scarfComplex -- gives the hull complex of a monomial ideal

Synopsis

• Usage:

  scarfComplex I

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

Description

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 : chainComplex C

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

o4 : ChainComplex

i5 : cells(1,C)/cellLabel

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

o5 : List

i6 : cells(2,C)/cellLabel

o6 = {}

o6 : List

i7 : isMinimal C

o7 = true

See also

• taylorComplex(MonomialIdeal) -- gives the Taylor complex of a monomial ideal
• hullComplex(MonomialIdeal) -- gives the hull complex of a monomial ideal