{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T17:08:29Z","timestamp":1760202509125},"reference-count":17,"publisher":"Elsevier BV","issue":"2","license":[{"start":{"date-parts":[[1992,4,1]],"date-time":"1992-04-01T00:00:00Z","timestamp":702086400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":7777,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information and Computation"],"published-print":{"date-parts":[[1992,4]]},"DOI":"10.1016\/0890-5401(92)90037-g","type":"journal-article","created":{"date-parts":[[2004,12,2]],"date-time":"2004-12-02T00:24:20Z","timestamp":1101947060000},"page":"262-276","source":"Crossref","is-referenced-by-count":3,"title":["Polynomial time algorithms for sentences over number fields"],"prefix":"10.1016","volume":"97","author":[{"given":"Shih Ping","family":"Tung","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/0890-5401(92)90037-G_BIB1","author":"Knuth","year":"1981"},{"key":"10.1016\/0890-5401(92)90037-G_BIB2","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1137\/0214015","article-title":"Factoring polynomials over algebraic number fields","volume":"14","author":"Landau","year":"1985","journal-title":"SIAM J. Comput."},{"key":"10.1016\/0890-5401(92)90037-G_BIB3","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/0022-0000(85)90013-3","article-title":"Solvability by radicals is in polynomial time","volume":"30","author":"Landau","year":"1985","journal-title":"J. Comput. System Sci."},{"key":"10.1016\/0890-5401(92)90037-G_BIB4","series-title":"Algebra","author":"Lang","year":"1971"},{"key":"10.1016\/0890-5401(92)90037-G_BIB5","author":"Lenstra","year":"1982"},{"key":"10.1016\/0890-5401(92)90037-G_BIB6","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1137\/0216040","article-title":"Factoring multivariate polynomials over algebraic number fields","volume":"16","author":"Lenstra","year":"1987","journal-title":"SIAM J. Comput."},{"key":"10.1016\/0890-5401(92)90037-G_BIB7","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1007\/BF01457454","article-title":"Factoring polynomials with rational coefficients","volume":"261","author":"Lenstra","year":"1982","journal-title":"Math. Ann."},{"key":"10.1016\/0890-5401(92)90037-G_BIB8","doi-asserted-by":"crossref","first-page":"1153","DOI":"10.1090\/S0025-5718-1974-0354624-3","article-title":"An inequality about factors of polynomials","volume":"28","author":"Mignotte","year":"1974","journal-title":"Math. Comp."},{"key":"10.1016\/0890-5401(92)90037-G_BIB9","author":"Pollard","year":"1975"},{"key":"10.1016\/0890-5401(92)90037-G_BIB10","doi-asserted-by":"crossref","first-page":"98","DOI":"10.2307\/2266510","article-title":"Definability and decision problems in arithmetic","volume":"14","author":"Robinson","year":"1949","journal-title":"J. Symbolic Logic"},{"key":"10.1016\/0890-5401(92)90037-G_BIB11","first-page":"950","article-title":"The undecidability of algebraic rings and fields","volume":"10","author":"Robinson","year":"1959"},{"key":"10.1016\/0890-5401(92)90037-G_BIB12","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1002\/malq.19640101803","article-title":"The undecidability of pure transcendental extensions of real fields","volume":"10","author":"Robinson","year":"1964","journal-title":"Z. Math. Logik Grundlog. Math."},{"key":"10.1016\/0890-5401(92)90037-G_BIB13","author":"Schinzel","year":"1982"},{"key":"10.1016\/0890-5401(92)90037-G_BIB14","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1112\/blms\/18.3.241","article-title":"Provability and decidability of arithmetical universal-existential sentences","volume":"18","author":"Tung","year":"1986","journal-title":"Bull. London Math. Soc."},{"key":"10.1016\/0890-5401(92)90037-G_BIB15","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1016\/0196-6774(87)90013-7","article-title":"Computational complexities of diophantine equations with parameters","volume":"8","author":"Tung","year":"1987","journal-title":"J. Algorithms"},{"key":"10.1016\/0890-5401(92)90037-G_BIB16","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.2307\/2274469","article-title":"Decidable fragments of field theories","volume":"55","author":"Tung","year":"1990","journal-title":"J. Symbolic Logic"},{"key":"10.1016\/0890-5401(92)90037-G_BIB17","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1137\/0220007","article-title":"Complexity of sentences over number rings","volume":"20","author":"Tung","year":"1991","journal-title":"SIAM J. Comput."}],"container-title":["Information and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:089054019290037G?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:089054019290037G?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,2,1]],"date-time":"2019-02-01T18:24:57Z","timestamp":1549045497000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/089054019290037G"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,4]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1992,4]]}},"alternative-id":["089054019290037G"],"URL":"https:\/\/doi.org\/10.1016\/0890-5401(92)90037-g","relation":{},"ISSN":["0890-5401"],"issn-type":[{"value":"0890-5401","type":"print"}],"subject":[],"published":{"date-parts":[[1992,4]]}}}