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Counting Points of Semi-Algebraic Subsets

  • T. Aliashvili
Conference paper
Part of the NATO Science Series II: Mathematics, Physics and Chemistry book series (NAII, volume 147)

Abstract

Effective computing of the number of points of a semi-algebraic subset given in explicit form is approached by a general algorithm.

Keywords

semialgebraic subsets algorithm for effictive computing Maxwell problem 

Mathematics Subject Classification (2000)

14Q20 

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References

  1. [1]
    Aliashvili, T. (2002) Counting real roots of polynomial endomorphisms, J. Math. Sci., Vol. 135, pp. 1–22.Google Scholar
  2. [2]
    Aliashvili, T. (1996) Signature method for counting points in semi-algebraic subsets, Bull. Georgian Acad. Sci., Vol. 154, pp. 34–36.zbMATHMathSciNetGoogle Scholar
  3. [3]
    Breker, T., Lander, L. (1977) Di erential germs and catastrophes, Mir, Moscow (Russian).Google Scholar
  4. [4]
    Hodge, W.V.N., Pedoe, D. (1947) Methods of algebraic geometry, 1. Cambridge Univ. Press, Cambridge.Google Scholar
  5. [5]
    Mumford, D. (1976) Algebraic geometry, I. Springer-Verlag, Berlin.Google Scholar
  6. [6]
    Griffths, P., Harris, J. (1978) Principles of algebraic geometry, John Wiley, New-York, Brisben, Toronto.Google Scholar
  7. [7]
    Kelley, J.-L. (1955) General topology, van Nostrand, Toronto, London, New-York.Google Scholar
  8. [8]
    Khimshiashvili, G. (1977) On the local degree of a smooth mapping, Bull. Acad. Sci. Georgian SSR, Vol. 85, pp. 309–312 (Russian).zbMATHGoogle Scholar
  9. [9]
    Khimshiashvili, G. (1982) The Euler characteristic of a manifold and critical points of smooth functions, Trudy. Tbiliss. Mat. Inst. Razmadze, Vol. 85, pp. 123–141 (Russian).MathSciNetGoogle Scholar
  10. [10]
    Khimshiashvili, G. (2001) Signature formulae for topological invariants, Proc. A. Razmadze Math. Institute, Vol. 125, pp. 1–121.zbMATHMathSciNetGoogle Scholar
  11. [11]
    Krein, M., Neimark, M. (1981) The method of symmetric and hermitian forms for the theory of separation of roots of algebraic polynomials, GNTI, Kharkov, 1936 (Russian); Linear and Multilinear Algebra, Vol. 10, pp. 265–308.Google Scholar
  12. [12]
    Postnikov, M. Stable polynomials, Nauka, Moscow (Russian).Google Scholar
  13. [13]
    Scheja, G., Storch, U. (1975) Über Spurfunktionen bei vollständigen Durchschnitten, J. Reine Angew. Math. Vol. 278/279, pp. 174–190.MathSciNetGoogle Scholar
  14. [14]
    Szafraniec, Z. (1989) The Euler characteristic of algebraic complete intersection, J. Reine Angew. Math., Vol. 397, pp. 194–201.zbMATHMathSciNetGoogle Scholar
  15. [15]
    Tsikh, A. (1988) Multidimensional residues and their applications, Nauka, Novosibirsk (Russian).Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • T. Aliashvili
    • 1
  1. 1.Chair of Mathematics #99Georgian Technical UniversityTbilisiGeorgia

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