## SE3.txt # List of shift operators for the shift a\pm1, c\pm1, g\pm2 # which are denoted Pap, ## PQoperators Pgp:= 4+4*a-8*x^2*c*g^2-20*x^2*c^2*g-16*x^2*c^2*b-16*x^2*c^2*a-8*x^2*c*a^2-8*x^2*c*b^2+4*c*b*g+16*x*c^2*b+16*x*c^2*a+28*x*c*b+20*x*c^2*g+12*x*c*b*g+4*c+8*g+4*b+28*x*c+4*c*b+6*c*g+4*a*b+6*a*g+6*b*g+5*g^2-32*x^2*c*a-32*x^2*c*b-30*x^2*c*g+36*x*c*a+30*x*c*g-36*x^2*c^2-28*x^2*c+36*x*c^2+20*x*c*a*g+16*x*c*a*b-16*x^2*c*a*g-16*x^2*c*a*b-16*x^2*c*b*g+8*x*c*a^2+8*x*c*b^2+8*x*c*g^2+8*x*c^3+2*c*g^2+2*a*g^2-8*x^2*c^3+g^3+2*b*g^2+2*x*(x-1)*(-2-7*a+4*x+6*x*c*b-7*c-3*g+7*x*a+14*x*c+6*x*g+7*x*b-2*c^2-4*c*a-2*c*b-4*c*g-2*a^2-2*a*b-4*a*g-g^2+6*x*c*a+8*x*c*g+4*x*a*b+4*x*a*g+4*x*b*g+4*x*c^2+2*x*a^2+2*x*g^2+2*x*b^2)*dx+4*a*g*b-x^2*(x-1)^2*dx^2*(2*a+2*c+2*b+3*g+6): Qgp:= 24+22*a-8*x^2*c*g^2-20*x^2*c^2*g-16*x^2*c^2*b-16*x^2*c^2*a-8*x^2*c*a^2-8*x^2*c*b^2+4*c*b*g+16*x*c^2*b+16*x*c^2*a-20*x+28*x*c*b+20*x*c^2*g+12*x*c*b*g+22*c+26*g+12*b+20*x^2-28*x*a+20*x*c-18*x*g-8*x*b+4*c^2+8*c*a+8*c*b+14*c*g+4*a^2+8*a*b+14*a*g+10*b*g+9*g^2-28*x^2*c*a-28*x^2*c*b-26*x^2*c*g+8*x^2*a*b+8*x^2*a*g+8*x^2*b*g+28*x*c*a+26*x*c*g-8*x*a*b-12*x*a*g-4*x*b*g-36*x^2*c^2-20*x^2*c+4*x^2*a^2+18*x^2*a+4*x^2*b^2+18*x^2*b+4*x^2*g^2+18*x^2*g+36*x*c^2-8*x*a^2-4*x*g^2+20*x*c*a*g+16*x*c*a*b-16*x^2*c*a*g-16*x^2*c*a*b-16*x^2*c*b*g+8*x*c*a^2+8*x*c*b^2+8*x*c*g^2+8*x*c^3+2*c*g^2+2*a*g^2-8*x^2*c^3+g^3+2*b*g^2+2*x*(x-1)*(-2-7*a+4*x+6*x*c*b-7*c-3*g+7*x*a+14*x*c+6*x*g+7*x*b-2*c^2-4*c*a-2*c*b-4*c*g-2*a^2-2*a*b-4*a*g-g^2+6*x*c*a+8*x*c*g+4*x*a*b+4*x*a*g+4*x*b*g+4*x*c^2+2*x*a^2+2*x*g^2+2*x*b^2)*dx+4*a*g*b-x^2*(x-1)^2*dx^2*(2*a+2*c+2*b+3*g+6): Pcp:= 