Elias' Article

A CGAL-based univariate algebraic kernel and applications to arrangements.
Sylvain Lazard, Luis Pe naranda, and Elias P. Tsigaridas.
In 24th European Workshop on Computational Geometry (EuroCG), pp. 91–94, Nancy, France, Mar 18--20 2008.

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Abstract:

Solving univariate polynomials and multivariate polynomial systems is critical in geometric computing with curved objects. Moreover, the real roots need to be computed in a certified way in order to avoid possible inconsistency in geometric algorithms. We present a \cgal-based univariate algebraic kernel, which follows the \cgal specifications for univariate kernels. It provides certified real-root isolation of univariate polynomials with integer coefficients (based on the library \rs) and standard functionalities such as basic arithmetic operations, gcd and square-free factorization. We compare our implementation with that of other univariate algebraic kernels that follow the same \cgal specifications. In particular, we compare it to the one developed at MPII. We also apply this kernel to the computation of arrangements of univariate polynomial functions.

@InProceedings{lpt-eurocg-2008,
  author =       {Sylvain Lazard and Luis Pe\~naranda and
                  Elias~P. Tsigaridas},
  title =        {{A CGAL-based univariate algebraic kernel and
                  applications to arrangements}},
  booktitle =    {24th European Workshop on Computational Geometry
                  (EuroCG)},
  pages =        {91--94},
  year =         2008,
  month =        {Mar 18--20},
  address =      {Nancy, France},
  abstract =     "Solving univariate polynomials and multivariate
                  polynomial systems is critical in geometric
                  computing with curved objects. Moreover, the real
                  roots need to be computed in a certified way in
                  order to avoid possible inconsistency in geometric
                  algorithms.  We present a \cgal-based univariate
                  algebraic kernel, which follows the
                  \cgal~specifications for univariate kernels.  It
                  provides certified real-root isolation of univariate
                  polynomials with integer coefficients (based on the
                  library \rs) and standard functionalities such as
                  basic arithmetic operations, gcd and square-free
                  factorization.  We compare our implementation with
                  that of other univariate algebraic kernels that
                  follow the same \cgal~specifications. In particular,
                  we compare it to the one developed at MPII. We also
                  apply this kernel to the computation of arrangements
                  of univariate polynomial functions. ",
}

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