restart;
with(LinearAlgebra):

# Define indeterminates

QParam := [q1,q2,q3,q4,q5,q6,q7,q8]:
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],
[1,0,-1,0,0,0,-1,0,1],
[1,1,1,-1,-1,-1,1,1,1],
[1,-1,1,-1,1,-1,1,-1,1],
[1,1/2,0,1/2,0,-1/2,0,-1/2,-1],
[1,-1,1,0,0,0,-1,1,-1],
[1,0,-1,-1,0,1,1,0,-1]
]):

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

# List of polynomial parametrizations

P0 := [
-1/(-f0^2+f1^2)*b0^2*d0^3*f0^3*h0^4-1/(-f0^2+f1^2)*b0^2*d0^3*f0^3*h1^4+1/(-f0^2+f1^2)*b0^2*d0^3*f0^2*f1*h0^3*h1+1/(-f0^2+f1^2)*b0^2*d0^3*f0^2*f1*h0*h1^3-1/(-f0^2+f1^2)*b0^2*d0^3*f0*f1^2*h0^3*h1-1/(-f0^2+f1^2)*b0^2*d0^3*f0*f1^2*h0*h1^3+1/(-f0^2+f1^2)*b0^2*d0^3*f1^3*h0^4+1/(-f0^2+f1^2)*b0^2*d0^3*f1^3*h1^4-2/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^3*h0^3*h1-2/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^3*h0^2*h1^2-2/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^3*h0*h1^3+1/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h0^4+1/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h0^3*h1+2/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h0^2*h1^2+1/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h0*h1^3+1/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h1^4-1/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h0^4-1/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h0^3*h1-2/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h0^2*h1^2-1/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h0*h1^3-1/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h1^4+2/(-f0^2+f1^2)*b0^2*d0^2*d1*f1^3*h0^3*h1+2/(-f0^2+f1^2)*b0^2*d0^2*d1*f1^3*h0^2*h1^2+2/(-f0^2+f1^2)*b0^2*d0^2*d1*f1^3*h0*h1^3-2/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^3*h0^3*h1-2/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^3*h0^2*h1^2-2/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^3*h0*h1^3+1/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h0^4+1/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h0^3*h1+2/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h0^2*h1^2+1/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h0*h1^3+1/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h1^4-1/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h0^4-1/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h0^3*h1-2/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h0^2*h1^2-1/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h0*h1^3-1/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h1^4+2/(-f0^2+f1^2)*b0^2*d0*d1^2*f1^3*h0^3*h1+2/(-f0^2+f1^2)*b0^2*d0*d1^2*f1^3*h0^2*h1^2+2/(-f0^2+f1^2)*b0^2*d0*d1^2*f1^3*h0*h1^3-1/(-f0^2+f1^2)*b0^2*d1^3*f0^3*h0^4-1/(-f0^2+f1^2)*b0^2*d1^3*f0^3*h1^4+1/(-f0^2+f1^2)*b0^2*d1^3*f0^2*f1*h0^3*h1+1/(-f0^2+f1^2)*b0^2*d1^3*f0^2*f1*h0*h1^3-1/(-f0^2+f1^2)*b0^2*d1^3*f0*f1^2*h0^3*h1-1/(-f0^2+f1^2)*b0^2*d1^3*f0*f1^2*h0*h1^3+1/(-f0^2+f1^2)*b0^2*d1^3*f1^3*h0^4+1/(-f0^2+f1^2)*b0^2*d1^3*f1^3*h1^4-2/(-f0^2+f1^2)*b0*b1*d0^3*f0^3*h0^3*h1-2/(-f0^2+f1^2)*b0*b1*d0^3*f0^3*h0*h1^3+4/(-f0^2+f1^2)*b0*b1*d0^3*f0^2*f1*h0^2*h1^2-4/(-f0^2+f1^2)*b0*b1*d0^3*f0*f1^2*h0^2*h1^2+2/(-f0^2+f1^2)*b0*b1*d0^3*f1^3*h0^3*h1+2/(-f0^2+f1^2)*b0*b1*d0^3*f1^3*h0*h1^3-2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^3*h0^4-2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^3*h0^3*h1-4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^3*h0^2*h1^2-2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^3*h0*h1^3-2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^3*h1^4+2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h0^4+4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h0^3*h1+4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h0*h1^3+2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h1^4-2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h0^4-4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h0^3*h1-4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h0*h1^3-2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h1^4+2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f1^3*h0^4+2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f1^3*h0^3*h1+4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f1^3*h0^2*h1^2+2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f1^3*h0*h1^3