Book Review
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MathSciNet review: 1568145
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Book Information:
Author: Henri Cohen
Title: A course in computational algebraic number theory
Additional book information: Springer-Verlag, New York, 1993, xxi+534 pp., US$49.00. ISBN 3-540-55640-0.
- [Be1] E. R. Berlekamp, Factoring polynomials over finite fields, Bell System Tech. J. 46 (1967), 1853–1859. MR 219231, https://doi.org/10.1002/j.1538-7305.1967.tb03174.x
- [Be2] E. R. Berlekamp, Factoring polynomials over large finite fields, Math. Comp. 24 (1970), 713–735. MR 276200, https://doi.org/10.1090/S0025-5718-1970-0276200-X
- [Bi1] J. Binet, Recherches sur la théorie des nombres entiers et sur la résolution de l'équation indeterminée du premier degré qui n'admet que des solutions entières, J. Math. Pures Appl. (1) 6 (1841), 449-494.
- [Bi2] -, Note sur le nombre des divisions à effectuer pour obtenir le plus grand diviseur commun de deux nombres entiers; suivie d'une remarque sur une classe de séries récurrentes, Comptes Rendus 19 (1844), 937-941.
- [C] George E. Collins, Factoring univariate integral polynomials in polynomial average time, Symbolic and algebraic computation (EUROSAM ’79, Internat. Sympos., Marseille, 1979) Lecture Notes in Comput. Sci., vol. 72, Springer, Berlin-New York, 1979, pp. 317–329. MR 575695
- [CZ] David G. Cantor and Hans Zassenhaus, A new algorithm for factoring polynomials over finite fields, Math. Comp. 36 (1981), no. 154, 587–592. MR 606517, https://doi.org/10.1090/S0025-5718-1981-0606517-5
- [JT] M. A. Jenkins and J. F. Traub, A three-stage variable-shift iteration for polynomial zeros and its relation to generalized Rayleigh iteration, Numer. Math. 14 (1969/70), 252–263. MR 258271, https://doi.org/10.1007/BF02163334
- [K] Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms; Addison-Wesley Series in Computer Science and Information Processing. MR 633878
- [L] G. Lamé, Note sur la limite du nombre des divisions dans la recherche du plus grand diviseur entre deux nombres entiers, Comptes Rendus 19 (1844), 867-870.
- [LLL] A. K. Lenstra, H. W. Lenstra Jr., and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982), no. 4, 515–534. MR 682664, https://doi.org/10.1007/BF01457454
- [M] M. Mignotte, An inequality about factors of polynomials, Math. Comp. 28 (1974), 1153–1157. MR 354624, https://doi.org/10.1090/S0025-5718-1974-0354624-3
- [P] C. Pomerance, Analysis and comparison of some integer factoring algorithms, Computational methods in number theory, Part I, Math. Centre Tracts, vol. 154, Math. Centrum, Amsterdam, 1982, pp. 89–139. MR 700260
- [Z1] Hans Zassenhaus, On Hensel factorization. I, J. Number Theory 1 (1969), 291–311. MR 242793, https://doi.org/10.1016/0022-314X(69)90047-X
- [Z2] Hans Zassenhaus, A remark on the Hensel factorization method, Math. Comp. 32 (1978), no. 141, 287–292. MR 476692, https://doi.org/10.1090/S0025-5718-1978-0476692-4
Review Information:
Reviewer: Hale Trotter
Journal: Bull. Amer. Math. Soc. 31 (1994), 312-318
DOI: https://doi.org/10.1090/S0273-0979-1994-00542-7