PseudomonomialPrimaryDecomposition -- primary decomposition of a square free pseudomonomial ideal

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