P. , A. Des, and . Finis, efficacité en pratique de cette méthode, nous l'avons appliquée à un problème de la théorie des graphes que nous rappelons dans la partie 12.3.1. Nous donnons ensuite les résultats expérimentaux dans la partie 12.3.2. 12.3. APPLICATION ET EXPÉRIMENTATIONS égaux (voir [12] à ce sujet) En testant si le degré du polynôme minimal calculé est égal à n, on a un certificat du résultat. Ainsi, l'algorithme est probabiliste du type Las-Vegas : le résultat retourné est toujours correct, mais plusieurs calculs peuvent être nécessaires. L'implémentation de l'algorithme de Wiedemann est spécialisée pour les matrices symétriques, ce qui permet d'économiser la moitié des produits matrice-vecteurs. De plus les matrices sont représentées par des boîtes noires dont le produit matrice-vecteur tient compte du fait que les coefficients sont dans l'ensemble {0, 1}. Le test des 3854 matrices de paramètre, APPLICATION ET EXPÉRIMENTATIONS 12.3 Application et expérimentations Pour illustrer l) a été effectué en 131,35 heures CPU d'un Itanium2 cadencé à 1,5Ghz (soit 16h25 effectives sur les 8 processeurs). Pour toutes les matrices A i , nous avons calculé det

. De-la-même-façon, le test des 32 548 matrices de paramètres (36, 15, 6, 6) a été effectué en 588 heures : après un premier calcul des det(A + 1234547I) mod 67 108 859, il restait 12 paires identiques et le calcul de det(A + 1234543I) mod 67 108 819 les a toutes

. Dans-nos-algorithmes-boîte-noire, nous avons utilisé la remontée de Hensel pour la factorisation en polynômes irréductibles du polynôme minimal, pour des raisons de simplicité de mise en oeuvre. Il est pourtant préférable de cantonner cette remontée à une base pgcd-libre décrivant le polynôme minimal et le polynôme caractéristique, comme l'a montré Storjohann

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