The following functions allow simple access to basic properties of invariant rings.

Group(R) : RngInvar -> Grp

Given the invariant ring R=K[V]^G of the group G over the field K, return the group G.

CoefficientField(R) : RngInvar -> Rng

Given the invariant ring R=K[V]^G of the group G over the field K, return the coefficient field K.

Given an invariant ring R=K[V]^G of the group G of degree n over the field K, return the polynomial ring P = K[x_1, ..., x_n] in which the invariants of R lie. P has the print names "x1", "x2", etc. -- the angle bracket notation or the . operator should be used to assign the variables of P to actual Magma variables.

Return whether the polynomial f is in R=K[V]^G. Note that the parent of f is always the polynomial ring P, never R, so a true result does not mean that the parent of f is R.