restart;
with(LinearAlgebra):

# Define indeterminates

QParam := [q1,q2,q3,q4,q5,q6,q7]:
PParam := Matrix([[p1],[p2],[p3],[p4],[p5],[p6],[p7],[p8],[p9]]):

# Special Fourier parameterization and inverse

F := Matrix([[1,1,1,1,1,1,1,1,1],
[1,-1,1,1,-1,1,1,-1,1],
[1,1/4,-1/2,0,-1/4,-1/2,1/4,0,-1/4],
[1,-1,1,-1,1,-1,0,0,0],
[1,1,1,1,1,1,-1,-1,-1],
[1,-1,1,1,-1,1,-1,1,-1],
[1,0,-1,-1,0,1,-1,0,1]]):

FI := Matrix([
[1/16,1/16,1/2,1/8,1/16,1/16,1/8],
[1/8,-1/8,1/4,-1/4,1/8,-1/8,0],
[1/16,1/16,-1/4,1/8,1/16,1/16,-1/8],
[1/16,1/16,0,-1/8,1/16,1/16,-1/8],
[1/8,-1/8,-1/4,1/4,1/8,-1/8,0],
[1/16,1/16,-1/4,-1/8,1/16,1/16,1/8],
[1/8,1/8,1/4,0,-1/8,-1/8,-1/4],
[1/4,-1/4,0,0,-1/4,1/4,0],
[1/8,1/8,-1/4,0,-1/8,-1/8,1/4]
]):

# List of polynomial parametrizations

P0 := [
-1/(-e0^2+e1^2)*c0^3*e0^3*g0^4-1/(-e0^2+e1^2)*c0^3*e0^3*g1^4+1/(-e0^2+e1^2)*c0^3*e0^2*e1*g0^3*g1+1/(-e0^2+e1^2)*c0^3*e0^2*e1*g0*g1^3-1/(-e0^2+e1^2)*c0^3*e0*e1^2*g0^3*g1-1/(-e0^2+e1^2)*c0^3*e0*e1^2*g0*g1^3+1/(-e0^2+e1^2)*c0^3*e1^3*g0^4+1/(-e0^2+e1^2)*c0^3*e1^3*g1^4-2/(-e0^2+e1^2)*c0^2*c1*e0^3*g0^3*g1-2/(-e0^2+e1^2)*c0^2*c1*e0^3*g0^2*g1^2-2/(-e0^2+e1^2)*c0^2*c1*e0^3*g0*g1^3+1/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^4+1/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^3*g1+2/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^2*g1^2+1/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0*g1^3+1/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g1^4-1/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^4-1/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^3*g1-2/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^2*g1^2-1/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0*g1^3-1/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g1^4+2/(-e0^2+e1^2)*c0^2*c1*e1^3*g0^3*g1+2/(-e0^2+e1^2)*c0^2*c1*e1^3*g0^2*g1^2+2/(-e0^2+e1^2)*c0^2*c1*e1^3*g0*g1^3-2/(-e0^2+e1^2)*c0*c1^2*e0^3*g0^3*g1-2/(-e0^2+e1^2)*c0*c1^2*e0^3*g0^2*g1^2-2/(-e0^2+e1^2)*c0*c1^2*e0^3*g0*g1^3+1/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^4+1/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^3*g1+2/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^2*g1^2+1/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0*g1^3+1/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g1^4-1/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^4-1/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^3*g1-2/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^2*g1^2-1/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0*g1^3-1/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g1^4+2/(-e0^2+e1^2)*c0*c1^2*e1^3*g0^3*g1+2/(-e0^2+e1^2)*c0*c1^2*e1^3*g0^2*g1^2+2/(-e0^2+e1^2)*c0*c1^2*e1^3*g0*g1^3-1/(-e0^2+e1^2)*c1^3*e0^3*g0^4-1/(-e0^2+e1^2)*c1^3*e0^3*g1^4+1/(-e0^2+e1^2)*c1^3*e0^2*e1*g0^3*g1+1/(-e0^2+e1^2)*c1^3*e0^2*e1*g0*g1^3-1/(-e0^2+e1^2)*c1^3*e0*e1^2*g0^3*g1-1/(-e0^2+e1^2)*c1^3*e0*e1^2*g0*g1^3+1/(-e0^2+e1^2)*c1^3*e1^3*g0^4+1/(-e0^2+e1^2)*c1^3*e1^3*g1^4,
-2/(-e0^2+e1^2)*c0^3*e0^3*g0^3*g1-2/(-e0^2+e1^2)*c0^3*e0^3*g0*g1^3+4/(-e0^2+e1^2)*c0^3*e0^2*e1*g0^2*g1^2-4/(-e0^2+e1^2)*c0^3*e0*e1^2*g0^2*g1^2+2/(-e0^2+e1^2)*c0^3*e1^3*g0^3*g1+2/(-e0^2+e1^2)*c0^3*e1^3*g0*g1^3-2/(-e0^2+e1^2)*c0^2*c1*e0^3*g0^3*g1-8/(-e0^2+e1^2)*c0^2*c1*e0^3*g0^2*g1^2-2/(-e0^2+e1^2)*c0^2*c1*e0^3*g0*g1^3+4/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^3*g1+4/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^2*g1^2+4/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0*g1^3-4/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^3*g1-4/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^2*g1^2-4/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0*g1^3+2/(-e0^2+e1^2)*c0^2*c1*e1^3*g0^3*g1+8/(-e0^2+e1^2)*c0^2*c1*e1^3*g0^2*g1^2+2/(-e0^2+e1^2)*c0^2*c1*e1^3*g0*g1^3-2/(-e0^2+e1^2)*c0*c1^2*e0^3*g0^3*g1-8/(-e0^2+e1^2)*c0*c1^2*e0^3*g0^2*g1^2-2/(-e0^2+e1^2)*c0*c1^2*e0^3*g0*g1^3+4/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^3*g1+4/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^2*g1^2+4/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0*g1^3-4/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^3*g1-4/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^2*g1^2-4/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0*g1^3+2/(-e0^2+e1^2)*c0*c1^2*e1^3*g0^3*g1+8/(-e0^2+e1^2)*c0*c1^2*e1^3*g0^2*g1^2+2/(-e0^2+e1^2)*c0*c1^2*e1^3*g0*g1^3-2/(-e0^2+e1^2)*c1^3*e0^3*g0^3*g1-2/(-e0^2+e1^2)*c1^3*e0^3*g0*g1^3+4/(-e0^2+e1^2)*c1^3*e0^2*e1*g0^2*g1^2-4/(-e0^2+e1^2)*c1^3*e0*e1^2*g0^2*g1^2+2/(-e0^2+e1^2)*c1^3*e1^3*g0^3*g1+2/(-e0^2+e1^2)*c1^3*e1^3*g0*g1^3,
