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An efficient algorithm for factoring polynomials over algebraic extension field

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Abstract

An efficient algorithm is proposed for factoring polynomials over an algebraic extension field defined by a polynomial ring modulo a maximal ideal. If the maximal ideal is given by its Gröbner basis, no extra Gröbner basis computation is needed for factoring a polynomial over this extension field. Nothing more than linear algebraic technique is used to get a characteristic polynomial of a generic linear map. Then this polynomial is factorized over the ground field. From its factors, the factorization of the polynomial over the extension field is obtained. The algorithm has been implemented in Magma and computer experiments indicate that it is very efficient, particularly for complicated examples.

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Authors and Affiliations

  1. SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Yao Sun

  2. KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Yao Sun & DingKang Wang

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  1. Yao Sun
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  2. DingKang Wang
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Correspondence to DingKang Wang.

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Sun, Y., Wang, D. An efficient algorithm for factoring polynomials over algebraic extension field. Sci. China Math. 56, 1155–1168 (2013). https://doi.org/10.1007/s11425-013-4586-0

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  • DOI: https://doi.org/10.1007/s11425-013-4586-0

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