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Book Review
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Book Information
Author(s):
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
References:
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- [Be1]
- E. R. Berlekamp, Factoring polynomials over finite fields, Bell System Tech. J. 46 (1967), 1853-1859. MR 0219231 (36:2314)
- [Be2]
- -, Factoring polynomials over large finite fields, Math. Comp. 24 (1970), 713-735. MR 0276200 (43:1948)
- [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]
- G. Collins, Factoring univariate integral polynomials in polynomial average time, Symbolic and Algebraic Computation, Lecture Notes in Comput. Sci., vol. 72, Springer, New York, 1969, pp. 317-329. MR 575695 (81g:68064)
- [CZ]
- D. Cantor and H. Zassenhaus, A new algorithm for factoring polynomials over finite fields, Math. Comp. 36 (1981), 587-592. MR 606517 (82e:12020)
- [JT]
- M. A. Jenkins and J. F. Traub, A three-stage variable shift iteration for polynomial zeroes and its relation to generalized Rayleigh iteration, Numer. Math. 14 (1970), 252-263. MR 0258271 (41:2918)
- [K]
- D. E. Knuth, The art of computer programming, Vol. 2, Seminumerical algorithms, 2nd ed., Addison-Wesley, Reading, MA, 1981. MR 633878 (83i:68003)
- [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, and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982), 515-534. MR 682664 (84a:12002)
- [M]
- M. Mignotte, An inequality about factors of polynomials, Math. Comp. 28 (1974), 1153-1157. MR 0354624 (50:7102)
- [P]
- C. Pomerance, Analysis and comparison of some integer factoring algorithms, Computational Methods in Number Theory, Part I (H. W. Lenstra and R. Tijdeman, eds.), Math. Centre Tracts 154/155, Math. Centrum, Amsterdam, 1982. MR 700260 (84i:10005)
- [Z1]
- H. Zassenhaus, On Hensel factorization. I, J. Number Theory 1 (1969), 291-311. MR 0242793 (39:4120)
- [Z2]
- -, A remark on the Hensel factorization method, Math. Comp. 32 (1978), 287-292. MR 0476692 (57:16251)
Additional Information:
Reviewer(s):
Hale
Trotter
Review Information:
Journal:
Bull. Amer. Math. Soc.
31
(1994),
312-318.
DOI:
10.1090/S0273-0979-1994-00542-7
PII:
S 0273-0979(1994)00542-7
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