Determining Liouvillian first integrals for dynamical systems in the plane

Here we present/implement an algorithm to find Liouvillian first integrals of dynamical systems in the plane. In [1], we have introduced the basis for the present implementation. The particular form of such systems allows reducing it to a single rational first order ordinary differential equation (rational first order ODE). We present a set of software routines in Maple 10 for solving rational first order ODEs. The package present commands permitting research incursions of some algebraic properties of the system that is being studied. Keyword: Liouvillian functions, first integrals, dynamical systems in the plane, first order ordinary differential equations, computer algebra, Prelle-Singer (PS) PACS: 02.30.Hq (Submitted to Computer Physics Communications) E-mails: [email protected], [email protected], [email protected] and [email protected]