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By Fallah F

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5 NTL . . . . . . . . . . . 6 Performances et surcoˆ ut des wrappers . . 3 Extension alg´ ebrique GF (pk ) . . . . . 1 Givaro . . . . . . . . . . . 2 NTL . . . . . . . . . . . 3 LiDIA . . . . . . . . . . . 4 Performances et surcoˆ ut des wrappers . . 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28 29 31 34 38 45 45 48 48 50 51 53 59 59 60 61 63 65 28 Arithm´etique des corps finis L’algorithmique en calcul exact et plus particuli`erement en alg`ebre lin´eaire n´ecessite des calculs sur de tr`es grands entiers.

4 Performances vs g´ en´ ericit´ es L’utilisation de l’arch´etype pour l’instanciation d’un corps fini entraˆıne un surcoˆ ut dˆ u `a la manipulation abstraite des objets et des fonctions. 1. Arch´etype de donn´ees 39 a` quantifier ces diff´erents surcoˆ uts et `a observer les diff´erents impacts sur les implantations concr`etes. Nous effectuons nos tests `a la fois pour une architecture 32 bits (Pentium III 1Ghz, 512 Mo RAM) et pour une architecture 64 bits (Itanium I 733 Mhz, 1Go RAM). 3 pour l’Itanium avec dans les deux cas l’option -O3.

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Algorithm for factorization of logic expressions by Fallah F


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