GeometricDecomposability Changelog

Version 1.5

Currently in development and available on github. We hope to include this in version 1.24 of Macaulay2.

• Added an optional input AllowSub, implementing the notion of a geometric vertex decomposition allowing substitution.

Version 1.4

Included in version 1.23 of Macaulay2.

• Added an optional input UniversalGB for when the given generating set of an ideal is a universal Gröbner basis. In this setting, the ideals C_y,I and N_y,I each inherit a universal Gröbner basis, and hence we can avoid computing Gröbner bases when checking whether I is geometrically vertex decomposable.
• Added an optional input SquarefreeOnly for the function findOneStepGVD. For an ideal I to have a geometric vertex decomposition with respect to y, it is sufficient for y to appear in the given generating set for I with maximum degree 1. When SquarefreeOnly=>true, we return only the variables that are squarefree in the generating set for I. This is much quicker, but does not necessarily provide an exhaustive list. The GVD methods now prefer these squarefree variables when computing C_y,I and N_y,I.
• Implemented suggestions from Patricia Klein:
  • Since Cohen-Macaulay implies unmixed, we need not always check unmixedness.
  • To check whether a homogeneous ideal is Cohen-Macaulay, we now check for equality between projective dimension and codimension. This is quicker than what it replaces, the isCM method from the Depth package, which verifies equality between dimension and depth. That these methods are equivalent in the homogeneous setting is guaranteed by Auslander–Buchsbaum.
  • The isGVD method now checks whether N_y,I is geometrically vertex decomposable before C_y,I. The link of a Cohen-Macaulay ideal will be Cohen-Macaulay, but the deletion need not be. So it may be more likely for N_y,I to not be Cohen-Macaulay and hence not geometrically vertex decomposable.

Version 1.3

Currently available on github.

• Renamed methods:
  • CyI has been renamed oneStepGVDCyI,
  • NyI has been renamed oneStepGVDNyI,
  • yInit has been renamed initialYForms.
• Updated isUnmixed; it should now run quicker

Version 1.2

Included in version 1.22 of Macaulay2.

• Fixed the error that would appear upon loading the package.
• Removed the documentation page for the optional input Verbose.

Version 1.1

First version of the package, included in version 1.21 of Macaulay2.