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.


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.