Computer Algebra Systems: A Practical Guide
Some Computer Algebra benchmarks
Doron Zeilberger's home
page, where you'll find the classic book A=B (by Petkovsek, Wilf and
Comparison of mathematical programs for data analysis by Stefan Steinhaus
Modern Computer Algebra
by Joachim von zur Gathen and Juergen Gerhard (to appear)
Handbook of Differential
Equations, by Daniel Zwillinger, 3rd edition.
A review of the ODE solvers of Axiom, Derive,
Mathematica, Macsyma, MuPAD and Reduce by Frank Postel and Paul Zimmermann.
Proceedings of the 5th RHINE WORKSHOP ON COMPUTER ALGEBRA, April 1-3, 1996,
This paper compares the capabilities of the ODE solvers
of several computer algebra systems
on a set of more than 50 ODEs and systems. The input/output files for
for Maple V.3 and
for Mathematica 2.2.3
(with the Calculus`DSolve package),
for Macsyma 420,
for MuPAD 1.3,
for Reduce 3.6 are also available.
Look also at the results obtained with the
CONVODE program, which is a huge Reduce
solver for ODEs and PDEs available on-line.
Here are some scores of some CAS integrators on the test database created by
Richard Fateman for his system
On the 2145 integrals (both definite and indefinite),
can do 1841 of them with 0 error, 0 timeout.
can do 1869 of them with 23 errors during the integration
and 2 timeouts
(more than 3 minutes of computing time)
for int(1/(A^2+cos(C*X)^2),X) and int(1/(B^2*cos(C*X)^2+1),X).
can do 1002 of them with 125 errors during the integration and 20 timeouts.