Pair Ordering

 

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 

1.   to order pairs in a set ascending w.r.t. the least common multiple of the leading monomials of the two polynomials or
2. to order pairs in a set ascending w.r.t. the leading monomial of the S-polynomial of the two polynomials or
3. ...

(In the present stage, only strategy 1 is implemented.)

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.