{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,24]],"date-time":"2025-01-24T05:07:29Z","timestamp":1737695249523,"version":"3.33.0"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2007,12,4]],"date-time":"2007-12-04T00:00:00Z","timestamp":1196726400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/2.0"},{"start":{"date-parts":[[2007,12,4]],"date-time":"2007-12-04T00:00:00Z","timestamp":1196726400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/2.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Algorithmica"],"published-print":{"date-parts":[[2009,9]]},"DOI":"10.1007\/s00453-007-9132-4","type":"journal-article","created":{"date-parts":[[2007,12,3]],"date-time":"2007-12-03T23:51:28Z","timestamp":1196725888000},"page":"14-28","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Separation Bound for Real Algebraic Expressions"],"prefix":"10.1007","volume":"55","author":[{"given":"Christoph","family":"Burnikel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Funke","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kurt","family":"Mehlhorn","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Schirra","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Susanne","family":"Schmitt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2007,12,4]]},"reference":[{"key":"9132_CR1","doi-asserted-by":"crossref","unstructured":"Burnikel, C., Fleischer, R., Mehlhorn, K., Schirra, S.: Exact efficient computational geometry made easy. In: Proceedings of the 15th Annual Symposium on Computational Geometry (SCG\u201999), pp. 341\u2013350 (1999)","DOI":"10.1145\/304893.304988"},{"key":"9132_CR2","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/s004530010005","volume":"27","author":"C. Burnikel","year":"2000","unstructured":"Burnikel, C., Fleischer, R., Mehlhorn, K., Schirra, S.: A strong and easily computable separation bound for arithmetic expressions involving radicals. Algorithmica 27, 87\u201399 (2000)","journal-title":"Algorithmica"},{"key":"9132_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/BFb0049411","volume-title":"Proceedings of the 2nd Annual European Symposium on Algorithms\u2014ESA\u201994","author":"C. Burnikel","year":"1994","unstructured":"Burnikel, C., Mehlhorn, K., Schirra, S.: How to compute the Voronoi diagram of line segments: Theoretical and experimental results. In: Proceedings of the 2nd Annual European Symposium on Algorithms\u2014ESA\u201994. Lecture Notes in Computer Science, vol. 855, pp. 227\u2013239. Springer, Berlin (1994)"},{"key":"9132_CR4","unstructured":"Burnikel, C., Mehlhorn, K., Schirra, S.: The LEDA class real number. Technical report MPI-I-96-1-001, Max-Planck-Institut f\u00fcr Informatik, Saarbr\u00fccken (1996)"},{"key":"9132_CR5","volume-title":"The Complexity of Robot Motion Planning","author":"J.F. Canny","year":"1987","unstructured":"Canny, J.F.: The Complexity of Robot Motion Planning. MIT Press, Cambridge (1987)"},{"key":"9132_CR6","volume-title":"Vorlesungen \u00fcber die Theorie der Algebraischen Zahlen","author":"E. Hecke","year":"1970","unstructured":"Hecke, E.: Vorlesungen \u00fcber die Theorie der Algebraischen Zahlen. Chelsea, New York (1970)"},{"key":"9132_CR7","doi-asserted-by":"crossref","unstructured":"Karamcheti, V., Li, C., Pechtchanski, I., Yap, C.: A core library for robust numeric and geometric computation. In: Proceedings of the 15th Annual ACM Symposium on Computational Geometry, pp.\u00a0351\u2013359. Miami, FL, 1999","DOI":"10.1145\/304893.304989"},{"key":"9132_CR8","unstructured":"LEDA (Library of Efficient Data Types and Algorithms): www.mpi-sb.mpg.de\/LEDA\/leda.html"},{"key":"9132_CR9","unstructured":"Li, C., Yap, C.: A new constructive root bound for algebraic expressions. In: Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA\u201901), pp. 496\u2013505 (2001)"},{"key":"9132_CR10","series-title":"Computing Supplementum","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/978-3-7091-3406-1_12","volume-title":"Computer Algebra. Symbolic and Algebraic Computation","author":"R. Loos","year":"1982","unstructured":"Loos, R.: Computing in algebraic extensions. In: Buchberger, B., Collins, G.E., Loos, R. (eds.) Computer Algebra. Symbolic and Algebraic Computation. Computing Supplementum, vol. 4, pp. 173\u2013188. Springer, Vienna (1982)"},{"key":"9132_CR11","volume-title":"The LEDA Platform for Combinatorial and Geometric Computing","author":"K. Mehlhorn","year":"1999","unstructured":"Mehlhorn, K., N\u00e4her, S.: The LEDA Platform for Combinatorial and Geometric Computing. Cambridge University Press, Cambridge (1999)"},{"key":"9132_CR12","volume-title":"Symbolic Algebraic Methods and Verification Methods","author":"K. Mehlhorn","year":"2001","unstructured":"Mehlhorn, K., Schirra, S.: Exact computation with leda_real - theory and geometric applications. In: Alefeld, G., Rohn, J., Rumpf, S., Yamamoto, T. (eds.) Symbolic Algebraic Methods and Verification Methods. Springer, Vienna (2001)"},{"issue":"3","key":"9132_CR13","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/0196-6774(82)90019-0","volume":"3","author":"M. Mignotte","year":"1982","unstructured":"Mignotte, M.: Identification of algebraic numbers. J. Algorithms 3(3), 197\u2013204 (1982)","journal-title":"J. Algorithms"},{"key":"9132_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-9171-5","volume-title":"Mathematics for Computer Algebra","author":"M. Mignotte","year":"1992","unstructured":"Mignotte, M.: Mathematics for Computer Algebra. Springer, Berlin (1992)"},{"key":"9132_CR15","volume-title":"Algebraische Zahlentheorie","author":"J. Neukirch","year":"1990","unstructured":"Neukirch, J.: Algebraische Zahlentheorie. Springer, Berlin (1990)"},{"key":"9132_CR16","doi-asserted-by":"publisher","first-page":"489","DOI":"10.2307\/2589344","volume":"107","author":"E.R. Scheinerman","year":"2000","unstructured":"Scheinerman, E.R.: When close enough is close enough. Am. Math. Mon. 107, 489\u2013499 (2000)","journal-title":"Am. Math. Mon."},{"key":"9132_CR17","doi-asserted-by":"crossref","unstructured":"Yap, C.K.: Towards exact geometric computation. Comput. Geom. Theory Appl. 7 (1997)","DOI":"10.1016\/0925-7721(95)00040-2"},{"key":"9132_CR18","volume-title":"Fundamental Problems in Algorithmic Algebra","author":"C.K. Yap","year":"1999","unstructured":"Yap, C.K.: Fundamental Problems in Algorithmic Algebra. Oxford University Press, Oxford (1999)"},{"key":"9132_CR19","volume-title":"Computing in Euclidean Geometry II","author":"C.K. Yap","year":"1995","unstructured":"Yap, C.K., Dube, T.: The exact computation paradigm. In: Computing in Euclidean Geometry II. World Scientific, Singapore (1995)"}],"container-title":["Algorithmica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00453-007-9132-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00453-007-9132-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00453-007-9132-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00453-007-9132-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,23]],"date-time":"2025-01-23T05:37:55Z","timestamp":1737610675000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00453-007-9132-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,12,4]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,9]]}},"alternative-id":["9132"],"URL":"https:\/\/doi.org\/10.1007\/s00453-007-9132-4","relation":{},"ISSN":["0178-4617","1432-0541"],"issn-type":[{"type":"print","value":"0178-4617"},{"type":"electronic","value":"1432-0541"}],"subject":[],"published":{"date-parts":[[2007,12,4]]},"assertion":[{"value":"7 November 2006","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 April 2007","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 November 2007","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 December 2007","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}