### Integral minimalisations improvement for Murphy's polynomial selection algorithm.

Jedlička, Přemysl (2010)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Jedlička, Přemysl (2010)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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We present an algorithm that returns a proper factor of a polynomial $\Phi \left(x\right)$ over the $p$-adic integers ${\mathbb{Z}}_{p}$ (if $\Phi \left(x\right)$ is reducible over ${\mathbb{Q}}_{p}$) or returns a power basis of the ring of integers of ${\mathbb{Q}}_{p}\left[x\right]/\Phi \left(x\right){\mathbb{Q}}_{p}\left[x\right]$ (if $\Phi \left(x\right)$ is irreducible over ${\mathbb{Q}}_{p}$). 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.

Michele Elia, Davide Schipani (2015)

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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...

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