## Z3PQ.txt 
# List of P and Q for the shifts
#  0p1p:={A0,A1} --> {A0+1,A1+1} and similarly,
#  0p3p, 0p2p, 0p2n, 2p3p, 2n3p;
#  0n1p, 0p1n, 0n1n; 
#  0pp:={A0 --> A0+2} and smilarly,
#  0nn, 1pp, 1nn, 2pp, 2nn, 3pp, 3nn.

P0p1p:=x*(x-1)*dx^2+(A0-A2-1+2*x-x*A0-x*A1+2*x*A2)*dx+1/2*A1^2+A2+1/2+1/2*A0^2+1/2*A2^2-1/2*A3^2-A0*A2+A1*A0-A1*A2:

Q0p1p:=x*(x-1)*dx^2+(A0-A2-x*A0-x*A1+2*x*A2)*dx+1/2*(A0+1+A3-A2+A1)*(A0+1-A3-A2+A1):

P0p3p:=x*(x-1)^2*dx^2+(x-1)*(3*x*A2+3*x+x*A3+A0-1-A2)*dx-2*A2+A3*A0+x*A3+3*x*A2+x+2*x*A2^2+2*x*A2*A3-1/2+A0*A2+1/2*A0^2+1/2*A3^2-1/2*A1^2-3/2*A2^2+A0-A2*A3:

Q0p3p:=x*(x-1)^2*dx^2+(x-1)*(4*x+3*x*A2+x*A3+A0-A2)*dx+1/2*A0^2+A3*A0+2*A0+A0*A2+1/2+1/2*A3^2-3/2*A2^2-A2*A3+A3-2*A2-1/2*A1^2+x*A3+5*x*A2+2*x+2*x*A2^2+2*x*A2*A3:     

P0p2p:=(x-1)*dx^2-1/2*(-10*x*A2-4*x*A0-5*x+x*A0^2-4*x*A0*A2-x*A1^2-5*x*A2^2+x*A3^2+4*A2+2-2*A0^2+2*A2^2)*dx/((A2+A0+1)*x)-1/2*(2*A2+1)*(-A2^2-2*A2-1-A1^2+A0^2+A3^2)/((A2+A0+1)*x):

Q0p2p:=(x-1)*dx^2-1/2*(x*A0^2-4*x*A0*A2-2*x*A0-x*A1^2-8*x*A2-5*x*A2^2+x*A3^2-3*x+2*A2^2-2*A0^2-4*A0-2)*dx/(x*(A2+A0+1))-1/2*(-2*A2^2+2*x*A0^2*A2-x*A2^2-x*A1^2+x*A0^2+x+4*x*A0*A2+2*x*A2*A3^2+x*A3^2-2*x*A2*A1^2+2*x*A0+2*x*A2-2*x*A2^3+2*A0^2+4*A0+2)/((A2+A0+1)*x^2):

P0p2n:=x^2*(x-1)^2*dx^2+x*(x-1)*(2*x*A2+3*x-2)*dx+A2-A0-A0^2-A2^2+2*A0*A2-3*x*A2-x+x*A2^2+x*A0^2-2*x*A0*A2+x*A0-x*A1^2+x*A3^2+x^2*A2^2+2*x^2*A2+x^2-x^2*A3^2: 

Q0p2n:=x^2*(x-1)^2*dx^2+x*(x-1)*(2*x*A2+3*x-2)*dx+3*A2-3*A0-2-A0^2-A2^2+2*A0*A2+x^2*A2^2+2*x^2*A2+x^2-x^2*A3^2-5*x*A2+x+x*A2^2+x*A0^2-2*x*A0*A2+3*x*A0-x*A1^2+x*A3^2: 

P2p3p:=x*(x-1)*dx^2+1/2*(-A0^2-A3^2-4*A3-3-6*A2-3*A2^2+A1^2-4*A2*A3+6*x*A2^2+8*x*A2*A3+12*x*A2+8*x*A3+6*x+2*x*A3^2)*dx/(A2+A3+1)+(2*A2+1)*(A2+A3+1): 

Q2p3p:=x*(x-1)*dx^2+1/2*(-A0^2-A3^2-6*A3-5-8*A2-3*A2^2+A1^2-4*A2*A3+16*x*A2+12*x*A3+10*x+8*x*A2*A3+2*x*A3^2+6*x*A2^2)*dx/(A2+A3+1)+2*(A2+1)*(A2+A3+2): 

P2n3p:=x^2*(x-1)^2*dx^2+x*(-1+2*x)*(x-1)*(2*A2+1)*dx-A0^2+A2^2-3*x*A2+x*A0^2-3*x*A2^2+x*A3^2-x*A1^2+x*A3-2*x*A2*A3+3*x^2*A2^2+3*x^2*A2+2*x^2*A2*A3-x^2*A3^2-x^2*A3: 

Q2n3p:=x^2*(x-1)^2*dx^2+x*(-1+2*x)*(x-1)*(2*A2+1)*dx-A0^2+A2^2-5*x*A2+2*x+x*A0^2-3*x*A2^2+x*A3^2-x*A1^2+3*x*A3-2*x*A2*A3+3*x^2*A2^2+5*x^2*A2+2*x^2*A2*A3-2*x^2-x^2*A3^2-3*x^2*A3: 

