From 51f46b5e2a2a6eb1b73f635cecccac10f3d8d289 Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Wed, 6 Jul 2016 21:16:17 0400
Subject: [PATCH] books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
\index{Johnson, M.E.}
\index{Rogers, C.}
\index{Schief, W.K.}
\index{Seiler, W.M.}
\begin{chunk}{axiom.bib}
@article{John94,
author = "Johnson, M.E. and Rogers, C. and Schief, W.K. and Seiler, W.M.",
title = "On moving pseudospherical surfaces: a generalised Weingarten
system and its formal analysis",
journal = "Lie Groups Appl.",
volume = "1",
pages = "124136",
year = "1994",
keywords = "axiomref",
abstract =
"The connection between the motion of certain curves in $\mathbb{R}^3$
and $1+1$dimensional soliton equations is by now wellestablished. On the
other hand, the sineGordon and other integrable equations may be
readily derived via the classical geometry of stationary
pseudospherical surfaces. Here, the motion of pseudospherical surfaces
$S$ is considered in a natural orthonormal triad formulation. In one case,
in a motion in which the Gaussian curvature of $S$ remains constant in
time, an integrable nonlinear evolution equation is derived which has
its origin in the description of wave propagation in an anharmonic
crystal. In a second case, wherein the Gaussian curvature is allowed
to vary in time, a classical generalised Weingarten system is derived
in connection with the purely normal propagation of a pseudospherical
surface. This is linked to triply orthogonal coordinate systems of
Bianchi type. The generalised Weingarten system incorporates an
integrable $2+1$dimensional sineGordon equation. The arbitrariness of the
solutions of the generalised Weingarten system is determined via a
completion procedure."
}
\end{chunk}
\index{Kajler, Norbert}
\index{Soiffer, Neil}
\begin{chunk}{axiom.bib}
author = "Kajler, Norbert and Soiffer, Neil",
title = "Some human interaction issues in computer algebra",
journal = "SIGSAM Bulletin",
volume = "28",
number = "1",
pages = "1828",
year = "1994",
abstract =
"This paper addresses some of the current issues concerning the
improvement of user interfaces for computer algebra systems. Some
state of the art commercial software as well as research prototypes
are presented, followed by a description of present research
directions."
}
\end{chunk}
\index{Kripfganz, Jochen}
\index{Perlt, Holger}
\begin{chunk}{axiom.bib}
@misc{Krip94,
author = "Kripfganz, Jochen and Perlt, Holger",
title = "Working with Mathematica. An Introduction with examples",
comment = "Arbeiten mit Mathematica. Eine Einfuhrung mit Beispielen",
book = "Hander",
year = "1994",
keywords = "axiomref"
}
\end{chunk}
\index{Schwarz, Fritz}
\begin{chunk}{axiom.bib}
@InProceedings{Schw94,
author = "Schwarz, Fritz",
title = "Computer algebra software for scientific applications",
booktitle = "Computerized symbolic manipulation in mechanics",
year = "1994",
publisher = "SpringerVerlag",
pages = "67117",
series = "CISM Courses Lecture 343",
keywords = "axiomref",
abstract =
"The central subject of this article are two basic questions: How to
make the process of developing computer algebra software on a large
scale ($10^4 to $10^5$) lines of code or more) more efficient and
how to improve the quality of the result. Taking procedures from well
established engineering sciences as a guide, two fundamental
principles turned out to be of overwhelming importance: Modularization
and limitation of growth through reuse. Important means for achieving
these goals turned out to be concept of an abstract data type and the
principles of objectoriented design. It is advocated to install an
additional abstraction level between the mathematics and the machine
in order to render it possible to develop (computer algebra) system
independent mathematical software. Basic constituents of this level
are a type system and a highlevel language."
}
\end{chunk}
\index{Kajler, Norbert}
\begin{chunk}{axiom.bib}
@article{Kajl92,
author = "Kajler, Norbert",
title = "CAS/PI: a Portable and Extensible Interface for Computer
Algebra Systems",
year = "1992",
booktitle = "Proc. ISSAC 1992",
series = "ISSAC 1992",
pages = "376386",
isbn = "0897914899 (soft cover) 0897914902 (hard cover)",
keywords = "axiomref",
paper = "Kajl92.pdf",
abstract =
"CAS/$\pi$ is a Computer Algebra System graphic user interface
designed to be highly portable and extensible. It has been developed
by composition of preexisting software tools such as Maple, Sisyphe,
or Ulysse systems, ZicVis 3D plotting library, etc, using control
integration technology and a set of high level graphic toolkits to
build the formula editor and the dialog manager. The main aim of
CAS/$\pi$ is to allow a wide range of runtime recon gurations and
extensions. For instance, it is possible to add new tools to a running
system, to modify connections between working tools, to extend the set
of graphic symbols managed by the formula editor, to design new high
level editing commands based on the syntax or semantics of
mathematical formulas, to customize and extend the menubutton based
user interface, etc. More generally, CAS/$\pi$ can be seen equally as
a powerful systemindependent graphic user interface enabling
intersystems communications, a toolkit to allow fast development of
custommade scientific software environments, or a very convenient
framework for experimenting with computer algebra systems protocols
and manmachine interfaces."
}
\end{chunk}
\index{Schu, J.}
\index{Seiler, Werner Markus}
\index{Calmet, Jacques}
\begin{chunk}{axiom.bib}
@InProceedings{Schu92,
author = "Schu, J. and Seiler, Werner Markus and Calmet, Jacques",
title = "Algorithmic Methods For Lie Pseudogroups'",
booktitle = "Proc. Modern Group Analysis: Advanced Analytical and
Computational Methods in Mathematical Physics",
pages = "337344",
location = "Acireale (Italy)",
year = "1992",
publisher = "Kluwer",
url =
"http://www.iks.kti.edu/fileadmin/User/calmet/papers/Acireale93.ps.gz",
keywords = "axiomref"
}
\end{chunk}
\index{Seiler, Werner Markus}
\begin{chunk}{axiom.bib}
@article{Seil99,
author = "Seiler, Werner Markus",
title = "DETools: A Library for Differential Equations",
paper = "Seil99.pdf",
year = "1999",
keywords = "axiomref",
abstract =
"This article tries to give at least a brief introduction. The MuPAD
library is extended on two levels. The first one consists of a new
library detools containing a number of routines for treating
differential equations. This includes support for the graphical
presentation of the output of the numerical routines in MuPAD, some
methods for analysing or generating differential equations and also
routines for solving some classes of partial differential
equations. The use of this new library will be described in this
article. The second level is somewhat more advanced and requires a
certain familiarity with the objectoriented domains."
}
\end{chunk}
\index{Bradford, Russell}
\index{Davenport, James H.}
\index{England, Matthew}
\index{McCallum, Scott}
\index{Wilson, David}
\begin{chunk}{axiom.bib}
@misc{Brad15,
author = "Bradford, Russell and Davenport, James H. and England, Matthew and
McCallum, Scott",
title = "Truth Table Invariant Cylindrical Algebraic Decomposition",
url = "https://arxiv.org/pdf/1401.0645.pdf",
paper = "Brad15.pdf",
year = "2015",
abstract =
"When using cylindrical algebraic decomposition (CAD) to solve a
problem with respect to a set of polynomials, it is likely not the
signs of those polynomials that are of paramount importance but rather
the truth values of certain quantifier free formulae involving
them. This observation motivates our article and definition of a Truth
Table Invariant CAD (TTICAD). In ISSAC 2013 the current authors
presented an algorithm that can efficiently and directly construct a
TTICAD for a list of formulae in which each has an equational
constraint. This was achieved by generalising McCallum's theory of
reduced projection operators. In this paper we present an extended
version of our theory which can be applied to an arbitrary list of
formulae, achieving savings if at least one has an equational
constraint. We also explain how the theory of reduced projection
operators can allow for further improvements to the lifting phase of
CAD algorithms, even in the context of a single equational constraint.
The algorithm is implemented fully in Maple and we present both
promising results from experimentation and a complexity analysis
showing the benefits of our contributions."
}
\end{chunk}
\index{Bradford, Russell}
\index{Chen, Changbo}
\index{Davenport, James H.}
\index{England, Matthew}
\index{Maza, Marc Moreno}
\index{Wilson, David}
\begin{chunk}{axiom.bib}
@misc{Brad14,
author = "Bradford, Russell and Chen, Changbo and Davenport, James H. and
England, Matthew and Maza, Marc Moreno and Wilson, David",
title = "Truth Table Invariant Cylindrical Algebraic Decomposition by
Regular Chains",
url = "https://arxiv.org/pdf/1401.6310.pdf",
paper = "Brad14.pdf",
year = "2014",
abstract =
"A new algorithm to compute cylindrical algebraic decompositions
(CADs) is presented, building on two recent advances. Firstly, the
output is truth table invariant (a TTICAD) meaning given formulae have
constant truth value on each cell of the decomposition. Secondly, the
computation uses regular chains theory to first build a cylindrical
decomposition of complex space (CCD) incrementally by polynomial.
Significant modification of the regular chains technology wa s used to
achieve the more sophisticated invariance criteria. Experimental
results on an implementation in the {\tt RegularChains} Library for Maple
verify that combining these advances gives an algorithm superior to
its individual components and competitive with the state of the art."
}
\end{chunk}
\index{Wilson, David}
\index{Bradford, Russell}
\index{Davenport, James H.}
\index{England, Matthew}
\begin{chunk}{axiom.bib}
@misc{Wils14,
author = "Wilson, David and Bradford, Russell and Davenport, James H. and
England, Matthew",
title = "Cylindrical Algebraic SubDecompositions",
url = "https://arxiv.org/pdf/1401.0647.pdf",
paper = "Wils14.pdf",
year = "2014",
abstract =
"Cylindrical algebraic decompositions (CADs) are a key tool in real
algebraic geometry, used primarily for eliminating quantifiers over
the reals and studying semialgebraic sets. In this paper we
introduce cylindrical algebraic subdecompositions (subCADs), which
are subsets of CADs containing all the information needed to specify a
solution for a given problem. We define two new types of subCAD:
variety subCADs which are those cells in a CAD lying on a designated
variety; and layered subCADs which have only those cells of
dimension higher than a specified value. We present algorithms to
produce these and describe how the two approaches may be combined with
each other and the recent theory of truthtable invariant CAD. We
give a complexity analysis showing that these techniques can offer
substantial theoretical savings, which is supported by experimentation
using an implementation in Maple."
}
\end{chunk}
\index{England, Matthew}
\index{Wilson, David}
\index{Bradford, Russell}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@misc{Engl14,
author = "England, Matthew and Wilson, David and Bradford, Russell and
Davenport, James H.",
title = "Using the Regular Chains Library to build cylindrical algebraic
decompositions by projecting and lifting",
url = "https://arxiv.org/pdf/1405.6090.pdf",
paper = "Engl14.pdf",
year = "2014",
abstract =
"Cylindrical algebraic decomposition (CAD) is an important tool, both
for quantifier elimination over the reals and a range of other
applications. Traditionally, a CAD is built through a process of
projection and lifting to move the problem within Euclidean spaces of
changing dimension. Recently, an alternative approach which first
decomposes complex space using triangular decomposition before
refining to real space has been introduced and implemented within the
RegularChains Library of Maple. We here describe a freely available
package ProjectionCAD which utilises the routines within the
RegularChains Library to build CADs by projection and lifting. We
detail how the projection and lifting algorithms were modified to
allow this, discuss the motivation and survey the functionality of the
package."
}
\end{chunk}
\index{England, Matthew}
\index{Bradford, Russell}
\index{Davenport, James H.}
\index{Wilson, David}
\begin{chunk}{axiom.bib}
@misc{Engl14a,
author = "England, Matthew and Bradford, Russell and Davenport, James H. and
Wilson, David",
title = "Choosing a variable ordering for truthtable invariant cylindrical
algebraic decomposition by incremental triangular decomposition",
url = "https://arxiv.org/pdf/1405.6094.pdf",
paper = "Engl14a.pdf",
year = "2014",
abstract =
"Cylindrical algebraic decomposition (CAD) is a key tool for solving
problems in real algebraic geometry and beyond. In recent years a new
approach has been developed, where regular chains technology is used
to first build a decomposition in complex space. We consider the
latest variant of this which builds the complex decomposition
incrementally by polynomial and produces CADs on whose cells a
sequence of formulae are truthinvariant. Like all CAD algorithms the
user must provide a variable ordering which can have a profound impact
on the tractability of a problem. We evaluate existing heuristics to
help with the choice for this algorithm, suggest improvements and then
derive a new heuristic more closely aligned with the mechanics of the
new algorithm."
}
\end{chunk}
\index{England, Matthew}
\index{Bradford, Russell}
\index{Chen, Changbo}
\index{Davenport, James H.}
\index{Maza, Marc Moreno}
\index{Wilson, David}
\begin{chunk}{axiom.bib}
@misc{Engl14b,
author = "England, Matthew and Bradford, Russell and Chen, Changbo and
Davenport, James H. and Maza, Marc Moreno",
title = "Problem formulation for truthtable invariant cylindrical
algebraic decomposition by incremental triangular decomposition",
url = "https://arxiv.org/pdf/1404.6371.pdf",
paper = "Engl14b.pdf",
year = "2014",
abstract =
"Cylindrical algebraic decompositions (CADs) are a key tool for
solving problems in real algebraic geometry and beyond. We recently
presented a new CAD algorithm combining two advances: truthtable
invariance, making the CAD invariant with respect to the truth of
logical formulae rather than the signs of polynomials; and CAD
construction by regular chains technology, where first a complex
decomposition is constructed by refining a tree incrementally by
constraint. We here consider how best to formulate problems for input
to this algorithm. We focus on a choice (not relevant for other CAD
algorithms) about the order in which constraints are presented. We
develop new heuristics to help make this choice and thus allow the
best use of the algorithm in practice. We also consider other choices
of problem formulation for CAD, as discussed in CICM 2013, revisiting
these in the context of the new algorithm."
}
\end{chunk}
\index{Chen, Changbo}
\index{Maza, Marc Moreno}
\begin{chunk}{axiom.bib}
@misc{Chen12,
author = "Chen, Changbo and Maza, Marc Moreno",
title = "An Incremental Algorithm for Computing Cylindrical Algebraic
Decompositions",
url = "https://arxiv.org/pdf/1210.5543.pdf",
paper = "Chen12.pdf",
year = "2012",
abstract =
"In this paper, we propose an incremental algorithm for computing
cylindrical al gebraic decompositions. The algorithm consists of two
parts: computing a complex cylindrical tree and refining this complex
tree into a cylindrical tree in real space. The incrementality comes
from the first part of the algorithm, where a complex cylindrical tree
is constructed by refining a previous complex cylindrical tree with a
polynomial constraint. We have implemented our algorithm in Maple. The
experimentation shows that the proposed algorithm outperforms existing
ones for many examples taken from the literature"
}
\end{chunk}

