Displaying similar documents to “Integral minimalisations improvement for Murphy's polynomial selection algorithm.”

A polynomial reduction algorithm

Henri Cohen, Francisco Diaz Y Diaz (1991)

Journal de théorie des nombres de Bordeaux


The algorithm described in this paper is a practical approach to the problem of giving, for each number field K a polynomial, as canonical as possible, a root of which is a primitive element of the extension K / . Our algorithm uses the L L L algorithm to find a basis of minimal vectors for the lattice of n determined by the integers of K under the canonical map.

Improvements on the Cantor-Zassenhaus factorization algorithm

Michele Elia, Davide Schipani (2015)

Mathematica Bohemica


The paper presents a careful analysis of the Cantor-Zassenhaus polynomial factorization algorithm, thus obtaining tight bounds on the performances, and proposing useful improvements. In particular, a new simplified version of this algorithm is described, which entails a lower computational cost. The key point is to use linear test polynomials, which not only reduce the computational burden, but can also provide good estimates and deterministic bounds of the number of operations needed...

A unified approach to some strategies for the treatment of breakdown in Lanczos-type algorithms

A. El Guennouni (1999)

Applicationes Mathematicae


The Lanczos method for solving systems of linear equations is implemented by using some recurrence relationships between polynomials of a family of formal orthogonal polynomials or between those of two adjacent families of formal orthogonal polynomials. A division by zero can occur in these relations, thus producing a breakdown in the algorithm which has to be stopped. In this paper, three strategies to avoid this drawback are discussed: the MRZ and its variants, the normalized and unnormalized...