The predicate `is_pa_greater` (in the case, where the variant of the Gröbner bases algorithm is used, where
criteria are applied when the pair set is created or updated, we use the
predicate `is_labeled_pa_greater` ) determines the *basic strategy* for the
ordering of polynomial pairs in a set of polynomial pairs (see also
Section 3.17). Possible strategies are

- to order pairs in a set ascending w.r.t. the least common multiple of the leading monomials of the two polynomials or
- to order pairs in a set ascending w.r.t. the leading monomial of the S-polynomial of the two polynomials or
- ...

Whatever strategy one might choose, some ordering on monomials will also be
required in the ordering of the pair set. Since this ordering need not be
equal to the ordering chosen for monomials in a polynomial, we have an
additional predicate `
is_greater_mon_pair_order` , for which we have
again the choices listed in Section 5.1.

A possible (i.e. plausible) setting is to order the pair set by ascending
*total degree* of the least common multiple of the leading monomials
when computing a lexical Gröbner basis. This strategy has turned out to be in some
examples significantly faster than having lexical ordering for the least
common multiple of the leading monomials as well (see [10], Section
on timing statistics). A similar strategy is also described in [5].

Choosing an appropriate setting is done in the file `GB.po.setup`.

Thu Sep 3 14:50:07 MDT 1998