books/bookvolbib.pamphlet  410 ++++++++++
changelog  2 +
patch  1608 +++++++++
src/axiomwebsite/patches.html  2 +
4 files changed, 724 insertions(+), 1298 deletions()
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 5ec7407..e39c1ba 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 9940,6 +9940,73 @@ J. Symbolic Computation 5, 237259 (1988)
\end{chunk}
+\index{Bradford, Russell}
+\index{Chen, Changbo}
+\index{Davenport, James H.}
+\index{England, Matthew}
+\index{Maza, Marc Moreno}
+\index{Wilson, David}
+\begin{chunk}{axiom.bib}
+@misc{Brad14,
+ author = "Bradford, Russell and Chen, Changbo and Davenport, James H. and
+ England, Matthew and Maza, Marc Moreno and Wilson, David",
+ title = "Truth Table Invariant Cylindrical Algebraic Decomposition by
+ Regular Chains",
+ url = "https://arxiv.org/pdf/1401.6310.pdf",
+ paper = "Brad14.pdf",
+ year = "2014",
+ abstract =
+ "A new algorithm to compute cylindrical algebraic decompositions
+ (CADs) is presented, building on two recent advances. Firstly, the
+ output is truth table invariant (a TTICAD) meaning given formulae have
+ constant truth value on each cell of the decomposition. Secondly, the
+ computation uses regular chains theory to first build a cylindrical
+ decomposition of complex space (CCD) incrementally by polynomial.
+ Significant modification of the regular chains technology wa s used to
+ achieve the more sophisticated invariance criteria. Experimental
+ results on an implementation in the {\tt RegularChains} Library for Maple
+ verify that combining these advances gives an algorithm superior to
+ its individual components and competitive with the state of the art."
+}
+
+\end{chunk}
+
+\index{Bradford, Russell}
+\index{Davenport, James H.}
+\index{England, Matthew}
+\index{McCallum, Scott}
+\index{Wilson, David}
+\begin{chunk}{axiom.bib}
+@misc{Brad15,
+ author = "Bradford, Russell and Davenport, James H. and England, Matthew and
+ McCallum, Scott",
+ title = "Truth Table Invariant Cylindrical Algebraic Decomposition",
+ url = "https://arxiv.org/pdf/1401.0645.pdf",
+ paper = "Brad15.pdf",
+ year = "2015",
+ abstract =
+ "When using cylindrical algebraic decomposition (CAD) to solve a
+ problem with respect to a set of polynomials, it is likely not the
+ signs of those polynomials that are of paramount importance but rather
+ the truth values of certain quantifier free formulae involving
+ them. This observation motivates our article and definition of a Truth
+ Table Invariant CAD (TTICAD). In ISSAC 2013 the current authors
+ presented an algorithm that can efficiently and directly construct a
+ TTICAD for a list of formulae in which each has an equational
+ constraint. This was achieved by generalising McCallum's theory of
+ reduced projection operators. In this paper we present an extended
+ version of our theory which can be applied to an arbitrary list of
+ formulae, achieving savings if at least one has an equational
+ constraint. We also explain how the theory of reduced projection
+ operators can allow for further improvements to the lifting phase of
+ CAD algorithms, even in the context of a single equational constraint.
+ The algorithm is implemented fully in Maple and we present both
+ promising results from experimentation and a complexity analysis
+ showing the benefits of our contributions."
+}
+
+\end{chunk}
+
\index{Brown, Christopher W.}
\begin{chunk}{axiom.bib}
@phdthesis{Brow99,
@@ 10024,12 +10091,15 @@ J. Symbolic Computation 5, 237259 (1988)
\end{chunk}
\index{Brown, Christopher W.}
\begin{chunk}{ignore}
\bibitem[Brown 02]{Brow02} Brown, Christopher W.
 title = "QEPCAD B  A program for computing with semialgebraic sets using CADs",
+\begin{chunk}{axiom.bib}
+@misc{Brow02,
+ author = "Brown, Christopher W.",
+ title = "QEPCAD B  A program for computing with semialgebraic sets
+ using CADs",
paper = "Brow02.pdf",
 abstract = "
 This report introduces QEPCAD B, a program for computing with real
+ year = "2002",
+ abstract =
+ "This report introduces QEPCAD B, a program for computing with real
algebraic sets using cylindrical algebraic decomposition (CAD). QEPCAD
B both extends and improves upon the QEPCAD system for quantifier
elimination by partial cylindrical algebraic decomposition written by
@@ 10040,6 +10110,31 @@ J. Symbolic Computation 5, 237259 (1988)
most of the extended features of QEPCAD B, but improvements to the
basic CAD implementation and to the SACLIB library on which QEPCAD is
based are the results of many people's work."
+}
+
+\end{chunk}
+
+\index{Chen, Changbo}
+\index{Maza, Marc Moreno}
+\begin{chunk}{axiom.bib}
+@misc{Chen12,
+ author = "Chen, Changbo and Maza, Marc Moreno",
+ title = "An Incremental Algorithm for Computing Cylindrical Algebraic
+ Decompositions",
+ url = "https://arxiv.org/pdf/1210.5543.pdf",
+ paper = "Chen12.pdf",
+ year = "2012",
+ abstract =
+ "In this paper, we propose an incremental algorithm for computing
+ cylindrical al gebraic decompositions. The algorithm consists of two
+ parts: computing a complex cylindrical tree and refining this complex
+ tree into a cylindrical tree in real space. The incrementality comes
+ from the first part of the algorithm, where a complex cylindrical tree
+ is constructed by refining a previous complex cylindrical tree with a
+ polynomial constraint. We have implemented our algorithm in Maple. The
+ experimentation shows that the proposed algorithm outperforms existing
+ ones for many examples taken from the literature"
+}
\end{chunk}
@@ 10087,6 +10182,101 @@ J. Symbolic Computation 5, 237259 (1988)
\end{chunk}
\index{England, Matthew}
+\index{Wilson, David}
+\index{Bradford, Russell}
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@misc{Engl14,
+ author = "England, Matthew and Wilson, David and Bradford, Russell and
+ Davenport, James H.",
+ title = "Using the Regular Chains Library to build cylindrical algebraic
+ decompositions by projecting and lifting",
+ url = "https://arxiv.org/pdf/1405.6090.pdf",
+ paper = "Engl14.pdf",
+ year = "2014",
+ abstract =
+ "Cylindrical algebraic decomposition (CAD) is an important tool, both
+ for quantifier elimination over the reals and a range of other
+ applications. Traditionally, a CAD is built through a process of
+ projection and lifting to move the problem within Euclidean spaces of
+ changing dimension. Recently, an alternative approach which first
+ decomposes complex space using triangular decomposition before
+ refining to real space has been introduced and implemented within the
+ RegularChains Library of Maple. We here describe a freely available
+ package ProjectionCAD which utilises the routines within the
+ RegularChains Library to build CADs by projection and lifting. We
+ detail how the projection and lifting algorithms were modified to
+ allow this, discuss the motivation and survey the functionality of the
+ package."
+}
+
+\end{chunk}
+
+\index{England, Matthew}
+\index{Bradford, Russell}
+\index{Davenport, James H.}
+\index{Wilson, David}
+\begin{chunk}{axiom.bib}
+@misc{Engl14a,
+ author = "England, Matthew and Bradford, Russell and Davenport, James H. and
+ Wilson, David",
+ title = "Choosing a variable ordering for truthtable invariant cylindrical
+ algebraic decomposition by incremental triangular decomposition",
+ url = "https://arxiv.org/pdf/1405.6094.pdf",
+ paper = "Engl14a.pdf",
+ year = "2014",
+ abstract =
+ "Cylindrical algebraic decomposition (CAD) is a key tool for solving
+ problems in real algebraic geometry and beyond. In recent years a new
+ approach has been developed, where regular chains technology is used
+ to first build a decomposition in complex space. We consider the
+ latest variant of this which builds the complex decomposition
+ incrementally by polynomial and produces CADs on whose cells a
+ sequence of formulae are truthinvariant. Like all CAD algorithms the
+ user must provide a variable ordering which can have a profound impact
+ on the tractability of a problem. We evaluate existing heuristics to
+ help with the choice for this algorithm, suggest improvements and then
+ derive a new heuristic more closely aligned with the mechanics of the
+ new algorithm."
+}
+
+\end{chunk}
+
+\index{England, Matthew}
+\index{Bradford, Russell}
+\index{Chen, Changbo}
+\index{Davenport, James H.}
+\index{Maza, Marc Moreno}
+\index{Wilson, David}
+\begin{chunk}{axiom.bib}
+@misc{Engl14b,
+ author = "England, Matthew and Bradford, Russell and Chen, Changbo and
+ Davenport, James H. and Maza, Marc Moreno",
+ title = "Problem formulation for truthtable invariant cylindrical
+ algebraic decomposition by incremental triangular decomposition",
+ url = "https://arxiv.org/pdf/1404.6371.pdf",
+ paper = "Engl14b.pdf",
+ year = "2014",
+ abstract =
+ "Cylindrical algebraic decompositions (CADs) are a key tool for
+ solving problems in real algebraic geometry and beyond. We recently
+ presented a new CAD algorithm combining two advances: truthtable
+ invariance, making the CAD invariant with respect to the truth of
+ logical formulae rather than the signs of polynomials; and CAD
+ construction by regular chains technology, where first a complex
+ decomposition is constructed by refining a tree incrementally by
+ constraint. We here consider how best to formulate problems for input
+ to this algorithm. We focus on a choice (not relevant for other CAD
+ algorithms) about the order in which constraints are presented. We
+ develop new heuristics to help make this choice and thus allow the
+ best use of the algorithm in practice. We also consider other choices
+ of problem formulation for CAD, as discussed in CICM 2013, revisiting
+ these in the context of the new algorithm."
+}
+
+\end{chunk}
+
+\index{England, Matthew}
\index{Bradford, Russell}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@@ 10200,6 +10390,37 @@ J. Symbolic Computation 5, 237259 (1988)
\end{chunk}
+\index{Wilson, David}
+\index{Bradford, Russell}
+\index{Davenport, James H.}
+\index{England, Matthew}
+\begin{chunk}{axiom.bib}
+@misc{Wils14,
+ author = "Wilson, David and Bradford, Russell and Davenport, James H. and
+ England, Matthew",
+ title = "Cylindrical Algebraic SubDecompositions",
+ url = "https://arxiv.org/pdf/1401.0647.pdf",
+ paper = "Wils14.pdf",
+ year = "2014",
+ abstract =
+ "Cylindrical algebraic decompositions (CADs) are a key tool in real
+ algebraic geometry, used primarily for eliminating quantifiers over
+ the reals and studying semialgebraic sets. In this paper we
+ introduce cylindrical algebraic subdecompositions (subCADs), which
+ are subsets of CADs containing all the information needed to specify a
