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Goal: Axiom Literate Programming
\index{Schwardmann, Ulrich}
\begin{chunk}{axiom.bib}
@book{Schw95,
author = "Schwardmann, Ulrich",
title = "Computer algebra systems",
comment = "ComputeralgebraSysteme, German",
publisher = "AddisonWesley",
year = "1995",
keywords = "axiomref"
}
\end{chunk}
\index{Storme, L.}
\index{van Maldeghem, H.}
\begin{chunk}{axiom.bib}
@article{Stor95,
author = "Storme, L. and van Maldeghem, H.",
title = "Cyclic caps in PG(3,q)",
journal = "Geom. Dedicata",
volume = "56",
number = "3",
pages = "271284",
year = "1995",
keywords = "axiomref",
url = "https://cage.ugent.be/~hvm/artikels/44.pdf",
paper = "Stor95.pdf",
abstract =
"A $k$cap $K$ on $PG(n,q)$ is a set of $k$ points, no three of which
are collinear. $K$ is complete if it cannot be extended to a $k+1$
cap. If $K$ is invariant under a cyclic subgroup (which acts regularly
on $K$) of $PGL(n+1,q)$, the $K$ is cyclic.
This article investigates cyclic complete $k$caps in
$PG(3,q). Namely, the different types of complete $k$caps $K$ in
$PG(3,q)$ stabilized by a cyclic projective group $G$ of order $k$,
acting regularly on the points of $K$, are determined. We show that in
$PG(3,q)$, $q$ even, the elliptic quadric is the only cyclic complete
$k$cap. For $q$ odd, it is shown that besides the elliptic quadric,
there also exist cyclic $k$caps containing $k/2$ points of two
disjoint elliptic quadrics or two disjoint hyperbolic quadrics and
that there exist cyclic $k$caps stabilized by a transitive cyclic
group $G$ fixed precisely one point and one plane of
$PG(3,q)$. Concrete examples of such caps, found using AXIOM and
CAYLEY, are presented."
}
\end{chunk}
\index{Weber, Andreas}
\begin{chunk}{axiom.bib}
@article{Webe95,
author = "Weber, Andreas",
title = "On coherence in computer algebra",
journal = "J. Symb. Comput.",
volume = "19",
number = "13",
pages = "2538",
year = "1995",
url =
"http://cg.cs.unibonn.de/personalpages/weber/publications/pdf/WeberA/Weber94e.pdf",
paper = "Webe95.pdf",
keywords = "axiomref",
abstract = "
Modern computer algebra systems (e.g. AXIOM) support a rich type
system including parameterized data types and the possibility of
implicit coercions between types. In such a type system it will be
frequently the case that there are different ways of building
coercions between types. An important requirement is that all
coercions between two types coincide, a property which is called {\sl
coherence}. We will prove a coherence theorem for a formal type system
having several possibilities of coercions covering many important
examples. Moreover, we will give some informal reasoning why the
formally defined restrictions can be satisfied by an actual system."
}
\end{chunk}
\index{Williamson, Clifton J.}
\begin{chunk}{axiom.bib}
@InProceedings{Will95,
author = "Williamson, Clifton J.",
title = "On the algebraic construction of tridiagonal matrices with given
characteristic polynomial",
booktitle = "4th Conf. of Canadian Number Theory Association",
year = "1995",
location = "Halifax, Nova Scotia, Canada",
pages = "417431",
keywords = "axiomref",
paper = "Will95.pdf",
abstract =
"Let $K$ be a field of characteristic zero and assume
\[f(x)=x^ns_1x^{n1}+\cdots+s_n \in L[x]\]
where $L=K(s_1,\cdots,s_n)$. Call, for the purposes of this review, an
$n\times n$ matrix 1tridiagonal if its entries above and below the
main diagonal are all 1, the entries on it are $d_1,\cdots,d_n$, and
all other entries are 0. Under which conditions can
$d_1,d_2,\cdots,d_n$ be chosen in a radical extension of $L$ such that
the resulting 1tridiagonal matrix has $f$ as its characteristic
polynomial? The author’s answer: for $n=3$ always. The $d_i,s_i$
are related by a system of algebraic equations of the form
$\overline{f}_i(d_1,d_2,d_3)=s_i$. If this is satisfied, then by
a resultant or Groebner basis computation with respect to the
lexicographic order, $d_3$ (say) must be a root of a certain
irreducible polynomial $\varphi$ of degree 6. Joining this
with a Galois group computation for $\varphi$ over $L$, it is shown
that a solvable and necessarily transitive Gal($\varphi$) will be a
necessary and sufficient condition for expressibility of $d_3$ (clear)
and, thanks to the form of the Groebner basis, also of $d_1,d_2$ in
radicals. Upon a discriminant computation of $\varphi$ and use of
results of G. Butler and J. McKay [Commun. Algebra 11,
863911 (1983; Zbl 0518.20003)] and J. McKay and L. Soicher [J. Number
Theory 20, 273281 (1985; Zbl 0579.12006)], this allows the author to
deduce the mentioned result. For $n=4$, though the author cannot get as
complete information about Galois groups etc., he can deduce e.g. that
if $s_1,\cdots,s_4$ are algebraically independent over $\mathbb{Q}$,
then $d_1,\cdots,d_4$ are not expressible in radicals over
$\mathbb{Q}(s_1,\cdots,s_4)$. He mentions, however, a solvable subcase."
}
\end{chunk}
\index{Bosma, Wieb}
\index{Cannon, John}
\index{Matthews, Graham}
\begin{chunk}{axiom.bib}
@InProceedings{Bosm94,
author = "Bosma, Wieb and Cannon, John and Matthews, Graham",
title = "Programming with algebraic structures: Design of the Magma
language",
booktitle = "Proc. ISSAC 94",
series = "ISSAC 94",
year = "1994",
publisher = "ACM Press",
location = "Baltimore, MD",
pages = "5257",
keywords = "axiomref",
paper = "Bosm94.pdf",
url = "http://www.math.ru.nl/~bosma/pubs/ISSAC94.pdf",
abstract =
"MAGMA is a new software system for computational algebra, number
theory and geometry whose design is centred on the concept of
algebraic structure (magma). The use of algebraic structure as a
design paradigm provides a natural strong typing mechanism. Further,
structures and their morphisms appear in the language as first class
objects. Standard mathematical notions are used for the basic data
types. The result is a powerful, clean language which deals with
objects in a mathematically rigorous manner. The conceptual and
implementation ideas behind MAGMA will be examined in this paper. This
conceptual base differs significantly from those underlying other
computer algebra systems."
}
\end{chunk}
\index{Dingle, Adam}
\index{Fateman, Richard J.}
\begin{chunk}{axiom.bib}
@InProceedings{Ding94,
author = "Dingle, Adam and Fateman, Richard",
title = "Branch Cuts in Computer Algebra",
year = "1994",
booktitle = "Proc. ISSAC 1994",
series = "ISSAC 94",
url = "http://www.cs.berkeley.edu/~fateman/papers/ding.ps",
paper = "Ding94.pdf",
keywords = "axiomref",
abstract =
"Many standard functions, such as the logarithms and square root
functions, cannot be defined continuously on the complex
plane. Mistaken assumptions about the properties of these functions
lead computer algebra systems into various conundrums. We discuss how
they can manipulate such functions in a useful fashion."
}
\end{chunk}
\index{Duval, Dominique}
\index{Senechaud, Pascale}
\begin{chunk}{axiom.bib}
@article{Duva94d,
author = "Duval, Dominique and Senechaud, Pascale",
title = "Sketches and parametrization",
journal = "Theor. Comput. Sci.",
volume = "123",
number = "1",
pages = "117130",
year = "1994",
keywords = "axiomref",
abstract =
"The paper deals with problems about conception and design of
highlevel computer algebra systems. Here we use a categorical
approach given by the notion of sketches. Sketches allow to describe
computation mechanisms in a syntactic way, well adapted to
implementation.
A computer algebra system must allow the manipulation of algebraic
structures, in particular, the construction of new structures from
known ones. In the paper we give a definition, at the sketch level, of
parametrization of a structure by another one."
}
\end{chunk}
\index{Duval, Dominique}
\begin{chunk}{axiom.bib}
@misc{Duva94e,
author = "Duval, Dominique",
title = "Symbolic or algebraic computation?",
booktitle = "Publication du LACO",
year = "1995",
location = "Madrid Spain",
comment = "NAG conference",
keywords = "axiomref"
}
\end{chunk}
\index{Duval, Dominique}
\index{Reynaud, J.C.}
\begin{chunk}{axiom.bib}
@article{Duva94a,
author = "Duval, D. and Reynaud, J.C.",
title = "Sketches and Computation (Part I):
Basic Definitions and Static Evaluation",
journal = "Mathematical Structures in Computer Science",
volume = "4",
pages = "185238",
publisher = "Cambridge University Press",
year = "1994",
url = "http://journals.cambridge.org/abstract_S0960129500000438",
paper = "Duva94a.pdf",
abstract =
"We define a categorical framework, based on the notion of {\sl
sketch}, for specification and evaluation in the sense of algebraic
specifications and algebraic programming. This framework goes far
beyond our initial motivations, which was to specify computation with
algebraic numbers. We begin by redefining sketches in order to deal
explicitly with programs. Expressions and terms are carefully defined
and studied, then {\sl quasiprojective sketches} are introduced. We
describe {\sl static evaluation} in these sketches: we propose a
rigorous basis for evaluation in the corresponding structures. These
structures admit an initial model, but are not necessarily
equational. In Part II (Duval and Reynaud 1994), we study a more
general process, called {\sl dynamic evaluation}, for structures that
may have no initial model."
}
\end{chunk}
\index{Duval, Dominique}
\index{Reynaud, JeanClaude}
\begin{chunk}{axiom.bib}
@article{Duva94b,
author = "Duval, Dominique and Reynaud, JeanClaude",
title = "Sketches and Computation (Part II):
Dynamic Evaluation and Applications",
journal = "Mathematical Structures in Computer Science",
volume = "4",
pages = "239271",
publisher = "Cambridge University Press",
year = "1994",
url = "http://journals.cambridge.org/abstract_S096012950000044X",
paper = "Duva94b.pdf",
abstract =
"In the first part of this paper (Duval and Reynaud 1994), we defined a
categorical framework, based on the notion of {\sl sketch}, for
specification and evaluation in the senses of algebraic specification
and algebraic programming. {\sl Static evaluation} in {\sl
quasiprojective sketches} was defined in Part I; in this paper, {\sl
dynamic evaluation} is introduced. It deals with more general
structures, which may have no initial model. Until now, this process
has not been used in algebraic specification systems, but computer
algebra systems are beginning to use it as a basic tool. Finally, we
give some applications of dynamic evaluation to computation in field
extensions."
}
\end{chunk}
\index{Duval, Dominique}
\begin{chunk}{axiom.bib}
@article{Duva94c,
author = "Duval, Dominique",
title = "Algebraic Numbers: An Example of Dynamic Evaluation",
journal = "J. Symbolic Computation",
volume = "18",
pages = "429445",
year = "1994",
url = "http://www.sciencedirect.com/science/article/pii/S0747717106000551",
paper = "Duva94c.pdf",
keywords = "axiomref",
abstract = "
Dynamic evaluation is presented through examples: computations
involving algebraic numbers, automatic case discussion according to
the characteristic of a field. Implementation questions are addressed
too. Finally, branches are presented as ``dual'' to binary functions,
according to the approach of sketch theory."
}
\end{chunk}
\index{Duval, Dominique}
\index{Reynaud, JeanClaude}
\begin{chunk}{axiom.bib}
@article{Duva96,
author = "Duval, D. and Reynaud, JeanClaude",
title = "Sketches and Computations over Fields",
journal = "Mathematics and Computers in Simulation",
volume = "42",
pages = "363373",
year = "1996",
paper = "Duva96.pdf",
abstract =
"The goal of this short paper is to describe one possible use of
sketches in computer algebra. We show that sketches are a powerful
tool for the description of mathematical structures and for the
description of computations."
}
\end{chunk}
\index{Duval, Dominique}
\index{Gonz\'alezVega, L.}
\begin{chunk}{axiom.bib}
@article{Duva96a,
author = {Duval, Dominique and Gonz\'alezVega, L.},
title = "Dynamic Evaluation and Real Closure",
journal = "Mathematics and Computers in Simulation",
volume = "42",
pages = "551560",
year = "1996",
paper = "Duva96a.pdf",
abstract = "
The aim of this paper is to present how the dynamic evaluation method
can be used to deal with the real closure of an ordered field. Two
kinds of questions, or tests, may be asked in an ordered field:
equality tests $(a=b?)$ and sign tests $(a > b?)$. Equality tests are
handled through splittings, exactly as in the algebraic closure of a
field. Sign tests are handled throug a structure called ``Tarski data
type''."
}
\end{chunk}
\index{Fritzson, D.}
\index{Fritzson, P.}
\index{Viklund, L.}
\index{Herber, J.}
\begin{chunk}{axiom.bib}
@article{Frit94,
author = "Fritzson, D. and Fritzson, P. and Viklund, L. and Herber, J.",
title = "Objectoriented mathematical modelling  applied to machine
elements",
journal = "Comput. Struct.",
volume = "51",
number = "3",
pages = "241253",
year = "1994",
keywords = "axiomref",
paper = "Frit94.pdf",
abstract =
"Machine element analysis has a goal of describing function and other
aspects of machine elements in a theoretical form. This paper shows
how ideas from objectoriented modelling can be applied to machine
elment analysis. The models thus obtained are both easier to
understand, better structured, and allow a higher degree of reuse
than conventional models. An objectoriented model description is
natural and suitable for machine element analysis. As a realistic
example an equational model of rolling bearings is presented. The
structure of the model is general, and applies to many types of
rolling bearings. The model and one solution require approximately
200+200 equations. The model is extensible, e.g. simple submodels of
detailed properties can be made more complex without altering the
overall structure. The example model has been implemented in a
language of our own design. ObjectMath (Objectoriented Mathematical
language for scientific computing). Using ObjectMath, it is possible
to model classes of equation objects, to support multiple and single
inheritance of equations, to support composition of equations, and to
solve systems of equations. Algebraic transformations can conveniently
be done since ObjectMath models are translated into the Mathematica
computer algebra language. When necessary, equations can be
transformed int C++ code for efficient numerical solution. The reuse
of equations through inheritance reduced the size of the model by a
factor of two, compared to a direct representation of the model in the
Mathematica computer algebra language."
}
\end{chunk}
\index{Ioakimidis, N.I.}
\begin{chunk}{axiom.bib}
@article{Ioak94,
author = "Ioakimidis, N.I.",
title = "Symbolic computations for the solution of inverse/design
problems with Maple",
journal = "Comput. Struct.",
volume = "53",
number = "1",
pages = "6368",
year = "1994",
keywords = "axiomref"
}
\end{chunk}
\index{Jenks, Richard D.}
\index{Trager, Barry M.}
\begin{chunk}{axiom.bib}
@InProceedings{Jenk94,
author = "Jenks, Richard D. and Trager, Barry M.",
title = "How to make AXIOM into a scratchpad",
booktitle = "Proceedings of the ACMSIGSAM 1989 International
Symposium on Symbolic and Algebraic Computation, ISSAC '94",
series = "ISSAC 94",
year = "1994",
pages = "3240",
isbn = "0897916387",
keywords = "axiomref",
publisher = "ACM Press",
address = "New York, NY, USA",
paper = "Jenk94.pdf",
abstract =
"Scratchpad [GrJe71] was a computer algebra system developed in the
early 1970s. Like M\&M (Maple [CGG91ab] and Mathematical [W01S92]) and
other systems today, Scratchpad had one principal representation for
mathematical formulae based on ``expression trees''. Its user interface
design was based on a patternmatching paradigm with infinite rewrite
rule semantics, providing what we believe to be the most natural
paradigm for interactive symbolic problem solving. Like M\&M, however,
user programs were interpreted, often resulting in poor performance
relative to similar facilities coded in standard programming languages
such as FORTRAN and C.
Scratchpad development stopped in 1976 giving way to a new system
design ([JenR79], [JeTr81]) that evolved into AXIOM [JeSu92].
AXIOM has a stronglytyped programming language for building a library
of parameterized types and algorithms, and a typeinferencing
interpreter that accesses the library and can build any of an infinite
number of types for interactive use.
We suggest that the addition of an expression tree type to AXIOM can
allow users to operate with the same freedom and convenience of
untyped systems without giving up the expressive power and runtime
efficiency provided by the type system. We also present a design that
supports a multiplicity of programming styles, from the Scratchpad
patternmatching paradigm to functional programming to more
conventional procedural programming. The resulting design seems to us
to combine the best features of Scratchpad with current AXIOM and to
offer a most attractive, flexible, and userfriendly environment for
interactive problem solving.
Section 2 is a discussion of design issues contrasting AXIOM with
other symbolic systems. Sections 3 and 4 is an assessment of AXIOM’s
current design for building libraries and interactive use. Section 5
describes a new interface design for AXIOM, its resulting paradigms,
and its underlying semantic model. Section 6 compares this work with
others."
}
\end{chunk}
\index{Bernard, Joey}
\begin{chunk}{axiom.bib}
@misc{Bern14,
author = "Bernard, Joey",
title = "Open Axiom",
url = "http://www.linuxjournal.com/content/openaxiom",
keywords = "axiomref",
year = "2014"
}
\end{chunk}
\index{Davenport, James H.}
\index{Trager, Barry M.}
\begin{chunk}{axiom.bib}
@InProceedings{Dave90,
author = "Davenport, James H. and Trager, Barry M.",
title = "Scratchpad's view of algebra I: Basic commutative algebra",
booktitle = "Design and Implementation of Symbolic Computation Systems",
year = "1990",
series = "DISCO '90",
location = "Capri, Italy",
publisher = "SpringerVerlag",
isbn = "0387525319",
keywords = "axiomref",
url = "http://opus.bath.ac.uk/32336/1/Davenport\_DISCO\_1990.pdf",
paper = "Dave90.pdf",
comment = "AXIOM Technical Report, ATR/1, NAG Ltd., Oxford, 1992",
keywords = "axiomref",
abstract =
"While computer algebra systems have dealt with polynomials and
rational functions with integer coefficients for many years, dealing
with more general constructs from commutative algebra is a more recent
problem. In this paper we explain how one system solves this problem,
what types and operators it is necessary to introduce and, in short,
how one can construct a computational theory of commutative
algebra. Of necessity, such a theory is rather different from the
conventional, nonconstructive, theory. It is also somewhat different
from the theories of Seidenberg [1974] and his school, who are not
particularly concerned with practical questions of efficiency."
}
\end{chunk}
\index{Jenks, Richard D.}
\index{Trager, Barry M.}
\begin{chunk}{axiom.bib}
@article{Jenk81,
author = "Jenks, Richard D. and Trager, Barry M.",
title = "A Language for Computational Algebra",
year = "1981",
booktitle = "Proc. Symp. on Symbolic and Algebraic Manipulation",
series = "SYMSAC 1981",
location = "Snowbird, Utah",
keywords = "axiomref",
comment = "IBM Research Report 8930",
abstract =
"This paper reports ongoing research at the IBM Research Center on the
development of a language with extensible parameterized types and
generic operators for computational algebra. The language provides an
abstract data type mechanism for defining algorithms which work in as
general a setting as possible. The language is based on the notions of
domains and categories. Domains represent algebraic
structures. Categories designate collections of domains having common
operations with stated mathematical properties. Domains and categories
are computed objects which may be dynamically assigned to variables,
passed as arguments, and returned by functions. Although the language
has been carefully tailored for the application of algebraic
computation, it actually provides a very general abstract data type
mechanism. Our notion of a category to group domains with common
properties appears novel among programming languages (cf. image
functor of RUSSELL) and leads to a very powerful notion of abstract
algorithms missing from other work on data types known to the authors."
}
\end{chunk}
\index{Kapur, D.}
\index{Musser, D.R.}
\index{Stepanov, A.A.}
\begin{chunk}{axiom.bib}
@misc{Kapu81,
author = "Kapur, D. and Musser, D.R. and Stepanov, A.A.",
title = "Operators and Algebraic Structures",
url = "http://www.stepanovpapers.com/p59kapur.pdf",
paper = "Kapu81.pdf",
year = "1981",
abstract =
"Operators in functional languages such as APL and FFP are a useful
programming concept. However, this concept cannot be ful ly
exploited in these languages because of certain constraints. It is
proposed that an operator should be associated with a structure hav
ing the algebraic properties on which the operator's behavior depends.
This is illustrated by introducing a language that provides mechanisms
for defining structures and operators on them. Using this language,
it is possible to describe algorithms abstractly, thus empliasizing
the algebraic properties on which the algorithms depend. The role
that formal representation of mathematical knowledge can play in the
development of programs is illustrated through an example. An
approach for associating complexity mea sures with a structure and
operators is also suggested. This ap proach is useful in analyzing
the complexity of algorithms in an abstract setting."
}
\end{chunk}
\index{Jenks, Richard D.}
\index{Sutor, Robert S.}
\index{Watt, Stephen M.}
\begin{chunk}{axiom.bib}
@techreport{Jenk86,
author = "Jenks, Richard D. and Sutor, Robert S. and Watt, Stephen M.",
title = "Scratchpad II: An Abstract Datatype System for Mathematical
Computation",
institution = "IBM Research",
year = "1986",
type = "Research Report",
number = "RC 12327 (\#55257)",
url = "http://www.csd.uwo.ca/~watt/pub/reprints/1987imaspadadt.pdf",
paper = "Jenk86.pdf",
keywords = "axiomref",
abstract = "
Scratchpad II is an abstract datatype language and system that is
under development in the Computer Algebra Group, Mathematical Sciences
Department, at the IBM Thomas J. Watson Research Center. Some features
of APL that made computation particularly elegant have been borrowed.
Many different kinds of computational objects and data structures are
provided. Facilities for computation include symbolic integration,
differentiation, factorization, solution of equations and linear
algebra. Code economy and modularity is achieved by having
polymorphic packages of functions that may create datatypes. The use
of categories makes these facilities as general as possible."
}
\end{chunk}
\index{Lloyd, Michael}
\index{Oancea, Cosmin}
\index{Watt, Stephen}
\begin{chunk}{axiom.bib}
@misc{Chic04,
author = "Chicha, Yannis and Lloyd, Michael Oancea, Cosmin",
title = "Parametric Polymorphism for Computer Algebra Software Components",
booktitle = "6th Int. Symp. on Symbolic and Numeric Algorithms for
Scientific Computing",
series = "SYNASC 04",
location = "Imisoara, Romania",
keywords = "axiomref",
year = "2004",
paper = "Chic04.pdf",
url = "http://www.csd.uwo.ca/~watt/pub/reprints/2004synascppca.pdf",
abstract =
"This paper presents our experiments in providing mechanisms for
parametric polymorphism for computer algebra software components.
Specific interfaces between Aldor and C++ and between Aldor and Maple
are described. We then present a general solution, Generic IDL (GIDL),
an extension to CORBA IDL supporting generic types. We describe our
language bindings for C++, Java 1.5 and Aldor as well as aspects of
our implementation, consisting of a GIDL to IDL compiler and tools for
generating interface code for the various language bindings."
}
\end{chunk}
\index{Watt, Stephen}
\begin{chunk}{axiom.bib}
@InProceedings{Watt07,
author = "Watt, Stephen",
title = "What Happened to Languages for Symolic Mathematical Computation?",
booktitle = "Proc. Prog. Lang. for Mechanized Mathematics",
series = "PLMMS 07",
year = "2007",
location = "RISCLinz, Austria",
pages = "8190",
keywords = "axiomref",
paper = "Watt07.pdf",
url =
"http://www.csd.uwo.ca/~watt/pub/reprints/2007plmmswhat\_happened.pdf",
abstract =
"While the state of the art is relatively sophisticated in programming
language support for computer algebra, there has been less development
in programming language support for symbolic computation over the past
two decades. We summarize certain advances in programming languages
for computer algebra and propose a set of directions and challenges
for programming languages for symbolic computation."
