On One Method of Proving Inequalities in Automated Way
The paper describes proving geometric inequalities in automated way without cell decomposition. Firstly an overview of known methods of proving inequalities is given including the method which is based on reduction of a conclusion polynomial to the canonical form modulo a hypotheses ideal. Then a parametrization method of proving geometric inequalities is introduced. Further a method of proving geometric inequalities which introduces an auxiliary polynomial is described.
Keywordsgeometric inequalities automated geometry theorem proving
Unable to display preview. Download preview PDF.
- 1.Bottema, O., et al.: Geometric inequalities, Groningen (1969)Google Scholar
- 4.Chou, S.C., Gao, X.S., Arnon, D.S.: On the mechanical proof of geometry theorems involving inequalities. Advances in Computing Research 6, 139–181 (1992)Google Scholar
- 5.Collins, G.E.: Quantifier elimination for the elementary theory of real closed fields by cylindrical algebraic decomposition. In: Brakhage, H. (ed.) GI-Fachtagung 1975. LNCS, vol. 33, pp. 134–183. Springer, Heidelberg (1975)Google Scholar
- 12.Nelsen, R.: Proofs Without Words. MAA (1993)Google Scholar
- 13.Parrilo, P.A.: Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization. PhD. thesis. California Institute of Technology, Pasadena, California (2000)Google Scholar
- 20.Weitzenböck, R.: Math. Zeitschrift 5, 137–146 (1919)Google Scholar
- 21.Wu, W.-T.: Mathematics Mechanization. Science Press, Kluwer Academic Publishers, Beijing, Dordrecht (2000)Google Scholar
- 24.Yao, Y.: Termination od the sequence of SDS and machine decision for positive semi-definite forms. arXiv:0904.4030v1 (2009)Google Scholar