Rewriting Techniques and Applications

Volume 1232 of the series Lecture Notes in Computer Science pp 269-283


Solving linear Diophantine equations using the geometric structure of the solution space

  • Ana Paula TomásAffiliated withLIACC, Universidade do Porto
  • , Miguel FilgueirasAffiliated withLIACC, Universidade do Porto

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In the development of algorithms for finding the minimal solutions of systems of linear Diophantine equations, little use has been made (to our knowledge) of the results by Stanley using the geometric properties of the solution space. Building upon these results, we present a new algorithm, and we suggest the use of geometric properties of the solution space in finding bounds for searching solutions and in having a qualitative evaluation of the difficulty in solving a given system.