On Wednesday 25 June 2008, Daniel Loughran wrote: > thanks for the help dudes, > > Although Im sorry Michael but I dont really understand any of your > last paragraph (rather Jargon heavy!) Swap? Bad Locality? FGB? F4? Are > you saying that I might be able to solve my problem using singular?
Hi there, you are using Singular (this is what does the heavy lifting behind the scenes). Jargon buster: Swap: Gröbner basis computations are exponential in time and memory on average. Thus, if you "increase" it only slightly your memory usage might increase a lot, you run out of fast RAM and hit the slow swap. Locality: An algorithm which uses say 20GB of data but loads e.g. 200MB at a time and computes 1 minute with those has better locality than a computation which jumps around in those 20GB all the time. Since these 20GB don't fit in RAM on most computers the later has to ask Swap (harddisk) quite often which is ~ 100 times slower than RAM if not more. FGB: A program by Jean-Charles Faugere which implements Buchberger's algorithm and F4: http://fgbrs.lip6.fr/jcf/ F4: An algorithm developed by Jean-Charles Faugere to compute Gröbner bases. It reduces several pairs at once by using linear algebra which makes it quite efficient but memory hungry. F4 is implemented in FGB and Magma. Singular (and thus Sage) has "a variant" of F4 called SlimGB which also does multi-reduction but without linear algebra. See I.groebner_basis? for details if I is your ideal. Hope that helps, Cheers, Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 _www: http://www.informatik.uni-bremen.de/~malb _jab: [EMAIL PROTECTED] --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
