+ the property that $\eta \ne 0$ implies $\vert\eta\vert \ge sep(E)$. We
+ propose a new separation bound that is easy to compute and stronger
+ than previous bounds."
+}
+
+\end{chunk}
+
+\index{Corless, Robert M.}
+\index{Jeffrey, David J.}
+\index{Knuth, Donald E.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Corl97,
+ author = "Corless, Robert M. and Jeffrey, David J. and Knuth, Donald E.",
+ title = "A Sequence of Series for The Lambert W Function",
+ booktitle = "Proc. ISSAC 1997",
+ series = "ISSAC '97",
+ pages = "197204",
+ year = "1997",
+ paper = "Corl97.pdf",
+ abstract =
+ "We give a uniform treatment of several series expansions for the
+ Lambert $W$ function, leading to an infinite family of new series.
+ We also discuss standardization, complex branches, a family of
+ arbitraryorder iterative methods for computation of $W_i$, and
+ give a theorem showing how to correctly solve another simple and
+ frequently occurring nonlinear equation in terms of $W$ and the
+ unwinding number"
+}
+
+\end{chunk}
+
+\index{Corless, Robert M.}
+\index{Jeffrey, David J.}
+\begin{chunk}{axiom.bib}
+@article{Corl96,
+ author = "Corless, Robert M. and Jeffrey, David J.",
+ title = "Editor's Corner: The Unwinding Number",
+ journal = "SIGSAM Bulletin",
+ volume = "30",
+ number = "1",
+ issue = "115",
+ pages = "2835",
+ year = "1996",
+ paper = "Corl96.pdf",
+ abstract =
+ "From the Oxford English Dictionary we find that {\sl to unwind}
+ can mean ``to become free from a convoluted state''. Further down
+ we find the quationation ``The solutoin of all knots, and unwinding
+ of all intricacies'', from H. Brooke (The Fool of Quality, 1809).
+ While we do not promise that the unwinding number, defined below,
+ will solve {\sl all} intricacies, we do show that it may help for
+ quite a few problems."
+}
+
+\end{chunk}
+
+\index{Corless, Robert M.}
+\index{Jeffrey, David J.}
+\begin{chunk}{axiom.bib}
+@article{Corl98,
+ author = "Corless, Robert M. and Jeffrey, David J.",
+ title = "Graphing Elementary Riemann Surfaces",
+ journal = "SIGSAM Bulletin",
+ volume = "32",
+ number = "1",
+ pages = "1117",
+ year = "1998",
+ paper = "Corl98.pdf",
+ abstract =
+ "This paper discusses one of the prettiest pieces of elementary
+ mathematics or computer algebra, that we have ever had the pleasure
+ to learn. The tricks that we discuss here are certainly ``wellknown''
+ (that is, in the literature), but we didn't know them until recently,
+ and none of our immediate colleagues knew them either. Therefore we
+ believe that it is useful to publicize them further. We hope that
+ you find these ideas as pleasant and useful as we do."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang93,
+ author = "Wang, Dongming",
+ title = "An Elimination Method for Polynomial Systems",
+ journal = "J. Symbolic Computation",
+ volume = "16",
+ number = "2",
+ pages = "83114",
+ year = "1993",
+ paper = "Wang93.pdf",
+ abstract =
+ "We present an elimination method for polynomial systems, in the form
+ of three main algorithms. For any given system [$\mathbb{P}$,$\mathbb{Q}$]
+ of two sets of multivariate polynomials, one of the algorithms computes a
+ sequence of triangular forms $\mathbb{T}_1,\ldots,\mathbb{T}_e$ and
+ polynomial sets $\mathbb{U}_1,\ldots,\mathbb{U}_e$ such that
+ Zero($\mathbb{P}$/$\mathbb{Q}$)
+ $= \cup_{i=1}^e {\rm\ Zero}(\mathbb{T}_i/\mathbb{U}_i)$,
+ where Zero($\mathbb{P}$/$\mathbb{Q}$) denotes the set of common zeros of
+ the polynomials in $\mathbb{P}$ which are not zeros of any polynomial in
+ $\mathbb{Q}$, and similarly for Zero($\mathbb{T}_i$/$\mathbb{U}_i$).
+ The two other algorithms compute the same zero decomposition but with nicer
+ properties such as Zero$(\mathbb{T}_i/\mathbb{U}_i) \ne 0$ for each $i$.
+ One of them, for which the computed triangular systems
+ [$\mathbb{T}_i$, $\mathbb{U}_i$] possess the projection property, provides
+ a quantifier elimination procedure for algebraically closed fields.
+ For the other, the computed triangular forms $\mathbb{T}_i$ are
+ irreducible. The relationship between our method and some existing
+ elimination methods is explained. Experimental data for a set of test
+ examples by a draft implementation of the method are provided, and show
+ that the efficiency of our method is comparable with that of some
+ wellknown methods. A few encouraging examples are given in detail for
+ illustration."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang94,
+ author = "Wang, Dongming",
+ title = "Differentiation and Integration of Indefinite Summations with
+ Respect to Indexed Variables  Some Rules and Applications",
+ journal = "J. Symbolic Computation",
+ volume = "18",
+ number = "3",
+ pages = "249263",
+ year = "1994",
+ paper = "Wang94.pdf",
+ abstract =
+ "In this paper we present some rules for the differentiation and
+ integration of expressions involving indefinite summations with
+ respect to indexed variables which have not yet been taken into
+ account of current computer algebra systems. These rules, together
+ with several others, have been implemented in MACSYMA and MAPLE as a
+ toolkit for manipulating indefinite summations. We discuss some
+ implementation issues and report our experiments with a set of typical
+ examples. The present work is motivated by our investigation in the
+ computeraided analysis and derivation of artificial neural systems.
+ The application of our rules to this subject is briefly explained."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@article{Wang95a,
+ author = "Wang, Dongming",
+ title = "A Method for Proving Theorems in Differential Geometry and
+ Mechanics",
+ journal = "J. Universal Computer Science",
+ volume = "1",
+ number = "9",
+ pages = "658673",
+ year = "1995",
+ url = "http://www.jucs.org/jucs\_1\_9/a\_method\_for\_proving",
+ paper = "Wang95a.pdf",
+ abstract =
+ "A zero decomposition algorithm is presented and used to devise a
+ method for proving theorems automatically in differential geometry and
+ mechanics. The method has been implemented and its practical
+ efficiency is demonstrated by several nontrivial examples including
+ Bertrand s theorem, Schell s theorem and KeplerNewton s laws."
+}
+
+\end{chunk}
+
+\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@article{Wang98,
author = "Wang, Dongming",
@@ 11777,6 +12336,7 @@ techniques."
\S4.2.17 FoxBox and other blackbox systems, pages 383385.",
isbn = "3540654666",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/01/symnum.pdf",
+ keywords = "axiomref",
paper = "Grab03.pdf",
}
@@ 12472,6 +13032,46 @@ techniques."
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Augot:1991:MDS,
+ author = "D. Augot and P. Charpin and N. Sendrier",
+ title = "The minimum distance of some binary codes via the
+ {Newton}'s identities",
+ crossref = "Cohen:1991:EIS",
+ pages = "6573",
+ month = "",
+ year = "1991",
+ bibdate = "Tue Sep 17 06:41:20 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "The authors propose a natural way of deciding whether
+ a given cyclic code contains a word of given weight.
+ The method is based on the manipulation of the locators
+ and of the locator polynomial of a codeword x. Because
+ of the dimensions of the problem, one needs to use
+ symbolic computation software, like Maple or Scratchpad
+ II. The method can be ineffective when the length is
+ too large. The paper is in two parts: In the first
+ part, they present the main definitions and properties
+ needed. In the second part, they explain how to use
+ these properties, and, as illustration, prove the three
+ following facts: the dual of the BCH code of length 63
+ and designed distance 9 has true minimum distance 14
+ (which was already known). The BCH code of length 1023
+ and designed distance 253 has minimum distance 253. The
+ cyclic codes of length 2/sup 11/, 2/sup 13/, 2/sup 17/,
+ with generator polynomial m/sub 1/(x) and m/sub 7/(x)
+ have minimum distance 4.",
+ acknowledgement = acknhfb,
+ affiliation = "Paris 6 Univ., France",
+ classification = "B6120B (Codes)",
+ keywords = "BCH code; Binary codes; Codeword; Cyclic codes;
+ Generator polynomial; Locator polynomial; Minimum
+ distance; Newton identities; Symbolic computation",
+ language = "English",
+ thesaurus = "Codes",
+}
+
+\end{chunk}
\index{Adams, William W.}
\index{Loustaunau, Philippe}
@@ 12499,6 +13099,18 @@ American Mathematical Society (1994)
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Andrews:1984:RS,
+ author = "George E. Andrews",
+ title = "{Ramanujan} and {SCRATCHPAD}",
+ crossref = "Golden:1984:PMU",
+ pages = "383??",
+ year = "1984",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.1.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+}
+
+\end{chunk}
\index{Andrews, George E.}
\begin{chunk}{axiom.bib}
@@ 12544,6 +13156,20 @@ American Mathematical Society (1994)
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Andrews:1988:ASP,
+ author = "G. E. Andrews",
+ title = "Application of {Scratchpad} to problems in special
+ functions and combinatorics",
+ crossref = "Janssen:1988:TCA",
+ pages = "158??",
+ year = "1988",
+ bibdate = "Fri Dec 29 18:28:25 1995",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.1.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+}
+
+\end{chunk}
\begin{chunk}{axiom.bib}
@book{Anon91,
@@ 12810,14 +13436,23 @@ American Mathematical Society (1994)
\index{Blair, Fred W.}
\index{Griesmer, James H.}
\index{Jenks, Richard D.}
\begin{chunk}{ignore}
\bibitem[Blair 70]{BGJ70}
+\begin{chunk}{axiom.bib}
+@inproceedings{Blai70,
author = "Blair, Fred W. and Griesmer, James H. and Jenks, Richard D.",
title = "An interactive facility for symbolic mathematics",
+ booktitle = "Proc. International Computing Symposium, Bonn, Germany",
year = "1970",
pages = "394419",
keywords = "axiomref",
Proc. International Computing Symposium, Bonn, Germany,
+ abstract =
+ "The SCRATCHPAD/1 system is designed to provide an interactive symbolic
+ coputational facility for the mathematician user. The system features
+ a user language designed to capture the style and succinctness of
+ mathematical notation, together with a facility for conveniently
+ introducing new notations into the language. A comprehensive system
+ library incorporates symbolic capabilities provided by such systems as
+ SIN, MATHLAB, and REDUCE."
+}
\end{chunk}
@@ 13130,6 +13765,65 @@ IBM Research Report, RC3062 Sept
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@Article{Boehm:1989:TIP,
+ author = "HansJ. Boehm",
+ title = "Type inference in the presence of type abstraction",
+ journal = jSIGPLAN,
+ volume = "24",
+ number = "7",
+ pages = "192206",
+ month = jul,
+ year = "1989",
+ CODEN = "SINODQ",
+ ISSN = "03621340 (print), 15232867 (print), 15581160
+ (electronic)",
+ ISSNL = "03621340",
+ bibdate = "Thu May 13 12:31:07 MDT 1999",
+ bibsource = "http://www.acm.org/pubs/contents/proceedings/pldi/73141/index.html;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.acm.org:80/pubs/citations/proceedings/pldi/73141/p192boehm/",
+ abstract = "A number of recent programming language designs
+ incorporate a type checking system based on the
+ GirardReynolds polymorphic \$lambda@calculus. This
+ allows the construction of general purpose, reusable
+ software without sacrificing compiletime type
+ checking. A major factor constraining the
+ implementation of these languages is the difficulty of
+ automatically inferring the lengthy type information
+ that is otherwise required if full use is made of these
+ languages. There is no known algorithm to solve any
+ natural and fully general formulation of this `type
+ inference' problem. One very reasonable formulation of
+ the problem is known to be undecidable. Here we define
+ a restricted version of the type inference problem and
+ present an efficient algorithm for its solution. We
+ argue that the restriction is sufficiently weak to be
+ unobtrusive in practice.",
+ acknowledgement = acknhfb,
+ affiliationaddress = "Houston, TX, USA",
+ annote = "Published as part of the Proceedings of PLDI'89.",
+ classification = "723",
+ conference = "Proceedings of the SIGPLAN '89 Conference on
+ Programming Language Design and Implementation",
+ fjournal = "ACM SIGPLAN Notices",
+ journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
+ journalabr = "SIGPLAN Not",
+ keywords = "Abstract Data Types (ADT); algorithms; Computer
+ Programming LanguagesDesign; Data Processing; Data
+ Structures; design; languages; Scratchpad; theory",
+ meetingaddress = "Portland, OR, USA",
+ meetingdate = "Jun 2123 1989",
+ meetingdate2 = "06/2123/89",
+ sponsor = "ACM, Special Interest Group on Programming Languages,
+ New York; SS NY, USA",
+ subject = "{\bf F.4.1} Theory of Computation, MATHEMATICAL LOGIC
+ AND FORMAL LANGUAGES, Mathematical Logic. {\bf F.3.3}
+ Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS,
+ Studies of Program Constructs, Type structure.",
+}
+
+\end{chunk}
\index{Boulton, Richard}
\index{Hardy, Ruth}
@@ 13262,6 +13956,35 @@ in [Wit87], p18
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Bronstein:1989:SRE,
+ author = "M. Bronstein",
+ title = "Simplification of real elementary functions",
+ crossref = "ACM:1989:PAI",
+ pages = "207211",
+ month = "",
+ year = "1989",
+ bibdate = "Tue Sep 17 06:46:18 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "The author describes an algorithm, based on Risch's
+ real structure theorem, that determines explicitly all
+ the algebraic relations among a given set of real
+ elementary functions. He provides examples from its
+ implementation in the Scratchpad computer algebra
+ system that illustrate the advantages over the use of
+ complex logarithms and exponentials.",
+ acknowledgement = acknhfb,
+ affiliation = "IBM Res. Div., T. J. Watson Res. Center, Yorktown
+ Heights, NY, USA",
+ classification = "C1110 (Algebra); C7310 (Mathematics)",
+ keywords = "Computer algebra system; Real elementary functions;
+ Real structure theorem; Scratchpad",
+ language = "English",
+ thesaurus = "Functions; Mathematics computing; Symbol
+ manipulation",
+}
+
+\end{chunk}
\index{Bronstein, Manuel}
\begin{chunk}{axiom.bib}
@@ 13286,6 +14009,39 @@ in [Wit87], p18
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Bronstein:1991:RDE,
+ author = "M. Bronstein",
+ title = "The {Risch} differential equation on an algebraic
+ curve",
+ crossref = "Watt:1991:PIS",
+ pages = "241246",
+ month = "",
+ year = "1991",
+ bibdate = "Tue Sep 17 06:44:07 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "The author presents a new rational algorithm for
+ solving Risch differential equations over algebraic
+ curves. This algorithm can also be used to solve n/sup
+ th/order linear ordinary differential equations with
+ coefficients in an algebraic extension of the rational
+ functions. In the general ('mixed function') case, this
+ algorithm finds the denominator of any solution of the
+ equation. The algorithm has been implemented in the
+ Maple and Scratchpad computer algebra systems.",
+ acknowledgement = acknhfb,
+ affiliation = "Inf. ETHZentrum, Zurich, Switzerland",
+ classification = "C4170 (Differential equations); C7310
+ (Mathematics)",
+ keywords = "Algebraic curve; Computer algebra systems; Maple;
+ N/sup th/order linear ordinary differential equations;
+ Rational algorithm; Rational functions; Risch
+ differential equation; Scratchpad",
+ language = "English",
+ thesaurus = "Differential equations; Symbol manipulation",
+}
+
+\end{chunk}
\index{Bronstein, Manuel}
\begin{chunk}{ignore}
@@ 13595,6 +14351,32 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Burge:1991:SRI,
+ author = "W. H. Burge",
+ title = "{Scratchpad} and the {RogersRamanujan} identities",
+ crossref = "Watt:1991:PIS",
+ pages = "189190",
+ month = "",
+ year = "1991",
+ bibdate = "Tue Sep 17 06:44:07 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "This note sketches the part played by Scratchpad in
+ obtaining new proofs of Euler's theorem and the
+ RogersRamanujan Identities.",
+ acknowledgement = acknhfb,
+ affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
+ NY, USA",
+ classification = "C1160 (Combinatorial mathematics); C7310
+ (Mathematics)",
+ keywords = "Euler theorem; Infinite series; Restricted partition
+ pairs; RogersRamanujan identities; Scratchpad",
+ language = "English",
+ thesaurus = "Mathematics computing; Number theory; Symbol
+ manipulation",
+}
+
+\end{chunk}
\index{Burge, William H.}
\index{Watt, Stephen M.}
@@ 13626,6 +14408,20 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@TechReport{Burge:1987:ISS,
+ author = "W. Burge and S. Watt",
+ title = "Infinite Structures in {SCRATCHPAD II}",
+ number = "RC 12794 (\#57573)",
+ institution = "IBM Thomas J. Watson Research Center",
+ address = "Bos 218, Yorktown Heights, NY 10598, USA",
+ pages = "??",
+ year = "1987",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+}
+
+\end{chunk}
\index{Burge, William H.}
\index{Watt, Stephen M.}
@@ 13643,15 +14439,71 @@ in [Wit87], pp912
\index{Burge, William H.}
\index{Watt, Stephen M.}
\begin{chunk}{ignore}
\bibitem[Burge 89]{BW89}
 author = "Burge, W. H. and Watt, S. M.",
+\begin{chunk}{axiom.bib}
+@inproceedings{Burg87b,
+ author = "Burge, William H. and Watt, Stephen M.",
title = "Infinite structures in Scratchpad II",
 year = "1989",
+ booktitle = "EUROCAL '87. European Conference on Computer Algebra
+ Proceedings",
+ year = "1987",
pages = "138148",
isbn = "3540515178",
keywords = "axiomref",
in Davenport [Dav89], LCCN QA155.7.E4E86 1987
+ abstract =
+ "An 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 either 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}
+\begin{chunk}{beebe.bib}
+@InProceedings{Burge:1989:ISS, DATE WRONG. SHOULD BE 87
+ author = "W. H. Burge and S. M. Watt",
+ title = "Infinite structures in {Scratchpad} {II}",
+ crossref = "Davenport:1989:EEC",
+ pages = "138148",
+ month = "",
+ year = "1989",
+ bibdate = "Tue Sep 17 06:46:18 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "An 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 either 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.",
+ acknowledgement = acknhfb,
+ affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
+ NY, USA",
+ classification = "C6120 (File organisation); C7310 (Mathematics)",
+ keywords = "Continued fractions; Higher level manipulations;
+ Infinite sequences; Infinite structure; Lazy
+ evaluation; Mathematical objects; Power series; Radix
+ expansions; Scratchpad II; Selfreferential data
+ structures",
+ language = "English",
+ thesaurus = "Algebra; Data structures; Mathematics computing;
+ Series [mathematics]; Software packages; Symbol
+ manipulation",
+}
\end{chunk}
@@ 13729,6 +14581,38 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@TechReport{Camion:1992:PCG,
+ author = "Paul Camion and Bernard Courteau and Andre Montpetit",
+ title = "Un probl{\`e}me combinatoire dans les graphes de
+ {Hamming} et sa solution en {Scratchpad}. ({English}:
+ {A} combinatorial problem in {Hamming} graphs and its
+ solution in {Scratchpad})",
+ type = "Rapports de recherche",
+ number = "1586",
+ institution = "Institut National de Recherche en Informatique et en
+ Automatique",
+ address = "Le Chesnay, France",
+ pages = "12",
+ month = jan,
+ year = "1992",
+ bibdate = "Sat Dec 30 08:42:16 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "We present a combinatorial problem which arises in the
+ determination of the complete weight coset enumerators
+ of errorcorrecting codes [1]. In solving this problem
+ by exponential power series with coefficients in a ring
+ of multivariate polynomials, we fall on a system of
+ differential equations with coefficients in a field of
+ rational functions. Thanks to the abstraction
+ capabilities of Scratchpad this differential equation
+ may be solved simply and naturally, which seems not to
+ be the case for the other computer algebra systems now
+ available.",
+ acknowledgement = acknhfb,
+}
+
+\end{chunk}
\index{Capriotti, Olga}
\index{Cohen, Arjeh M.}
@@ 13977,6 +14861,36 @@ Universit{\"a}t Karsruhe, Karlsruhe, Germany 1994
\end{chunk}
+\index{Chan, L.}
+\index{ChebTerrab, E.S.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Chan04,
+ author = "Chan, L. and ChebTerrab, E.S.",
+ title = "NonLiouvillian solutions for second order linear ODEs",
+ booktitle = "Proc. ISSAC 04",
+ pages = "8086",
+ isbn = "158113827X",
+ url = "http://www.cecm.sfu.ca/CAG/papers/edgardoIS04.pdf",
+ keywords = "axiomref",
+ paper = "Chan04.pdf",
+ abstract =
+ "There exist sound literature and algorithms for computing Liouvillian
+ solutions for the important problem of linear ODEs with rational
+ coefficients. Taking as sample the 363 second order equations of that
+ type found in Kamke's book, for instance, 51\% of them admit Liouvillian
+ solutions and so are solvable using Kovacic's algorithm. On the other
+ hand, special function solutions not admitting Liouvillian form appear
+ frequently in mathematical physics, but there are not so general
+ algorithms for computing them. In this paper we present an algorithm
+ for computing special function solutions which can be expressed using
+ the $_2F_1$, $_1F_1$ or $_0F_1$ hypergeometric functions. They algorithm
+ is easy to implement in the framework of a computer algebra system and
+ systematically solves 91\% of the 363 Kamke's linear ODE examples
+ mentioned."
+}
+
+\end{chunk}
+
\index{Chicha, Yannis}
\index{Lloyd, Michael}
\index{Oancea, Cosmin}
@@ 14581,6 +15495,41 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Dalmas:1992:PFL,
+ author = "S. Dalmas",
+ title = "A polymorphic functional language applied to symbolic
+ computation",
+ crossref = "Wang:1992:ISS",
+ pages = "369375",
+ month = "",
+ year = "1992",
+ bibdate = "Tue Sep 17 06:35:39 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "The programming language in which to describe
+ mathematical objects and algorithms is a fundamental
+ issue in the design of a symbolic computation system.
