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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.

Menu

Enumerating monomial ideals with given generator degrees or number of elements

Enumerating monomial ideals with given Hilbert function

Options limiting the type of ideals generated

Authors

Version

This documentation describes version 1.5 of MonomialOrbits.

Citation

If you have used this package in your research, please cite it as follows:

@misc{MonomialOrbitsSource,
  title = {{MonomialOrbits: Orbit representatives of monomial ideals. Version~1.5}},
  author = {David Eisenbud and Mike Stillman},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

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 a package, defined in MonomialOrbits.m2.

The source of this document is in MonomialOrbits.m2:324:0.