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.
The object ReduceNewGenerators is a symbol.