+ XFun is a strongly typed functional programming
+ language. Although it was not designed as a specialized
+ language, its sophisticated type system can be
+ successfully applied to describe mathematical objects
+ and structures. After illustrating its main features,
+ the author sketches how it could be applied to symbolic
+ computation. A comparison with Scratchpad II is
+ attempted. XFun seems to exhibit more flexibility
+ simplicity and uniformity.",
+ acknowledgement = acknhfb,
+ affiliation = "Inst. Nat. de Recherche d'Inf. et d'Autom., Valbonne,
+ France",
+ classification = "C6140D (High level languages); C7310 (Mathematics)",
+ keywords = "Mathematical objects; Polymorphic functional language;
+ Scratchpad II; Symbolic computation; XFun",
+ language = "English",
+ thesaurus = "Functional programming; High level languages; Symbol
+ manipulation",
+}
+
+\end{chunk}
\index{Daly, Timothy}
\begin{chunk}{axiom.bib}
@@ 14607,13 +15556,18 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
\end{chunk}
\index{Daly, Timothy}
\begin{chunk}{ignore}TPDHERE
\bibitem[Daly 02]{Dal02} Daly, Timothy
+\begin{chunk}{axiom.bib}
+@article{Daly02,
+ author = "Daly, Timothy",
title = "Axiom as open source",
SIGSAM Bulletin (ACM Special Interest Group
on Symbolic and Algebraic Manipulation) 36(1) pp28?? March 2002
CODEN SIGSBZ ISSN 01635824
 keywords = "axiomref",
+ journal = "SIGSAM Bulletin",
+ volume = "36",
+ number = "1",
+ pages = "2828",
+ month = "March",
+ year = "2002",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 14628,12 +15582,16 @@ CODEN SIGSBZ ISSN 01635824
\index{Daly, Timothy}
\begin{chunk}{ignore}
\bibitem[Daly 06]{Dal06} Daly, Timothy
+@book{Daly06,
+ author = "Daly, Timothy",
title = "Axiom Volume 1: Tutorial",
Lulu, Inc. 860 Aviation Parkway,
Suite 300, Morrisville, NC 27560 USA, 2006 ISBN 141166597X 287pp
+ publisher = "Lulu, Inc.",
+ address = "860 Aviation Parkway, Suite 300, Morrisville, NC 27560 USA",
+ year = "2006",
+ isbn = "141166597X",
url = "http://www.lulu.com/content/190827",
 keywords = "axiomref",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 14734,13 +15692,32 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
\index{Sundaresan, Christine}
\index{Sutor, Robert S.}
\index{Trager, Barry M.}
\begin{chunk}{ignore}
\bibitem[Davenport 84]{DGJ84} Davenport, J.; Gianni, P.; Jenks, R.;
Miller, V.; Morrison, S.; Rothstein, M.; Sundaresan, C.; Sutor, R.;
Trager, B.
+\begin{chunk}{axiom.bib}
+@manual{Dave84,
+ author = "Davenport, James H. and Gianni, Patrizia and Jenks, Richard D. and
+ Miller, Victor and Morrison, Scott C. and Rothstein, Michael and
+ Sundaresan, Christine and Sutor, Robert S. and Trager, Barry M.",
title = "Scratchpad",
Mathematical Sciences Department, IBM Thomas Watson Research Center 1984
+ organization = "Mathematical Sciences Department",
+ address = "IBM Thomas Watson Research Center, Yorktown Heights, NY",
keywords = "axiomref",
+ year = "1984"
+}
+
+\end{chunk}
+\begin{chunk}{beebe.bib}
+@Manual{Davenport:1984:S,
+ author = "J. Davenport and P. Gianni and R. Jenks and V. Miller
+ and S. Morrison and M. Rothstein and C. Sundaresan and
+ R. Sutor and B. Trager",
+ title = "{Scratchpad}",
+ organization = "Mathematical Sciences Department",
+ address = "IBM Thomas Watson Research Center",
+ pages = "??",
+ year = "1984",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.1.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+}
\end{chunk}
@@ 14801,8 +15778,8 @@ Mathematical Sciences Department, IBM Thomas Watson Research Center 1984
\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",
+ title = "Computer Algebra: Systems and Algorithms for Algebraic
+ Computation",
publisher = "Academic Press",
year = "1988",
isbn ="0122042301",
@@ 14812,6 +15789,42 @@ Mathematical Sciences Department, IBM Thomas Watson Research Center 1984
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@Book{Davenport:1988:CA,
+ author = "J. H. Davenport and Y. Siret and E. Tournier",
+ title = "Computer Algebra: Systems and Algorithms for Algebraic
+ Computation",
+ publisher = pubAP,
+ address = pubAP:adr,
+ pages = "xix + 267",
+ year = "1988",
+ ISBN = "0122042301",
+ ISBN13 = "9780122042300",
+ LCCN = "QA155.7.E4 D38 1988",
+ bibdate = "Fri Dec 29 18:14:51 1995",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ notes = "{\footnotesize Dies ist die englische Ausgabe des
+ urspr{\"u}nglich bei Masson 1987 erschienen Buches {\em
+ Calcul Formel}. Es ist die erste Monographie {\"u}ber
+ Computeralgebra. Es wird in etwa die Theorie behandelt,
+ die heute in den gr{\"o}{\ss}eren Systemen wie MACSYMA,
+ MAPLE, REDUCE oder SCRATCHPAD II realisiert ist. Das
+ erste Kapitel ist der Diskussion verschiedener \CA\
+ Systeme mit Beispielen gewidmet. Die wichtige Frage der
+ Repr{\"a}sentation der mathematischen Objekte auf einem
+ Computer ist das Thema des zweiten Kapitels. Der
+ Algorithmus von Buchberger, zylindrische Dekomposition,
+ Berechnung von gr{\"o}{\ss}ten gemeinsamen Teilern,
+ padische Methoden und Faktorisierung,
+ Differentialgleichungen und Stammfunktionen sind die
+ wichtigsten behandelten Gegenst{\"a}nde des Buches, das
+ mit einer ausf{\"u}hrlichen Bibliographie und einer
+ Beschreibung von REDUCE im Anhang endet. \hfill J.
+ Grabmeier}",
+}
+
+\end{chunk}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@@ 14986,6 +15999,50 @@ UK / etc., 1989 ISBN 3540515178 LCCN QA155.7.E4E86 1987
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Davenport:1990:SVA,
+ author = "J. H. Davenport and B. M. Trager",
+ title = "{Scratchpad}'s View of Algebra {I}: Basic Commutative
+ Algebra",
+ crossref = "Miola:1990:DIS",
+ pages = "4054",
+ month = "",
+ year = "1990",
+ bibdate = "Tue Sep 17 06:44:07 MDT 1996",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ note = "auch in: {AXIOM} Technical Report, ATR/1, NAG Ltd.,
+ Oxford, 1992.",
+ abstract = "The paper describes the constructive theory of
+ commutative algebra which underlies that part of
+ Scratchpad which deals with commutative algebra. The
+ authors begin by explaining the background that led the
+ Scratchpad group to construct such a general theory.
+ They contrast the general theory in Scratchpad with
+ Reduce3's theory of domains, which is in many ways
+ more limited, but is the closest approach to an
+ implemented general theory to be found outside
+ Scratchpad. This leads them to describe the general
+ Scratchpad view of data types and categories, and the
+ possibilities it offers. They then digress a little to
+ ask what criteria should be adopted in choosing what
+ types to define. Having discussed the philosophical
+ issues, they then discuss commutative algebra proper,
+ breaking this up into the sections `up to Ring',
+ `Integral Domain', `Gcd Domain' and `Euclidean
+ Domain'.",
+ acknowledgement = acknhfb,
+ affiliation = "Sch. of Math. Sci., Bath Univ., UK",
+ classification = "C1110 (Algebra); C7310 (Mathematics)",
+ keywords = "Categories; Commutative algebra; Constructive theory;
+ Data types; Euclidean Domain; Gcd Domain; Greatest
+ common divisors; Integral Domain; Philosophical issues;
+ Ring; Scratchpad",
+ language = "English",
+ thesaurus = "Algebra; Software packages; Symbol manipulation",
+}
+
+\end{chunk}
\index{Davenport, James H.}
\index{Gianni, Patrizia}
@@ 15033,26 +16090,162 @@ UK / etc., 1989 ISBN 3540515178 LCCN QA155.7.E4E86 1987
}
\end{chunk}

\index{Davenport, James H.}
\index{Gianni, Patrizia}
\index{Trager, Barry M.}
\begin{chunk}{ignore}
\bibitem[Davenport 92]{DGT92} Davenport, J. H.;, Gianni, P.; Trager, B. M.
 title = "Scratchpad's view of algebra II: A categorical view of factorization",
Technical Report TR4/92 (ATR/2) (NP2491), Numerical Algorithms Group, Inc.,
Downer's Grove, IL, USA and Oxford, UK, December 1992
 url = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
 keywords = "axiomref",
+\begin{chunk}{beebe.bib}
+@InProceedings{Davenport:1991:SVA,
+ author = "J. H. Davenport and P. Gianni and B. M. Trager",
+ title = "{Scratchpad}'s view of algebra. {II}. {A} categorical
+ view of factorization",
+ crossref = "Watt:1991:PIS",
+ pages = "3238",
+ month = "",
+ year = "1991",
+ bibdate = "Tue Sep 17 06:44:07 MDT 1996",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ note = "auch in: {AXIOM} Technical Report, ATR/2, NAG Ltd.,
+ Oxford, 1992.",
+ abstract = "For pt.I see Proc. DISCO 1990 (p.4054). The paper
+ explains how Scratchpad solves the problem of
+ presenting a categorical view of factorization in
+ unique factorization domains, i.e. a view which can be
+ propagated by functors such as
+ SparseUnivariatePolynomial or Fraction. This is not
+ easy, as the constructive version of the classical
+ concept of UniqueFactorizationdomain cannot be so
+ propagated. The solution adopted is based largely on
+ the Seidenberg conditions (F) and (P), but there are
+ several additional points that have to be borne in mind
+ to produce reasonably efficient algorithms in the
+ required generality. The consequence of the algorithms
+ and interfaces presented is that Scratchpad can
+ factorize in any extension of the integers or finite
+ fields by any combination of polynomial, fraction and
+ algebraic extensions: a capability far more general
+ than any other computer algebra system possesses.",
+ acknowledgement = acknhfb,
+ affiliation = "Sch. of Math., Bath Univ., Claverton Down, UK",
+ classification = "C4130 (Interpolation and function approximation);
+ C7310 (Mathematics)",
+ keywords = "Algebraic extensions; Categorical view; Computer
+ algebra system; Factorization; Finite fields; Fraction;
+ Integers; Polynomial; Scratchpad; Seidenberg
+ conditions",
+ language = "English",
+ thesaurus = "Mathematics computing; Polynomials; Symbol
+ manipulation",
+}
\end{chunk}
\index{Davenport, James H.}
+\index{Trager, Barry M.}
\begin{chunk}{axiom.bib}
@techreport{Dave92a,
 author = "Davenport, James H.",
 title = "The AXIOM system",
 type = "technical report",
+@techreport{Dave92c,
+ author = "Davenport, James H. and Trager, Barry M.",
+ title = "Scratchpad's view of algebra I: Basic commutative algebra",
+ number = "TR3/92 (ATR/1) (NP2490)",
+ institution = "Numerical Algorithm Group (NAG) Ltd.",
+ year = "1992",
+ keywords = "axiomref",
+ paper = "Dave90.pdf",
+ abstract =
+ "While computer algebra systems have dealt with polynomials and
+ rational functions with integer coefficients for many years, dealing
+ with more general constructs from commutative algebra is a more recent
+ problem. In this paper we explain how one system solves this problem,
+ what types and operators it is necessary to introduce and, in short,
+ how one can construct a computational theory of commutative
+ algebra. Of necessity, such a theory is rather different from the
+ conventional, nonconstructive, theory. It is also somewhat different
+ from the theories of Seidenberg [1974] and his school, who are not
+ particularly concerned with practical questions of efficiency."
+}
+
+\end{chunk}
+\begin{chunk}{beebe.bib}
+@TechReport{Davenport:1992:SVAa,
+ author = "J. H. Davenport and B. M. Trager",
+ title = "{Scratchpad}'s View of Algebra {I}: Basic Commutative
+ Algebra",
+ number = "TR3/92 (ATR/1) (NP2490)",
+ institution = instNAG,
+ address = instNAG:adr,
+ pages = "??",
+ month = dec,
+ year = "1992",
+ bibdate = "Fri Dec 29 16:31:49 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
+ acknowledgement = acknhfb,
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
+\index{Gianni, Patrizia}
+\index{Trager, Barry M.}
+\begin{chunk}{axiom.bib}
+@techreport{Dave92d,
+ author = "Davenport, James H. and Gianni, Patrizia and Trager, Barry M.",
+ title = "Scratchpad's view of algebra II:
+ A categorical view of factorization",
+ type = "Technical Report",
+ number = "TR4/92 (ATR/2) (NP2491)",
+ institution = "Numerical Algorithms Group, Inc.",
+ address = "Downer's Grove, IL, USA and Oxford, UK",
+ year = "1992",
+ url = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
+ keywords = "axiomref",
+ paper = "Dave91.pdf",
+ abstract = "
+ This paper explains how Scratchpad solves the problem of presenting a
+ categorical view of factorization in unique factorization domains,
+ i.e. a view which can be propagated by functors such as
+ SparseUnivariatePolynomial or Fraction. This is not easy, as the
+ constructive version of the classical concept of
+ UniqueFactorizationDomain cannot be so propagated. The solution
+ adopted is based largely on Seidenberg's conditions (F) and (P), but
+ there are several additional points that have to be borne in mind to
+ produce reasonably efficient algorithms in the required generality.
+
+ The consequence of the algorithms and interfaces presented in this
+ paper is that Scratchpad can factorize in any extension of the
+ integers or finite fields by any combination of polynomial, fraction
+ and algebraic extensions: a capability far more general than any other
+ computer algebra system possesses. The solution is not perfect: for
+ example we cannot use these general constructions to factorize
+ polyinmoals in $\overline{Z[\sqrt{5}]}[x]$ since the domain
+ $Z[\sqrt{5}]$ is not a unique factorization domain, even though
+ $\overline{Z[\sqrt{5}]}$ is, since it is a field. Of course, we can
+ factor polynomials in $\overline{Z}[\sqrt{5}][x]$"
+}
+
+\end{chunk}
+\begin{chunk}{beebe.bib}
+@TechReport{Davenport:1992:SVAb,
+ author = "J. H. Davenport and P. Gianni and B. M. Trager",
+ title = "{Scratchpad}'s View of Algebra {II}: {A} Categorical
+ View of Factorization",
+ number = "TR4/92 (ATR/2) (NP2491)",
+ institution = instNAG,
+ address = instNAG:adr,
+ pages = "??",
+ month = dec,
+ year = "1992",
+ bibdate = "Fri Dec 29 16:31:49 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
+ acknowledgement = acknhfb,
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@techreport{Dave92a,
+ author = "Davenport, James H.",
+ title = "The AXIOM system",
+ type = "technical report",
number = "TR5/92 (ATR/3) (NP2492)",
institution = "Numerical Algorithms Group, Inc.",
year = "1992",
@@ 15076,6 +16269,25 @@ Downer's Grove, IL, USA and Oxford, UK, December 1992
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@TechReport{Davenport:1992:AS,
+ author = "J. H. Davenport",
+ title = "The {AXIOM} System",
+ type = "AXIOM Technical Report",
+ number = "TR5/92 (ATR/3) (NP2492)",
+ institution = instNAG,
+ address = instNAG:adr,
+ pages = "??",
+ month = dec,
+ year = "1992",
+ bibdate = "Fri Dec 29 16:31:49 1995",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
+ acknowledgement = acknhfb,
+}
+
+\end{chunk}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@@ 15098,6 +16310,25 @@ Downer's Grove, IL, USA and Oxford, UK, December 1992
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@TechReport{Davenport:1992:HDO,
+ author = "J. H. Davenport",
+ title = "How Does One Program in the {AXIOM} System?",
+ type = "AXIOM Technical Report",
+ number = "TR6/92 (ATR/4) (NP2493)",
+ institution = instNAG,
+ address = instNAG:adr,
+ pages = "??",
+ month = dec,
+ year = "1992",
+ bibdate = "Fri Dec 29 16:31:49 1995",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
+ acknowledgement = acknhfb,
+}
+
+\end{chunk}
\index{Davenport, James H.}
\index{Trager, Barry M.}
@@ 15623,6 +16854,38 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Dicrescenzo:1989:AEA, DATE WRONG, SHOULD BE 1988
+ author = "C. Dicrescenzo and D. Duval",
+ title = "Algebraic extensions and algebraic closure in
+ {Scratchpad} {II}",
+ crossref = "Gianni:1989:SAC",
+ pages = "440446",
+ year = "1989",
+ bibdate = "Tue Sep 17 06:46:18 MDT 1996",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ 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. The authors
+ describe an implementation of an algebraic closure
+ domain constructor in the language Scratchpad II. In
+ the first part they analyze the problem, and in the
+ second part they describe a solution based on the D5
+ system.",
+ acknowledgement = acknhfb,
+ affiliation = "TIM3, INPG, Grenoble, France",
+ classification = "C7310 (Mathematics)",
+ keywords = "Algebraic closure domain constructor; D5 system;
+ Language Scratchpad II",
+ language = "English",
+ thesaurus = "Mathematics computing; Symbol manipulation",
+}
+
+\end{chunk}
\index{Dicrescenzo, C.}
\index{Jung, Francoise}
@@ 15639,6 +16902,22 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
\end{chunk}
+\index{Dicrescenzo, C.}
+\index{Duval, Dominique}
+\begin{chunk}{axiom.bib}
+@book{Dicr05,
+ author = "Dicrescenzo, C. and Duval, D.",
+ title = "Algebraic extensions and algebraic closure in Scratchpad II",
+ booktitle = "Symbolic and Algebraic Computation",
+ series = "Lecture Notes in Computer Science 358",
+ year = "2005",
+ publisher = "Springer",
+ pages = "440446",
+ keywords = "axiomref",
+}
+
+\end{chunk}
+
\index{Dingle, Adam}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@@ 16141,6 +17420,55 @@ TPHOLS 2001, Edinburgh
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@Article{Duval:1992:EPS,
+ author = "D. Duval and F. Jung",
+ title = "Examples of problem solving using computer algebra",
+ journal = jIFIPTRANSA,
+ volume = "A2",
+ pages = "133141, 143",
+ month = "",
+ year = "1992",
+ CODEN = "ITATEC",
+ ISSN = "09265473",
+ bibdate = "Tue Sep 17 06:41:20 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "Computer algebra, in contrast with numerical analysis,
+ aims at returning exact solutions to given problems.
+ One consequence is that the shape of the solutions may,
+ at first, look somewhat surprising. The authors present
+ two examples of problem solving using computer algebra,
+ with emphasis on the shape of the solutions. The first
+ example is the resolution of linear differential
+ equations with polynomial coefficients, and the second
+ one is the resolution of polynomial equations in one
+ variable. In the first example the solution may look
+ useless since it makes use of divergent series, and in
+ the second example the solution may look rather
+ awkward. But in both examples it is shown that these
+ solutions are in the right shape for a lot of
+ applications, including numerical ones. It is also
+ shown that some features of the computer algebra system
+ Scratchpad, especially strong typing and genericity,
+ are useful for the implementation of a method for a
+ second problem, i.e. for the implementation of the
+ `dynamic' algebraic closure of a field.",
+ acknowledgement = acknhfb,
+ affiliation = "Lab. de Theorie des Nombres et Algorithmique, Limoges
+ Univ., France",
+ classification = "C7310 (Mathematics)",
+ fjournal = "IFIP Transactions. A. Computer Science and
+ Technology",
+ keywords = "Algebraic closure; Computer algebra; Divergent series;
+ Exact solutions; Genericity; Linear differential
+ equations; Polynomial coefficients; Polynomial
+ equations; Problem solving; Scratchpad; Strong typing",
+ language = "English",
+ thesaurus = "Linear differential equations; Polynomials; Symbol
+ manipulation",
+}
+
+\end{chunk}
\index{Duval, Dominique}
\begin{chunk}{axiom.bib}
@@ 16371,51 +17699,88 @@ TPHOLS 2001, Edinburgh
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate94,
+@inproceedings{Fate90,
author = "Fateman, Richard J.",
 title = "On the Design and Construction of Algebraic Manipulation Systems",
+ title = "Advances and trends in the design and construction of algebraic
+ manipulation systems",
+ booktitle = "Proc. ISSAC 1990",
+ publisher = "ACM",
+ pages = "6067",
+ isbn = "0897914015",
+ year = "1990",
+ paper = "Fate90.pdf",
+ url = "http://people.eecs.berkeley.edu/~fateman/papers/advances.pdf",
keywords = "axiomref",
 url = "http://www.cs.berkeley.edu/~fateman/papers/asmerev94.ps",
 paper = "Fate94.pdf",
abstract =
"We compare and contrast several techniques for the implementation of
components of an algebraic manipulation system. On one hand is the
 mathematicalalgebraic approach which characterizes (for example)
 IBM's Axiom. On the other hand is the more {\sl adhoc} approach which
+ mathematicalalgebraic approach which chaaracterizes (for example)
+ IBM's Axiom. On the other hand is the more {\sl ad hoc} approach which
characterizes many other popular systems (for example, Macsyma,
Reduce, Maple, and Mathematica). While the algebraic approach has
generally positive results, careful examination suggests that there
 are significant remaining problems, especially in the representation
+ are significant remaining problems, expecially in the representation
and manipulation of analytical, as opposed to algebraic,
mathematics. We describe some of these problems and some general
approaches for solutions."
