What is the best way of writing out code to calculate the symmetry group of the Klein Quartic (The klein quatric is the set of the solutions to f=0, where f is the polynomial x^3*y+y^3*z+z^3+x in QQ[x,y,z]) I know of 2 symmetry types one is the rotation of terms of order 3 ( (x,y,z), (z,x,y), (y,z,x)) and one is the mapping of x->v*x, y->v^4*y, z->v^2*z, where v is a 7th root of unity (v=(1/7)*(142)) this is a symmetry of order 7 thoughts?
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