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Factoring polynomials with rational coefficients

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References

  1. Adleman, L.M., Odlyzko, A.M.: Irreducibility testing and factorization of polynomials, to appear. Extended abstract: Proc. 22nd Annual IEEE Symp. Found. Comp. Sci., pp. 409–418 (1981)

  2. Brentjes, A.J.: Multi-dimensional continued fraction algorithms. Mathematical Centre Tracts 145. Amsterdam: Mathematisch Centrum 1981

    Google Scholar 

  3. Cantor, D.G.: Irreducible polynomials with integral coefficients have succinct certificates. J. Algorithms2, 385–392 (1981)

    Article  Google Scholar 

  4. Cassels, J.W.S.: An introduction to the geometry of numbers. Berlin, Heidelberg, New York: Springer 1971

    Google Scholar 

  5. Ferguson, H.R.P., Forcade, R.W.: Generalization of the Euclidean algorithm for real numbers to all dimensions higher than two. Bull. Am. Math. Soc.1, 912–914 (1979)

    Google Scholar 

  6. Hardy, G.H., Wright, E.M.: An introduction to the theory of numbers. Oxford: Oxford University Press 1979

    Google Scholar 

  7. Knuth, D.E.: The art of computer programming, Vol. 2, Seminumerical algorithms. Reading: Addison-Wesley 1981

    Google Scholar 

  8. Lenstra, A.K.: Lattices and factorization of polynomials, Report IW 190/81. Amsterdam: Mathematisch Centrum 1981

    Google Scholar 

  9. Lenstra, H.W., Jr.: Integer programming with a fixed number of variables. Math. Oper. Res. (to appear)

  10. Mignotte, M.: An inequality about factors of polynomials. Math. Comp.28, 1153–1157 (1974)

    Google Scholar 

  11. Pritchard, P.: A sublinear additive sieve for finding prime numbers. Comm. ACM24, 18–23 (1981)

    Google Scholar 

  12. Barkley Rosser, J., Schoenfeld, L.: Approximate formulas for some functions of prime numbers. Ill. J. Math.6, 64–94 (1962)

    Google Scholar 

  13. Yun, D.Y.Y.: The Hensel lemma in algebraic manipulation. Cambridge: MIT 1974; reprint: New York: Garland 1980

    Google Scholar 

  14. Zassenhaus, H.: On Hensel factorization. I. J. Number. Theory1, 291–311 (1969)

    Google Scholar 

  15. Zassenhaus, H.: A remark on the Hensel factorization method. Math. Comp.32, 287–292 (1978)

    Google Scholar 

  16. Zassenhaus, H.: A new polynomial factorization algorithm (unpublished manuscript, 1981)

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Lenstra, A.K., Lenstra, H.W. & Lovász, L. Factoring polynomials with rational coefficients. Math. Ann. 261, 515–534 (1982). https://doi.org/10.1007/BF01457454

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