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MonomialOrbits :: MonomialOrbits

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, in orbitRepresentatives or by the Hilbert function, in hilbertRepresentatives. If the option MonomialType => "SquareFree" is given, then only square-free monomial ideals are considered.

Authors

Version

This documentation describes version 0.9 of MonomialOrbits.

Source code

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

Exports

  • Functions and commands
  • Methods
    • "hilbertRepresentatives(Ring,VisibleList)" -- see hilbertRepresentatives -- find representatives of monomial ideals under permutations of the variables
    • "orbitRepresentatives(Ring,MonomialIdeal,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.

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Enumerating monomial ideals with given generator degrees

Enumerating monomial ideals with given Hilbert function

Options limiting the type of ideals generated