From b52503575a629869644cd2f5ec5b43a45687ff4e Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Sat, 2 Jul 2016 19:20:52 0400
Subject: [PATCH] books/bookvolbib Axiom Citations in the Literature
MIMEVersion: 1.0
ContentType: text/plain; charset=UTF8
ContentTransferEncoding: 8bit
Goal: Axiom Literate Programming
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate99,
author = "Fateman, Richard J.",
title = "Symbolic mathematics system evaluators",
year = "1999",
keywords = "axiomref",
url = "http://people.eecs.berkeley.edu/~fateman/papers/evalnew.pdf",
paper = "Fate99.pdf",
abstract =
"``Evaluation'' of expressions and programs in a computer algebra
system is central to every system, but inevitably fails to provide
complete satisfaction. Here we explain the conflicting requirements,
describe some solutions from current systems, and propose alternatives
that might be preferable sometimes. We give examples primarily from
Axiom, Macsyma, Maple, Mathematica, with passing metion of a few other
systems."
}
\end{chunk}
\index{G{\'o}mezD{\'\i}az, Teresa}
\begin{chunk}{axiom.bib}
@phdthesis{Gome92,
author = "GomezDias, Teresa",
title = {Quelques applications de l`\'evaluation dynamique},
school = "L'Universite de Limoges",
year = "1992",
month = "March",
paper = "Gome92.pdf"
}
\end{chunk}
\index{G{\'o}mezD{\'\i}az, Teresa}
\begin{chunk}{axiom.bib}
@article{Gome96,
author = "GomezDiaz, Theresa",
title = "Examples of using dynamic constructible closure",
journal = "Math. Comput. Simul.",
volume = "42",
number = "46",
pages = "375383",
year = "1996",
keywords = "axiomref",
abstract =
"We present here some examples of using the ``Dynamic Constructible
Closure'' program, which performs automatic case distinctions in
computations involving parameters over a base field ``K''. This
program is an application of the ``Dynamic Evaluation'' principle
which generalizes tradional evaluation and was first used to deal with
algebraic numbers."
}
\end{chunk}
\index{Green, Edward L.}
\begin{chunk}{axiom.bib}
@book{Gree01,
author = "Green, Edward L.",
title = "Symbolic Computation: Solving Equations in Algebra, Geometry, and
Engineering",
booktitle = "Proc. AMSIMSSIAM Joint Summer Research Conference on Symbolic
Computation",
volume = "232",
publisher = "American Mathematical Society",
year = "2001",
keywords = "axiomref",
abstract =
"This volume contains papers related to the research conference,
``Symbolic Computation: Solving Equations in Algebra, Analysis, and
Engineering,'' held at Mount Holyoke College (MA). It provides a broad
range of active research areas in symbolic computation as it applies
to the solution of polynomial systems. The conference brought together
pure and applied mathematicians, computer scientists, and engineers,
who use symbolic computation to solve systems of equations or who
develop the theoretical background and tools needed for this
purpose. Within this general framework, the conference focused on
several themes: systems of polynomials, systems of differential
equations, noncommutative systems, and applications."
}
\end{chunk}
\index{Dragan, Laurentiu}
\index{Watt, Stephen}
\begin{chunk}{axiom.bib}
@InProceedings{Drag10,
author = "Dragan, Laurentiu and Watt, Stephen",
title = "Type Specialization in Aldor",
booktitle = "Computer algebra in scientific computing",
series = "CASC 2010",
year = "2010",
location = "Tsakhadzor, Armenia",
pages = "7384",
keywords = "axiomref",
url = "http://www.csd.uwo.ca/~watt/pub/reprints/2010cascspecdom.pdf",
paper = "Drag10.pdf",
abstract =
"Computer algebra in scientific computation squarely faces the dilemma
of natural mathematical expression versus efficiency. While
higherorder programming constructs and parametric polymorphism
provide a natural and expressive language for mathematical
abstractions, they can come at a considerable cost. We investigate how
deeply nested type constructions may be optimized to achieve
performance similar to that of handtuned code written in lowerlevel
languages."
}
\end{chunk}
\index{Delliere, Stephane}
\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@techreport{Dell00,
author = "Delliere, Stephane and Wang, Dongming",
title = "simple systems and dynamic constructible closure",
institution = "Universite de Limoges",
year = "2000",
type = "technical report",
number = "200016",
paper = "Dell00.pdf",
url = "http://www.unilim.fr/laco/rapports/2000/R2000\_16.pdf",
keywords = "axiomref",
abstract =
"Dynamic evaluation is a general method for computing with parameters
[6, 9]. In 1994, T. GomezDiaz implemented the dynamic constructible
closure in the scientific computation system Axiom [17]: by simulating
dynamic evaluation, it offers the possibility to compute with
parameters in a very large way [13]. The outputs of a calculs with
T. GomezDiaz programs are represented by a finite collection of
constructible triangular systems defined in [12, definition
p.106]. Though there are numerous applications of these programs
(notably polynomial system solving with parameters [11], automatic
geometric theorem proving [14, 15], computation of Jordan forms with
parameters [16]), nobody gives theorical interest to this kind of
triangular systems. The main reason of this phenomenon is that they
are definied in [12] within the dynamic evaluation context. On the
opposite, most notions of triangular systems (J.F. RittW.T. Wu
characteristic sets [24, 28], M. Kalkbrener regular chains [18],
D. Lazard triangular sets [20], M. Moreno Maza regular sets [22],
D.M. Wang simple systems [26, 27]) are defined in terms of commutative
algebra. This problem is at the origin of the work done in [7] where
we give a relevant algebraic model of T. GomezDiaz systems within
commutative algebra terminology. This allows us to relate them to many
concepts of triangular systems [7]. Thus, we give interest to the
connections with D. Lazard triangular sets in [8]. In a way, this
paper is the continuation of this previous work. This time, we study
relationships between T. GomezDiaz systems and D.M. Wang simple
systems. The paper is structured as follows. We have collected in
section 2 some needed notations. In section 3, we give all the
terminology related to our algebraic model of T. GomezDiaz
systems. Thus, we define the notion of weak constructible triangular
systems and introduce the properties of normalization and
squarefreeness. Section 4 is more detailed. First of all, we study a
weaker form of normalization called $L$normalization. Then we give
many properties of constructible triangular systems verifying this new
notion. We obtain an algebraic and geometric framework which permits,
in section 5, to explore the connections between T. GomezDiaz systems
and D.M. Wang simple systems. In particular, this last section will
demonstrate well the importance of our $L$normalization
property. Indeed, we show that simple systems and squarefree
$L$normalized constructible triangular systems are equivalent."
