Quasidegrees

Macaulay2 package Quasidegrees: Quasidegrees is a package that enables the user to construct multigraded rings and look at the graded structure of multigraded finitely generated modules over a polynomial ring. The quasidegree set of a ℤd-graded module M is the Zariski closure in Cd of the degrees of the nonzero homogeneous components of M. This package can compute the quasidegree set of a finitely generated module over a ℤd-graded polynomial ring. This package also computes the quasidegree sets of local cohomology modules supported at the maximal irrelevant ideal of modules over a ℤd-graded polynomial ring. The motivation for this package comes from A-hypergeometric functions and the relation between the rank jumps of A-hypergeometric systems and the quasidegree sets of non-top local cohomology modules supported at the maximal irrelevant ideal of the associated toric ideal as described in the paper: Laura Felicia Matusevich, Ezra Miller, and Uli Walther. Homological methods for hypergeometric families. J. Am. Math. Soc., 18(4):919-941, 2005. This package requires FourTiTwo, Depth, and Polyhedra.

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