P0n1p:=x*(x-1)*dx^2+(-1-A2-A0+2*x+x*A0-x*A1+2*x*A2)*dx+1/2*A1^2+A2+1/2+1/2*A0^2+1/2*A2^2-1/2*A3^2+A0*A2-A1*A0-A1*A2: 

Q0n1p:=x*(x-1)*dx^2+(-A2-A0+x*A0-x*A1+2*x*A2)*dx+1/2*(A0-1+A2-A3-A1)*(A0-1+A2+A3-A1): 

P0p1n:=x*(x-1)*dx^2+(2*x-x*A0+2*x*A2+x*A1+A0-A2-1)*dx+1/2*A1^2+A2+1/2+1/2*A0^2+1/2*A2^2-1/2*A3^2-A0*A2-A1*A0+A1*A2: 

Q0p1n:=x*(x-1)*dx^2+(A0-A2-x*A0+2*x*A2+x*A1)*dx+1/2*(A0-A2-A1+A3+1)*(A0-A2+1-A1-A3): 

P0n1n:=x*(x-1)*dx^2+(2*x+x*A0+x*A1+2*x*A2-1-A2-A0)*dx+1/2*A1^2+A2+1/2+1/2*A0^2+1/2*A2^2-1/2*A3^2+A0*A2+A1*A0+A1*A2: 

Q0n1n:=x*(x-1)*dx^2+(-A2-A0+x*A0+x*A1+2*x*A2)*dx+1/2*(A0-1+A2+A1-A3)*(A0-1+A2+A1+A3): 

P0pp:=(x-1)^2*dx^2-1/2*(x-1)*(-10*x*A2-4*x*A0-5*x+x*A0^2-4*x*A0*A2-x*A1^2-5*x*A2^2+x*A3^2+4*A2+2-2*A0^2+2*A2^2)*dx/(x*(A2+A0+1))+1/8*(-4+8*A0^2*A2-20*A2^2-4*A1^2+4*A0^2+5*x-12*x*A2*A3^2*A0+4*x*A2*A1^2*A0-16*A0*A2+8*A2*A3^2+4*A0*A3^2+4*A3^2-8*A2*A1^2+8*A2*A3^2*A0-8*A2*A1^2*A0+8*A0^3*A2-8*A2^3*A0-4*A1^2*A0-4*A0-16*A2+8*x*A0+20*x*A2+4*x*A2*A1^2-12*x*A2*A3^2+4*x*A0^2*A2+4*A0^3-20*A2^2*A0+2*x*A0^2+2*x*A1^2-6*x*A3^2+28*x*A0*A2+x*A2^4+x*A0^4+x*A1^4+x*A3^4-2*x*A0^2*A3^2-4*x*A0^3*A2+12*x*A2^3*A0-2*x*A1^2*A0^2+32*x*A2^2*A0+6*x*A2^2*A0^2-2*x*A1^2*A3^2-2*x*A2^2*A1^2-8*x*A0*A3^2-2*x*A2^2*A3^2+12*x*A2^3+26*x*A2^2-8*A2^3)/(x*(A2+A0+1)*(A0+1)): 

Q0pp:=(x-1)^2*dx^2-1/2*(x-1)*(-6*x*A2-x+x*A0^2-4*x*A0*A2-x*A1^2-5*x*A2^2+x*A3^2-6-2*A0^2-4*A2+2*A2^2-8*A0)*dx/(x*(A2+A0+1))+1/8*(24-8*A2^2+40*A0^2-12*x+8*x*A2*A3^2*A0-8*x*A2*A1^2*A0-12*x^2*A2*A3^2*A0+4*x^2*A2*A1^2*A0+16*A0*A2+x^2+56*A0+16*A2-28*x*A0+16*x*A2-8*x*A2*A1^2+8*x*A2*A3^2+40*x*A0^2*A2+8*A0^3-4*x^2*A2-2*x^2*A3^2-8*A2^2*A0-20*x*A0^2+4*x*A1^2-4*x*A3^2+6*x^2*A2^2+48*x*A0*A2-4*x*A0^3-2*x^2*A1^2+6*x^2*A0^2+x^2*A2^4+4*x^2*A0+x^2*A0^4+x^2*A1^4+x^2*A3^4+8*x*A0^3*A2-8*x*A2^3*A0+4*x*A1^2*A0+20*x*A2^2*A0-4*x*A0*A3^2-12*x^2*A0^2*A2-12*x^2*A0*A2-12*x^2*A2*A3^2-2*x^2*A0^2*A3^2-4*x^2*A0*A3^2+4*x^2*A2*A1^2-4*x^2*A0^3*A2+12*x^2*A2^3*A0-2*x^2*A1^2*A0^2-2*x^2*A2^2*A1^2-2*x^2*A2^2*A3^2+12*x^2*A2^2*A0+6*x^2*A2^2*A0^2-2*x^2*A1^2*A3^2+12*x^2*A2^3-8*x*A2^3+20*x*A2^2-4*x^2*A1^2*A0+4*x^2*A0^3)/(x^2*(A2+A0+1)*(A0+1)): 