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Fateman:1990:ATD,
+ author = "R. J. Fateman",
+ title = "Advances and trends in the design and construction of
+ algebraic manipulation systems",
+ crossref = "Watanabe:1990:IPI",
+ pages = "6067",
+ year = "1990",
+ DOI = "http://dx.doi.org/10.1145.96895",
+ bibdate = "Thu Jul 26 09:04:25 2001",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "Compares and contrasts several techniques for the
+ implementation of components of an algebraic
+ manipulation system. On one hand is the mathematical
+ algebraic approach which characterizes (for example)
+ IBM's Scratchpad II. On the other hand is the more ad
+ hoc approach which characterizes many other popular
+ systems (for example, Macsyma, Reduce, Maple, and
+ Mathematica). While the algebraic approach has
+ generally positive results, careful examination
+ suggests that there are significant remaining problems,
+ especially in the representation and manipulation of
+ analytical, as opposed to algebraic mathematics. The
+ author describes some of these problems, and some
+ general approaches for solutions.",
+ acknowledgement = acknhfb,
+ affiliation = "California Univ., Berkeley, CA, USA",
+ classification = "C4240 (Programming and algorithm theory); C7310
+ (Mathematics)",
+ keywords = "Algebraic manipulation systems; Algebraic mathematics;
+ Macsyma; Maple; Mathematica; Mathematical algebraic;
+ Reduce; Scratchpad II",
+ language = "English",
+ thesaurus = "Algebra; Symbol manipulation",
+}
+
+\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@inproceedings{Fate90,
+@misc{Fate94,
author = "Fateman, Richard J.",
 title = "Advances and trends in the design and construction of algebraic
 manipulation systems",
 booktitle = "Proc. ISSAC 1990",
 publisher = "ACM",
 pages = "6067",
 isbn = "0897914015",
 year = "1990",
 paper = "Fate90.pdf",
 url = "http://people.eecs.berkeley.edu/~fateman/papers/advances.pdf",
+ title = "On the Design and Construction of Algebraic Manipulation Systems",
keywords = "axiomref",
+ url = "http://www.cs.berkeley.edu/~fateman/papers/asmerev94.ps",
+ paper = "Fate94.pdf",
abstract =
"We compare and contrast several techniques for the implementation of
components of an algebraic manipulation system. On one hand is the
 mathematicalalgebraic approach which chaaracterizes (for example)
 IBM's Axiom. On the other hand is the more {\sl ad hoc} approach which
+ mathematicalalgebraic approach which characterizes (for example)
+ IBM's Axiom. On the other hand is the more {\sl adhoc} approach which
characterizes many other popular systems (for example, Macsyma,
Reduce, Maple, and Mathematica). While the algebraic approach has
generally positive results, careful examination suggests that there
 are significant remaining problems, expecially in the representation
+ are significant remaining problems, especially in the representation
and manipulation of analytical, as opposed to algebraic,
mathematics. We describe some of these problems and some general
approaches for solutions."
@@ 16475,7 +17840,7 @@ TPHOLS 2001, Edinburgh
author = "Fateman, Richard J. and Caspi, Eylon",
title = "Parsing TeX into Mathematics",
year = "1999",
 url = "http://lib.org.by/_djvu/_Papers/Computer_algebra/CAS%20systems/",
+ url = "http://lib.org.by/\_djvu/\_Papers/Computer\_algebra/CAS%20systems/",
paper = "Fate99a.djvu",
keywords = "axiomref",
abstract =
@@ 16531,6 +17896,32 @@ TPHOLS 2001, Edinburgh
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
+@article{Fate01,
+ author = "Fateman, Richard J.",
+ title = "A Review of Macsyma",
+ journal = "IEEE Trans. Knowl. Eng.",
+ volume = "1",
+ number = "1",
+ year = "2001",
+ url = "http://people.eecs.berkeley.edu/~fateman/papers/mac82b.pdf",
+ paper = "Fate01.pdf",
+ keywords = "axiomref",
+ abstract =
+ "We review the successes and failures of the Macsyma algebraic
+ manipulation system from the point of view of one of the original
+ contributors. We provide a retrospective examination of some of the
+ controversial ideas that worked, and some that did not. We consider
+ input/output, language semantics, data types, pattern matching,
+ knowledgeadjunction, mathematical semantics, the user community,
+ and software engineering. We also comment on the porting of this
+ system to a variety of computing systems, and possible future
+ directions for algebraic manipulation systembuilding."
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
@misc{Fate05,
author = "Fateman, Richard J.",
title = "An incremental approach to building a mathematical
@@ 16765,6 +18156,46 @@ LCCN QA155.7.E4 I57 1984
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Fortenbacher:1990:ETI,
+ author = "A. Fortenbacher",
+ title = "Efficient type inference and coercion in computer
+ algebra",
+ crossref = "Miola:1990:DIS",
+ pages = "5660",
+ month = "",
+ year = "1990",
+ bibdate = "Tue Sep 17 06:44:07 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "Computer algebra systems of the new generation, like
+ Scratchpad, are characterized by a very rich type
+ concept, which models the relationship between
+ mathematical domains of computation. To use these
+ systems interactively, however, the user should be
+ freed of type information. A type inference mechanism
+ determines the appropriate function to call. All known
+ models which define a semantics for type inference
+ cannot express the rich `mathematical' type structure,
+ so presently type inference is done heuristically. The
+ following paper defines a semantics for a subproblem,
+ namely coercion, which is based on rewrite rules. From
+ this definition, an efficient coercion algorithm for
+ Scratchpad is constructed using graph techniques.",
+ acknowledgement = acknhfb,
+ affiliation = "Sci. Center Heidelberg, IBM Deutschland GmbH,
+ Germany",
+ classification = "C1110 (Algebra); C4210 (Formal logic); C6120 (File
+ organisation); C7310 (Mathematics)",
+ keywords = "Coercion algorithm; Computer algebra; Graph
+ techniques; Rewrite rules; Scratchpad; Type inference
+ mechanism",
+ language = "English",
+ thesaurus = "Algebra; Data structures; Inference mechanisms;
+ Mathematics computing; Rewriting systems; Symbol
+ manipulation",
+}
+
+\end{chunk}
\index{Fortuna, E.}
\index{Gianni, P.}
@@ 16807,7 +18238,23 @@ LCCN QA155.7.E4 I57 1984
year = "1990",
institution = {Institut de Recherche Math{\'{e}}matique Avanc{\'{e}}e''},
location = "Strasbourg, France",
 keywords = "axiomref"
+ keywords = "axiomref",
+}
+
+\end{chunk}
+\begin{chunk}{beebe.bib}
+@TechReport{Fouche:1990:ILK,
+ author = "Francois Fouche",
+ title = "Une Implantation de l'algorithme de {Kovacic} en
+ {Scratchpad}",
+ institution = "Institut de Recherche Math{\'{e}}matique
+ Avanc{\'{e}}e",
+ address = "Strasbourg, France",
+ pages = "31",
+ year = "1990",
+ bibdate = "Sat Dec 30 08:25:26 MST 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
}
\end{chunk}
@@ 16952,6 +18399,30 @@ LCCN QA155.7.E4 I57 1984
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Gebauer:1986:BAS,
+ author = "R{\"u}diger Gebauer and H. Michael M{\"o}ller",
+ editor = "Bruce W. Char",
+ booktitle = "Proceedings of the 1986 Symposium on Symbolic and
+ Algebraic Computation: Symsac '86, July 2123, 1986,
+ Waterloo, Ontario",
+ title = "{Buchberger}'s algorithm and staggered linear bases",
+ publisher = pubACM,
+ address = pubACM:adr,
+ pages = "218221",
+ year = "1986",
+ DOI = "http://dx.doi.org/10.1145.32482",
+ ISBN = "0897911997",
+ ISBN13 = "9780897911993",
+ LCCN = "QA155.7.E4 A281 1986",
+ bibdate = "Thu Jul 26 09:06:12 2001",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ note = "ACM order number 505860.",
+ acknowledgement = acknhfb,
+ bookpages = "254",
+}
+
+\end{chunk}
\index{Gebauer, R{\"u}diger}
\index{M{\"o}ller, H. Michael}
@@ 16981,6 +18452,51 @@ LCCN QA155.7.E4 I57 1984
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@Article{Gebauer:1988:IBA,
+ author = "R. Gebauer and H. M. M{\"o}ller",
+ title = "On an installation of {Buchberger}'s algorithm",
+ journal = jJSYMBOLICCOMP,
+ volume = "6",
+ number = "23",
+ pages = "275286",
+ month = oct # "" # dec,
+ year = "1988",
+ CODEN = "JSYCEH",
+ ISSN = "07477171 (print), 1095855X (electronic)",
+ ISSNL = "07477171",
+ bibdate = "Tue Sep 17 08:24:38 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "Buchberger's algorithm calculates Gr{\"o}bner 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 The authors 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 the 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.",
+ acknowledgement = acknhfb,
+ affiliation = "SpringerVerlag, New York, NY, USA",
+ classification = "C4130 (Interpolation and function approximation);
+ C6130 (Data handling techniques); C7310 (Mathematics)",
+ fjournal = "Journal of Symbolic Computation",
+ journalURL = "http://www.sciencedirect.com/science/journal/07477171",
+ keywords = "Buchberger algorithm installation; Gr{\"o}bner bases;
+ Polynomial ideals; Superfluous reductions; Redundant
+ elements; Module of syzygies; SCRATCHPAD II; REDUCE
+ 3.3; Computational properties",
+ language = "English",
+ pubcountry = "UK",
+ thesaurus = "Polynomials; Symbol manipulation",
+}
+
+\end{chunk}
\index{Geddes, K. O.}
\index{Czapor, S.R.}
@@ 17191,15 +18707,138 @@ LCCN QA76.95.I57 1988 Conference held jointly with AAECC6
}
\end{chunk}

\index{Gil, I. }
\begin{chunk}{ignore}
\bibitem[Gil 92]{Gil92} Gil, I.
 title = "Computation of the Jordan canonical form of a square matrix (using the Axiom programming language)",
In Wang [Wan92], pp138145.
ISBN 0897914899 (soft cover), 0897914902 (hard cover)
LCCN QA76.95.I59 1992
 keywords = "axiomref",
+\begin{chunk}{beebe.bib}
+@InProceedings{Gianni:1989:ASS,
+ author = "P. Gianni and T. Mora",
+ title = "Algebraic solution of systems of polynomial equations
+ using {Gr{\"o}bner} bases",
+ crossref = "Huguet:1989:AAA",
+ pages = "247257",
+ month = "",
+ year = "1989",
+ bibdate = "Tue Sep 17 06:46:18 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "One of the most important applications of Buchberger's
+ algorithm for Gr{\"o}bner 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 Gr{\"o}bner bases w.r.t. a
+ lexicographical ordering and elimination ideals. The
+ algorithms discussed in this paper are implemented in
+ SCRATCHPAD II. In the first section the authors recall
+ some wellknown properties of Gr{\"o}bner bases and
+ properties on the structure of Gr{\"o}bner bases of
+ zerodimensional ideals; in the second section they
+ recall the Gr{\"o}bner basis algorithm for solving
+ systems of algebraic equations. The original results
+ are then presented. The authors first take advantage of
+ the obvious fact that density can be controlled
+ performing `small' changes of coordinates: they show
+ that such approach is possible during a Gr{\"o}bner
+ basis computation, in such a way that computations done
+ before a change of coordinates are valid also after it;
+ they propose a `linear algebra' approach to obtain the
+ Gr{\"o}bner basis w.r.t. the lexicographical ordering
+ from the one w.r.t. the totaldegree ordering; and
+ finally they present a zerodimensional radical
+ algorithm and show how to apply it to the present
+ problem.",
+ acknowledgement = acknhfb,
+ affiliation = "Pisa Univ., Italy",
+ classification = "C1110 (Algebra); C4140 (Linear algebra); C7310
+ (Mathematics)",
+ keywords = "Coordinate changes; Polynomial equations; Gr{\"o}bner
+ bases; Buchberger's algorithm; Gr{\"o}bner basis
+ computation; Zeros; 0Dimensional polynomial ideals;
+ Lexicographical ordering; Elimination ideals;
+ SCRATCHPAD II; Algebraic equations; Linear algebra;
+ Totaldegree ordering; Zerodimensional radical
+ algorithm",
+ language = "English",
+ thesaurus = "Equations; Linear algebra; Mathematics computing;
+ Poles and zeros; Polynomials",
+}
+
+\end{chunk}
+
+\index{Gil, Isabelle}
+\begin{chunk}{axiom.bib}
+@inproceedings{Gilx92,
+ author = "Gil, Isabelle",
+ title = "Computation of the Jordan canonical form of a square matrix
+ (using the Axiom programming language)",
+ booktitle = "Proc ISSAC 1992",
+ series = "ISSAC '92",
+ publisher = "ACM",
+ pages = "138145",
+ isbn = "0897914899 (soft cover), 0897914902 (hard cover)",
+ keywords = "axiomref",
+ abstract =
+ "Presents an algorithm for computing: the Jordan form of a square
+ matrix with coefficients in a field K using the computer algebra
+ system Axiom. This system presents the advantage of allowing generic
+ programming. That is to say, the algorithm can first be implemented
+ for matrices with rational coefficients and then generalized to
+ matrices with coefficients in any field. Therefore the author
+ presents the general method which is essentially based on the use of
+ the Frobenius form of a matrix in order to compute its Jordan form;
+ and then restricts attention to matrices with rational
+ coefficients. On the one hand the author streamlines the algorithm
+ froben which computes the Frobenius form of a matrix, and on the other
+ she examines in some detail the transformation from the Frobenius form
+ to the Jordan form, and gives the so called algorithm Jordform. The
+ author studies in particular, the complexity of this algorithm and
+ proves that it is polynomial when the coefficients of the matrix are
+ rational. Finally the author gives some experiments and a conclusion."
+}
+
+\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Gil:1992:CJC,
+ author = "I. Gil",
+ title = "Computation of the {Jordan} canonical form of a square
+ matrix (using the {Axiom} programming language)",
+ crossref = "Wang:1992:ISS",
+ pages = "138145",
+ month = "",
+ year = "1992",
+ bibdate = "Tue Sep 17 06:35:39 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "Presents an algorithm for computing: the Jordan form
+ of a square matrix with coefficients in a field K using
+ the computer algebra system Axiom. This system presents
+ the advantage of allowing generic programming. That is
+ to say, the algorithm can first be implemented for
+ matrices with rational coefficients and then
+ generalized to matrices with coefficients in any field.
+ Therefore the author presents the general method which
+ is essentially based on the use of the Frobenius form
+ of a matrix in order to compute its Jordan form; and
+ then restricts attention to matrices with rational
+ coefficients. On the one hand the author streamlines
+ the algorithm froben which computes the Frobenius form
+ of a matrix, and on the other she examines in some
+ detail the transformation from the Frobenius form to
+ the Jordan form, and gives the so called algorithm
+ Jordform. The author studies in particular, the
+ complexity of this algorithm and proves that it is
+ polynomial when the coefficients of the matrix are
+ rational. Finally the author gives some experiments and
+ a conclusion.",
+ acknowledgement = acknhfb,
+ affiliation = "LMC, IMAG, Grenoble, France",
+ classification = "C4130 (Interpolation and function approximation);
+ C4140 (Linear algebra); C4240 (Programming and
+ algorithm theory); C7310 (Mathematics)",
+ keywords = "Axiom programming language; Complexity; Computer
+ algebra system; Froben; Frobenius form; Generic
+ programming; Jordan canonical form; Jordform;
+ Polynomial; Rational coefficients; Square matrix",
+ language = "English",
+ thesaurus = "Computational complexity; Matrix algebra; Polynomials;
+ Symbol manipulation",
+}
\end{chunk}
@@ 17278,6 +18917,39 @@ IMACS Symposium SC1993
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Goodwin:1991:UMT,
+ author = "B. M. Goodwin and R. A. Buonopane and A. Lee",
+ title = "Using {MathCAD} in teaching material and energy
+ balance concepts",
+ crossref = "Anonymous:1991:PAC",
+ pages = "345349 (vol. 1)",
+ year = "1991",
+ bibdate = "Tue Sep 17 06:37:45 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "The authors show how PCbased applications software,
+ specifically MathCAD, is used in the teaching of
+ material and energy balance concepts. MathCAD is a
+ microcomputer software package which acts as a
+ mathematical scratchpad. It has proven to be a very
+ useful instructional tool in introductory chemical
+ engineering courses. MathCAD solutions to typical
+ course problems are presented.",
+ acknowledgement = acknhfb,
+ affiliation = "Northeastern Univ., Boston, MA, USA",
+ classification = "C7450 (Chemical engineering); C7810C (Computeraided
+ instruction)",
+ keywords = "Energy balance concepts; Instructional tool;
+ Introductory chemical engineering courses; MathCAD;
+ Mathematical scratchpad; PCbased applications
+ software",
+ language = "English",
+ thesaurus = "Chemical engineering computing; Computer aided
+ instruction; Microcomputer applications; Spreadsheet
+ programs",
+}
+
+\end{chunk}
\index{Golden, V. Ellen}
\index{Hussain, M. A.}
@@ 17435,18 +19107,115 @@ In Fitch [Fit93], pp193202. ISBN 0387572724 (New York),
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@TechReport{Grabmeier:1991:CSA,
+ author = "J. Grabmeier and K. Huber and U. Krieger",
+ title = "{Das ComputeralgebraSystem AXIOM bei kryptologischen
+ und verkehrstheoretischen Untersuchungen des
+ Forschungsinstituts der Deutschen Bundespost TELEKOM}",
+ type = "Technischer Report",
+ number = "TR 75.91.20",
+ institution = "IBM Wissenschaftliches Zentrum",
+ address = "Heidelberg, Germany",
+ pages = "??",
+ year = "1991",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+}
+
+\end{chunk}
\index{Grabmeier, Johannes}
\index{Scheerhorn, A.}
\begin{chunk}{ignore}
\bibitem[Grabmeier 92]{GS92} Grabmeier, J.; Scheerhorn, A.
+\begin{chunk}{axiom.bib}
+@article{Grab91b,
+ author = "Grabmeier, Johannes",
+ title = "Axiom, ein Computeralgebrasystem mit abstrakten Datentypen",
+ journal = "mathPAD",
+ volume = "1",
+ number = "3",
+ pages = "1315",
+ keywords = "axiomref",
+ paper = "Grab91b.pdf",
+}
+
+\end{chunk}
+
+\index{CharacteristicNonZero}
+\index{FieldOfPrimeCharacteristic}
+\index{ExtensionField}
+\index{FiniteFieldCategory}
+\index{FiniteAlgebraicExtensionField}
+\index{SimpleAlgebraicExtension}
+\index{InnerPrimeField}
+\index{PrimeField}
+\index{FiniteFieldExtensionByPolynomial}
+\index{FiniteFieldCyclicGroupExtensionByPolynomial}
+\index{FiniteFieldNormalBasisExtensionByPolynomial}
+\index{FiniteFieldExtension}
+\index{FiniteFieldCyclicGroupExtension}
+\index{FiniteFieldNormalBasisExtension}
+\index{InnerFiniteField}
+\index{FiniteField}
+\index{FiniteFieldCyclicGroup}
+\index{FiniteFieldNormalBasis}
+\index{DiscreteLogarithmPackage}
+\index{FiniteFieldFunctions}
+\index{InnerNormalBasisFieldFunctions}
+\index{FiniteFieldPolynomialPackage}
+\index{FiniteFieldPolynomialPackage2}
+\index{FiniteFieldHomomorphisms}
+\index{FiniteFieldFactorizationWithSizeParseBySideEffect}
+\index{Grabmeier, Johannes}
+\index{Scheerhorn, Alfred}
+\begin{chunk}{axiom.bib}
+@techreport{Grab92,
+ author = "Grabmeier, Johannes and Scheerhorn, Alfred",
title = "Finite fields in Axiom",
AXIOM Technical Report TR7/92 (ATR/5)(NP2522),
Numerical Algorithms Group, Inc., Downer's
Grove, IL, USA and Oxford, UK, 1992
+ type = "technical report",
+ number = "AXIOM Technical Report TR7/92 (ATR/5)(NP2522)",
+ institution = "Numerical Algorithms Group, Inc.",
+ address = "Downer's Grove, IL, USA and Oxford, UK",
+ year = "1992",
url = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
and Technical Report, IBM Heidelberg Scientific Center, 1992
keywords = "axiomref",
+ paper = "Grab92.pdf",
+ algebra =
+ "\newline\refto{category CHARNZ CharacteristicNonZero}
+ \newline\refto{category FPC FieldOfPrimeCharacteristic}
+ \newline\refto{category XF ExtensionField}
+ \newline\refto{category FFIELDC FiniteFieldCategory}
+ \newline\refto{category FAXF FiniteAlgebraicExtensionField}
+ \newline\refto{domain SAE SimpleAlgebraicExtension}
+ \newline\refto{domain IPF InnerPrimeField}
+ \newline\refto{domain PF PrimeField}
+ \newline\refto{domain FFP FiniteFieldExtensionByPolynomial}
+ \newline\refto{domain FFCGP FiniteFieldCyclicGroupExtensionByPolynomial}
+ \newline\refto{domain FFNBP FiniteFieldNormalBasisExtensionByPolynomial}
+ \newline\refto{domain FFX FiniteFieldExtension}
+ \newline\refto{domain FFCGX FiniteFieldCyclicGroupExtension}
+ \newline\refto{domain FFNBX FiniteFieldNormalBasisExtension}
+ \newline\refto{domain IFF InnerFiniteField}
+ \newline\refto{domain FF FiniteField}
+ \newline\refto{domain FFCG FiniteFieldCyclicGroup}
+ \newline\refto{domain FFNB FiniteFieldNormalBasis}
+ \newline\refto{package DLP DiscreteLogarithmPackage}
+ \newline\refto{package FFF FiniteFieldFunctions}
+ \newline\refto{package INBFF InnerNormalBasisFieldFunctions}
+ \newline\refto{package FFPOLY FiniteFieldPolynomialPackage}
+ \newline\refto{package FFPOLY2 FiniteFieldPolynomialPackage2}
+ \newline\refto{package FFHOM FiniteFieldHomomorphisms}
+ \newline\refto
+ {package FFFACTSE FiniteFieldFactorizationWithSizeParseBySideEffect}",
+ abstract =
+ "Finite fields play an important role for many applications (e.g. coding
+ theory, cryptograpy). There are different ways to construct a finite
+ field for a given prime power. The paper describes the different
+ constructions implemented in AXIOM. These are {\sl polynomial basis
+ representation}, {\sl cyclic group representation}, and {\sl normal
+ basis representation}. Furthermore, the concept of the implementation,
+ the used algorithms and the various datatype coercions between these
+ representations are discussed."
