Sieving in function fields

We present the first implementation of sieving techniques in the context of function fields. More precisely, we compute in class groups of quadratic c ongruence function fields by combining the algorithm of Hafner and McCurley with sieving ideas known from factoring. We apply our methods to the compu tation of generators and relations of the Jacobian variety of hyperelliptic curves over finite fields. The algorithms introduced here were implemented in C++ with the help of LED A and LiDIA. We provide examples of running times and comparisons with earl ier algorithms.