Rational Parametric Algebraic Curves (Subprojekt des DK W-1214)

We propose to investigate rational parametric algebraic curves both with respect to to their mathematical and geometric properties and also with respect to their manipulation by symbolic computation software. Rational curves and surfaces play an important role in geometric design or the integration theory of algebraic functions, but recently they have also been successfully use in diophantine analysis, and for finding general solutions of differential equations. Although algorithms for rational algebraic curves are already migrating from special purpose software systems (such as the CASA system developed by the proposer's research group) into mainstream computer algebra systems like \textsc{Maple}, there is in our view a demand for implementation of modern methods on such curves.