[SADE] a Maple package for the symmetry analysis of differential equations

We present the package SADE (Symmetry Analysis of Differential Equations) for the determination of symmetries and related properties of systems of differential equations. The main methods implemented are: Lie, nonclassical, Lie–Bäcklund and potential symmetries, invariant solutions, first-integrals, Nöther theorem for both discrete and continuous systems, solution of ordinary differential equations, order and dimension reductions using Lie symmetries, classification of differential equations, Casimir invariants, and the quasi-polynomial formalism for ODE's (previously implemented by the authors in the package QPSI) for the determination of quasi-polynomial first-integrals, Lie symmetries and invariant surfaces. Examples of use of the package are given.Program summaryProgram title: SADECatalogue identifier: AEHL_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHL_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 27 704No. of bytes in distributed program, including test data, etc.: 346 954Distribution format: tar.gzProgramming language: MAPLE 13 and MAPLE 14Computer: PCs and workstationsOperating system: UNIX/LINUX systems and WINDOWSClassification: 4.3Nature of problem: Determination of analytical properties of systems of differential equations, including symmetry transformations, analytical solutions and conservation laws.Solution method: The package implements in MAPLE some algorithms (discussed in the text) for the study of systems of differential equations.Restrictions: Depends strongly on the system and on the algorithm required. Typical restrictions are related to the solution of a large over-determined system of linear or non-linear differential equations.Running time: Depends strongly on the order, the complexity of the differential system and the object computed. Ranges from seconds to hours.