Limit Computation in Computer Algebra

Limit computation is an important topic in computer algebra. Limits may be computed either directly or by various other functions, as e.g. definite integration, summation or differential equations. We describe an algorithm for computing symbolic limits, i.e. limits of expressions in symbolic form for a large class of expressions.\\ This algorithm is based on the idea of the most rapidly varying subexpression of a given expression. It solves the dominance problem for exp--log functions, and also for a much wider class of functions. The algorithm is simple and very efficient.\\ We also outline an algorithm for computing asymptotic series which is induced directly by the limit computation algorithm and show some examples.