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

Synopsis

Usage:
irreducibleDecomposition I
Function: irreducibleDecomposition
Inputs:
- I, a monomial ideal
Outputs:
- a list, a list of irreducible monomial ideals whose intersection is I

Description

i1 : 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 QQ[x, y, z]

i3 : w = irreducibleDecomposition I

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

o3 : List

i4 : assert( I == intersect w )