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,-1/3,1,-1/3,1,-1/3,-1/3,1,-1/3],
[1,1/3,-1/3,-1/3,1/3,1/3,0,-1/3,-1/3],
[1,-1/3,-1/3,1/3,1/3,-1/3,0,-1/3,1/3],
[1,1,1,1,-1/3,-1/3,-1/3,-1/3,-1/3],
[1,-1/3,1,-1/3,-1/3,1/9,1/9,-1/3,1/9],
[1,1/3,-1/3,-1/3,-1/3,-1/3,0,1/3,1/3],
[1,-1/3,-1/3,1/3,-1/3,1/3,0,1/3,-1/3]
]):

FI := Matrix([
[1/64,3/64,3/16,3/16,3/64,9/64,3/16,3/16],
[3/32,-3/32,3/8,-3/8,9/32,-9/32,3/8,-3/8],
[3/64,9/64,-3/16,-3/16,9/64,27/64,-3/16,-3/16],
[3/32,-3/32,-3/8,3/8,9/32,-9/32,-3/8,3/8],
[3/32,9/32,3/8,3/8,-3/32,-9/32,-3/8,-3/8],
[3/32,-3/32,3/8,-3/8,-3/32,3/32,-3/8,3/8],
[3/8,-3/8,0,0,-3/8,3/8,0,0],
[3/32,9/32,-3/8,-3/8,-3/32,-9/32,3/8,3/8],
[3/32,-3/32,-3/8,3/8,-3/32,3/32,3/8,-3/8]
]):
  
