linearlyReductiveAction(I, M, R)
linearlyReductiveAction(I, M, Q)
In order to encode a linearly reductive group action, we represent the group as an affine variety. The polynomial ring S is the coordinate ring of the ambient affine space containing the group, while I is the ideal of S defining the group as a subvariety. In other words, the elements of the group are the points of the affine variety with coordinate ring S/I. The group acts linearly on the polynomial ring R via the matrix M with entries in S.
The next example constructs a cyclic group of order 2 as a set of two affine points. Then it introduces an action of this group on a polynomial ring in two variables.






This function is also used to define linearly reductive group actions on quotients of polynomial rings. We illustrate by a slight variation on the previous example.





The object linearlyReductiveAction is a method function.