//This is the ideal Fourier invariants.

ring rQ = 0,(q1,q2,q3,q4,q5,q6,q7,q8,q9),dp; 

ideal Invariants = 
q7*q8-q6*q9,
q6*q8-q5*q9,
q4*q8-q3*q9,
q6^2-q5*q7,
q4*q6-q3*q7,
q4*q5-q3*q6,
q2*q5-q1*q7,
q2*q3*q8-q1*q4*q9,
q4*q6*q7-q2*q9^2,
q4*q6^2-q2*q8*q9,
q4*q5*q6-q1*q9^2,
q4*q5*q6-q2*q8^2,
q4*q5^2-q1*q8*q9,
q3*q5^2-q1*q8^2,
q2*q3^2-q1*q4^2;

// This is the inverse of the Fourier transform.

matrix ptoq[11][9] =
1/64,3/64,3/32,3/32,9/64,3/32,9/64,3/16,3/16,
3/32,-3/32,3/16,-3/16,15/32,-3/16,-9/32,3/8,-3/8,
3/64,9/64,-3/32,-3/32,3/64,-3/32,27/64,-3/16,-3/16,
3/32,-3/32,-3/16,3/16,3/32,3/16,-9/32,-3/8,3/8,
3/64,9/64,-3/32,-3/32,15/64,9/32,-9/64,-3/16,-3/16,
3/32,-3/32,3/16,-3/16,3/32,-3/16,3/32,-3/8,3/8,
3/16,-3/16,-3/8,3/8,3/16,-3/8,3/16,0,0,
3/64,9/64,9/32,9/32,-9/64,-3/32,-9/64,-3/16,-3/16,
3/16,-3/16,3/8,-3/8,-9/16,3/8,3/16,0,0,
3/32,9/32,-3/16,-3/16,-9/32,-3/16,-9/32,3/8,3/8,
3/32,-3/32,-3/16,3/16,-9/32,3/16,3/32,3/8,-3/8;

// This is the ring of probability distributions. 

ring rP = 0,(p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11),dp;

//This is the Fourier transform.

matrix qtop[9][11] =
1,1,1,1,1,1,1,1,1,1,1,
1,-1/3,1,-1/3,1,-1/3,-1/3,1,-1/3,1,-1/3,
1,1/3,-1/3,-1/3,-1/3,1/3,-1/3,1,1/3,-1/3,-1/3,
1,-1/3,-1/3,1/3,-1/3,-1/3,1/3,1,-1/3,-1/3,1/3,
1,5/9,1/9,1/9,5/9,1/9,1/9,-1/3,-1/3,-1/3,-1/3,
1,-1/3,-1/3,1/3,1,-1/3,-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,-1/3,1/9,
1,1/3,-1/3,-1/3,-1/3,-1/3,0,-1/3,0,1/3,1/3,
1,-1/3,-1/3,1/3,-1/3,1/3,0,-1/3,0,1/3,-1/3;


ideal Fourier = qtop*transpose(maxideal(1));

// This is the list of polynomial invariants.

map F = rQ, Fourier;
ideal PInvariants =  F(Invariants); 

// This is the polynomial parametrization.

ring r = 0,(b0,b1,d0,d1,f0,f1),dp;

