On Sat, May 15, 2010 at 12:55 PM, Tom Coates <t.coa...@imperial.ac.uk> wrote: > > 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
1. On what hardware? 2. Can you post something so that somebody else (e.g., me) could replicate this benchmark? I want to make sure that, e.g., your Sage wasn't built incorrectly. -- William > > 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 > -- William Stein Professor of Mathematics University of Washington http://wstein.org -- 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
