restart;
with(LinearAlgebra):

# Define indeterminates

QParam := [q1,q2,q3,q4,q5,q6,q7,q8,q9,q10,q11,q12,q13]:
PParam := Matrix([[p1],[p2],[p3],[p4],[p5],[p6],[p7],[p8],[p9],[p10],[p11],[p12],[p13],[p14],[p15],[p16],[p17],[p18],[p19],[p20]]):

# 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],
[1,1/9,1/9,-1/3,1,1/9,-1/3,1,1/9,1/9,1/9,-1/3,1/9,-1/3,1,1/9,1/9,-1/3,1,1/9],
[1,-1/3,-1/3,1/3,1,-1/3,1/3,1,-1/3,-1/3,-1/3,1/3,-1/3,1/3,1,-1/3,-1/3,1/3,1,-1/3],
[1,5/9,1/9,1/9,-1/3,-1/3,-1/3,-1/3,1/9,-1/3,5/9,1/9,-1/3,-1/3,1,5/9,1/9,1/9,-1/3,-1/3],
[1,1/9,-1/3,-1/9,-1/3,1/9,1/3,-1/3,-1/3,1/9,1/9,-1/9,1/9,1/3,1,1/9,-1/3,-1/9,-1/3,1/9],
[1,-1/3,5/21,1/21,-1/3,1/21,-1/7,-1/3,5/21,1/21,-1/3,1/21,1/21,-1/7,1,-1/3,5/21,1/21,-1/3,1/21],
[1,2/3,1/3,1/3,0,0,0,2/3,1/3,1/3,0,0,0,0,-1/3,-1/3,-1/3,-1/3,-1/3,-1/3],
[1,1/9,-1/3,-1/9,-1/3,1/9,1/3,1,1/9,1/9,-1/3,-1/9,-1/3,-1/9,-1/3,1/9,1/9,1/3,-1/3,1/9],
[1,-1/12,1/6,-1/6,5/12,1/12,-1/4,1/4,-1/6,-1/6,1/12,1/12,1/12,1/12,-1/3,0,0,0,-1/3,0],
[1,-1/3,-1/3,1/3,1,-1/3,1/3,-1/3,1/9,1/9,1/9,-1/9,1/9,-1/9,-1/3,1/9,1/9,-1/9,-1/3,1/9],
[1,5/9,1/9,1/9,-1/3,-1/3,-1/3,-1/3,-1/3,-1/9,-1/3,-1/9,1/9,1/9,-1/3,-1/9,1/9,1/9,1/3,1/3],
[1,1/9,-1/3,-1/9,-1/3,1/9,1/3,-1/3,1/9,-1/9,1/9,1/9,1/9,-1/9,-1/3,-1/9,1/9,-1/9,1/3,-1/9],
[1,-1/3,5/21,1/21,-1/3,1/21,-1/7,-1/3,1/21,1/7,1/21,-1/21,-1/7,1/21,-1/3,1/7,-1/7,1/21,1/3,-1/21]]):

FI := Matrix([
[1/256,9/256,3/128,9/256,9/128,21/256,3/64,9/128,3/16,9/128,9/128,9/64,21/128],
[9/256,9/256,-9/128,45/256,9/128,-63/256,9/32,9/128,-9/64,-27/128,45/128,9/64,-63/128],
[9/256,9/256,-9/128,9/256,-27/128,45/256,9/64,-27/128,9/32,-27/128,9/128,-27/64,45/128],
[9/128,-27/128,9/64,9/128,-9/64,9/128,9/32,-9/64,-9/16,27/64,9/64,-9/32,9/64],
[3/256,27/256,9/128,-9/256,-9/128,-21/256,0,-9/128,15/64,27/128,-9/128,-9/64,-21/128],