ideal P = 
b0^2*d0^3*f0^4+3*b0^2*d0^3*f1^4+6*b0^2*d0^2*d1*f0^3*f1+6*b0^2*d0^2*d1*f0^2*f1^2+6*b0^2*d0^2*d1*f0*f1^3+18*b0^2*d0^2*d1*f1^4+6*b0^2*d0*d1^2*f0^3*f1+24*b0^2*d0*d1^2*f0^2*f1^2+42*b0^2*d0*d1^2*f0*f1^3+36*b0^2*d0*d1^2*f1^4+3*b0^2*d1^3*f0^4+12*b0^2*d1^3*f0^3*f1+18*b0^2*d1^3*f0^2*f1^2+24*b0^2*d1^3*f0*f1^3+51*b0^2*d1^3*f1^4+6*b0*b1*d0^3*f0^3*f1+6*b0*b1*d0^3*f0*f1^3+12*b0*b1*d0^3*f1^4+6*b0*b1*d0^2*d1*f0^4+18*b0*b1*d0^2*d1*f0^3*f1+36*b0*b1*d0^2*d1*f0^2*f1^2+66*b0*b1*d0^2*d1*f0*f1^3+90*b0*b1*d0^2*d1*f1^4+6*b0*b1*d0*d1^2*f0^4+54*b0*b1*d0*d1^2*f0^3*f1+144*b0*b1*d0*d1^2*f0^2*f1^2+174*b0*b1*d0*d1^2*f0*f1^3+270*b0*b1*d0*d1^2*f1^4+12*b0*b1*d1^3*f0^4+66*b0*b1*d1^3*f0^3*f1+108*b0*b1*d1^3*f0^2*f1^2+186*b0*b1*d1^3*f0*f1^3+276*b0*b1*d1^3*f1^4+3*b1^2*d0^3*f0^4+6*b1^2*d0^3*f0^3*f1+6*b1^2*d0^3*f0*f1^3+21*b1^2*d0^3*f1^4+6*b1^2*d0^2*d1*f0^4+36*b1^2*d0^2*d1*f0^3*f1+54*b1^2*d0^2*d1*f0^2*f1^2+84*b1^2*d0^2*d1*f0*f1^3+144*b1^2*d0^2*d1*f1^4+6*b1^2*d0*d1^2*f0^4+72*b1^2*d0*d1^2*f0^3*f1+216*b1^2*d0*d1^2*f0^2*f1^2+300*b1^2*d0*d1^2*f0*f1^3+378*b1^2*d0*d1^2*f1^4+21*b1^2*d1^3*f0^4+102*b1^2*d1^3*f0^3*f1+162*b1^2*d1^3*f0^2*f1^2+258*b1^2*d1^3*f0*f1^3+429*b1^2*d1^3*f1^4,
6*b0^2*d0^3*f0^3*f1+6*b0^2*d0^3*f0*f1^3+12*b0^2*d0^3*f1^4+6*b0^2*d0^2*d1*f0^3*f1+60*b0^2*d0^2*d1*f0^2*f1^2+78*b0^2*d0^2*d1*f0*f1^3+72*b0^2*d0^2*d1*f1^4+6*b0^2*d0*d1^2*f0^3*f1+132*b0^2*d0*d1^2*f0^2*f1^2+366*b0^2*d0*d1^2*f0*f1^3+144*b0^2*d0*d1^2*f1^4+30*b0^2*d1^3*f0^3*f1+144*b0^2*d1^3*f0^2*f1^2+270*b0^2*d1^3*f0*f1^3+204*b0^2*d1^3*f1^4+48*b0*b1*d0^3*f0^2*f1^2+48*b0*b1*d0^3*f0*f1^3+48*b0*b1*d0^3*f1^4+48*b0*b1*d0^2*d1*f0^3*f1+264*b0*b1*d0^2*d1*f0^2*f1^2+624*b0*b1*d0^2*d1*f0*f1^3+360*b0*b1*d0^2*d1*f1^4+120*b0*b1*d0*d1^2*f0^3*f1+840*b0*b1*d0*d1^2*f0^2*f1^2+1848*b0*b1*d0*d1^2*f0*f1^3+1080*b0*b1*d0*d1^2*f1^4+120*b0*b1*d1^3*f0^3*f1+864*b0*b1*d1^3*f0^2*f1^2+1800*b0*b1*d1^3*f0*f1^3+1104*b0*b1*d1^3*f1^4+18*b1^2*d0^3*f0^3*f1+48*b1^2*d0^3*f0^2*f1^2+66*b1^2*d0^3*f0*f1^3+84*b1^2*d0^3*f1^4+66*b1^2*d0^2*d1*f0^3*f1+444*b1^2*d0^2*d1*f0^2*f1^2+858*b1^2*d0^2*d1*f0*f1^3+576*b1^2*d0^2*d1*f1^4+138*b1^2*d0*d1^2*f0^3*f1+1236*b1^2*d0*d1^2*f0^2*f1^2+2946*b1^2*d0*d1^2*f0*f1^3+1512*b1^2*d0*d1^2*f1^4+210*b1^2*d1^3*f0^3*f1+1296*b1^2*d1^3*f0^2*f1^2+2610*b1^2*d1^3*f0*f1^3+1716*b1^2*d1^3*f1^4,
6*b0^2*d0^3*f0^2*f1^2+6*b0^2*d0^3*f1^4+3*b0^2*d0^2*d1*f0^4+6*b0^2*d0^2*d1*f0^3*f1+24*b0^2*d0^2*d1*f0^2*f1^2+30*b0^2*d0^2*d1*f0*f1^3+45*b0^2*d0^2*d1*f1^4+3*b0^2*d0*d1^2*f0^4+42*b0^2*d0*d1^2*f0^3*f1+42*b0^2*d0*d1^2*f0^2*f1^2+102*b0^2*d0*d1^2*f0*f1^3+135*b0^2*d0*d1^2*f1^4+6*b0^2*d1^3*f0^4+24*b0^2*d1^3*f0^3*f1+72*b0^2*d1^3*f0^2*f1^2+84*b0^2*d1^3*f0*f1^3+138*b0^2*d1^3*f1^4+6*b0*b1*d0^3*f0^3*f1+12*b0*b1*d0^3*f0^2*f1^2+30*b0*b1*d0^3*f0*f1^3+24*b0*b1*d0^3*f1^4+6*b0*b1*d0^2*d1*f0^4+66*b0*b1*d0^2*d1*f0^3*f1+120*b0*b1*d0^2*d1*f0^2*f1^2+186*b0*b1*d0^2*d1*f0*f1^3+270*b0*b1*d0^2*d1*f1^4+42*b0*b1*d0*d1^2*f0^4+174*b0*b1*d0*d1^2*f0^3*f1+372*b0*b1*d0*d1^2*f0^2*f1^2+510*b0*b1*d0*d1^2*f0*f1^3+846*b0*b1*d0*d1^2*f1^4+24*b0*b1*d1^3*f0^4+186*b0*b1*d1^3*f0^3*f1+360*b0*b1*d1^3*f0^2*f1^2+570*b0*b1*d1^3*f0*f1^3+804*b0*b1*d1^3*f1^4+6*b1^2*d0^3*f0^3*f1+30*b1^2*d0^3*f0^2*f1^2+30*b1^2*d0^3*f0*f1^3+42*b1^2*d0^3*f1^4+15*b1^2*d0^2*d1*f0^4+84*b1^2*d0^2*d1*f0^3*f1+192*b1^2*d0^2*d1*f0^2*f1^2+276*b1^2*d0^2*d1*f0*f1^3+405*b1^2*d0^2*d1*f1^4+51*b1^2*d0*d1^2*f0^4+300*b1^2*d0*d1^2*f0^3*f1+498*b1^2*d0*d1^2*f0^2*f1^2+816*b1^2*d0*d1^2*f0*f1^3+1251*b1^2*d0*d1^2*f1^4+42*b1^2*d1^3*f0^4+258*b1^2*d1^3*f0^3*f1+576*b1^2*d1^3*f0^2*f1^2+822*b1^2*d1^3*f0*f1^3+1218*b1^2*d1^3*f1^4,
6*b0^2*d0^3*f0^2*f1^2+12*b0^2*d0^3*f0*f1^3+6*b0^2*d0^3*f1^4+12*b0^2*d0^2*d1*f0^3*f1+30*b0^2*d0^2*d1*f0^2*f1^2+120*b0^2*d0^2*d1*f0*f1^3+54*b0^2*d0^2*d1*f1^4+12*b0^2*d0*d1^2*f0^3*f1+174*b0^2*d0*d1^2*f0^2*f1^2+264*b0^2*d0*d1^2*f0*f1^3+198*b0^2*d0*d1^2*f1^4+24*b0^2*d1^3*f0^3*f1+126*b0^2*d1^3*f0^2*f1^2+324*b0^2*d1^3*f0*f1^3+174*b0^2*d1^3*f1^4+24*b0*b1*d0^3*f0^2*f1^2+96*b0*b1*d0^3*f0*f1^3+24*b0*b1*d0^3*f1^4+24*b0*b1*d0^2*d1*f0^3*f1+312*b0*b1*d0^2*d1*f0^2*f1^2+600*b0*b1*d0^2*d1*f0*f1^3+360*b0*b1*d0^2*d1*f1^4+168*b0*b1*d0*d1^2*f0^3*f1+816*b0*b1*d0*d1^2*f0^2*f1^2+1752*b0*b1*d0*d1^2*f0*f1^3+1152*b0*b1*d0*d1^2*f1^4+96*b0*b1*d1^3*f0^3*f1+864*b0*b1*d1^3*f0^2*f1^2+1872*b0*b1*d1^3*f0*f1^3+1056*b0*b1*d1^3*f1^4+42*b1^2*d0^3*f0^2*f1^2+132*b1^2*d0^3*f0*f1^3+42*b1^2*d0^3*f1^4+60*b1^2*d0^2*d1*f0^3*f1+402*b1^2*d0^2*d1*f0^2*f1^2+960*b1^2*d0^2*d1*f0*f1^3+522*b1^2*d0^2*d1*f1^4+204*b1^2*d0*d1^2*f0^3*f1+1338*b1^2*d0*d1^2*f0^2*f1^2+2544*b1^2*d0*d1^2*f0*f1^3+1746*b1^2*d0*d1^2*f1^4+168*b1^2*d1^3*f0^3*f1+1242*b1^2*d1^3*f0^2*f1^2+2844*b1^2*d1^3*f0*f1^3+1578*b1^2*d1^3*f1^4,
3*b0^2*d0^3*f0^3*f1+3*b0^2*d0^3*f0*f1^3+6*b0^2*d0^3*f1^4+3*b0^2*d0^2*d1*f0^4+9*b0^2*d0^2*d1*f0^3*f1+18*b0^2*d0^2*d1*f0^2*f1^2+33*b0^2*d0^2*d1*f0*f1^3+45*b0^2*d0^2*d1*f1^4+3*b0^2*d0*d1^2*f0^4+27*b0^2*d0*d1^2*f0^3*f1+72*b0^2*d0*d1^2*f0^2*f1^2+87*b0^2*d0*d1^2*f0*f1^3+135*b0^2*d0*d1^2*f1^4+6*b0^2*d1^3*f0^4+33*b0^2*d1^3*f0^3*f1+54*b0^2*d1^3*f0^2*f1^2+93*b0^2*d1^3*f0*f1^3+138*b0^2*d1^3*f1^4+24*b0*b1*d0^3*f0^2*f1^2+24*b0*b1*d0^3*f0*f1^3+24*b0*b1*d0^3*f1^4+6*b0*b1*d0^2*d1*f0^4+60*b0*b1*d0^2*d1*f0^3*f1+132*b0*b1*d0^2*d1*f0^2*f1^2+180*b0*b1*d0^2*d1*f0*f1^3+270*b0*b1*d0^2*d1*f1^4+42*b0*b1*d0*d1^2*f0^4+204*b0*b1*d0*d1^2*f0^3*f1+312*b0*b1*d0*d1^2*f0^2*f1^2+540*b0*b1*d0*d1^2*f0*f1^3+846*b0*b1*d0*d1^2*f1^4+24*b0*b1*d1^3*f0^4+168*b0*b1*d1^3*f0^3*f1+396*b0*b1*d1^3*f0^2*f1^2+552*b0*b1*d1^3*f0*f1^3+804*b0*b1*d1^3*f1^4+9*b1^2*d0^3*f0^3*f1+24*b1^2*d0^3*f0^2*f1^2+33*b1^2*d0^3*f0*f1^3+42*b1^2*d0^3*f1^4+15*b1^2*d0^2*d1*f0^4+87*b1^2*d0^2*d1*f0^3*f1+186*b1^2*d0^2*d1*f0^2*f1^2+279*b1^2*d0^2*d1*f0*f1^3+405*b1^2*d0^2*d1*f1^4+51*b1^2*d0*d1^2*f0^4+285*b1^2*d0*d1^2*f0^3*f1+528*b1^2*d0*d1^2*f0^2*f1^2+801*b1^2*d0*d1^2*f0*f1^3+1251*b1^2*d0*d1^2*f1^4+42*b1^2*d1^3*f0^4+267*b1^2*d1^3*f0^3*f1+558*b1^2*d1^3*f0^2*f1^2+831*b1^2*d1^3*f0*f1^3+1218*b1^2*d1^3*f1^4,
12*b0^2*d0^3*f0^2*f1^2+12*b0^2*d0^3*f1^4+12*b0^2*d0^2*d1*f0^3*f1+36*b0^2*d0^2*d1*f0^2*f1^2+108*b0^2*d0^2*d1*f0*f1^3+60*b0^2*d0^2*d1*f1^4+12*b0^2*d0*d1^2*f0^3*f1+144*b0^2*d0*d1^2*f0^2*f1^2+324*b0^2*d0*d1^2*f0*f1^3+168*b0^2*d0*d1^2*f1^4+24*b0^2*d1^3*f0^3*f1+144*b0^2*d1^3*f0^2*f1^2+288*b0^2*d1^3*f0*f1^3+192*b0^2*d1^3*f1^4+12*b0*b1*d0^3*f0^3*f1+24*b0*b1*d0^3*f0^2*f1^2+60*b0*b1*d0^3*f0*f1^3+48*b0*b1*d0^3*f1^4+36*b0*b1*d0^2*d1*f0^3*f1+312*b0*b1*d0^2*d1*f0^2*f1^2+564*b0*b1*d0^2*d1*f0*f1^3+384*b0*b1*d0^2*d1*f1^4+108*b0*b1*d0*d1^2*f0^3*f1+816*b0*b1*d0*d1^2*f0^2*f1^2+1932*b0*b1*d0*d1^2*f0*f1^3+1032*b0*b1*d0*d1^2*f1^4+132*b0*b1*d1^3*f0^3*f1+864*b0*b1*d1^3*f0^2*f1^2+1764*b0*b1*d1^3*f0*f1^3+1128*b0*b1*d1^3*f1^4+12*b1^2*d0^3*f0^3*f1+60*b1^2*d0^3*f0^2*f1^2+60*b1^2*d0^3*f0*f1^3+84*b1^2*d0^3*f1^4+72*b1^2*d0^2*d1*f0^3*f1+420*b1^2*d0^2*d1*f0^2*f1^2+888*b1^2*d0^2*d1*f0*f1^3+564*b1^2*d0^2*d1*f1^4+144*b1^2*d0*d1^2*f0^3*f1+1248*b1^2*d0*d1^2*f0^2*f1^2+2904*b1^2*d0*d1^2*f0*f1^3+1536*b1^2*d0*d1^2*f1^4+204*b1^2*d1^3*f0^3*f1+1296*b1^2*d1^3*f0^2*f1^2+2628*b1^2*d1^3*f0*f1^3+1704*b1^2*d1^3*f1^4,
12*b0^2*d0^3*f0^2*f1^2+24*b0^2*d0^3*f0*f1^3+12*b0^2*d0^3*f1^4+12*b0^2*d0^2*d1*f0^3*f1+96*b0^2*d0^2*d1*f0^2*f1^2+204*b0^2*d0^2*d1*f0*f1^3+120*b0^2*d0^2*d1*f1^4+48*b0^2*d0*d1^2*f0^3*f1+276*b0^2*d0*d1^2*f0^2*f1^2+600*b0^2*d0*d1^2*f0*f1^3+372*b0^2*d0*d1^2*f1^4+36*b0^2*d1^3*f0^3*f1+288*b0^2*d1^3*f0^2*f1^2+612*b0^2*d1^3*f0*f1^3+360*b0^2*d1^3*f1^4+48*b0*b1*d0^3*f0^2*f1^2+192*b0*b1*d0^3*f0*f1^3+48*b0*b1*d0^3*f1^4+72*b0*b1*d0^2*d1*f0^3*f1+552*b0*b1*d0^2*d1*f0^2*f1^2+1272*b0*b1*d0^2*d1*f0*f1^3+696*b0*b1*d0^2*d1*f1^4+288*b0*b1*d0*d1^2*f0^3*f1+1776*b0*b1*d0*d1^2*f0^2*f1^2+3360*b0*b1*d0*d1^2*f0*f1^3+2352*b0*b1*d0*d1^2*f1^4+216*b0*b1*d1^3*f0^3*f1+1656*b0*b1*d1^3*f0^2*f1^2+3816*b0*b1*d1^3*f0*f1^3+2088*b0*b1*d1^3*f1^4+84*b1^2*d0^3*f0^2*f1^2+264*b1^2*d0^3*f0*f1^3+84*b1^2*d0^3*f1^4+108*b1^2*d0^2*d1*f0^3*f1+840*b1^2*d0^2*d1*f0^2*f1^2+1884*b1^2*d0^2*d1*f0*f1^3+1056*b1^2*d0^2*d1*f1^4+432*b1^2*d0*d1^2*f0^3*f1+2604*b1^2*d0*d1^2*f0^2*f1^2+5160*b1^2*d0*d1^2*f0*f1^3+3468*b1^2*d0*d1^2*f1^4+324*b1^2*d1^3*f0^3*f1+2520*b1^2*d1^3*f0^2*f1^2+5652*b1^2*d1^3*f0*f1^3+3168*b1^2*d1^3*f1^4,
3*b0^2*d0^3*f0^3*f1+3*b0^2*d0^3*f0*f1^3+6*b0^2*d0^3*f1^4+3*b0^2*d0^2*d1*f0^4+9*b0^2*d0^2*d1*f0^3*f1+18*b0^2*d0^2*d1*f0^2*f1^2+33*b0^2*d0^2*d1*f0*f1^3+45*b0^2*d0^2*d1*f1^4+3*b0^2*d0*d1^2*f0^4+27*b0^2*d0*d1^2*f0^3*f1+72*b0^2*d0*d1^2*f0^2*f1^2+87*b0^2*d0*d1^2*f0*f1^3+135*b0^2*d0*d1^2*f1^4+6*b0^2*d1^3*f0^4+33*b0^2*d1^3*f0^3*f1+54*b0^2*d1^3*f0^2*f1^2+93*b0^2*d1^3*f0*f1^3+138*b0^2*d1^3*f1^4+6*b0*b1*d0^3*f0^4+12*b0*b1*d0^3*f0^3*f1+12*b0*b1*d0^3*f0*f1^3+42*b0*b1*d0^3*f1^4+12*b0*b1*d0^2*d1*f0^4+72*b0*b1*d0^2*d1*f0^3*f1+108*b0*b1*d0^2*d1*f0^2*f1^2+168*b0*b1*d0^2*d1*f0*f1^3+288*b0*b1*d0^2*d1*f1^4+12*b0*b1*d0*d1^2*f0^4+144*b0*b1*d0*d1^2*f0^3*f1+432*b0*b1*d0*d1^2*f0^2*f1^2+600*b0*b1*d0*d1^2*f0*f1^3+756*b0*b1*d0*d1^2*f1^4+42*b0*b1*d1^3*f0^4+204*b0*b1*d1^3*f0^3*f1+324*b0*b1*d1^3*f0^2*f1^2+516*b0*b1*d1^3*f0*f1^3+858*b0*b1*d1^3*f1^4+6*b1^2*d0^3*f0^4+21*b1^2*d0^3*f0^3*f1+21*b1^2*d0^3*f0*f1^3+60*b1^2*d0^3*f1^4+21*b1^2*d0^2*d1*f0^4+99*b1^2*d0^2*d1*f0^3*f1+162*b1^2*d0^2*d1*f0^2*f1^2+267*b1^2*d0^2*d1*f0*f1^3+423*b1^2*d0^2*d1*f1^4+21*b1^2*d0*d1^2*f0^4+225*b1^2*d0*d1^2*f0^3*f1+648*b1^2*d0*d1^2*f0^2*f1^2+861*b1^2*d0*d1^2*f0*f1^3+1161*b1^2*d0*d1^2*f1^4+60*b1^2*d1^3*f0^4+303*b1^2*d1^3*f0^3*f1+486*b1^2*d1^3*f0^2*f1^2+795*b1^2*d1^3*f0*f1^3+1272*b1^2*d1^3*f1^4,
12*b0^2*d0^3*f0^2*f1^2+24*b0^2*d0^3*f0*f1^3+12*b0^2*d0^3*f1^4+12*b0^2*d0^2*d1*f0^3*f1+96*b0^2*d0^2*d1*f0^2*f1^2+204*b0^2*d0^2*d1*f0*f1^3+120*b0^2*d0^2*d1*f1^4+48*b0^2*d0*d1^2*f0^3*f1+276*b0^2*d0*d1^2*f0^2*f1^2+600*b0^2*d0*d1^2*f0*f1^3+372*b0^2*d0*d1^2*f1^4+36*b0^2*d1^3*f0^3*f1+288*b0^2*d1^3*f0^2*f1^2+612*b0^2*d1^3*f0*f1^3+360*b0^2*d1^3*f1^4+24*b0*b1*d0^3*f0^3*f1+72*b0*b1*d0^3*f0^2*f1^2+72*b0*b1*d0^3*f0*f1^3+120*b0*b1*d0^3*f1^4+96*b0*b1*d0^2*d1*f0^3*f1+576*b0*b1*d0^2*d1*f0^2*f1^2+1152*b0*b1*d0^2*d1*f0*f1^3+768*b0*b1*d0^2*d1*f1^4+168*b0*b1*d0*d1^2*f0^3*f1+1656*b0*b1*d0*d1^2*f0^2*f1^2+3960*b0*b1*d0*d1^2*f0*f1^3+1992*b0*b1*d0*d1^2*f1^4+288*b0*b1*d1^3*f0^3*f1+1728*b0*b1*d1^3*f0^2*f1^2+3456*b0*b1*d1^3*f0*f1^3+2304*b0*b1*d1^3*f1^4+24*b1^2*d0^3*f0^3*f1+108*b1^2*d0^3*f0^2*f1^2+144*b1^2*d0^3*f0*f1^3+156*b1^2*d0^3*f1^4+132*b1^2*d0^2*d1*f0^3*f1+864*b1^2*d0^2*d1*f0^2*f1^2+1764*b1^2*d0^2*d1*f0*f1^3+1128*b1^2*d0^2*d1*f1^4+312*b1^2*d0*d1^2*f0^3*f1+2484*b1^2*d0*d1^2*f0^2*f1^2+5760*b1^2*d0*d1^2*f0*f1^3+3108*b1^2*d0*d1^2*f1^4+396*b1^2*d1^3*f0^3*f1+2592*b1^2*d1^3*f0^2*f1^2+5292*b1^2*d1^3*f0*f1^3+3384*b1^2*d1^3*f1^4,
6*b0^2*d0^3*f0^2*f1^2+12*b0^2*d0^3*f0*f1^3+6*b0^2*d0^3*f1^4+24*b0^2*d0^2*d1*f0^3*f1+42*b0^2*d0^2*d1*f0^2*f1^2+60*b0^2*d0^2*d1*f0*f1^3+90*b0^2*d0^2*d1*f1^4+18*b0^2*d0*d1^2*f0^4+60*b0^2*d0*d1^2*f0^3*f1+114*b0^2*d0*d1^2*f0^2*f1^2+168*b0^2*d0*d1^2*f0*f1^3+288*b0^2*d0*d1^2*f1^4+6*b0^2*d1^3*f0^4+60*b0^2*d1^3*f0^3*f1+126*b0^2*d1^3*f0^2*f1^2+192*b0^2*d1^3*f0*f1^3+264*b0^2*d1^3*f1^4+12*b0*b1*d0^3*f0^3*f1+36*b0*b1*d0^3*f0^2*f1^2+36*b0*b1*d0^3*f0*f1^3+60*b0*b1*d0^3*f1^4+24*b0*b1*d0^2*d1*f0^4+108*b0*b1*d0^2*d1*f0^3*f1+252*b0*b1*d0^2*d1*f0^2*f1^2+372*b0*b1*d0^2*d1*f0*f1^3+540*b0*b1*d0^2*d1*f1^4+60*b0*b1*d0*d1^2*f0^4+396*b0*b1*d0*d1^2*f0^3*f1+684*b0*b1*d0*d1^2*f0^2*f1^2+1092*b0*b1*d0*d1^2*f0*f1^3+1656*b0*b1*d0*d1^2*f1^4+60*b0*b1*d1^3*f0^4+348*b0*b1*d1^3*f0^3*f1+756*b0*b1*d1^3*f0^2*f1^2+1092*b0*b1*d1^3*f0*f1^3+1632*b0*b1*d1^3*f1^4+12*b1^2*d0^3*f0^3*f1+54*b1^2*d0^3*f0^2*f1^2+72*b1^2*d0^3*f0*f1^3+78*b1^2*d0^3*f1^4+24*b1^2*d0^2*d1*f0^4+180*b1^2*d0^2*d1*f0^3*f1+378*b1^2*d0^2*d1*f0^2*f1^2+552*b1^2*d0^2*d1*f0*f1^3+810*b1^2*d0^2*d1*f1^4+114*b1^2*d0*d1^2*f0^4+576*b1^2*d0*d1^2*f0^3*f1+1026*b1^2*d0*d1^2*f0^2*f1^2+1596*b1^2*d0*d1^2*f0*f1^3+2520*b1^2*d0*d1^2*f1^4+78*b1^2*d1^3*f0^4+528*b1^2*d1^3*f0^3*f1+1134*b1^2*d1^3*f0^2*f1^2+1668*b1^2*d1^3*f0*f1^3+2424*b1^2*d1^3*f1^4,
24*b0^2*d0^3*f0*f1^3+60*b0^2*d0^2*d1*f0^2*f1^2+96*b0^2*d0^2*d1*f0*f1^3+60*b0^2*d0^2*d1*f1^4+36*b0^2*d0*d1^2*f0^3*f1+132*b0^2*d0*d1^2*f0^2*f1^2+276*b0^2*d0*d1^2*f0*f1^3+204*b0^2*d0*d1^2*f1^4+12*b0^2*d1^3*f0^3*f1+144*b0^2*d1^3*f0^2*f1^2+324*b0^2*d1^3*f0*f1^3+168*b0^2*d1^3*f1^4+36*b0*b1*d0^3*f0^2*f1^2+72*b0*b1*d0^3*f0*f1^3+36*b0*b1*d0^3*f1^4+48*b0*b1*d0^2*d1*f0^3*f1+252*b0*b1*d0^2*d1*f0^2*f1^2+648*b0*b1*d0^2*d1*f0*f1^3+348*b0*b1*d0^2*d1*f1^4+120*b0*b1*d0*d1^2*f0^3*f1+900*b0*b1*d0*d1^2*f0^2*f1^2+1728*b0*b1*d0*d1^2*f0*f1^3+1140*b0*b1*d0*d1^2*f1^4+120*b0*b1*d1^3*f0^3*f1+828*b0*b1*d1^3*f0^2*f1^2+1872*b0*b1*d1^3*f0*f1^3+1068*b0*b1*d1^3*f1^4+36*b1^2*d0^3*f0^2*f1^2+144*b1^2*d0^3*f0*f1^3+36*b1^2*d0^3*f1^4+48*b1^2*d0^2*d1*f0^3*f1+432*b1^2*d0^2*d1*f0^2*f1^2+936*b1^2*d0^2*d1*f0*f1^3+528*b1^2*d0^2*d1*f1^4+228*b1^2*d0*d1^2*f0^3*f1+1296*b1^2*d0*d1^2*f0^2*f1^2+2556*b1^2*d0*d1^2*f0*f1^3+1752*b1^2*d0*d1^2*f1^4+156*b1^2*d1^3*f0^3*f1+1260*b1^2*d1^3*f0^2*f1^2+2844*b1^2*d1^3*f0*f1^3+1572*b1^2*d1^3*f1^4;

// This checks that the polynomial parametrization
// lies on the probability simplex.
// It requires suma.sing. Most likely, you should 
// change the directory where you saved this file. 

// If you do have this file, you should uncomment
// the following two lines.

// < "/home/lgp/singular/suma.sing";

// Suma(Substitute(1,P));

// This checks that the PInvariants vanish at
// the polynomial parametrization.

map Evaluate = rP, P;

// The following command takes a lot of space and time to
// finish for larger models.

// ideal Z = Evaluate(PInvariants);

setring rP;
ideal Z;
int i;
for (i=1; i<= size(PInvariants); i++)
{
  i;
  Z = PInvariants[i];
  setring r;
  Evaluate(Z);
  setring rP;
}