+2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f1^3*h1^4-2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^3*h0^4-2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^3*h0^3*h1-4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^3*h0^2*h1^2-2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^3*h0*h1^3-2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^3*h1^4+2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h0^4+4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h0^3*h1+4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h0*h1^3+2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h1^4-2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h0^4-4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h0^3*h1-4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h0*h1^3-2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h1^4+2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f1^3*h0^4+2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f1^3*h0^3*h1+4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f1^3*h0^2*h1^2+2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f1^3*h0*h1^3+2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f1^3*h1^4-2/(-f0^2+f1^2)*b0*b1*d1^3*f0^3*h0^3*h1-2/(-f0^2+f1^2)*b0*b1*d1^3*f0^3*h0*h1^3+4/(-f0^2+f1^2)*b0*b1*d1^3*f0^2*f1*h0^2*h1^2-4/(-f0^2+f1^2)*b0*b1*d1^3*f0*f1^2*h0^2*h1^2+2/(-f0^2+f1^2)*b0*b1*d1^3*f1^3*h0^3*h1+2/(-f0^2+f1^2)*b0*b1*d1^3*f1^3*h0*h1^3-1/(-f0^2+f1^2)*b1^2*d0^3*f0^3*h0^4-1/(-f0^2+f1^2)*b1^2*d0^3*f0^3*h1^4+1/(-f0^2+f1^2)*b1^2*d0^3*f0^2*f1*h0^3*h1+1/(-f0^2+f1^2)*b1^2*d0^3*f0^2*f1*h0*h1^3-1/(-f0^2+f1^2)*b1^2*d0^3*f0*f1^2*h0^3*h1-1/(-f0^2+f1^2)*b1^2*d0^3*f0*f1^2*h0*h1^3+1/(-f0^2+f1^2)*b1^2*d0^3*f1^3*h0^4+1/(-f0^2+f1^2)*b1^2*d0^3*f1^3*h1^4-2/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^3*h0^3*h1-2/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^3*h0^2*h1^2-2/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^3*h0*h1^3+1/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h0^4+1/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h0^3*h1+2/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h0^2*h1^2+1/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h0*h1^3+1/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h1^4-1/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h0^4-1/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h0^3*h1-2/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h0^2*h1^2-1/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h0*h1^3-1/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h1^4+2/(-f0^2+f1^2)*b1^2*d0^2*d1*f1^3*h0^3*h1+2/(-f0^2+f1^2)*b1^2*d0^2*d1*f1^3*h0^2*h1^2+2/(-f0^2+f1^2)*b1^2*d0^2*d1*f1^3*h0*h1^3-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^3*h0^3*h1-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^3*h0^2*h1^2-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^3*h0*h1^3+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0^4+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0^3*h1+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0^2*h1^2+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0*h1^3+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h1^4-1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0^4-1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0^3*h1-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0^2*h1^2-1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0*h1^3-1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h1^4+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h0^3*h1+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h0^2*h1^2+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h0*h1^3-1/(-f0^2+f1^2)*b1^2*d1^3*f0^3*h0^4-1/(-f0^2+f1^2)*b1^2*d1^3*f0^3*h1^4+1/(-f0^2+f1^2)*b1^2*d1^3*f0^2*f1*h0^3*h1+1/(-f0^2+f1^2)*b1^2*d1^3*f0^2*f1*h0*h1^3-1/(-f0^2+f1^2)*b1^2*d1^3*f0*f1^2*h0^3*h1-1/(-f0^2+f1^2)*b1^2*d1^3*f0*f1^2*h0*h1^3+1/(-f0^2+f1^2)*b1^2*d1^3*f1^3*h0^4+1/(-f0^2+f1^2)*b1^2*d1^3*f1^3*h1^4,
