We review computations of joint invariants on a linear symplectic space,
discuss variations for an extension of group and space and relate this to other
equivalence problems and approaches, most importantly to differential
invariants.Comment: In this revision we added missing references, and essentially changed
the presentation into a review. We corrected small errors, reduced the
material on algebraic part, and extended it on geometric part. Thus we
elaborate on known results from the classical invariant theory, discuss some
extensions and draw relations to the differential invariants theory via
symplectic invariant discretization
