Proving Geometric Theorems by Partitioned-Parametric Gröbner Bases

  • Xuefeng Chen
  • Peng Li
  • Long Lin
  • Dingkang Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3763)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xuefeng Chen
    • 1
  • Peng Li
    • 1
  • Long Lin
    • 1
  • Dingkang Wang
    • 1
  1. 1.Key Laboratory of Mathematics Mechanization, Academy of Mathematics and System SciencesChinese Academy of SciencesBeijingP.R. China

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