An Efficient Incremental Algorithm for Solving Systems of Linear Diophantine Equations

On Solving Linear Diophantine Systems Using Generalized Rosser's Algorithm

Complete Solving of Linear

In this paper, we present an algorithm for solving directly linear Diophantine systems of both equations and inequations. Here directly means without adding slack variables for encoding inequalities as equalities. This algorithm is an extension of the algorithm due to Con-tejean and Devie 9] for solving linear Diophantine systems of equations, which is itself a generalization of the algorithm o...

On Solving Linear Diophantine Systems Using Generalized Rosser’s Algorithm

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...

Presentations of finitely generated cancellative commutative monoids and nonnegative solutions of systems of linear equations

Varying methods exist for computing a presentation of a finitely generated commutative cancellative monoid.We use an algorithm of Contejean andDevie [An efficient incremental algorithm for solving systems of linear diophantine equations, Inform. andComput. 113 (1994) 143–172] to show how these presentations can be obtained from the nonnegative integer solutions to a linear system of equations. ...

An Efficient Numerical Algorithm For Solving Linear Differential Equations of Arbitrary Order And Coefficients

Referring to one of the recent works of the authors, presented in~cite{differentialbpf}, for numerical solution of linear differential equations, an alternative scheme is proposed in this article to considerably improve the accuracy and efficiency. For this purpose, triangular functions as a set of orthogonal functions are used. By using a special representation of the vector forms of triangula...