{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T01:52:44Z","timestamp":1775872364071,"version":"3.50.1"},"reference-count":5,"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>\n            Sparse polynomial representations are used in a number of algebraic manipulation systems, including Altran. This paper discusses the arithmetic operations with sparsely represented polynomials; we give particular attention to multiplication and division. We give new algorithms for multiplying two polynomials, with\n            <jats:italic>n<\/jats:italic>\n            and\n            <jats:italic>m<\/jats:italic>\n            terms, in time\n            <jats:italic>mn<\/jats:italic>\n            log\n            <jats:italic>m<\/jats:italic>\n            ;, these algorithms have the property that, in the usual univariate dense case, the algorithm is bounded by\n            <jats:italic>mn.<\/jats:italic>\n            Division algorithms are discussed which run in comparable time.\n          <\/jats:p>","DOI":"10.1145\/1086837.1086847","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"63-71","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":46,"title":["Sparse polynomial arithmetic"],"prefix":"10.1145","volume":"8","author":[{"given":"Stephen C.","family":"Johnson","sequence":"first","affiliation":[{"name":"Bell Telephone Labs, Murray Hill, N. J."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[1974,8]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/13.1.32"},{"key":"e_1_2_1_2_1","unstructured":"Knuth D. E. The Art of Computer Programming Vol 2 Addison-Wesley 1969.   Knuth D. E. The Art of Computer Programming Vol 2 Addison-Wesley 1969."},{"key":"e_1_2_1_3_1","volume-title":"Addison-Wesley","author":"Aho A. V.","year":"1974"},{"key":"e_1_2_1_4_1","unstructured":"Knuth D. E. The Art of Computer Programming Vol 3 Addison-Wesley 1973.   Knuth D. E. The Art of Computer Programming Vol 3 Addison-Wesley 1973."},{"key":"e_1_2_1_5_1","unstructured":"Brown W. S. etal ALTRAN Vols I and II (1973) Bell Telephone Labs.  Brown W. S. et al ALTRAN Vols I and II (1973) Bell Telephone Labs."}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1086837.1086847","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1086837.1086847","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\/1086837.1086847"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1974,8]]},"references-count":5,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1974,8]]}},"alternative-id":["10.1145\/1086837.1086847"],"URL":"https:\/\/doi.org\/10.1145\/1086837.1086847","relation":{},"ISSN":["0163-5824"],"issn-type":[{"value":"0163-5824","type":"print"}],"subject":[],"published":{"date-parts":[[1974,8]]},"assertion":[{"value":"1974-08-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}