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Part of the book series: Algorithms and Computation in Mathematics ((AACIM,volume 10))

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14.6 Bibliographical Notes

  1. S. Basu, New Results on Quantifier Elimination over Real Closed Fields and Applications to Constraint Databases, Journal of the ACM, 46(4), 537–555 (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, Computing the Dimension of a Semi-Algebraic Set, Zap. Nauchn. Semin. POMI 316 42–54 (2004).

    MATH  Google Scholar 

  4. D. Grigor’ev, The Complexity of deciding Tarski algebra, Journal of Symbolic Computation 5 65–108 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  5. 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 

  6. 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 

  7. N. N. Vorobjov. Complexity of computing the dimension of a semi-algebraic set. J. of Symbolic Comput., 27: 565–579 (1999).

    Article  MATH  MathSciNet  Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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(2006). Quantifier Elimination. 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_15

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