explicit_chain_criterion( LP lp1, LP lp2, PS G, PaS B)

Type:

Predicate

Defined in:

reductions.c.trace

The version of the chain criterion (i.e. Criterion1 in [1]), which is used in the variant of the Gröbner bases algorithm, where criteria are applied before S-polynomial computation. It returns TRUE if there is a polynomial p in G s.t.

the least common multiple of the leading monomials of lp1 and lp2 is a multiple of the leading monomial of p,

and , and

the pairs (p, lp1) and (p, lp2) are not contained in B, which means that they have already been considered for S-polynomial computation.

See also:

[1], criteria.