{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:41:53Z","timestamp":1750308113439,"version":"3.41.0"},"reference-count":21,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[1974,8,1]],"date-time":"1974-08-01T00:00:00Z","timestamp":144547200000},"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":[[1974,8]]},"abstract":"<jats:p>Recent literature (e.g., [12]) shows a growing interest in the representation of algebraic numbers in terms of the polynomials they satisfy. The basis of this interest is the observation that for every algebraic number \u03b1 there exists a unique polynomial p(x) having the following properties:<\/jats:p>","DOI":"10.1145\/1086837.1086853","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"91-95","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Formal representations for algebraic numbers"],"prefix":"10.1145","volume":"8","author":[{"given":"Dennis","family":"Weeks","sequence":"first","affiliation":[{"name":"Xebec Systems, Inc., Sunnyvale, Calif."}]}],"member":"320","published-online":{"date-parts":[[1974,8]]},"reference":[{"volume-title":"MacMillan","year":"1927","author":"B\u00f4cher M.","key":"e_1_2_1_1_1"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/321250.321258"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/363427.363465"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/321662.321666"},{"key":"e_1_2_1_5_1","first-page":"128","article-title":"aux sommes des racines, prises deux \u00e0 deux, d'une \u00e9quation donn\u00e9e","volume":"2","author":"Gerono G. C.","year":"1843","journal-title":"Nouv. Ann. Math"},{"volume-title":"Wiley","year":"1947","author":"Griffiths L. W.","key":"e_1_2_1_6_1"},{"key":"e_1_2_1_7_1","unstructured":"Hancock H. Introduction to the theory of algebraic numbers. Vol. 1. (reprint) Dover 1965.  Hancock H. Introduction to the theory of algebraic numbers. Vol. 1. (reprint) Dover 1965."},{"volume-title":"Cambridge","year":"1938","author":"Hardy G. H.","key":"e_1_2_1_8_1"},{"key":"e_1_2_1_9_1","first-page":"23","article-title":"\u00dcber die Verallgemeinerung einer Gauss'schen Formel aus der Theorie der h\u00f6heren Kongruenzen","volume":"20","author":"J\u00e4nichen W","year":"1921","journal-title":"S-b. Berliner Math. Gesellschaft"},{"volume-title":"London: Heineman, 1958","year":"1970","author":"Littlewood D. E.","key":"e_1_2_1_10_1"},{"volume-title":"Washington: Catholic University of America","year":"1940","author":"Lloyd D. B.","key":"e_1_2_1_11_1"},{"key":"e_1_2_1_12_1","unstructured":"Loos R. A constructive approach to algebraic numbers. SIAM Jour. Comp. (to appear)  Loos R. A constructive approach to algebraic numbers. SIAM Jour. Comp. (to appear)"},{"key":"e_1_2_1_13_1","first-page":"30","article-title":"A general formula for the equation whose roots are the products in pairs of the roots of any algebraic equation","volume":"13","author":"Malet J. C","year":"1875","journal-title":"Quart. Jour. Pure and Applied Math."},{"key":"e_1_2_1_14_1","first-page":"519","article-title":"On a class of properties connected with linear differential equations","volume":"3","author":"Malet J. C","year":"1876","journal-title":"Trinity College Hermathena (Dublin)"},{"key":"e_1_2_1_15_1","first-page":"306","article-title":"On a problem in algebra. Annali di matematiche pura ed applicada, Tomo 9","volume":"2","author":"Malet J. C","year":"1879","journal-title":"Serie"},{"key":"e_1_2_1_16_1","first-page":"158","article-title":"equations for the power sums","volume":"11","author":"Selmer E. S.","year":"1970","journal-title":"BIT"},{"key":"e_1_2_1_17_1","first-page":"132","article-title":"Observation\" appended to {5})","volume":"2","author":"Terquem O.","year":"1843","journal-title":"Nouv. Ann. Math."},{"volume-title":"McGraw-Hill","year":"1938","author":"Thomas J. M.","key":"e_1_2_1_18_1"},{"volume-title":"Washington: Catholic University of America","year":"1939","author":"Varnhorn M. C.","key":"e_1_2_1_19_1"},{"key":"e_1_2_1_20_1","unstructured":"Waring E. Meditationes algebraic\u00e6. Editio tertia. Cambridge 1782.  Waring E. Meditationes algebraic\u00e6. Editio tertia. Cambridge 1782."},{"key":"e_1_2_1_21_1","doi-asserted-by":"crossref","unstructured":"Zassenhaus H. A real root calculus. in Leech J. ed. Computational problems in abstract algebra (pp. 383--393) London and New York: Pergamon 1970.  Zassenhaus H. A real root calculus. in Leech J. ed. Computational problems in abstract algebra (pp. 383--393) London and New York: Pergamon 1970.","DOI":"10.1016\/B978-0-08-012975-4.50038-2"}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1086837.1086853","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1086837.1086853","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T16:08:13Z","timestamp":1750262893000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1086837.1086853"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1974,8]]},"references-count":21,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1974,8]]}},"alternative-id":["10.1145\/1086837.1086853"],"URL":"https:\/\/doi.org\/10.1145\/1086837.1086853","relation":{},"ISSN":["0163-5824"],"issn-type":[{"type":"print","value":"0163-5824"}],"subject":[],"published":{"date-parts":[[1974,8]]},"assertion":[{"value":"1974-08-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}