Skip to main content

Polynomial time algorithms in the theory of linear diophantine equations

  • Section C Computability, Decidability & Arithmetic Complexity
  • Conference paper
  • First Online:
Fundamentals of Computation Theory (FCT 1977)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 56))

Included in the following conference series:

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. W.A.Blankinship. A new version of the Euclidian algorithm. Amer. Math. Monthly, v. 70(1967), No. 3.

    Google Scholar 

  2. J. Bond. Calculation the general solution of a linear diophantine equation. Amer. Math. Monthly, v.74(1971), No. 8.

    Google Scholar 

  3. I. Borosh, A.S. Fraenkel. Exact solution of linear equations with rational coefficients by congruence techniques. Math. Comp., v. 20 (1966), No. 93.

    Google Scholar 

  4. G.H. Bradly. Algorithm and bound for the gratest common divisor of n integers. Comm. of ACM, v. 3(1970) No. 7.

    Google Scholar 

  5. G.H. Bradly. Algorithms for Hermite and Smith normal matrices and linear diophantine equations. Math. Comp., v. 25(1971), No. 116.

    Google Scholar 

  6. J.W.S. Cassels. An Introduction to The Geometry of numbers. Springer-Verlag, 1959.

    Google Scholar 

  7. M.A. Frumkin. Application of modular arithmetic to the construction of algorithms of solving systems of linear equations. Soviet Math. Dokl., v. 17(1976), No.4.

    Google Scholar 

  8. М.А. Фрумкин. Алгоритмы решения систем илнейных уравнений в целых числах. сб. "Исследования по дискретной оптимизации", М. "Наука", 1976, 97–127.

    Google Scholar 

  9. М.А. Фрумкин. Алгоритм приведения целочисленной матрицы к треугольному виду со степенной сложностью вычислений. Экономика и мат. методы, т. XII (1976), No I.

    Google Scholar 

  10. T.C. Hu and R.D. Young. Integer programming and network flows. Addison-Wesley, Reading, Mass., 1969.

    Google Scholar 

  11. А.А. Вотяков, М.А. Фрумкин. Алгоритм нахождения общего целочисленного решения системы линейных диофантовых уравнений. сб. "Исследования по дискретной оптимизации", М. "Наука", 1976, 128–140.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Marek Karpiński

Rights and permissions

Reprints and permissions

Copyright information

© 1977 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Frumkin, M.A. (1977). Polynomial time algorithms in the theory of linear diophantine equations. In: Karpiński, M. (eds) Fundamentals of Computation Theory. FCT 1977. Lecture Notes in Computer Science, vol 56. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08442-8_106

Download citation

  • DOI: https://doi.org/10.1007/3-540-08442-8_106

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08442-6

  • Online ISBN: 978-3-540-37084-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics