A Geometric Procedure with Prover9

  • Ranganathan Padmanabhan
  • Robert Veroff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7788)


Here we give an automated proof of the fact that a cubic curve admits at most one group law. This is achieved by proving the tight connection between the chord-tangent law of composition and any potential group law (as a morphism) on the curve. An automated proof of this is accomplished by implementing the rigidity lemma and the Cayley-Bacharach theorem of algebraic geometry as formal inference rules in Prover9, a first-order theorem prover developed by Dr. William McCune.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ranganathan Padmanabhan
    • 1
  • Robert Veroff
    • 2
  1. 1.University of ManitobaWinnipegCanada
  2. 2.University of New MexicoAlbuquerqueUSA

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