Univariate Algebraic Kernel and Application to Arrangements

We present a cgal-based univariate algebraic kernel, which provides certi ed real-root isolation of univariate polynomials with integer coe cients 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 e ciency of our approach. Our experiments are performed on large data sets including polynomials of high degree (up to 2 000) and with very large coe cients (up to 25 000 bits per coe cient). We also address the problem of computing arrangements of x-monotone polynomial curves. We apply our kernel to this problem and demonstrate its e ciency compared to previous solutions available in cgal.