By Gábor Bodnár (auth.), Franz Winkler (eds.)
This ebook constitutes the completely refereed post-proceedings of the 4th foreign Workshop on automatic Deduction in Geometry, ADG 2002, held at Hagenberg citadel, Austria in September 2002.
The thirteen revised complete papers awarded 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 number of geometric theorem proving structures are explored; and functions of automatic deduction in geometry are established 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
It’s obvious to see that we can predetermine the variables occurring in nondegenerate conditions. So it’s convenient for us to observe the range of possible value for any variables. As a rule, we will eliminate all the dependent variables . Moreover, we can be certain that the conditions found through this method are the weakest compared to the condition obtained by Wu’s method and the others based on Gr¨obner basis such as Kapur’s and Winkler’s approaches. Now we consider the application of projection method on formula deduction.
If we want to compute P rojx1 ,··· ,xn Zero(P S/D). The computing process can be divided into two steps. The variable ordering should be xn > · · · > xm+1 > xm > · · · > x1 . t. Zero(P S/D) = i Zero(ASi /Ji D). Each ASi is an ascending set for the variable ordering xn > · · · > xm+1 > xm > · · · > x1 . Then for each Zero(ASi /Ji D) we can compute its projection. In the following, we will give the algorithm in detail. Step 1. t. Zero(ASi /Ji D) Zero(P S/D) = i where Ji is the product of the initials of the polynomials in ASi .
Elimination Methods. Springer-Verlag,Wien New York, 2001. 33  P. Wenger. Classiﬁcation of 3r positioning manipulators. Journal of Mechanical Design, 120:327–332, June 1998. 32, 42  Ph. Wenger and J. El Omri. Changing posture for cuspidal robot manipulators. In Proceeding of the 1996 IEEE Int. Conf on Robotics and Automation, pages 3173–3178, 1996. cn Abstract. We introduce a software package, MMP/Geometer, developed by us to automate some of the basic geometric activities including geometric theorem proving, geometric theorem discovering, and geometric diagram generation.
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.)