On Solving Linear Diophantine Systems Using Generalized Rosser’s Algorithm
چکیده
A difficulty in solving linear Diophantine systems is the rapid growth of intermediate results. Rosser’s algorithm for solving a single linear Diophatine equation is an efficient algorithm that effectively controls the growth of intermediate results. Here, we propose an approach to generalize Rosser’s algorithm and present two algorithms for solving systems of linear Diophantine equations. Then, we show that the generalized approach provides us with a new formulation of the LDSSBR of Chou and Collins and a more efficient implementation of Rosser’s approach. The new formulation also enables us to propose an efficient algorithm for solving rank one perturbed linear Diophantine systems based on the LDSSBR, and to improve and extend the class of integer ABS algorithms for solving linear Diophantine systems.