From dab1ac42801dd1cb534f61ea80d6d913bdbb1683 Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Mon, 27 Jun 2016 21:45:15 0400
Subject: [PATCH] books/bookvolbib Axiom Citations in the Literature
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Goal: Axiom Literate Programming
\index{Rigal, Alain}
\begin{chunk}{axiom.bib}
@article{Riga99,
author = "Rigal, Alain",
title = "Highorder compact schemes: Application to bidimensional unsteady
diffusionconvection problems.",
journal = "C. R. Acad. Sci.",
volume = "328",
number = "6",
pages = "535538",
year = "1999",
keywords = "axiomref",
abstract =
"For unsteady 2D diffusionconvection problems, we present two classes
of compact difference schemes of order 2 in time and 4 in space. These
finite difference schemes are essentially derived from 1D schemes,
extensively analyzed in our previous paper [J. Comput. Phys. 114,
No. 1, 5976 (1994; Zbl 0807.65056)]. We propose two approaches:
construction of 2D schemes as product of 1D schemes and global
formulation of 2D schemes. Part II by M. Fournié [C. R. Acad. Sci.,
Paris, Sér. I, Math. 328, No. 6, 539542 (1999; reviewed below)]
focuses on the development and analysis of global schemes with the
assistance of symbolic computation software (AXIOM)."
}
\end{chunk}
\index{Roesner, K. G.}
\begin{chunk}{axiom.bib}
@article{Roes99,
author = "Roesner, K. G.",
title = "Supersonic flow around accelerated and decelerated bodies,
analysed by analytical methods",
journal = "Z. Angew. Math. Mech.",
volume = "79",
number = "3",
pages = "815816",
year = "1999",
keywords = "axiomref",
abstract =
"By an extensive use of the computer algebra system AXIOM, a power
series expansion with respect to the radial variable $r$ is used to
describe the accelerated or decelerated supersonic flow field around
the tip of slender conical bodies. The set of coupled nonlinear
differential equations for the coefficient functions, depending on
$\theta$ and $t$, is derived in closed form, and the first and second
approximation of the coefficient functions are determined
numerically."
}
\end{chunk}
\index{Stroeker, Roelof J.}
\index{Kaashoek, Johan F.}
\begin{chunk}{axiom.bib}
@book{Stro99,
author = "Stroeker, Roelof J. and Kaashoek, Johan F.",
title = "Discovering mathematics with Maple. An interactive exploration for
mathematicians, engineers and econometricians",
year = "1999",
publisher = "Birkhauser",
keywords = "axiomref",
abstract =
"During the past decade, the mathematical computer software packages
such as Mathematica, Maple, MATLAB (Axiom, Derive, Macsyma, MuPad are
some further examples of such software) [see Macsyma 2.3. Lite – the
student edition (1998; Zbl 0911.68089); B. W. Char, K. O. Geddes,
G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt, Maple V
Library reference manual (1991; Zbl 0763.68046); J. L. Zachary,
Introduction to scientific programming. Computational problem solving
using Mathematica and C (1997; Zbl 0891.68053); The student edition of
MATLAB. Student user guide. The problemsolving tool for engineers,
mathematicians, and scientists (1992; Zbl 0782.65001); H. Benker,
Ingenieurmathematik mit ComputeralgebraSystemen. AXIOM, DERIVE,
MACSYMA, MAPLE, MATHCAD, MATHEMATICA, MATLAB und MuPAD in der
Anwendung (1998; Zbl 0909.68109); W. Koepf, Hohere Analysis mit DERIVE
(1994; Zbl 0819.26003)] have greatly faciliated mathematical
experiments and have thus become popular tools for the modern
mathematician. It is a pity that most of these packages are quite
expensive, and that the frequently upgraded versions are not free for
the owners of the earlier versions (fortunately, there are inexpensive
student versions of some of these packages). There is a constant
demand of instructional textbooks by users of these packages. This
demand is reflected in the growing number of such textbooks. Many of
these books provide software support (diskette, CDROM, access by
ftp). Such a textbook should meet, in my opinion, the following
criteria: (1) The size should be small, not bulky like the complete
technical descriptions of the software. (2) There should be a lot of
examples of the use of the software covering a wide range of
mathematical topics. Electronic versions of these examples should be
made available for free to the users of the textbook
(e.g. diskette/CDROM, access by ftp). (3) There should be a good
supply of exercises covering the basic mathematical applications. (4)
The book should be visually pleasing, easy to read, have good indexes
and provide pointers to other books and electronic sources of
information. The book under review provides, in addition to the actual
text, an interactive exploratorium of its topics, based on the
mechanism of Maple worksheets. These worksheets can be ``opened'' by
the Maple program and they form a mixture of usual text, hypertext,
and Maple commands and have a nice style appearance. They also can be
``exported'' in a file and included in a file for further treatment.
The book meets all the aforementioned criteria (1)(4) with elegance.
There are many exercises which cover all the usual mathematical topics
from linear algebra to differential equations and statistics. A
valuable feature is an appendix with hints and answers for all
exercises. One of the highlights of the book is the examination of
Riemann's nondifferentiable function
\[x \mapsto \sum_{k=1}^\infty{k^{2}} sin(\pi kx)\]
which is differentiable only at the rational points $p/q$ with $p$
and $q$ odd and relatively prime, where its derivative is $1/2$.
The book is intended for students of mathematics, engineering
sciences, and econometry. This book is an ideal guide for this purpose
and it could probably be used along, without the bulky technical
documentation of the Maple language. Note that Maple has a
comprehensive online help program, which contains large parts of the
original documentation."
}
\end{chunk}
\index{Wester, Michael J.}
\begin{chunk}{axiom.bib}
@book{West99,
author = "Wester, Michael J.",
title = "Computer Algebra Systems. A practical guide",
year = "1999",
publisher = "Wiley",
keywords = "axiomref",
abstract =
"In this book some of the most popular general purpose computer
algebra systems (CAS), such as Mathematica, Maple, Derive, Axiom,
MuPAD, and Macsyma, are examined. The strengths and weaknesses of
these programs are compared and contrasted, and tutorial information
for using these systems in various ways is given. The different
packages are quantitatively compared using standard test suites,
giving the possibility to asses the most appropriate for a particular
user or application. The origins of these systems are revealed and
many of their behaviors analyzed. This furnishes a feel for where the
current computer algebra system state of the art stays and what can be
expected for existing and future systems. The book is organized in
several chapters written by different authors. Chapters 1,2, and 3 are
organized as reviews, comparisons, and critiques of CAS
capabilities. Then more technical issues are discussed considering
different approaches taken by different CAS: simplifying square roots
of square roots by denesting (chapter 4), complex number calculation
(chapter 5), efficiently computing Chebyshev polynomials (chapter 6),
solving single equations and systems of polynomial equations (chapters
7, 8), computing limits (chapter 9), multiple integration (chapter
10), solving ordinary differential equation (chapter 11), integration
of nonlinear evolution equations (chapter 12), code generation
(chapter 13), evaluation of expressions and programs in the embedded
computer algebra programming language (chapter 14), and computer
algebra in education (chapter 15). Chapter 16 covers the origin of CA,
and, finally chapter 17 gives a list of most CAS available today."
