partialCharacter -- Computing the partial character of a cellular binomial ideal

Synopsis

• Usage:

  partialCharacter I

• Inputs:

  • I, a cellular binomial ideal
• Optional inputs:

  • cellVariables => ..., -- Computing the partial character of a cellular binomial ideal
• Outputs:

  • cv, the cellular variables
  • L, A matrix whose columns are generators for the lattice supporting the character
  • c, The values that the character takes on the generator

Description

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : I = ideal(x^3-1,y-x)

             3
o2 = ideal (x  - 1, - x + y)

o2 : Ideal of R

i3 : cv = isCellular (I,returnCellVars=>true)

o3 = {x, y}

o3 : List

i4 : pc = partialCharacter (I,cellVariables=>cv)

o4 = ({x, y}, | 1  0 |, {1, 1})
              | -1 3 |

o4 : Sequence