
Directory of Activities
This page contains references to benchmark activities in computer algebra.
The content was compiled from the results of the
Benchmark Meeting at
ISSAC'98.
Please send an email to me
to get your activities included in this list.
Breadth and Scope Benchmarks
Average Quality Benchmarks
 Medicis Benchs
by Joel Marchand and others.
A collection of timings on various application problems,
computer algebra systems and hardware platforms from the
Medicis group.
The timings are compiled from a user survey
in a physics lab and are from codes in Maple, C, C++ and Fortran.
Contact Joel Marchand for details.
Performance Benchmarks, Polynomial Systems
 PolyData Project
by Olaf Bachmann, Hans Schoenemann,
HansGert Graebe, JeanCharles Faugere and Michael Dengel.
From the WebPage:
The PolyData project has the following two main goals:
 To provide a framework and general tools that are capable for

a systematic and uniform collection of problems (together
with their solutions and other related background
information) from different areas of Symbolic Computation

convenient extensions, manipulations, and categorizations
of the collected data

the specification of (inter)relations of the collected
data

trusted benchmarking on various Computer Algebra Systems
of (a significant part of) the collected problems

electronic transformation of the collected data into other
representation formats, like HTML, or SQL, in order to
conveniently view and/or (re)process the data

easy and comfortable reuse and extensions of the provided
tools, so that people from all areas of Computer Algebra
can conveniently contribute and use the results of our
work

To use these tools to systematically collect and maintain
polynomial systems that
were considered in papers or elsewhere, and to publish results
of benchmark tests for computing various properties of these
polynomial systems (like Groebner basis, szyzygies, free
resolutions, decompositions, "solutions", etc).
 PoSSo Examples
by Marco Silvestri.
A collection of systems of polynomial equations used by the
PoSSo Group for testing.
Dated 28. Sept. 1994.
 Handbook of Polynomial Systems
by D. Bini and B. Mourrain
The aim of this data base is to provide a consequent list of
polynomial systems which could be used to illustrate,
compare, evaluate different methods for solving polynomial systems.
We will gather polynomial systems (including the list of the
PoSSo project) and add to each of these systems short descriptions
of methods, results of computations, timing, ...
 Gb Benchs
by JeanCharles Faugere.
Benchmarks used by the Gb, FGb and RS systems.
 ccNbody
by Ilias Kotsireas.
Polynomial systems arising in the study of central
configurations in the Nbody problem of Celestial Mechanics
 Some Examples for Solving Systems of Algebraic Equations by
Calculating Groebner Bases
by W. Boege, R. Gebauer and H. Kredel.
One of the first papers with timings from 1984.
(Grand) Challenges Benchmarks
 Great Internet Mersenne Prime Search (GIMP)
From the Background:
The Great Internet Mersenne Prime Search (GIMPS) harnesses the power
of thousands of small computers like yours to solve the seemingly
intractable problem of finding HUGE prime numbers.
Specifically, GIMPS looks for
Mersenne Primes,
expressed by the formula 2^{P}1. Over 8,000 people
have contributed computer time to help discover worldrecord
Mersenne primes. Thoughout history, the largest known prime number
has usually been a Mersenne prime.
 A Polynomial Factorisation Challenge
by Joachim von zur Gathen.
SIGSAM Bulletin, Vol. 26, No. 2, April 1992, Issue 100.
MuPad results by Paul Zimmermann.
 Record Number Field Sieve Factorisations
by PeterLawrence Montgomery.
A team of researchers from Amsterdam and Oregon have factored the
162digit Cunningham number (12^151  1)/11 using the Special Number Field
Sieve (SNFS). This team also factored a 105digit cofactor of 3^367  1
using the General Number Field Sieve (GNFS), These beat the prior records
of 158 digits (SNFS) and 75 digits (GNFS). The Amsterdam group also factored
the 123digit cofactor of the Most Wanted number 2^511  1 using SNFS.
 Factorbymail project
by Bob Silverman.
Others
 Comparison of mathematical programs for data analysis
by Stefan Steinhaus. (New edition May 1999)
From the Abstract:
This comparison should give an overview about the functionality,
the availability for different operating systems and the speed of
mathematical programs for analysing huge or very huge data sets in
mathematical, statistical or graphical ways. The focus of this test
is therefor set to mathematical functions which are mainly used
in economics, financial analysis, biology, chemistry, physics and
some other subjects where the numerical analyse of data is very
important.
 SATLIB  The Satisfiability Library
by Holger Hoos and Thomas Stuetzle.
From the Abstract:
SATLIB is a collection of benchmark problems, solvers, and tools we are
using for our own SAT related research. One strong motivation for
creating SATLIB is to provide a uniform testbed for SAT solvers as well
as a site for collecting SAT problem instances, algorithms, and
empirical characterisations of the algorithms' performance.
 Jacques Morgenstern Challenge