}
\end{chunk}
\index{Benker, Hans}
\begin{chunk}{axiom.bib}
@book{Benk98,
author = "Benker, Hans",
title = "Engineering mathematics with computer algebra systems",
year = "1998",
keywords = "axiomref",
comment = "german"
}
\end{chunk}
\index{Breuer, Thomas}
\index{Linton, Steve}
\begin{chunk}{axiom.bib}
@InProceedings{Breu98,
author = "Breuer, Thomas and Linton, Steve",
title = "The GAP 4 type system organising algebraic algorithms",
booktitle = "Proc. ISSAC 98",
series = "ISSAC 98",
year = "1998",
publisher = "ACM Press",
location = "Rostock, Germany",
pages = "1315",
keywords = "axiomref",
paper = "Breu98.pdf",
url = "http://www.gapsystem.org/Doc/Talks/paper.ps",
abstract =
"Version 4 of the GAP (Groups, Algorithms, Programming) system for
computational discrete mathematics has a number of novel features. In
this paper, we describe the type system, and the way in which it is
used for method selection. This system is central to the organization
of the library which is the main part of the GAP system. Unlike
simpler objectoriented systems, GAP allows method selection based on
the types of all arguments and on certain aspects of the relationship
between the arguments. In addition, the type of an object can change,
in a controlled way, during its life. This reflects information about
the object which has been computed and stored. Individual methods can
be written and installed independently. Furthermore, most checking of
the arguments is done in a uniform way by the method selection system,
making individual methods simpler and less prone to error. The methods
are combined automatically to produce a powerful and usable system for
interactive use or programming."
}
\end{chunk}
\index{Linton, Stephen}
\begin{chunk}{axiom.bib}
@misc{Lint98,
author = "Linton, Stephen",
title = "The GAP 4 Type System Organising Algebraic Algorithms",
paper = "Lint98.pdf",
url = "http://www.gapsystem.org/Doc/Talks/kobe.ps",
keywords = "axiomref"
}
\end{chunk}
\index{Diaz, Angel}
\index{Kaltofen, Erich}
\begin{chunk}{axiom.bib}
@InProceedings{Diaz98,
author = "Diaz, A. and Kaltofen, E.",
title = "{FoxBox}, a System for Manipulating Symbolic Objects in Black Box
Representation",
booktitle = "Proc. 1998 Internat. Symp. Symbolic Algebraic Comput.",
crossref = "ISSAC98",
publisher = "ACM Press",
year = "1998",
pages = "3037",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/98/DiKa98.pdf",
paper = "Diaz98.pdf",
abstract =
"The FOXBOX system puts in practice the black box representation of
symbolic objects and provides algorithms for performing the symbolic
calculus with such representations. Black box objects are stored as
functions. For instance: a black box polynomial is a procedure that
takes values for the variables as input and evaluates the polynomial
at that given point. FOXBOX can compute the greatest common divisor
and factorize polynomials in black box representation, producing as
output new black boxes. It also can compute the standard sparse
distributed representation of a black box polynomial, for example, one
which was computed for an irreducible factor. We establish that the
black box representation of objects can push the size of symbolic
expressions far beyond what standard data structures could handle
before.
Furthermore, FOXBOX demonstrates the generic program design
methodology. The FOXBOX system is written in C++. C++ template
arguments provide for abstract domain types. Currently, FOXBOX can be
compiled with SACLIB 1.1, GnuMP 1.0, and NTL 2.0 as its underlying
field and polynomial arithmetic. Multiple arithmetic plugins can be
used in the same computation. FOXBOX provides an MPI compliant
distribution mechanism that allows for parallel and distributed
execution of FOXBOX programs. Finally, FOXBOX plugs into a
server/clientstyle Maple application interface."
}
\end{chunk}
\index{Dooley, Samuel S.}
\begin{chunk}{axiom.bib}
@InProceedings{Dool98,
author = "Dooley, Samuel S.",
title = "Coordinating mathematical content and presentation markup in
interactive mathematical documents",
booktitle = "Proc. ISSAC 1998",
series = "ISSAC 98",
year = "1998",
publisher = "ACM Press",
location = "Rostock, Germany",
pages = "1315",
keywords = "axiomref",
abstract =
"This paper presents a method for representing mathematical content
and presentation markup in interactive mathematical documents that
treats each view of the information on a separate and equal
footing. By providing extensible, overridable, default mappings from
content to presentation in a way that supports efficient mappings back
from the presentation to the underlying content, a user interface for
an interactive textbook has been implemented where the user interacts
with highquality presentation markup that supports user operations
defined in terms of the mathematical content. In addition, the user
interface can be insulated from contentspecific information, while
still being enabled to transfer that information to other programs for
computation. This method has been employed to embed interactive
mathematical content into the IBM techexplorer Interactive Textbook
for Linear Algebra. The issues involved in the implementation of the
interactive textbook also shed some light on the problems faced by the
MathML working group in representing both presentation and content for
mathematics for interactive web documents."
}
\end{chunk}
\index{Dunstan, Martin}
\index{Kelsey, Tom}
\index{Linton, Steve A.}
\index{Martin, Ursula}
\begin{chunk}{axiom.bib}
@InProceedings{Duns98,
author = "Dunstan, Martin and Kelsey, Tom and Linton, Steve and
Martin, Ursula",
title = "Lightweight Formal Methods For Computer Algebra Systems",
publisher = "ACM Press",
booktitle = "Proc. ISSAC 1998",
year = "1998",
location = "Rostock, Germany",
pages = "8087",
url = "http://www.cs.standrews.ac.uk/~tom/pub/issac98.pdf",
paper = "Duns98.pdf",
keywords = "axiomref",
abstract =
"Demonstrates the use of formal methods tools to provide a semantics
for the type hierarchy of the Axiom computer algebra system, and a
methodology for Aldor program analysis and verification. There are
examples of abstract specifications of Axiom primitives."
}
\end{chunk}
\index{Harrison, J.}
\index{Thery, L.}
\begin{chunk}{axiom.bib}
@article{Harr98,
author = "Harrison, J. and Thery, L.",
title = "A Skeptic's approach to combining HOL and Maple",
journal = "J. Autom. Reasoning",
volume = "21",
number = "3",
pages = "279294",
year = "1998",
keywords = "axiomref",
paper = "Harr98.pdf",
url = "http://www.cl.cam.ac.uk/~jrh13/papers/cas.ps.gz",
abstract =
"We contrast theorem provers and computer algebra systems, pointing
out the advantages and disadvantages of each, and suggest a simple way
to achieve a synthesis of some of the best features of both. Our
method is based on the systematic separation of search for a solution
and checking the solution, using a physical connection between
systems. We describe the separation of proof search and checking in
some detail, relating it to proof planning and to the complexity class
NP, and discuss different ways of exploiting a physical link between
systems. Finally, the method is illustrated by some concrete examples
of computer algebra results proved formally in the HOL theorem prover
with the aid of Maple."
}
\end{chunk}
\index{Kerber, Manfred}
\index{Kohlhase, Michael}
\index{Volker, Sorge}
\begin{chunk}{axiom.bib}
@article{Kerb98,
author = "Kerber, Manfred and Kohlhase, Michael and Volker, Sorge",
title = "Integrating computer algebra into proof planning",
journal = "J. Autom. Reasoning",
volume = "21",
number = "3",
pages = "327355",
keywords = "axiomref",
paper = "Kerb98.pdf",
url =
"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.40.3914&rep=rep1&type=pdf",
abstract =
"Mechanized reasoning systems and computer algebra systems have
different objectives. Their integration is highly desirable, since
formal proofs often involve both of the two different tasks proving
and calculating. Even more important, proof and computation are often
interwoven and not easily separable.
In this article, we advocate an integration of computer algebra into
mechanized reasoning systems at the proof plan level. This approach
allows us to view the computer algebra algorithms as methods, that is,
declarative representations of the problemsolving knowledge specific
to a certain mathematical domain. Automation can be achieved in many
cases by searching for a hierarchic proof plan at the method level by
using suitable domainspecific control knowledge about the
mathematical algorithms. In other words, the uniform framework of
proof planning allows us to solve a large class of problems that are
not automatically solvable by separate systems.
Our approach also gives an answer to the correctness problems inherent
in such an integration. We advocate an approach where the computer
algebra system produces highlevel protocol information that can be
processed by an interface to derive proof plans. Such a proof plan in
turn can be expanded to proofs at different levels of abstraction, so
the approach is well suited for producing a highlevel verbalized
explication as well as for a lowlevel, machinecheckable,
calculuslevel proof. We present an implementation of our ideas and
exemplify them using an automatically solved example."
