## Z6PQ1.txt 20221208 # parameters are u, g1, g4, A1, A2, A3, A4 # u\pm1, g1\pm1, g4\pm1 are denoted as up, un, g1p, g1n, g4p, g4n # A1\pm2, A2\pm2, A3\pm2, A4\pm2 are denoted as A1p, A1n and so on. ## data for shifts such as (A0,A1) to (A0+1,A1+1) are given in Z6PQ2.txt ## Svalues are as follows # Sunp= Pup*Pun Sunp:=-(u-1)*(u-2)*(u-3)*(-A3-A2-1+g1+g4+u)*(-2*A2-1+g1+g4+u) *(-A2-1+A3+g1+g4+u): # Sg1np= Pg1p*Pg1n, Sg4np= Pg4p*Pg4n Sg1np:=(u-1)^2*(u-2)^2*g1*(A2-g1+A0)*(-A2+g1+A0)*(-2*A2-1+g1+g4+u) *(-A2-1+A3+g1+g4+u)*(-A3-A2-1+g1+g4+u): Sg4np:=-(u-1)^2*(u-2)^2*(-A1+A2-g4)*(A1+A2-g4)*(-2*A2-1+g1+g4+u) *(-A2-1+A3+g1+g4+u)*(-A3-A2-1+g1+g4+u)*g4: # Sung4p=Pupg4n*Pung4p, Sung1p=Pupg1n*Pung1p Sung4p:=(u-1)*(u-2)*(u-3)*(g4+1)*(A2-1-A1-g4)*(-1+A2+A1-g4): Sung1p:=(u-1)*(u-2)*(u-3)*(g1+1)*(A0-1+A2-g1)*(A0+1-A2+g1): # SvA0np = PA0p*PA0n SvA0np:=(u-1)^2*(u-2)^2*(g1-A2+A0)*(g1-1-A2+A0)*(-g1-1+A2+A0) *(-g1-2+A2+A0)*(-A3-1-A2+A1+A0)*(A3-1-A2-A1+A0)*(-A3-1+A2-A1+A0) *(A3-1+A2+A1+A0)*(-A3-1-A2-A1+A0)*(A3-1-A2+A1+A0)*(-A3-1+A2+A1+A0) *(A3-1+A2-A1+A0)/(A0-1)^2: # SvA1np = PA1p*PA1n SvA1np:=-1/16*(u-1)^2*(u-2)^2*(-g4-1+A2+A1)*(-g4-2+A2+A1)*(g4-A2+A1) *(g4-1-A2+A1)*(-A3+1-A2-A1+A0)*(A3+1-A2-A1+A0)*(-A3+1+A2-A1+A0) *(A3+1+A2-A1+A0)*(-A3-1-A2+A1+A0)*(A3-1-A2+A1+A0)*(-A3-1+A2+A1+A0) *(A3-1+A2+A1+A0)/(A1-1)^2: # SvA3pn = PA3p*PA3n SvA3pn:=-1/16*(u-1)^2*(u-2)^2*(-u-g4-g1+A3+A2)*(A3-1+A2-g1-g4-u) *(-u+2-g4-g1-A3+A2)*(A2+1-A3-g1-g4-u)*(A3-1-A2-A1+A0)*(A3-1+A2-A1+A0) *(-A3+1-A2-A1+A0)*(-A3+1+A2-A1+A0)*(A3-1-A2+A1+A0)*(A3-1+A2+A1+A0) *(-A3+1-A2+A1+A0)*(-A3+1+A2+A1+A0)/(A3-1)^2: ## PQ-operators # Pun,Pup,Qun,Qup: u\pm1 # Pg1n,Pg1p,Qg1n,Qg1p: g1\pm1 # Pg4n,Pg4p,Qg4n,Qg4p: g4\pm1 # Pupg4n, Pupg1n