From 75a386e00fc2bf886ae356616ea2266103251ab7 Mon Sep 17 00:00:00 2001
From: Tim Daly
Date: Fri, 1 Jul 2016 01:45:50 0400
Subject: [PATCH] books/bookvolbib Axiom Citations in the Literature
MIMEVersion: 1.0
ContentType: text/plain; charset=UTF8
ContentTransferEncoding: 8bit
Goal: Axiom Literate Programming
\index{Petitjean, S.}
\begin{chunk}{axiom.bib}
@article{Peti99,
author = "Petitjean, S.",
title = "Algebraic Geometry and Computer Vision: Polynomial Systems, Real
and Complex Roots",
journal = "J. of Mathematical Imaging and Vision",
volume = "10",
number = "1",
year = "1999",
keywords = "axiomref",
paper = "Peti99.pdf",
url = "http://www.loria.fr/~petitjea/papers/jmiv99.pdf",
abstract =
"We review the different techniques known for doing exact computations
on polynomial systems. Some are based on the use of Groebner bases and
linear algebra, others on the more classical resultants and its modern
counterparts. Many theoretical examples of the use of these techniques
are given. Furthermore, a full set of examples of applications in the
domain of artificial vision, where many constraints boil down to
polynomial systems, are presented. Emphasis is also put on very recent
methods for determining the number of (isolated) real and complex
roots of such systems."
}
\end{chunk}
\index{Kreuzer, Edwin}
\begin{chunk}{axiom.bib}
@book{Kreu14,
author = "Kreuzer, Edwin",
title = "Computerized Symbolic Manipulation in Mechanics",
publisher = "Springer",
year = "2014",
abstract =
"The aim of this book is to present important software tools, basic
concepts, methods, and highly sophisticated applications of
computerized symbolic manipulation to mechanics problems. An overview
about generalpurpose symbolic software is followed by general
guidelines how to develop and implement highquality computer algebra
code. The theoretical background including modeling techniques for
mechanical systems is provided which allows for the computer aided
generation of the symbolic equation of motion for multibody
systems. It is shown how the governing equations for different types
of problems in structural mechanics can be automatically derived and
how to implement finite element techniques via computer algebra
software. Perturbation methods as a very powerful approach for
nonlinear problems are discussed in detail and are demonstrated for a
number of applications. The applications covered in this book
represent some of the most advanced topics in the rapidly growing
field of research on symbolic computation."
}
\end{chunk}
\index{Dom\'inguez, C\'esar}
\index{Rubio, Julio}
\begin{chunk}{axiom.bib}
@InProceedings{Domi01,
author = {Dom\'inguez, C\'esar; Rubio, Julio},
title = "Modeling Inheritance as Coercion in a Symbolic Computation System",
booktitle = "Proc. ISSAC 2001",
series = "ISSAC 2001",
year = "2001",
keywords = "axiomref",
paper = "Domi01.pdf",
abstract =
"In this paper the analysis of the data structures used in a symbolic
computation system, called Kenzo, is undertaken. We deal with the
specification of the inheritance relationship since Kenzo is an
objectoriented system, written in CLOS, the Common Lisp Object
System. We focus on a particular case, namely the relationship between
simplicial sets and chain complexes, showing how the ordersorted
algebraic specifications formalisms can be adapted, through the
``inheritance as coercion'' metaphor, in order to model this Kenzo
fragment."
}
\end{chunk}
\index{Weber, Andreas}
\begin{chunk}{axiom.bib}
@InProceedings{Webe94,
author = "Weber, Andreas",
title = "Algorithms for Type Inference with Coercions",
booktitle = "Proc ISSAC 94",
series = "ISSAC 94",
year = "1994",
keywords = "axiomref",
paper = "Webe94.pdf",
abstract =
"This paper presents algorithms that perform a type inference for a
type system occurring in the context of computer algebra. The type
system permits various classes of coercions between types and the
algorithms are complete for the precisely defined system, which can be
seen as a formal description of an important subset of the type system
supported by the computer algebra program Axiom.
Previously only algorithms for much more restricted cases of coercions
have been described or the frameworks used have been so general that
the corresponding type inference problems were known to be
undecidable."
}
\end{chunk}
\index{Sutor, Robert S.}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@article{Suto87,
author = "Sutor, Robert S. and Jenks, Richard D.",
title = "The type inference and coercion facilities in the Scratchpad II
interpreter",
journal = "SIGPLAN Notices",
volume = "22",
number = "7",
pages = "5663",
year = "1987",
isbn = "0897912357",
paper = "Suto87.pdf",
keywords = "axiomref",
abstract =
"The Scratchpad II system is an abstract datatype programming
language, a compiler for the language, a library of packages of
polymorphic functions and parametrized abstract datatypes, and an
interpreter that provides sophisticated type inference and coercion
facilities . Although originally designed for the implementation of
symbolic mathematical algorithms, Scratchpad 11 is a general purpose
programming language . This paper discusses aspects of the
implementation of the interpreter and how it attempts to provide a
user friendly and relatively weakly typed front end for the strongly
typed programming language."
}
\end{chunk}
\index{van Leeuwen, Andr\'e M.A.}
\begin{chunk}{axiom.bib}
@misc{Leeuxx,
author = {van Leeuwen, Andr\'e M.A.},
title = "Representation of mathematical object in interactive books",
paper = "Leeuxx.pdf",
abstract = "
We present a model for the representation of mathematical objects in
structured electronic documents, in a way that allows for interaction
with applications such as computer algebra systems and proof checkers.
Using a representation that reflects only the intrinsic information of
an object, and storing applicationdependent information in socalled
{\sl application descriptions}, it is shown how the translation from
the internal to an external representation and {\sl vice versa} can be
achieved. Hereby a formalisation of the concept of {\sl context} is
introduced. The proposed scheme allows for a high degree of
application integration, e.g., parallel evaluation of subexpressions
(by different computer algebra systems), or a proof checker using a
computer algebra system to verify an equation involving a symbolic
computation."
}
\end{chunk}
\index{Jenks, Richard D.}
\index{Trager, Barry M.}
\begin{chunk}{ignore}
@InProceedings{Jenk94,
author = "Jenks, Richard D. and Trager, Barry M.",
booktitle = "Proceedings of the ACMSIGSAM 1989 International
Symposium on Symbolic and Algebraic Computation, ISSAC '94",
series = "ISSAC 94",
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{Poll, Erik}
\index{Thompson, Simon}
\begin{chunk}{axiom.bib}
@misc{Poll99a,
author = "Poll, Erik and Thompson, Simon",
title = "The Type System of Aldor",
url = "http://www.cs.kent.ac.uk/pubs/1999/874/content.ps",
paper = "Poll99a.pdf",
keywords = "axiomref",
abstract =
"This paper gives a formal description of  at least a part of 
the type system of Aldor, the extension language of the Axiom.
In the process of doing this a critique of the design of the system
emerges."
}
\end{chunk}
\index{Boulanger, JeanLouis}
\begin{chunk}{axiom.bib}
@misc{Boul93b,
author = "Boulanger, JeanLouis",
title = "AXIOM, A Functional Language with Object Oriented Development",
year = "1993",
paper = "Boul93b.pdf",
keywords = "axiomref",
abstract =
"We present in this paper, a study about the computer algebra system
Axiom, which gives us many very interesting Software engineering
concepts. This language is a functional language with an Object
Oriented Development. This feature is very important for modeling the
mathematical world (Hierarchy) and provides a running with
mathematical sense. (All objects are functions). We present many
problems of running and development in Axiom. We can note that Aiom is
the only system of this category."
}
\end{chunk}
\index{Brown, Ronald}
\index{Dreckmann, Winfried}
\begin{chunk}{axiom.bib}
@misc{Brow95,
author = "Brown, Ronald and Dreckmann, Winfried",
title = "Domains of data and domains of terms in AXIOM",
year = "1995",
keywords = "axiomref",
url = "http://axiomwiki.newsynthesis.org/public/refs/brownfreecg.pdf",
paper = "Brow95.pdf",
abstract = "
The main new concept we wish to illustrate in this paper is a
distinction between ``domains of data'' and ``domains of terms'', and
its use in the programming of certain mathematical structures.
Although this distinction is implicit in much of the programming work
that has gone into the construction of Axiom categories and domains,
we believe that a formalisation of this is new, that standards and
conventions are necessary and will be useful in various other
contexts. We shall show how this concept may be used for the coding of
free categories and groupoids on directed graphs."
}
\end{chunk}
\index{Danielsson, Nils Anders}
\index{Hughes, John}
\index{Jansson, Patrik}
\index{Gibbons, Jeremy}
\begin{chunk}{axiom.bib}
@InProceedings{Dani06,
author = "Danielsson, Nils Anders and Hughes, John and Jansson, Patrik and
Gibbons, Jeremy",
title = "Fast and Loose Reasoning is Morally Correct",
booktitle = "Proc. of ACM POPL '06",
series = "POPL '06",
year = "2006",
location = "Charleston, South Carolina",
keywords = "axiomref",
paper = "Dani06.pdf",
abstract =
"Functional programmers often reason about programs as if they were
written in a total language, expecting the results to carry over to
nontoal (partial) languages. We justify such reasoning.
Two languages are defined, one total and one partial, with identical
syntax. The semantics of the partial language includes partial and
infinite values, and all types are lifted, including the function
spaces. A partial equivalence relation (PER) is then defined, the
domain of which is the total subset of the partial language. For types
not containing function spaces the PER relates equal values, and
functions are related if they map related values to related values.
It is proved that if two closed terms have the same semantics in the
total language, then they have related semantics in the partial
language. It is also shown that the PER gives rise to a bicartesian
closed category which can be used to reason about values in the domain
of the relation."
}
\end{chunk}
\index{Doye, Nicolas James}
\begin{chunk}{axiom.bib}
@phdthesis{Doye97,
author = "Doye, Nicolas James",
title = "Order Sorted Computer Algebra and Coercions",
school = "University of Bath",
year = "1997",
keywords = "axiomref",
paper = "Doye97.pdf",
abstract =
"Computer algebra systems are large collections of routines for solving
mathematical problems algorithmically, efficiently and above all,
symbolically. The more advanced and rigorous computer algebra systems
(for example, Axiom) use the concept of strong types based on
ordersorted algebra and category theory to ensure that operations are
only applied to expressions when they ``make sense''.
In cases where Axiom uses notions which are not covered by current
mathematics we shall present new mathematics which will allow us to
prove that all such cases are reducible to cases covered by the
current theory. On the other hand, we shall also point out all the
cases where Axiom deviates undesirably from the mathematical ideal.
Furthermore we shall propose solutions to these deviations.
Strongly typed systems (especially of mathematics) become unusable
unless the system can change the type in a way a user expects. We wish
any change expected by a user to be automated, ``natural'', and
unique. ``Coercions'' are normally viewed as ``natural type changing
maps''. This thesis shall rigorously define the word ``coercion'' in
the context of computer algebra systems.
We shall list some assumptions so that we may prove new results so
that all coercions are unique. This concept is called ``coherence''.
We shall give an algorithm for automatically creating all coercions in
type system which adheres to a set of assumptions. We shall prove that
this is an algorithm and that it always returns a coercion when one
exists. Finally, we present a demonstration implementation of this
automated coerion algorithm in Axiom."
}
\end{chunk}
\index{Dunstan, Martin}
\index{Kelsey, Tom}
\index{Martin, Ursula}
\index{Linton, Steve A.}
\begin{chunk}{axiom.bib}
@InProceedings{Duns99,
author = "Dunstan, Martin and Kelsey, Tom and Martin, Ursula and
Linton, Steve A.",
title = "Formal Methods for Extensions to CAS",
booktitle = "Proc. of FME'99",
series = "FME'99",
location = "Toulouse, France",
year = "1999",
pages = "17581777",
url = "http://tom.host.cs.standrews.ac.uk/pub/fm99.ps",
paper = "Duns99.pdf",
keywords = "axiomref",
abstract =
"We demonstrate the use of formal methods tools to provide a semantics
for the type hierarchy of the AXIOM computer algebra system, and a
methodology for Aldor program analysis and verification. We give a
case study of abstract specifications of AXIOM primitives, and provide
an interface between these abstractions and Aldor code."
}
\end{chunk}
\index{Boehm, HansJ.}
\index{Cartwright, Robert}
\index{Riggle, Mark}
\index{O'Donnell, Michael J.}
\begin{chunk}{axiom.bib}
author = "Boehm, HansJ. and Cartwright, Robert and Riggle, Mark and
O'Donnell, Michael J.",
title = "Exact Real Arithmetic: A Case Study in Higher Order Programming",
url = "http://dev.acm.org/pubs/citations/proceedings/lfp/319838/p162boehm",
paper = "Boeh86.pdf",
abstract =
"Two methods for implementing {\sl exact} real arithmetic are explored
One method is based on formulating real numbers as functions that map
rational tolerances to rational approximations. This approach, which
was developed by constructive mathematicians as a concrete
formalization of the real numbers, has lead to a surpris ingly
successful implementation. The second method formulates real numbers
as potentially infinite sequences of digits, evaluated on demand.
This approach has frequently been advocated by proponents of lazy
functional languages in the computer science community. Ironically,
it leads to much less satisfactory implementations. We discuss the
theoretical problems involved m both methods, give algortthms for the
basic arithmetic operations, and give an empirical comparison of the
two techniques. We conclude wtth some general observations about the
lazy evaluation paradigm and its implementation."
}
\end{chunk}
\index{Gruntz, Dominik}
\begin{chunk}{axiom.bib}
@phdthesis{Grun96,
author = "Gruntz, Dominik",
title = "On Computing Limits in a Symbolic Manipulation System",
school = "Swiss Federal Institute of Technology Zurich",
year = "1996",
paper = "Grun96.pdf",
url = "http://www.cybertester.com/data/gruntz.pdf",
keywords = "axiomref",
abstract = "
This thesis presents an algorithm for computing (onesided) limits
within a symbolic manipulation system. Computing limtis is an
important facility, as limits are used both by other functions such as
the definite integrator and to get directly some qualitative
information about a given function.
The algorithm we present is very compact, easy to understand and easy
to implement. It overcomes the cancellation problem other algorithms
suffer from. These goals were achieved using a uniform method, namely
by expanding the whole function into a series in terms of its most
rapidly varying subexpression instead of a recursive bottom up
expansion of the function. In the latter approach exact error terms
have to be kept with each approximation in order to resolve the
cancellation problem, and this may lead to an intermediate expression
swell. Our algorithm avoids this problem and is thus suited to be
implemented in a symbolic manipulation system."
}
\end{chunk}
\index{Boulm\'e, S.}
\index{Hardin, T.}
\index{Rioboo, Renaud}
\begin{chunk}{axiom.bib}
@misc{Boul00,
author = "Boulme, S. and Hardin, T. and Rioboo, R.",
title = "Polymorphic Data Types, Objects, Modules and Functors,:
is it too much?",
url = "ftp://ftp.lip6.fr/lip6/reports/2000/lip6.2000.014.ps.gz",
paper = "Boul00.pdf",
keywords = "axiomref",
abstract = "
Abstraction is a powerful tool for developers and it is offered by
numerous features such as polymorphism, classes, modules, and
functors, $\ldots$ A working programmer may be confused by this
abundance. We develop a computer algebra library which is being
certificed. Reporting this experience made with a language (Ocaml)
offering all these features, we argue that the are all needed
together. We compare several ways of using classes to represent
algebraic concepts, trying to follow as close as possible mathematical
specification. Then we show how to combine classes and modules to
produce code having very strong typing properties. Currently, this
library is made of one hundred units of functional code and behaves
faster than analogous ones such as Axiom."
}
\end{chunk}
\index{Conrad, Marc}
\index{French, Tim}
\index{Maple, Carsten}
\index{Pott, Sandra}
\begin{chunk}{axiom.bib}
@misc{Conrxxb,
author = "Conrad, Marc and French, Tim and Maple, Carsten and Pott, Sandra",
title = "Mathematical Use Cases lead naturally to nonstandard Inheritance
Relationships: How to make them accessible in a mainstream language?",
paper = "Conrxxb.pdf",
keywords = "axiomref",
abstract = "
Conceptually there is a strong correspondence between Mathematical
Reasoning and ObjectOriented techniques. We investigate how the ideas
of Method Renaming, Dynamic Inheritance and Interclassing can be used
to strengthen this relationship. A discussion is initiated concerning
the feasibility of each of these features."
}
\end{chunk}
\index{Dunstan, Martin N.}
\begin{chunk}{axiom.bib}
@phdthesis{Duns99a,
author = "Dunstan, Martin N.",
title = "Larch/Aldor  A Larch BISL for AXIOM and Aldor",