}
\end{chunk}
\index{Naudin, Patrice}
\index{Quitte, Claude}
\begin{chunk}{axiom.bib}
@article{Naud98,
author = "Naudin, Patrice and Quitte, Claude",
title = "Univariate polynomial factorization over finite fields",
journal = "Theor. Comput. Sci.",
volume = "191",
number = "12",
pages = "136",
year = "1998",
paper = "Naud98.pdf",
abstract =
"This paper is a tutorial introduction to univariate polynomial
factorization over finite fields. The authors recall the classical
methods that induced most factorization algorithms (Berlekamp’s and
the CantorZassenhaus ones) and some refinements which can be applied
to these methods. Explicit algorithms are presented in a form suitable
for almost immediate implementation. They give a detailed description
of an efficient implementation of the CantorZassenhaus algorithm used
in the release 2 of the Axiom computer algebra system."
}
\end{chunk}

books/bookvolbib.pamphlet  397 ++++++++++++++++++++++++++++++
changelog  2 +
patch  519 +++++++++++++++++++++++++++++
src/axiomwebsite/patches.html  2 +
4 files changed, 772 insertions(+), 148 deletions()
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 4adfd54..fa94aaf 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 1764,10 +1764,35 @@ when shown in factored form.
Representation",
booktitle = "Proc. 1998 Internat. Symp. Symbolic Algebraic Comput.",
crossref = "ISSAC98",
+ publisher = "ACM Press",
year = "1998",
pages = "3037",
url = "http://www.math.ncsu.edu/~kaltofen/bibliography/98/DiKa98.pdf",
paper = "Diaz98.pdf",
+ abstract =
+ "The FOXBOX system puts in practice the black box representation of
+ symbolic objects and provides algorithms for performing the symbolic
+ calculus with such representations. Black box objects are stored as
+ functions. For instance: a black box polynomial is a procedure that
+ takes values for the variables as input and evaluates the polynomial
+ at that given point. FOXBOX can compute the greatest common divisor
+ and factorize polynomials in black box representation, producing as
+ output new black boxes. It also can compute the standard sparse
+ distributed representation of a black box polynomial, for example, one
+ which was computed for an irreducible factor. We establish that the
+ black box representation of objects can push the size of symbolic
+ expressions far beyond what standard data structures could handle
+ before.
+
+ Furthermore, FOXBOX demonstrates the generic program design
+ methodology. The FOXBOX system is written in C++. C++ template
+ arguments provide for abstract domain types. Currently, FOXBOX can be
+ compiled with SACLIB 1.1, GnuMP 1.0, and NTL 2.0 as its underlying
+ field and polynomial arithmetic. Multiple arithmetic plugins can be
+ used in the same computation. FOXBOX provides an MPI compliant
+ distribution mechanism that allows for parallel and distributed
+ execution of FOXBOX programs. Finally, FOXBOX plugs into a
+ server/clientstyle Maple application interface."
}
\end{chunk}
@@ 4741,18 +4766,25 @@ Calculemus (2011) Springer
\index{Kelsey, Tom}
\index{Linton, Steve A.}
\index{Martin, Ursula}
\begin{chunk}{ignore}
\bibitem[Dunstan 98]{Dun98} Dunstan, Martin; Kelsey, Tom; Linton, Steve;
Martin, Ursula
+\begin{chunk}{axiom.bib}
+@InProceedings{Duns98,
+ author = "Dunstan, Martin and Kelsey, Tom and Linton, Steve and
+ Martin, Ursula",
title = "Lightweight Formal Methods For Computer Algebra Systems",
+ publisher = "ACM Press",
+ booktitle = "Proc. ISSAC 1998",
+ year = "1998",
+ location = "Rostock, Germany",
+ pages = "8087",
url = "http://www.cs.standrews.ac.uk/~tom/pub/issac98.pdf",
 paper = "Dun98.pdf",
+ paper = "Duns98.pdf",
keywords = "axiomref",
 abstract = "
 Demonstrates the use of formal methods tools to provide a semantics
+ abstract =
+ "Demonstrates the use of formal methods tools to provide a semantics
for the type hierarchy of the Axiom computer algebra system, and a
methodology for Aldor program analysis and verification. There are
examples of abstract specifications of Axiom primitives."
+}
\end{chunk}
@@ 10942,6 +10974,18 @@ American Mathematical Society (1994)
\end{chunk}
+\index{Benker, Hans}
+\begin{chunk}{axiom.bib}
+@book{Benk98,
+ author = "Benker, Hans",
+ title = "Engineering mathematics with computer algebra systems",
+ year = "1998",
+ keywords = "axiomref",
+ comment = "german"
+}
+
+\end{chunk}
+
\index{Betten, Anton}
\index{Kohnert, Axel}
\index{Laue, Reinhard}
@@ 11064,6 +11108,41 @@ Soc. for Industrial and Applied Mathematics, Philadelphia (1990)
\end{chunk}
+\index{Breuer, Thomas}
+\index{Linton, Steve}
+\begin{chunk}{axiom.bib}
+@InProceedings{Breu98,
+ author = "Breuer, Thomas and Linton, Steve",
+ title = "The GAP 4 type system organising algebraic algorithms",
+ booktitle = "Proc. ISSAC 98",
+ series = "ISSAC 98",
+ year = "1998",
+ publisher = "ACM Press",
+ location = "Rostock, Germany",
+ pages = "1315",
+ keywords = "axiomref",
+ paper = "Breu98.pdf",
+ url = "http://www.gapsystem.org/Doc/Talks/paper.ps",
+ abstract =
+ "Version 4 of the GAP (Groups, Algorithms, Programming) system for
+ computational discrete mathematics has a number of novel features. In
+ this paper, we describe the type system, and the way in which it is
+ used for method selection. This system is central to the organization
+ of the library which is the main part of the GAP system. Unlike
+ simpler objectoriented systems, GAP allows method selection based on
+ the types of all arguments and on certain aspects of the relationship
+ between the arguments. In addition, the type of an object can change,
+ in a controlled way, during its life. This reflects information about
+ the object which has been computed and stored. Individual methods can
+ be written and installed independently. Furthermore, most checking of
+ the arguments is done in a uniform way by the method selection system,
+ making individual methods simpler and less prone to error. The methods
+ are combined automatically to produce a powerful and usable system for
+ interactive use or programming."
+}
+
+\end{chunk}
+
\index{Broadbery, Peter A.}
\index{G{\'o}mezD{\'\i}az, Teresa}
\index{Watt, Stephen M.}
@@ 12645,6 +12724,41 @@ LCCN QA76.95.I57 1998 Conference held jointly with AAECC6
\end{chunk}
+\index{Dooley, Samuel S.}
+\begin{chunk}{axiom.bib}
+@InProceedings{Dool98,
+ author = "Dooley, Samuel S.",
+ title = "Coordinating mathematical content and presentation markup in
+ interactive mathematical documents",
+ booktitle = "Proc. ISSAC 1998",
+ series = "ISSAC 98",
+ year = "1998",
+ publisher = "ACM Press",
+ location = "Rostock, Germany",
+ pages = "1315",
+ keywords = "axiomref",
+ abstract =
+ "This paper presents a method for representing mathematical content
+ and presentation markup in interactive mathematical documents that
+ treats each view of the information on a separate and equal
+ footing. By providing extensible, overridable, default mappings from
+ content to presentation in a way that supports efficient mappings back
+ from the presentation to the underlying content, a user interface for
+ an interactive textbook has been implemented where the user interacts
+ with highquality presentation markup that supports user operations
+ defined in terms of the mathematical content. In addition, the user
+ interface can be insulated from contentspecific information, while
+ still being enabled to transfer that information to other programs for
+ computation. This method has been employed to embed interactive
+ mathematical content into the IBM techexplorer Interactive Textbook
+ for Linear Algebra. The issues involved in the implementation of the
+ interactive textbook also shed some light on the problems faced by the
+ MathML working group in representing both presentation and content for
+ mathematics for interactive web documents."
