Download e-book for kindle: Automated Deduction in Geometry: Second International by Xiao-Shan Gao, Dongming Wang, Lu Yang (auth.)

By Xiao-Shan Gao, Dongming Wang, Lu Yang (auth.)

ISBN-10: 3540666729

ISBN-13: 9783540666721

The moment overseas Workshop on automatic Deduction in Geometry (ADG ’98) used to be 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 striking variety of greater than forty individuals from ten nations and the robust tech- cal software of 25 shows, of which one-hour invited talks got through Professors Wen-tsun ¨ Wu and Jing-Zhong Zhang. The workshop supplied the individuals with a well-focused discussion board for e?ective alternate of latest rules and well timed document of analysis development. perception surveys, algorithmic advancements, and purposes in CAGD/CAD and machine imaginative and prescient offered by way of lively - searchers, including geometry software program demos, make clear the positive factors of this moment workshop. ADG ’98 used to be hosted via the maths Mechanization study middle (MMRC) with ?nancial help from the chinese language Academy of Sciences and the French nationwide heart for Scienti?c learn (CNRS), and was once equipped through the 3 co-editors of this court cases quantity. The papers inside the quantity have been chosen, below a strict refereeing technique, from these awarded at ADG ’98 and submitted afterwards. many of the 14 authorised papers have been conscientiously revised and a few of the revised models have been checked back via exterior reviewers. we are hoping that those papers hide one of the most fresh and signi?cant study effects and advancements and re?ect the present cutting-edge of ADG.

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Extra resources for Automated Deduction in Geometry: Second International Workshop, ADG’98 Beijing, China, August 1–3, 1998 Proceedings

Example text

Fs }, by Ii (i = 1, 2, . . , s) denote the leading coefficient of fi in xi . The triangular set {f1 , f2 , . . , fs } is called a normal ascending chain if I1 = 0, res(Ii , fi−1 , . . , f1 ) = 0, i = 2, . . , s. 2 (Simplicial [33,34]). A normal ascending chain {f1 , f2 , . . , fs } is simplicial with respect to a polynomial g if either prem(g, fs , . . , f1 ) = 0 or res(g, fs , . . , f1 ) = 0. 3 (Discrimination Matrix [30]). Given a polynomial with general symbolic coefficients f (x) = a0 xn + a1 xn−1 + · · · + an , the following 2n × 2n matrix in terms of the coefficients   a0 a1 a2 · · · an  0 na0 (n − 1)a1 · · · an−1      a a · · · a a 0 1 n−1 n     0 na · · · 2a a 0 n−2 n−1     · · · · · ·     · · · · · ·    a0 a1 a2 · · · an  0 na0 (n − 1)a1 · · · an−1 is called the discrimination matrix of f (x), and denoted by Discr(f ).

110–134, 1992. 31 33. , Zhang, J. Z. & Hou, X. , An Efficient Decomposition Algorithm for Geometry Theorem Proving Without Factorization, Proc. of Asian Symposium on Computer Mathematics, H. Shi & H. ), Scientists Incorporated, Japan, pp. 33–41, 1995. 32, 33, 40 34. , Zhang, J. Z. & Hou, X. , Nonlinear Algebraic Equation System and Automated Theorem Proving, Shanghai Scientific and Technological Education Publ. House, Shanghai, 1996. (in Chinese) 31, 32, 33, 40 35. Zhang, J. , Yang, L. & Hou, X. , A Criterion for Dependency of Algebraic Equations with Applications to Automated Theorem Proving, Science in China, Series A 37, 547–554, 1994.

When dealing with geometry proofs, we often take for granted conditions that need to be stated explicitly for machine proofs: for example, two points making up a line should not coincide. The machine proofs are valid only if these conditions are met. These are known as non-degenerate conditions and are required in many cases to prevent the denominators of fractions from becoming zero in the various algebraic statements. 2 The Full-Angle Method A full-angle u, v is the angle from line u to line v measured anti-clockwise.

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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.)

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