Practical Aurifeuillian factorization

Bill Allombert; Karim Belabas

doi:10.5802/jtnb.641

Bill Allombert ; Karim Belabas

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

Résumé
Abstract

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 $\tilde{O} (d^{2} L)$ , utilisant un espace $O (d L)$ , où l’on a noté $L ≔ log (|a| + 1)$ .

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 $\tilde{O} (d^{2} L)$ , using $O (d L)$ space, where $L ≔ log (|a| + 1)$ .

Reçu le : 2008-03-21
Publié le : 2009-06-04

MR 2523308 | Zbl pre05572692

DOI : https://doi.org/10.5802/jtnb.641

@article{JTNB_2008__20_3_543_0,
     author = {Bill Allombert and Karim Belabas},
     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},
     zbl = {pre05572692},
     mrnumber = {2523308},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.641/}
}

Bill Allombert; Karim Belabas. Practical Aurifeuillian factorization. Journal de Théorie des Nombres de Bordeaux, Tome 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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