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VirtualResolutions :: findGensUpToIrrelevance

findGensUpToIrrelevance -- creates a list of subsets of the minimal generators that generate a given ideal up to saturation

Synopsis

Description

Given an ideal I, integer n, and irrelevant ideal irr, findGensUpToIrrelevance searches through all n-subsets of the generators of I. If a subset generates the same irr-saturated ideal as the irr-saturation of I, then that subset is added to a list. After running through all subsets, the list is returned.

i1 : R = ZZ/101[x_0,x_1,x_2,x_3,x_4,Degrees=>{2:{1,0},3:{0,1}}];
i2 : B = intersect(ideal(x_0,x_1),ideal(x_2,x_3,x_4));

o2 : Ideal of R
i3 : I = ideal(x_0^2*x_2^2+x_1^2*x_3^2+x_0*x_1*x_4^2, x_0^3*x_4+x_1^3*(x_2+x_3));

o3 : Ideal of R
i4 : findGensUpToIrrelevance(2,I,B)

o4 = {{0, 1}}

o4 : List

Caveat

If no subset of generators generates the ideal up to saturation, then the empty list is returned.

Ways to use findGensUpToIrrelevance :