Univariate Algebraic Kernel and Application to Arrangements

  • Sylvain Lazard
  • Luis Peñaranda
  • Elias Tsigaridas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5526)


We present a cgal-based univariate algebraic kernel, which provides certified real-root isolation of univariate polynomials with integer coefficients and standard functionalities such as basic arithmetic operations, greatest common divisor (gcd) and square-free factorization, as well as comparison and sign evaluations of real algebraic numbers.

We compare our kernel with other comparable kernels, demonstrating the efficiency of our approach. Our experiments are performed on large data sets including polynomials of high degree (up to 2 000) and with very large coefficients (up to 25 000 bits per coefficient).

We also address the problem of computing arrangements of x-monotone polynomial curves. We apply our kernel to this problem and demonstrate its efficiency compared to previous solutions available in cgal.


Real Root Algebraic Number Interval Arithmetic Univariate Polynomial Random Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Sylvain Lazard
    • 1
  • Luis Peñaranda
    • 1
  • Elias Tsigaridas
    • 2
  1. 1.INRIA Nancy - Grand Est, LORIAFrance
  2. 2.INRIA Sophia-Antipolis - MéditerranéFrance

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