P0nn:=(x-1)^2*dx^2+1/2*(x-1)*(-5*x*A2^2-10*x*A2+4*x*A0*A2+x*A3^2+x*A0^2-5*x-x*A1^2+4*x*A0+2+2*A2^2-2*A0^2+4*A2)*dx/(x*(A0-A2-1))+1/8*(-4+8*A0^2*A2-20*A2^2-4*A1^2+4*A0^2+5*x+12*x*A2*A3^2*A0-4*x*A2*A1^2*A0+16*A0*A2+8*A2*A3^2-4*A0*A3^2+4*A3^2-8*A2*A1^2-8*A2*A3^2*A0+8*A2*A1^2*A0-8*A0^3*A2+8*A2^3*A0+4*A1^2*A0+4*A0-16*A2-8*x*A0+20*x*A2+4*x*A2*A1^2-12*x*A2*A3^2+4*x*A0^2*A2-4*A0^3+20*A2^2*A0+2*x*A0^2+2*x*A1^2-6*x*A3^2-28*x*A0*A2+x*A2^4+x*A0^4+x*A1^4+x*A3^4-2*x*A0^2*A3^2+4*x*A0^3*A2-12*x*A2^3*A0-2*x*A1^2*A0^2-32*x*A2^2*A0+6*x*A2^2*A0^2-2*x*A1^2*A3^2-2*x*A2^2*A1^2+8*x*A0*A3^2-2*x*A2^2*A3^2+12*x*A2^3+26*x*A2^2-8*A2^3)/(x*(A0-A2-1)*(A0-1)): 

Q0nn:=(x-1)^2*dx^2+1/2*(x-1)*(-5*x*A2^2-6*x*A2+4*x*A0*A2+x*A3^2+x*A0^2-x-x*A1^2+8*A0-4*A2-6+2*A2^2-2*A0^2)*dx/(x*(A0-A2-1))+1/8*(24-8*A2^2+40*A0^2-12*x-8*x*A2*A3^2*A0+8*x*A2*A1^2*A0+12*x^2*A2*A3^2*A0-4*x^2*A2*A1^2*A0-16*A0*A2+x^2-56*A0+16*A2+28*x*A0+16*x*A2-8*x*A2*A1^2+8*x*A2*A3^2+40*x*A0^2*A2-8*A0^3-4*x^2*A2-2*x^2*A3^2+8*A2^2*A0-20*x*A0^2+4*x*A1^2-4*x*A3^2+6*x^2*A2^2-48*x*A0*A2+4*x*A0^3-2*x^2*A1^2+6*x^2*A0^2+x^2*A2^4-4*x^2*A0+x^2*A0^4+x^2*A1^4+x^2*A3^4-8*x*A0^3*A2+8*x*A2^3*A0-4*x*A1^2*A0-20*x*A2^2*A0+4*x*A0*A3^2-12*x^2*A0^2*A2+12*x^2*A0*A2-12*x^2*A2*A3^2-2*x^2*A0^2*A3^2+4*x^2*A0*A3^2+4*x^2*A2*A1^2+4*x^2*A0^3*A2-12*x^2*A2^3*A0-2*x^2*A1^2*A0^2-2*x^2*A2^2*A1^2-2*x^2*A2^2*A3^2-12*x^2*A2^2*A0+6*x^2*A2^2*A0^2-2*x^2*A1^2*A3^2+12*x^2*A2^3-8*x*A2^3+20*x*A2^2+4*x^2*A1^2*A0-4*x^2*A0^3)/(x^2*(A0-A2-1)*(A0-1)): 

P1pp:=x^2*dx^2+1/2*x*(-4*A1-A1^2-4*A1*A2-3-A0^2+A3^2-3*A2^2-6*A2+x*A0^2+10*x*A2-x*A3^2+4*x*A1*A2+4*x*A1-x*A1^2+5*x+5*x*A2^2)*dx/((A1+A2+1)*(x-1))+1/8*(-1+4*A0^2*A2+4*A1*A2*A0^2-6*A2^2-6*A1^2+2*A0^2+5*x+4*A3^2*A1*A2+4*A2*A3^2-12*A1*A2^2+2*A0^2*A3^2-12*A1*A2+2*A3^2-12*A2*A1^2-4*A2^3*A1+4*A3^2*A1+4*A0^2*A1-4*A2*A1^3+2*A1^2*A0^2-A2^4-4*A1-4*A2+8*x*A1+20*x*A2+4*x*A2*A1^2-12*x*A2*A3^2+4*x*A0^2*A2-A0^4-A1^4+4*x*A1*A2*A0^2-12*x*A3^2*A1*A2+2*A2^2*A0^2+2*A1^2*A3^2+2*x*A0^2+2*x*A1^2-6*x*A3^2+x*A2^4+x*A0^4+x*A1^4+x*A3^4-6*A2^2*A1^2-2*x*A0^2*A3^2-2*x*A1^2*A0^2-2*x*A2^2*A0^2-2*x*A1^2*A3^2+6*x*A2^2*A1^2-2*x*A2^2*A3^2+2*A2^2*A3^2+12*x*A2^3+26*x*A2^2-4*A2^3-A3^4-4*A1^3+32*x*A1*A2^2+28*x*A1*A2+12*x*A2^3*A1-8*x*A3^2*A1-4*x*A2*A1^3)/((A1+1)*(A1+A2+1)*(x-1)):