2+4*a-8*x-6*x*c*b+4*c+g+8*x^2-12*x*a-18*x*c-6*x*g-4*x*b+2*c^2+4*c*a+c*g+2*a^2+a*g+10*x^2*c*a+10*x^2*c*b+7*x^2*c*g+4*x^2*a*b+3*x^2*a*g+3*x^2*b*g-14*x*c*a-7*x*c*g-4*x*a*b-4*x*a*g-2*x*b*g+10*x^2*c^2+18*x^2*c+2*x^2*a^2+8*x^2*a+2*x^2*b^2+8*x^2*b+x^2*g^2+6*x^2*g-10*x*c^2-4*x*a^2-x*g^2+x^2*(x-1)^2*dx^2-(x-1)*x*(3*x*a+6*x*c+2*x*g+4*x+3*x*b-3*a-3*c-g-2)*dx: Qcp:= 3+5*a-14*x-6*x*c*b+5*c+g+14*x^2-16*x*a-24*x*c-8*x*g-6*x*b+2*c^2+4*c*a+c*g+2*a^2+a*g+10*x^2*c*a+10*x^2*c*b+7*x^2*c*g+4*x^2*a*b+3*x^2*a*g+3*x^2*b*g-14*x*c*a-7*x*c*g-4*x*a*b-4*x*a*g-2*x*b*g+10*x^2*c^2+24*x^2*c+2*x^2*a^2+11*x^2*a+2*x^2*b^2+11*x^2*b+x^2*g^2+8*x^2*g-10*x*c^2-4*x*a^2-x*g^2-(x-1)*x*(3*x*a+6*x*c+6*x+2*x*g+3*x*b-3*a-3*c-3-g)*dx+x^2*(x-1)^2*dx^2: Pap:= x^2*(x-1)^2*dx^2-(x-1)*x*(4*x*c+x*a+x*b+x*g-3*a-3*c-2-g)*dx+2-6*x*c*a-6*x*c^2-2*x*c*b-3*x*c*g-6*x*c+g+2*c^2+4*c*a+c*g+a*g+4*c+4*a+2*a^2+2*x^2*c*b+4*x^2*c^2+2*x^2*c*a+2*x^2*c*g+2*x^2*c: Qap:= 3+5*a+2*x-2*x*c*b+5*c+g-x^2+2*x*a-6*x*c+x*g+2*c^2+4*c*a+c*g+2*a^2+a*g+2*x^2*c*a+2*x^2*c*b+2*x^2*c*g-6*x*c*a-3*x*c*g+4*x^2*c^2-x^2*a-x^2*b-x^2*g-6*x*c^2-(x-1)*x*(4*x*c-x+x*g+x*a+x*b-3*a-3*c-3-g)*dx+x^2*(x-1)^2*dx^2: # a-1 pan2:=(x-1)^2: pan1:=-(x-1)*(3*a*x+3*b*x+4*c*x+2*g*x-a-c+2*x)/x: pan0:=(2*a+2+2*b+2*c+g)*(a*x+b*x+2*c*x+g*x-c+x)/x: Pan:=pan2*dx^2+pan1*dx+pan0: # c-1 pcn2:=1: pcn1:=-(a*x + b*x + 2*c*x - a - c)/((x - 1)*x): pcn0:=c*(2*a + 2 + 2*b + 2*c + g)/((x - 1)*x): Pcn:=pcn2*dx^2+pcn1*dx+pcn0: # g-2 pgn2:=(2*a*c*x^2 + a*g*x^2 + 2*b*c*x^2 + b*g*x^2 + 2*c*g*x^2 + g^2*x^2 - 4*b*c*x - 2*b*g*x - 2*c*g*x - g^2*x + 2*a*b + a*g + 2*b*c + 2*b*g + c*g + g^2): pgn1:=-(6*a^2*c*x^3 + 3*a^2*g*x^3 + 12*a*b*c*x^3 + 6*a*b*g*x^3 + 8*a*c^2*x^3 + 14*a*c*g*x^3 + 5*a*g^2*x^3 + 6*b^2*c*x^3 + 3*b^2*g*x^3 + 8*b*c^2*x^3 + 