resolution => Algorithm

Algorithm => n -- an option for resolution which specifies which algorithm to use. Algorithms are specified by number and the algorithms available are
  • Algorithm => 0 -- Compute syzygies on the Groebner bases of each syzygy module. The algorithm uses important speedups due to R. Lascala. This algorithm appears to be on the average the fastest.
  • Algorithm => 1 -- An older version of algorithm 0, which doesn't allow as much experimentation, but can sometimes be marginally faster.
  • Algorithm => 2 -- Compute syzygies on the minimal generators of each matrix in the resolution. Over quotient rings, preferred.
  • Algorithm => 3 -- Same as algorithm 2, but compute those Hilbert functions which allow removal of S-pairs (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.

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