all_reduced( PS reducibles, PS reducers, PS basis, PaS pairs)

Type:

Function

Defined in:

gb_reduce_all.c.trace

Performs interreduction during the Gröbner bases algorithm. reducibles contains polynomials, whose head term is reducible by one of the polynomials in reducers, which contains candidates to be adjoined to the basis. basis and pairs contain the current basis and pair set respectively.

An element from reducibles is reduced by polynomials from reducers and the basis. If this reduction yields a non-zero polynomial p, then p is adjoined to reducers and all polynomials in reducers and in the basis, whose head term can be reduced by p, change to reducibles. This can lead to a cascade of reductions until reducibles is empty. When this state is reached, the ``reducers'' are adjoined to the basis and the pair set is updated.

A list containing the basis and the updated pair set is returned.

See also:

[1].