{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:58:20Z","timestamp":1760061500163},"reference-count":27,"publisher":"Elsevier BV","issue":"3-4","license":[{"start":{"date-parts":[[2003,9,1]],"date-time":"2003-09-01T00:00:00Z","timestamp":1062374400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":3607,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Symbolic Computation"],"published-print":{"date-parts":[[2003,9]]},"DOI":"10.1016\/s0747-7171(03)00093-2","type":"journal-article","created":{"date-parts":[[2003,7,16]],"date-time":"2003-07-16T16:18:16Z","timestamp":1058372296000},"page":"513-533","source":"Crossref","is-referenced-by-count":8,"title":["Towards faster real algebraic numbers"],"prefix":"10.1016","volume":"36","author":[{"given":"Renaud","family":"Rioboo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"issue":"6","key":"10.1016\/S0747-7171(03)00093-2_B1","doi-asserted-by":"crossref","first-page":"1002","DOI":"10.1145\/235809.235813","article-title":"On the combinatorial and algebraic complexity of quantifier elimination","volume":"43","author":"Basu","year":"1996","journal-title":"Journal of the ACM"},{"key":"10.1016\/S0747-7171(03)00093-2_B2","series-title":"G\u00e9om\u00e9trie Alg\u00e9brique R\u00e9elle","author":"Bochnak","year":"1988"},{"key":"10.1016\/S0747-7171(03)00093-2_B3","series-title":"Computer Algebra","first-page":"83","article-title":"Real zeros of polynomials","author":"Collins","year":"1982"},{"key":"10.1016\/S0747-7171(03)00093-2_B4","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/S0747-7171(88)80008-7","article-title":"Thom\u2019s lemma, the coding of real algebraic numbers and the computation of the topology of semi-algebraic sets","volume":"5","author":"Coste","year":"1988","journal-title":"Journal of Symbolic Computation"},{"key":"10.1016\/S0747-7171(03)00093-2_B5","series-title":"Calcul Formel: syst\u00e8mes et algorithmes de manipulations alg\u00e9briques","author":"Davenport","year":"1987"},{"key":"10.1016\/S0747-7171(03)00093-2_B6","doi-asserted-by":"crossref","unstructured":"Della Dora, J., Discrescenzo, D., Duval, D., 1985. About a new method for computing in algebraic number fields. In: Lecture Notes in Computer Science, vol.\u00a0204","DOI":"10.1007\/3-540-15984-3_279"},{"key":"10.1016\/S0747-7171(03)00093-2_B7","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/S0022-4049(98)00081-4","article-title":"Optimizations of the subresultant algorithm","volume":"145","author":"Ducos","year":"2000","journal-title":"Journal of Pure and Applied Algebra"},{"key":"10.1016\/S0747-7171(03)00093-2_B8","doi-asserted-by":"crossref","first-page":"551","DOI":"10.1016\/S0378-4754(96)00032-8","article-title":"Dynamic evaluation and real closure","volume":"42","author":"Duval","year":"1996","journal-title":"Mathematics and Computers in Simulation"},{"key":"10.1016\/S0747-7171(03)00093-2_B9","unstructured":"Gonzalez Vega, L., Rouillier, F., Roy, M.-F., Trujillo, G., 1998a. Symbolic recipes for real solutions. In: Cohen et al. (1998), pp.\u00a0121\u2013167"},{"key":"10.1016\/S0747-7171(03)00093-2_B10","unstructured":"Gonzalez Vega, L., Roy, M.-F., Rouillier, F., 1998b. Symbolic recipes for polynomial system solving. In: Cohen et al. (1998), pp.\u00a034\u201365"},{"key":"10.1016\/S0747-7171(03)00093-2_B11","unstructured":"Hollcott, A., 1941. Finite konstruktion geordneter algebraischer erweterungen von geordneten grundkorpern. Ph.D. Thesis, Univ. of Hamburg"},{"key":"10.1016\/S0747-7171(03)00093-2_B12","series-title":"Algebraic Numbers","author":"Lang","year":"1964"},{"key":"10.1016\/S0747-7171(03)00093-2_B13","series-title":"Algebra","author":"Lang","year":"1969"},{"key":"10.1016\/S0747-7171(03)00093-2_B14","unstructured":"Lecerf, G., 1996. Dynamic evaluation and real closure. Implementation in Axiom. Available from http:\/\/www.medicis.polytechnique.fr\/~lecerf\/"},{"key":"10.1016\/S0747-7171(03)00093-2_B15","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1006\/jsco.2000.0427","article-title":"Sylvester-Habicht sequences and fast Cauchy index computations","volume":"31","author":"Lickteig","year":"2001","journal-title":"Journal of Symbolic Computation"},{"key":"10.1016\/S0747-7171(03)00093-2_B16","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1016\/S0378-4754(96)00031-6","article-title":"Generic closure of an ordered field, implementation in Axiom","volume":"42","author":"Ligatsikas","year":"1996","journal-title":"Mathematics and Computers in Simulation"},{"key":"10.1016\/S0747-7171(03)00093-2_B17","first-page":"249","article-title":"Elementary constructive theory of ordered fields","volume":"34","author":"Lombardi","year":"1991","journal-title":"Progress in Mathematics"},{"key":"10.1016\/S0747-7171(03)00093-2_B18","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1006\/jsco.1999.0322","article-title":"New structure theorems for subresultants","volume":"29","author":"Lombardi","year":"2000","journal-title":"Journal of Symbolic Computation"},{"key":"10.1016\/S0747-7171(03)00093-2_B19","series-title":"Computer Algebra","first-page":"115","article-title":"Generalized polynomial remainder sequences","author":"Loos","year":"1982"},{"key":"10.1016\/S0747-7171(03)00093-2_B20","doi-asserted-by":"crossref","unstructured":"Moreno Maza, M., Rioboo, R., 1996. Polynomial gcd computations over towers of algebraic extensions. In: Lecture Notes in Computer Science, vol.\u00a0948","DOI":"10.1007\/3-540-60114-7_28"},{"key":"10.1016\/S0747-7171(03)00093-2_B21","series-title":"ISSAC\u201992","article-title":"Computation of the real closure of an ordered field","author":"Rioboo","year":"1992"},{"key":"10.1016\/S0747-7171(03)00093-2_B22","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1006\/jsco.1997.0158","article-title":"Computing in the field of complex algebraic numbers","author":"Strzebo\u0144ski","year":"1997","journal-title":"Journal of Symbolic Computation"},{"key":"10.1016\/S0747-7171(03)00093-2_B23","series-title":"Computational Problems in Abstract Algebra","first-page":"383","article-title":"A real root calculus","author":"Zassenhauss","year":"1970"},{"key":"10.1016\/S0747-7171(03)00093-2_F1","series-title":"Computer Algebra","author":"Buchberger","year":"1982"},{"key":"10.1016\/S0747-7171(03)00093-2_F2","series-title":"Some Tapas of Computer Algebra","volume":"vol. 4","year":"1998"},{"key":"10.1016\/S0747-7171(03)00093-2_F3","series-title":"Computer Algebra","first-page":"173","article-title":"Computing in algebraic extensions","author":"Loos","year":"1982"},{"key":"10.1016\/S0747-7171(03)00093-2_F4","unstructured":"Rioboo, R., 1991. Quelques aspects du calcul exact avec les nombres r\u00e9els. Ph.D. Thesis, Laboratoire d\u2019Informatique Th\u00e9orique et Programmationg"}],"container-title":["Journal of Symbolic Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0747717103000932?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0747717103000932?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,3,24]],"date-time":"2020-03-24T18:26:51Z","timestamp":1585074411000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0747717103000932"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,9]]},"references-count":27,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2003,9]]}},"alternative-id":["S0747717103000932"],"URL":"https:\/\/doi.org\/10.1016\/s0747-7171(03)00093-2","relation":{},"ISSN":["0747-7171"],"issn-type":[{"value":"0747-7171","type":"print"}],"subject":[],"published":{"date-parts":[[2003,9]]}}}