+}
\end{chunk}
@@ 17501,7 +19270,7 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
Manipulation",
series = "SYMSAC 71",
year = "1971",
 pages = "4258",
+ pages = "4258",
doi = "http://dx.doi.org/10.1145806266",
url = "http://delivery.acm.org/10.1145/810000/806266/p42griesmer.pdf",
paper = "Grie71.pdf",
@@ 17513,7 +19282,23 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
mathematical notation, together with a facility for conveniently
introducing new notations into the language. A comprehensive system
library incorporates symbolic capabilities provided by such systems as
 SIN, MATHLAB, and REDUCE."
+ SIN, MATHLAB, and REDUCE.",
+}
+
+\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Griesmer:1971:SIF,
+ author = "J. H. Griesmer and R. D. Jenks",
+ title = "{SCRATCHPAD/1}  an interactive facility for
+ symbolic mathematics",
+ crossref = "Petrick:1971:PSS",
+ pages = "4258",
+ year = "1971",
+ DOI = "http://dx.doi.org/10.1145806266",
+ bibdate = "Thu Jul 26 08:45:53 2001",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/obscure.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ URL = "http://delivery.acm.org/10.1145/810000/806266/p42griesmer.pdf",
}
\end{chunk}
@@ 17530,6 +19315,28 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Griesmer:1972:EOSb,
+ author = "J. Griesmer and R. Jenks",
+ title = "Experience with an online symbolic math. system
+ {SCRATCHPAD}",
+ crossref = "Online:1972:OCP",
+ pages = "????",
+ year = "1972",
+ bibsource = "/usr/local/src/bib/bibliography/Distributed/QLD.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ bydate = "Le",
+ byrev = "Le",
+ date = "00/00/00",
+ descriptors = "Formula manipulation",
+ enum = "1209",
+ language = "English",
+ location = "PKIOG: LiOrd.Le",
+ references = "0",
+ revision = "21/04/91",
+}
+
+\end{chunk}
\index{Griesmer, James H.}
\index{Jenks, Richard D.}
@@ 17558,6 +19365,53 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@Article{Griesmer:1972:SCV,
+ author = "James H. Griesmer and Richard D. Jenks",
+ title = "{SCRATCHPAD}: {A} capsule view",
+ journal = jSIGPLAN,
+ volume = "7",
+ number = "10",
+ pages = "93102",
+ year = "1972",
+ CODEN = "SINODQ",
+ DOI = "http://dx.doi.org/10.1145807019",
+ ISSN = "03621340 (print), 15232867 (print), 15581160
+ (electronic)",
+ ISSNL = "03621340",
+ bibdate = "Thu Jul 26 10:33:16 2001",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ note = "Proceedings of the symposium on Twodimensional
+ manmachine communication, Mark B. Wells and James B.
+ Morris (eds.)",
+ acknowledgement = acknhfb,
+ bookpages = "iii + 160",
+ fjournal = "ACM SIGPLAN Notices",
+ journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
+}
+
+\end{chunk}
+
+\index{Griesmer, James H.}
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@article{Grie74,
+ author = "Griesmer, James H. and Jenks, Richard D.",
+ title = "A solution to problem \#4: the lie transform",
+ journal = "SIGSAM Bulletin",
+ volume = "8",
+ number = "4",
+ pages = "1213",
+ year = "1974",
+ keywords = "axiomref",
+ abstract =
+ "The following SCRATCHPAD conversation for carrying out the Lie
+ Transform computation represents a slight modification of one written
+ by Dr. David Barton, when he was a summer visitor during 1972 at the
+ Watson Research Center."
+}
+
+\end{chunk}
\index{Griesmer, James H.}
\index{Jenks, Richard D.}
@@ 17576,6 +19430,44 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
\index{Griesmer, James H.}
\index{Jenks, Richard D.}
+\index{Yun, David Y.Y.}
+\begin{chunk}{axiom.bib}
+@article{Grie75a,
+ author = "Griesmer, James H. and Jenks, Richard D. and Yun, David Y.Y.",
+ title = "A SCRATCHPAD solution to problem \#7",
+ journal = "SIGSAM",
+ volume = "9",
+ number = "3",
+ pages = "1317",
+ year = "1975"
+}
+
+\end{chunk}
+
+\index{Griesmer, James H.}
+\index{Jenks, Richard D.}
+\index{Yun, David Y.Y.}
+\begin{chunk}{axiom.bib}
+@article{Grie75b,
+ author = "Griesmer, James H. and Jenks, Richard D. and Yun, David Y.Y.",
+ title = "A FORMAT statement in SCRATCHPAD",
+ journal = "SIGSAM",
+ volume = "9",
+ number = "3",
+ pages = "2425",
+ year = "1975",
+ keywords = "axiomref",
+ abstract =
+ "Algebraic manipulation covers branches of software, particularly list
+ processing, mathematics, notably logic and number theory, and
+ applications largely in physics. The lectures will deal with all of these
+ to a varying extent."
+}
+
+\end{chunk}
+
+\index{Griesmer, James H.}
+\index{Jenks, Richard D.}
\index{Yun, David Y.Y}
\begin{chunk}{ignore}
\bibitem[Griesmer 76]{GJY76} Griesmer, J.H.; Jenks, R.D.; Yun, D.Y.Y
@@ 17585,6 +19477,21 @@ April 1976 (private copy)
\end{chunk}
+\index{Griesmer, James H.}
+\begin{chunk}{axiom.bib}
+@article{Grie79,
+ author = "Griesmer, James H.",
+ title = "The state of symbolic computation",
+ journal = "SIGSAM Bulletin",
+ volume = "13",
+ number = "3",
+ pages = "2528",
+ year = "1979",
+ keywwords = "axiomref"
+}
+
+\end{chunk}
+
\index{Gruntz, Dominik}
\index{Monagan, Michael B.}
\begin{chunk}{ignore}
@@ 17809,6 +19716,38 @@ in [Wit87], pp58
\index{ASP9}
\index{Hearn, Anthony C.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Hear80,
+ author = "Hearn, Anthony C.",
+ title = "Symbolic Computation and its Application to High Energy Physics",
+ booktitle = "Proc. 1980 CERN School of Computing",
+ pages = "390406",
+ year = "1980",
+ paper = "Hear80.pdf",
+ url =
+"http://www.iaea.org/inis/collection/NCLCollectionStore/\_Public/12/631/12631585.pdf",
+ abstract =
+ "It is clear that we are in the middle of an electronic revolution
+ whose effect will be as profound as the in dustrial revolution. The
+ continuing advances in computing technology will provide us with
+ devices which will make present day computers appear primitive. In
+ this environment, the algebraic and other nonnumerical capabilities
+ of such devices will become increasingly important. These lectures
+ will review the present state of the field of algebraic computation
+ and its potential for problem solving in high energy physics and
+ related areas. We shall begin with a brief description of the
+ available systems and examine the data objects which they consider.
+ As an example of the facilities which these systems can offer, we
+ shall then consider the problem of analytic integration, since this â€¢
+ is so fundamental to many of the calculational techniques used by high
+ energy physicists. Finally, we shall study the implications which the
+ current developments in hardware technology hold for scientific
+ problem solving."
+}
+
+\end{chunk}
+
+\index{Hearn, Anthony C.}
\index{Eberhard, Schrufer}
\begin{chunk}{axiom.bib}
@article{Hear95,
@@ 18555,6 +20494,47 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@TechReport{Jenks:1971:MPS,
+ author = "R. D. Jenks",
+ title = "{META\slash PLUS}: The Syntax Extension Facility for
+ {SCRATCHPAD}",
+ type = "Research Report",
+ number = "RC 3259",
+ institution = "International Business Machines Inc., Thomas J. Watson
+ Research Center",
+ address = "Yorktown Heights, NY, USA",
+ pages = "??",
+ month = feb,
+ year = "1971",
+ bibdate = "Sat Dec 30 08:53:02 1995",
+ bibsource = "/usr/local/src/bib/bibliography/Ai/lisp.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@article{Jenk72,
+ author = "Jenks, Richard D.",
+ title = "SCRATCHPAD",
+ volume = "??",
+ number = "24",
+ pages = "1617",
+ month = "October",
+ year = "1972",
+ keywords = "axiomref",
+ abstract =
+ "The following SCRATCHPAD solution of Problem \#2 was run on a 1280K
+ virtual machine under CP/CMS time sharing system on a System/360
+ model 67. The conversation below is a modification of a program
+ originally written by Yngve Sundblad, August 1972. The program uses
+ symmetrised formulae, saves certain intermediate results, but does not
+ eliminate numerical factors in denominators"
+}
+
+\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@@ 18562,7 +20542,7 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
author = "Jenks, Richard D.",
title = "The SCRATCHPAD language",
journal = "ACM SIGPLAN Notices",
 comment = "reprinted in SIGSAM Bulletin, Vol 8, No. 2, May 1974",
+ comment = "reprinted in SIGSAM Bulletin, Vol 8, No. 2, pp 2030 May 1974",
volume = "9",
number = "4",
pages = "101111",
@@ 18581,6 +20561,62 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@Article{Jenks:1974:SL,
+ author = "R. D. Jenks",
+ title = "The {SCRATCHPAD} language",
+ journal = jSIGPLAN,
+ volume = "9",
+ number = "4",
+ pages = "101111",
+ month = apr,
+ year = "1974",
+ CODEN = "SINODQ",
+ DOI = "http://dx.doi.org/10.1145807051",
+ ISSN = "03621340 (print), 15232867 (print), 15581160
+ (electronic)",
+ ISSNL = "03621340",
+ bibdate = "Sat Apr 25 11:46:37 MDT 1998",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ classification = "C6140D (High level languages); C7310 (Mathematics
+ computing)",
+ conflocation = "Santa Monica, CA, USA; 2829 March 1974",
+ conftitle = "ACM SIGPLAN Symposium on Very High Level Languages",
+ corpsource = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
+ NY, USA",
+ fjournal = "ACM SIGPLAN Notices",
+ journalURL = "http://portal.acm.org/browse_dl.cfm?idx=J706",
+ keywords = "formal description; formal programming language; high
+ level programming language; interactive system;
+ mathematical algorithms; natural sciences applications
+ of computers; online problem solving; problem oriented
+ languages; SCRATCHPAD language; symbolic mathematical
+ computation; user language",
+ sponsororg = "ACM",
+ treatment = "A Application; P Practical",
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@article{Jenk76a,
+ author = "Jenks, Richard D.",
+ title = "Problem \#11: generation of RungeKutta equations",
+ journal = "SIGSAM Bulletin",
+ volume = "10",
+ number = "1",
+ year = "1976",
+ abstract =
+ "Generate a set of equations for an explicit kth order, m stage,
+ RungeKutta method for integrating an autonomous system of ordinary
+ differential equations, k and m as large as possible. The number of
+ conditions and variables for various k and m are given in Table
+ 1. Tabulate the costs C(m,k)."
+}
+
+\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@@ 18607,6 +20643,51 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Jenks:1976:PC,
+ author = "Richard D. Jenks",
+ editor = "Richard D. Jenks",
+ booktitle = "Symsac '76: proceedings of the 1976 ACM Symposium on
+ Symbolic and Algebraic Computation, August 1012,
+ 1976, Yorktown Heights, New York",
+ title = "A pattern compiler",
+ publisher = pubACM,
+ address = pubACM:adr,
+ pages = "6065",
+ year = "1976",
+ DOI = "http://dx.doi.org/10.1145806324",
+ ISBN = "????",
+ ISBN13 = "????",
+ LCCN = "QA155.7.E4 .A15 1976; QA9.58 .A11 1976",
+ bibdate = "Thu Jul 26 08:56:43 2001",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ bookpages = "384",
+ keywords = "Scratchpad",
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@article{Jenk77,
+ author = "Jenks, Richard D.",
+ title = "On the design of a modebased symbolic system",
+ journal = "SIGGAM Bulletin",
+ volume = "11",
+ number = "1",
+ pages = "1619",
+ year = "1977",
+ keywords = "axiomref",
+ abstract =
+ "This paper is a preliminary report on the design and implementation
+ of a modebased symbolic programming system and compiler which allows
+ programming with rewrite rules and LET and IS patternmatch constructs.
+ An important feature of this design is the provision for modevalued
+ variables which allow algebraic domains to be runtime parameters."
+}
+
+\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@@ 18626,6 +20707,28 @@ Watson Research Center, Yorktown Heights, NY, USA, 1969 RC2968 July 1970
\end{chunk}
\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@article{Jenk79a,
+ author = "Jenks, Richard D.",
+ title = "SCRATCHPAD/360: reflections on a language design",
+ journal = "SIGSAM",
+ volume = "13",
+ number = "1",
+ pages = "1626",
+ year = "1979",
+ keywords = "axiomref",
+ comment = "IBM Research RC 7405",
+ abstract =
+ "The key concepts of the SCRATCHPAD language are described, assessed,
+ and illustrated by an example. The language was originally intended as
+ an interactive problem solving language for symbolic mathematics.
+ Nevertheless, as this paper intends to show, it can be used as a
+ programming language as well."
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
\index{Trager, Barry M.}
\begin{chunk}{axiom.bib}
@article{Jenk81,
@@ 18680,6 +20783,19 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Jenks:1984:NSL,
+ author = "Richard D. Jenks",
+ title = "The New {SCRATCHPAD} Language and System for Computer
+ Algebra",
+ crossref = "Golden:1984:PMU",
+ pages = "409??",
+ year = "1984",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.1.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+}
+
+\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@@ 18737,6 +20853,18 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Jenks:1984:PKN,
+ author = "Richard D. Jenks",
+ title = "A primer: 11 keys to {New Scratchpad}",
+ crossref = "Fitch:1984:E",
+ pages = "123147",
+ year = "1984",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.1.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+}
+
+\end{chunk}
\index{Jenks, Richard D.}
\index{Sundaresan, Christine J.}
@@ 18816,6 +20944,27 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@TechReport{Jenks:1986:SIA,
+ author = "Richard D. Jenks and Robert S. Sutor and Stephen M.
+ Watt",
+ title = "Scratchpad {II}: an abstract datatype system for
+ mathematical computation",
+ type = "Research Report",
+ number = "RC 12327 (\#55257)",
+ institution = "International Business Machines Inc., Thomas J. Watson
+ Research Center",
+ address = "Yorktown Heights, NY, USA",
+ pages = "23",
+ year = "1986",
+ bibdate = "Thu Oct 31 17:23:28 2002",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ keywords = "Abstract data types (Computer science); Operating
+ systems (Computers)",
+}
+
+\end{chunk}
\index{Jenks, Richard D.}
\index{Sutor, Robert S.}
@@ 18827,10 +20976,22 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
Mathematical Computation'",
booktitle = "Proceedings Trends in Computer Algebra",
series = "Lecture Notes in Computer Science 296",
+ pages = "157182",
publisher = "SpringerVerlag",
+ isbn = "0387189289",
year = "1987",
comment = "IBM Research Report RC 12327 (\#55257) See Jenks86.pdf",
 keywords = "axiomref"
+ 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}
@@ 18838,7 +20999,7 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
\index{Jenks, Richard D.}
\index{Sutor, Robert S.}
\index{Watt, Stephen M.}
\begin{chunk}{ignore}
+\begin{chunk}{axiom.bib}
@inproceedings{Jenk88,
author = "Jenks, Richard D. and Sutor, Robert S. and Watt, Stephen M.",
title = "Scratchpad II: An Abstract Datatype System for Mathematical
@@ 18862,6 +21023,19 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Jenks:1988:SIA,
+ author = "R. D. Jenks and R. S. Sutor and S. M. Watt",
+ title = "{Scratchpad II}: An Abstract Datatype System for
+ Mathematical Computation",
+ crossref = "Janssen:1988:TCA",
+ pages = "1237",
+ year = "1988",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+}
+
+\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{ignore}
@@ 19463,12 +21637,60 @@ University of St Andrews, 6th April 2000
\end{chunk}
\index{Kendall, W.S.}
\begin{chunk}{ignore}
\bibitem[Kendall 99b]{Ken99b} Kendall, W.S.
+\index{Kendall, Wilfrid S.}
+\begin{chunk}{axiom.bib}
+@article{Kend01,
+ author = "Kendall, Wilfrid S.",
title = "Symbolic It\^o calculus in AXIOM: an ongoing story",
+ journal = "Statistics and Computing",
+ volume = "11",
+ pages = "2535",
+ year = "2001",
url = "http://www2.warwick.ac.uk/fac/sci/statistics/staff/academicresearch/kendall/personal/ppt/327.ps.gz",
+ paper = "Kend01.pdf",
+ keywords = "axiomref",
+ abstract =
+ "Symbolic It\^o calculus refers both to the implementation of the
+ It\^o calculus algebra package and to its application. This article
+ reports on progress in the implementation of It\^o calculus in the
+ powerful and innovative computer algebra package AXIOM, in the context
+ of a decade of previous implementations and applications. It is shown
+ how the elegant algebraic structure underylying the expressive and
+ effective formalism of It\^o calculus can be implemented directly in
+ AXIOM using the package's programmable facilities for ``strong
+ typing'' of computational objects. An application is given of the use
+ of the implementation to provide calculations for a new proof, based
+ on stochastic differentials, of the MardiaDryden distribution from
+ statistical shape theory."
+}
+
+\end{chunk}
+
+\index{Kendall, Wilfrid S.}
+\begin{chunk}{axiom.bib}
+@article{Kend07,
+ author = "Kendall, Wilfrid S.",
+ title = "Coupling all the Levy Stochastic Areas of Multidimensional
+ Brownian Motion",
+ journal = "The Annals of Probability",
+ volume = "35",
+ number = "3",
+ pages = "935953",
+ year = "2007",
keywords = "axiomref",
+ comment = "Author used Axiom for computation but says missed citation",
+ url = "http://arxiv.org/pdf/math/0512336v2.pdf",
+ paper = "Kend07.pdf",
+ abstract =
+ "It is shown how to construct a successful coadapted coupling of two
+ copies of an $n$dimensional Brownian motion ($B_1,\ldots,B_n$) while
+ simultaneously coupling all corresponding copies of the L{\'e}vy
+ stochastic areas $\int B_idB_j$  \int B_j dB_i$. It is conjectured
+ that successful coadapted couplings still exist when the L{\'e}vy
+ stochastic areas are replaced by a finite set of multiply iterated
+ path and timeintegrals, subject to algebraic compatibility of the
+ initial conditions."
+}
\end{chunk}
@@ 19700,6 +21922,43 @@ University of St Andrews, 6th April 2000
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@Article{Koseleff:1991:WGF,
+ author = "P.V. Koseleff",
+ title = "Word games in free {Lie} algebras: several bases and
+ formulas",
+ journal = jTHEORCOMPSCI,
+ volume = "79",
+ number = "1",
+ pages = "241256",
+ month = feb,
+ year = "1991",
+ CODEN = "TCSCDI",
+ ISSN = "03043975 (print), 18792294 (electronic)",
+ ISSNL = "03043975",
+ bibdate = "Tue Sep 17 06:44:07 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "The author compares the efficiency of many methods
+ which allow calculations in Lie algebras. Many
+ construction methods exist for the base of free Lie
+ algebras developed from finite sets. They use two
+ algorithms for calculation of several
+ CampbellHausdorf formulas. Diverse implementations
+ are realised in LISP on Scratchpad II.",
+ acknowledgement = acknhfb,
+ affiliation = "IBM, Paris, France",
+ classification = "C6130 (Data handling techniques); C7310
+ (Mathematics)",
+ fjournal = "Theoretical Computer Science",
+ journalURL = "http://www.sciencedirect.com/science/journal/03043975",
+ keywords = "Bases; CampbellHausdorf formulas; Finite sets; Free
+ Lie algebras; LISP; Scratchpad II",
+ language = "English",
+ pubcountry = "Netherlands",
+ thesaurus = "Mathematics computing; Symbol manipulation",
+}
+
+\end{chunk}
\index{Kredel, Heinz}
\begin{chunk}{axiom.bib}
@@ 19964,6 +22223,51 @@ University of St Andrews, 6th April 2000
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Kusche:1989:IGT,
+ author = "K. Kusche and B. Kutzler and H. Mayr",
+ title = "Implementation of a geometry theorem proving package
+ in {SCRATCHPAD} {II}",
+ crossref = "Davenport:1989:EEC",
+ pages = "246257",
+ month = "",
+ year = "1989",
+ bibdate = "Tue Sep 17 06:46:18 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ 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
+ Gr{\"o}bner bases have been implemented by groups at
+ Academia Sinica Beijing (China), U. Texas at Austin
+ (USA), General Electric Schenectady (USA), and Research
+ Institute for Symbolic Computation Linz (Austria). So
+ far, 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
+ these provers in the computer algebra system and
+ language SCRATCHPAD II. The authors 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 computing
+ time statistics of 24 examples.",
+ acknowledgement = acknhfb,
+ affiliation = "Res. Inst. for Symbolic Comput., RISCLINZ, Johannes
+ Kepler Univ., Linz, Austria",
+ classification = "C1230 (Artificial intelligence); C7310
+ (Mathematics)",
+ keywords = "Geometry theorem proving package; SCRATCHPAD II;
+ Characteristic sets; Gr{\"o}bner bases; Computer
+ algebra system; Computing time statistics",
+ language = "English",
+ thesaurus = "Algebra; Computational geometry; Mathematics
+ computing; Symbol manipulation; Theorem proving",
+}
+
+\end{chunk}
\subsection{L} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ 20056,6 +22360,56 @@ University of St Andrews, 6th April 2000
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@Article{Lambe:1991:RHP,
+ author = "L. A. Lambe",
+ title = "Resolutions via homological perturbation",
+ journal = jJSYMBOLICCOMP,
+ volume = "12",
+ number = "1",
+ pages = "7187",
+ month = jul,
+ year = "1991",
+ CODEN = "JSYCEH",
+ ISSN = "07477171 (print), 1095855X (electronic)",
+ ISSNL = "07477171",
+ bibdate = "Tue Sep 17 06:44:07 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "There is a tradeoff between the size of the
+ resolutions which arise from the perturbation method
+ and the complexity of the new differential. In order to
+ keep the modules relatively small, there is a
+ considerable increase in the algebraic complexity of
+ the resulting differentials. In order to study such
+ complexes systematically, examples are needed. To
+ facilitate such study, the Scratchpad system was used
+ to set up and perform the necessary calculations.
