Thank you (everyone!) for the many extremely helpful comments and links. Recall that I need to compute
1, f, f^2, ..., f^K for f in ZZ[x,y,z] and K known but large. (In fact I only need certain coefficients of the f^i, but this does not seem to help very much.) I have implemented the most naive possible approach in Sage, MAGMA, and Maple, and also written C code that first encodes f as a univariate polynomial and then uses the flint library to do the multiplication. The results so far, for a typical f that occurs in my problem: Sage: K=70 96.9 secs K=100 439.4 secs MAGMA: K=70 42.9 secs K=100 191.7 secs Also Sage uses almost twice the amount of memory as MAGMA (1587 Mb rather than 910 Mb for the K=100 case). My C code is substantially slower than either MAGMA or Sage. The Maple code is by far the slowest and uses the most memory, but this is not a fair comparison because at the moment I only have access to Maple 12 and this does not have the Johnson/Monaghan--Pearce algorithm available (this is in Maple 14, which I should have in a week or so) . Also I have very little experience with Maple and so I might be doing something stupid. All these timings are from the same machine, which has an Intel Core 2 CPU running at 2.4GHz. More details on the problem. In my situation f starts off as a Laurent polynomial, but I convert it into an element of ZZ[x,y,z] by multiplying by an appropriate monomial. The original Laurent polynomial is "small and dense": its Newton polytope is a 3- dimensional reflexive polytope, so in particular has only one integer point in the interior (this interior point is the origin). Also the exponents are all quite close together: the Newton polytope of a typical f would fit in a 5x5x5 cube. Again, many thanks for all of the advice. I look forward to trying out Bill's new code. Best, Tom -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
