Univariate Algebraic Kernel and Application to Arrangements

Sylvain Lazard 1 Luis Peñaranda 1 Elias P. Tsigaridas 2
1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : We present a cgal-based univariate algebraic kernel, which provides certied real-root isolation of univariate polynomials with integer coecients 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 eciency of our approach. Our experiments are performed on large data sets including polynomials of high degree (up to 2 000) and with very large coecients (up to 25 000 bits per coecient). We also address the problem of computing arrangements of x-monotone polynomial curves. We apply our kernel to this problem and demonstrate its eciency compared to previous solutions available in cgal.
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Conference papers
Jan Vahrenhold. 8th International Symposium SEA 2009, Jun 2009, Dortmund, Germany. Springer-Verlag, LNCS 5526/2009, pp.209-220, 2009, Lecture Notes in Computer Science; Experimental Algorithms, 8th International Symposium, SEA 2009. <http://www.springerlink.com/content/86154423035p3265/?p=65a469d9bf0643db8b0d9da60f98bd60&pi=19>. <10.1007/978-3-642-02011-7>
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Sylvain Lazard, Luis Peñaranda, Elias P. Tsigaridas. Univariate Algebraic Kernel and Application to Arrangements. Jan Vahrenhold. 8th International Symposium SEA 2009, Jun 2009, Dortmund, Germany. Springer-Verlag, LNCS 5526/2009, pp.209-220, 2009, Lecture Notes in Computer Science; Experimental Algorithms, 8th International Symposium, SEA 2009. <http://www.springerlink.com/content/86154423035p3265/?p=65a469d9bf0643db8b0d9da60f98bd60&pi=19>. <10.1007/978-3-642-02011-7>. <inria-00431559>

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