We introduce a presentation for central simple algebras over a field k using Amitsur
cohomology. We provide efficient algorithms for computing a cocycle corresponding to any …

We consider the algorithmic problem of computing a primitive idempotent of a central simple
algebra over the field of rational functions over a finite field. The algebra is given by a set of …

We represent vector bundles over a regular algebraic curve as pairs of lattices over the
maximal orders of its function field and we give polynomial algorithms for several tasks …

We propose a randomized polynomial time algorithm for computing non-trivial zeros of
quadratic forms in 4 or more variables over F q (t), where F q is a finite field of odd …

We present an efficient computational representation of central simple algebras using
Brauer factor sets. Using this representation and polynomial quantum algorithms for number …

We propose polynomial-time algorithms for finding nontrivial zeros of quadratic forms with
four variables over rational function fields of characteristic 2. We apply these results to find …

Let L be a separable quadratic extension of either Q \documentclass[12pt]{minimal} \usepackage{amsmath}
\usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} …

We propose an algorithm for finding zero divisors in quaternion algebras over quadratic
number fields, or equivalently, solving homogeneous quadratic equations in three variables …

Let $\mathbb {F} _q $ be the finite field of size $ q $ and let $\ell:\mathbb {F} _q^ n\to\mathbb
{F} _q $ be a linear function. We introduce the {\em Learning From Subset} problem LFS $(q …

We propose polynomial-time algorithms for finding nontrivial zeros of quadratic forms with
four variables over rational function fields of characteristic 2. We apply these results to find …