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

Synopsis

Description

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 )

Ways to use irreducibleDecomposition :

For the programmer

The object irreducibleDecomposition is a method function.