Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
Interval arithmetic in cylindrical algebraic decomposition
Journal of Symbolic Computation
Efficient isolation of polynomial's real roots
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Towards and open curved kernel
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
On the complexity of real root isolation using continued fractions
Theoretical Computer Science
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Real algebraic numbers and polynomial systems of small degree
Theoretical Computer Science
EXACUS: efficient and exact algorithms for curves and surfaces
ESA'05 Proceedings of the 13th annual European conference on Algorithms
A descartes algorithm for polynomials with bit-stream coefficients
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Exact geometric and algebraic computations in CGAL
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
A generic algebraic kernel for non-linear geometric applications
Proceedings of the twenty-seventh annual symposium on Computational geometry
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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 .