Automated reasoning in differential geometry and mechanics using the characteristic set method

Abstract

We clarify the formulation problem of mechanical theorem proving in difierential geometry and mechanics and propose two formulations. We present complete methods of mechanical theorem proving for the two formulations. We also introduce predicates and a language to translate geometry statements into difierential polynomial equations. A program based on our methods has proved more than 100 nontrivial theorems in difierential geometry and elementary mechanics including various classiflcation theorems for space curves, Bertrand's Theorem, Newton's gravitational laws, etc.