Let L be an algebraic function field in k parameters t1,..,tk.
Let f1, f2 be nonzero polynomials in L[x]. We give two algorithms
for computing their gcd. The first, a modular GCD algorithm, is
an extension of the modular GCD algorithm of Brown for Z[x1,..,xn]
and Encarnacion for Q(alpha)[x] to function fields. The second, a
fractionfree algorithm, is a modification of the MorenoMaza and
Rioboo algorithm for computing gcds over triangular sets. The
modification reduces coefficient growth in L to be linear. We give
an empirical comparison of the two algorithms using implementations
in Maple.
