{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:58:39Z","timestamp":1760061519569,"version":"3.41.0"},"publisher-location":"New York, NY, USA","reference-count":26,"publisher":"ACM","license":[{"start":{"date-parts":[[2016,7,20]],"date-time":"2016-07-20T00:00:00Z","timestamp":1468972800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"Institut universitaire de France"},{"name":"ANR-DFG program Explosys","award":["ANR-14-CE35-0013-01; GL203\/9-1"],"award-info":[{"award-number":["ANR-14-CE35-0013-01; GL203\/9-1"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2016,7,20]]},"DOI":"10.1145\/2930889.2930916","type":"proceedings-article","created":{"date-parts":[[2016,7,19]],"date-time":"2016-07-19T11:59:33Z","timestamp":1468929573000},"page":"103-110","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Determinantal Sets, Singularities and Application to Optimal Control in Medical Imagery"],"prefix":"10.1145","author":[{"given":"Bernard","family":"Bonnard","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Bourgogne, Inria Sophia Antipolis, McTao project, Dijon, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Charles","family":"Faug\u00e8re","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9s, UPMC Univ. Paris 06, Inria Paris, PolSys project, CNRS UMR 7606, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alain","family":"Jacquemard","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9s, UPMC Univ. Paris 06, Inria Paris, PolSys project, CNRS UMR 7606, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohab","family":"Safey El Din","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9s, UPMC Univ. Paris 06, Inria Paris, PolSys project, CNRS UMR 7606, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thibaut","family":"Verron","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9s, UPMC Univ. Paris 06, Inria Paris, PolSys project, CNRS UMR 7606, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2016,7,20]]},"reference":[{"key":"e_1_3_2_1_1_1","series-title":"Ergebnisse der Mathematik und ihrer Grenzgebiete (3) {Results in Mathematics and Related Areas (3)}","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03718-8","volume-title":"Real algebraic geometry","author":"Bochnak J.","year":"1998","unstructured":"J. Bochnak , M. Coste , and M.-F. Roy . Real algebraic geometry , volume 36 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3) {Results in Mathematics and Related Areas (3)} . Springer-Verlag , Berlin , 1998 . Translated from the 1987 French original, Revised by the authors. J. Bochnak, M. Coste, and M.-F. Roy. Real algebraic geometry, volume 36 of Ergebnisse der Mathematik und ihrer Grenzgebiete (3) {Results in Mathematics and Related Areas (3)}. Springer-Verlag, Berlin, 1998. Translated from the 1987 French original, Revised by the authors."},{"key":"e_1_3_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.3934\/mcrf.2013.3.397"},{"key":"e_1_3_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2012.2195859"},{"key":"e_1_3_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/1277548.1277557"},{"key":"e_1_3_2_1_5_1","volume-title":"Determinantal Rings","author":"Bruns W.","year":"2014","unstructured":"W. Bruns and U. Vetter . Determinantal Rings . Springer , 2014 . W. Bruns and U. Vetter. Determinantal Rings. Springer, 2014."},{"key":"e_1_3_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10440-014-9950-8"},{"key":"e_1_3_2_1_7_1","first-page":"134","volume-title":"Kaiserslautern","volume":"33","author":"Collins G. E.","year":"1975","unstructured":"G. E. Collins . Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In Automata theory and formal languages (Second GI Conf ., Kaiserslautern , 1975 ), pages 134 -- 183 . Lecture Notes in Comput. Sci. , Vol. 33 . Springer, Berlin, 1975. G. E. Collins. Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In Automata theory and formal languages (Second GI Conf., Kaiserslautern, 1975), pages 134--183. Lecture Notes in Comput. Sci., Vol. 33. Springer, Berlin, 1975."},{"key":"e_1_3_2_1_8_1","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1007\/BFb0084605","volume-title":"Real analytic and algebraic geometry (Trento","author":"Coste M.","year":"1992","unstructured":"M. Coste and M. Shiota . Thom's first isotopy lemma: a semialgebraic version, with uniform bound . In Real analytic and algebraic geometry (Trento , 1992 ), pages 83 -- 101 . de Gruyter , Berlin , 1995. M. Coste and M. Shiota. Thom's first isotopy lemma: a semialgebraic version, with uniform bound. In Real analytic and algebraic geometry (Trento, 1992), pages 83--101. de Gruyter, Berlin, 1995."},{"key":"e_1_3_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(88)80004-X"},{"key":"e_1_3_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-57134-3"},{"key":"e_1_3_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/780506.780516"},{"key":"e_1_3_2_1_12_1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1007\/978-3-642-15582-6_17","volume-title":"Mathematical Software - ICMS","author":"Faug\u00e8re J.