}
\end{chunk}
\index{Santas, Philip S.}
\begin{chunk}{axiom.bib}
@inproceedings{Sant96,
author = "Santas, Philip S.",
title = "Conditional Categories and Domains",
keywords = "axiomref",
booktitle = "Proc. DISCO 1996",
year = "1996",
pages = "112125",
isbn = "3540616977"
}
\end{chunk}
\index{Santas, Philip S.}
\begin{chunk}{axiom.bib}
@book{Sant05,
author = "Santas, Philip S.",
title = "Conditional Categories and Domains",
keywords = "axiomref",
booktitle = "Design and Implementation of Symbolic Computation Systems",
year = "2005",
series = "Lecture Notes in Computer Science",
volume = "1128",
publisher = "Springer",
abstract =
"We extend the Type system defined in [Sant95] with Axiomlike
Conditional Categories with the additional property of Static Typing
and Checking. Categories and Domains may contain conditionals in their
bodies, which are elaborated by our compiler by techniques used in
standard typing. We define an appropriate calculus and discuss its
properties. Examples inspired by the Axiom library illustrate the
power of our apprach and its application in constructing algebraic
concepts. The full calculus has been implemented and tested with our
LA compiler which generated executable files."
}
\end{chunk}
\begin{chunk}{axiom.bib}
@misc{Gute16,
author = "Gutenberg SelfPublishing Press",
title = "OpenAxiom",
keywords = "axiomref",
url = "http://self.gutenberg.org/articles/openaxiom",
year = "2016"
}
\end{chunk}
\index{Baker, Martin}
\begin{chunk}{axiom.bib}
@misc{Bake16,
author = "Baker, Martin",
title = "Axiom Maths Program",
keywords = "axiomref",
year = "2016",
url = "http://www.euclideanspace.com/prog/scratchpad/axiom/index.htm"
}
\end{chunk}
\index{Caviness, Bob}
\index{Trager, Barry}
\index{Gianni, Patrizia}
\begin{chunk}{axiom.bib}
@misc{Cavi03,
author = "Caviness, Bob and Trager, Barry and Gianni, Patrizia",
title = "Dedicated to the Memory of Richard Dimick Jenks",
year = "2003",
url = "https://www.eecis.udel.edu/~caviness/jenks/issacded.pdf",
keywords = "axiomref",
paper = "Cavi03.pdf",
abstract =
"On December 30, 2003, Dick Jenks died at the age of 66, after an
extended and courageous battle with multiple system atrophy.
He received his PhD in mathematics from the University of Illinois at
UrbanaChampaign in 1966. The title of his dissertation was
“Quadratic Differential Systems for Mathematical Models” and was
written under the supervision of Donald Gilles. After completing his
PhD, he was a postdoctoral fellow at Brookhaven National Laboratory
on Long Island. In 1968 he joined IBM Research where he worked until
his retirement in 2002.
At IBM he was one of the principal architects of the Scratchpad
system, one of the earliest computer algebra systems(1971). Dick
always believed that natural user interfaces were essential and
developed a userfriendly rulebased system for Scratchpad. Although
this rulebased approach was easy to use, as algorithms for computer
algebra became more complicated, he began to understand that an
abstract data type approach would give sophisticated algorithm
development considerably more leverage. In 1977 he began the Axiom
development (originally called Scratchpad II) with the design of
MODLISP, a merger of Lisp with types (modes). In 1980, with the help
of many others, he completed an initial prototype design based on
categories and domains that were intended to be natural for
mathematically sophisticated users.
During this period many researchers in computer algebra visited IBM
Research in Yorktown Heights and contributed to the development of
the Axiom system. All this activity made the computer algebra group at
IBM one of the leading centers for research in this area and Dick was
always there to organize the visits and provide a stimulating and
pleasant working environment for everyone. He had a good perspective
on the most important research directions and worked to attract
worldrenowned experts to visit and interact with his group. He was an
ideal manager for whom to work, one who always put the project and the
needs of the group members first. It was a joy to work in such a
vibrant and stimulating environment.
After many years of development, a decision was made to rename
Scratch pad II to Axiom and to release it as a product. Dick and
Robert Sutor were the primary authors of the book {\sl Axiom: The
Scientific Computation System}. In the foreword of the book, written
by David and Gregory Chudnovsky, it is stated that ``The Scratchpad
system took its time to blossom into the beautiful Axiom
product. There is no rival to this powerful environment in its scope
and, most importantly, in its structure and organization.'' Axiom was
recently made available as free software. See
http://savannah.nongnu.org/projects/axiom
Dick was active in service to the computer algebra community as
well. Here are some highlights. He served as Chair of ACM SIGSAM
(197981) and Conference Cochair (with J. A. van Hulzen) of EUROSAM
’84, a precursor of the ISSAC meetings. Dick also had a long period of
service on the editorial board of the {\sl Journal of Symbolic
Computation}. At ISSAC ’95 in Montreal, Dick was elected to the
initial ISSAC Steering Committee and was elected as the second Chair
of the Committee in 1997. He, along with David Chudnovsky, organized
the highly successful meetings on Computers and Mathematics that were
held at Stanford in 1986 and MIT in 1989. As a legacy of those
meetings, the Jenks Prize for outstanding contributions to software
engineering in computer algebra has been established.
Dick had many interests outside of his professional pursuits including
reading, travel, physical fitness, and especially music. Dick was an
accomplished pianist, organist, and vocalist. At one point he was the
organist and choir master of the Church of the Holy Communion in
Mahopac, NY. In the 1980s and 1990s, he sang in choral groups under
the direction of Dr. Dennis Keene that performed at Lincoln Center in
New York city.
Personally, Dick was warm, generous, and outgoing with many
friends. He will be missed for his technical accomplishments, his
artist talents, and most of all for his positive, gentle, charming
spirit."
}
\end{chunk}
\index{Davenport, James H.}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@article{Dave81,
author = "Davenport, James H. and Jenks, Richard D.",
title = "MODLISP",
year = "1981",
journal = "ACM SIGSAM Bulletin",
volume = "15",
issue = "1",
pages = "1120",
publisher = "ACM",
keywords = "axiomref",
abstract =
"This paper discusses the design and implementation of MODLISP, a
LISPlike language enhanced with the idea of MODes. This extension
permits, but does not require, the user to declare the types of
various variables, and to compile functions with the arguments
declared to be of a particular type. It is possible to declare several
functions of the same name, with arguments of different type
(e.g. PLUS could be declared for Integer arguments, or Rational, or
Real, or even Polynomial arguments) and the system will apply the
correct function for the types of the arguments."
}
\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@inproceedings{Jenk79,
author = "Jenks, Richard D.",
title = "MODLISP: An Introduction",
booktitle = "Proc. ISSAC 1979",
series = "EUROSAM 79",
pages = "466480",
year = "1979",
publisher = "SpringerVerlag",
isbn = "3540095195",
comment = "IBM Research Report RC 8073 Jan 1980",
keywords = "axiomref"
}
\end{chunk}
\index{Davenport, James H.}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@techreport{Dave80,
author = "Davenport, James H. and Jenks, Richard D.",
title = "MODLISP: A Preliminary Design",
institution = "IBM Research",
type = "Research Report",
year = "1980",
number = "RC 8073",
keywords = "axiomref"
}
\end{chunk}
\index{Davenport, James H.}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@techreport{Dave80,
author = "Davenport, James H. and Jenks, Richard D.",
title = "MODLISP",
institution = "IBM Research",
type = "Research Report",
year = "1980",
number = "RC 8537 (\#37198)",
keywords = "axiomref",
comment = "http://www.computerhistory.org/collections/catalog/102719109"
}
\end{chunk}
\index{Hoeven, Joris van der}
\index{Lecerf, Gregoire}
\begin{chunk}{axiom.bib}
@misc{Hoev15,
author = "Hoeven, Joris van der and Lecerf, Gregoire",
title = "Interfacing Mathemagix with C++",
keywords = "axiomref",
url = "http://www.texmacs.org/joris/mmxcpp/mmxcpp.html",
abstract =
"In this paper, we give a detailed description of the interface
between the Mathemagix language and C++. In particular, we describe
the mechanism which allows us to import a C++ template library
(which only permits static instantiation) as a fully generic
Mathemagix template library."
}
\end{chunk}
\index{Fortenbacher, A.}
\index{Jenks, Richard}
\index{Lucks, Michael}
\index{Sutor, Robert}
\index{Trager, Barry}
\index{Watt, Stephen}
\begin{chunk}{axiom.bib}
@techreport{Fort85,
author = "Fortenbacher, A. and Jenks, Richard and Lucks, Michael and
Sutor, Robert and Trager, Barry and Watt, Stephen",
title = "An Overview of the Scratchpad II Language and System",
year = "1985",
type = "Research Report",
publisher = "IBM Research Computer Algebra Group",
keywords = "axiomref"
}
\end{chunk}
\begin{chunk}{axiom.bib}
@misc{Maxi16,
author = "Maxima",
title = "Other Free Computer Algebra Systems",
url = "http://maxima.sourceforge.net/compalg.html",
year = "2016",
keywords = "axiomref",
abstract =
“Axiom is a general purpose Computer Algebra system. It is useful for
doing mathematics by computer and for research and development of
mathematical algorithms. It defines a strongly typed, mathematically
correct type hierarchy. It has a programming language and a builtin
compiler.
There is also an interesting Rosetta Stone which offers translations
of many basic operations for several computer algebra systems,
including Maxima."
}
\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@inproceedings{Jenk84b,
author = "Jenks, Richard D.",
title = "A primer: 11 keys to New Scratchpad",
booktitle = "Proc. EUROSAM ISSAC 1984",
year = "1984",
publisher = "SpringerVerlag",
pages = "123147",
isbn = "038713350X",
keywords = "axiomref",
abstract =
"This paper is an abbreviated primer for the language of new
SCRATCHPAD, a new implementation of SCRATCHPAD which has been under
design and development by the Computer Algebra Group at the IBM
Research Center during the past 6 years. The basic design goals of the
new SCRATCHPAD language and interface to the user are to provde:
\begin{itemize}
\item a ``typeless'' interactive language suitable for online solution
of mathematical problems by novice users with little or no programming
required, and
\item a programming language suitable for the formal description of
algorithms and algebraic structures which can be compiled into runtime
efficient object code.
\end{itemize}
The new SCRATCHPAD language is introduced by 11 keys with each
successive key introducing an additional capability of the
language. The language is thus described as a ``concentric'' language
with each of the 11 levels corresponding to a language subset. These
levels are more than just a pedagogic device, since they correspond to
levels at which the system can be effectively used. Level 1 is
sufficient for naive interactive use; levels 28 progressively
introduce interactive users to capabilities of the language; levels
911 are for system programmers and advanced users. Levesl 2, 4, 6,
and 7 give users the full power of LISP with a highlevel language;
level 8 introduces ``type declarations;'' level 9 allows polymorphic
functions to be defined and compiled; levels 1011 give users an
Adalike facility for defining types and packages (those of new
SCRATCHPAD are dynamically constructable, however). One language is
used for both interactive and system programming language use,
although several freedomes such as abbreviation and optional
typedeclarations allowed at toplevel are not permitted in system
code. The interactive language (levels 18) is a blend of original
SCRATCHPAD [GRJY75], some proposed extensions [JENK74], work by Loos
[LOOS74], SETL [DEWA79], SMP [COWO81], and new ideas; the system
programming language (levels 111) superficially resembles Ada but is
more similar to CLU [LISK74] in its semantic design.
This presentation of the language in this paper omits many details to
be covered in the SCRATCHPAD System Programming Manual [SCRA84] and an
expanded version of this paper will serve as a primer for SCRATCHPAD
users [JESU84]."
}
\end{chunk}
\index{Griesmer, James H.}
\index{Jenks, Richard D.}
\index{Yun, David Y.Y}
\begin{chunk}{axiom.bib}
@techreport{Grie75,
author = "Griesmer, James H. and Jenks, Richard D. and Yun, David Y.Y",
title = "SCRATCHPAD User's Manual",
year = "1975",
type = "Research Report",
number = "RA70",
keywords = "axiomref"
}
\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@article{Jenk74,
author = "Jenks, Richard D.",
title = "The SCRATCHPAD language",
journal = "ACM SIGPLAN Notices",
comment = "reprinted in SIGSAM Bulletin, Vol 8, No. 2, May 1974",
volume = "9",
number = "4",
pages = "101111",
year = "1974",
keywords = "axiomref"
}
\end{chunk}
\index{Jenks, Richard D.}
\index{Sundaresan, Christine J.}
\begin{chunk}{axiom.bib}
@misc{Jenk84c,
author = "Jenks, Richard D. and Sundaresan, Christine J.",
title = "The 11 Keys to SCRATCHPAD: A Primer",
year = "1984",
keywords = "axiomref"
}
\index{Davenport, James H.}
\index{Gianni, Patrizia}
\index{Jenks, Ricard D.}
\index{Miller, Victor}
\index{Morrison, Scott}
\index{Rothstein, Michael}
\index{Sundaresan, Christine J.}
\index{Sutor, Robert S.}
\index{Trager, Barry M.}
\begin{chunk}{axiom.bib}
@misc{Dave84b,
author = "Davenport, James H. and Gianni, Patrizia and Jenks, Ricard D. and
Miller, Victor and Morrison, Scott and Rothstein, Michael and
Sundaresan, Christine J. and Sutor, Robert S. and Trager, Barry",
title = "SCRATCHPAD System Programming Language Manual",
year = "1984",
keywords = "axiomref",
}
\end{chunk}
\index{Constable, Robert L.}
\index{Jackson, Paul B.}
\begin{chunk}{axiom.bib}
@misc{Cons98,
author = "Constable, Robert L. and Jackson, Paul B.",
title = "Towards Integrated Systems for Symbolic Algebra and Formal
Constructive Mathematics",
url = "http://www.nuprl.org/documents/Constable/towardsintegrated.pdf",
paper = "Cons98.pdf",
year = "1998",
abstract =
"The purpose of this paper is to report on our efforts to give e a
formal account of some of the algebra used in Computer Algebra Systems
(CAS). In particular, we look at the concepts used in the so called
3rd generation algebra systems, such as Axiom[4] and Weyl[9]. It is
our claim that the Nuprl proof development system is especially well
suited to support this kind of mathematics."
}
\end{chunk}
\begin{chunk}{axiom.bib}
@misc{Acad16,
author = "Academic Search",
title = "A Primer: 11 Keys to New Scratchpad",
url =
"http://libra.msra.cn/publication/645035/aprimer11keystonewscratchpad",
year = "2016",
keywords = "axiomref"
}
\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@misc{Jenk86a,
author = "Jenks, Richard D.",
title = "Basic Algebraic Facilities of the Scratchpad II Computer
Algebra System",
institution = "IBM Research",
year = "1986",
keywords = "axiomref"
}
\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@misc{Jenk86b,
author = "Jenks, Richard D.",
title = "Scratchpad II Examples from INPUT files",
institution = "IBM Research",
year = "1986",
keywords = "axiomref"
}
\end{chunk}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@article{Dave85,
author = "Davenport, James H.",
title = "The LISP/VM Foundation of Scratchpad II",
journal = "The Scratchpad II Newsletter",
volume = "1",
number = "1",
year = "1985",
month = "September",
institution = "IBM Research",
keywords = "axiomref"
}
\end{chunk}
\index{Wityak, Sandra}
\begin{chunk}{ignore}
@misc{Wity85,
author = "Wityak, Sandra",
title = "The Scratchpad II Newsletter",
volume = "1",
number = "1",
year = "1985",
month = "September",
institution = "IBM Research",
keywords = "axiomref"
}
\end{chunk}
\index{Wityak, Sandra}
\begin{chunk}{ignore}
@misc{Wity86,
author = "Wityak, Sandra",
title = "The Scratchpad II Newsletter",
volume = "1",
number = "2",
year = "1986",
month = "January",
institution = "IBM Research",
keywords = "axiomref"
}
\end{chunk}
\index{Wityak, Sandra}
\begin{chunk}{ignore}
@misc{Wity86a,
author = "Wityak, Sandra",
title = "The Scratchpad II Newsletter",
volume = "1",
number = "3",
year = "1986",
month = "May",
institution = "IBM Research",
keywords = "axiomref"
}
\end{chunk}
\index{Watt, Stephen M.}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@misc{Watt87,
author = "Watt, Stephen M. and Jenks, Richard D.",
title = "Abstract Datatypes, Multiple Views and Multiple Inheritance in
Scratchpad II",
keywords = "axiomref",
year = "1987",
url = "https://cs.uwaterloo.ca/~smatt/pub/reprints/1987itlspadviews.pdf",
paper = "Watt87.pdf",
abstract =
"Scratchpad II is an abstract datatype language developed at Yorktown
Heights for the implementation of a new computer algebra system. It
provides packages of polymorphic functions and parameterized, abstract
datatypes with operator overloading and multiple inheritance. To
express the intricate interrelationships between the datatypes
necessary for the description of mathematical objects, a number of
techniques based on the notion of {\sl category} have been
used. Categories are used to enforce relationships between type
parameters and to provide the mechanism for multiple inheritance. They
also allow the language to be statically type checked and the
generation of efficient code. This paper describes the role of
categories in Scratchpad II."
}
\end{chunk}
\index{Watt, Stephen M.}
\index{Jenks, Richard D.}
\index{Sutor, Robert S.}
\index{Trager, Barry M.}
\begin{chunk}{axiom.bib}
@inproceedings{Watt90,
author = "Watt, Stephen M. and Jenks, Richard D. and Sutor, Robert S. and
Trager, Barry M.",
title = "The Scratchpad II type system: Domains and Subdomains",
booktitle = "Computing Tools for Scientific Problem Solving",
year = "1990",
publisher = "Academic Press",
url =
"https://cs.uwaterloo.ca/~smwatt/pub/reprints/1990miolaspadtypes.pdf",
paper = "Watt90.pdf",
keywords = "axiomref",
abstract =
"Scratchpad II is a language developed at Yorktown Heights for the
implementation of a new computer algebra system. The need to model the
intricate relationships among the datatypes representing mathematical
objects has provided a number of challenges in the design of a type
system for the programming language.
In languages in which a datatype constructor may take multiple
parameters, ensuring compatibility between them is extremely
important. Scratchpad II addresses this issue by basing its
implementation of abstract datatypes on {\cl categories}. Categories
provide a convenient and useful method for specifying requirements on
operations from datatypes. These requirements can be very complex when
modelling mathematics.
We show how categories provide multiple inheritance and how
inheritance of specification is separated from inheritance of
implementation. We also present implications of the type system on
compilation of efficient code and flexibility of a weakly typed
interactive user interface.
Finally, the mechanisms of Scratchpad II are compared with those of
traditional abstract datatype and objectoriented programming
languages."
}
\end{chunk}
\index{Zippel, Richard}
\begin{chunk}{axiom.bib}
@misc{Zipp93,
author = "Zippel, Richard",
title = "The Weyl Computer Algebra Substrate",
paper = "Zipp93.pdf",
keywords = "axiomref",
booktitle = "Proc. of DISCO 1993",
series = "DISCO 93",
pages = "303=307",
year = "1993"
}
\end{chunk}
\index{Sutor, Robert S.}
\begin{chunk}{axiom.bib}
@inproceedings{Suto85,
author = "Sutor, Robert S.",
title = "The Scratchpad II computer algebra language and system",
booktitle = "Research Contributions from the Euro. Conf. on Comp. Alg.",
series = "Lecture Notes in Computer Science Volume 204",
volume = "2",
pages = "3233",
year = "1985",
isbn = "0387159835 (vol. 1),0387159843 (vol. 2)",
keywords = "axiomref"
}
\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{axiom.bib}
@article{Jenk88d,
author = "Jenks, Richard D.",
title = "Scratchpad II: A computer algebra language and system",
journal = "The Journal of the Acoustical Society of America",
year = "1988",
volume = "83",
number = "S1",
pages = "S106",
keywords = "axiomref",
abstract =
"The Scratchpad II system represents a new generation of systems for
doing symbolic mathematics, based on modern algebra and abstract data
types. A large number of facilities are provided, for example:
symbolic integration, ``infinite'' power series, differential operators,
Cartesian tensors, and solution of nonlinear systems. Scratchpad II
has been designed from the outset to be extendible. The system
introduces a new data abstraction notion, the ``category,'' to express
intricate interrelationships between data types. The result design
permits the compilation of algorithms described in their most natural
mathematical setting. The use of categories guarantees user defined
types and packages are compatible with each other and with built in
facilities. This system provides a single high‐level language with an
intepreter and compiler. The language can be used by the naive user
for convenient interactive mathematics calculations and by the
advanced user for the efficient implementation of
algorithms. Scratchpad II is built on Lisp/VM and runs on IBM/370
class mainframes. An implementation of the system on the RT/PC is
expected soon."
}
\end{chunk}
\index{Jenks, Richard D.}
\index{Sutor, Robert S.}
\index{Watt, Stephen M.}
\begin{chunk}{axiom.bib}
@book{Jenk88e,
author = "Jenks, Richard D. and Sutor, Robert S. and Watt, Stephen M.",
title = "Scratchpad II: An Abstract Datatype System for Mathematical
Computation",
booktitle = "Mathematical Aspects of Scientific Software",
year = "1988",
pages = "157182",
publisher = "Springer",
isbn = "0387189289",
keywords = "axiomref",
abstract =
"Scratchpad II is an abstract datatype language and system that is
under development in the Computer Algebra Group, Mathematical Sciences
Department, at the IBM Thomas J. Watson Research Center. Many
different kinds of computational objects and data structures are
provided. Facilities for computation include symbolic integration,
differentation, factorization, solution of equations and linear
algebra. Code economy and modularity is achieved by having polymorphic
packages of functions that may create datatypes. The use of categories
makes these facilities as general as possible."
}
\end{chunk}

books/bookvolbib.pamphlet  1641 +++++++++++++++++++++++++++++++++++
changelog  2 +
patch  1343 ++++++++++++++++++++++++++++++++
src/axiomwebsite/patches.html  2 +
4 files changed, 2768 insertions(+), 220 deletions()
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index 1f39b2f..5ec7407 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 21,6 +21,7 @@ paragraph for those unfamiliar with the terms.
\section{Algebra Documentation References}
\index{Gonshor, H.}
+\index{AlgebraGivenByStructuralConstants}
\begin{chunk}{axiom.bib}
@article{Gons71,
author = "Gonshor, H.",
@@ 45,6 +46,7 @@ paragraph for those unfamiliar with the terms.
\end{chunk}
+\index{AlgebraGivenByStructuralConstants}
\index{Reed, Mary Lynn}
\begin{chunk}{axiom.bib}
@article{Reed97,
@@ 83,6 +85,7 @@ paragraph for those unfamiliar with the terms.
\end{chunk}
+\index{PermutationGroup}
\index{Sims, Charles}
\begin{chunk}{axiom.bib}
@article{Sims71,
@@ 98,6 +101,7 @@ paragraph for those unfamiliar with the terms.
\end{chunk}
+\index{AlgebraGivenByStructuralConstants}
\index{W\"orzBusekros, A.}
\begin{chunk}{axiom.bib}
@article{Worz80,
@@ 2099,6 +2103,7 @@ when shown in factored form.
\end{chunk}
+\index{BlasLevelOne}
\index{Chellappa, Srinivas}
\index{Franchetti, Franz}
\index{P\"uschel, Markus}
@@ 3441,6 +3446,7 @@ when shown in factored form.
\end{chunk}
+\index{DoubleFloatSpecialFunctions}
\index{Segletes, S.B.}
\begin{chunk}{axiom.bib}
@techreport{Segl98,
@@ 3971,6 +3977,27 @@ Martin, U.
\end{chunk}
+\index{Constable, Robert L.}
+\index{Jackson, Paul B.}
+\begin{chunk}{axiom.bib}
+@misc{Cons98,
+ author = "Constable, Robert L. and Jackson, Paul B.",
+ title = "Towards Integrated Systems for Symbolic Algebra and Formal
+ Constructive Mathematics",
+ url = "http://www.nuprl.org/documents/Constable/towardsintegrated.pdf",
+ paper = "Cons98.pdf",
+ year = "1998",
+ abstract =
+ "The purpose of this paper is to report on our efforts to give e a
+ formal account of some of the algebra used in Computer Algebra Systems
+ (CAS). In particular, we look at the concepts used in the so called
+ 3rd generation algebra systems, such as Axiom[4] and Weyl[9]. It is
+ our claim that the Nuprl proof development system is especially well
+ suited to support this kind of mathematics."
+}
+
+\end{chunk}
+
\index{Geuvers, Herman}
\index{Pollack, Randy}
\index{Wiedijk, Freek}
@@ 5534,6 +5561,18 @@ Petkovsek, Marko
\end{chunk}
+\index{UnivariateSkewPolynomialCategory}
+\index{LinearOrdinaryDifferentialOperatorCategory}
+\index{Automorphism}
+\index{SparseUnivariateSkewPolynomial}
+\index{UnivariateSkewPolynomial}
+\index{LinearOrdinaryDifferentialOperator}
+\index{LinearOrdinaryDifferentialOperator1}
+\index{LinearOrdinaryDifferentialOperator2}
+\index{ApplyUnivariateSkewPolynomial}
+\index{UnivariateSkewPolynomialCategoryOps}
+\index{LinearOrdinaryDifferentialOperatorFactorizer}
+\index{LinearOrdinaryDifferentialOperatorsOps}
\index{Abramov, Sergei A.}
\index{Bronstein, Manuel}
\begin{chunk}{axiom.bib}
@@ 5544,7 +5583,8 @@ Petkovsek, Marko
url =
"http://wwwsop.inria.fr/cafe/Manuel.Bronstein/publications/mb_papers.html",
paper = "Abra01.pdf",
 algebra = "\newline\refto{category OREPCAT UnivariateSkewPolynomialCategory}
+ algebra =
+ "\newline\refto{category OREPCAT UnivariateSkewPolynomialCategory}
\newline\refto{category LODOCAT LinearOrdinaryDifferentialOperatorCategory}
\newline\refto{domain AUTOMOR Automorphism}
\newline\refto{domain ORESUP SparseUnivariateSkewPolynomial}
@@ 5586,6 +5626,7 @@ Mathematics and Computers in Simulation 42 pp 387389 (1996)
\end{chunk}
+\index{LeftOreRing}
\index{Bronstein, Manuel}
\index{Petkovsek, Marko}
\begin{chunk}{axiom.bib}
@@ 7462,6 +7503,7 @@ Proc ISSAC 97 pp172175 (1997)
\end{chunk}
+\index{LeftOreRing}
\index{Delenclos, Jonathon}
\index{Leroy, Andr\'e}
\begin{chunk}{axiom.bib}
@@ 7875,6 +7917,7 @@ Proc ISSAC 97 pp172175 (1997)
\end{chunk}
+\index{IdealDecompositionPackage}
\index{Gianni, Patrizia}
\index{Trager, Barry M.}
\index{Zacharias, Gail}
@@ 9694,6 +9737,7 @@ rational righthand sides etc."
\end{chunk}
+\index{DeRhamComplex}
\index{Flanders, Harley}
\begin{chunk}{axiom.bib}
@book{Flan03,
@@ 9999,6 +10043,7 @@ J. Symbolic Computation 5, 237259 (1988)
\end{chunk}
+\index{RealClosure}
\index{Emiris, Ioannis Z.}
\index{Tsigaridas, Elias P.}
\begin{chunk}{axiom.bib}
@@ 10125,6 +10170,7 @@ J. Symbolic Computation 5, 237259 (1988)
\end{chunk}
+\index{RealClosure}
\index{Rioboo, Renaud}
\begin{chunk}{axiom.bib}
@InProceedings{Riob92,
@@ 11521,6 +11567,7 @@ American Mathematical Society (1994)
\end{chunk}
+\index{IntegerPrimesPackage}
\index{Arnault, Francois}
\begin{chunk}{axiom.bib}
@Article{Arna95,
@@ 11610,6 +11657,18 @@ American Mathematical Society (1994)
\end{chunk}
+\index{Baker, Martin}
+\begin{chunk}{axiom.bib}
+@misc{Bake16,
+ author = "Baker, Martin",
+ title = "Axiom Maths Program",
+ keywords = "axiomref",
+ year = "2016",
+ url = "http://www.euclideanspace.com/prog/scratchpad/axiom/index.htm"
+}
+
+\end{chunk}
+
\index{Ballarin, Clemens}
\begin{chunk}{axiom.bib}
@article{Ball14,
@@ 11693,6 +11752,18 @@ American Mathematical Society (1994)
\end{chunk}
+\index{Bernard, Joey}
+\begin{chunk}{axiom.bib}
+@misc{Bern14,
+ author = "Bernard, Joey",
+ title = "Open Axiom",
+ url = "http://www.linuxjournal.com/content/openaxiom",
+ keywords = "axiomref",
+ year = "2014"
+}
+
+\end{chunk}
+
\index{Betten, Anton}
\index{Kohnert, Axel}
\index{Laue, Reinhard}
@@ 11736,6 +11807,39 @@ IBM Research Report, RC3062 Sept
\end{chunk}
+\index{Bosma, Wieb}
+\index{Cannon, John}
+\index{Matthews, Graham}
+\begin{chunk}{axiom.bib}
+@InProceedings{Bosm94,
+ author = "Bosma, Wieb and Cannon, John and Matthews, Graham",
+ title = "Programming with algebraic structures: Design of the Magma
+ language",
+ booktitle = "Proc. ISSAC 94",
+ series = "ISSAC 94",
+ year = "1994",
+ publisher = "ACM Press",
+ location = "Baltimore, MD",
+ pages = "5257",
+ keywords = "axiomref",
+ paper = "Bosm94.pdf",
+ url = "http://www.math.ru.nl/~bosma/pubs/ISSAC94.pdf",
+ abstract =
+ "MAGMA is a new software system for computational algebra, number
+ theory and geometry whose design is centred on the concept of
+ algebraic structure (magma). The use of algebraic structure as a
+ design paradigm provides a natural strong typing mechanism. Further,
+ structures and their morphisms appear in the language as first class
+ objects. Standard mathematical notions are used for the basic data
+ types. The result is a powerful, clean language which deals with
+ objects in a mathematically rigorous manner. The conceptual and
+ implementation ideas behind MAGMA will be examined in this paper. This
+ conceptual base differs significantly from those underlying other
+ computer algebra systems."
+}
+
+\end{chunk}
+
\index{Boyle, Ann}
\begin{chunk}{ignore}
\bibitem[Boyle 88]{Boyl88} Boyle, Ann
@@ 11779,6 +11883,7 @@ Soc. for Industrial and Applied Mathematics, Philadelphia (1990)
\end{chunk}
+\index{NonAssociativeRng}
\index{Bremner, Murray R.}
\index{Murakami, Lucia I.}
\index{Shestakov, Ivan P.}
@@ 12116,6 +12221,11 @@ SpringerVerlag, NY (1991)
\end{chunk}
+\index{ConstantLODE}
+\index{ElementaryFunctionLODESolver}
+\index{PureAlgebraicLODE}
+\index{RationalLODE}
+\index{ReduceLODE}
\index{Bronstein, Manuel}
\begin{chunk}{axiom.bib}
@misc{Bron92,
@@ 12626,6 +12736,124 @@ Informatique et en Automatique, Le Chesnay, France, 12pp
\end{chunk}
+\index{Caviness, Bob}
+\index{Trager, Barry}
+\index{Gianni, Patrizia}
+\begin{chunk}{axiom.bib}
+@misc{Cavi03,
+ author = "Caviness, Bob and Trager, Barry and Gianni, Patrizia",
+ title = "Dedicated to the Memory of Richard Dimick Jenks",
+ year = "2003",
+ url = "https://www.eecis.udel.edu/~caviness/jenks/issacded.pdf",
+ keywords = "axiomref",
+ paper = "Cavi03.pdf",
+ abstract =
+ "On December 30, 2003, Dick Jenks died at the age of 66, after an
+ extended and courageous battle with multiple system atrophy.
+
+ He received his PhD in mathematics from the University of Illinois at
+ UrbanaChampaign in 1966. The title of his dissertation was
+ “Quadratic Differential Systems for Mathematical Models” and was
+ written under the supervision of Donald Gilles. After completing his
+ PhD, he was a postdoctoral fellow at Brookhaven National Laboratory
+ on Long Island. In 1968 he joined IBM Research where he worked until
+ his retirement in 2002.
+
+ At IBM he was one of the principal architects of the Scratchpad
+ system, one of the earliest computer algebra systems(1971). Dick
+ always believed that natural user interfaces were essential and
+ developed a userfriendly rulebased system for Scratchpad. Although
+ this rulebased approach was easy to use, as algorithms for computer
+ algebra became more complicated, he began to understand that an
+ abstract data type approach would give sophisticated algorithm
+ development considerably more leverage. In 1977 he began the Axiom
+ development (originally called Scratchpad II) with the design of
+ MODLISP, a merger of Lisp with types (modes). In 1980, with the help
+ of many others, he completed an initial prototype design based on
+ categories and domains that were intended to be natural for
+ mathematically sophisticated users.
+
+ During this period many researchers in computer algebra visited IBM
+ Research in Yorktown Heights and contributed to the development of
+ the Axiom system. All this activity made the computer algebra group at
+ IBM one of the leading centers for research in this area and Dick was
+ always there to organize the visits and provide a stimulating and
+ pleasant working environment for everyone. He had a good perspective
+ on the most important research directions and worked to attract
+ worldrenowned experts to visit and interact with his group. He was an
+ ideal manager for whom to work, one who always put the project and the
+ needs of the group members first. It was a joy to work in such a
+ vibrant and stimulating environment.
+
+ After many years of development, a decision was made to rename
+ Scratch pad II to Axiom and to release it as a product. Dick and
+ Robert Sutor were the primary authors of the book {\sl Axiom: The
+ Scientific Computation System}. In the foreword of the book, written
+ by David and Gregory Chudnovsky, it is stated that ``The Scratchpad
+ system took its time to blossom into the beautiful Axiom
+ product. There is no rival to this powerful environment in its scope
+ and, most importantly, in its structure and organization.'' Axiom was
+ recently made available as free software. See
+ http://savannah.nongnu.org/projects/axiom
+
+ Dick was active in service to the computer algebra community as
+ well. Here are some highlights. He served as Chair of ACM SIGSAM
+ (197981) and Conference Cochair (with J. A. van Hulzen) of EUROSAM
+ ’84, a precursor of the ISSAC meetings. Dick also had a long period of
+ service on the editorial board of the {\sl Journal of Symbolic
+ Computation}. At ISSAC ’95 in Montreal, Dick was elected to the
+ initial ISSAC Steering Committee and was elected as the second Chair
+ of the Committee in 1997. He, along with David Chudnovsky, organized
+ the highly successful meetings on Computers and Mathematics that were
+ held at Stanford in 1986 and MIT in 1989. As a legacy of those
+ meetings, the Jenks Prize for outstanding contributions to software
+ engineering in computer algebra has been established.
+
+ Dick had many interests outside of his professional pursuits including
+ reading, travel, physical fitness, and especially music. Dick was an
+ accomplished pianist, organist, and vocalist. At one point he was the
+ organist and choir master of the Church of the Holy Communion in
+ Mahopac, NY. In the 1980s and 1990s, he sang in choral groups under
+ the direction of Dr. Dennis Keene that performed at Lincoln Center in
+ New York city.
+
+ Personally, Dick was warm, generous, and outgoing with many
+ friends. He will be missed for his technical accomplishments, his
+ artist talents, and most of all for his positive, gentle, charming
+ spirit."
+}
+
+\end{chunk}
+
+\index{Chicha, Yannis}
+\index{Lloyd, Michael}
+\index{Oancea, Cosmin}
+\index{Watt, Stephen}
+\begin{chunk}{axiom.bib}
+@misc{Chic04,
+ author = "Chicha, Yannis and Lloyd, Michael Oancea, Cosmin",
+ title = "Parametric Polymorphism for Computer Algebra Software Components",
+ booktitle = "6th Int. Symp. on Symbolic and Numeric Algorithms for
+ Scientific Computing",
+ series = "SYNASC 04",
+ location = "Imisoara, Romania",
+ keywords = "axiomref",
+ year = "2004",
+ paper = "Chic04.pdf",
+ url = "http://www.csd.uwo.ca/~watt/pub/reprints/2004synascppca.pdf",
+ abstract =
+ "This paper presents our experiments in providing mechanisms for
+ parametric polymorphism for computer algebra software components.
+ Specific interfaces between Aldor and C++ and between Aldor and Maple
+ are described. We then present a general solution, Generic IDL (GIDL),
+ an extension to CORBA IDL supporting generic types. We describe our
+ language bindings for C++, Java 1.5 and Aldor as well as aspects of
+ our implementation, consisting of a GIDL to IDL compiler and tools for
+ generating interface code for the various language bindings."
+}
+
+\end{chunk}
+
\index{Chou, ShangChing}
\index{Gao, XiaoShan}
\index{Liu, ZhuoJun}
@@ 12981,6 +13209,12 @@ Coding Theory and Applications Proceedings. SpringerVerlag, Berlin, Germany
\end{chunk}
+\index{GroebnerPackage}
+\index{PseudoLinearNormalForm}
+\index{PolyGroebner}
+\index{DistributedMultivariatePolynomial}
+\index{GeneralDistributedMultivariatePolynomial}
+\index{HomogeneousDistributedMultivariatePolynomial}
\index{Cox, David}
\index{Little, John}
\index{O'Shea, Donal}
@@ 13221,11 +13455,59 @@ VM/370 SPAD.SCRIPTS August 24, 1979 SPAD.SCRIPT
\index{Davenport, James H.}
\index{Jenks, Richard D.}
\begin{chunk}{ignore}
\bibitem[Davenport 80]{Dav80} Davenport, J.H.; Jenks, R.D.
 title = "MODLISP  an Introduction",
Proc LISP80, 1980, and IBM RC8357 Oct 1980
+\begin{chunk}{axiom.bib}
+@techreport{Dave80,
+ author = "Davenport, James H. and Jenks, Richard D.",
+ title = "MODLISP: A Preliminary Design",
+ institution = "IBM Research",
+ type = "Research Report",
+ year = "1980",
+ number = "RC 8073",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@techreport{Dave80,
+ author = "Davenport, James H. and Jenks, Richard D.",
+ title = "MODLISP",
+ institution = "IBM Research",
+ type = "Research Report",
+ year = "1980",
+ number = "RC 8537 (\#37198)",
+ keywords = "axiomref",
+ comment = "http://www.computerhistory.org/collections/catalog/102719109"
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@article{Dave81,
+ author = "Davenport, James H. and Jenks, Richard D.",
+ title = "MODLISP",
+ year = "1981",
+ journal = "ACM SIGSAM Bulletin",
+ volume = "15",
+ issue = "1",
+ pages = "1120",
+ publisher = "ACM",
keywords = "axiomref",
+ abstract =
+ "This paper discusses the design and implementation of MODLISP, a
+ LISPlike language enhanced with the idea of MODes. This extension
+ permits, but does not require, the user to declare the types of
+ various variables, and to compile functions with the arguments
+ declared to be of a particular type. It is possible to declare several
+ functions of the same name, with arguments of different type
+ (e.g. PLUS could be declared for Integer arguments, or Rational, or
+ Real, or even Polynomial arguments) and the system will apply the
+ correct function for the types of the arguments."
+}
\end{chunk}
@@ 13263,12 +13545,39 @@ Mathematical Sciences Department, IBM Thomas Watson Research Center 1984
\end{chunk}
\index{Davenport, James H.}
\begin{chunk}{ignore}
\bibitem[Davenport 85]{Dav85} Davenport, James H.
 title = "The LISP/VM Foundation of Scratchpad II",
The Scratchpad II Newsletter, Volume 1, Number 1, September 1, 1985
IBM Corporation, Yorktown Heights, NY
+\index{Gianni, Patrizia}
+\index{Jenks, Ricard D.}
+\index{Miller, Victor}
+\index{Morrison, Scott}
+\index{Rothstein, Michael}
+\index{Sundaresan, Christine J.}
+\index{Sutor, Robert S.}
+\index{Trager, Barry M.}
+\begin{chunk}{axiom.bib}
+@misc{Dave84b,
+ author = "Davenport, James H. and Gianni, Patrizia and Jenks, Ricard D. and
+ Miller, Victor and Morrison, Scott and Rothstein, Michael and
+ Sundaresan, Christine J. and Sutor, Robert S. and Trager, Barry",
+ title = "SCRATCHPAD System Programming Language Manual",
+ year = "1984",
keywords = "axiomref",
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@article{Dave85,
+ author = "Davenport, James H.",
+ title = "The LISP/VM Foundation of Scratchpad II",
+ journal = "The Scratchpad II Newsletter",
+ volume = "1",
+ number = "1",
+ year = "1985",
+ month = "September",
+ institution = "IBM Research",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 13428,13 +13737,33 @@ UK / etc., 1989 ISBN 3540515178 LCCN QA155.7.E4E86 1987
\index{Davenport, James H.}
\index{Trager, Barry M.}
\begin{chunk}{ignore}
\bibitem[Davenport 90]{DT90} Davenport, J. H.; Trager, B. M.
+\begin{chunk}{axiom.bib}
+@InProceedings{Dave90,
+ author = "Davenport, James H. and Trager, Barry M.",
title = "Scratchpad's view of algebra I: Basic commutative algebra",
In Miola [Mio90], pp4054. ISBN 0387525319 (New York),
3540525319 (Berlin). LCCN QA76.9.S88I576 1990 also in AXIOM Technical
Report, ATR/1, NAG Ltd., Oxford, 1992
+ booktitle = "Design and Implementation of Symbolic Computation Systems",
+ year = "1990",
+ series = "DISCO '90",
+ location = "Capri, Italy",
+ publisher = "SpringerVerlag",
+ isbn = "0387525319",
keywords = "axiomref",
+ url = "http://opus.bath.ac.uk/32336/1/Davenport\_DISCO\_1990.pdf",
+ paper = "Dave90.pdf",
+ comment = "AXIOM Technical Report, ATR/1, NAG Ltd., Oxford, 1992",
+ keywords = "axiomref",
+ abstract =
+ "While computer algebra systems have dealt with polynomials and
+ rational functions with integer coefficients for many years, dealing
+ with more general constructs from commutative algebra is a more recent
+ problem. In this paper we explain how one system solves this problem,
+ what types and operators it is necessary to introduce and, in short,
+ how one can construct a computational theory of commutative
+ algebra. Of necessity, such a theory is rather different from the
+ conventional, nonconstructive, theory. It is also somewhat different
+ from the theories of Seidenberg [1974] and his school, who are not
+ particularly concerned with practical questions of efficiency."
+}
\end{chunk}
@@ 13546,6 +13875,7 @@ December 1992.
\end{chunk}
+\index{IntegerPrimesPackage}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@article{Dave92,
@@ 13751,6 +14081,34 @@ May 1984
\end{chunk}
+\index{d01ajfAnnaType}
+\index{d01akfAnnaType}
+\index{d01alfAnnaType}
+\index{d01amfAnnaType}
+\index{d01anfAnnaType}
+\index{d01apfAnnaType}
+\index{d01aqfAnnaType}
+\index{d01asfAnnaType}
+\index{d01fcfAnnaType}
+\index{d01gbfAnnaType}
+\index{d01TransformFunctionType}
+\index{d02bbfAnnaType}
+\index{d02bhfAnnaType}
+\index{d02cjfAnnaType}
+\index{d02ejfAnnaType}
+\index{d03eefAnnaType}
+\index{d03fafAnnaType}
+\index{e04dgfAnnaType}
+\index{e04fdfAnnaType}
+\index{e04gcfAnnaType}
+\index{e04jafAnnaType}
+\index{e04mbfAnnaType}
+\index{e04nafAnnaType}
+\index{e04ucfAnnaType}
+\index{NumericalIntegrationProblem}
+\index{NumericalODEProblem}
+\index{NumericalOptimizationProblem}
+\index{NumericalPDEProblem}
\index{Dewar, Michael C.}
\begin{chunk}{axiom.bib}
@InProceedings{Dewa92,
@@ 13934,19 +14292,23 @@ and Laine, M. and Valkeila, E. pp112 University of Helsinki, Finland (1994)
\index{Dingle, Adam}
\index{Fateman, Richard J.}
\begin{chunk}{ignore}
\bibitem[Dingle 94]{Din94} Dingle, Adam; Fateman, Richard
+\begin{chunk}{axiom.bib}
+@InProceedings{Ding94,
+ author = "Dingle, Adam and Fateman, Richard",
title = "Branch Cuts in Computer Algebra",
1994 ISSAC, Oxford (UK), July 1994
+ year = "1994",
+ booktitle = "Proc. ISSAC 1994",
+ series = "ISSAC 94",
url = "http://www.cs.berkeley.edu/~fateman/papers/ding.ps",
 paper = "Din94.pdf",
+ paper = "Ding94.pdf",
keywords = "axiomref",
 abstract = "
 Many standard functions, such as the logarithms and square root
+ abstract =
+ "Many standard functions, such as the logarithms and square root
functions, cannot be defined continuously on the complex
plane. Mistaken assumptions about the properties of these functions
lead computer algebra systems into various conundrums. We discuss how
they can manipulate such functions in a useful fashion."
+}
\end{chunk}
@@ 14188,6 +14550,34 @@ Grant citation GR/L48256 Nov 1, 1997Feb 28, 2001
\end{chunk}
+\index{d01ajfAnnaType}
+\index{d01akfAnnaType}
+\index{d01alfAnnaType}
+\index{d01amfAnnaType}
+\index{d01anfAnnaType}
+\index{d01apfAnnaType}
+\index{d01aqfAnnaType}
+\index{d01asfAnnaType}
+\index{d01fcfAnnaType}
+\index{d01gbfAnnaType}
+\index{d01TransformFunctionType}
+\index{d02bbfAnnaType}
+\index{d02bhfAnnaType}
+\index{d02cjfAnnaType}
+\index{d02ejfAnnaType}
+\index{d03eefAnnaType}
+\index{d03fafAnnaType}
+\index{e04dgfAnnaType}
+\index{e04fdfAnnaType}
+\index{e04gcfAnnaType}
+\index{e04jafAnnaType}
+\index{e04mbfAnnaType}
+\index{e04nafAnnaType}
+\index{e04ucfAnnaType}
+\index{NumericalIntegrationProblem}
+\index{NumericalODEProblem}
+\index{NumericalOptimizationProblem}
+\index{NumericalPDEProblem}
\index{Dupee, Brian J.}
\index{Davenport, James H.}
\begin{chunk}{axiom.bib}
@@ 14302,24 +14692,56 @@ CODEN ITATEC. ISSN 09265473
\end{chunk}
\index{Duval, Dominique}
\begin{chunk}{ignore}
\bibitem[Duval 94]{Duv94} Duval, Dominique
+\begin{chunk}{axiom.bib}
+@misc{Duva94e,
+ author = "Duval, Dominique",
title = "Symbolic or algebraic computation?",
Madrid Spain, NAG conference (private copy of paper)
+ booktitle = "Publication du LACO",
+ year = "1995",
+ location = "Madrid Spain",
+ comment = "NAG conference",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Duval, Dominique}
+\index{Senechaud, Pascale}
+\begin{chunk}{axiom.bib}
+@article{Duva94d,
+ author = "Duval, Dominique and Senechaud, Pascale",
+ title = "Sketches and parametrization",
+ journal = "Theor. Comput. Sci.",
+ volume = "123",
+ number = "1",
+ pages = "117130",
+ year = "1994",
keywords = "axiomref",
+ abstract =
+ "The paper deals with problems about conception and design of
+ highlevel computer algebra systems. Here we use a categorical
+ approach given by the notion of sketches. Sketches allow to describe
+ computation mechanisms in a syntactic way, well adapted to
+ implementation.
+
+ A computer algebra system must allow the manipulation of algebraic
+ structures, in particular, the construction of new structures from
+ known ones. In the paper we give a definition, at the sketch level, of
+ parametrization of a structure by another one."
