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PARALLEL COMPUTATION OF LAGRANGE RESOLVENTS BY MULTI-RESOLVENTS

Annotation

The goal of this paper is the parallel computation of Lagrange resolvents of a univariate polynomial. The computation of Lagrange resolvents of a univariate polynomial has significance for Galois Theory. Since Lagrange's algorithms, many other algorithms for computing some particular resolvents, called absolute, were developed from the fundamental theorem of symmetric functions. The algebraic algorithms for non absolute resolvents are few and recent because they use galoisian ideals that were introduced recently. However these algorithms become time and space consuming when the degree of the polynomial increases. This motivates their parallelization. Rennert proposed a multi-modular method for computing absolute resolvents of polynomials with integer coefficients. We show that the same techniques can be extended to any resolvent. This method is naturally parallelizable. Moreover, we give a decomposition formula of resolvents which makes possible another level of parallelization. This leads to an algorithm with a doubly parallel character.

Keywords

Lagrange resolvent; Galois group; galoisian ideal; triangular ideal; double class; parallel computation

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UDC

519.688

Pages

1328-1341

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