A Las Vegas randomized algorithm is given to compute the Smith multipliers for a
nonsingular integer matrix A, that is, unimodular matrices U and V such that AV= US, with S …

Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation:
Computing a Basis for an Integer Lattice: Page 1 Computing a Basis for an Integer Lattice: A …

A Las Vegas randomized algorithm is given to compute the Hermite normal form of a
nonsingular integer matrix A of dimension n. The algorithm uses quadratic integer …

En modélisation géométrique à base topologique, les objets manipulés sont subdivisés en
cellules de différentes dimensions (sommets, arêtes, faces, volumes...). Dans ce cadre, le …

We present a proof under a generalization of the Riemann Hypothesis that the class group
algorithm of Hafner and McCurley runs in expected time\begin {document} $ e^{\left (3/\sqrt …

The ideal class group is a fundamental concept in algebraic number theory, providing
insights into the structure and factorization properties of the ring of integers of a number field …

One of the main goals of the International Workshops on Computer Algebra in Scientific
Computing, which started in 1998 and since then have been held annually, is the timely in …

Transition to quantum-safe cryptogrpahy is being carried on to resist menace of the
developing powerful quantum computers, and lattice-based cryptosystems are among the …

The focus of this thesis is on fundamental computational problems in exact integer linear
algebra. Specifically, for a nonsingular integer input matrix A of dimension n, we consider …

The extended gcd problem takes as input two integers, and asks as output an integer linear
combination of the integers that are equal to their gcd. The classical extended Euclidean …