Computer Algebra System REDUCE Research Articles

Computer algebra application for determining Lie and Lie-Bäcklund symmetries of differential equations

The application of computer algebra for determining Lie and Lie-Bäcklund (LB) symmetries of differential equations is considered. Algorithms for calculating the symmetries are developed and implemented on the basis of computer algebra systems REDUCE, AMP and FORMAC. The most effective and advanced program is written in FORMAC. It finds LB symmetries completely automatically. In many cases the program yields the full algebra of symmetries. If the program fails in full integration of the determining system, it reduces the remaining determining equations to the system in involution.

Exterior calculus on the computer: The REDUCE-package EXCALC applied to general relativity and to the Poincaré gauge theory

The computer algebra system REDUCE has recently been enriched by a package on exterior calculus. Here we apply the EXCALC package to the calculation of quantities within the Poincare gauge theory of gravity, general relativity being included in this scheme as a spcial case. Thereby we simplify and streamline earlier results found by means of tensor-analytical REDUCE calculations.

The Riquier-Janet theory and its application to nonlinear evolution equations

It is shown that by taking into account all integrability conditions for a given system of partial differential equations a more systematic treatment of several problems in the theory of nonlinear evolution equations may be performed. The basic prerequisites are the theory of Riquier and Janet of partial differential equations and the application of the computer algebra system REDUCE. Several kinds of Bäcklund transformations and the prolongation of Estabrook and Wahlquist are discussed in detail.