To Be Presented in the 11th Asian Technology Conference in Mathematics
December 12-16, 2006, Hong Kong SAR, China
Geometric Reasoning with Invariant Algebras
Key Laboratory of Mathematics Mechanization
Chinese Academy of Sciences
Geometric reasoning is a common task in Mathematics
Education, Computer-Aided Design, Computer Vision and Robot Navigation.
Traditional geometric reasoning follows either a logical approach in Artificial
Intelligence, or a coordinate approach in Computer Algebra, or an approach
of basic geometric invariants such as areas, volumes and distances. In
algebraic approaches to geometric reasoning, geometric interpretation
is needed for the result after algebraic manipulation, but in general
this is a difficult task. It is hoped that more advanced geometric invariants
can make some contribution to the problem.
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