+}
\end{chunk}
\index{Duval, Dominique}
\begin{chunk}{axiom.bib}
@article{Duva95,
 author = "Duval, D.",
+ author = "Duval, Dominique",
title = "Dynamic evaluation and algebraic closure in Axiom",
comment = "Evaluation dynamique et cl\^oture alg\'ebrique en Axiom",
journal = "Journal of Pure and Applied Algebra",
volume = "99",
year = "1995",
 pages = "267295.",
+ pages = "267295",
keywords = "axiomref",
paper = "Duva95.pdf",
abstract =
@@ 14738,6 +15160,25 @@ LCCN QA155.7.E4 I57 1984
\end{chunk}
\index{Fortenbacher, A.}
+\index{Jenks, Richard}
+\index{Lucks, Michael}
+\index{Sutor, Robert}
+\index{Trager, Barry}
+\index{Watt, Stephen}
+\begin{chunk}{axiom.bib}
+@techreport{Fort85,
+ author = "Fortenbacher, A. and Jenks, Richard and Lucks, Michael and
+ Sutor, Robert and Trager, Barry and Watt, Stephen",
+ title = "An Overview of the Scratchpad II Language and System",
+ year = "1985",
+ type = "Research Report",
+ publisher = "IBM Research Computer Algebra Group",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Fortenbacher, A.}
\begin{chunk}{ignore}
\bibitem[Fortenbacher 90]{For90} Fortenbacher, A.
title = "Efficient type inference and coercion in computer algebra",
@@ 14804,6 +15245,51 @@ Strasbourg, France, 1990 31pp
\end{chunk}
+\index{Fritzson, D.}
+\index{Fritzson, P.}
+\index{Viklund, L.}
+\index{Herber, J.}
+\begin{chunk}{axiom.bib}
+@article{Frit94,
+ author = "Fritzson, D. and Fritzson, P. and Viklund, L. and Herber, J.",
+ title = "Objectoriented mathematical modelling  applied to machine
+ elements",
+ journal = "Comput. Struct.",
+ volume = "51",
+ number = "3",
+ pages = "241253",
+ year = "1994",
+ keywords = "axiomref",
+ paper = "Frit94.pdf",
+ abstract =
+ "Machine element analysis has a goal of describing function and other
+ aspects of machine elements in a theoretical form. This paper shows
+ how ideas from objectoriented modelling can be applied to machine
+ elment analysis. The models thus obtained are both easier to
+ understand, better structured, and allow a higher degree of reuse
+ than conventional models. An objectoriented model description is
+ natural and suitable for machine element analysis. As a realistic
+ example an equational model of rolling bearings is presented. The
+ structure of the model is general, and applies to many types of
+ rolling bearings. The model and one solution require approximately
+ 200+200 equations. The model is extensible, e.g. simple submodels of
+ detailed properties can be made more complex without altering the
+ overall structure. The example model has been implemented in a
+ language of our own design. ObjectMath (Objectoriented Mathematical
+ language for scientific computing). Using ObjectMath, it is possible
+ to model classes of equation objects, to support multiple and single
+ inheritance of equations, to support composition of equations, and to
+ solve systems of equations. Algebraic transformations can conveniently
+ be done since ObjectMath models are translated into the Mathematica
+ computer algebra language. When necessary, equations can be
+ transformed int C++ code for efficient numerical solution. The reuse
+ of equations through inheritance reduced the size of the model by a
+ factor of two, compared to a direct representation of the model in the
+ Mathematica computer algebra language."
+}
+
+\end{chunk}
+
\subsection{G} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Gallopoulos, Stratis}
@@ 15254,11 +15740,15 @@ James B. Morris (eds.).
\index{Griesmer, James H.}
\index{Jenks, Richard D.}
\index{Yun, David Y.Y}
\begin{chunk}{ignore}
\bibitem[Griesmer 75]{GJY75} Griesmer, J.H.; Jenks, R.D.; Yun, D.Y.Y
+\begin{chunk}{axiom.bib}
+@techreport{Grie75,
+ author = "Griesmer, James H. and Jenks, Richard D. and Yun, David Y.Y",
title = "SCRATCHPAD User's Manual",
IBM Research Publication RA70 June 1975
 keywords = "axiomref",
+ year = "1975",
+ type = "Research Report",
+ number = "RA70",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 15315,6 +15805,17 @@ Manipulation), 28(3) pp319 August 1994 CODEN SIGSBZ ISSN 01635824
\end{chunk}
+\begin{chunk}{axiom.bib}
+@misc{Gute16,
+ author = "Gutenberg SelfPublishing Press",
+ title = "OpenAxiom",
+ keywords = "axiomref",
+ url = "http://self.gutenberg.org/articles/openaxiom",
+ year = "2016"
+}
+
+\end{chunk}
+
\subsection{H} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Harrison, J.}
@@ 15808,6 +16309,25 @@ Vol. 8 No. 3 pp195210 (2001)
\end{chunk}
+\index{Hoeven, Joris van der}
+\index{Lecerf, Gregoire}
+\begin{chunk}{axiom.bib}
+@misc{Hoev15,
+ author = "Hoeven, Joris van der and Lecerf, Gregoire",
+ title = "Interfacing Mathemagix with C++",
+ keywords = "axiomref",
+ url = "http://www.texmacs.org/joris/mmxcpp/mmxcpp.html",
+ abstract =
+ "In this paper, we give a detailed description of the interface
+ between the Mathemagix language and C++. In particular, we describe
+ the mechanism which allows us to import a C++ template library
+ (which only permits static instantiation) as a fully generic
+ Mathemagix template library."
+}
+
+\end{chunk}
+
+\index{ProjectiveSpaceCategory}
\index{Hohold, Tom}
\index{van Lint, Jacobus H.}
\index{Pellikaan, Ruud}
@@ 15944,6 +16464,7 @@ Developments. LIFL Univ. Lille, Lille France, 1993
\end{chunk}
+\index{IntegerPrimesPackage}
\index{Jaeschke, Gerhard}
\begin{chunk}{axiom.bib}
@article{Jaes93,
@@ 16029,11 +16550,18 @@ Watson Research Center, Yorktown Heights, NY, USA, 1971
\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{ignore}
\bibitem[Jenks 74]{Jen74} Jenks, R. D.
 title = "The SCRATCHPAD language'",
ACM SIGPLAN Notices, 9(4) pp101111 1974 CODEN SINODQ. ISSN 03621340
 keywords = "axiomref",
+\begin{chunk}{axiom.bib}
+@article{Jenk74,
+ author = "Jenks, Richard D.",
+ title = "The SCRATCHPAD language",
+ journal = "ACM SIGPLAN Notices",
+ comment = "reprinted in SIGSAM Bulletin, Vol 8, No. 2, May 1974",
+ volume = "9",
+ number = "4",
+ pages = "101111",
+ year = "1974",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 16051,22 +16579,52 @@ QA9.58.A11 1976
\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{ignore}
\bibitem[Jenks 79]{Jen79} Jenks, R. D.
+\begin{chunk}{axiom.bib}
+@inproceedings{Jenk79,
+ author = "Jenks, Richard D.",
title = "MODLISP: An Introduction",
Proc EUROSAM 79, pp466480, 1979 and IBMRC8073 Jan 1980
 keywords = "axiomref",
+ booktitle = "Proc. ISSAC 1979",
+ series = "EUROSAM 79",
+ pages = "466480",
+ year = "1979",
+ publisher = "SpringerVerlag",
+ isbn = "3540095195",
+ comment = "IBM Research Report RC 8073 Jan 1980",
+ keywords = "axiomref"
+}
\end{chunk}
\index{Jenks, Richard D.}
\index{Trager, Barry M.}
\begin{chunk}{ignore}
\bibitem[Jenks 81]{JT81} Jenks, R.D.; Trager, B.M.
+\begin{chunk}{axiom.bib}
+@article{Jenk81,
+ author = "Jenks, Richard D. and Trager, Barry M.",
title = "A Language for Computational Algebra",
Proceedings of SYMSAC81, Symposium on Symbolic and Algebraic Manipulation,
Snowbird, Utah August, 1981
+ year = "1981",
+ booktitle = "Proc. Symp. on Symbolic and Algebraic Manipulation",
+ series = "SYMSAC 1981",
+ location = "Snowbird, Utah",
keywords = "axiomref",
+ comment = "IBM Research Report 8930",
+ abstract =
+ "This paper reports ongoing research at the IBM Research Center on the
+ development of a language with extensible parameterized types and
+ generic operators for computational algebra. The language provides an
+ abstract data type mechanism for defining algorithms which work in as
+ general a setting as possible. The language is based on the notions of
+ domains and categories. Domains represent algebraic
+ structures. Categories designate collections of domains having common
+ operations with stated mathematical properties. Domains and categories
+ are computed objects which may be dynamically assigned to variables,
+ passed as arguments, and returned by functions. Although the language
+ has been carefully tailored for the application of algebraic
+ computation, it actually provides a very general abstract data type
+ mechanism. Our notion of a category to group domains with common
+ properties appears novel among programming languages (cf. image
+ functor of RUSSELL) and leads to a very powerful notion of abstract
+ algorithms missing from other work on data types known to the authors."
+}
\end{chunk}
@@ 16081,16 +16639,6 @@ SIGPLAN Notices, New York: Association for Computing Machiner, Nov 1981
\end{chunk}
\index{Jenks, Richard D.}
\index{Trager, Barry M.}
\begin{chunk}{ignore}
\bibitem[Jenks 81b]{JT81b} Jenks, R.D.; Trager, B.M.
 title = "A Language for Computational Algebra",
IBM Research Report RC8930 IBM Yorktown Heights, NY
 keywords = "axiomref",

\end{chunk}

\index{Jenks, Richard D.}
\begin{chunk}{ignore}
\bibitem[Jenks 84a]{Jen84a} Jenks, Richard D.
title = "The new SCRATCHPAD language and system for computer algebra",
@@ 16100,42 +16648,141 @@ In Golden and Hussain [GH84], pp409??
\end{chunk}
\index{Jenks, Richard D.}
\begin{chunk}{ignore}
\bibitem[Jenks 84b]{Jen84b} Jenks, Richard D.
+\begin{chunk}{axiom.bib}
+@inproceedings{Jenk84b,
+ author = "Jenks, Richard D.",
title = "A primer: 11 keys to New Scratchpad",
In Fitch [Fit84], pp123147. ISBN 038713350X LCCN QA155.7.E4 I57 1984
+ booktitle = "Proc. EUROSAM ISSAC 1984",
+ year = "1984",
+ publisher = "SpringerVerlag",
+ pages = "123147",
+ isbn = "038713350X",
keywords = "axiomref",
+ abstract =
+ "This paper is an abbreviated primer for the language of new
+ SCRATCHPAD, a new implementation of SCRATCHPAD which has been under
+ design and development by the Computer Algebra Group at the IBM
+ Research Center during the past 6 years. The basic design goals of the
+ new SCRATCHPAD language and interface to the user are to provde:
+ \begin{itemize}
+ \item a ``typeless'' interactive language suitable for online solution
+ of mathematical problems by novice users with little or no programming
+ required, and
+ \item a programming language suitable for the formal description of
+ algorithms and algebraic structures which can be compiled into runtime
+ efficient object code.
+ \end{itemize}
+
+ The new SCRATCHPAD language is introduced by 11 keys with each
+ successive key introducing an additional capability of the
+ language. The language is thus described as a ``concentric'' language
+ with each of the 11 levels corresponding to a language subset. These
+ levels are more than just a pedagogic device, since they correspond to
+ levels at which the system can be effectively used. Level 1 is
+ sufficient for naive interactive use; levels 28 progressively
+ introduce interactive users to capabilities of the language; levels
+ 911 are for system programmers and advanced users. Levesl 2, 4, 6,
+ and 7 give users the full power of LISP with a highlevel language;
+ level 8 introduces ``type declarations;'' level 9 allows polymorphic
+ functions to be defined and compiled; levels 1011 give users an
+ Adalike facility for defining types and packages (those of new
+ SCRATCHPAD are dynamically constructable, however). One language is
+ used for both interactive and system programming language use,
+ although several freedomes such as abbreviation and optional
+ typedeclarations allowed at toplevel are not permitted in system
+ code. The interactive language (levels 18) is a blend of original
+ SCRATCHPAD [GRJY75], some proposed extensions [JENK74], work by Loos
+ [LOOS74], SETL [DEWA79], SMP [COWO81], and new ideas; the system
+ programming language (levels 111) superficially resembles Ada but is
+ more similar to CLU [LISK74] in its semantic design.
+
+ This presentation of the language in this paper omits many details to
+ be covered in the SCRATCHPAD System Programming Manual [SCRA84] and an
+ expanded version of this paper will serve as a primer for SCRATCHPAD
+ users [JESU84]."
+}
\end{chunk}
\index{Jenks, Richard D.}
\index{Sutor, Robert S.}
\index{Watt, Stephen M.}
\begin{chunk}{ignore}
\bibitem[Jenks 86]{JWS86} Jenks, Richard D.; Sutor, Robert S.;
Watt, Stephen M.
 title = "Scratchpad II: An Abstract Datatype System for Mathematical Computation",
Research Report RC 12327 (\#55257), Iinternational Business Machines, Inc.,
Thomas J. Watson Research Center, Yorktown Heights, NY, USA, 1986 23pp
 url = "http://www.csd.uwo.ca/~watt/pub/reprints/1987imaspadadt.pdf",
 paper = "JWS86.pdf",
 keywords = "axiomref",
 abstract = "
 Scratchpad II is an abstract datatype language and system that is
 under development in the Computer Algebra Group, Mathematical Sciences
 Department, at the IBM Thomas J. Watson Research Center. Some features
 of APL that made computation particularly elegant have been borrowed.
 Many different kinds of computational objects and data structures are
 provided. Facilities for computation include symbolic integration,
 differentiation, factorization, solution of equations and linear
 algebra. Code economy and modularity is achieved by having
 polymorphic packages of functions that may create datatypes. The use
 of categories makes these facilities as general as possible."

\end{chunk}
+\index{Sundaresan, Christine J.}
+\begin{chunk}{axiom.bib}
+@misc{Jenk84c,
+ author = "Jenks, Richard D. and Sundaresan, Christine J.",
+ title = "The 11 Keys to SCRATCHPAD: A Primer",
+ year = "1984",
+ keywords = "axiomref"
+}
\index{Jenks, Richard D.}
\index{Sutor, Robert S.}
+\begin{chunk}{axiom.bib}
+@misc{Acad16,
+ author = "Academic Search",
+ title = "A Primer: 11 Keys to New Scratchpad",
+ url =
+ "http://libra.msra.cn/publication/645035/aprimer11keystonewscratchpad",
+ year = "2016",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@misc{Jenk86a,
+ author = "Jenks, Richard D.",
+ title = "Basic Algebraic Facilities of the Scratchpad II Computer
+ Algebra System",
+ institution = "IBM Research",
+ year = "1986",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@misc{Jenk86b,
+ author = "Jenks, Richard D.",
+ title = "Scratchpad II Examples from INPUT files",
+ institution = "IBM Research",
+ year = "1986",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\index{Sutor, Robert S.}
+\index{Watt, Stephen M.}
+\begin{chunk}{axiom.bib}
+@techreport{Jenk86,
+ author = "Jenks, Richard D. and Sutor, Robert S. and Watt, Stephen M.",
+ title = "Scratchpad II: An Abstract Datatype System for Mathematical
+ Computation",
+ institution = "IBM Research",
+ year = "1986",
+ type = "Research Report",
+ number = "RC 12327 (\#55257)",
+ url = "http://www.csd.uwo.ca/~watt/pub/reprints/1987imaspadadt.pdf",
+ paper = "Jenk86.pdf",
+ keywords = "axiomref",
+ abstract = "
+ Scratchpad II is an abstract datatype language and system that is
+ under development in the Computer Algebra Group, Mathematical Sciences
+ Department, at the IBM Thomas J. Watson Research Center. Some features
+ of APL that made computation particularly elegant have been borrowed.
+ Many different kinds of computational objects and data structures are
+ provided. Facilities for computation include symbolic integration,
+ differentiation, factorization, solution of equations and linear
+ algebra. Code economy and modularity is achieved by having
+ polymorphic packages of functions that may create datatypes. The use
+ of categories makes these facilities as general as possible."
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\index{Sutor, Robert S.}
\index{Watt, Stephen M.}
\begin{chunk}{ignore}
\bibitem[Jenks 87]{JWS87} Jenks, Richard D.; Sutor, Robert S.;
@@ 16179,14 +16826,64 @@ Draft September 5, 1988
\end{chunk}
\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@article{Jenk88d,
+ author = "Jenks, Richard D.",
+ title = "Scratchpad II: A computer algebra language and system",
+ journal = "The Journal of the Acoustical Society of America",
+ year = "1988",
+ volume = "83",
+ number = "S1",
+ pages = "S106",
+ keywords = "axiomref",
+ abstract =
+ "The Scratchpad II system represents a new generation of systems for
+ doing symbolic mathematics, based on modern algebra and abstract data
+ types. A large number of facilities are provided, for example:
+ symbolic integration, ``infinite'' power series, differential operators,
+ Cartesian tensors, and solution of nonlinear systems. Scratchpad II
+ has been designed from the outset to be extendible. The system
+ introduces a new data abstraction notion, the ``category,'' to express
+ intricate interrelationships between data types. The result design
+ permits the compilation of algorithms described in their most natural
+ mathematical setting. The use of categories guarantees user defined
+ types and packages are compatible with each other and with built in
+ facilities. This system provides a single high‐level language with an
+ intepreter and compiler. The language can be used by the naive user
+ for convenient interactive mathematics calculations and by the
+ advanced user for the efficient implementation of
+ algorithms. Scratchpad II is built on Lisp/VM and runs on IBM/370
+ class mainframes. An implementation of the system on the RT/PC is
+ expected soon."
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
\index{Sutor, Robert S.}
\index{Watt, Stephen M.}
\begin{chunk}{ignore}
\bibitem[Jenks 88c]{JWS88} Jenks, R. D.; Sutor, R. S.; Watt, S. M.
 title = "Scratchpad II: an abstract datatype system for mathematical computation",
In Jan{\ss}en
[Jan88], pp1237. ISBN 3540189289, 0387189289 LCCN QA155.7.E4T74 1988
+\begin{chunk}{axiom.bib}
+@book{Jenk88e,
+ author = "Jenks, Richard D. and Sutor, Robert S. and Watt, Stephen M.",
+ title = "Scratchpad II: An Abstract Datatype System for Mathematical
+ Computation",
+ booktitle = "Mathematical Aspects of Scientific Software",
+ year = "1988",
+ pages = "157182",
+ publisher = "Springer",
+ isbn = "0387189289",
keywords = "axiomref",
+ abstract =
+ "Scratchpad II is an abstract datatype language and system that is
+ under development in the Computer Algebra Group, Mathematical Sciences
+ Department, at the IBM Thomas J. Watson Research Center. Many
+ different kinds of computational objects and data structures are
+ provided. Facilities for computation include symbolic integration,
+ differentation, factorization, solution of equations and linear
+ algebra. Code economy and modularity is achieved by having polymorphic
+ packages of functions that may create datatypes. The use of categories
+ makes these facilities as general as possible."
+}
\end{chunk}
@@ 16206,9 +16903,10 @@ In Jan{\ss}en
\index{Jenks, Richard D.}
\index{Trager, Barry M.}
\begin{chunk}{ignore}
+\begin{chunk}{axiom.bib}
@InProceedings{Jenk94,
author = "Jenks, Richard D. and Trager, Barry M.",
+ title = "How to make AXIOM into a scratchpad",
booktitle = "Proceedings of the ACMSIGSAM 1989 International
Symposium on Symbolic and Algebraic Computation, ISSAC '94",
series = "ISSAC 94",
@@ 16403,6 +17101,21 @@ SIGSAM Communications in Computer Algebra, 157 2006
\subsection{K} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{Kajler, Norbert}
+\begin{chunk}{axiom.bib}
+ author = "Kajler, Norbert",
+ title = "CAS/PI: a Portable and Extensible Interface for Computer
+ Algebra Systems",
+ year = "1992",
+ booktitle = "Proc. ISSAC 1992",
+ series = "ISSAC 1992",
+ pages = "376386",
+ isbn = "0897914899 (soft cover) 0897914902 (hard cover)",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
\index{Kaplan, Michael}
\begin{chunk}{axiom.bib}
@book{Kapl05,
@@ 16417,17 +17130,31 @@ SIGSAM Communications in Computer Algebra, 157 2006
\end{chunk}
\index{Kajler, Norbert}
+\index{Kapur, D.}
+\index{Musser, D.R.}
+\index{Stepanov, A.A.}
\begin{chunk}{axiom.bib}
 author = "Kajler, Norbert",
 title = "CAS/PI: a Portable and Extensible Interface for Computer
 Algebra Systems",
 year = "1992",
 booktitle = "Proc. ISSAC 1992",
 series = "ISSAC 1992",
 pages = "376386",
 isbn = "0897914899 (soft cover) 0897914902 (hard cover)",
 keywords = "axiomref"
+@misc{Kapu81,
+ author = "Kapur, D. and Musser, D.R. and Stepanov, A.A.",
+ title = "Operators and Algebraic Structures",
+ url = "http://www.stepanovpapers.com/p59kapur.pdf",
+ paper = "Kapu81.pdf",
+ year = "1981",
+ abstract =
+ "Operators in functional languages such as APL and FFP are a useful
+ programming concept. However, this concept cannot be ful ly
+ exploited in these languages because of certain constraints. It is
+ proposed that an operator should be associated with a structure hav
+ ing the algebraic properties on which the operator's behavior depends.
+ This is illustrated by introducing a language that provides mechanisms
+ for defining structures and operators on them. Using this language,
+ it is possible to describe algorithms abstractly, thus empliasizing
+ the algebraic properties on which the algorithms depend. The role
+ that formal representation of mathematical knowledge can play in the
+ development of programs is illustrated through an example. An
+ approach for associating complexity mea sures with a structure and
+ operators is also suggested. This ap proach is useful in analyzing
+ the complexity of algorithms in an abstract setting."
}
\end{chunk}
@@ 16993,6 +17720,7 @@ CODEN JSYCEH ISSN 07477171
\end{chunk}
+\index{FreeModuleCat}
\index{Lambe, Larry A.}
\begin{chunk}{axiom.bib}
@article{Lamb92,
@@ 17720,6 +18448,32 @@ ISSN 07308639
\end{chunk}
+\begin{chunk}{axiom.bib}
+@misc{Maxi16,
+ author = "Maxima",
+ title = "Other Free Computer Algebra Systems",
+ url = "http://maxima.sourceforge.net/compalg.html",
+ year = "2016",
+ keywords = "axiomref",
+ abstract =
+ "Axiom is a general purpose Computer Algebra system. It is useful for
+ doing mathematics by computer and for research and development of
+ mathematical algorithms. It defines a strongly typed, mathematically
+ correct type hierarchy. It has a programming language and a builtin
+ compiler.
+
+ There is also an interesting Rosetta Stone which offers translations
+ of many basic operations for several computer algebra systems,
+ including Maxima."