Q1pp:=x^2*dx^2+1/2*(6*x*A2+x+x*A0^2-x*A3^2+4*x*A1*A2-x*A1^2+5*x*A2^2-8*A1-4*A1*A2-7-A0^2+A3^2-3*A2^2-10*A2-A1^2)*x*dx/((x-1)*(A1+A2+1))+1/8*(13-4*A0^2*A2-4*A1*A2*A0^2+18*A2^2+26*A1^2+2*A0^2+10*x-4*A3^2*A1*A2-4*A2*A3^2+24*A1*A2^2-2*A0^2*A3^2+x^2+52*A1*A2-6*A3^2+28*A2*A1^2+4*A2^3*A1-8*A3^2*A1+4*A2*A1^3-2*A1^2*A0^2+A2^4+32*A1+28*A2+20*x*A1-8*x*A2-16*x*A2*A1^2+16*x*A2*A3^2+A0^4+A1^4+16*x*A3^2*A1*A2+4*x^2*A1*A2*A0^2-12*x^2*A3^2*A1*A2-4*x^2*A2-2*x^2*A3^2-2*A2^2*A0^2-2*A1^2*A3^2+8*x*A1^2+8*x*A3^2+6*x^2*A2^2-2*x*A2^4-2*x*A0^4-2*x*A1^4-2*x*A3^4+6*x^2*A1^2-2*x^2*A0^2+x^2*A2^4+x^2*A0^4+x^2*A1^4+x^2*A3^4+6*A2^2*A1^2+4*x*A0^2*A3^2+4*x*A1^2*A0^2+4*x*A2^2*A0^2+4*x*A1^2*A3^2-12*x*A2^2*A1^2+4*x*A2^2*A3^2+4*x^2*A0^2*A2-12*x^2*A2*A3^2-2*x^2*A0^2*A3^2-12*x^2*A2*A1^2-2*x^2*A1^2*A0^2+6*x^2*A2^2*A1^2-2*x^2*A2^2*A3^2-2*x^2*A2^2*A0^2-2*x^2*A1^2*A3^2+12*x^2*A2^3-2*A2^2*A3^2-4*x*A1^3-16*x*A2^3-32*x*A2^2+4*A2^3+A3^4+8*A1^3+4*x*A0^2*A1+12*x^2*A1*A2^2-12*x^2*A1*A2+12*x^2*A2^3*A1-4*x^2*A3^2*A1-4*x^2*A0^2*A1-4*x^2*A2*A1^3+4*x^2*A1-44*x*A1*A2^2-24*x*A1*A2-16*x*A2^3*A1+12*x*A3^2*A1+4*x^2*A1^3)/((A1+1)*(A1+A2+1)*(x-1)^2):

P1nn:=x^2*dx^2-1/2*x*(-A0^2+4*A1+4*A1*A2-A1^2-3-6*A2+A3^2-3*A2^2+x*A0^2+10*x*A2-x*A3^2-4*x*A1*A2-4*x*A1-x*A1^2+5*x+5*x*A2^2)*dx/((A1-A2-1)*(x-1))+1/8*(-1+4*A0^2*A2-4*A1*A2*A0^2-6*A2^2-6*A1^2+2*A0^2+5*x-4*A3^2*A1*A2+4*A2*A3^2+12*A1*A2^2+2*A0^2*A3^2+12*A1*A2+2*A3^2-12*A2*A1^2+4*A2^3*A1-4*A3^2*A1-4*A0^2*A1+4*A2*A1^3+2*A1^2*A0^2-A2^4+4*A1-4*A2-8*x*A1+20*x*A2+4*x*A2*A1^2-12*x*A2*A3^2+4*x*A0^2*A2-A0^4-A1^4-4*x*A1*A2*A0^2+12*x*A3^2*A1*A2+2*A2^2*A0^2+2*A1^2*A3^2+2*x*A0^2+2*x*A1^2-6*x*A3^2+x*A2^4+x*A0^4+x*A1^4+x*A3^4-6*A2^2*A1^2-2*x*A0^2*A3^2-2*x*A1^2*A0^2-2*x*A2^2*A0^2-2*x*A1^2*A3^2+6*x*A2^2*A1^2-2*x*A2^2*A3^2+2*A2^2*A3^2+12*x*A2^3+26*x*A2^2-4*A2^3-A3^4+4*A1^3-32*x*A1*A2^2-28*x*A1*A2-12*x*A2^3*A1+8*x*A3^2*A1+4*x*A2*A1^3)/((A1-1)*(A1-A2-1)*(x-1)): 