-2/(-e0^2+e1^2)*c0^3*e0^3*g0^2*g1^2+1/(-e0^2+e1^2)*c0^3*e0^2*e1*g0^3*g1+1/(-e0^2+e1^2)*c0^3*e0^2*e1*g0*g1^3-1/(-e0^2+e1^2)*c0^3*e0*e1^2*g0^3*g1-1/(-e0^2+e1^2)*c0^3*e0*e1^2*g0*g1^3+2/(-e0^2+e1^2)*c0^3*e1^3*g0^2*g1^2-1/(-e0^2+e1^2)*c0^2*c1*e0^3*g0^4-2/(-e0^2+e1^2)*c0^2*c1*e0^3*g0^3*g1-2/(-e0^2+e1^2)*c0^2*c1*e0^3*g0*g1^3-1/(-e0^2+e1^2)*c0^2*c1*e0^3*g1^4+1/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^4+1/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^3*g1+2/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^2*g1^2+1/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0*g1^3+1/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g1^4-1/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^4-1/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^3*g1-2/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^2*g1^2-1/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0*g1^3-1/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g1^4+1/(-e0^2+e1^2)*c0^2*c1*e1^3*g0^4+2/(-e0^2+e1^2)*c0^2*c1*e1^3*g0^3*g1+2/(-e0^2+e1^2)*c0^2*c1*e1^3*g0*g1^3+1/(-e0^2+e1^2)*c0^2*c1*e1^3*g1^4-1/(-e0^2+e1^2)*c0*c1^2*e0^3*g0^4-2/(-e0^2+e1^2)*c0*c1^2*e0^3*g0^3*g1-2/(-e0^2+e1^2)*c0*c1^2*e0^3*g0*g1^3-1/(-e0^2+e1^2)*c0*c1^2*e0^3*g1^4+1/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^4+1/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^3*g1+2/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^2*g1^2+1/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0*g1^3+1/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g1^4-1/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^4-1/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^3*g1-2/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^2*g1^2-1/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0*g1^3-1/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g1^4+1/(-e0^2+e1^2)*c0*c1^2*e1^3*g0^4+2/(-e0^2+e1^2)*c0*c1^2*e1^3*g0^3*g1+2/(-e0^2+e1^2)*c0*c1^2*e1^3*g0*g1^3+1/(-e0^2+e1^2)*c0*c1^2*e1^3*g1^4-2/(-e0^2+e1^2)*c1^3*e0^3*g0^2*g1^2+1/(-e0^2+e1^2)*c1^3*e0^2*e1*g0^3*g1+1/(-e0^2+e1^2)*c1^3*e0^2*e1*g0*g1^3-1/(-e0^2+e1^2)*c1^3*e0*e1^2*g0^3*g1-1/(-e0^2+e1^2)*c1^3*e0*e1^2*g0*g1^3+2/(-e0^2+e1^2)*c1^3*e1^3*g0^2*g1^2,
-1/(-e0^2+e1^2)*c0^3*e0^3*g0^3*g1-1/(-e0^2+e1^2)*c0^3*e0^3*g0*g1^3+2/(-e0^2+e1^2)*c0^3*e0^2*e1*g0^2*g1^2-2/(-e0^2+e1^2)*c0^3*e0*e1^2*g0^2*g1^2+1/(-e0^2+e1^2)*c0^3*e1^3*g0^3*g1+1/(-e0^2+e1^2)*c0^3*e1^3*g0*g1^3-1/(-e0^2+e1^2)*c0^2*c1*e0^3*g0^4-1/(-e0^2+e1^2)*c0^2*c1*e0^3*g0^3*g1-2/(-e0^2+e1^2)*c0^2*c1*e0^3*g0^2*g1^2-1/(-e0^2+e1^2)*c0^2*c1*e0^3*g0*g1^3-1/(-e0^2+e1^2)*c0^2*c1*e0^3*g1^4+1/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^4+2/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^3*g1+2/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0*g1^3+1/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g1^4-1/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^4-2/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^3*g1-2/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0*g1^3-1/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