+}
+
+\end{chunk}
+
\index{Dooley, Sam}
\begin{chunk}{ignore}
\bibitem[Dooley 99]{Doo99} Dooley, Sam editor.
@@ 13551,6 +13665,36 @@ Diss. ETH No. 11432
\subsection{H} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{Harrison, J.}
+\index{Thery, L.}
+\begin{chunk}{axiom.bib}
+@article{Harr98,
+ author = "Harrison, J. and Thery, L.",
+ title = "A Skeptic's approach to combining HOL and Maple",
+ journal = "J. Autom. Reasoning",
+ volume = "21",
+ number = "3",
+ pages = "279294",
+ year = "1998",
+ keywords = "axiomref",
+ paper = "Harr98.pdf",
+ url = "http://www.cl.cam.ac.uk/~jrh13/papers/cas.ps.gz",
+ abstract =
+ "We contrast theorem provers and computer algebra systems, pointing
+ out the advantages and disadvantages of each, and suggest a simple way
+ to achieve a synthesis of some of the best features of both. Our
+ method is based on the systematic separation of search for a solution
+ and checking the solution, using a physical connection between
+ systems. We describe the separation of proof search and checking in
+ some detail, relating it to proof planning and to the complexity class
+ NP, and discuss different ways of exploiting a physical link between
+ systems. Finally, the method is illustrated by some concrete examples
+ of computer algebra results proved formally in the HOL theorem prover
+ with the aid of Maple."
+}
+
+\end{chunk}
+
\index{Hassner, Martin}
\index{Burge, William H.}
\index{Watt, Stephen M.}
@@ 14411,6 +14555,52 @@ University of St Andrews, 6th April 2000
\end{chunk}
+\index{Kerber, Manfred}
+\index{Kohlhase, Michael}
+\index{Volker, Sorge}
+\begin{chunk}{axiom.bib}
+@article{Kerb98,
+ author = "Kerber, Manfred and Kohlhase, Michael and Volker, Sorge",
+ title = "Integrating computer algebra into proof planning",
+ journal = "J. Autom. Reasoning",
+ volume = "21",
+ number = "3",
+ pages = "327355",
+ keywords = "axiomref",
+ paper = "Kerb98.pdf",
+ url =
+"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.40.3914&rep=rep1&type=pdf",
+ abstract =
+ "Mechanized reasoning systems and computer algebra systems have
+ different objectives. Their integration is highly desirable, since
+ formal proofs often involve both of the two different tasks proving
+ and calculating. Even more important, proof and computation are often
+ interwoven and not easily separable.
+
+ In this article, we advocate an integration of computer algebra into
+ mechanized reasoning systems at the proof plan level. This approach
+ allows us to view the computer algebra algorithms as methods, that is,
+ declarative representations of the problemsolving knowledge specific
+ to a certain mathematical domain. Automation can be achieved in many
+ cases by searching for a hierarchic proof plan at the method level by
+ using suitable domainspecific control knowledge about the
+ mathematical algorithms. In other words, the uniform framework of
+ proof planning allows us to solve a large class of problems that are
+ not automatically solvable by separate systems.
+
+ Our approach also gives an answer to the correctness problems inherent
+ in such an integration. We advocate an approach where the computer
+ algebra system produces highlevel protocol information that can be
+ processed by an interface to derive proof plans. Such a proof plan in
+ turn can be expanded to proofs at different levels of abstraction, so
+ the approach is well suited for producing a highlevel verbalized
+ explication as well as for a lowlevel, machinecheckable,
+ calculuslevel proof. We present an implementation of our ideas and
+ exemplify them using an automatically solved example."
+}
+
+\end{chunk}
+
\index{Koepf, Wolfram}
\begin{chunk}{axiom.bib}
@InProceedings{Koep99,
@@ 15228,6 +15418,18 @@ Math. and Computers in Simulation 42 pp 541549 (1996)
\end{chunk}
+\index{Linton, Stephen}
+\begin{chunk}{axiom.bib}
+@misc{Lint98,
+ author = "Linton, Stephen",
+ title = "The GAP 4 Type System Organising Algebraic Algorithms",
+ paper = "Lint98.pdf",
+ url = "http://www.gapsystem.org/Doc/Talks/kobe.ps",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
\index{Liska, Richard}
\index{Drska, Ladislav}
\index{Limpouch, Jiri}
@@ 15960,6 +16162,33 @@ A281 1986 ACM order number 505860
\end{chunk}
+\index{Rigal, Alain}
+\begin{chunk}{axiom.bib}
+@article{Riga99,
+ author = "Rigal, Alain",
+ title = "Highorder compact schemes: Application to bidimensional unsteady
+ diffusionconvection problems.",
+ journal = "C. R. Acad. Sci.",
+ volume = "328",
+ number = "6",
+ pages = "535538",
+ year = "1999",
+ keywords = "axiomref",
+ abstract =
+ "For unsteady 2D diffusionconvection problems, we present two classes
+ of compact difference schemes of order 2 in time and 4 in space. These
+ finite difference schemes are essentially derived from 1D schemes,
+ extensively analyzed in our previous paper [J. Comput. Phys. 114,
+ No. 1, 5976 (1994; Zbl 0807.65056)]. We propose two approaches:
+ construction of 2D schemes as product of 1D schemes and global
+ formulation of 2D schemes. Part II by M. Fournié [C. R. Acad. Sci.,
+ Paris, Sér. I, Math. 328, No. 6, 539542 (1999; reviewed below)]
+ focuses on the development and analysis of global schemes with the
+ assistance of symbolic computation software (AXIOM)."
+}
+
+\end{chunk}
+
\index{Rioboo, Renaud}
\begin{chunk}{axiom.bib}
@article{Riob09,
@@ 16102,6 +16331,31 @@ J. of Symbolic Computation 36 pp 513533 (2003)
\end{chunk}
+\index{Roesner, K. G.}
+\begin{chunk}{axiom.bib}
+@article{Roes99,
+ author = "Roesner, K. G.",
+ title = "Supersonic flow around accelerated and decelerated bodies,
+ analysed by analytical methods",
+ journal = "Z. Angew. Math. Mech.",
+ volume = "79",
+ number = "3",
+ pages = "815816",
+ year = "1999",
+ keywords = "axiomref",
+ abstract =
+ "By an extensive use of the computer algebra system AXIOM, a power
+ series expansion with respect to the radial variable $r$ is used to
+ describe the accelerated or decelerated supersonic flow field around
+ the tip of slender conical bodies. The set of coupled nonlinear
+ differential equations for the coefficient functions, depending on
+ $\theta$ and $t$, is derived in closed form, and the first and second
+ approximation of the coefficient functions are determined
+ numerically."
