Details:
Title  Automatic discovery of geometry theorems using minimal canonical comprehensive Gr\"obner systems.  Author(s)  Antonio Montes, Tomás Recio  Type  Book, Chapter in Book, Conference Proceeding  Abstract  The main proposal in this paper is the merging of two techniques that have been recently developed. On the one hand, we consider a new approach for computing some specializable Gröbner basis, the so called Minimal Canonical Comprehensive Gröbner Systems (MCCGS) that is roughly speaking a computational procedure 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 is related to automatic theorem discovery in elementary geometry. Automatic discovery aims to obtain complementary (equality and inequality type) 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.  Keywords  automatic discovering, comprehensive Gröbner system, automatic theorem proving  ISBN  9783540773559/pbk 
URL 
http://link.springer.com/chapter/10.1007%2F9783540773566_8 
Language  English  Pages  113138  Publisher  Berlin: Springer  Year  2007  Edition  0  Translation 
No  Refereed 
No 
