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

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.

See also

Ways to use EKResolution:

  • EKResolution(MonomialIdeal)

For the programmer

The object EKResolution is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.06+ds/M2/Macaulay2/packages/ChainComplexExtras.m2:2071:0.