Computational Thinking Process of Prospective Mathematics Teacher in Solving Diophantine Linear Equation Problems

Solving Linear Diophantine Equations

An overview of a family of methods for nding the minimal solutions to a single linear Diophantine equation over the natural numbers is given. Most of the formal details were dropped, some illustrations that might give some intuition on the methods being presented instead.

Solving Linear Diophantine Constraints Incrementally

In this paper, we show how to handle linear Diophantine constraints incre-mentally by using several variations of the algorithm by Contejean and Devie (hereafter called ABCD) for solving linear Diophantine systems 4, 5]. The basic algorithm is based on a certain enumeration of the potential solutions of a system, and termination is ensured by an adequate restriction on the search. This algorith...

On Solving Linear Diophantine Systems Using Generalized Rosser's Algorithm

Fast Methods for Solving Linear Diophantine Equations

We present some recent results from our research on methods for finding the minimal solutions to linear Diophantine equations over the naturals. We give an overview of a family of methods we developed and describe two of them, called Slopes algorithm and Rectangles algorithm. From empirical evidence obtained by directly comparing our methods with others, and which is partly presented here, we a...

Computational advances in solving Mixed Integer Linear Programming problems

In this paper, we identify some of the computational advances that have been contributing to the efficient solution of mixed-integer linear programming (MILP) problems. Recent features added to MILP solvers at the algorithmic level and at the hardware level have been contributing to the increasingly efficient solution of more difficult and larger problems. Therefore, we will focus on the main a...