-2/(-f0^2+f1^2)*b0^2*d0^3*f0^3*h0^3*h1-2/(-f0^2+f1^2)*b0^2*d0^3*f0^3*h0*h1^3+4/(-f0^2+f1^2)*b0^2*d0^3*f0^2*f1*h0^2*h1^2-4/(-f0^2+f1^2)*b0^2*d0^3*f0*f1^2*h0^2*h1^2+2/(-f0^2+f1^2)*b0^2*d0^3*f1^3*h0^3*h1+2/(-f0^2+f1^2)*b0^2*d0^3*f1^3*h0*h1^3-2/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^3*h0^3*h1-8/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^3*h0^2*h1^2-2/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^3*h0*h1^3+4/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h0^3*h1+4/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h0^2*h1^2+4/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h0*h1^3-4/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h0^3*h1-4/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h0^2*h1^2-4/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h0*h1^3+2/(-f0^2+f1^2)*b0^2*d0^2*d1*f1^3*h0^3*h1+8/(-f0^2+f1^2)*b0^2*d0^2*d1*f1^3*h0^2*h1^2+2/(-f0^2+f1^2)*b0^2*d0^2*d1*f1^3*h0*h1^3-2/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^3*h0^3*h1-8/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^3*h0^2*h1^2-2/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^3*h0*h1^3+4/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h0^3*h1+4/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h0^2*h1^2+4/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h0*h1^3-4/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h0^3*h1-4/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h0^2*h1^2-4/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h0*h1^3+2/(-f0^2+f1^2)*b0^2*d0*d1^2*f1^3*h0^3*h1+8/(-f0^2+f1^2)*b0^2*d0*d1^2*f1^3*h0^2*h1^2+2/(-f0^2+f1^2)*b0^2*d0*d1^2*f1^3*h0*h1^3-2/(-f0^2+f1^2)*b0^2*d1^3*f0^3*h0^3*h1-2/(-f0^2+f1^2)*b0^2*d1^3*f0^3*h0*h1^3+4/(-f0^2+f1^2)*b0^2*d1^3*f0^2*f1*h0^2*h1^2-4/(-f0^2+f1^2)*b0^2*d1^3*f0*f1^2*h0^2*h1^2+2/(-f0^2+f1^2)*b0^2*d1^3*f1^3*h0^3*h1+2/(-f0^2+f1^2)*b0^2*d1^3*f1^3*h0*h1^3-8/(-f0^2+f1^2)*b0*b1*d0^3*f0^3*h0^2*h1^2+4/(-f0^2+f1^2)*b0*b1*d0^3*f0^2*f1*h0^3*h1+4/(-f0^2+f1^2)*b0*b1*d0^3*f0^2*f1*h0*h1^3-4/(-f0^2+f1^2)*b0*b1*d0^3*f0*f1^2*h0^3*h1-4/(-f0^2+f1^2)*b0*b1*d0^3*f0*f1^2*h0*h1^3+8/(-f0^2+f1^2)*b0*b1*d0^3*f1^3*h0^2*h1^2-8/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^3*h0^3*h1-8/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^3*h0^2*h1^2-8/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^3*h0*h1^3+4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h0^3*h1+16/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h0^2*h1^2+4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h0*h1^3-4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h0^3*h1-16/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h0^2*h1^2-4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h0*h1^3+8/(-f0^2+f1^2)*b0*b1*d0^2*d1*f1^3*h0^3*h1+8/(-f0^2+f1^2)*b0*b1*d0^2*d1*f1^3*h0^2*h1^2+8/(-f0^2+f1^2)*b0*b1*d0^2*d1*f1^3*h0*h1^3-8/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^3*h0^3*h1-8/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^3*h0^2*h1^2-8/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^3*h0*h1^3+4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h0^3*h1+16/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h0^2*h1^2+4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h0*h1^3-4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h0^3*h1-16/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h0^2*h1^2-4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h0*h1^3+8/(-f0^2+f1^2)*b0*b1*d0*d1^2*f1^3*h0^3*h1+8/(-f0^2+f1^2)*b0*b1*d0*d1^2*f1^3*h0^2*h1^2+8/(-f0^2+f1^2)*b0*b1*d0*d1^2*f1^3*h0*h1^3-8/(-f0^2+f1^2)*b0*b1*d1^3*f0^3*h0^2*h1^2+4/(-f0^2+f1^2)*b0*b1*d1^3*f0^2*f1*h0^3*h1+4/(-f0^2+f1^2)*b0*b1*d1^3*f0^2*f1*h0*h1^3-4/(-f0^2+f1^2)*b0*b1*d1^3*f0*f1^2*h0^3*h1-4/(-f0^2+f1^2)*b0*b1*d1^3*f0*f1^2*h0*h1^3+8/(-f0^2+f1^2)*b0*b1*d1^3*f1^3*h0^2*h1^2-2/(-f0^2+f1^2)*b1^2*d0^3*f0^3*h0^3*h1-2/(-f0^2+f1^2)*b1^2*d0^3*f0^3*h0*h1^3+4/(-f0^2+f1^2)*b1^2*d0^3*f0^2*f1*h0^2*h1^2-4/(-f0^2+f1^2)*b1^2*d0^3*f0*f1^2*h0^2*h1^2+2/(-f0^2+f1^2)*b1^2*d0^3*f1^3*h0^3*h1+2/(-f0^2+f1^2)*b1^2*d0^3*f1^3*h0*h1^3-2/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^3*h0^3*h1-8/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^3*h0^2*h1^2-2/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^3*h0*h1^3+4/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h0^3*h1+4/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h0^2*h1^2+4/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h0*h1^3-4/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