{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,12,13]],"date-time":"2024-12-13T06:40:01Z","timestamp":1734072001465,"version":"3.30.2"},"reference-count":12,"publisher":"Elsevier BV","issue":"5","license":[{"start":{"date-parts":[[2003,10,1]],"date-time":"2003-10-01T00:00:00Z","timestamp":1064966400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,8,22]],"date-time":"2013-08-22T00:00:00Z","timestamp":1377129600000},"content-version":"vor","delay-in-days":3613,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Complexity"],"published-print":{"date-parts":[[2003,10]]},"DOI":"10.1016\/s0885-064x(03)00047-5","type":"journal-article","created":{"date-parts":[[2003,7,16]],"date-time":"2003-07-16T15:02:03Z","timestamp":1058367723000},"page":"631-637","source":"Crossref","is-referenced-by-count":3,"title":["Use of algebraically independent numbers for zero recognition of polynomial terms"],"prefix":"10.1016","volume":"19","author":[{"given":"Daniel","family":"Richardson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmed","family":"El-Sonbaty","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"year":"1975","series-title":"Transcendental Number Theory","author":"Baker","key":"10.1016\/S0885-064X(03)00047-5_BIBBAKER"},{"key":"10.1016\/S0885-064X(03)00047-5_BIBBESICOVITCH","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1112\/jlms\/s1-15.1.3","article-title":"On the linear independence of fractional powers of integers","volume":"15","author":"Besicovitch","year":"1940","journal-title":"J. London Math. Soc."},{"year":"1987","series-title":"Pi and the AGM","author":"Borwein","key":"10.1016\/S0885-064X(03)00047-5_BIBBORWEIN"},{"issue":"4","key":"10.1016\/S0885-064X(03)00047-5_BIBBORWEIN1988","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1137\/1030134","article-title":"On the complexity of familiar functions and numbers","volume":"30","author":"Borwein","year":"1988","journal-title":"SIAM Rev."},{"key":"10.1016\/S0885-064X(03)00047-5_BIBBRENT74","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1145\/321812.321815","article-title":"The parallel evaluation of generic arithmetic expressions","volume":"21","author":"Brent","year":"1974","journal-title":"J. ACM"},{"key":"10.1016\/S0885-064X(03)00047-5_BIBBRENT","series-title":"Analytic Computational Complexity","first-page":"151","article-title":"Multiple-precision zero-finding methods and the complexity of elementary functions","author":"Brent","year":"1975"},{"key":"10.1016\/S0885-064X(03)00047-5_BIBRICHARDSON97","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1006\/jsco.1997.0157","article-title":"How to recognise zero","volume":"24","author":"Richardson","year":"1997","journal-title":"J. Symbolic Comput."},{"key":"10.1016\/S0885-064X(03)00047-5_BIBRICHARDSON2000","unstructured":"D. Richardson, The uniformity conjecture, Proceedings of Computability and Complexity in Analysis, CCA2000, September 17\u201319, Swansea, Wales. Also in associated Springer Lecture Notes in Computer Science, Vol. 2064, Springer, Berlin, 2000, pp. 253\u2013272."},{"key":"10.1016\/S0885-064X(03)00047-5_BIBRICHARDSON2001","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/S0022-4049(00)00156-0","article-title":"Multiplicative independence of algebraic numbers and expressions","volume":"164","author":"Richardson","year":"2001","journal-title":"J. Pure Appl. Algebra"},{"key":"10.1016\/S0885-064X(03)00047-5_BIBRICHARDSONLA","doi-asserted-by":"crossref","unstructured":"in: T. Mora (Ed.), Some Observations about Familiar Numbers, ISSAC2002, ACM Press, pp. 214\u2013220.","DOI":"10.1145\/780506.780534"},{"key":"10.1016\/S0885-064X(03)00047-5_BIBVDHOEVEN","unstructured":"J. Van Der Hoeven, Automatic asymptotics, Ph.D. Thesis, Ecole Polytechnique, 1997."},{"year":"1993","series-title":"Effective Polynomial Computation","author":"Zippel","key":"10.1016\/S0885-064X(03)00047-5_BIBZIPPEL"}],"container-title":["Journal of Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0885064X03000475?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0885064X03000475?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2024,12,13]],"date-time":"2024-12-13T05:59:08Z","timestamp":1734069548000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0885064X03000475"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,10]]},"references-count":12,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2003,10]]}},"alternative-id":["S0885064X03000475"],"URL":"https:\/\/doi.org\/10.1016\/s0885-064x(03)00047-5","relation":{},"ISSN":["0885-064X"],"issn-type":[{"type":"print","value":"0885-064X"}],"subject":[],"published":{"date-parts":[[2003,10]]}}}