Proving and discovering geometric theorems by using comprehensive Groebner system
Dingkang Wang, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Wednesday July 27th, K9509, 1:30pm.
Abstract For a polynomial system with parameters, different specifications of the parameters will lead to different Groebner basis. Both comprehensive Groebner system (CGS) and comprehensive Groebner basis (CGB) are introduced by Weispfenning to describe the Groeber bases for all possible specifications of the parameters. We proposed an algorithm to compute CGS, and the experimental result show that it is efficient, further more, this algorithm can be extended to compute CGS and CGB simultaneously. Based on CGS, a method for automatic discovery of geometric theorems is given.