h0^3*h1-4/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h0^2*h1^2-4/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h0*h1^3+2/(-f0^2+f1^2)*b1^2*d0^2*d1*f1^3*h0^3*h1+8/(-f0^2+f1^2)*b1^2*d0^2*d1*f1^3*h0^2*h1^2+2/(-f0^2+f1^2)*b1^2*d0^2*d1*f1^3*h0*h1^3-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^3*h0^3*h1-8/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^3*h0^2*h1^2-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^3*h0*h1^3+4/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0^3*h1+4/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0^2*h1^2+4/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0*h1^3-4/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0^3*h1-4/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0^2*h1^2-4/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0*h1^3+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h0^3*h1+8/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h0^2*h1^2+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h0*h1^3-2/(-f0^2+f1^2)*b1^2*d1^3*f0^3*h0^3*h1-2/(-f0^2+f1^2)*b1^2*d1^3*f0^3*h0*h1^3+4/(-f0^2+f1^2)*b1^2*d1^3*f0^2*f1*h0^2*h1^2-4/(-f0^2+f1^2)*b1^2*d1^3*f0*f1^2*h0^2*h1^2+2/(-f0^2+f1^2)*b1^2*d1^3*f1^3*h0^3*h1+2/(-f0^2+f1^2)*b1^2*d1^3*f1^3*h0*h1^3,
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*f0^3*h0^4-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^3*h0^3*h1-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^3*h0*h1^3-1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^3*h1^4+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0^4+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0^3*h1+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0^2*h1^2+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0*h1^3+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h1^4-1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0^4-1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0^3*h1-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0^2*h1^2-1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0*h1^3-1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h1^4+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h0^4+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h0^3*h1+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h0*h1^3+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h1^4-2/(-f0^2+f1^2)*b1^2*d1^3*f0^3*h0^2*h1^2+1/(-f0^2+f1^2)*b1^2*d1^3*f0^2*f1*h0^3*h1+1/(-f0^2+f1^2)*b1^2*d1^3*f0^2*f1*h0*h1^3-1/(-f0^2+f1^2)*b1^2*d1^3*f0*f1^2*h0^3*h1-1/(-f0^2+f1^2)*b1^2*d1^3*f0*f1^2*h0*h1^3+2/(-f0^2+f1^2)*b1^2*d1^3*f1^3*h0^2*h1^2,
-2/(-f0^2+f1^2)*b0^2*d0^3*f0^2*f1*h0^4-2/(-f0^2+f1^2)*b0^2*d0^3*f0^2*f1*h0^3*h1-2/(-f0^2+f1^2)*b0^2*d0^3*f0^2*f1*h0*h1^3-2/(-f0^2+f1^2)*b0^2*d0^3*f0^2*f1*h1^4+2/(-f0^2+f1^2)*b0^2*d0^3*f0*f1^2*h0^4+2/(-f0^2+f1^2)*b0^2*d0^3*f0*f1^2*h0^3*h1+2/(-f0^2+f1^2)*b0^2*d0^3*f0*f1^2*h0*h1^3+2/(-f0^2+f1^2)*b0^2*d0^3*f0*f1^2*h1^4-2/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h0^4-6/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h0^3*h1-8/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h0^2*h1^2-6/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h0*h1^3-2/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h1^4+2/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h0^4+6/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h0^3*h1+8/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h0^2*h1^2+6/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h0*h1^3+2/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h1^4-2/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h0^4-6/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h0^3*h1-8/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h0^2*h1^2-6/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h0*h1^3-2/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h1^4+2/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h0^4+6/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h0^3*h1+8/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h0^2*h1^2+6/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h0*h1^3+2/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h1^4-2/(-f0^2+f1^2)*b0^2*d1^3*f0^2*f1*h0^4-2/(-f0^2+f1^2