Directory of Activities
This page contains references to benchmark activities in computer algebra.
The content was compiled from the results of the
Please send an e-mail 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
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,
Hans-Gert Graebe, Jean-Charles Faugere and Michael Dengel.
From the Web-Page:
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
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
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 Jean-Charles Faugere.
Benchmarks used by the Gb, FGb and RS systems.
by Ilias Kotsireas.
Polynomial systems arising in the study of central
configurations in the N-body 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
expressed by the formula 2P-1. Over 8,000 people
have contributed computer time to help discover world-record
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 Peter-Lawrence Montgomery.
A team of researchers from Amsterdam and Oregon have factored the
162-digit Cunningham number (12^151 - 1)/11 using the Special Number Field
Sieve (SNFS). This team also factored a 105-digit 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 123-digit cofactor of the Most Wanted number 2^511 - 1 using SNFS.
- Factor-by-mail project
by Bob Silverman.
- 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
- 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 test-bed for SAT solvers as well
as a site for collecting SAT problem instances, algorithms, and
empirical characterisations of the algorithms' performance.
- Jacques Morgenstern Challenge