|\^/| Maple V Release 5 (University of California, Davis) ._|\| |/|_. Copyright (c) 1981-1997 by Waterloo Maple Inc. All rights \ MAPLE / reserved. Maple and Maple V are registered trademarks of <____ ____> Waterloo Maple Inc. | Type ? for help. # Ok, here is an example of when the GB for plex is the graph E # but if we change the monomial order the graph is different! > > with(Groebner); [fglm, gbasis, gsolve, hilbertdim, hilbertpoly, hilbertseries, inter_reduce, is_finite, is_solvable, leadcoeff, leadmon, leadterm, normalf, pretend_gbasis, reduce, spoly, termorder, testorder, univpoly] > > F:=[x1*x2-x3*x6, x1*x3,x1*x4, x1*x5, x1*x6, x2*x3,x2*x4, x2*x5, > x2*x6, x3*x4, x3*x7, x4*x5,x4*x7, x4*x8, x5*x8]; F := [x1 x2 - x3 x6, x1 x3, x1 x4, x1 x5, x1 x6, x2 x3, x2 x4, x2 x5, x2 x6, x3 x4, x3 x7, x4 x5, x4 x7, x4 x8, x5 x8] > > > > U:=map(y->leadterm(y,plex(x1,x2,x3,x4,x5,x6,x7,x8)),gbasis(F,plex(x1,x2,x3,x4,x5,x6,x7,x8))); bytes used=1000864, alloc=917336, time=0.16 bytes used=2001168, alloc=1310480, time=0.37 2 2 U := [x5 x8, x4 x8, x4 x7, x4 x5, x3 x7, x3 x6 , x5 x3 x6, x3 x4, x3 x6, x2 x6, x2 x5, x2 x4, x2 x3, x1 x6, x1 x5, x1 x4, x1 x3, x1 x2] > > hilbertdim(U,plex(x1,x2,x3,x4,x5,x6,x7,x8)); bytes used=3001484, alloc=1376004, time=0.58 bytes used=4001752, alloc=1507052, time=0.84 3 > > print(`------------------------------`); ------------------------------ > U:=map(y->leadterm(y,plex(x8,x7,x6,x5,x4,x3,x1,x2)), gbasis(F,plex(x8,x7,x6,x5,x4,x3,x1,x2))); bytes used=5001944, alloc=1507052, time=1.07 bytes used=6002728, alloc=1507052, time=1.31 2 2 U := [x1 x2 , x1 x2, x2 x3, x1 x3, x2 x4, x1 x4, x3 x4, x2 x5, x1 x5, x4 x5, x2 x6, x1 x6, x3 x6, x7 x1 x2, x3 x7, x4 x7, x4 x8, x5 x8] > > hilbertdim(U,plex(x6,x7,x8,x5,x4,x3,x1,x2)); bytes used=7003320, alloc=1572576, time=1.53 bytes used=8003512, alloc=1572576, time=1.79 3 > print(`-------------------------------`); ------------------------------- > > U:=map(x->leadterm(x,tdeg(x1,x2,x3,x4,x5,x6,x7,x8)),gbasis(F,tdeg(x1,x2,x3,x4,x5,x6,x7,x8))); bytes used=9004488, alloc=1572576, time=2.02 bytes used=10005248, alloc=1572576, time=2.25 U := [x5 x8, x4 x8, x4 x7, x3 x7, x2 x6, x1 x6, x4 x5, x2 x5, x1 x5, x3 x4, 2 2 x2 x4, x1 x4, x2 x3, x1 x3, x1 x2, x3 x6 , x5 x3 x6, x3 x6] > > hilbertdim(U,tdeg(x1,x2,x3,x4,x5,x6,x7,x8)); bytes used=11005416, alloc=1572576, time=2.50 3 > quit bytes used=11755180, alloc=1572576, time=2.66