# MonomialOrbits -- find orbit representatives of monomial ideals, under permutations of the variables

## Description

This package contains functions for the construction of representatives of the orbits of monomial ideals of a given type in a polynomial ring $S$ under the group of permutations of the variables of $S$.

The type of the ideals may be defined either by the number of minimal generators of each degree, or by the set of monomials from which to choose or by the set of monomials from which to subtract in orbitRepresentatives or by the Hilbert function, in hilbertRepresentatives. If the option MonomialType => "SquareFree" is given, then only square-free monomial ideals are considered.

## Version

This documentation describes version 1.5 of MonomialOrbits.

## Source code

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

## Exports

• Functions and commands
• hilbertRepresentatives -- find representatives of monomial ideals under permutations of the variables
• normalForms -- chooses orbit representatives from a list of monomial ideals, under a group of permutations
• orbitRepresentatives -- find representatives of monomial ideals under permutations of variables
• Methods
• "hilbertRepresentatives(Ring,VisibleList)" -- see hilbertRepresentatives -- find representatives of monomial ideals under permutations of the variables
• "normalForms(List,List)" -- see normalForms -- chooses orbit representatives from a list of monomial ideals, under a group of permutations
• "orbitRepresentatives(Ring,Ideal,Ideal,ZZ)" -- see orbitRepresentatives -- find representatives of monomial ideals under permutations of variables
• "orbitRepresentatives(Ring,Ideal,VisibleList)" -- see orbitRepresentatives -- find representatives of monomial ideals under permutations of variables
• "orbitRepresentatives(Ring,VisibleList)" -- see orbitRepresentatives -- find representatives of monomial ideals under permutations of variables
• Symbols

## For the programmer

The object MonomialOrbits is .