school = "University of St. Andrews",
year = "1999",
paper = "Duns99a.pdf",
keywords = "axiomref",
abstract = "
In this thesis we investigate the use of lightweight formal methods
and verification conditions (VCs) to help improve the reliability of
components constructed within a computer algebra system. We follow the
Larch approach to formal methods and have designed a new behavioural
interface specification language (BISL) for use with Aldor: the
compiled extension language of Axiom and a fullyfeatured programming
language in its own right. We describe our idea of lightweight formal
methods, present a design for a lightweight verification condition
generator and review our implementation of a prototype verification
condition generator for Larch/Aldor."
}
\end{chunk}
\index{Thompson, Simon}
\index{Timochouk, Leonid}
\begin{chunk}{axiom.bib}
@misc{Thomxx,
author = "Thompson, Simon and Timochouk, Leonid",
title = "The Aldor\\ language",
paper = "Thomxx.pdf",
keywords = "axiomref",
abstract = "
This paper introduces the \verbAldor language, which is a
functional programming language with dependent types and a powerful,
typebased, overloading mechanism. The language is built on a subset
of Aldor, the 'library compiler' language for the Axiom computer
algebra system. \verbAldor is designed with the intention of
incorporating logical reasoning into computer algebra computations.
The paper contains a formal account of the semantics and type system
of \verbAldor; a general discussion of overloading and how the
overloading in \verbAldor fits into the general scheme; examples
of logic within \verbAldor and notes on the implementation of the
system."
}
\end{chunk}
\index{Davenport, James H.}
\index{Fitch, John}
\begin{chunk}{axiom.bib}
@misc{Dave07,
author = "Davenport, James H. and Fitch, John",
title = "Computer Algebra and the three 'E's: Efficiency, Elegance, and
Expressiveness",
url = "http://staff.bath.ac.uk/masjhd/Drafts/PLMMS2007",
paper = "Dave07.pdf",
keywords = "axiomref",
abstract =
"What author of a programming language would not claim that the 3 'E's
were the goals? Nevertheless, we claim that computer algebra does lead
to particular emphases, and constraints, in these areas.
We restrict ``efficiency'' to mean machine efficiency, since the other
'E's cover programmer efficiency. For the sake of clarity, we describe
as ``expressiveness'', what can be expressed in the language, and
``elegance'' as how it can be expressed."
}
\end{chunk}
\index{Jager, Bram De}
\index{van Asch, Bram}
\begin{chunk}{axiom.bib}
@article{Jage96,
author = "Jager, Bram De and van Asch, Bram",
title = "Symbolic Solutions for a Class of Partial Differential Equations",
journal = "J. Symbolic Computation",
volume = "22",
pages = "459468",
paper = "Jage96.pdf",
url = "http://www.mate.tue.nl/mate/pdfs/1610.pdf",
keywords = "axiomref",
abstract =
"An algorithm to generate solutions for members of a class of
completely integrable partial differential equations has been derived
from a constructive proof of Frobenius' Theorem. The algorithm is
implemented as a procedure in the computer algebra system
Maple. Because the implementation uses the facilities of Maple for
solving sets of ordinary differential equations and for sets of
nonlinear equations, and those facilities are limited, the problems
that actually can be solved are restricted in size and
complexity. Several examples, some derived from industrial practice,
are presented to illustrate the use of the algorithm and to
demonstrate the advantages and shortcomings of the implementation."
}
\end{chunk}
\index{Hereman, Willy}
\begin{chunk}{axiom.bib}
@article{Here97,
author = "Hereman, Willy",
title = "Review of Symbolic Software for Lie Symmetry Analysis",
journal = "Math. Comput. Modelling",
volume = "25",
number = "8/9",
pages = "115132",
year = "1997",
keywords = "axiomref",
paper = "Here97.pdf",
abstract =
"Sophus Lie (18421899) pioneered the study of continuous
transformation groups that leave systems of differential equations
invariant. Lie’s work [l3] brought diverse and ad hoc integration
methods for solving special classes of differential equations under a
common conceptual umbrella. Indeed, Lie’s infinitesimal
transformation method provides a widely applicable technique to find
closed form solutions of ordinary differential equations (ODES).
Standard solution methods for firstorder or linear ODES can be
characterized in terms of symmetries. Through the group
classification of ODES, Lie succeeded in identifying all ODES that can
either be reduced to lowerorder ones or be completely integrated via
group theoretic techniques.
Applied to partial differential equations (PDEs), Lie’s method [2]
leads to groupinvariant solutions and conservation laws. Exploiting
the symmetries of PDEs, new solutions can be derived from known ones,
and PDEs can be classified into equivalence classes. Furthermore,
groupinvariant solutions obtained via Lie’s approach may provide
insight into the physical models themselves, and explicit solutions
can serve as benchmarks in the design, accuracy testing, and
comparison of numerical algorithms.
Nowadays, the concept of symmetry plays a key role in the study and
development of mathematics and physics. Indeed, the theory of Lie
groups and Lie algebras is applied to diverse fields of mathematics
including differential geometry, algebraic topology, bifurcation
theory, to name a few. Lie’s original ideas greatly influenced the
study of physically important systems of differential equations in
classical and quantum mechanics, fluid dynamics, elasticity, and many
other applied areas [481].
The application of Lie group methods to concrete physical systems
involves tedious computations. Even the calculation of the
continuous symmetry group of a modest system of differential equations
is prone to errors, if done with pencil and paper. Computer algebra
systems (CAS) such as Mathematica, MACSYMA, Maple, REDUCE, AXIOM and
MuPAD are extremely useful for such computations. Symbolic packages
[911], written in the language of these GAS, can find the determining
equations of the Lie symmetry group. The most sophisticated packages
then reduce these into an equivalent but more suitable system,
subsequently solve that system in closed form, and go on to calculate
the infinitesimal generators that span the Lie algebra of symmetries.
In Section 2, we discuss methods and algorithms used in the
computation of Lie symmetries. We address the computation of
determining systems, their reduction to standard form, solution
techniques, and the computation of the size of the symmetry group.
In Section 3, we look beyond Liepoint symmetries, addressing contact
and generalized symmetries, as well as nonclassical or conditional
symmetries.
Section 4 is devoted to a review of modern Lie symmetry
programs, classified according to the underlying CAS. The review
focuses on Lie symmetry software for classical Liepoint symmetries,
contact (or dynamical), generalized (or LieBacklund) symmetries,
nonclassical (or conditional) symmetries. Most of these packages were
written in the last decade. Researchers interested in details about
pioneering work should consult [9,10,12]. In Section 5, two examples
illustrate results that can be obtained with Lie symmetry software.
In Section 6 we draw some conclusions.
Lack of space forces us to give only a few key references for the Lie
symmetry packages. A comprehensive survey of the literature devoted
to theoretical as well as computational aspects of Lie symmetries,
with over 300 references, can be found elsewhere [11]."
}
\end{chunk}
\index{Minoiu, N.}
\index{Netto, M}
\index{Mammar, S}
\begin{chunk}{axiom.bib}
@misc{Mino07,
author = "Minoiu, N. and Netto, M and Mammar, S",
title = "Assistance control based on a composite Lyapunov function for
lane departure avoidance",
booktitle = "Proc. 15 Med. Conf. on Control \& Automation",
year = "2007",
keywords = "axiomref",
abstract =
"This paper presents a vehicle steering assistance designed to avoid
lane departure during driver inattention periods. Activated for a
driver loss of concentration during a lane keeping maneuver the
steering assistance drives the vehicle back to the center of the
lane. In order to ensure a vehicle trajectory as close as possible to
the centerline, the control law has been developed based on invariant
sets theory and on composite Lyapunov functions. The computation has
been performed using LMI methods, which allow in addition imposing a
maximum bound for the control steering angle."
}
\end{chunk}
\index{Davenport, James H.}
\begin{chunk}{ignore}
@misc{Dave12a,
author = "Davenport, James H.",
title = "Computer Algebra or Computer Mathematics?",
year = "2012",
url = "http://people.bath.ac.uk/masjhd/Slides/CalculemusSchool2002.pdf",
paper = "Dave12a.pdf",
abstract =
"Scope: ``polynomialtype'' systems: Axiom, Macsyma/Maxima, Maple,
Mathematica, and Reduce."
}
\index{Dicrescenzo, C.}
\index{Duval, Dominique}
\begin{chunk}{axiom.bib}
@InProceedings{Dicr88,
author = "Dicrescenzo, C. and Duval, D.",
title = "Algebraic extensions and algebraic closure in Scratchpad II",
booktitle = "Proc. ISSAC 1988",
series = "ISSAC 1998",
year = "1998",
pages = "440446",
isbn = "3540510842",
keywords = "axiomref"
}
\end{chunk}
\begin{chunk}{axiom.bib}
@misc{Unkn16,
title = "Computer Algebra Systems",
url = "http://www.mhtlab.uwaterloo.ca/courses/me755/web\_intro.pdf",
paper = "Unkn16.pdf"
}
\end{chunk}
\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@InProceedings{Wang02,
author = "Wang, Dongming",
title = "Epsilon: A Library of Software Tools for Polynomial Elimination",
booktitle = "Proc. 1st Int. Congress of Mathematical Software",
series = "ICMS 2002",
year = "2002",
location = "Beijing China",
pages = "379389",
keywords = "axiomref",
paper = "Wang02.pdf",
url = "https://hal.inria.fr/inria00107607/file/A02R314.pdf",
abstract =
"This article presents a Maple library of functions for decomposing
systems of multivariate polynomials into triangular systems of
various kinds (regular, simple, or irreducible), with an application
package for manipulating and proving geometric theorems."
}
\end{chunk}
\index{Gr\"abe, HansGert}
\begin{chunk}{axiom.bib}
@InProceedings{Grab02,
author = "Grabe, HansGert",
title = "The SymbolicData Benchmark Problems Collection of Polynomial
Systems",
booktitle = "Workshop on Under and Overdetermined Systems of Algebraic or
Differential Equations",
location = "Karlsruhe, Germany",
pages = "5776",
url = "http://symbolicdata.org/Papers/karlsruhe02.pdf",
paper = "Grab02.pdf",
keywords = "axiomref"
}
\end{chunk}
\index{Norman, Arthur C.}
\begin{chunk}{axiom.bib}
@misc{Norm94,
author = "Norman, Arthur C.",
title = "Algebraic Manipulation",
paper = "Norm94.pdf",
keywords = "axiomref"
}
\end{chunk}
\index{Joyner, David}
\begin{chunk}{axiom.bib}
@misc{Joyn16,
author = "Joyner, David",
title = "Links to some open source mathematical programs",
keywords = "axiomref",
url = "http://www.opensourcemath.org/opensource\_math.html"
}
\end{chunk}
\index{Cohen, Joel S.}
\begin{chunk}{axiom.bib}
@book{Cohe03b,
author = "Cohen, Joel S.",
title = "Computer algebra and symbolic computation. Elementary Algorithms",
year = "2003",
publisher = "A. K. Peters",
isbn = "1568811594",
keywords = "axiomref",
paper = "Cohe03b.pdf"
}
\end{chunk}
\index{Decker, Wolfram}
\begin{chunk}{axiom.bib}
@misc{Deckxx,
author = "Decker, Wolfram",
title = "Some Introductory Remarks on Computer Algebra",
url =
"https://www.math.unibielefeld.de/~rehmann/ECM/cdrom/3ecm/pdfs/pant3/decker.pdf",
paper = "Deckxx.pdf",
keywords = "axiomref",
abstract =
"Computer algebra is a relatively young but rapidly growing field. In
this introductory note to the minisymposium on computer algebra
organized as part of the third European Congress of Mathematics I will
not even attempt to adress all major streams of research and the many
applications of computer algebra. I will concentrate on a few aspects,
mostly from a mathematical point of view, and I will discuss a few
typical applications in mathematics. I will present a couple of
examples which underline the fact that computer algebra systems
provide easy access to powerful computing tools. And, I will quote
from and refer to a couple of survey papers, textbooks and webpages
which I recommend for further reading."
}
\end{chunk}
\index{Chew, Paul}
\index{Constable, Robert L.}
\index{Pingali, Keshav}
\index{Vavasis, Steve}
\index{Zippel, Richard}
\begin{chunk}{axiom.bib}
@misc{Chew95,
author = "Chew, Paul and Constable, Robert L. and Pingali, Keshav and
Vavasis, Steve and Zippel, Richard",
title = "Collaborative Mathematics Environment",
url = "http://www.cs.cornell.edu/rz/MathBus95/TechSummary.html",
keywords = "axiomref"
}
\end{chunk}
\index{Simon, Barry}
\begin{chunk}{axiom.bib}
@misc{Simo97,
author = "Simon, Barry",
title = "The PC Is Now Axiomatic",
publisher = "PC Mag",
year = "1997",
month = "March",
day = "25",
keywords = "axiomref"
}
\end{chunk}
\index{Batut, C.}
\index{Belabas, K.}
\index{Bernardi, D.}
\index{Cohen, H.}
\index{Olivier, M.}
\begin{chunk}{axiom.bib}
@misc{Batu03,
author = "Batut, C. and Belabas, K. and Bernardi, D. and Cohen, H. and
Olivier, M.",
title = "User's Guide to PARI/GP",
url = "http://math.mit.edu/~brubaker/PARI/PARIusers.pdf",
paper = "Batu03.pdf",
keywords = "axiomref"
}
\end{chunk}
\index{Gianni, Patrizia}
\index{Trager, Barry M.}
\index{Zacharias, Gail}
\begin{chunk}{axiom.bib}
@article{Gian88,
author = "Gianni, Patrizia. and Trager, Barry. and Zacharias, Gail",
title = "Groebner Bases and Primary Decomposition of Polynomial Ideals",
journal = "J. Symbolic Computation",
volume = "6",
pages = "149167",
year = "1988",
url = "http://www.sciencedirect.com/science/article/pii/S0747717188800403/pdf?md5=40c29b67947035884904fd4597ddf710&pid=1s2.0S0747717188800403main.pdf",
paper = "Gian88.pdf"
}
\end{chunk}
\begin{chunk}{axiom.bib}
@misc{Wikixx,
title = "List of opensource software for mathematics",
url = "https://en.wikipedia.org/wiki/List\_of\_opensource\_software\_for\_mathematics",
keywords = "axiomref"
}
\end{chunk}
\index{Joyner, David}
\index{Stein, William}
\begin{chunk}{axiom.bib}
@misc{Joyn08,
author = "Joyner, David and Stein, William",
title = "Open Source Mathematical Software: A White Paper",
year = "2008",
url =
"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.124.7499&rep=rep1&type=pdf",
paper = "Joyn08.pdf",
keywords = "axiomref",
abstract =
"Open source software has had a profound effect on computing during
the last decade, especially on web servers (Apache), web browsers
(Firefox), operating systems (Linux and OS X), and programming
languages (GC C, Java, Python, Perl, etc.). The purpose of this paper
is to put forward the case that open source development methodologies
might also have a positive effect on mathematical software,
especially if the National Science Foundation (NSF) increases their
support of open source mathematical software de velopment. We argue
that careful funding of open source mathematical software may lead to
a lower total cost of ownership in the research and education
community, and to more efficient and trustworthy mathematical software."
}
\end{chunk}
\index{Nguyen, Minh Van}
\begin{chunk}{axiom.bib}
@phdthesis{Nguy09,
author = "Nguyen, Minh Van",
title = "Exploring Cryptography Using the Sage Computer Algebra System",
school = "Victoria University",
year = "2009",
keywords = "axiomref",
paper = "Nguy09.pdf",
abstract =
"Cryptography has become indispensable in areas such as ecommerce,
the legal safeguarding of medical records, and secure electronic
communication. Hence, it is incumbent upon software engineers to
understand the concepts and techniques underlying the cryptosystems
that they implement. An educator needs to consider which topics to
cover in a course on cryptography as well as how to present the
concepts and techniques to be covered in the course. This thesis
contributes to the field of cryptography pedagogy by discussing and
implementing smallscale cryptosystems whose encryption and
decryption processes can be stepped through by hand. Our
implementation has been accepted and integrated into the code base of
the computer algebra system Sage. As Sage is free and open source,
students and educators of cryptology need not worry about paying
license fees in order to use Sage, but can instead concentrate on
exploring cryptography using Sage’s builtin support for cryptography."
}
\end{chunk}
\index{Hoeven, Joris van der}
\index{Lecerf, Gregoire}
\begin{chunk}{axiom.bib}
@misc{Hoev13,
author = "Hoeven, Joris van der and Lecerf, Gregoire",
title = "Interfacing Mathemagix with C++",
keywords = "axiomref",
url = "http://www.texmacs.org/joris/mmxcpp/mmxcpp.pdf",
paper = "Hoev13.pdf",
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{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate94,
author = "Fateman, Richard J.",
title = "On the Design and Construction of Algebraic Manipulation Systems",
keywords = "axiomref",
url = "http://www.cs.berkeley.edu/~fateman/papers/asmerev94.ps",
paper = "Fate94.pdf",
abstract =
"We compare and contrast several techniques for the implementation of
components of an algebraic manipulation system. On one hand is the
mathematicalalgebraic approach which characterizes (for example)
IBM's Axiom. On the other hand is the more {\sl adhoc} approach which
characterizes many other popular systems (for example, Macsyma,
Reduce, Maple, and Mathematica). While the algebraic approach has
generally positive results, careful examination suggests that there
are significant remaining problems, especially in the representation
and manipulation of analytical, as opposed to algebraic,
mathematics. We describe some of these problems and some general
approaches for solutions."
}
\end{chunk}

