Algorithmic Invariant Theory of Nonreductive Groups

The main purpose of this paper is to give a survey of algorithms in invariant theory, with emphasis on nonreductive groups and on recent developments. But the article has some novel elements: it contains a new algorithm for computing invariant rings, which works under the condition that the invariant field is the field of fractions of the invariant ring. We also prove that if n is the dimension of the invariant ring, then there exists a separating set of invariants whose size is at most 2n + 1.