  We develop explicit formulas and algorithms for arithmetic in radical
function fields K/k(x) over finite constant fields. First, we classify which
places of k(x) whose local integral bases have an easy monogenic form, and give
explicit formulas for these bases. Then, for a fixed place p of k(x), we give
formulas for functions whose valuation is zero for all places P | p except one,
for which it is one. We extend a result by Q. Wu on a k[x]-basis of its
integral closure in K, show how to compute certain Riemann-Roch spaces and how
to compute the exact constant field, resulting in explicit formulas for the
exact constant field together with easy to evaluate formulas for the genus of
K. Finally, we show how to approximate the Euler product to obtain the class
number using ideas of R. Scheidler and A. Stein and give an algorithm. We give
bounds on the running time for all algorithms.
