Book Review
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MathSciNet review:
1568145
Full text of review:
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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.
E. R. Berlekamp, Factoring polynomials over finite fields, Bell System Tech. J. 46 (1967), 1853–1859. MR 219231, DOI 10.1002/j.1538-7305.1967.tb03174.x
E. R. Berlekamp, Factoring polynomials over large finite fields, Math. Comp. 24 (1970), 713–735. MR 276200, DOI 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.
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
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, DOI 10.1090/S0025-5718-1981-0606517-5
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, DOI 10.1007/BF02163334
Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms. 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.
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, DOI 10.1007/BF01457454
M. Mignotte, An inequality about factors of polynomials, Math. Comp. 28 (1974), 1153–1157. MR 354624, DOI 10.1090/S0025-5718-1974-0354624-3
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
Hans Zassenhaus, On Hensel factorization. I, J. Number Theory 1 (1969), 291–311. MR 242793, DOI 10.1016/0022-314X(69)90047-X
Hans Zassenhaus, A remark on the Hensel factorization method, Math. Comp. 32 (1978), no. 141, 287–292. MR 476692, DOI 10.1090/S0025-5718-1978-0476692-4
- [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)
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
