Univariate Algebraic Kernel and Application to Arrangements

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.

• Type: Conference
• Year: 2009
• Where: WEA
• Authors: Sylvain Lazard, Luis Mariano Peñaranda, Elias P. Tsigaridas
• Keywords: Algorithms, Greatest Common Divisor, Polynomial, Univariate Algebraic Kernel, WEA 2009