2. Sequential Algorithms

For any Groebner or standard basis computation the efficiency of
an algorithm depends essentially on the strategy how to chose
the next pair from the pairset constructed so far. The major criteria
to sort (and select from) a pairset are usually order-dependend (** O**)
(the order of the leading term of the s-polynomial or of the syzygy
of the initial monomials) or the module index (** M**) for implementations of
free resolutions. Moreover, there are some secondary criteria like
the length of polynomials etc.

Of course, the organization of the pairset depends also on the sequence
(** S**) with which new generators are added to the set of known generators.
The following table gives an overview about the use of the major types of
known criteria within the different algorithms:

Naive | Schreyer | LaScala | Hilbert-driven | Sequential | |

1. criterion | M | M | O | O | S |

2. criterion | O | O | M | M | |

3. criterion | S | S | S | S |