, Volume 55, Issue 1, pp 14–28 | Cite as

A Separation Bound for Real Algebraic Expressions

  • Christoph Burnikel
  • Stefan Funke
  • Kurt Mehlhorn
  • Stefan Schirra
  • Susanne Schmitt
Open Access


Real algebraic expressions are expressions whose leaves are integers and whose internal nodes are additions, subtractions, multiplications, divisions, k-th root operations for integral k, and taking roots of polynomials whose coefficients are given by the values of subexpressions. We consider the sign computation of real algebraic expressions, a task vital for the implementation of geometric algorithms. We prove a new separation bound for real algebraic expressions and compare it analytically and experimentally with previous bounds. The bound is used in the sign test of the number type leda::real.


Exact geometric computation Separation bound Zero testing 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Christoph Burnikel
    • 1
  • Stefan Funke
    • 2
  • Kurt Mehlhorn
    • 3
  • Stefan Schirra
    • 4
  • Susanne Schmitt
    • 3
  1. 1.ENCOM GmbHSaarlouisGermany
  2. 2.Institut für Mathematik und InformatikErnst-Moritz-Arndt Universität GreifswaldGreifswaldGermany
  3. 3.MPI für InformatikSaarbrückenGermany
  4. 4.Fakultät für InformatikOtto-von-Guericke Universität MagdeburgMagdeburgGermany

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