Download Algorithmes paralleles pour le calcul formel: algebre by Dumas J.-G. PDF

By Dumas J.-G.

Summary: In each fi eld of scientifi с and commercial study, the extension of using desktop technological know-how has led to an expanding desire for computing energy. it really is therefore very important to exploit those computing assets in parallel. during this thesis we search to compute the canonical kind of very huge sparse matrices with integer coeffi cients, particularly the integer Smith general shape. by means of 'Very large'', we suggest 1000000 indeterminates and one million equations, i.e. thousand billion of coeffi cients. these days, such structures aren't even storable. besides the fact that, we're drawn to structures for which lots of those coeffi cients are exact; for that reason we discuss sparse structures. we wish to resolve those structures in a precise manner, i.e. we paintings with integers or in smaller algebraic buildings the place the entire uncomplicated mathematics operations are nonetheless legitimate, particularly fi nitefi elds. The rebuilding of the entire answer from the smaller strategies is then fairly effortless.

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Extra resources for Algorithmes paralleles pour le calcul formel: algebre lineaire creuse et extensions algebriques

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1 : Si et ✁ Oui, si ✁ ✁ ✕ ✗. ✁✡✂☛☎✞✝ ✟ ☞ irréductible de degré ✠ ✕ ✗. dans ✁✡✂ ☎✞✝ ✟ ☞ est générateur de l’extension ✁✄✂✆☎✞✝ ✟ [X]✒ F ; Non dans le cas ✓ Faire ne sont pas premiers entre eux Alors Renvoyer “Non”. ☞ 2 : Pour tout , premier et divisant ✝ ☞ ✞ ✏ ✠ ✑✔✓✖✕ ✗ Alors Renvoyer “Non”. {Factorisation de ✝ ☞ ✞ ✓} ✞✄✂✡✟ Si 3 : ✁ {Calcul récursif par carrés} 4 : Renvoyer “Oui”. Un algorithme cherchant au hasard un générateur, une fois le corps construit, est alors aisé. En outre, V. Shoup [151 - Shoup (1992), Théorème 1] a montré que l’on peut restreindre l’ensemble de recherche à des polynômes de faible degré ✝ ( ☎ ☎ ☎ ✡ ✡ ).

1 – Comparaison de différents langages de programmation parallèle de « haut niveau » [65 - Galilée (1999)] Enfin, le parallélisme peut être de type « série-parallèle » si les synchronisations entre les tâches sont effectuées par fratrie : la tâche mère est seule capable de synchroniser ses filles, et cette synchronisation est globale sur l’ensemble des filles créées. Par exemple, une tâche créant du parallélisme à l’aide d’une séquence est bloquée jusqu’à la terminaison du calcul de tous les éléments de la séquence.

Pour expliquer ces fonctionnalités, nous proposons un exemple, l’élimination de Gauß sur matrice dense, stockée par lignes . 2 É LIMINATION DE G AUSS AVEC ATHAPASCAN -1 Nous donnons ici à titre d’exemple le code Athapascan-1 pour l’élimination de Gauß exacte sur une matrice dense, a priori non inversible. 1 Élimination de Gauß avec Athapascan-1 1 5 struct SearchPivot { // pivot_row : la ligne de recherche // i : le numéro de ligne courante // rank : le rang actuel // permutation : indique l’indice du prochain pivot void operator() (Shared_r > pivot_row, int i, int n_col, Shared_cw rank, Shared_w permutation) { // recherche un élément non nul dans la ligne // ajoute 1 au rang si un élément non nul est trouvé // indique l’emplacement de ce pivot.

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