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SubalgebraBases : Index
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ambient(SAGBIBasis)
-- The ambient ring of a SAGBIBasis computation object
ambient(Subring)
-- The ambient ring of a subring
AutoSubduce
-- Flag for autosubduction before the sagbi algorithm
AutoSubduceOnPartialCompletion
-- Subduct subalgebra generators at the end of the sagbi algorithm
CheckFullIntersection
-- Flag for deciding if isFullIntersection is called
Compute
-- Flag for performing computations while checking the completeness of a subalgebra basis
Example: Translation and rotation sub-actions of the adjoint action of SE(3)
flattenedRing
-- The flattened ring of a subring or sagbiBasis
flattenedRing(SAGBIBasis)
-- The flattened ring of a subring or sagbiBasis
flattenedRing(Subring)
-- The flattened ring of a subring or sagbiBasis
forceSB
-- declare the generators to be a complete subalgebra basis
forceSB(SAGBIBasis)
-- declare the generators to be a complete subalgebra basis
forceSB(SAGBIBasis,AutoSubduce=>...)
-- Flag for autosubduction before the sagbi algorithm
forceSB(SAGBIBasis,Limit=>...)
-- Bound for subalgebra basis computation
forceSB(SAGBIBasis,PrintLevel=>...)
-- Levels of information displayed during Sagbi algorithm
forceSB(SAGBIBasis,RenewOptions=>...)
-- Flag for reselecting the options for a subalgebra bases computation
forceSB(SAGBIBasis,Strategy=>...)
-- Update procedure for the Sagbi algorithm
forceSB(SAGBIBasis,SubductionMethod=>...)
-- Subduction method for the Sagbi algorithm
forceSB(SAGBIBasis,UseSubringGens=>...)
-- Flag for using the subring generators when checking a subalgebra basis
forceSB(Subring)
-- declare the generators to be a complete subalgebra basis
forceSB(Subring,AutoSubduce=>...)
-- Flag for autosubduction before the sagbi algorithm
forceSB(Subring,Limit=>...)
-- Bound for subalgebra basis computation
forceSB(Subring,PrintLevel=>...)
-- Levels of information displayed during Sagbi algorithm
forceSB(Subring,RenewOptions=>...)
-- Flag for reselecting the options for a subalgebra bases computation
forceSB(Subring,Strategy=>...)
-- Update procedure for the Sagbi algorithm
forceSB(Subring,SubductionMethod=>...)
-- Subduction method for the Sagbi algorithm
forceSB(Subring,UseSubringGens=>...)
-- Flag for using the subring generators when checking a subalgebra basis
generators(SAGBIBasis)
-- Returns generators of a SAGBIBasis computation object
generators(Subring)
-- A generating set of a subring
GeneratorSymbol
-- variables for the presentationRing
groebnerMembershipTest
-- Extrinsic method for subring membership
groebnerMembershipTest(RingElement,Subring)
-- Extrinsic method for subring membership
groebnerSubductionQuotient
-- Extrinsic method for subduction quotients
groebnerSubductionQuotient(RingElement,Subring)
-- Extrinsic method for subduction quotients
intersect(Subring,Subring)
-- Intersection of subrings
intersect(Subring,Subring,CheckFullIntersection=>...)
-- Flag for deciding if isFullIntersection is called
intersect(Subring,Subring,Compute=>...)
-- Flag for performing computations while checking the completeness of a subalgebra basis
intersect(Subring,Subring,Limit=>...)
-- Bound for subalgebra basis computation
intersect(Subring,Subring,PrintLevel=>...)
-- Levels of information displayed during Sagbi algorithm
intersect(Subring,Subring,SAGBILimitType=>...)
-- Flag for calculating degree limit in intersections
intersect(Subring,Subring,Strategy=>...)
-- Update procedure for the Sagbi algorithm
intersect(Subring,Subring,SubductionMethod=>...)
-- Subduction method for the Sagbi algorithm
IntersectedSubring
-- The type of all subrings arising from intersection
isFullIntersection
-- check correctness of intersection computation
isFullIntersection(IntersectedSubring)
-- check correctness of intersection computation
isSAGBI
-- Check if the generators are a subalgebra basis
isSAGBI(List)
-- Check if the generators are a subalgebra basis
isSAGBI(List,Compute=>...)
