A procedure to prove statements in differential geometry
Journal of Automated Reasoning
Mechanical theorem proving of differential geometries and some of its applications in mechanics
Journal of Automated Reasoning - Special issue on new trends in automated reasoning
Representation for the radical of a finitely generated differential ideal
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Decomposing polynomial systems into simple systems
Journal of Symbolic Computation
Algorithmic properties of polynomial rings
Journal of Symbolic Computation
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Factorization-free decomposition algorithms in differential algebra
Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
Computing canonical representatives of regular differential ideals
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Clifford Algebraic Reduction Method for Automated Theorem Proving in Differential Geometry
Journal of Automated Reasoning
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This paper presents methods for zero and ideal decomposition of partial differential polynomial systems and the application of these methods and their implementations to deal with problems from the local theory of surfaces. We show how to prove known geometric theorems and to derive unknown relations automatically. In particular, an algebraic relation between the first and the second fundamental coefficients in a very compact form has been derived, which is more general and has smaller degree than a relation discovered previously by Z. Li. Moreover, we provide symmetric expressions for Li's relation and clarify his statement. Some examples of theorem proving and computational difficulties encountered in our experiments are also discussed.