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• GeometricDecomposability -- a package to check whether ideals are geometrically vertex decomposable
• CheckCM -- when to perform a Cohen-Macaulay check on the ideal
• CheckDegenerate -- check whether the geometric vertex decomposition is degenerate
• CheckUnmixed -- check whether ideals encountered are unmixed
• findLexCompatiblyGVDOrders -- finds all lexicographic monomial orders $<$ such that the ideal is $<$-compatibly geometrically vertex decomposable
• findOneStepGVD -- for which indeterminates does there exist a geometric vertex decomposition
• getGVDIdeal -- computes the $C_{y,I}$ or $N_{y,I}$ ideal at any point in the GVD recursion tree
• initialYForms -- computes the ideal of initial y-forms
• isGeneratedByIndeterminates -- checks whether the ideal is generated by indeterminates
• isGVD -- checks whether an ideal is geometrically vertex decomposable
• IsIdealHomogeneous -- specify whether an ideal is homogeneous
• IsIdealUnmixed -- specify whether an ideal is unmixed
• isLexCompatiblyGVD -- checks whether an ideal is <-compatibly geometrically vertex decomposable for a given order
• isUnmixed -- checks whether an ideal is unmixed
• isWeaklyGVD -- checks whether an ideal is weakly geometrically vertex decomposable
• oneStepGVD -- computes a geometric vertex decomposition
• oneStepGVDCyI -- computes the ideal $C_{y,I}$ for a given ideal and indeterminate
• oneStepGVDNyI -- computes the ideal $N_{y,I}$ for a given ideal and indeterminate
• OnlyDegenerate -- restrict to degenerate geometric vertex decompositions
• OnlyNondegenerate -- restrict to nondegenerate geometric vertex decompositions
• SquarefreeOnly -- only return the squarefree variables from the generators
• UniversalGB -- whether the generators for an ideal form a universal Gröbner basis