  First order algebraic differential equations are considered. An necessary
condition for a first order algebraic differential equation to have a rational
general solution is given: the algebraic genus of the equation should be zero.
Combining with Fuchs' conditions for algebraic differential equations without
movable critical point, an algorithm is given for the computation of rational
general solutions of these equations if they exist under the assumption that a
rational parametrization is provided. It is based on an algorithmic reduction
of first order algebraic differential equations with algebraic genus zero and
without movable critical point to classical Riccati equations.
