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}}];
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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 $M$.
The object isSupportedInZeroLocus is a method function.