Description
Strategy => n  an option for
resolution which specifies which algorithm to use. Strategies are specified by number and the algorithms available are

Strategy => 0  Compute syzygies on the GrÃ¶bner bases of each syzygy module. The algorithm uses important speedups due to R. La Scala. This algorithm appears to be on the average the fastest.

Strategy => 1  An older version of algorithm 0, which doesn't allow as much experimentation, but can sometimes be marginally faster.

Strategy => 2  Compute syzygies on the minimal generators of each matrix in the resolution. Over quotient rings, it's preferred.

Strategy => 3  Same as algorithm 2, but compute those Hilbert functions which allow removal of Spairs (a la Robbiano, et al.). Sometimes this improvement can be very dramatic.
All algorithms use induced monomial orders (Schreyer orders), since this makes an enormous improvement to the efficiency of the algorithm.