+}
+
+\end{chunk}
+
+\index{TriangularSetCategory}
+\index{RegularTriangularSetCategory}
+\index{NormalizedTriangularSetCategory}
+\index{SquareFreeRegularTriangularSetCategory}
+\index{RegularSetDecompositionPackage}
\index{Maza, Marc Moreno}
\begin{chunk}{axiom.bib}
@techreport{Maza00,
@@ 17733,11 +18487,12 @@ ISSN 07308639
paper = "Maza00.pdf",
url = "http://www.csd.uwo.ca/~moreno//Publications",
keywords = "axiomref",
 algebra = "\newline\refto{category TSETCAT TriangularSetCategory}
 \newline\refto{category RSETCAT RegularTriangularSetCategory}
 \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
 \newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
 \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
+ algebra =
+ "\newline\refto{category TSETCAT TriangularSetCategory}
+ \newline\refto{category RSETCAT RegularTriangularSetCategory}
+ \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
+ \newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
+ \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
abstract =
"Different kinds of triangular decompositions of algebraic varieties
are presented. The main result is an efficient method for obtaining
@@ 18074,6 +18829,18 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
\end{chunk}
+\index{UnivariateSkewPolynomialCategory}
+\index{LinearOrdinaryDifferentialOperatorCategory}
+\index{Automorphism}
+\index{SparseUnivariateSkewPolynomial}
+\index{UnivariateSkewPolynomial}
+\index{LinearOrdinaryDifferentialOperator}
+\index{LinearOrdinaryDifferentialOperator1}
+\index{LinearOrdinaryDifferentialOperator2}
+\index{ApplyUnivariateSkewPolynomial}
+\index{UnivariateSkewPolynomialCategoryOps}
+\index{LinearOrdinaryDifferentialOperatorFactorizer}
+\index{LinearOrdinaryDifferentialOperatorsOps}"
\index{Mulders, Thom}
\begin{chunk}{axiom.bib}
@misc{Muld95,
@@ 18084,7 +18851,8 @@ Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago
url =
"ftp://ftp.inf.ethz.ch/org/cathode/workshops/jan95/abstracts/mulders.ps",
keywords = "axiomref",
 algebra = "\newline\refto{category OREPCAT UnivariateSkewPolynomialCategory}
+ algebra =
+ "\newline\refto{category OREPCAT UnivariateSkewPolynomialCategory}
\newline\refto{category LODOCAT LinearOrdinaryDifferentialOperatorCategory}
\newline\refto{domain AUTOMOR Automorphism}
\newline\refto{domain ORESUP SparseUnivariateSkewPolynomial}
@@ 18194,6 +18962,15 @@ Dec. 1975 CODEN ACMSCU ISSN 00983500
\end{chunk}
+\index{AffineAlgebraicSetComputeWithGroebnerBasis}
+\index{EuclideanGroebnerBasisPackage}
+\index{GroebnerFactorizationPackage}
+\index{GroebnerInternalPackage}
+\index{GroebnerPackage}
+\index{GroebnerSolve}
+\index{InterfaceGroebnerPackage}
+\index{LinGroebnerPackage}
+\index{PolyGroebner}
\index{Norman, Arthur C.}
\begin{chunk}{axiom.bib}
@misc{Normxx,
@@ 18873,17 +19650,23 @@ Mathematik und Physik, 75 (suppl. 2):S435S438, 1995 ISSN 00442267
\end{chunk}
+\index{TriangularSetCategory}
+\index{RegularTriangularSetCategory}
+\index{NormalizedTriangularSetCategory}
+\index{SquareFreeRegularTriangularSetCategory}
+\index{RegularSetDecompositionPackage}
\begin{chunk}{axiom.bib}
@misc{SALSA,
author = "SALSA",
title = "Solvers for Algebraic Systems and Applications",
url =
"http://www.enslyon.fr/LIP/Arenaire/SYMB/teams/salsa/proposalsalsa.pdf",
 algebra = "\newline\refto{category TSETCAT TriangularSetCategory}
 \newline\refto{category RSETCAT RegularTriangularSetCategory}
 \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
+ algebra =
+ "\newline\refto{category TSETCAT TriangularSetCategory}
+ \newline\refto{category RSETCAT RegularTriangularSetCategory}
+ \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
\newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
 \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
+ \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
paper = "SALSA.pdf"
}
@@ 18943,6 +19726,45 @@ April 1991 CODEN SIGSBZ ISSN 01635824
\end{chunk}
+\index{Santas, Philip S.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Sant96,
+ author = "Santas, Philip S.",
+ title = "Conditional Categories and Domains",
+ keywords = "axiomref",
+ booktitle = "Proc. DISCO 1996",
+ year = "1996",
+ pages = "112125",
+ isbn = "3540616977"
+}
+
+\end{chunk}
+
+\index{Santas, Philip S.}
+\begin{chunk}{axiom.bib}
+@book{Sant05,
+ author = "Santas, Philip S.",
+ title = "Conditional Categories and Domains",
+ keywords = "axiomref",
+ booktitle = "Design and Implementation of Symbolic Computation Systems",
+ year = "2005",
+ series = "Lecture Notes in Computer Science",
+ volume = "1128",
+ publisher = "Springer",
+ abstract =
+ "We extend the Type system defined in [Sant95] with Axiomlike
+ Conditional Categories with the additional property of Static Typing
+ and Checking. Categories and Domains may contain conditionals in their
+ bodies, which are elaborated by our compiler by techniques used in
+ standard typing. We define an appropriate calculus and discuss its
+ properties. Examples inspired by the Axiom library illustrate the
+ power of our apprach and its application in constructing algebraic
+ concepts. The full calculus has been implemented and tested with our
+ LA compiler which generated executable files."
+}
+
+\end{chunk}
+
\index{Saunders, B. David}
\begin{chunk}{axiom.bib}
@article{Saun80,
@@ 18978,6 +19800,19 @@ Kognitive Systeme, Universit\"t Karlsruhe 1992
\end{chunk}
+\index{Schwardmann, Ulrich}
+\begin{chunk}{axiom.bib}
+@book{Schw95,
+ author = "Schwardmann, Ulrich",
+ title = "Computer algebra systems",
+ comment = "ComputeralgebraSysteme, German",
+ publisher = "AddisonWesley",
+ year = "1995",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
\index{Schwarz, Fritz}
\begin{chunk}{ignore}
\bibitem[Schwarz 88]{Sch88} Schwarz, F.
@@ 19371,6 +20206,42 @@ Physics, pp337344, Acireale (Italy), 1992 Kluwer, Dordrecht 1993
\end{chunk}
+\index{Storme, L.}
+\index{van Maldeghem, H.}
+\begin{chunk}{axiom.bib}
+@article{Stor95,
+ author = "Storme, L. and van Maldeghem, H.",
+ title = "Cyclic caps in PG(3,q)",
+ journal = "Geom. Dedicata",
+ volume = "56",
+ number = "3",
+ pages = "271284",
+ year = "1995",
+ keywords = "axiomref",
+ url = "https://cage.ugent.be/~hvm/artikels/44.pdf",
+ paper = "Stor95.pdf",
+ abstract =
+ "A $k$cap $K$ on $PG(n,q)$ is a set of $k$ points, no three of which
+ are collinear. $K$ is complete if it cannot be extended to a $k+1$
+ cap. If $K$ is invariant under a cyclic subgroup (which acts regularly
+ on $K$) of $PGL(n+1,q)$, the $K$ is cyclic.
+
+ This article investigates cyclic complete $k$caps in
+ $PG(3,q). Namely, the different types of complete $k$caps $K$ in
+ $PG(3,q)$ stabilized by a cyclic projective group $G$ of order $k$,
+ acting regularly on the points of $K$, are determined. We show that in
+ $PG(3,q)$, $q$ even, the elliptic quadric is the only cyclic complete
+ $k$cap. For $q$ odd, it is shown that besides the elliptic quadric,
+ there also exist cyclic $k$caps containing $k/2$ points of two
+ disjoint elliptic quadrics or two disjoint hyperbolic quadrics and
+ that there exist cyclic $k$caps stabilized by a transitive cyclic
+ group $G$ fixed precisely one point and one plane of
+ $PG(3,q)$. Concrete examples of such caps, found using AXIOM and
+ CAYLEY, are presented."
+}
+
+\end{chunk}
+
\index{Stroeker, Roelof J.}
\index{Kaashoek, Johan F.}
\begin{chunk}{axiom.bib}
@@ 19441,12 +20312,18 @@ Physics, pp337344, Acireale (Italy), 1992 Kluwer, Dordrecht 1993
\end{chunk}
\index{Sutor, Robert S.}
\begin{chunk}{ignore}
\bibitem[Sutor 85]{Sut85} Sutor, R.S.
+\begin{chunk}{axiom.bib}
+@inproceedings{Suto85,
+ author = "Sutor, Robert S.",
title = "The Scratchpad II computer algebra language and system",
In Buchberger and Caviness [BC85], pp3233 ISBN 0387159835 (vol. 1),
0387159843 (vol. 2) LCCN QA155.7.E4 E86 1985 Two volumes.
 keywords = "axiomref",
+ booktitle = "Research Contributions from the Euro. Conf. on Comp. Alg.",
+ series = "Lecture Notes in Computer Science Volume 204",
+ volume = "2",
+ pages = "3233",
+ year = "1985",
+ isbn = "0387159835 (vol. 1),0387159843 (vol. 2)",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 19458,6 +20335,7 @@ In Buchberger and Caviness [BC85], pp3233 ISBN 0387159835 (vol. 1),
title = "The type inference and coercion facilities in the Scratchpad II
interpreter",
journal = "SIGPLAN Notices",
+ comment = "IBM Research Report RC 12595",
volume = "22",
number = "7",
pages = "5663",
@@ 19873,6 +20751,34 @@ in [Wit87], pp1317
\end{chunk}
\index{Watt, Stephen M.}
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@misc{Watt87,
+ author = "Watt, Stephen M. and Jenks, Richard D.",
+ title = "Abstract Datatypes, Multiple Views and Multiple Inheritance in
+ Scratchpad II",
+ keywords = "axiomref",
+ year = "1987",
+ url = "https://cs.uwaterloo.ca/~smatt/pub/reprints/1987itlspadviews.pdf",
+ paper = "Watt87.pdf",
+ abstract =
+ "Scratchpad II is an abstract datatype language developed at Yorktown
+ Heights for the implementation of a new computer algebra system. It
+ provides packages of polymorphic functions and parameterized, abstract
+ datatypes with operator overloading and multiple inheritance. To
+ express the intricate interrelationships between the datatypes
+ necessary for the description of mathematical objects, a number of
+ techniques based on the notion of {\sl category} have been
+ used. Categories are used to enforce relationships between type
+ parameters and to provide the mechanism for multiple inheritance. They
+ also allow the language to be statically type checked and the
+ generation of efficient code. This paper describes the role of
+ categories in Scratchpad II."
+}
+
+\end{chunk}
+
+\index{Watt, Stephen M.}
\begin{chunk}{ignore}
\bibitem[Watt 89]{Wat89} Watt, S. M.
title = "A fixed point method for power series computation",
@@ 19886,12 +20792,43 @@ In Gianni [Gia89], pp206217 ISBN 3540510842 LCCN QA76.95.I57
\index{Jenks, Richard D.}
\index{Sutor, Robert S.}
\index{Trager, Barry M.}
\begin{chunk}{ignore}
\bibitem[Watt 90]{WJST90} Watt, S.M.; Jenks, R.D.; Sutor, R.S.; Trager, B.M.
 title = "The Scratchpad II type system: Domains and subdomains",
in A.M. Miola, editor Computing Tools
for Scientific Problem Solving, Academic Press, New York, 1990
+\begin{chunk}{axiom.bib}
+@inproceedings{Watt90,
+ author = "Watt, Stephen M. and Jenks, Richard D. and Sutor, Robert S. and
+ Trager, Barry M.",
+ title = "The Scratchpad II type system: Domains and Subdomains",
+ booktitle = "Computing Tools for Scientific Problem Solving",
+ year = "1990",
+ publisher = "Academic Press",
+ url =
+ "https://cs.uwaterloo.ca/~smwatt/pub/reprints/1990miolaspadtypes.pdf",
+ paper = "Watt90.pdf",
keywords = "axiomref",
+ abstract =
+ "Scratchpad II is a language developed at Yorktown Heights for the
+ implementation of a new computer algebra system. The need to model the
+ intricate relationships among the datatypes representing mathematical
+ objects has provided a number of challenges in the design of a type
+ system for the programming language.
+
+ In languages in which a datatype constructor may take multiple
+ parameters, ensuring compatibility between them is extremely
+ important. Scratchpad II addresses this issue by basing its
+ implementation of abstract datatypes on {\cl categories}. Categories
+ provide a convenient and useful method for specifying requirements on
+ operations from datatypes. These requirements can be very complex when
+ modelling mathematics.
+
+ We show how categories provide multiple inheritance and how
+ inheritance of specification is separated from inheritance of
+ implementation. We also present implications of the type system on
+ compilation of efficient code and flexibility of a weakly typed
+ interactive user interface.
+
+ Finally, the mechanisms of Scratchpad II are compared with those of
+ traditional abstract datatype and objectoriented programming
+ languages."
+}
\end{chunk}
@@ 20059,6 +20996,31 @@ IBM T. J. Watson Research Center (2001)
\end{chunk}
+\index{Watt, Stephen}
+\begin{chunk}{axiom.bib}
+@InProceedings{Watt07,
+ author = "Watt, Stephen",
+ title = "What Happened to Languages for Symolic Mathematical Computation?",
+ booktitle = "Proc. Prog. Lang. for Mechanized Mathematics",
+ series = "PLMMS 07",
+ year = "2007",
+ location = "RISCLinz, Austria",
+ pages = "8190",
+ keywords = "axiomref",
+ paper = "Watt07.pdf",
+ url =
+ "http://www.csd.uwo.ca/~watt/pub/reprints/2007plmmswhat\_happened.pdf",
+ abstract =
+ "While the state of the art is relatively sophisticated in programming
+ language support for computer algebra, there has been less development
+ in programming language support for symbolic computation over the past
+ two decades. We summarize certain advances in programming languages
+ for computer algebra and propose a set of directions and challenges
+ for programming languages for symbolic computation."
+}
+
+\end{chunk}
+
\index{Weber, Andreas}
\begin{chunk}{axiom.bib}
@phdthesis{Webe93b,
@@ 20153,10 +21115,17 @@ IBM T. J. Watson Research Center (2001)
\end{chunk}
\index{Weber, Andreas}
\begin{chunk}{ignore}
\bibitem[Weber 95]{Webe95} Weber, A.
+\begin{chunk}{axiom.bib}
+@article{Webe95,
+ author = "Weber, Andreas",
title = "On coherence in computer algebra",
 url = "http://cg.cs.unibonn.de/personalpages/weber/publications/pdf/WeberA/Weber94e.pdf",
+ journal = "J. Symb. Comput.",
+ volume = "19",
+ number = "13",
+ pages = "2538",
+ year = "1995",
+ url =
+"http://cg.cs.unibonn.de/personalpages/weber/publications/pdf/WeberA/Weber94e.pdf",
paper = "Webe95.pdf",
keywords = "axiomref",
abstract = "
@@ 20170,6 +21139,7 @@ IBM T. J. Watson Research Center (2001)
having several possibilities of coercions covering many important
examples. Moreover, we will give some informal reasoning why the
formally defined restrictions can be satisfied by an actual system."
+}
\end{chunk}
@@ 20297,6 +21267,50 @@ LCCN QA76.7.S54 v22:7 SIGPLAN Notices, vol 22, no 7 (July 1987)
\end{chunk}
+\index{Williamson, Clifton J.}
+\begin{chunk}{axiom.bib}
+@InProceedings{Will95,
+ author = "Williamson, Clifton J.",
+ title = "On the algebraic construction of tridiagonal matrices with given
+ characteristic polynomial",
+ booktitle = "4th Conf. of Canadian Number Theory Association",
+ year = "1995",
+ location = "Halifax, Nova Scotia, Canada",
+ pages = "417431",
+ keywords = "axiomref",
+ paper = "Will95.pdf",
+ abstract =
+ "Let $K$ be a field of characteristic zero and assume
+ \[f(x)=x^ns_1x^{n1}+\cdots+s_n \in L[x]\]
+ where $L=K(s_1,\cdots,s_n)$. Call, for the purposes of this review, an
+ $n\times n$ matrix 1tridiagonal if its entries above and below the
+ main diagonal are all 1, the entries on it are $d_1,\cdots,d_n$, and
+ all other entries are 0. Under which conditions can
+ $d_1,d_2,\cdots,d_n$ be chosen in a radical extension of $L$ such that
+ the resulting 1tridiagonal matrix has $f$ as its characteristic
+ polynomial? The author’s answer: for $n=3$ always. The $d_i,s_i$
+ are related by a system of algebraic equations of the form
+ $\overline{f}_i(d_1,d_2,d_3)=s_i$. If this is satisfied, then by
+ a resultant or Groebner basis computation with respect to the
+ lexicographic order, $d_3$ (say) must be a root of a certain
+ irreducible polynomial $\varphi$ of degree 6. Joining this
+ with a Galois group computation for $\varphi$ over $L$, it is shown
+ that a solvable and necessarily transitive Gal($\varphi$) will be a
+ necessary and sufficient condition for expressibility of $d_3$ (clear)
+ and, thanks to the form of the Groebner basis, also of $d_1,d_2$ in
+ radicals. Upon a discriminant computation of $\varphi$ and use of
+ results of G. Butler and J. McKay [Commun. Algebra 11,
+ 863911 (1983; Zbl 0518.20003)] and J. McKay and L. Soicher [J. Number
+ Theory 20, 273281 (1985; Zbl 0579.12006)], this allows the author to
+ deduce the mentioned result. For $n=4$, though the author cannot get as
+ complete information about Galois groups etc., he can deduce e.g. that
+ if $s_1,\cdots,s_4$ are algebraically independent over $\mathbb{Q}$,
+ then $d_1,\cdots,d_4$ are not expressible in radicals over
+ $\mathbb{Q}(s_1,\cdots,s_4)$. He mentions, however, a solvable subcase."
+}
+
+\end{chunk}
+
\index{Winkler, Franz}
\begin{chunk}{axiom.bib}
@article{Wink89,
@@ 20401,10 +21415,46 @@ LCCN QA76.7.S54 v22:7 SIGPLAN Notices, vol 22, no 7 (July 1987)
\index{Wityak, Sandra}
\begin{chunk}{ignore}
\bibitem[Wityak 87]{Wit87} Wityak, Sandra
 title = "Scratchpad II Newsletter",
Volume 2, Number 1, Nov 1987
 keywords = "axiomref",
+@misc{Wity85,
+ author = "Wityak, Sandra",
+ title = "The Scratchpad II Newsletter",
+ volume = "1",
+ number = "1",
+ year = "1985",
+ month = "September",
+ institution = "IBM Research",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Wityak, Sandra}
+\begin{chunk}{ignore}
+@misc{Wity86,
+ author = "Wityak, Sandra",
+ title = "The Scratchpad II Newsletter",
+ volume = "1",
+ number = "2",
+ year = "1986",
+ month = "January",
+ institution = "IBM Research",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Wityak, Sandra}
+\begin{chunk}{ignore}
+@misc{Wity86a,
+ author = "Wityak, Sandra",
+ title = "The Scratchpad II Newsletter",
+ volume = "1",
+ number = "3",
+ year = "1986",
+ month = "May",
+ institution = "IBM Research",
+ keywords = "axiomref"
+}
\end{chunk}
@@ 20416,6 +21466,7 @@ Software Preservation Group
\end{chunk}
+\index{DoubleFloatSpecialFunctions}
\begin{chunk}{axiom.bib}
@misc{WikiG,
author = "Wikipedia Authors",
@@ 20501,6 +21552,35 @@ Karlsruhe, Germany, 1992
\end{chunk}
+\index{Zippel, Richard}
+\begin{chunk}{axiom.bib}
+@misc{Zipp89,
+ author = "Zippel, Richard",
+ title = "The Weyl Computer Algebra Substrate",
+ paper = "Zipp89.pdf",
+ keywords = "axiomref",
+ year = "1989",
+ paper = "Zipp89.pdf",
+ url = "https://ecommons.cornell.edu/bitstream/handle/1813/6917/901077.pdf"
+}
+
+\end{chunk}
+
+\index{Zippel, Richard}
+\begin{chunk}{axiom.bib}
+@misc{Zipp93,
+ author = "Zippel, Richard",
+ title = "The Weyl Computer Algebra Substrate",
+ paper = "Zipp93.pdf",
+ keywords = "axiomref",
+ booktitle = "Proc. of DISCO 1993",
+ series = "DISCO 93",
+ pages = "303=307",
+ year = "1993"
+}
+
+\end{chunk}
+
\index{Zwillinger, Daniel}
\begin{chunk}{ignore}
\bibitem[Zwi92]{Zwi92} Zwillinger, Daniel
@@ 20610,6 +21690,11 @@ National Physical Laboratory. (1982)
\end{chunk}
+\index{TriangularSetCategory}
+\index{RegularTriangularSetCategory}
+\index{NormalizedTriangularSetCategory}
+\index{SquareFreeRegularTriangularSetCategory}
+\index{RegularSetDecompositionPackage}
\index{Aubry, Phillippe}
\index{Lazard, Daniel}
\index{Maza, Marc Moreno}
@@ 20623,11 +21708,12 @@ National Physical Laboratory. (1982)
volume = "28",
url = "http://www.csd.uwo.ca/~moreno/Publications/AubryLazardMorenoMaza1999JSC.pdf",
papers = "Aubr99.pdf",
 algebra = "\newline\refto{category TSETCAT TriangularSetCategory}
 \newline\refto{category RSETCAT RegularTriangularSetCategory}
 \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
+ algebra =
+ "\newline\refto{category TSETCAT TriangularSetCategory}
+ \newline\refto{category RSETCAT RegularTriangularSetCategory}
+ \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
\newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
 \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
+ \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
abstract =
"Different notions of triangular sets are presented. The relationship
between these notions are studied. The main result is that four
@@ 20637,6 +21723,11 @@ National Physical Laboratory. (1982)
\end{chunk}
+\index{TriangularSetCategory}
+\index{RegularTriangularSetCategory}
+\index{NormalizedTriangularSetCategory}
+\index{SquareFreeRegularTriangularSetCategory}
+\index{RegularSetDecompositionPackage}
\index{Aubry, Phillippe}
\index{Maza, Marc Moreno}
\begin{chunk}{axiom.bib}
@@ 20647,11 +21738,12 @@ National Physical Laboratory. (1982)
year = "1996",
url = "http://www.lip6.fr/lip6/reports/1997/lip6.1997.009.ps.gz",
paper = "Aubr96.pdf",
 algebra = "\newline\refto{category TSETCAT TriangularSetCategory}
 \newline\refto{category RSETCAT RegularTriangularSetCategory}
 \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
+ algebra =
+ "\newline\refto{category TSETCAT TriangularSetCategory}
+ \newline\refto{category RSETCAT RegularTriangularSetCategory}
+ \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
\newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
 \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
+ \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
keywords = "axiomref",
abstract =
"Four methods for solving polynomial systems by means of triangular
@@ 20663,6 +21755,11 @@ National Physical Laboratory. (1982)
\end{chunk}
+\index{TriangularSetCategory}
+\index{RegularTriangularSetCategory}
+\index{NormalizedTriangularSetCategory}
+\index{SquareFreeRegularTriangularSetCategory}
+\index{RegularSetDecompositionPackage}
\index{Aubry, Phillippe}
\index{Maza, Marc Moreno}
\begin{chunk}{axiom.bib}
@@ 20678,11 +21775,12 @@ National Physical Laboratory. (1982)
url =
"http://www.csd.uwo.ca/~moreno/Publications/AubryMorenoMaza1999JSC.pdf",
paper = "Aubr99a.pdf",
 algebra = "\newline\refto{category TSETCAT TriangularSetCategory}
 \newline\refto{category RSETCAT RegularTriangularSetCategory}
 \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
+ algebra =
+ "\newline\refto{category TSETCAT TriangularSetCategory}
+ \newline\refto{category RSETCAT RegularTriangularSetCategory}
+ \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
\newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
 \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
+ \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
keywords = "axiomref",
abstract =
"Four methods for solving polynomial systems by means of triangular
@@ 20986,6 +22084,18 @@ Mathematics of Computation, vol. 35, num. 35, Oct. 1980, 13791381
\end{chunk}
+\index{UnivariateSkewPolynomialCategory}
+\index{LinearOrdinaryDifferentialOperatorCategory}
+\index{Automorphism}
+\index{SparseUnivariateSkewPolynomial}
+\index{UnivariateSkewPolynomial}
+\index{LinearOrdinaryDifferentialOperator}
+\index{LinearOrdinaryDifferentialOperator1}
+\index{LinearOrdinaryDifferentialOperator2}
+\index{ApplyUnivariateSkewPolynomial}
+\index{UnivariateSkewPolynomialCategoryOps}
+\index{LinearOrdinaryDifferentialOperatorFactorizer}
+\index{LinearOrdinaryDifferentialOperatorsOps}
\index{Bronstein, Manuel}
\begin{chunk}{axiom.bib}
@misc{Bron95,
@@ 20995,7 +22105,8 @@ Mathematics of Computation, vol. 35, num. 35, Oct. 1980, 13791381
year = "1995",
url =
"ftp://ftp.inf.ethz.ch/org/cathode/workshops/jan95/abstracts/bronstein.ps",
 algebra = "\newline\refto{category OREPCAT UnivariateSkewPolynomialCategory}
+ algebra =
+ "\newline\refto{category OREPCAT UnivariateSkewPolynomialCategory}
\newline\refto{category LODOCAT LinearOrdinaryDifferentialOperatorCategory}
\newline\refto{domain AUTOMOR Automorphism}
\newline\refto{domain ORESUP SparseUnivariateSkewPolynomial}
@@ 21613,10 +22724,14 @@ A.E.R.E. Report R.8730. HMSO. (1977)
\index{Duval, Dominique}
\index{Gonz\'alezVega, L.}
\begin{chunk}{ignore}
\bibitem[Duval 96a]{Duva96a} Duval, D.; Gonz\'alezVega, L.
+\begin{chunk}{axiom.bib}
+@article{Duva96a,
+ author = {Duval, Dominique and Gonz\'alezVega, L.},
title = "Dynamic Evaluation and Real Closure",
Mathematics and Computers in Simulation 42 pp 551560 (1996)
+ journal = "Mathematics and Computers in Simulation",
+ volume = "42",
+ pages = "551560",
+ year = "1996",
paper = "Duva96a.pdf",
abstract = "
The aim of this paper is to present how the dynamic evaluation method
@@ 21626,34 +22741,46 @@ Mathematics and Computers in Simulation 42 pp 551560 (1996)
handled through splittings, exactly as in the algebraic closure of a
field. Sign tests are handled throug a structure called ``Tarski data
type''."
