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Moving Frame Based Strategies for Reduction of Ordinary Differential/Recurrence Systems using their Expanded Lie Point Symmetries.

When an ordinary differential/recurrence system presents a m-parameters solvable group of symmetries, Lie group theory states that its number of variables could be reduce by m. This reduction process is classically done by rewriting original problem in an invariant coordinates set for these symmetries. We show how to use computational strategies using non explicit (infinitesimal) data representation in the reduction process and thus, how to avoid—for differential systems—the explicit expansive computation of these invariants. Thus, these strategies lead to efficient algorithms that were used in the maple implementation.