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N-1st Betti multidegrees of monomial ideals using Mayer-Vietoris trees

MayerVietorisTreeN1(I: IDEAL): INT

Implemented in CoCoALib by Eduardo Saenz-de-Cabezon.

This function returns the list of multidegrees M such that the N-1st Betti number of a monomial ideal I at multidegree M is not zero. It is computed via a version of its Mayer-Vietoris tree.

The length of this list is the number of irreducible components of I, the number of maximal standard monomials, and the number of generators of its Alexander Dual.

/**/  Use QQ[x,y,z];
/**/  I := ideal(x, y, z)^2;
/**/  MayerVietorisTreeN1(I);
[x^2*y*z, x*y^2*z, x*y*z^2]

See Also