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