[9/128,9/128,-9/64,-27/128,9/64,9/128,0,9/64,9/32,-27/64,-27/64,9/32,9/64],
[3/128,-9/128,3/64,-9/128,9/64,-9/128,0,9/64,-9/32,9/64,-9/64,9/32,-9/64],
[3/256,27/256,9/128,-9/256,-9/128,-21/256,3/32,27/128,9/64,-9/128,-9/128,-9/64,-21/128],
[9/256,9/256,-9/128,9/256,-27/128,45/256,9/64,9/128,-9/32,9/128,-27/128,9/64,9/128],
[9/128,9/128,-9/64,-27/128,9/64,9/128,9/32,9/64,-9/16,9/64,-9/64,-9/32,27/64],
[9/256,9/256,-9/128,45/256,9/128,-63/256,0,-27/128,9/64,9/128,-27/128,9/64,9/128],
[9/64,-27/64,9/32,9/64,-9/32,9/64,0,-9/32,9/16,-9/32,-9/32,9/16,-9/32,
9/128,9/128,-9/64,-27/128,9/64,9/128,0,-27/64,9/32,9/64,9/64,9/32,-27/64],
[9/128,-27/128,9/64,-27/128,27/64,-27/128,0,-9/64,9/32,-9/64,9/64,-9/32,9/64],
[3/256,27/256,9/128,27/256,27/128,63/256,-3/64,-9/128,-3/16,-9/128,-9/128,-9/64,-21/128],
[9/128,9/128,-9/64,45/128,9/64,-63/128,-9/32,9/64,0,9/64,-9/64,-9/32,27/64],
[9/128,9/128,-9/64,9/128,-27/64,45/128,-9/32,9/64,0,9/64,9/64,9/32,-27/64],
[9/128,-27/128,9/64,9/128,-9/64,9/128,-9/32,27/64,0,-9/64,9/64,-9/32,9/64],
[3/128,27/128,9/64,-9/128,-9/64,-21/128,-3/32,-9/64,-3/8,-9/64,9/64,9/32,21/64],
[9/128,9/128,-9/64,-27/128,9/64,9/128,-9/32,9/64,0,9/64,27/64,-9/32,-9/64]
]):

# List of polynomial parametrizations

P0 := [
b0^2*d0^3*g0^5+3*b0^2*d0^3*g1^5+6*b0^2*d0^2*d1*g0^4*g1+3*b0^2*d0^2*d1*g0^3*g1^2+3*b0^2*d0^2*d1*g0^2*g1^3+6*b0^2*d0^2*d1*g0*g1^4+18*b0^2*d0^2*d1*g1^5+6*b0^2*d0*d1^2*g0^4*g1+21*b0^2*d0*d1^2*g0^3*g1^2+3*b0^2*d0*d1^2*g0^2*g1^3+42*b0^2*d0*d1^2*g0*g1^4+36*b0^2*d0*d1^2*g1^5+3*b0^2*d1^3*g0^5+12*b0^2*d1^3*g0^4*g1+12*b0^2*d1^3*g0^3*g1^2+6*b0^2*d1^3*g0^2*g1^3+24*b0^2*d1^3*g0*g1^4+51*b0^2*d1^3*g1^5+6*b0*b1*d0^3*g0^4*g1+6*b0*b1*d0^3*g0*g1^4+12*b0*b1*d0^3*g1^5+6*b0*b1*d0^2*d1*g0^5+18*b0*b1*d0^2*d1*g0^4*g1+30*b0*b1*d0^2*d1*g0^3*g1^2+6*b0*b1*d0^2*d1*g0^2*g1^3+66*b0*b1*d0^2*d1*g0*