{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T03:53:30Z","timestamp":1759118010774,"version":"3.41.0"},"reference-count":23,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2004,9,1]],"date-time":"2004-09-01T00:00:00Z","timestamp":1093996800000},"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":[[2004,9]]},"abstract":"<jats:p>We discuss the multiple definitions of multivalued functions and their suitability for computer algebra systems. We focus the discussion by taking one specific problem and considering how it is solved using different definitions. Our example problem is the classical one of calculating the roots of a cubic polynomial from the Cardano formulae, which contain fractional powers. We show that some definitions of these functions result in formulae that are correct only in the sense that they give candidates for solutions; these candidates must then be tested. Formulae that are based on single-valued functions, in contrast, are efficient and direct.<\/jats:p>","DOI":"10.1145\/1040034.1040036","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"57-66","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":13,"title":["Not seeing the roots for the branches"],"prefix":"10.1145","volume":"38","author":[{"given":"D. J.","family":"Jeffrey","sequence":"first","affiliation":[{"name":"The University of Western Ontario, London, Ontario, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. C.","family":"Norman","sequence":"additional","affiliation":[{"name":"Trinity College, Cambridge, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2004,9]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Handbook of Mathematical Functions","author":"Abramowitz Milton","year":"1965","unstructured":"Milton Abramowitz and Irene A. Stegun . Handbook of Mathematical Functions . Dover , New York , 1965 .]] Milton Abramowitz and Irene A. Stegun. Handbook of Mathematical Functions. Dover, New York, 1965.]]"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/235699.235702"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/860854.860867"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016007415899"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/780506.780509"},{"key":"e_1_2_1_6_1","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1515\/dmvm-2000-0038","article-title":"Das ende der mathematik?","volume":"2","author":"Buchberger Bruno","year":"2000","unstructured":"Bruno Buchberger . Computer-algebra : Das ende der mathematik? Mitteilungen der Deutschen Mathematiker-Vereinigung , 2 : 16 -- 19 , 2000 .]] Bruno Buchberger. Computer-algebra: Das ende der mathematik? Mitteilungen der Deutschen Mathematiker-Vereinigung, 2:16--19, 2000.]]","journal-title":"Mitteilungen der Deutschen Mathematiker-Vereinigung"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/565145.565147"},{"key":"e_1_2_1_8_1","volume-title":"Chelsea","author":"Carath\u00e9odory C.","year":"1958","unstructured":"C. Carath\u00e9odory . Theory of functions of a complex variable (trans. F. Steinhardt), 2nd. ed . Chelsea , New York , 1958 .]] C. Carath\u00e9odory. Theory of functions of a complex variable (trans. F. Steinhardt), 2nd. ed. Chelsea, New York, 1958.]]"},{"key":"e_1_2_1_9_1","volume-title":"Algebra: an elementary text-book","author":"Chrystal G.","year":"1964","unstructured":"G. Chrystal . Algebra: an elementary text-book , 7 th ed. Chelsea , 1964 .]] G. Chrystal. Algebra: an elementary text-book, 7th ed. Chelsea, 1964.]]","edition":"7"},{"key":"e_1_2_1_10_1","volume-title":"Reasoning about the elementary functions of complex analysis","author":"Corless R. M.","year":"1930","unstructured":"R. M. Corless , J. H. Davenport , D. J. Jeffrey , G. Litt , and S. M. Watt . Reasoning about the elementary functions of complex analysis . Springer lecture notes on Artificial Intelligence (LNAI), 1930 :115--126, 2001.]] R. M. Corless, J. H. Davenport, D. J. Jeffrey, G. Litt, and S. M. Watt. Reasoning about the elementary functions of complex analysis. Springer lecture notes on Artificial Intelligence (LNAI), 1930:115--126, 2001.]]"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/362001.362023"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/235699.235705"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/190347.190424"},{"key":"e_1_2_1_14_1","volume-title":"Abstract Algebra","author":"Dummit David S.","year":"1991","unstructured":"David S. Dummit and Richard M. Foote . Abstract Algebra . Prentice-Hall , 1991 .]] David S. Dummit and Richard M. Foote. Abstract Algebra. Prentice-Hall, 1991.]]"},{"key":"e_1_2_1_15_1","volume-title":"Encyclopaedia of Mathematics","author":"Hazewinkel M.","year":"1995","unstructured":"M. Hazewinkel (Ed.). Encyclopaedia of Mathematics . Kluwer Academic Publishers , 1995 .]] M. Hazewinkel (Ed.). Encyclopaedia of Mathematics. Kluwer Academic Publishers, 1995.]]"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1997.0152"},{"key":"e_1_2_1_17_1","first-page":"165","volume-title":"The State of the Art in Numerical Analysis (Eds Iserles and Powell)","author":"Kahan W.","year":"1987","unstructured":"W. Kahan . Branch cuts for complex elementary functions, or much ado about nothing's sign bit . In The State of the Art in Numerical Analysis (Eds Iserles and Powell) , pages 165 -- 211 . Clarendon Press , Oxford , 1987 .]] W. Kahan. Branch cuts for complex elementary functions, or much ado about nothing's sign bit. In The State of the Art in Numerical Analysis (Eds Iserles and Powell), pages 165--211. Clarendon Press, Oxford, 1987.]]"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1137\/1028001"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/235699.235703"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/281508.281614"},{"key":"e_1_2_1_21_1","volume-title":"Numerical Recipes in C","author":"Press William H.","year":"1992","unstructured":"William H. Press , Saul A. Teukolsky , William T. Vetterling , and Brian P. Flannery . Numerical Recipes in C , 2 nd Edition. Cambridge University Press , 1992 .]] William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. Numerical Recipes in C, 2nd Edition. Cambridge University Press, 1992.]]","edition":"2"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/235699.235704"},{"key":"e_1_2_1_23_1","volume-title":"Longman","author":"Tignol Jean-Pierre","year":"1988","unstructured":"Jean-Pierre Tignol . Galois' theory of algebraic equations . Longman , 1988 .]] Jean-Pierre Tignol. Galois' theory of algebraic equations. Longman, 1988.]]"}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1040034.1040036","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1040034.1040036","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T16:31:45Z","timestamp":1750264305000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1040034.1040036"}},"subtitle":["multivalued functions in computer algebra"],"short-title":[],"issued":{"date-parts":[[2004,9]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2004,9]]}},"alternative-id":["10.1145\/1040034.1040036"],"URL":"https:\/\/doi.org\/10.1145\/1040034.1040036","relation":{},"ISSN":["0163-5824"],"issn-type":[{"type":"print","value":"0163-5824"}],"subject":[],"published":{"date-parts":[[2004,9]]},"assertion":[{"value":"2004-09-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}