2007/03/16 by Antônio Montes, Antonio Montes, Montes, Antonio +3
Computer Science · Engineering · Mathematics · Medicine · #13P10 #68T15 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Cancer Treatment and Pharmacology #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:13P10 #msc:68T15
paper · pdf · doi:10.48550/arxiv.math/0703483
25 pages, 8 figures
openalex publication_date 2007/03/16 · arxiv created 2007/10/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main idea in this paper is merging two techniques that have been recently developed. On the one hand, we consider MCCGS, standing for Minimal Canonical Comprehensive Groebner Systems, a recently introduced computational tool yielding "good" bases for ideals of polynomials over a field depending on several parameters, that specialize "well", for instance, regarding the number of solutions for the given ideal, for different values of the parameters. The second ingredient concerns automatic theorem discovery in elementary geometry. Automatic discovery aims to obtain complementary hypotheses for a (generally false) geometric statement to become true. The paper shows how to use MCCGS for automatic discovering of theorems and gives relevant examples.