14*b*c*g*x^3 + 5*b*g^2*x^3 + 8*c^2*g*x^3 + 8*c*g^2*x^3 + 2*g^3*x^3 - 6*a^2*c*x^2 - 3*a^2*g*x^2 - 18*a*b*c*x^2 - 9*a*b*g*x^2 - 6*a*c^2*x^2 - 17*a*c*g*x^2 + 4*a*c*x^3 - 7*a*g^2*x^2 + 2*a*g*x^3 - 12*b^2*c*x^2 - 6*b^2*g*x^2 - 18*b*c^2*x^2 - 25*b*c*g*x^2 + 4*b*c*x^3 - 8*b*g^2*x^2 + 2*b*g*x^3 - 12*c^2*g*x^2 - 12*c*g^2*x^2 + 4*c*g*x^3 - 3*g^3*x^2 + 2*g^2*x^3 + 2*a^2*b*x + a^2*g*x + 2*a*b^2*x + 14*a*b*c*x + 7*a*b*g*x + 7*a*c*g*x - 4*a*c*x^2 + 3*a*g^2*x - 2*a*g*x^2 + 6*b^2*c*x + 4*b^2*g*x + 12*b*c^2*x + 15*b*c*g*x - 8*b*c*x^2 + 4*b*g^2*x - 4*b*g*x^2 + 6*c^2*g*x + 6*c*g^2*x - 6*c*g*x^2 + g^3*x - 3*g^2*x^2 - 2*a^2*b - a^2*g - 4*a*b*c - 2*a*b*g - 2*a*c*g - a*g^2 - 2*b*c^2 - 2*b*c*g + 4*b*c*x + 2*b*g*x - c^2*g - c*g^2 + 2*c*g*x + g^2*x)/(x*(x - 1)): pgn0:=(2*a + 2 + 2*b + 2*c + g)*(2*a^2*c*x^2 + a^2*g*x^2 + 4*a*b*c*x^2 + 2*a*b*g*x^2 + 4*a*c^2*x^2 + 6*a*c*g*x^2 + 2*a*g^2*x^2 + 2*b^2*c*x^2 + b^2*g*x^2 + 4*b*c^2*x^2 + 6*b*c*g*x^2 + 2*b*g^2*x^2 + 4*c^2*g*x^2 + 4*c*g^2*x^2 + g^3*x^2 - 2*a^2*c*x - a^2*g*x - 4*a*b*c*x - 2*a*b*g*x - 2*a*c^2*x - 5*a*c*g*x + 2*a*c*x^2 - 2*a*g^2*x + a*g*x^2 - 2*b^2*c*x - b^2*g*x - 6*b*c^2*x - 7*b*c*g*x + 2*b*c*x^2 - 2*b*g^2*x + b*g*x^2 - 4*c^2*g*x - 4*c*g^2*x + 2*c*g*x^2 - g^3*x + g^2*x^2 + 2*a*b*c + a*c*g - 2*a*c*x - a*g*x + 2*b*c^2 + 2*b*c*g - 2*b*c*x - b*g*x + c^2*g + c*g^2 - 2*c*g*x - g^2*x)/(x*(x - 1)): Pgn:=pgn2*dx^2+pgn1*dx+pgn0: Qan:=(x-1)^2*dx^2-(x-1)*(x+2*g*x+3*b*x+4*c*x+3*a*x-1-a-c)*dx/x+(1+4*x^2*a*b+a-2*a*c*x-c*g*x-2*x+3*a*g*x^2+3*b*g*x^2+6*a*c*x^2+6*b*c*x^2+4*c*g*x^2-2*b*c*x+c-2*a*x-2*b*x-4*c*x-g*x+g^2*x^2-2*x*c^2+x^2+4*x^2*c^2+4*x^2*c+2*x^2*g+2*x^2*a^2+3*x^2*a+2*x^2*b^2+3*x^2*b)/x^2: Qcn:= dx^2-(b*x+2*c*x+2*x+a*x-a-1-c)*dx/(x*(x-1))+(2*a*c*x^2+4*x^2*c+c*g*x^2+x^2*b+2*b*c*x^2+2*x^2+x^2*a+2*x^2*c^2-2*x-2*a*x-4*c*x-c*g*x-2*b*c*x-2*x*c^2-2*a*c*x+1+a+c)/(x^2*(x-1)^2): Qgn:= (2*a*c*x^2+a*g*x^2+2*b*c*x^2+b*g*x^2+2*c*g*x^2+g^2*x^2-4*b*c*x-2*b*g*x-2*c*g*x-g^2*x+2*a*b+a*g+2*b*c+2*b*g+c*g+g^2)*dx^2-(6*b^2*c*x^3-6*a*c^2*x^2+6*c*g^2*x+3*a^2*g*x^3-6*a^2*c*x^2-8*b*g^2*x^2+4*c*g*x+2*a^2*b*x+4*b^2*g*x+12*a*b*c*x^3+6*a*b*g*x^3+14*a*c*g*x^3+14*b*c*g*x^3-18*a*b*c*x^2-9*a*b*g*x^2-17*a*c*g*x^2-25*b*c*g*x^2+14*a*b*c*x+7*a*b*g*x+7*a*c*g*x+15*b*c*g*x+2*a*g*x^2-2*b*g*x^2+4*a*c*x^2-4*b*c*x^2+8*b*c*x+8*b*g*x+4*g^2*x-2*a*g-2*c*g-4*a*b-4*b*c-4*b*g+2*g^3*x^3-3*g^3*x^2-2*a^2*b-2*b*c^2-2*g^2-c*g^2-a^2*g+g^3*x+a^2*g*x-c^2*g-a*g^2+6*a^2*c*x^3+8*a*c^2*x^3+5*a*g^2*x^3+3*b^2*g*x^3+8*b*c^2*x^3+5*b*g^2*x^3+8*c^2*g*x^3+8*c*g^2*x^3-3*a^2*g*x^2-7*a*g^2*x^2-12*b^2*c*x^2-6*b^2*g*x^2-18*b*c^2*x^2-12*c^2*g*x^2-12*c*g^2*x^2+2*a*b^2*x+3*a*g^2*x+6*b^2*c*x+12*b*c^2*x+4*b*g^2*x+6*c^2*g*x-4*a*b*c-2*a*b*g-2*a*c*g-2*b*c*g+4*a*g*x+8*x*a*b)*dx/(x*(x-1))+(-4*c^3*x*b-12*c*x^3*g^3+12*x^2*a*b-2*c^3*x*g-8*b^2*c*x^3+10*c^3*x^2*g-2*a*c^2*x^2-7*c*g^2*x+8*c^2*x^2*a^2-2*a^2*c*x^2+8*b*g^2*x^2-20*c^2*x^3*a^2-6*c*g*x-3*c^2*x*g^2-8*a^2*b*x+6*x^2*a*b^2+4*c^2*x^4*a+4*c^2*x^4*b+4*c^2*x^4*g+4*c*x^2*a^3-20*c^3*x^3*b-4*b^2*g*x-8*a*b*c*x^3-4*a*b*g*x^3-6*a*c*g*x^3-18*b*c*g*x^3+24*a*b*c*x^2+14*a*b*g*x^2+10*a*c*g*x^2+28*b*c*g*x^2-20*a*b*c*x-12*a*b*g*x-10*a*c*g*x-16*b*c*g*x+23*c*x^2*b*g^2+6*a*g*x^2+12*b*g*x^2+12*b*c*x^2+6*c*g*x^2-12*b*c*x-12*b*g*x+6*g^2*x^2-6*g^2*x+2*a*g+2*c*g+4*a*b+4*b*c+4*b*g-2*g^3*x^3+2*g^3*x^2+2*a^2*b+2*b*c^2+2*g^2+c*g^2+a^2*g-g^3*x-4*a^2*g*x+c^2*g+a*g^2-3*a*g^2*x^3-4*b^2*g*x^3-16*b*c^2*x^3+15*c^2*x^2*