Implementation of the Painlevé test for ordinary differential systems
Theoretical Computer Science - Special volume on computer algebra
Involutive bases of polynomial ideals
Mathematics and Computers in Simulation - Special issue: Simplification of systems of algebraic and differential equations with applications
Fast Search for the Janet Divisor
Programming and Computing Software
Introduction to Maple
Interdependence between the laurent-series and elliptic solutions of nonintegrable systems
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
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A package facilitating search for analytic solutions of nonintegrable systems of autonomous ordinary differential equations is suggested. The algorithm discussed, which is a generalization of the Conte-Musette method, allows one to obtain single-valued and multivalued analytical solutions that were known to exist only in the form of formal Laurent and Puiseux series (obtained, for example, by means of the Painlevé analysis), respectively. Solutions in the form of the formal Laurent series and procedures from the package discussed are used not only for constructing elliptic solutions but also for proving impossibility of such construction. The suggested procedures have been implemented as packages in Maple and REDUCE.