isStable -- test whether a monomial ideal is stable

Usage:

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

Description

A monomial ideal I in S = k[x_1, ..., x_n] is stable if for every minimal generator g and every variable x_j of index strictly less than the largest index appearing in g, the monomial (g / x_{maxVar(g)}) * x_j lies in I. Stability depends on the variable order of the ring. Stable monomial ideals are exactly the ones for which the Eliahou-Kervaire formula gives a minimal free resolution; see EKResolution.

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

o1 = R

o1 : PolynomialRing

i2 : isStable monomialIdeal(x^3, x^2*y, x*y^2, y^3)

o2 = true

i3 : isStable monomialIdeal(x^3, x*y^2, y^3)

o3 = false

Ways to use isStable:

isStable(MonomialIdeal)

For the programmer

The object isStable is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.06+ds/M2/Macaulay2/packages/ChainComplexExtras.m2:1971:0.

isStable -- test whether a monomial ideal is stable

Description

See also

Ways to use isStable:

For the programmer