Fast arithmetic for the algebraic closure of finite fields

Abstract : We present algorithms to construct and do arithmetic operations in the algebraic closure of the finite field Fp. Our approach is inspired by algorithms for constructing irreducible polynomials, which first reduce to prime power degrees, then use composita techniques. We use similar ideas to give efficient algorithms for embeddings and isomorphisms. Copyright is held by the owner/author(s).
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Submitted on : Monday, July 8, 2019 - 5:15:23 PM
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L. de Feo, J. Doliskani, É. Schost. Fast arithmetic for the algebraic closure of finite fields. 2014 39th International Symposium on Symbolic and Algebraic Computation, ISSAC 2014, Jul 2014, kobe, Japan. pp.122-129, ⟨10.1145/2608628.2608672⟩. ⟨hal-02177228⟩

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