}
\end{chunk}
\index{Aubry, Phillippe}
\begin{chunk}{axiom.bib}
@phdthesis{Aubr99b,
author = "Aubry, Philippe",
title = "Ensembles triangulaires de polynomes et resolution de systemes
algebriques. Implantation en Axiom",
school = "l'Universite de Paris VI",
year = "1999",
month = "January",
paper = "Aubr99b.pdf",
comment = "French"
}
\end{chunk}
\index{Duval, Dominique}
\begin{chunk}{axiom.bib}
@article{Duva94c,
author = "Duval, Dominique",
title = "Algebraic Numbers: An Example of Dynamic Evaluation",
journal = "J. Symbolic Computation",
volume = "18",
pages = "429445",
year = "1994",
url = "http://www.sciencedirect.com/science/article/pii/S0747717106000551",
paper = "Duva94c.pdf",
keywords = "axiomref",
abstract = "
Dynamic evaluation is presented through examples: computations
involving algebraic numbers, automatic case discussion according to
the characteristic of a field. Implementation questions are addressed
too. Finally, branches are presented as ``dual'' to binary functions,
according to the approach of sketch theory."
}
\end{chunk}
\index{Hubert, Evelyne}
\begin{chunk}{axiom.bib}
@InProceedings{Hube03,
author = "Hubert, Evelyne",
title = "Notes on Triangular Sets and TriangulationDecomposition I:
Polynomial Systems",
booktitle = "Symbolic and Numerical Scientific Computing",
series = "Lecture Notes in Computer Science 2630",
year = "2003",
pages = "139",
keywords = "axiomref",
paper = "Hube03.pdf",
url = "http://www.cecm.sfu.ca/~rpearcea/sdmp/sdmp\_paper.pdf",
abstract =
"This is the first in a series of two tutorial articles devoted to
triangulation decomposition algorithms. The value of these notes
resides in the uniform presen tation of triangulationdecomposition
of polynomial and differential radical ideals with detailed proofs of
all the presented results.We emphasize the study of the mathematical
objects manipulated by the algorithms and show their properties in
independently of those. We also detail a selection of algorithms, one
for each task. We address here polynomial systems and some of the
material we develop here will be used in the second part, devoted to
differential systems."
}
\end{chunk}
\index{Hubert, Evelyne}
\begin{chunk}{axiom.bib}
@InProceedings{Hube03a,
author = "Hubert, Evelyne",
title = "Notes on Triangular Sets and TriangulationDecomposition II:
Differential Systems",
booktitle = "Symbolic and Numerical Scientific Computing",
series = "Lecture Notes in Computer Science 2630",
year = "2003",
pages = "4087",
keywords = "axiomref",
paper = "Hube03a.pdf",
url =
"http://wwwsop.inria.fr/members/Evelyne.Hubert/publications/sncsd.pdf",
abstract =
"This is the second in a series of two tutorial articles devoted to
triangulationdecomposition algorithms. The value of these notes
resides in the uniform presentation of triangulationdecomposition of
polynomial and differential radical ideals with detailed proofs of all
the presented results.We emphasize the study of the mathematical
objects manipulated by the algorithms and show their properties
independently of those. We also detail a selection of algorithms, one
for each task. The present article deals with differential systems. It
uses results presented in the first article on polynomial systems but
can be read independently."
}
\end{chunk}
\index{Philippe, M. Trebuchet}
\begin{chunk}{axiom.bib}
@phdthesis{Phil02,
author = "Philippe, M. Trebuchet",
title = "Toward a fast and numerically stable algebraic equation solving",
comment = "Vers une resolution stable et rapide des equations algebriques",
school = "l'Universite de Paris 6",
year = "2002",
month = "December",
paper = "Phil02.pdf",
abstract =
"Polynomial systems can be found in many industrial applications. They
are also in the heart of effective algebraic geometry. A fundamental
tool for studying them is the Groebner bases. The knowledge of this
paricular base of the ideal generated by the polynomials composing the
system allows us to compute in $A=K[x_1,\ldots,x_n]/I$, the quotient
algebra, and this is necessary when we try to solve. Nevertheless,
Groebner bases computations rely heavily on the introduction of
monomial ordering. This introduces a certain rigidity in the
computation and thus numerical instability. We propose a new algorithm
that tries to remedy that problem. It generalises Groebner bases
computation and is much less numerically instable. To do this, we
decrease the requirement of monomial ordering, and use a new normal
form criterion. We then give an algorithm and prove its termination
and correctness when the input polynomial system is
0dimensional. After, we compare it with the previously known methods
and show how it can be seen as a generalisation of them. Next, we
detail how we implemented it in C++ using the Synaps library. We also
describe the sparse matrix elimination algorithm we used in or
program. Finally, we present some of the experiments we have done with
our program in domains like computer vision, algorithmic geometry,
robotics, or pharmacology."
}
\end{chunk}
\index{Duval, Dominique}
\begin{chunk}{axiom.bib}
@article{Duva95,
author = "Duval, D.",
title = "Evaluation dynamique et cl\^oture alg\'ebrique en Axiom",
journal = "Journal of Pure and Applied Algebra",
volume = "99",
year = "1995",
pages = "267295.",
keywords = "axiomref",
abstract =
"Dynamic evaluation allows to compute with algebraic numbers without
factorizing polynomials. It also allows to manipulate parameters in a
flexible and userfriendly way. The aim of this paper is the
following: Explain what is dynamic evaluation, with its basic notions
of dynamic set and splitting. Present its application to computations
involving algebraic numbers, which amounts to defining the dynamic
algebraic closure of a field. Describe the Axiom program which
implements this, and give a user guide for it (only this last point
assumes some knowledge of Axiom) Dynamic evaluation is described here
without any reference to sketch theory, however our presentation, less
rigourous, may be considered as more accessible."
}
\end{chunk}
\index{Montes, Antonio}
\begin{chunk}{axiom.bib}
@misc{Mont07,
author = "Montes, Antonio",
title = "On the canonical discussion of polynomial systems with parameters",
year = "2007",
url = "http://arxiv.org/pdf/math/0601674.pdf",
paper = "Mont07.pdf",
keywords = "axiomref",
abstract =
"Given a parametric polynomial ideal $I$, the algorithm DISPGB,
introduced by the author in 2002, builds up a binary tree describing a
dichotomic discussion of the different reduced Groebner bases
depending on the values of the parameters, whose set of terminal
vertices form a Comprehensive Groebner System (CGS). It is relevant
to obtain CGS’s having further properties in order to make them more
useful for the applications. In this paper the interest is focused on
obtaining a canonical CGS. We define the objective, show the
difficulties and formulate a natural conjecture. If the conjecture is
true then such a canonical CGS will exist and can be computed. We also
give an algorithm to transform our original CGS in this direction and
show its utility in applications."
}
\end{chunk}

books/bookvolbib.pamphlet  337 +++++++++++++++++++++++++++++
changelog  2 +
patch  448 ++++++++++++++++++++++++++++
src/axiomwebsite/patches.html  2 +
4 files changed, 647 insertions(+), 142 deletions()
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 8e09d68..c3af887 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 78,7 +78,7 @@ paragraph for those unfamiliar with the terms.
survey article as another example of the breadth of mathematics that
has biological significance. The most comprehensive reference for the
mathematical research done in this area (through 1980) is
 W\:orzBusekros."