)*b0^2*d1^3*f0^2*f1*h0^3*h1-2/(-f0^2+f1^2)*b0^2*d1^3*f0^2*f1*h0*h1^3-2/(-f0^2+f1^2)*b0^2*d1^3*f0^2*f1*h1^4+2/(-f0^2+f1^2)*b0^2*d1^3*f0*f1^2*h0^4+2/(-f0^2+f1^2)*b0^2*d1^3*f0*f1^2*h0^3*h1+2/(-f0^2+f1^2)*b0^2*d1^3*f0*f1^2*h0*h1^3+2/(-f0^2+f1^2)*b0^2*d1^3*f0*f1^2*h1^4-4/(-f0^2+f1^2)*b0*b1*d0^3*f0^2*f1*h0^3*h1-8/(-f0^2+f1^2)*b0*b1*d0^3*f0^2*f1*h0^2*h1^2-4/(-f0^2+f1^2)*b0*b1*d0^3*f0^2*f1*h0*h1^3+4/(-f0^2+f1^2)*b0*b1*d0^3*f0*f1^2*h0^3*h1+8/(-f0^2+f1^2)*b0*b1*d0^3*f0*f1^2*h0^2*h1^2+4/(-f0^2+f1^2)*b0*b1*d0^3*f0*f1^2*h0*h1^3-8/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h0^4-12/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h0^3*h1-8/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h0^2*h1^2-12/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h0*h1^3-8/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h1^4+8/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h0^4+12/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h0^3*h1+8/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h0^2*h1^2+12/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h0*h1^3+8/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h1^4-8/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h0^4-12/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h0^3*h1-8/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h0^2*h1^2-12/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h0*h1^3-8/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h1^4+8/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h0^4+12/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h0^3*h1+8/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h0^2*h1^2+12/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h0*h1^3+8/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h1^4-4/(-f0^2+f1^2)*b0*b1*d1^3*f0^2*f1*h0^3*h1-8/(-f0^2+f1^2)*b0*b1*d1^3*f0^2*f1*h0^2*h1^2-4/(-f0^2+f1^2)*b0*b1*d1^3*f0^2*f1*h0*h1^3+4/(-f0^2+f1^2)*b0*b1*d1^3*f0*f1^2*h0^3*h1+8/(-f0^2+f1^2)*b0*b1*d1^3*f0*f1^2*h0^2*h1^2+4/(-f0^2+f1^2)*b0*b1*d1^3*f0*f1^2*h0*h1^3-2/(-f0^2+f1^2)*b1^2*d0^3*f0^2*f1*h0^4-2/(-f0^2+f1^2)*b1^2*d0^3*f0^2*f1*h0^3*h1-2/(-f0^2+f1^2)*b1^2*d0^3*f0^2*f1*h0*h1^3-2/(-f0^2+f1^2)*b1^2*d0^3*f0^2*f1*h1^4+2/(-f0^2+f1^2)*b1^2*d0^3*f0*f1^2*h0^4+2/(-f0^2+f1^2)*b1^2*d0^3*f0*f1^2*h0^3*h1+2/(-f0^2+f1^2)*b1^2*d0^3*f0*f1^2*h0*h1^3+2/(-f0^2+f1^2)*b1^2*d0^3*f0*f1^2*h1^4-2/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h0^4-6/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h0^3*h1-8/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h0^2*h1^2-6/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h0*h1^3-2/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h1^4+2/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h0^4+6/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h0^3*h1+8/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h0^2*h1^2+6/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h0*h1^3+2/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h1^4-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0^4-6/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0^3*h1-8/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0^2*h1^2-6/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0*h1^3-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h1^4+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0^4+6/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0^3*h1+8/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0^2*h1^2+6/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0*h1^3+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h1^4-2/(-f0^2+f1^2)*b1^2*d1^3*f0^2*f1*h0^4-2/(-f0^2+f1^2)*b1^2*d1^3*f0^2*f1*h0^3*h1-2/(-f0^2+f1^2)*b1^2*d1^3*f0^2*f1*h0*h1^3-2/(-f0^2+f1^2)*b1^2*d1^3*f0^2*f1*h1^4+2/(-f0^2+f1^2)*b1^2*d1^3*f0*f1^2*h0^4+2/(-f0^2+f1^2)*b1^2*d1^3*f0*f1^2*h0^3*h1+2/(-f0^2+f1^2)*b1^2*d1^3*f0*f1^2*h0*h1^3+2/(-f0^2+f1^2)*b1^2*d1^3*f0*f1^2*h1^4,
