{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T08:54:37Z","timestamp":1743152077385,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":24,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642250699"},{"type":"electronic","value":"9783642250705"}],"license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011]]},"DOI":"10.1007\/978-3-642-25070-5_9","type":"book-chapter","created":{"date-parts":[[2011,11,8]],"date-time":"2011-11-08T20:30:55Z","timestamp":1320784255000},"page":"152-168","source":"Crossref","is-referenced-by-count":0,"title":["On One Method of Proving Inequalities in Automated Way"],"prefix":"10.1007","author":[{"given":"Pavel","family":"Pech","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"9_CR1","unstructured":"Bottema, O., et al.: Geometric inequalities, Groningen (1969)"},{"key":"9_CR2","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1007\/978-94-009-5225-6_6","volume-title":"Multidimensional Systems Theory","author":"B. Buchberger","year":"1985","unstructured":"Buchberger, B.: Groebner bases: an algorithmic method in polynomial ideal theory. In: Bose, N.-K. (ed.) Multidimensional Systems Theory, pp. 184\u2013232. Reidel, Dordrecht (1985)"},{"key":"9_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-4037-6","volume-title":"Mechanical Geometry Theorem Proving","author":"S.C. Chou","year":"1987","unstructured":"Chou, S.C.: Mechanical Geometry Theorem Proving. D. Reidel Publishing Company, Dordrecht (1987)"},{"key":"9_CR4","first-page":"139","volume":"6","author":"S.C. Chou","year":"1992","unstructured":"Chou, S.C., Gao, X.S., Arnon, D.S.: On the mechanical proof of geometry theorems involving inequalities. Advances in Computing Research\u00a06, 139\u2013181 (1992)","journal-title":"Advances in Computing Research"},{"key":"9_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1007\/3-540-07407-4_17","volume-title":"Automata Theory and Formal Languages","author":"G.E. Collins","year":"1975","unstructured":"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.\u00a033, pp. 134\u2013183. Springer, Heidelberg (1975)"},{"key":"9_CR6","volume-title":"Ideals, Varieties and Algorithms","author":"D. Cox","year":"1997","unstructured":"Cox, D., Little, J., O\u2019Shea, D.: Ideals, Varieties and Algorithms. Springer, Berlin (1997)"},{"key":"9_CR7","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/s10817-009-9133-x","volume":"43","author":"G. Dalzotto","year":"2009","unstructured":"Dalzotto, G., Recio, T.: On protocols for the automated discovery of theorems in elementary geometry. Journal of Automated Reasoning\u00a043, 203\u2013236 (2009)","journal-title":"Journal of Automated Reasoning"},{"key":"9_CR8","doi-asserted-by":"publisher","first-page":"97","DOI":"10.2140\/pjm.1975.56.97","volume":"56","author":"L. Gerber","year":"1975","unstructured":"Gerber, L.: The orthocentric simplex as an extreme simplex. Pacific J. of Math.\u00a056, 97\u2013111 (1975)","journal-title":"Pacific J. of Math."},{"key":"9_CR9","doi-asserted-by":"publisher","first-page":"778","DOI":"10.1007\/s11432-010-4178-3","volume":"54","author":"X. Hou","year":"2011","unstructured":"Hou, X., Xu, S., Shao, J.: Some geometric properties of successive difference substitutions. Science China, Information Sciences\u00a054, 778\u2013786 (2011)","journal-title":"Science China, Information Sciences"},{"key":"9_CR10","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/0004-3702(88)90050-1","volume":"37","author":"D. Kapur","year":"1988","unstructured":"Kapur, D.: A Refutational Approach to Geometry Theorem Proving. Artificial Intelligence Journal\u00a037, 61\u201393 (1988)","journal-title":"Artificial Intelligence Journal"},{"key":"9_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-7842-4","volume-title":"Recent Advances in Geometric Inequalities","author":"D.S. Mitrinovic","year":"1989","unstructured":"Mitrinovic, D.S., Pecaric, J.E., Volenec, V.: Recent Advances in Geometric Inequalities. Kluwer Acad. Publ., Dordrecht (1989)"},{"key":"9_CR12","unstructured":"Nelsen, R.: Proofs Without Words. MAA (1993)"},{"key":"9_CR13","unstructured":"Parrilo, P.A.: Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization. PhD. thesis. California Institute of Technology, Pasadena, California (2000)"},{"key":"9_CR14","doi-asserted-by":"publisher","DOI":"10.1142\/6556","volume-title":"Selected topics in geometry with classical vs. computer proving","author":"P. Pech","year":"2007","unstructured":"Pech, P.: Selected topics in geometry with classical vs. computer proving. World Scientific Publishing, New Jersey (2007)"},{"key":"9_CR15","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1007\/978-3-662-03891-8_12","volume-title":"Some Tapas of Computer Algebra, Algorithms and Computations in Mathematics","author":"T. Recio","year":"1998","unstructured":"Recio, T., Sterk, H., V\u00e9lez, M.P.: Project 1. Automatic Geometry Theorem Proving. In: Cohen, A., Cuipers, H., Sterk, H. (eds.) Some Tapas of Computer Algebra, Algorithms and Computations in Mathematics, vol.\u00a04, pp. 276\u2013296. Springer, Heidelberg (1998)"},{"key":"9_CR16","first-page":"257","volume":"253","author":"B. Reznick","year":"2000","unstructured":"Reznick, B.: Some concrete aspects of Hilbert\u2019s 17th Problem. Contemp. Math.\u00a0253, 257\u2013272 (2000)","journal-title":"Contemp. Math."},{"key":"9_CR17","series-title":"Lecture Notes of Computer Algebra","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1017\/CBO9780511565847.016","volume-title":"Gr\u00f6bner Bases and Applications","author":"D. Wang","year":"1998","unstructured":"Wang, D.: Gr\u00f6bner Bases Applied to Geometric Theorem Proving and Discovering. In: Buchberger, B., Winkler, F. (eds.) Gr\u00f6bner Bases and Applications. Lecture Notes of Computer Algebra, pp. 281\u2013301. Cambridge Univ. Press, Cambridge (1998)"},{"key":"9_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-6202-6","volume-title":"Elimination Methods","author":"D. Wang","year":"2001","unstructured":"Wang, D.: Elimination Methods. Springer, Wien (2001)"},{"key":"9_CR19","doi-asserted-by":"publisher","DOI":"10.1142\/9781848161207","volume-title":"Elimination Practice. Software Tools and Applications","author":"D. Wang","year":"2004","unstructured":"Wang, D.: Elimination Practice. Software Tools and Applications. Imperial College Press, London (2004)"},{"key":"9_CR20","first-page":"137","volume":"5","author":"R. Weitzenb\u00f6ck","year":"1919","unstructured":"Weitzenb\u00f6ck, R.: Math. Zeitschrift\u00a05, 137\u2013146 (1919)","journal-title":"Zeitschrift"},{"key":"9_CR21","volume-title":"Mathematics Mechanization","author":"W.-T. Wu","year":"2000","unstructured":"Wu, W.-T.: Mathematics Mechanization. Science Press, Kluwer Academic Publishers, Beijing, Dordrecht (2000)"},{"key":"9_CR22","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/3-540-45410-1_4","volume-title":"Automated Deduction in Geometry","author":"L. Yang","year":"2001","unstructured":"Yang, L., Zhang, J.: A Practical Program of Automated Proving for a Class of Geometric Inequalities. In: Richter-Gebert, J., Wang, D. (eds.) ADG 2000. LNCS (LNAI), vol.\u00a02061, pp. 41\u201357. Springer, Heidelberg (2001)"},{"issue":"2","key":"9_CR23","first-page":"1","volume":"5","author":"L. Yang","year":"2006","unstructured":"Yang, L.: Difference substitution and automated inequality proving. Journal of Guangzhou Univ., Natural Science Edition\u00a05(2), 1\u20137 (2006)","journal-title":"Journal of Guangzhou Univ., Natural Science Edition"},{"key":"9_CR24","unstructured":"Yao, Y.: Termination od the sequence of SDS and machine decision for positive semi-definite forms. arXiv:0904.4030v1 (2009)"}],"container-title":["Lecture Notes in Computer Science","Automated Deduction in Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-25070-5_9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,19]],"date-time":"2019-05-19T20:30:04Z","timestamp":1558297804000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-25070-5_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642250699","9783642250705"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-25070-5_9","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2011]]}}}