books/bookvolbib.pamphlet  801 ++++++++++++++++
changelog  2 +
patch  1783 ++++++++++++++++++
src/axiomwebsite/patches.html  2 +
4 files changed, 1512 insertions(+), 1076 deletions()
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 8e72be5..a22a1d2 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 4664,11 +4664,14 @@ Martin, U.
\index{Boulm\'e, S.}
\index{Hardin, T.}
\index{Rioboo, Renaud}
\begin{chunk}{ignore}
\bibitem[Boulme 00]{BHR00} Boulm\'e, S.; Hardin, T.; Rioboo, R.
+\begin{chunk}{axiom.bib}
+@misc{Boul00,
+ author = "Boulme, S. and Hardin, T. and Rioboo, R.",
title = "Polymorphic Data Types, Objects, Modules and Functors,:
is it too much?",
 paper = "BHR00.pdf",
+ url = "ftp://ftp.lip6.fr/lip6/reports/2000/lip6.2000.014.ps.gz",
+ paper = "Boul00.pdf",
+ keywords = "axiomref",
abstract = "
Abstraction is a powerful tool for developers and it is offered by
numerous features such as polymorphism, classes, modules, and
@@ 4678,10 +4681,11 @@ Martin, U.
offering all these features, we argue that the are all needed
together. We compare several ways of using classes to represent
algebraic concepts, trying to follow as close as possible mathematical
 specification. Thenwe show how to combine classes and modules to
+ specification. Then we show how to combine classes and modules to
produce code having very strong typing properties. Currently, this
library is made of one hundred units of functional code and behaves
faster than analogous ones such as Axiom."
+}
\end{chunk}
@@ 4741,15 +4745,19 @@ Martin, U.
\index{Hughes, John}
\index{Jansson, Patrik}
\index{Gibbons, Jeremy}
\begin{chunk}{ignore}
\bibitem[Danielsson 06]{Dani06} Danielsson, Nils Anders; Hughes, John;
Jansson, Patrik; Gibbons, Jeremy
+\begin{chunk}{axiom.bib}
+@InProceedings{Dani06,
+ author = "Danielsson, Nils Anders and Hughes, John and Jansson, Patrik and
+ Gibbons, Jeremy",
title = "Fast and Loose Reasoning is Morally Correct",
 year = "2005",
ACM POPL'06 January 2006, Charleston, South Carolina, USA
+ booktitle = "Proc. of ACM POPL '06",
+ series = "POPL '06",
+ year = "2006",
+ location = "Charleston, South Carolina",
+ keywords = "axiomref",
paper = "Dani06.pdf",
 abstract = "
 Functional programmers often reason about programs as if they were
+ abstract =
+ "Functional programmers often reason about programs as if they were
written in a total language, expecting the results to carry over to
nontoal (partial) languages. We justify such reasoning.
@@ 4766,6 +4774,7 @@ ACM POPL'06 January 2006, Charleston, South Carolina, USA
language. It is also shown that the PER gives rise to a bicartesian
closed category which can be used to reason about values in the domain
of the relation."
+}
\end{chunk}
@@ 4890,14 +4899,14 @@ Calculemus (2011) Springer
\end{chunk}
\index{Dunstan, Martin}
\begin{chunk}{ignore}
\bibitem[Dunstan 99a]{Dun99a} Dunstan, MN
+\index{Dunstan, Martin N.}
+\begin{chunk}{axiom.bib}
+@phdthesis{Duns99a,
+ author = "Dunstan, Martin N.",
title = "Larch/Aldor  A Larch BISL for AXIOM and Aldor",
+ school = "University of St. Andrews",
year = "1999",
PhD Thesis, 1999
 url = "http://www.cs.standrews.uk/files/publications/Dun99.php",
 paper = "Dun99a.pdf",
+ paper = "Duns99a.pdf",
keywords = "axiomref",
abstract = "
In this thesis we investigate the use of lightweight formal methods
@@ 4910,6 +4919,7 @@ PhD Thesis, 1999
methods, present a design for a lightweight verification condition
generator and review our implementation of a prototype verification
condition generator for Larch/Aldor."
+}
\end{chunk}
@@ 4917,19 +4927,26 @@ PhD Thesis, 1999
\index{Kelsey, Tom}
\index{Martin, Ursula}
\index{Linton, Steve A.}
\begin{chunk}{ignore}
\bibitem[Dunstan 00]{Dun00} Dunstan, Martin; Kelsey, Tom; Martin, Ursula;
Linton, Steve
+\begin{chunk}{axiom.bib}
+@InProceedings{Duns99,
+ author = "Dunstan, Martin and Kelsey, Tom and Martin, Ursula and
+ Linton, Steve A.",
title = "Formal Methods for Extensions to CAS",
FME'99, Toulouse, France, Sept 2024, 1999, pp 17581777
+ booktitle = "Proc. of FME'99",
+ series = "FME'99",
+ location = "Toulouse, France",
+ year = "1999",
+ pages = "17581777",
url = "http://tom.host.cs.standrews.ac.uk/pub/fm99.ps",
 paper = "Dun00.pdf",
 abstract = "
 We demonstrate the use of formal methods tools to provide a semantics
+ paper = "Duns99.pdf",
+ keywords = "axiomref",
+ abstract =
+ "We demonstrate the use of formal methods tools to provide a semantics
for the type hierarchy of the AXIOM computer algebra system, and a
methodology for Aldor program analysis and verification. We give a
case study of abstract specifications of AXIOM primitives, and provide
an interface between these abstractions and Aldor code."
+}
\end{chunk}
@@ 5154,16 +5171,19 @@ Munteanu, Bogdan; Brooker, Marc; Deardeuff, Michael
\index{Poll, Erik}
\index{Thompson, Simon}
\begin{chunk}{ignore}
\bibitem[Poll 99]{PT99} Poll, Erik; Thompson, Simon
+\begin{chunk}{axiom.bib}
+@misc{Poll99a,
+ author = "Poll, Erik and Thompson, Simon",
title = "The Type System of Aldor",
url = "http://www.cs.kent.ac.uk/pubs/1999/874/content.ps",
 paper = "PT99.pdf",
 abstract = "
 This paper gives a formal description of  at least a part of 
+ paper = "Poll99a.pdf",
+ keywords = "axiomref",
+ abstract =
+ "This paper gives a formal description of  at least a part of 
the type system of Aldor, the extension language of the Axiom.
In the process of doing this a critique of the design of the system
emerges."
+}
\end{chunk}
@@ 5184,12 +5204,28 @@ Munteanu, Bogdan; Brooker, Marc; Deardeuff, Michael
\index{Cartwright, Robert}
\index{Riggle, Mark}
\index{O'Donnell, Michael J.}
\begin{chunk}{ignore}
\bibitem[Boehm 86]{Boe86} Boehm, HansJ.; Cartwright, Robert; Riggle, Mark;
O'Donnell, Michael J.
+\begin{chunk}{axiom.bib}
+ author = "Boehm, HansJ. and Cartwright, Robert and Riggle, Mark and
+ O'Donnell, Michael J.",
title = "Exact Real Arithmetic: A Case Study in Higher Order Programming",
url = "http://dev.acm.org/pubs/citations/proceedings/lfp/319838/p162boehm",
 paper = "Boe86.pdf",
+ paper = "Boeh86.pdf",
+ abstract =
+ "Two methods for implementing {\sl exact} real arithmetic are explored
+ One method is based on formulating real numbers as functions that map
+ rational tolerances to rational approximations. This approach, which
+ was developed by constructive mathematicians as a concrete
+ formalization of the real numbers, has lead to a surpris ingly
+ successful implementation. The second method formulates real numbers
+ as potentially infinite sequences of digits, evaluated on demand.
+ This approach has frequently been advocated by proponents of lazy
+ functional languages in the computer science community. Ironically,
+ it leads to much less satisfactory implementations. We discuss the
+ theoretical problems involved m both methods, give algortthms for the
+ basic arithmetic operations, and give an empirical comparison of the
+ two techniques. We conclude wtth some general observations about the
+ lazy evaluation paradigm and its implementation."
+}
\end{chunk}
@@ 5403,10 +5439,11 @@ in Lecture Notes in Computer Science, Springer ISBN 9783540855200
\end{chunk}
\index{van Leeuwen, Andr\'e M.A.}
\begin{chunk}{ignore}
\bibitem[Leeuwen]{Leexx} {van Leeuwen}, Andr\'e M.A.
+\begin{chunk}{axiom.bib}
+@misc{Leeuxx,
+ author = {van Leeuwen, Andr\'e M.A.},
title = "Representation of mathematical object in interactive books",
 paper = "Leexx.pdf",
+ paper = "Leeuxx.pdf",
abstract = "
We present a model for the representation of mathematical objects in
structured electronic documents, in a way that allows for interaction
@@ 5421,6 +5458,7 @@ in Lecture Notes in Computer Science, Springer ISBN 9783540855200
(by different computer algebra systems), or a proof checker using a
computer algebra system to verify an equation involving a symbolic
computation."
+}
\end{chunk}
@@ 7820,6 +7858,23 @@ Proc ISSAC 97 pp172175 (1997)
\end{chunk}
+\index{Gianni, Patrizia}
+\index{Trager, Barry M.}
+\index{Zacharias, Gail}
+\begin{chunk}{axiom.bib}
+@article{Gian88,
+ author = "Gianni, Patrizia. and Trager, Barry. and Zacharias, Gail",
+ title = "Groebner Bases and Primary Decomposition of Polynomial Ideals",
+ journal = "J. Symbolic Computation",
+ volume = "6",
+ pages = "149167",
+ year = "1988",
+ url = "http://www.sciencedirect.com/science/article/pii/S0747717188800403/pdf?md5=40c29b67947035884904fd4597ddf710&pid=1s2.0S0747717188800403main.pdf",
+ paper = "Gian88.pdf"
+}
+
+\end{chunk}
+
\index{Gianni, P.}
\index{Trager, B.}
\begin{chunk}{axiom.bib}
@@ 11824,14 +11879,14 @@ Soc. for Industrial and Applied Mathematics, Philadelphia (1990)
\index{Boulanger, JeanLouis}
\begin{chunk}{axiom.bib}
@misc{Bou93b,
+@misc{Boul93b,
author = "Boulanger, JeanLouis",
title = "AXIOM, A Functional Language with Object Oriented Development",
year = "1993",
 paper = "Bou93b.pdf",
+ paper = "Boul93b.pdf",
keywords = "axiomref",
 abstract = "
 We present in this paper, a study about the computer algebra system
+ abstract =
+ "We present in this paper, a study about the computer algebra system
Axiom, which gives us many very interesting Software engineering
concepts. This language is a functional language with an Object
Oriented Development. This feature is very important for modeling the
@@ 11851,7 +11906,7 @@ Soc. for Industrial and Applied Mathematics, Philadelphia (1990)
year = "1995",
month = "February",
pages = "3341",
 paper = "Bou94.pdf",
+ paper = "Boul95.pdf",
publisher = "ACM SIGPLAN Notices, 30(2) CODEN SINODQ ISSN 03621340",
keywords = "axiomref",
abstract = "
@@ 12135,7 +12190,8 @@ Elektronik, 43(15) CODEN EKRKAR ISSN 00135658
title = "Domains of data and domains of terms in AXIOM",
year = "1995",
keywords = "axiomref",
 paper = "DB95.pdf",
+ url = "http://axiomwiki.newsynthesis.org/public/refs/brownfreecg.pdf",
+ paper = "Brow95.pdf",
abstract = "
The main new concept we wish to illustrate in this paper is a
distinction between ``domains of data'' and ``domains of terms'', and
@@ 12657,7 +12713,8 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
year = "2003",
publisher = "A. K. Peters",
isbn = "1568811594",
 keywords = "axiomref"
+ keywords = "axiomref",
+ paper = "Cohe03b.pdf"
}
\end{chunk}
@@ 12693,11 +12750,11 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
\index{Maple, Carsten}
\index{Pott, Sandra}
\begin{chunk}{axiom.bib}
@misc{CFMPxxb,
+@misc{Conrxxb,
author = "Conrad, Marc and French, Tim and Maple, Carsten and Pott, Sandra",
title = "Mathematical Use Cases lead naturally to nonstandard Inheritance
Relationships: How to make them accessible in a mainstream language?",
 paper = "CFMPxxb.pdf",
+ paper = "Conrxxb.pdf",
keywords = "axiomref",
abstract = "
Conceptually there is a strong correspondence between Mathematical
@@ 13069,6 +13126,29 @@ Academic Press, New York, NY, USA, 1988, ISBN 0122042329
\end{chunk}
\index{Davenport, James H.}
+\index{Fitch, John}
+\begin{chunk}{axiom.bib}
+@misc{Dave07,
+ author = "Davenport, James H. and Fitch, John",
+ title = "Computer Algebra and the three 'E's: Efficiency, Elegance, and
+ Expressiveness",
+ url = "http://staff.bath.ac.uk/masjhd/Drafts/PLMMS2007",
+ paper = "Dave07.pdf",
+ keywords = "axiomref",
+ abstract =
+ "What author of a programming language would not claim that the 3 'E's
+ were the goals? Nevertheless, we claim that computer algebra does lead
+ to particular emphases, and constraints, in these areas.
+
+ We restrict ``efficiency'' to mean machine efficiency, since the other
+ 'E's cover programmer efficiency. For the sake of clarity, we describe
+ as ``expressiveness'', what can be expressed in the language, and
+ ``elegance'' as how it can be expressed."
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
\begin{chunk}{ignore}
\bibitem[Davenport 14]{Dav14} Davenport, James H.
title = "Computer Algebra textbook",
@@ 13263,10 +13343,48 @@ May 1984
\index{Davenport, James H.}
\begin{chunk}{ignore}
+@misc{Dave12a,
+ author = "Davenport, James H.",
+ title = "Computer Algebra or Computer Mathematics?",
+ year = "2012",
+ url = "http://people.bath.ac.uk/masjhd/Slides/CalculemusSchool2002.pdf",
+ paper = "Dave12a.pdf",
+ abstract =
+ "Scope: ``polynomialtype'' systems: Axiom, Macsyma/Maxima, Maple,
+ Mathematica, and Reduce."
+}
+
+\index{Davenport, James H.}
+\begin{chunk}{ignore}
\bibitem[Davenport 12]{Dav12} Davenport, J.H.
title = "Computer Algebra",
url = "http://staff.bath.ac.uk/masjhd/JHDCA.pdf",
+ keywords = "axiomref"}
+
+\end{chunk}
+
+\index{Decker, Wolfram}
+\begin{chunk}{axiom.bib}
+@misc{Deckxx,
+ author = "Decker, Wolfram",
+ title = "Some Introductory Remarks on Computer Algebra",
+ url =
+"https://www.math.unibielefeld.de/~rehmann/ECM/cdrom/3ecm/pdfs/pant3/decker.pdf",
+ paper = "Deckxx.pdf",
keywords = "axiomref",
+ abstract =
+ "Computer algebra is a relatively young but rapidly growing field. In
+ this introductory note to the minisymposium on computer algebra
+ organized as part of the third European Congress of Mathematics I will
+ not even attempt to adress all major streams of research and the many
+ applications of computer algebra. I will concentrate on a few aspects,
+ mostly from a mathematical point of view, and I will discuss a few
+ typical applications in mathematics. I will present a couple of
+ examples which underline the fact that computer algebra systems
+ provide easy access to powerful computing tools. And, I will quote
+ from and refer to a couple of survey papers, textbooks and webpages
+ which I recommend for further reading."
+}
\end{chunk}
@@ 13393,12 +13511,17 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
\index{Dicrescenzo, C.}
\index{Duval, Dominique}
\begin{chunk}{ignore}
\bibitem[Dicrescenzo 89]{DD89} Dicrescenzo, C.; Duval, D.
+\begin{chunk}{axiom.bib}
+@InProceedings{Dicr88,
+ author = "Dicrescenzo, C. and Duval, D.",
title = "Algebraic extensions and algebraic closure in Scratchpad II",
In Gianni [Gia89], pp440446 ISBN 3540510842
LCCN QA76.95.I57 1998 Conference held jointly with AAECC6
 keywords = "axiomref",
+ booktitle = "Proc. ISSAC 1988",
+ series = "ISSAC 1998",
+ year = "1998",
+ pages = "440446",
+ isbn = "3540510842",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 13542,14 +13665,16 @@ ISBN 1581130732 LCCN QA76.95.I57 1999
\end{chunk}
\index{Doye, Nicolas James}
\begin{chunk}{ignore}
\bibitem[Doye 97]{Doy97} Doye, Nicolas James
+\begin{chunk}{axiom.bib}
+@phdthesis{Doye97,
+ author = "Doye, Nicolas James",
title = "Order Sorted Computer Algebra and Coercions",
Ph.D. Thesis University of Bath 1997
 paper = "Doy97.pdf",
+ school = "University of Bath",
+ year = "1997",
keywords = "axiomref",
 abstract = "
 Computer algebra systems are large collections of routines for solving
+ paper = "Doye97.pdf",
+ abstract =
+ "Computer algebra systems are large collections of routines for solving
mathematical problems algorithmically, efficiently and above all,
symbolically. The more advanced and rigorous computer algebra systems
(for example, Axiom) use the concept of strong types based on
@@ 13578,6 +13703,7 @@ Ph.D. Thesis University of Bath 1997
this is an algorithm and that it always returns a coercion when one
exists. Finally, we present a demonstration implementation of this
automated coerion algorithm in Axiom."
+}
\end{chunk}
@@ 13594,12 +13720,15 @@ ISBN 1581130732 LCCN QA76.95.I57 1999 ACM Press
\index{Dom\'inguez, C\'esar}
\index{Rubio, Julio}
\begin{chunk}{ignore}
\bibitem[Dominguez 01]{DR01} Dom\'inguez, C\'esar; Rubio, Julio
+\begin{chunk}{axiom.bib}
+@InProceedings{Domi01,
+ author = {Dom\'inguez, C\'esar; Rubio, Julio},
title = "Modeling Inheritance as Coercion in a Symbolic Computation System",
ISSAC 2001 ACM 1581134177/01/0007
 paper = "DR01.pdf",
+ booktitle = "Proc. ISSAC 2001",
+ series = "ISSAC 2001",
+ year = "2001",
keywords = "axiomref",
+ paper = "Domi01.pdf",
abstract = "
In this paper the analysis of the data structures used in a symbolic
computation system, called Kenzo, is undertaken. We deal with the
@@ 13610,6 +13739,7 @@ ISSAC 2001 ACM 1581134177/01/0007
algebraic specifications formalisms can be adapted, through the
``inheritance as coercion'' metaphor, in order to model this Kenzo
fragment."
+}
\end{chunk}
@@ 13786,6 +13916,30 @@ Madrid Spain, NAG conference (private copy of paper)
\end{chunk}
\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@misc{Fate94,
+ author = "Fateman, Richard J.",
+ title = "On the Design and Construction of Algebraic Manipulation Systems",
+ keywords = "axiomref",
+ url = "http://www.cs.berkeley.edu/~fateman/papers/asmerev94.ps",
+ paper = "Fate94.pdf",
+ abstract =
+ "We compare and contrast several techniques for the implementation of
+ components of an algebraic manipulation system. On one hand is the
+ mathematicalalgebraic approach which characterizes (for example)
+ IBM's Axiom. On the other hand is the more {\sl adhoc} approach which
+ characterizes many other popular systems (for example, Macsyma,
+ Reduce, Maple, and Mathematica). While the algebraic approach has
+ generally positive results, careful examination suggests that there
+ are significant remaining problems, especially in the representation
+ and manipulation of analytical, as opposed to algebraic,
+ mathematics. We describe some of these problems and some general
+ approaches for solutions."
+}
+
+\end{chunk}
+
+\index{Fateman, Richard J.}
\begin{chunk}{ignore}
\bibitem[Fateman 90]{Fat90} Fateman, R. J.
title = "Advances and trends in the design and construction of algebraic manipulation systems",
@@ 14170,19 +14324,6 @@ in [Wit87], pp1213
\end{chunk}
\index{Gianni, Patrizia}
\index{Trager, Barry M.}
\begin{chunk}{ignore}
\bibitem[Gianni 88]{Gia88} Gianni, Patrizia.; Trager, Barry.;
Zacharias, Gail.
 title = "Gr\"obner Bases and Primary Decomposition of Polynomial Ideals",
J. Symbolic Computation 6, 149167 (1988)
 url = "http://www.sciencedirect.com/science/article/pii/S0747717188800403/pdf?md5=40c29b67947035884904fd4597ddf710&pid=1s2.0S0747717188800403main.pdf",
 paper = "Gia88.pdf",
 keywords = "axiomref",