+ WorzBusekros."
}
\end{chunk}
@@ 13428,6 +13428,62 @@ May 1984
\end{chunk}
\index{Delliere, Stephane}
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@techreport{Dell00,
+ author = "Delliere, Stephane and Wang, Dongming",
+ title = "simple systems and dynamic constructible closure",
+ institution = "Universite de Limoges",
+ year = "2000",
+ type = "technical report",
+ number = "200016",
+ paper = "Dell00.pdf",
+ url = "http://www.unilim.fr/laco/rapports/2000/R2000\_16.pdf",
+ keywords = "axiomref",
+ abstract =
+ "Dynamic evaluation is a general method for computing with parameters
+ [6, 9]. In 1994, T. GomezDiaz implemented the dynamic constructible
+ closure in the scientific computation system Axiom [17]: by simulating
+ dynamic evaluation, it offers the possibility to compute with
+ parameters in a very large way [13]. The outputs of a calculs with
+ T. GomezDiaz programs are represented by a finite collection of
+ constructible triangular systems defined in [12, definition
+ p.106]. Though there are numerous applications of these programs
+ (notably polynomial system solving with parameters [11], automatic
+ geometric theorem proving [14, 15], computation of Jordan forms with
+ parameters [16]), nobody gives theorical interest to this kind of
+ triangular systems. The main reason of this phenomenon is that they
+ are definied in [12] within the dynamic evaluation context. On the
+ opposite, most notions of triangular systems (J.F. RittW.T. Wu
+ characteristic sets [24, 28], M. Kalkbrener regular chains [18],
+ D. Lazard triangular sets [20], M. Moreno Maza regular sets [22],
+ D.M. Wang simple systems [26, 27]) are defined in terms of commutative
+ algebra. This problem is at the origin of the work done in [7] where
+ we give a relevant algebraic model of T. GomezDiaz systems within
+ commutative algebra terminology. This allows us to relate them to many
+ concepts of triangular systems [7]. Thus, we give interest to the
+ connections with D. Lazard triangular sets in [8]. In a way, this
+ paper is the continuation of this previous work. This time, we study
+ relationships between T. GomezDiaz systems and D.M. Wang simple
+ systems. The paper is structured as follows. We have collected in
+ section 2 some needed notations. In section 3, we give all the
+ terminology related to our algebraic model of T. GomezDiaz
+ systems. Thus, we define the notion of weak constructible triangular
+ systems and introduce the properties of normalization and
+ squarefreeness. Section 4 is more detailed. First of all, we study a
+ weaker form of normalization called $L$normalization. Then we give
+ many properties of constructible triangular systems verifying this new
+ notion. We obtain an algebraic and geometric framework which permits,
+ in section 5, to explore the connections between T. GomezDiaz systems
+ and D.M. Wang simple systems. In particular, this last section will
+ demonstrate well the importance of our $L$normalization
+ property. Indeed, we show that simple systems and squarefree
+ $L$normalized constructible triangular systems are equivalent."
+}
+
+\end{chunk}
+
+\index{Delliere, Stephane}
\begin{chunk}{axiom.bib}
@article{Dell01,
author = "Delliere, Stephane",
@@ 13782,6 +13838,33 @@ ISBN 1581130732 LCCN QA76.95.I57 1999 ACM Press
\end{chunk}
+\index{Dragan, Laurentiu}
+\index{Watt, Stephen}
+\begin{chunk}{axiom.bib}
+@InProceedings{Drag10,
+ author = "Dragan, Laurentiu and Watt, Stephen",
+ title = "Type Specialization in Aldor",
+ booktitle = "Computer algebra in scientific computing",
+ series = "CASC 2010",
+ year = "2010",
+ location = "Tsakhadzor, Armenia",
+ pages = "7384",
+ keywords = "axiomref",
+ url = "http://www.csd.uwo.ca/~watt/pub/reprints/2010cascspecdom.pdf",
+ paper = "Drag10.pdf",
+ abstract =
+ "Computer algebra in scientific computation squarely faces the dilemma
+ of natural mathematical expression versus efficiency. While
+ higherorder programming constructs and parametric polymorphism
+ provide a natural and expressive language for mathematical
+ abstractions, they can come at a considerable cost. We investigate how
+ deeply nested type constructions may be optimized to achieve
+ performance similar to that of handtuned code written in lowerlevel
+ languages."
+}
+
+\end{chunk}
+
\index{Dunstan, Martin}
\index{Martin, Ursula}
\index{Linton, Steve A.}
@@ 13850,7 +13933,19 @@ Madrid Spain, NAG conference (private copy of paper)
volume = "99",
year = "1995",
pages = "267295.",
 keywords = "axiomref"
+ keywords = "axiomref",
+ abstract =
+ "Dynamic evaluation allows to compute with algebraic numbers without
+ factorizing polynomials. It also allows to manipulate parameters in a
+ flexible and userfriendly way. The aim of this paper is the
+ following: Explain what is dynamic evaluation, with its basic notions
+ of dynamic set and splitting. Present its application to computations
+ involving algebraic numbers, which amounts to defining the dynamic
+ algebraic closure of a field. Describe the Axiom program which
+ implements this, and give a user guide for it (only this last point
+ assumes some knowledge of Axiom) Dynamic evaluation is described here
+ without any reference to sketch theory, however our presentation, less
+ rigourous, may be considered as more accessible."
}
\end{chunk}
@@ 13997,7 +14092,6 @@ In Watanabe and Nagata [WN90], pp6067 ISBN 0897914015 LCCN QA76.95.I57 1990
year = "1996",
pages = "8694",
keywords = "axiomref",
 keywords = "axiomref",
paper = "Fate96.pdf",
url = "http://http.cs.berkeley.edu/~fateman/papers/eval.ps",
abstract =
@@ 14014,6 +14108,27 @@ In Watanabe and Nagata [WN90], pp6067 ISBN 0897914015 LCCN QA76.95.I57 1990
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
+@misc{Fate99,
+ author = "Fateman, Richard J.",
+ title = "Symbolic mathematics system evaluators",
+ year = "1999",
+ keywords = "axiomref",
+ url = "http://people.eecs.berkeley.edu/~fateman/papers/evalnew.pdf",
+ paper = "Fate99.pdf",
+ abstract =
+ "``Evaluation'' of expressions and programs in a computer algebra
+ system is central to every system, but inevitably fails to provide
+ complete satisfaction. Here we explain the conflicting requirements,
+ describe some solutions from current systems, and propose alternatives
+ that might be preferable sometimes. We give examples primarily from
+ Axiom, Macsyma, Maple, Mathematica, with passing metion of a few other
+ systems."