+ Because of the way Scratchpad is organized, this could
+ be done in a way that minimizes programming effort and
+ provides the natural mathematical environment for such
+ calculations. The author discusses some of the general
+ theory behind homological perturbation theory, gives an
+ idea of what is needed to make calculations within that
+ theory in Scratchpad, and calculates a resolution of
+ the integers over the integral group ring of the 4*4
+ upper triangular matrices with ones along the
+ diagonal.",
+ acknowledgement = acknhfb,
+ affiliation = "Illinois Univ., Chicago, IL, USA",
+ classification = "C4240 (Programming and algorithm theory); C7310
+ (Mathematics)",
+ fjournal = "Journal of Symbolic Computation",
+ journalURL = "http://www.sciencedirect.com/science/journal/07477171",
+ keywords = "Algebraic complexity; Complexity; Homological
+ perturbation; Integers; Mathematical environment;
+ Resolutions; Scratchpad system",
+ language = "English",
+ pubcountry = "UK",
+ thesaurus = "Computational complexity; Perturbation theory; Symbol
+ manipulation",
+}
+
+\end{chunk}
\index{FreeModuleCat}
\index{Lambe, Larry A.}
@@ 20348,6 +22702,54 @@ PhD thesis, Nov 2008 Florida State University
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{LeBlanc:1991:UMT,
+ author = "S. E. LeBlanc",
+ title = "The use of {MathCAD} and {Theorist} in the {ChE}
+ classroom",
+ crossref = "Anonymous:1991:PAC",
+ pages = "287299 (vol. 1)",
+ year = "1991",
+ bibdate = "Tue Sep 17 06:37:45 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "MathCAD and Theorist are two powerful mathematical
+ packages available for instruction in the ChE
+ classroom. MathCAD is advertised as an `electronic
+ scratchpad' and it certainly lives up to its billing.
+ It is an extremely userfriendly collection of
+ numerical routines that eliminates the drudgery of
+ solving many of the types of problems encountered by
+ undergraduate ChE's (and engineers in general). MathCAD
+ is available for both the Macintosh and IBM PC
+ compatibles. The PC version is available as a
+ fullfunctioned student version for around US\$40 (less
+ than many textbooks). Theorist is a symbolic
+ mathematical package for the Macintosh. Many
+ interesting and instructive things can be done with it
+ in the ChE curriculum. One of its many attractive
+ features includes the ability to generate high quality
+ three dimensional plots that can be very instructive in
+ examining the behavior of an engineering system. The
+ author discusses the application and use of these
+ packages in chemical engineering and give example
+ problems and their solutions for a number of courses
+ including stoichiometry, unit operations,
+ thermodynamics and design.",
+ acknowledgement = acknhfb,
+ affiliation = "Toledo Univ., OH, USA",
+ classification = "C7450 (Chemical engineering); C7810C (Computeraided
+ instruction)",
+ keywords = "Chemical engineering; MathCAD; Mathematical packages;
+ Numerical routines; Stoichiometry; Symbolic
+ mathematical package; Theorist; Thermodynamics; Unit
+ operations",
+ language = "English",
+ thesaurus = "Chemical engineering computing; Computer aided
+ instruction; Spreadsheet programs; Symbol
+ manipulation",
+}
+
+\end{chunk}
\index{Lecerf, Gr{\'e}goire}
\begin{chunk}{axiom.bib}
@@ 20647,6 +23049,41 @@ ISBN 0897916999 LCCN QA76.95 I59 1995 ACM order number 505950
\end{chunk}
\index{Li, Xin}
+\index{Maza, Marc Moreno}
+\index{Schost, Eric}
+\begin{chunk}{axiom.bib}
+@inproceedings{LIxx07,
+ author = "Li, Xin and Maza, Marc Moreno and Schost, Eric",
+ title = "On the Virtues of Generic Programming for Symbolic Computation",
+ booktitle = "Computational Science  ICCS 2007",
+ series = "Lecture Notes in Computer Science",
+ isbn = "3540725857",
+ pages = "251258",
+ year = "2007",
+ book = "Lixx07.pdf",
+ keywords = "axiomref",
+ abstract =
+ "The purpose of this study is to measure the impact of C level code
+ polynomial arithmetic on the performances of Axiom highlevel algorithms,
+ such as polynomial factorization. More precisely, given a highlevel
+ Axiom package P parameterized by a univariate polynomial domain U, we
+ have compared the performances of P when applied to different U's,
+ including an Axiom wrapper for our C level code.
+
+ Our experiments show that when P relies on U for its univariate
+ polynomial computations, our specialized C level code can provide a
+ significant speedup. For instance, the improved implementation of
+ squarefree factorization in Axiom is 7 times faster than the one in
+ Maple and very close to the one in Magma. On the contrary, when P does
+ not rely much on the operations of U and implements its private univariate
+ polynomial operation, the P cannot benefit from our highly optimized C
+ level code. Consequently, code which is poorly generic reduces the
+ speedup opportunities when applied to highly efficient and specialized."
+}
+
+\end{chunk}
+
+\index{Li, Xin}
\begin{chunk}{axiom.bib}
@phdthesis{Lixx09a,
author = "Li, Xin",
@@ 20765,16 +23202,31 @@ PASCO 2010
\index{Li, Yue}
\index{Dos Reis, Gabriel}
\begin{chunk}{ignore}
\bibitem[Li 11]{YL11} Li, Yue; Dos Reis, Gabriel
 title = "An Automatic Parallelization Framework for Algebraic Computation Systems",
ISSAC 2011
+\begin{chunk}{axiom.bib}
+@inproceedings{Lixx11,
+ author = "Li, Yue and Dos Reis, Gabriel",
+ title = "An Automatic Parallelization Framework for Algebraic
+ Computation Systems",
+ booktitle = "Proc. ISSAC 2011",
+ pages = "233240",
+ isbn = "9781450306751",
+ year = "2011",
url = "http://www.axiomatics.org/~gdr/concurrency/oaconcissac11.pdf",
 paper = "YL11.pdf",
+ paper = "Lixx11.pdf",
keywords = "axiomref",
 abstract = "
 This paper proposes a nonintrusive automatic parallelization
 framework for typeful and propertyaware computer algebra systems."
+ abstract =
+ "This paper proposes a nonintrusive automatic parallelization
+ framework for typeful and propertyaware computer algebra systems.
+ Automatic parallelization remains a promising computer program
+ transformation for exploiting ubiquitous concurrency facilities
+ available in modern computers. The framework uses semanticsbased
+ static analysis to extract reductions in library components based on
+ algebraic properties. An early implementation shows up to 5 times
+ speedup for library functions and homotopybased polynomial system
+ solver. The general framework is applicable to algebraic computation
+ systems and programming languages with advanced type systems that
+ support userdefined axioms or annotation systems."
+}
\end{chunk}
@@ 20913,6 +23365,30 @@ June 2, 1997
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Lucks:1986:FIP,
+ author = "Michael Lucks",
+ editor = "Bruce W. Char",
+ booktitle = "Proceedings of the 1986 Symposium on Symbolic and
+ Algebraic Computation: Symsac '86, July 2123, 1986,
+ Waterloo, Ontario",
+ title = "A fast implementation of polynomial factorization",
+ publisher = pubACM,
+ address = pubACM:adr,
+ pages = "228232",
+ year = "1986",
+ DOI = "http://dx.doi.org/10.1145.32485",
+ ISBN = "0897911997",
+ ISBN13 = "9780897911993",
+ LCCN = "QA155.7.E4 A281 1986",
+ bibdate = "Thu Jul 26 09:06:12 2001",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ note = "ACM order number 505860.",
+ acknowledgement = acknhfb,
+ keywords = "Scratchpad",
+}
+
+\end{chunk}
\index{Lueken, E.}
\begin{chunk}{axiom.bib}
@@ 20926,6 +23402,24 @@ June 2, 1997
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@MastersThesis{Lueken:1977:UIF,
+ author = "E. Lueken",
+ title = "{Ueberlegungen zur Implementierung eines
+ Formelmanipulationssystemes}",
+ school = "Technischen Universit{\"{a}}t CaroloWilhelmina zu
+ Braunschweig",
+ address = "Braunschweig, Germany",
+ pages = "??",
+ year = "1977",
+ bibsource = "/usr/local/src/bib/bibliography/Misc/TUBScsd.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ descriptor = "Alpak, Altran, Formac, Funktion, G.g.t., Kanonische
+ Darstellung von Polynomen, Macsyma, Mathlab, Polynom,
+ Rationale Funktion, Reduce, Sac1, Scratchpad",
+}
+
+\end{chunk}
\index{Lynch, R.}
\index{Mavromatis, H. A.}
@@ 20954,6 +23448,58 @@ June 2, 1997
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@Article{Lynch:1991:NQM,
+ author = "R. Lynch and H. A. Mavromatis",
+ title = "New quantum mechanical perturbation technique using an
+ `electronic scratchpad' on an inexpensive computer",
+ journal = jAMERJPHYSICS,
+ volume = "59",
+ number = "3",
+ pages = "270273",
+ month = mar,
+ year = "1991",
+ CODEN = "AJPIAS",
+ ISSN = "00029505 (print), 19432909 (electronic)",
+ ISSNL = "00029505",
+ bibdate = "Tue Sep 17 06:44:07 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "The authors have developed a new method for doing
+ numerical quantum mechanical perturbation theory. It
+ has the flavor of RayleighSchr{\"o}dinger
+ perturbation theory (division of the Hamiltonian into
+ an unperturbed Hamiltonian and a perturbing term, use
+ of the basis formed by the eigenfunctions of the
+ unperturbed Hamiltonian) while turning out to be a
+ variational technique. Furthermore, it is easily
+ implemented by means of the widely used `electronic
+ scratchpad,' MathCAD 2.0, using an inexpensive
+ computer. As an example of the method, the problem of a
+ harmonic oscillator with a quartic perturbing term is
+ examined.",
+ acknowledgement = acknhfb,
+ affiliation = "Dept. of Phys., King Fahd Univ. of Pet. and Miner.,
+ Dhahran, Saudi Arabia",
+ classification = "A0150H (Instructional computer use); A0210 (Algebra,
+ set theory, and graph theory); A0230 (Function theory,
+ analysis); A0365D (Functional analytical methods);
+ A0365F (Algebraic methods); A0365G (Solutions of wave
+ equations: bound state); C7810C (Computeraided
+ instruction)",
+ fjournal = "American Journal of Physics",
+ keywords = "Electronic scratchpad; Eigenvalues; Eigenfunctions;
+ Quantum mechanical perturbation technique;
+ RayleighSchr{\"o}dinger perturbation theory;
+ Hamiltonian; Variational technique; MathCAD 2.0;
+ Harmonic oscillator",
+ language = "English",
+ pubcountry = "USA",
+ thesaurus = "Computer aided instruction; Eigenvalues and
+ eigenfunctions; Harmonic oscillators; Perturbation
+ theory; Quantum theory; Variational techniques",
+}
+
+\end{chunk}
\subsection{M} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ 20967,8 +23513,8 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
\end{chunk}
\index{Mathews, J. }
\begin{chunk}{ignore}
+\index{Mathews, J.}
+\begin{chunk}{axiom.bib}
@article{Math89,
author = "Mathews, J.",
title = "Symbolic computational algebra applied to Picard iteration",
@@ 20981,6 +23527,7 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
"http://mathfaculty.fullerton.edu/mathews/articles/1989PicardIteration.pdf",
paper = "Math89.pdf",
keywords = "axiomref",
+ abstract =
"The term ``Picard iteration'' occurs two places in undergraduate
mathematics. In numerical analysis it is used when discussing fixed
point iteration for finding a numerical approximation to the equation
@@ 21004,6 +23551,55 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@Article{Mathews:1989:SCA,
+ author = "J. Mathews",
+ title = "Symbolic computational algebra applied to {Picard}
+ iteration",
+ journal = jMATHCOMPEDU,
+ volume = "23",
+ number = "2",
+ pages = "117122",
+ month = "Spring",
+ year = "1989",
+ CODEN = "MCEDDA",
+ ISSN = "07308639",
+ bibdate = "Tue Sep 17 06:48:10 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "Picard iteration occurs in differential equations as a
+ constructive procedure for establishing the existence
+ of a solution to a differential equation. This
+ application of Picard iteration illustrates how to use
+ a computer to generate a sequence of functions which
+ converges to a solution. The article shows the step by
+ step process in translating mathematical theory into
+ the symbolic manipulation setting. Systems such as
+ MACSYMA, ALTRAN, REDUCE, SMP, MAPLE, SCRATCHPAD, and
+ muMATH are being introduced in undergraduate
+ mathematics courses to assist in keeping track of
+ equations during complicated manipulations. The product
+ muMATH is illustrated because of its availability. It
+ runs on all 16bit computers which are IBM compatible.
+ The way has been opened to see how computers can be
+ used as a symbol cruncher.",
+ acknowledgement = acknhfb,
+ affiliation = "California State Univ., Fullerton, CA, USA",
+ classification = "C4130 (Interpolation and function approximation);
+ C4170 (Differential equations); C6130 (Data handling
+ techniques); C7310 (Mathematics)",
+ fjournal = "Mathematics and computer education",
+ keywords = "Differential equations; IBM compatible; Mathematical
+ theory; Mathematics computing; MuMATH; Picard
+ iteration; Symbol cruncher; Symbolic manipulation;
+ Undergraduate mathematics",
+ language = "English",
+ pubcountry = "USA",
+ thesaurus = "Differential equations; Iterative methods; Mathematics
+ computing; Microcomputer applications; Symbol
+ manipulation",
+}
+
+\end{chunk}
\begin{chunk}{axiom.bib}
@misc{Maxi16,
@@ 21115,6 +23711,48 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@Article{Melachrinoudis:1990:TAT,
+ author = "E. Melachrinoudis and D. L. Rumpf",
+ title = "Teaching advantages of transparent computer software
+  {MathCAD}",
+ journal = jCOED,
+ volume = "10",
+ number = "1",
+ pages = "7176",
+ month = jan # "" # mar,
+ year = "1990",
+ CODEN = "CWLJDP",
+ ISSN = "07368607",
+ bibdate = "Tue Sep 17 06:46:18 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "The case is presented for using mathematical
+ scratchpad software, such as MathCAD, in undergraduate
+ and graduate engineering courses. The pedagogical
+ benefits, especially relative to the usual black box
+ engineering software, are described. Several examples
+ of student written projects are presented. The projects
+ solve problems in operations research, control theory
+ and statistical regression analysis.",
+ acknowledgement = acknhfb,
+ affiliation = "Dept. of Ind. Eng., Northeastern Univ., Boston, MA,
+ USA",
+ classification = "C7110 (Education); C7310 (Mathematics); C7400
+ (Engineering); C7810C (Computeraided instruction)",
+ fjournal = "CoED",
+ keywords = "Black box engineering software; Control theory;
+ Graduate engineering courses; MathCAD; Mathematical
+ scratchpad software; Operations research; Pedagogical
+ benefits; Statistical regression analysis; Student
+ written projects; Transparent computer software;
+ Undergraduate",
+ language = "English",
+ pubcountry = "USA",
+ thesaurus = "CAD; Educational computing; Engineering computing;
+ Mathematics computing; Teaching",
+}
+
+\end{chunk}
\index{Melenk, H.}
\index{M\"oller, H. M.}
@@ 21170,6 +23808,27 @@ Seminar Proceedings, Schloss Dagstuhl (2005)
\end{chunk}
+\index{Miller, Bruce R.}
+\begin{chunk}{axiom.bib}
+@misc{Mill95,
+ author = "Miller, Bruce R.",
+ title = "An expression formatter for MACSYMA",
+ keywords = "axiomref",
+ year = "1995",
+ paper = "Mill95.pdf",
+ abstract =
+ "A package for formatting algebraic expressions in MACSYA is described.
+ It provides facilities for userdirected hierarchical structuring of
+ expressions, as well as for directing simplifications to selected
+ subexpressions. It emphasizes a semantic rther than syntactic description
+ of the desired form. The package also provides utilities for obtaining
+ efficiently the coefficients of polynomials, trigonometric sums and
+ power series. Similar capabilities would be useful in other computer
+ algebra systems."
+}
+
+\end{chunk}
+
\index{Minoiu, N.}
\index{Netto, M}
\index{Mammar, S}
@@ 21583,6 +24242,36 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
\end{chunk}
+\index{Ng, Edward W.}
+\begin{chunk}{axiom.bib}
+@techreport{Ngxx80,
+ author = "Ng, Edward W.",
+ title = "SymbolicNumeric Interface: A Review",
+ type = "technical report",
+ number = "NASACR162690 HC A02/MF A01",
+ institution = "NASA Jet Propulsion Lab",
+ url = "http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19800008508.pdf",
+ paper = "Ngxx80.pdf",
+ keywords = "axiomref",
+ abstract =
+ "This is a survey of recent activities that either used or encouraged the
+ potential use of a combination of symbolic and numerical calculations.
+ Symbolic calculations here primarily refer to the computer processing of
+ procedures from classical algebra, analysis and calculus. Numerical
+ calculations refer to both numerical mathematics research and scientific
+ computation. This survey is inteded to point out a large number of problem
+ areas where a cooperation of symbolic and numeric methods is likely to
+ bear many fruits. These areas include such classical operations as
+ differentiation and integration, such diverse activities as function
+ approximations andqualitative analysis, and such contemporary topics as
+ finite element calculations and computational complexity. It is contended
+ that other less obvious topics such as the fast Fourier transform, linear
+ algebra, nonlinear analysis and error analysis would also benefti from a
+ synergistic approach advocated here."
+}
+
+\end{chunk}
+
\index{Norman, Arthur C.}
\begin{chunk}{axiom.bib}
@article{Norm75,
@@ 21598,6 +24287,28 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@Article{Norman:1975:CFP,
+ author = "A. C. Norman",
+ title = "Computing with Formal Power Series",
+ journal = jTOMS,
+ volume = "1",
+ number = "4",
+ pages = "346356",
+ month = dec,
+ year = "1975",
+ CODEN = "ACMSCU",
+ ISSN = "00983500 (print), 15577295 (electronic)",
+ ISSNL = "00983500",
+ bibdate = "Sat Aug 27 00:22:26 1994",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ fjournal = "ACM Transactions on Mathematical Software",
+ journalURL = "http://portal.acm.org/toc.cfm?idx=J782",
+ keywords = "Scratchpad",
+}
+
+\end{chunk}
\index{AffineAlgebraicSetComputeWithGroebnerBasis}
\index{EuclideanGroebnerBasisPackage}
@@ 21630,11 +24341,18 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
\end{chunk}
\index{Norman, Arthur C.}
\begin{chunk}{ignore}
\bibitem[Norman 75a]{Nor75a} Norman, A.C.
+\begin{chunk}{axiom.bib}
+@article{Norm75a,
+ author = "Norman, Arthur C.",
title = "The SCRATCHPAD Power Series Package",
IBM T.J. Watson Research RC4998
 keywords = "axiomref",
+ journal = "SIGSAM",
+ volume = "9",
+ number = "1",
+ pages = "1220",
+ year = "1975",
+ comment = "IBM T.J. Watson Research RC4998",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 21806,6 +24524,49 @@ IBM T.J. Watson Research RC4998
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Ollivier:1989:IRM,
+ author = "F. Ollivier",
+ title = "Inversibility of rational mappings and structural
+ identifiability in automatics",
+ crossref = "ACM:1989:PAI",
+ pages = "4354",
+ month = "",
+ year = "1989",
+ bibdate = "Tue Sep 17 06:46:18 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "The author investigates different methods for testing
+ whether a rational mapping f from k/sup n/ to k/sup m/
+ admits a rational inverse, or whether a polynomial
+ mapping admits a polynomial one. He gives a new
+ solution, which seems much more efficient in practice
+ than previously known ones using `tag' variables and
+ standard basis, and a majoration for the degree of the
+ standard basis calculations which is valid for both
+ methods in the case of a polynomial map which is
+ birational. He shows that a better bound can be given
+ for the method, under some assumption on the form of f.
+ The method can also extend to check whether a given
+ polynomial belongs to the subfield generated by a
+ finite set of fractions. The author illustrates the
+ algorithm with an application to structural
+ identifiability. The implementation has been done in
+ the IBM computer algebra system Scratchpad II.",
+ acknowledgement = acknhfb,
+ affiliation = "Lab. d'Inf. de l'X, Ecole Polytech., Palaiseau,
+ France",
+ classification = "C1110 (Algebra); C1120 (Analysis); C7310
+ (Mathematics)",
+ keywords = "Computer algebra system; Fractions; IBM;
+ Inversibility; Polynomial inverse; Polynomial mapping;
+ Rational inverse; Rational mappings; Scratchpad II;
+ Structural identifiability",
+ language = "English",
+ thesaurus = "Inverse problems; Mathematics computing; Polynomials;
+ Set theory; Symbol manipulation",
+}
+
+\end{chunk}
\begin{chunk}{ignore}
\bibitem[Online 72]{Onl72}.
@@ 21837,7 +24598,30 @@ interactive computing, Brunel University, Uxbridge, England, 47 September
volume = "41",
number = "3",
pages = "114",
 keywords = "axiomref"
+ keywords = "axiomref",
+ abstract =
+ "Axiom has been in development since 1971. Originally called
+ Scratchpad II, it was developed by IBM under the direction of Richard
+ Jenks[1]. The project evolved over a period of 20 years as a research
+ platform for developing new ideas in computational mathematics.
+ ScratchPad also attracted the interest and contributions of a large
+ number of mathematicians and computer scientists outside of IBM. In
+ the 1990s, the Scratchpad project was renamed to Axiom, and sold to
+ the Numerical Algorithms Group (NAG) in England who marketed it as a
+ commercial system. NAG withdrew Axiom from the market in October 2001
+ and agreed to release Axiom as free software, under an open source
+ license.
+
+ Tim Daly (a former ScratchPad developer at IBM) setup a pubic open
+ source Axiom project[2] in October 2002 with a primary goal to improve
+ the documentation of Axiom through the extensive use of literate
+ programming[3]. The first free open source version of Axiom was
+ released in 2003. Since that time the project has attracted a small
+ but very active group of developers and a growing number of users.
+
+ This exhibit includes a laptop computer running a recent version
+ of Axiom, Internet access (if available) to the Axiom Wiki website[4],
+ and CDs containing Axiom software for free distribution[5]."
