{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T07:13:44Z","timestamp":1776755624448,"version":"3.51.2"},"publisher-location":"Berlin, Heidelberg","reference-count":23,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540123170","type":"print"},{"value":"9783540400387","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1983]]},"DOI":"10.1007\/bfb0036913","type":"book-chapter","created":{"date-parts":[[2006,1,25]],"date-time":"2006-01-25T12:38:14Z","timestamp":1138192694000},"page":"250-263","source":"Crossref","is-referenced-by-count":7,"title":["Polynomial-time factorization of multivariate polynomials over finite fields"],"prefix":"10.1007","author":[{"given":"J.","family":"von zur Gathen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E.","family":"Kaltofen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2005,12,26]]},"reference":[{"key":"21_CR1","volume-title":"The design and analysis of computer algorithms","author":"A.V. Aho","year":"1974","unstructured":"A.V. Aho, J.E. Hopcroft and J.D. Ullman, The design and analysis of computer algorithms. Addison-Wesley, Reading MA, 1974."},{"key":"21_CR2","doi-asserted-by":"crossref","unstructured":"M. Ben-Or, Probabilistic algorithms in finite fields. Proc. 22nd Symp. Foundations Comp. Sci. IEEE, 1981, 394\u2013398.","DOI":"10.1109\/SFCS.1981.37"},{"key":"21_CR3","doi-asserted-by":"crossref","first-page":"1853","DOI":"10.1002\/j.1538-7305.1967.tb03174.x","volume":"46","author":"E.R. Berlekamp","year":"1967","unstructured":"E.R. Berlekamp, Factoring polynomials over finite fields. Bell System Tech. J. 46 (1967), 1853\u20131859.","journal-title":"Bell System Tech. J."},{"key":"21_CR4","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1090\/S0025-5718-1970-0276200-X","volume":"24","author":"E.R. Berlekamp","year":"1970","unstructured":"E.R. Berlekamp, Factoring polynomials over large finite fields. Math. Comp. 24 (1970), 713\u2013735.","journal-title":"Math. Comp."},{"key":"21_CR5","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1145\/321662.321664","volume":"18","author":"W.S. Brown","year":"1971","unstructured":"W.S. Brown, On Euclid's algorithm and the computation of polynomial Greatest Common Divisors. J. ACM 18 (1971), 478\u2013504.","journal-title":"J. ACM"},{"key":"21_CR6","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1090\/S0025-5718-1981-0606517-5","volume":"36","author":"D.G. Cantor","year":"1981","unstructured":"D.G. Cantor and H. Zassenhaus, On algorithms for factoring polynomials over finite fields. Math. Comp. 36 (1981), 587\u2013592.","journal-title":"Math. Comp."},{"key":"21_CR7","unstructured":"A.L. Chistov and D.Yu. Grigoryev, Polynomial-time factoring of the multivariable polynomials over a global field. LOMI preprint E-5-82, Leningrad, 1982."},{"key":"21_CR8","doi-asserted-by":"crossref","unstructured":"J.H. Davenport and B.M. Trager, Factorization over finitely generated fields. Proc. 1981 ACM Symp. Symbolic and Algebraic Computation, ed. by P. Wang, 1981, 200\u2013205.","DOI":"10.1145\/800206.806396"},{"key":"21_CR9","unstructured":"J. von zur Gathen, Hensel and Newton methods in valuation rings. Tech. Report 155(1981), Dept. of Computer Science, University of Toronto. To appear in Math. Comp."},{"key":"21_CR10","doi-asserted-by":"crossref","unstructured":"J. von zur Gathen, Parallel algorithms for algebraic problems. Proc. 15th ACM Symp. Theory of Computing, Boston, 1983.","DOI":"10.1145\/800061.808728"},{"key":"21_CR11","doi-asserted-by":"crossref","unstructured":"J. von zur Gathen [83a], Factoring sparse multivariate polynomials. Manuscript, 1983.","DOI":"10.1109\/SFCS.1983.15"},{"key":"21_CR12","volume-title":"An introduction to the theory of numbers","author":"G.H. Hardy","year":"1962","unstructured":"G.H. Hardy and E.M. Wright, An introduction to the theory of numbers. Clarendon Press, Oxford, 1962."