  This is the continuation of Montes' paper "On the canonical discussion of
polynomial systems with parameters". In this paper we define the Minimal
Canonical Comprehensive Groebner System (MCCGS) of a parametric ideal and fix
under which hypothesis it exists and is computable. An algorithm to obtain a
canonical description of the segments of the MCCGS is given, completing so the
whole MCCGS algorithm (implemented in Maple). We show its high utility for
applications, like automatic theorem proving and discovering, and compare it
with other existing methods. A way to detect a counterexample is outlined,
although the high number of tests done give evidence of the existence of the
MCCGS.
