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

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 Llog(a+1).

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 Llog(a+1).

@article{JTNB_2008__20_3_543_0,
     author = {Allombert, Bill and Belabas, Karim},
     title = {Practical Aurifeuillian factorization},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {543--553},
     publisher = {Universit\'e Bordeaux 1},
     volume = {20},
     number = {3},
     year = {2008},
     doi = {10.5802/jtnb.641},
     mrnumber = {2523308},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/jtnb.641/}
}
Allombert, Bill; Belabas, Karim. Practical Aurifeuillian factorization. Journal de Théorie des Nombres de Bordeaux, Tome 20 (2008) no. 3, pp. 543-553. doi : 10.5802/jtnb.641. http://archive.numdam.org/articles/10.5802/jtnb.641/

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