-- Flag for performing computations while checking the completeness of a subalgebra basis
isSAGBI(List,ModifySAGBIBasis=>...)
-- Flag for allowing the cached computation object to be modified
isSAGBI(List,PrintLevel=>...)
-- Levels of information displayed during Sagbi algorithm
isSAGBI(List,Recompute=>...)
-- Flag for restarting a sagbi or isSAGBI computation
isSAGBI(List,RenewOptions=>...)
-- Flag for reselecting the options for a subalgebra bases computation
isSAGBI(List,Strategy=>...)
-- Update procedure for the Sagbi algorithm
isSAGBI(List,SubductionMethod=>...)
-- Subduction method for the Sagbi algorithm
isSAGBI(List,UseSubringGens=>...)
-- Flag for using the subring generators when checking a subalgebra basis
isSAGBI(Matrix)
-- Check if the generators are a subalgebra basis
isSAGBI(Matrix,Compute=>...)
-- Flag for performing computations while checking the completeness of a subalgebra basis
isSAGBI(Matrix,ModifySAGBIBasis=>...)
-- Flag for allowing the cached computation object to be modified
isSAGBI(Matrix,PrintLevel=>...)
-- Levels of information displayed during Sagbi algorithm
isSAGBI(Matrix,Recompute=>...)
-- Flag for restarting a sagbi or isSAGBI computation
isSAGBI(Matrix,RenewOptions=>...)
-- Flag for reselecting the options for a subalgebra bases computation
isSAGBI(Matrix,Strategy=>...)
-- Update procedure for the Sagbi algorithm
isSAGBI(Matrix,SubductionMethod=>...)
-- Subduction method for the Sagbi algorithm
isSAGBI(Matrix,UseSubringGens=>...)
-- Flag for using the subring generators when checking a subalgebra basis
isSAGBI(SAGBIBasis)
-- Check if the generators are a subalgebra basis
isSAGBI(SAGBIBasis,Compute=>...)
-- Flag for performing computations while checking the completeness of a subalgebra basis
isSAGBI(SAGBIBasis,ModifySAGBIBasis=>...)
-- Flag for allowing the cached computation object to be modified
isSAGBI(SAGBIBasis,PrintLevel=>...)
-- Levels of information displayed during Sagbi algorithm
isSAGBI(SAGBIBasis,Recompute=>...)
-- Flag for restarting a sagbi or isSAGBI computation
isSAGBI(SAGBIBasis,RenewOptions=>...)
-- Flag for reselecting the options for a subalgebra bases computation
isSAGBI(SAGBIBasis,Strategy=>...)
-- Update procedure for the Sagbi algorithm
isSAGBI(SAGBIBasis,SubductionMethod=>...)
-- Subduction method for the Sagbi algorithm
isSAGBI(SAGBIBasis,UseSubringGens=>...)
-- Flag for using the subring generators when checking a subalgebra basis
isSAGBI(Subring)
-- Check if the generators are a subalgebra basis
isSAGBI(Subring,Compute=>...)
-- Flag for performing computations while checking the completeness of a subalgebra basis
isSAGBI(Subring,ModifySAGBIBasis=>...)
-- Flag for allowing the cached computation object to be modified
isSAGBI(Subring,PrintLevel=>...)
-- Levels of information displayed during Sagbi algorithm
isSAGBI(Subring,Recompute=>...)
-- Flag for restarting a sagbi or isSAGBI computation
isSAGBI(Subring,RenewOptions=>...)
-- Flag for reselecting the options for a subalgebra bases computation
isSAGBI(Subring,Strategy=>...)
-- Update procedure for the Sagbi algorithm
isSAGBI(Subring,SubductionMethod=>...)
-- Subduction method for the Sagbi algorithm
isSAGBI(Subring,UseSubringGens=>...)