+ solution for a given problem. We define two new types of subCAD:
+ variety subCADs which are those cells in a CAD lying on a designated
+ variety; and layered subCADs which have only those cells of
+ dimension higher than a specified value. We present algorithms to
+ produce these and describe how the two approaches may be combined with
+ each other and the recent theory of truthtable invariant CAD. We
+ give a complexity analysis showing that these techniques can offer
+ substantial theoretical savings, which is supported by experimentation
+ using an implementation in Maple."
+}
+
+\end{chunk}
+
\section{Comparison of Computer Algebra System} %%%%%%%%%%%%%%%%%%%%%%
\index{Bernardin, Laurent}
@@ 17000,6 +17221,42 @@ Draft September 5, 1988
\end{chunk}
+\index{Johnson, M.E.}
+\index{Rogers, C.}
+\index{Schief, W.K.}
+\index{Seiler, Werner Markus}
+\begin{chunk}{axiom.bib}
+@article{John94,
+ author = "Johnson, M.E. and Rogers, C. and Schief, W.K. and Seiler, W.M.",
+ title = "On moving pseudospherical surfaces: a generalised Weingarten
+ system and its formal analysis",
+ journal = "Lie Groups Appl.",
+ volume = "1",
+ pages = "124136",
+ year = "1994",
+ keywords = "axiomref",
+ abstract =
+ "The connection between the motion of certain curves in $\mathbb{R}^3$
+ and $1+1$dimensional soliton equations is by now wellestablished. On the
+ other hand, the sineGordon and other integrable equations may be
+ readily derived via the classical geometry of stationary
+ pseudospherical surfaces. Here, the motion of pseudospherical surfaces
+ $S$ is considered in a natural orthonormal triad formulation. In one case,
+ in a motion in which the Gaussian curvature of $S$ remains constant in
+ time, an integrable nonlinear evolution equation is derived which has
+ its origin in the description of wave propagation in an anharmonic
+ crystal. In a second case, wherein the Gaussian curvature is allowed
+ to vary in time, a classical generalised Weingarten system is derived
+ in connection with the purely normal propagation of a pseudospherical
+ surface. This is linked to triply orthogonal coordinate systems of
+ Bianchi type. The generalised Weingarten system incorporates an
+ integrable $2+1$dimensional sineGordon equation. The arbitrariness of the
+ solutions of the generalised Weingarten system is determined via a
+ completion procedure."
+}
+
+\end{chunk}
+
\index{Joswig, Rainer}
\begin{chunk}{ignore}
\bibitem[Rainer 14]{Rain14} Joswig, Rainer
@@ 17103,6 +17360,7 @@ SIGSAM Communications in Computer Algebra, 157 2006
\index{Kajler, Norbert}
\begin{chunk}{axiom.bib}
+@article{Kajl92,
author = "Kajler, Norbert",
title = "CAS/PI: a Portable and Extensible Interface for Computer
Algebra Systems",
@@ 17111,7 +17369,49 @@ SIGSAM Communications in Computer Algebra, 157 2006
series = "ISSAC 1992",
pages = "376386",
isbn = "0897914899 (soft cover) 0897914902 (hard cover)",
 keywords = "axiomref"
+ keywords = "axiomref",
+ paper = "Kajl92.pdf",
+ abstract =
+ "CAS/$\pi$ is a Computer Algebra System graphic user interface
+ designed to be highly portable and extensible. It has been developed
+ by composition of preexisting software tools such as Maple, Sisyphe,
+ or Ulysse systems, ZicVis 3D plotting library, etc, using control
+ integration technology and a set of high level graphic toolkits to
+ build the formula editor and the dialog manager. The main aim of
+ CAS/$\pi$ is to allow a wide range of runtime recon gurations and
+ extensions. For instance, it is possible to add new tools to a running
+ system, to modify connections between working tools, to extend the set
+ of graphic symbols managed by the formula editor, to design new high
+ level editing commands based on the syntax or semantics of
+ mathematical formulas, to customize and extend the menubutton based
+ user interface, etc. More generally, CAS/$\pi$ can be seen equally as
+ a powerful systemindependent graphic user interface enabling
+ intersystems communications, a toolkit to allow fast development of
+ custommade scientific software environments, or a very convenient
+ framework for experimenting with computer algebra systems protocols
+ and manmachine interfaces."
+}
+
+\end{chunk}
+
+\index{Kajler, Norbert}
+\index{Soiffer, Neil}
+\begin{chunk}{axiom.bib}
+@article{Kajl94,
+ author = "Kajler, Norbert and Soiffer, Neil",
+ title = "Some human interaction issues in computer algebra",
+ journal = "SIGSAM Bulletin",
+ volume = "28",
+ number = "1",
+ pages = "1828",
+ year = "1994",
+ keywords = "axiomref",
+ abstract =
+ "This paper addresses some of the current issues concerning the
+ improvement of user interfaces for computer algebra systems. Some
+ state of the art commercial software as well as research prototypes
+ are presented, followed by a description of present research
+ directions."
}
\end{chunk}
@@ 17615,6 +17915,20 @@ ISSN 03043975
\end{chunk}
+\index{Kripfganz, Jochen}
+\index{Perlt, Holger}
+\begin{chunk}{axiom.bib}
+@misc{Krip94,
+ author = "Kripfganz, Jochen and Perlt, Holger",
+ title = "Working with Mathematica. An Introduction with examples",
+ comment = "Arbeiten mit Mathematica. Eine Einfuhrung mit Beispielen",
+ book = "Hander",
+ year = "1994",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
\index{Kumar, P.}
\index{Pellegrino, S.}
\begin{chunk}{axiom.bib}
@@ 17860,7 +18174,7 @@ CODEN JSYCEH ISSN 07477171
\end{chunk}
\index{Lambe, Larry A.}
\index{Seiler, Werner M.}
+\index{Seiler, Werner Markus}
\begin{chunk}{axiom.bib}
@article{Lamb02,
author = "Lambe, Larry A. and Seiler, Werner M.",
@@ 19833,6 +20147,16 @@ In ACM [ACM89], pp1725 ISBN 0897913256 LCCN QA76.95.I59 1989
\end{chunk}
\index{Schwarz, Fritz}
+\begin{chunk}{ignore}
+\bibitem[Schwarz 91]{Sch91} Schwarz, F.
+ title = "Monomial orderings and Gr{\"o}bner bases",
+SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic
+Manipulation) 2591) pp1023 Jan. 1991 CODEN SIGSBZ ISSN 01635824
+ keywords = "axiomref",
+
+\end{chunk}
+
+\index{Schwarz, Fritz}
\begin{chunk}{axiom.bib}
@InProceedings{Schw02,
author = "Schwarz, Fritz",
@@ 19866,12 +20190,31 @@ In ACM [ACM89], pp1725 ISBN 0897913256 LCCN QA76.95.I59 1989
\end{chunk}
\index{Schwarz, Fritz}
\begin{chunk}{ignore}
\bibitem[Schwarz 91]{Sch91} Schwarz, F.
 title = "Monomial orderings and Gr{\"o}bner bases",
SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic
Manipulation) 2591) pp1023 Jan. 1991 CODEN SIGSBZ ISSN 01635824
+\begin{chunk}{axiom.bib}
+@InProceedings{Schw94,
+ author = "Schwarz, Fritz",
+ title = "Computer algebra software for scientific applications",
+ booktitle = "Computerized symbolic manipulation in mechanics",
+ year = "1994",
+ publisher = "SpringerVerlag",
+ pages = "67117",
+ series = "CISM Courses Lecture 343",
keywords = "axiomref",
+ abstract =
+ "The central subject of this article are two basic questions: How to
+ make the process of developing computer algebra software on a large
+ scale ($10^4 to $10^5$) lines of code or more) more efficient and
+ how to improve the quality of the result. Taking procedures from well
+ established engineering sciences as a guide, two fundamental
+ principles turned out to be of overwhelming importance: Modularization
+ and limitation of growth through reuse. Important means for achieving
+ these goals turned out to be concept of an abstract data type and the
+ principles of objectoriented design. It is advocated to install an
+ additional abstraction level between the mathematics and the machine
+ in order to render it possible to develop (computer algebra) system
+ independent mathematical software. Basic constituents of this level
+ are a type system and a highlevel language."
+}
\end{chunk}
@@ 19999,11 +20342,25 @@ in Calmet [Cal94] pp103104
\end{chunk}
\index{Seiler, Werner Markus}
\begin{chunk}{ignore}
\bibitem[Seiler (a)]{Seixx} Seiler, W.M.
+\begin{chunk}{axiom.bib}
+@article{Seil99,
+ author = "Seiler, Werner Markus",
title = "DETools: A Library for Differential Equations",
 url = "http://iakswww.ira.uka.de/iakscalmet/werner/werner.html",
+ paper = "Seil99.pdf",
+ year = "1999",
keywords = "axiomref",
+ abstract =
+ "This article tries to give at least a brief introduction. The MuPAD
+ library is extended on two levels. The first one consists of a new
+ library detools containing a number of routines for treating
+ differential equations. This includes support for the graphical
+ presentation of the output of the numerical routines in MuPAD, some
+ methods for analysing or generating differential equations and also
+ routines for solving some classes of partial differential
+ equations. The use of this new library will be described in this
+ article. The second level is somewhat more advanced and requires a
+ certain familiarity with the objectoriented domains."
+}
\end{chunk}
@@ 20165,14 +20522,23 @@ LCCN QA76.76.A65 S95 1992
\end{chunk}
\begin{chunk}{ignore}
\bibitem[SSC92]{SSC92}.
+\index{Schu, J.}
+\index{Seiler, Werner Markus}
+\index{Calmet, Jacques}
+\begin{chunk}{axiom.bib}
+@InProceedings{Schu92,
+ author = "Schu, J. and Seiler, Werner Markus and Calmet, Jacques",
title = "Algorithmic Methods For Lie Pseudogroups'",
In N. Ibragimov, M. Torrisi and A. Valenti, editors, Proc. Modern Group
Analysis: Advanced Analytical and Computational Methods in Mathematical
Physics, pp337344, Acireale (Italy), 1992 Kluwer, Dordrecht 1993
 url = "http://iakswww.ira.uka.de/iakscalmet/werner/Papers/Acireale92.ps.gz",
 keywords = "axiomref",
+ booktitle = "Proc. Modern Group Analysis: Advanced Analytical and
+ Computational Methods in Mathematical Physics",
+ pages = "337344",
+ location = "Acireale (Italy)",
+ year = "1992",
+ publisher = "Kluwer",
+ url =
+ "http://www.iks.kti.edu/fileadmin/User/calmet/papers/Acireale93.ps.gz",
+ keywords = "axiomref"
+}
\end{chunk}
diff git a/changelog b/changelog
index e7fa296..5107e24 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,5 @@
+20160704 tpd src/axiomwebsite/patches.html 20160706.01.tpd.patch
+20160705 tpd books/bookvolbib Axiom Citations in the Literature
20160704 tpd src/axiomwebsite/patches.html 20160705.01.tpd.patch
20160705 tpd books/bookvolbib Axiom Citations in the Literature
20160704 tpd src/axiomwebsite/patches.html 20160704.04.tpd.patch
diff git a/patch b/patch
index f339a05..6639aab 100644
 a/patch
+++ b/patch
@@ 2,1341 +2,397 @@ books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
\index{Schwardmann, Ulrich}
\begin{chunk}{axiom.bib}
@book{Schw95,
 author = "Schwardmann, Ulrich",
 title = "Computer algebra systems",
 comment = "ComputeralgebraSysteme, German",
 publisher = "AddisonWesley",
 year = "1995",
 keywords = "axiomref"
}