}
\end{chunk}
@@ 21997,6 +24781,31 @@ Computers and Mathematics November 1993, Vol 40, Number 9 pp12031210
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Purtilo:1986:ASI,
+ author = "J. Purtilo",
+ editor = "Bruce W. Char",
+ booktitle = "Proceedings of the 1986 Symposium on Symbolic and
+ Algebraic Computation: Symsac '86, July 2123, 1986,
+ Waterloo, Ontario",
+ title = "Applications of a software interconnection system in
+ mathematical problem solving environments",
+ publisher = pubACM,
+ address = pubACM:adr,
+ pages = "1623",
+ year = "1986",
+ DOI = "http://dx.doi.org/10.1145.32443",
+ ISBN = "0897911997",
+ ISBN13 = "9780897911993",
+ LCCN = "QA155.7.E4 A281 1986",
+ bibdate = "Thu Jul 26 09:26:18 2001",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ note = "ACM order number 505860.",
+ acknowledgement = acknhfb,
+ keywords = "Scratchpad",
+}
+
+\end{chunk}
\subsection{R} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ 22374,6 +25183,38 @@ Mathematik und Physik, 75 (suppl. 2):S435S438, 1995 ISSN 00442267
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@TechReport{Salvy:1989:EAA,
+ author = "B. Salvy",
+ title = "Examples of automatic asymptotic expansions",
+ number = "114",
+ institution = "Inst. Nat. Recherche Inf. Autom.",
+ address = "Le Chesnay, France",
+ pages = "18",
+ month = dec,
+ year = "1989",
+ bibdate = "Tue Sep 17 06:46:18 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "Describes the current state of a Maple library, gdev,
+ designed to perform asymptotic expansions for a large
+ class of expressions. Many examples are provided, along
+ with a short sketch of the underlying principles. A
+ striking feature of these examples is that none of them
+ can be computed directly with any of the most
+ widespread symbolic computation systems (Macsyma,
+ Mathematica, Maple or Scratchpad II).",
+ acknowledgement = acknhfb,
+ classification = "C1120 (Analysis); C6130 (Data handling techniques);
+ C7310 (Mathematics)",
+ keywords = "Asymptotic expansions; Gdev; Maple library; Symbolic
+ computation systems",
+ language = "English",
+ pubcountry = "France",
+ thesaurus = "Mathematical analysis; Mathematics computing;
+ Subroutines; Symbol manipulation",
+}
+
+\end{chunk}
\index{Salvy, Bruno}
\begin{chunk}{ignore}
@@ 22585,6 +25426,19 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InCollection{Schwarz:1988:PAD,
+ author = "F. Schwarz",
+ title = "Programming with abstract data types: the symmetry
+ package {SPDE} in {Scratchpad}",
+ crossref = "Janssen:1988:TCA",
+ pages = "167176",
+ year = "1988",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/cathode.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+}
+
+\end{chunk}
\index{Schwarz, Fritz}
\begin{chunk}{axiom.bib}
@@ 22616,6 +25470,50 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Schwarz:1989:FAL,
+ author = "F. Schwarz",
+ title = "A factorization algorithm for linear ordinary
+ differential equations",
+ crossref = "ACM:1989:PAI",
+ pages = "1725",
+ month = "",
+ year = "1989",
+ bibdate = "Tue Sep 17 06:46:18 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "The reducibility and factorization of linear
+ homogeneous differential equations are of great
+ theoretical and practical importance in mathematics.
+ Although it has been known for a long time that
+ factorization is in principle a decision procedure, its
+ use in an automatic differential equation solver
+ requires a more detailed analysis of the various steps
+ involved. Especially important are certain auxiliary
+ equations, the socalled associated equations. An upper
+ bound for the degree of its coefficients is derived.
+ Another important ingredient is the computation of
+ optimal estimates for the size of polynomial and
+ rational solutions of certain differential equations
+ with rotational coefficients. Applying these results,
+ the design of the factorization algorithm LODEF and its
+ implementation in the Scratchpad II Computer Algebra
+ System is described.",
+ acknowledgement = acknhfb,
+ affiliation = "GMD, Inst. F1, St. Augustin, West Germany",
+ classification = "C1120 (Analysis); C4170 (Differential equations);
+ C7310 (Mathematics)",
+ keywords = "Associated equations; Automatic differential equation
+ solver; Factorization algorithm; Linear ordinary
+ differential equations; LODEF; Optimal estimates;
+ Polynomial solutions; Rational solutions; Rotational
+ coefficients; Scratchpad II Computer Algebra System;
+ Upper bound",
+ language = "English",
+ thesaurus = "Linear differential equations; Mathematics computing;
+ Polynomials; Symbol manipulation",
+}
+
+\end{chunk}
\index{Schwarz, Fritz}
\begin{chunk}{axiom.bib}
@@ 22641,6 +25539,51 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@Article{Schwarz:1991:MOG,
+ author = "F. Schwarz",
+ title = "Monomial orderings and {Gr{\"o}bner} bases",
+ journal = jSIGSAM,
+ volume = "25",
+ number = "1",
+ pages = "1023",
+ month = jan,
+ year = "1991",
+ CODEN = "SIGSBZ",
+ ISSN = "01635824 (print), 15579492 (electronic)",
+ ISSNL = "01635824",
+ bibdate = "Tue Sep 17 06:44:07 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "Let there be given a set of monomials in n variables
+ and some order relations between them. The following
+ fundamental problem of monomial ordering is considered.
+ Is it possible to decide whether these ordering
+ relations are consistent and if so to extend them to an
+ admissible ordering for all monomials? The answer is
+ given in terms of the algorithm MACOT which constructs
+ a matrix of socalled cotes which establishes the
+ desired ordering relations. The main area of
+ application of this algorithm, i.e. the construction of
+ Gr{\"o}bner bases for different orderings and of
+ universal Gr{\"o}bner bases, is presented. An
+ implementation in Scratchpad is also briefly
+ described.",
+ acknowledgement = acknhfb,
+ affiliation = "GMD Inst., St. Augustin, Germany",
+ classification = "C1110 (Algebra); C4140 (Linear algebra); C7310
+ (Mathematics)",
+ fjournal = "SIGSAM Bulletin",
+ keywords = "Computer algebra; Thomas theorem; Multivariate
+ polynomial; Gr{\"o}bner bases; Monomial ordering;
+ Ordering relations; Admissible ordering; MACOT; Matrix;
+ Cotes; Scratchpad",
+ language = "English",
+ pubcountry = "USA",
+ thesaurus = "Algebra; Matrix algebra; Polynomials; Symbol
+ manipulation",
+}
+
+\end{chunk}
\index{Schwarz, Fritz}
\begin{chunk}{axiom.bib}
@@ 22813,17 +25756,25 @@ in Calmet [Cal94] pp103104
\end{chunk}
\index{Seiler, Werner Markus}
\begin{chunk}{ignore}
\bibitem[Seiler 97]{Sei97} Seiler, Werner M.
+\begin{chunk}{axiom.bib}
+@article{Seil97,
+ author = "Seiler, Werner M.",
title = "Computer Algebra and Differential Equations: An Overview",
 url = "http://www.mathematik.unikassel.di/~seiler/Papers/Postscript/CADERep.ps.gz",
+ journal = "mathPAD7",
+ volume = "7",
+ pages = "3449",
+ year = "1997",
+ url =
+"http://www.mathematik.unikassel.di/~seiler/Papers/Postscript/CADERep.ps.gz",
keywords = "axiomref",
 abstract = "
 We present an informal overview of a number of approaches to
+ paper = "Seil97.pdf",
+ abstract =
+ "We present an informal overview of a number of approaches to
differential equations which are popular in computer algebra. This
includes symmetry and completion theory, local analysis, differential
ideal and Galois theory, dynamical systems and numerical analysis. A
large bibliography is provided."
+}
\end{chunk}
@@ 22867,6 +25818,40 @@ in Calmet [Cal94] pp103104
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@TechReport{Senechaud:1987:SIP,
+ author = "P. Senechaud and F. Siebert and G. Villard",
+ title = "Scratchpad {II}: Pr{\'e}sentation d'un nouveau langage
+ de calcul formel",
+ number = "640M",
+ institution = "TIM 3 (IMAG)",
+ address = "Grenoble, France",
+ pages = "??",
+ month = feb,
+ year = "1987",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.1.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+}
+
+\end{chunk}
+
+\index{Senechaud, Pascale}
+\index{Siebert, F.}
+\begin{chunk}{axiom.bib}
+@techreport{Sene87a,
+ author = "Senechaud, Pascale and Siebert, F.",
+ title = "Etude dl l'algorithme de Kovacic et son implantation sur
+ Scratchpad II",
+ type = "Technical Report",
+ number = "639",
+ institution = "Institut IMAG, Informatique et Mathematiques Appliquees
+ de Grenoble",
+ address = "Grenoble, France",
+ year = "1987",
+ keywords = "axiomref"
+}
+
+\end{chunk}
\index{Shannon, D.}
\index{Sweedler, M.}
@@ 22903,6 +25888,81 @@ in Calmet [Cal94] pp103104
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@Article{Shannon:1988:UGB,
+ author = "D. Shannon and M. Sweedler",
+ title = "Using {Gr{\"o}bner} bases to determine algebra
+ membership, split surjective algebra homomorphisms
+ determine birational equivalence",
+ journal = jJSYMBOLICCOMP,
+ volume = "6",
+ number = "23",
+ pages = "267273",
+ month = oct # "" # dec,
+ year = "1988",
+ CODEN = "JSYCEH",
+ ISSN = "07477171 (print), 1095855X (electronic)",
+ ISSNL = "07477171",
+ bibdate = "Tue Sep 17 06:48:10 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "This paper presents a simple algorithm, based on
+ Gr{\"o}bner bases, to test if a given polynomial g of
+ k(X/sub 1/,\ldots{}, X/sub n/) lies in k(f/sub
+ 1/,\ldots{}, f/sub m/) where k is a field, X/sub
+ i/,\ldots{}, X/sub n/ are indeterminates over k and
+ f/sub 1/,\ldots{}, f/sub m/ in k(X/sub 1/,\ldots{},
+ X/sub n/). If so, the algorithm produces a polynomial P
+ of m variables where g=P(f/sub 1/,\ldots{}, f/sub m/).
+ Say omega:B to k(X/sub 1/,\ldots{}, X/sub n/) is a
+ homomorphism where omega (b/sub i/)=f/sub i/, for
+ algebra generators (b/sub i/) contained in/implied by
+ B. If omega is onto, the algorithm gives a homomorphism
+ lambda:k(X/sub 1/,\ldots{}, X/sub 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/sub 1/,\ldots{}, f/sub
+ m/)=k(X/sub 1/,\ldots{}, X/sub n/), tells if k(f/sub
+ 1/,\ldots{}, f/sub m/)=k(X/sub 1/,\ldots{}, X/sub n/).
+ Existing computer algebra systems, such as IBM'S
+ SCRATCHPAD II, have Gr{\"o}bner basis packages which
+ allow the user to specify a term ordering sufficient to
+ carry out the algorithm.",
+ acknowledgement = acknhfb,
+ affiliation = "Dept. of Math., Transylvania Univ., Lexington, KY,
+ USA",
+ classification = "C4130 (Interpolation and function approximation);
+ C6130 (Data handling techniques); C7310 (Mathematics)",
+ fjournal = "Journal of Symbolic Computation",
+ journalURL = "http://www.sciencedirect.com/science/journal/07477171",
+ keywords = "IBM; Gr{\"o}bner bases; Algebra membership; Split
+ surjective algebra homomorphisms; Birational
+ equivalence; Polynomial; Homomorphism; Algebra
+ generators; Identity map; Algebra automorphisms;
+ Computer algebra systems; SCRATCHPAD II",
+ language = "English",
+ pubcountry = "UK",
+ thesaurus = "Polynomials; Symbol manipulation",
+}
+
+\end{chunk}
+
+\begin{chunk}{axiom.bib}
+@misc{SIGS16,
+ author = "SIGSAM, ACM",
+ title = "Axiom",
+ url = "http://www.sigsam.org/software/axiom.html",
+ year = "2016",
+ contact = "Infodir\_SIGSAM\@acm.org",
+ abstract =
+ "Axiom is a free, open source, generalpurpose computer algebra
+ system. It features a strongly typed language. The system has an
+ interactive interpreter and a compiler. It includes over 1100
+ supported categories, domains, and packages covering large areas of
+ Mathematics."
+}
+
+\end{chunk}
\index{Singer, Michael F.}
\index{Ulmer, Felix}
@@ 23057,6 +26117,42 @@ in Calmet [Cal94] pp103104
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Sit:1989:GAS,
+ author = "W. Y. Sit",
+ title = "On {Goldman}'s algorithm for solving firstorder
+ multinomial autonomous systems",
+ crossref = "Mora:1989:AAA",
+ pages = "386395",
+ month = "",
+ year = "1989",
+ bibdate = "Tue Sep 17 06:46:18 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "A brief exposition of a method for finding first
+ integrals for first order multinomial autonomous
+ systems (FOMAS) of ordinary differential equations with
+ constant coefficients is given. The method is a
+ simplified as well as a redesigned version based on a
+ paper of Goldman (1987). The author shows how it can be
+ applied to FOMAS with parametric coefficients. The
+ algorithm is currently being implemented using the
+ SCRATCHPAD II computer algebra language and system at
+ the IBM TJ Watson Research Center.",
+ acknowledgement = acknhfb,
+ affiliation = "Dept. of Math., City Coll. of New York, NY, USA",
+ classification = "B0290P (Differential equations); B0290R (Integral
+ equations); C4170 (Differential equations); C4180
+ (Integral equations); C7310 (Mathematics)",
+ keywords = "Computer algebra language; Constant coefficients;
+ First integrals; First order multinomial autonomous
+ systems; FOMAS; Goldman algorithm; IBM; Ordinary
+ differential equations; SCRATCHPAD II",
+ language = "English",
+ thesaurus = "Differential equations; Integral equations;
+ Mathematics computing",
+}
+
+\end{chunk}
\index{Sit, William Y.}
\begin{chunk}{ignore}
@@ 23487,6 +26583,19 @@ LCCN QA76.76.A65 S95 1992
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Sutor:1985:SIC,
+ author = "R. S. Sutor",
+ title = "The {Scratchpad II} Computer Algebra Language and
+ System",
+ crossref = "Buchberger:1985:EEC",
+ pages = "3233",
+ year = "1985",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/Comp.Alg.1.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+}
+
+\end{chunk}
\index{Sutor, Robert S.}
\index{Jenks, Richard D.}
@@ 23518,6 +26627,42 @@ LCCN QA76.76.A65 S95 1992
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Sutor:1987:TICb,
+ author = "R. S. Sutor and R. D. Jenks",
+ title = "The Type Inference and Coercion Facilities in the
+ {Scratchpad II} Interpreter",
+ crossref = "Wexelblat:1987:IIT",
+ pages = "5663",
+ year = "1987",
+ bibsource = "/usr/local/src/bib/bibliography/Compiler/bevan.bib;
+ /usr/local/src/bib/bibliography/Misc/sigplan.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "The Scratchpad II system is an abstract datatype
+ programming language, a compiler for the language, a
+ library of packages of polymorphic functions and
+ parameterized abstract datatypes, and an interpreter
+ that provides sophisticated type inference and coercion
+ facilities. Although originally designed for the
+ implementation of symbolic mathematical algorithms,
+ Scratchpad II is a general purpose programming
+ language. This paper discusses aspects of the
+ implementation of the interpreter and how it attempts
+ to provide a user friendly ad relatively weakly typed
+ front end for the strongly typed programming
+ language.",
+ acknowledgement = acknhfb,
+ checked = "19940516",
+ keywords = "scratchpad",
+ refs = "8",
+ subject = "D.3.4 Software, PROGRAMMING LANGUAGES, Processors,
+ Interpreters \\ I.1.3 Computing Methodologies,
+ ALGEBRAIC MANIPULATION, Languages and Systems,
+ SCRATCHPAD \\ D.3.3 Software, PROGRAMMING LANGUAGES,
+ Language Constructs, Abstract data types",
+}
+
+\end{chunk}
\index{Sutor, Robert S.}
\begin{chunk}{ignore}
@@ 23530,15 +26675,20 @@ IBM Course presentation slide deck Spring 1987
\index{Sutor, Robert S.}
\index{Jenks, Richard D.}
\begin{chunk}{ignore}
\bibitem[Sutor 87c]{SJ87c} Sutor, Robert S.; Jenks, Richard
 title = "The type inference and coercion facilities in the Scratchpad II interpreter'",
Research report RC 12595 (\#56575),
IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA, 1987, 11pp
 paper = "SJ87c.pdf",
+\begin{chunk}{axiom.bib}
+@techreport{Suto87c,
+ author = "Sutor, Robert S. and Jenks, Richard D.",
+ title = "The type inference and coercion facilities in the
+ Scratchpad II interpreter'",
+ type = "Research Report",
+ number = "RC 12595 (\#56575)",
+ institution = "Mathematical Sciences Department",
+ address = "IBM Thomas J. Watson Research Center, Yorktown Heights, NY",
+ year = "1987",
+ paper = "Suto87c.pdf",
keywords = "axiomref",
 abstract = "
 The Scratchpad II system is an abstract datatype programming language,
+ abstract =
+ "The Scratchpad II system is an abstract datatype programming language,
a compiler for the language, a library of packages of polymorphic
functions and parameterized abstract datatypes, and an interpreter
that provides sophisticated type inference and coercion facilities.
@@ 23548,6 +26698,26 @@ IBM Thomas J. Watson Research Center, Yorktown Heights, NY, USA, 1987, 11pp
implementation of the intepreter and how it attempts to provide a user
friendly and relatively weakly typed front end for the strongly typed
programming language."
+}
+
+\end{chunk}
+\begin{chunk}{beebe.bib}
+@TechReport{Sutor:1987:TICa,
+ author = "Robert S. Sutor and Richard D. Jenks",
+ title = "The type inference and coercion facilities in the
+ {Scratchpad II} interpreter",
+ type = "Research Report",
+ number = "RC 12595 (\#56575)",
+ institution = "IBM Thomas J. Watson Research Center",
+ address = "Yorktown Heights, NY, USA",
+ pages = "11",
+ year = "1987",
+ bibdate = "Sat Dec 30 08:25:26 MST 1995",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ acknowledgement = acknhfb,
+ keywords = "Abstract data types (Computer science); Programming
+ languages (Electronic computers)",
+}
\end{chunk}
@@ 23814,6 +26984,7 @@ ISBN 3540213112
pages = "2531",
year = "1989",
keywords = "axiomref",
+ paper = "Wang89.pdf",
abstract =
"This report describes the implementation and use of a program for
computing the Liapunov functions and Liapunov constants for a class
@@ 23821,6 +26992,45 @@ ISBN 3540213112
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@Article{Wang:1989:PCL,
+ author = "D. Wang",
+ title = "A program for computing the {Liapunov} functions and
+ {Liapunov} constants in {Scratchpad} {II}",
+ journal = jSIGSAM,
+ volume = "23",
+ number = "4",
+ pages = "2531",
+ month = oct,
+ year = "1989",
+ CODEN = "SIGSBZ",
+ ISSN = "01635824 (print), 15579492 (electronic)",
+ ISSNL = "01635824",
+ bibdate = "Tue Sep 17 06:46:18 MDT 1996",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/sigsam.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "The report describes the implementation and use of a
+ program for computing the Liapunov functions and
+ Liapunov constants for a class of differential systems
+ in Scratchpad II.",
+ acknowledgement = acknhfb,
+ affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
+ Univ., Linz, Austria",
+ classification = "C1320 (Stability); C4170 (Differential equations);
+ C7420 (Control engineering)",
+ fjournal = "SIGSAM Bulletin",
+ keywords = "Differential systems, design; Liapunov constants;
+ Liapunov functions; performance; Scratchpad II",
+ language = "English",
+ pubcountry = "USA",
+ subject = "E.4 Data, CODING AND INFORMATION THEORY, Data
+ compaction and compression \\ G.2.0 Mathematics of
+ Computing, DISCRETE MATHEMATICS, General",
+ thesaurus = "Control system CAD; Differential equations; Lyapunov
+ methods; Polynomials",
+}
+
+\end{chunk}
\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@@ 23855,6 +27065,7 @@ ISBN 3540213112
year = "1991",
keywords = "axiomref",
paper = "Wang91.pdf",
+ comment = "See Wang89 for the implementation code",
abstract =
"In this paper we describe a mechanical procedure for computing the
Liapunov functions and Liapunov constants for a class of differential
@@ 23877,6 +27088,68 @@ ISBN 3540213112
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@Article{Wang:1991:MMC,
+ author = "Dongming Wang",
+ title = "Mechanical manipulation for a class of differential
+ systems",
+ journal = jJSYMBOLICCOMP,
+ volume = "12",
+ number = "2",
+ pages = "233254",
+ month = aug,
+ year = "1991",
+ CODEN = "JSYCEH",
+ ISSN = "07477171 (print), 1095855X (electronic)",
+ ISSNL = "07477171",
+ bibdate = "Tue Sep 17 06:44:07 MDT 1996",
+ bibsource = "/usr/local/src/bib/bibliography/Theory/cathode.bib;
+ http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "The author describes a mechanical procedure for
+ computing the Liapunov functions and Liapunov constants
+ for a class of differential systems. These functions
+ and constants are used for establishing the stability
+ criteria, the conditions for the existence of a center
+ and for the investigation of limit cycles. Some
+ problems for handling the computer constants, which are
+ usually large polynomials in terms of the coefficients
+ of the differential system, and an approach towards
+ their solution by using computer algebraic methods are
+ proposed. This approach has been successfully applied
+ to check some known results mechanically. The author
+ has implemented a system DEMS on an HP1000 and in
+ Scratchpad II on an IBM4341 for computing and
+ manipulating the Liapunov functions and Liapunov
+ constants. As examples, two particular cubic systems
+ are discussed in detail. The explicit algebraic
+ relations between the computed Liapunov constants and
+ the conditions given by Saharnikov are established,
+ which leads to a rediscovery of the incompleteness of
+ his conditions. A class of cubic systems with 6tuple
+ focus is presented to demonstrate the feasibility of
+ the approach for finding systems with higher multiple
+ focus.",
+ acknowledgement = acknhfb,
+ affiliation = "Res. Inst. for Symbolic Comput., Johannes Kepler
+ Univ., Linz, Austria",
+ classification = "C1320 (Stability); C4170 (Differential equations);
+ C7420 (Control engineering)",
+ fjournal = "Journal of Symbolic Computation",
+ journalURL = "http://www.sciencedirect.com/science/journal/07477171",
+ keywords = "6Tuple focus; Computer algebraic methods; Cubic
+ systems; DEMS; Differential systems; HP1000; IBM4341;
+ Incompleteness; Large polynomials; Liapunov constants;
+ Liapunov functions; Limit cycles; Limit cycles
+ SCRATCHPAD, Nonlinear DEs; Mechanical procedure;
+ Scratchpad II; Stability criteria",
+ language = "English",
+ pubcountry = "UK",
+ thesaurus = "Control system analysis computing; Lyapunov methods;
+ Nonlinear differential equations; Stability; Symbol
+ manipulation",
+}
+
+\end{chunk}
\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@@ 24104,6 +27377,48 @@ in [Wit87], pp1317
}
\end{chunk}
+\begin{chunk}{beebe.bib}
+@InProceedings{Watt:1989:FPM,
+ author = "S. M. Watt",
+ title = "A fixed point method for power series computation",
+ crossref = "Gianni:1989:SAC",
+ pages = "206217",
+ month = "",
+ year = "1989",
+ bibdate = "Tue Sep 17 06:46:18 MDT 1996",
+ bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib",
+ abstract = "Presents a novel technique for manipulating structures
+ which represent infinite power series. The technique
+ described allows a power series to be defined in a very
+ natural but computationally inefficient way and
+ transforms it to an equivalent, efficient form. This is
+ achieved by using a fixed point operator on the delayed
+ part to remove redundant calculations. The paper
+ describes this fixed point method and the class of
+ problems to which it is applicable. It has been used in
+ Scratchpad II to improve the performance of a number of
+ operations on infinite series, including division,
+ reversion, special functions and the solution of linear
+ and nonlinear ordinary differential equations. A few
+ examples are given of the method and of the speed up
+ obtained. To illustrate, the computation of the first n
+ terms of exp(u) for a dense, infinite series u is
+ reduced from O(n/sup 4/) to O(n/sup 2/) coefficient
+ operations, the same as required by the standard
+ online algorithms.",
+ acknowledgement = acknhfb,
+ affiliation = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
+ NY, USA",
+ classification = "C4240 (Programming and algorithm theory); C7310
+ (Mathematics)",
+ keywords = "Delayed part; Fixed point method; Fixed point
+ operator; Infinite power series; Power series
+ computation; Redundant calculations; Scratchpad II",
+ language = "English",
+ thesaurus = "Computational complexity; Mathematics computing",
+}
+
+\end{chunk}
\index{Watt, Stephen M.}
\index{Jenks, Richard D.}
@@ 26779,7 +30094,8 @@ J. of Pure and Applied Algebra, 45, 225240 (1987)
journal = "Bayreuther Mathematische Schriften",
volume = "33",
year = "1990",
 pages = "123"
+ pages = "123",
+ keywords = "axiomref"
}
\end{chunk}
@@ 27278,15 +30594,22 @@ Dept. G68, P.O. Box 1900, Boulder, Colorado, USA 803019191.
