There are three possible values for Strategy: DegreeByDegree, Incremental, or Master.
At the beginning of each loop inside of sagbi, the main SAGBIBasis computation object is updated. There are two types of update procedures, and the update procedure that is used is determined by the value of Strategy.
The DegreeByDegree strategy computes a partial groebner basis of the reduction ideal from scratch. The DegreeByDegree strategy is better when many new generators are added during each loop of the sagbi algorithm. The Incremental strategy computes a full groebner basis of the reduction ideal by using the previous full groebner basis together with the data of the new subalgebra generators. The Incremental strategy is better when there is little change to the number of subalgebra generators.
For many examples, it is observed that many new generators are added at the beginning of subalgebra basis computations, but, towards the end of the computation, there are very few new generators that are added at each step. By setting Strategy to Master (default), the DegreeByDegree strategy is used at the beginning, and the strategy switches to Incremental part-of-the-way through the algorithm.