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Automated Discovering and Proving for Geometric Inequalities

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Automated Deduction in Geometry (ADG 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1669))

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Abstract

Automated discovering and proving for geometric inequalities have been considered a difficult topic in the area of automated reasoning for manyy ears. Some well-known algorithms are complete theoreticallyb ut inefficient in practice, and cannot verify non-trivial propositions in batches. In this paper, we present an efficient algorithm to discover and prove a class of inequality-type theorems automatically by combining discriminant sequence for polynomials with Wu’s elimination and a partial cylindrical algebraic decomposition. Also this algorithm is applied to the classification of the real physical solutions of geometric constraint problems. Manygeom etric inequalities have been discovered byou r program, DISCOVERER, which implements the algorithm in Maple.

This work is supported in part by CAS and CNRS under a cooperative project between CICA and LEIBNIZ, and in part by the National “937” Project of China

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Authors and Affiliations

  1. Chengdu Institute of Computer Applications Academia Sinica, Chengdu, 610041, China

    Lu Yang, Xiaorong Hou & Bican Xia

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  1. Lu Yang
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  2. Xiaorong Hou
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  3. Bican Xia
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© 1999 Springer-Verlag Berlin Heidelberg

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Yang, L., Hou, X., Xia, B. (1999). Automated Discovering and Proving for Geometric Inequalities. In: Automated Deduction in Geometry. ADG 1998. Lecture Notes in Computer Science(), vol 1669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47997-X_3

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  • DOI: https://doi.org/10.1007/3-540-47997-X_3

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  • Print ISBN: 978-3-540-66672-1

  • Online ISBN: 978-3-540-47997-0

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