Abstract
In this paper we present algorithmic considerations and theoretical results about the relation between the orders of certain groups associated to the components of a polynomial and the order of the group that corresponds to the polynomial, proving it for arbitrary tame polynomials, and considering the case of rational functions.
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References
Alonso, C., Gutierrez, J., Recio, T.: A rational function decomposition algorithm by near-separated polynomials. J. Symbolic Comput. 19(6), 527–544 (1995)
Beardon, A.F., Ng, T.W.: On Ritt’s factorization of polynomials. J. London Math. Soc. (2) 62(1), 127–138 (2000)
Cade, J.: A new public-key cipher which allows signatures. In: Proc. 2nd SIAM Conf. on Appl. Linear Algebra, Raleigh NC (1985)
Casperson, D., Ford, D., McKay, J.: An ideal decomposition Algorithm. J. Symbolic Comput. 21(2), 133–137 (1996)
von zur Gathen, J.: Functional decomposition of polynomials: the tame case. J. Symbolic Comput. 9(3), 281–299 (1990)
von zur Gathen, J.: Functional decomposition of polynomials: the wild case. J. Symbolic Comput. 10(5), 437–452 (1990)
Gutierrez, J.: A polynomial decomposition algorithm over factorial domains. C. R. Math. Rep. Acad. Sci. Canada 13(2-3), 81–86 (1991)
Gutierrez, J., Recio, T., Ruiz de Velasco, C.: A polynomial decomposition algorithm of almost quadratic complexity. In: Mora, T. (ed.) AAECC 1988. LNCS, vol. 357, pp. 471–476. Springer, Heidelberg (1989)
Gutierrez, J., Rubio, R.: CADECOM: Computer Algebra software for functional DECOMposition. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds.) Proceedings of the Second Workshop on Computer Algebra in Scientific Computing, Samarkand, Uzbekistan, pp. 233–248. Springer, Heidelberg (2000)
Gutierrez, J., Rubio, R., Sevilla, D.: On Multivariate Rational Function Decomposition. J. Symbolic Comput. 33(5), 545–562 (2002)
Gutierrez, J., Rubio, R., von zur Gathen, J.: Multivariate Polynomial decomposition. Applicable Algebra in Engineering, Communication and Computing 14(1), 11–31 (2003)
Gutierrez, J., Sevilla, D.: On Ritt’s decomposition Theorem in the case of finite fields. Finite Fields and Their Applications 12(3), 403–412 (2006)
Kozen, D., Landau, S.: Polynomial decomposition algorithms. J. Symbolic Comput. 7(5), 445–456 (1989)
Nagata, M.: Theory of Commutative Fields. Translations of Mathematical Monographs, Amer. Math. Soc. 125 (1993)
Netto, E.: Ünber einen Lüroth-Gordaschen Satz. Math. Ann. 9, 310–318 (1895)
Schinzel, A.: Selected Topics on Polynomials. University Michigan Press, Ann Arbor (1982)
Schinzel, A.: Polynomials with special regard to reducibility. Cambridge University Press, New York (2000)
Zippel, R.: Rational Function Decomposition. In: Proc. ISSAC 1991, pp. 1–6. ACM Press, New York (1991)
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Gutierrez, J., Sevilla, D. (2006). On Decomposition of Tame Polynomials and Rational Functions. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2006. Lecture Notes in Computer Science, vol 4194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11870814_18
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DOI: https://doi.org/10.1007/11870814_18
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