flearex / workshop-2016-warwick

Collaboration area for the Macaulay2 workshop at the University of Warwick, May 23-26, 2016.

Workshop-2016-Warwick

Collaboration area for the Macaulay2 workshop at the University of Warwick, May 23-26, 2016.

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• The directory "RandomIdeals" contains packages created or refined at the M2 workshop in Utah. David Eisenbud wants to work on them and polish them for possible inclusion in Macaulay2 v 1.9.1, and perhaps for a publication in JSAG.

• One of the packages, RandomIdeal.m2, contains code for constructing various sorts of ideals at random; in particular, it can create random (in some distribution) shellable simplicial complexes of given dimension and degree, and thus random square-free monomial ideals that are Cohen-Macaulay.

• The other package, ResidualIntersection.m2, contains tests for many of the special properties of Cohen-Macaulay ideals that have been used in the theory of residual intersections; things such as "strongly Cohen-Macaulay" and "sliding depth" and "G_d"

• Eisenbud hopes to use these two packages together to construct interesting new families of square-free monomial ideals for which these strong Cohen-Macaulay properties hold, and to try in this way to understand them combinatorially.

• Dan Grayson adds something to this file