\end{chunk}

\index{Storme, L.}
\index{van Maldeghem, H.}
\begin{chunk}{axiom.bib}
@article{Stor95,
 author = "Storme, L. and van Maldeghem, H.",
 title = "Cyclic caps in PG(3,q)",
 journal = "Geom. Dedicata",
 volume = "56",
 number = "3",
 pages = "271284",
 year = "1995",
 keywords = "axiomref",
 url = "https://cage.ugent.be/~hvm/artikels/44.pdf",
 paper = "Stor95.pdf",
 abstract =
 "A $k$cap $K$ on $PG(n,q)$ is a set of $k$ points, no three of which
 are collinear. $K$ is complete if it cannot be extended to a $k+1$
 cap. If $K$ is invariant under a cyclic subgroup (which acts regularly
 on $K$) of $PGL(n+1,q)$, the $K$ is cyclic.

 This article investigates cyclic complete $k$caps in
 $PG(3,q). Namely, the different types of complete $k$caps $K$ in
 $PG(3,q)$ stabilized by a cyclic projective group $G$ of order $k$,
 acting regularly on the points of $K$, are determined. We show that in
 $PG(3,q)$, $q$ even, the elliptic quadric is the only cyclic complete
 $k$cap. For $q$ odd, it is shown that besides the elliptic quadric,
 there also exist cyclic $k$caps containing $k/2$ points of two
 disjoint elliptic quadrics or two disjoint hyperbolic quadrics and
 that there exist cyclic $k$caps stabilized by a transitive cyclic
 group $G$ fixed precisely one point and one plane of
 $PG(3,q)$. Concrete examples of such caps, found using AXIOM and
 CAYLEY, are presented."
}

\end{chunk}

\index{Weber, Andreas}
\begin{chunk}{axiom.bib}
@article{Webe95,
 author = "Weber, Andreas",
 title = "On coherence in computer algebra",
 journal = "J. Symb. Comput.",
 volume = "19",
 number = "13",
 pages = "2538",
 year = "1995",
 url =
"http://cg.cs.unibonn.de/personalpages/weber/publications/pdf/WeberA/Weber94e.pdf",
 paper = "Webe95.pdf",
 keywords = "axiomref",
 abstract = "
 Modern computer algebra systems (e.g. AXIOM) support a rich type
 system including parameterized data types and the possibility of
 implicit coercions between types. In such a type system it will be
 frequently the case that there are different ways of building
 coercions between types. An important requirement is that all
 coercions between two types coincide, a property which is called {\sl
 coherence}. We will prove a coherence theorem for a formal type system
 having several possibilities of coercions covering many important
 examples. Moreover, we will give some informal reasoning why the
 formally defined restrictions can be satisfied by an actual system."
}

\end{chunk}

\index{Williamson, Clifton J.}
\begin{chunk}{axiom.bib}
@InProceedings{Will95,
 author = "Williamson, Clifton J.",
 title = "On the algebraic construction of tridiagonal matrices with given
 characteristic polynomial",
 booktitle = "4th Conf. of Canadian Number Theory Association",
 year = "1995",
 location = "Halifax, Nova Scotia, Canada",
 pages = "417431",
 keywords = "axiomref",
 paper = "Will95.pdf",
 abstract =
 "Let $K$ be a field of characteristic zero and assume
 \[f(x)=x^ns_1x^{n1}+\cdots+s_n \in L[x]\]
 where $L=K(s_1,\cdots,s_n)$. Call, for the purposes of this review, an
 $n\times n$ matrix 1tridiagonal if its entries above and below the
 main diagonal are all 1, the entries on it are $d_1,\cdots,d_n$, and
 all other entries are 0. Under which conditions can
 $d_1,d_2,\cdots,d_n$ be chosen in a radical extension of $L$ such that
 the resulting 1tridiagonal matrix has $f$ as its characteristic
 polynomial? The author’s answer: for $n=3$ always. The $d_i,s_i$
 are related by a system of algebraic equations of the form
 $\overline{f}_i(d_1,d_2,d_3)=s_i$. If this is satisfied, then by
 a resultant or Groebner basis computation with respect to the
 lexicographic order, $d_3$ (say) must be a root of a certain
 irreducible polynomial $\varphi$ of degree 6. Joining this
 with a Galois group computation for $\varphi$ over $L$, it is shown
 that a solvable and necessarily transitive Gal($\varphi$) will be a
 necessary and sufficient condition for expressibility of $d_3$ (clear)
 and, thanks to the form of the Groebner basis, also of $d_1,d_2$ in
 radicals. Upon a discriminant computation of $\varphi$ and use of
 results of G. Butler and J. McKay [Commun. Algebra 11,
 863911 (1983; Zbl 0518.20003)] and J. McKay and L. Soicher [J. Number
 Theory 20, 273281 (1985; Zbl 0579.12006)], this allows the author to
 deduce the mentioned result. For $n=4$, though the author cannot get as
 complete information about Galois groups etc., he can deduce e.g. that
 if $s_1,\cdots,s_4$ are algebraically independent over $\mathbb{Q}$,
 then $d_1,\cdots,d_4$ are not expressible in radicals over
 $\mathbb{Q}(s_1,\cdots,s_4)$. He mentions, however, a solvable subcase."
}

\end{chunk}

\index{Bosma, Wieb}
\index{Cannon, John}
\index{Matthews, Graham}
\begin{chunk}{axiom.bib}
@InProceedings{Bosm94,
 author = "Bosma, Wieb and Cannon, John and Matthews, Graham",
 title = "Programming with algebraic structures: Design of the Magma
 language",
 booktitle = "Proc. ISSAC 94",
 series = "ISSAC 94",
+\index{Johnson, M.E.}
+\index{Rogers, C.}
+\index{Schief, W.K.}
+\index{Seiler, W.M.}
+\begin{chunk}{axiom.bib}
+@article{John94,
+ author = "Johnson, M.E. and Rogers, C. and Schief, W.K. and Seiler, W.M.",
+ title = "On moving pseudospherical surfaces: a generalised Weingarten
+ system and its formal analysis",
+ journal = "Lie Groups Appl.",
+ volume = "1",
+ pages = "124136",
year = "1994",
 publisher = "ACM Press",
 location = "Baltimore, MD",
 pages = "5257",
keywords = "axiomref",
 paper = "Bosm94.pdf",
 url = "http://www.math.ru.nl/~bosma/pubs/ISSAC94.pdf",
abstract =
 "MAGMA is a new software system for computational algebra, number
 theory and geometry whose design is centred on the concept of
 algebraic structure (magma). The use of algebraic structure as a
 design paradigm provides a natural strong typing mechanism. Further,
 structures and their morphisms appear in the language as first class
 objects. Standard mathematical notions are used for the basic data
 types. The result is a powerful, clean language which deals with
 objects in a mathematically rigorous manner. The conceptual and
 implementation ideas behind MAGMA will be examined in this paper. This
 conceptual base differs significantly from those underlying other
 computer algebra systems."
}

\end{chunk}

\index{Dingle, Adam}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@InProceedings{Ding94,
 author = "Dingle, Adam and Fateman, Richard",
 title = "Branch Cuts in Computer Algebra",
 year = "1994",
 booktitle = "Proc. ISSAC 1994",
 series = "ISSAC 94",
 url = "http://www.cs.berkeley.edu/~fateman/papers/ding.ps",
 paper = "Ding94.pdf",
 keywords = "axiomref",
 abstract =
 "Many standard functions, such as the logarithms and square root
 functions, cannot be defined continuously on the complex
 plane. Mistaken assumptions about the properties of these functions
 lead computer algebra systems into various conundrums. We discuss how
 they can manipulate such functions in a useful fashion."
}

\end{chunk}

\index{Duval, Dominique}
\index{Senechaud, Pascale}
\begin{chunk}{axiom.bib}
@article{Duva94d,
 author = "Duval, Dominique and Senechaud, Pascale",
 title = "Sketches and parametrization",
 journal = "Theor. Comput. Sci.",
 volume = "123",
+ "The connection between the motion of certain curves in $\mathbb{R}^3$
+ and $1+1$dimensional soliton equations is by now wellestablished. On the
+ other hand, the sineGordon and other integrable equations may be
+ readily derived via the classical geometry of stationary
+ pseudospherical surfaces. Here, the motion of pseudospherical surfaces
+ $S$ is considered in a natural orthonormal triad formulation. In one case,
+ in a motion in which the Gaussian curvature of $S$ remains constant in
+ time, an integrable nonlinear evolution equation is derived which has
+ its origin in the description of wave propagation in an anharmonic
+ crystal. In a second case, wherein the Gaussian curvature is allowed
+ to vary in time, a classical generalised Weingarten system is derived
+ in connection with the purely normal propagation of a pseudospherical
+ surface. This is linked to triply orthogonal coordinate systems of
+ Bianchi type. The generalised Weingarten system incorporates an
+ integrable $2+1$dimensional sineGordon equation. The arbitrariness of the
+ solutions of the generalised Weingarten system is determined via a
+ completion procedure."
+}
+
+\end{chunk}
+
+\index{Kajler, Norbert}
+\index{Soiffer, Neil}
+\begin{chunk}{axiom.bib}
+ author = "Kajler, Norbert and Soiffer, Neil",
+ title = "Some human interaction issues in computer algebra",
+ journal = "SIGSAM Bulletin",
+ volume = "28",
number = "1",
 pages = "117130",
 year = "1994",
 keywords = "axiomref",
 abstract =
 "The paper deals with problems about conception and design of
 highlevel computer algebra systems. Here we use a categorical
 approach given by the notion of sketches. Sketches allow to describe
 computation mechanisms in a syntactic way, well adapted to
 implementation.

 A computer algebra system must allow the manipulation of algebraic
 structures, in particular, the construction of new structures from
 known ones. In the paper we give a definition, at the sketch level, of
 parametrization of a structure by another one."
}

\end{chunk}

\index{Duval, Dominique}
\begin{chunk}{axiom.bib}
@misc{Duva94e,
 author = "Duval, Dominique",
 title = "Symbolic or algebraic computation?",
 booktitle = "Publication du LACO",
 year = "1995",
 location = "Madrid Spain",
 comment = "NAG conference",
 keywords = "axiomref"
}

\end{chunk}

\index{Duval, Dominique}
\index{Reynaud, J.C.}
\begin{chunk}{axiom.bib}
@article{Duva94a,
 author = "Duval, D. and Reynaud, J.C.",
 title = "Sketches and Computation (Part I):
 Basic Definitions and Static Evaluation",
 journal = "Mathematical Structures in Computer Science",
 volume = "4",
 pages = "185238",
 publisher = "Cambridge University Press",
 year = "1994",
 url = "http://journals.cambridge.org/abstract_S0960129500000438",
 paper = "Duva94a.pdf",
 abstract =
 "We define a categorical framework, based on the notion of {\sl
 sketch}, for specification and evaluation in the sense of algebraic
 specifications and algebraic programming. This framework goes far
 beyond our initial motivations, which was to specify computation with
 algebraic numbers. We begin by redefining sketches in order to deal
 explicitly with programs. Expressions and terms are carefully defined
 and studied, then {\sl quasiprojective sketches} are introduced. We
 describe {\sl static evaluation} in these sketches: we propose a
 rigorous basis for evaluation in the corresponding structures. These
 structures admit an initial model, but are not necessarily
 equational. In Part II (Duval and Reynaud 1994), we study a more
 general process, called {\sl dynamic evaluation}, for structures that
 may have no initial model."
}

\end{chunk}

\index{Duval, Dominique}
\index{Reynaud, JeanClaude}
\begin{chunk}{axiom.bib}
@article{Duva94b,
 author = "Duval, Dominique and Reynaud, JeanClaude",
 title = "Sketches and Computation (Part II):
 Dynamic Evaluation and Applications",
 journal = "Mathematical Structures in Computer Science",
 volume = "4",
 pages = "239271",
 publisher = "Cambridge University Press",
 year = "1994",
 url = "http://journals.cambridge.org/abstract_S096012950000044X",
 paper = "Duva94b.pdf",
 abstract =
 "In the first part of this paper (Duval and Reynaud 1994), we defined a
 categorical framework, based on the notion of {\sl sketch}, for
 specification and evaluation in the senses of algebraic specification
 and algebraic programming. {\sl Static evaluation} in {\sl
 quasiprojective sketches} was defined in Part I; in this paper, {\sl
 dynamic evaluation} is introduced. It deals with more general
 structures, which may have no initial model. Until now, this process
 has not been used in algebraic specification systems, but computer
 algebra systems are beginning to use it as a basic tool. Finally, we
 give some applications of dynamic evaluation to computation in field
 extensions."
}

