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

## Synopsis

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

## 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 :

• "irreducibleDecomposition(MonomialIdeal)"

## For the programmer

The object irreducibleDecomposition is .