-- Flag for using the subring generators when checking a subalgebra basis
Matrix % SAGBIBasis
-- Remainder modulo a subring
Matrix % Subring
-- Remainder modulo a subring
ModifySAGBIBasis
-- Flag for allowing the cached computation object to be modified
net(SAGBIBasis)
-- Short summary of a subalgebra basis computation object
net(Subring)
-- Short summary of a subring
numgens(SAGBIBasis)
-- The number of generators of a SAGBIBasis
numgens(Subring)
-- The number of generators of a subring
originalSubringGens
-- generators of the original subrings
originalSubringGens(IntersectedSubring)
-- generators of the original subrings
presentationRing
-- returns the presentation ring of a subring
presentationRing(Subring)
-- returns the presentation ring of a subring
PrintLevel
-- Levels of information displayed during Sagbi algorithm
Recompute
-- Flag for restarting a sagbi or isSAGBI computation
ReduceNewGenerators
-- Flag for reducing new generators in Sagbi algorithm
Reduction in subrings
-- Remainder modulo a subring
RenewOptions
-- Flag for reselecting the options for a subalgebra bases computation
ring(SAGBIBasis)
-- The lifted ring of a SAGBIBasis computation object
RingElement % SAGBIBasis
-- Remainder modulo a subring
RingElement % Subring
-- Remainder modulo a subring
RingElement // Subring
-- Subduction quotient with respect to a subring
sagbi
-- Compute a subalgebra basis (sagbi basis)
sagbi(...,AutoSubduce=>...)
-- Flag for autosubduction before the sagbi algorithm
sagbi(...,AutoSubduceOnPartialCompletion=>...)
-- Subduct subalgebra generators at the end of the sagbi algorithm
sagbi(...,Limit=>...)
-- Bound for subalgebra basis computation
sagbi(...,PrintLevel=>...)
-- Levels of information displayed during Sagbi algorithm
sagbi(...,Recompute=>...)
-- Flag for restarting a sagbi or isSAGBI computation
sagbi(...,ReduceNewGenerators=>...)
-- Flag for reducing new generators in Sagbi algorithm
sagbi(...,RenewOptions=>...)
-- Flag for reselecting the options for a subalgebra bases computation
sagbi(...,StorePending=>...)
-- Flag for storing the pending list to the result of the Sagbi algorithm
sagbi(...,Strategy=>...)
-- Update procedure for the Sagbi algorithm
sagbi(...,SubductionMethod=>...)
-- Subduction method for the Sagbi algorithm
sagbi(List)
-- Compute a subalgebra basis (sagbi basis)
sagbi(Matrix)
-- Compute a subalgebra basis (sagbi basis)
sagbi(SAGBIBasis)
-- Compute a subalgebra basis (sagbi basis)
sagbi(Subring)
-- Compute a subalgebra basis (sagbi basis)
SAGBIBasis
-- The type of all subalgebra bases
sagbiBasis
-- Constructs a computation object from a subring.
sagbiBasis(...,AutoSubduce=>...)
-- Flag for autosubduction before the sagbi algorithm
sagbiBasis(...,AutoSubduceOnPartialCompletion=>...)
-- Subduct subalgebra generators at the end of the sagbi algorithm
sagbiBasis(...,Limit=>...)
-- Bound for subalgebra basis computation
sagbiBasis(...,PrintLevel=>...)
-- Levels of information displayed during Sagbi algorithm
sagbiBasis(...,Recompute=>...)
-- Flag for restarting a sagbi or isSAGBI computation
sagbiBasis(...,ReduceNewGenerators=>...)
-- Flag for reducing new generators in Sagbi algorithm
sagbiBasis(...,RenewOptions=>...)
-- Flag for reselecting the options for a subalgebra bases computation
sagbiBasis(...,StorePending=>...)
-- Flag for storing the pending list to the result of the Sagbi algorithm
sagbiBasis(...,Strategy=>...)
-- Update procedure for the Sagbi algorithm
sagbiBasis(...,SubductionMethod=>...)