\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{Duval, Dominique}
\index{Reynaud, JeanClaude}
\begin{chunk}{axiom.bib}
@article{Duva96,
 author = "Duval, D. and Reynaud, JeanClaude",
 title = "Sketches and Computations over Fields",
 journal = "Mathematics and Computers in Simulation",
 volume = "42",
 pages = "363373",
 year = "1996",
 paper = "Duva96.pdf",
 abstract =
 "The goal of this short paper is to describe one possible use of
 sketches in computer algebra. We show that sketches are a powerful
 tool for the description of mathematical structures and for the
 description of computations."
}

\end{chunk}

\index{Duval, Dominique}
\index{Gonz\'alezVega, L.}
\begin{chunk}{axiom.bib}
@article{Duva96a,
 author = {Duval, Dominique and Gonz\'alezVega, L.},
 title = "Dynamic Evaluation and Real Closure",
 journal = "Mathematics and Computers in Simulation",
 volume = "42",
 pages = "551560",
 year = "1996",
 paper = "Duva96a.pdf",
 abstract = "
 The aim of this paper is to present how the dynamic evaluation method
 can be used to deal with the real closure of an ordered field. Two
 kinds of questions, or tests, may be asked in an ordered field:
 equality tests $(a=b?)$ and sign tests $(a > b?)$. Equality tests are
 handled through splittings, exactly as in the algebraic closure of a
 field. Sign tests are handled throug a structure called ``Tarski data
 type''."
}

\end{chunk}

\index{Fritzson, D.}
\index{Fritzson, P.}
\index{Viklund, L.}
\index{Herber, J.}
\begin{chunk}{axiom.bib}
@article{Frit94,
 author = "Fritzson, D. and Fritzson, P. and Viklund, L. and Herber, J.",
 title = "Objectoriented mathematical modelling  applied to machine
 elements",
 journal = "Comput. Struct.",
 volume = "51",
 number = "3",
 pages = "241253",
+ pages = "1828",
year = "1994",
 keywords = "axiomref",
 paper = "Frit94.pdf",
abstract =
 "Machine element analysis has a goal of describing function and other
 aspects of machine elements in a theoretical form. This paper shows
 how ideas from objectoriented modelling can be applied to machine
 elment analysis. The models thus obtained are both easier to
 understand, better structured, and allow a higher degree of reuse
 than conventional models. An objectoriented model description is
 natural and suitable for machine element analysis. As a realistic
 example an equational model of rolling bearings is presented. The
 structure of the model is general, and applies to many types of
 rolling bearings. The model and one solution require approximately
 200+200 equations. The model is extensible, e.g. simple submodels of
 detailed properties can be made more complex without altering the
 overall structure. The example model has been implemented in a
 language of our own design. ObjectMath (Objectoriented Mathematical
 language for scientific computing). Using ObjectMath, it is possible
 to model classes of equation objects, to support multiple and single
 inheritance of equations, to support composition of equations, and to
 solve systems of equations. Algebraic transformations can conveniently
 be done since ObjectMath models are translated into the Mathematica
 computer algebra language. When necessary, equations can be
 transformed int C++ code for efficient numerical solution. The reuse
 of equations through inheritance reduced the size of the model by a
 factor of two, compared to a direct representation of the model in the
 Mathematica computer algebra language."
+ "This paper addresses some of the current issues concerning the
+ improvement of user interfaces for computer algebra systems. Some
+ state of the art commercial software as well as research prototypes
+ are presented, followed by a description of present research
+ directions."
}
\end{chunk}
\index{Ioakimidis, N.I.}
+\index{Kripfganz, Jochen}
+\index{Perlt, Holger}
\begin{chunk}{axiom.bib}
@article{Ioak94,
 author = "Ioakimidis, N.I.",
 title = "Symbolic computations for the solution of inverse/design
 problems with Maple",
 journal = "Comput. Struct.",
 volume = "53",
 number = "1",
 pages = "6368",
+@misc{Krip94,
+ author = "Kripfganz, Jochen and Perlt, Holger",
+ title = "Working with Mathematica. An Introduction with examples",
+ comment = "Arbeiten mit Mathematica. Eine Einfuhrung mit Beispielen",
+ book = "Hander",
year = "1994",
keywords = "axiomref"
}
\end{chunk}
\index{Jenks, Richard D.}
\index{Trager, Barry M.}
+\index{Schwarz, Fritz}
\begin{chunk}{axiom.bib}
@InProceedings{Jenk94,
 author = "Jenks, Richard D. and Trager, Barry M.",
 title = "How to make AXIOM into a scratchpad",
 booktitle = "Proceedings of the ACMSIGSAM 1989 International
 Symposium on Symbolic and Algebraic Computation, ISSAC '94",
 series = "ISSAC 94",
+@InProceedings{Schw94,
+ author = "Schwarz, Fritz",
+ title = "Computer algebra software for scientific applications",
+ booktitle = "Computerized symbolic manipulation in mechanics",
year = "1994",
 pages = "3240",
 isbn = "0897916387",
 keywords = "axiomref",
 publisher = "ACM Press",
 address = "New York, NY, USA",
 paper = "Jenk94.pdf",
 abstract =
 "Scratchpad [GrJe71] was a computer algebra system developed in the
 early 1970s. Like M\&M (Maple [CGG91ab] and Mathematical [W01S92]) and
 other systems today, Scratchpad had one principal representation for
 mathematical formulae based on ``expression trees''. Its user interface
 design was based on a patternmatching paradigm with infinite rewrite
 rule semantics, providing what we believe to be the most natural
 paradigm for interactive symbolic problem solving. Like M\&M, however,
 user programs were interpreted, often resulting in poor performance
 relative to similar facilities coded in standard programming languages
 such as FORTRAN and C.

 Scratchpad development stopped in 1976 giving way to a new system
 design ([JenR79], [JeTr81]) that evolved into AXIOM [JeSu92].
 AXIOM has a stronglytyped programming language for building a library
 of parameterized types and algorithms, and a typeinferencing
 interpreter that accesses the library and can build any of an infinite
 number of types for interactive use.

 We suggest that the addition of an expression tree type to AXIOM can
 allow users to operate with the same freedom and convenience of
 untyped systems without giving up the expressive power and runtime
 efficiency provided by the type system. We also present a design that
 supports a multiplicity of programming styles, from the Scratchpad
 patternmatching paradigm to functional programming to more
 conventional procedural programming. The resulting design seems to us
 to combine the best features of Scratchpad with current AXIOM and to
 offer a most attractive, flexible, and userfriendly environment for
 interactive problem solving.

 Section 2 is a discussion of design issues contrasting AXIOM with
 other symbolic systems. Sections 3 and 4 is an assessment of AXIOM’s
 current design for building libraries and interactive use. Section 5
 describes a new interface design for AXIOM, its resulting paradigms,
 and its underlying semantic model. Section 6 compares this work with
 others."
}

\end{chunk}

\index{Bernard, Joey}
\begin{chunk}{axiom.bib}
@misc{Bern14,
 author = "Bernard, Joey",
 title = "Open Axiom",
 url = "http://www.linuxjournal.com/content/openaxiom",
 keywords = "axiomref",
 year = "2014"
}

\end{chunk}

\index{Davenport, James H.}
\index{Trager, Barry M.}
\begin{chunk}{axiom.bib}
@InProceedings{Dave90,
 author = "Davenport, James H. and Trager, Barry M.",
 title = "Scratchpad's view of algebra I: Basic commutative algebra",
 booktitle = "Design and Implementation of Symbolic Computation Systems",
 year = "1990",
 series = "DISCO '90",
 location = "Capri, Italy",
publisher = "SpringerVerlag",
 isbn = "0387525319",
 keywords = "axiomref",
 url = "http://opus.bath.ac.uk/32336/1/Davenport\_DISCO\_1990.pdf",
 paper = "Dave90.pdf",
 comment = "AXIOM Technical Report, ATR/1, NAG Ltd., Oxford, 1992",
+ pages = "67117",
+ series = "CISM Courses Lecture 343",
keywords = "axiomref",
abstract =
 "While computer algebra systems have dealt with polynomials and
 rational functions with integer coefficients for many years, dealing
 with more general constructs from commutative algebra is a more recent
 problem. In this paper we explain how one system solves this problem,
 what types and operators it is necessary to introduce and, in short,
 how one can construct a computational theory of commutative
 algebra. Of necessity, such a theory is rather different from the
 conventional, nonconstructive, theory. It is also somewhat different
 from the theories of Seidenberg [1974] and his school, who are not
 particularly concerned with practical questions of efficiency."
}

\end{chunk}

\index{Jenks, Richard D.}
\index{Trager, Barry M.}
\begin{chunk}{axiom.bib}
@article{Jenk81,
 author = "Jenks, Richard D. and Trager, Barry M.",
 title = "A Language for Computational Algebra",
 year = "1981",
 booktitle = "Proc. Symp. on Symbolic and Algebraic Manipulation",
 series = "SYMSAC 1981",
 location = "Snowbird, Utah",
 keywords = "axiomref",
 comment = "IBM Research Report 8930",
 abstract =
 "This paper reports ongoing research at the IBM Research Center on the
 development of a language with extensible parameterized types and
 generic operators for computational algebra. The language provides an
 abstract data type mechanism for defining algorithms which work in as
 general a setting as possible. The language is based on the notions of
 domains and categories. Domains represent algebraic
 structures. Categories designate collections of domains having common
 operations with stated mathematical properties. Domains and categories
 are computed objects which may be dynamically assigned to variables,
 passed as arguments, and returned by functions. Although the language
 has been carefully tailored for the application of algebraic
 computation, it actually provides a very general abstract data type
 mechanism. Our notion of a category to group domains with common
 properties appears novel among programming languages (cf. image
 functor of RUSSELL) and leads to a very powerful notion of abstract
 algorithms missing from other work on data types known to the authors."
}

\end{chunk}

\index{Kapur, D.}
\index{Musser, D.R.}
\index{Stepanov, A.A.}
\begin{chunk}{axiom.bib}
@misc{Kapu81,
 author = "Kapur, D. and Musser, D.R. and Stepanov, A.A.",
 title = "Operators and Algebraic Structures",
 url = "http://www.stepanovpapers.com/p59kapur.pdf",
 paper = "Kapu81.pdf",
 year = "1981",
 abstract =
 "Operators in functional languages such as APL and FFP are a useful
 programming concept. However, this concept cannot be ful ly
 exploited in these languages because of certain constraints. It is
 proposed that an operator should be associated with a structure hav
 ing the algebraic properties on which the operator's behavior depends.
 This is illustrated by introducing a language that provides mechanisms
 for defining structures and operators on them. Using this language,
 it is possible to describe algorithms abstractly, thus empliasizing
 the algebraic properties on which the algorithms depend. The role
 that formal representation of mathematical knowledge can play in the
 development of programs is illustrated through an example. An
 approach for associating complexity mea sures with a structure and
 operators is also suggested. This ap proach is useful in analyzing
 the complexity of algorithms in an abstract setting."
}

\end{chunk}

\index{Jenks, Richard D.}
\index{Sutor, Robert S.}
\index{Watt, Stephen M.}
\begin{chunk}{axiom.bib}
@techreport{Jenk86,
 author = "Jenks, Richard D. and Sutor, Robert S. and Watt, Stephen M.",
 title = "Scratchpad II: An Abstract Datatype System for Mathematical
 Computation",
 institution = "IBM Research",
 year = "1986",
 type = "Research Report",
 number = "RC 12327 (\#55257)",
 url = "http://www.csd.uwo.ca/~watt/pub/reprints/1987imaspadadt.pdf",
 paper = "Jenk86.pdf",
 keywords = "axiomref",
 abstract = "
 Scratchpad II is an abstract datatype language and system that is
 under development in the Computer Algebra Group, Mathematical Sciences
 Department, at the IBM Thomas J. Watson Research Center. Some features
 of APL that made computation particularly elegant have been borrowed.
 Many different kinds of computational objects and data structures are
 provided. Facilities for computation include symbolic integration,
 differentiation, factorization, solution of equations and linear
 algebra. Code economy and modularity is achieved by having
 polymorphic packages of functions that may create datatypes. The use
 of categories makes these facilities as general as possible."
}

