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scarfComplex -- gives the hull complex of a monomial ideal

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

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

o5 : List
 
i6 : cells(2,C)/cellLabel

o6 = {}

o6 : List
 
i7 : isMinimal C

o7 = true

See also

Ways to use scarfComplex:

  • scarfComplex(MonomialIdeal)

For the programmer

The object scarfComplex is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/CellularResolutions/doc.m2:1309:0.