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13.5 Bibliographical Notes

  1. S. Basu, On Bounding the Betti Numbers and Computing the Euler Characteristics of Semi-algebraic Sets, Discrete and Computational Geometry, 22 1–18 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  2. S. Basu, R. Pollack, M.-F. Roy, On the Combinatorial and Algebraic Complexity of Quantifier Elimination, Journal of the ACM, 43 1002–1045, (1996).

    Article  MATH  MathSciNet  Google Scholar 

  3. S. Basu, R. Pollack, M.-F. Roy, On Computing a Set of Points meeting every Semi-algebraically Connected Component of a Family of Polynomials on a Variety, Journal of Complexity, March 1997, 13(1), 28–37.

    Article  MATH  MathSciNet  Google Scholar 

  4. J. Canny, Some Algebraic and Geometric Computations in PSPACE, Proc. Twentieth ACM Symp. on Theory of Computing, 460–467, (1988).

    Google Scholar 

  5. A. Chistov, H. Fournier, L. Gurvits, P. Koiran, Vandermonde Matrices, NP-Completeness and Transversal Subspaces, Foundations of Computational Mathematics, 3(4) 421–427 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  6. D. Grigor’ev, N. Vorobjov, Solving Systems of Polynomial Inequalities in Subexponential Time, Journal of Symbolic Computation, 5 37–64 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Heintz, M.-F. Roy, P. Solernò, Sur la complexité du principe de Tarski-Seidenberg, Bull. Soc. Math. France 118 101–126 (1990).

    MATH  MathSciNet  Google Scholar 

  8. J. Renegar. On the computational complexity and geometry of the first order theory of the reals, Journal of Symbolic Computation, 13: 255–352 (1992).

    Article  MATH  MathSciNet  Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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(2006). Existential Theory of the Reals. In: Algorithms in Real Algebraic Geometry. Algorithms and Computation in Mathematics, vol 10. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-33099-2_14

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