We provide algorithms to count and enumerate representatives of the (right) ideal classes of
an Eichler order in a quaternion algebra defined over a number field. We analyze the run …

We discuss the relationship between quaternion algebras and quadratic forms with a focus
on computational aspects. Our basic motivating problem is to determine if a given algebra of …

Let K be a fixed algebraic number field and let A be an associative algebra over K given by
structure constants such that A≅ Mn (K) holds for some positive integer n. Suppose that n is …

It is well known that a Severi–Brauer surface has a rational point if and only if it is isomorphic
to the projective plane. Given a Severi–Brauer surface, we study the problem to decide …

Computing the Cassels-Tate Pairing for Jacobian Varieties of Genus Two Curves Page 1
University of Cambridge TRINITY COLLEGE Doctoral Thesis Computing the Cassels-Tate …

Selected Applications of LLL in Number Theory Page 1 Chapter 7 Selected Applications of LLL
in Number Theory Denis Simon Abstract In this survey, I describe some applications of LLL in …

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 …

The main results in this dissertation concern the computational complexity of structural
decomposition problems in finite dimensional associative algebras over global fields …

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 …

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