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EK -- n-th map in the Eliahou-Kervaire resolution

Description

Returns the n-th map in the Eliahou-Kervaire resolution of S/I, following the formulas in [EK]. For n == 0 this is just the generator matrix gens I. The function does not check whether I is stable; on a non-stable ideal the resulting complex may not be a resolution.

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 : EK(0, I)

o3 = | x2 xy y2 yz |

             1      4
o3 : Matrix R  <-- R
 
i4 : EK(2, I)

o4 = {3} | 0  |
     {3} | z  |
     {3} | -y |
     {3} | x  |

             4      1
o4 : Matrix R  <-- R

Caveat

Does not verify stability of I; use isStable to check.

See also

Ways to use EK:

  • EK(ZZ,MonomialIdeal)

For the programmer

The object EK is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.06+ds/M2/Macaulay2/packages/ChainComplexExtras.m2:2036:0.