Automatic generation of vertices for the Schroedinger functional

We present a multiplication algorithm to recursively construct vertices for the Schroedinger functional in the abelian background field case. The algorithm is suited for automatic perturbative calculations with a variety of actions. As first applications, we derive ratios of the lambda parameters between the lattice scheme (improved gauge actions including six link loops) and the $\overline{\mathrm{M}\mathrm{S}}$ scheme, and one-loop results for the Schroedinger functional coupling with a lattice $T=L\pm a$, which is motivated by considering staggered fermions.