Q1nn:=x^2*dx^2-1/2*(6*x*A2+x+x*A0^2-x*A3^2-4*x*A1*A2-x*A1^2+5*x*A2^2-A0^2+8*A1+4*A1*A2-7-10*A2+A3^2-3*A2^2-A1^2)*x*dx/((x-1)*(A1-A2-1))+1/8*(13-4*A0^2*A2+4*A1*A2*A0^2+18*A2^2+26*A1^2+2*A0^2+10*x+4*A3^2*A1*A2-4*A2*A3^2-24*A1*A2^2-2*A0^2*A3^2+x^2-52*A1*A2-6*A3^2+28*A2*A1^2-4*A2^3*A1+8*A3^2*A1-4*A2*A1^3-2*A1^2*A0^2+A2^4-32*A1+28*A2-20*x*A1-8*x*A2-16*x*A2*A1^2+16*x*A2*A3^2+A0^4+A1^4-16*x*A3^2*A1*A2-4*x^2*A1*A2*A0^2+12*x^2*A3^2*A1*A2-4*x^2*A2-2*x^2*A3^2-2*A2^2*A0^2-2*A1^2*A3^2+8*x*A1^2+8*x*A3^2+6*x^2*A2^2-2*x*A2^4-2*x*A0^4-2*x*A1^4-2*x*A3^4+6*x^2*A1^2-2*x^2*A0^2+x^2*A2^4+x^2*A0^4+x^2*A1^4+x^2*A3^4+6*A2^2*A1^2+4*x*A0^2*A3^2+4*x*A1^2*A0^2+4*x*A2^2*A0^2+4*x*A1^2*A3^2-12*x*A2^2*A1^2+4*x*A2^2*A3^2+4*x^2*A0^2*A2-12*x^2*A2*A3^2-2*x^2*A0^2*A3^2-12*x^2*A2*A1^2-2*x^2*A1^2*A0^2+6*x^2*A2^2*A1^2-2*x^2*A2^2*A3^2-2*x^2*A2^2*A0^2-2*x^2*A1^2*A3^2+12*x^2*A2^3-2*A2^2*A3^2+4*x*A1^3-16*x*A2^3-32*x*A2^2+4*A2^3+A3^4-8*A1^3-4*x*A0^2*A1-12*x^2*A1*A2^2+12*x^2*A1*A2-12*x^2*A2^3*A1+4*x^2*A3^2*A1+4*x^2*A0^2*A1+4*x^2*A2*A1^3-4*x^2*A1+44*x*A1*A2^2+24*x*A1*A2+16*x*A2^3*A1-12*x*A3^2*A1-4*x^2*A1^3)/((A1-1)*(A1-A2-1)*(x-1)^2):

P2pp:=dx^2+4*(A2+1)*(1+6*A2^2-A1^2-2*x-2*A2*A3^2+A0^2*A3^2-A3^2-2*A2*A1^2+A1^2*A0^2+A2^4+4*A2-8*x*A2+2*x*A2*A1^2+4*x*A2*A3^2+2*x*A0^2*A2-A0^4+x*A0^2+x*A1^2+2*x*A3^2-2*x*A2^4+x*A0^4+x*A1^4-A2^2*A1^2-x*A0^2*A3^2-2*x*A1^2*A0^2+x*A2^2*A0^2-x*A1^2*A3^2+x*A2^2*A1^2+2*x*A2^2*A3^2-A2^2*A3^2-8*x*A2^3-12*x*A2^2+4*A2^3)*dx/((-3*A2^4-12*A2^3+2*A2^2*A1^2+2*A2^2*A3^2-18*A2^2+2*A2^2*A0^2+4*A2*A3^2+4*A2*A1^2+4*A0^2*A2-12*A2+2*A1^2-3+2*A0^2-2*A1^2*A3^2+A0^4+A1^4+2*A3^2-2*A1^2*A0^2-2*A0^2*A3^2+A3^4)*x*(x-1))+2*(A2+1)*(2*A2+1)*(A0^2+1-A1^2+2*A2+A2^2-A3^2)*(-A2^2-2*A2-1-A1^2+A0^2+A3^2)/((-3*A2^4-12*A2^3+2*A2^2*A1^2+2*A2^2*A3^2-18*A2^2+2*A2^2*A0^2+4*A2*A3^2+4*A2*A1^2+4*A0^2*A2-12*A2+2*A1^2-3+2*A0^2-2*A1^2*A3^2+A0^4+A1^4+2*A3^2-2*A1^2*A0^2-2*A0^2*A3^2+A3^4)*x*(x-1)): 