g1^4+1/(-e0^2+e1^2)*c0^2*c1*e1^3*g0^4+1/(-e0^2+e1^2)*c0^2*c1*e1^3*g0^3*g1+2/(-e0^2+e1^2)*c0^2*c1*e1^3*g0^2*g1^2+1/(-e0^2+e1^2)*c0^2*c1*e1^3*g0*g1^3+1/(-e0^2+e1^2)*c0^2*c1*e1^3*g1^4-1/(-e0^2+e1^2)*c0*c1^2*e0^3*g0^4-1/(-e0^2+e1^2)*c0*c1^2*e0^3*g0^3*g1-2/(-e0^2+e1^2)*c0*c1^2*e0^3*g0^2*g1^2-1/(-e0^2+e1^2)*c0*c1^2*e0^3*g0*g1^3-1/(-e0^2+e1^2)*c0*c1^2*e0^3*g1^4+1/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^4+2/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^3*g1+2/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0*g1^3+1/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g1^4-1/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^4-2/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^3*g1-2/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0*g1^3-1/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g1^4+1/(-e0^2+e1^2)*c0*c1^2*e1^3*g0^4+1/(-e0^2+e1^2)*c0*c1^2*e1^3*g0^3*g1+2/(-e0^2+e1^2)*c0*c1^2*e1^3*g0^2*g1^2+1/(-e0^2+e1^2)*c0*c1^2*e1^3*g0*g1^3+1/(-e0^2+e1^2)*c0*c1^2*e1^3*g1^4-1/(-e0^2+e1^2)*c1^3*e0^3*g0^3*g1-1/(-e0^2+e1^2)*c1^3*e0^3*g0*g1^3+2/(-e0^2+e1^2)*c1^3*e0^2*e1*g0^2*g1^2-2/(-e0^2+e1^2)*c1^3*e0*e1^2*g0^2*g1^2+1/(-e0^2+e1^2)*c1^3*e1^3*g0^3*g1+1/(-e0^2+e1^2)*c1^3*e1^3*g0*g1^3,
-4/(-e0^2+e1^2)*c0^3*e0^3*g0^2*g1^2+2/(-e0^2+e1^2)*c0^3*e0^2*e1*g0^3*g1+2/(-e0^2+e1^2)*c0^3*e0^2*e1*g0*g1^3-2/(-e0^2+e1^2)*c0^3*e0*e1^2*g0^3*g1-2/(-e0^2+e1^2)*c0^3*e0*e1^2*g0*g1^3+4/(-e0^2+e1^2)*c0^3*e1^3*g0^2*g1^2-4/(-e0^2+e1^2)*c0^2*c1*e0^3*g0^3*g1-4/(-e0^2+e1^2)*c0^2*c1*e0^3*g0^2*g1^2-4/(-e0^2+e1^2)*c0^2*c1*e0^3*g0*g1^3+2/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^3*g1+8/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^2*g1^2+2/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0*g1^3-2/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^3*g1-8/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^2*g1^2-2/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0*g1^3+4/(-e0^2+e1^2)*c0^2*c1*e1^3*g0^3*g1+4/(-e0^2+e1^2)*c0^2*c1*e1^3*g0^2*g1^2+4/(-e0^2+e1^2)*c0^2*c1*e1^3*g0*g1^3-4/(-e0^2+e1^2)*c0*c1^2*e0^3*g0^3*g1-4/(-e0^2+e1^2)*c0*c1^2*e0^3*g0^2*g1^2-4/(-e0^2+e1^2)*c0*c1^2*e0^3*g0*g1^3+2/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^3*g1+8/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^2*g1^2+2/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0*g1^3-2/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^3*g1-8/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^2*g1^2-2/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0*g1^3+4/(-e0^2+e1^2)*c0*c1^2*e1^3*g0^3*g1+4/(-e0^2+e1^2)*c0*c1^2*e1^3*g0^2*g1^2+4/(-e0^2+e1^2)*c0*c1^2*e1^3*g0*g1^3-4/(-e0^2+e1^2)*c1^3*e0^3*g0^2*g1^2+2/(-e0^2+e1^2)*c1^3*e0^2*e1*g0^3*g1+2/(-e0^2+e1^2)*c1^3*e0^2*e1*g0*g1^3-2/(-e0^2+e1^2)*c1^3*e0*e1^2*g0^3*g1-2/(-e0^2+e1^2)*c1^3*e0*e1^2*g0*g1^3+4/(-e0^2+e1^2)*c1^3*e1^3*g0^2*g1^2,
-1/(-e0^2+e1^2)*c0^3*e0^3*g0^3*g1-1/(-e0^2+e1^2)*c0^3*e0^3*g0*g1^3+1/(-e0^2+e1^2)*c0^3*e0^2*e1*g0^4+1/(-e0^2+e1^2)*c0^3*e0^2*e1*g1^4-1/(-e0^2+e1^2)*c0^3*e0*e1^2*g0^4-1/(-e0^2+e1^2)*c0^3*e0*e1^2*g1^4+1/(-e0^2+e1^2)*c0^3*e1^3*g0^3*g1+1/(-e0^2+e1^2)*c0^3*e1^3*g0*g1^3-1/(-e0^2+e1^2)*c0^2*c1*e0^3*g0^4-1/(-e0^2+e1^2)*c0^2*c1*e0^3*g0^3*g1-2/(-e0^2+e1^2)*c0^2*c1*e0^3*g0^2*g1^2-1/(-e0^2+e1^2)*c0^2*c1*e0^3*g0*g1^3-1/(-e0^2+e1^2)*c0^2*c1*e0^3*g1^4+2/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^3*g1+2/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^2*g1^2+2/