{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T07:19:28Z","timestamp":1742973568591,"version":"3.40.3"},"publisher-location":"Cham","reference-count":15,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319491295"},{"type":"electronic","value":"9783319491301"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-49130-1_14","type":"book-chapter","created":{"date-parts":[[2016,11,4]],"date-time":"2016-11-04T14:13:59Z","timestamp":1478268839000},"page":"179-191","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Subdivision Approach to the Solution of Polynomial Constraints over Finite Domains Using the Modified Bernstein Form"],"prefix":"10.1007","author":[{"given":"Federico","family":"Bergenti","sequence":"first","affiliation":[]},{"given":"Stefania","family":"Monica","sequence":"additional","affiliation":[]},{"given":"Gianfranco","family":"Rossi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,11,5]]},"reference":[{"key":"14_CR1","unstructured":"Bergenti, F., Monica, S., Rossi, G.: Polynomial constraint solving over finite domains with the modified Bernstein form. In: Fiorentini, C., Momigliano, A. (eds.) Proceedings of the 31st Italian Conference on Computational Logic, vol. 1645. CEUR Workshop Proceedings, pp. 118\u2013131. RWTH Aachen (2016)"},{"key":"14_CR2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511615320","volume-title":"Principles of Constraint Programming","author":"K Apt","year":"2003","unstructured":"Apt, K.: Principles of Constraint Programming. Cambridge University Press, Cambridge (2003)"},{"key":"14_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1007\/978-3-642-29822-6_24","volume-title":"Functional and Logic Programming","author":"M Triska","year":"2012","unstructured":"Triska, M.: The finite domain constraint solver of SWI-prolog. In: Schrijvers, T., Thiemann, P. (eds.) FLOPS 2012. LNCS, vol. 7294, pp. 307\u2013316. Springer, Heidelberg (2012). doi:10.1007\/978-3-642-29822-6_24"},{"issue":"1\u20132","key":"14_CR4","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1017\/S1471068411000494","volume":"12","author":"J Wielemaker","year":"2012","unstructured":"Wielemaker, J., Schrijvers, T., Triska, M., Lager, T.: SWI-prolog. Theory Pract. Logic Program. 12(1\u20132), 67\u201396 (2012)","journal-title":"Theory Pract. Logic Program."},{"issue":"1","key":"14_CR5","first-page":"1","volume":"2:XIII","author":"SN Bernstein","year":"1912","unstructured":"Bernstein, S.N.: D\u00e9monstration du th\u00e9or\u00e8me de Weierstrass fond\u00e9e sur le calcul des probabilit\u00e9s. Commun. Soc. Math. de Kharkov 2:XIII(1), 1\u20132 (1912)","journal-title":"Commun. Soc. Math. de Kharkov"},{"key":"14_CR6","volume-title":"Bernstein Polynomials","author":"GG Lorentz","year":"1953","unstructured":"Lorentz, G.G.: Bernstein Polynomials. University of Toronto Press, Toronto (1953)"},{"key":"14_CR7","doi-asserted-by":"publisher","first-page":"959","DOI":"10.1016\/S0010-4485(03)00021-6","volume":"35","author":"J S\u00e1nchez-Reyes","year":"2003","unstructured":"S\u00e1nchez-Reyes, J.: Algebraic manipulation in the Bernstein form made simple via convolutions. Comput. Aided Des. 35, 959\u2013967 (2003)","journal-title":"Comput. Aided Des."},{"issue":"1","key":"14_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0167-8396(88)90016-7","volume":"5","author":"RT Farouki","year":"1988","unstructured":"Farouki, R.T., Rajan, V.T.: Algorithms for polynomials in Bernstein form. Comput. Aided Geom. Des. 5(1), 1\u201326 (1988)","journal-title":"Comput. Aided Geom. Des."},{"issue":"4","key":"14_CR9","doi-asserted-by":"publisher","first-page":"342","DOI":"10.1007\/s11633-007-0342-7","volume":"4","author":"P Nataraj","year":"2007","unstructured":"Nataraj, P., Arounassalame, M.: A new subdivision algorithm for the Bernstein polynomial approach to global optimization. Int. J. Autom. Comput. 4(4), 342\u2013352 (2007)","journal-title":"Int. J. Autom. Comput."},{"issue":"3","key":"14_CR10","doi-asserted-by":"publisher","first-page":"292","DOI":"10.1016\/j.jsc.2008.04.016","volume":"44","author":"B Mourrain","year":"2009","unstructured":"Mourrain, B., Pavone, J.: Subdivision methods for solving polynomial equations. J. Symbolic Comput. 44(3), 292\u2013306 (2009)","journal-title":"J. Symbolic Comput."},{"key":"14_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/3-540-16437-5_5","volume-title":"Interval Mathematics 1985","author":"J Garloff","year":"1986","unstructured":"Garloff, J.: Convergent bounds for the range of multivariate polynomials. In: Nickel, K. (ed.) IMath 1985. LNCS, vol. 212, pp. 37\u201356. Springer, Heidelberg (1986). doi:10.1007\/3-540-16437-5_5"},{"key":"14_CR12","first-page":"154","volume":"2","author":"J Garloff","year":"1993","unstructured":"Garloff, J.: The Bernstein algorithm. Interval Comput. 2, 154\u2013168 (1993)","journal-title":"Interval Comput."},{"issue":"6","key":"14_CR13","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1016\/j.cagd.2012.03.001","volume":"29","author":"RT Farouki","year":"2012","unstructured":"Farouki, R.T.: The Bernstein polynomial basis: a centennial retrospective. Comput. Aided Geom. Des. 29(6), 379\u2013419 (2012)","journal-title":"Comput. Aided Geom. Des."},{"key":"14_CR14","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/978-3-7091-6280-4_9","volume-title":"Symbolic Algebraic Methods and Verification Methods","author":"J Garloff","year":"2001","unstructured":"Garloff, J., Smith, A.P.: Solution of systems of polynomial equations by using Bernstein expansion. In: Alefeld, G., Rohn, J., Rump, S., Yamamoto, T. (eds.) Symbolic Algebraic Methods and Verification Methods, pp. 87\u201397. Springer, Vienna (2001)"},{"key":"14_CR15","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1007\/s10898-008-9382-y","volume":"45","author":"S Ray","year":"2009","unstructured":"Ray, S., Nataraj, P.: An efficient algorithm for range computation of polynomials using the Bernstein form. J. Global Optim. 45, 403\u2013426 (2009)","journal-title":"J. Global Optim."}],"container-title":["Lecture Notes in Computer Science","AI*IA 2016 Advances in Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-49130-1_14","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,12]],"date-time":"2024-03-12T17:54:32Z","timestamp":1710266072000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-49130-1_14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319491295","9783319491301"],"references-count":15,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-49130-1_14","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2016]]},"assertion":[{"value":"5 November 2016","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"AI*IA","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Conference of the Italian Association for Artificial Intelligence","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Genova","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Italy","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2016","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29 November 2016","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1 December 2016","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"XV","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"aiia2016","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.aixia2016.unige.it\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}