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
@InProceedings{Fate00,
author = "Fateman, Richard J.",
title = "Problem solving environments and symbolic computing",
@@ 14396,16 +14511,21 @@ LCCN QA76.95.I59 1992
\end{chunk}
\index{G{\'o}mezD{\'\i}az, Teresa}
\begin{chunk}{ignore}
\bibitem[GomezDiaz 92]{Gom92} G\'omezD'iaz, Teresa
 title = "Quelques applications de l`\'evaluation dynamique",
Ph.D. Thesis L'Universite De Limoges March 1992
 keywords = "axiomref",
+\begin{chunk}{axiom.bib}
+@phdthesis{Gome92,
+ author = "GomezDias, Teresa",
+ title = {Quelques applications de l`\'evaluation dynamique},
+ school = "L'Universite de Limoges",
+ year = "1992",
+ month = "March",
+ paper = "Gome92.pdf"
+}
\end{chunk}
\index{G{\'o}mezD{\'\i}az, Teresa}
\begin{chunk}{ignore}
+@article{Gome93
\bibitem[GomezDiaz 93]{Gom93} G\'omezD\'iaz, Teresa
title = "Examples of using Dynamic Constructible Closure",
IMACS Symposium SC1993
@@ 14421,6 +14541,28 @@ IMACS Symposium SC1993
\end{chunk}
+\index{G{\'o}mezD{\'\i}az, Teresa}
+\begin{chunk}{axiom.bib}
+@article{Gome96,
+ author = "GomezDiaz, Theresa",
+ title = "Examples of using dynamic constructible closure",
+ journal = "Math. Comput. Simul.",
+ volume = "42",
+ number = "46",
+ pages = "375383",
+ year = "1996",
+ keywords = "axiomref",
+ abstract =
+ "We present here some examples of using the ``Dynamic Constructible
+ Closure'' program, which performs automatic case distinctions in
+ computations involving parameters over a base field ``K''. This
+ program is an application of the ``Dynamic Evaluation'' principle
+ which generalizes tradional evaluation and was first used to deal with
+ algebraic numbers."
+}
+
+\end{chunk}
+
\index{Goodwin, B. M.}
\index{Buonopane, R. A.}
\index{Lee, A.}
@@ 14610,6 +14752,34 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
\end{chunk}
+\index{Green, Edward L.}
+\begin{chunk}{axiom.bib}
+@book{Gree01,
+ author = "Green, Edward L.",
+ title = "Symbolic Computation: Solving Equations in Algebra, Geometry, and
+ Engineering",
+ booktitle = "Proc. AMSIMSSIAM Joint Summer Research Conference on Symbolic
+ Computation",
+ volume = "232",
+ publisher = "American Mathematical Society",
+ year = "2001",
+ keywords = "axiomref",
+ abstract =
+ "This volume contains papers related to the research conference,
+ ``Symbolic Computation: Solving Equations in Algebra, Analysis, and
+ Engineering,'' held at Mount Holyoke College (MA). It provides a broad
+ range of active research areas in symbolic computation as it applies
+ to the solution of polynomial systems. The conference brought together
+ pure and applied mathematicians, computer scientists, and engineers,
+ who use symbolic computation to solve systems of equations or who
+ develop the theoretical background and tools needed for this
+ purpose. Within this general framework, the conference focused on
+ several themes: systems of polynomials, systems of differential
+ equations, noncommutative systems, and applications."
+}
+
+\end{chunk}
+
\index{Griesmer, James H.}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@@ 17285,6 +17455,32 @@ In Miola [Mio93], pp8194 ISBN 354057235X LCCN QA76.9.S88I576 1993
\end{chunk}
+\index{Montes, Antonio}
+\begin{chunk}{axiom.bib}
+@misc{Mont07,
+ author = "Montes, Antonio",
+ title = "On the canonical discussion of polynomial systems with parameters",
+ year = "2007",
+ url = "http://arxiv.org/pdf/math/0601674.pdf",
+ paper = "Mont07.pdf",
+ keywords = "axiomref",
+ abstract =
+ "Given a parametric polynomial ideal $I$, the algorithm DISPGB,
+ introduced by the author in 2002, builds up a binary tree describing a
+ dichotomic discussion of the different reduced Groebner bases
+ depending on the values of the parameters, whose set of terminal
+ vertices form a Comprehensive Groebner System (CGS). It is relevant
+ to obtain CGS’s having further properties in order to make them more
+ useful for the applications. In this paper the interest is focused on
+ obtaining a canonical CGS. We define the objective, show the
+ difficulties and formulate a natural conjecture. If the conjecture is
+ true then such a canonical CGS will exist and can be computed. We also
+ give an algorithm to transform our original CGS in this direction and
+ show its utility in applications."
+}
+
+\end{chunk}
+
\index{Mora, T.}
\begin{chunk}{ignore}
\bibitem[Mora 89]{Mor89} Mora, T. (ed)
@@ 19761,6 +19957,21 @@ National Physical Laboratory. (1982)
\end{chunk}
+\index{Aubry, Phillippe}
+\begin{chunk}{axiom.bib}
+@phdthesis{Aubr99b,
+ author = "Aubry, Philippe",
+ title = "Ensembles triangulaires de polynomes et resolution de systemes
+ algebriques. Implantation en Axiom",
+ school = "l'Universite de Paris VI",
+ year = "1999",
+ month = "January",
+ paper = "Aubr99b.pdf",
+ comment = "French"
+}
+
+\end{chunk}
+
\subsection{B} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Bailey P. B.}
@@ 20780,18 +20991,24 @@ Mathematical Structures in Computer Science, 4, p 239271. Cambridge University
\end{chunk}
\index{Duval, Dominique}
\begin{chunk}{ignore}
\bibitem[Duval 94c]{Duva94c} Duval, Dominique
+\begin{chunk}{axiom.bib}
+@article{Duva94c,
+ author = "Duval, Dominique",
title = "Algebraic Numbers: An Example of Dynamic Evaluation",
J. Symbolic Computation 18, 429445 (1994)
+ journal = "J. Symbolic Computation",
+ volume = "18",
+ pages = "429445",
+ year = "1994",
url = "http://www.sciencedirect.com/science/article/pii/S0747717106000551",
paper = "Duva94c.pdf",
+ keywords = "axiomref",
abstract = "
Dynamic evaluation is presented through examples: computations
involving algebraic numbers, automatic case discussion according to
the characteristic of a field. Implementation questions are addressed
too. Finally, branches are presented as ``dual'' to binary functions,
according to the approach of sketch theory."
+}
\end{chunk}
@@ 21574,6 +21791,64 @@ IEEE Comput. Soc. Press, pp. 678687.
