  The Painleve test is very useful to construct not only the Laurent-series
solutions but also the elliptic and trigonometric ones. Such single-valued
functions are solutions of some polynomial first order differential equations.
To find the elliptic solutions we transform an initial nonlinear differential
equation in a nonlinear algebraic system in parameters of the Laurent-series
solutions of the initial equation. The number of unknowns in the obtained
nonlinear system does not depend on number of arbitrary coefficients of the
used first order equation. In this paper we describe the corresponding
algorithm, which has been realized in REDUCE and Maple.