Pupg4n:=x^3*(x-1)^5*dx^5-x^2*(x-1)^4*(-4*x*A2-16*x+3*x*g1+3*x*g4+5*x*u+9+2*A2-3*g1-3*u)*dx^4+x*(x-1)^3*(19-15*u-85*x+3*u^2+6*g1*u+3*g1^2-4*A2*u-4*A2*g1+A2^2+10*A2-15*g1+75*x^2+63*x*u-48*x*A2+48*x*g1+24*x*g4+x*A3^2-8*x^2*A2*g1+6*x^2*g1*g4-8*x^2*A2*g4+3*x^2*g1^2+5*x^2*A2^2-x^2*A3^2+3*x^2*g4^2-16*x^2*A2*u-54*x^2*u-x*A1^2-9*x*u*g4-18*x*g1*u+18*x*A2*u+12*x*A2*g1-6*x*g1*g4+4*x*A2*g4+10*x^2*u^2+12*x^2*g1*u+12*x^2*u*g4-A0^2-5*x*A2^2-6*x*g1^2-12*x*u^2+44*x^2*A2-33*x^2*g1-33*x^2*g4+x*A0^2)*dx^3-1/2*(x-1)^2*(-2*g1^3-2*u^3-50*x^2*u*A2^2+84*x^2*A2*u^2-42*x^2*u*g1^2-72*x^2*g1*u^2-54*x^2*u^2*g4-18*x^2*u*g4^2+16-24*u-181*x-6*x^2*g1^3+6*x^2*A2^3-20*x^2*A2^2*g1-12*x^2*g1^2*g4+20*x^2*g1^2*A2-6*x^2*g1*g4^2+2*x^2*A3^2*g4+4*x^2*g1*A3^2+10*x^2*u*A3^2-6*x^2*A2*A3^2-230*x^3+2*x^2*A0^2*g1+4*x^2*u*A0^2+2*u*A0^2-2*u*A2^2+4*A2*u^2-6*u*g1^2-6*g1*u^2+12*u^2+24*g1*u+12*g1^2-16*A2*u-16*A2*g1+4*A2^2-2*x^2*A0^2*A2+2*A0^2*g1-2*A2^2*g1+4*g1^2*A2+24*x^2*A2*g1*g4+36*x^3*u^2*g4+36*x^3*g1*u^2-48*x^3*A2*u^2+14*x^3*A3^2+2*x^2*A1^2*A2-2*x^2*A1^2*g4-4*x^2*A1^2*u+16*A2-24*g1+2*x^2*A0^2*g4+395*x^2+246*x*u-188*x*A2+196*x*g1+86*x*g4+186*x^3*g4+186*x^3*g1+298*x^3*u-248*x^3*A2+9*x*A3^2+30*x^3*u*A2^2+18*x^3*u*g1^2+36*x^3*g1*u*g4+18*x^3*u*g4^2-48*x^3*A2*u*g4-48*x^3*u*A2*g1+2*x*A1^2*g1-9*x^2*A0^2-2*x^2*A1^2*g1-132*x^3*u^2+20*x^3*u^3-220*x^2*A2*g1+138*x^2*g1*g4-148*x^2*A2*g4-60*x^2*g1*u*g4+64*x^2*A2*u*g4+96*x^2*u*A2*g1+96*x^2*g1^2+115*x^2*A2^2-23*x^2*A3^2+42*x^2*g4^2+22*x*u*A2^2-40*x*A2*u^2+30*x*u*g1^2+42*x*g1*u^2+2*x*A2^2*g4+12*x*A2^2*g1+6*x*g1^2*g4-16*x*g1^2*A2+18*x*u^2*g4-2*x*g1*A3^2-4*x*u*A3^2+2*x*A2*A3^2-36*x^2*u^3-6*x^3*u*A3^2+4*x*A1^2*u-162*x^3*g1*u+2*x^3*g1^3+216*x^3*A2*u-4*x^3*A2^3-16*x^3*A2*g1*g4+2*x^3*g4^3-2*x^3*g1*A3^2+4*x^3*A2*A3^2-2*x^3*A3^2*g4+6*x^3*g1*g4^2+10*x^3*A2^2*g1-8*x^3*g1^2*A2+6*x^3*g1^2*g4+10*x^3*A2^2*g4-162*x^3*u*g4-8*x^3*g4^2*A2-372*x^2*A2*u+112*x^3*A2*g1-520*x^2*u-9*x*A1^2+112*x^3*A2*g4-84*x^3*g1*g4+24*x*g1*u*g4-16*x*A2*u*g4-8*x*A2*g1*g4-56*x*u*A2*g1-78*x*u*g4-180*x*g1*u+172*x*A2*u+124*x*A2*g1-54*x*g1*g4+36*x*A2*g4+8*u*A2*g1+234*x^2*u^2+318*x^2*g1*u-2*x*A0^2*g4+240*x^2*u*g4-4*A0^2-2*x*A2^3+6*x*g1^3+18*x*u^3-6*x*u*A0^2-4*x*A0^2*g1+2*x*A0^2*A2-49*x*A2^2+4*x^2*g