Abstract
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.
Acknowledgements
Part of this work has been supported by the SPACES Project (http://wwwspaces. lip6.fr/) and by the Chinese National 973 Project NKBRSF G19980306.
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Aubry, P., Wang, D. (2001). Reasoning about Surfaces Using Differential Zero and Ideal Decomposition. In: Richter-Gebert, J., Wang, D. (eds) Automated Deduction in Geometry. ADG 2000. Lecture Notes in Computer Science(), vol 2061. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45410-1_10
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DOI: https://doi.org/10.1007/3-540-45410-1_10
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