Hi! I think, multivariate gcd is a neverending topic, discussed very often in many communities. Actually, I never tried to implement that and hopefully I never will. But I *enjoyed* ;-) many discussions about it.
So, I think, if you want to have success, the first task is, what Roman said: Learning, that the multivariate GCD is a big project and cannot be accomplished in a weeks project or studying a few examples. I have seen many cases, where multivariate gcd computations (as part of a big complex computation) took "forever" in one version of Singular and were immediately calculated in the next version (but for another set of examples we had just the opposite phenomenon). And this isn't a Singular problem, but it is related to the problem itself. So stop this nonsense, find the *easy secret* of fast multivariate gcd and realize, that it is hard work. In fact, we know, that part of the strength of the implementation in Magma was the hard work Allan Steel put in, treating all these special cases. I didn't try maxima and I don't know anything about the efficiency of its polynomial data structures. But I know that this statement looks very true: >My experience shows that its the algorithm changes that matter most. So it might be the case, that the code in Maxima or Singular provides a good basis for really fast gcd (but that needs work) A statement to the Singular gcd: As far as I know the gcd in Singular is part of Singular-factory, a quite independent C++-library. I features a recursive polynomial representation (which is probably a good data structure for multivariate gcds). Pro: - quite small - also used in Macaulay 2 - improving it will speed up other parts of SAGEs commutative algebra (which relies on libSingular) Contra: - quite old (not everything works) Best regards, Michael --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
