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MayerVietorisTreeN1

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

Syntax
MayerVietorisTreeN1(I: IDEAL): INT

Description
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.

Example
/**/  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