**Type:**- Function
**Defined in:**- gb_small_ps.c.trace
- Returns the reduced Gröbner basis of the ideal
generated by the polynomials in the set
`F`.The algorithm applies the criteria for a-priori detection of zero-reductions already when the pair set is created and cancels all unnecessary pairs immediately. This keeps the pair set in each stage as small as possible. The pair set is totally ordered by

`is_labeled_pa_greater`. This refinement of the ordering for pairs is required for correct application of the criteria in this version of the algorithm. **See also:**-
Section 3.17, Section 5.1, Section 5.2,
Section 5.3,

`is_greater_mon`,`is_labeled_pa_greater`, and

`is_greater_mon_pair_order`.

Thu Sep 3 14:50:07 MDT 1998