Get Automated Deduction in Geometry: 4th International Workshop, PDF

By Gábor Bodnár (auth.), Franz Winkler (eds.)

ISBN-10: 3540209271

ISBN-13: 9783540209270

This publication constitutes the completely refereed post-proceedings of the 4th overseas Workshop on automatic Deduction in Geometry, ADG 2002, held at Hagenberg fortress, Austria in September 2002.

The thirteen revised complete papers provided have been conscientiously chosen in the course of rounds of reviewing and development. one of the concerns addressed are theoretical and methodological issues, resembling the solution of singularities, algebraic geometry and laptop algebra; a variety of geometric theorem proving structures are explored; and purposes of automatic deduction in geometry are validated in fields like computer-aided layout and robotics.

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Extra info for Automated Deduction in Geometry: 4th International Workshop, ADG 2002, Hagenberg Castle, Austria, September 4-6, 2002. Revised Papers

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4, Ins. of Systems Science, Academia Sinica,(1991) 22, 23, 25 [8] Dongming Wang: Elimination method, Springer 2001. 23, 27 [9] Dingkang Wang: Zero Decomposition Algorithms for System of Polynomial Equations, Computer Mathematics, World Scientific, (2000) 67-70 24, 25 [10] X. Gao, S. Chou: Solving Parametric Algebraic Systems, Proc. fr Abstract. In this paper we present a classification of 3-revolute-jointed manipulators based on the cuspidal behaviour. It was shown in a previous work [16] that this ability to change posture without meeting a singularity is equivalent to the existence of a point in the workspace, such that a polynomial of degree four depending on the parameters of the manipulator and on the cartesian coordinates of the effector has a triple root.

Wu’s method might be the most powerful method in terms of proving difficult geometric theorems and applying to more geometries [33, 36]. Wu’s method is a coordinate-based method. It first transfers geometric conditions into polynomial or differential equations in the coordinates of the points involved, then deals with the equations with the characteristic set method. The area method uses high-level geometric lemmas about geometric invariants such as the area and the Pythagorean difference as the basic tool of proving geometric theorems [8].

T. (a1 , · · · , an ) ∈ Zero(ASi /Ji ). According to the definition of projection, (a1 , · · · , am ) ∈ P rojxm+1 ,··· ,xn Zero(ASi /Ji ), it follows that a = (a1 , · · · , am ) ∈ ∪i P rojxm+1 ,··· ,xn Zero(ASi /Ji D). It shows P rojxm+1 ,··· ,xn i Zero(ASi /Ji D) ⊂ i P rojxm+1 ,··· ,xn Zero(ASi /Ji D). The inclusion of reversal direction also can be proved by the same way. Lemma 2. t. variable ordering (x1 < x2 < · · · < xn ),AS = {A1 , · · · , As−1 }, J and J are the products of the initials of polynomials in AS and AS respectively.

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Automated Deduction in Geometry: 4th International Workshop, ADG 2002, Hagenberg Castle, Austria, September 4-6, 2002. Revised Papers by Gábor Bodnár (auth.), Franz Winkler (eds.)


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