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ExteriorIdeals :: ExteriorIdeals

ExteriorIdeals -- a package for working with ideals over exterior algebra

Description

ExteriorIdeals is a package for creating and manipulating ideals over exterior algebra

Other acknowledgements:

The method isLexIdeal was taken from Chris Francisco's package: LexIdeals, which is available at LexIdeals

Authors

Certification a gold star

Version 1.0 of this package was accepted for publication in volume 8 of the journal The Journal of Software for Algebra and Geometry on 24 June 2018, in the article ExteriorIdeals: a package for computing monomial ideals in an exterior algebra. That version can be obtained from the journal or from the Macaulay2 source code repository, http://github.com/Macaulay2/M2/blob/master/M2/Macaulay2/packages/ExteriorIdeals.m2, commit number 1073789664ba1f00096121613a8b6d932a0e5c4e.

Version

This documentation describes version 1.0 of ExteriorIdeals.

Source code

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

Exports

  • Functions and commands
    • allHilbertSequences -- compute all Hilbert sequences of quotients in an exterior algebra
    • hilbertSequence -- compute the Hilbert sequence of a given ideal in an exterior algebra
    • initialDegree -- compute the initial degree of a graded ideal
    • isHilbertSequence -- whether the given sequence is a Hilbert sequence
    • isLexIdeal -- whether an ideal is lex
    • isStableIdeal -- whether a monomial ideal in an exterior algebra is stable
    • isStronglyStableIdeal -- whether a monomial ideal in an exterior algebra is strongly stable
    • lexIdeal -- compute the lex ideal with a given Hilbert function in an exterior algebra
    • macaulayExpansion -- compute the Macaulay expansion of a positive integer
    • solveMacaulayExpansion -- compute the sum of a Macaulay expansion
    • stableIdeal -- compute the smallest stable ideal in an exterior algebra containing a given monomial ideal
    • stronglyStableIdeal -- compute the smallest strongly stable ideal in an exterior algebra containing a given monomial ideal
  • Symbols
    • Shift -- optional argument for macaulayExpansion