Automated reasoning about cubic curves

✍ Scribed by R. Padmanabhan; W. McCune

• Book ID: 103931339
• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 529 KB
• Volume: 29
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(94)00214-6

✦ Synopsis

It is well known that the n-ary morphisms defined on projective algebraic curves satisfy some strong local-to-global equational rules of derivation not satisfied in general by universal algebras. For example, every rationally defined group law on a cubic curve must be commutative. Here, we extract from the geometry of curves a first-order property (gL) satisfied by all morphisms defined on these curves such that the equational consequences known for projective curves can be derived automatically from a set of six rules (stated within the first-order logic with equality). First, the rule (gL) is implemented in the theorem-proving program OTTER. Then, we use OTTER to automatically prove some incidence theorems on projective curves without any further reference to the underlying geometry or topology of the curves.