  We describe a new algorithm for calculating the topological degree deg (f, B,
0) where B \subseteq Rn is a product of closed real intervals and f : B
\rightarrow Rn is a real-valued continuous function given in the form of
arithmetical expressions. The algorithm cleanly separates numerical from
combinatorial computation. Based on this, the numerical part provably computes
only the information that is strictly necessary for the following combinatorial
part, and the combinatorial part may optimize its computation based on the
numerical information computed before. We also present computational
experiments based on an implementation of the algorithm. Also, in contrast to
previous work, the algorithm does not assume knowledge of a Lipschitz constant
of the function f, and works for arbitrary continuous functions for which some
notion of interval arithmetic can be defined.
