Le samedi 7 mai 2016 07:30:42 UTC+2, john_perry_usm a écrit : > > I'm sorry. I got the name mixed up; the function you want to look at is > sba(), not dstd() (which is something experimental of mine that never saw > the light of day). > > http://www.singular.uni-kl.de/Manual/latest/sing_391.htm#SEC430 > > Because my copy of Singular is a little... "tinkered with" I'd have to > redownload and recompile Singular, but replace std() with sba() in your > example and see how the timings compare, but for example when I run your > example the timing my version reports falls from 169 to 114. -- Again, I > tinkered with mine, so the timings won't be reflective of actual > performance. > > sba is indeed a little faster for cyclic7 in Z/pZ (25%) but not for cyclic8 in Z/pZ (10 minutes here compared to groebner 40s, giac 3.3s) and it eats a lot of memory (1.5G, compared to 45M for giac) //timer=1; system("--ticks-per-sec",100); //option(prot); ring r=16777213,(x1,x2,x3,x4,x5,x6,x7,x8),dp; ideal k=x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8, x1*x2 + x2*x3 + x3*x4 + x4*x5 + x5*x6 + x6*x7 + x1*x8 + x7*x8, x1*x2*x3 + x2*x3*x4 + x3*x4*x5 + x4*x5*x6 + x5*x6*x7 + x1*x2*x8 + x1*x7*x8 + x6*x7*x8, x1*x2*x3*x4 + x2*x3*x4*x5 + x3*x4*x5*x6 + x4*x5*x6*x7 + x1*x2*x3*x8 + x1*x2*x7*x8 + x1*x6*x7*x8 + x5*x6*x7*x8, x1*x2*x3*x4*x5 + x2*x3*x4*x5*x6 + x3*x4*x5*x6*x7 + x1*x2*x3*x4*x8 + x1*x2*x3*x7*x8 + x1*x2*x6*x7*x8 + x1*x5*x6*x7*x8 + x4*x5*x6*x7*x8, x1*x2*x3*x4*x5*x6 + x2*x3*x4*x5*x6*x7 + x1*x2*x3*x4*x5*x8 + x1*x2*x3*x4*x7*x8 + x1*x2*x3*x6*x7*x8 + x1*x2*x5*x6*x7*x8 + x1*x4*x5*x6*x7*x8 + x3*x4*x5*x6*x7*x8, x1*x2*x3*x4*x5*x6*x7 + x1*x2*x3*x4*x5*x6*x8 + x1*x2*x3*x4*x5*x7*x8 + x1*x2*x3*x4*x6*x7*x8 + x1*x2*x3*x5*x6*x7*x8 + x1*x2*x4*x5*x6*x7*x8 + x1*x3*x4*x5*x6*x7*x8 + x2*x3*x4*x5*x6*x7*x8, x1*x2*x3*x4*x5*x6*x7*x8 - 1; //int RT = rtimer; int T=timer; size(groebner(k)); rtimer-RT; timer-T; int RT = rtimer; int T=timer; size(sba(k)); rtimer-RT; timer-T; This does not change the comparison (especially if you consider that giac is now a little faster than in Roman reported timings and this might also be the case for mgb and magma), singular is still much slower than the 3 others for dense inputs.
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