The function sagbi computes a subalgebra basis by subducting S-pairs. Any resulting non-zero polynomials are added to the list of subalgebra generators. If ReduceNewGenerators is set to true, then the new generators are reduced (using Gaussian elimination) against the other new generators. This process is quick and ensures that duplicate generators are not added to the list of subalgebra generators.

- sagbi -- Compute a subalgebra basis (sagbi basis)
- sagbiBasis -- Constructs a computation object from a subring.
- subalgebraBasis -- Compute subalgebra basis generators
- subduction -- Subduction against a set elements
- AutoSubduce -- Flag for autosubduction before the sagbi algorithm
- ReduceNewGenerators -- Flag for reducing new generators in Sagbi algorithm
- StorePending -- Flag for storing the pending list to the result of the Sagbi algorithm
- SubductionMethod -- Subduction method for the Sagbi algorithm
- AutoSubduceOnPartialCompletion -- Subduct subalgebra generators at the end of the sagbi algorithm
- PrintLevel -- Levels of information displayed during Sagbi algorithm
- Recompute -- Flag for restarting a sagbi or isSAGBI computation
- RenewOptions -- Flag for reselecting the options for a subalgebra bases computation

- sagbi(...,ReduceNewGenerators=>...)
- sagbiBasis(...,ReduceNewGenerators=>...)
- subalgebraBasis(...,ReduceNewGenerators=>...)
- subduction(...,ReduceNewGenerators=>...)

The object ReduceNewGenerators is a symbol.