4^2*A2-10*x^2*A2^2*g4-70*x^3*A2^2-42*x^3*g1^2-66*x*g1^2-114*x*u^2-42*x^3*g4^2+420*x^2*A2-358*x^2*g1-272*x^2*g4-2*x*A1^2*A2+13*x*A0^2+9*x^2*A1^2)*dx^2+1/2*(x-1)*(u-2)*(-12*g1*u*g4+2*A2^3-4*g1^3-4*u^3-70*x^2*u*A2^2+76*x^2*A2*u^2-48*x^2*u*g1^2-60*x^2*g1*u^2-54*x^2*u^2*g4-36*x^2*u*g4^2+15-28*u-76*x-12*x^2*g1^3+18*x^2*A2^3-50*x^2*A2^2*g1-30*x^2*g1^2*g4+44*x^2*g1^2*A2-24*x^2*g1*g4^2+8*x^2*A3^2*g4+10*x^2*g1*A3^2+14*x^2*u*A3^2-18*x^2*A2*A3^2-2*A1^2*u-2*A1^2*g1+2*A1^2*A2-46*x^3+2*x^2*A0^2*g1+2*x^2*u*A0^2+18*u*g4+2*u*A0^2-10*u*A2^2+12*A2*u^2-12*u*g1^2-12*g1*u^2+18*u^2+36*g1*u+18*g1^2-36*A2*u-36*A2*g1+15*A2^2-2*x^2*A0^2*A2+2*A0^2*g4+2*A0^2*g1+18*g1*g4-12*A2*g4-2*A2^2*g4-10*A2^2*g1-6*g1^2*g4+12*g1^2*A2-6*u^2*g4+72*x^2*A2*g1*g4+24*x^3*u^2*g4+24*x^3*g1*u^2-32*x^3*A2*u^2+10*x^3*A3^2+2*x^2*A1^2*A2-2*x^2*A1^2*g4-2*x^2*A1^2*u+2*g1*A3^2+2*u*A3^2-2*A2*A3^2+28*A2-28*g1-14*g4+2*x^2*A0^2*g4+3*A1^2+107*x^2+136*x*u-144*x*A2+122*x*g1+94*x*g4-6*x^2*g4^3+66*x^3*g4+66*x^3*g1+80*x^3*u-88*x^3*A2+16*x*A3^2+30*x^3*u*A2^2+18*x^3*u*g1^2+36*x^3*g1*u*g4+18*x^3*u*g4^2-48*x^3*A2*u*g4-48*x^3*u*A2*g1+4*x*A1^2*g1-3*x^2*A0^2-2*x^2*A1^2*g1-48*x^3*u^2+10*x^3*u^3-196*x^2*A2*g1+138*x^2*g1*g4-172*x^2*A2*g4-84*x^2*g1*u*g4+104*x^2*A2*u*g4+120*x^2*u*A2*g1+78*x^2*g1^2+115*x^2*A2^2-23*x^2*A3^2+60*x^2*g4^2+50*x*u*A2^2-56*x*A2*u^2+42*x*u*g1^2+48*x*g1*u^2-8*x*g4^2*A2+20*x*A2^2*g4+40*x*A2^2*g1+24*x*g1^2*g4-40*x*g1^2*A2+36*x*u^2*g4+12*x*g1*g4^2-4*x*A3^2*g4-8*x*g1*A3^2-10*x*u*A3^2+12*x*A2*A3^2+18*x*u*g4^2-24*x^2*u^3+4*x*A1^2*g4-6*x^3*u*A3^2+4*x*A1^2*u-78*x^3*g1*u+4*x^3*g1^3+104*x^3*A2*u-8*x^3*A2^3-32*x^3*A2*g1*g4+4*x^3*g4^3-4*x^3*g1*A3^2+8*x^3*A2*A3^2-4*x^3*A3^2*g4+12*x^3*g1*g4^2+20*x^3*A2^2*g1-16*x^3*g1^2*A2+12*x^3*g1^2*g4+20*x^3*A2^2*g4-78*x^3*u*g4-16*x^3*g4^2*A2-244*x^2*A2*u+80*x^3*A2*g1+8*A2*u*g4+8*A2*g1*g4-188*x^2*u-6*x*A1^2-3*A3^2+80*x^3*A2*g4-60*x^3*g1*g4+60*x*g1*u*g4-64*x*A2*u*g4-48*x*A2*g1*g4-96*x*u*A2*g1-114*x*u*g4-150*x*g1*u+176*x*A2*u+152*x*A2