\end{chunk}

\index{Gianni, Patrizia}
\begin{chunk}{ignore}
\bibitem[Gianni 89a]{Gia89} Gianni, P. (Patrizia) (ed)
Symbolic and Algebraic Computation.
@@ 14306,6 +14447,23 @@ In Fitch [Fit93], pp193202. ISBN 0387572724 (New York),
\index{Gr\"abe, HansGert}
\begin{chunk}{axiom.bib}
+@InProceedings{Grab02,
+ author = "Grabe, HansGert",
+ title = "The SymbolicData Benchmark Problems Collection of Polynomial
+ Systems",
+ booktitle = "Workshop on Under and Overdetermined Systems of Algebraic or
+ Differential Equations",
+ location = "Karlsruhe, Germany",
+ pages = "5776",
+ url = "http://symbolicdata.org/Papers/karlsruhe02.pdf",
+ paper = "Grab02.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Gr\"abe, HansGert}
+\begin{chunk}{axiom.bib}
@misc{Grab06,
author = "Grabe, HansGert",
title = "The Groebner Factorizer and Polynomial System Solving",
@@ 14495,13 +14653,14 @@ Manipulation), 28(3) pp319 August 1994 CODEN SIGSBZ ISSN 01635824
\end{chunk}
\index{Gruntz, Dominik}
\begin{chunk}{ignore}
\bibitem[Gruntz 96]{Gru96} Gruntz, Dominik
+\begin{chunk}{axiom.bib}
+@phdthesis{Grun96,
+ author = "Gruntz, Dominik",
title = "On Computing Limits in a Symbolic Manipulation System",
Thesis, Swiss Federal Institute of Technology Z\"urich 1996
Diss. ETH No. 11432
+ school = "Swiss Federal Institute of Technology Zurich",
+ year = "1996",
+ paper = "Grun96.pdf",
url = "http://www.cybertester.com/data/gruntz.pdf",
 paper = "Gru96.pdf",
keywords = "axiomref",
abstract = "
This thesis presents an algorithm for computing (onesided) limits
@@ 14520,6 +14679,7 @@ Diss. ETH No. 11432
cancellation problem, and this may lead to an intermediate expression
swell. Our algorithm avoids this problem and is thus suited to be
implemented in a symbolic manipulation system."
+}
\end{chunk}
@@ 14728,6 +14888,88 @@ Vol. 8 No. 3 pp195210 (2001)
\end{chunk}
+\index{Hereman, Willy}
+\begin{chunk}{axiom.bib}
+@article{Here97,
+ author = "Hereman, Willy",
+ title = "Review of Symbolic Software for Lie Symmetry Analysis",
+ journal = "Math. Comput. Modelling",
+ volume = "25",
+ number = "8/9",
+ pages = "115132",
+ year = "1997",
+ keywords = "axiomref",
+ paper = "Here97.pdf",
+ abstract =
+ "Sophus Lie (18421899) pioneered the study of continuous
+ transformation groups that leave systems of differential equations
+ invariant. Lie’s work [l3] brought diverse and ad hoc integration
+ methods for solving special classes of differential equations under a
+ common conceptual umbrella. Indeed, Lie’s infinitesimal
+ transformation method provides a widely applicable technique to find
+ closed form solutions of ordinary differential equations (ODES).
+ Standard solution methods for firstorder or linear ODES can be
+ characterized in terms of symmetries. Through the group
+ classification of ODES, Lie succeeded in identifying all ODES that can
+ either be reduced to lowerorder ones or be completely integrated via
+ group theoretic techniques.
+
+ Applied to partial differential equations (PDEs), Lie’s method [2]
+ leads to groupinvariant solutions and conservation laws. Exploiting
+ the symmetries of PDEs, new solutions can be derived from known ones,
+ and PDEs can be classified into equivalence classes. Furthermore,
+ groupinvariant solutions obtained via Lie’s approach may provide
+ insight into the physical models themselves, and explicit solutions
+ can serve as benchmarks in the design, accuracy testing, and
+ comparison of numerical algorithms.
+
+ Nowadays, the concept of symmetry plays a key role in the study and
+ development of mathematics and physics. Indeed, the theory of Lie
+ groups and Lie algebras is applied to diverse fields of mathematics
+ including differential geometry, algebraic topology, bifurcation
+ theory, to name a few. Lie’s original ideas greatly influenced the
+ study of physically important systems of differential equations in
+ classical and quantum mechanics, fluid dynamics, elasticity, and many
+ other applied areas [481].
+
+ The application of Lie group methods to concrete physical systems
+ involves tedious computations. Even the calculation of the
+ continuous symmetry group of a modest system of differential equations
+ is prone to errors, if done with pencil and paper. Computer algebra
+ systems (CAS) such as Mathematica, MACSYMA, Maple, REDUCE, AXIOM and
+ MuPAD are extremely useful for such computations. Symbolic packages
+ [911], written in the language of these GAS, can find the determining
+ equations of the Lie symmetry group. The most sophisticated packages
+ then reduce these into an equivalent but more suitable system,
+ subsequently solve that system in closed form, and go on to calculate
+ the infinitesimal generators that span the Lie algebra of symmetries.
+
+ In Section 2, we discuss methods and algorithms used in the
+ computation of Lie symmetries. We address the computation of
+ determining systems, their reduction to standard form, solution
+ techniques, and the computation of the size of the symmetry group.
+ In Section 3, we look beyond Liepoint symmetries, addressing contact
+ and generalized symmetries, as well as nonclassical or conditional
+ symmetries.
+
+ Section 4 is devoted to a review of modern Lie symmetry
+ programs, classified according to the underlying CAS. The review
+ focuses on Lie symmetry software for classical Liepoint symmetries,
+ contact (or dynamical), generalized (or LieBacklund) symmetries,
+ nonclassical (or conditional) symmetries. Most of these packages were
+ written in the last decade. Researchers interested in details about
+ pioneering work should consult [9,10,12]. In Section 5, two examples
+ illustrate results that can be obtained with Lie symmetry software.
+ In Section 6 we draw some conclusions.
+
+ Lack of space forces us to give only a few key references for the Lie
+ symmetry packages. A comprehensive survey of the literature devoted
+ to theoretical as well as computational aspects of Lie symmetries,
+ with over 300 references, can be found elsewhere [11]."
+}
+
+\end{chunk}
+
\index{Hivert, Florent}
\index{Thiery, Nicolas M.}
\begin{chunk}{axiom.bib}
@@ 14867,6 +15109,25 @@ Vol. 8 No. 3 pp195210 (2001)
\end{chunk}
+\index{Hoeven, Joris van der}
+\index{Lecerf, Gregoire}
+\begin{chunk}{axiom.bib}
+@misc{Hoev13,
+ author = "Hoeven, Joris van der and Lecerf, Gregoire",
+ title = "Interfacing Mathemagix with C++",
+ keywords = "axiomref",
+ url = "http://www.texmacs.org/joris/mmxcpp/mmxcpp.pdf",
+ paper = "Hoev13.pdf",
+ 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{Hohold, Tom}
\index{van Lint, Jacobus H.}
\index{Pellikaan, Ruud}
@@ 15026,6 +15287,34 @@ Developments. LIFL Univ. Lille, Lille France, 1993
\end{chunk}
+\index{Jager, Bram De}
+\index{van Asch, Bram}
+\begin{chunk}{axiom.bib}
+@article{Jage96,
+ author = "Jager, Bram De and van Asch, Bram",
+ title = "Symbolic Solutions for a Class of Partial Differential Equations",
+ journal = "J. Symbolic Computation",
+ volume = "22",
+ pages = "459468",
+ paper = "Jage96.pdf",
+ url = "http://www.mate.tue.nl/mate/pdfs/1610.pdf",
+ keywords = "axiomref",
+ abstract =
+ "An algorithm to generate solutions for members of a class of
+ completely integrable partial differential equations has been derived
+ from a constructive proof of Frobenius' Theorem. The algorithm is
+ implemented as a procedure in the computer algebra system
+ Maple. Because the implementation uses the facilities of Maple for
+ solving sets of ordinary differential equations and for sets of
+ nonlinear equations, and those facilities are limited, the problems
+ that actually can be solved are restricted in size and
+ complexity. Several examples, some derived from industrial practice,
+ are presented to illustrate the use of the algorithm and to
+ demonstrate the advantages and shortcomings of the implementation."
+}
+
+\end{chunk}
+
\index{Jan{\ss}en, R.}
\begin{chunk}{ignore}
\bibitem[Janssen 88]{Jan88} Jan{\ss}en, R. (ed)
@@ 15238,11 +15527,55 @@ In Jan{\ss}en
\index{Jenks, Richard D.}
\index{Trager, Barry M.}
\begin{chunk}{ignore}
\bibitem[Jenks 94]{JT94} Jenks, R. D.; Trager, B. M.
 title = "How to make AXIOM into a Scratchpad",
In ACM [ACM94], pp3240 ISBN 0897916387 LCCN QA76.95.I59 1994
 paper = "JT94.pdf",
+@InProceedings{Jenk94,
+ author = "Jenks, Richard D. and Trager, Barry M.",
+ booktitle = "Proceedings of the ACMSIGSAM 1989 International
+ Symposium on Symbolic and Algebraic Computation, ISSAC '94",
+ series = "ISSAC 94",
+ 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}
@@ 15299,6 +15632,44 @@ In ACM [ACM94], pp3240 ISBN 0897916387 LCCN QA76.95.I59 1994
\end{chunk}
\index{Joyner, David}
+\index{Stein, William}
+\begin{chunk}{axiom.bib}
+@misc{Joyn08,
+ author = "Joyner, David and Stein, William",
+ title = "Open Source Mathematical Software: A White Paper",
+ year = "2008",
+ url =
+"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.124.7499&rep=rep1&type=pdf",
+ paper = "Joyn08.pdf",
+ keywords = "axiomref",
+ abstract =
+ "Open source software has had a profound effect on computing during
+ the last decade, especially on web servers (Apache), web browsers
+ (Firefox), operating systems (Linux and OS X), and programming
+ languages (GC C, Java, Python, Perl, etc.). The purpose of this paper
+ is to put forward the case that open source development methodologies
+ might also have a positive effect on mathematical software,
+ especially if the National Science Foundation (NSF) increases their
+ support of open source mathematical software de velopment. We argue
+ that careful funding of open source mathematical software may lead to
+ a lower total cost of ownership in the research and education
+ community, and to more efficient and trustworthy mathematical software."
+}
+
+\end{chunk}
+
+\index{Joyner, David}
+\begin{chunk}{axiom.bib}
+@misc{Joyn16,
+ author = "Joyner, David",
+ title = "Links to some open source mathematical programs",
+ keywords = "axiomref",
+ url = "http://www.opensourcemath.org/opensource\_math.html"
+}
+
+\end{chunk}
+
+\index{Joyner, David}
\begin{chunk}{axiom.bib}
@article{Joyn08,
author = "Joyner, David",
@@ 15755,6 +16126,34 @@ ISSN 03043975
\end{chunk}
+\index{Kreuzer, Edwin}
+\begin{chunk}{axiom.bib}
+@book{Kreu14,
+ author = "Kreuzer, Edwin",
+ title = "Computerized Symbolic Manipulation in Mechanics",
+ publisher = "Springer",
+ year = "2014",
+ abstract =
+ "The aim of this book is to present important software tools, basic
+ concepts, methods, and highly sophisticated applications of
+ computerized symbolic manipulation to mechanics problems. An overview
+ about generalpurpose symbolic software is followed by general
+ guidelines how to develop and implement highquality computer algebra
+ code. The theoretical background including modeling techniques for
+ mechanical systems is provided which allows for the computer aided
+ generation of the symbolic equation of motion for multibody
+ systems. It is shown how the governing equations for different types
+ of problems in structural mechanics can be automatically derived and
+ how to implement finite element techniques via computer algebra
+ software. Perturbation methods as a very powerful approach for
+ nonlinear problems are discussed in detail and are demonstrated for a
+ number of applications. The applications covered in this book
+ represent some of the most advanced topics in the rapidly growing
+ field of research on symbolic computation."
+}
+
+\end{chunk}
+
\index{Kumar, P.}
\index{Pellegrino, S.}
\begin{chunk}{axiom.bib}
@@ 16689,6 +17088,31 @@ CoED, 10(1) pp7176, JanuaryMarch 1990 CODEN CWLJDP ISSN 07368607
\end{chunk}
+\index{Minoiu, N.}
+\index{Netto, M}
+\index{Mammar, S}
+\begin{chunk}{axiom.bib}
+@misc{Mino07,
+ author = "Minoiu, N. and Netto, M and Mammar, S",
+ title = "Assistance control based on a composite Lyapunov function for
+ lane departure avoidance",
+ booktitle = "Proc. 15 Med. Conf. on Control \& Automation",
+ year = "2007",
+ keywords = "axiomref",
+ abstract =
+ "This paper presents a vehicle steering assistance designed to avoid
+ lane departure during driver inattention periods. Activated for a
+ driver loss of concentration during a lane keeping maneuver the
+ steering assistance drives the vehicle back to the center of the
+ lane. In order to ensure a vehicle trajectory as close as possible to
+ the centerline, the control law has been developed based on invariant
+ sets theory and on composite Lyapunov functions. The computation has
+ been performed using LMI methods, which allow in addition imposing a
+ maximum bound for the control steering angle."
+}
+
+\end{chunk}
+
\index{Miola, A.}
\begin{chunk}{ignore}
\bibitem[Miola 90]{Mio90} Miola, A. (ed)
@@ 16975,6 +17399,46 @@ IBM T.J. Watson Research RC4998
\end{chunk}
+\index{Norman, Arthur C.}
+\begin{chunk}{axiom.bib}
+@misc{Norm94,
+ author = "Norman, Arthur C.",
+ title = "Algebraic Manipulation",
+ paper = "Norm94.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Nguyen, Minh Van}
+\begin{chunk}{axiom.bib}
+@phdthesis{Nguy09,
+ author = "Nguyen, Minh Van",
+ title = "Exploring Cryptography Using the Sage Computer Algebra System",
+ school = "Victoria University",
+ year = "2009",
+ keywords = "axiomref",
+ paper = "Nguy09.pdf",
+ abstract =
+ "Cryptography has become indispensable in areas such as ecommerce,
+ the legal safeguarding of medical records, and secure electronic
+ communication. Hence, it is incumbent upon software engineers to
+ understand the concepts and techniques underlying the cryptosystems
+ that they implement. An educator needs to consider which topics to
+ cover in a course on cryptography as well as how to present the
+ concepts and techniques to be covered in the course. This thesis
+ contributes to the field of cryptography pedagogy by discussing and
+ implementing smallscale cryptosystems whose encryption and
+ decryption processes can be stepped through by hand. Our
+ implementation has been accepted and integrated into the code base of
+ the computer algebra system Sage. As Sage is free and open source,
+ students and educators of cryptology need not worry about paying
+ license fees in order to use Sage, but can instead concentrate on
+ exploring cryptography using Sage’s builtin support for cryptography."
+}
+
+\end{chunk}
+
\subsection{O} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Oancea, Cosmin E.}
@@ 17084,6 +17548,33 @@ interactive computing, Brunel University, Uxbridge, England, 47 September
\end{chunk}
+\index{Petitjean, S.}
+\begin{chunk}{axiom.bib}
+@article{Peti99,
+ author = "Petitjean, S.",
+ title = "Algebraic Geometry and Computer Vision: Polynomial Systems, Real
+ and Complex Roots",
+ journal = "J. of Mathematical Imaging and Vision",
+ volume = "10",
+ number = "1",
+ year = "1999",
+ keywords = "axiomref",
+ paper = "Peti99.pdf",
+ url = "http://www.loria.fr/~petitjea/papers/jmiv99.pdf",
+ abstract =
+ "We review the different techniques known for doing exact computations
+ on polynomial systems. Some are based on the use of Groebner bases and
+ linear algebra, others on the more classical resultants and its modern
+ counterparts. Many theoretical examples of the use of these techniques
+ are given. Furthermore, a full set of examples of applications in the
+ domain of artificial vision, where many constraints boil down to
+ polynomial systems, are presented. Emphasis is also put on very recent
+ methods for determining the number of (isolated) real and complex
+ roots of such systems."
+}
+
+\end{chunk}
+
\index{Petitot, Michel}
\begin{chunk}{ignore}
\bibitem[Petitot 90]{Pet90} Petitot, Michel
@@ 18043,13 +18534,31 @@ In Buchberger and Caviness [BC85], pp3233 ISBN 0387159835 (vol. 1),
\index{Sutor, Robert S.}
\index{Jenks, Richard D.}
\begin{chunk}{ignore}
\bibitem[Sutor 87a]{SJ87a} Sutor, R. S.; Jenks, R. D.
 title = "The type inference and coercion facilities in the Scratchpad II interpreter",
 In Wexelblat [Wex87], pp5663
ISBN 0897912357 LCCN QA76.7.S54 v22:7 SIGPLAN Notices, v22 n7 (July 1987)
 paper = "SJ87a.pdf",
+\begin{chunk}{axiom.bib}
+@article{Suto87,
+ author = "Sutor, Robert S. and Jenks, Richard D.",
+ title = "The type inference and coercion facilities in the Scratchpad II
+ interpreter",
+ journal = "SIGPLAN Notices",
+ volume = "22",
+ number = "7",
+ pages = "5663",
+ year = "1987",
+ isbn = "0897912357",
+ paper = "Suto87.pdf",
keywords = "axiomref",
+ abstract =
+ "The Scratchpad II system is an abstract datatype programming
+ language, a compiler for the language, a library of packages of
+ polymorphic functions and parametrized abstract datatypes, and an
+ interpreter that provides sophisticated type inference and coercion
+ facilities . Although originally designed for the implementation of
+ symbolic mathematical algorithms, Scratchpad 11 is a general purpose
+ programming language . This paper discusses aspects of the
+ implementation of the interpreter and how it attempts to provide a
+ user friendly and relatively weakly typed front end for the strongly
+ typed programming language."
+}
\end{chunk}
@@ 18146,10 +18655,11 @@ IBM Manual, March 1988
\index{Thompson, Simon}
\index{Timochouk, Leonid}
\begin{chunk}{ignore}
\bibitem[Thompson (a)]{TTxx} Thompson, Simon; Timochouk, Leonid
+\begin{chunk}{axiom.bib}
+@misc{Thomxx,
+ author = "Thompson, Simon and Timochouk, Leonid",
title = "The Aldor\\ language",
 paper = "TTxx.pdf",
+ paper = "Thomxx.pdf",
keywords = "axiomref",
abstract = "
This paper introduces the \verbAldor language, which is a
@@ 18164,6 +18674,7 @@ IBM Manual, March 1988
overloading in \verbAldor fits into the general scheme; examples
of logic within \verbAldor and notes on the implementation of the
system."
+}
\end{chunk}
@@ 18195,6 +18706,17 @@ IBM Manual, March 1988
\end{chunk}
+\subsection{U} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{chunk}{axiom.bib}
+@misc{Unkn16,
+ title = "Computer Algebra Systems",
+ url = "http://www.mhtlab.uwaterloo.ca/courses/me755/web\_intro.pdf",
+ paper = "Unkn16.pdf"
+}
+
+\end{chunk}
+
\subsection{V} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{van der Hoeven, Joris}
@@ 18321,6 +18843,28 @@ CODEN JSYCEH ISSN 07477171
\end{chunk}
+\index{Wang, Dongming}
+\begin{chunk}{axiom.bib}
+@InProceedings{Wang02,
+ author = "Wang, Dongming",
+ title = "Epsilon: A Library of Software Tools for Polynomial Elimination",
+ booktitle = "Proc. 1st Int. Congress of Mathematical Software",
+ series = "ICMS 2002",
+ year = "2002",
+ location = "Beijing China",
+ pages = "379389",
+ keywords = "axiomref",
+ paper = "Wang02.pdf",
+ url = "https://hal.inria.fr/inria00107607/file/A02R314.pdf",
+ abstract =
+ "This article presents a Maple library of functions for decomposing
+ systems of multivariate polynomials into triangular systems of
+ various kinds (regular, simple, or irreducible), with an application
+ package for manipulating and proving geometric theorems."
+}
+
+\end{chunk}
+
\index{Wang, Paul S.}
\begin{chunk}{ignore}
\bibitem[Wang 92]{Wan92} Wang, Paul S. (ed)
@@ 18521,8 +19065,7 @@ The Numerical Algorithms Group (NAG) Ltd, 1994
Morrison, Scott C.; Steinbach, Jonathan M.
title = "FOAM: A First Order Abstract Machine Version 0.35",
IBM T. J. Watson Research Center (2001)
 paper = "Wat01.pdf",
 keywords = "axiomref",
+ paper = "Wat01.pdf"
\end{chunk}
@@ 18594,14 +19137,17 @@ IBM T. J. Watson Research Center (2001)
\end{chunk}
\index{Weber, Andreas}
\begin{chunk}{ignore}
\bibitem[Weber 94]{Web94} Weber, Andreas
+\begin{chunk}{axiom.bib}
+@InProceedings{Webe94,
+ author = "Weber, Andreas",
title = "Algorithms for Type Inference with Coercions",
ISSAC 94 ACM 0897916387/94/0007
 paper = "Web94.pdf",
+ booktitle = "Proc ISSAC 94",
+ series = "ISSAC 94",
+ year = "1994",
keywords = "axiomref",
 abstract = "
 This paper presents algorithms that perform a type inference for a
+ paper = "Webe94.pdf",
+ abstract =
+ "This paper presents algorithms that perform a type inference for a
type system occurring in the context of computer algebra. The type
system permits various classes of coercions between types and the
algorithms are complete for the precisely defined system, which can be
@@ 18612,6 +19158,7 @@ ISSAC 94 ACM 0897916387/94/0007
have been described or the frameworks used have been so general that
the corresponding type inference problems were known to be
undecidable."
+}
\end{chunk}
@@ 18751,6 +19298,15 @@ LCCN QA76.7.S54 v22:7 SIGPLAN Notices, vol 22, no 7 (July 1987)
\end{chunk}
+\begin{chunk}{axiom.bib}
+@misc{Wikixx,
+ title = "List of opensource software for mathematics",
+ url = "https://en.wikipedia.org/wiki/List\_of\_opensource\_software\_for\_mathematics",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
\index{Winkler, Franz}
\begin{chunk}{axiom.bib}
@article{Wink89,
@@ 19195,6 +19751,23 @@ Comm. ACM. 17, 6 319320. (1974)
\end{chunk}
+\index{Batut, C.}
+\index{Belabas, K.}
+\index{Bernardi, D.}
+\index{Cohen, H.}
+\index{Olivier, M.}
+\begin{chunk}{axiom.bib}
+@misc{Batu03,
+ author = "Batut, C. and Belabas, K. and Bernardi, D. and Cohen, H. and
+ Olivier, M.",
+ title = "User's Guide to PARI/GP",
+ url = "http://math.mit.edu/~brubaker/PARI/PARIusers.pdf",
+ paper = "Batu03.pdf",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
\index{Beauzamy, Bernard}
\begin{chunk}{ignore}
\bibitem[Beauzamy 92]{Bea92} Beauzamy, Bernard
@@ 19607,6 +20180,22 @@ GauthierVillars, Paris, 1891).
\end{chunk}
+\index{Chew, Paul}
+\index{Constable, Robert L.}
+\index{Pingali, Keshav}
+\index{Vavasis, Steve}
+\index{Zippel, Richard}
+\begin{chunk}{axiom.bib}
+@misc{Chew95,
+ author = "Chew, Paul and Constable, Robert L. and Pingali, Keshav and
+ Vavasis, Steve and Zippel, Richard",
+ title = "Collaborative Mathematics Environment",
+ url = "http://www.cs.cornell.edu/rz/MathBus95/TechSummary.html",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
\index{Ch\'eze, Guillaume}
\index{Lecerf, Gr{\'e}goire}
\begin{chunk}{ignore}
@@ 22610,6 +23199,20 @@ Mathematics and Computers in Simulation 42 pp 509528 (1996)
\end{chunk}
+\index{Simon, Barry}
+\begin{chunk}{axiom.bib}
+@misc{Simo97,
+ author = "Simon, Barry",
+ title = "The PC Is Now Axiomatic",
+ publisher = "PC Mag",
+ year = "1997",
+ month = "March",
+ day = "25",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
\index{Singer, Michael F.}
\begin{chunk}{ignore}
\bibitem[Singer 89]{Sing89} Singer, M.F.
diff git a/changelog b/changelog
index cb9d427..e22c45d 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,5 @@
+20160630 tpd src/axiomwebsite/patches.html 20160630.01.tpd.patch
+20160630 tpd books/bookvolbib Axiom Citations in the Literature
20160629 tpd src/axiomwebsite/patches.html 20160629.01.tpd.patch
20160629 tpd books/bookvolbib Axiom Citations in the Literature
20160628 tpd src/axiomwebsite/patches.html 20160628.02.tpd.patch
diff git a/patch b/patch
index 285ea86..bb0c6ec 100644
 a/patch
+++ b/patch
@@ 2,1186 +2,1015 @@ books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
\index{Colin, Antoine}
+\index{Petitjean, S.}
\begin{chunk}{axiom.bib}
@article{Coli97,
 author = "Colin, Antoine",
 title = "Solving a system of algebraic equations with symmetries",
 journal = "J. Pure Appl. Algebra",
 volume = "117118",
 pages = "195215",
 year = "1997",
 keywords = "axiomref",
 abstract =
 "Let $(F)$ be a system of $p$ polynomial equations
 $F_i({\bf X}) \in k[{\bf X}]$, where $k$ is a commutative field and
 ${\bf X} := (X_1,\cdots,X_n)$ are indeterminates. Let $G$ be a subgroup
 of $GL_n(k)$. A polynomial $P \in k[{\bf X}]$ (resp. rational function
 $P \in k({\bf X})$ ) is an invariant of $G$ if and only if for all
 $A \in G$ we have $A\cdot P = P$. We denote $k[{\bf X}]^G$ by (resp.
 $k({\bf X})^G$) the algebra of polynomial (resp. rational function)
 invariants of $G$. If $L$ is another subgroup of $GL_n(k)$ such that
 $G \subset L$, $P$ is called a primary invariant of $G$ relative to $L$ if
 and only if $Stab_L(P) = G$ (where $Stab_L(P)$ is the stabilizer of
 $P$ in $L$).