+}
+
+\end{chunk}
+
\index{RojasBruna, Carlos}
\begin{chunk}{axiom.bib}
\article{Roja13,
@@ 16660,6 +16914,75 @@ Physics, pp337344, Acireale (Italy), 1992 Kluwer, Dordrecht 1993
\end{chunk}
+\index{Stroeker, Roelof J.}
+\index{Kaashoek, Johan F.}
+\begin{chunk}{axiom.bib}
+@book{Stro99,
+ author = "Stroeker, Roelof J. and Kaashoek, Johan F.",
+ title = "Discovering mathematics with Maple. An interactive exploration for
+ mathematicians, engineers and econometricians",
+ year = "1999",
+ publisher = "Birkhauser",
+ keywords = "axiomref",
+ abstract =
+ "During the past decade, the mathematical computer software packages
+ such as Mathematica, Maple, MATLAB (Axiom, Derive, Macsyma, MuPad are
+ some further examples of such software) [see Macsyma 2.3. Lite – the
+ student edition (1998; Zbl 0911.68089); B. W. Char, K. O. Geddes,
+ G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt, Maple V
+ Library reference manual (1991; Zbl 0763.68046); J. L. Zachary,
+ Introduction to scientific programming. Computational problem solving
+ using Mathematica and C (1997; Zbl 0891.68053); The student edition of
+ MATLAB. Student user guide. The problemsolving tool for engineers,
+ mathematicians, and scientists (1992; Zbl 0782.65001); H. Benker,
+ Ingenieurmathematik mit ComputeralgebraSystemen. AXIOM, DERIVE,
+ MACSYMA, MAPLE, MATHCAD, MATHEMATICA, MATLAB und MuPAD in der
+ Anwendung (1998; Zbl 0909.68109); W. Koepf, Hohere Analysis mit DERIVE
+ (1994; Zbl 0819.26003)] have greatly faciliated mathematical
+ experiments and have thus become popular tools for the modern
+ mathematician. It is a pity that most of these packages are quite
+ expensive, and that the frequently upgraded versions are not free for
+ the owners of the earlier versions (fortunately, there are inexpensive
+ student versions of some of these packages). There is a constant
+ demand of instructional textbooks by users of these packages. This
+ demand is reflected in the growing number of such textbooks. Many of
+ these books provide software support (diskette, CDROM, access by
+ ftp). Such a textbook should meet, in my opinion, the following
+ criteria: (1) The size should be small, not bulky like the complete
+ technical descriptions of the software. (2) There should be a lot of
+ examples of the use of the software covering a wide range of
+ mathematical topics. Electronic versions of these examples should be
+ made available for free to the users of the textbook
+ (e.g. diskette/CDROM, access by ftp). (3) There should be a good
+ supply of exercises covering the basic mathematical applications. (4)
+ The book should be visually pleasing, easy to read, have good indexes
+ and provide pointers to other books and electronic sources of
+ information. The book under review provides, in addition to the actual
+ text, an interactive exploratorium of its topics, based on the
+ mechanism of Maple worksheets. These worksheets can be ``opened'' by
+ the Maple program and they form a mixture of usual text, hypertext,
+ and Maple commands and have a nice style appearance. They also can be
+ ``exported'' in a file and included in a file for further treatment.
+ The book meets all the aforementioned criteria (1)(4) with elegance.
+ There are many exercises which cover all the usual mathematical topics
+ from linear algebra to differential equations and statistics. A
+ valuable feature is an appendix with hints and answers for all
+ exercises. One of the highlights of the book is the examination of
+ Riemann's nondifferentiable function
+ \[x \mapsto \sum_{k=1}^\infty{k^{2}} sin(\pi kx)\]
+ which is differentiable only at the rational points $p/q$ with $p$
+ and $q$ odd and relatively prime, where its derivative is $1/2$.
+
+ The book is intended for students of mathematics, engineering
+ sciences, and econometry. This book is an ideal guide for this purpose
+ and it could probably be used along, without the bulky technical
+ documentation of the Maple language. Note that Maple has a
+ comprehensive online help program, which contains large parts of the
+ original documentation."
+}
+
+\end{chunk}
+
\index{Sutor, Robert S.}
\begin{chunk}{ignore}
\bibitem[Sutor 85]{Sut85} Sutor, R.S.
@@ 17296,11 +17619,40 @@ ISSAC 94 ACM 0897916387/94/0007
\end{chunk}
\index{Wester, Michael J.}
\begin{chunk}{ignore}
\bibitem[Wester 99]{Wes99} Wester, Michael J.
 title = "Computer Algebra Systems",
John Wiley and Sons 1999 ISBN 0471983535
+\begin{chunk}{axiom.bib}
+@book{West99,
+ author = "Wester, Michael J.",
+ title = "Computer Algebra Systems. A practical guide",
+ year = "1999",
+ publisher = "Wiley",
keywords = "axiomref",
+ abstract =
+ "In this book some of the most popular general purpose computer
+ algebra systems (CAS), such as Mathematica, Maple, Derive, Axiom,
+ MuPAD, and Macsyma, are examined. The strengths and weaknesses of
+ these programs are compared and contrasted, and tutorial information
+ for using these systems in various ways is given. The different
+ packages are quantitatively compared using standard test suites,
+ giving the possibility to asses the most appropriate for a particular
+ user or application. The origins of these systems are revealed and
+ many of their behaviors analyzed. This furnishes a feel for where the
+ current computer algebra system state of the art stays and what can be
+ expected for existing and future systems. The book is organized in
+ several chapters written by different authors. Chapters 1,2, and 3 are
+ organized as reviews, comparisons, and critiques of CAS
+ capabilities. Then more technical issues are discussed considering
+ different approaches taken by different CAS: simplifying square roots
+ of square roots by denesting (chapter 4), complex number calculation
+ (chapter 5), efficiently computing Chebyshev polynomials (chapter 6),
+ solving single equations and systems of polynomial equations (chapters
+ 7, 8), computing limits (chapter 9), multiple integration (chapter
+ 10), solving ordinary differential equation (chapter 11), integration
+ of nonlinear evolution equations (chapter 12), code generation
+ (chapter 13), evaluation of expressions and programs in the embedded
+ computer algebra programming language (chapter 14), and computer
+ algebra in education (chapter 15). Chapter 16 covers the origin of CA,
+ and, finally chapter 17 gives a list of most CAS available today."
+}
\end{chunk}
@@ 20304,6 +20656,31 @@ Journal of the ACM, Vol. 25, No. 2, April 1978, pp. 271282
\subsection{N} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{Naudin, Patrice}
+\index{Quitte, Claude}
+\begin{chunk}{axiom.bib}
+@article{Naud98,
+ author = "Naudin, Patrice and Quitte, Claude",
+ title = "Univariate polynomial factorization over finite fields",
+ journal = "Theor. Comput. Sci.",
+ volume = "191",
+ number = "12",
+ pages = "136",
+ year = "1998",
+ paper = "Naud98.pdf",
+ abstract =
+ "This paper is a tutorial introduction to univariate polynomial
+ factorization over finite fields. The authors recall the classical
+ methods that induced most factorization algorithms (Berlekamp’s and
+ the CantorZassenhaus ones) and some refinements which can be applied
+ to these methods. Explicit algorithms are presented in a form suitable
+ for almost immediate implementation. They give a detailed description
+ of an efficient implementation of the CantorZassenhaus algorithm used
+ in the release 2 of the Axiom computer algebra system."
+}
+
+\end{chunk}
+
\index{Nijenhuis}
\index{Wilf}
\begin{chunk}{ignore}
diff git a/changelog b/changelog
index 4856bfc..eddcd5a 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,5 @@
+20160627 tpd src/axiomwebsite/patches.html 20160626.04.tpd.patch
+20160627 tpd books/bookvolbib Axiom Citations in the Literature
20160627 tpd src/axiomwebsite/patches.html 20160626.03.tpd.patch
20160627 tpd books/bookvolbib Axiom Citations in the Literature
20160627 tpd src/axiomwebsite/patches.html 20160626.02.tpd.patch
diff git a/patch b/patch
index f1687d5..6ccb2f7 100644
 a/patch
+++ b/patch
@@ 2,181 +2,424 @@ books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
\index{Koepf, Wolfram}
+\index{Rigal, Alain}
\begin{chunk}{axiom.bib}
@InProceedings{Koep99,
 author = "Koepf, Wolfram",
 title = "Orthogonal polnomials and computer algebra",
 booktitle = "Recent developments in complex analysis and computer algebra",
 series = "ISSAC 97",
+@article{Riga99,
+ author = "Rigal, Alain",
+ title = "Highorder compact schemes: Application to bidimensional unsteady
+ diffusionconvection problems.",
+ journal = "C. R. Acad. Sci.",
+ volume = "328",
+ number = "6",
+ pages = "535538",
year = "1999",
 publisher = "Kluwer Adademic Publishers",
 location = "Newark, DE",
 pages = "205234",
keywords = "axiomref",
 paper = "Koep99.pdf",
abstract =
 "Orthogonal polynomials have a long history, and are still important
 objects of consideration in mathematical research as well as in
 applications in Mathematical Physics, Chemistry, and
 Engineering. Quite a lot is known about them. Particularly wellknown
 are differential equations, recurrence equations, Rodrigues formulas,
 generating functions and hypergeometric representations for the
 classical systems of Jacobi, Laguerre and Hermite which can be found
 in mathematical dictionaries. Less wellknown are the corresponding
 representations for the classical discrete systems of Hahn,
 Krawtchouk, Meixner and Charlier, as well as addition theorems,
 connection relations between different systems and other identities
 for these and other systems of orthogonal polynomials. The ongoing
 research in this still very active subject of mathematics expands the
 knowledge database about orthogonal polynomials continuously. In the
 last few decades the classical families have been extended to a rather
 large collection of polynomial systems, the socalled AskeyWilson
 scheme, and they have been generalized in other ways as well.

