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Effective Hilbert irreducibility

  • Pactorization And GCD Computations
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EUROSAM 84 (EUROSAM 1984)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 174))

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References

  1. Berlekamp, E.R.: Factoring Polynomials over Large Finite Fields. Math. Comp. 24, 713–735 (1970).

    Google Scholar 

  2. Chistov, A.L., Grigoryev, D.Y.: Polynomial-Time Factoring of Multivariate Polynomials over a Global Field. Lomi preprint E-5-82, Leningrad 1982.

    Google Scholar 

  3. Dörge, K.: Zum Hilbertschen Irreduzibilitätssatz. Mathematische Annalen 95, 84–97 (1926).

    Google Scholar 

  4. von zur Gathen, J.: Factoring Sparse Multivariate Polynomials. Proceedings 1983 IEEE Symposium on Foundations of Computer Science, 172–179.

    Google Scholar 

  5. von zur Gathen, J., Kaltofen, E.: A Polynomial-Time Algorithm for Factoring Multivariate Polynomials Over Finite Fields. Proc. 1983 Internat. Conf. Automata, Languages and Programming. Springer Lec. Notes Comp. Sci. 154, 250–263.

    Google Scholar 

  6. Heintz, J., Sieveking, M.: Absolute Primality of Polynomials is Decidable in Random Polynomial Time in the Number of Variables. Proc. 1981 Internat. Conf. Automata, Languages and Programming. Springer Lec. Notes Comp. Sci. 115, 16–28.

    Google Scholar 

  7. Kaltofen, E.: A Polynomial Reduction from Multivariate to Bivariate Integer Polynomial Factorization. Proc. 1982 ACM Symp. Theory Comp., 261–266.

    Google Scholar 

  8. Kaltofen, E.: A Polynomial-Time Reduction from Bivariate to Univariate Integral Polynomial Factorization. Proceedings 23rd Symposium on Foundations of Computer Science. IEEE, 57–64 (1982).

    Google Scholar 

  9. Kaltofen, E.: Polynomial-Time Reductions from Multivariate to Bi-and Univariate Integral Polynomial Factorization. SIAM J. Comp., in press.

    Google Scholar 

  10. Landau, S.: Factoring Polynomials over Algebraic Number Fields is in Polynomial Time. SIAM J. Comp., to appear.

    Google Scholar 

  11. Lenstra, A.K.: Factoring Polynomials over Algebraic Number Fields. Manuscript 1982.

    Google Scholar 

  12. Lenstra, A.K.: Factoring Multivariate Polynomials over a Finite Field. Proc. 1983 ACM Symp. Theory Comp., 189–192.

    Google Scholar 

  13. Lenstra, A.K.: Factoring Multivariate Integral Polynomials. Proc. 1983 Internat. Conf. Automata, Languages and Programming. Springer Lec. Notes Comp. Sci. 154, 189–192.

    Google Scholar 

  14. Lenstra, A.K.: Factoring Multivariate Polynomials over Algebraic Number Fields. Manuscript 1983.

    Google Scholar 

  15. Lenstra, A. K., Lenstra, H. W., Lovász, L.: Factoring Polynomials with Rational Coefficients. Math. Ann. 261, 515–534 (1982).

    Google Scholar 

  16. Schönhage, A.: Factorization of Univariate Integer Polynomials by Diophantine Approximation and by an Improved Reduction Algorithm. Manuscript 1983.

    Google Scholar 

  17. Schwartz, J.T.: Fast Probabilistic Algorithms for Verification of Polynomial Identities. J. ACM 27, 701–717 (1980).

    Google Scholar 

  18. Zippel, R. E.: Newton's Iteration and the Sparse Hensel Algorithm. Proc. 1981 ACM Symp. Symbolic Alg. Comp., 68–72.

    Google Scholar 

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Author notes

  1. Erich Kaltofen

    Present address: Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 12181, Troy, New York

Authors and Affiliations

  1. Department of Computer Science, University of Toronto, M5S1A4, Toronto, Ontario, Canada

    Erich Kaltofen

Authors
  1. Erich Kaltofen
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John Fitch

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© 1984 Springer-Verlag Berlin Heidelberg

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Kaltofen, E. (1984). Effective Hilbert irreducibility. In: Fitch, J. (eds) EUROSAM 84. EUROSAM 1984. Lecture Notes in Computer Science, vol 174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032850

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  • DOI: https://doi.org/10.1007/BFb0032850

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13350-6

  • Online ISBN: 978-3-540-38893-7

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