# List of polynomial parametrizations

P0 := [
1/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^5*f0^3+3/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^5*f1^3-3/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0^2*f1-3/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0*f1^2-6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f1^3-3/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0^3+9/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0^2*f1+9/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0*f1^2+9/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f1^3-1/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0^3-9/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0^2*f1-9/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0*f1^2-21/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f1^3+6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0^3+3/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0^2*f1+3/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0*f1^2+24/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f1^3-3/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f0^3-9/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f1^3+6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^5*f0^2*f1+6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^5*f0*f1^2+12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^5*f1^3-6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0^3-12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0^2*f1-12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0*f1^2-42/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f1^3+18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0^3+18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0^2*f1+18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0*f1^2+90/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f1^3-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0^3-42/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0^2*f1-42/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0*f1^2-138/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f1^3+6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0^3+48/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0^2*f1+48/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0*f1^2+114/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f1^3-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0^2*f1-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0*f1^2-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f1^3+3/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^5*f0^3+6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^5*f0^2*f1+6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^5*f0*f1^2+21/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^5*f1^3-6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0^3-21/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0^2*f1-21/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0*f1^2-60/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f1^3+9/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0^3+45/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0^2*f1+45/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0*f1^2+117/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f1^3-21/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0^3-69/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0^2*f1-69/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0*f1^2-201/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f1^3+24/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0^3+57/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0^2*f1+57/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0*f1^2+186/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f1^3-9/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0^3-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0^2*f1-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0*f1^2-63/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f1^3,
6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^5*f0^2*f1+6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^5*f0*f1^2+12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^5*f1^3-6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0^2*f1-42/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0*f1^2-24/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f1^3+108/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0*f1^2+36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f1^3-24/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0^2*f1-132/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0*f1^2-84/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f1^3+42/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0^2*f1+78/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0*f1^2+96/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f1^3-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f0^2*f1-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f0*f1^2-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f1^3+12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^5*f0^2*f1+84/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^5*f0*f1^2+48/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^5*f1^3-60/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0^2*f1-204/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0*f1^2-168/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f1^3+144/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0^2*f1+360/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0*f1^2+360/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f1^3-192/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0^2*f1-696/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0*f1^2-552/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f1^3+132/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0^2*f1+708/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0*f1^2+456/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f1^3-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0^2*f1-252/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0*f1^2-144/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f1^3+30/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^5*f0^2*f1+102/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^5*f0*f1^2+84/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^5*f1^3-78/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0^2*f1-330/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0*f1^2-240/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f1^3+144/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0^2*f1+684/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0*f1^2+468/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f1^3-264/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0^2*f1-1092/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0*f1^2-804/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f1^3+258/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0^2*f1+942/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0*f1^2+744/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f1^3-90/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0^2*f1-306/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0*f1^2-252/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f1^3,
3/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^5*f0^2*f1+3/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^5*f0*f1^2+6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^5*f1^3-3/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0^3-6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0^2*f1-6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0*f1^2-21/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f1^3+9/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0^3+9/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0^2*f1+9/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0*f1^2+45/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f1^3-9/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0^3-21/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0^2*f1-21/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0*f1^2-69/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f1^3+3/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0^3+24/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0^2*f1+24/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0*f1^2+57/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f1^3-9/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f0^2*f1-9/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f0*f1^2-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f1^3+6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^5*f0^3+12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^5*f0^2*f1+12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^5*f0*f1^2+42/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^5*f1^3-12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0^3-42/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0^2*f1-42/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0*f1^2-120/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f1^3+18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0^3+90/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0^2*f1+90/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0*f1^2+234/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f1^3-42/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0^3-138/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0^2*f1-138/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0*f1^2-402/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f1^3+48/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0^3+114/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0^2*f1+114/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0*f1^2+372/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f1^3-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0^3-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0^2*f1-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0*f1^2-126/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f1^3+6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^5*f0^3+21/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^5*f0^2*f1+21/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^5*f0*f1^2+60/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^5*f1^3-21/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0^3-60/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0^2*f1-60/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0*f1^2-183/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f1^3+45/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0^3+117/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0^2*f1+117/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0*f1^2+369/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f1^3-69/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0^3-201/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0^2*f1-201/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0*f1^2-609/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f1^3+57/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0^3+186/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0^2*f1+186/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0*f1^2+543/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f1^3-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0^3-63/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0^2*f1-63/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0*f1^2-180/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f1^3,
18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^5*f0*f1^2+6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^5*f1^3-12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0^2*f1-30/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0*f1^2-30/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f1^3+36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0^2*f1+36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0*f1^2+72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f1^3-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0^2*f1-108/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0*f1^2-96/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f1^3+12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0^2*f1+138/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0*f1^2+66/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f1^3-54/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f0*f1^2-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f1^3+24/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^5*f0^2*f1+60/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^5*f0*f1^2+60/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^5*f1^3-48/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0^2*f1-228/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0*f1^2-156/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f1^3+72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0^2*f1+504/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0*f1^2+288/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f1^3-168/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0^2*f1-744/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0*f1^2-528/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f1^3+192/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0^2*f1+588/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0*f1^2+516/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f1^3-72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0^2*f1-180/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0*f1^2-180/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f1^3+24/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^5*f0^2*f1+114/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^5*f0*f1^2+78/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^5*f1^3-84/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0^2*f1-318/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0*f1^2-246/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f1^3+180/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0^2*f1+612/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0*f1^2+504/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f1^3-276/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0^2*f1-1068/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0*f1^2-816/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f1^3+228/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0^2*f1+1002/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0*f1^2+714/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f1^3-72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0^2*f1-342/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0*f1^2-234/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f1^3,