 The paper describes the algebra of the invariants of a finite group
 and how to express these invariants in terms of a small number of
 them, from both the CohenMacaulay algebra and the field theory points
 of view. A method is proposed to solve $(F)$ by expressing it in terms of
 primary invariants $\Pi_1,\cdots,\Pi_n$
 (e.g. the elementary symmetric polynomials) and one
 ``primitive'' secondary invariant.

 The main thrust of the paper is contained in the following theorem.
 Let $(F)$ be a set of invariants of $G$. Let $L$ be a subgroup of
 $GL_n(k)$ such that $G \subset L$ and $k({\bf X})^L$ is a purely
 transcendental extension of $k_i$, let $\Pi_1,\cdots,\Pi_n$ be
 polynomials such that $k({\bf X})^L = k(\Pi_1,\cdots,\Pi_n)$,
 and let $\Theta \in k[{\bf X}]^G$ be a primitive polynomial invariant
 of $G$ relative to $L$.
 When possible, it is convenient to choose $\Theta$ to be one of the
 polynomials in $(F)$. – An algorithm is given that allows each polynomial
 $F_i$ to be expressed as $F_i({\bf X}) = H_i(\Pi_1,\cdots,\Pi_n,\Theta)$,
 an algebraic fraction in $\Pi_1,\cdots,\Pi_n$ and a polynomial in
 $\Theta$. Now let $L$ be the minimal polynomial of $\Theta$ over
 $k[{\bf X}]^L$; we have
 \[L({\bf X},T)=\prod_{\Theta^{'} \in L\cdot \Theta}(T\Theta^{'})
 \in k[{\bf X}]^L[T]\]
 (where $L$ is called a generic Lagrange resolvent).
 As $k(\Pi_1,\cdots,\Pi_n)=k({\bf X})^L$, we can write
 $L({\bf X},T)=H_0(\Pi_1,\cdots,\Pi_n,T)$ where $H_0$ is some
 rational function. The question
 $H_0(\Pi_1,\cdots,\Pi_n,\Theta)=0$ is always satisfied because
 $\Theta$ is a root of $L$. Then, we solve the system of ($p=1$)
 algebraic equations $H_i(\Pi_1,\cdots,\Pi_n,\Theta)=0$,
 $0 \le i \le p$ for $\Pi_1,\cdots,\Pi_n,\Theta$ as indeterminates.

 Theorem 1: Let $D \in k[\Pi_1,\cdots,\Pi_n]$ be the LCM of the
 denominators of all the fractions $H_i$,$0 \le i \le p$ and let
 $H_i^{'}=DH_i$. For every solution
 $x:=(x_1,\cdots,x_n)$ of the system $(F)$:$F_i({\bf X})=0$,
 $1 \le i \le p$, there exists a solution ($\pi_1,\cdots,\pi_n,\Theta$)
 of the system
 $(H^{'}):H_i^{'}(\Pi_1,\cdots,\Pi_n,\Theta)=0$, $0 \le i \le p$ such
 that $x$ is a solution of the system
 $(P_\pi):\Pi_i({\bf X})=\pi_i$, $1 \le i \le n$ , and of the equation
 $\Theta({\bf X})=0$. Conversely, for any solution
 $(\[i_1,\cdots,\pi_n,\theta)$ of the system $(H^{'})$ such that
 $D(\pi_1,\cdots,\pi_n) \ne 0$, if $x$ is a solution of the system
 $(P_\pi)$ relative to $(\pi_1,\cdots,\pi_n)$, then there exists
 some $A \in L$ such that $\Theta(A\cdot x)=\theta$, and then for all
 $B \in G$, $BA\cdot x$, is a solution of the system $(F)$.

 A slighly more general version of this theorem is also given. The
 paper then presents an algorithm that applies the theory and has been
 implemented in AXIOM. It is followed by several examples."
}

\end{chunk}

\index{DiBlasio, Paolo}
\index{Temperini, Marco}
\begin{chunk}{axiom.bib}
@article{DiBl95,
 author = "DiBlasio, Paolo and Temperini, Marco",
 title = "Subtyping Inheritance and Its Application in Languages for
 Symbolic Computation Systems",
 journal = "J. Symbolic Computation",
 volume = "19",
 pages = "3963",
 year = "1995",
 paper = "DiBl95.pdf",
+@article{Peti99,
+ author = "Petitjean, S.",
+ title = "Algebraic Geometry and Computer Vision: Polynomial Systems, Real
+ and Complex Roots",
+ journal = "J. of Mathematical Imaging and Vision",
+ volume = "10",
+ number = "1",
+ year = "1999",
keywords = "axiomref",
+ paper = "Peti99.pdf",
+ url = "http://www.loria.fr/~petitjea/papers/jmiv99.pdf",
abstract =
 "Application of objectoriented programming techniques to design and
 implementation of symbolic computation is investigated. We show the
 significance of certain correctness problems, occurring in programming
 environments based on specialization inheritance, due to use of method
 redefinition and polymorphism. We propose a solution to these
 problems, by defining a mechanism of subtyping inheritance and the
 prototype of an objectoriented programming language for a symbolic
 computation system. We devise the subtyping inheritance {\sl ESI
 (Enhanced String Inheritance)} by lifting to programming language
 constructs a given model of subtyping, which is established by a
 monotonic (covariant) subtyping rule. Type safeness of language
 instructions is proved.

 The adoption of {\sl ESI} allows to model method and class
 specialization in a natural way. The {\sl ESI} mechanism verifies the
 type correctness of language statements by means of type checking
 rules and preserves their correctness at runtime by a suitable method
 lookup algorithm."
+ "We review the different techniques known for doing exact computations
+ on polynomial systems. Some are based on the use of Groebner bases and
+ linear algebra, others on the more classical resultants and its modern
+ counterparts. Many theoretical examples of the use of these techniques
+ are given. Furthermore, a full set of examples of applications in the
+ domain of artificial vision, where many constraints boil down to
+ polynomial systems, are presented. Emphasis is also put on very recent
+ methods for determining the number of (isolated) real and complex
+ roots of such systems."
}
\end{chunk}
\index{DiBlasio, Paolo}
\index{Temperini, Marco}
+\index{Kreuzer, Edwin}
\begin{chunk}{axiom.bib}
@InProceedings{DiBl97,
 author = "DiBlasio, Paolo and Temperini, Marco",
 title = "On subtyping in languages for symbolic computation systems",
 booktitle = "Advances in the design of symbolic computation systems",
 series = "Monographs in Symbolic Computation",
 year = "1997",
+@book{Kreu14,
+ author = "Kreuzer, Edwin",
+ title = "Computerized Symbolic Manipulation in Mechanics",
publisher = "Springer",
 pages = "164178",
 keywords = "axiomref",
+ year = "2014",
abstract =
 "We want to define a strongly typed OOP language suitable as the
 software development tool of a symbolic computation system, which
 provides class structure to manage ADTs and supports multiple
 inheritance to model specialization hierarchies. In this paper, we
 provide the theoretical background for such a task."
}

\end{chunk}

\index{Fakler, Winfried}
\begin{chunk}{axiom.bib}
@article{Fakl97,
 author = "Fakler, Winfried",
 title = "On second order homogeneous linear differential equations with
 Liouvillian solutions",
 journal = "Theor. Comput. Sci.",
 volume = "187",
 number = "12",
 pages = "2748",
 year = "1997",
 paper = "Fakl97.pdf",
+ "The aim of this book is to present important software tools, basic
+ concepts, methods, and highly sophisticated applications of
+ computerized symbolic manipulation to mechanics problems. An overview
+ about generalpurpose symbolic software is followed by general
+ guidelines how to develop and implement highquality computer algebra
+ code. The theoretical background including modeling techniques for
+ mechanical systems is provided which allows for the computer aided
+ generation of the symbolic equation of motion for multibody
+ systems. It is shown how the governing equations for different types
+ of problems in structural mechanics can be automatically derived and
+ how to implement finite element techniques via computer algebra
+ software. Perturbation methods as a very powerful approach for
+ nonlinear problems are discussed in detail and are demonstrated for a
+ number of applications. The applications covered in this book
+ represent some of the most advanced topics in the rapidly growing
+ field of research on symbolic computation."
+}
+
+\end{chunk}
+
+\index{Dom\'inguez, C\'esar}
+\index{Rubio, Julio}
+\begin{chunk}{axiom.bib}
+@InProceedings{Domi01,
+ author = {Dom\'inguez, C\'esar; Rubio, Julio},
+ title = "Modeling Inheritance as Coercion in a Symbolic Computation System",
+ booktitle = "Proc. ISSAC 2001",
+ series = "ISSAC 2001",
+ year = "2001",
keywords = "axiomref",
 abstract =
 "We determine all minimal polynomials for second order homogeneous
 linear differential equations with algebraic solutions decomposed into
 invariants and we show how easily one can recover the known conditions
 on differential Galois groups [J. Kovacic, J. Symb. Comput. 2, 343
 (1986; Zbl 0603.68035), M. F. Singer and F. Ulmer,
 J. Symb. Comput. 16, 936, 3773 (1993; Zbl 0802.12004, Zbl
 0802.12005), F.Ulmer and J. A. Weil, J. Symb. Comput. 22, 179200
 (1996; Zbl 0871.12008)] using invariant theory. Applying these
 conditions and the differential invariants of a differential equation
 we deduce an alternative method to the algorithms given in (loc. cit.)
 for computing Liouvillian solutions. For irreducible second order
 equations our method determines solutions by formulas in all but three
 cases."
+ paper = "Domi01.pdf",
+ abstract =
+ "In this paper the analysis of the data structures used in a symbolic
+ computation system, called Kenzo, is undertaken. We deal with the
+ specification of the inheritance relationship since Kenzo is an
+ objectoriented system, written in CLOS, the Common Lisp Object
+ System. We focus on a particular case, namely the relationship between
+ simplicial sets and chain complexes, showing how the ordersorted
+ algebraic specifications formalisms can be adapted, through the
+ ``inheritance as coercion'' metaphor, in order to model this Kenzo
+ fragment."
}
\end{chunk}
\index{Jacquemard, Alain}
\index{KhechichineMourtada, F.Z.}
\index{Mourtada, A.}
+\index{Weber, Andreas}
\begin{chunk}{axiom.bib}
@article{Jacq97,
 author = "Jacquemard, Alain and KhechichineMourtada, F.Z. and Mourtada, A.",
 title = "Formal algorithms applied to the study of the cyclicity of a
 generic algebraic polycycle with four hyperbolic crests",
 journal = "Nonlinearity",
 volume = "10",
 number = "1",
 pages = "1953",
 year = "1997",
+@InProceedings{Webe94,
+ author = "Weber, Andreas",
+ title = "Algorithms for Type Inference with Coercions",
+ booktitle = "Proc ISSAC 94",
+ series = "ISSAC 94",
+ year = "1994",
keywords = "axiomref",
 comment = "french",
+ paper = "Webe94.pdf",
abstract =
 "Drawing on the work of Mourtada, we show that a family of vector
 fields with a generic algebraic polycycle of four hyperbolic apices
 possesses a maximum capacity of four limit cycles. This cyclicity is
 attained in an opening connecting the parameters which the edge
 contains, in particular a generic line of singularities of dovetail
 type. We also give an asymptotic estimation of the volume of this
 opening, as well as an explicit example of a family of polynomial
 vector fields replicating the abovedescribed conditions and
 possessing five limit cycles. The methods employed are very diverse:
 geometrical arguments (Thom’s theory of catastrophes and the theory of
 algebraic singularities), developments from Puiseux, the number of
 major roots by Descartes’ law and calculated exactly by Sturm series,
 and other specific methods for formal calculus, such as for example
 the cylindrical algebraic decomposition and the resolution of
 algebraic systems via the construction of Gröbner bases. The
 calculations have been executed formally, that is to say without
 making the least appeal to numerical approximation, in using the
 formal calculus system AXIOM."
+ "This paper presents algorithms that perform a type inference for a
+ type system occurring in the context of computer algebra. The type
+ system permits various classes of coercions between types and the
+ algorithms are complete for the precisely defined system, which can be
+ seen as a formal description of an important subset of the type system
+ supported by the computer algebra program Axiom.
+
+ Previously only algorithms for much more restricted cases of coercions
+ have been described or the frameworks used have been so general that
+ the corresponding type inference problems were known to be
+ undecidable."
}
\end{chunk}
\index{Lambe, Larry A.}
\index{Radford, David E.}
+\index{Sutor, Robert S.}
+\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@book{Lamb97,
 author = "Lambe, Larry A. and Radford, David E.",
 title = "Introduction to the quantum YangBaxter equation and quantum
 groups: an algebraic approach",
 booktitle = "Mathematics and its Applications",
 publisher = "Kluwer Adademic Publishers",
 year = "1997",
+@article{Suto87,
+ author = "Sutor, Robert S. and Jenks, Richard D.",
+ title = "The type inference and coercion facilities in the Scratchpad II
+ interpreter",
+ journal = "SIGPLAN Notices",
+ volume = "22",
+ number = "7",
+ pages = "5663",
+ year = "1987",
+ isbn = "0897912357",
+ paper = "Suto87.pdf",
keywords = "axiomref",
 abstract =
 "The quantum YangBaxter equation (QYBE) has roots in statistical
 mechanics and the inverse scattering method and leads to a natural
 construction of a bialgebra. It turns out to have important
 connections with knot theory and invariants of 3manifolds. There are
 now available many reference books to quantum groups and these various
 applications. The book under review develops the algebraic
 underpinning and theory of the QYBE, including the constant form and
 the one and two parameter forms.

 We give a brief description of the chapters. Chapter 1 (together with
 an Appendix) gives the algebraic preliminaries involving coalgebras,
 bialgebras, Hopf algebras, modules and comodules. Chapter 2 introduces
 the various forms of the QYBE, and the basic algebraic structures
 associated to them, including FaddeevReshetikhinTakhtadzhan (FRT)
 construction. Chapter 3 explores various categorical settings for the
 constant form of the QYBE, the most basic being the category of left
 QYB modules over a bialgebra and the notion of algebras, coalgebras,
 etc. in this category. Chapter 4 develops universal mapping properties
 of the FRT construction and its reduced version, and the authors
 investigate when the reduced FRT construction leads to a pointed
 bialgebra or a pointed Hopf algebra. Chapter 5 develops the quantum
 groups associated to $SL(2)$, i.e., the quantum universal enveloping
 algebra, and the quantum function algebra. Chapter 6 introduces
 quasitriangular Hopf algebras, and discusses how the
 finitedimensional ones give rise to solutions of the QYBE through
 their representation theory. The most important example is the
 Drinfeld double of a finitedimensional Hopf algebra. The authors note
 (through an exercise!) that every finitedimensional Hopf algebra is
 the reduced FRT construction of some solution to the QYBE. Chapter 7
 introduces coquasitriangular bialgebras, the most important being the
 FRT and the reduced FRT constructions. There are some generalizations
 here to the oneparameter form of the QYBE. Chapter 8 uses all the
 previously developed techniques to find solutions of the QYBE in
 certain cases, including the oneparameter form. Some of these were
 discovered by computer algebra methods. The final chapter 9 gives a
 brief discussion of certain categorical constructions and the QYBE is
 certain fairly abstract categories, motivated by the fact that the FRT
 construction is a coend.

 This book fills an important niche in the literature involving the
 QYBE by highlighting the algebraic aspects and applications. Although
 this is basically a reference book, it includes so many important
 parts of the study of Hopf algebras that it could be used as a
 textbook for a certain type of course on Hopf algebras and quantum
 groups, and certainly as supplementary reading material for such a
 course. There are frequent exercises which would be useful for such
 purposes. Besides being a basic source book, the authors include some
 new results and some novel approaches to earlier results. All this
 makes this book a most welcome addition to the quantum group
 literature."
+ abstract =
+ "The Scratchpad II system is an abstract datatype programming
+ language, a compiler for the language, a library of packages of
+ polymorphic functions and parametrized abstract datatypes, and an
+ interpreter that provides sophisticated type inference and coercion
+ facilities . Although originally designed for the implementation of
+ symbolic mathematical algorithms, Scratchpad 11 is a general purpose
+ programming language . This paper discusses aspects of the
+ implementation of the interpreter and how it attempts to provide a
+ user friendly and relatively weakly typed front end for the strongly
+ typed programming language."
}
\end{chunk}
\index{Letichevskij, A. Alexander}
\index{Marinchenko, V. G.}
+\index{van Leeuwen, Andr\'e M.A.}
\begin{chunk}{axiom.bib}
@article{Leti97,
 author = "Letichevskij, A. Alexander and Marinchenko, V. G.",
 title = "Objects in algebraic programming system",
 journal = "Cybern. Syst. Anal.",
 volume = "33",
 number = "2",
 pages = "283299",
 year = "1997",
 keywords = "axiomref",
 comment = "translated from Russian",
 abstract =
 "The algebraic programming system (APS) developed at the
 V. M. Glushkov Institute of Cybernetics of the Academy of Sciences of
 the Ukrainian SSR integrates the basic programming paradigms,
 including procedural, functional, algebraic, and logic programming.

 Algebraic programming in APS relies on special data structures, the
 socalled graph terms, which permit using diverse data and knowledge
 representations in relevant application domains. In the language
 APLAN, graph terms are described by expressions or systems of
 expressions of a manysorted algebra of data. They may represent both
 objects of the application domain and reasoning about these
 objects. The option of setting an arbitrary interpretation of the
 operations in the algebra of data makes it possible to use APS as a
 basis for various extensions.

 Symbolic computation systems such as Scratchpad/AXIOM have acquired
 special importance. They provide various possibilities of manipulating
 typed mathematical objects, including objects of complex hierarchical
 structure. This is a natural requirement when working with algebraic
 objects. In particular, the properties of many algebraic structures
 (such as groups, rings, fields, etc.) are naturally
 hierarchicalmodular.

 The Institute of Cybernetics and the Kherson Teachers’ College have
 developed an instructionoriented computer algebra system AIST. The
 AIST kernel is a hierarchical structure of mathematical concepts
 described in the APS language. However, construction of new
 applications on the basis of this hierarchical structure has proved
 difficult. The system kernel can be made more flexible by providing
 tools for flexible description of hierarchical structures of
 mathematical concepts.