-4/(-f0^2+f1^2)*b0^2*d0^3*f0^2*f1*h0^3*h1-8/(-f0^2+f1^2)*b0^2*d0^3*f0^2*f1*h0^2*h1^2-4/(-f0^2+f1^2)*b0^2*d0^3*f0^2*f1*h0*h1^3+4/(-f0^2+f1^2)*b0^2*d0^3*f0*f1^2*h0^3*h1+8/(-f0^2+f1^2)*b0^2*d0^3*f0*f1^2*h0^2*h1^2+4/(-f0^2+f1^2)*b0^2*d0^3*f0*f1^2*h0*h1^3-12/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h0^3*h1-24/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h0^2*h1^2-12/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h0*h1^3+12/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h0^3*h1+24/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h0^2*h1^2+12/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h0*h1^3-12/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h0^3*h1-24/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h0^2*h1^2-12/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h0*h1^3+12/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h0^3*h1+24/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h0^2*h1^2+12/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h0*h1^3-4/(-f0^2+f1^2)*b0^2*d1^3*f0^2*f1*h0^3*h1-8/(-f0^2+f1^2)*b0^2*d1^3*f0^2*f1*h0^2*h1^2-4/(-f0^2+f1^2)*b0^2*d1^3*f0^2*f1*h0*h1^3+4/(-f0^2+f1^2)*b0^2*d1^3*f0*f1^2*h0^3*h1+8/(-f0^2+f1^2)*b0^2*d1^3*f0*f1^2*h0^2*h1^2+4/(-f0^2+f1^2)*b0^2*d1^3*f0*f1^2*h0*h1^3-8/(-f0^2+f1^2)*b0*b1*d0^3*f0^2*f1*h0^3*h1-16/(-f0^2+f1^2)*b0*b1*d0^3*f0^2*f1*h0^2*h1^2-8/(-f0^2+f1^2)*b0*b1*d0^3*f0^2*f1*h0*h1^3+8/(-f0^2+f1^2)*b0*b1*d0^3*f0*f1^2*h0^3*h1+16/(-f0^2+f1^2)*b0*b1*d0^3*f0*f1^2*h0^2*h1^2+8/(-f0^2+f1^2)*b0*b1*d0^3*f0*f1^2*h0*h1^3-24/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h0^3*h1-48/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h0^2*h1^2-24/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h0*h1^3+24/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h0^3*h1+48/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h0^2*h1^2+24/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h0*h1^3-24/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h0^3*h1-48/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h0^2*h1^2-24/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h0*h1^3+24/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h0^3*h1+48/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h0^2*h1^2+24/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h0*h1^3-8/(-f0^2+f1^2)*b0*b1*d1^3*f0^2*f1*h0^3*h1-16/(-f0^2+f1^2)*b0*b1*d1^3*f0^2*f1*h0^2*h1^2-8/(-f0^2+f1^2)*b0*b1*d1^3*f0^2*f1*h0*h1^3+8/(-f0^2+f1^2)*b0*b1*d1^3*f0*f1^2*h0^3*h1+16/(-f0^2+f1^2)*b0*b1*d1^3*f0*f1^2*h0^2*h1^2+8/(-f0^2+f1^2)*b0*b1*d1^3*f0*f1^2*h0*h1^3-4/(-f0^2+f1^2)*b1^2*d0^3*f0^2*f1*h0^3*h1-8/(-f0^2+f1^2)*b1^2*d0^3*f0^2*f1*h0^2*h1^2-4/(-f0^2+f1^2)*b1^2*d0^3*f0^2*f1*h0*h1^3+4/(-f0^2+f1^2)*b1^2*d0^3*f0*f1^2*h0^3*h1+8/(-f0^2+f1^2)*b1^2*d0^3*f0*f1^2*h0^2*h1^2+4/(-f0^2+f1^2)*b1^2*d0^3*f0*f1^2*h0*h1^3-12/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h0^3*h1-24/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h0^2*h1^2-12/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h0*h1^3+12/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h0^3*h1+24/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h0^2*h1^2+12/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h0*h1^3-12/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0^3*h1-24/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0^2*h1^2-12/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0*h1^3+12/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0^3*h1+24/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0^2*h1^2+12/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0*h1^3-4/(-f0^2+f1^2)*b1^2*d1^3*f0^2*f1*h0^3*h1-8/(-f0^2+f1^2)*b1^2*d1^3*f0^2*f1*h0^2*h1^2-4/(-f0^2+f1^2)*b1^2*d1^3*f0^2*f1*h0*h1^3+4/(-f0^2+f1^2)*b1^2*d1^3*f0*f1^2*h0^3*h1+8/(-f0^2+f1^2)*b1^2*d1^3*f0*f1^2*h0^2*h1^2+4/(-f0^2+f1^2)*b1^2*d1^3*f0*f1^2*h0*h1^3,
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2+f1^2)*b1^2*d0*d1^2*f0^3*h0^3*h1-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^3*h0^2*h1^2-1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^3*h0*h1^3-1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^3*h1^4+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0^3*h1+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0^2*h1^2+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0*h1^3-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0^3*h1-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0^2*h1^2-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0*h1^3+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h0^4+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h0^3*h1+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h0^2*h1^2+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h0*h1^3+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h1^4-1/(-f0^2+f1^2)*b1^2*d1^3*f0^3*h0^3*h1-1/(-f0^2+f1^2)*b1^2*d1^3*f0^3*h0*h1^3+1/(-f0^2+f1^2)*b1^2*d1^3*f0^2*f1*h0^4+1/(-f0^2+f1^2)*b1^2*d1^3*f0^2*f1*h1^4-1/(-f0^2+f1^2)*b1^2*d1^3*f0*f1^2*h0^4-1/(-f0^2+f1^2)*b1^2*d1^3*f0*f1^2*h1^4+1/(-f0^2+f1^2)*b1^2*d1^3*f1^3*h0^3*h1+1/(-f0^2+f1^2)*b1^2*d1^3*f1^3*h0*h1^3,