-C.","year":"2010","unstructured":"J.-C. Faug\u00e8re . FGb: A Library for Computing Gr\u00f6bner Bases . In Komei Fukuda, Joris Hoeven, Michael Joswig, and Nobuki Takayama, editors, Mathematical Software - ICMS 2010 , volume 6327 of Lecture Notes in Computer Science , pages 84 -- 87 , Berlin, Heidelberg, September 2010. Springer Berlin \/ Heidelberg . J.-C. Faug\u00e8re. FGb: A Library for Computing Gr\u00f6bner Bases. In Komei Fukuda, Joris Hoeven, Michael Joswig, and Nobuki Takayama, editors, Mathematical Software - ICMS 2010, volume 6327 of Lecture Notes in Computer Science, pages 84--87, Berlin, Heidelberg, September 2010. Springer Berlin \/ Heidelberg."},{"key":"e_1_3_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/2442829.2442855"},{"key":"e_1_3_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2013.03.004"},{"key":"e_1_3_2_1_15_1","volume-title":"August","author":"Henrion D.","year":"2015","unstructured":"D. Henrion , S. Naldi , and M. Safey El Din. Exact algorithms for linear matrix inequalities. Submitted ., August 2015 . D. Henrion, S. Naldi, and M. Safey El Din. Exact algorithms for linear matrix inequalities. Submitted., August 2015."},{"key":"e_1_3_2_1_16_1","volume-title":"June","author":"Henrion D.","year":"2015","unstructured":"D. Henrion , S. Naldi , and M. Safey El Din. Real root finding for low rank linear matrices. Submitted ., June 2015 . D. Henrion, S. Naldi, and M. Safey El Din. Real root finding for low rank linear matrices. Submitted., June 2015."},{"key":"e_1_3_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/2755996.2756667"},{"key":"e_1_3_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2015.06.010"},{"key":"e_1_3_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2011.05.014"},{"key":"e_1_3_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2007.01.007"},{"key":"e_1_3_2_1_21_1","first-page":"355","volume-title":"Maple conference","volume":"5","author":"Lemaire F.","year":"2005","unstructured":"F. Lemaire , M. Moreno Maza , and Y. Xie . The regularchains library . In Maple conference , volume 5 , pages 355 -- 368 , 2005 . F. Lemaire, M. Moreno Maza, and Y. Xie. The regularchains library. In Maple conference, volume 5, pages 355--368, 2005."},{"key":"e_1_3_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/309831.309892"},{"key":"e_1_3_2_1_23_1","volume-title":"The mathematical theory of optimal processes. Translated from the Russian by K. N. Trirogoff","author":"Pontryagin L. S.","year":"1962","unstructured":"L. S. Pontryagin , V. G. Boltyanskii , R. V. Gamkrelidze , and E. F. Mishchenko . The mathematical theory of optimal processes. Translated from the Russian by K. N. Trirogoff ; edited by L. W. Neustadt. Interscience Publishers John Wiley & Sons , Inc., New York-London, 1962 . L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko. The mathematical theory of optimal processes. Translated from the Russian by K. N. Trirogoff; edited by L. W. Neustadt. Interscience Publishers John Wiley & Sons, Inc., New York-London, 1962."},{"key":"e_1_3_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/2755996.2756649"},{"key":"e_1_3_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1137\/130936294"},{"issue":"1","key":"e_1_3_2_1_26_1","first-page":"33","article-title":"A complete algorithm for automated discovering of a class of inequality-type theorems","volume":"44","author":"Yang L.","year":"2001","unstructured":"L. Yang , X. Hou , and B. Xia . A complete algorithm for automated discovering of a class of inequality-type theorems . Sci. China Ser. F , 44 ( 1 ): 33 -- 49 , 2001 . L. Yang, X. Hou, and B. Xia. A complete algorithm for automated discovering of a class of inequality-type theorems. Sci. China Ser. F, 44(1):33--49, 2001.","journal-title":"Sci. China Ser. F"}],"event":{"name":"ISSAC '16: International Symposium on Symbolic and Algebraic Computation","sponsor":["SIGSAM ACM Special Interest Group on Symbolic and Algebraic Manipulation"],"location":"Waterloo ON Canada","acronym":"ISSAC '16"},"container-title":["Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2930889.2930916","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2930889.2930916","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:55:48Z","timestamp":1750222548000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2930889.2930916"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,20]]},"references-count":26,"alternative-id":["10.1145\/2930889.2930916","10.1145\/2930889"],"URL":"https:\/\/doi.org\/10.1145\/2930889.2930916","relation":{},"subject":[],"published":{"date-parts":[[2016,7,20]]},"assertion":[{"value":"2016-07-20","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}