\end{chunk}

\index{Lloyd, Michael}
\index{Oancea, Cosmin}
\index{Watt, Stephen}
\begin{chunk}{axiom.bib}
@misc{Chic04,
 author = "Chicha, Yannis and Lloyd, Michael Oancea, Cosmin",
 title = "Parametric Polymorphism for Computer Algebra Software Components",
 booktitle = "6th Int. Symp. on Symbolic and Numeric Algorithms for
 Scientific Computing",
 series = "SYNASC 04",
 location = "Imisoara, Romania",
 keywords = "axiomref",
 year = "2004",
 paper = "Chic04.pdf",
 url = "http://www.csd.uwo.ca/~watt/pub/reprints/2004synascppca.pdf",
+ "The central subject of this article are two basic questions: How to
+ make the process of developing computer algebra software on a large
+ scale ($10^4 to $10^5$) lines of code or more) more efficient and
+ how to improve the quality of the result. Taking procedures from well
+ established engineering sciences as a guide, two fundamental
+ principles turned out to be of overwhelming importance: Modularization
+ and limitation of growth through reuse. Important means for achieving
+ these goals turned out to be concept of an abstract data type and the
+ principles of objectoriented design. It is advocated to install an
+ additional abstraction level between the mathematics and the machine
+ in order to render it possible to develop (computer algebra) system
+ independent mathematical software. Basic constituents of this level
+ are a type system and a highlevel language."
+}
+
+\end{chunk}
+
+\index{Kajler, Norbert}
+\begin{chunk}{axiom.bib}
+@article{Kajl92,
+ author = "Kajler, Norbert",
+ title = "CAS/PI: a Portable and Extensible Interface for Computer
+ Algebra Systems",
+ year = "1992",
+ booktitle = "Proc. ISSAC 1992",
+ series = "ISSAC 1992",
+ pages = "376386",
+ isbn = "0897914899 (soft cover) 0897914902 (hard cover)",
+ keywords = "axiomref",
+ paper = "Kajl92.pdf",
abstract =
 "This paper presents our experiments in providing mechanisms for
 parametric polymorphism for computer algebra software components.
 Specific interfaces between Aldor and C++ and between Aldor and Maple
 are described. We then present a general solution, Generic IDL (GIDL),
 an extension to CORBA IDL supporting generic types. We describe our
 language bindings for C++, Java 1.5 and Aldor as well as aspects of
 our implementation, consisting of a GIDL to IDL compiler and tools for
 generating interface code for the various language bindings."
}

\end{chunk}

\index{Watt, Stephen}
\begin{chunk}{axiom.bib}
@InProceedings{Watt07,
 author = "Watt, Stephen",
 title = "What Happened to Languages for Symolic Mathematical Computation?",
 booktitle = "Proc. Prog. Lang. for Mechanized Mathematics",
 series = "PLMMS 07",
 year = "2007",
 location = "RISCLinz, Austria",
 pages = "8190",
 keywords = "axiomref",
 paper = "Watt07.pdf",
+ "CAS/$\pi$ is a Computer Algebra System graphic user interface
+ designed to be highly portable and extensible. It has been developed
+ by composition of preexisting software tools such as Maple, Sisyphe,
+ or Ulysse systems, ZicVis 3D plotting library, etc, using control
+ integration technology and a set of high level graphic toolkits to
+ build the formula editor and the dialog manager. The main aim of
+ CAS/$\pi$ is to allow a wide range of runtime recon gurations and
+ extensions. For instance, it is possible to add new tools to a running
+ system, to modify connections between working tools, to extend the set
+ of graphic symbols managed by the formula editor, to design new high
+ level editing commands based on the syntax or semantics of
+ mathematical formulas, to customize and extend the menubutton based
+ user interface, etc. More generally, CAS/$\pi$ can be seen equally as
+ a powerful systemindependent graphic user interface enabling
+ intersystems communications, a toolkit to allow fast development of
+ custommade scientific software environments, or a very convenient
+ framework for experimenting with computer algebra systems protocols
+ and manmachine interfaces."
+}
+
+\end{chunk}
+
+\index{Schu, J.}
+\index{Seiler, Werner Markus}
+\index{Calmet, Jacques}
+\begin{chunk}{axiom.bib}
+@InProceedings{Schu92,
+ author = "Schu, J. and Seiler, Werner Markus and Calmet, Jacques",
+ title = "Algorithmic Methods For Lie Pseudogroups'",
+ booktitle = "Proc. Modern Group Analysis: Advanced Analytical and
+ Computational Methods in Mathematical Physics",
+ pages = "337344",
+ location = "Acireale (Italy)",
+ year = "1992",
+ publisher = "Kluwer",
url =
 "http://www.csd.uwo.ca/~watt/pub/reprints/2007plmmswhat\_happened.pdf",
 abstract =
 "While the state of the art is relatively sophisticated in programming
 language support for computer algebra, there has been less development
 in programming language support for symbolic computation over the past
 two decades. We summarize certain advances in programming languages
 for computer algebra and propose a set of directions and challenges
 for programming languages for symbolic computation."
}

\end{chunk}

\index{Santas, Philip S.}
\begin{chunk}{axiom.bib}
@inproceedings{Sant96,
 author = "Santas, Philip S.",
 title = "Conditional Categories and Domains",
 keywords = "axiomref",
 booktitle = "Proc. DISCO 1996",
 year = "1996",
 pages = "112125",
 isbn = "3540616977"
}

\end{chunk}


\index{Santas, Philip S.}
\begin{chunk}{axiom.bib}
@book{Sant05,
 author = "Santas, Philip S.",
 title = "Conditional Categories and Domains",
 keywords = "axiomref",
 booktitle = "Design and Implementation of Symbolic Computation Systems",
 year = "2005",
 series = "Lecture Notes in Computer Science",
 volume = "1128",
 publisher = "Springer",
 abstract =
 "We extend the Type system defined in [Sant95] with Axiomlike
 Conditional Categories with the additional property of Static Typing
 and Checking. Categories and Domains may contain conditionals in their
 bodies, which are elaborated by our compiler by techniques used in
 standard typing. We define an appropriate calculus and discuss its
 properties. Examples inspired by the Axiom library illustrate the
 power of our apprach and its application in constructing algebraic
 concepts. The full calculus has been implemented and tested with our
 LA compiler which generated executable files."
}

\end{chunk}

\begin{chunk}{axiom.bib}
@misc{Gute16,
 author = "Gutenberg SelfPublishing Press",
 title = "OpenAxiom",
 keywords = "axiomref",
 url = "http://self.gutenberg.org/articles/openaxiom",
 year = "2016"
}

\end{chunk}

\index{Baker, Martin}
\begin{chunk}{axiom.bib}
@misc{Bake16,
 author = "Baker, Martin",
 title = "Axiom Maths Program",
 keywords = "axiomref",
 year = "2016",
 url = "http://www.euclideanspace.com/prog/scratchpad/axiom/index.htm"
+ "http://www.iks.kti.edu/fileadmin/User/calmet/papers/Acireale93.ps.gz",
+ keywords = "axiomref"
}
\end{chunk}
\index{Caviness, Bob}
\index{Trager, Barry}
\index{Gianni, Patrizia}
+\index{Seiler, Werner Markus}
\begin{chunk}{axiom.bib}
@misc{Cavi03,
 author = "Caviness, Bob and Trager, Barry and Gianni, Patrizia",
 title = "Dedicated to the Memory of Richard Dimick Jenks",
 year = "2003",
 url = "https://www.eecis.udel.edu/~caviness/jenks/issacded.pdf",
+@article{Seil99,
+ author = "Seiler, Werner Markus",
+ title = "DETools: A Library for Differential Equations",
+ paper = "Seil99.pdf",
+ year = "1999",
keywords = "axiomref",
 paper = "Cavi03.pdf",
abstract =
 "On December 30, 2003, Dick Jenks died at the age of 66, after an
 extended and courageous battle with multiple system atrophy.

 He received his PhD in mathematics from the University of Illinois at
 UrbanaChampaign in 1966. The title of his dissertation was
 “Quadratic Differential Systems for Mathematical Models” and was
 written under the supervision of Donald Gilles. After completing his
 PhD, he was a postdoctoral fellow at Brookhaven National Laboratory
 on Long Island. In 1968 he joined IBM Research where he worked until
 his retirement in 2002.

 At IBM he was one of the principal architects of the Scratchpad
 system, one of the earliest computer algebra systems(1971). Dick
 always believed that natural user interfaces were essential and
 developed a userfriendly rulebased system for Scratchpad. Although
 this rulebased approach was easy to use, as algorithms for computer
 algebra became more complicated, he began to understand that an
 abstract data type approach would give sophisticated algorithm
 development considerably more leverage. In 1977 he began the Axiom
 development (originally called Scratchpad II) with the design of
 MODLISP, a merger of Lisp with types (modes). In 1980, with the help
 of many others, he completed an initial prototype design based on
 categories and domains that were intended to be natural for
 mathematically sophisticated users.

 During this period many researchers in computer algebra visited IBM
 Research in Yorktown Heights and contributed to the development of
 the Axiom system. All this activity made the computer algebra group at
 IBM one of the leading centers for research in this area and Dick was
 always there to organize the visits and provide a stimulating and
 pleasant working environment for everyone. He had a good perspective
 on the most important research directions and worked to attract
 worldrenowned experts to visit and interact with his group. He was an
 ideal manager for whom to work, one who always put the project and the
 needs of the group members first. It was a joy to work in such a
 vibrant and stimulating environment.

 After many years of development, a decision was made to rename
 Scratch pad II to Axiom and to release it as a product. Dick and
 Robert Sutor were the primary authors of the book {\sl Axiom: The
 Scientific Computation System}. In the foreword of the book, written
 by David and Gregory Chudnovsky, it is stated that ``The Scratchpad
 system took its time to blossom into the beautiful Axiom
 product. There is no rival to this powerful environment in its scope
 and, most importantly, in its structure and organization.'' Axiom was
 recently made available as free software. See
 http://savannah.nongnu.org/projects/axiom

 Dick was active in service to the computer algebra community as
 well. Here are some highlights. He served as Chair of ACM SIGSAM
 (197981) and Conference Cochair (with J. A. van Hulzen) of EUROSAM
 ’84, a precursor of the ISSAC meetings. Dick also had a long period of
 service on the editorial board of the {\sl Journal of Symbolic
 Computation}. At ISSAC ’95 in Montreal, Dick was elected to the
 initial ISSAC Steering Committee and was elected as the second Chair
 of the Committee in 1997. He, along with David Chudnovsky, organized
 the highly successful meetings on Computers and Mathematics that were
 held at Stanford in 1986 and MIT in 1989. As a legacy of those
 meetings, the Jenks Prize for outstanding contributions to software
 engineering in computer algebra has been established.

 Dick had many interests outside of his professional pursuits including
 reading, travel, physical fitness, and especially music. Dick was an
 accomplished pianist, organist, and vocalist. At one point he was the
 organist and choir master of the Church of the Holy Communion in
 Mahopac, NY. In the 1980s and 1990s, he sang in choral groups under
 the direction of Dr. Dennis Keene that performed at Lincoln Center in
 New York city.

 Personally, Dick was warm, generous, and outgoing with many
 friends. He will be missed for his technical accomplishments, his
 artist talents, and most of all for his positive, gentle, charming
 spirit."
+ "This article tries to give at least a brief introduction. The MuPAD
+ library is extended on two levels. The first one consists of a new
+ library detools containing a number of routines for treating
+ differential equations. This includes support for the graphical
+ presentation of the output of the numerical routines in MuPAD, some
+ methods for analysing or generating differential equations and also
+ routines for solving some classes of partial differential
+ equations. The use of this new library will be described in this
+ article. The second level is somewhat more advanced and requires a
+ certain familiarity with the objectoriented domains."
}
\end{chunk}
+\index{Bradford, Russell}
\index{Davenport, James H.}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@article{Dave81,
 author = "Davenport, James H. and Jenks, Richard D.",
 title = "MODLISP",
 year = "1981",
 journal = "ACM SIGSAM Bulletin",
 volume = "15",
 issue = "1",
 pages = "1120",
 publisher = "ACM",
 keywords = "axiomref",
+\index{England, Matthew}
+\index{McCallum, Scott}
+\index{Wilson, David}
+\begin{chunk}{axiom.bib}
+@misc{Brad15,
+ author = "Bradford, Russell and Davenport, James H. and England, Matthew and
+ McCallum, Scott",
+ title = "Truth Table Invariant Cylindrical Algebraic Decomposition",
+ url = "https://arxiv.org/pdf/1401.0645.pdf",
+ paper = "Brad15.pdf",
+ year = "2015",
abstract =
 "This paper discusses the design and implementation of MODLISP, a
 LISPlike language enhanced with the idea of MODes. This extension
 permits, but does not require, the user to declare the types of
 various variables, and to compile functions with the arguments
 declared to be of a particular type. It is possible to declare several
 functions of the same name, with arguments of different type
 (e.g. PLUS could be declared for Integer arguments, or Rational, or
 Real, or even Polynomial arguments) and the system will apply the
 correct function for the types of the arguments."
}