g^2-5*b*g^2*x^3-8*c^2*g*x^3-8*c*g^2*x^3+2*a^2*g*x^2+4*a*c*x^3+5*a*g^2*x^2+2*a*g*x^3+10*b^2*c*x^2+8*b^2*g*x^2+22*b*c^2*x^2-4*b*c*x^3-2*b*g*x^3+10*c^2*g*x^2+11*c*g^2*x^2-4*a*b^2*x-5*a*g^2*x-4*b^2*c*x-12*b*c^2*x-4*b*g^2*x-6*c^2*g*x+4*a*b*c+2*a*b*g+2*a*c*g+2*b*c*g-6*a*g*x-12*x*a*b+20*c^2*x^2*b^2-4*b^2*c^2*x-c*g^3*x-24*c^2*x^3*g^2+22*c*x^2*b^2*g-8*c*x*a*b*g+5*b^2*g^2*x^2+4*b^3*c*x^2+2*c*x^4*a^2+2*c*x^4*b^2+4*c*x^4*g^2+6*a^2*b*x^2+x^4*a^2*g+2*x^4*a*g^2+x^4*b^2*g+2*x^4*b*g^2-4*x^3*a^3*g-10*x^3*b^2*g^2-4*x^3*b^3*g-8*x^3*b*g^3+2*b^3*g*x^2-4*a*b^2*c*x-4*b^2*c*g*x-4*b*c*g^2*x-4*c*x*a^2*b-2*c*x*a^2*g-3*c*x*a*g^2-8*c^2*x*a*b-4*c^2*x*a*g-8*c^2*x*b*g+32*c^2*x^2*a*b+24*c^2*x^2*a*g+36*c^2*x^2*b*g-44*c^2*x^3*a*g-52*c^2*x^3*b*g-48*c^2*x^3*a*b+4*c^3*x^2*a-8*c*x^3*a^3+16*c^3*x^2*b-12*c^3*x^3*a-16*c^3*x^3*g-30*c*x^3*a^2*g-35*c*x^3*a*g^2+16*c*x^2*a^2*g-34*c*x^3*b^2*g-37*c*x^3*b*g^2-24*c*x^3*a^2*b+20*c*x^2*a*g^2+16*c*x^2*a^2*b-24*c*x^3*a*b^2+16*c*x^2*a*b^2-28*c^2*x^3*b^2+7*c*x^2*g^3-8*c*x^3*b^3-64*c*x^3*a*g*b+40*c*x^2*b*g*a+6*x^4*a^2*b*g+6*x^4*a*b^2*g+10*x^4*a*b*g^2-12*x^3*a^2*g*b-20*x^3*a*g^2*b-12*x^3*a*g*b^2+10*a*g^2*x^2*b+6*a*g*x^2*b^2+12*c*x^4*a^2*b+12*c*x^4*a*b^2+x^4*g^3+x^4*g^4-2*x^3*g^4+g^4*x^2+5*a^2*g^2*x^2+2*a^3*g*x^2+4*a*g^3*x^2+8*c^3*x^4*a+8*c^3*x^4*b+8*c^3*x^4*g+12*c^2*x^4*a^2+12*c^2*x^4*b^2+12*c^2*x^4*g^2+4*c*x^4*a^3+4*c*x^4*b^3+6*c*x^4*g^3+6*a^2*g*x^2*b+5*x^4*a^2*g^2+2*x^4*a^3*g+4*x^4*a*g^3+5*x^4*b^2*g^2+2*x^4*b^3*g+4*x^4*b*g^3-10*x^3*a^2*g^2-8*x^3*a*g^3+2*x^4*a*b*g+32*c*x^4*a*b*g+16*c*x^4*a^2*g+18*c*x^4*a*g^2+16*c*x^4*b^2*g+18*c*x^4*b*g^2+24*c^2*x^4*a*b+24*c^2*x^4*a*g+24*c^2*x^4*b*g+4*b*g^3*x^2+4*c*x^4*a*b+6*c*x^4*a*g+6*c*x^4*b*g)/(x^2*(x-1)^2):