 Recently new algorithmic approaches have been discovered to compute
 differential, recurrence and similar equations from series or integral
 representations. These methods turn out to be quite useful to prove or
 detect identities for orthogonal polynomial systems. Further
 algorithms to detect connection coefficients or to identify polynomial
 systems from given recurrence equations have been developed. Although
 some algorithmic methods had been known already in the last century,
 their use was rather limited due to the immense amount of
 calculations. Only the existence and distribution of computer algebra
 systems makes their use simple and useful for everybody.

 In this plenary lecture an overview is given of how algorithmic
 methods implemented in computer algebra systems can be used to prove
 identities about and to detect new knowledge for orthogonal
 polynomials and other hypergeometric type special functions.
 Implementations for this type of algorithms exist in Maple,
 Mathematica and REDUCE, and maybe also in other computer algebra
 systems. Online demonstrations will be given using Maple V.5."
+ "For unsteady 2D diffusionconvection problems, we present two classes
+ of compact difference schemes of order 2 in time and 4 in space. These
+ finite difference schemes are essentially derived from 1D schemes,
+ extensively analyzed in our previous paper [J. Comput. Phys. 114,
+ No. 1, 5976 (1994; Zbl 0807.65056)]. We propose two approaches:
+ construction of 2D schemes as product of 1D schemes and global
+ formulation of 2D schemes. Part II by M. Fournié [C. R. Acad. Sci.,
+ Paris, Sér. I, Math. 328, No. 6, 539542 (1999; reviewed below)]
+ focuses on the development and analysis of global schemes with the
+ assistance of symbolic computation software (AXIOM)."
}
\end{chunk}
\index{Koepf, Wolfram}
+\index{Roesner, K. G.}
\begin{chunk}{axiom.bib}
@misc{Koep14,
 author = "Koepf, Wolfram",
 title = "Methods of Computer Algebra for Orthogonal Polynomials",
 year = "2014",
 location = "Rutgers, NJ, USA",
 url =
"http://www.mathematik.unikassel.de/~koepf/Vortrag/2014ZeilbergerVortrag.pdf",
 paper = "Koep14.pdf",
 video1 = "https://vimeo.com/85573338",
 video2 = "https://vimeo.com/85573712",
 website = "http://www.caop.org"
+@article{Roes99,
+ author = "Roesner, K. G.",
+ title = "Supersonic flow around accelerated and decelerated bodies,
+ analysed by analytical methods",
+ journal = "Z. Angew. Math. Mech.",
+ volume = "79",
+ number = "3",
+ pages = "815816",
+ year = "1999",
+ keywords = "axiomref",
+ abstract =
+ "By an extensive use of the computer algebra system AXIOM, a power
+ series expansion with respect to the radial variable $r$ is used to
+ describe the accelerated or decelerated supersonic flow field around
+ the tip of slender conical bodies. The set of coupled nonlinear
+ differential equations for the coefficient functions, depending on
+ $\theta$ and $t$, is derived in closed form, and the first and second
+ approximation of the coefficient functions are determined
+ numerically."
}
\end{chunk}
\index{Daly, Timothy}
+\index{Stroeker, Roelof J.}
+\index{Kaashoek, Johan F.}
\begin{chunk}{axiom.bib}
@misc{Daly08,
 author = "Daly, Timothy",
 title = "Axiom Computer Algebra System Information Sources",
 video = "https://www.youtube.com/watch?v=CV8y3UrpadY",
+@book{Stro99,
+ author = "Stroeker, Roelof J. and Kaashoek, Johan F.",
+ title = "Discovering mathematics with Maple. An interactive exploration for
+ mathematicians, engineers and econometricians",
+ year = "1999",
+ publisher = "Birkhauser",
keywords = "axiomref",
 year = "2008"
+ abstract =
+ "During the past decade, the mathematical computer software packages
+ such as Mathematica, Maple, MATLAB (Axiom, Derive, Macsyma, MuPad are
+ some further examples of such software) [see Macsyma 2.3. Lite – the
+ student edition (1998; Zbl 0911.68089); B. W. Char, K. O. Geddes,
+ G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt, Maple V
+ Library reference manual (1991; Zbl 0763.68046); J. L. Zachary,
+ Introduction to scientific programming. Computational problem solving
+ using Mathematica and C (1997; Zbl 0891.68053); The student edition of
+ MATLAB. Student user guide. The problemsolving tool for engineers,
+ mathematicians, and scientists (1992; Zbl 0782.65001); H. Benker,
+ Ingenieurmathematik mit ComputeralgebraSystemen. AXIOM, DERIVE,
+ MACSYMA, MAPLE, MATHCAD, MATHEMATICA, MATLAB und MuPAD in der
+ Anwendung (1998; Zbl 0909.68109); W. Koepf, Hohere Analysis mit DERIVE
+ (1994; Zbl 0819.26003)] have greatly faciliated mathematical
+ experiments and have thus become popular tools for the modern
+ mathematician. It is a pity that most of these packages are quite
+ expensive, and that the frequently upgraded versions are not free for
+ the owners of the earlier versions (fortunately, there are inexpensive
+ student versions of some of these packages). There is a constant
+ demand of instructional textbooks by users of these packages. This
+ demand is reflected in the growing number of such textbooks. Many of
+ these books provide software support (diskette, CDROM, access by
+ ftp). Such a textbook should meet, in my opinion, the following
+ criteria: (1) The size should be small, not bulky like the complete
+ technical descriptions of the software. (2) There should be a lot of
+ examples of the use of the software covering a wide range of
+ mathematical topics. Electronic versions of these examples should be
+ made available for free to the users of the textbook
+ (e.g. diskette/CDROM, access by ftp). (3) There should be a good
+ supply of exercises covering the basic mathematical applications. (4)
+ The book should be visually pleasing, easy to read, have good indexes
+ and provide pointers to other books and electronic sources of
+ information. The book under review provides, in addition to the actual
+ text, an interactive exploratorium of its topics, based on the
+ mechanism of Maple worksheets. These worksheets can be ``opened'' by
+ the Maple program and they form a mixture of usual text, hypertext,
+ and Maple commands and have a nice style appearance. They also can be
+ ``exported'' in a file and included in a file for further treatment.
+ The book meets all the aforementioned criteria (1)(4) with elegance.
+ There are many exercises which cover all the usual mathematical topics
+ from linear algebra to differential equations and statistics. A
+ valuable feature is an appendix with hints and answers for all
+ exercises. One of the highlights of the book is the examination of
+ Riemann's nondifferentiable function
+ \[x \mapsto \sum_{k=1}^\infty{k^{2}} sin(\pi kx)\]
+ which is differentiable only at the rational points $p/q$ with $p$
+ and $q$ odd and relatively prime, where its derivative is $1/2$.
+
+ The book is intended for students of mathematics, engineering
+ sciences, and econometry. This book is an ideal guide for this purpose
+ and it could probably be used along, without the bulky technical
+ documentation of the Maple language. Note that Maple has a
+ comprehensive online help program, which contains large parts of the
+ original documentation."
