{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:42:03Z","timestamp":1750308123035,"version":"3.41.0"},"reference-count":0,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[1980,2,1]],"date-time":"1980-02-01T00:00:00Z","timestamp":318211200000},"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":[[1980,2]]},"abstract":"<jats:p>In 1973 G. E. Collins gave a new quantifier elimination algorithm for the first order theory of real closed fields. We utilize the main ideas of this algorithm to prove that any real algebraic variety (in fact, any semi-algebraic set) can be decomposed into a finite union of open cells.<\/jats:p>","DOI":"10.1145\/1089212.1089213","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"6-7","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Titles and abstracts"],"prefix":"10.1145","volume":"14","author":[{"given":"Paul S.","family":"Wang","sequence":"first","affiliation":[{"name":"Kent State University, Kent, Ohio"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[1980,2]]},"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1089212.1089213","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1089212.1089213","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\/1089212.1089213"}},"subtitle":["mathematical symbolic manipulation on the computer and applications"],"short-title":[],"issued":{"date-parts":[[1980,2]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1980,2]]}},"alternative-id":["10.1145\/1089212.1089213"],"URL":"https:\/\/doi.org\/10.1145\/1089212.1089213","relation":{},"ISSN":["0163-5824"],"issn-type":[{"type":"print","value":"0163-5824"}],"subject":[],"published":{"date-parts":[[1980,2]]},"assertion":[{"value":"1980-02-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}