A Geometric Procedure with Prover9

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

Abstract

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.

Keywords

Elliptic Curve Inference Rule Elliptic Curf Theorem Prover Abelian Variety 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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