Q2pp:=dx^2+4*(A2+1)*(1+6*A2^2-A1^2-2*x-2*A2*A3^2+A0^2*A3^2-A3^2-2*A2*A1^2+A1^2*A0^2+A2^4+4*A2-8*x*A2+2*x*A2*A1^2+4*x*A2*A3^2+2*x*A0^2*A2-A0^4+x*A0^2+x*A1^2+2*x*A3^2-2*x*A2^4+x*A0^4+x*A1^4-A2^2*A1^2-x*A0^2*A3^2-2*x*A1^2*A0^2+x*A2^2*A0^2-x*A1^2*A3^2+x*A2^2*A1^2+2*x*A2^2*A3^2-A2^2*A3^2-8*x*A2^3-12*x*A2^2+4*A2^3)*dx/((-3*A2^4-12*A2^3+2*A2^2*A1^2+2*A2^2*A3^2-18*A2^2+2*A2^2*A0^2+4*A2*A3^2+4*A2*A1^2+4*A0^2*A2-12*A2+2*A1^2-3+2*A0^2-2*A1^2*A3^2+A0^4+A1^4+2*A3^2-2*A1^2*A0^2-2*A0^2*A3^2+A3^4)*x*(x-1))+2*(A2+1)*(2+12*A2^2-2*A1^2-x-4*A2*A3^2+2*A0^2*A3^2+x^2-2*A3^2-4*A2*A1^2+2*A1^2*A0^2+2*A2^4+8*A2-2*x^2*A2^5-2*x*A2+8*x*A2*A1^2-8*x*A2*A3^2-2*A0^4+2*x^2*A2+2*x^2*A3^2+4*x^2*A2^3*A3^2-2*x^2*A3^4*A2+2*x^2*A2*A0^4+2*x^2*A2*A1^4-4*x^2*A0^2*A2*A1^2+4*x*A1^2-2*x*A3^2-2*x^2*A2^2+7*x*A2^4+x*A0^4-3*x*A1^4+3*x*A3^4-2*x^2*A1^2-2*x^2*A0^2-7*x^2*A2^4+x^2*A0^4+x^2*A1^4-3*x^2*A3^4-2*A2^2*A1^2-4*x*A0^2*A3^2+2*x*A1^2*A0^2+4*x*A2^2*A1^2-10*x*A2^2*A3^2-4*x^2*A0^2*A2+8*x^2*A2*A3^2+2*x^2*A0^2*A3^2-4*x^2*A2*A1^2-2*x^2*A1^2*A0^2-2*x^2*A2^2*A1^2+10*x^2*A2^2*A3^2-2*x^2*A2^2*A0^2+2*x^2*A1^2*A3^2-8*x^2*A2^3-2*A2^2*A3^2+8*x*A2^3+2*x*A2^2+8*A2^3+2*x*A2*A3^4+2*x*A2^5+4*x*A0^2*A2*A1^2-4*x*A2^3*A3^2-2*x*A2*A0^4-2*x*A2*A1^4)/((-3*A2^4-12*A2^3+2*A2^2*A1^2+2*A2^2*A3^2-18*A2^2+2*A2^2*A0^2+4*A2*A3^2+4*A2*A1^2+4*A0^2*A2-12*A2+2*A1^2-3+2*A0^2-2*A1^2*A3^2+A0^4+A1^4+2*A3^2-2*A1^2*A0^2-2*A0^2*A3^2+A3^4)*x^2*(x-1)^2): 

P2nn:=(x-1)^2*(-2*x^2*A2+x^2+x^2*A2^2-x^2*A3^2+x*A3^2+2*x*A2-x*A2^2-x-x*A1^2+x*A0^2+A2^2-A0^2+1-2*A2)*x^2*dx^2/((A2-1+A3)*(-1+A2-A3))+1/2*(x-1)*(-2+4*A0^2*A2+6*A2^2+2*A0^2+7*x-9*x^2+6*x^3-4*x*A2+2*x*A2*A1^2-2*x*A2*A3^2-10*x*A0^2*A2+12*x^2*A2+9*x^2*A3^2-7*x*A0^2+3*x*A1^2-3*x*A3^2+3*x^2*A2^2-5*x^2*A1^2+5*x^2*A0^2+6*x^2*A0^2*A2+6*x^2*A2*A3^2-6*x^2*A2*A1^2-6*x^2*A2^3-2*x^3*A2^2-8*x^3*A2-6*x^3*A3^2-4*x^3*A2*A3^2+10*x*A2^3-13*x*A2^2-4*A2^3+4*x^3*A2^3)*x*dx/((A2-1+A3)*(-1+A2-A3))+1/2*(4*A0^2*A2+2*A2^2-2*A0^2-x+3*x^2-4*x^3+2*A2^4-2*x*A2-4*x*A0^2*A2+2*x^4+2*A0^4+2*x^2*A2-5*x^2*A3^2-4*A2^2*A0^2+5*x*A0^2-x*A1^2+x*A3^2-3*x^2*A2^2-8*x*A2^4-4*x*A0^4+x^2*A1^2-5*x^2*A0^2+10*x^2*A2^4+2*x^2*A0^4+2*x^2*A1^4+2*x^2*A3^4-4*x*A0^2*A3^2+4*x*A1^2*A0^2+12*x*A2^2*A0^2-4*x^2*A0^2*A2+8*x^2*A0^2*A3^2+8*x^2*A2*A1^2-4*x^2*A1^2*A0^2-4*x^2*A2^2*A3^2-12*x^2*A2^2*A0^2-4*x^2*A1^2*A3^2-12*x^2*A2^3-2*x^3*A1^2+8*x^3*A2^2+8*x^3*A3^2-4*x^4*A2^2-4*x^4*A3^2+2*x^3*A0^2+12*x*A2^3-x*A2^2-4*A2^3+4*x^3*A0^2*A2-4*x^4*A2^2*A3^2+2*x^4*A3^4+2*x^4*A2^4-4*x^3*A2^4-4*x^3*A2*A1^2-4*x^3*A0^2*A3^2-4*x^3*A3^4+8*x^3*A2^2*A3^2-4*x^3*A2^2*A1^2+4*x^3*A1^2*A3^2+4*x^3*A2^2*A0^2)/((A2-1+A3)*(-1+A2-A3)): 