+}
\end{chunk}
\index{Duval, Dominique}
\index{Reynaud, J.C.}
\begin{chunk}{ignore}
\bibitem[Duval 96]{Duva96} Duval, D.; Reynaud, J.C.
+\index{Reynaud, JeanClaude}
+\begin{chunk}{axiom.bib}
+@article{Duva96,
+ author = "Duval, D. and Reynaud, JeanClaude",
title = "Sketches and Computations over Fields",
Mathematics and Computers in Simulation 42 pp 363373 (1996)
+ journal = "Mathematics and Computers in Simulation",
+ volume = "42",
+ pages = "363373",
+ year = "1996",
paper = "Duva96.pdf",
 abstract = "
 The goal of this short paper is to describe one possible use of
+ abstract =
+ "The goal of this short paper is to describe one possible use of
sketches in computer algebra. We show that sketches are a powerful
tool for the description of mathematical structures and for the
description of computations."
+}
\end{chunk}
\index{Duval, Dominique}
\index{Reynaud, J.C.}
\begin{chunk}{ignore}
\bibitem[Duval 94a]{Duva94a} Duval, D.; Reynaud, J.C.
 title = "Sketches and Computation (Part I): Basic Definitions and Static Evaluation",
Mathematical Structures in Computer Science, 4, p 185238 Cambridge University Press (1994)
+\begin{chunk}{axiom.bib}
+@article{Duva94a,
+ author = "Duval, D. and Reynaud, J.C.",
+ title = "Sketches and Computation (Part I):
+ Basic Definitions and Static Evaluation",
+ journal = "Mathematical Structures in Computer Science",
+ volume = "4",
+ pages = "185238",
+ publisher = "Cambridge University Press",
+ year = "1994",
url = "http://journals.cambridge.org/abstract_S0960129500000438",
paper = "Duva94a.pdf",
 abstract = "
 We define a categorical framework, based on the notion of {\sl
+ abstract =
+ "We define a categorical framework, based on the notion of {\sl
sketch}, for specification and evaluation in the sense of algebraic
specifications and algebraic programming. This framework goes far
beyond our initial motivations, which was to specify computation with
@@ 21666,19 +22793,26 @@ Mathematical Structures in Computer Science, 4, p 185238 Cambridge University P
equational. In Part II (Duval and Reynaud 1994), we study a more
general process, called {\sl dynamic evaluation}, for structures that
may have no initial model."
+}
\end{chunk}
\index{Duval, Dominique}
\index{Reynaud, J.C.}
\begin{chunk}{ignore}
\bibitem[Duval 94b]{Duva94b} Duval, D.; Reynaud, J.C.
 title = "Sketches and Computation (Part II): Dynamic Evaluation and Applications",
Mathematical Structures in Computer Science, 4, p 239271. Cambridge University Press (1994)
+\index{Reynaud, JeanClaude}
+\begin{chunk}{axiom.bib}
+@article{Duva94b,
+ author = "Duval, Dominique and Reynaud, JeanClaude",
+ title = "Sketches and Computation (Part II):
+ Dynamic Evaluation and Applications",
+ journal = "Mathematical Structures in Computer Science",
+ volume = "4",
+ pages = "239271",
+ publisher = "Cambridge University Press",
+ year = "1994",
url = "http://journals.cambridge.org/abstract_S096012950000044X",
paper = "Duva94b.pdf",
 abstract = "
 In the first part of this paper (Duval and Reynaud 1994), we defined a
+ abstract =
+ "In the first part of this paper (Duval and Reynaud 1994), we defined a
categorical framework, based on the notion of {\sl sketch}, for
specification and evaluation in the senses of algebraic specification
and algebraic programming. {\sl Static evaluation} in {\sl
@@ 21689,6 +22823,7 @@ Mathematical Structures in Computer Science, 4, p 239271. Cambridge University
algebra systems are beginning to use it as a basic tool. Finally, we
give some applications of dynamic evaluation to computation in field
extensions."
+}
\end{chunk}
@@ 21858,6 +22993,9 @@ AddisonWesley. 181187. (1965)
\end{chunk}
+\index{GeneralPackageForAlgebraicFunctionField}
+\index{PackageForAlgebraicFunctionFieldOverFiniteField}
+\index{PackageForAlgebraicFunctionField}
\index{Fulton, William}
\begin{chunk}{axiom.bib}
@misc{Fult08,
@@ 21910,6 +23048,7 @@ Journal of Symbolic Computation (1990) 9, 281299
\end{chunk}
+\index{PolynomialGcdPackage}
\index{von zur Gathen, Joachim}
\index{Gerhard, J\"urgen}
\begin{chunk}{axiom.bib}
@@ 22249,6 +23388,9 @@ Grove, IL, USA and Oxford, UK, 1992
\subsection{H} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{GeneralPackageForAlgebraicFunctionField}
+\index{PackageForAlgebraicFunctionFieldOverFiniteField}
+\index{PackageForAlgebraicFunctionField}
\index{Hach\'e, G.}
\index{Le Brigand, D.}
\begin{chunk}{axiom.bib}
@@ 22400,6 +23542,13 @@ J. Inst. Math. Appl. 14 89103. (1974)
\end{chunk}
+\index{Guess}
+\index{GuessAlgebraicNumber}
+\index{GuessFinite}
+\index{GuessFiniteFunctions}
+\index{GuessInteger}
+\index{GuessPolynomial}
+\index{GuessUnivariatePolynomial}
\index{Hebisch, Waldemar}
\index{Rubey, Martin}
\begin{chunk}{axiom.bib}
@@ 22409,13 +23558,14 @@ J. Inst. Math. Appl. 14 89103. (1974)
year = "2010",
url = "https://arxiv.org/abs/math/0702086v2",
paper = "Hebi10.pdf",
 algebra = "\newline\refto{package GUESS Guess}
 \newline\refto{package GUESSAN GuessAlgebraicNumber}
 \newline\refto{package GUESSF GuessFinite}
 \newline\refto{package GUESSF1 GuessFiniteFunctions}
 \newline\refto{package GUESSINT GuessInteger}
 \newline\refto{package GUESSP GuessPolynomial}
 \newline\refto{package GUESSUP GuessUnivariatePolynomial}",
+ algebra =
+ "\newline\refto{package GUESS Guess}
+ \newline\refto{package GUESSAN GuessAlgebraicNumber}
+ \newline\refto{package GUESSF GuessFinite}
+ \newline\refto{package GUESSF1 GuessFiniteFunctions}
+ \newline\refto{package GUESSINT GuessInteger}
+ \newline\refto{package GUESSP GuessPolynomial}
+ \newline\refto{package GUESSUP GuessUnivariatePolynomial}",
abstract =
"We present a software package that guesses formulae for sequences of,
for example, rational numbers or rational functions, given the first
@@ 22493,6 +23643,7 @@ IEEE Comput. Soc. Press, pp. 678687.
\end{chunk}
+\index{DifferentialVariableCategory}
\index{Hubbard, John H.}
\index{Lundell, Benjamin}
\begin{chunk}{axiom.bib}
@@ 22596,6 +23747,22 @@ Dept. G68, P.O. Box 1900, Boulder, Colorado, USA 803019191.
\end{chunk}
+\index{Ioakimidis, N.I.}
+\begin{chunk}{axiom.bib}
+@article{Ioak94,
+ author = "Ioakimidis, N.I.",
+ title = "Symbolic computations for the solution of inverse/design
+ problems with Maple",
+ journal = "Comput. Struct.",
+ volume = "53",
+ number = "1",
+ pages = "6368",
+ year = "1994",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
\index{Itoh, T.}
\index{Tsujii, S.}
\begin{chunk}{ignore}
@@ 22623,6 +23790,7 @@ Inf. and Comp. 78, pp.171177, 1988
\end{chunk}
+\index{GradedAlgebra}
\index{Iyanaga, Shokichi}
\index{Iyanaga, Yukiyosi Kawada}
\begin{chunk}{axiom.bib}
@@ 22639,6 +23807,7 @@ Inf. and Comp. 78, pp.171177, 1988
\subsection{J} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{Monad}
\index{Jacobson, Nathan}
\begin{chunk}{axiom.bib}
@article{Jaco51,
@@ 22656,6 +23825,8 @@ Inf. and Comp. 78, pp.171177, 1988
\end{chunk}
+\index{Monad},
+\index{MonadWithUnit}
\index{Jacobson, Nathan}
\begin{chunk}{axiom.bib}
@article{Jaco68,
@@ 22667,8 +23838,9 @@ Inf. and Comp. 78, pp.171177, 1988
year = "1973",
pages = "509514",
url = "http://projecteuclid.org/euclid.bams/1183534656",
 algebra = "\newline\refto{category MONAD Monad},
 \newline\refto{category MONADWU MonadWithUnit}"
+ algebra =
+ "\newline\refto{category MONAD Monad},
+ \newline\refto{category MONADWU MonadWithUnit}"
}
\end{chunk}
@@ 22710,6 +23882,11 @@ Comput. J. 9 281285. (1966)
\subsection{K} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{TriangularSetCategory}
+\index{RegularTriangularSetCategory}
+\index{NormalizedTriangularSetCategory}
+\index{SquareFreeRegularTriangularSetCategory}
+\index{RegularSetDecompositionPackage}
\index{Kalkbrener, M.}
\begin{chunk}{axiom.bib}
@phdthesis{Kalk91,
@@ 22717,26 +23894,33 @@ Comput. J. 9 281285. (1966)
title = "Three contributions to elimination theory",
school = "University of Linz, Austria",
year = "1991",
 algebra = "\newline\refto{category TSETCAT TriangularSetCategory}
 \newline\refto{category RSETCAT RegularTriangularSetCategory}
 \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
+ algebra =
+ "\newline\refto{category TSETCAT TriangularSetCategory}
+ \newline\refto{category RSETCAT RegularTriangularSetCategory}
+ \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
\newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
 \newline\refto{package RSDCMPK RegularSetDecompositionPackage}"
+ \newline\refto{package RSDCMPK RegularSetDecompositionPackage}"
}
\end{chunk}
+\index{TriangularSetCategory}
+\index{RegularTriangularSetCategory}
+\index{NormalizedTriangularSetCategory}
+\index{SquareFreeRegularTriangularSetCategory}
+\index{RegularSetDecompositionPackage}
\index{Kalkbrener, M.}
\begin{chunk}{axiom.bib}
@article{Kalk98,
author = "Kalkbrener, M.",
title = "Algorithmic properties of polynomial rings",
journal = "Journal of Symbolic Computation",
 algebra = "\newline\refto{category TSETCAT TriangularSetCategory}
 \newline\refto{category RSETCAT RegularTriangularSetCategory}
 \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
+ algebra =
+ "\newline\refto{category TSETCAT TriangularSetCategory}
+ \newline\refto{category RSETCAT RegularTriangularSetCategory}
+ \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
\newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
 \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
+ \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
year = "1998",
paper = "Kalk98.pdf",
abstract =
@@ 22928,6 +24112,11 @@ PrenticeHall. (1974)
\end{chunk}
+\index{TriangularSetCategory}
+\index{RegularTriangularSetCategory}
+\index{NormalizedTriangularSetCategory}
+\index{SquareFreeRegularTriangularSetCategory}
+\index{RegularSetDecompositionPackage}
\index{Lazard, Daniel}
\begin{chunk}{axiom.bib}
@article{Laza91,
@@ 22938,11 +24127,12 @@ PrenticeHall. (1974)
year = "1991",
pages = "147160",
paper = "Laza91.pdf",
 algebra = "\newline\refto{category TSETCAT TriangularSetCategory}
 \newline\refto{category RSETCAT RegularTriangularSetCategory}
 \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
+ algebra =
+ "\newline\refto{category TSETCAT TriangularSetCategory}
+ \newline\refto{category RSETCAT RegularTriangularSetCategory}
+ \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
\newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
 \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
+ \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
abstract =
"A new algorithm is presented for solving algebraic systems of
equations, which is designed from the structure which is wanted for
@@ 23098,6 +24288,7 @@ The Benjamin/Cummings Publishing Company, Inc.Menlo Park, California, 1981.
\end{chunk}
+\index{DoubleFloatSpecialFunctions}
\index{L\"osch, Friedrich}
\begin{chunk}{axiom.bib}
@book{Losc60,
@@ 23117,6 +24308,7 @@ The Benjamin/Cummings Publishing Company, Inc.Menlo Park, California, 1981.
\end{chunk}
+\index{DoubleFloatSpecialFunctions}
\index{Luke, Yudell L.}
\begin{chunk}{axiom.bib}
@book{Luke69a,
@@ 23131,6 +24323,7 @@ The Benjamin/Cummings Publishing Company, Inc.Menlo Park, California, 1981.
\end{chunk}
+\index{DoubleFloatSpecialFunctions}
\index{Luke, Yudell L.}
\begin{chunk}{axiom.bib}
@book{Luke69b,
@@ 23212,6 +24405,11 @@ Mathematical Surveys. 3 Am. Math. Soc., Providence, RI. (1966)
\end{chunk}
+\index{TriangularSetCategory}
+\index{RegularTriangularSetCategory}
+\index{NormalizedTriangularSetCategory}
+\index{SquareFreeRegularTriangularSetCategory}
+\index{RegularSetDecompositionPackage}
\index{Maza, Marc Moreno}
\index{Rioboo, Renaud}
\begin{chunk}{axiom.bib}
@@ 23222,11 +24420,12 @@ Mathematical Surveys. 3 Am. Math. Soc., Providence, RI. (1966)
journal = "Proceedings of AAECC11",
keywords = "axiomref",
paper = "Maza95.pdf",
 algebra = "\newline\refto{category TSETCAT TriangularSetCategory}
 \newline\refto{category RSETCAT RegularTriangularSetCategory}
 \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
+ algebra =
+ "\newline\refto{category TSETCAT TriangularSetCategory}
+ \newline\refto{category RSETCAT RegularTriangularSetCategory}
+ \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
\newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
 \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
+ \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
abstract =
"Some methods for polynomial system solving require efficient
techniques for computing univariate polynomial gcd over algebraic
@@ 23242,6 +24441,11 @@ Mathematical Surveys. 3 Am. Math. Soc., Providence, RI. (1966)
\end{chunk}
+\index{TriangularSetCategory}
+\index{RegularTriangularSetCategory}
+\index{NormalizedTriangularSetCategory}
+\index{SquareFreeRegularTriangularSetCategory}
+\index{RegularSetDecompositionPackage}
\index{Maza, Marc Moreno}
\begin{chunk}{axiom.bib}
@phdthesis{Maza97,
@@ 23252,11 +24456,12 @@ Mathematical Surveys. 3 Am. Math. Soc., Providence, RI. (1966)
year = "1997",
paper = "Maza97.pdf",
keyword = "axiomref",
 algebra = "\newline\refto{category TSETCAT TriangularSetCategory}
 \newline\refto{category RSETCAT RegularTriangularSetCategory}
 \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
+ algebra =
+ "\newline\refto{category TSETCAT TriangularSetCategory}
+ \newline\refto{category RSETCAT RegularTriangularSetCategory}
+ \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
\newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
 \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
+ \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
url =
"http://www.csd.uwo.ca/~moreno//Publications/MorenoMazaThesis1997.ps.gz",
abstract =
@@ 23279,6 +24484,11 @@ Mathematical Surveys. 3 Am. Math. Soc., Providence, RI. (1966)
\end{chunk}
+\index{TriangularSetCategory}
+\index{RegularTriangularSetCategory}
+\index{NormalizedTriangularSetCategory}
+\index{SquareFreeRegularTriangularSetCategory}
+\index{RegularSetDecompositionPackage}
\index{Maza, Marc Moreno}
\begin{chunk}{axiom.bib}
@techreport{Maza98,
@@ 23286,11 +24496,12 @@ Mathematical Surveys. 3 Am. Math. Soc., Providence, RI. (1966)
title = "A new algorithm for computing triangular decomposition of
algebraic varieties",
institution = "Numerical Algorithms Group (NAG)",
 algebra = "\newline\refto{category TSETCAT TriangularSetCategory}
 \newline\refto{category RSETCAT RegularTriangularSetCategory}
 \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
+ algebra =
+ "\newline\refto{category TSETCAT TriangularSetCategory}
+ \newline\refto{category RSETCAT RegularTriangularSetCategory}
+ \newline\refto{category NTSCAT NormalizedTriangularSetCategory}
\newline\refto{category SFRTCAT SquareFreeRegularTriangularSetCategory}
 \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
+ \newline\refto{package RSDCMPK RegularSetDecompositionPackage}",
year = "1998"
}
@@ 23647,6 +24858,7 @@ Science of Computer Programming V25 No.1 Oct 1995 pp4161 Elesevier
\end{chunk}
+\index{DoubleFloatSpecialFunctions}
\index{Pearcey, T.}
\begin{chunk}{axiom.bib}
@book{Pear56,
@@ 24098,6 +25310,7 @@ November 1996.
\end{chunk}
+\index{DifferentialVariableCategory}
\index{Ritt, Joseph Fels}
\begin{chunk}{axiom.bib}
@article{Ritt50,
@@ 24123,6 +25336,13 @@ in Computational Discrete Mathematics ISBN 3540427759 pp119135
\end{chunk}
+\index{Guess}
+\index{GuessAlgebraicNumber}
+\index{GuessFinite}
+\index{GuessFiniteFunctions}
+\index{GuessInteger}
+\index{GuessPolynomial}
+\index{GuessUnivariatePolynomial}
\index{Rubey, Martin}
\begin{chunk}{axiom.bib}
@InProceedings{Rube06,
@@ 24135,13 +25355,14 @@ in Computational Discrete Mathematics ISBN 3540427759 pp119135
pages = "431434",
paper = "Rube06.pdf",
url = "http://mathinfo06.iecn.unancy.fr/papers/dmAG431434.pdf",
 algebra = "\newline\refto{package GUESS Guess}
 \newline\refto{package GUESSAN GuessAlgebraicNumber}
 \newline\refto{package GUESSF GuessFinite}
 \newline\refto{package GUESSF1 GuessFiniteFunctions}
 \newline\refto{package GUESSINT GuessInteger}
 \newline\refto{package GUESSP GuessPolynomial}
 \newline\refto{package GUESSUP GuessUnivariatePolynomial}",
+ algebra =
+ "\newline\refto{package GUESS Guess}
+ \newline\refto{package GUESSAN GuessAlgebraicNumber}
+ \newline\refto{package GUESSF GuessFinite}
+ \newline\refto{package GUESSF1 GuessFiniteFunctions}
+ \newline\refto{package GUESSINT GuessInteger}
+ \newline\refto{package GUESSP GuessPolynomial}
+ \newline\refto{package GUESSUP GuessUnivariatePolynomial}",
abstract =
"We present a software package that guesses formulas from sequences
of, for example, rational numbers or rational functions, given the
@@ 24178,6 +25399,7 @@ Num. Math. 16 205223. (1970)
\subsection{S} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\index{GradedModule}
\index{MacLane, Saunders}
\index{Birkhoff, Garrett}
\begin{chunk}{axiom.bib}
@@ 24191,6 +25413,7 @@ Num. Math. 16 205223. (1970)
\end{chunk}
+\index{NonAssociativeRng}
\index{Schafer, R.D.}
\begin{chunk}{axiom.bib}
@article{Scha61,
@@ 24219,6 +25442,9 @@ Num. Math. 16 205223. (1970)
\end{chunk}
+\index{NonAssociativeRng}
+\index{NonAssociativeRing}
+\index{AlgebraGivenByStructuralConstants}
\index{Schafer, R.D.}
\begin{chunk}{axiom.bib}
@book{Scha66,
@@ 24226,13 +25452,15 @@ Num. Math. 16 205223. (1970)
title = "An Introduction to Nonassociative Algebras",
year = "1966",
publisher = "Academic Press, New York",
 algebra = "\newline\refto{category NARNG NonAssociativeRng}
 \newline\refto{category NASRING NonAssociativeRing}
 \newline\refto{domain ALGSC AlgebraGivenByStructuralConstants}"
+ algebra =
+ "\newline\refto{category NARNG NonAssociativeRng}
+ \newline\refto{category NASRING NonAssociativeRing}
+ \newline\refto{domain ALGSC AlgebraGivenByStructuralConstants}"
}
\end{chunk}
+\index{NonAssociativeRng}
\index{Schafer, R.D.}
\begin{chunk}{axiom.bib}
@book{Scha10,
@@ 24394,6 +25622,7 @@ The University of Chicago Press. 1974
\end{chunk}
+\index{DoubleFloatSpecialFunctions}
\index{Steele, Guy L.}
\begin{chunk}{axiom.bib}
@book{Stee90,
@@ 24622,6 +25851,9 @@ SIAM Philadelphia. (1992)
\end{chunk}
+\index{GeneralPackageForAlgebraicFunctionField}
+\index{PackageForAlgebraicFunctionFieldOverFiniteField}
+\index{PackageForAlgebraicFunctionField}
\index{Vogler, Doctor}
\begin{chunk}{axiom.bib}
@misc{Vogl07,
@@ 24648,6 +25880,9 @@ Wiley. (1985)
\end{chunk}
+\index{GeneralPackageForAlgebraicFunctionField}
+\index{PackageForAlgebraicFunctionFieldOverFiniteField}
+\index{PackageForAlgebraicFunctionField}
\index{Walker, Robert J.}
\begin{chunk}{axiom.bib}
@book{Walk78,
diff git a/changelog b/changelog
index e175137..e7fa296 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,5 @@
+20160704 tpd src/axiomwebsite/patches.html 20160705.01.tpd.patch
+20160705 tpd books/bookvolbib Axiom Citations in the Literature
20160704 tpd src/axiomwebsite/patches.html 20160704.04.tpd.patch
20160704 tpd books/bookvolbib Axiom Citations in the Literature
20160704 tpd src/axiomwebsite/patches.html 20160704.03.tpd.patch
diff git a/patch b/patch
index d0fb360..f339a05 100644
 a/patch
+++ b/patch
@@ 2,33 +2,1342 @@ books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
\index{Kajler, Norbert}
+\index{Schwardmann, Ulrich}
\begin{chunk}{axiom.bib}
 author = "Kajler, Norbert",
 title = "CAS/PI: a Portable and Extensible Interface for Computer
 Algebra Systems",
 year = "1992",
 booktitle = "Proc. ISSAC 1992",
 series = "ISSAC 1992",
 pages = "376386",
 isbn = "0897914899 (soft cover) 0897914902 (hard cover)",
+@book{Schw95,
+ author = "Schwardmann, Ulrich",
+ title = "Computer algebra systems",
+ comment = "ComputeralgebraSysteme, German",
+ publisher = "AddisonWesley",
+ year = "1995",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Storme, L.}
+\index{van Maldeghem, H.}
+\begin{chunk}{axiom.bib}
+@article{Stor95,
+ author = "Storme, L. and van Maldeghem, H.",
+ title = "Cyclic caps in PG(3,q)",
+ journal = "Geom. Dedicata",
+ volume = "56",
+ number = "3",
+ pages = "271284",
+ year = "1995",
+ keywords = "axiomref",
+ url = "https://cage.ugent.be/~hvm/artikels/44.pdf",
+ paper = "Stor95.pdf",
+ abstract =
+ "A $k$cap $K$ on $PG(n,q)$ is a set of $k$ points, no three of which
+ are collinear. $K$ is complete if it cannot be extended to a $k+1$
+ cap. If $K$ is invariant under a cyclic subgroup (which acts regularly
+ on $K$) of $PGL(n+1,q)$, the $K$ is cyclic.
+
+ This article investigates cyclic complete $k$caps in
+ $PG(3,q). Namely, the different types of complete $k$caps $K$ in
+ $PG(3,q)$ stabilized by a cyclic projective group $G$ of order $k$,
+ acting regularly on the points of $K$, are determined. We show that in
+ $PG(3,q)$, $q$ even, the elliptic quadric is the only cyclic complete
+ $k$cap. For $q$ odd, it is shown that besides the elliptic quadric,
+ there also exist cyclic $k$caps containing $k/2$ points of two
+ disjoint elliptic quadrics or two disjoint hyperbolic quadrics and
+ that there exist cyclic $k$caps stabilized by a transitive cyclic
+ group $G$ fixed precisely one point and one plane of
+ $PG(3,q)$. Concrete examples of such caps, found using AXIOM and
+ CAYLEY, are presented."