*g1-96*x*g1*g4+104*x*A2*g4+24*u*A2*g1+114*x^2*u^2+192*x^2*g1*u-4*x*A0^2*g4+174*x^2*u*g4-3*A0^2-30*x*g4^2-2*A0^2*A2-12*x*A2^3+12*x*g1^3+18*x*u^3-4*x*u*A0^2-4*x*A0^2*g1+4*x*A0^2*A2-80*x*A2^2+28*x^2*g4^2*A2-40*x^2*A2^2*g4-50*x^3*A2^2-30*x^3*g1^2-66*x*g1^2-84*x*u^2-30*x^3*g4^2+204*x^2*A2-160*x^2*g1-146*x^2*g4-4*x*A1^2*A2+6*x*A0^2+3*x^2*A1^2)*dx-(u-1)*(u-2)*(-6*g1*u*g4+2*A2^3-g1^3-u^3-15*x^2*u*A2^2+12*x^2*A2*u^2-9*x^2*u*g1^2-9*x^2*g1*u^2-9*x^2*u^2*g4-9*x^2*u*g4^2+1-3*u-3*x-3*x^2*g1^3+6*x^2*A2^3-15*x^2*A2^2*g1-9*x^2*g1^2*g4+12*x^2*g1^2*A2-9*x^2*g1*g4^2+3*x^2*A3^2*g4+3*x^2*g1*A3^2+3*x^2*u*A3^2-6*x^2*A2*A3^2-A1^2*g4-x^3+6*u*g4-5*u*A2^2+4*A2*u^2-3*u*g1^2-3*g1*u^2+3*u^2+6*g1*u+3*g1^2-8*A2*u-8*A2*g1+5*A2^2+2*g4^2*A2+6*g1*g4-8*A2*g4-4*A2^2*g4-5*A2^2*g1-3*g1^2*g4+4*g1^2*A2-3*u^2*g4-3*g1*g4^2+24*x^2*A2*g1*g4+3*x^3*u^2*g4+3*x^3*g1*u^2-4*x^3*A2*u^2+x^3*A3^2+A3^2*g4+g1*A3^2+u*A3^2-2*A2*A3^2+4*A2-3*g1-3*g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Pupg1n:=x^5*(x-1)^3*dx^5-x^4*(x-1)^2*(-16*x-4*x*A2+3*x*g1+3*x*g4+5*x*u-2*u+7-3*g1+2*A2)*dx^4+(x-1)*(9-6*u-65*x+u^2+3*g1*u+3*g1^2-2*A2*u-4*A2*g1+A2^2+6*A2-9*g1+75*x^2+45*x*u-40*x*A2+42*x*g1+18*x*g4+x*A3^2-8*x^2*A2*g1+6*x^2*g1*g4-8*x^2*A2*g4+3*x^2*g1^2+5*x^2*A2^2-x^2*A3^2+3*x^2*g4^2-16*x^2*A2*u-54*x^2*u-x*A1^2-6*x*u*g4-15*x*g1*u+14*x*A2*u+12*x*A2*g1-6*x*g1*g4+4*x*A2*g4+10*x^2*u^2+12*x^2*g1*u+12*x^2*u*g4-A0^2-5*x*A2^2-6*x*g1^2-8*x*u^2+44*x^2*A2-33*x^2*g1-33*x^2*g4+x*A0^2)*x^3*dx^3-1/2*(-2*g1^3-40*x^2*u*A2^2+60*x^2*A2*u^2-36*x^2*u*g1^2-54*x^2*g1*u^2-36*x^2*u^2*g4-12*x^2*u*g4^2-81*x-6*x^2*g1^3+6*x^2*A2^3-20*x^2*A2^2*g1-12*x^2*g1^2*g4+20*x^2*g1^2*A2-6*x^2*g1*g4^2+2*x^2*A3^2*g4+4*x^2*g1*A3^2+8*x^2*u*A3^2-6*x^2*A2*A3^2-230*x^3+2*x^2*A0^2*g1+4*x^2*u*A0^2-2*x^2*A0^2*A2+2*A0^2*g1-2*A2^2*g1+4*g1^2*A2+24*x^2*A2*g1*g4+36*x^3*u^2*g4+36*x^3*g1*u^2-48*x^3*A2*u^2+14*x^3*A3^2+2*x^2*A1^2*A2-2*x^2*A1^2*g4-4*x^2*A1^2*u+2*x^2*A0^2*g4+295*x^2+100*x*u-92*x*A2+100*x*g1+38*x*g4+186*x^3*g4+186