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