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