Q2nn:=(x-1)^2*(-2*x^2*A2+x^2+x^2*A2^2-x^2*A3^2+x*A3^2+2*x*A2-x*A2^2-x-x*A1^2+x*A0^2+A2^2-A0^2+1-2*A2)*x^2*dx^2/((A2-1+A3)*(-1+A2-A3))+1/2*(x-1)*(2+4*A0^2*A2+10*A2^2-2*A0^2+x-15*x^2+10*x^3-8*A2+8*x*A2+2*x*A2*A1^2-2*x*A2*A3^2-10*x*A0^2*A2+24*x^2*A2+15*x^2*A3^2-x*A0^2+5*x*A1^2-5*x*A3^2-3*x^2*A2^2-3*x^2*A1^2+3*x^2*A0^2+6*x^2*A0^2*A2+6*x^2*A2*A3^2-6*x^2*A2*A1^2-6*x^2*A2^3+2*x^3*A2^2-16*x^3*A2-10*x^3*A3^2-4*x^3*A2*A3^2+10*x*A2^3-19*x*A2^2-4*A2^3+4*x^3*A2^3)*x*dx/((A2-1+A3)*(-1+A2-A3))+1/2*(2+8*A0^2*A2+12*A2^2-4*A0^2-3*x+11*x^2-16*x^3+2*A2^4-8*A2+14*x*A2-4*x*A2*A1^2+4*x*A2*A3^2-16*x*A0^2*A2+8*x^4+2*A0^4-22*x^2*A2-9*x^2*A3^2-4*A2^2*A0^2+7*x*A0^2+x*A1^2-x*A3^2+21*x^2*A2^2-8*x*A2^4-4*x*A0^4-7*x^2*A1^2-x^2*A0^2+10*x^2*A2^4+2*x^2*A0^4+2*x^2*A1^4+2*x^2*A3^4-4*x*A0^2*A3^2+4*x*A1^2*A0^2+12*x*A2^2*A0^2+4*x^2*A0^2*A2-8*x^2*A2*A3^2+8*x^2*A0^2*A3^2+16*x^2*A2*A1^2-4*x^2*A1^2*A0^2-4*x^2*A2^2*A3^2-12*x^2*A2^2*A0^2-4*x^2*A1^2*A3^2-20*x^2*A2^3+4*x^4*A2^3+2*x^3*A1^2+12*x^3*A2^2+16*x^3*A2+20*x^3*A3^2-6*x^4*A2^2-8*x^4*A2-10*x^4*A3^2-2*x^3*A0^2+8*x^3*A2*A3^2-4*x^4*A2*A3^2+24*x*A2^3-27*x*A2^2-8*A2^3+4*x^3*A0^2*A2-4*x^4*A2^2*A3^2+2*x^4*A3^4+2*x^4*A2^4-4*x^3*A2^4-4*x^3*A2*A1^2-4*x^3*A0^2*A3^2-4*x^3*A3^4+8*x^3*A2^2*A3^2-4*x^3*A2^2*A1^2+4*x^3*A1^2*A3^2+4*x^3*A2^2*A0^2-8*x^3*A2^3)/((A2-1+A3)*(-1+A2-A3)): 

P3pp:=x^2*(x-1)^2*dx^2+1/2*(x-1)*(-A0^2-A3^2-4*A3-3-6*A2-3*A2^2+A1^2-4*A2*A3+6*x*A2^2+8*x*A2*A3+12*x*A2+8*x*A3+6*x+2*x*A3^2)*x*dx/(A2+A3+1)+1/8*(1-4*A0^2*A2+6*A2^2-2*A1^2-2*A0^2-8*x-16*x*A2*A3^3+16*x^2*A2*A3^3+72*x^2*A2^2*A3+16*x^2*A2^3*A3-72*x*A2^2*A3-16*x*A2^3*A3-8*x*A3^3-4*A0^2*A3+4*A2*A3^3+12*A2*A3^2-2*A0^2*A3^2+8*x^2+6*A3^2-4*A3*A2*A1^2-4*A2*A1^2+8*x^2*A3^3-2*A1^2*A0^2+4*A3^3+80*x^2*A2*A3+A2^4+4*A2+4*A3-32*x*A2-64*x*A2*A3^2-4*A3*A1^2+A0^4+A1^4+24*x^2*A3+32*x^2*A2+24*x^2*A3^2-4*A3*A0^2*A2-2*A2^2*A0^2-2*A1^2*A3^2-24*x*A3^2+40*x^2*A2^2+12*A2*A3-2*A2^2*A1^2-32*x*A2^2*A3^2+64*x^2*A2*A3^2+4*A2^3*A3+32*x^2*A2^2*A3^2+16*x^2*A2^3+6*A2^2*A3^2-16*x*A2^3-24*x*A3-40*x*A2^2+4*A2^3-80*x*A2*A3+A3^4+12*A2^2*A3)/((A3+1)*(A2+A3+1)): 

Q3pp:=x^2*(x-1)^2*dx^2+1/2*(x-1)*(14*x+6*x*A2^2+20*x*A2+2*x*A3^2+8*x*A2*A3+16*x*A3+A1^2-A0^2-4*A2*A3-A3^2-7-10*A2-8*A3-3*A2^2)*x*dx/(A2+A3+1)+1/8*(13-4*A0^2*A2+18*A2^2-6*A1^2+2*A0^2-64*x+8*x*A3*A1^2-16*x*A2*A3^3-8*x*A0^2*A3+16*x^2*A2*A3^3+128*x^2*A2^2*A3+16*x^2*A2^3*A3-128*x*A2^2*A3-16*x*A2^3*A3-16*x*A3^3+4*A2*A3^3+28*A2*A3^2-2*A0^2*A3^2+64*x^2+26*A3^2-4*A3*A2*A1^2-4*A2*A1^2+16*x^2*A3^3-2*A1^2*A0^2+8*A3^3+256*x^2*A2*A3+A2^4+28*A2+32*A3-144*x*A2-128*x*A2*A3^2-8*A3*A1^2+A0^4+A1^4+144*x^2*A3+144*x^2*A2+96*x^2*A3^2-4*A3*A0^2*A2-2*A2^2*A0^2-2*A1^2*A3^2-8*x*A0^2+8*x*A1^2-96*x*A3^2+96*x^2*A2^2+52*A2*A3-2*A2^2*A1^2-32*x*A2^2*A3^2+128*x^2*A2*A3^2+4*A2^3*A3+32*x^2*A2^2*A3^2+16*x^2*A2^3+6*A2^2*A3^2-16*x*A2^3-144*x*A3-96*x*A2^2+4*A2^3-256*x*A2*A3+A3^4+24*A2^2*A3)/((A3+1)*(A2+A3+1)):

P3nn:=x^2*(x-1)^2*dx^2+1/2*(x-1)*(6*x+2*x*A3^2+6*x*A2^2+12*x*A2-8*x*A2*A3-8*x*A3-3-3*A2^2+A1^2-A0^2-6*A2+4*A2*A3-A3^2+4*A3)*x*dx/(1+A2-A3)+1/8*(-1+4*A0^2*A2-6*A2^2+2*A1^2+2*A0^2+8*x-16*x*A2*A3^3+16*x^2*A2*A3^3+72*x^2*A2^2*A3+16*x^2*A2^3*A3-72*x*A2^2*A3-16*x*A2^3*A3-8*x*A3^3-4*A0^2*A3+4*A2*A3^3-12*A2*A3^2+2*A0^2*A3^2-8*x^2-6*A3^2-4*A3*A2*A1^2+4*A2*A1^2+8*x^2*A3^3+2*A1^2*A0^2+4*A3^3+80*x^2*A2*A3-A2^4-4*A2+4*A3+32*x*A2+64*x*A2*A3^2-4*A3*A1^2-A0^4-A1^4+24*x^2*A3-32*x^2*A2-24*x^2*A3^2-4*A3*A0^2*A2+2*A2^2*A0^2+2*A1^2*A3^2+24*x*A3^2-40*x^2*A2^2+12*A2*A3+2*A2^2*A1^2+32*x*A2^2*A3^2-64*x^2*A2*A3^2+4*A2^3*A3-32*x^2*A2^2*A3^2-16*x^2*A2^3-6*A2^2*A3^2+16*x*A2^3-24*x*A3+40*x*A2^2-4*A2^3-80*x*A2*A3-A3^4+12*A2^2*A3)/((A3-1)*(1+A2-A3)): 

Q3nn:=x^2*(x-1)^2*dx^2+1/2*(x-1)*(20*x*A2+14*x-8*x*A2*A3+6*x*A2^2-16*x*A3+2*x*A3^2-7-A3^2-3*A2^2-10*A2-A0^2+A1^2+8*A3+4*A2*A3)*x*dx/(1+A2-A3)+1/8*(-13+4*A0^2*A2-18*A2^2+6*A1^2-2*A0^2+64*x+8*x*A3*A1^2-16*x*A2*A3^3-8*x*A0^2*A3+16*x^2*A2*A3^3+128*x^2*A2^2*A3+16*x^2*A2^3*A3-128*x*A2^2*A3-16*x*A2^3*A3-16*x*A3^3+4*A2*A3^3-28*A2*A3^2+2*A0^2*A3^2-64*x^2-26*A3^2-4*A3*A2*A1^2+4*A2*A1^2+16*x^2*A3^3+2*A1^2*A0^2+8*A3^3+256*x^2*A2*A3-A2^4-28*A2+32*A3+144*x*A2+128*x*A2*A3^2-8*A3*A1^2-A0^4-A1^4+144*x^2*A3-144*x^2*A2-96*x^2*A3^2-4*A3*A0^2*A2+2*A2^2*A0^2+2*A1^2*A3^2+8*x*A0^2-8*x*A1^2+96*x*A3^2-96*x^2*A2^2+52*A2*A3+2*A2^2*A1^2+32*x*A2^2*A3^2-128*x^2*A2*A3^2+4*A2^3*A3-32*x^2*A2^2*A3^2-16*x^2*A2^3-6*A2^2*A3^2+16*x*A2^3-144*x*A3+96*x*A2^2-4*A2^3-256*x*A2*A3-A3^4+24*A2^2*A3)/((A3-1)*(1+A2-A3)):