chal@CS.CMU.EDU (Prasad Chalasani) (11/02/90)
Here are responses I got from the University of Sidney,
where Cayley was developed.
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From: Anne Cannon <anne@maths.su.oz.au>
Message-Id: <9010220924.AA03855@galois.maths.su.oz.au>
Received: by galois.maths.su.oz.au (4.1/6.3 to SMTP)
id AA03855; Mon, 22 Oct 90 19:24:52 EST
To: prasad.chalasani@REDNECK.PC.CS.CMU.EDU
Subject: Cayley brochure
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Thank you for your message about Cayley. The system is made available
on a subscription basis upon payment of a distribution and maintenance
fee of US$2,000 for a mainframe or network for University users. In the case of
developing countries, a discount fee of US$1,000 applies.
This fee entitles the licencee to an initial copy of the software, a set of
manuals,a subscription to the Cayley Bulletin and all updates and new releases
for the period of the licence, which is usually three years. In the case of
a single Sun or Apollo workstation, a discount price of US$1,000 is available.
The system has been implemented on a range of processors and information about
this is included in the brochure which I will also send to you.
Please contact us if we can supply any further information,
Yours faithfully, Anne O'Kane, Secretary, Computer Algebra Group
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THE CAYLEY SYSTEM FOR DISCRETE ALGEBRAIC AND COMBINATORIAL COMPUTATION
Announcement of Versions 3.7 and 3.8
1. Introduction
The Cayley system for discrete algebra and combinatorial theory is designed
to solve hard problems in related areas of algebra, number theory and finite
geometry.
Cayley is not simply an alternative to other Computer Algebra systems. It
supports computation in important new areas of algebra (eg group theory,
modules) which are not included in the standard systems. Moreover, its design
is based on a computational model arising from the structural principles of
modern abstract algebra.
Cayley enables users to define and to compute in structures such as finite
and infinite groups, rings, fields and modules. Features include:
(*) User definition of the particular algebraic structures needed to solve a
problem. Each object arising in the course of the computation is then
defined in terms of these structures;
(*) Fast computation in important classes of algebraic structures;
(*) Correspondence of the user language data types to the central concepts
of modern algebra: algebraic structures, algebraic elements, sets,
sequences, and mappings;
(*) Several hundred built-in functions capable of determining deep
structural properties of groups and other structures; and
(*) Data bases containing many useful examples of structures (mainly groups
at present) are available which further enhance the knowledge-base of the
system.
Approximately 200 institutions spread over 28 countries have installed the
system and it has found wide application to problems arising in many branches
of mathematical research including group theory, representation theory,
topology, knot theory, finite geometry, number theory, combinatorial theory and
graph theory. Further, the system has successfully solved problems arising in
application areas such as complexity theory, coding theory, data encryption,
communication network design, discrete fourier transforms, mathematical
crystallography and solid state physics. Cayley has been cited in approximately
400 papers and theses.
[ ..... sections 2-5 omitted for brevity --Prasad Chalasani .... ]
6. Applications
An estimated 400 papers and theses cite some application of Cayley (a list
containing some 250 of these citations may be obtained from the Computational
Algebra Group). We list a few examples of published applications.
