EKResolution -- Eliahou-Kervaire minimal free resolution of a stable monomial ideal

Usage:

EKResolution I
Inputs:
- I, a monomial ideal, that is stable
Outputs:
- a chain complex, the Eliahou-Kervaire resolution of S/I

Description

Assembles the maps produced by EK into a chain complex. For a stable monomial ideal the result is a minimal free resolution of S/I, by the theorem of Eliahou and Kervaire [EK].

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

o1 = R

o1 : PolynomialRing

i2 : I = monomialIdeal(x^2, x*y, y^2, y*z)

                     2        2
o2 = monomialIdeal (x , x*y, y , y*z)

o2 : MonomialIdeal of R

i3 : EKR = EKResolution I

      1      4      4      1
o3 = R  <-- R  <-- R  <-- R
                           
     0      1      2      3

o3 : Complex

i4 : betti EKR == betti res I

o4 = true

i5 : isResolution(EKR, I)

o5 = true

Caveat

The function does not check that I is stable; on a non-stable ideal the result may not be a resolution.

Ways to use EKResolution:

EKResolution(MonomialIdeal)

For the programmer

The object EKResolution is a method function.

The source of this document is in ChainComplexExtras.m2:2071:0.

EKResolution -- Eliahou-Kervaire minimal free resolution of a stable monomial ideal

Description

Caveat

See also

Ways to use EKResolution:

For the programmer