Computing Hypercircles by Moving Hyperplanes
arXiv:1106.1378 · doi:10.1016/j.jsc.2012.09.001
Abstract
Let K be a field of characteristic zero, alpha algebraic of degree n over K. Given a proper parametrization psi of a rational curve C, we present a new algorithm to compute the hypercircle associated to the parametrization psi. As a consequence, we can decide if the curve C is defined over K and, if not, to compute the minimum field of definition of C containing K. The algorithm exploits the conjugate curves of C but avoids computation in the normal closure of K(alpha) over K.
16 pages