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Factoring multivariate polynomials over the integers. (English) Zbl 0311.10052

MSC:
11C08 Polynomials in number theory
11A41 Primes
12D05 Polynomials in real and complex fields: factorization
Software:
MACSYMA
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References:
[1] E. R. Berlekamp, Factoring polynomials over finite fields, Bell System Tech. J. 46 (1967), 1853 – 1859. · Zbl 0166.04901
[2] E. R. Berlekamp, Factoring polynomials over large finite fields, Math. Comp. 24 (1970), 713 – 735. · Zbl 0247.12014
[3] W. S. Brown, On Euclid’s algorithm and the computation of polynomial greatest common divisors, J. Assoc. Comput. Mach. 18 (1971), 478 – 504. · Zbl 0226.65040
[4] G. E. COLLINS, SAC-1 Modular Arithmetic System, University of Wisconsin Technical Report No. 10, June 1969.
[5] A. O. Gel\(^{\prime}\)fond, Transcendental and algebraic numbers, Translated from the first Russian edition by Leo F. Boron, Dover Publications, Inc., New York, 1960.
[6] Donald E. Knuth, The art of computer programming. Vol. 2: Seminumerical algorithms, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont, 1969. · Zbl 0191.18001
[7] J. McCARTHY et al., LISP 1.5 Programmer’s Manual, M.I.T. Press, Cambridge, Mass., 1963.
[8] J. MOSES & D. Y. Y. YUN, ”The EZ GCD algorithm,” Proceedings of ACM Annual Conference, August 1973.
[9] D. R. MUSSER, Algorithms for Polynomial Factorization, Ph. D. Thesis, Computer Science Department, The University of Wisconsin, Madison, Wis., 1971.
[10] B. L. VAN DER WAERDEN, Modern Algebra. Vol. 1, Springer, Berlin, 1930; English transl., Ungar, New York, 1949. MR 10, 587. · JFM 56.0138.01
[11] D. Y. Y. YUN, The Hensel Lemma in Algebraic Manipulation, Ph. D. Thesis, Department of Mathematics, M.I.T., Nov. 1973 (also Project MAC TR-138, November 1974).
[12] Hans Zassenhaus, On Hensel factorization. I, J. Number Theory 1 (1969), 291 – 311. · Zbl 0188.33703
[13] MACSYMA Reference Manual, the MATHLAB group, Project MAC, M.I.T., Cambridge, Mass., Sept. 1974.
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