binomialCellularDecomposition -- Binomial Cellular Decomposition

• Usage:

  binomialCellularDecomposition I

• Inputs:
  • I, a binomial ideal
• Optional inputs:
  • ReturnCellVars => ..., default value false
  • Verbose => ..., default value false, generate informative output
• Outputs:
  • a list of cellular ideals whose intersection is I or a list of pairs of these ideals and their cellular variables if the option ReturnCellVars => true is used

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : I = ideal (x*y-z, x*z-y^2)

                        2
o2 = ideal (x*y - z, - y  + x*z)

o2 : Ideal of R

i3 : bcd = binomialCellularDecomposition I

              2                  2
o3 = {ideal (y  - x*z, x*y - z, x  - y), ideal (z, y)}

o3 : List

i4 : intersect bcd == I

o4 = true

i5 : binomialCellularDecomposition (I, ReturnCellVars=>true, Verbose=>false)

               2                  2
o5 = {{ideal (y  - x*z, x*y - z, x  - y), {x, y, z}}, {ideal (z, y), {x}}}

o5 : List