\end{chunk}
+\index{Hubert, Evelyne}
+\begin{chunk}{axiom.bib}
+@InProceedings{Hube03,
+ author = "Hubert, Evelyne",
+ title = "Notes on Triangular Sets and TriangulationDecomposition I:
+ Polynomial Systems",
+ booktitle = "Symbolic and Numerical Scientific Computing",
+ series = "Lecture Notes in Computer Science 2630",
+ year = "2003",
+ pages = "139",
+ keywords = "axiomref",
+ paper = "Hube03.pdf",
+ url =
+ "http://wwwsop.inria.fr/members/Evelyne.Hubert/publications/sncsp.pdf",
+ abstract =
+ "This is the first in a series of two tutorial articles devoted to
+ triangulation decomposition algorithms. The value of these notes
+ resides in the uniform presen tation of triangulationdecomposition
+ of polynomial and differential radical ideals with detailed proofs of
+ all the presented results.We emphasize the study of the mathematical
+ objects manipulated by the algorithms and show their properties in
+ independently of those. We also detail a selection of algorithms, one
+ for each task. We address here polynomial systems and some of the
+ material we develop here will be used in the second part, devoted to
+ differential systems."
+}
+
+\end{chunk}
+
+\index{Hubert, Evelyne}
+\begin{chunk}{axiom.bib}
+@InProceedings{Hube03a,
+ author = "Hubert, Evelyne",
+ title = "Notes on Triangular Sets and TriangulationDecomposition II:
+ Differential Systems",
+ booktitle = "Symbolic and Numerical Scientific Computing",
+ series = "Lecture Notes in Computer Science 2630",
+ year = "2003",
+ pages = "4087",
+ keywords = "axiomref",
+ paper = "Hube03a.pdf",
+ url =
+ "http://wwwsop.inria.fr/members/Evelyne.Hubert/publications/sncsd.pdf",
+ abstract =
+ "This is the second in a series of two tutorial articles devoted to
+ triangulationdecomposition algorithms. The value of these notes
+ resides in the uniform presentation of triangulationdecomposition of
+ polynomial and differential radical ideals with detailed proofs of all
+ the presented results.We emphasize the study of the mathematical
+ objects manipulated by the algorithms and show their properties
+ independently of those. We also detail a selection of algorithms, one
+ for each task. The present article deals with differential systems. It
+ uses results presented in the first article on polynomial systems but
+ can be read independently."
+}
+
+\end{chunk}
+
\subsection{I} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{chunk}{ignore}
@@ 22691,6 +22966,42 @@ J. Inst. Maths Applics. 8 1635. (1971)
\end{chunk}
+\index{Philippe, M. Trebuchet}
+\begin{chunk}{axiom.bib}
+@phdthesis{Phil02,
+ author = "Philippe, M. Trebuchet",
+ title = "Toward a fast and numerically stable algebraic equation solving",
+ comment = "Vers une resolution stable et rapide des equations algebriques",
+ school = "l'Universite de Paris 6",
+ year = "2002",
+ month = "December",
+ paper = "Phil02.pdf",
+ abstract =
+ "Polynomial systems can be found in many industrial applications. They
+ are also in the heart of effective algebraic geometry. A fundamental
+ tool for studying them is the Groebner bases. The knowledge of this
+ paricular base of the ideal generated by the polynomials composing the
+ system allows us to compute in $A=K[x_1,\ldots,x_n]/I$, the quotient
+ algebra, and this is necessary when we try to solve. Nevertheless,
+ Groebner bases computations rely heavily on the introduction of
+ monomial ordering. This introduces a certain rigidity in the
+ computation and thus numerical instability. We propose a new algorithm
+ that tries to remedy that problem. It generalises Groebner bases
+ computation and is much less numerically instable. To do this, we
+ decrease the requirement of monomial ordering, and use a new normal
+ form criterion. We then give an algorithm and prove its termination
+ and correctness when the input polynomial system is
+ 0dimensional. After, we compare it with the previously known methods
+ and show how it can be seen as a generalisation of them. Next, we
+ detail how we implemented it in C++ using the Synaps library. We also
+ describe the sparse matrix elimination algorithm we used in or
+ program. Finally, we present some of the experiments we have done with
+ our program in domains like computer vision, algorithmic geometry,
+ robotics, or pharmacology."
+}
+
+\end{chunk}
+
\index{Pierce, R.S.}
\begin{chunk}{ignore}
\bibitem[Pierce 82]{Pie82} R.S. Pierce
@@ 23178,8 +23489,8 @@ Num. Math. 16 205223. (1970)
year = "1966",
publisher = "Academic Press, New York",
algebra = "\newline\refto{category NARNG NonAssociativeRng}
 \newline\refto{category NASRING NonAssociativeRing}",
 algebra = "\newline\refto{domain ALGSC AlgebraGivenByStructuralConstants}"
+ \newline\refto{category NASRING NonAssociativeRing}
+ \newline\refto{domain ALGSC AlgebraGivenByStructuralConstants}"
}
\end{chunk}
diff git a/changelog b/changelog
index 333beea..e47a477 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,5 @@
+20160702 tpd src/axiomwebsite/patches.html 20160702.02.tpd.patch
+20160702 tpd books/bookvolbib Axiom Citations in the Literature
20160702 tpd src/axiomwebsite/patches.html 20160702.01.tpd.patch
20160702 tpd books/bookvolbib Axiom Citations in the Literature
20160701 tpd src/axiomwebsite/patches.html 20160701.01.tpd.patch
diff git a/patch b/patch
index d7b04b4..5dac759 100644
 a/patch
+++ b/patch
@@ 2,161 +2,351 @@ books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
\index{Chou, ShangChing}
\index{Gao, XiaoShan}
\index{Liu, ZhuoJun}
\index{Wang, DingKang}
\index{Wang, Dongming}
+\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Chouxx,
 author = "Chou, ShangChing and Gao, XiaoShan and Liu, ZhuoJun and
 Wang, DingKang and Wang, Dongming",
 title = "Geometric Theorem Provers and Algebraic Equations Solvers",
 comment = "Chapter 20",
 url = "http://www.mmrc.iss.ac.cn/~xgao/papers/soft1.pdf",
 paper = "Chouxx.pdf",
+@misc{Fate99,
+ author = "Fateman, Richard J.",
+ title = "Symbolic mathematics system evaluators",
+ year = "1999",
+ keywords = "axiomref",
+ url = "http://people.eecs.berkeley.edu/~fateman/papers/evalnew.pdf",
+ paper = "Fate99.pdf",
abstract =
 "The methods of mechanizing mathematics are realized by means of
 compputer software for solving scientiØc and engineering problems via
 symbolic and hybrid computation. This chapter provides a collection of
 geometric theorem provers and algebraic equations solvers that are
 pieces of mathematical software based mostly on Wu's method and were
 developed mainly by members of the extended Wu group. The early
 theorem provers, though e±cient, were written in basic programming
 languages and on primitive computers. Now there exist more powerful
 and mature geometric theorem provers of which some have already been
 published as commercial software. On the other hand, building ef
 fective equations solvers is still at the experimental stage and
 remains for further research and development."
