GeometricDecomposability : Table of Contents

• 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