},{"key":"21_CR13","doi-asserted-by":"crossref","unstructured":"E. Kaltofen, A Polynomial Time Reduction from Bivariate to Univariate Integral Polynomial Factorization. Proc. 23rd Symp. Foundations of Comp. Sci., IEEE, 1982, 57\u201364.","DOI":"10.1109\/SFCS.1982.56"},{"key":"21_CR14","doi-asserted-by":"crossref","unstructured":"E. Kaltofen, Polynomial-time Reduction from Multivariate to Bivariate and Univariate Integer Polynomial Factorization. Manuscript, 1983, submitted to SIAM J. Comput.","DOI":"10.1145\/800070.802200"},{"key":"21_CR15","volume-title":"The Art of Computer Programming, Vol.2","author":"D.E. Knuth","year":"1981","unstructured":"D.E. Knuth, The Art of Computer Programming, Vol.2, 2nd Ed. Addison-Wesley, Reading MA, 1981.","edition":"2nd Ed."},{"key":"21_CR16","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/0304-3975(83)90108-1","volume":"22","author":"A. Lempel","year":"1983","unstructured":"A. Lempel, G. Seroussi and S. Winograd, On the complexity of multiplication in finite fields. Theor. Comp. Science 22 (1983), 285\u2013296.","journal-title":"Theor. Comp. Science"},{"key":"21_CR17","doi-asserted-by":"crossref","unstructured":"A.K. Lenstra, Factoring multivariate polynomials over finite fields. Proc. 15th ACM Symp. Theory of Computing, Boston, 1983.","DOI":"10.1145\/800061.808748"},{"key":"21_CR18","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1007\/BF01457454","volume":"261","author":"A.K. Lenstra","year":"1982","unstructured":"A.K. Lenstra, H.W. Lenstra, and L. Lov\u00e1sz, Factoring polynomials with rational coefficients. Math. Ann. 261 (1982), 515\u2013534.","journal-title":"Math. Ann."},{"key":"21_CR19","unstructured":"D.R. Musser, Algorithms for Polynomial Factorization. Ph.D. thesis and TR 134, Univ. of Wisconsin, 1971."},{"key":"21_CR20","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1137\/0209024","volume":"9","author":"M.O. Rabin","year":"1980","unstructured":"M.O. Rabin, Probabilistic algorithms in finite fields. SIAM J. Comp. 9 (1980), 273\u2013280.","journal-title":"SIAM J. Comp."},{"key":"21_CR21","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1515\/crll.1846.31.269","volume":"31","author":"T. Sch\u00f6nemann","year":"1846","unstructured":"T. Sch\u00f6nemann, Grundz\u00fcge einer allgemeinen Theorie der h\u00f6heren Congruenzen, deren Modul eine reelle Primzahl ist. J. f. d. reine u. angew. Math. 31 (1846), 269\u2013325.","journal-title":"J. f. d. reine u. angew. Math."},{"key":"21_CR22","volume-title":"Modern Algebra, vol. 1","author":"B.L. Waerden van der","year":"1953","unstructured":"B.L. van der Waerden, Modern Algebra, vol. 1. Ungar, New York, 1953."},{"key":"21_CR23","doi-asserted-by":"crossref","unstructured":"H. Weyl, Algebraic theory of numbers. Princeton University Press, 1940.","DOI":"10.1515\/9781400882809"}],"container-title":["Lecture Notes in Computer Science","Automata, Languages and Programming"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BFb0036913","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,16]],"date-time":"2019-04-16T11:16:27Z","timestamp":1555413387000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BFb0036913"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983]]},"ISBN":["9783540123170","9783540400387"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/bfb0036913","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[1983]]}}}