On Geometric Theorem Proving with Null Geometric Algebra
نویسندگان
چکیده
In algebraic approaches to geometric computing, the general procedure is as follows [11]: first, the geometric configuration, including both the hypotheses and the conclusion, is translated into an algebraic formulation in a prerequisite algebraic language; second, algebraic computations are carried out to the conclusion by utilizing the computational rules of the algebra and the given hypotheses; third, the result of the computations is translated back to geometry, or in other words, is given a geometric interpretation. In geometric reasoning and theorem proving, the input of a geometric problem is formulated by a set of symbols and their algebraic relations, and the algebraic computing, if geometrically meaningful, is called “symbolic geometric computation” [10]. The most commonly used algebraic formulation is Cartesian coordinates and its variations. In this setting, geometric relations are represented by polynomial equalities of coordinates. When coordinates are used in geometric computation, two typical difficulties occur:
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