The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

Single scale quantities, as anomalous dimensions and hard scattering cross sections, in
renormalizable Quantum Field Theories are found to obey difference equations of finite …

We speed up existing decoding algorithms for three code classes in different metrics:
interleaved Gabidulin codes in the rank metric, lifted interleaved Gabidulin codes in the …

This is an overview over standard techniques for holonomic functions, written for readers
who are new to the subject. We state the definition for holonomy in a couple of different …

Given a nonsingular n× n matrix of univariate polynomials over a field K, we give fast and
deterministic algorithms to compute its determinant and its Hermite normal form. Our …

In this paper we give formulas for performing row reduction of a matrix of Ore polynomials in
a fraction-free way. The reductions can be used for finding the rank and left nullspace of …

Le calcul formel traite des objets mathématiques exacts d'un point de vue informatique. Cet
ouvrage «Algorithmes efficaces en calcul formel» explore deux directions: la calculabilité et …

We consider the problem of computing univariate polynomial matrices over a field that
represent minimal solution bases for a general interpolation problem, some forms of which …

We present an algorithm for the computation of a shifted Popov normal form of a rectangular
polynomial matrix. For specific input shifts, we obtain methods for computing the matrix …

Linear systems with structures such as Toeplitz, Vandermonde or Cauchy-likeness can be
solved in Õ (α2n) operations, where n is the matrix size, α is its displacement rank, and Õ …