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Sets of Polynomial Pairs


Type Name:
tex2html_wrap_inline6568 for some tex2html_wrap_inline6570 .
A (possibly empty) list of polynomial pairs tex2html_wrap_inline6572 . 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).

windsteiger wolfgang
Thu Sep 3 14:50:07 MDT 1998