5. Conclusion

The algorithmic theory of difference equations has developed considerably in recent years, providing a general and comprehensive framework for linear difference equations or systems. This work completes the studies carried out in the case of linear differential equations with regular or irregular singularities.

Several university programs exist for this theory. Other areas are beginning to be explored by techniques extending those outlined in this article: nonlinear differential or difference equations, algebraic differential equations, equations with parameters.

The actual numerical calculation of solutions from the formal solutions found by previous algorithms is a difficult problem that calls on resumption theories.