SAGBIBasis -- The type of all sagbi bases

Description

This is a computation object for sagbi bases. It stores a partial sagbi computation for picking up a computation where it left off. An instance of a SAGBIBasis is constructed with the function sagbiBasis and as the output of sagbi.

Every instance of SAGBIBasis contains the following hashtables:

SAGBIdata: contains parameters for the sagbi computation
degree: current degree of the S-pairs in the sagbi algorithm.
limit: degree limit of the computation.
sagbiGenerators: generators in the sagbi basis (default none)
subalgebraGenerators: original generating set of the subring.
SAGBIideals
I: the ideal defining the ambient ring = liftedRing / I
leadTermsI: initial ideal of I
reductionIdeal: SIdeal+I lifted to the tensorRing
SIdeal: ideal generated by (SagbiGenerators - TagVariables)
SAGBIrings
liftedRing: the polynomial ring of the quotient ring
quotientRing: ambient ring of the underlying subring
tensorRing: tensor product of the liftedRing with a polynomial ring that has one variable for each sagbi generator
SAGBImaps: a collection of useful maps between the 'rings'
SAGBIoptions: supplied options for the sagbi computation
SAGBIpending: newly computed sagbi generators before they are added to the sagbiGenerators in 'data'

Functions and methods returning an object of class SAGBIBasis :

isSAGBI -- Check if the generators are a sagbi basis

Methods that use an object of class SAGBIBasis :

ambient(SAGBIBasis) -- The ambient ring of a SAGBIBasis computation object
"forceSB(SAGBIBasis)" -- see forceSB -- declare the generators of a subring or SAGBIBasis to be a complete sagbi basis
generators(SAGBIBasis) -- Returns a partial sagbi generating set
"isSAGBI(SAGBIBasis)" -- see isSAGBI -- Check if the generators are a sagbi basis
Matrix % SAGBIBasis -- Remainder modulo a subring
net(SAGBIBasis) -- Short summary of a sagbi basis computation object
numgens(SAGBIBasis) -- The number of generators of a SAGBIBasis
ring(SAGBIBasis) -- The lifted ring of a SAGBIBasis computation object
RingElement % SAGBIBasis -- Remainder modulo a subring
"sagbi(SAGBIBasis)" -- see sagbi -- Compute a subalgebra basis (sagbi basis)
"sagbiDegree(SAGBIBasis)" -- see sagbiDegree -- The current degree of the sagbi computation
"sagbiLimit(SAGBIBasis)" -- see sagbiLimit -- The current limit of the sagbi computation
"sagbiStatus(SAGBIBasis)" -- see sagbiStatus -- returns if the sagbi computation is done
status(SAGBIBasis) -- status of the sagbi computation
"subduction(SAGBIBasis,Matrix)" -- see subduction -- Subduction of polynomials
"subduction(SAGBIBasis,RingElement)" -- see subduction -- Subduction of polynomials
"subring(SAGBIBasis)" -- see subring -- Constructs a subring of a polynomial ring.

For the programmer

The object SAGBIBasis is a type, with ancestor classes HashTable < Thing.

SAGBIBasis -- The type of all sagbi bases

Description

See also

Functions and methods returning an object of class SAGBIBasis :

Methods that use an object of class SAGBIBasis :

For the programmer