Factoring skew polynomials over Hamilton's quaternion algebra and the complex numbers

Factoring Rational Polynomials Over the Complex Numbers

NC algorithms are given for determining the number and degrees of the factors, irreducible over the complex numbers C, of a multivariate polynomial with rational coeÆcients and for approximating each irreducible factor. NC is the class of functions computable by logspace-uniform boolean circuits of polynomial size and polylogarithmic depth. The measures of size of the input polynomial are its d...

Matrix Theory over the Complex Quaternion Algebra

We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex quaternion matrices, and so on. AMS Mathematics Subject Classification: 15A06; 15A24; 15A33

Factoring Polynomials over Local Fields

Factoring Polynomials over Number Fields

The purpose of these notes is to give a substantially self-contained introduction to the factorization of polynomials over number fields. In particular, we present Zassenhaus’ algorithm and a factoring algorithm using lattice reduction, which were, respectively, the best in practice and in theory, before 2002. We give references for the van Hoeij-Novocin algorithm, currently the best both in pr...

Factoring Polynomials over Local Fields