**Type Name:**`PaS`**Structure:**- for some .
**Description:**- A (possibly empty) list of polynomial pairs .
For the advanced versions of the Gröbner bases algorithm the pair set is kept in
ascending order w.r.t. the chosen ordering
`is_pa_greater`. The first element in the pair set is always the next pair that is considered for S-polynomial computation, hence, the ordering on the pair set determines the strategy for choosing S-polynomials .Up to now, the only strategy being tested is ``take the pair with smallest

*least common multiple*of the leading monomials'', however, the interface for choosing a different strategy is implemented. A possible (i.e. reasonable) strategy to be tested is ``take the pair with smallest*leading monomial*of the S-polynomial''.For the variant of the Gröbner bases algorithm, in which pairs for which a criterion can be applied are deleted immediately, we also have to fix an ordering on the pairs with equal ``lcm''. This ordering is called

`is_labeled_pa_greater`and is a refinement of`is_pa_greater`in the way that pairs with equal ``lcm'' are ordered by a lexical ordering on the pairs of labels (of the polynomials in the pair).

Thu Sep 3 14:50:07 MDT 1998