scarfComplex -- gives the hull complex of a monomial ideal

Usage:

scarfComplex I
Inputs:
- I, a monomial ideal,
Outputs:
- a cell complex, the scarf complex of $I$

Description

Given a monomial ideal $I$, this function returns the Scarf complex of that ideal. This complex, which is a subcomplex of the Taylor complex, if it is a resolution is always minimal, but it need not be a resolution in general.

i1 : S = QQ[x,y,z];

i2 : I = monomialIdeal (x^2*z, x*y*z, y^2*z, x^3*y^5, x^4*y^4, x^5*y^3);

o2 : MonomialIdeal of S

i3 : C = scarfComplex I

o3 = C

o3 : CellComplex

i4 : complex C

      1      6      4
o4 = S  <-- S  <-- S
                    
     -1     0      1

o4 : Complex

i5 : cells(1,C)/cellLabel

       5 4     2    2      4 5
o5 = {x y , x*y z, x y*z, x y }

o5 : List

i6 : cells(2,C)/cellLabel

o6 = {}

o6 : List

i7 : isMinimal C

o7 = true

Ways to use scarfComplex:

scarfComplex(MonomialIdeal)

For the programmer

The object scarfComplex is a method function.

The source of this document is in CellularResolutions/doc.m2:1309:0.

scarfComplex -- gives the hull complex of a monomial ideal

Description

See also

Ways to use scarfComplex:

For the programmer