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Parametrization over prescribed coefficient fields
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Franz Winkler
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Date:  July 18th (Thursday) \\
Time:  08:30-09:00\\

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Abstract
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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. 

