{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:59:17Z","timestamp":1760061557230,"version":"3.41.0"},"reference-count":9,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[1977,5,1]],"date-time":"1977-05-01T00:00:00Z","timestamp":231292800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGSAM Bull."],"published-print":{"date-parts":[[1977,5]]},"abstract":"<jats:p>Several algorithms are known to separate the real zeros of a polynomial. In his thesis Heindel [He70] showed, that the computing time of his algorithm using Sturm sequences is polynomially bounded in the length of the coefficients. The polynomials are assumed to have integral coefficients. In his Diplomarbeit [L\u00fc76] Ludicke gave a modified Sturm algorithm for real algebraic polynomials with a polynomially bounded, but very high computing time. He described and analyzed the algorithm, but did not implement it. In the present paper we extend the Collins\/Loos - algorithm [CL76] from integral to real algebraic coefficients and gain empirical computing times.<\/jats:p>","DOI":"10.1145\/1088240.1088241","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"2-3","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Real root isolation for algebraic polynomials"],"prefix":"10.1145","volume":"11","author":[{"given":"Siegfried M.","family":"Rump","sequence":"first","affiliation":[{"name":"University of Karlsruhe, Karlsruhe"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[1977,5]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Math. Comp.","volume":"28","author":"Collins G. E.","year":"1976"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/800205.806319"},{"key":"e_1_2_1_3_1","doi-asserted-by":"crossref","unstructured":"{He76} Heindel L. E. Algorithms for exact Polynomial Root Calculation Ph.D. Thesis Computer Science Department University of Wisconsin Madison Wisconsin 1970   {He76} Heindel L. E. Algorithms for exact Polynomial Root Calculation Ph.D. Thesis Computer Science Department University of Wisconsin Madison Wisconsin 1970","DOI":"10.1145\/1093415.1093416"},{"key":"e_1_2_1_4_1","unstructured":"{Lo76} Loos R. G. K. private communication  {Lo76} Loos R. G. K. private communication"},{"key":"e_1_2_1_5_1","unstructured":"{L\u00fc76} L\u00fcdicke L. Diplomarbeit Frankfurt 1976  {L\u00fc76} L\u00fcdicke L. Diplomarbeit Frankfurt 1976"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/800205.806339"},{"key":"e_1_2_1_7_1","unstructured":"{Rb74} Rubald C. M. Algorithms for Polynomials over Real Algebraic Number Field Ph.D. Thesis Computer Science Technical Report Nr. 206 January 1974   {Rb74} Rubald C. M. Algorithms for Polynomials over Real Algebraic Number Field Ph.D. Thesis Computer Science Technical Report Nr. 206 January 1974"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/800205.806341"},{"key":"e_1_2_1_9_1","unstructured":"{Ru76} Rump S. Isolierung der Reellen Nullstellen algebraischer Polynome Bericht der Arbeitsgruppe Computer Algebra 10 Fachbereich Informatik Kaiserslautern November 1976 121 Seiten  {Ru76} Rump S. Isolierung der Reellen Nullstellen algebraischer Polynome Bericht der Arbeitsgruppe Computer Algebra 10 Fachbereich Informatik Kaiserslautern November 1976 121 Seiten"}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1088240.1088241","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1088240.1088241","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T22:43:44Z","timestamp":1750286624000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1088240.1088241"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1977,5]]},"references-count":9,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1977,5]]}},"alternative-id":["10.1145\/1088240.1088241"],"URL":"https:\/\/doi.org\/10.1145\/1088240.1088241","relation":{},"ISSN":["0163-5824"],"issn-type":[{"type":"print","value":"0163-5824"}],"subject":[],"published":{"date-parts":[[1977,5]]},"assertion":[{"value":"1977-05-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}