{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T13:16:00Z","timestamp":1725455760167},"publisher-location":"Berlin, Heidelberg","reference-count":31,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540642978"},{"type":"electronic","value":"9783540697176"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1997]]},"DOI":"10.1007\/bfb0022721","type":"book-chapter","created":{"date-parts":[[2005,11,19]],"date-time":"2005-11-19T08:02:06Z","timestamp":1132387326000},"page":"87-101","source":"Crossref","is-referenced-by-count":2,"title":["Probabilistic verification of elementary geometry statements"],"prefix":"10.1007","author":[{"given":"Giuseppa","family":"Carr\u00e1 Ferro","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giovanni","family":"Gallo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rosario","family":"Gennaro","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2005,6,17]]},"reference":[{"key":"4_CR1","doi-asserted-by":"crossref","first-page":"577","DOI":"10.2307\/1971361","volume":"126","author":"D. Brownawell","year":"1987","unstructured":"D. Brownawell: Bounds for the Degree in the Nullstellensatz. Ann. Math. 126 (1987),577\u2013591","journal-title":"Ann. Math."},{"key":"4_CR2","first-page":"255","volume":"307","author":"L. Caniglia","year":"1988","unstructured":"L. Caniglia, A. Galligo, J. Heintz: Borne simple exponentielle pour le degr\u00e9s dans le th\u00e9or\u00e8me des z\u00e9ros sur un corps de caract\u00e9ristique quelconque. C.R.A.S. Paris 307 (1988), 255\u2013258","journal-title":"C.R.A.S. Paris"},{"key":"4_CR3","first-page":"141","volume":"365","author":"G. Carri","year":"1986","unstructured":"G. Carri, G. Gallo: A Procedure to Prove Geometrical Statements. Proc. AAECC5 (Menorca) Lecture Notes in Computer Science 365 (1986), 141\u2013150","journal-title":"Proc. AAECC5 (Menorca) Lecture Notes in Computer Science"},{"key":"4_CR4","volume-title":"Mechanical Geometry Theorem Proving","author":"S.-C. Chou","year":"1988","unstructured":"S.-C. Chou: Mechanical Geometry Theorem Proving. D. Reidel Publishing Company, Kluwer Academic Publishers Group, Dordrecht Boston (1988)"},{"key":"4_CR5","unstructured":"S.-C. Chou: Proving and Discovering Theorems in Elementary Geometries Using Wu's Method. PhD. Thesis, Department of Mathematics, University of Texas at Austin (1985)"},{"key":"4_CR6","first-page":"1066","volume":"34","author":"M.K. Deng","year":"1989","unstructured":"M.K. Deng: The Parallel Numerical Method of Proving the Constructive Geometric Theorems. Chinese Sci. Bull. 34 (1989), 1066\u20131070","journal-title":"Chinese Sci. Bull."},{"key":"4_CR7","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1002\/mana.19901490118","volume":"149","author":"N. Fitchas","year":"1990","unstructured":"N. Fitchas, A. Galligo: Nulstellensatz effective et conjecture de Serre (Theoreme de Quillen-Suslin) pour le calcul formel. Math. Nachr. 149 (1990), 231\u2013253","journal-title":"Math. Nachr."},{"key":"4_CR8","unstructured":"G. Gallo: La Dimostrazione Automatica in Geometria e Questioni di Complessita' Correlate. Tesi di Dottorato di Ricerca, Catania (1989)"},{"key":"4_CR9","first-page":"119","volume":"94","author":"G. Gallo","year":"1990","unstructured":"G. Gallo, B. Mishra: Efficient Algorithms and Bounds for Wu-Ritt Characteristic Sets. Progress in Math. 94, Proc. of MEGA 90, Birkh\u00e4user (1990), 119\u2013142","journal-title":"Progress in Math."