Computing Hypercircles by Moving Hyperplanes

Details Computing Hypercircles by Moving Hyperplanes Computing Hypercircles by Moving Hyperplanes

2011-06-07

arxiv.org/abs/1106.1378v1

Mathematics

Algebraic Geometry

16 pages

Scientific paper

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.

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