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-1/(-f0^2+f1^2)*b0^2*d0^3*f0^3*h0^3*h1-1/(-f0^2+f1^2)*b0^2*d0^3*f0^3*h0*h1^3+2/(-f0^2+f1^2)*b0^2*d0^3*f0^2*f1*h0^2*h1^2-2/(-f0^2+f1^2)*b0^2*d0^3*f0*f1^2*h0^2*h1^2+1/(-f0^2+f1^2)*b0^2*d0^3*f1^3*h0^3*h1+1/(-f0^2+f1^2)*b0^2*d0^3*f1^3*h0*h1^3-1/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^3*h0^4-1/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^3*h0^3*h1-2/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^3*h0^2*h1^2-1/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^3*h0*h1^3-1/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^3*h1^4+1/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h0^4+2/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h0^3*h1+2/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h0*h1^3+1/(-f0^2+f1^2)*b0^2*d0^2*d1*f0^2*f1*h1^4-1/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h0^4-2/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h0^3*h1-2/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h0*h1^3-1/(-f0^2+f1^2)*b0^2*d0^2*d1*f0*f1^2*h1^4+1/(-f0^2+f1^2)*b0^2*d0^2*d1*f1^3*h0^4+1/(-f0^2+f1^2)*b0^2*d0^2*d1*f1^3*h0^3*h1+2/(-f0^2+f1^2)*b0^2*d0^2*d1*f1^3*h0^2*h1^2+1/(-f0^2+f1^2)*b0^2*d0^2*d1*f1^3*h0*h1^3+1/(-f0^2+f1^2)*b0^2*d0^2*d1*f1^3*h1^4-1/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^3*h0^4-1/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^3*h0^3*h1-2/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^3*h0^2*h1^2-1/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^3*h0*h1^3-1/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^3*h1^4+1/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h0^4+2/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h0^3*h1+2/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h0*h1^3+1/(-f0^2+f1^2)*b0^2*d0*d1^2*f0^2*f1*h1^4-1/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h0^4-2/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h0^3*h1-2/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h0*h1^3-1/(-f0^2+f1^2)*b0^2*d0*d1^2*f0*f1^2*h1^4+1/(-f0^2+f1^2)*b0^2*d0*d1^2*f1^3*h0^4+1/(-f0^2+f1^2)*b0^2*d0*d1^2*f1^3*h0^3*h1+2/(-f0^2+f1^2)*b0^2*d0*d1^2*f1^3*h0^2*h1^2+1/(-f0^2+f1^2)*b0^2*d0*d1^2*f1^3*h0*h1^3+1/(-f0^2+f1^2)*b0^2*d0*d1^2*f1^3*h1^4-1/(-f0^2+f1^2)*b0^2*d1^3*f0^3*h0^3*h1-1/(-f0^2+f1^2)*b0^2*d1^3*f0^3*h0*h1^3+2/(-f0^2+f1^2)*b0^2*d1^3*f0^2*f1*h0^2*h1^2-2/(-f0^2+f1^2)*b0^2*d1^3*f0*f1^2*h0^2*h1^2+1/(-f0^2+f1^2)*b0^2*d1^3*f1^3*h0^3*h1+1/(-f0^2+f1^2)*b0^2*d1^3*f1^3*h0*h1^3-2/(-f0^2+f1^2)*b0*b1*d0^3*f0^3*h0^4-2/(-f0^2+f1^2)*b0*b1*d0^3*f0^3*h1^4+2/(-f0^2+f1^2)*b0*b1*d0^3*f0^2*f1*h0^3*h1+2/(-f0^2+f1^2)*b0*b1*d0^3*f0^2*f1*h0*h1^3-2/(-f0^2+f1^2)*b0*b1*d0^3*f0*f1^2*h0^3*h1-2/(-f0^2+f1^2)*b0*b1*d0^3*f0*f1^2*h0*h1^3+2/(-f0^2+f1^2)*b0*b1*d0^3*f1^3*h0^4+2/(-f0^2+f1^2)*b0*b1*d0^3*f1^3*h1^4-4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^3*h0^3*h1-4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^3*h0^2*h1^2-4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^3*h0*h1^3+2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h0^4+2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h0^3*h1+4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h0^2*h1^2+2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h0*h1^3+2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0^2*f1*h1^4-2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h0^4-2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h0^3*h1-4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h0^2*h1^2-2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h0*h1^3-2/(-f0^2+f1^2)*b0*b1*d0^2*d1*f0*f1^2*h1^4+4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f1^3*h0^3*h1+4