Practical Aurifeuillian factorization
Journal de Théorie des Nombres de Bordeaux, Volume 20 (2008) no. 3, pp. 543-553.

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 O ˜(d 2 L), using O(dL) space, where L≔log(a+1).

Nous décrivons un algorithme simple pour déterminer les facteurs d’Aurifeuille des entiers Φ d (a), où Φ d est le d-ème polynôme cyclotomique, et a un entier. Sous une hypothèse de Riemann convenable, l’algorithme termine en temps polynomial déterministe O ˜(d 2 L), utilisant un espace O(dL), où l’on a noté L≔log(a+1).

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DOI: 10.5802/jtnb.641 
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Bill Allombert; Karim Belabas. Practical Aurifeuillian factorization. Journal de Théorie des Nombres de Bordeaux, Volume 20 (2008) no. 3, pp. 543-553. doi : 10.5802/jtnb.641. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.641/

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