This is not a feature of Sage as such but of Groebner basis computations generally. They go very quickly from easy to impossible when, for example, you increase the number of variables.
I have not tried it but I would not be surprised if other packages (including the expensive ones) have the same difficulty. But perhaps someone will prove me wrong? John Cremona 2008/6/24 Daniel Loughran <[EMAIL PROTECTED]>: > > Dear Sage Community, > I havnt been using Sage that long but iv noticed a trend, in that my > sage doesnt seem to complete some more difficult tasks. Either it > completes the task in less than 10 seconds or it doesnt complete it > all! It feels like once I have crossed a certain threshold the > computation will never finish and I have to interupt it. > > Here is my spec: > OS: Windows XP (latest version) > Sage Version: SAGE Version 3.0.1, Release Date: 2008-05-05 > Using firefox notebook through VMware player. > Machine: 2.40GHz, 1.97Gb RAM, Plently of free Hard disk space. > > As an example, iv been trying to compute the following Groebner Bases > (apologises for the code overload! I wasnt sure how else to present > it...) > > ---------------------------------------------------------------------------------------------------------------------------------------------------------------- > > R.<x0,x1,x2,x3,x4,x5,x6,R10,R11,R12,R13,R14,R15,R16,R17,R18,R19,R110,R111,R112,R113,R114,R115> > =PolynomialRing(QQ); > > I=ideal([-x4*R14 - x6*R16 + x6*R17 + x5*R19 + x3*R113,x5*R11 + x2*R14 > + x4*R17 > - x3*R110 + x6*R112, -x6*R11 - x2*R12 - x2*R16 + x1*R17 + x6*R18 + > x1*R110 - x3*R115 - x4*R115, -x5*R11 - x4*R12 - x2*R14 + x3*R16 - > x4*R17 > + x5*R18 + x6*R19 + x3*R110 + x1*R113 + x6*R115, -x6*R11 - x2*R12 + > x6*R13 + x0*R14 + x5*R15 - x2*R16 + x1*R110 - x3*R114 - x4*R115,x0*R12 > - x3*R13 - x4*R13 + x6*R15 + x0*R16 + x4*R18 - x1*R112 - x1*R114],R); > > len(I.gens()); > 6 > > len(I.groebner_basis()); > 30 > > (calculated in less than 3 seconds) > > > However if I add just one more generator it never completes the > computation: > > J=ideal([-x4*R14 - x6*R16 + x6*R17 + x5*R19 + x3*R113,x5*R11 + x2*R14 > + x4*R17 > - x3*R110 + x6*R112, -x6*R11 - x2*R12 - x2*R16 + x1*R17 + x6*R18 + > x1*R110 - x3*R115 - x4*R115, -x5*R11 - x4*R12 - x2*R14 + x3*R16 - > x4*R17 > + x5*R18 + x6*R19 + x3*R110 + x1*R113 + x6*R115, -x6*R11 - x2*R12 + > x6*R13 + x0*R14 + x5*R15 - x2*R16 + x1*R110 - x3*R114 - x4*R115,x0*R12 > - x3*R13 - x4*R13 + x6*R15 + x0*R16 + x4*R18 - x1*R112 - x1*R114, > x3*R10 - x4*R10 + x3*R11 + x0*R17 - x2*R19 + x0*R110 + x6*R111 - > x2*R112 - x2*R114],R); > > len(J.gens()); > 7 > > len(J.groebner_basis()); > ? > > I actually want to calculate the groebner basis for the following > ideal: > K=ideal([-x4*R14 - x6*R16 + x6*R17 + x5*R19 + x3*R113, x5*R11 + x2*R14 > + x4*R17 > - x3*R110 + x6*R112, -x6*R11 - x2*R12 - x2*R16 + x1*R17 + x6*R18 + > x1*R110 - x3*R115 - x4*R115, -x5*R11 - x4*R12 - x2*R14 + x3*R16 - > x4*R17 > + x5*R18 + x6*R19 + x3*R110 + x1*R113 + x6*R115, -x6*R11 - x2*R12 + > x6*R13 + x0*R14 + x5*R15 - x2*R16 + x1*R110 - x3*R114 - x4*R115, > x0*R12 > - x3*R13 - x4*R13 + x6*R15 + x0*R16 + x4*R18 - x1*R112 - x1*R114, > -x3*R10 - x4*R10 + x3*R11 + x0*R17 - x2*R19 + x0*R110 + x6*R111 - > x2*R112 - x2*R114, x6*R10 - x6*R11 - x2*R16 + x5*R111 + x0*R113 - > x4*R114, -x1*R10 + x1*R11 + x2*R13 + x4*R15 - x2*R18 + x0*R19 - > x3*R111 > + x0*R115, -x3*x6*R10 + x3*x6*R11 + x0*x6*R12 - x3*x6*R13 + x4*x5*R15 > + > x6^2*R15 + x2*x3*R16 - x1*x4*R17 + x0*x6*R17 + x0*x5*R19 - x3*x5*R111 > - > x1*x6*R112 - x1*x6*R114 + x3*x4*R115, -x3^2*R10 - x3*x4*R10 + x3^2*R11 > + > x0*x5*R11 - x2*x6*R13 - x2*x5*R15 + x1*x2*R17 + x0*x3*R17 + x0*x4*R17 > + > x2*x6*R18 - x2*x3*R19 + x3*x6*R111 - x2*x3*R112 + x0*x6*R112 - > x2*x3*R115, x1*x4*R11 - x0*x6*R11 + x3*x4*R15 + x4^2*R15 + x2*x6*R15 - > x2*x3*R18 + x0*x6*R18 + x1*x2*R19 + x0*x3*R19 + x0*x4*R19 - x3^2*R111 > - > x3*x4*R111 - x1*x6*R111, -x0*x3*x6^2*R12 - x0*x4*x6^2*R12 + > x3^2*x6^2*R13 + x3*x4*x6^2*R13 - x2*x6^3*R13 - x3*x6^3*R15 - > x4*x6^3*R15 > + x1*x2*x6^2*R16 - x3*x4*x6^2*R18 + x0*x5*x6^2*R18 + x2*x6^3*R18 - > x1*x5*x6^2*R111 + x3*x6^3*R111 + x1*x3*x6^2*R112 + x0*x6^3*R112 + > x1*x3*x6^2*R114 + x1*x4*x6^2*R114],R); > > len(K.gens()); > 13 > > Seems a long way off.... > > > Am I really pushing Sage beyond its limits or is there something else > more subtle going on? > > Thanks! > Dan > > > > > --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
