Automated Reasoning and Mathematics

Volume 7788 of the series Lecture Notes in Computer Science pp 139-150

A Geometric Procedure with Prover9

  • Ranganathan PadmanabhanAffiliated withUniversity of Manitoba
  • , Robert VeroffAffiliated withUniversity of New Mexico

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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.