*x^3*g1+298*x^3*u-248*x^3*A2+5*x*A3^2+30*x^3*u*A2^2+18*x^3*u*g1^2+36*x^3*g1*u*g4+18*x^3*u*g4^2-48*x^3*A2*u*g4-48*x^3*u*A2*g1+2*x*A1^2*g1-9*x^2*A0^2-2*x^2*A1^2*g1-132*x^3*u^2+20*x^3*u^3-188*x^2*A2*g1+114*x^2*g1*g4-116*x^2*A2*g4-48*x^2*g1*u*g4+48*x^2*A2*u*g4+80*x^2*u*A2*g1+84*x^2*g1^2+95*x^2*A2^2-19*x^2*A3^2+30*x^2*g4^2+12*x*u*A2^2-16*x*A2*u^2+18*x*u*g1^2+18*x*g1*u^2+2*x*A2^2*g4+12*x*A2^2*g1+6*x*g1^2*g4-16*x*g1^2*A2+6*x*u^2*g4-2*x*g1*A3^2-2*x*u*A3^2+2*x*A2*A3^2-24*x^2*u^3-6*x^3*u*A3^2+2*x*A1^2*u-162*x^3*g1*u+2*x^3*g1^3+216*x^3*A2*u-4*x^3*A2^3-16*x^3*A2*g1*g4+2*x^3*g4^3-2*x^3*g1*A3^2+4*x^3*A2*A3^2-2*x^3*A3^2*g4+6*x^3*g1*g4^2+10*x^3*A2^2*g1-8*x^3*g1^2*A2+6*x^3*g1^2*g4+10*x^3*A2^2*g4-162*x^3*u*g4-8*x^3*g4^2*A2-276*x^2*A2*u+112*x^3*A2*g1-374*x^2*u-5*x*A1^2+112*x^3*A2*g4-84*x^3*g1*g4+12*x*g1*u*g4-8*x*A2*u*g4-8*x*A2*g1*g4-32*x*u*A2*g1-30*x*u*g4-84*x*g1*u+76*x*A2*u+76*x*A2*g1-30*x*g1*g4+20*x*A2*g4+162*x^2*u^2+246*x^2*g1*u-2*x*A0^2*g4+168*x^2*u*g4-2*x*A2^3+6*x*g1^3+6*x*u^3-4*x*u*A0^2-4*x*A0^2*g1+2*x*A0^2*A2-29*x*A2^2+4*x^2*g4^2*A2-10*x^2*A2^2*g4-70*x^3*A2^2-42*x^3*g1^2-42*x*g1^2-42*x*u^2-42*x^3*g4^2+324*x^2*A2-286*x^2*g1-200*x^2*g4-2*x*A1^2*A2+9*x*A0^2+9*x^2*A1^2)*x^2*dx^2+1/2*(u-2)*(2*g1^3-20*x^2*u*A2^2+20*x^2*A2*u^2-18*x^2*u*g1^2-18*x^2*g1*u^2-12*x^2*u^2*g4-6*x^2*u*g4^2-6*x^2*g1^3+6*x^2*A2^3-20*x^2*A2^2*g1-12*x^2*g1^2*g4+20*x^2*g1^2*A2-6*x^2*g1*g4^2+2*x^2*A3^2*g4+4*x^2*g1*A3^2+4*x^2*u*A3^2-6*x^2*A2*A3^2-46*x^3+2*x^2*A0^2*g1+2*x^2*u*A0^2-2*x^2*A0^2*A2-2*A0^2*g1+2*A2^2*g1-4*g1^2*A2+24*x^2*A2*g1*g4+24*x^3*u^2*g4+24*x^3*g1*u^2-32*x^3*A2*u^2+10*x^3*A3^2+2*x^2*A1^2*A2-2*x^2*A1^2*g4-2*x^2*A1^2*u+2*x^2*A0^2*g4+31*x^2+66*x^3*g4+66*x^3*g1+80*x^3*u-88*x^3*A2+30*x^3*u*A2^2+18*x^3*u*g1^2+36*x^3*g1*u*g4+18*x^3*u*g4^2-48*x^3*A2*u*g4-48*x^3*u*A2*g1-3*x^2*A0^2-2*x^2*A1^2*g1-48*x^3*u^2+10*x^3*u^3-68*x^2*A2*g1+42*x^2*g1*g4-44*x^2*A2*g4-24*x^2*g1*u*g4+24*x^2*A2*u*g4+40*x^2*u*A2*g1+30*x^2*g1^2+35*x^2*A2^2-7*x^2*A3^2+12*x^2*