{"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":1750308113646,"version":"3.41.0"},"reference-count":12,"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>In this paper we present detailed algorithms for the basic arithmetic operations on symbolic rational expressions represented by formal quotients of factored polynomials. These algorithms are currently implemented in the ALTRAN system for symbolic algebra but the descriptions given in this paper are system independent.First we describe the representation and examine the need for options to permit control over the amount of effort expended in the search for factors or in canonicalizing results. We then present algorithms in the form of programs for equality-test, exponentiation, multiplication, and addition, and mention the modifications required for division and subtraction.We conclude by presenting the results of several benchmark tests comparing the performance of these algorithms with others previously used.<\/jats:p>","DOI":"10.1145\/1086837.1086843","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"35-45","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["Factored rational expressions in ALTRAN"],"prefix":"10.1145","volume":"8","author":[{"suffix":"Jr.","given":"Andrew D.","family":"Hall","sequence":"first","affiliation":[{"name":"Bell Laboratories, Murray Hill, New Jersey"}]}],"member":"320","published-online":{"date-parts":[[1974,8]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1086837.1086842"},{"key":"e_1_2_1_2_1","unstructured":"W. S. Brown ALTRAN User's Manual Third Edition Bell Laboratories 1973.  W. S. Brown ALTRAN User's Manual Third Edition Bell Laboratories 1973."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/362637.362644"},{"key":"e_1_2_1_4_1","first-page":"32","volume":"13","author":"Barton D.","year":"1970","journal-title":"An Algebra System, Computer Journal"},{"key":"e_1_2_1_5_1","unstructured":"S. MacLane and G. Birkhoff Algebra The MacMillan Company New York (1967).  S. MacLane and G. Birkhoff Algebra The MacMillan Company New York (1967)."},{"key":"e_1_2_1_6_1","first-page":"2081","volume":"42","author":"Brown W. S.","year":"1963","journal-title":"The ALPAK System for Non-numerical Algebra on a Digital Computer, B.S.T.J."},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/1086793.1086794"},{"key":"e_1_2_1_8_1","unstructured":"A. D. Hall Solving a Problem in Eigenvalue Approximation with a Symbolic Algebra System SIGSAM Bulletin No. 26 15--23 (June 1973).  A. D. Hall Solving a Problem in Eigenvalue Approximation with a Symbolic Algebra System SIGSAM Bulletin No. 26 15--23 (June 1973)."},{"key":"e_1_2_1_9_1","volume":"70","author":"Sconzo P.","year":"1965","journal-title":"Symbolic Computation of F and G Series by Computer, Astronomical Journal"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1086830.1086831"},{"key":"e_1_2_1_11_1","doi-asserted-by":"crossref","unstructured":"L. Takacs A Single-Server Queue with Feedback B.S.T.J. 42 503--519 (March 1963).  L. Takacs A Single-Server Queue with Feedback B.S.T.J. 42 503--519 (March 1963).","DOI":"10.1002\/j.1538-7305.1963.tb00510.x"},{"key":"e_1_2_1_12_1","unstructured":"S. C. Johnson Sparse Polynomial Arithmetic this issue.  S. C. Johnson Sparse Polynomial Arithmetic this issue."}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1086837.1086843","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1086837.1086843","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\/1086837.1086843"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1974,8]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1974,8]]}},"alternative-id":["10.1145\/1086837.1086843"],"URL":"https:\/\/doi.org\/10.1145\/1086837.1086843","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"}}]}}