cellularBinomialPrimaryDecomposition -- Primary decomposition of a cellular binomial ideal

Synopsis

• Usage:

  cellularBinomialPrimaryDecomposition I

• Inputs:
  • I, a cellular binomial ideal
• Optional inputs:
  • CellVariables => ..., default value null, cellular variables
  • Verbose => ..., default value false, generate informative output
• Outputs:
  • a binomial primary decomposition of I

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 : pd = cellularBinomialPrimaryDecomposition (I,CellVariables=>cv)

o4 = {ideal (y - 1, x - 1), ideal (y - ww , x - ww ), ideal (y + ww  + 1, x +
                                         3        3                3         
     ------------------------------------------------------------------------
     ww  + 1)}
       3

o4 : List

i5 : mingens \ pd

o5 = {| y-1 x-1 |, | y-ww_3 x-ww_3 |, | y+ww_3+1 x+ww_3+1 |}

o5 : List

Caveat

See also

• binomialAssociatedPrimes -- Associated primes of a binomial ideal