g4^2-6*x^2*u^3-6*x^3*u*A3^2-78*x^3*g1*u+4*x^3*g1^3+104*x^3*A2*u-8*x^3*A2^3-32*x^3*A2*g1*g4+4*x^3*g4^3-4*x^3*g1*A3^2+8*x^3*A2*A3^2-4*x^3*A3^2*g4+12*x^3*g1*g4^2+20*x^3*A2^2*g1-16*x^3*g1^2*A2+12*x^3*g1^2*g4+20*x^3*A2^2*g4-78*x^3*u*g4-16*x^3*g4^2*A2-68*x^2*A2*u+80*x^3*A2*g1-52*x^2*u+80*x^3*A2*g4-60*x^3*g1*g4+30*x^2*u^2+60*x^2*g1*u+42*x^2*u*g4+4*x^2*g4^2*A2-10*x^2*A2^2*g4-50*x^3*A2^2-30*x^3*g1^2-30*x^3*g4^2+60*x^2*A2-52*x^2*g1-38*x^2*g4+3*x^2*A1^2)*x*dx-(u-1)*(u-2)*(-g1^3-x^3+A0^2*g1-A2^2*g1+2*g1^2*A2+3*x^3*u^2*g4+3*x^3*g1*u^2-4*x^3*A2*u^2+x^3*A3^2+3*x^3*g4+3*x^3*g1+3*x^3*u-4*x^3*A2+5*x^3*u*A2^2+3*x^3*u*g1^2+6*x^3*g1*u*g4+3*x^3*u*g4^2-8*x^3*A2*u*g4-8*x^3*u*A2*g1-3*x^3*u^2+x^3*u^3-x^3*u*A3^2-6*x^3*g1*u+x^3*g1^3+8*x^3*A2*u-2*x^3*A2^3-8*x^3*A2*g1*g4+x^3*g4^3-x^3*g1*A3^2+2*x^3*A2*A3^2-x^3*A3^2*g4+3*x^3*g1*g4^2+5*x^3*A2^2*g1-4*x^3*g1^2*A2+3*x^3*g1^2*g4+5*x^3*A2^2*g4-6*x^3*u*g4-4*x^3*g4^2*A2+8*x^3*A2*g1+8*x^3*A2*g4-6*x^3*g1*g4-5*x^3*A2^2-3*x^3*g1^2-3*x^3*g4^2): ### Pun:=dx: Qun:=dx: 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Qup:=x^3*(x-1)^3*dx^5-x^2*(x-1)^2*(-4*x*A2-18*x+3*x*g1+3*x*g4+6*x*u+9-3*g1+2*A2-3*u)*dx^4+x*(x-1)*(19-15*u-97*x+3*u^2+6*g1*u+3*g1^2-4*A2*u-4*A2*g1+A2^2+10*A2-15*g1+97*x^2+75*x*u-52*x*A2+54*x*g1+24*x*g4+x*A3^2-8*x^2*A2*g1+6*x^2*g1*g4-8*x^2*A2*g4+3*x^2*g1^2+5*x^2*A2^2-x^2*A3^2+3*x^2*g4^2-20*x^2*A2*u-75*x^2*u-x*A1^2-9*x*u*g4-21*x*g1*u+20*x*A2*u+12*x*A2*g1-6*x*g1*g4+4*x*A2*g4+15*x^2*u^2+15*x^2*g1*u+15*x^2*u*g4-A0^2-5*x*A2^2-6*x*g1^2-15*x*u^2+52*x^2*A2-39*x^2*g1-39*x^2*g4+x*A0^2)*dx^3+(g1^3+u^3+30*x^2*u*A2^2-60*x^2*A2*u^2+27*x^2*u*g1^2+54*x^2*g1*u^2+36*x^2*u^2*g4+9*x^2*u*g4^2-8+12*u+209/2*x+3*x^2*g1^3-3*x^2*A2^3+10*x^2*A2^2*g1+6*x^2*g1^2*g4-10*x^2*g1^2*A2+3*x^2*g1*g4^2-x^2*A3^2*g4-2*x^2*g1*A3^2-6*x^2*u*A3^2+3*x^2*A2*A3^2+177*x^3-x^2*A0^2*g1-3*x^2*u*A0^2-u*A0^2+u*A2^2-2*A2*u^2+3*u*g1^2+3*g1*u^2-6*u^2-12*g1*u-6*g1^2+8*A2*u+8*A2*g1-2*A2^2+x^2*A0^2*A2-A0^2*g1+A2^2*g1-2*g1^2*A2-12*x^2*A2