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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]
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