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The decidability of real algebraic sets by the index formula

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1524)

Abstract

We propose an algorithm to decide if a real algebraic set defined by polynomials with integer coefficients has a non empty intersection with a given ball by the index formula of Kronecker. We approximate the integral by a Riemann sum and we give an estimate of the time of computation which is needed. The method is well adapted to the use of parallel time computations.

Keywords

  • Real algebraic geometry
  • index formula
  • NP-problems
  • 1980 Mathematics subject classifications
  • Primary 32C05
  • Secondary 12-04

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References

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© 1992 Springer-Verlag

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Françoise, JP., Ronga, F. (1992). The decidability of real algebraic sets by the index formula. In: Coste, M., Mahé, L., Roy, MF. (eds) Real Algebraic Geometry. Lecture Notes in Mathematics, vol 1524. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084623

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  • DOI: https://doi.org/10.1007/BFb0084623

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55992-4

  • Online ISBN: 978-3-540-47337-4

  • eBook Packages: Springer Book Archive