I will geve a short answer to Rene Grognard, and to D.Tweed, since it is late and people will close the campus in a few minutes. Prof. Malaquias, from time to time, disappears. I do not know where he goes when this happens. However, he does not answer mails, and does not update his home page. This is one of those periods, when it is impossible to contact him. For this reason, I will try to answer your questions, instead of handling them to him. A few years ago, Prof. Malaquias developed a very good (IMHO) computer algebra system in Scheme. The system was small, fast and fairly complete. It is known as CICS. It was written in a functional subset of Scheme. It could simplify expressions, put them in the canonical form, compare them for equality (this involves putting them in the canonical form), differentiate expressions, integrate expressions, solve many types of differential equations, do matrix and tensor algebra, etc. CICS was indeed a good system. However, Prof. Malaquias is very fond of Haskell and ML. Therefore, he decided to drop his efforts to develop CICS in Scheme, and create an entirely new system in Haskell. Since he could not find an appropriate Haskell compiler (a compiler that could handle matrices well), he decide to test his ideas using Clean. In the end, he did a double implementation, in Haskell and Clean (as far as I know). What he did was to overload arithmetic operators and functions. His expressions carry an environment around. This environment tells the simplifying functions how to act (simplification is different if the expression is a multiplication factor, or the argument of a sin, or the argument of a logarithm, etc.). He says in his monography that the heart of an algebraic system is the subsystem that puts expressions in the canonical form, that allows semantic unification and comparisons. He also believes that a language like Haskell is better to implement computer algebra systems than Scheme or Lisp, because they are faster and safer. I happen to have Prof. Malaquias unpublished monography. I will try to contact him. If he answer my mail, I will ask him to contact you. In Haskell, he did only the simplification of expressions, the subsystem that put them in the canonical form, and an integrator. However, he says that this is the heart, and the most difficult part of the system. If people have this, voluntaries could easily add their contributions. Tomorrow, I will finished this letter... Ed. Costa ------------------------------------------------------------ This e-mail has been sent to you courtesy of OperaMail, as a free service from Opera Software, makers of the award-winning Web Browser, Opera. Visit us at http://www.opera.com/ or our portal at: http://www.myopera.com/ Your free e-mail account is waiting at: http://www.operamail.com/ ------------------------------------------------------------
