Factoring polynomials over global fields

Karim Belabas; Mark van Hoeij; Jürgen Klüners; Allan Steel

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Displaying similar documents to “Factoring polynomials over global fields”

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The main contribution of this work is to provide an algorithm for the computation of the GCD of 2-D polynomials, based on DFT techniques. The whole theory is implemented via illustrative examples.

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We describe a simple procedure to find Aurifeuillian factors of values of cyclotomic polynomials $Φ_{d} (a)$ for integers $a$ and $d > 0$ . Assuming a suitable Riemann Hypothesis, the algorithm runs in deterministic time $\tilde{O} (d^{2} L)$ , using $O (d L)$ space, where $L ≔ log (|a| + 1)$ .

On Garcia numbers.

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