DMS Algebra/Linear Algebra Seminar

Speaker: Doug Leonard

Title: Standard monomial generating functions

Abstract: For  ideals I of a multivariate polynomial ring R,  a minimal, reduced Gröbner basis describes the leading monomials, and leads to elementary methods for computing their complement, the set of standard monomials.

In this context, this would be a generalization of Hilbert series, which only counts the number of such of given degree, grading, multi-grading,.... So it is natural to see how this is related to free resolutions of R/I and all things related to same, especially as this is not restricted to homogeneous ideals in graded/multi-graded rings.

Singular has several ways of computing free resolutions, whereas Macaulay2 has only one. So we'll look at some of them to see if any come close to what we will produce.