{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T12:15:38Z","timestamp":1772367338535,"version":"3.50.1"},"reference-count":19,"publisher":"Elsevier BV","issue":"1-2","license":[{"start":{"date-parts":[[2003,2,1]],"date-time":"2003-02-01T00:00:00Z","timestamp":1044057600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2003,2,1]],"date-time":"2003-02-01T00:00:00Z","timestamp":1044057600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":3819,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Advances in Applied Mathematics"],"published-print":{"date-parts":[[2003,2]]},"DOI":"10.1016\/s0196-8858(02)00529-8","type":"journal-article","created":{"date-parts":[[2003,4,4]],"date-time":"2003-04-04T17:33:30Z","timestamp":1049477610000},"page":"137-159","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":12,"title":["A direct algorithm to construct the minimal Z-pairs for rational functions"],"prefix":"10.1016","volume":"30","author":[{"given":"H.Q.","family":"Le","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0196-8858(02)00529-8_BIB001","first-page":"1035","article-title":"Rational component of the solutions of a first-order linear recurrence relation with a rational right-hand side","volume":"14","author":"Abramov","year":"1975","journal-title":"USSR Comput. Math. Phys."},{"key":"10.1016\/S0196-8858(02)00529-8_BIB002","series-title":"Proceedings ISSAC'93","first-page":"152","article-title":"On the greatest common divisor of polynomials which depend on a parameter","author":"Abramov","year":"1993"},{"key":"10.1016\/S0196-8858(02)00529-8_BIB003","series-title":"Proceedings ISSAC'95","first-page":"303","article-title":"Indefinite sums of rational functions","author":"Abramov","year":"1995"},{"key":"10.1016\/S0196-8858(02)00529-8_BIB004","series-title":"Proceedings FPSAC'2000","first-page":"91","article-title":"Applicability of Zeilberger's algorithm to rational functions","author":"Abramov","year":"2000"},{"key":"10.1016\/S0196-8858(02)00529-8_BIB005","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0012-365X(02)00442-9","article-title":"A criterion for the applicability of Zeilberger's algorithm to rational functions","volume":"259","author":"Abramov","year":"2002","journal-title":"Discrete Math."},{"key":"10.1016\/S0196-8858(02)00529-8_BIB006","series-title":"Proc. ISSAC'2001","first-page":"7","article-title":"Minimal decomposition of indefinite hypergeometric sums","author":"Abramov","year":"2001"},{"key":"10.1016\/S0196-8858(02)00529-8_BIB007","series-title":"Concrete Mathematics","author":"Graham","year":"1994"},{"key":"10.1016\/S0196-8858(02)00529-8_BIB008","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/0377-0427(93)90317-5","article-title":"On Zeilberger's algorithm and its q-analogue","volume":"48","author":"Koornwinder","year":"1993","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/S0196-8858(02)00529-8_BIB009","series-title":"Proc. FPSAC'2001","first-page":"303","article-title":"A direct algorithm to construct Zeilberger's recurrences for rational functions","author":"Le","year":"2001"},{"key":"10.1016\/S0196-8858(02)00529-8_BIB010","first-page":"49","article-title":"On the q-analogue of Zeilberger's algorithm to rational functions","volume":"27","author":"Le","year":"2001","journal-title":"Progr. Comput. Software (Programmirovanie)"},{"key":"10.1016\/S0196-8858(02)00529-8_BIB011","unstructured":"H.Q. Le, S.A. Abramov, K.O. Geddes, A direct algorithm to construct the minimal telescopers for rational functions (q-difference case), Technical Report CS-2001-25, Department of Computer Science, University of Waterloo, ON, Canada"},{"key":"10.1016\/S0196-8858(02)00529-8_BIB012","unstructured":"H.Q. Le, S.A. Abramov, K.O. Geddes, HypergeometricSum: A Maple package for finding closed forms of indefinite and definite sums of hypergeometric type, Technical Report CS-2001-24, Department of Computer Science, University of Waterloo, ON, Canada"},{"key":"10.1016\/S0196-8858(02)00529-8_BIB013","series-title":"Maple 7 Programming Guide","author":"Monagan","year":"2001"},{"key":"10.1016\/S0196-8858(02)00529-8_BIB014","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1006\/jsco.1995.1049","article-title":"Greatest factorial factorization and symbolic summation","volume":"20","author":"Paule","year":"1995","journal-title":"J. Symbolic Comput."},{"key":"10.1016\/S0196-8858(02)00529-8_BIB015","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1006\/jsco.1995.1071","article-title":"A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities","volume":"20","author":"Paule","year":"1995","journal-title":"J. Symbolic Comput."},{"key":"10.1016\/S0196-8858(02)00529-8_BIB016","series-title":"A=B","author":"Petkov\u0161ek","year":"1996"},{"key":"10.1016\/S0196-8858(02)00529-8_BIB017","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1006\/jsco.1995.1068","article-title":"Rational summation and Gosper\u2013Petkov\u0161ek representation","volume":"20","author":"Pirastu","year":"1995","journal-title":"J. Symbolic Comput."},{"key":"10.1016\/S0196-8858(02)00529-8_BIB018","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1007\/BF02100618","article-title":"An algorithmic proof theory for hypergeometric (ordinary and \u201cq\u201d) multisum\/integral identities","volume":"108","author":"Wilf","year":"1992","journal-title":"Invent. Math."},{"key":"10.1016\/S0196-8858(02)00529-8_BIB019","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/S0747-7171(08)80044-2","article-title":"The method of creative telescoping","volume":"11","author":"Zeilberger","year":"1991","journal-title":"J. Symbolic Comput."}],"container-title":["Advances in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0196885802005298?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0196885802005298?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T06:44:33Z","timestamp":1759301073000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0196885802005298"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,2]]},"references-count":19,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2003,2]]}},"alternative-id":["S0196885802005298"],"URL":"https:\/\/doi.org\/10.1016\/s0196-8858(02)00529-8","relation":{},"ISSN":["0196-8858"],"issn-type":[{"value":"0196-8858","type":"print"}],"subject":[],"published":{"date-parts":[[2003,2]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A direct algorithm to construct the minimal Z-pairs for rational functions","name":"articletitle","label":"Article Title"},{"value":"Advances in Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/S0196-8858(02)00529-8","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"converted-article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2003 Elsevier Science (USA). All rights reserved.","name":"copyright","label":"Copyright"}]}}