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isSupportedInZeroLocus -- whether support of a module is contained in the zero locus of the (irrelevant) ideal



Given an module $M$ and an ideal $B$, isSupportedInZeroLocus checks whether $\mathrm{ann}(M):B^\infty=R$. If it is, isSupportedInZeroLocus returns true otherwise it returns false. If the first argument is an ideal, $M = R^1/I$ is taken as the module.

i1 : S = ZZ/32003[x_0..x_4, Degrees=>{2:{1,0}, 3:{0,1}}];
i2 : irr = intersect(ideal(x_0,x_1), ideal(x_2,x_3,x_4));

o2 : Ideal of S
i3 : M = S^1/(irr^2);
i4 : isSupportedInZeroLocus_irr M

o4 = true

This is done without computing saturation of $M$. Instead, we check whether for each generator of $B$ some power of it annihilates the module $M$.

Ways to use isSupportedInZeroLocus :

For the programmer

The object isSupportedInZeroLocus is a method function.