\end{chunk}
+\index{InnerNormalBasisFieldFunctions}
\index{Itoh, T.}
\index{Tsujii, S.}
\begin{chunk}{ignore}
\bibitem[Itoh 88]{Itoh88} Itoh, T.;, Tsujii, S.
 title = "A fast algorithm for computing multiplicative inverses in $GF(2^m)$ using normal bases",
Inf. and Comp. 78, pp.171177, 1988
+\begin{chunk}{axiom.bib}
+@article{Itoh88,
+ author = "Itoh, T. and Tsujii, S.",
+ title = "A fast algorithm for computing multiplicative inverses in
+ $GF(2^m)$ using normal bases",
+ journal = "Inf. and Comp.",
+ volume = "78",
+ pages = "171177",
+ year = "1988",
paper = "Itoh88.pdf",
 abstract = "
 This paper proposes a fast algorithm for computing multiplicative
+ algebra = "\newline\refto{package INBFF InnerNormalBasisFieldFunctions}",
+ abstract =
+ "This paper proposes a fast algorithm for computing multiplicative
inverses in $GF(2^m)$ using normal bases. Normal bases have the
following useful property: In the case that an element $x$ in
$GF(2^m)$ is represented by normal bases, $2^k$ power operation of an
@@ 27302,6 +30625,7 @@ Inf. and Comp. 78, pp.171177, 1988
algorithm is applicable to the general power operation in $GF(2^m)$
and the computation of multiplicative inverses in $GF(q^m)$
$(q=2^n)$."
+}
\end{chunk}
@@ 27744,12 +31068,25 @@ Journal of Symbolic Computation, 1992, 13, 117131
\end{chunk}
+\index{FiniteFieldPolynomialPackage}
\index{Lenstra, H. W.}
\index{Schoof, R. J.}
\begin{chunk}{ignore}
\bibitem[Lenstra 87]{LS87} Lenstra, H. W.; Schoof, R. J.
 title = "Primitivive Normal Bases for Finite Fields",
Math. Comp. 48, 1987, pp. 217231
+\begin{chunk}{axiom.bib}
+@article{Lens87,
+ author = "Lenstra, H. W. and Schoof, R. J.",
+ title = "Primitive Normal Bases for Finite Fields",
+ journal = "Mathematics of Computation",
+ volume = "48",
+ number = "177",
+ year = "1987",
+ pages = "217231",
+ url = "http://www.math.leidenuniv.nl/~hwl/PUBLICATIONS/",
+ paper = "Lens87.pdf",
+ algebra = "\newline\refto{package FFPOLY FiniteFieldPolynomialPackage}",
+ abstract =
+ "It is proved that any finite extension of a finite field has a normal
+ basis consisting of primitive roots"
+}
\end{chunk}
@@ 27774,12 +31111,54 @@ Stanford University. (1977)
\end{chunk}
\index{Lidl, R.}
\index{Niederreiter, H.}
\begin{chunk}{ignore}
\bibitem[Lidl 83]{LN83} Lidl, R.; Niederreiter, H.
 title = "Finite Field, Encycoldia of Mathematics and Its Applications",
Vol. 20, Cambridge Univ. Press, 1983 ISBN 0521302404
+\index{FiniteAlgebraicExtensionField}
+\index{FiniteField}
+\index{FiniteFieldCyclicGroup}
+\index{FiniteFieldCyclicGroupExtension}
+\index{FiniteFieldCyclicGroupExtensionByPolynomial}
+\index{FiniteFieldExtension}
+\index{FiniteFieldExtensionByPolynomial}
+\index{FiniteFieldNormalBasis}
+\index{FiniteFieldNormalBasisExtension}
+\index{FiniteFieldNormalBasisExtensionByPolynomial}
+\index{InnerFiniteField}
+\index{InnerPrimeField}
+\index{PrimeField}
+\index{InnerNormalBasisFieldFunctions}
+\index{FiniteFieldPolynomialPackage2}
+\index{FiniteFieldPolynomialPackage}
+\index{FiniteFieldHomomorphisms}
+\index{FiniteFieldFunctions}
+\index{Lidl, Rudolf}
+\index{Niederreiter, Harald}
+\begin{chunk}{axiom.bib}
+@book{Lidl83,
+ author = "Lidl, Rudolf and Niederreiter, Harald",
+ title = "Finite Field, Encyclopedia of Mathematics and Its Applications",
+ volume = "20",
+ publishier = "Cambridge Univ. Press",
+ year = "1983",
+ isbn = "0521302404",
+ algebra =
+ "\newline\refto{category FAXF FiniteAlgebraicExtensionField}
+ \newline\refto{domain FF FiniteField}
+ \newline\refto{domain FFCG FiniteFieldCyclicGroup}
+ \newline\refto{domain FFCGX FiniteFieldCyclicGroupExtension}
+ \newline\refto{domain FFCGP FiniteFieldCyclicGroupExtensionByPolynomial}
+ \newline\refto{domain FFX FiniteFieldExtension}
+ \newline\refto{domain FFP FiniteFieldExtensionByPolynomial}
+ \newline\refto{domain FFNB FiniteFieldNormalBasis}
+ \newline\refto{domain FFNBX FiniteFieldNormalBasisExtension}
+ \newline\refto{domain FFNBP FiniteFieldNormalBasisExtensionByPolynomial}
+ \newline\refto{domain IFF InnerFiniteField}
+ \newline\refto{domain IPF InnerPrimeField}
+ \newline\refto{domain PF PrimeField}
+ \newline\refto{package INBFF InnerNormalBasisFieldFunctions}
+ \newline\refto{package FFPOLY2 FiniteFieldPolynomialPackage2}
+ \newline\refto{package FFPOLY FiniteFieldPolynomialPackage}
+ \newline\refto{package FFHOM FiniteFieldHomomorphisms}
+ \newline\refto{package FFF FiniteFieldFunctions}"
+}
\end{chunk}
@@ 27793,11 +31172,17 @@ AddisonWesley (March 1979) ISBN 0201144611
\end{chunk}
\index{Lipson, D.}
\begin{chunk}{ignore}
\bibitem[Lipson 81]{Lip81} Lipson, D.
+\index{FiniteFieldCategory}
+\index{Lipson, John D.}
+\begin{chunk}{axiom.bib}
+@book{Lips81,
+ author = "Lipson, John D.",
title = "Elements of Algebra and Algebraic Computing",
The Benjamin/Cummings Publishing Company, Inc.Menlo Park, California, 1981.
+ publisher = "AddisonWesley Educational Publishers",
+ year = "1981",
+ isbn = "9780201041156",
+ algebra = "\newline\refto{category FFIELDC FiniteFieldCategory}"
+}
\end{chunk}
@@ 27943,6 +31328,14 @@ Mathematical Surveys. 3 Am. Math. Soc., Providence, RI. (1966)
\end{chunk}
+\begin{chunk}{axiom.bib}
+@misc{Maxi16a,
+ author = "Maxima",
+ title = "Symbolic Integration: The Algorithms",
+ url =
+"http://maxima.sourceforge.net/docs/tutorial/en/gaertnertutorialrevision/Pages/SI001.htm"
+}
+
\index{TriangularSetCategory}
\index{RegularTriangularSetCategory}
\index{NormalizedTriangularSetCategory}
@@ 29187,20 +32580,28 @@ The University of Chicago Press. 1974
\end{chunk}
+\index{InnerNormalBasisFieldFunctions}
\index{Stinson, D.R.}
\begin{chunk}{ignore}
\bibitem[Stinson 90]{Stin90} Stinson, D.R.
``Some observations on parallel Algorithms for fast exponentiation
in $GF(2^n)$''
Siam J. Comp., Vol.19, No.4, pp.711717, August 1990
+\begin{chunk}{axiom.bib}
+@article{Stin90,
+ author = "Stinson, D.R.",
+ title = "Some observations on parallel Algorithms for fast exponentiation
+ in $GF(2^n)$",
+ journal = "Siam J. Comp.",
+ volume = "19",
+ number = "4",
+ pages = "711717",
+ year = "1990",
paper = "Stin90.pdf",
 abstract = "
 A normal basis represention in $GF(2^n)$ allows squaring to be
+ algebra = "\newline\refto{package INBFF InnerNormalBasisFieldFunctions}",
+ abstract =
+ "A normal basis represention in $GF(2^n)$ allows squaring to be
accomplished by a cyclic shift. Algorithms for multiplication in
$GF(2^n)$ using a normal basis have been studied by several
researchers. In this paper, algorithms for performing exponentiation
in $GF(2^n)$ using a normal basis, and how they can be speeded up by
using parallelization, are investigated."
+}
\end{chunk}
diff git a/changelog b/changelog
index 3944157..22d7536 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,8 @@
+20160717 tpd src/axiomwebsite/patches.html 20160717.01.tpd.patch
+20160717 tpd books/bookvol10.2 add citations to algebra
+20160717 tpd books/bookvol10.3 add citations to algebra
+20160717 tpd books/bookvol10.4 add citations to algebra
+20160717 tpd books/bookvolbib Axiom Citations in the Literature
20160714 tpd src/axiomwebsite/patches.html 20160714.06.tpd.patch
20160714 tpd books/bookvol2 Add Davenport chapters
20160714 tpd src/axiomwebsite/patches.html 20160714.05.tpd.patch
diff git a/patch b/patch
index 75cfd2e..58e4160 100644
 a/patch
+++ b/patch
@@ 1,4 +1,820 @@
books/bookvol2 Add Davenport chapters
+books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
+\index{Corless, Robert M.}
+\index{Jeffrey, David J.}
+\begin{chunk}{axiom.bib}
+@article{Corl98,
+ author = "Corless, Robert M. and Jeffrey, David J.",
+ title = "Graphing Elementary Riemann Surfaces",
+ journal = "SIGSAM Bulletin",
+ volume = "32",
+ number = "1",
+ pages = "1117",
+ year = "1998",
+ paper = "Corl98.djvu",
+ abstract =
+ "This paper discusses one of the prettiest pieces of elementary
+ mathematics or computer algebra, that we have ever had the pleasure
+ to learn. The tricks that we discuss here are certainly ``wellknown''
+ (that is, in the literature), but we didn't know them until recently,
+ and none of our immediate colleagues knew them either. Therefore we
+ believe that it is useful to publicize them further. We hope that
+ you find these ideas as pleasant and useful as we do."
+}
+
+\end{chunk}
+
+\index{Corless, Robert M.}
+\index{Jeffrey, David J.}
+\index{Knuth, Donald E.}
+\begin{chunk}{axiom.bib}
+@misc{Corl97,
+ author = "Corless, Robert M. and Jeffrey, David J. and Knuth, Donald E.",
+ title = "A Sequence of Series for The Lambert W Function",
+ year = "1997",
+ paper = "Corl97.pdf",
+ abstract =
+ "We give a uniform treatment of several series expansions for the
+ Lambert $W$ function, leading to an infinite family of new series.
+ We also discuss standardization, complex branches, a family of
+ arbitraryorder iterative methods for computation of $W_i$, and
+ give a theorem showing how to correctly solve another simple and
+ frequently occurring nonlinear equation in terms of $W$ and the
+ unwinding number"
+}
+
+\end{chunk}
+
+\index{Chow, Timothy Y.}
+\begin{chunk}{axiom.bib}
+@article{Chow99,
+ author = "Chow, Timothy Y.",
+ title = "What is a closedform number?",
+ journal = "The American Mathematical Monthly",
+ volume = "106",
+ number = "5",
+ pages = "440448",
+ paper = "Chowxx.pdf",
+ year = "1999"
+}
+
+\end{chunk}
+
+\index{Hur, Namhyun}
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Hurx00,
+ author = "Hur, Namhyun and Davenport, James H.",
+ title = "An exact real algebraic arithmetic with equality determination",
+ booktitle = "Proc. ISSAC 2000",
+ series = "ISSAC '00",
+ pages = "169174",
+ year = "2000",
+ paper = "Hurx00.djvu",
+ abstract =
+ "We describe a new arithmetic model for real algebraic numbers with
+ an exact equality determination. The model represents a real algebraic
+ number as a pair of an arbitrary precision numerical value and a
+ symbolic expression. For the numerical part we currently (another
+ representation could be used) use the dyadic exact real number and
+ for the symbolic part we use a squarefree polynomial for the real
+ algebraic number. In this model we show that we can decide exactly
+ the equality of real algebraic numbers."
+}
+
+\end{chunk}
+
+\index{Langley, Simon}
+\index{Richardson, Daniel}
+\begin{chunk}{axiom.bib}
+@article{Lang02,
+ author = "Langley, Simon and Richardson, Daniel",
+ title = "What can we do with a Solution?",
+ journal = "Electronic Notes in Theoretical Computer Science",
+ volume = "66",
+ number = "1",
+ year = "2002",
+ url = "http://www.elsevier.nl/locate/entcs/volume66.html",
+ paper = "Lang02.pdf",
+ abstract =
+ "If $S=0$ is a system of $n$ equations and unknowns over $\mathbb{C}$
+ and $S(\alpha)=0$ to what extent can we compute with the point $\alpha$?
+ In particular, can we decide whether or not a polynomial expressions
+ in the components of $\alpha$ with integral coefficients is zero?
+ This question is considered for both algebraic and elementary systems
+ of equations."
+}
+
+\end{chunk}
+
+\index{Wang, Paul S.}
+\begin{chunk}{axiom.bib}
+@article{Wang74,
+ author = "Wang, Paul S.",
+ title = "The Undecidability of the Existence of Zeros of Real Elementary
+ Functions",
+ journal = "J. ACM",
+ volume = "21",
+ number = "4",
+ pages = "586589",
+ year = "1974",
+ paper = "Wang74.djvu",
+ abstract =
+ "From Richardson's undecidability results, it is shown that the predicate
+ ``there exists a real number $r$ such that $G(r)=0$'' is recursively
+ undecidable for $G(x)$ in a class of functions which involves polynomials
+ and the sine function. The deduction follows that the convergence of a
+ class of improper integrals is recursively undecidable."
+}
+
+\end{chunk}
+
+\index{Daly, Timothy}
+\begin{chunk}{axiom.bib}
+@article{Daly02
+ author = "Daly, Timothy",
+ title = "Axiom as open source",
+ journal = "SIGSAM Bulletin",
+ volume = "36",
+ number = "1",
+ pages = "2828",
+ month = "March",
+ year = "2002",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@article{Jenk92,
+ author = "Jenks, Richard D.",
+ title = "SCRATCHPAD",
+ volume = "??",
+ number = "24",
+ pages = "1617",
+ month = "October",
+ year = "1972",
+ keywords = "axiomref",
+ abstract =
+ "The following SCRATCHPAD solution of Problem \#2 was run on a 1280K
+ virtual machine under CP/CMS time sharing system on a System/360
+ model 67. The conversation below is a modification of a program
+ originally written by Yngve Sundblad, August 1972. The program uses
+ symmetrised formulae, saves certain intermediate results, but does not
+ eliminate numerical factors in denominators"
+}
+
+\end{chunk}
+
+\index{Norman, Arthur C.}
+\begin{chunk}{axiom.bib}
+@article{Norm75a,
+ author = "Norman, Arthur C.",
+ title = "The SCRATCHPAD Power Series Package",
+ journal = "SIGSAM",
+ volume = "9",
+ number = "1",
+ pages = "1220",
+ year = "1975",
+ comment = "IBM T.J. Watson Research RC4998",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Griesmer, James H.}
+\index{Jenks, Richard D.}
+\index{Yun, David Y.Y.}
+\begin{chunk}{axiom.bib}
+@article{Grie75a,
+ author = "Griesmer, James H. and Jenks, Richard D. and Yun, David Y.Y."
+ title = "A SCRATCHPAD solution to problem \#7",
+ journal = "SIGSAM",
+ volume = "9",
+ number = "3",
+ pages = "1317",
+ year = "1975"
+}
+
+\end{chunk}
+
+\index{Miller, Bruce R.}
+\begin{chunk}{axiom.bib}
+@misc{Mill95,
+ author = "Miller, Bruce R.",
+ title = "An expression formatter for MACSYMA",
+ keywords = "axiomref",
+ year = "1995",
+ paper = "Mill95.pdf",
+ abstract =
+ "A package for formatting algebraic expressions in MACSYA is described.
+ It provides facilities for userdirected hierarchical structuring of
+ expressions, as well as for directing simplifications to selected
+ subexpressions. It emphasizes a semantic rther than syntactic description
+ of the desired form. The package also provides utilities for obtaining
+ efficiently the coefficients of polynomials, trigonometric sums and
+ power series. Similar capabilities would be useful in other computer
+ algebra systems."
+}
+
+\end{chunk}
+
+\index{Griesmer, James H.}
+\index{Jenks, Richard D.}
+\index{Yun, David Y.Y.}
+\begin{chunk}{axiom.bib}
+@article{Grie75b,
+ author = "Griesmer, James H. and Jenks, Richard D. and Yun, David Y.Y."
+ title = "A FORMAT statement in SCRATCHPAD",
+ journal = "SIGSAM",
+ volume = "9",
+ number = "3",
+ pages = "2425",
+ year = "1975",
+ keywords = "axiomref",
+ abstract =
+ "Algebraic manipulation covers branches of software, particularly list
+ processing, mathematics, notably logic and number theory, and
+ applications largely in physics. The lectures will deal with all of these
+ to a varying extent.
+}
+
+\end{chunk}
+
+\index{Blair, Fred W.}
+\index{Griesmer, James H.}
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Blai70,
+ author = "Blair, Fred W. and Griesmer, James H. and Jenks, Richard D.",
+ title = "An interactive facility for symbolic mathematics",
+ booktitle = "Proc. International Computing Symposium, Bonn, Germany",
+ year = "1970",
+ pages = "394419",
+ keywords = "axiomref",
+ abstract =
+ "The SCRATCHPAD/1 system is designed to provide an interactive symbolic
+ coputational facility for the mathematician user. The system features
+ a user language designed to capture the style and succinctness of
+ mathematical notation, together with a facility for conveniently
+ introducing new notations into the language. A comprehensive system
+ library incorporates symbolic capabilities provided by such systems as
+ SIN, MATHLAB, and REDUCE."
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@article{Jenk79a,
+ author = "Jenks, Richard D.",
+ title = "SCRATCHPAD/360: reflections on a language design",
+ journal = "SIGSAM",
+ volume = "13",
+ number = "1",
+ pages = "1626",
+ year = "1979",
+ keywords = "axiomref",
+ comment = "IBM Research RC 7405",
+ abstract =
+ "The key concepts of the SCRATCHPAD language are described, assessed,
+ and illustrated by an example. The language was originally intended as
+ an interactive problem solving language for symbolic mathematics.
+ Nevertheless, as this paper intends to show, it can be used as a
+ programming language as well."
+}
+
+\end{chunk}
+
+\index{Ng, Edward W.}
+\begin{chunk}{axiom.bib}
+@techreport{Ngxx80,
+ author = "Ng, Edward W.",
+ title = "SymbolicNumeric Interface: A Review",
+ type = "technical report",
+ number = "NASACR162690 HC A02/MF A01"
+ institution = "NASA Jet Propulsion Lab",
+ url = "http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19800008508.pdf",
+ paper = "Ngxx80.pdf",
+ keywords = "axiomref",
+ abstract =
+ "This is a survey of recent activities that either used or encouraged the
+ potential use of a combination of symbolic and numerical calculations.