\end{chunk}

\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@inproceedings{Jenk79,
 author = "Jenks, Richard D.",
 title = "MODLISP: An Introduction",
 booktitle = "Proc. ISSAC 1979",
 series = "EUROSAM 79",
 pages = "466480",
 year = "1979",
 publisher = "SpringerVerlag",
 isbn = "3540095195",
 comment = "IBM Research Report RC 8073 Jan 1980",
 keywords = "axiomref"
}

\end{chunk}

\index{Davenport, James H.}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@techreport{Dave80,
 author = "Davenport, James H. and Jenks, Richard D.",
 title = "MODLISP: A Preliminary Design",
 institution = "IBM Research",
 type = "Research Report",
 year = "1980",
 number = "RC 8073",
 keywords = "axiomref"
}

\end{chunk}

+ "When using cylindrical algebraic decomposition (CAD) to solve a
+ problem with respect to a set of polynomials, it is likely not the
+ signs of those polynomials that are of paramount importance but rather
+ the truth values of certain quantifier free formulae involving
+ them. This observation motivates our article and definition of a Truth
+ Table Invariant CAD (TTICAD). In ISSAC 2013 the current authors
+ presented an algorithm that can efficiently and directly construct a
+ TTICAD for a list of formulae in which each has an equational
+ constraint. This was achieved by generalising McCallum's theory of
+ reduced projection operators. In this paper we present an extended
+ version of our theory which can be applied to an arbitrary list of
+ formulae, achieving savings if at least one has an equational
+ constraint. We also explain how the theory of reduced projection
+ operators can allow for further improvements to the lifting phase of
+ CAD algorithms, even in the context of a single equational constraint.
+ The algorithm is implemented fully in Maple and we present both
+ promising results from experimentation and a complexity analysis
+ showing the benefits of our contributions."
+}
+
+\end{chunk}
+
+\index{Bradford, Russell}
+\index{Chen, Changbo}
\index{Davenport, James H.}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@techreport{Dave80,
 author = "Davenport, James H. and Jenks, Richard D.",
 title = "MODLISP",
 institution = "IBM Research",
 type = "Research Report",
 year = "1980",
 number = "RC 8537 (\#37198)",
 keywords = "axiomref",
 comment = "http://www.computerhistory.org/collections/catalog/102719109"
}

\end{chunk}

\index{Hoeven, Joris van der}
\index{Lecerf, Gregoire}
\begin{chunk}{axiom.bib}
@misc{Hoev15,
 author = "Hoeven, Joris van der and Lecerf, Gregoire",
 title = "Interfacing Mathemagix with C++",
 keywords = "axiomref",
 url = "http://www.texmacs.org/joris/mmxcpp/mmxcpp.html",
 abstract =
 "In this paper, we give a detailed description of the interface
 between the Mathemagix language and C++. In particular, we describe
 the mechanism which allows us to import a C++ template library
 (which only permits static instantiation) as a fully generic
 Mathemagix template library."
}

\end{chunk}

\index{Fortenbacher, A.}
\index{Jenks, Richard}
\index{Lucks, Michael}
\index{Sutor, Robert}
\index{Trager, Barry}
\index{Watt, Stephen}
\begin{chunk}{axiom.bib}
@techreport{Fort85,
 author = "Fortenbacher, A. and Jenks, Richard and Lucks, Michael and
 Sutor, Robert and Trager, Barry and Watt, Stephen",
 title = "An Overview of the Scratchpad II Language and System",
 year = "1985",
 type = "Research Report",
 publisher = "IBM Research Computer Algebra Group",
 keywords = "axiomref"
}

\end{chunk}

\begin{chunk}{axiom.bib}
@misc{Maxi16,
 author = "Maxima",
 title = "Other Free Computer Algebra Systems",
 url = "http://maxima.sourceforge.net/compalg.html",
 year = "2016",
 keywords = "axiomref",
 abstract =
 “Axiom is a general purpose Computer Algebra system. It is useful for
 doing mathematics by computer and for research and development of
 mathematical algorithms. It defines a strongly typed, mathematically
 correct type hierarchy. It has a programming language and a builtin
 compiler.

 There is also an interesting Rosetta Stone which offers translations
 of many basic operations for several computer algebra systems,
 including Maxima."
}

\end{chunk}

\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@inproceedings{Jenk84b,
 author = "Jenks, Richard D.",
 title = "A primer: 11 keys to New Scratchpad",
 booktitle = "Proc. EUROSAM ISSAC 1984",
 year = "1984",
 publisher = "SpringerVerlag",
 pages = "123147",
 isbn = "038713350X",
 keywords = "axiomref",
+\index{England, Matthew}
+\index{Maza, Marc Moreno}
+\index{Wilson, David}
+\begin{chunk}{axiom.bib}
+@misc{Brad14,
+ author = "Bradford, Russell and Chen, Changbo and Davenport, James H. and
+ England, Matthew and Maza, Marc Moreno and Wilson, David",
+ title = "Truth Table Invariant Cylindrical Algebraic Decomposition by
+ Regular Chains",
+ url = "https://arxiv.org/pdf/1401.6310.pdf",
+ paper = "Brad14.pdf",
+ year = "2014",
abstract =
 "This paper is an abbreviated primer for the language of new
 SCRATCHPAD, a new implementation of SCRATCHPAD which has been under
 design and development by the Computer Algebra Group at the IBM
 Research Center during the past 6 years. The basic design goals of the
 new SCRATCHPAD language and interface to the user are to provde:
 \begin{itemize}
 \item a ``typeless'' interactive language suitable for online solution
 of mathematical problems by novice users with little or no programming
 required, and
 \item a programming language suitable for the formal description of
 algorithms and algebraic structures which can be compiled into runtime
 efficient object code.
 \end{itemize}

 The new SCRATCHPAD language is introduced by 11 keys with each
 successive key introducing an additional capability of the
 language. The language is thus described as a ``concentric'' language
 with each of the 11 levels corresponding to a language subset. These
 levels are more than just a pedagogic device, since they correspond to
 levels at which the system can be effectively used. Level 1 is
 sufficient for naive interactive use; levels 28 progressively
 introduce interactive users to capabilities of the language; levels
 911 are for system programmers and advanced users. Levesl 2, 4, 6,
 and 7 give users the full power of LISP with a highlevel language;
 level 8 introduces ``type declarations;'' level 9 allows polymorphic
 functions to be defined and compiled; levels 1011 give users an
 Adalike facility for defining types and packages (those of new
 SCRATCHPAD are dynamically constructable, however). One language is
 used for both interactive and system programming language use,
 although several freedomes such as abbreviation and optional
 typedeclarations allowed at toplevel are not permitted in system
 code. The interactive language (levels 18) is a blend of original
 SCRATCHPAD [GRJY75], some proposed extensions [JENK74], work by Loos
 [LOOS74], SETL [DEWA79], SMP [COWO81], and new ideas; the system
 programming language (levels 111) superficially resembles Ada but is
 more similar to CLU [LISK74] in its semantic design.

 This presentation of the language in this paper omits many details to
 be covered in the SCRATCHPAD System Programming Manual [SCRA84] and an
 expanded version of this paper will serve as a primer for SCRATCHPAD
 users [JESU84]."
+ "A new algorithm to compute cylindrical algebraic decompositions
+ (CADs) is presented, building on two recent advances. Firstly, the
+ output is truth table invariant (a TTICAD) meaning given formulae have
+ constant truth value on each cell of the decomposition. Secondly, the
+ computation uses regular chains theory to first build a cylindrical
+ decomposition of complex space (CCD) incrementally by polynomial.
+ Significant modification of the regular chains technology wa s used to
+ achieve the more sophisticated invariance criteria. Experimental
+ results on an implementation in the {\tt RegularChains} Library for Maple
+ verify that combining these advances gives an algorithm superior to
+ its individual components and competitive with the state of the art."
}
\end{chunk}
\index{Griesmer, James H.}
\index{Jenks, Richard D.}
\index{Yun, David Y.Y}
\begin{chunk}{axiom.bib}
@techreport{Grie75,
 author = "Griesmer, James H. and Jenks, Richard D. and Yun, David Y.Y",
 title = "SCRATCHPAD User's Manual",
 year = "1975",
 type = "Research Report",
 number = "RA70",
 keywords = "axiomref"
}

\end{chunk}

\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@article{Jenk74,
 author = "Jenks, Richard D.",
 title = "The SCRATCHPAD language",
 journal = "ACM SIGPLAN Notices",
 comment = "reprinted in SIGSAM Bulletin, Vol 8, No. 2, May 1974",
 volume = "9",
 number = "4",
 pages = "101111",
 year = "1974",
 keywords = "axiomref"
}

\end{chunk}

\index{Jenks, Richard D.}
\index{Sundaresan, Christine J.}
\begin{chunk}{axiom.bib}
@misc{Jenk84c,
 author = "Jenks, Richard D. and Sundaresan, Christine J.",
 title = "The 11 Keys to SCRATCHPAD: A Primer",
 year = "1984",
 keywords = "axiomref"
}

+\index{Wilson, David}
+\index{Bradford, Russell}
\index{Davenport, James H.}
\index{Gianni, Patrizia}
\index{Jenks, Ricard D.}
\index{Miller, Victor}
\index{Morrison, Scott}
\index{Rothstein, Michael}
\index{Sundaresan, Christine J.}
\index{Sutor, Robert S.}
\index{Trager, Barry M.}
\begin{chunk}{axiom.bib}
@misc{Dave84b,
 author = "Davenport, James H. and Gianni, Patrizia and Jenks, Ricard D. and
 Miller, Victor and Morrison, Scott and Rothstein, Michael and
 Sundaresan, Christine J. and Sutor, Robert S. and Trager, Barry",
 title = "SCRATCHPAD System Programming Language Manual",
 year = "1984",
 keywords = "axiomref",
}

\end{chunk}

\index{Constable, Robert L.}
\index{Jackson, Paul B.}
\begin{chunk}{axiom.bib}
@misc{Cons98,
 author = "Constable, Robert L. and Jackson, Paul B.",
 title = "Towards Integrated Systems for Symbolic Algebra and Formal
 Constructive Mathematics",
 url = "http://www.nuprl.org/documents/Constable/towardsintegrated.pdf",
 paper = "Cons98.pdf",
 year = "1998",
+\index{England, Matthew}
+\begin{chunk}{axiom.bib}
+@misc{Wils14,
+ author = "Wilson, David and Bradford, Russell and Davenport, James H. and
+ England, Matthew",
+ title = "Cylindrical Algebraic SubDecompositions",
+ url = "https://arxiv.org/pdf/1401.0647.pdf",
+ paper = "Wils14.pdf",
+ year = "2014",
abstract =
 "The purpose of this paper is to report on our efforts to give e a
 formal account of some of the algebra used in Computer Algebra Systems
 (CAS). In particular, we look at the concepts used in the so called
 3rd generation algebra systems, such as Axiom[4] and Weyl[9]. It is
 our claim that the Nuprl proof development system is especially well
 suited to support this kind of mathematics."
}

\end{chunk}

\begin{chunk}{axiom.bib}
@misc{Acad16,
 author = "Academic Search",
 title = "A Primer: 11 Keys to New Scratchpad",
 url =
 "http://libra.msra.cn/publication/645035/aprimer11keystonewscratchpad",
 year = "2016",
 keywords = "axiomref"
}

\end{chunk}

\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@misc{Jenk86a,
 author = "Jenks, Richard D.",
 title = "Basic Algebraic Facilities of the Scratchpad II Computer
 Algebra System",
 institution = "IBM Research",
 year = "1986",
 keywords = "axiomref"
}

\end{chunk}

\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@misc{Jenk86b,
 author = "Jenks, Richard D.",
 title = "Scratchpad II Examples from INPUT files",
 institution = "IBM Research",
 year = "1986",
 keywords = "axiomref"
}

\end{chunk}

+ "Cylindrical algebraic decompositions (CADs) are a key tool in real
+ algebraic geometry, used primarily for eliminating quantifiers over
+ the reals and studying semialgebraic sets. In this paper we
+ introduce cylindrical algebraic subdecompositions (subCADs), which
+ are subsets of CADs containing all the information needed to specify a
+ solution for a given problem. We define two new types of subCAD:
+ variety subCADs which are those cells in a CAD lying on a designated
+ variety; and layered subCADs which have only those cells of
+ dimension higher than a specified value. We present algorithms to
+ produce these and describe how the two approaches may be combined with
+ each other and the recent theory of truthtable invariant CAD. We
+ give a complexity analysis showing that these techniques can offer
+ substantial theoretical savings, which is supported by experimentation
+ using an implementation in Maple."
+}
+
+\end{chunk}
+
+\index{England, Matthew}
+\index{Wilson, David}
+\index{Bradford, Russell}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@article{Dave85,
 author = "Davenport, James H.",
 title = "The LISP/VM Foundation of Scratchpad II",
 journal = "The Scratchpad II Newsletter",
 volume = "1",
 number = "1",
 year = "1985",
 month = "September",
 institution = "IBM Research",
 keywords = "axiomref"
}

