{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,7]],"date-time":"2024-09-07T21:41:52Z","timestamp":1725745312369},"publisher-location":"Cham","reference-count":26,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319022963"},{"type":"electronic","value":"9783319022970"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-319-02297-0_24","type":"book-chapter","created":{"date-parts":[[2013,8,14]],"date-time":"2013-08-14T07:37:38Z","timestamp":1376465858000},"page":"288-300","source":"Crossref","is-referenced-by-count":0,"title":["A Note on the Need for Radical Membership Checking in Mechanical Theorem Proving in Geometry"],"prefix":"10.1007","author":[{"given":"Eugenio","family":"Roanes-Lozano","sequence":"first","affiliation":[]},{"given":"Eugenio","family":"Roanes-Mac\u00edas","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"24_CR1","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1007\/3-540-45410-1_7","volume-title":"Automated Deduction in Geometry","author":"L. Bazzotti","year":"2001","unstructured":"Bazzotti, L., Dalzotto, G., Robbiano, L.: Remarks on geometric theorem proving. In: Richter-Gebert, J., Wang, D. (eds.) ADG 2000. LNCS (LNAI), vol.\u00a02061, pp. 104\u2013128. Springer, Heidelberg (2001)"},{"issue":"2","key":"24_CR2","first-page":"141","volume":"61","author":"F. Botana","year":"2003","unstructured":"Botana, F., Valcarce, J.L.: A software tool for the investigation of plane loci. Mat. Comp. Simul.\u00a061(2), 141\u2013154 (2003)","journal-title":"Mat. Comp. Simul."},{"issue":"1","key":"24_CR3","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1023\/A:1025636820683","volume":"8","author":"F. Botana","year":"2003","unstructured":"Botana, F.: A web-based resource for automatic discovery in plane geometry. Intl. J. Comp. Mat. Learning\u00a08(1), 109\u2013121 (2003)","journal-title":"Intl. J. Comp. Mat. Learning"},{"key":"24_CR4","doi-asserted-by":"crossref","unstructured":"Buchberger, B: Applications of Gr\u00f6bner bases in non-linear computational geometry, in: Rice, J.R. (ed.) Mathematical Aspects of Scientific Software, pp. 59\u201387. Springer (1988)","DOI":"10.1007\/978-1-4684-7074-1_3"},{"key":"24_CR5","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/3-540-45410-1_8","volume-title":"Automated Deduction in Geometry","author":"M. Bulmer","year":"2001","unstructured":"Bulmer, M., Fearnley-Sander, D., Stokes, T.: The kinds of truth of geometry theorems. In: Richter-Gebert, J., Wang, D. (eds.) ADG 2000. LNCS (LNAI), vol.\u00a02061, pp. 129\u2013142. Springer, Heidelberg (2001)"},{"key":"24_CR6","volume-title":"Mechanical geometry theorem proving","author":"S.-C. Chou","year":"1988","unstructured":"Chou, S.-C.: Mechanical geometry theorem proving. Reidel, Dordrecht (1988)"},{"key":"24_CR7","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/3-540-45410-1_6","volume-title":"Automated Deduction in Geometry","author":"P. Conti","year":"2001","unstructured":"Conti, P., Traverso, C.: Algebraic and Semialgebraic Proofs: Methods and Paradoxes. In: Richter-Gebert, J., Wang, D. (eds.) ADG 2000. LNCS (LNAI), vol.\u00a02061, pp. 83\u2013103. Springer, Heidelberg (2001)"},{"key":"24_CR8","series-title":"Undergraduate Texts in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2693-0","volume-title":"Ideals, Varieties, and Algorithms","author":"D. Cox","year":"1997","unstructured":"Cox, D., Little, J., O\u2019Shea, D.: Ideals, Varieties, and Algorithms. Undergraduate Texts in Mathematics. Springer, New York (1997)"},{"key":"24_CR9","first-page":"254","volume-title":"Proc. ISSAC 1989","author":"B. Kutzler","year":"1989","unstructured":"Kutzler, B.: Careful algebraic translations of geometry theorems. In: Gonnet, G.H. (ed.) Proc. ISSAC 1989, pp. 254\u2013263. ACM Press, Portland (1989)"},{"issue":"4","key":"24_CR10","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1016\/S0747-7171(86)80006-2","volume":"2","author":"B. Kutzler","year":"1986","unstructured":"Kutzler, B., Stifter, S.: On the application of Buchberger\u2019s algorithm to automated geometry theorem proving. J. Symb. Comp.