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N1st Betti multidegrees of monomial ideals using MayerVietoris trees
MayerVietorisTreeN1(I: IDEAL): INT 
Implemented in CoCoALib by Eduardo SaenzdeCabezon.
This function returns the list of multidegrees
M
such that the N1st
Betti number of a monomial ideal
I
at multidegree
M
is not zero.
It is computed via a version of its MayerVietoris 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]
