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

  • Ana Paula Tomás
  • Miguel Filgueiras
Conference paper

DOI: 10.1007/3-540-62950-5_77

Volume 1232 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Tomás A.P., Filgueiras M. (1997) Solving linear Diophantine equations using the geometric structure of the solution space. In: Comon H. (eds) Rewriting Techniques and Applications. RTA 1997. Lecture Notes in Computer Science, vol 1232. Springer, Berlin, Heidelberg

Abstract

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.

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Ana Paula Tomás
    • 1
  • Miguel Filgueiras
    • 1
  1. 1.LIACCUniversidade do PortoPortugal