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Geometry theorem proving by decomposing polynomial system into strong regular sets

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Abstract

This paper presents a complete method to prove geometric theorem by decomposing the corresponding polynomial system into strong regular sets, by which one can compute some components for which the geometry theorem is true and exclude other components for which the geometry theorem is false. Two examples are given to show that the geometry theorems are conditionally true for some components which are excluded by other methods.

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Authors and Affiliations

  1. Mathematical College, Sichuan University, 610041, Chengdu, P.R. China

    Yong-Bin Li & Xiao-Lin Xiang

  2. College of Information Technology, Sichuan Normal University, 610068, Chengdu, P.R. China

    Yong-Bin Li

  3. Department of Computer Science and Technology, Sichuan Agriculture University, 611830, Dujiangyan, P. R. China

    Wu Liu

Authors
  1. Yong-Bin Li
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  2. Wu Liu
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  3. Xiao-Lin Xiang
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Corresponding author

Correspondence to Yong-Bin Li.

Additional information

Yong-Bin Li was born in 1965. He is a Ph.D. in the Mathematical College of Sichuan University. His major research interests include computer algebra and analysis and geometric reasoning.

Wu Liu was born in 1966. He is a Ph.D. in the Chengdu Institute of Computer Applications, The Chinese Academy of Sciences. His major interests include computer algebra and security of network information.

Xiao-Lin Xiang was born in 1965. He is a Ph.D. candidate in the Mathematical College of Sichuan University. His major research interests include computer algebra and analysis and geometric reasoning.

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Li, YB., Liu, W. & Xiang, XL. Geometry theorem proving by decomposing polynomial system into strong regular sets. J. Comput. Sci. & Technol. 19, 820–827 (2004). https://doi.org/10.1007/BF02973445

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  • DOI: https://doi.org/10.1007/BF02973445

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