BOTTEMA

Automated Proving for a Class of Constructive Geometric Inequalities. An automated inequality-proving algorithm is presented based on a mixed method including a so-called cell-decomposition. That is implemented by a Maple program named “BOTTEMA” which can prove or disprove propositions in an extensive class of geometric and algebraic inequalities involving radicals. Most of the theorems in “Geometric Inequalities”　writed by Bottema et al., can be proven efficiently in this way.

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References in zbMATH (referenced in 9 articles )

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  1. Chen, Shiping; Liu, Zhong: Automated proof of mixed trigonometric-polynomial inequalities (2020)
  2. Chen, Shiping; Liu, Zhong: Automated proving of exponent polynomial inequalities (2017)
  3. Chen, Shiping; Liu, Zhong: Automated proving of trigonometric function inequalities using Taylor expansion (2016)
  4. Xia, Bican; Yang, Lu: Automated inequality proving and discovering (2016)
  5. Chen, Shengli; Chen, Liangyu: The degree-decreasing decomposition of symmetric forms with a program for algebraic inequality decision (2013)
  6. Wu, Yu-Dong; Lokesha, V.; Srivastava, H. M.: Another refinement of the Pólya-Szegő inequality (2010)
  7. Guan, Qiang; Wang, Long; Xia, Bican; Yang, Lu; Yu, Wensheng; Zeng, Zhenbing: Solution to the generalized champagne problem on simultaneous stabilization of linear systems (2007)
  8. Yang, Lu; Feng, Yong; Yao, Yong: A class of mechanically decidable problems beyond Tarski’s model (2007)
  9. Bottema, O.; Đorđević, Radosav Ž.; Janić, Racovan R.; Mitrinović, D. S.; Vasić, Petar M.: Geometric inequalities (1969)