多項式の因数分解
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^ An example of degree 2401, taking 7.35 seconds, is found in Section 4 in: Hart, van Hoeij, Novocin: Practical Polynomial Factoring in Polynomial Time ISSAC'2011 Proceedings, p. 163-170 (2011).
^ van der Waerden 1970, §5.4, 5.6.
^ M. van Hoeij: Factoring polynomials and the knapsack problem. Journal of Number Theory, 95, 167-189, (2002).
参考文献
Frohlich, A.; Shepherson, J. C. (1955), “On the factorisation of polynomials in a finite number of steps”, Mathematische Zeitschrift 62 (1): 331?334, doi:10.1007/BF01180640, .mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation.cs-ja1 q,.mw-parser-output .citation.cs-ja2 q{quotes:"「""」""『""』"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:#d33}.mw-parser-output .cs1-visible-error{color:#d33}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}ISSN 0025-5874
Trager, B.M., ⇒“Algebraic Factoring and Rational Function Integration”, Proc. SYMSAC 76, ⇒http://dl.acm.org/citation.cfm?id=806338
Bernard Beauzamy, Per Enflo, Paul Wang (October 1994). “Quantitative Estimates for Polynomials in One or Several Variables: From Analysis and Number Theory to Symbolic and Massively Parallel Computation”. Mathematics Magazine 67 (4): 243?257. doi:10.2307/2690843. JSTOR 2690843. (accessible to readers with undergraduate mathematics)
Cohen, Henri (1993). A course in computational algebraic number theory. Graduate Texts in Mathematics. 138. Berlin, New York: Springer-Verlag. ISBN 978-3-540-55640-4. MR1228206
Kaltofen, Erich (1982), “Factorization of polynomials”, in B. Buchberger; R. Loos; G. Collins, Computer Algebra, Springer Verlag, doi:10.1007/978-3-7091-3406-1_8, MR780381, Zbl 0519.68059
Knuth, Donald E (1997). “4.6.2 Factorization of Polynomials”. Seminumerical Algorithms. The Art of Computer Programming. 2 (Third ed.). Reading, Massachusetts: Addison-Wesley. pp. 439?461, 678?691. ISBN 0-201-89684-2
Lenstra, A. K.; Lenstra, H. W.; Lovasz, Laszlo (1982). “Factoring polynomials with rational coefficients”. Mathematische Annalen 261 (4): 515?534. doi:10.1007/BF01457454. ISSN 0025-5831. MR682664
van der Waerden, B. L. (1970), Algebra, trans. Blum and Schulenberger, Frederick Ungar
関連文献
Kaltofen, Erich (1990), “Polynomial Factorization 1982-1986”, in D. V. Chudnovsky; R. D. Jenks, Computers in Mathematics, Lecture Notes in Pure and Applied Mathematics, 125, Marcel Dekker, Inc.
Kaltofen, Erich (1992), ⇒“Polynomial Factorization 1987?1991”, Proceedings of Latin ’92, Springer Lect. Notes Comput. Sci., 583, Springer, ⇒http://www4.ncsu.edu/~kaltofen/bibliography/92/Ka92_latin.pdf 2012年10月14日閲覧。
Ivanyos, Gabor; Marek, Karpinski; Saxena, Nitin (2009), “Schemes for Deterministic Polynomial Factoring”, Proc. ISSAC 2009: 191?198, arXiv:0804.1974, doi:10.1145/1576702.1576730
外部リンク
Weisstein, Eric W. "Polynomial Factorization". mathworld.wolfram.com (英語).
factorization of primitive polynomial - PlanetMath.（英語）
Hazewinkel, Michiel, ed. (2001), “Factorization of polynomials”, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=Factorization_of_polynomials
Hazewinkel, Michiel, ed. (2001), “Kronecker method”, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=Kronecker_method
関連項目
因数分解#多項式の因数分解
表
話
編
歴
多項式
元数
多変数
次数
多項式
零多項式
定数多項式
斉次多項式
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