[GAP Forum] group action on polynomials

[Bill Chin]

I have defined a polynomial ring Q[x_1,...,x_5] over the rationals. How do
you define an action of S_5 such that gx_i=x_g(i) for all g in S_5, i.e. an
action permuting the vertices? I am interested in this and other actions on
the polynomial ring.

I have defined

Q:=Rationals
R:=PolynomialRing(Q,5)
G:=Group[(12),(1,2,3,4,5)]

Thanks in advance.