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

Author

Alan A. Veliz-Cuba <[email protected]>

Certification

Version 0.3 of this package was accepted for publication in volume 12 of The Journal of Software for Algebra and Geometry on 18 July 2022, in the article Primary decomposition of squarefree pseudomonomial ideals. That version can be obtained from the journal or from the Macaulay2 source code repository.

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.

Exports

Functions and commands
- isSquarefreePseudomonomialIdeal -- determine if an ideal is a square free pseudomonomial ideal
- primaryDecompositionPseudomonomial -- primary decomposition of a square free pseudomonomial ideal
Methods
- "isSquarefreePseudomonomialIdeal(Ideal)" -- see isSquarefreePseudomonomialIdeal -- determine if an ideal is a square free pseudomonomial ideal
- "primaryDecompositionPseudomonomial(Ideal)" -- see primaryDecompositionPseudomonomial -- primary decomposition of a square free pseudomonomial ideal

For the programmer

The object PseudomonomialPrimaryDecomposition is a package.