Computing the Algebraic Relations of C-finite Sequences and Multisequences

We present an algorithm for computing generators for the ideal of algebraic relations among sequences which are given by homogeneous linear recurrence equations with constant coefficients. Knowing these generators makes it possible to use Gr\"obner basis methods for carrying out certain basic operations in the ring of such sequences effectively. In particular, one can answer the question whether a given sequence can be represented in terms of other given sequences. A collection of examples, which were done with an implementation of our algorithm, is included.