*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 *ℤ ^{d}*-graded module

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 is written when the ambient ring of the modules in question are positively graded and are presented by a monomial matrix, that is, a matrix whose entries are monomials. This is due to the algorithms depending on finding standard pairs of monomial ideals generated by rows of a presentation matrix.

Version **1.0** of this package was accepted for publication in volume 9 of the journal The Journal of Software for Algebra and Geometry on 26 February 2019, in the article Computing quasidegrees of A-graded modules. That version can be obtained from the journal or from the *Macaulay2* source code repository, http://github.com/Macaulay2/M2/blob/master/M2/Macaulay2/packages/Quasidegrees.m2, commit number d76252d2c8d38f0ec55212eb458869503b1f0312.

- Functions and commands
- exceptionalSet -- returns the exceptional set of a matrix
- makeGradedRing -- makes a polynomial ring graded by a matrix
- quasidegrees -- compute the quasidegree set of a module
- quasidegreesAsVariables -- quasidegrees represented as variables
- quasidegreesLocalCohomology -- quasidegrees of local cohomology of module
- removeRedundancy -- removes redundancies from a list of planes
- toGradedRing -- grade a polynomial ring by a matrix
- toricIdeal -- returns a toric ideal