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f1^3*h0^2*h1^2+4/(-f0^2+f1^2)*b0*b1*d0^2*d1*f1^3*h0*h1^3-4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^3*h0^3*h1-4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^3*h0^2*h1^2-4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^3*h0*h1^3+2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h0^4+2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h0^3*h1+4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h0^2*h1^2+2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h0*h1^3+2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0^2*f1*h1^4-2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h0^4-2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h0^3*h1-4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h0^2*h1^2-2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h0*h1^3-2/(-f0^2+f1^2)*b0*b1*d0*d1^2*f0*f1^2*h1^4+4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f1^3*h0^3*h1+4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f1^3*h0^2*h1^2+4/(-f0^2+f1^2)*b0*b1*d0*d1^2*f1^3*h0*h1^3-2/(-f0^2+f1^2)*b0*b1*d1^3*f0^3*h0^4-2/(-f0^2+f1^2)*b0*b1*d1^3*f0^3*h1^4+2/(-f0^2+f1^2)*b0*b1*d1^3*f0^2*f1*h0^3*h1+2/(-f0^2+f1^2)*b0*b1*d1^3*f0^2*f1*h0*h1^3-2/(-f0^2+f1^2)*b0*b1*d1^3*f0*f1^2*h0^3*h1-2/(-f0^2+f1^2)*b0*b1*d1^3*f0*f1^2*h0*h1^3+2/(-f0^2+f1^2)*b0*b1*d1^3*f1^3*h0^4+2/(-f0^2+f1^2)*b0*b1*d1^3*f1^3*h1^4-1/(-f0^2+f1^2)*b1^2*d0^3*f0^3*h0^3*h1-1/(-f0^2+f1^2)*b1^2*d0^3*f0^3*h0*h1^3+2/(-f0^2+f1^2)*b1^2*d0^3*f0^2*f1*h0^2*h1^2-2/(-f0^2+f1^2)*b1^2*d0^3*f0*f1^2*h0^2*h1^2+1/(-f0^2+f1^2)*b1^2*d0^3*f1^3*h0^3*h1+1/(-f0^2+f1^2)*b1^2*d0^3*f1^3*h0*h1^3-1/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^3*h0^4-1/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^3*h0^3*h1-2/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^3*h0^2*h1^2-1/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^3*h0*h1^3-1/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^3*h1^4+1/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h0^4+2/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h0^3*h1+2/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h0*h1^3+1/(-f0^2+f1^2)*b1^2*d0^2*d1*f0^2*f1*h1^4-1/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h0^4-2/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h0^3*h1-2/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h0*h1^3-1/(-f0^2+f1^2)*b1^2*d0^2*d1*f0*f1^2*h1^4+1/(-f0^2+f1^2)*b1^2*d0^2*d1*f1^3*h0^4+1/(-f0^2+f1^2)*b1^2*d0^2*d1*f1^3*h0^3*h1+2/(-f0^2+f1^2)*b1^2*d0^2*d1*f1^3*h0^2*h1^2+1/(-f0^2+f1^2)*b1^2*d0^2*d1*f1^3*h0*h1^3+1/(-f0^2+f1^2)*b1^2*d0^2*d1*f1^3*h1^4-1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^3*h0^4-1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^3*h0^3*h1-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^3*h0^2*h1^2-1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^3*h0*h1^3-1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^3*h1^4+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0^4+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0^3*h1+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h0*h1^3+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0^2*f1*h1^4-1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0^4-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0^3*h1-2/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h0*h1^3-1/(-f0^2+f1^2)*b1^2*d0*d1^2*f0*f1^2*h1^4+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h0^4+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h0^3*h1+2/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h0^2*h1^2+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h0*h1^3+1/(-f0^2+f1^2)*b1^2*d0*d1^2*f1^3*h1^4-1/(-f0^2+f1^2)*b1^2*d1^3*f0^3*h0^3*h1-1/(-f0^2+f1^2)*b1^2*d1^3*f0^3*h0*h1^3+2/(-f0^2+f1^2)*b1^2*d1^3*f0^2*f1*h0^2*h1^2-2/(-f0^2+f1^2)*b1^2*d1^3*f0*f1^2*h0^2*h1^2+1/(-f0^2+f1^2)*b1^2*d1^3*f1^3*h0^3*h1+1/(-f0^2+f1^2)*b1^2*d1^3*f1^3*h0*h1^3
]:

# Substitutions based on the model

P := P0:
P := subs(b0 = 1-b1, P):
P := subs(d0 = 1-d1, P):
P := subs(f0 = 1-f1, P):
P := subs(h0 = 1-h1, 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([
q5*q6-q4*q7,
q5*q6-q2*q8,
q4*q6-q1*q8,
q2*q6-q1*q7,
q2*q4-q1*q5
]):

# 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: