Mathematica or axiom or Maple or MuPAD or REDUCE or Form ?

Can and Cannot Do

2. Mathematica or axiom or Maple or MuPAD or REDUCE or Form ?

This cannot be answered here. It depends largely on what you require from a computer algebra system. For the opinions of several reviewers, see the references listed in the Appendix. You should make an informed decision yourself whether Mathematica is the correct system for your special applications. Some of the things that can be done with Mathematica will be shown in the following chapters of this book.

At the time this book was written, a good (objective) indication existed that Mathematica is the right choice for the reader. It was the only system that was able to solve all of the ten (easy to state, but not so easy to solve) problems from the 1997 ISSAC [International Symposium on Symbolic and Algebraic Computation] system challenge [1282÷], http://www.wolfram.com/news/archive/issac. The summary of the challenge session states: “… there can really be only one choice. Only one team correctly solved all problems. Only one team solved every problem in more than one way as a check for their solution. … The team was Mathematica’s team.” [308÷].

A more recent, and more hard-core numerical oriented, problem set was Nick Trefethen’s 100$–100-digit challenge [1280÷], [173÷]. Comparing the solutions and the solution techniques employed by users of a variety of programs [1281÷] shows that frequently Mathematica allowed for the most straightforward, shortest, most elegant solutions, frequently even in a symbolic form using the special functions of mathematical physics (which are discussed in the Symbolics volume [1285÷] of the GuideBooks). (And again, the Mathematica team, among others, was be able to solve all problems correctly.

(See http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/hundred.html for details.)

And although we cannot ask David Hilbert directly anymore, G. J. Chaitin says “I think that Hilbert would have loved Mathematica … because in a funny way it carries out Hilbert’s dream, as much as it was possible.” [259÷].

3. Improvements?

Just try it!

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