-- Subduction method for the Sagbi algorithm
sagbiBasis(Subring)
-- Constructs a computation object from a subring.
sagbiDegree
-- The current degree of the subalgebra bases computation
sagbiDegree(SAGBIBasis)
-- The current degree of the subalgebra bases computation
sagbiLimit
-- The current limit of the subalgebra bases computation
sagbiLimit(SAGBIBasis)
-- The current limit of the subalgebra bases computation
SAGBILimitType
-- Flag for calculating degree limit in intersections
sagbiStatus
-- checks if the subalgebra bases computation is done
sagbiStatus(SAGBIBasis)
-- checks if the subalgebra bases computation is done
status(SAGBIBasis)
-- status of the subalgebra bases computation
StorePending
-- Flag for storing the pending list to the result of the Sagbi algorithm
SubalgebraBases
-- A package for finding canonical subalgebra bases (SAGBI bases)
subalgebraBasis
-- Compute subalgebra basis generators
subalgebraBasis(...,AutoSubduce=>...)
-- Flag for autosubduction before the sagbi algorithm
subalgebraBasis(...,AutoSubduceOnPartialCompletion=>...)
-- Subduct subalgebra generators at the end of the sagbi algorithm
subalgebraBasis(...,Limit=>...)
-- Bound for subalgebra basis computation
subalgebraBasis(...,PrintLevel=>...)
-- Levels of information displayed during Sagbi algorithm
subalgebraBasis(...,Recompute=>...)
-- Flag for restarting a sagbi or isSAGBI computation
subalgebraBasis(...,ReduceNewGenerators=>...)
-- Flag for reducing new generators in Sagbi algorithm
subalgebraBasis(...,RenewOptions=>...)
-- Flag for reselecting the options for a subalgebra bases computation
subalgebraBasis(...,StorePending=>...)
-- Flag for storing the pending list to the result of the Sagbi algorithm
subalgebraBasis(...,Strategy=>...)
-- Update procedure for the Sagbi algorithm
subalgebraBasis(...,SubductionMethod=>...)
-- Subduction method for the Sagbi algorithm
subalgebraBasis(List)
-- Compute subalgebra basis generators
subalgebraBasis(Matrix)
-- Compute subalgebra basis generators
subalgebraBasis(Subring)
-- Compute subalgebra basis generators
subduction
-- Subduction against a set elements
Subduction computation limit
-- Bound for subalgebra basis computation
Subduction strategies
-- Update procedure for the Sagbi algorithm
subduction(...,AutoSubduce=>...)
-- Flag for autosubduction before the sagbi algorithm
subduction(...,AutoSubduceOnPartialCompletion=>...)
-- Subduct subalgebra generators at the end of the sagbi algorithm
subduction(...,Limit=>...)
-- Bound for subalgebra basis computation
subduction(...,PrintLevel=>...)
-- Levels of information displayed during Sagbi algorithm
subduction(...,Recompute=>...)
-- Flag for restarting a sagbi or isSAGBI computation
subduction(...,ReduceNewGenerators=>...)
-- Flag for reducing new generators in Sagbi algorithm
subduction(...,RenewOptions=>...)
-- Flag for reselecting the options for a subalgebra bases computation
subduction(...,StorePending=>...)
-- Flag for storing the pending list to the result of the Sagbi algorithm
subduction(...,Strategy=>...)
-- Update procedure for the Sagbi algorithm
subduction(...,SubductionMethod=>...)
-- Subduction method for the Sagbi algorithm
subduction(List,List)
-- Subduction against a set elements
subduction(List,RingElement)
-- Subduction against a set elements
subduction(Matrix,Matrix)
-- Subduction against a set elements
subduction(Matrix,RingElement)
-- Subduction against a set elements
subduction(SAGBIBasis,Matrix)
-- Subduction against a set elements
subduction(SAGBIBasis,RingElement)
-- Subduction against a set elements
subduction(Subring,Matrix)
-- Subduction against a set elements
subduction(Subring,RingElement)
-- Subduction against a set elements
SubductionMethod
-- Subduction method for the Sagbi algorithm
Subring
-- The type of all subrings
subring
-- Constructs a subring of a polynomial ring.
subring(...,GeneratorSymbol=>...)
-- Constructs a subring of a polynomial ring.
subring(List)
-- Constructs a subring of a polynomial ring.
subring(Matrix)
-- Constructs a subring of a polynomial ring.
subring(SAGBIBasis)
-- Constructs a subring of a polynomial ring.
UseSubringGens
-- Flag for using the subring generators when checking a subalgebra basis