A Geometric Procedure with Prover9
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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- 1.Knapp, A.: Elliptic Curves. Princeton University Press (1992)Google Scholar
- 2.McCune, W.: Otter 3.0 Reference Manual and Guide. Tech. Report ANL-94/6, Argonne National Laboratory, Argonne, IL (1994), http://www.mcs.anl.gov/AR/otter/
- 3.McCune, W.: Prover9, version 2009-02A, http://www.cs.unm.edu/~mccune/prover9/
- 8.Padmanabhan, R., Veroff, R.: A geometric procedure with Prover9 (Web support) (2012), http://www.cs.unm.edu/~veroff/gL_Paper/
- 9.Padmanabhan, R., Veroff, R.: A gL clause generator (2012), http://www.cs.unm.edu/~veroff/gL_Paper/gL_gen.html
- 10.Silverman, J., Tate, J.: Rational Points on Elliptic Curves. Springer (1992)Google Scholar