GeometricDecomposability Changelog
Version 1.5
Currently in development and available on github (currently, this version is out of date). We hope to include this in a later version of Macaulay2.
- Added an optional input
AllowSub
, implementing the notion of a geometric vertex decomposition allowing substitution.
Version 1.4.1
Submitted to be included in version 1.24 of Macaulay2.
- Fixed how geometric vertex decompositions are checked when a universal Gröbner basis is provided.
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 Cy,I and Ny,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 functionfindOneStepGVD
. 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. WhenSquarefreeOnly=>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 Cy,I and Ny,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 theDepth
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 Ny,I is geometrically vertex decomposable before Cy,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 Ny,I to not be Cohen-Macaulay and hence not geometrically vertex decomposable.
Version 1.3
Currently available on github.
- Renamed methods:
CyI
has been renamedoneStepGVDCyI
,NyI
has been renamedoneStepGVDNyI
,yInit
has been renamedinitialYForms
.
- 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.