*g1*g4-30*x^3*u^2*g4-30*x^3*g1*u^2+40*x^3*A2*u^2-9*x^3*A3^2-x^2*A1^2*A2+x^2*A1^2*g4+3*x^2*A1^2*u-8*A2+12*g1-x^2*A0^2*g4-531/2*x^2-148*x*u+106*x*A2-116*x*g1-43*x*g4-135*x^3*g4-135*x^3*g1-248*x^3*u+180*x^3*A2-9/2*x*A3^2-20*x^3*u*A2^2-12*x^3*u*g1^2-24*x^3*g1*u*g4-12*x^3*u*g4^2+32*x^3*A2*u*g4+32*x^3*u*A2*g1-x*A1^2*g1+13/2*x^2*A0^2+x^2*A1^2*g1+120*x^3*u^2-20*x^3*u^3+134*x^2*A2*g1-81*x^2*g1*g4+82*x^2*A2*g4+36*x^2*g1*u*g4-36*x^2*A2*u*g4-60*x^2*u*A2*g1-60*x^2*g1^2-135/2*x^2*A2^2+27/2*x^2*A3^2-21*x^2*g4^2-12*x*u*A2^2+24*x*A2*u^2-18*x*u*g1^2-27*x*g1*u^2-x*A2^2*g4-6*x*A2^2*g1-3*x*g1^2*g4+8*x*g1^2*A2-9*x*u^2*g4+x*g1*A3^2+2*x*u*A3^2-x*A2*A3^2+30*x^2*u^3+4*x^3*u*A3^2-2*x*A1^2*u+126*x^3*g1*u-x^3*g1^3-168*x^3*A2*u+2*x^3*A2^3+8*x^3*A2*g1*g4-x^3*g4^3+x^3*g1*A3^2-2*x^3*A2*A3^2+x^3*A3^2*g4-3*x^3*g1*g4^2-5*x^3*A2^2*g1+4*x^3*g1^2*A2-3*x^3*g1^2*g4-5*x^3*A2^2*g4+126*x^3*u*g4+4*x^3*g4^2*A2+252*x^2*A2*u-72*x^3*A2*g1+372*x^2*u+9/2*x*A1^2-72*x^3*A2*g4+54*x^3*g1*g4-12*x*g1*u*g4+8*x*A2*u*g4+4*x*A2*g1*g4+32*x*u*A2*g1+39*x*u*g4+111*x*g1*u-100*x*A2*u-70*x*A2*g1+27*x*g1*g4-18*x*A2*g4-4*u*A2*g1-180*x^2*u^2-225*x^2*g1*u+x*A0^2*g4-153*x^2*u*g4+2*A0^2+x*A2^3-3*x*g1^3-12*x*u^3+4*x*u*A0^2+2*x*A0^2*g1-x*A0^2*A2+53/2*x*A2^2-2*x^2*g4^2*A2+5*x^2*A2^2*g4+45*x^3*A2^2+27*x^3*g1^2+39*x*g1^2+72*x*u^2+27*x^3*g4^2-270*x^2*A2+239*x^2*g1+166*x^2*g4+x*A1^2*A2-17/2*x*A0^2-13/2*x^2*A1^2)*dx^2+1/2*(u-2)*(12*g1*u*g4-2*A2^3+6*g1^3+6*u^3+60*x^2*u*A2^2-80*x^2*A2*u^2+36*x^2*u*g1^2+60*x^2*g1*u^2+60*x^2*u^2*g4+36*x^2*u*g4^2-17+34*u+90*x+6*x^2*g1^3-12*x^2*A2^3+30*x^2*A2^2*g1+18*x^2*g1^2*g4-24*x^2*g1^2*A2+18*x^2*g1*g4^2-6*x^2*A3^2*g4-6*x^2*g1*A3^2-12*x^2*u*A3^2+12*x^2*A2*A3^2+2*A1^2*u+2*A1^2*g1-2*A1^2*A2-18*u*g4-4*u*A0^2+12*u*A2^2-16*A2*u^2+18*u*g1^2+18*g1*u^2-24*u^2-48*g1*u-24*g1^2+44*A2*u+44*A2*g1-17*A2^2-2*A0^2*g4-4*A0^2*g1-18*g1*g4+12*A2*g4+2*A2^2*g4+12*A2^2*g1+6*g1^2*g4-16*g1^2*A2+6*u^2*g4-48*x^2*A2*g1*g4-2*g1*A3^2-2*u*A3^2+2*A2*A3^2-32*A2+34*g1+14*g4-3*A1^2