}
\end{chunk}
\index{Koepf, Wolfram}
+\index{Wester, Michael J.}
\begin{chunk}{axiom.bib}
@article{Koep99a,
 author = "Koepf, Wolfram",
 title = "Software for the algorithmic work with orthogonal polynomials
 and special functions",
 journal = "Electron. Trans. Numer. Anal.",
 volume = "9",
+@book{West99,
+ author = "Wester, Michael J.",
+ title = "Computer Algebra Systems. A practical guide",
year = "1999",
+ publisher = "Wiley",
keywords = "axiomref",
 paper = "Koep99a.pdf",
 url = "http://arxiv.org/pdf/math/9809125v1.pdf",
abstract =
 "An overview of the MAPLE routines that can be used for hypergeometric
 and basic hypergeometric series with some discussion of how and why
 they work."
+ "In this book some of the most popular general purpose computer
+ algebra systems (CAS), such as Mathematica, Maple, Derive, Axiom,
+ MuPAD, and Macsyma, are examined. The strengths and weaknesses of
+ these programs are compared and contrasted, and tutorial information
+ for using these systems in various ways is given. The different
+ packages are quantitatively compared using standard test suites,
+ giving the possibility to asses the most appropriate for a particular
+ user or application. The origins of these systems are revealed and
+ many of their behaviors analyzed. This furnishes a feel for where the
+ current computer algebra system state of the art stays and what can be
+ expected for existing and future systems. The book is organized in
+ several chapters written by different authors. Chapters 1,2, and 3 are
+ organized as reviews, comparisons, and critiques of CAS
+ capabilities. Then more technical issues are discussed considering
+ different approaches taken by different CAS: simplifying square roots
+ of square roots by denesting (chapter 4), complex number calculation
+ (chapter 5), efficiently computing Chebyshev polynomials (chapter 6),
+ solving single equations and systems of polynomial equations (chapters
+ 7, 8), computing limits (chapter 9), multiple integration (chapter
+ 10), solving ordinary differential equation (chapter 11), integration
+ of nonlinear evolution equations (chapter 12), code generation
+ (chapter 13), evaluation of expressions and programs in the embedded
+ computer algebra programming language (chapter 14), and computer
+ algebra in education (chapter 15). Chapter 16 covers the origin of CA,
+ and, finally chapter 17 gives a list of most CAS available today."
}
\end{chunk}
\index{Martin, Ursula}
+\index{Benker, Hans}
\begin{chunk}{axiom.bib}
@InProceedings{Mart99,
 author = "Martin, Ursula",
 title = "Computers, reasoning and mathematical practice",
 booktitle = "Computational Logic",
 publisher = "Springer",
 year = "1999",
 location = "Marktoberdorf, Germany",
 pages = "301346",
+@book{Benk98,
+ author = "Benker, Hans",
+ title = "Engineering mathematics with computer algebra systems",
+ year = "1998",
+ keywords = "axiomref",
+ comment = "german"
+}
+
+\end{chunk}
+
+\index{Breuer, Thomas}
+\index{Linton, Steve}
+\begin{chunk}{axiom.bib}
+@InProceedings{Breu98,
+ author = "Breuer, Thomas and Linton, Steve",
+ title = "The GAP 4 type system organising algebraic algorithms",
+ booktitle = "Proc. ISSAC 98",
+ series = "ISSAC 98",
+ year = "1998",
+ publisher = "ACM Press",
+ location = "Rostock, Germany",
+ pages = "1315",
+ keywords = "axiomref",
+ paper = "Breu98.pdf",
+ url = "http://www.gapsystem.org/Doc/Talks/paper.ps",
+ abstract =
+ "Version 4 of the GAP (Groups, Algorithms, Programming) system for
+ computational discrete mathematics has a number of novel features. In
+ this paper, we describe the type system, and the way in which it is
+ used for method selection. This system is central to the organization
+ of the library which is the main part of the GAP system. Unlike
+ simpler objectoriented systems, GAP allows method selection based on
+ the types of all arguments and on certain aspects of the relationship
+ between the arguments. In addition, the type of an object can change,
+ in a controlled way, during its life. This reflects information about
+ the object which has been computed and stored. Individual methods can
+ be written and installed independently. Furthermore, most checking of
+ the arguments is done in a uniform way by the method selection system,
+ making individual methods simpler and less prone to error. The methods
+ are combined automatically to produce a powerful and usable system for
+ interactive use or programming."
+}
+
+\end{chunk}
+
+\index{Linton, Stephen}
+\begin{chunk}{axiom.bib}
+@misc{Lint98,
+ author = "Linton, Stephen",
+ title = "The GAP 4 Type System Organising Algebraic Algorithms",
+ paper = "Lint98.pdf",
+ url = "http://www.gapsystem.org/Doc/Talks/kobe.ps",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Diaz, Angel}
+\index{Kaltofen, Erich}
+\begin{chunk}{axiom.bib}
+@InProceedings{Diaz98,
+ author = "Diaz, A. and Kaltofen, E.",
+ title = "{FoxBox}, a System for Manipulating Symbolic Objects in Black Box
+ Representation",
+ booktitle = "Proc. 1998 Internat. Symp. Symbolic Algebraic Comput.",
+ crossref = "ISSAC98",
+ publisher = "ACM Press",
+ year = "1998",
+ pages = "3037",
+ url = "http://www.math.ncsu.edu/~kaltofen/bibliography/98/DiKa98.pdf",
+ paper = "Diaz98.pdf",
+ abstract =
+ "The FOXBOX system puts in practice the black box representation of
+ symbolic objects and provides algorithms for performing the symbolic
+ calculus with such representations. Black box objects are stored as
+ functions. For instance: a black box polynomial is a procedure that
+ takes values for the variables as input and evaluates the polynomial
+ at that given point. FOXBOX can compute the greatest common divisor
+ and factorize polynomials in black box representation, producing as
+ output new black boxes. It also can compute the standard sparse
+ distributed representation of a black box polynomial, for example, one
+ which was computed for an irreducible factor. We establish that the
+ black box representation of objects can push the size of symbolic
+ expressions far beyond what standard data structures could handle
+ before.
+
+ Furthermore, FOXBOX demonstrates the generic program design
+ methodology. The FOXBOX system is written in C++. C++ template
+ arguments provide for abstract domain types. Currently, FOXBOX can be
+ compiled with SACLIB 1.1, GnuMP 1.0, and NTL 2.0 as its underlying
+ field and polynomial arithmetic. Multiple arithmetic plugins can be
+ used in the same computation. FOXBOX provides an MPI compliant
+ distribution mechanism that allows for parallel and distributed
+ execution of FOXBOX programs. Finally, FOXBOX plugs into a
+ server/clientstyle Maple application interface."
+}
+
+\end{chunk}
+
+\index{Dooley, Samuel S.}
+\begin{chunk}{axiom.bib}
+@InProceedings{Dool98,
+ author = "Dooley, Samuel S.",
+ title = "Coordinating mathematical content and presentation markup in
+ interactive mathematical documents",
+ booktitle = "Proc. ISSAC 1998",
+ series = "ISSAC 98",
+ year = "1998",
+ publisher = "ACM Press",
+ location = "Rostock, Germany",
+ pages = "1315",
keywords = "axiomref",
 paper = "Mart99.pdf",
 url =
"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.50.2061&rep=rep1&type=pdf",
abstract =
 "We identify three main objectives for computer aided reasoning
 enhancing the techniques available for mathematical experimentation,
 developing community standards for experiment and modelling and
 developing methods which will make computation more acceptable as part
 of a proof. We discuss three areas of research which address these:
 the use of theorem proving techniques to enhance or extend
 mathematical software systems, support for formal methods techniques
 to increase the reliability of such systems, and the use of computer
 aided formal reasoning in support of mathematical practice. This last
 includes activities such as formalizing systems for computational
 mathematics or visualization so that they can still be used informally
 but generate a formal development, and developing techniques to
 provide assistance in the initial stages of developing a new theory.

