Abstract
The notion of partitioned-parametric Gröbner bases of a polynomial ideal under constraints is introduced and an algorithm for constructing partitioned-parametric Gröbner bases is given; the correctness and the termination of the algorithm are proved. We also present a method based on computing partitioned-parametric Gröbner bases for proving geometric theorems mechanically. By this method, besides proving the generic truth of a geometric theorem, we can give the necessary and sufficient conditions on the free parameters for the theorem to be true. An example for proving geometric theorems by the partitioned-parametric Gröbner bases method is given. © Springer-Verlag Berlin Heidelberg 2006.
Cite
CITATION STYLE
Chen, X., Li, P., Lin, L., & Wang, D. (2006). Proving geometric theorems by partitioned-parametric Gröbner bases. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3763 LNAI, pp. 34–43). Springer Verlag. https://doi.org/10.1007/11615798_3
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