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0*g1^3-2/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^3*g1-2/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^2*g1^2-2/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0*g1^3+1/(-e0^2+e1^2)*c0^2*c1*e1^3*g0^4+1/(-e0^2+e1^2)*c0^2*c1*e1^3*g0^3*g1+2/(-e0^2+e1^2)*c0^2*c1*e1^3*g0^2*g1^2+1/(-e0^2+e1^2)*c0^2*c1*e1^3*g0*g1^3+1/(-e0^2+e1^2)*c0^2*c1*e1^3*g1^4-1/(-e0^2+e1^2)*c0*c1^2*e0^3*g0^4-1/(-e0^2+e1^2)*c0*c1^2*e0^3*g0^3*g1-2/(-e0^2+e1^2)*c0*c1^2*e0^3*g0^2*g1^2-1/(-e0^2+e1^2)*c0*c1^2*e0^3*g0*g1^3-1/(-e0^2+e1^2)*c0*c1^2*e0^3*g1^4+2/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^3*g1+2/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^2*g1^2+2/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0*g1^3-2/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^3*g1-2/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^2*g1^2-2/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0*g1^3+1/(-e0^2+e1^2)*c0*c1^2*e1^3*g0^4+1/(-e0^2+e1^2)*c0*c1^2*e1^3*g0^3*g1+2/(-e0^2+e1^2)*c0*c1^2*e1^3*g0^2*g1^2+1/(-e0^2+e1^2)*c0*c1^2*e1^3*g0*g1^3+1/(-e0^2+e1^2)*c0*c1^2*e1^3*g1^4-1/(-e0^2+e1^2)*c1^3*e0^3*g0^3*g1-1/(-e0^2+e1^2)*c1^3*e0^3*g0*g1^3+1/(-e0^2+e1^2)*c1^3*e0^2*e1*g0^4+1/(-e0^2+e1^2)*c1^3*e0^2*e1*g1^4-1/(-e0^2+e1^2)*c1^3*e0*e1^2*g0^4-1/(-e0^2+e1^2)*c1^3*e0*e1^2*g1^4+1/(-e0^2+e1^2)*c1^3*e1^3*g0^3*g1+1/(-e0^2+e1^2)*c1^3*e1^3*g0*g1^3,
-2/(-e0^2+e1^2)*c0^3*e0^2*e1*g0^4-2/(-e0^2+e1^2)*c0^3*e0^2*e1*g0^3*g1-2/(-e0^2+e1^2)*c0^3*e0^2*e1*g0*g1^3-2/(-e0^2+e1^2)*c0^3*e0^2*e1*g1^4+2/(-e0^2+e1^2)*c0^3*e0*e1^2*g0^4+2/(-e0^2+e1^2)*c0^3*e0*e1^2*g0^3*g1+2/(-e0^2+e1^2)*c0^3*e0*e1^2*g0*g1^3+2/(-e0^2+e1^2)*c0^3*e0*e1^2*g1^4-2/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^4-6/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^3*g1-8/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^2*g1^2-6/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0*g1^3-2/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g1^4+2/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^4+6/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^3*g1+8/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^2*g1^2+6/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0*g1^3+2/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g1^4-2/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^4-6/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^3*g1-8/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^2*g1^2-6/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0*g1^3-2/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g1^4+2/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^4+6/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^3*g1+8/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^2*g1^2+6/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0*g1^3+2/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g1^4-2/(-e0^2+e1^2)*c1^3*e0^2*e1*g0^4-2/(-e0^2+e1^2)*c1^3*e0^2*e1*g0^3*g1-2/(-e0^2+e1^2)*c1^3*e0^2*e1*g0*g1^3-2/(-e0^2+e1^2)*c1^3*e0^2*e1*g1^4+2/(-e0^2+e1^2)*c1^3*e0*e1^2*g0^4+2/(-e0^2+e1^2)*c1^3*e0*e1^2*g0^3*g1+2/(-e0^2+e1^2)*c1^3*e0*e1^2*g0*g1^3+2/(-e0^2+e1^2)*c1^3*e0*e1^2*g1^4,