 In this article, we describe an extension of the language APLAN, which
 provides tools for the objectoriented style of programming. This is
 one of the possible ways of introducing types in APS. The
 objectoriented technology also can be used to develop a hierarchical
 system of mathematical objects."
+@misc{Leeuxx,
+ author = {van Leeuwen, Andr\'e M.A.},
+ title = "Representation of mathematical object in interactive books",
+ paper = "Leeuxx.pdf",
+ abstract = "
+ We present a model for the representation of mathematical objects in
+ structured electronic documents, in a way that allows for interaction
+ with applications such as computer algebra systems and proof checkers.
+ Using a representation that reflects only the intrinsic information of
+ an object, and storing applicationdependent information in socalled
+ {\sl application descriptions}, it is shown how the translation from
+ the internal to an external representation and {\sl vice versa} can be
+ achieved. Hereby a formalisation of the concept of {\sl context} is
+ introduced. The proposed scheme allows for a high degree of
+ application integration, e.g., parallel evaluation of subexpressions
+ (by different computer algebra systems), or a proof checker using a
+ computer algebra system to verify an equation involving a symbolic
+ computation."
}
\end{chunk}
\index{Schwarzweller, Christoph}
\begin{chunk}{axiom.bib}
@phdthesis{Schw97,
 author = "Schwarzweller, Christoph",
 title = "MIZAR verification of generic algebraic algorithms",
 school = "University of Tubingen",
 year = "1997",
 paper = "Schw97.pdf",
+\index{Jenks, Richard D.}
+\index{Trager, Barry M.}
+\begin{chunk}{ignore}
+@InProceedings{Jenk94,
+ author = "Jenks, Richard D. and Trager, Barry M.",
+ booktitle = "Proceedings of the ACMSIGSAM 1989 International
+ Symposium on Symbolic and Algebraic Computation, ISSAC '94",
+ series = "ISSAC 94",
+ year = "1994",
+ pages = "3240",
+ isbn = "0897916387",
keywords = "axiomref",
+ publisher = "ACM Press",
+ address = "New York, NY, USA",
+ paper = "Jenk94.pdf",
abstract =
 "Although generic programming founds more and more attention –
 nowadays generic programming languages as well as generic libraries
 exist – there are hardly approaches for the verification of generic
 algorithms or generic libraries. This thesis deals with generic
 algorithms in the field of computer algebra. We propose the Mizar
 system as a theorem prover capable of verifying generic algorithms on
 an appropriate abstract level. The main advantage of the MIZAR theorem
 prover is its special input language that enables textbook style
 presentation of proofs. For generic versions of Brown/Henrici addition
 and of Euclidean’s algorithm we give complete correctness proofs
 written in the MIZAR language.
+ "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.
 Moreover, we do not only prove algorithms correct in the usual
 sense. In addition we show how to check, using the MIZAR system, that
 a generic algebraic algorithm is correctly instantiated with a
 particular domain. Answering this question that especially arises if
 one wants to implement generic programming languages, in the field of
 computer algebra requires nontrivial mathematical knowledge.
+ 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.
 To build a verification system using the MIZAR theorem prover, we also
 implemented a generator which almost automatically computes for a
 given algorithm a set of theorems that imply the correctness of this
 algorithm."
}

\end{chunk}

\index{Zenger, Christoph}
\begin{chunk}{axiom.bib}
@article{Zeng97,
 article = "Zenger, Christoph",
 title = "Indexed types",
 journal = "Theor. Comput. Sci.",
 volume = "187",
 numbers = "12",
 pages = "147165",
 year = "1997",
 keywords = "axiomref",
 paper = "Zeng97.pdf",
 abstract =
 "A new extension of the Hindley/Milner type system is proposed. The
 type system has algebraic types, that have not only type parameters
 but also value parameters (indices). This allows for example to
 parameterize matrices and vectors by their size and to check size
 compatibility statically. This is especially of interest in computer
 algebra."
+ 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{Bernardin, Laurent}
+\index{Poll, Erik}
+\index{Thompson, Simon}
\begin{chunk}{axiom.bib}
@article{Bern96,
 author = "Benardin, Laurent",
 title = "A review of symbolic solvers",
 journal = "SIGSAM Bull.",
 volume = "30",
 number = "1",
 pages = "920",
 year = "1996",
+@misc{Poll99a,
+ author = "Poll, Erik and Thompson, Simon",
+ title = "The Type System of Aldor",
+ url = "http://www.cs.kent.ac.uk/pubs/1999/874/content.ps",
+ paper = "Poll99a.pdf",
keywords = "axiomref",
 paper = "Bern96.pdf",
 abstract =
 "Solving equations and systems of equations symbolically is a key
 feature of every Computer Algebra System. This review examines the
 capabilities of the six best known general purpose systems to date in
 the area of general algebraic and transcendental equation
 solving. Areas explicitly not covered by this review are differential
 equations and numeric or polynomial system solving as special purpose
 systems exist for these kinds of problems. The aim is to provide a
 benchmark for comparing Computer Algebra Systems in a specific
 domain. We do not intend to give a rating of overall capabilities as
 for example in [9]. 1 The Contestants We compare six major Computer
 Algebra Systems. Axiom 2.0 [7], Derive 3.06 [1], Macsyma 420 [8],
 Maple V R4 [3], Mathematica 2.2 [10], MuPAD 1.2.9 [5] and Reduce 3.6
 [6]. When available, we tried to use the latest shipping version of
 each system. 2 The Problem Set The following table presents the set of
 80 problems that we used to evaluate the different solvers..."
+ abstract =
+ "This paper gives a formal description of  at least a part of 
+ the type system of Aldor, the extension language of the Axiom.
+ In the process of doing this a critique of the design of the system
+ emerges."
}
\end{chunk}
\index{Wester, Michael J.}
+\index{Boulanger, JeanLouis}
\begin{chunk}{axiom.bib}
@misc{Westxx,
 author = "Wester, Michael J.",
 title = "Computer Algebra Synonyms",
+@misc{Boul93b,
+ author = "Boulanger, JeanLouis",
+ title = "AXIOM, A Functional Language with Object Oriented Development",
+ year = "1993",
+ paper = "Boul93b.pdf",
keywords = "axiomref",
 url = "http://math.unm.edu/~wester/cas/synonyms.pdf",
 paper = "Westxx.pdf",
abstract =
 "The following is a collection of synonyms for various operations in
 the seven general purpose computer algebra systems {\bf Axiom}, {\bf
 Derive}, {\bf Macsyma}, {\bf Maple}, {\bf Mathematica}, {\bf MuPAD},
 and {\bf Reduce}. This collection does not attempt to be
 comprehensive, but hopefully it will be useful in giving an indication
 of how to translate between the syntaxes used by the different systems
 in many common situations. Note that for a blank entry means that
 there is no exact translation of a particular operation for the
 indicated system, but it may still be possible to work around this
 lack with a related functionality."
+ "We present in this paper, a study about the computer algebra system
+ Axiom, which gives us many very interesting Software engineering
+ concepts. This language is a functional language with an Object
+ Oriented Development. This feature is very important for modeling the
+ mathematical world (Hierarchy) and provides a running with
+ mathematical sense. (All objects are functions). We present many
+ problems of running and development in Axiom. We can note that Aiom is
+ the only system of this category."
}
\end{chunk}
\index{Wester, Michael J.}
+\index{Brown, Ronald}
+\index{Dreckmann, Winfried}
\begin{chunk}{axiom.bib}
@misc{West95,
 author = "Wester, Michael J.",
 title = "A Review of CAS Mathematical Capabilities",
+@misc{Brow95,
+ author = "Brown, Ronald and Dreckmann, Winfried",
+ title = "Domains of data and domains of terms in AXIOM",
year = "1995",
keywords = "axiomref",
 paper = "West95.pdf",
 url = "http://math.unm.edu/~wester/cas/Paper.ps",
 abstract =
 "Computer algebra systems (CASs) have become an important
 computational tool in the last decade. General purpose CASs, which are
 designed to solve a wide variety of problems, have gained special
 prominance. In this paper, the capabilities of seven major general
 purpose CASs (Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, and
 Reduce) are reviewed on 131 short problems covering a broad range of
 (primarily) symbolic mathematics.

 A demo was developed for each CAS, run and the results
 evaluated. Problems were graded in terms of whether it was easy or
 difficult or possible to produce an answer and if an answer was
 produced, whether it was correct. It is the author's hope that this
 review will encourage the development of a comprehensive CAS test
 suite."
}
+ url = "http://axiomwiki.newsynthesis.org/public/refs/brownfreecg.pdf",
+ paper = "Brow95.pdf",
+ abstract = "
+ The main new concept we wish to illustrate in this paper is a
+ distinction between ``domains of data'' and ``domains of terms'', and
+ its use in the programming of certain mathematical structures.
+ Although this distinction is implicit in much of the programming work
+ that has gone into the construction of Axiom categories and domains,
+ we believe that a formalisation of this is new, that standards and
+ conventions are necessary and will be useful in various other
+ contexts. We shall show how this concept may be used for the coding of
+ free categories and groupoids on directed graphs."
+}
+
+\end{chunk}
+
+\index{Danielsson, Nils Anders}
+\index{Hughes, John}
+\index{Jansson, Patrik}
+\index{Gibbons, Jeremy}
+\begin{chunk}{axiom.bib}
+@InProceedings{Dani06,
+ author = "Danielsson, Nils Anders and Hughes, John and Jansson, Patrik and
+ Gibbons, Jeremy",
+ title = "Fast and Loose Reasoning is Morally Correct",
+ booktitle = "Proc. of ACM POPL '06",
+ series = "POPL '06",
+ year = "2006",
+ location = "Charleston, South Carolina",
+ keywords = "axiomref",
+ paper = "Dani06.pdf",
+ abstract =
+ "Functional programmers often reason about programs as if they were
+ written in a total language, expecting the results to carry over to
+ nontoal (partial) languages. We justify such reasoning.
\end{chunk}
+ Two languages are defined, one total and one partial, with identical
+ syntax. The semantics of the partial language includes partial and
+ infinite values, and all types are lifted, including the function
+ spaces. A partial equivalence relation (PER) is then defined, the
+ domain of which is the total subset of the partial language. For types
+ not containing function spaces the PER relates equal values, and
+ functions are related if they map related values to related values.
\index{Apel, Joachim}
\index{Klaus, Uwe}
\begin{chunk}{axiom.bib}
@misc{Apel94,
 author = "Apel, Joachim and Klaus, Uwe",
 title = "Representing Polynomials in Computer Algebra Systems",
 year = "1994",
 paper = "Apel94.pdf",
 abstract =
 "There are discussed implementational aspects of the specialpurpose
 computer algebra system FELIX designed for computations in
 constructive algebra. In particular, data types developed for the
 representation of and computation with commutative and noncommuative
 polynomials are described. Furthermore, comparison of time and memory
 requirements of different polynomial representations are reported."
+ It is proved that if two closed terms have the same semantics in the
+ total language, then they have related semantics in the partial
+ language. It is also shown that the PER gives rise to a bicartesian
+ closed category which can be used to reason about values in the domain
+ of the relation."
}
\end{chunk}
\index{Stoutemyer, David R.}
+\index{Doye, Nicolas James}
\begin{chunk}{axiom.bib}
@article{Stou91,
 author = "Stoutemyer, David R.",
 title = "Crimes and misdemeanors in the computer algebra trade",
 journal = "Notices of the American Mathematical Society",
 volume = "38",
 number = "7",
 pages = "778785",
 year = "1991"
}
+@phdthesis{Doye97,
+ author = "Doye, Nicolas James",
+ title = "Order Sorted Computer Algebra and Coercions",
+ school = "University of Bath",
+ year = "1997",
+ keywords = "axiomref",
+ paper = "Doye97.pdf",
+ abstract =
+ "Computer algebra systems are large collections of routines for solving
+ mathematical problems algorithmically, efficiently and above all,
+ symbolically. The more advanced and rigorous computer algebra systems
+ (for example, Axiom) use the concept of strong types based on
+ ordersorted algebra and category theory to ensure that operations are
+ only applied to expressions when they ``make sense''.
\end{chunk}
+ In cases where Axiom uses notions which are not covered by current
+ mathematics we shall present new mathematics which will allow us to
+ prove that all such cases are reducible to cases covered by the
+ current theory. On the other hand, we shall also point out all the
+ cases where Axiom deviates undesirably from the mathematical ideal.
+ Furthermore we shall propose solutions to these deviations.
\index{Sangwin, Chris}
\begin{chunk}{axiom.bib}
@misc{Sang10,
 author = "Sangwin, Chris",
 title = "Intriguing Integrals: Part I and II",
 year = "2010",
 url1 =
 "https://plus.maths.org/issue54/features/sangwin/2pdf/index.html/op.pdf",
 paper1 = "Sang10a.pdf",
 url2 =
 "https://plus.maths.org/issue54/features/sangwin2/2pdf/index.html/op.pdf",
 paper2 = "Sang10b.pdf"
}
+ Strongly typed systems (especially of mathematics) become unusable
+ unless the system can change the type in a way a user expects. We wish
+ any change expected by a user to be automated, ``natural'', and
+ unique. ``Coercions'' are normally viewed as ``natural type changing
+ maps''. This thesis shall rigorously define the word ``coercion'' in
+ the context of computer algebra systems.
\end{chunk}
+ We shall list some assumptions so that we may prove new results so
+ that all coercions are unique. This concept is called ``coherence''.
\index{Evans, Brian}
\begin{chunk}{axiom.bib}
@misc{Evanxx,
 author = "Evans, Brian",
 title = "History of CA Systems",
 url = "http://felix.unife.it/Root/dMathematics/dThemathematician/dHistoryofmathematics/tHistoryofcomputeralgebra",
 paper = "Evanxx.txt"
+ We shall give an algorithm for automatically creating all coercions in
+ type system which adheres to a set of assumptions. We shall prove that
+ this is an algorithm and that it always returns a coercion when one
+ exists. Finally, we present a demonstration implementation of this
+ automated coerion algorithm in Axiom."
}
\end{chunk}
+\index{Dunstan, Martin}
+\index{Kelsey, Tom}
\index{Martin, Ursula}
\index{Shand, D.}
\begin{chunk}{axiom.bib}
@misc{Mart97,
 author = "Martin, Ursula and Shand, D",
 title = "Investigating some Embedded Verification Techniques for
 Computer Algebra Systems",
 url = "http://www.risc.jku.at/conferences/Theorema/papers/shand.ps.gz",
 paper = "Mart97.ps",
 abstract = "
 This paper reports some preliminary ideas on a collaborative project
 between St. Andrews University in the UK and NAG Ltd. The project aims
 to use embedded verification techniques to improve the reliability and
 mathematical soundness of computer algebra systems. We give some
 history of attempts to integrate computer algebra systems and
 automated theorem provers and discuss possible advantages and
 disadvantages of these approaches. We also discuss some possible case
 studies."
+\index{Linton, Steve A.}
+\begin{chunk}{axiom.bib}
+@InProceedings{Duns99,
+ author = "Dunstan, Martin and Kelsey, Tom and Martin, Ursula and
+ Linton, Steve A.",
+ title = "Formal Methods for Extensions to CAS",
+ booktitle = "Proc. of FME'99",
+ series = "FME'99",
+ location = "Toulouse, France",
+ year = "1999",
+ pages = "17581777",
+ url = "http://tom.host.cs.standrews.ac.uk/pub/fm99.ps",
+ paper = "Duns99.pdf",
+ keywords = "axiomref",
+ abstract =
+ "We demonstrate the use of formal methods tools to provide a semantics
+ for the type hierarchy of the AXIOM computer algebra system, and a
+ methodology for Aldor program analysis and verification. We give a
+ case study of abstract specifications of AXIOM primitives, and provide
+ an interface between these abstractions and Aldor code."
}
\end{chunk}
\index{Tonisson, Eno}
+\index{Boehm, HansJ.}
+\index{Cartwright, Robert}
+\index{Riggle, Mark}
+\index{O'Donnell, Michael J.}
\begin{chunk}{axiom.bib}
@article{Tonixx,
 author = "Tonisson, Eno",
 title = "Branch Completeness in School Mathematics and in Computer Algebra
 Systems",
 journal = "The Electronic Journal of Mathematics and Technology",
 volume = "1",
 number = "1",
 issn = "19332823",
 paper = "Tonixx.pdf",
 url = "https://php.radford.edu/~ejmt/deliveryBoy.php?paper=eJMT_v1n3p5",
+ author = "Boehm, HansJ. and Cartwright, Robert and Riggle, Mark and
+ O'Donnell, Michael J.",
+ title = "Exact Real Arithmetic: A Case Study in Higher Order Programming",
+ url = "http://dev.acm.org/pubs/citations/proceedings/lfp/319838/p162boehm",
+ paper = "Boeh86.pdf",
abstract =
 "In many cases when solving school algebra problems (e.g. simplifying
 an expression, solving an equation), the solution is separable into
 branches in some manner. The paper describes some approaches to
 branches that are used in school textbooks and computer algebra
 systems and compares them with mathematically branchcomplete
 solutions. It tries to identify possible reasons behind different
 approaches and also indicate some ideas how such differences could be
 explained to the students."
+ "Two methods for implementing {\sl exact} real arithmetic are explored
+ One method is based on formulating real numbers as functions that map
+ rational tolerances to rational approximations. This approach, which
+ was developed by constructive mathematicians as a concrete
+ formalization of the real numbers, has lead to a surpris ingly
+ successful implementation. The second method formulates real numbers
+ as potentially infinite sequences of digits, evaluated on demand.
+ This approach has frequently been advocated by proponents of lazy
+ functional languages in the computer science community. Ironically,
+ it leads to much less satisfactory implementations. We discuss the
+ theoretical problems involved m both methods, give algortthms for the
+ basic arithmetic operations, and give an empirical comparison of the
+ two techniques. We conclude wtth some general observations about the
+ lazy evaluation paradigm and its implementation."
+}
+
+\end{chunk}
+
+\index{Gruntz, Dominik}
+\begin{chunk}{axiom.bib}
+@phdthesis{Grun96,
+ author = "Gruntz, Dominik",
+ title = "On Computing Limits in a Symbolic Manipulation System",
+ school = "Swiss Federal Institute of Technology Zurich",
+ year = "1996",
+ paper = "Grun96.pdf",
+ url = "http://www.cybertester.com/data/gruntz.pdf",
+ keywords = "axiomref",
+ abstract = "
+ This thesis presents an algorithm for computing (onesided) limits
+ within a symbolic manipulation system. Computing limtis is an
+ important facility, as limits are used both by other functions such as
+ the definite integrator and to get directly some qualitative
+ information about a given function.
+
+ The algorithm we present is very compact, easy to understand and easy
+ to implement. It overcomes the cancellation problem other algorithms
+ suffer from. These goals were achieved using a uniform method, namely
+ by expanding the whole function into a series in terms of its most
+ rapidly varying subexpression instead of a recursive bottom up
+ expansion of the function. In the latter approach exact error terms
+ have to be kept with each approximation in order to resolve the
+ cancellation problem, and this may lead to an intermediate expression
+ swell. Our algorithm avoids this problem and is thus suited to be
+ implemented in a symbolic manipulation system."
+}
+
+\end{chunk}
+
+\index{Boulm\'e, S.}
+\index{Hardin, T.}
+\index{Rioboo, Renaud}
+\begin{chunk}{axiom.bib}
+@misc{Boul00,
+ author = "Boulme, S. and Hardin, T. and Rioboo, R.",
+ title = "Polymorphic Data Types, Objects, Modules and Functors,:
+ is it too much?",
+ url = "ftp://ftp.lip6.fr/lip6/reports/2000/lip6.2000.014.ps.gz",
+ paper = "Boul00.pdf",
+ keywords = "axiomref",
+ abstract = "
+ Abstraction is a powerful tool for developers and it is offered by
+ numerous features such as polymorphism, classes, modules, and
+ functors, $\ldots$ A working programmer may be confused by this
+ abundance. We develop a computer algebra library which is being
+ certificed. Reporting this experience made with a language (Ocaml)
+ offering all these features, we argue that the are all needed
+ together. We compare several ways of using classes to represent
+ algebraic concepts, trying to follow as close as possible mathematical
+ specification. Then we show how to combine classes and modules to
+ produce code having very strong typing properties. Currently, this
+ library is made of one hundred units of functional code and behaves
+ faster than analogous ones such as Axiom."
}
\end{chunk}
\index{Beeson, Michael}
+\index{Conrad, Marc}
+\index{French, Tim}
+\index{Maple, Carsten}
+\index{Pott, Sandra}
\begin{chunk}{axiom.bib}
@misc{Beesxx,
 author = "Beeson, Michael",
 title = "Automatic Generation of EpsilonDelta Proofs of Continuity",
 url = "http://www.michaelbeeson.com/research/papers/aisc.pdf",
 paper = "Beesxx.pdf",
 abstract =
 "As part of a project on automatic generation of proofs involving both
 logic and computation, we have automated the production of some proofs
 involving epsilondelta arguments. These proofs involve two or three
 quantifiers on the logical side, and on the computational side, they
 involve algebra, trigonometry, and some calculus. At the border of
 logic and computation, they involve several types of arguments
 involving inequalities, including transitivity chaining and several
 types of bounding arguments, in which bounds are sought that do not
 depend on certain variables. Control mechanisms have been developed
 for intermixing logical deduction steps with computational steps and
 with inequality reasoning. Problems discussed here as examples involve
 the continuity and uniform continuity of various specific functions."
+@misc{Conrxxb,
+ author = "Conrad, Marc and French, Tim and Maple, Carsten and Pott, Sandra",
+ title = "Mathematical Use Cases lead naturally to nonstandard Inheritance
+ Relationships: How to make them accessible in a mainstream language?",
+ paper = "Conrxxb.pdf",
+ keywords = "axiomref",
+ abstract = "
+ Conceptually there is a strong correspondence between Mathematical
+ Reasoning and ObjectOriented techniques. We investigate how the ideas
+ of Method Renaming, Dynamic Inheritance and Interclassing can be used
+ to strengthen this relationship. A discussion is initiated concerning
+ the feasibility of each of these features."
}
\end{chunk}
\index{Ballarin, Clemens}
\index{Paulson, Lawrence C.}
\begin{chunk}
@misc{Ball98,
 author = "Ballarin, Clemens and Paulson, Lawrence C.",
 title = "Reasoning about Coding Theory: The Benefits We Get from
 Computer Algebra",
 year = "1998",
 url = http://www21.in.tum.de/~ballarin/publications/aisc98.pdf",
 paper = "Ball98.pdf",
 abstract =
 "The use of computer algebra is usually considered beneficial for
 mechanised reasoning in mathematical domains. We present a case study,
 in the application domain of coding theory, that supports this claim:
 the mechanised proof depends on nontrivial algorithms from computer
 algebra and increase the reasoning power of the theorem prover. The
 unsoundness of computer algebra systems is a major problem in
 interfacing them to theorem provers. Our approach to obtaining a sound
 overall system is not blanket distrust but based on the distinction
 between algorithms we call sound and {\sl ad hoc} respectively. This
 distinction is blurred in most computer algebra systems OUr
 experimental interface therefore uses a computer algebra library. It
 is based on theorem templates, which provide formal specifications for
 the algorithms."
+\index{Dunstan, Martin N.}
+\begin{chunk}{axiom.bib}
+@phdthesis{Duns99a,
+ author = "Dunstan, Martin N.",
+ title = "Larch/Aldor  A Larch BISL for AXIOM and Aldor",
+ school = "University of St. Andrews",
+ year = "1999",
+ paper = "Duns99a.pdf",
+ keywords = "axiomref",
+ abstract = "
+ In this thesis we investigate the use of lightweight formal methods
+ and verification conditions (VCs) to help improve the reliability of
+ components constructed within a computer algebra system. We follow the
+ Larch approach to formal methods and have designed a new behavioural
+ interface specification language (BISL) for use with Aldor: the
+ compiled extension language of Axiom and a fullyfeatured programming
+ language in its own right. We describe our idea of lightweight formal
+ methods, present a design for a lightweight verification condition
+ generator and review our implementation of a prototype verification
+ condition generator for Larch/Aldor."
}
\end{chunk}
\index{Aslaksen, Helmer}
+\index{Thompson, Simon}
+\index{Timochouk, Leonid}
\begin{chunk}{axiom.bib}
@article{Asla96,
 author = "Aslaksen, Helmer",
 title = "Multiplevalued complex functions and computer algebra",
 journal = "SIGSAM Bulletin",
 volume = "30",
 number = "2",
 year = "1996",
 pages = "1220",
 paper = "Asla96.pdf",
 url = "http://www.math.nus.edu.sg/aslaksen/papers/cacas.pdf",
 abstract =
 "I recently taught a course on complex analysis. That forced me to
 think more carefully about branches. Being interested in computer
 algebra, it was only natural that I wanted to see how such programs
 dealt with these problems. I was also inspired by a paper by
 Stoutemyer.

 While programs like Derive, Maple, Mathematica and Reduce are very
 powerful, they also have their fair share of problems. In particular,
 branches are somewhat of an Achilles' heel for them. As is wellknown,
 the complex logarithm function is properly defined as a
 multiplevalued function. And since the general power and exponential
 functions are defined in terms of the logarithm function, they are
 also multiplevalued. But for actual computations, we need to make
 them single valued, which we do by choosing a branch. In Section 2, we
 will consider some transformation rules for branches of
 multiplevalued complex functions in painstaking detail.
+@misc{Thomxx,
+ author = "Thompson, Simon and Timochouk, Leonid",
+ title = "The Aldor\\ language",
+ paper = "Thomxx.pdf",
+ keywords = "axiomref",
+ abstract = "
+ This paper introduces the \verbAldor language, which is a
+ functional programming language with dependent types and a powerful,
+ typebased, overloading mechanism. The language is built on a subset
+ of Aldor, the 'library compiler' language for the Axiom computer
+ algebra system. \verbAldor is designed with the intention of
+ incorporating logical reasoning into computer algebra computations.
 The purpose of this short article is not to do a comprehensive
 comparative study of different computer algebra systems. My goal is
 simply to make the readers aware of some of the problems, and to
 encourage the readers to sit down and experiment with their favourite
 programs."
+ The paper contains a formal account of the semantics and type system
+ of \verbAldor; a general discussion of overloading and how the
+ overloading in \verbAldor fits into the general scheme; examples
+ of logic within \verbAldor and notes on the implementation of the
+ system."
}
\end{chunk}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@InProceedings{Fate96,
 author = "Fateman, Richard J.",
 title = "A Review of Symbolic Solvers",
 booktitle = "Proc 1996 ISSAC",
 series = "ISSAC 96",
 year = "1996",
 pages = "8694",
 keywords = "axiomref",
+\index{Davenport, James H.}
+\index{Fitch, John}
+\begin{chunk}{axiom.bib}
+@misc{Dave07,
+ author = "Davenport, James H. and Fitch, John",
+ title = "Computer Algebra and the three 'E's: Efficiency, Elegance, and
+ Expressiveness",
+ url = "http://staff.bath.ac.uk/masjhd/Drafts/PLMMS2007",
+ paper = "Dave07.pdf",
keywords = "axiomref",
 paper = "Fate96.pdf",
 url = "http://http.cs.berkeley.edu/~fateman/papers/eval.ps",
abstract =
 "``Evaluation'' of expressions and programs in a computer algebra
 system is central to every system, but inevitably fails to provide
 complete satisfaction. Here we explain the conflicting requirements,
 describe some solutions from current systems, and propose alternatives
 that might be preferable sometimes. We give examples primarily from
 Axiom, Macsyma, Maple, Mathematica, with passing metion of a few other
 systems."
}

\end{chunk}

\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Fate05,
 author = "Fateman, Richard J.",
 title = "An incremental approach to building a mathematical
 expert out of software",
 conference = "Axiom Computer Algebra Conference",
 location = "City College of New York, CAISS project",
 year = "2005",
 month = "April",
 day = "19",
 url = "http://www.cs.berkeley.edu/~fateman/papers/axiom.pdf",
 paper = "Fat05.pdf",
 keywords = "axiomref"
+ "What author of a programming language would not claim that the 3 'E's
+ were the goals? Nevertheless, we claim that computer algebra does lead
+ to particular emphases, and constraints, in these areas.
+
+ We restrict ``efficiency'' to mean machine efficiency, since the other
+ 'E's cover programmer efficiency. For the sake of clarity, we describe
+ as ``expressiveness'', what can be expressed in the language, and
+ ``elegance'' as how it can be expressed."
}
\end{chunk}
\index{Gr\"abe, HansGert}
+\index{Jager, Bram De}
+\index{van Asch, Bram}
\begin{chunk}{axiom.bib}
@misc{Grab98,
 author = "Grabe, HansGert",
 title = "About the Polynomial System Solve Facility of Axiom, Macsyma,
 Maple Mathematica, MuPAD, and Reduce",
 paper = "Grab98.pdf",
 url =
"https://www.informatik.unileipzig.de/~graebe/ComputerAlgebra/Publications/WesterBook.pdf",
+@article{Jage96,
+ author = "Jager, Bram De and van Asch, Bram",
+ title = "Symbolic Solutions for a Class of Partial Differential Equations",
+ journal = "J. Symbolic Computation",
+ volume = "22",
+ pages = "459468",
+ paper = "Jage96.pdf",
+ url = "http://www.mate.tue.nl/mate/pdfs/1610.pdf",
keywords = "axiomref",
 abstract =
 "We report on some experiences with the general purpose Computer
 Algebra Systems (CAS) Axiom, Macsyma, Maple, Mathematica, MuPAD, and
 Reduce solving systems of polynomial equations and the way they
 present their solutions. This snapshot (taken in the spring of 1996)
 of the current power of the different systems in a special area
 concentrates on both CPUtimes and the quality of the output."
}

\end{chunk}

\index{Gr\"abe, HansGert}
\begin{chunk}{axiom.bib}
@misc{Grab06,
 author = "Grabe, HansGert",
 title = "The Groebner Factorizer and Polynomial System Solving",
 year = "2006",
+ abstract =
+ "An algorithm to generate solutions for members of a class of
+ completely integrable partial differential equations has been derived
+ from a constructive proof of Frobenius' Theorem. The algorithm is
+ implemented as a procedure in the computer algebra system
+ Maple. Because the implementation uses the facilities of Maple for
+ solving sets of ordinary differential equations and for sets of
+ nonlinear equations, and those facilities are limited, the problems
+ that actually can be solved are restricted in size and
+ complexity. Several examples, some derived from industrial practice,
+ are presented to illustrate the use of the algorithm and to
+ demonstrate the advantages and shortcomings of the implementation."
+}
+
+\end{chunk}
+
+\index{Hereman, Willy}
+\begin{chunk}{axiom.bib}
+@article{Here97,
+ author = "Hereman, Willy",
+ title = "Review of Symbolic Software for Lie Symmetry Analysis",
+ journal = "Math. Comput. Modelling",
+ volume = "25",
+ number = "8/9",
+ pages = "115132",
+ year = "1997",
keywords = "axiomref",
 report = "Special Semester on Groebner Bases",
 location = "Linz",
 paper = "Grab06.pdf",
 url =
"https://www.ricam.oeaw.ac.at/specsem/srs/groeb/download/06\_02\_Solver.pdf",
+ paper = "Here97.pdf",
abstract =
 "Let $S := k[x_1,\ldots, x_n]$ be the polynomial ring in the
 variables $x_1,\ldots,x_n$ over the field $k$ and
 $B := \{f_1,\ldots,f_m\} \subset S$
 be a finite system of polynomials. Denote by $I(B)$ the
 ideal generated by these polynomials. One of the major tasks of
 constructive commutative algebra is the derivation of information
 about the structure of
 \[V(B):=\{a \in K^n : \forall f \in B{\rm\ such\ that\ }f(a)=0\}\]
 the set of common zeroes of the system $B$ over an
 algebraically closed extension $K$ of $k$. Splitting the system into
 smaller ones, solving them separately, and patching all solutions
 together is often a good guess for a quick solution of even highly
 nontrivial problems. This can be done by several techniques, e.g.,
 characteristic sets, resultants, the Groebner factorizer or some ad
 hoc methods. Of course, such a strategy makes sense only for problems
 that really will split, i.e., for reducible varieties of
 solutions. Surprisingly often, problems coming from 11real life''
 fulfill this condition.
+ "Sophus Lie (18421899) pioneered the study of continuous
+ transformation groups that leave systems of differential equations
+ invariant. Lie’s work [l3] brought diverse and ad hoc integration
+ methods for solving special classes of differential equations under a
+ common conceptual umbrella. Indeed, Lie’s infinitesimal
+ transformation method provides a widely applicable technique to find
+ closed form solutions of ordinary differential equations (ODES).
+ Standard solution methods for firstorder or linear ODES can be
+ characterized in terms of symmetries. Through the group
+ classification of ODES, Lie succeeded in identifying all ODES that can
+ either be reduced to lowerorder ones or be completely integrated via
+ group theoretic techniques.
+
+ Applied to partial differential equations (PDEs), Lie’s method [2]
+ leads to groupinvariant solutions and conservation laws. Exploiting
+ the symmetries of PDEs, new solutions can be derived from known ones,
+ and PDEs can be classified into equivalence classes. Furthermore,
+ groupinvariant solutions obtained via Lie’s approach may provide
+ insight into the physical models themselves, and explicit solutions
+ can serve as benchmarks in the design, accuracy testing, and
+ comparison of numerical algorithms.
 Among the methods to split polynomial systems into smaller pieces
 probably the Groebner factor izer method attracted the most
 theoretical attention, see Czapor ([4, 5]), Davenport ([6]), Melenk, M
 ̈oller and Neun ([16, 17]) and Gr ̈abe ([13, 14]). General purpose
 Computer Algebra Systems (CAS) are well suited for such an approach,
 since they make available both a (more or less) well tuned
 implementation of the classical Groebner algorithm and an effective
 multivariate polynomial factorizer.
+ Nowadays, the concept of symmetry plays a key role in the study and
+ development of mathematics and physics. Indeed, the theory of Lie
+ groups and Lie algebras is applied to diverse fields of mathematics
+ including differential geometry, algebraic topology, bifurcation
+ theory, to name a few. Lie’s original ideas greatly influenced the
+ study of physically important systems of differential equations in
+ classical and quantum mechanics, fluid dynamics, elasticity, and many
+ other applied areas [481].
 Furthermore it turned out that the Groebner factorizer is not only a
 good heuristic approach for splitting, but its output is also usually
 a collection of almost prime components. Their description allows a
 much deeper understanding of the structure of the set of zeroes
 compared to the result of a sole Groebner basis computation.
+ The application of Lie group methods to concrete physical systems
+ involves tedious computations. Even the calculation of the
+ continuous symmetry group of a modest system of differential equations
+ is prone to errors, if done with pencil and paper. Computer algebra
+ systems (CAS) such as Mathematica, MACSYMA, Maple, REDUCE, AXIOM and
+ MuPAD are extremely useful for such computations. Symbolic packages
+ [911], written in the language of these GAS, can find the determining
+ equations of the Lie symmetry group. The most sophisticated packages
+ then reduce these into an equivalent but more suitable system,
+ subsequently solve that system in closed form, and go on to calculate
+ the infinitesimal generators that span the Lie algebra of symmetries.
 Of course, for special purposes a general CAS as a multipurpose
 mathematical assistant can’t offer the same power as specialized
 software with efficiently implemented and well adapted algorithms and
 data types. For polynomial system solving, such specialized software
 has to implement two algorithmically complex tasks, solving and
 splitting, and until recently none of the specialized systems (as
 e.g., GB, Macaulay, Singular, CoCoA, etc.) did both
 efficiently. Meanwhile, being very efficient computing (classical)
 Groebner bases, development efforts are also directed, not only
 for performance reasons, towards a better inclusion of factorization
 into such specialized systems. Needless to remark that it needs some
 skill to force a special system to answer questions and the user will
 probably first try his ``home system'' for an answer. Thus the
 polynomial systems solving facility of the different CAS should behave
 especially well on such polynomial systems that are hard enough not to
 be done by hand, but not really hard to require special efforts. It
 should invoke a convenient interface to get the solutions in a form
 that is (correct and) well suited for further analysis in the familiar
 environment of the given CAS as the personal mathematical assistant."
+ In Section 2, we discuss methods and algorithms used in the
+ computation of Lie symmetries. We address the computation of
+ determining systems, their reduction to standard form, solution
+ techniques, and the computation of the size of the symmetry group.
+ In Section 3, we look beyond Liepoint symmetries, addressing contact
+ and generalized symmetries, as well as nonclassical or conditional
+ symmetries.
+
+ Section 4 is devoted to a review of modern Lie symmetry
+ programs, classified according to the underlying CAS. The review
+ focuses on Lie symmetry software for classical Liepoint symmetries,
+ contact (or dynamical), generalized (or LieBacklund) symmetries,
+ nonclassical (or conditional) symmetries. Most of these packages were
+ written in the last decade. Researchers interested in details about
+ pioneering work should consult [9,10,12]. In Section 5, two examples
+ illustrate results that can be obtained with Lie symmetry software.
+ In Section 6 we draw some conclusions.
+
+ Lack of space forces us to give only a few key references for the Lie
+ symmetry packages. A comprehensive survey of the literature devoted
+ to theoretical as well as computational aspects of Lie symmetries,
+ with over 300 references, can be found elsewhere [11]."
}
\end{chunk}
\index{Corless, Robert M.}
\index{Jeffrey, David J.}
\index{Watt, Stephen M.}
\index{Bradford, Russell}
\index{Davenport, James H.}
+\index{Minoiu, N.}
+\index{Netto, M}
+\index{Mammar, S}
\begin{chunk}{axiom.bib}
@misc{Corl0,
 author = "Corless, Robert M. and Jeffrey, David J. and Watt, Stephen M.
 and Bradford, Russell and Davenport, James H.",
 title = "Reasoning about the elementary functions of complex analysis",
 url = "http://www.csd.uwo.ca/~watt/pub/reprints/2002amaireasoning.pdf",
 paper = "Corl05.pdf",
 abstract = "
 There are many problems with the simplification of elementary
 functions, particularly over the complex plane. Systems tend to make
 ``howlers'' or not to simplify enough. In this paper we outline the
 ``unwinding number'' approach to such problems, and show how it can be
 used to prevent errors and to systematise such simplification, even
 though we have not yet reduced the simplification process to a
 complete algorithm. The unsolved problems are probably more amenable
 to the techniques of artificial intelligence and theorem proving than
 the original problem of complexvariable analysis."
+@misc{Mino07,
+ author = "Minoiu, N. and Netto, M and Mammar, S",
+ title = "Assistance control based on a composite Lyapunov function for
+ lane departure avoidance",
+ booktitle = "Proc. 15 Med. Conf. on Control \& Automation",
+ year = "2007",
+ keywords = "axiomref",
+ abstract =
+ "This paper presents a vehicle steering assistance designed to avoid
+ lane departure during driver inattention periods. Activated for a
+ driver loss of concentration during a lane keeping maneuver the
+ steering assistance drives the vehicle back to the center of the
+ lane. In order to ensure a vehicle trajectory as close as possible to
+ the centerline, the control law has been developed based on invariant
+ sets theory and on composite Lyapunov functions. The computation has
+ been performed using LMI methods, which allow in addition imposing a
+ maximum bound for the control steering angle."
}
\end{chunk}
\index{Touratier, Emmanuel}
+\index{Davenport, James H.}
+\begin{chunk}{ignore}
+@misc{Dave12a,
+ author = "Davenport, James H.",
+ title = "Computer Algebra or Computer Mathematics?",
+ year = "2012",
+ url = "http://people.bath.ac.uk/masjhd/Slides/CalculemusSchool2002.pdf",
+ paper = "Dave12a.pdf",
+ abstract =
+ "Scope: ``polynomialtype'' systems: Axiom, Macsyma/Maxima, Maple,
+ Mathematica, and Reduce."
+}
+
+\index{Dicrescenzo, C.}
+\index{Duval, Dominique}
\begin{chunk}{axiom.bib}
@misc{Tour98,
 author = "Touratier, Emmanuel",
 title = {Etude du typage dans le syst\`eme de calcul scientifique Aldor},
 comment = "Study of types in the Aldor scientific computation system",
+@InProceedings{Dicr88,
+ author = "Dicrescenzo, C. and Duval, D.",
+ title = "Algebraic extensions and algebraic closure in Scratchpad II",
+ booktitle = "Proc. ISSAC 1988",
+ series = "ISSAC 1998",
year = "1998",
 paper = "Tour98.pdf",
 url = "http://axiomwiki.newsynthesis.org/public/refs/AldorT1998_04.pdf",
+ pages = "440446",
+ isbn = "3540510842",
keywords = "axiomref"
}
\end{chunk}
\index{Seiler, Werner Markus}
\begin{chunk}{axiom.bib}
@misc{Seil95,
 author = "Seiler, Werner Markus",
 title = "Applying AXIOM to partial differential equations",
 institution = {Universit\"at Karlsruhe, Fakult\"at f\"ur Informatik},
 year = "1995",
 type = "Internal Report",
 number = "9517",
 url = "http://axiomwiki.newsynthesis.org/public/refs/Axiompdf.pdf",
 paper = "Seil95.pdf",
 keywords = "axiomref",
 abstract =
 "We present an Axiom environment called JET for geometric computations
 with partial differential equations within the framework of the jet
 bundle formalism. This comprises expecially the completion of a given
 differential equation to an involutive one according to the
 CartanKuranishi Theorem and the setting up of the determining system
 for the generators of classical and nonclassical Lie
 symmetries. Details of the implementations are described and
 applications are given. An appendix contains tables of all exported
 functions."
+@misc{Unkn16,
+ title = "Computer Algebra Systems",
+ url = "http://www.mhtlab.uwaterloo.ca/courses/me755/web\_intro.pdf",
+ paper = "Unkn16.pdf"
}
\end{chunk}
\index{Davenport, James H.}
+\index{Wang, Dongming}
\begin{chunk}{axiom.bib}
@misc{Dave84a,
 author = "Davenport, James H.",
 title = "A New Algebra System",
 paper = "Dave84a.pdf",
+@InProceedings{Wang02,
+ author = "Wang, Dongming",
+ title = "Epsilon: A Library of Software Tools for Polynomial Elimination",
+ booktitle = "Proc. 1st Int. Congress of Mathematical Software",
+ series = "ICMS 2002",
+ year = "2002",
+ location = "Beijing China",
+ pages = "379389",
keywords = "axiomref",
 url = "http://axiomwiki.newsynthesis.org/public/refs/Davenport1984a\_new\_algebra\_system.pdf",
+ paper = "Wang02.pdf",
+ url = "https://hal.inria.fr/inria00107607/file/A02R314.pdf",
abstract =
 "Seminal internal paper discussing Axiom design decisions."
+ "This article presents a Maple library of functions for decomposing
+ systems of multivariate polynomials into triangular systems of
+ various kinds (regular, simple, or irreducible), with an application
+ package for manipulating and proving geometric theorems."
}
\end{chunk}
\index{Conrad, Marc}
\index{French, Tim}
\index{Maple, Carsten}
\index{Pott, Sandra}
+\index{Gr\"abe, HansGert}
\begin{chunk}{axiom.bib}
@misc{Conrxxa,
 author = "Conrad, Marc and French, Tim and Maple, Carsten and Pott, Sandra",
 title = "Approaching Inheritance from a Natural Mathematical Perspective
 and from a Java Driven Viewpoint: a Comparative Review",
 keywords = "axiomref",
 url = "http://axiomwiki.newsynthesis.org/public/refs/McTfCmSpaxiom.pdf",
 paper = "Conrxxa.pdf",
 abstract = "
 It is wellknown that few objectoriented programming languages allow
 objects to change their nature at runtime. There have been a number
 of reasons presented for this, but it appears that there is a real
 need for matters to change. In this paper we discuss the need for
 objectoriented programming languages to reflect the dynamic nature of
 problems, particularly those arising in a mathematical context. It is
 from this context that we present a framework that realistically
 represents the dynamic and evolving characteristic of problems and
 algorithms."
+@InProceedings{Grab02,
+ author = "Grabe, HansGert",
+ title = "The SymbolicData Benchmark Problems Collection of Polynomial
+ Systems",
+ booktitle = "Workshop on Under and Overdetermined Systems of Algebraic or
+ Differential Equations",
+ location = "Karlsruhe, Germany",
+ pages = "5776",
+ url = "http://symbolicdata.org/Papers/karlsruhe02.pdf",
+ paper = "Grab02.pdf",
+ keywords = "axiomref"
}
\end{chunk}
\index{Meijer, Erik}
\index{Fokkinga, Maarten}
\index{Paterson, Ross}
+\index{Norman, Arthur C.}
\begin{chunk}{axiom.bib}
@misc{Meij91,
 author = "Meijer, Erik and Fokkinga, Maarten and Paterson, Ross",
 title = "Functional Programming with Bananas, Lenses, Envelopes and
 Barbed Wire",
 url = "http://eprints.eemcs.utwente.nl/7281/01/dbutwente40501F46.pdf",
 paper = "Meij91.pdf",
 abstract = "
 We develop a calculus for lazy functional programming based on
 recursion operators associated with data type definitions. For these
 operators we derive various algebraic laws that are useful in deriving
 and manipulating programs. We shall show that all example functions in
 Bird and Wadler's ``Introduction to Functional Programming'' can be
 expressed using these operators."
+@misc{Norm94,
+ author = "Norman, Arthur C.",
+ title = "Algebraic Manipulation",
+ paper = "Norm94.pdf",
+ keywords = "axiomref"
}
\end{chunk}
\index{Robidoux, Nicolas}
+\index{Joyner, David}
\begin{chunk}{axiom.bib}
@misc{Robi93,
 author = "Robidoux, Nicolas",
 title = "Does Axiom Solve Systems of O.D.E's Like Mathematica?",
 year = "1993",
 paper = "Robi93.pdf",
 url = "http://axiomwiki.newsynthesis.org/public/refs/Robidoux.pdf",
+@misc{Joyn16,
+ author = "Joyner, David",
+ title = "Links to some open source mathematical programs",
keywords = "axiomref",
 abstract = "
 If I were demonstrating Axiom and were asked this question, my reply
 would be ``No, but I am not sure that this is a bad thing''. And I
 would illustrate this with the following example.

