**Type:**- Function
**Defined in:**- gb_reduce_all.c.trace
- Returns the reduced Gröbner basis of the ideal
generated by the polynomials in the set
`F`.The algorithm used is the improved version sketched in [1], where criteria are applied and, whenever a reduction yields a non-zero polynomial, interreduction is performed

*before*this polynomial is adjoined to the basis. Like in`GB_criteria`, pairs are kept ordered. **See also:**- Section 5.1, Section 5.2, Section 5.3,

`is_greater_mon`,`is_pa_greater`,

`is_greater_mon_pair_order`,`all_reduced`.

Thu Sep 3 14:50:07 MDT 1998