Download Arithmetique et algorithmique en algebre lineaire exacte by Pascal G. PDF

By Pascal G.

Summary: For a number of many years, numerical linear algebra has visible extensive advancements in either mathematical and computing device technology thought that have ended in real ordinary software program like BLAS or lapack. In laptop algebra the placement has no longer complex as a lot, specifically due to the range of the issues and thanks to a lot of the theoretical development were performed lately. This thesis falls right into a contemporary category of labor which goals at uniforming high-performance codes from many really expert libraries right into a unmarried platform of computation. particularly, the emergence of strong and transportable libraries like GMP or ntl for precise computation has grew to become out to be a true asset for the advance of purposes in specified linear algebra. during this thesis, we examine the feasibility and the relevance of the re-use of specialised codes to enhance a excessive functionality targeted linear algebra library, specifically the LinBox library. We use the regular programming mechanisms of C++ (abstract classification, template type) to supply an abstraction of the mathematical items and therefore to permit the plugin of exterior parts. Our goal is then to layout and validate, in LinBox. excessive point usual toolboxes for the implementation of algorithms in designated linear algebra. particularly, we suggest ''exact/numeric'' hybrid computation workouts for dense matrices over finite fields which almost fit with the functionality acquired through numerical libraries like LAPACK. On a better point, we reuse those hybrid workouts to unravel very successfully a classical challenge of desktop algebra : fixing diophantine linear structures. therefore, this allowed us to validate the primary of code reuse in LinBox library and extra typically in machine algebra. The LinBox library is accessible at www.linalg.org.

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4 Performances vs g´en´ericit´es . . . . . 2 Corps finis premiers . . . . . . . 1 Modular . . . . . . . . . . 2 GivaroZpz standard . . . . . . . 4 GivaroZpz : base de Montgomery . . . 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 .

L’instanciation de ce pointeur par un objet d´eriv´e de l’interface abstraite permet donc de fixer le polymorphisme dynamique de l’interface. L’utilisation de l’enveloppe pour instancier ce pointeur permet d’assurer le bon comportement des allocations m´emoire pour toutes les implantations de corps finis. function();} }; Fig. 3 – Code pour une interface abstraite compilable. Nous nous int´eressons maintenant aux d´etails d’implantation de l’arch´etype de donn´ees des corps finis. 3 d´ecrit les diff´erents m´ecanismes C++ utilis´es pour obtenir une interface de donn´ees compilable.

L’objectif de la biblioth`eque LinBox est de proposer un moyen simple et efficace pour configurer `a la demande les implantations d’algorithmes en fonction des corps finis, aussi bien dans des codes compil´es que dans des codes interpr´et´es. L’int´erˆet est de pouvoir r´eutiliser des corps finis provenant de biblioth`eques externes sans avoir `a r´ecrire l’ensemble de la biblioth`eque, et `a plus long terme, de b´en´eficier des ´evolutions futures en arithm´etique des corps finis. L’utilisation de biblioth`eques externes permet de b´en´eficier de corps finis performants sans avoir `a r´e´ecrire leurs implantations.

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