2006/11/30 by Antônio Montes, Antonio Montes, Montes, Antonio +2
Computer Science · Mathematics · Medicine · #13F10 #13P10 #68W30 #Cancer Treatment and Pharmacology #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #msc:13F10 #msc:13P10 #msc:68W30
paper · pdf · doi:10.48550/arxiv.math/0611948
23 pages, 7 figures. New version
openalex publication_date 2006/11/30 · arxiv created 2007/05/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.