Abstract : If $K$/$k$ is a function field in one variable of positive characteristic, we describe a general algorithm to factor one-variable polynomials with coefficients in $K$. The algorithm is flexible enough to find factors subject to additional restrictions, e.g., to find all roots that belong to a given finite dimensional $k$-subspace of $K$ more efficiently. This has an application to list decoding of AG codes that we also describe.

Keywords : polynomial factorization; function fields; list decoding