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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 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.

Version

This documentation describes version 1.1 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
    • initialIdeal -- compute the initial ideal of a given 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
    • minimalBettiNumbers -- compute the minimal Betti numbers of a given graded ideal
    • 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
  • Methods
    • "allHilbertSequences(Ring)" -- see allHilbertSequences -- compute all Hilbert sequences of quotients in an exterior algebra
    • "hilbertSequence(Ideal)" -- see hilbertSequence -- compute the Hilbert sequence of a given ideal in an exterior algebra
    • "initialDegree(Ideal)" -- see initialDegree -- compute the initial degree of a graded ideal
    • "initialIdeal(Ideal)" -- see initialIdeal -- compute the initial ideal of a given ideal
    • "isHilbertSequence(List,Ring)" -- see isHilbertSequence -- whether the given sequence is a Hilbert sequence
    • "isLexIdeal(Ideal)" -- see isLexIdeal -- whether an ideal is lex
    • "isStableIdeal(Ideal)" -- see isStableIdeal -- whether a monomial ideal in an exterior algebra is stable
    • "isStronglyStableIdeal(Ideal)" -- see isStronglyStableIdeal -- whether a monomial ideal in an exterior algebra is strongly stable
    • "lexIdeal(Ideal)" -- see lexIdeal -- compute the lex ideal with a given Hilbert function in an exterior algebra
    • "lexIdeal(List,Ring)" -- see lexIdeal -- compute the lex ideal with a given Hilbert function in an exterior algebra
    • "macaulayExpansion(ZZ,ZZ)" -- see macaulayExpansion -- compute the Macaulay expansion of a positive integer
    • "minimalBettiNumbers(Ideal)" -- see minimalBettiNumbers -- compute the minimal Betti numbers of a given graded ideal
    • "solveMacaulayExpansion(List)" -- see solveMacaulayExpansion -- compute the sum of a Macaulay expansion
    • "stableIdeal(Ideal)" -- see stableIdeal -- compute the smallest stable ideal in an exterior algebra containing a given monomial ideal
    • "stronglyStableIdeal(Ideal)" -- see stronglyStableIdeal -- compute the smallest strongly stable ideal in an exterior algebra containing a given monomial ideal
  • Symbols
    • Shift -- optional argument for macaulayExpansion

For the programmer

The object ExteriorIdeals is a package.