g1^4+90*b0*b1*d0^2*d1*g1^5+6*b0*b1*d0*d1^2*g0^5+54*b0*b1*d0*d1^2*g0^4*g1+102*b0*b1*d0*d1^2*g0^3*g1^2+42*b0*b1*d0*d1^2*g0^2*g1^3+174*b0*b1*d0*d1^2*g0*g1^4+270*b0*b1*d0*d1^2*g1^5+12*b0*b1*d1^3*g0^5+66*b0*b1*d1^3*g0^4*g1+84*b0*b1*d1^3*g0^3*g1^2+24*b0*b1*d1^3*g0^2*g1^3+186*b0*b1*d1^3*g0*g1^4+276*b0*b1*d1^3*g1^5+3*b1^2*d0^3*g0^5+6*b1^2*d0^3*g0^4*g1+6*b1^2*d0^3*g0*g1^4+21*b1^2*d0^3*g1^5+6*b1^2*d0^2*d1*g0^5+36*b1^2*d0^2*d1*g0^4*g1+39*b1^2*d0^2*d1*g0^3*g1^2+15*b1^2*d0^2*d1*g0^2*g1^3+84*b1^2*d0^2*d1*g0*g1^4+144*b1^2*d0^2*d1*g1^5+6*b1^2*d0*d1^2*g0^5+72*b1^2*d0*d1^2*g0^4*g1+165*b1^2*d0*d1^2*g0^3*g1^2+51*b1^2*d0*d1^2*g0^2*g1^3+300*b1^2*d0*d1^2*g0*g1^4+378*b1^2*d0*d1^2*g1^5+21*b1^2*d1^3*g0^5+102*b1^2*d1^3*g0^4*g1+120*b1^2*d1^3*g0^3*g1^2+42*b1^2*d1^3*g0^2*g1^3+258*b1^2*d1^3*g0*g1^4+429*b1^2*d1^3*g1^5,
9*b0^2*d0^3*g0^4*g1+9*b0^2*d0^3*g0*g1^4+18*b0^2*d0^3*g1^5+63*b0^2*d0^2*d1*g0^3*g1^2+63*b0^2*d0^2*d1*g0^2*g1^3+90*b0^2*d0^2*d1*g0*g1^4+108*b0^2*d0^2*d1*g1^5+63*b0^2*d0*d1^2*g0^3*g1^2+333*b0^2*d0*d1^2*g0^2*g1^3+360*b0^2*d0*d1^2*g0*g1^4+216*b0^2*d0*d1^2*g1^5+27*b0^2*d1^3*g0^4*g1+126*b0^2*d1^3*g0^3*g1^2+216*b0^2*d1^3*g0^2*g1^3+297*b0^2*d1^3*g0*g1^4+306*b0^2*d1^3*g1^5+54*b0*b1*d0^3*g0^3*g1^2+18*b0*b1*d0^3*g0^2*g1^3+72*b0*b1*d0^3*g0*g1^4+72*b0*b1*d0^3*g1^5+54*b0*b1*d0^2*d1*g0^4*g1+180*b0*b1*d0^2*d1*g0^3*g1^2+504*b0*b1*d0^2*d1*g0^2*g1^3+666*b0*b1*d0^2*d1*g0*g1^4+540*b0*b1*d0^2*d1*g1^5+54*b0*b1*d0*d1^2*g0^4*g1+612*b0*b1*d0*d1^2*g0^3*g1^2+1692*b0*b1*d0*d1^2*g0^2*g1^3+1854*b0*b1*d0*d1^2*g0*g1^4+1620*b0*b1*d0*d1^2*g1^5+108*b0*b1*d1^3*g0^4*g1+666*b0*b1*d1^3*g0^3*g1^2+1458*b0*b1*d1^3*g0^2*g1^3+1944*b0*b1*d1^3*g0*g1^4+1656*b0*b1*d1^3*g1^5+27*b1^2*d0^3*g0^4*g1+54*b1^2*d0^3*g0^3*g1^2+18*b1^2*d0^3*g0^2*g1^3+99*b1^2*d0^3*g0*g1^4+126*b1^2*d0^3*g1^5+54*b1^2*d0^2*d1*g0^4*g1+369*b1^2*d0^2*d1*g0^3*g1^2+693*b1^