\end{chunk}

\index{Wityak, Sandra}
\begin{chunk}{ignore}
@misc{Wity85,
 author = "Wityak, Sandra",
 title = "The Scratchpad II Newsletter",
 volume = "1",
 number = "1",
 year = "1985",
 month = "September",
 institution = "IBM Research",
 keywords = "axiomref"
}

\end{chunk}

\index{Wityak, Sandra}
\begin{chunk}{ignore}
@misc{Wity86,
 author = "Wityak, Sandra",
 title = "The Scratchpad II Newsletter",
 volume = "1",
 number = "2",
 year = "1986",
 month = "January",
 institution = "IBM Research",
 keywords = "axiomref"
}

\end{chunk}

\index{Wityak, Sandra}
\begin{chunk}{ignore}
@misc{Wity86a,
 author = "Wityak, Sandra",
 title = "The Scratchpad II Newsletter",
 volume = "1",
 number = "3",
 year = "1986",
 month = "May",
 institution = "IBM Research",
 keywords = "axiomref"
}

\end{chunk}

\index{Watt, Stephen M.}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@misc{Watt87,
 author = "Watt, Stephen M. and Jenks, Richard D.",
 title = "Abstract Datatypes, Multiple Views and Multiple Inheritance in
 Scratchpad II",
 keywords = "axiomref",
 year = "1987",
 url = "https://cs.uwaterloo.ca/~smatt/pub/reprints/1987itlspadviews.pdf",
 paper = "Watt87.pdf",
+@misc{Engl14,
+ author = "England, Matthew and Wilson, David and Bradford, Russell and
+ Davenport, James H.",
+ title = "Using the Regular Chains Library to build cylindrical algebraic
+ decompositions by projecting and lifting",
+ url = "https://arxiv.org/pdf/1405.6090.pdf",
+ paper = "Engl14.pdf",
+ year = "2014",
abstract =
 "Scratchpad II is an abstract datatype language developed at Yorktown
 Heights for the implementation of a new computer algebra system. It
 provides packages of polymorphic functions and parameterized, abstract
 datatypes with operator overloading and multiple inheritance. To
 express the intricate interrelationships between the datatypes
 necessary for the description of mathematical objects, a number of
 techniques based on the notion of {\sl category} have been
 used. Categories are used to enforce relationships between type
 parameters and to provide the mechanism for multiple inheritance. They
 also allow the language to be statically type checked and the
 generation of efficient code. This paper describes the role of
 categories in Scratchpad II."
+ "Cylindrical algebraic decomposition (CAD) is an important tool, both
+ for quantifier elimination over the reals and a range of other
+ applications. Traditionally, a CAD is built through a process of
+ projection and lifting to move the problem within Euclidean spaces of
+ changing dimension. Recently, an alternative approach which first
+ decomposes complex space using triangular decomposition before
+ refining to real space has been introduced and implemented within the
+ RegularChains Library of Maple. We here describe a freely available
+ package ProjectionCAD which utilises the routines within the
+ RegularChains Library to build CADs by projection and lifting. We
+ detail how the projection and lifting algorithms were modified to
+ allow this, discuss the motivation and survey the functionality of the
+ package."
}
\end{chunk}
\index{Watt, Stephen M.}
\index{Jenks, Richard D.}
\index{Sutor, Robert S.}
\index{Trager, Barry M.}
\begin{chunk}{axiom.bib}
@inproceedings{Watt90,
 author = "Watt, Stephen M. and Jenks, Richard D. and Sutor, Robert S. and
 Trager, Barry M.",
 title = "The Scratchpad II type system: Domains and Subdomains",
 booktitle = "Computing Tools for Scientific Problem Solving",
 year = "1990",
 publisher = "Academic Press",
 url =
 "https://cs.uwaterloo.ca/~smwatt/pub/reprints/1990miolaspadtypes.pdf",
 paper = "Watt90.pdf",
 keywords = "axiomref",
+\index{England, Matthew}
+\index{Bradford, Russell}
+\index{Davenport, James H.}
+\index{Wilson, David}
+\begin{chunk}{axiom.bib}
+@misc{Engl14a,
+ author = "England, Matthew and Bradford, Russell and Davenport, James H. and
+ Wilson, David",
+ title = "Choosing a variable ordering for truthtable invariant cylindrical
+ algebraic decomposition by incremental triangular decomposition",
+ url = "https://arxiv.org/pdf/1405.6094.pdf",
+ paper = "Engl14a.pdf",
+ year = "2014",
abstract =
 "Scratchpad II is a language developed at Yorktown Heights for the
 implementation of a new computer algebra system. The need to model the
 intricate relationships among the datatypes representing mathematical
 objects has provided a number of challenges in the design of a type
 system for the programming language.

 In languages in which a datatype constructor may take multiple
 parameters, ensuring compatibility between them is extremely
 important. Scratchpad II addresses this issue by basing its
 implementation of abstract datatypes on {\cl categories}. Categories
 provide a convenient and useful method for specifying requirements on
 operations from datatypes. These requirements can be very complex when
 modelling mathematics.

 We show how categories provide multiple inheritance and how
 inheritance of specification is separated from inheritance of
 implementation. We also present implications of the type system on
 compilation of efficient code and flexibility of a weakly typed
 interactive user interface.

 Finally, the mechanisms of Scratchpad II are compared with those of
 traditional abstract datatype and objectoriented programming
 languages."
}

\end{chunk}

\index{Zippel, Richard}
\begin{chunk}{axiom.bib}
@misc{Zipp93,
 author = "Zippel, Richard",
 title = "The Weyl Computer Algebra Substrate",
 paper = "Zipp93.pdf",
 keywords = "axiomref",
 booktitle = "Proc. of DISCO 1993",
 series = "DISCO 93",
 pages = "303=307",
 year = "1993"
+ "Cylindrical algebraic decomposition (CAD) is a key tool for solving
+ problems in real algebraic geometry and beyond. In recent years a new
+ approach has been developed, where regular chains technology is used
+ to first build a decomposition in complex space. We consider the
+ latest variant of this which builds the complex decomposition
+ incrementally by polynomial and produces CADs on whose cells a
+ sequence of formulae are truthinvariant. Like all CAD algorithms the
+ user must provide a variable ordering which can have a profound impact
+ on the tractability of a problem. We evaluate existing heuristics to
+ help with the choice for this algorithm, suggest improvements and then
+ derive a new heuristic more closely aligned with the mechanics of the
+ new algorithm."
}
\end{chunk}
\index{Sutor, Robert S.}
\begin{chunk}{axiom.bib}
@inproceedings{Suto85,
 author = "Sutor, Robert S.",
 title = "The Scratchpad II computer algebra language and system",
 booktitle = "Research Contributions from the Euro. Conf. on Comp. Alg.",
 series = "Lecture Notes in Computer Science Volume 204",
 volume = "2",
 pages = "3233",
 year = "1985",
 isbn = "0387159835 (vol. 1),0387159843 (vol. 2)",
 keywords = "axiomref"
}

\end{chunk}

\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@article{Jenk88d,
 author = "Jenks, Richard D.",
 title = "Scratchpad II: A computer algebra language and system",
 journal = "The Journal of the Acoustical Society of America",
 year = "1988",
 volume = "83",
 number = "S1",
 pages = "S106",
 keywords = "axiomref",
+\index{England, Matthew}
+\index{Bradford, Russell}
+\index{Chen, Changbo}
+\index{Davenport, James H.}
+\index{Maza, Marc Moreno}
+\index{Wilson, David}
+\begin{chunk}{axiom.bib}
+@misc{Engl14b,
+ author = "England, Matthew and Bradford, Russell and Chen, Changbo and
+ Davenport, James H. and Maza, Marc Moreno",
+ title = "Problem formulation for truthtable invariant cylindrical
+ algebraic decomposition by incremental triangular decomposition",
+ url = "https://arxiv.org/pdf/1404.6371.pdf",
+ paper = "Engl14b.pdf",
+ year = "2014",
abstract =
 "The Scratchpad II system represents a new generation of systems for
 doing symbolic mathematics, based on modern algebra and abstract data
 types. A large number of facilities are provided, for example:
 symbolic integration, ``infinite'' power series, differential operators,
 Cartesian tensors, and solution of nonlinear systems. Scratchpad II
 has been designed from the outset to be extendible. The system
 introduces a new data abstraction notion, the ``category,'' to express
 intricate interrelationships between data types. The result design
 permits the compilation of algorithms described in their most natural
 mathematical setting. The use of categories guarantees user defined
 types and packages are compatible with each other and with built in
 facilities. This system provides a single high‐level language with an
 intepreter and compiler. The language can be used by the naive user
 for convenient interactive mathematics calculations and by the
 advanced user for the efficient implementation of
 algorithms. Scratchpad II is built on Lisp/VM and runs on IBM/370
 class mainframes. An implementation of the system on the RT/PC is
 expected soon."
}

\end{chunk}

\index{Jenks, Richard D.}
\index{Sutor, Robert S.}
\index{Watt, Stephen M.}
\begin{chunk}{axiom.bib}
@book{Jenk88e,
 author = "Jenks, Richard D. and Sutor, Robert S. and Watt, Stephen M.",
 title = "Scratchpad II: An Abstract Datatype System for Mathematical
 Computation",
 booktitle = "Mathematical Aspects of Scientific Software",
 year = "1988",
 pages = "157182",
 publisher = "Springer",
 isbn = "0387189289",
 keywords = "axiomref",
+ "Cylindrical algebraic decompositions (CADs) are a key tool for
+ solving problems in real algebraic geometry and beyond. We recently
+ presented a new CAD algorithm combining two advances: truthtable
+ invariance, making the CAD invariant with respect to the truth of
+ logical formulae rather than the signs of polynomials; and CAD
+ construction by regular chains technology, where first a complex
+ decomposition is constructed by refining a tree incrementally by
+ constraint. We here consider how best to formulate problems for input
+ to this algorithm. We focus on a choice (not relevant for other CAD
+ algorithms) about the order in which constraints are presented. We
+ develop new heuristics to help make this choice and thus allow the
+ best use of the algorithm in practice. We also consider other choices
+ of problem formulation for CAD, as discussed in CICM 2013, revisiting
+ these in the context of the new algorithm."
+}
+
+\end{chunk}
+
+\index{Chen, Changbo}
+\index{Maza, Marc Moreno}
+\begin{chunk}{axiom.bib}
+@misc{Chen12,
+ author = "Chen, Changbo and Maza, Marc Moreno",
+ title = "An Incremental Algorithm for Computing Cylindrical Algebraic
+ Decompositions",
+ url = "https://arxiv.org/pdf/1210.5543.pdf",
+ paper = "Chen12.pdf",
+ year = "2012",
abstract =
 "Scratchpad II is an abstract datatype language and system that is
 under development in the Computer Algebra Group, Mathematical Sciences
 Department, at the IBM Thomas J. Watson Research Center. Many
 different kinds of computational objects and data structures are
 provided. Facilities for computation include symbolic integration,
 differentation, factorization, solution of equations and linear
 algebra. Code economy and modularity is achieved by having polymorphic
 packages of functions that may create datatypes. The use of categories
 makes these facilities as general as possible."
+ "In this paper, we propose an incremental algorithm for computing
+ cylindrical al gebraic decompositions. The algorithm consists of two
+ parts: computing a complex cylindrical tree and refining this complex
+ tree into a cylindrical tree in real space. The incrementality comes
+ from the first part of the algorithm, where a complex cylindrical tree
+ is constructed by refining a previous complex cylindrical tree with a
+ polynomial constraint. We have implemented our algorithm in Maple. The
+ experimentation shows that the proposed algorithm outperforms existing
+ ones for many examples taken from the literature"
}
\end{chunk}
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 2b68804..e751a9d 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5454,6 +5454,8 @@ books/bookvol10.4 add Bronstein citations for LODE code
books/bookvolbib Axiom Citations in the Literature
20160705.01.tpd.patch
books/bookvolbib Axiom Citations in the Literature
+20160706.01.tpd.patch
+books/bookvolbib Axiom Citations in the Literature

1.7.5.4