irreducibleDecomposition -- express a monomial ideal as an intersection of irreducible monomial ideals

• Usage:

  irreducibleDecomposition I

• Inputs:
  • I, an ideal,
• Outputs:
  • a list, containing the irreducible monomial ideals whose intersection is I

i1 : R = QQ[x..z];

i2 : I = monomialIdeal (x*y^3, x*y^2*z)

                       3     2
o2 = monomialIdeal (x*y , x*y z)

o2 : MonomialIdeal of R

i3 : w = irreducibleDecomposition I

                                      2                  3
o3 = {monomialIdeal x, monomialIdeal y , monomialIdeal (y , z)}

o3 : List

i4 : assert( I == intersect w )