},{"key":"4_CR10","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1090\/dimacs\/006\/07","volume":"6","author":"G. Gallo","year":"1991","unstructured":"G. Gallo, B. Mishra: Wu-Ritt Characteristic Sets and Their Complexity. DIMACS series in Discrete Mathematics and Theoretical Computer Science 6 (1991), 111\u2013136","journal-title":"DIMACS series in Discrete Mathematics and Theoretical Computer Science"},{"key":"4_CR11","doi-asserted-by":"crossref","unstructured":"J.W. Hong: Proving by Example and Gap Theorem. 27th Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press (1986), 107\u2013116","DOI":"10.1109\/SFCS.1986.48"},{"key":"4_CR12","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1016\/S0747-7171(86)80007-4","volume":"2","author":"D. Kapur","year":"1986","unstructured":"D. Kapur: Using Gr\u00f6bner Bases to Reason about Geometry Problems. Journal of Symbolic Computation\n2 (1986), 399\u2013408","journal-title":"Journal of Symbolic Computation"},{"key":"4_CR13","doi-asserted-by":"crossref","unstructured":"D. Kapur, T. Saxena, L. Yang: Algebraic and Geometric Reasoning using Dixon Resultants. Proc. ISSAC-94 (Oxford, July 20\u201322, 1994), 97\u2013107","DOI":"10.1145\/190347.190372"},{"key":"4_CR14","doi-asserted-by":"crossref","first-page":"963","DOI":"10.2307\/1990996","volume":"1","author":"J. Kollar","year":"1988","unstructured":"J. Kollar: Sharp Effective Nullstellensatz. J. Amer. Math. Soc. 1 (1988), 963\u2013975","journal-title":"J. Amer. Math. Soc."},{"key":"4_CR15","doi-asserted-by":"crossref","unstructured":"B. Kutzler, S. Stifter: Automated Geometry Theorem Proving Using Buchberger's Algorithm. Proceedings of the 1986 Symposium on Symbolic and Algebraic Computation (Waterloo, July 21\u201323, 1986), 209\u2013214","DOI":"10.1145\/32439.32480"},{"key":"4_CR16","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4344-1","volume-title":"Algorithmic Algebra","author":"B. Mishra","year":"1993","unstructured":"B. Mishra: Algorithmic Algebra. Springer Verlag, New York (1993)"},{"key":"4_CR17","volume-title":"Differential Equations from an Algebraic Standpoint","author":"J.F. Ritt","year":"1932","unstructured":"J.F. Ritt: Differential Equations from an Algebraic Standpoint. AMS Colloquium Publications XIV, New York (1932)"},{"key":"4_CR18","volume-title":"Differential Algebra","author":"J.F. Ritt","year":"1950","unstructured":"J.F. Ritt: Differential Algebra. AMS Colloquium Publications XXXII, New York (1950)"},{"key":"4_CR19","doi-asserted-by":"publisher","first-page":"701","DOI":"10.1145\/322217.322225","volume":"27","author":"J.T. Schwartz","year":"1980","unstructured":"J.T. Schwartz: Fast Probabilistic Algorithms for Verification of Polynomial Identities. Journal of ACM 27 (1980), 701\u2013717","journal-title":"Journal of ACM"},{"issue":"4","key":"4_CR20","first-page":"2015","volume":"33","author":"D. Wang","year":"1988","unstructured":"D. Wang: Proving-by-Examples Method and Inclusion of Varieties. Kexue Tongbao 33(4) (1988), 2015\u20132018","journal-title":"Kexue Tongbao"},{"key":"4_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01531321","volume":"3","author":"D. Wang","year":"1995","unstructured":"D. Wang: Elimination Procedures for Mechanical Theorem Proving in Geometry. Ann. Math. Artif. Intell. 3 (1995), 1\u201324","journal-title":"Ann. Math. Artif. Intell."