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Approximate factorization of multivariate polynomials and absolute irreducibility testing

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Abstract

A concept of approximate factorization of multivariate polynomial is introduced and an algorithm for approximate factorization is presented. The algorithm handles polynomials with complex coefficients represented approximately, hence it can be used to test the absolute irreducibility of multivariate polynomials. The algorithm works as follows: given a monic square-free polynomialF(x,y,…,z), it calculates the roots ofF(x,y o , ...,z 0) numerically, wherey o, … z0 are suitably chosen numbers, then it constructs power series F1, …, Fn such thatF(x,y, …, z) ∈F1 (x,y., ...,z)...F n (x,y, ...z) (mod Se+2), where n=degx (F),S=(y-y 0, ...,z-z 0), ande=max{degy(F), …, degx (F)}; finally it finds the approximate divisors ofF as products of elements of {F 1, …,F n}.

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Authors and Affiliations

  1. RIKEN (Institute of Physical and Chemical Research), Wako-shi, 351-01, Saitama, Japan

    Tateaki Sasaki, Masayuki Suzuki, Miroslav Kolár & Mutsuko Sasaki

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  1. Tateaki Sasaki
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  2. Masayuki Suzuki
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  3. Miroslav Kolár
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  4. Mutsuko Sasaki
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Sasaki, T., Suzuki, M., Kolár, M. et al. Approximate factorization of multivariate polynomials and absolute irreducibility testing. Japan J. Indust. Appl. Math. 8, 357–375 (1991). https://doi.org/10.1007/BF03167142

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  • DOI: https://doi.org/10.1007/BF03167142

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