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SubalgebraBases : Table of Contents
SubalgebraBases
-- A package for finding canonical subalgebra bases (SAGBI bases)
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
forceSB
-- declare the generators to be a complete subalgebra basis
forceSB(SAGBIBasis)
-- declare the generators to be a complete subalgebra basis
forceSB(Subring)
-- declare the generators to be a complete 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
groebnerSubductionQuotient
-- Extrinsic method for subduction quotients
intersect(Subring,Subring)
-- Intersection of subrings
IntersectedSubring
-- The type of all subrings arising from intersection
isFullIntersection
-- check correctness of intersection computation
isSAGBI
-- Check if the generators are a subalgebra basis
isSAGBI(SAGBIBasis)
-- Check if the generators are a subalgebra basis
isSAGBI(Subring)
-- Check if the generators are a subalgebra basis
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
presentationRing
-- 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 // Subring
-- Subduction quotient with respect to a subring
sagbi
-- Compute a subalgebra basis (sagbi basis)
SAGBIBasis
-- The type of all subalgebra bases
sagbiBasis
-- Constructs a computation object from a subring.
sagbiDegree
-- The current degree of the subalgebra bases computation
sagbiLimit
-- 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
status(SAGBIBasis)
-- status of the subalgebra bases computation
StorePending
-- Flag for storing the pending list to the result of the Sagbi algorithm
subalgebraBasis
-- 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
SubductionMethod
-- Subduction method for the Sagbi algorithm
Subring
-- The type of all subrings
subring
-- Constructs a subring of a polynomial ring.
UseSubringGens
-- Flag for using the subring generators when checking a subalgebra basis