# PseudomonomialPrimaryDecomposition -- primary decomposition of a square free pseudomonomial ideal

## Description

A pseudomonomial is a polynomial in K[x1,x2,...,xn] that can be written as a product of factors of the form (xi-ai)^ni, where ai is 0 or 1. The xi's in the product should be distinct. A square free pseudomonomial ideal is an ideal generated by pseudomonomials such that each ni=1.

This package finds the primary decomposition of square free pseudomonomial ideals. It also determines if an ideal is a pseudomonomial ideal.

For example, x1^2*(x3-1) is a pseudomonomial, but not square free. The polynomial x1*(x3-1) is a square free pseudomonomial. The ideal ideal(x1*(x3-1),(x1-1)*(x2-1)*x4,x1*x2*x3,(x1-1)*x2*(x5-1)) is a square free pseudomonomial ideal.

 i1 : R = ZZ/2[x1,x2,x3,x4,x5]; i2 : I = ideal(x1*(x3-1),(x1-1)*(x2-1)*x4,x1*x2*x3,(x1-1)*x2*(x5-1)); o2 : Ideal of R i3 : isSquarefreePseudomonomialIdeal I o3 = true i4 : C = primaryDecompositionPseudomonomial I o4 = {ideal (x5 + 1, x1, x2 + 1), ideal (x2, x3 + 1, x1 + 1), ideal (x1, x4, ------------------------------------------------------------------------ x2), ideal (x1, x4, x5 + 1), ideal (x3 + 1, x4, x2)} o4 : List i5 : intersect C == I o5 = true

## Version

This documentation describes version 0.3 of PseudomonomialPrimaryDecomposition.

## Source code

The source code from which this documentation is derived is in the file PseudomonomialPrimaryDecomposition.m2.

## For the programmer

The object PseudomonomialPrimaryDecomposition is .