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 are convinced that ours are the fastest known to date when the equation coefficients are not too small (ie., greater than 2 or 3).

• Type: Conference
• Year: 1993
• Where: EPIA
• Authors: Miguel Filgueiras, Ana Paula Tomás
• Keywords: Artificial Intelligence, Diophantine Equations, EPIA 1993, Minimal Solutions, Slopes Algorithm