Computing with root subgroups of twisted reductive groups (preprint

Abstract. We present algorithms to compute with relative root subgroups of twisted reductive groups. Given a Galois cocycle specifying a twisted form, we can find the relative root datum and Tits index, and carry out operations involving root elements. We can also find a presentation of the unipotent subgroup. Given a Tits index and the anisotropic subgroup, we can determine a cocycle with that index, if one exists. 1