Michael Wester (wester@math.unm.edu)

1801 Quincy, SE

Albuquerque, New Mexico

USA 87108-4427

Tel: 1-(505) 243-2800

**User Friendly Reviews of Computer Algebra Systems**

Nicolas Robidoux (mia@math.unm.edu)

*Abstract:*So far, comparative reviews of computer algebra systems have, for the most part, consisted of lists of implemented packages with a sampling of related bugs. Organizing this information into a coherent whole must begin with an explicit model of the users and what they do with and expect from the systems. "Scores" must be accompanied by a description of the attributes of the yardstick user: her skill level, her model and use of the computer algebra system (oracle, table book, compute engine, high level programming language, teaching aid, driver for numerical or graphics libraries...), her willingness to hand hold and check answers (for some users, a wrong answer which can easily be found to be wrong may be quite acceptable, unlike one which is quite difficult to "back plug"), the size of typical problems... Some "yardstick users" and their attributes will be presented.**A Review of Symbolic Solvers**

Laurent Bernardin (bernardin@inf.ethz.ch)

*Abstract:*Solving equations and systems of equations symbolically is a key feature of every computer algebra system. This review examines the capabilities of the six best known general purpose systems to date in the area of general algebraic and transcendental equation solving. Areas explicitly not covered by this review are differential equations and numeric or polynomial system solving as special purpose systems exist for these kinds of problems.**Factorized Gröbner Bases and Polynomial Systems**

Hans-Gert Gräbe (graebe@informatik.uni-leipzig.de)

*Abstract:*Solving complicated polynomial systems with special purpose CASs (as proposed in L. Bernardin's abstract) is often only of restricted benefit due to the complicated output structure. Especially for systems with infinitely many solutions, algorithms near to a prime decompositions must be involved instead to obtain more insight into the structure of the set of solutions. A central tool for such a purpose is the Gröbner algorithm with factorization. No special purpose systems offer both facilities (yet) on a satisfactory level. In my report, I will present both a comparison of the Gröbner factorizer capabilities of the big general purpose CASs (as far as these capabilities are accessible) and a survey about the output quality of this algorithm compared to a full prime decomposition.**A review of the ODE solvers of Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD and Reduce**

Frank Postel (frankp@uni-paderborn.de) and Paul Zimmermann (Paul.Zimmermann@loria.fr)

*Abstract:*Using a wide set of more than 50 different kinds of ordinary differential equations and systems, we try to give an idea of the capabilities of Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD and Reduce in solving differential equations. In our conclusion we firstly want to give the user an answer to the question "What system should I use?" and secondly to point out to developers of computer algebra systems the advantages and/or drawbacks of their ODE solver, to help to improve it.**Multiple-valued Complex Functions and Computer Algebra**

Helmer Aslaksen (aslaksen@math.nus.sg)

*Abstract:*I will discuss some elementary, but not very well-known facts about multiple-valued complex functions, and see how computer algebra systems deal with these problems.**Computer Algebra Systems: Pitfalls, Pratfalls and also Elegance**

Michael Wester (wester@math.unm.edu)

*Abstract:*General purpose computer algebra systems have many wonderful abilities. But how easy are they really to use in practice? Can the answers they produce be trusted? In this talk, I will give some examples of both the good and the bad (selected from a collection of now more than 400 problems) with an occasional philosophical digression.**Computer Algebra and Problem Solving Environments**

Stanly Steinberg (stanly@math.unm.edu)

*Abstract:*Problem Solving Environments provide a promising new approach for solving modeling problems that occur in engineering and science. Such environments will provide easy access to integrated symbolic and numeric computing and this will greatly enhance the tools available to modelers. However, this will place new demands on computer algebra systems.

(extended abstract)**Commercial vs Free Computer Algebra Systems**

Paul Zimmermann (Paul.Zimmermann@loria.fr)

*Abstract:*Today, the two or three leading computer algebra systems are commercial. However, in some other fields, some leading products are free systems, for example gcc for compilers, gnu-emacs for editors, TeX for (scientific) text processing. In this talk, we will try to figure out the reasons (if any) why the situation is different for computer algebra systems, and try to guess what the future market of symbolic computation will be.**Discussion of Issues Raised and Not Raised**

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