Abstract
Let G be an algebraic group acting on an irreducible variety X. We present an algorithm for computing the invariant field k(X)G. Moreover, we give a constructive version of a theorem of Rosenlicht, which says that almost all orbits can be separated by rational invariants. More precisely, we give an algorithm for computing a nonempty open subset of X with a geometric quotient.
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Kemper, G. The Computation of Invariant Fields and a Constructive Version of a Theorem by Rosenlicht. Transformation Groups 12, 657–670 (2007). https://doi.org/10.1007/s00031-007-0056-5
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DOI: https://doi.org/10.1007/s00031-007-0056-5