+ "``Evaluation'' of expressions and programs in a computer algebra
+ system is central to every system, but inevitably fails to provide
+ complete satisfaction. Here we explain the conflicting requirements,
+ describe some solutions from current systems, and propose alternatives
+ that might be preferable sometimes. We give examples primarily from
+ Axiom, Macsyma, Maple, Mathematica, with passing metion of a few other
+ systems."
+}
+
+\end{chunk}
+
+\index{G{\'o}mezD{\'\i}az, Teresa}
+\begin{chunk}{axiom.bib}
+@phdthesis{Gome92,
+ author = "GomezDias, Teresa",
+ title = {Quelques applications de l`\'evaluation dynamique},
+ school = "L'Universite de Limoges",
+ year = "1992",
+ month = "March",
+ paper = "Gome92.pdf"
}
\end{chunk}
\index{Melenk, H.}
\index{M\"oller, H. M.}
\index{Neun, W.}
+\index{G{\'o}mezD{\'\i}az, Teresa}
\begin{chunk}{axiom.bib}
@misc{Mele88,
 author = "Melenk, H. and Moller, H. M. and Neun, W.",
 title = "On Groebner Bases Computation on a Supercomputer Using REDUCE",
 paper = "Mele88.pdf",
 url = "https://opus4.kobv.de/opus4zib/files/10/SC8802.pdf",
+@article{Gome96,
+ author = "GomezDiaz, Theresa",
+ title = "Examples of using dynamic constructible closure",
+ journal = "Math. Comput. Simul.",
+ volume = "42",
+ number = "46",
+ pages = "375383",
+ year = "1996",
keywords = "axiomref",
 abstract =
 "Groebner bases are the main tool for solving systems of algebraic
 equations and some other problems in connection with polynomial ideals
 using Computer Algebra Systems. The procedure for the computation of
 Groebner bases in REDUCE 3.3 has been modified in order to solve more
 complicated algebraic systems of equations by some general
 improvements and by some tools based on the specific resources of the
 CRAY XMP. We present this modification and illustrate it by examples."
+ abstract =
+ "We present here some examples of using the ``Dynamic Constructible
+ Closure'' program, which performs automatic case distinctions in
+ computations involving parameters over a base field ``K''. This
+ program is an application of the ``Dynamic Evaluation'' principle
+ which generalizes tradional evaluation and was first used to deal with
+ algebraic numbers."
}
\end{chunk}
\index{Norman, Arthur C.}
+\index{Green, Edward L.}
\begin{chunk}{axiom.bib}
@misc{Normxx,
 author = "Norman, Arthur C.",
 title = "Notes 13: How to Compute a Groebner Basis",
 url = "http://people.math.umass.edu/~norman/462\_11/notes/m462notes13.pdf",
 paper = "Normxx.pdf",
 comment =
 "\newline\refto{package AFALGGRO AffineAlgebraicSetComputeWithGroebnerBasis}
 \newline\refto{package GBEUCLID EuclideanGroebnerBasisPackage}
 \newline\refto{package GBF GroebnerFactorizationPackage}
 \newline\refto{package GBINTERN GroebnerInternalPackage}
 \newline\refto{package GB GroebnerPackage}
 \newline\refto{package GROEBSOL GroebnerSolve}
 \newline\refto{package INTERGB InterfaceGroebnerPackage}
 \newline\refto{package LGROBP LinGroebnerPackage}
 \newline\refto{package PGROEB PolyGroebner}"
+@book{Gree01,
+ author = "Green, Edward L.",
+ title = "Symbolic Computation: Solving Equations in Algebra, Geometry, and
+ Engineering",
+ booktitle = "Proc. AMSIMSSIAM Joint Summer Research Conference on Symbolic
+ Computation",
+ volume = "232",
+ publisher = "American Mathematical Society",
+ year = "2001",
+ keywords = "axiomref",
+ abstract =
+ "This volume contains papers related to the research conference,
+ ``Symbolic Computation: Solving Equations in Algebra, Analysis, and
+ Engineering,'' held at Mount Holyoke College (MA). It provides a broad
+ range of active research areas in symbolic computation as it applies
+ to the solution of polynomial systems. The conference brought together
+ pure and applied mathematicians, computer scientists, and engineers,
+ who use symbolic computation to solve systems of equations or who
+ develop the theoretical background and tools needed for this
+ purpose. Within this general framework, the conference focused on
+ several themes: systems of polynomials, systems of differential
+ equations, noncommutative systems, and applications."
}
\end{chunk}
\index{Cox, David}
\index{Little, John}
\index{O'Shea, Donal}
+\index{Dragan, Laurentiu}
+\index{Watt, Stephen}
\begin{chunk}{axiom.bib}
@book{Coxx07,
 author = "Cox, David and Little, John and O'Shea, Donald",
 title = "Ideals, varieties and algorithms. An introduction to computational
 algebraic geometry and commutative algebra",
 publisher = "Springer",
 isbn = "9780387356501",
 year = "2007",
+@InProceedings{Drag10,
+ author = "Dragan, Laurentiu and Watt, Stephen",
+ title = "Type Specialization in Aldor",
+ booktitle = "Computer algebra in scientific computing",
+ series = "CASC 2010",
+ year = "2010",
+ location = "Tsakhadzor, Armenia",
+ pages = "7384",
keywords = "axiomref",
 url = "http://www.dm.unipi.it/~caboara/Misc/Cox,\%20Little,\%20O'Shea\%20\%20Ideals,\%20varieties\%20and%20algorithms.pdf",
 paper = "Coxx07.pdf",
 comment = "\newline\refto{package GB GroebnerPackage}
 \newline\refto{package PSEUDLIN PseudoLinearNormalForm}
 \newline\refto{package PGROEB PolyGroebner}
 \newline\refto{domain DMP DistributedMultivariatePolynomial}
 \newline\refto{domain GDMP GeneralDistributedMultivariatePolynomial}
 \newline\refto{domain HDMP HomogeneousDistributedMultivariatePolynomial}",
+ url = "http://www.csd.uwo.ca/~watt/pub/reprints/2010cascspecdom.pdf",
+ paper = "Drag10.pdf",
abstract =
 "Around 1980 two new directions in science and technique came
 together. One was Buchberger’s algorithms in order to handle Groebner
 bases in an effective way for solving polynomial equations. The second
 one was the development of the personal computers. This was the
 starting point of a computational perspective in commutative algebra
 and algebraic geometry. In 1991 the three authors invented the first
 edition of their book as an introduction for undergraduates to some
 interesting ideas in commutative algebra and algebraic geometry with a
 strong perspective to practical and computational aspects. A second
 revised edition appeared in 1996. That means from the very beginning
 the book provides a bridge for the new, computational aspects in the
 field of commutative algebra and algebraic geometry.