 By mathematics here we mean the activities of working research
 mathematicians, producing new results in pure or applied mathematics,
 although we touch briefly on some questions concerning the
 applications of computational mathematics and simulation in research
 science and engineering. We have left out several other related areas
 entirely: logical questions of decidability, soundness or
 completeness, theoretical computer science issues of semantics,
 computability or complexity, foundational issues such as
 constructivity, computer aided proofs about software and hardware, and
 the use of computers in mathematical education at all levels and in
 heuristic discovery. In particular foundational questions about
 computation have transformed mathematical logic, computation has made
 constructive proof feasible, and effective notions of practice for
 proofs about hardware and software are by no means well understood.
 However these matters fall outside the scope of this paper."
+ "This paper presents a method for representing mathematical content
+ and presentation markup in interactive mathematical documents that
+ treats each view of the information on a separate and equal
+ footing. By providing extensible, overridable, default mappings from
+ content to presentation in a way that supports efficient mappings back
+ from the presentation to the underlying content, a user interface for
+ an interactive textbook has been implemented where the user interacts
+ with highquality presentation markup that supports user operations
+ defined in terms of the mathematical content. In addition, the user
+ interface can be insulated from contentspecific information, while
+ still being enabled to transfer that information to other programs for
+ computation. This method has been employed to embed interactive
+ mathematical content into the IBM techexplorer Interactive Textbook
+ for Linear Algebra. The issues involved in the implementation of the
+ interactive textbook also shed some light on the problems faced by the
+ MathML working group in representing both presentation and content for
+ mathematics for interactive web documents."
}
\end{chunk}
\index{Brown, Ronald}
\index{Tonks, Andrew}
+\index{Dunstan, Martin}
+\index{Kelsey, Tom}
+\index{Linton, Steve A.}
+\index{Martin, Ursula}
\begin{chunk}{axiom.bib}
@article{Brow94,
 author = "Brown, Ronald and Tonks, Andrew",
 title = "Calculations with simplicial and cubical groups in AXIOM",
 journal = "Journal of Symbolic Computation",
 volume = "17",
 number = "2",
 pages = "159179",
 year = "1994",
 month = "February",
 misc = "CODEN JSYCEH ISSN 07477171",
+@InProceedings{Duns98,
+ author = "Dunstan, Martin and Kelsey, Tom and Linton, Steve and
+ Martin, Ursula",
+ title = "Lightweight Formal Methods For Computer Algebra Systems",
+ publisher = "ACM Press",
+ booktitle = "Proc. ISSAC 1998",
+ year = "1998",
+ location = "Rostock, Germany",
+ pages = "8087",
+ url = "http://www.cs.standrews.ac.uk/~tom/pub/issac98.pdf",
+ paper = "Duns98.pdf",
keywords = "axiomref",
 paper = "Brow94.pdf",
abstract =
 "Work on calculations with simplical and cubical groups in AXIOM was
 carried out using loan equipment and software from IBM UK and guidance
 from L. A. Lambe. We report on the results of this work, and present
 the AXIOM code written by the second author during this period. This
 includes an implementation of the monoids which model cubes and
 simplices, together with a new AXIOM category of nearrings with which
 to carry out nonabelian calculations. Examples of the use of this
 code in interactive AXIOM sessions are also given."
+ "Demonstrates the use of formal methods tools to provide a semantics
+ for the type hierarchy of the Axiom computer algebra system, and a
+ methodology for Aldor program analysis and verification. There are
+ examples of abstract specifications of Axiom primitives."
+}
+
+\end{chunk}
+
+\index{Harrison, J.}
+\index{Thery, L.}
+\begin{chunk}{axiom.bib}
+@article{Harr98,
+ author = "Harrison, J. and Thery, L.",
+ title = "A Skeptic's approach to combining HOL and Maple",
+ journal = "J. Autom. Reasoning",
+ volume = "21",
+ number = "3",
+ pages = "279294",
+ year = "1998",
+ keywords = "axiomref",
+ paper = "Harr98.pdf",
+ url = "http://www.cl.cam.ac.uk/~jrh13/papers/cas.ps.gz",
+ abstract =
+ "We contrast theorem provers and computer algebra systems, pointing
+ out the advantages and disadvantages of each, and suggest a simple way
+ to achieve a synthesis of some of the best features of both. Our
+ method is based on the systematic separation of search for a solution
+ and checking the solution, using a physical connection between
+ systems. We describe the separation of proof search and checking in
+ some detail, relating it to proof planning and to the complexity class
+ NP, and discuss different ways of exploiting a physical link between
+ systems. Finally, the method is illustrated by some concrete examples
+ of computer algebra results proved formally in the HOL theorem prover
+ with the aid of Maple."
+}
+
+\end{chunk}
+
+\index{Kerber, Manfred}
+\index{Kohlhase, Michael}
+\index{Volker, Sorge}
+\begin{chunk}{axiom.bib}
+@article{Kerb98,
+ author = "Kerber, Manfred and Kohlhase, Michael and Volker, Sorge",
+ title = "Integrating computer algebra into proof planning",
+ journal = "J. Autom. Reasoning",
+ volume = "21",
+ number = "3",
+ pages = "327355",
+ keywords = "axiomref",
+ paper = "Kerb98.pdf",
+ url =
+"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.40.3914&rep=rep1&type=pdf",
+ abstract =
+ "Mechanized reasoning systems and computer algebra systems have
+ different objectives. Their integration is highly desirable, since
+ formal proofs often involve both of the two different tasks proving
+ and calculating. Even more important, proof and computation are often
+ interwoven and not easily separable.
+
+ In this article, we advocate an integration of computer algebra into
+ mechanized reasoning systems at the proof plan level. This approach
+ allows us to view the computer algebra algorithms as methods, that is,
+ declarative representations of the problemsolving knowledge specific
+ to a certain mathematical domain. Automation can be achieved in many
+ cases by searching for a hierarchic proof plan at the method level by
+ using suitable domainspecific control knowledge about the
+ mathematical algorithms. In other words, the uniform framework of
+ proof planning allows us to solve a large class of problems that are
+ not automatically solvable by separate systems.
+
+ Our approach also gives an answer to the correctness problems inherent
+ in such an integration. We advocate an approach where the computer
+ algebra system produces highlevel protocol information that can be
+ processed by an interface to derive proof plans. Such a proof plan in
+ turn can be expanded to proofs at different levels of abstraction, so
+ the approach is well suited for producing a highlevel verbalized
+ explication as well as for a lowlevel, machinecheckable,
+ calculuslevel proof. We present an implementation of our ideas and
+ exemplify them using an automatically solved example."
+}
+
+\end{chunk}
+
+\index{Naudin, Patrice}
+\index{Quitte, Claude}
+\begin{chunk}{axiom.bib}
+@article{Naud98,
+ author = "Naudin, Patrice and Quitte, Claude",
+ title = "Univariate polynomial factorization over finite fields",
+ journal = "Theor. Comput. Sci.",
+ volume = "191",
+ number = "12",
+ pages = "136",
+ year = "1998",
+ paper = "Naud98.pdf",
+ abstract =
+ "This paper is a tutorial introduction to univariate polynomial
+ factorization over finite fields. The authors recall the classical
+ methods that induced most factorization algorithms (Berlekamp’s and
+ the CantorZassenhaus ones) and some refinements which can be applied
+ to these methods. Explicit algorithms are presented in a form suitable
+ for almost immediate implementation. They give a detailed description
+ of an efficient implementation of the CantorZassenhaus algorithm used
+ in the release 2 of the Axiom computer algebra system."
}
\end{chunk}
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 7022942..1006490 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5418,6 +5418,8 @@ buglist: add todo 339: missing side conditions
books/bookvolbib Axiom Citations in the Literature
20160627.03.tpd.patch
books/bookvolbib Axiom Citations in the Literature
+20160627.04.tpd.patch
+books/bookvolbib Axiom Citations in the Literature

1.7.5.4