},{"key":"4_CR22","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/3-540-61732-9_60","volume":"1138","author":"D. Wang","year":"1996","unstructured":"D. Wang: Geometry Machines: From AI to SMC. Proc. AISMC-3 (Steyr, Sept. 23-25) Lecture Notes in Computer Science 1138 (1996), 213\u2013239","journal-title":"Lecture Notes in Computer Science"},{"key":"4_CR23","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1007\/3-540-51084-2_34","volume":"358","author":"F. Winkler","year":"1988","unstructured":"F. Winkler: A Geometric Decision Algorithm Based on the Gr\u00f6bner Bases Algorithm. Proc. ISSAC-88 (Rome) Lecture Notes in Computer Science 358 (1988), 356\u2013363","journal-title":"Proc. ISSAC-88 (Rome) Lecture Notes in Computer Science"},{"key":"4_CR24","first-page":"157","volume":"21","author":"W-T. Wu","year":"1978","unstructured":"W-T. Wu: On the Decision Problem and the Mechanization of Theorem Proving in Elementary Geometry. Scientia Sinica 21 (1978), 157\u2013179","journal-title":"Scientia Sinica"},{"key":"4_CR25","first-page":"207","volume":"4","author":"W-T. Wu","year":"1984","unstructured":"W-T. Wu: Basic Principles of Mechanical Theorem Proving in Elementary Geometries. Journal of Sys. Sci. and Math. Sci. 4 (1984), 207\u2013235; also in Journal of Automated Reasoning 4 (1986), 221\u2013252","journal-title":"Journal of Sys. Sci. and Math. Sci."},{"key":"4_CR26","first-page":"235","volume":"29","author":"W-T. Wu","year":"1984","unstructured":"26.W-T. Wu: Some Recent Advances in Mechanical Theorem-Proving of Geometries. Automated Theorem Proving: After 25 Years, Contemporary Mathematics. American Mathematical Society. 29 (1984), 235\u2013242","journal-title":"American Mathematical Society"},{"key":"4_CR27","volume-title":"Mechanical Theorem Proving in Geometries: Basic Principles (translated from the Chinese by Xiaofan Jin and Dongming Wang)","author":"W-T. Wu","year":"1994","unstructured":"W-T. Wu: Mechanical Theorem Proving in Geometries: Basic Principles (translated from the Chinese by Xiaofan Jin and Dongming Wang). Springer-Verlag, Wien New York (1994)"},{"key":"4_CR28","first-page":"115","volume-title":"A New Method of Automated Theorem Proving. The Mathematical Revolution Inspired by Computing","author":"L. Yang","year":"1991","unstructured":"L. Yang:A New Method of Automated Theorem Proving. The Mathematical Revolution Inspired by Computing. Oxford Univ. Press, New York (1991), 115\u2013126"},{"key":"4_CR29","unstructured":"L. Yang, J.Z. Zhang, C.Z. Li: A Prover for Parallel Numerical Verification of a Class of Constructive Geometry Theorems. Proc. IWMM 92 (Beijing, July 16\u201318, 1992),244\u2013250"},{"key":"4_CR30","first-page":"147","volume-title":"Searching Dependency between Algebraic Equations: An Algorithm Applied to Automated Reasoning. Artificial Intelligence in Mathematics","author":"L. Yang","year":"1994","unstructured":"L. Yang, J.Z. Zhang: Searching Dependency between Algebraic Equations: An Algorithm Applied to Automated Reasoning. Artificial Intelligence in Mathematics, Oxford University Press, Oxford (1994), 147\u2013156"},{"key":"4_CR31","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1016\/0304-3975(90)90077-U","volume":"74","author":"J.Z. Zhang","year":"1990","unstructured":"J.Z. Zhang, L. Yang, M.K. Deng: The Parallel Numerical Methods in Mechanical Theorem Proving. Theoret. Comput. Sci. 74 (1990), 253\u2013271","journal-title":"Theoret. Comput. Sci."}],"container-title":["Lecture Notes in Computer Science","Automated Deduction in Geometry"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BFb0022721","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,2,4]],"date-time":"2019-02-04T22:16:09Z","timestamp":1549318569000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BFb0022721"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997]]},"ISBN":["9783540642978","9783540697176"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/bfb0022721","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[1997]]}}}