 To be more precise, the book gives an introduction to Buchberger’s
 algorithm with applications to syzygies, Hilbert polynomials, primary
 decompositions. There is an introduction to classical algebraic
 geometry with applications to the ideal membership problem, solving
 polynomial equations, and elimination theory. Some more spectacular
 applications are about robotics, automatic geometric theorem proving,
 and invariants of finite groups. It seems to the reviewer to carry
 coals to Newcastle for estimating the importance and usefulness of the
 book. It should be of some interest to ask how many undergraduates
 have been introduced to algorithmic aspects of commutative algebra and
 algebraic geometry following the line of the book. The reviewer will
 be sure that this will continue in the future too.

 What are the changes to the previous editions? There is a significant
 shorter proof of the Extension Theorem, see 3.6 in Chapter 3,
 suggested by A.H.M. Levelt. A major update has been done in Appendix C
 ``Computer Algebra Systems''. This concerns in the main the section
 about MAPLE. Some minor updated information concern the use of AXIOM,
 CoCoA, Macaulay2, Magma, Mathematica, and SINGULAR. This reflects
 about the recent developments in Computer Algebra Systems. It
 encourages an interested reader to more practical exercises. The
 authors have made changes on over 200 pages to enhance clarity and
 correctness. Many individuals have reported typographical errors and
 gave the authors feedback on the earlier editions. The book is
 wellwritten. The reviewer guesses that it will become more and more
 difficult to earn 1 dollar (sponsored by the authors) for every new
 typographical error as it was the case also with the first and second
 edition. The reviewer is sure that it will be a excellent guide to
 introduce further undergraduates in the algorithmic aspect of
 commutative algebra and algebraic geometry."
+ "Computer algebra in scientific computation squarely faces the dilemma
+ of natural mathematical expression versus efficiency. While
+ higherorder programming constructs and parametric polymorphism
+ provide a natural and expressive language for mathematical
+ abstractions, they can come at a considerable cost. We investigate how
+ deeply nested type constructions may be optimized to achieve
+ performance similar to that of handtuned code written in lowerlevel
+ languages."
}
\end{chunk}
\index{Gianni, Patrizia}
\index{Trager, Barry M.}
\index{Zacharias, Gail}
+\index{Delliere, Stephane}
+\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@article{Gian88,
 author = "Gianni, Patrizia. and Trager, Barry. and Zacharias, Gail",
 title = "Groebner Bases and Primary Decomposition of Polynomial Ideals",
+@techreport{Dell00,
+ author = "Delliere, Stephane and Wang, Dongming",
+ title = "simple systems and dynamic constructible closure",
+ institution = "Universite de Limoges",
+ year = "2000",
+ type = "technical report",
+ number = "200016",
+ paper = "Dell00.pdf",
+ url = "http://www.unilim.fr/laco/rapports/2000/R2000\_16.pdf",
+ keywords = "axiomref",
+ abstract =
+ "Dynamic evaluation is a general method for computing with parameters
+ [6, 9]. In 1994, T. GomezDiaz implemented the dynamic constructible
+ closure in the scientific computation system Axiom [17]: by simulating
+ dynamic evaluation, it offers the possibility to compute with
+ parameters in a very large way [13]. The outputs of a calculs with
+ T. GomezDiaz programs are represented by a finite collection of
+ constructible triangular systems defined in [12, definition
+ p.106]. Though there are numerous applications of these programs
+ (notably polynomial system solving with parameters [11], automatic
+ geometric theorem proving [14, 15], computation of Jordan forms with
+ parameters [16]), nobody gives theorical interest to this kind of
+ triangular systems. The main reason of this phenomenon is that they
+ are definied in [12] within the dynamic evaluation context. On the
+ opposite, most notions of triangular systems (J.F. RittW.T. Wu
+ characteristic sets [24, 28], M. Kalkbrener regular chains [18],
+ D. Lazard triangular sets [20], M. Moreno Maza regular sets [22],
+ D.M. Wang simple systems [26, 27]) are defined in terms of commutative
+ algebra. This problem is at the origin of the work done in [7] where
+ we give a relevant algebraic model of T. GomezDiaz systems within
+ commutative algebra terminology. This allows us to relate them to many
+ concepts of triangular systems [7]. Thus, we give interest to the
+ connections with D. Lazard triangular sets in [8]. In a way, this
+ paper is the continuation of this previous work. This time, we study
+ relationships between T. GomezDiaz systems and D.M. Wang simple
+ systems. The paper is structured as follows. We have collected in
+ section 2 some needed notations. In section 3, we give all the
+ terminology related to our algebraic model of T. GomezDiaz
+ systems. Thus, we define the notion of weak constructible triangular
+ systems and introduce the properties of normalization and
+ squarefreeness. Section 4 is more detailed. First of all, we study a
+ weaker form of normalization called $L$normalization. Then we give
+ many properties of constructible triangular systems verifying this new
+ notion. We obtain an algebraic and geometric framework which permits,
+ in section 5, to explore the connections between T. GomezDiaz systems
+ and D.M. Wang simple systems. In particular, this last section will
+ demonstrate well the importance of our $L$normalization
+ property. Indeed, we show that simple systems and squarefree
+ $L$normalized constructible triangular systems are equivalent."
+}
+
+\end{chunk}
+
+\index{Aubry, Phillippe}
+\begin{chunk}{axiom.bib}
+@phdthesis{Aubr99b,
+ author = "Aubry, Philippe",
+ title = "Ensembles triangulaires de polynomes et resolution de systemes
+ algebriques. Implantation en Axiom",
+ school = "l'Universite de Paris VI",
+ year = "1999",
+ month = "January",
+ paper = "Aubr99b.pdf",
+ comment = "French"
+}
+
+\end{chunk}
+
+\index{Duval, Dominique}
+\begin{chunk}{axiom.bib}
+@article{Duva94c,
+ author = "Duval, Dominique",
+ title = "Algebraic Numbers: An Example of Dynamic Evaluation",
journal = "J. Symbolic Computation",
 volume = "6",
 pages = "149167",
 year = "1988",
 url = "http://www.sciencedirect.com/science/article/pii/S0747717188800403/pdf?md5=40c29b67947035884904fd4597ddf710&pid=1s2.0S0747717188800403main.pdf",
 paper = "Gian88.pdf",
 comment = "\newline\refto{package IDECOMP IdealDecompositionPackage}"
+ volume = "18",
+ pages = "429445",
+ year = "1994",
+ url = "http://www.sciencedirect.com/science/article/pii/S0747717106000551",
+ paper = "Duva94c.pdf",
+ keywords = "axiomref",
+ abstract = "
+ Dynamic evaluation is presented through examples: computations
+ involving algebraic numbers, automatic case discussion according to
+ the characteristic of a field. Implementation questions are addressed
+ too. Finally, branches are presented as ``dual'' to binary functions,
+ according to the approach of sketch theory."
+}
+
+\end{chunk}
+
+\index{Hubert, Evelyne}
+\begin{chunk}{axiom.bib}
+@InProceedings{Hube03,
+ author = "Hubert, Evelyne",
+ title = "Notes on Triangular Sets and TriangulationDecomposition I:
+ Polynomial Systems",
+ booktitle = "Symbolic and Numerical Scientific Computing",
+ series = "Lecture Notes in Computer Science 2630",
+ year = "2003",
+ pages = "139",
+ keywords = "axiomref",
+ paper = "Hube03.pdf",
+ url = "http://www.cecm.sfu.ca/~rpearcea/sdmp/sdmp\_paper.pdf",
+ abstract =
+ "This is the first in a series of two tutorial articles devoted to
+ triangulation decomposition algorithms. The value of these notes
+ resides in the uniform presen tation of triangulationdecomposition
+ of polynomial and differential radical ideals with detailed proofs of
+ all the presented results.We emphasize the study of the mathematical
+ objects manipulated by the algorithms and show their properties in
+ independently of those. We also detail a selection of algorithms, one
+ for each task. We address here polynomial systems and some of the
+ material we develop here will be used in the second part, devoted to
+ differential systems."
+}
+
+\end{chunk}
+
+\index{Hubert, Evelyne}
+\begin{chunk}{axiom.bib}
+@InProceedings{Hube03a,
+ author = "Hubert, Evelyne",
+ title = "Notes on Triangular Sets and TriangulationDecomposition II:
+ Differential Systems",
+ booktitle = "Symbolic and Numerical Scientific Computing",
+ series = "Lecture Notes in Computer Science 2630",
+ year = "2003",
+ pages = "4087",
+ keywords = "axiomref",
+ paper = "Hube03a.pdf",
+ url =
+ "http://wwwsop.inria.fr/members/Evelyne.Hubert/publications/sncsd.pdf",
+ abstract =
+ "This is the second in a series of two tutorial articles devoted to
+ triangulationdecomposition algorithms. The value of these notes
+ resides in the uniform presentation of triangulationdecomposition of
+ polynomial and differential radical ideals with detailed proofs of all
+ the presented results.We emphasize the study of the mathematical
+ objects manipulated by the algorithms and show their properties
+ independently of those. We also detail a selection of algorithms, one
+ for each task. The present article deals with differential systems. It
+ uses results presented in the first article on polynomial systems but
+ can be read independently."
+}
+
+\end{chunk}
+
+\index{Philippe, M. Trebuchet}
+\begin{chunk}{axiom.bib}
+@phdthesis{Phil02,
+ author = "Philippe, M. Trebuchet",
+ title = "Toward a fast and numerically stable algebraic equation solving",
+ comment = "Vers une resolution stable et rapide des equations algebriques",
+ school = "l'Universite de Paris 6",
+ year = "2002",
+ month = "December",
+ paper = "Phil02.pdf",
+ abstract =
+ "Polynomial systems can be found in many industrial applications. They
+ are also in the heart of effective algebraic geometry. A fundamental
+ tool for studying them is the Groebner bases. The knowledge of this
+ paricular base of the ideal generated by the polynomials composing the
+ system allows us to compute in $A=K[x_1,\ldots,x_n]/I$, the quotient
+ algebra, and this is necessary when we try to solve. Nevertheless,
+ Groebner bases computations rely heavily on the introduction of
+ monomial ordering. This introduces a certain rigidity in the
+ computation and thus numerical instability. We propose a new algorithm
+ that tries to remedy that problem. It generalises Groebner bases
+ computation and is much less numerically instable. To do this, we
+ decrease the requirement of monomial ordering, and use a new normal
+ form criterion. We then give an algorithm and prove its termination
+ and correctness when the input polynomial system is
+ 0dimensional. After, we compare it with the previously known methods
+ and show how it can be seen as a generalisation of them. Next, we
+ detail how we implemented it in C++ using the Synaps library. We also
+ describe the sparse matrix elimination algorithm we used in or
+ program. Finally, we present some of the experiments we have done with
+ our program in domains like computer vision, algorithmic geometry,
+ robotics, or pharmacology."
+}
+
+\end{chunk}
+
+\index{Duval, Dominique}
+\begin{chunk}{axiom.bib}
+@article{Duva95,
+ author = "Duval, D.",
+ title = "Evaluation dynamique et cl\^oture alg\'ebrique en Axiom",
+ journal = "Journal of Pure and Applied Algebra",
+ volume = "99",
+ year = "1995",
+ pages = "267295.",
+ keywords = "axiomref",
+ abstract =
+ "Dynamic evaluation allows to compute with algebraic numbers without
+ factorizing polynomials. It also allows to manipulate parameters in a
+ flexible and userfriendly way. The aim of this paper is the
+ following: Explain what is dynamic evaluation, with its basic notions
+ of dynamic set and splitting. Present its application to computations
+ involving algebraic numbers, which amounts to defining the dynamic
+ algebraic closure of a field. Describe the Axiom program which
+ implements this, and give a user guide for it (only this last point
+ assumes some knowledge of Axiom) Dynamic evaluation is described here
+ without any reference to sketch theory, however our presentation, less
+ rigourous, may be considered as more accessible."
+}
+
+\end{chunk}
+
+\index{Montes, Antonio}
+\begin{chunk}{axiom.bib}
+@misc{Mont07,
+ author = "Montes, Antonio",
+ title = "On the canonical discussion of polynomial systems with parameters",
+ year = "2007",
+ url = "http://arxiv.org/pdf/math/0601674.pdf",
+ paper = "Mont07.pdf",
+ keywords = "axiomref",
+ abstract =
+ "Given a parametric polynomial ideal $I$, the algorithm DISPGB,
+ introduced by the author in 2002, builds up a binary tree describing a
+ dichotomic discussion of the different reduced Groebner bases
+ depending on the values of the parameters, whose set of terminal
+ vertices form a Comprehensive Groebner System (CGS). It is relevant
+ to obtain CGS’s having further properties in order to make them more
+ useful for the applications. In this paper the interest is focused on
+ obtaining a canonical CGS. We define the objective, show the
+ difficulties and formulate a natural conjecture. If the conjecture is
+ true then such a canonical CGS will exist and can be computed. We also
+ give an algorithm to transform our original CGS in this direction and
+ show its utility in applications."
}
\end{chunk}
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 73ba53f..2204973 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5434,6 +5434,8 @@ books/bookvol0 add backmatter quotes to Jenks book
books/axiom.bst Include new 'algebra' keyword for Spad refs
20160702.01.tpd.patch
books/bookvolbib Axiom Citations in the Literature
+20160702.02.tpd.patch
+books/bookvolbib Axiom Citations in the Literature

1.7.5.4