*Autosubduction* is a procedure which performs subduction on a collection of ring elements against each other, one at a time. This is typically performed on a set of generators of a Subring or SAGBIBasis. The result of each subduction replaces the original element in the collection and zeros are removed from the collection. If the elements form a subalgebra basis, then the result of autosubduction is unique.

- sagbi -- Compute a subalgebra basis (sagbi basis)
- subalgebraBasis -- Compute subalgebra basis generators
- ReduceNewGenerators -- Flag for reducing new generators in Sagbi algorithm
- subduction -- Subduction against a set elements
- 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
- ReduceNewGenerators -- Flag for reducing new generators in Sagbi algorithm
- RenewOptions -- Flag for reselecting the options for a subalgebra bases computation

- forceSB(SAGBIBasis,AutoSubduce=>...)
- forceSB(Subring,AutoSubduce=>...)
- sagbi(...,AutoSubduce=>...)
- sagbiBasis(...,AutoSubduce=>...)
- subalgebraBasis(...,AutoSubduce=>...)
- subduction(...,AutoSubduce=>...)

The object AutoSubduce is a symbol.