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?
Thanks, Dan On Jun 25, 12:42 am, mabshoff <[EMAIL PROTECTED] dortmund.de> wrote: > On Jun 24, 1:31 pm, "John Cremona" <[EMAIL PROTECTED]> wrote: > > > 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? > > Yes, GB computations have some of the worst case complexities I know > about. And adding innocent looking generators or even changing > something seemingly innocent like coefficients or adding "small" terms > to the generators can radically change the computations time and > memory consumption. > > Additionally you are using a 32 bit VMWare image with limited RAM and > swap, so once you hit swap it is basically game over for the GB > computations since it tends to have bad locality. If other packages > can easily compute the problem in question it is likely a coincidence > since I am sure one can find examples where the opposite occurs. Note > that Maple uses FGB and Magama implemented F4, both which tend to be > more memory hungry than slimgb implemented in Singular. > > > John Cremona > > Cheers, > > Michael > > > 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 -~----------~----~----~----~------~----~------~--~---