\u00a02(4), 389\u2013397 (1986)","journal-title":"J. Symb. Comp."},{"key":"24_CR11","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1016\/j.jsc.2007.07.022","volume":"44","author":"M. Manubens","year":"2006","unstructured":"Manubens, M., Montes, A.: Minimal Canomical Comprehensive Groebner system. J. Symb. Comput.\u00a044, 463\u2013478 (2006)","journal-title":"J. Symb. Comput."},{"key":"24_CR12","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/978-3-540-77356-6_8","volume-title":"Automated Deduction in Geometry","author":"A. Montes","year":"2007","unstructured":"Montes, A., Recio, T.: Automatic discovery of geometry theorems using minimal canonical comprehensive gr\u00f6bner systems. In: Botana, F., Recio, T. (eds.) ADG 2006. LNCS (LNAI), vol.\u00a04869, pp. 113\u2013138. Springer, Heidelberg (2007)"},{"key":"24_CR13","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1007\/978-3-540-77356-6_10","volume-title":"Automated Deduction in Geometry","author":"P. Pech","year":"2007","unstructured":"Pech, P.: On the need of radical ideals in automatic proving: A theorem about regular polygons. In: Botana, F., Recio, T. (eds.) ADG 2006. LNCS (LNAI), vol.\u00a04869, pp. 157\u2013170. Springer, Heidelberg (2007)"},{"key":"24_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 Co. Pte. Ltd, Singapore (2007)"},{"key":"24_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1007\/978-3-540-24709-8_80","volume-title":"Computational Science and Its Applications \u2013 ICCSA 2004","author":"T. Recio","year":"2004","unstructured":"Recio, T., Botana, F.: Where the truth lies (in automatic theorem proving in elementary geometry). In: Lagan\u00e1, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds.) ICCSA 2004. LNCS, vol.\u00a03044, pp. 761\u2013770. Springer, Heidelberg (2004)"},{"key":"24_CR16","series-title":"Texts & Monographs in Symbolic Computation","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1007\/978-3-7091-0794-2_12","volume-title":"Numerical and Symbolic Scientific Computing","author":"T. Recio","year":"2012","unstructured":"Recio, T., V\u00e9lez, M.P.: An Introduction to Automated Discovery in Geometry through Symbolic Computation. In: Langer, U., Paule, P. (eds.) Numerical and Symbolic Scientific Computing. Texts & Monographs in Symbolic Computation, vol.\u00a01, pp. 257\u2013271. Springer, Vienna (2012)"},{"issue":"9-10","key":"24_CR17","doi-asserted-by":"publisher","first-page":"1005","DOI":"10.1016\/S0895-7177(03)00115-8","volume":"37","author":"E. Roanes-Lozano","year":"2003","unstructured":"Roanes-Lozano, E., Roanes-Mac\u00edas, E., Villar-Mena, M.: A bridge between dynamic geometry and computer algebra. Mat. Comp. Mod.\u00a037(9-10), 1005\u20131028 (2003)","journal-title":"Mat. Comp. Mod."},{"issue":"2","key":"24_CR18","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1109\/MCISE.2004.1267612","volume":"6","author":"E. Roanes-Lozano","year":"2004","unstructured":"Roanes-Lozano, E., Roanes-Mac\u00edas, Laita, L.M.: The geometry of algebraic systems and their exact solving using Groebner bases. Comp. Sci. Eng.