Displaying similar documents to “Complexity bound of absolute factoring of parametric polynomials.”

Improvements on the Cantor-Zassenhaus factorization algorithm

Michele Elia, Davide Schipani (2015)

Mathematica Bohemica

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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 polynomial reduction algorithm

Henri Cohen, Francisco Diaz Y Diaz (1991)

Journal de théorie des nombres de Bordeaux

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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.

Some Algebraic Properties of Polynomial Rings

Christoph Schwarzweller, Artur Korniłowicz (2016)

Formalized Mathematics

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In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based on [2], [3]. After introducing constant and monic polynomials we present the canonical embedding of R into R[X] and deal with both unit and irreducible elements. We also define polynomial GCDs and show that for fields F and irreducible polynomials p the field F[X]/ is isomorphic to the field of polynomials with degree smaller than the one of p.

Subresultant Polynomial Remainder Sequences Obtained by Polynomial Divisions in Q[x] or in Z[x]

Akritas, Alkiviadis G., Malaschonok, Gennadi I., Vigklas, Panagiotis S. (2016)

Serdica Journal of Computing

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In this paper we present two new methods for computing the subresultant polynomial remainder sequence (prs) of two polynomials f, g ∈ Z[x]. We are now able to also correctly compute the Euclidean and modified Euclidean prs of f, g by using either of the functions employed by our methods to compute the remainder polynomials. Another innovation is that we are able to obtain subresultant prs’s in Z[x] by employing the function rem(f, g, x) to compute the remainder polynomials in [x]. This...

A fast algorithm for polynomial factorization over p

David Ford, Sebastian Pauli, Xavier-François Roblot (2002)

Journal de théorie des nombres de Bordeaux

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We present an algorithm that returns a proper factor of a polynomial Φ ( x ) over the p -adic integers p (if Φ ( x ) is reducible over p ) or returns a power basis of the ring of integers of p [ x ] / Φ ( x ) p [ x ] (if Φ ( x ) is irreducible over p ). Our algorithm is based on the Round Four maximal order algorithm. Experimental results show that the new algorithm is considerably faster than the Round Four algorithm.