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SubalgebraBases :: SAGBIBasis

SAGBIBasis -- The type of all sagbi bases


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'

See also

Functions and methods returning an object of class SAGBIBasis :

Methods that use an object of class SAGBIBasis :

For the programmer

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