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# 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

## 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 a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/PrimaryDecomposition/doc.m2:750:0.