-4/(-e0^2+e1^2)*c0^3*e0^2*e1*g0^3*g1-8/(-e0^2+e1^2)*c0^3*e0^2*e1*g0^2*g1^2-4/(-e0^2+e1^2)*c0^3*e0^2*e1*g0*g1^3+4/(-e0^2+e1^2)*c0^3*e0*e1^2*g0^3*g1+8/(-e0^2+e1^2)*c0^3*e0*e1^2*g0^2*g1^2+4/(-e0^2+e1^2)*c0^3*e0*e1^2*g0*g1^3-12/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^3*g1-24/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^2*g1^2-12/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0*g1^3+12/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^3*g1+24/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^2*g1^2+12/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0*g1^3-12/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^3*g1-24/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^2*g1^2-12/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0*g1^3+12/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^3*g1+24/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^2*g1^2+12/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0*g1^3-4/(-e0^2+e1^2)*c1^3*e0^2*e1*g0^3*g1-8/(-e0^2+e1^2)*c1^3*e0^2*e1*g0^2*g1^2-4/(-e0^2+e1^2)*c1^3*e0^2*e1*g0*g1^3+4/(-e0^2+e1^2)*c1^3*e0*e1^2*g0^3*g1+8/(-e0^2+e1^2)*c1^3*e0*e1^2*g0^2*g1^2+4/(-e0^2+e1^2)*c1^3*e0*e1^2*g0*g1^3,
-2/(-e0^2+e1^2)*c0^3*e0^2*e1*g0^3*g1-4/(-e0^2+e1^2)*c0^3*e0^2*e1*g0^2*g1^2-2/(-e0^2+e1^2)*c0^3*e0^2*e1*g0*g1^3+2/(-e0^2+e1^2)*c0^3*e0*e1^2*g0^3*g1+4/(-e0^2+e1^2)*c0^3*e0*e1^2*g0^2*g1^2+2/(-e0^2+e1^2)*c0^3*e0*e1^2*g0*g1^3-4/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^4-6/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^3*g1-4/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0^2*g1^2-6/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g0*g1^3-4/(-e0^2+e1^2)*c0^2*c1*e0^2*e1*g1^4+4/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^4+6/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^3*g1+4/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0^2*g1^2+6/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g0*g1^3+4/(-e0^2+e1^2)*c0^2*c1*e0*e1^2*g1^4-4/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^4-6/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^3*g1-4/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0^2*g1^2-6/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g0*g1^3-4/(-e0^2+e1^2)*c0*c1^2*e0^2*e1*g1^4+4/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^4+6/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^3*g1+4/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0^2*g1^2+6/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g0*g1^3+4/(-e0^2+e1^2)*c0*c1^2*e0*e1^2*g1^4-2/(-e0^2+e1^2)*c1^3*e0^2*e1*g0^3*g1-4/(-e0^2+e1^2)*c1^3*e0^2*e1*g0^2*g1^2-2/(-e0^2+e1^2)*c1^3*e0^2*e1*g0*g1^3+2/(-e0^2+e1^2)*c1^3*e0*e1^2*g0^3*g1+4/(-e0^2+e1^2)*c1^3*e0*e1^2*g0^2*g1^2+2/(-e0^2+e1^2)*c1^3*e0*e1^2*g0*g1^3]:

# Substitutions based on the model

P := P0:
P := subs(c0 = 1-c1, P):
P := subs(e0 = 1-e1, P):
P := subs(g0 = 1-g1, P):

# Check that the polynomial parametrization lies in the probability simplex

suma := 0:
for i from 1 to nops(P) do
suma := suma + P[i]:
od:
normal(expand(suma));

# Ideal of Invariants in Fourier coordinates

Invariants := Matrix([
q3*q6-q2*q7,
q4*q5-q2*q7,
q3*q5-q1*q7,
q2*q5-q1*q6,
q2*q3-q1*q4]):

# Ideal of Invariants in probability coordinates

Fourier := MatrixMatrixMultiply(F,PParam):

PInvariants := Invariants:
for i from 1 to nops(QParam) do
PInvariants := subs(QParam[i] = Fourier[i, 1], PInvariants):
od:

# Evaluation of Invariants at the polynomial/rational parametrization

num := op(PInvariants[1,1..-1])[1]:
for j from 1 to num do
coordpoly := PInvariants[1, j]:
for i from 1 to op(PParam[1..-1,1])[1] do
coordpoly := subs(PParam[i, 1] = P0[i], coordpoly):
od:
coordpoly :=expand(coordpoly):
lprint(j,coordpoly);
od: