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:

data: contains parameters for the sagbi computation

degree: current degree of the Spairs 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.

ideals

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)

rings

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

maps: a collection of useful maps between the 'rings'

options: supplied options for the sagbi computation

pending: newly computed sagbi generators before they are added to the sagbiGenerators in 'data'