6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0^3+6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0^2*f1+6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0*f1^2+30/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f1^3-6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0^3-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0^2*f1-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0*f1^2-54/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f1^3-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0^3+18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0^2*f1+18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0*f1^2-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f1^3+30/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0^3-6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0^2*f1-6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0*f1^2+78/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f1^3-12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f0^3-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f1^3+12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0^3+60/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0^2*f1+60/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0*f1^2+156/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f1^3-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0^3-108/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0^2*f1-108/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0*f1^2-324/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f1^3+36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0^3-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0^2*f1-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0*f1^2+36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f1^3-12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0^3+156/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0^2*f1+156/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0*f1^2+276/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f1^3-72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0^2*f1-72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0*f1^2-144/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f1^3+30/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0^3+78/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0^2*f1+78/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0*f1^2+246/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f1^3-54/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0^3-162/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0^2*f1-162/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0*f1^2-486/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f1^3-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0^3+18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0^2*f1+18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0*f1^2-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f1^3+78/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0^3+138/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0^2*f1+138/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0*f1^2+510/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f1^3-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0^3-72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0^2*f1-72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0*f1^2-252/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f1^3,
12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0^2*f1+12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0*f1^2+24/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f1^3-12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0^2*f1-48/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0*f1^2-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f1^3-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0^2*f1+72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0*f1^2-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f1^3+60/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0^2*f1-48/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0*f1^2+84/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f1^3-24/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f0^2*f1+12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f0*f1^2-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f1^3+24/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0^2*f1+168/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0*f1^2+96/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f1^3-72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0^2*f1-288/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0*f1^2-216/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f1^3+72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0^2*f1-144/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0*f1^2+72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f1^3-24/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0^2*f1+480/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0*f1^2+120/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f1^3-216/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0*f1^2-72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f1^3+60/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0^2*f1+204/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0*f1^2+168/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f1^3-108/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0^2*f1-432/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0*f1^2-324/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f1^3-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0^2*f1+72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0*f1^2-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f1^3+156/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0^2*f1+336/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0*f1^2+372/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f1^3-72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0^2*f1-180/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0*f1^2-180/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f1^3,
24/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0^2*f1+96/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0*f1^2+72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f1^3-48/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0^2*f1-192/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0*f1^2-144/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f1^3+48/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0^2*f1+192/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0*f1^2+144/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f1^3-24/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f0^2*f1-96/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f0*f1^2-72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f1^3+144/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0^2*f1+576/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0*f1^2+432/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f1^3-288/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0^2*f1-1152/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0*f1^2-864/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f1^3+288/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0^2*f1+1152/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0*f1^2+864/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f1^3-144/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0^2*f1-576/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0*f1^2-432/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f1^3+216/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0^2*f1+864/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0*f1^2+648/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f1^3-432/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0^2*f1-1728/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0*f1^2-1296/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f1^3+432/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0^2*f1+1728/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0*f1^2+1296/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f1^3-216/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0^2*f1-864/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0*f1^2-648/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f1^3,
12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0^2*f1+12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0*f1^2+24/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f1^3-6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0^3-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0^2*f1-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0*f1^2-54/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f1^3+18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0^3-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0^2*f1-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0*f1^2+18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f1^3-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0^3+42/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0^2*f1+42/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0*f1^2+30/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f1^3+6/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f0^3-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f0^2*f1-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f0*f1^2-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f1^3+24/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0^3+48/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0^2*f1+48/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0*f1^2+168/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f1^3-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0^3-108/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0^2*f1-108/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0*f1^2-324/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f1^3-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0^3+36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0^2*f1+36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0*f1^2-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f1^3+84/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0^3+60/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0^2*f1+60/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0*f1^2+372/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f1^3-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0^3-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0^2*f1-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0*f1^2-180/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f1^3+24/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0^3+84/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0^2*f1+84/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0*f1^2+240/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f1^3-54/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0^3-162/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0^2*f1-162/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0*f1^2-486/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f1^3+18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0^3-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0^2*f1-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0*f1^2+18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f1^3+30/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0^3+186/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0^2*f1+186/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0*f1^2+462/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f1^3-18/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0^3-90/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0^2*f1-90/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0*f1^2-234/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f1^3,
36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f0*f1^2+12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^4*d1*f1^3-12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0^2*f1-48/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f0*f1^2-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^3*d1^2*f1^3+36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0^2*f1-72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f0*f1^2+36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0^2*d1^3*f1^3-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0^2*f1+144/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f0*f1^2-12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d0*d1^4*f1^3+12/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f0^2*f1-60/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0^2*d1^5*f0*f1^2+48/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0^2*f1+120/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f0*f1^2+120/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^4*d1*f1^3-72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0^2*f1-288/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f0*f1^2-216/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^3*d1^2*f1^3-72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0^2*f1+144/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f0*f1^2-72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0^2*d1^3*f1^3+168/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0^2*f1+96/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f0*f1^2+312/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d0*d1^4*f1^3-72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0^2*f1-72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f0*f1^2-144/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b0*b1*d1^5*f1^3+48/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0^2*f1+228/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f0*f1^2+156/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^4*d1*f1^3-108/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0^2*f1-432/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f0*f1^2-324/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^3*d1^2*f1^3+36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0^2*f1-72/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f0*f1^2+36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0^2*d1^3*f1^3+60/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0^2*f1+528/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f0*f1^2+276/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d0*d1^4*f1^3-36/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0^2*f1-252/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f0*f1^2-144/(d0^4-6*d0^2*d1^2+8*d0*d1^3-3*d1^4)*b1^2*d1^5*f1^3
]:

# Substitutions based on the model

P := P0:
P := subs(d0 = 1-3*d1, P):
P := subs(b0 = 1-3*b1, P):
P := subs(f0 = 1-3*f1, 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([
q4*q7-q3*q8,
q2*q5-q1*q6,
q6*q7^2-q5*q8^2,
q3*q6*q7-q4*q5*q8,
q2*q3*q7-q1*q4*q8,
q4^2*q6-q2*q8^2,
q3*q4*q6-q2*q7*q8,
q4^2*q5-q3^2*q6,
q4^2*q5-q2*q7^2,
q4^2*q5-q1*q8^2,
q3*q4*q5-q1*q7*q8,
q3^2*q5-q1*q7^2,
q2*q3^2-q1*q4^2
]):

# 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: