{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T11:00:13Z","timestamp":1757588413217,"version":"3.41.0"},"reference-count":2,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[1981,11,1]],"date-time":"1981-11-01T00:00:00Z","timestamp":373420800000},"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":[[1981,11]]},"abstract":"<jats:p>\n            We describe a computer program for the automatic analysis of a real plane affine algebraic curve. The input to the program is a bivariate integral polynomial\n            <jats:italic>F<\/jats:italic>\n            (\n            <jats:italic>x, y<\/jats:italic>\n            ); the outputs are a report on the real curve defined by\n            <jats:italic>F<\/jats:italic>\n            (\n            <jats:italic>x, y<\/jats:italic>\n            ) = 0, and a picture of the curve. The report contains the following information: whether the curve is irreducible, whether singular, and whether bounded; the number of its connected components and the dimension of each; the number of singular, turning, and level points of the curve. Approximations to these special points can be obtained to any desired precision; the more precision, the more time required. The exact form of the picture is controlled by the user; a topologically correct but \"linearized\" picture can be produced relatively quickly, while a more accurate drawing can be generated but requires more time. The program makes essential use of the clustering cylindrical algebraic decomposition algorithm [Arnon DS: Algorithms for the geometry of semi-algebraic sets (Dissertation). Technical Report #436, Computer Science Department, University of Wisconsin-Madison, 1981].\n          <\/jats:p>","DOI":"10.1145\/1089270.1089271","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"3-9","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["Automatic analysis of real algebraic curves"],"prefix":"10.1145","volume":"15","author":[{"given":"Dennis S.","family":"Arnon","sequence":"first","affiliation":[{"name":"Purdue University, West Lafayette, Indiana"}]}],"member":"320","published-online":{"date-parts":[[1981,11]]},"reference":[{"key":"e_1_2_1_2_1","first-page":"134","volume-title":"Second GI Conference on Automata Theory and Formal Languages","volume":"33","author":"Collins GE","year":"1975","unstructured":"{COL75} Collins GE : Quantifier elimination for real closed fields by cylindrical algebraic decomposition , in Second GI Conference on Automata Theory and Formal Languages , vol. 33 of Lecture Notes in Computer Science, Springer-Verlag, Berlin , 1975 , pp 134 -- 183 . {COL75} Collins GE: Quantifier elimination for real closed fields by cylindrical algebraic decomposition, in Second GI Conference on Automata Theory and Formal Languages, vol. 33 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, 1975, pp 134--183."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1093390.1093393"}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1089270.1089271","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1089270.1089271","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T16:08:22Z","timestamp":1750262902000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1089270.1089271"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1981,11]]},"references-count":2,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1981,11]]}},"alternative-id":["10.1145\/1089270.1089271"],"URL":"https:\/\/doi.org\/10.1145\/1089270.1089271","relation":{},"ISSN":["0163-5824"],"issn-type":[{"type":"print","value":"0163-5824"}],"subject":[],"published":{"date-parts":[[1981,11]]},"assertion":[{"value":"1981-11-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}