Computation of Zolotarev Rational Functions

An algorithm is presented to compute Zolotarev rational functions, that is, rational functions r\astn of a given degree that are as small as possible on one set E C \BbbC \cup {oo\} relative to their size on another set F C \BbbC\cup {oo\} (the third Zolotarev problem). Along the way we also approximate the sign function relative to E and F (the fourth Zolotarev problem).