+}
+
+\end{chunk}
+
+\index{Weber, Andreas}
+\begin{chunk}{axiom.bib}
+@article{Webe95,
+ author = "Weber, Andreas",
+ title = "On coherence in computer algebra",
+ journal = "J. Symb. Comput.",
+ volume = "19",
+ number = "13",
+ pages = "2538",
+ year = "1995",
+ url =
+"http://cg.cs.unibonn.de/personalpages/weber/publications/pdf/WeberA/Weber94e.pdf",
+ paper = "Webe95.pdf",
+ keywords = "axiomref",
+ abstract = "
+ Modern computer algebra systems (e.g. AXIOM) support a rich type
+ system including parameterized data types and the possibility of
+ implicit coercions between types. In such a type system it will be
+ frequently the case that there are different ways of building
+ coercions between types. An important requirement is that all
+ coercions between two types coincide, a property which is called {\sl
+ coherence}. We will prove a coherence theorem for a formal type system
+ having several possibilities of coercions covering many important
+ examples. Moreover, we will give some informal reasoning why the
+ formally defined restrictions can be satisfied by an actual system."
+}
+
+\end{chunk}
+
+\index{Williamson, Clifton J.}
+\begin{chunk}{axiom.bib}
+@InProceedings{Will95,
+ author = "Williamson, Clifton J.",
+ title = "On the algebraic construction of tridiagonal matrices with given
+ characteristic polynomial",
+ booktitle = "4th Conf. of Canadian Number Theory Association",
+ year = "1995",
+ location = "Halifax, Nova Scotia, Canada",
+ pages = "417431",
+ keywords = "axiomref",
+ paper = "Will95.pdf",
+ abstract =
+ "Let $K$ be a field of characteristic zero and assume
+ \[f(x)=x^ns_1x^{n1}+\cdots+s_n \in L[x]\]
+ where $L=K(s_1,\cdots,s_n)$. Call, for the purposes of this review, an
+ $n\times n$ matrix 1tridiagonal if its entries above and below the
+ main diagonal are all 1, the entries on it are $d_1,\cdots,d_n$, and
+ all other entries are 0. Under which conditions can
+ $d_1,d_2,\cdots,d_n$ be chosen in a radical extension of $L$ such that
+ the resulting 1tridiagonal matrix has $f$ as its characteristic
+ polynomial? The author’s answer: for $n=3$ always. The $d_i,s_i$
+ are related by a system of algebraic equations of the form
+ $\overline{f}_i(d_1,d_2,d_3)=s_i$. If this is satisfied, then by
+ a resultant or Groebner basis computation with respect to the
+ lexicographic order, $d_3$ (say) must be a root of a certain
+ irreducible polynomial $\varphi$ of degree 6. Joining this
+ with a Galois group computation for $\varphi$ over $L$, it is shown
+ that a solvable and necessarily transitive Gal($\varphi$) will be a
+ necessary and sufficient condition for expressibility of $d_3$ (clear)
+ and, thanks to the form of the Groebner basis, also of $d_1,d_2$ in
+ radicals. Upon a discriminant computation of $\varphi$ and use of
+ results of G. Butler and J. McKay [Commun. Algebra 11,
+ 863911 (1983; Zbl 0518.20003)] and J. McKay and L. Soicher [J. Number
+ Theory 20, 273281 (1985; Zbl 0579.12006)], this allows the author to
+ deduce the mentioned result. For $n=4$, though the author cannot get as
+ complete information about Galois groups etc., he can deduce e.g. that
+ if $s_1,\cdots,s_4$ are algebraically independent over $\mathbb{Q}$,
+ then $d_1,\cdots,d_4$ are not expressible in radicals over
+ $\mathbb{Q}(s_1,\cdots,s_4)$. He mentions, however, a solvable subcase."
+}
+
+\end{chunk}
+
+\index{Bosma, Wieb}
+\index{Cannon, John}
+\index{Matthews, Graham}
+\begin{chunk}{axiom.bib}
+@InProceedings{Bosm94,
+ author = "Bosma, Wieb and Cannon, John and Matthews, Graham",
+ title = "Programming with algebraic structures: Design of the Magma
+ language",
+ booktitle = "Proc. ISSAC 94",
+ series = "ISSAC 94",
+ year = "1994",
+ publisher = "ACM Press",
+ location = "Baltimore, MD",
+ pages = "5257",
+ keywords = "axiomref",
+ paper = "Bosm94.pdf",
+ url = "http://www.math.ru.nl/~bosma/pubs/ISSAC94.pdf",
+ abstract =
+ "MAGMA is a new software system for computational algebra, number
+ theory and geometry whose design is centred on the concept of
+ algebraic structure (magma). The use of algebraic structure as a
+ design paradigm provides a natural strong typing mechanism. Further,
+ structures and their morphisms appear in the language as first class
+ objects. Standard mathematical notions are used for the basic data
+ types. The result is a powerful, clean language which deals with
+ objects in a mathematically rigorous manner. The conceptual and
+ implementation ideas behind MAGMA will be examined in this paper. This
+ conceptual base differs significantly from those underlying other
+ computer algebra systems."
+}
+
+\end{chunk}
+
+\index{Dingle, Adam}
+\index{Fateman, Richard J.}
+\begin{chunk}{axiom.bib}
+@InProceedings{Ding94,
+ author = "Dingle, Adam and Fateman, Richard",
+ title = "Branch Cuts in Computer Algebra",
+ year = "1994",
+ booktitle = "Proc. ISSAC 1994",
+ series = "ISSAC 94",
+ url = "http://www.cs.berkeley.edu/~fateman/papers/ding.ps",
+ paper = "Ding94.pdf",
+ keywords = "axiomref",
+ abstract =
+ "Many standard functions, such as the logarithms and square root
+ functions, cannot be defined continuously on the complex
+ plane. Mistaken assumptions about the properties of these functions
+ lead computer algebra systems into various conundrums. We discuss how
+ they can manipulate such functions in a useful fashion."
+}
+
+\end{chunk}
+
+\index{Duval, Dominique}
+\index{Senechaud, Pascale}
+\begin{chunk}{axiom.bib}
+@article{Duva94d,
+ author = "Duval, Dominique and Senechaud, Pascale",
+ title = "Sketches and parametrization",
+ journal = "Theor. Comput. Sci.",
+ volume = "123",
+ number = "1",
+ pages = "117130",
+ year = "1994",
+ keywords = "axiomref",
+ abstract =
+ "The paper deals with problems about conception and design of
+ highlevel computer algebra systems. Here we use a categorical
+ approach given by the notion of sketches. Sketches allow to describe
+ computation mechanisms in a syntactic way, well adapted to
+ implementation.
+
+ A computer algebra system must allow the manipulation of algebraic
+ structures, in particular, the construction of new structures from
+ known ones. In the paper we give a definition, at the sketch level, of
+ parametrization of a structure by another one."
+}
+
+\end{chunk}
+
+\index{Duval, Dominique}
+\begin{chunk}{axiom.bib}
+@misc{Duva94e,
+ author = "Duval, Dominique",
+ title = "Symbolic or algebraic computation?",
+ booktitle = "Publication du LACO",
+ year = "1995",
+ location = "Madrid Spain",
+ comment = "NAG conference",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Duval, Dominique}
+\index{Reynaud, J.C.}
+\begin{chunk}{axiom.bib}
+@article{Duva94a,
+ author = "Duval, D. and Reynaud, J.C.",
+ title = "Sketches and Computation (Part I):
+ Basic Definitions and Static Evaluation",
+ journal = "Mathematical Structures in Computer Science",
+ volume = "4",
+ pages = "185238",
+ publisher = "Cambridge University Press",
+ year = "1994",
+ url = "http://journals.cambridge.org/abstract_S0960129500000438",
+ paper = "Duva94a.pdf",
+ abstract =
+ "We define a categorical framework, based on the notion of {\sl
+ sketch}, for specification and evaluation in the sense of algebraic
+ specifications and algebraic programming. This framework goes far
+ beyond our initial motivations, which was to specify computation with
+ algebraic numbers. We begin by redefining sketches in order to deal
+ explicitly with programs. Expressions and terms are carefully defined
+ and studied, then {\sl quasiprojective sketches} are introduced. We
+ describe {\sl static evaluation} in these sketches: we propose a
+ rigorous basis for evaluation in the corresponding structures. These
+ structures admit an initial model, but are not necessarily
+ equational. In Part II (Duval and Reynaud 1994), we study a more
+ general process, called {\sl dynamic evaluation}, for structures that
+ may have no initial model."
+}
+
+\end{chunk}
+
+\index{Duval, Dominique}
+\index{Reynaud, JeanClaude}
+\begin{chunk}{axiom.bib}
+@article{Duva94b,
+ author = "Duval, Dominique and Reynaud, JeanClaude",
+ title = "Sketches and Computation (Part II):
+ Dynamic Evaluation and Applications",
+ journal = "Mathematical Structures in Computer Science",
+ volume = "4",
+ pages = "239271",
+ publisher = "Cambridge University Press",
+ year = "1994",
+ url = "http://journals.cambridge.org/abstract_S096012950000044X",
+ paper = "Duva94b.pdf",
+ abstract =
+ "In the first part of this paper (Duval and Reynaud 1994), we defined a
+ categorical framework, based on the notion of {\sl sketch}, for
+ specification and evaluation in the senses of algebraic specification
+ and algebraic programming. {\sl Static evaluation} in {\sl
+ quasiprojective sketches} was defined in Part I; in this paper, {\sl
+ dynamic evaluation} is introduced. It deals with more general
+ structures, which may have no initial model. Until now, this process
+ has not been used in algebraic specification systems, but computer
+ algebra systems are beginning to use it as a basic tool. Finally, we
+ give some applications of dynamic evaluation to computation in field
+ extensions."
+}
+
+\end{chunk}
+
+\index{Duval, Dominique}
+\begin{chunk}{axiom.bib}
+@article{Duva94c,
+ author = "Duval, Dominique",
+ title = "Algebraic Numbers: An Example of Dynamic Evaluation",
+ journal = "J. Symbolic Computation",
+ volume = "18",
+ pages = "429445",
+ year = "1994",
+ url = "http://www.sciencedirect.com/science/article/pii/S0747717106000551",
+ paper = "Duva94c.pdf",
+ keywords = "axiomref",
+ abstract = "
+ Dynamic evaluation is presented through examples: computations
+ involving algebraic numbers, automatic case discussion according to
+ the characteristic of a field. Implementation questions are addressed
+ too. Finally, branches are presented as ``dual'' to binary functions,
+ according to the approach of sketch theory."
+}
+
+\end{chunk}
+
+\index{Duval, Dominique}
+\index{Reynaud, JeanClaude}
+\begin{chunk}{axiom.bib}
+@article{Duva96,
+ author = "Duval, D. and Reynaud, JeanClaude",
+ title = "Sketches and Computations over Fields",
+ journal = "Mathematics and Computers in Simulation",
+ volume = "42",
+ pages = "363373",
+ year = "1996",
+ paper = "Duva96.pdf",
+ abstract =
+ "The goal of this short paper is to describe one possible use of
+ sketches in computer algebra. We show that sketches are a powerful
+ tool for the description of mathematical structures and for the
+ description of computations."
+}
+
+\end{chunk}
+
+\index{Duval, Dominique}
+\index{Gonz\'alezVega, L.}
+\begin{chunk}{axiom.bib}
+@article{Duva96a,
+ author = {Duval, Dominique and Gonz\'alezVega, L.},
+ title = "Dynamic Evaluation and Real Closure",
+ journal = "Mathematics and Computers in Simulation",
+ volume = "42",
+ pages = "551560",
+ year = "1996",
+ paper = "Duva96a.pdf",
+ abstract = "
+ The aim of this paper is to present how the dynamic evaluation method
+ can be used to deal with the real closure of an ordered field. Two
+ kinds of questions, or tests, may be asked in an ordered field:
+ equality tests $(a=b?)$ and sign tests $(a > b?)$. Equality tests are
+ handled through splittings, exactly as in the algebraic closure of a
+ field. Sign tests are handled throug a structure called ``Tarski data
+ type''."
+}
+
+\end{chunk}
+
+\index{Fritzson, D.}
+\index{Fritzson, P.}
+\index{Viklund, L.}
+\index{Herber, J.}
+\begin{chunk}{axiom.bib}
+@article{Frit94,
+ author = "Fritzson, D. and Fritzson, P. and Viklund, L. and Herber, J.",
+ title = "Objectoriented mathematical modelling  applied to machine
+ elements",
+ journal = "Comput. Struct.",
+ volume = "51",
+ number = "3",
+ pages = "241253",
+ year = "1994",
+ keywords = "axiomref",
+ paper = "Frit94.pdf",
+ abstract =
+ "Machine element analysis has a goal of describing function and other
+ aspects of machine elements in a theoretical form. This paper shows
+ how ideas from objectoriented modelling can be applied to machine
+ elment analysis. The models thus obtained are both easier to
+ understand, better structured, and allow a higher degree of reuse
+ than conventional models. An objectoriented model description is
+ natural and suitable for machine element analysis. As a realistic
+ example an equational model of rolling bearings is presented. The
+ structure of the model is general, and applies to many types of
+ rolling bearings. The model and one solution require approximately
+ 200+200 equations. The model is extensible, e.g. simple submodels of
+ detailed properties can be made more complex without altering the
+ overall structure. The example model has been implemented in a
+ language of our own design. ObjectMath (Objectoriented Mathematical
+ language for scientific computing). Using ObjectMath, it is possible
+ to model classes of equation objects, to support multiple and single
+ inheritance of equations, to support composition of equations, and to
+ solve systems of equations. Algebraic transformations can conveniently
+ be done since ObjectMath models are translated into the Mathematica
+ computer algebra language. When necessary, equations can be
+ transformed int C++ code for efficient numerical solution. The reuse
+ of equations through inheritance reduced the size of the model by a
+ factor of two, compared to a direct representation of the model in the
+ Mathematica computer algebra language."
+}
+
+\end{chunk}
+
+\index{Ioakimidis, N.I.}
+\begin{chunk}{axiom.bib}
+@article{Ioak94,
+ author = "Ioakimidis, N.I.",
+ title = "Symbolic computations for the solution of inverse/design
+ problems with Maple",
+ journal = "Comput. Struct.",
+ volume = "53",
+ number = "1",
+ pages = "6368",
+ year = "1994",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\index{Trager, Barry M.}
+\begin{chunk}{axiom.bib}
+@InProceedings{Jenk94,
+ author = "Jenks, Richard D. and Trager, Barry M.",
+ title = "How to make AXIOM into a scratchpad",
+ booktitle = "Proceedings of the ACMSIGSAM 1989 International
+ Symposium on Symbolic and Algebraic Computation, ISSAC '94",
+ series = "ISSAC 94",
+ year = "1994",
+ pages = "3240",
+ isbn = "0897916387",
+ keywords = "axiomref",
+ publisher = "ACM Press",
+ address = "New York, NY, USA",
+ paper = "Jenk94.pdf",
+ abstract =
+ "Scratchpad [GrJe71] was a computer algebra system developed in the
+ early 1970s. Like M\&M (Maple [CGG91ab] and Mathematical [W01S92]) and
+ other systems today, Scratchpad had one principal representation for
+ mathematical formulae based on ``expression trees''. Its user interface
+ design was based on a patternmatching paradigm with infinite rewrite
+ rule semantics, providing what we believe to be the most natural
+ paradigm for interactive symbolic problem solving. Like M\&M, however,
+ user programs were interpreted, often resulting in poor performance
+ relative to similar facilities coded in standard programming languages
+ such as FORTRAN and C.
+
+ Scratchpad development stopped in 1976 giving way to a new system
+ design ([JenR79], [JeTr81]) that evolved into AXIOM [JeSu92].
+ AXIOM has a stronglytyped programming language for building a library
+ of parameterized types and algorithms, and a typeinferencing
+ interpreter that accesses the library and can build any of an infinite
+ number of types for interactive use.
+
+ We suggest that the addition of an expression tree type to AXIOM can
+ allow users to operate with the same freedom and convenience of
+ untyped systems without giving up the expressive power and runtime
+ efficiency provided by the type system. We also present a design that
+ supports a multiplicity of programming styles, from the Scratchpad
+ patternmatching paradigm to functional programming to more
+ conventional procedural programming. The resulting design seems to us
+ to combine the best features of Scratchpad with current AXIOM and to
+ offer a most attractive, flexible, and userfriendly environment for
+ interactive problem solving.
+
+ Section 2 is a discussion of design issues contrasting AXIOM with
+ other symbolic systems. Sections 3 and 4 is an assessment of AXIOM’s
+ current design for building libraries and interactive use. Section 5
+ describes a new interface design for AXIOM, its resulting paradigms,
+ and its underlying semantic model. Section 6 compares this work with
+ others."
+}
+
+\end{chunk}
+
+\index{Bernard, Joey}
+\begin{chunk}{axiom.bib}
+@misc{Bern14,
+ author = "Bernard, Joey",
+ title = "Open Axiom",
+ url = "http://www.linuxjournal.com/content/openaxiom",
+ keywords = "axiomref",
+ year = "2014"
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
+\index{Trager, Barry M.}
+\begin{chunk}{axiom.bib}
+@InProceedings{Dave90,
+ author = "Davenport, James H. and Trager, Barry M.",
+ title = "Scratchpad's view of algebra I: Basic commutative algebra",
+ booktitle = "Design and Implementation of Symbolic Computation Systems",
+ year = "1990",
+ series = "DISCO '90",
+ location = "Capri, Italy",
+ publisher = "SpringerVerlag",
+ isbn = "0387525319",
+ keywords = "axiomref",
+ url = "http://opus.bath.ac.uk/32336/1/Davenport\_DISCO\_1990.pdf",
+ paper = "Dave90.pdf",
+ comment = "AXIOM Technical Report, ATR/1, NAG Ltd., Oxford, 1992",
+ keywords = "axiomref",
+ abstract =
+ "While computer algebra systems have dealt with polynomials and
+ rational functions with integer coefficients for many years, dealing
+ with more general constructs from commutative algebra is a more recent
+ problem. In this paper we explain how one system solves this problem,
+ what types and operators it is necessary to introduce and, in short,
+ how one can construct a computational theory of commutative
+ algebra. Of necessity, such a theory is rather different from the
+ conventional, nonconstructive, theory. It is also somewhat different
+ from the theories of Seidenberg [1974] and his school, who are not
+ particularly concerned with practical questions of efficiency."
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\index{Trager, Barry M.}
+\begin{chunk}{axiom.bib}
+@article{Jenk81,
+ author = "Jenks, Richard D. and Trager, Barry M.",
+ title = "A Language for Computational Algebra",
+ year = "1981",
+ booktitle = "Proc. Symp. on Symbolic and Algebraic Manipulation",
+ series = "SYMSAC 1981",
+ location = "Snowbird, Utah",
+ keywords = "axiomref",
+ comment = "IBM Research Report 8930",
+ abstract =
+ "This paper reports ongoing research at the IBM Research Center on the
+ development of a language with extensible parameterized types and
+ generic operators for computational algebra. The language provides an
+ abstract data type mechanism for defining algorithms which work in as
+ general a setting as possible. The language is based on the notions of
+ domains and categories. Domains represent algebraic
+ structures. Categories designate collections of domains having common
+ operations with stated mathematical properties. Domains and categories
+ are computed objects which may be dynamically assigned to variables,
+ passed as arguments, and returned by functions. Although the language
+ has been carefully tailored for the application of algebraic
+ computation, it actually provides a very general abstract data type
+ mechanism. Our notion of a category to group domains with common
+ properties appears novel among programming languages (cf. image
+ functor of RUSSELL) and leads to a very powerful notion of abstract
+ algorithms missing from other work on data types known to the authors."
+}
+
+\end{chunk}
+
+\index{Kapur, D.}
+\index{Musser, D.R.}
+\index{Stepanov, A.A.}
+\begin{chunk}{axiom.bib}
+@misc{Kapu81,
+ author = "Kapur, D. and Musser, D.R. and Stepanov, A.A.",
+ title = "Operators and Algebraic Structures",
+ url = "http://www.stepanovpapers.com/p59kapur.pdf",
+ paper = "Kapu81.pdf",
+ year = "1981",
+ abstract =
+ "Operators in functional languages such as APL and FFP are a useful
+ programming concept. However, this concept cannot be ful ly
+ exploited in these languages because of certain constraints. It is
+ proposed that an operator should be associated with a structure hav
+ ing the algebraic properties on which the operator's behavior depends.
+ This is illustrated by introducing a language that provides mechanisms
+ for defining structures and operators on them. Using this language,
+ it is possible to describe algorithms abstractly, thus empliasizing
+ the algebraic properties on which the algorithms depend. The role
+ that formal representation of mathematical knowledge can play in the
+ development of programs is illustrated through an example. An
+ approach for associating complexity mea sures with a structure and
+ operators is also suggested. This ap proach is useful in analyzing
+ the complexity of algorithms in an abstract setting."
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\index{Sutor, Robert S.}
+\index{Watt, Stephen M.}
+\begin{chunk}{axiom.bib}
+@techreport{Jenk86,
+ author = "Jenks, Richard D. and Sutor, Robert S. and Watt, Stephen M.",
+ title = "Scratchpad II: An Abstract Datatype System for Mathematical
+ Computation",
+ institution = "IBM Research",
+ year = "1986",
+ type = "Research Report",
+ number = "RC 12327 (\#55257)",
+ url = "http://www.csd.uwo.ca/~watt/pub/reprints/1987imaspadadt.pdf",
+ paper = "Jenk86.pdf",
+ keywords = "axiomref",
+ abstract = "
+ Scratchpad II is an abstract datatype language and system that is
+ under development in the Computer Algebra Group, Mathematical Sciences
+ Department, at the IBM Thomas J. Watson Research Center. Some features
+ of APL that made computation particularly elegant have been borrowed.
+ Many different kinds of computational objects and data structures are
+ provided. Facilities for computation include symbolic integration,
+ differentiation, factorization, solution of equations and linear
+ algebra. Code economy and modularity is achieved by having
+ polymorphic packages of functions that may create datatypes. The use
+ of categories makes these facilities as general as possible."
+}
+
+\end{chunk}
+
+\index{Lloyd, Michael}
+\index{Oancea, Cosmin}
+\index{Watt, Stephen}
+\begin{chunk}{axiom.bib}
+@misc{Chic04,
+ author = "Chicha, Yannis and Lloyd, Michael Oancea, Cosmin",
+ title = "Parametric Polymorphism for Computer Algebra Software Components",
+ booktitle = "6th Int. Symp. on Symbolic and Numeric Algorithms for
+ Scientific Computing",
+ series = "SYNASC 04",
+ location = "Imisoara, Romania",
+ keywords = "axiomref",
+ year = "2004",
+ paper = "Chic04.pdf",
+ url = "http://www.csd.uwo.ca/~watt/pub/reprints/2004synascppca.pdf",
+ abstract =
+ "This paper presents our experiments in providing mechanisms for
+ parametric polymorphism for computer algebra software components.
+ Specific interfaces between Aldor and C++ and between Aldor and Maple
+ are described. We then present a general solution, Generic IDL (GIDL),
+ an extension to CORBA IDL supporting generic types. We describe our
+ language bindings for C++, Java 1.5 and Aldor as well as aspects of
+ our implementation, consisting of a GIDL to IDL compiler and tools for
+ generating interface code for the various language bindings."
+}
+
+\end{chunk}
+
+\index{Watt, Stephen}
+\begin{chunk}{axiom.bib}
+@InProceedings{Watt07,
+ author = "Watt, Stephen",
+ title = "What Happened to Languages for Symolic Mathematical Computation?",
+ booktitle = "Proc. Prog. Lang. for Mechanized Mathematics",
+ series = "PLMMS 07",
+ year = "2007",
+ location = "RISCLinz, Austria",
+ pages = "8190",
+ keywords = "axiomref",
+ paper = "Watt07.pdf",
+ url =
+ "http://www.csd.uwo.ca/~watt/pub/reprints/2007plmmswhat\_happened.pdf",
+ abstract =
+ "While the state of the art is relatively sophisticated in programming
+ language support for computer algebra, there has been less development
+ in programming language support for symbolic computation over the past
+ two decades. We summarize certain advances in programming languages
+ for computer algebra and propose a set of directions and challenges
+ for programming languages for symbolic computation."
