By Xiao-Shan Gao, Dongming Wang, Lu Yang (auth.)
The moment foreign Workshop on automatic Deduction in Geometry (ADG ’98) was once held in Beijing, China, August 1–3, 1998. a rise of curiosity in ADG ’98 over the former workshop ADG ’96 is represented via the impressive variety of greater than forty individuals from ten international locations and the powerful tech- cal software of 25 shows, of which one-hour invited talks got by means of Professors Wen-tsun ¨ Wu and Jing-Zhong Zhang. The workshop supplied the members with a well-focused discussion board for e?ective alternate of recent rules and well timed document of study development. perception surveys, algorithmic advancements, and purposes in CAGD/CAD and computing device imaginative and prescient offered via lively - searchers, including geometry software program demos, make clear the gains of this moment workshop. ADG ’98 used to be hosted through the maths Mechanization learn heart (MMRC) with ?nancial help from the chinese language Academy of Sciences and the French nationwide heart for Scienti?c examine (CNRS), and was once prepared through the 3 co-editors of this lawsuits quantity. The papers inside the quantity have been chosen, less than a strict refereeing method, from these awarded at ADG ’98 and submitted afterwards. lots of the 14 approved papers have been conscientiously revised and a few of the revised types have been checked back via exterior reviewers. we are hoping that those papers conceal essentially the most fresh and signi?cant examine effects and advancements and re?ect the present state of the art of ADG.
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Extra info for Automated Deduction in Geometry: Second International Workshop, ADG’98 Beijing, China, August 1–3, 1998 Proceedings
30–46, 1999. c Springer-Verlag Berlin Heidelberg 1999 Automated Discovering and Proving for Geometric Inequalities 31 of polynomial equations only. This is a very eﬃcient method for mechanically proving elementary geometry theorems (of equality type). Chou  has successfully implemented Wu’s method for 512 examples which include almost all the well-known or historically interesting theorems in elementary geometry, and it was reported that for most of the examples the CPU time spent was only few seconds each, or less than 1 second!
Counting Real Zeros. D. dissertation, Courant Institute of Mathematical Sciences, New York, 1991. 18 20. Paul Pedersen, Marie-Fran¸coise Roy, and Aviva Szpirglas. Counting real zeroes in the multivariate case. In F. Eysette and A. Galigo, editors, Computational Algebraic Geometry, volume 109 of Progress in Mathematics, pages 203–224. Birkh¨ auser, Boston, Basel; Berlin, 1993. Proceedings of the MEGA 92. 18 21. Alfred Tarski. A decision method for elementary algebra and geometry. Technical report, RAND, Santa Monica, CA, 1948.
All these simpliﬁcations takes 434 s. The automatic tableau method can simplify some of the resulting conjunctive normal forms in about 1 s. After these simpliﬁcations we get a disjunction of eight conjunctive normal forms. From these eight conjunctive normal forms are six pure conjunctions of atomic formulas. The two other ones are conjunctions containing atomic formulas and only one disjunction of two atomic formulas. Using the equivalents (α 0 ∨ β = 0) ←→ (α · β 2 0) and (α = 0 ∨ β = 0) ←→ (α · β = 0) we can simplify the formula to a disjunctive normal form ψ with constituents ψi .
Automated Deduction in Geometry: Second International Workshop, ADG’98 Beijing, China, August 1–3, 1998 Proceedings by Xiao-Shan Gao, Dongming Wang, Lu Yang (auth.)