A PostScript / PDF version of the article (last revised January 4, 1999) [40 pages].

An earlier review of the same ilk is A Review of CAS Mathematical Capabilities. Also see a Comparison of Polynomial-Oriented Computer Algebra Systems for some timing studies.

A 14-page table of CAS synonyms.

*Results:*

**Boolean Logic and Quantifier Elimination**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Set Theory**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Numbers**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Numerical Analysis**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Statistics**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Combinatorial Theory**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Number Theory**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Algebra**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Trigonometry**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Special Functions**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**The Complex Domain**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Determining Zero Equivalence**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Equations**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Inequalities**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Vector Analysis**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Matrix Theory**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Tensor Analysis**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Sums**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Products**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Limits**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Calculus**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Indefinite Integrals**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Definite Integrals**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Series**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Transforms**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Axiom,
**Ordinary Difference and Differential Equations**- Axiom, Derive, Derive (ODE), Macsyma, Maple, Mathematica, MuPAD, Reduce
**Partial Differential Equations**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce (Heat equation)
**Operators**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
**Programming and Miscellaneous**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce
- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce (differentiation)
**Mathematics vs Computer Science**- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce (local variables)
- Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce (matching)

References:

- [Asl96]
- Helmer Aslaksen, ``Multiple-valued complex functions and computer algebra'', SIGSAM Bulletin, Volume 30, Number 2, June 1996, 12-20. (original)
- [Ber96]
- Laurent Bernardin, ``A Review of Symbolic Solvers'', SIGSAM Bulletin, Volume 30, Number 1, March 1996, 9-20. (original)
- [Fat96]
- Richard J. Fateman, ``Symbolic Mathematics System Evaluators'', Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation, 1996, 86-94. (original)
- [Fau95]
- J. C. Faugère, ``GB: State of GB + Tutorial, Proceedings of the POSSO Workshop on Software, draft version, edited by Jean-Charles Faugère, Joel Marchand and Renaud Rioboo, Paris, March 1-4, 1995, 55-60.
- [Grä95]
- Hans-Gert Gräbe, ``On Factorized Gröbner Bases'', Computer Algebra in Science and Engineering, edited by Fleischer, Grabmeier, Hehl and Küchlin, World Scientific Singapore 1995, 77-89. (original)
- [Grä96]
- Hans-Gert Gräbe, About the Polynomial System Solve Facility of Axiom, Macsyma, Maple, Mathematica, MuPAD, and Reduce, Preprint 11/96 des Instituts für Informatik, Universität Leipzig, Germany, December 1996. (original)
- [Gru96]
- Dominik Gruntz, On Computing Limits in a Symbolic Manipulation System, Ph.D. dissertation, Swiss Federal Institute of Technology, Zürich, Switzerland, Diss. ETH No. 11432, 1996. (original)
- [Har91]
- David Harper, Chris Wooff and David Hodgkinson, A Guide to COMPUTER ALGEBRA SYSTEMS, John Wiley & Sons, 1991.
- [Her94]
- W. Hereman, ``Review of Symbolic Software for the Computation of Lie Symmetries of Differential Equations'', Euromath Bulletin, Volume 1, Number 2, 1994, 45-79.
- [Her95]
- Willy Hereman, ``Visual data analysis: maths made easy'', Physics World, Volume 8, Number 4, April 1995, 49-53.
- [Her96]
- Willy Hereman, ``Computer algebra: lightening the load'', Physics World, Volume 9, Number 3, March 1996, 47-52.
- [Koe95]
- Wolfram Koepf, ``Efficient Computation of Orthogonal Polynomials in Computer Algebra'', Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), Preprint SC 95-42, December 1995. (original)
- [Pos96]
- Frank Postel and Paul Zimmermann, ``A review of the ODE solvers of Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD and Reduce'', submitted to the 5th Rhine Workshop on Computer Algebra to be held in Saint-Louis, France, April 1-3, 1996. (original)
- [Rob93]
- Nicolas Robidoux, ``Does Axiom Solve Systems of O.D.E.'s Like Mathematica?'', LA-UR-93-2235, Los Alamos National Laboratory, Los Alamos, New Mexico, 1993.
- [Sim92]
- Barry Simon, ``Comparative CAS Reviews'', Notices of the American Mathematical Society, Volume 39, Number 7, September 1992, 700-710.
- [Sim95]
- Barry Simon, ``Symbolic Math Powerhouses'', Desktop Engineering, Volume 1, Issue 1, September/October 1995, 42-51.
- [Sim97]
- Barry Simon, ``Symbolic Math Powerhouses Revisited'', Desktop Engineering, Volume 2, Issue 7, March 1997, 12-25, 52-53.
- [Sto91]
- David R. Stoutemyer, ``Crimes and Misdemeanors in the Computer Algebra Trade'', Notices of the American Mathematical Society, Volume 38, Number 7, September 1991, 778-785.
- [Wes94]
- Michael Wester, ``A Review of CAS Mathematical Capabilities'', Computer Algebra Nederland Nieuwsbrief, Number 13, December 1994, ISSN 1380-1260, 41-48 (newer version of the paper below).
- [Wes95]
- Michael Wester, ``A Review of CAS Mathematical Capabilities'', Applied Mechanics in the Americas, Volume III, edited by Luis A. Godoy, Sergio R. Idelsohn, Patricio A. A. Laura and Dean T. Mook, American Academy of Mechanics and Asociacion Argentina de Mecanica Computacional, Santa Fe, Argentina, 1995, 450-455.
- [Zim95]
- Paul Zimmermann, ``Wester's test suite in MuPAD 1.2.2'', Computer Algebra Nederland Nieuwsbrief, Number 14, April 1995, ISSN 1380-1260, 53-64. (original)
- [Zim96]
- Paul Zimmermann, ``Wester's test suite in MuPAD 1.3'', The SAC Newsletter, Number 1, December 1996, 53-69. (original)

Several of the above papers were presented in the
ACA'96 session on
*Comparative CAS Reviews and
Philosophy*.