\u00a06(2), 76\u201379 (2004)","journal-title":"Comp. Sci. Eng."},{"issue":"3","key":"24_CR19","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1109\/MCISE.2004.1289309","volume":"6","author":"E. Roanes-Lozano","year":"2004","unstructured":"Roanes-Lozano, E., Roanes-Mac\u00edas, Laita, L.M.: Some Applications of Groebner bases. Comp. Sci. Eng.\u00a06(3), 56\u201360 (2004)","journal-title":"Comp. Sci. Eng."},{"key":"24_CR20","volume-title":"Nuevas Tecnolog\u00edas en Geometr\u00eda","author":"E. Roanes-Mac\u00edas","year":"1994","unstructured":"Roanes-Mac\u00edas, E., Roanes-Lozano, E.: Nuevas Tecnolog\u00edas en Geometr\u00eda. Editorial Complutense, Madrid (1994)"},{"key":"24_CR21","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/978-3-540-77356-6_11","volume-title":"Automated Deduction in Geometry","author":"E. Roanes-Mac\u00edas","year":"2007","unstructured":"Roanes-Mac\u00edas, E., Roanes-Lozano, E.: A Maple package for automatic theorem proving and discovery in 3D-geometry. In: Botana, F., Recio, T. (eds.) ADG 2006. LNCS (LNAI), vol.\u00a04869, pp. 171\u2013188. Springer, Heidelberg (2007)"},{"key":"24_CR22","first-page":"38","volume":"80","author":"E. Roanes-Mac\u00edas","year":"2008","unstructured":"Roanes-Mac\u00edas, E., Roanes-Lozano, E., Fern\u00e1ndez-Biarge, J.: Extensi\u00f3n natural a 3D del teorema de Pappus y su configuraci\u00f3n completa. Bol. Soc. \u201cPuig Adam\u201d\u00a080, 38\u201356 (2008)","journal-title":"Bol. Soc. \u201cPuig Adam\u201d"},{"issue":"1","key":"24_CR23","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/BF03191837","volume":"103","author":"E. Roanes-Mac\u00edas","year":"2009","unstructured":"Roanes-Mac\u00edas, E., Roanes-Lozano, E., Fern\u00e1ndez-Biarge, J.: Obtaining a 3D extension of Pascal theorem for non-degenerated quadrics and its complete configuration with the aid of a computer algebra system. RACSAM (Rev. R. Acad. C. Exactas, F\u00eds. Nat., Serie A, Mat.)\u00a0103(1), 93\u2013109 (2009)","journal-title":"RACSAM (Rev. R. Acad. C. Exactas, F\u00eds. Nat., Serie A, Mat.)"},{"key":"24_CR24","first-page":"31","volume":"88","author":"E. Roanes-Mac\u00edas","year":"2011","unstructured":"Roanes-Mac\u00edas, E., Roanes-Lozano, E.: Un m\u00e9todo algebraico-computacional para demostraci\u00f3n autom\u00e1tica en geometr\u00eda eucl\u00eddea. Bol. Soc. \u201cPuig Adam\u201d\u00a088, 31\u201363 (2011)","journal-title":"Bol. Soc. \u201cPuig Adam\u201d"},{"key":"24_CR25","unstructured":"Sun, Y., Wang, D., Zhou, J.: A new method of automatic geometric theorem proving and discovery by comprehensive Groebner systems. In: Proc. ADG 2012 (2012) (to appear), \n                  \n                    http:\/\/dream.inf.ed.ac.uk\/events\/adg2012\/uploads\/proceedings\/ADG2012-proceedings.pdf#page=163"},{"key":"24_CR26","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1007\/978-3-540-24616-9_12","volume-title":"Automated Deduction in Geometry","author":"D. Wang","year":"2004","unstructured":"Wang, D.: GEOTHER 1.1: Handling and proving geometric theorems automatically. In: Winkler, F. (ed.) ADG 2002. LNCS (LNAI), vol.\u00a02930, pp. 194\u2013215. Springer, Heidelberg (2004)"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-02297-0_24","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T11:55:57Z","timestamp":1558007757000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-02297-0_24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783319022963","9783319022970"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-02297-0_24","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2013]]}}}