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