+}
+
+\end{chunk}
+
+\index{Santas, Philip S.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Sant96,
+ author = "Santas, Philip S.",
+ title = "Conditional Categories and Domains",
+ keywords = "axiomref",
+ booktitle = "Proc. DISCO 1996",
+ year = "1996",
+ pages = "112125",
+ isbn = "3540616977"
+}
+
+\end{chunk}
+
+
+\index{Santas, Philip S.}
+\begin{chunk}{axiom.bib}
+@book{Sant05,
+ author = "Santas, Philip S.",
+ title = "Conditional Categories and Domains",
+ keywords = "axiomref",
+ booktitle = "Design and Implementation of Symbolic Computation Systems",
+ year = "2005",
+ series = "Lecture Notes in Computer Science",
+ volume = "1128",
+ publisher = "Springer",
+ abstract =
+ "We extend the Type system defined in [Sant95] with Axiomlike
+ Conditional Categories with the additional property of Static Typing
+ and Checking. Categories and Domains may contain conditionals in their
+ bodies, which are elaborated by our compiler by techniques used in
+ standard typing. We define an appropriate calculus and discuss its
+ properties. Examples inspired by the Axiom library illustrate the
+ power of our apprach and its application in constructing algebraic
+ concepts. The full calculus has been implemented and tested with our
+ LA compiler which generated executable files."
+}
+
+\end{chunk}
+
+\begin{chunk}{axiom.bib}
+@misc{Gute16,
+ author = "Gutenberg SelfPublishing Press",
+ title = "OpenAxiom",
+ keywords = "axiomref",
+ url = "http://self.gutenberg.org/articles/openaxiom",
+ year = "2016"
+}
+
+\end{chunk}
+
+\index{Baker, Martin}
+\begin{chunk}{axiom.bib}
+@misc{Bake16,
+ author = "Baker, Martin",
+ title = "Axiom Maths Program",
+ keywords = "axiomref",
+ year = "2016",
+ url = "http://www.euclideanspace.com/prog/scratchpad/axiom/index.htm"
+}
+
+\end{chunk}
+
+\index{Caviness, Bob}
+\index{Trager, Barry}
+\index{Gianni, Patrizia}
+\begin{chunk}{axiom.bib}
+@misc{Cavi03,
+ author = "Caviness, Bob and Trager, Barry and Gianni, Patrizia",
+ title = "Dedicated to the Memory of Richard Dimick Jenks",
+ year = "2003",
+ url = "https://www.eecis.udel.edu/~caviness/jenks/issacded.pdf",
+ keywords = "axiomref",
+ paper = "Cavi03.pdf",
+ abstract =
+ "On December 30, 2003, Dick Jenks died at the age of 66, after an
+ extended and courageous battle with multiple system atrophy.
+
+ He received his PhD in mathematics from the University of Illinois at
+ UrbanaChampaign in 1966. The title of his dissertation was
+ “Quadratic Differential Systems for Mathematical Models” and was
+ written under the supervision of Donald Gilles. After completing his
+ PhD, he was a postdoctoral fellow at Brookhaven National Laboratory
+ on Long Island. In 1968 he joined IBM Research where he worked until
+ his retirement in 2002.
+
+ At IBM he was one of the principal architects of the Scratchpad
+ system, one of the earliest computer algebra systems(1971). Dick
+ always believed that natural user interfaces were essential and
+ developed a userfriendly rulebased system for Scratchpad. Although
+ this rulebased approach was easy to use, as algorithms for computer
+ algebra became more complicated, he began to understand that an
+ abstract data type approach would give sophisticated algorithm
+ development considerably more leverage. In 1977 he began the Axiom
+ development (originally called Scratchpad II) with the design of
+ MODLISP, a merger of Lisp with types (modes). In 1980, with the help
+ of many others, he completed an initial prototype design based on
+ categories and domains that were intended to be natural for
+ mathematically sophisticated users.
+
+ During this period many researchers in computer algebra visited IBM
+ Research in Yorktown Heights and contributed to the development of
+ the Axiom system. All this activity made the computer algebra group at
+ IBM one of the leading centers for research in this area and Dick was
+ always there to organize the visits and provide a stimulating and
+ pleasant working environment for everyone. He had a good perspective
+ on the most important research directions and worked to attract
+ worldrenowned experts to visit and interact with his group. He was an
+ ideal manager for whom to work, one who always put the project and the
+ needs of the group members first. It was a joy to work in such a
+ vibrant and stimulating environment.
+
+ After many years of development, a decision was made to rename
+ Scratch pad II to Axiom and to release it as a product. Dick and
+ Robert Sutor were the primary authors of the book {\sl Axiom: The
+ Scientific Computation System}. In the foreword of the book, written
+ by David and Gregory Chudnovsky, it is stated that ``The Scratchpad
+ system took its time to blossom into the beautiful Axiom
+ product. There is no rival to this powerful environment in its scope
+ and, most importantly, in its structure and organization.'' Axiom was
+ recently made available as free software. See
+ http://savannah.nongnu.org/projects/axiom
+
+ Dick was active in service to the computer algebra community as
+ well. Here are some highlights. He served as Chair of ACM SIGSAM
+ (197981) and Conference Cochair (with J. A. van Hulzen) of EUROSAM
+ ’84, a precursor of the ISSAC meetings. Dick also had a long period of
+ service on the editorial board of the {\sl Journal of Symbolic
+ Computation}. At ISSAC ’95 in Montreal, Dick was elected to the
+ initial ISSAC Steering Committee and was elected as the second Chair
+ of the Committee in 1997. He, along with David Chudnovsky, organized
+ the highly successful meetings on Computers and Mathematics that were
+ held at Stanford in 1986 and MIT in 1989. As a legacy of those
+ meetings, the Jenks Prize for outstanding contributions to software
+ engineering in computer algebra has been established.
+
+ Dick had many interests outside of his professional pursuits including
+ reading, travel, physical fitness, and especially music. Dick was an
+ accomplished pianist, organist, and vocalist. At one point he was the
+ organist and choir master of the Church of the Holy Communion in
+ Mahopac, NY. In the 1980s and 1990s, he sang in choral groups under
+ the direction of Dr. Dennis Keene that performed at Lincoln Center in
+ New York city.
+
+ Personally, Dick was warm, generous, and outgoing with many
+ friends. He will be missed for his technical accomplishments, his
+ artist talents, and most of all for his positive, gentle, charming
+ spirit."
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@article{Dave81,
+ author = "Davenport, James H. and Jenks, Richard D.",
+ title = "MODLISP",
+ year = "1981",
+ journal = "ACM SIGSAM Bulletin",
+ volume = "15",
+ issue = "1",
+ pages = "1120",
+ publisher = "ACM",
+ keywords = "axiomref",
+ abstract =
+ "This paper discusses the design and implementation of MODLISP, a
+ LISPlike language enhanced with the idea of MODes. This extension
+ permits, but does not require, the user to declare the types of
+ various variables, and to compile functions with the arguments
+ declared to be of a particular type. It is possible to declare several
+ functions of the same name, with arguments of different type
+ (e.g. PLUS could be declared for Integer arguments, or Rational, or
+ Real, or even Polynomial arguments) and the system will apply the
+ correct function for the types of the arguments."
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Jenk79,
+ author = "Jenks, Richard D.",
+ title = "MODLISP: An Introduction",
+ booktitle = "Proc. ISSAC 1979",
+ series = "EUROSAM 79",
+ pages = "466480",
+ year = "1979",
+ publisher = "SpringerVerlag",
+ isbn = "3540095195",
+ comment = "IBM Research Report RC 8073 Jan 1980",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@techreport{Dave80,
+ author = "Davenport, James H. and Jenks, Richard D.",
+ title = "MODLISP: A Preliminary Design",
+ institution = "IBM Research",
+ type = "Research Report",
+ year = "1980",
+ number = "RC 8073",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@techreport{Dave80,
+ author = "Davenport, James H. and Jenks, Richard D.",
+ title = "MODLISP",
+ institution = "IBM Research",
+ type = "Research Report",
+ year = "1980",
+ number = "RC 8537 (\#37198)",
+ keywords = "axiomref",
+ comment = "http://www.computerhistory.org/collections/catalog/102719109"
+}
+
+\end{chunk}
+
+\index{Hoeven, Joris van der}
+\index{Lecerf, Gregoire}
+\begin{chunk}{axiom.bib}
+@misc{Hoev15,
+ author = "Hoeven, Joris van der and Lecerf, Gregoire",
+ title = "Interfacing Mathemagix with C++",
+ keywords = "axiomref",
+ url = "http://www.texmacs.org/joris/mmxcpp/mmxcpp.html",
+ abstract =
+ "In this paper, we give a detailed description of the interface
+ between the Mathemagix language and C++. In particular, we describe
+ the mechanism which allows us to import a C++ template library
+ (which only permits static instantiation) as a fully generic
+ Mathemagix template library."
+}
+
+\end{chunk}
+
+\index{Fortenbacher, A.}
+\index{Jenks, Richard}
+\index{Lucks, Michael}
+\index{Sutor, Robert}
+\index{Trager, Barry}
+\index{Watt, Stephen}
+\begin{chunk}{axiom.bib}
+@techreport{Fort85,
+ author = "Fortenbacher, A. and Jenks, Richard and Lucks, Michael and
+ Sutor, Robert and Trager, Barry and Watt, Stephen",
+ title = "An Overview of the Scratchpad II Language and System",
+ year = "1985",
+ type = "Research Report",
+ publisher = "IBM Research Computer Algebra Group",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\begin{chunk}{axiom.bib}
+@misc{Maxi16,
+ author = "Maxima",
+ title = "Other Free Computer Algebra Systems",
+ url = "http://maxima.sourceforge.net/compalg.html",
+ year = "2016",
+ keywords = "axiomref",
+ abstract =
+ “Axiom is a general purpose Computer Algebra system. It is useful for
+ doing mathematics by computer and for research and development of
+ mathematical algorithms. It defines a strongly typed, mathematically
+ correct type hierarchy. It has a programming language and a builtin
+ compiler.
+
+ There is also an interesting Rosetta Stone which offers translations
+ of many basic operations for several computer algebra systems,
+ including Maxima."
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Jenk84b,
+ author = "Jenks, Richard D.",
+ title = "A primer: 11 keys to New Scratchpad",
+ booktitle = "Proc. EUROSAM ISSAC 1984",
+ year = "1984",
+ publisher = "SpringerVerlag",
+ pages = "123147",
+ isbn = "038713350X",
+ keywords = "axiomref",
+ abstract =
+ "This paper is an abbreviated primer for the language of new
+ SCRATCHPAD, a new implementation of SCRATCHPAD which has been under
+ design and development by the Computer Algebra Group at the IBM
+ Research Center during the past 6 years. The basic design goals of the
+ new SCRATCHPAD language and interface to the user are to provde:
+ \begin{itemize}
+ \item a ``typeless'' interactive language suitable for online solution
+ of mathematical problems by novice users with little or no programming
+ required, and
+ \item a programming language suitable for the formal description of
+ algorithms and algebraic structures which can be compiled into runtime
+ efficient object code.
+ \end{itemize}
+
+ The new SCRATCHPAD language is introduced by 11 keys with each
+ successive key introducing an additional capability of the
+ language. The language is thus described as a ``concentric'' language
+ with each of the 11 levels corresponding to a language subset. These
+ levels are more than just a pedagogic device, since they correspond to
+ levels at which the system can be effectively used. Level 1 is
+ sufficient for naive interactive use; levels 28 progressively
+ introduce interactive users to capabilities of the language; levels
+ 911 are for system programmers and advanced users. Levesl 2, 4, 6,
+ and 7 give users the full power of LISP with a highlevel language;
+ level 8 introduces ``type declarations;'' level 9 allows polymorphic
+ functions to be defined and compiled; levels 1011 give users an
+ Adalike facility for defining types and packages (those of new
+ SCRATCHPAD are dynamically constructable, however). One language is
+ used for both interactive and system programming language use,
+ although several freedomes such as abbreviation and optional
+ typedeclarations allowed at toplevel are not permitted in system
+ code. The interactive language (levels 18) is a blend of original
+ SCRATCHPAD [GRJY75], some proposed extensions [JENK74], work by Loos
+ [LOOS74], SETL [DEWA79], SMP [COWO81], and new ideas; the system
+ programming language (levels 111) superficially resembles Ada but is
+ more similar to CLU [LISK74] in its semantic design.
+
+ This presentation of the language in this paper omits many details to
+ be covered in the SCRATCHPAD System Programming Manual [SCRA84] and an
+ expanded version of this paper will serve as a primer for SCRATCHPAD
+ users [JESU84]."
+}
+
+\end{chunk}
+
+\index{Griesmer, James H.}
+\index{Jenks, Richard D.}
+\index{Yun, David Y.Y}
+\begin{chunk}{axiom.bib}
+@techreport{Grie75,
+ author = "Griesmer, James H. and Jenks, Richard D. and Yun, David Y.Y",
+ title = "SCRATCHPAD User's Manual",
+ year = "1975",
+ type = "Research Report",
+ number = "RA70",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@article{Jenk74,
+ author = "Jenks, Richard D.",
+ title = "The SCRATCHPAD language",
+ journal = "ACM SIGPLAN Notices",
+ comment = "reprinted in SIGSAM Bulletin, Vol 8, No. 2, May 1974",
+ volume = "9",
+ number = "4",
+ pages = "101111",
+ year = "1974",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\index{Sundaresan, Christine J.}
+\begin{chunk}{axiom.bib}
+@misc{Jenk84c,
+ author = "Jenks, Richard D. and Sundaresan, Christine J.",
+ title = "The 11 Keys to SCRATCHPAD: A Primer",
+ year = "1984",
+ keywords = "axiomref"
+}
+
+\index{Davenport, James H.}
+\index{Gianni, Patrizia}
+\index{Jenks, Ricard D.}
+\index{Miller, Victor}
+\index{Morrison, Scott}
+\index{Rothstein, Michael}
+\index{Sundaresan, Christine J.}
+\index{Sutor, Robert S.}
+\index{Trager, Barry M.}
+\begin{chunk}{axiom.bib}
+@misc{Dave84b,
+ author = "Davenport, James H. and Gianni, Patrizia and Jenks, Ricard D. and
+ Miller, Victor and Morrison, Scott and Rothstein, Michael and
+ Sundaresan, Christine J. and Sutor, Robert S. and Trager, Barry",
+ title = "SCRATCHPAD System Programming Language Manual",
+ year = "1984",
+ keywords = "axiomref",
+}
+
+\end{chunk}
+
+\index{Constable, Robert L.}
+\index{Jackson, Paul B.}
+\begin{chunk}{axiom.bib}
+@misc{Cons98,
+ author = "Constable, Robert L. and Jackson, Paul B.",
+ title = "Towards Integrated Systems for Symbolic Algebra and Formal
+ Constructive Mathematics",
+ url = "http://www.nuprl.org/documents/Constable/towardsintegrated.pdf",
+ paper = "Cons98.pdf",
+ year = "1998",
+ abstract =
+ "The purpose of this paper is to report on our efforts to give e a
+ formal account of some of the algebra used in Computer Algebra Systems
+ (CAS). In particular, we look at the concepts used in the so called
+ 3rd generation algebra systems, such as Axiom[4] and Weyl[9]. It is
+ our claim that the Nuprl proof development system is especially well
+ suited to support this kind of mathematics."
+}
+
+\end{chunk}
+
+\begin{chunk}{axiom.bib}
+@misc{Acad16,
+ author = "Academic Search",
+ title = "A Primer: 11 Keys to New Scratchpad",
+ url =
+ "http://libra.msra.cn/publication/645035/aprimer11keystonewscratchpad",
+ year = "2016",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@misc{Jenk86a,
+ author = "Jenks, Richard D.",
+ title = "Basic Algebraic Facilities of the Scratchpad II Computer
+ Algebra System",
+ institution = "IBM Research",
+ year = "1986",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@misc{Jenk86b,
+ author = "Jenks, Richard D.",
+ title = "Scratchpad II Examples from INPUT files",
+ institution = "IBM Research",
+ year = "1986",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@article{Dave85,
+ author = "Davenport, James H.",
+ title = "The LISP/VM Foundation of Scratchpad II",
+ journal = "The Scratchpad II Newsletter",
+ volume = "1",
+ number = "1",
+ year = "1985",
+ month = "September",
+ institution = "IBM Research",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Wityak, Sandra}
+\begin{chunk}{ignore}
+@misc{Wity85,
+ author = "Wityak, Sandra",
+ title = "The Scratchpad II Newsletter",
+ volume = "1",
+ number = "1",
+ year = "1985",
+ month = "September",
+ institution = "IBM Research",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Wityak, Sandra}
+\begin{chunk}{ignore}
+@misc{Wity86,
+ author = "Wityak, Sandra",
+ title = "The Scratchpad II Newsletter",
+ volume = "1",
+ number = "2",
+ year = "1986",
+ month = "January",
+ institution = "IBM Research",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
+\index{Wityak, Sandra}
+\begin{chunk}{ignore}
+@misc{Wity86a,
+ author = "Wityak, Sandra",
+ title = "The Scratchpad II Newsletter",
+ volume = "1",
+ number = "3",
+ year = "1986",
+ month = "May",
+ institution = "IBM Research",
keywords = "axiomref"
}
\end{chunk}
\index{Watt, Stephen M.}
\index{Della Dora, J.}
\index{Wityak, Sandy}
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@misc{Watt87,
+ author = "Watt, Stephen M. and Jenks, Richard D.",
+ title = "Abstract Datatypes, Multiple Views and Multiple Inheritance in
+ Scratchpad II",
+ keywords = "axiomref",
+ year = "1987",
+ url = "https://cs.uwaterloo.ca/~smatt/pub/reprints/1987itlspadviews.pdf",
+ paper = "Watt87.pdf",
+ abstract =
+ "Scratchpad II is an abstract datatype language developed at Yorktown
+ Heights for the implementation of a new computer algebra system. It
+ provides packages of polymorphic functions and parameterized, abstract
+ datatypes with operator overloading and multiple inheritance. To
+ express the intricate interrelationships between the datatypes
+ necessary for the description of mathematical objects, a number of
+ techniques based on the notion of {\sl category} have been
+ used. Categories are used to enforce relationships between type
+ parameters and to provide the mechanism for multiple inheritance. They
+ also allow the language to be statically type checked and the
+ generation of efficient code. This paper describes the role of
+ categories in Scratchpad II."
+}
+
+\end{chunk}
+
+\index{Watt, Stephen M.}
+\index{Jenks, Richard D.}
+\index{Sutor, Robert S.}
+\index{Trager, Barry M.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Watt90,
+ author = "Watt, Stephen M. and Jenks, Richard D. and Sutor, Robert S. and
+ Trager, Barry M.",
+ title = "The Scratchpad II type system: Domains and Subdomains",
+ booktitle = "Computing Tools for Scientific Problem Solving",
+ year = "1990",
+ publisher = "Academic Press",
+ url =
+ "https://cs.uwaterloo.ca/~smwatt/pub/reprints/1990miolaspadtypes.pdf",
+ paper = "Watt90.pdf",
+ keywords = "axiomref",
+ abstract =
+ "Scratchpad II is a language developed at Yorktown Heights for the
+ implementation of a new computer algebra system. The need to model the
+ intricate relationships among the datatypes representing mathematical
+ objects has provided a number of challenges in the design of a type
+ system for the programming language.
+
+ In languages in which a datatype constructor may take multiple
+ parameters, ensuring compatibility between them is extremely
+ important. Scratchpad II addresses this issue by basing its
+ implementation of abstract datatypes on {\cl categories}. Categories
+ provide a convenient and useful method for specifying requirements on
+ operations from datatypes. These requirements can be very complex when
+ modelling mathematics.
+
+ We show how categories provide multiple inheritance and how
+ inheritance of specification is separated from inheritance of
+ implementation. We also present implications of the type system on
+ compilation of efficient code and flexibility of a weakly typed
+ interactive user interface.
+
+ Finally, the mechanisms of Scratchpad II are compared with those of
+ traditional abstract datatype and objectoriented programming
+ languages."
+}
+
+\end{chunk}
+
+\index{Zippel, Richard}
\begin{chunk}{axiom.bib}
@misc{Watt86,
 author = "Watt, Stephen M. and Della Dora, J. and Wityak, Sandy (ed)",
 title = "Algebra Snapshot: Linear Ordinary Differential Operators",
 source = "Scratchpad II Newsletter: Vol 1 Num 2 (Jan 1986)",
 url = "http://www.csd.uwo.ca/~watt/pub/reprints/1986snewslodo.pdf",
 paper = "Watt86.pdf",
+@misc{Zipp93,
+ author = "Zippel, Richard",
+ title = "The Weyl Computer Algebra Substrate",
+ paper = "Zipp93.pdf",
+ keywords = "axiomref",
+ booktitle = "Proc. of DISCO 1993",
+ series = "DISCO 93",
+ pages = "303=307",
+ year = "1993"
+}
+
+\end{chunk}
+
+\index{Sutor, Robert S.}
+\begin{chunk}{axiom.bib}
+@inproceedings{Suto85,
+ author = "Sutor, Robert S.",
+ title = "The Scratchpad II computer algebra language and system",
+ booktitle = "Research Contributions from the Euro. Conf. on Comp. Alg.",
+ series = "Lecture Notes in Computer Science Volume 204",
+ volume = "2",
+ pages = "3233",
+ year = "1985",
+ isbn = "0387159835 (vol. 1),0387159843 (vol. 2)",
keywords = "axiomref"
}
\end{chunk}
+\index{Jenks, Richard D.}
+\begin{chunk}{axiom.bib}
+@article{Jenk88d,
+ author = "Jenks, Richard D.",
+ title = "Scratchpad II: A computer algebra language and system",
+ journal = "The Journal of the Acoustical Society of America",
+ year = "1988",
+ volume = "83",
+ number = "S1",
+ pages = "S106",
+ keywords = "axiomref",
+ abstract =
+ "The Scratchpad II system represents a new generation of systems for
+ doing symbolic mathematics, based on modern algebra and abstract data
+ types. A large number of facilities are provided, for example:
+ symbolic integration, ``infinite'' power series, differential operators,
+ Cartesian tensors, and solution of nonlinear systems. Scratchpad II
+ has been designed from the outset to be extendible. The system
+ introduces a new data abstraction notion, the ``category,'' to express
+ intricate interrelationships between data types. The result design
+ permits the compilation of algorithms described in their most natural
+ mathematical setting. The use of categories guarantees user defined
+ types and packages are compatible with each other and with built in
+ facilities. This system provides a single high‐level language with an
+ intepreter and compiler. The language can be used by the naive user
+ for convenient interactive mathematics calculations and by the
+ advanced user for the efficient implementation of
+ algorithms. Scratchpad II is built on Lisp/VM and runs on IBM/370
+ class mainframes. An implementation of the system on the RT/PC is
+ expected soon."
+}
+
+\end{chunk}
+
+\index{Jenks, Richard D.}
+\index{Sutor, Robert S.}
+\index{Watt, Stephen M.}
+\begin{chunk}{axiom.bib}
+@book{Jenk88e,
+ author = "Jenks, Richard D. and Sutor, Robert S. and Watt, Stephen M.",
+ title = "Scratchpad II: An Abstract Datatype System for Mathematical
+ Computation",
+ booktitle = "Mathematical Aspects of Scientific Software",
+ year = "1988",
+ pages = "157182",
+ publisher = "Springer",
+ isbn = "0387189289",
+ keywords = "axiomref",
+ abstract =
+ "Scratchpad II is an abstract datatype language and system that is
+ under development in the Computer Algebra Group, Mathematical Sciences
+ Department, at the IBM Thomas J. Watson Research Center. Many
+ different kinds of computational objects and data structures are
+ provided. Facilities for computation include symbolic integration,
+ differentation, factorization, solution of equations and linear
+ algebra. Code economy and modularity is achieved by having polymorphic
+ packages of functions that may create datatypes. The use of categories
+ makes these facilities as general as possible."
+}
+
+\end{chunk}
+
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index e339c64..2b68804 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5452,6 +5452,8 @@ books/bookvol10.3 add Dupee, Dewar citations to algebra
books/bookvol10.4 add Bronstein citations for LODE code
20160704.04.tpd.patch
books/bookvolbib Axiom Citations in the Literature
+20160705.01.tpd.patch
+books/bookvolbib Axiom Citations in the Literature

1.7.5.4