isSQStable -- test whether a squarefree monomial ideal is squarefree stable

Usage:

isSQStable I
Inputs:
- I, a monomial ideal,
Outputs:
- a Boolean value, whether I is squarefree stable in the variable order of its ring

Description

Stability for squarefree ideals: for every generator g and every variable x_j of index strictly less than maxVar(g) that does not already divide g, the monomial (g / x_{maxVar(g)}) * x_j lies in I. Squarefree stability is the natural hypothesis for the Aramova-Herzog-Hibi resolution; see AHHResolution. Note that "squarefree stable" is different from "squarefree and stable".

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : isSQStable monomialIdeal(x*y, x*z, y*z)

o2 = true

i3 : isSQStable monomialIdeal(x, y*z)

o3 = true

i4 : isSQStable monomialIdeal(x*z, y*z)

o4 = false

Ways to use isSQStable:

isSQStable(MonomialIdeal)

For the programmer

The object isSQStable is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.06+ds/M2/Macaulay2/packages/ChainComplexExtras.m2:2002:0.

isSQStable -- test whether a squarefree monomial ideal is squarefree stable

Description

See also

Ways to use isSQStable:

For the programmer