 Consider the following system of O.D.E.'s
 \[
 \begin{array}{rcl}
 \frac{dx_1}{dt} & = & \left(1+\frac{cos t}{2+sin t}\right)x_1\\
 \frac{dx_2}{dt} & = & x_1  x_2
 \end{array}
 \]
 This is a very simple system: $x_1$ is actually uncoupled from $x_2$"
+ url = "http://www.opensourcemath.org/opensource\_math.html"
}
\end{chunk}
\index{Davenport, James H.}
\index{Faure, Christ\'ele}
+\index{Cohen, Joel S.}
\begin{chunk}{axiom.bib}
@misc{Davexx,
 author = {Davenport, James; Faure, Christ\'ele},
 title = "The Unknown in Computer Algebra",
 url =
"http://axiomwiki.newsynthesis.org/public/refs/TheUnknownInComputerAlgebra.pdf",
 paper = "Davexx.pdf",
+@book{Cohe03b,
+ author = "Cohen, Joel S.",
+ title = "Computer algebra and symbolic computation. Elementary Algorithms",
+ year = "2003",
+ publisher = "A. K. Peters",
+ isbn = "1568811594",
keywords = "axiomref",
 abstract = "
 Computer algebra systems have to deal with the confusion between
 ``programming variables'' and ``mathematical symbols''. We claim that
 they should also deal with ``unknowns'', i.e. elements whose values
 are unknown, but whose type is known. For examples $x^p \ne x$ if $x$
 is a symbol, but $x^p = x$ if $x \in GF(p)$. We show how we have
 extended Axiom to deal with this concept."
+ paper = "Cohe03b.pdf"
}
\end{chunk}
\index{Davenport, James H.}
+\index{Decker, Wolfram}
\begin{chunk}{axiom.bib}
@techreport{Dave92b,
 author = "Davenport, James H.",
 title = "How does one program in the AXIOM system?",
 institution = "Numerical Algorithms Group, Inc.",
 year = "1992",
 type = "technical report",
 number = "TR6/92 (ATR/4)(NP2493)",
 url = "http://www.nag.co.uk/doc/TechRep/axiomtr.html",
 paper = "Dave92b.pdf",
+@misc{Deckxx,
+ author = "Decker, Wolfram",
+ title = "Some Introductory Remarks on Computer Algebra",
+ url =
+"https://www.math.unibielefeld.de/~rehmann/ECM/cdrom/3ecm/pdfs/pant3/decker.pdf",
+ paper = "Deckxx.pdf",
keywords = "axiomref",
abstract =
 "Axiom is a computer algebra system superficially like many others, but
 fundamentally different in its internal construction, and therefore in
 the possibilities it offers to its users and programmers. In these
 lecture notes, we will explain, by example, the methodology that the
 author uses for programming substantial bits of mathematics in Axiom."
+ "Computer algebra is a relatively young but rapidly growing field. In
+ this introductory note to the minisymposium on computer algebra
+ organized as part of the third European Congress of Mathematics I will
+ not even attempt to adress all major streams of research and the many
+ applications of computer algebra. I will concentrate on a few aspects,
+ mostly from a mathematical point of view, and I will discuss a few
+ typical applications in mathematics. I will present a couple of
+ examples which underline the fact that computer algebra systems
+ provide easy access to powerful computing tools. And, I will quote
+ from and refer to a couple of survey papers, textbooks and webpages
+ which I recommend for further reading."
+}
+
+\end{chunk}
+
+\index{Chew, Paul}
+\index{Constable, Robert L.}
+\index{Pingali, Keshav}
+\index{Vavasis, Steve}
+\index{Zippel, Richard}
+\begin{chunk}{axiom.bib}
+@misc{Chew95,
+ author = "Chew, Paul and Constable, Robert L. and Pingali, Keshav and
+ Vavasis, Steve and Zippel, Richard",
+ title = "Collaborative Mathematics Environment",
+ url = "http://www.cs.cornell.edu/rz/MathBus95/TechSummary.html",
+ keywords = "axiomref"
}
\end{chunk}
\index{Youssef, Saul}
+\index{Simon, Barry}
\begin{chunk}{axiom.bib}
@misc{Yous04,
 author = "Youssef, Saul",
 title = "Prospects for Category Theory in Aldor",
 year = "2004",
 url =
"http://axiomwiki.newsynthesis.org/public/refs/YoussefProspectsForCategoryTheoryInAldor.pdf",
 paper = "Yous04.pdf",
 abstract =
 "Ways of encorporating category theory constructions and results into
 the Aldor language are discussed. The main features of Aldor which
 make this possible are identified, examples of categorical
 constructions are provided and a suggestion is made for a foundation
 for rigorous results."
+@misc{Simo97,
+ author = "Simon, Barry",
+ title = "The PC Is Now Axiomatic",
+ publisher = "PC Mag",
+ year = "1997",
+ month = "March",
+ day = "25",
+ keywords = "axiomref"
}
\end{chunk}
\index{Carpent, Quentin}
\index{Conil, Christophe}
+\index{Batut, C.}
+\index{Belabas, K.}
+\index{Bernardi, D.}
+\index{Cohen, H.}
+\index{Olivier, M.}
\begin{chunk}{axiom.bib}
@misc{Carp04,
 author = "Carpent, Quentin and Conil, Christophe",
 title = "Utilisation de logiciels libres pour la r\'ealisation de TP MT26",
 year = "2004",
 paper = "Carp04.pdf",
 url = "http://axiomwiki.newsynthesis.org/public/refs/ac20.pdf",
 keywords = "axiomref",
 comment = "french",
 abstract = "radicalSolve(x**3+x**27=0,x)"
+@misc{Batu03,
+ author = "Batut, C. and Belabas, K. and Bernardi, D. and Cohen, H. and
+ Olivier, M.",
+ title = "User's Guide to PARI/GP",
+ url = "http://math.mit.edu/~brubaker/PARI/PARIusers.pdf",
+ paper = "Batu03.pdf",
+ keywords = "axiomref"
}
\end{chunk}
\index{Naylor, William A.}
\index{Padget, Julian}
+\index{Gianni, Patrizia}
+\index{Trager, Barry M.}
+\index{Zacharias, Gail}
\begin{chunk}{axiom.bib}
@InProceedings{Nayl06,
 author = "Naylor, William and Padget, Julian",
 title = "From Untyped to Polymorphically Typed Objects in Mathematical
 Web Services",
 paper = "NPxx.pdf",
 series = Lecture Notes in Computer Science",
 volume = "4108",
 pages = "222236",
 year = "2006",
 keywords = "axiomref",
 abstract =
 "OpenMath is a widely recognized approach to the semantic markup of
 mathematics that is often used for communication between OpenMath
 compliant systems. The Aldor language has a sophisticated
 categorybased type system that was specifically developed for the
 purpose of modelling mathematical structures, while the system itself
 supports the creation of smallfootprint applications suitable for
 deployment as web services. In this paper we present our first results
 of how one may perform translations from generic OpenMath objects into
 values in specific Aldor domains, describing how the Aldor interfae
 domain ExpresstionTree is used to achieve this. We outline our Aldor
 implementation of an OpenMath translator, and describe an efficient
 extention of this to the Parser category. In addition, the Aldor
 service creation and invocation mechanism are explained. Thus we are
 in a position to develop and deploy mathematical web services whose
 descriptions may be directly derived from Aldor's rich type language."
+@article{Gian88,
+ author = "Gianni, Patrizia. and Trager, Barry. and Zacharias, Gail",
+ title = "Groebner Bases and Primary Decomposition of Polynomial Ideals",
+ journal = "J. Symbolic Computation",
+ volume = "6",
+ pages = "149167",
+ year = "1988",
+ url = "http://www.sciencedirect.com/science/article/pii/S0747717188800403/pdf?md5=40c29b67947035884904fd4597ddf710&pid=1s2.0S0747717188800403main.pdf",
+ paper = "Gian88.pdf"
}
\end{chunk}
\index{Watt, Stephen M.}
\index{Broadbery, Peter A.}
\index{Dooley, Sam}
\index{Iglio, Pietro}
\begin{chunk}{axiom.bib}
@techreport{Watt94,
 author = "Watt, Stephen M. and Broadbery, Peter A. and Dooley, Samuel S.
 and Iglio, Pietro",
 title = "A First Report on the A\# Compiler (including benchmarks)",
 institution = "IBM Research",
 year = "1994",
 type = "technical report",
 number = "RC19529 (85075)",
 paper = "Watt94.pdf",
 url =
 "http://axiomwiki.newsynthesis.org/public/refs/axiomaldorasharp.pdf",
 keywords = "axiomref",
 abstract =
 "The $A^{#}$ compiler allows users of computer algebra to develop
 programs in a context where multiple programming languages are
 employed. The compiler translates programs written in the $A^{#}$
 programming language to a lowlevel intermediate language, Foam,
 from which it can generate standalone programs, native object
 libraries to be linked with other applications, or code to be read
 into closed environments. In addition, Foam code may be directly
 executed using an interpreter provided with the $A^{#}$ compiler.

 The $A^{#}$ programming language provides support for objectoriented
 and functional programming styles. It is ``higherorder'' in the sense
 that both types and functions are first class, and may be manipulated
 in the same ways as any other values. The primary considerations in
 the formulation of the language have been generality, composibility,
 and efficiency. The language has been designed to admit a number of
 important optimizations, allowing compilation to machine code which is
 in many instances of efficiency comparable to that produced by a C or
 Fortran compiler.

 The original motivation for $A^{#}$ comes from the field of computer
 algebra: to provide an improved extension language for the Axiom
 computer algebra system."
+@misc{Wikixx,
+ title = "List of opensource software for mathematics",
+ url = "https://en.wikipedia.org/wiki/List\_of\_opensource\_software\_for\_mathematics",
+ keywords = "axiomref"
}
\end{chunk}
\index{Lambe, Larry A.}
\index{Luczak, Richard}
+\index{Joyner, David}
+\index{Stein, William}
\begin{chunk}{axiom.bib}
@article{Lamb93a,
 article = "Lambe, Larry and Luczak, Richard",
 title = "ObjectOriented Mathematical Programming and
 Symbolic/Numeric Interface",
 journal = "3rd Int. Conf. on Expert Systems in Numerical Computing",
 year = "1993",
 url = "http://axiomwiki.newsynthesis.org/public/refs/axiomfem.pdf",
 paper = "Lamb93a.pdf",
+@misc{Joyn08,
+ author = "Joyner, David and Stein, William",
+ title = "Open Source Mathematical Software: A White Paper",
+ year = "2008",
+ url =
+"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.124.7499&rep=rep1&type=pdf",
+ paper = "Joyn08.pdf",
keywords = "axiomref",
 abstract =
 "The Axiom language is based on the notions of ``categories'',
 ``domains'', and ``packages''. These concepts are used to build an
 interface between symbolic and numeric calculations. In particular, an
 interface to the NAG Fortran Library and Axiom's algebra and graphics
 facilities is presented. Some examples of numerical calculations in a
 symbolic computational environment are also included using the finite
 element method. While the examples are elementary, we believe that
 they point to very powerful methods for combining numeric and symbolic
 computational techniques."
+ abstract =
+ "Open source software has had a profound effect on computing during
+ the last decade, especially on web servers (Apache), web browsers
+ (Firefox), operating systems (Linux and OS X), and programming
+ languages (GC C, Java, Python, Perl, etc.). The purpose of this paper
+ is to put forward the case that open source development methodologies
+ might also have a positive effect on mathematical software,
+ especially if the National Science Foundation (NSF) increases their
+ support of open source mathematical software de velopment. We argue
+ that careful funding of open source mathematical software may lead to
+ a lower total cost of ownership in the research and education
+ community, and to more efficient and trustworthy mathematical software."
}
\end{chunk}
\index{Griesmer, James H.}
\index{Jenks, Richard D.}
+\index{Nguyen, Minh Van}
\begin{chunk}{axiom.bib}
@InProceedings{Grie71,
 author = "Griesmer, James H. and Jenks, Richard D.",
 title = "SCRATCHPAD/1  an interactive facility for symbolic mathematics",
 booktitle = "Proc. second ACM Symposium on Symbolic and Algebraic
 Manipulation",
 series = "SYMSAC 71",
 year = "1971",
 pages = "4258",
 url = "http://delivery.acm.org/10.1145/810000/806266/p42griesmer.pdf",
 paper = "GJ71.pdf",
+@phdthesis{Nguy09,
+ author = "Nguyen, Minh Van",
+ title = "Exploring Cryptography Using the Sage Computer Algebra System",
+ school = "Victoria University",
+ year = "2009",
keywords = "axiomref",
 abstract = "
 The SCRATCHPAD/1 system is designed to provide an interactive symbolic
 computational facility for the mathematician user. The system features
 a user language designed to capture the style and succinctness of
 mathematical notation, together with a facility for conveniently
 introducing new notations into the language. A comprehensive system
 library incorporates symbolic capabilities provided by such systems as
 SIN, MATHLAB, and REDUCE."
+ paper = "Nguy09.pdf",
+ abstract =
+ "Cryptography has become indispensable in areas such as ecommerce,
+ the legal safeguarding of medical records, and secure electronic
+ communication. Hence, it is incumbent upon software engineers to
+ understand the concepts and techniques underlying the cryptosystems
+ that they implement. An educator needs to consider which topics to
+ cover in a course on cryptography as well as how to present the
+ concepts and techniques to be covered in the course. This thesis
+ contributes to the field of cryptography pedagogy by discussing and
+ implementing smallscale cryptosystems whose encryption and
+ decryption processes can be stepped through by hand. Our
+ implementation has been accepted and integrated into the code base of
+ the computer algebra system Sage. As Sage is free and open source,
+ students and educators of cryptology need not worry about paying
+ license fees in order to use Sage, but can instead concentrate on
+ exploring cryptography using Sage’s builtin support for cryptography."
+}
+
+\end{chunk}
+
+\index{Hoeven, Joris van der}
+\index{Lecerf, Gregoire}
+\begin{chunk}{axiom.bib}
+@misc{Hoev13,
+ author = "Hoeven, Joris van der and Lecerf, Gregoire",
+ title = "Interfacing Mathemagix with C++",
+ keywords = "axiomref",
+ url = "http://www.texmacs.org/joris/mmxcpp/mmxcpp.pdf",
+ paper = "Hoev13.pdf",
+ 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{Seiler, Werner Markus}
\index{Calmet, J.}
+\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@misc{Seil95a,
 author = "Seiler, Werner Markus and Calmet, J.",
 title = "JET  An Axiom Environment for Geometric Computations with
 Differential Equations",
 paper = "Seil95a.pdf",
 url = "http://axiomwiki.newsynthesis.org/public/refs/axiomjet95.pdf",
+@misc{Fate94,
+ author = "Fateman, Richard J.",
+ title = "On the Design and Construction of Algebraic Manipulation Systems",
keywords = "axiomref",
 abstract =
 "JET is an environment within the computer algebra system Axiom to
 perform such computations. The current implementation emphasises the
 two key concepts involution and symmetry. It provides some packages
 for the completion of a given system of differential equations to an
 equivalent involutive one based on the CartanKuranishi theorem and
 for setting up the determining equations for classical and
 nonclassical point symmetries."
+ url = "http://www.cs.berkeley.edu/~fateman/papers/asmerev94.ps",
+ paper = "Fate94.pdf",
+ abstract =
+ "We compare and contrast several techniques for the implementation of
+ components of an algebraic manipulation system. On one hand is the
+ mathematicalalgebraic approach which characterizes (for example)
+ IBM's Axiom. On the other hand is the more {\sl adhoc} approach which
+ characterizes many other popular systems (for example, Macsyma,
+ Reduce, Maple, and Mathematica). While the algebraic approach has
+ generally positive results, careful examination suggests that there
+ are significant remaining problems, especially in the representation
+ and manipulation of analytical, as opposed to algebraic,
+ mathematics. We describe some of these problems and some general
+ approaches for solutions."
}
\end{chunk}
+
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index 4c07d74..db1a136 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5426,6 +5426,8 @@ books/bookvolbib Axiom Citations in the Literature
src/input/Makefile fix typo
20160629.01.tpd.patch
books/bookvolbib Axiom Citations in the Literature
+20160630.01.tpd.patch
+books/bookvolbib Axiom Citations in the Literature

1.7.5.4