Group Theory:
(*) A new construction for the Rudvalis simple group (Delgado & Weiss)
(*) Subgroup structure of M12 (Buekenhout & Rees)
(*) Maximal subgroups of He and G(2, 4) (Butler)
(*) Classification of the minimal 2-groups which act uniserially in
dimension 8 and having class less than 8 (Leedham-Green & McKay)
(*) Determination of groups of order 128 and 256 (Newman & O'Brien)
(*) Classification of all transitive groups of degree up to 12 (Royle)
Representation theory:
(*) Character tables of Sylow normalizers of the sporadic simple groups
(Ostermann)
(*) Vertices and sources of the 2-modular representations of the Mathieu
groups (Schneider)
(*) Group of units in a modular group ring (Sandling)
Lattices:
(*) Maximal finite irreducible subgroups of GL(n, Z), n ge 5 (Plesken)
(*) Constructing lattices with prescribed minimum (Plesken & Pohst)
Ring Theory:
(*) Verbal embeddings of rings in groups (Fournelle & Weston)
Topology:
(*) A computer search for homology 3-spheres (Dunwoody)
(*) Classification of hyperbolic manifolds from regular polyhedra
(Richardson & Rubinstein)
Combinatorial Theory:
(*) Classification of vertex transitive graphs on 24 points (Praeger & Royle)
(*) Analysis of the groups of perfect shuffles (Morrison)
(*) Construction of designs by partitioning sets (Sharry & Street)
Finite Geometry:
(*) Construction of affine planes (Assmus & Key)
(*) Geometries of the groups PSL(2, q) (Cruyce)
(*) Collineation groups of spreads of PG(3, q) (Volcheck)
Differential Equations:
(*) Existence of Liouvillian solutions of third order homogeneous
linear differential equations (Ulmer)
(*) Construction of symmetry adapted bases for the solution of 3-dimensional
partial dirrerential equations (Ungricht)
Discrete Fourier Transforms
(*) Construction of discrete Fourier transforms on abelian groups and
p-groups (Clausen)
7. Implementations
Cayley comprises approximately 350,000 lines of C. The system is distributed
only in binary form. An interface is provided to enable users to link their own
code with the Cayley system and then to call it directly from within the Cayley
language.
As of June 1990, versions of Cayley are available for the following
processors:
(*) SUN 3, SUN 4
(*) Apollo M680x0 based models, DN10000
(*) VAX/VMS
(*) IBM 30xx, 43xx under VM/CMS
(*) IBM RT; IBM PS/2 Models 55, 70 and 80; IBM RS 6000 series
(*) Cadmus PCS
8. Ordering Information
Cayley is distributed on a subscription basis: a site acquires a licence
for a period (typically three years) and over that period is provided with
upgrades and new releases. At the present time the system is evolving
rapidly and a major new release is put out each year. The subscription price
varies according to processor type and whether the licencee is a university,
government, or industrial organization. As an illustration, the university
price for a version running on a SUN fileserver together with its clients is
currently $US2000. A discount is available in certain cases for single
workstation versions.
For more information, or to order the system, contact
The Secretary,
Computational Algebra Group, Pure Mathematics,
University of Sydney, NSW 2006, Australia
Email:cayley@maths.su.oz.au Telephone:(61)(02) 692 3338 Fax:(61)(02) 692 4534
REFERENCES
J.J. Cannon, Software tools for group theory, Proceedings of the
AMS Symposium on Pure Mathematics, 37 (1980) 495--502.
J.J. Cannon, A Language for Group Theory, Department of Pure
Mathematics (1982), 300 pages. (To be published in the series Springer
Lecture Notes in Computer Science).
J.J. Cannon, An introduction to the group theory language Cayley,
Computational Group Theory, (Proceedings of the LMS Symposium on
Computational Group Theory, Durham, July 30--August 9, 1982),
M.D. Atkinson (ed), Academic Press, London, 1984, 143--182.
J.J. Cannon, A computational toolkit for finite permutation groups,
In: Proceedings of the Rutgers Group Theory Year, 1983--1984,
M. Aschbacher et al (eds), Cambridge University Press, New York, 1984, 1--18.
J.J. Cannon, The Cayley system for group theory, J. Symbolic Computation,
To appear.
D.F. Holt, The CAYLEY group theory system, Notices Amer. Math. Soc.,
35 (1988), 1135--1140.
M.F. Newman and E.A. O'Brien, A CAYLEY library for the groups of order
dividing 128, In: Group Theory, (Proceedings of the Singapore Group Theory
Conference, Singapore, June, 1987), K.N. Cheng and Y.K. Leong (eds),
Walter de Gruyter, Berlin, New York, (1989), 437--442.
G.J.A. Schneider, Computing with endomorphism rings of modular
representations, J. Symbolic Computation, 9, 5/6 (1990).
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Prasad Chalasani Work: 412-268-3053
School of Computer Signs Home: 412-422-8897
Carnage Melon Drive chal@cs.cmu.edu
Pittsburgh PA 15213
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