+ Symbolic calculations here primarily refer to the computer processing of
+ procedures from classical algebra, analysis and calculus. Numerical
+ calculations refer to both numerical mathematics research and scientific
+ computation. This survey is inteded to point out a large number of problem
+ areas where a cooperation of symbolic and numeric methods is likely to
+ bear many fruits. These areas include such classical operations as
+ differentiation and integration, such diverse activities as function
+ approximations andqualitative analysis, and such contemporary topics as
+ finite element calculations and computational complexity. It is contended
+ that other less obvious topics such as the fast Fourier transform, linear
+ algebra, nonlinear analysis and error analysis would also benefti from a
+ synergistic approach advocated here."
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@article{Fate01,
+ author = "Fateman, Richard J.",
+ title = "A Review of Macsyma",
+ journal = "IEEE Trans. Knowl. Eng.",
+ volume = "1",
+ number = "1",
+ year = "2001",
+ url = "http://people.eecs.berkeley.edu/~fateman/papers/mac82b.pdf",
+ paper = "Fate01.pdf",
+ keywords = "axiomref",
+ abstract =
+ "We review the successes and failures of the Macsyma algebraic
+ manipulation system from the point of view of one of the original
+ contributors. We provide a retrospective examination of some of the
+ controversial ideas that worked, and some that did not. We consider
+ input/output, language semantics, data types, pattern matching,
+ knowledgeadjunction, mathematical semantics, the user community,
+ and software engineering. We also comment on the porting of this
+ system to a variety of computing systems, and possible future
+ directions for algebraic manipulation systembuilding."
+}
+
+\end{chunk}
+
+\index{Griesmer, James H.}
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@article{Grie74,
+ author = "Griesmer, James H. and Jenks, Richard D.",
+ title = "A solution to problem \#4": the lie transform",
+ journal = "SIGSAM Bulletin",
+ volume = "8",
+ number = "4",
+ pages = "1213",
+ year = "1974",
+ keywords = "axiomref",
+ abstract =
+ "The following SCRATCHPAD conversation for carrying out the Lie
+ Transform computation represents a slight modification of one written
+ by Dr. David Barton, when he was a summer visitor during 1972 at the
+ Watson Research Center."
+}
+
+\end{chunk}
+
+\begin{chunk}{axiom.bib}
+@misc{SIGS16,
+ author = "SIGSAM, ACM",
+ title = "Axiom"
+ url = "http://www.sigsam.org/software/axiom.html",
+ year = "2016",
+ contact = "Infodir\_SIGSAM\@acm.org",
+ abstract =
+ "Axiom is a free, open source, generalpurpose computer algebra
+ system. It features a strongly typed language. The system has an
+ interactive interpreter and a compiler. It includes over 1100
+ supported categories, domains, and packages covering large areas of
+ Mathematics."
+}
+
+\end{chunk}
+
+\index{Li, Yue}
+\index{Dos Reis, Gabriel}
+\begin{chunk}{axiom.bib}
+@inproceedings{Lixx11,
+ author = "Li, Yue and Dos Reis, Gabriel",
+ title = "An Automatic Parallelization Framework for Algebraic
+ Computation Systems",
+ booktitle = "Proc. ISSAC 2011",
+ pages = "233240",
+ isbn = "9781450306751",
+ year = "2011",
+ url = "http://www.axiomatics.org/~gdr/concurrency/oaconcissac11.pdf",
+ paper = "Lixx11.pdf",
+ keywords = "axiomref",
+ abstract =
+ "This paper proposes a nonintrusive automatic parallelization
+ framework for typeful and propertyaware computer algebra systems.
+ Automatic parallelization remains a promising computer program
+ transformation for exploiting ubiquitous concurrency facilities
+ available in modern computers. The framework uses semanticsbased
+ static analysis to extract reductions in library components based on
+ algebraic properties. An early implementation shows up to 5 times
+ speedup for library functions and homotopybased polynomial system
+ solver. The general framework is applicable to algebraic computation
+ systems and programming languages with advanced type systems that
+ support userdefined axioms or annotation systems."
+}
+
+\end{chunk}
+
+\index{Kendall, Wilfrid S.}
+\begin{chunk}{axiom.bib}
+@article{Kend01,
+ author = "Kendall, Wilfrid S.",
+ title = "Symbolic It\^o calculus in AXIOM: an ongoing story",
+ journal = "Statistics and Computing",
+ volume = "11",
+ pages = "2535",
+ year = "2001",
+ url = "http://www2.warwick.ac.uk/fac/sci/statistics/staff/academicresearch/kendall/personal/ppt/327.ps.gz",
+ paper = "Kend01.pdf",
+ keywords = "axiomref",
+ abstract =
+ "Symbolic It\^o calculus refers both to the implementation of the
+ It\^o calculus algebra package and to its application. This article
+ reports on progress in the implementation of It\^o calculus in the
+ powerful and innovative computer algebra package AXIOM, in the context
+ of a decade of previous implementations and applications. It is shown
+ how the elegant algebraic structure underylying the expressive and
+ effective formalism of It\^o calculus can be implemented directly in
+ AXIOM using the package's programmable facilities for ``strong
+ typing'' of computational objects. An application is given of the use
+ of the implementation to provide calculations for a new proof, based
+ on stochastic differentials, of the MardiaDryden distribution from
+ statistical shape theory."
+}
+
+\end{chunk}
+
+\index{Senechaud, Pascale}
+\index{Siebert, F.}
+\begin{chunk}{axiom.bib}
+@techreport{Sene87a,
+ author = "Senechaud, Pascale and Siebert, F.",
+ title = "Etude dl l'algorithme de Kovacic et son implantation sur
+ Scratchpad II",
+ type = "Technical Report",
+ number = "639",
+ institution = "Institut IMAG, Informatique et Mathematiques Appliquees
+ de Grenoble",
+ address = "Grenoble, France",
+ year = "1987",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Terelius, Bjorn}
+\begin{chunk}{axiom.bib}
+@mastersthesis{Tere09,
+ author = "Terelius, Bjorn",
+ title = "Symbolic Integration",
+ school = "Royal Institute of Technology",
+ address = "Stockholm, Sweden",
+ year = "2009",
+ paper = "Tere09.pdf",
+ abstract =
+ "Symbolic integration is the problem of expressing an indefinite integral
+ $\int{f}$ of a given function $f$ as a finite combination $g$ of elementary
+ functions, or more generally, to determine whether a certain class of
+ functions contains an element $g$ such that $g^\prime = f$."
+
+ In the first part of this thesis, we compare different algorithms for
+ symbolic integration. Specifically, we review the integration rules
+ taught in calculus courses and how they can be used systematically to
+ create a reasonable, but somewhat limited, integration method. Then we
+ present the differential algebra required to prove the transcendental
+ cases of Risch's algorithm. Risch's algorithm decides if the integral
+ of an elementary function is elementary and if so computes it. The
+ presentation is mostly selfcontained and, we hope, simpler than
+ previous descriptions of the algorithm. Finally, we describe
+ RischNorman's algorithm which, although it is not a decision
+ procedure, works well in practice and is considerably simpler than the
+ full Risch algorithm.
+
+ In the second part of this thesis, we briefly discuss an
+ implementation of a computer algebra system and some of the
+ experiences it has given us. We also demonstrate an implementation of
+ the rulebased approach and how it can be used, not only to compute
+ integrals, but also to generate readable derivations of the results."
+}
+
+\end{chunk}
+
+\index{Kendall, Wilfrid S.}
+\begin{chunk}{axiom.bib}
+@article{Kend07,
+ author = "Kendall, Wilfrid S.",
+ title = "Coupling all the Levy Stochastic Areas of Multidimensional
+ Brownian Motion",
+ journal = "The Annals of Probability",
+ volume = "35",
+ number = "3",
+ pages = "935953",
+ year = "2007",
+ keywords = "axiomref",
+ comment = "Author used Axiom for computation but says missed citation",
+ url = "http://arxiv.org/pdf/math/0512336v2.pdf",
+ paper = "Kend07.pdf",
+ abstract =
+ "It is shown how to construct a successful coadapted coupling of two
+ copies of an $n$dimensional Brownian motion ($B_1,\ldots,B_n$) while
+ simultaneously coupling all corresponding copies of the L{\'e}vy
+ stochastic areas $\int B_idB_j$  \int B_j dB_i$. It is conjectured
+ that successful coadapted couplings still exist when the L{\'e}vy
+ stochastic areas are replaced by a finite set of multiply iterated
+ path and timeintegrals, subject to algebraic compatibility of the
+ initial conditions."
+}
+
+\end{chunk}
+
+\index{Bronstein, Manuel}
+\index{Lafaille, S\'ebastien}
+\begin{chunk}{axiom.bib}
+@inproceedings{Bron02,
+ author = "Bronstein, Manuel and Lafaille, S\'ebastien",
+ title = "Solutions of linear ordinary differential equations in terms
+ of special functions",
+ booktitle = "Proc. ISSAC '02",
+ publisher = "ACM Press",
+ pages = "2328",
+ year = "2002",
+ isbn = "1581134843",
+ url =
+ "http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/issac2002.pdf",
+ paper = "Bron02.pdf",
+ url2 = "http://xena.hunter.cuny.edu/ksda/papers/bronstein2.pdf",
+ paper2 = "Bron02x.pdf",
+ abstract =
+ "We describe a new algorithm for computing special function solutions
+ of the form $y(x) = m(x)F(\eta(x))$ of second order linear ordinary
+ differential equations, where $m(x)$ is an arbitrary Liouvillian
+ function, $\eta(x)$ is an arbitrary rational function, and $F$
+ satisfies a given second order linear ordinary differential
+ equations. Our algorithm, which is base on finding an appropriate
+ point transformation between the equation defining $F$ and the one to
+ solve, is able to find all rational transformations for a large class
+ of functions $F$, in particular (but not only) the $_0F_1$ and $_1F_1$
+ special functions of mathematical physics, such as Airy, Bessel,
+ Kummer and Whittaker functions. It is also able to identify the values
+ of the parameters entering those special functions, and can be
+ generalized to equations of higher order."
+}
+
+\end{chunk}
+
+\index{Chan, L.}
+\index{ChebTerrab, E.S.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Chan04,
+ author = "Chan, L. and ChebTerrab, E.S.",
+ title = "NonLiouvillian solutions for second order linear ODEs",
+ booktitle = "Proc. ISSAC 04",
+ pages = "8086",
+ isbn = "158113827X",
+ url = "http://www.cecm.sfu.ca/CAG/papers/edgardoIS04.pdf",
+ keywords = "axiomref",
+ paper = "Chan04.pdf",
+ abstract =
+ "There exist sound literature and algorithms for computing Liouvillian
+ solutions for the important problem of linear ODEs with rational
+ coefficients. Taking as sample the 363 second order equations of that
+ type found in Kamke's book, for instance, 51\% of them admit Liouvillian
+ solutions and so are solvable using Kovacic's algorithm. On the other
+ hand, special function solutions not admitting Liouvillian form appear
+ frequently in mathematical physics, but there are not so general
+ algorithms for computing them. In this paper we present an algorithm
+ for computing special function solutions which can be expressed using
+ the $_2F_1$, $_1F_1$ or $_0F_1$ hypergeometric functions. They algorithm
+ is easy to implement in the framework of a computer algebra system and
+ systematically solves 91\% of the 363 Kamke's linear ODE examples
+ mentioned."
+}
+
+\end{chunk}
+
+\index{van Hoeij, Mark}
+\index{Monagan, Michael}
+\begin{chunk}{axiom.bib}
+@inproceedings{Hoei04,
+ author = "van Hoeij, Mark and Monagan, Michael",
+ title = "Algorithms for Polynomial GCD Computation over Algebraic
+ Function Fields",
+ booktitle = "Proc. ISSAC 04",
+ isbn = "158113827X",
+ url = "http://www.cecm.sfu.ca/personal/mmonagan/papers/AFGCD.pdf",
+ paper = "Hoei04.pdf",
+ abstract =
+ "Let $L$ be an algebraic function field in $k \ge 0$ parameters
+ $t_1,\ldots,t)k$. Let $f_1$, $f_2$ be nonzero polynomials in
+ $L[x]$. We give two algorithms for computing their gcd. The first, a
+ modular GCD algorithm, is an extension of the modular GCD algorithm
+ for Brown for {\bf Z}$[x_1,\ldots,x_n]$ and Encarnacion for {\bf
+ Q}$(\alpha[x])$ to function fields. The second, a fractionfree
+ algorithm, is a modification of the Moreno Maza and Rioboo algorithm
+ for computing gcds over triangular sets. The modification reduces
+ coefficient grownth in $L$ to be linear. We give an empirical
+ comparison of the two algorithms using implementations in Maple."
+}
+
+\end{chunk}
+
+\begin{chunk}{axiom.bib}
+@misc{Maxi16a,
+ author = "Maxima",
+ title = "Symbolic Integration: The Algorithms",
+ url =
+"http://maxima.sourceforge.net/docs/tutorial/en/gaertnertutorialrevision/Pages/SI001.htm"
+}
+
+\index{Gil, I.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Gilx92,
+ author = "Gil, I.",
+ title = "Computation of the Jordan canonical form of a square matrix
+ (using the Axiom programming language)",
+ booktitle = "Proc ISSAC 1992",
+ series = "ISSAC '92",
+ publisher = "ACM",
+ pages = "138145",
+ isbn = "0897914899 (soft cover), 0897914902 (hard cover)",
+ keywords = "axiomref",
+ abstract =
+ "Presents an algorithm for computing: the Jordan form of a square
+ matrix with coefficients in a field K using the computer algebra
+ system Axiom. This system presents the advantage of allowing generic
+ programming. That is to say, the algorithm can first be implemented
+ for matrices with rational coefficients and then generalized to
+ matrices with coefficients in any field. Therefore the author
+ presents the general method which is essentially based on the use of
+ the Frobenius form of a matrix in order to compute its Jordan form;
+ and then restricts attention to matrices with rational
+ coefficients. On the one hand the author streamlines the algorithm
+ froben which computes the Frobenius form of a matrix, and on the other
+ she examines in some detail the transformation from the Frobenius form
+ to the Jordan form, and gives the so called algorithm Jordform. The
+ author studies in particular, the complexity of this algorithm and
+ proves that it is polynomial when the coefficients of the matrix are
+ rational. Finally the author gives some experiments and a conclusion."
+}
+
+\end{chunk}
+
+\index{InnerNormalBasisFieldFunctions}
+\index{Stinson, D.R.}
+\begin{chunk}{axiom.bib}
+@article{Stin90,
+ author = "Stinson, D.R.",
+ title = "Some observations on parallel Algorithms for fast exponentiation
+ in $GF(2^n)$",
+ journal = "Siam J. Comp.",
+ volume = "19",
+ number = "4",
+ pages = "711717",
+ year = "1990",
+ paper = "Stin90.pdf",
+ algebra = "\newline\refto{package INBFF InnerNormalBasisFieldFunctions}",
+ abstract =
+ "A normal basis represention in $GF(2^n)$ allows squaring to be
+ accomplished by a cyclic shift. Algorithms for multiplication in
+ $GF(2^n)$ using a normal basis have been studied by several
+ researchers. In this paper, algorithms for performing exponentiation
+ in $GF(2^n)$ using a normal basis, and how they can be speeded up by
+ using parallelization, are investigated."
+}
+
+\end{chunk}
+
+\index{FiniteFieldPolynomialPackage}
+\index{Lenstra, H. W.}
+\index{Schoof, R. J.}
+\begin{chunk}{axiom.bib}
+@article{Lens87,
+ author = "Lenstra, H. W. and Schoof, R. J.",
+ title = "Primitive Normal Bases for Finite Fields",
+ journal = "Mathematics of Computation",
+ volume = "48",
+ number = "177",
+ year = "1987",
+ pages = "217231",
+ url = "http://www.math.leidenuniv.nl/~hwl/PUBLICATIONS/",
+ paper = "Lens87.pdf",
+ algebra = "\newline\refto{package FFPOLY FiniteFieldPolynomialPackage}",
+ abstract =
+ "It is proved that any finite extension of a finite field has a normal
+ basis consisting of primitive roots"
+}
+
+\end{chunk}
+
+\index{CharacteristicNonZero}
+\index{FieldOfPrimeCharacteristic}
+\index{ExtensionField}
+\index{FiniteFieldCategory}
+\index{FiniteAlgebraicExtensionField}
+\index{SimpleAlgebraicExtension}
+\index{InnerPrimeField}
+\index{PrimeField}
+\index{FiniteFieldExtensionByPolynomial}
+\index{FiniteFieldCyclicGroupExtensionByPolynomial}
+\index{FiniteFieldNormalBasisExtensionByPolynomial}
+\index{FiniteFieldExtension}
+\index{FiniteFieldCyclicGroupExtension}
+\index{FiniteFieldNormalBasisExtension}
+\index{InnerFiniteField}
+\index{FiniteField}
+\index{FiniteFieldCyclicGroup}
+\index{FiniteFieldNormalBasis}
+\index{DiscreteLogarithmPackage}
+\index{FiniteFieldFunctions}
+\index{InnerNormalBasisFieldFunctions}
+\index{FiniteFieldPolynomialPackage}
+\index{FiniteFieldPolynomialPackage2}
+\index{FiniteFieldHomomorphisms}
+\index{FiniteFieldFactorizationWithSizeParseBySideEffect}
+\index{Grabmeier, Johannes}
+\index{Scheerhorn, Alfred}
+\begin{chunk}{axiom.bib}
+@techreport{Grab92,
+ author = "Grabmeier, Johannes and Scheerhorn, Alfred",
+ title = "Finite fields in Axiom",
+ type = "technical report",
+ number = "AXIOM Technical Report TR7/92 (ATR/5)(NP2522)",
+ institution = "Numerical Algorithms Group, Inc.",
+ address = "Downer's Grove, IL, USA and Oxford, UK",
+ year = "1992",
+ url = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
+ keywords = "axiomref",
+ paper = "Grab92.pdf",
+ algebra =
+ "\newline\refto{category CHARNZ CharacteristicNonZero}
+ \newline\refto{category FPC FieldOfPrimeCharacteristic}
+ \newline\refto{category XF ExtensionField}
+ \newline\refto{category FFIELDC FiniteFieldCategory}
+ \newline\refto{category FAXF FiniteAlgebraicExtensionField}
+ \newline\refto{domain SAE SimpleAlgebraicExtension}
+ \newline\refto{domain IPF InnerPrimeField}
+ \newline\refto{domain PF PrimeField}
+ \newline\refto{domain FFP FiniteFieldExtensionByPolynomial}
+ \newline\refto{domain FFCGP FiniteFieldCyclicGroupExtensionByPolynomial}
+ \newline\refto{domain FFNBP FiniteFieldNormalBasisExtensionByPolynomial}
+ \newline\refto{domain FFX FiniteFieldExtension}
+ \newline\refto{domain FFCGX FiniteFieldCyclicGroupExtension}
+ \newline\refto{domain FFNBX FiniteFieldNormalBasisExtension}
+ \newline\refto{domain IFF InnerFiniteField}
+ \newline\refto{domain FF FiniteField}
+ \newline\refto{domain FFCG FiniteFieldCyclicGroup}
+ \newline\refto{domain FFNB FiniteFieldNormalBasis}
+ \newline\refto{package DLP DiscreteLogarithmPackage}
+ \newline\refto{package FFF FiniteFieldFunctions}
+ \newline\refto{package INBFF InnerNormalBasisFieldFunctions}
+ \newline\refto{package FFPOLY FiniteFieldPolynomialPackage}
+ \newline\refto{package FFPOLY2 FiniteFieldPolynomialPackage2}
+ \newline\refto{package FFHOM FiniteFieldHomomorphisms}
+ \newline\refto
+ {package FFFACTSE FiniteFieldFactorizationWithSizeParseBySideEffect}",
+ abstract =
+ "Finite fields play an important role for many applications (e.g. coding
+ theory, cryptograpy). There are different ways to construct a finite
+ field for a given prime power. The paper describes the different
+ constructions implemented in AXIOM. These are {\sl polynomial basis
+ representation}, {\sl cyclic group representation}, and {\sl normal
+ basis representation}. Furthermore, the concept of the implementation,
+ the used algorithms and the various datatype coercions between these
+ representations are discussed."
+}
+
+\end{chunk}
+
+\index{InnerNormalBasisFieldFunctions}
+\index{Itoh, T.}
+\index{Tsujii, S.}
+\begin{chunk}{axiom.bib}
+@article{Itoh88,
+ author = "Itoh, T. and Tsujii, S.",
+ title = "A fast algorithm for computing multiplicative inverses in
+ $GF(2^m)$ using normal bases",
+ journal = "Inf. and Comp.",
+ volume = "78",
+ pages = "171177",
+ year = "1988",
+ paper = "Itoh88.pdf",
+ algebra = "\newline\refto{package INBFF InnerNormalBasisFieldFunctions}",
+ abstract =
+ "This paper proposes a fast algorithm for computing multiplicative
+ inverses in $GF(2^m)$ using normal bases. Normal bases have the
+ following useful property: In the case that an element $x$ in
+ $GF(2^m)$ is represented by normal bases, $2^k$ power operation of an
+ element $x$ in $GF(2^m)$ can be carried out by $k$ times cyclic shift
+ of its vector representation. C.C. Wang et al. proposed an algorithm
+ for computing multiplicative inverses using normal bases, which
+ requires $(m2)$ multiplications in $GF(2^m)$ and $(m1)$ cyclic
+ shifts. The fast algorithm proposed in this paper also uses normal
+ bases, and computes multiplicative inverses iterating multiplications
+ in $GF(2^m)$. It requires at most $2[log_2(m1)]$ multiplications in
+ $GF(2^m)$ and $(m1)$ cyclic shifts, which are much less than those
+ required in Wang's method. The same idea of the proposed fast
+ algorithm is applicable to the general power operation in $GF(2^m)$
+ and the computation of multiplicative inverses in $GF(q^m)$
+ $(q=2^n)$."
+}
+
+\end{chunk}
+
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 2ccd632..721903c 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5480,6 +5480,8 @@ books/bookvolbib Axiom Citations in the Literature
books/bookvol10.* add literature references to algebra
20160714.06.tpd.patch
books/bookvol2 Add Davenport chapters
+20160717.01.tpd.patch
+books/bookvolbib Axiom Citations in the Literature

1.7.5.4