We develop an algorithm for solving a system of diophantine equations with lower and upper bounds on the variables. The algorithm is based on lattice basis reduction. It first finds a short vector ...

Research in group theory has long embraced equations as a means to elucidate the structure and behaviour of groups. In particular, Diophantine problems—those surrounding the existence and ...

New algorithms for constructing the Hermite normal form (triangular) and Smith normal form (diagonal) of an integer matrix are presented. A new algorithm for determining the set of solutions to a ...