2*d0^2*d1*g0^2*g1^3+936*b1^2*d0^2*d1*g0*g1^4+864*b1^2*d0^2*d1*g1^5+54*b1^2*d0*d1^2*g0^4*g1+801*b1^2*d0*d1^2*g0^3*g1^2+2691*b1^2*d0*d1^2*g0^2*g1^3+2934*b1^2*d0*d1^2*g0*g1^4+2268*b1^2*d0*d1^2*g1^5+189*b1^2*d1^3*g0^4*g1+1044*b1^2*d1^3*g0^3*g1^2+2106*b1^2*d1^3*g0^2*g1^3+2835*b1^2*d1^3*g0*g1^4+2574*b1^2*d1^3*g1^5,
9*b0^2*d0^3*g0^3*g1^2+9*b0^2*d0^3*g0^2*g1^3+18*b0^2*d0^3*g1^5+9*b0^2*d0^2*d1*g0^4*g1+18*b0^2*d0^2*d1*g0^3*g1^2+126*b0^2*d0^2*d1*g0^2*g1^3+63*b0^2*d0^2*d1*g0*g1^4+108*b0^2*d0^2*d1*g1^5+9*b0^2*d0*d1^2*g0^4*g1+126*b0^2*d0*d1^2*g0^3*g1^2+180*b0^2*d0*d1^2*g0^2*g1^3+441*b0^2*d0*d1^2*g0*g1^4+216*b0^2*d0*d1^2*g1^5+18*b0^2*d1^3*g0^4*g1+99*b0^2*d1^3*g0^3*g1^2+297*b0^2*d1^3*g0^2*g1^3+252*b0^2*d1^3*g0*g1^4+306*b0^2*d1^3*g1^5+18*b0*b1*d0^3*g0^3*g1^2+90*b0*b1*d0^3*g0^2*g1^3+36*b0*b1*d0^3*g0*g1^4+72*b0*b1*d0^3*g1^5+18*b0*b1*d0^2*d1*g0^4*g1+252*b0*b1*d0^2*d1*g0^3*g1^2+468*b0*b1*d0^2*d1*g0^2*g1^3+666*b0*b1*d0^2*d1*g0*g1^4+540*b0*b1*d0^2*d1*g1^5+126*b0*b1*d0*d1^2*g0^4*g1+576*b0*b1*d0*d1^2*g0^3*g1^2+1548*b0*b1*d0*d1^2*g0^2*g1^3+1962*b0*b1*d0*d1^2*g0*g1^4+1620*b0*b1*d0*d1^2*g1^5+72*b0*b1*d1^3*g0^4*g1+666*b0*b1*d1^3*g0^3*g1^2+1566*b0*b1*d1^3*g0^2*g1^3+1872*b0*b1*d1^3*g0*g1^4+1656*b0*b1*d1^3*g1^5+45*b1^2*d0^3*g0^3*g1^2+117*b1^2*d0^3*g0^2*g1^3+36*b1^2*d0^3*g0*g1^4+126*b1^2*d0^3*g1^5+45*b1^2*d0^2*d1*g0^4*g1+306*b1^2*d0^2*d1*g0^3*g1^2+846*b1^2*d0^2*d1*g0^2*g1^3+855*b1^2*d0^2*d1*g0*g1^4+864*b1^2*d0^2*d1*g1^5+153*b1^2*d0*d1^2*g0^4*g1+954*b1^2*d0*d1^2*g0^3*g1^2+2088*b1^2*d0*d1^2*g0^2*g1^3+3285*b1^2*d0*d1^2*g0*g1^4+2268*b1^2*d0*d1^2*g1^5+126*b1^2*d1^3*g0^4*g1+963*b1^2*d1^3*g0^3*g1^2+2457*b1^2*d1^3*g0^2*g1^3+2628*b1^2*d1^3*g0*g1^4+2574*b1^2*d1^3*g1^5,
18*b0^2*d0^3*g0^3*g1^2+36*b0^2*d0^3*g0*g1^4+18*b0^2*d0^3*g1^5+36*b0^2*d0^2*d1*g0^3*g1^2+198*b0^2*d0^2*d1*g0^2*g1^3+306*b0^2*d0^2*d1*g0*g1^4+108*b0^2*d0^2*d1*g1^5+36*b0^2*d0*d1^2*g0^3*g1^2+630*b0^2*d0*d1^2*g0^2*g1^3+1062*b0^2*d0*d1^2*g0*g1^4+216*b0^2*d0*d1^2*g1^5+126*b0^2*d1^3*g0^3*g1^2+540*b0^2*d1^3*g0^2*g1^3+972*b0^2*d1^3*g0*g1^4+306*b0^2*d1^3*g1^5+180*b0*b1*d0^3*g0^2*g1^3+180*b0*b1*d0^3*g0*g1^4+72*b0*b1*d0^3*g1^5+180*b0*b1*d0^2*d1*g0^3*g1^2+1152*b0*b1*d0^2*d1*g0^2*g1^3+2016*b0*b1*d0^2*d1*g0*g1^4+540*b0*b1*d0^2*d1*g1^5+612*b0*b1*d0*d1^2*g0^3*g1^2+3312*b0*b1*d0*d1^2*g0^2*g1^3+6120*b0*b1*d0*d1^2*g0*g1^4+1620*b0*b1*d0*d1^2*g1^5+504*b0*b1*d1^3*g0^3*g1^2+3564*b0*b1*d1^3*g0^2*g1^3+5940*b0*b1*d1^3*g0*g1^4+1656*b0*b1*d1^3*g1^5+54*b1^2*d0^3*g0^3*g1^2+180*b1^2*d0^3*g0^2*g1^3+288*b1^2*d0^3*g0*g1^4+126*b1^2*d0^3*g1^5+288*b1^2*d0^2*d1*g0^3*g1^2+1746*b1^2*d0^2*d1*g0^2*g1^3+2934*b1^2*d0^2*d1*g0*g1^4+864*b1^2*d0^2*d1*g1^5+720*b1^2*d0*d1^2*g0^3*g1^2+5202*b1^2*d0*d1^2*g0^2*g1^3+9306*b1^2*d0*d1^2*g0*g1^4+2268*b1^2*d0*d1^2*g1^5+882*b1^2*d1^3*g0^3*g1^2+5184*b1^2*d1^3*g0^2*g1^3+8856*b1^2*d1^3*g0*g1^4+2574*b1^2*d1^3*g1^5,
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36*b0^2*d0^3*g0^2*g1^3+18*b0^2*d0^3*g0*g1^4+18*b0^2*d0^3*g1^5+90*b0^2*d0^2*d1*g0^3*g1^2+162*b0^2*d0^2*d1*g0^2*g1^3+216*b0^2*d0^2*d1*g0*g1^4+180*b0^2*d0^2*d1*g1^5+54*b0^2*d0*d1^2*g0^4*g1+198*b0^2*d0*d1^2*g0^3*g1^2+486*b0^2*d0*d1^2*g0^2*g1^3+648*b0^2*d0*d1^2*g0*g1^4+558*b0^2*d0*d1^2*g1^5+18*b0^2*d1^3*g0^4*g1+216*b0^2*d1^3*g0^3*g1^2+540*b0^2*d1^3*g0^2*g1^3+630*b0^2*d1^3*g0*g1^4+540*b0^2*d1^3*g1^5+72*b0*b1*d0^3*g0^3*g1^2+144*b0*b1*d0^3*g0^2*g1^3+36*b0*b1*d0^3*g0*g1^4+180*b0*b1*d0^3*g1^5+72*b0*b1*d0^2*d1*g0^4*g1+396*b0*b1*d0^2*d1*g0^3*g1^2+1116*b0*b1*d0^2*d1*g0^2*g1^3+1152*b0*b1*d0^2*d1*g0*g1^4+1152*b0*b1*d0^2*d1*g1^5+180*b0*b1*d0*d1^2*g0^4*g1+1260*b0*b1*d0*d1^2*g0^3*g1^2+2844*b0*b1*d0*d1^2*g0^2*g1^3+4392*b0*b1*d0*d1^2*g0*g1^4+2988*b0*b1*d0*d1^2*g1^5+180*b0*b1*d1^3*g0^4*g1+1296*b0*b1*d1^3*g0^3*g1^2+3240*b0*b1*d1^3*g0^2*g1^3+3492*b0*b1*d1^3*g0*g1^4+3456*b0*b1*d1^3*g1^5+72*b1^2*d0^3*g0^3*g1^2+252*b1^2*d0^3*g0^2*g1^3+90*b1^2*d0^3*g0*g1^4+234*b1^2*d0^3*g1^5+72*b1^2*d0^2*d1*g0^4*g1+666*b1^2*d0^2*d1*g0^3*g1^2+1602*b1^2*d0^2*d1*g0^2*g1^3+1800*b1^2*d0^2*d1*g0*g1^4+1692*b1^2*d0^2*d1*g1^5+342*b1^2*d0*d1^2*g0^4*g1+1854*b1^2*d0*d1^2*g0^3*g1^2+4302*b1^2*d0*d1^2*g0^2*g1^3+6336*b1^2*d0*d1^2*g0*g1^4+4662*b1^2*d0*d1^2*g1^5+234*b1^2*d1^3*g0^4*g1+1944*b1^2*d1^3*g0^3*g1^2+4860*b1^2*d1^3*g0^2*g1^3+5382*b1^2*d1^3*g0*g1^4+5076*b1^2*d1^3*g1^5,
18*b0^2*d0^3*g0^2*g1^3+54*b0^2*d0^3*g0*g1^4+18*b0^2*d0^2*d1*g0^3*g1^2+216*b0^2*d0^2*d1*g0^2*g1^3+324*b0^2*d0^2*d1*g0*g1^4+90*b0^2*d0^2*d1*g1^5+126*b0^2*d0*d1^2*g0^3*g1^2+540*b0^2*d0*d1^2*g0^2*g1^3+972*b0^2*d0*d1^2*g0*g1^4+306*b0^2*d0*d1^2*g1^5+72*b0^2*d1^3*g0^3*g1^2+594*b0^2*d1^3*g0^2*g1^3+1026*b0^2*d1^3*g0*g1^4+252*b0^2*d1^3*g1^5+36*b0*b1*d0^3*g0^3*g1^2+144*b0*b1*d0^3*g0^2*g1^3+144*b0*b1*d0^3*g0*g1^4+108*b0*b1*d0^3*g1^5+216*b0*b1*d0^2*d1*g0^3*g1^2+1116*b0*b1*d0^2*d1*g0^2*g1^3+1980*b0*b1*d0^2*d1*g0*g1^4+576*b0*b1*d0^2*d1*g1^5+432*b0*b1*d0*d1^2*g0^3*g1^2+3492*b0*b1*d0*d1^2*g0^2*g1^3+6300*b0*b1*d0*d1^2*g0*g1^4+1440*b0*b1*d0*d1^2*g1^5+612*b0*b1*d1^3*g0^3*g1^2+3456*b0*b1*d1^3*g0^2*g1^3+5832*b0*b1*d1^3*g0*g1^4+1764*b0*b1*d1^3*g1^5+36*b1^2*d0^3*g0^3*g1^2+198*b1^2*d0^3*g0^2*g1^3+306*b1^2*d0^3*g0*g1^4+108*b1^2*d0^3*g1^5+270*b1^2*d0^2*d1*g0^3*g1^2+1764*b1^2*d0^2*d1*g0^2*g1^3+2952*b1^2*d0^2*d1*g0*g1^4+846*b1^2*d0^2*d1*g1^5+810*b1^2*d0*d1^2*g0^3*g1^2+5112*b1^2*d0*d1^2*g0^2*g1^3+9216*b1^2*d0*d1^2*g0*g1^4+2358*b1^2*d0*d1^2*g1^5+828*b1^2*d1^3*g0^3*g1^2+5238*b1^2*d1^3*g0^2*g1^3+8910*b1^2*d1^3*g0*g1^4+2520*b1^2*d1^3*g1^5,
6*b0^2*d0^3*g0^3*g1^2+12*b0^2*d0^3*g0*g1^4+6*b0^2*d0^3*g1^5+24*b0^2*d0^2*d1*g0^4*g1+30*b0^2*d0^2*d1*g0^3*g1^2+12*b0^2*d0^2*d1*g0^2*g1^3+60*b0^2*d0^2*d1*g0*g1^4+90*b0^2*d0^2*d1*g1^5+18*b0^2*d0*d1^2*g0^5+60*b0^2*d0*d1^2*g0^4*g1+84*b0^2*d0*d1^2*g0^3*g1^2+30*b0^2*d0*d1^2*g0^2*g1^3+168*b0^2*d0*d1^2*g0*g1^4+288*b0^2*d0*d1^2*g1^5+6*b0^2*d1^3*g0^5+60*b0^2*d1^3*g0^4*g1+96*b0^2*d1^3*g0^3*g1^2+30*b0^2*d1^3*g0^2*g1^3+192*b0^2*d1^3*g0*g1^4+264*b0^2*d1^3*g1^5+12*b0*b1*d0^3*g0^4*g1+24*b0*b1*d0^3*g0^3*g1^2+12*b0*b1*d0^3*g0^2*g1^3+36*b0*b1*d0^3*g0*g1^4+60*b0*b1*d0^3*g1^5+24*b0*b1*d0^2*d1*g0^5+108*b0*b1*d0^2*d1*g0^4*g1+192*b0*b1*d0^2*d1*g0^3*g1^2+60*b0*b1*d0^2*d1*g0^2*g1^3+372*b0*b1*d0^2*d1*g0*g1^4+540*b0*b1*d0^2*d1*g1^5+60*b0*b1*d0*d1^2*g0^5+396*b0*b1*d0*d1^2*g0^4*g1+516*b0*b1*d0*d1^2*g0^3*g1^2+168*b0*b1*d0*d1^2*g0^2*g1^3+1092*b0*b1*d0*d1^2*g0*g1^4+1656*b0*b1*d0*d1^2*g1^5+60*b0*b1*d1^3*g0^5+348*b0*b1*d1^3*g0^4*g1+564*b0*b1*d1^3*g0^3*g1^2+192*b0*b1*d1^3*g0^2*g1^3+1092*b0*b1*d1^3*g0*g1^4+1632*b0*b1*d1^3*g1^5+12*b1^2*d0^3*g0^4*g1+42*b1^2*d0^3*g0^3*g1^2+12*b1^2*d0^3*g0^2*g1^3+72*b1^2*d0^3*g0*g1^4+78*b1^2*d0^3*g1^5+24*b1^2*d0^2*d1*g0^5+180*b1^2*d0^2*d1*g0^4*g1+282*b1^2*d0^2*d1*g0^3*g1^2+96*b1^2*d0^2*d1*g0^2*g1^3+552*b1^2*d0^2*d1*g0*g1^4+810*b1^2*d0^2*d1*g1^5+114*b1^2*d0*d1^2*g0^5+576*b1^2*d0*d1^2*g0^4*g1+768*b1^2*d0*d1^2*g0^3*g1^2+258*b1^2*d0*d1^2*g0^2*g1^3+1596*b1^2*d0*d1^2*g0*g1^4+2520*b1^2*d0*d1^2*g1^5+78*b1^2*d1^3*g0^5+528*b1^2*d1^3*g0^4*g1+852*b1^2*d1^3*g0^3*g1^2+282*b1^2*d1^3*g0^2*g1^3+1668*b1^2*d1^3*g0*g1^4+2424*b1^2*d1^3*g1^5,
18*b0^2*d0^3*g0^2*g1^3+54*b0^2*d0^3*g0*g1^4+72*b0^2*d0^2*d1*g0^3*g1^2+198*b0^2*d0^2*d1*g0^2*g1^3+198*b0^2*d0^2*d1*g0*g1^4+180*b0^2*d0^2*d1*g1^5+54*b0^2*d0*d1^2*g0^4*g1+234*b0^2*d0*d1^2*g0^3*g1^2+468*b0^2*d0*d1^2*g0^2*g1^3+576*b0^2*d0*d1^2*g0*g1^4+612*b0^2*d0*d1^2*g1^5+18*b0^2*d1^3*g0^4*g1+198*b0^2*d1^3*g0^3*g1^2+540*b0^2*d1^3*g0^2*g1^3+684*b0^2*d1^3*g0*g1^4+504*b0^2*d1^3*g1^5+36*b0*b1*d0^3*g0^3*g1^2+144*b0*b1*d0^3*g0^2*g1^3+144*b0*b1*d0^3*g0*g1^4+108*b0*b1*d0^3*g1^5+72*b0*b1*d0^2*d1*g0^4*g1+396*b0*b1*d0^2*d1*g0^3*g1^2+1008*b0*b1*d0^2*d1*g0^2*g1^3+1368*b0*b1*d0^2*d1*g0*g1^4+1044*b0*b1*d0^2*d1*g1^5+180*b0*b1*d0*d1^2*g0^4*g1+1368*b0*b1*d0*d1^2*g0^3*g1^2+3060*b0*b1*d0*d1^2*g0^2*g1^3+3636*b0*b1*d0*d1^2*g0*g1^4+3420*b0*b1*d0*d1^2*g1^5+180*b0*b1*d1^3*g0^4*g1+1224*b0*b1*d1^3*g0^3*g1^2+3132*b0*b1*d1^3*g0^2*g1^3+3924*b0*b1*d1^3*g0*g1^4+3204*b0*b1*d1^3*g1^5+36*b1^2*d0^3*g0^3*g1^2+198*b1^2*d0^3*g0^2*g1^3+306*b1^2*d0^3*g0*g1^4+108*b1^2*d0^3*g1^5+72*b1^2*d0^2*d1*g0^4*g1+612*b1^2*d0^2*d1*g0^3*g1^2+1602*b1^2*d0^2*d1*g0^2*g1^3+1962*b1^2*d0^2*d1*g0*g1^4+1584*b1^2*d0^2*d1*g1^5+342*b1^2*d0*d1^2*g0^4*g1+2070*b1^2*d0*d1^2*g0^3*g1^2+4464*b1^2*d0*d1^2*g0^2*g1^3+5364*b1^2*d0*d1^2*g0*g1^4+5256*b1^2*d0*d1^2*g1^5+234*b1^2*d1^3*g0^4*g1+1818*b1^2*d1^3*g0^3*g1^2+4752*b1^2*d1^3*g0^2*g1^3+5976*b1^2*d1^3*g0*g1^4+4716*b1^2*d1^3*g1^5]:

# Substitutions based on the model

P := P0:
P := subs(b0 = 1-3*b1, P):
P := subs(d0 = 1-3*d1, P):
P := subs(g0 = 1-3*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([
q12^2-q11*q13,
q10*q12-q9*q13,
q9*q12-q8*q13,
q8*q12-q7*q13,
q6*q12-q5*q13,
q5*q12-q4*q13,
q3*q12-q2*q13,
q10*q11-q8*q13,
q9*q11-q7*q13,
q8*q11-q7*q12,
q6*q11-q4*q13,
q5*q11-q4*q12,
q3*q11-q2*q12,
q2*q11-q1*q13,
q9^2-q8*q10,
q8*q9-q7*q10,
q6*q9-q5*q10,
q5*q9-q4*q10,
q3*q9-q2*q10,
q8^2-q7*q9,
q6*q8-q4*q10,
q5*q8-q4*q9,
q3*q8-q2*q9,
q2*q8-q1*q10,
q6*q7-q4*q9,
q5*q7-q4*q8,
q3*q7-q1*q10,
q2*q7-q1*q9,
q5^2-q4*q6,
q3*q5-q2*q6,
q3*q4-q2*q5,
q2*q4-q1*q6,
q5*q10^2-q3*q13^2,
q4*q10^2-q2*q13^2,
q4*q9*q10-q2*q12*q13,
q4*q8*q10-q1*q13^2,
q4*q7*q10-q1*q12*q13,
q4*q7*q9-q1*q11*q13,
q4*q7*q8-q1*q11*q12,
q4*q7^2-q1*q11^2,
q2^3-q1*q3^2]):

# 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: