Parametrization over prescribed coefficient fields.
Date: July 18th (Thursday)
Time: 08:30-09:00
Abstract
In parametrizing an algebraic curves we often actually want the parametrization to
have coefficients in some desirable field. For instance, if the curve equation $f(x,y)=0$ has
integral coefficients, we might want to determine a parametrization with rational
coefficients, if possible. Or in the context of computer aided geometric design, we might
want to parametrize a real curve in such a way that the parametrization has only real
coefficients. Some surfaces $S(x,y,z)=0$ can be parametrized by considering one of the
variables as a parameter $t$, determining a uniform parametrization of the curves
$S(x,y,t)=0$, and extracting from this a parametrization of the surface. In this context we
want to compute parametrizations of curves with coefficients in $Q(t)$, i.e. rational
functions in $t$.
We describe algorithmic approaches to the question of parametrization over such prescribed
coefficient fields.
