Cybernetics and Systems Analysis

, Volume 43, Issue 2, pp 171–178 | Cite as

Algorithms for solution of systems of linear diophantine equations in residue fields

  • S. L. Kryvyi


Algorithms are proposed for computing the basis of the solution set of a system of linear Diophantine homogeneous or inhomogeneous equations in the residue field modulo a prime number.


residue field linear Diophantine equation basis of a solution set 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. A. Donets, “Solution of the safe problem on (0,1)-matrices,” Cybernetics and Systems Analysis, No. 1, 98–105 (2002).Google Scholar
  2. 2.
    A. V. Cheremushkin, Lectures on Arithmetic Algorithms in Cryptography [in Russian], MTsNMO, Moscow (2002).Google Scholar
  3. 3.
    F. Baader and J. Ziekmann, “Unification theory,” in: Handbook of Logic in Artificial Intelligence and Logic Programming, Oxford University Press (1994), pp. 1–85.Google Scholar
  4. 4.
    R. Allen and K. Kennedy, “Automatic translation of FORTRAN programs to vector form,” ACM Transactions on Programming Languages and Systems, 9, No. 4, 491–542 (1987).MATHCrossRefGoogle Scholar
  5. 5.
    E. Contejan and F. Ajili, “Avoiding slack variables in the solving of linear Diophantine equations and inequations,” Theoretical Comp. Science, 173, 183–208 (1997).CrossRefGoogle Scholar
  6. 6.
    L. Pottier, “Minimal solution of linear diophantine systems: Bounds and algorithms,” in: Proc. 4th Intern. Conf. on Rewriting Techniques and Applications, Como, Italy (1991), pp. 162–173.Google Scholar
  7. 7.
    E. Domenjoud, “Outils pour la deduction automatique dans les theories associatives-commutatives,” These de Doctorat de l’universite de Nancy I (1991).Google Scholar
  8. 8.
    M. Clausen and A. Fortenbacher, “Efficient solution of linear diophantine equations,” J. Symbolic Computation, 8, Nos. 1–2, 201–216 (1989).MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    J. F. Romeuf, “A polinomial algorithm for solving systems of two linear Diophantine equations,” TCS, 74, No. 3, 329–340 (1990).MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    M. Filgueiras and A. P. Tomas, “A fast method for finding the basis of non-negative solutions to a linear Diophantine equation,” J. Symbolic Computation, 19, No. 2, 507–526 (1995).MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    H. Comon, “Constraint solving on terms: Automata techniques (Preliminary lecture notes),” in: Intern. Summer School on Constraints in Computational Logics, Gif-sur-Yvette, France (1999), p. 22.Google Scholar
  12. 12.
    S. L. Kryvyi, “Algorithms of solution of systems of linear Diophantine equations in integer domains,” Cybernetics and Systems Analysis, No. 2, 3–17 (2006).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • S. L. Kryvyi
    • 1
  1. 1.Cybernetics InstituteNational Academy of Sciences of UkraineKievUkraine

Personalised recommendations