Hi. I have the following ideal, which turns out to be the maximal ideal generated by all the variables. Magma can compute a Groebner basis in a few seconds, while in Singular, "std(I)" seems to take forever. Is there a trick that one can use to speed up the computation, or is Magma using voodoo magic? Thanks! Code: ring R = 0,(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28),dp; ideal I = -x6*x9+x5*x10-x8*x11+x7*x12,-2*x1*x10-x2*x11-x2*x12+x3*x12,x3*x9+2*x0*x10+x4*x10-2*x6,-x3*x10-x8*x10+x0*x11+x0*x12+x6*x12-x3-x7-x8,-x1*x9+x2*x10-x0*x12+x2+x4+x8,-x7*x9-x1*x10+x5*x11-x3,x7*x10-x4*x11-x6*x11-x10,-x7*x9+x5*x11-x2*x12+2*x1+x9,x4*x9+x6*x9-x5*x10+x2-x12,x2*x10+x2-x3+x11,-x6*x13+x5*x14-x8*x15+x7*x16,-2*x1*x14-x2*x15-x2*x16+x3*x16+2*x6,x3*x13+2*x0*x14+x4*x14,-x3*x14-x8*x14+x0*x15+x0*x16+x6*x16+x4,-x1*x13+x2*x14-x0*x16+x5,-x7*x13-x1*x14+x5*x15-x2+x6,x7*x14-x4*x15-x6*x15-x3-x14,-x7*x13+x5*x15-x2*x16-2*x0-x4+x13,x4*x13+x6*x13-x5*x14-x16,x2*x14+x15,-x6*x17+x5*x18-x8*x19+x7*x20,-2*x1*x18-x2*x19-x2*x20+x3*x20+x3+x7+x8,x3*x17+2*x0*x18+x4*x18-x4,-x3*x18-x8*x18+x0*x19+x0*x20+x6*x20,-x1*x17+x2*x18-x0*x20-x0-x6,-x7*x17-x1*x18+x5*x19+x1,x7*x18-x4*x19-x6*x19-x18,-x7*x17+x5*x19-x2*x20+x3+x8+x17,x4*x17+x6*x17-x5*x18-x0-x20,x2*x18-x0-x6+x19,-x6*x21+x5*x22-x8*x23+x7*x24,-2*x1*x22-x2*x23-x2*x24+x3*x24-x2-x4-x8,x3*x21+2*x0*x22+x4*x22-x5,-x3*x22-x8*x22+x0*x23+x0*x24+x6*x24+x0+x6,-x1*x21+x2*x22-x0*x24,-x7*x21-x1*x22+x5*x23+x0,x7*x22-x4*x23-x6*x23+x1-x22,-x7*x21+x5*x23-x2*x24-x2+x21,x4*x21+x6*x21-x5*x22-x24,x2*x22+x0+x23,-x6*x25+x5*x26-x8*x27+x7*x28,-2*x1*x26-x2*x27-x2*x28+x3*x28+x3,x3*x25+2*x0*x26+x4*x26+x2-x6,-x3*x26-x8*x26+x0*x27+x0*x28+x6*x28-x1,-x1*x25+x2*x26-x0*x28-x0,-x7*x25-x1*x26+x5*x27,x7*x26-x4*x27-x6*x27+x7-x26,-x7*x25+x5*x27-x2*x28+x1+x25,x4*x25+x6*x25-x5*x26-x5-x28,x2*x26+x27;
Hi. I have the following ideal, which turns out to be the maximal ideal generated by all the variables. Magma can compute a Groebner basis in a few seconds, while in Singular, "std(I)" seems to take forever. Is there a trick that one can use to speed up the computation, or is Magma using voodoo magic? Thanks!
[code]ring R = 0,(x0,x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28),dp; ideal I = -x6*x9+x5*x10-x8*x11+x7*x12,-2*x1*x10-x2*x11-x2*x12+x3*x12,x3*x9+2*x0*x10+x4*x10-2*x6,-x3*x10-x8*x10+x0*x11+x0*x12+x6*x12-x3-x7-x8,-x1*x9+x2*x10-x0*x12+x2+x4+x8,-x7*x9-x1*x10+x5*x11-x3,x7*x10-x4*x11-x6*x11-x10,-x7*x9+x5*x11-x2*x12+2*x1+x9,x4*x9+x6*x9-x5*x10+x2-x12,x2*x10+x2-x3+x11,-x6*x13+x5*x14-x8*x15+x7*x16,-2*x1*x14-x2*x15-x2*x16+x3*x16+2*x6,x3*x13+2*x0*x14+x4*x14,-x3*x14-x8*x14+x0*x15+x0*x16+x6*x16+x4,-x1*x13+x2*x14-x0*x16+x5,-x7*x13-x1*x14+x5*x15-x2+x6,x7*x14-x4*x15-x6*x15-x3-x14,-x7*x13+x5*x15-x2*x16-2*x0-x4+x13,x4*x13+x6*x13-x5*x14-x16,x2*x14+x15,-x6*x17+x5*x18-x8*x19+x7*x20,-2*x1*x18-x2*x19-x2*x20+x3*x20+x3+x7+x8,x3*x17+2*x0*x18+x4*x18-x4,-x3*x18-x8*x18+x0*x19+x0*x20+x6*x20,-x1*x17+x2*x18-x0*x20-x0-x6,-x7*x17-x1*x18+x5*x19+x1,x7*x18-x4*x19-x6*x19-x18,-x7*x17+x5*x19-x2*x20+x3+x8+x17,x4*x17+x6*x17-x5*x18-x0-x20,x2*x18-x0-x6+x19,-x6*x21+x5*x22-x8*x23+x7*x24,-2*x1*x22-x2*x23-x2*x24+x3*x24-x2-x4-x8,x3*x21+2*x0*x22+x4*x22-x5,-x3*x22-x8*x22+x0*x23+x0*x24+x6*x24+x0+x6,-x1*x21+x2*x22-x0*x24,-x7*x21-x1*x22+x5*x23+x0,x7*x22-x4*x23-x6*x23+x1-x22,-x7*x21+x5*x23-x2*x24-x2+x21,x4*x21+x6*x21-x5*x22-x24,x2*x22+x0+x23,-x6*x25+x5*x26-x8*x27+x7*x28,-2*x1*x26-x2*x27-x2*x28+x3*x28+x3,x3*x25+2*x0*x26+x4*x26+x2-x6,-x3*x26-x8*x26+x0*x27+x0*x28+x6*x28-x1,-x1*x25+x2*x26-x0*x28-x0,-x7*x25-x1*x26+x5*x27,x7*x26-x4*x27-x6*x27+x7-x26,-x7*x25+x5*x27-x2*x28+x1+x25,x4*x25+x6*x25-x5*x26-x5-x28,x2*x26+x27;[/code]
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