Computing Roots of Polynomials over Function Fields of Curves

We design algorithms for nding roots of polynomials over function elds of curves. Such algorithms are useful for list decoding of Reed-Solomon and algebraic-geometric codes. In the rst half of the paper we will focus on bivariate polynomials, i.e., polynomials over the coordinate ring of the aane line. In the second half we will design algorithms for computing roots of polynomials over the function eld of a nonsingular absolutely irreducible plane algebraic curve. Several examples are included.