-90*x^2-174*x*u+168*x*A2-146*x*g1-106*x*g4+6*x^2*g4^3-18*x*A3^2-4*x*A1^2*g1+144*x^2*A2*g1-108*x^2*g1*g4+144*x^2*A2*g4+72*x^2*g1*u*g4-96*x^2*A2*u*g4-96*x^2*u*A2*g1-54*x^2*g1^2-90*x^2*A2^2+18*x^2*A3^2-54*x^2*g4^2-60*x*u*A2^2+80*x*A2*u^2-54*x*u*g1^2-72*x*g1*u^2+8*x*g4^2*A2-20*x*A2^2*g4-40*x*A2^2*g1-24*x*g1^2*g4+40*x*g1^2*A2-48*x*u^2*g4-12*x*g1*g4^2+4*x*A3^2*g4+8*x*g1*A3^2+12*x*u*A3^2-12*x*A2*A3^2-18*x*u*g4^2+30*x^2*u^3-4*x*A1^2*g4-6*x*A1^2*u+224*x^2*A2*u-8*A2*u*g4-8*A2*g1*g4+174*x^2*u+8*x*A1^2+3*A3^2-72*x*g1*u*g4+72*x*A2*u*g4+48*x*A2*g1*g4+120*x*u*A2*g1+138*x*u*g4+198*x*g1*u-224*x*A2*u-176*x*A2*g1+108*x*g1*g4-112*x*A2*g4-32*u*A2*g1-120*x^2*u^2-168*x^2*g1*u+4*x*A0^2*g4-168*x^2*u*g4+5*A0^2+30*x*g4^2+2*A0^2*A2+12*x*A2^3-12*x*g1^3-30*x*u^3+6*x*u*A0^2+4*x*A0^2*g1-4*x*A0^2*A2+90*x*A2^2-24*x^2*g4^2*A2+30*x^2*A2^2*g4+78*x*g1^2+120*x*u^2-168*x^2*A2+126*x^2*g1+126*x^2*g4+4*x*A1^2*A2-8*x*A0^2)*dx-1/2*(u-1)*(u-2)*(-24*g1*u*g4+6*A2^3-6*g1^3-6*u^3+3-10*u-6*x-2*A1^2*u-2*A1^2*g1-2*A1^2*g4+2*A1^2*A2+18*u*g4+2*u*A0^2-20*u*A2^2+20*A2*u^2-18*u*g1^2-18*g1*u^2+12*u^2+24*g1*u+12*g1^2-28*A2*u-28*A2*g1+15*A2^2+4*g4^2*A2+2*A0^2*g4+2*A0^2*g1+18*g1*g4-20*A2*g4-10*A2^2*g4-20*A2^2*g1-12*g1^2*g4+20*g1^2*A2-12*u^2*g4-6*g1*g4^2+2*A3^2*g4+4*g1*A3^2+4*u*A3^2-6*A2*A3^2+12*A2-10*g1-8*g4+A1^2+20*x*u-24*x*A2+18*x*g1+18*x*g4+6*x*A3^2+40*x*u*A2^2-40*x*A2*u^2+24*x*u*g1^2+30*x*g1*u^2-24*x*g4^2*A2+30*x*A2^2*g4+30*x*A2^2*g1+18*x*g1^2*g4-24*x*g1^2*A2+30*x*u^2*g4+18*x*g1*g4^2-6*x*A3^2*g4-6*x*g1*A3^2-8*x*u*A3^2+12*x*A2*A3^2+24*x*u*g4^2+24*A2*u*g4+24*A2*g1*g4-3*A3^2+6*g4^2+48*x*g1*u*g4-64*x*A2*u*g4-48*x*A2*g1*g4-64*x*u*A2*g1-42*x*u*g4-42*x*g1*u+56*x*A2*u+48*x*A2*g1-36*x*g1*g4+48*x*A2*g4+40*u*A2*g1+6*x*g4^3-A0^2-6*u*g4^2-18*x*g4^2-2*A0^2*A2-12*x*A2^3+6*x*g1^3+12*x*u^3-30*x*A2^2-18*x*g1^2-24*x*u^2): Pg1n:=x^4*(x-1)^3*dx^5-x^3*(x-1)^2*(-16*x-4*x*A2+3*x*g1+3*x*g4+5*x*u-2*u+7-3*g1+2*A2)*dx^4+x^2*(x-1)*(9-6*u-65*x+u^2+3*g1*u+3*g1^2-2*A2*u-4*A2*g1+A2^2+6*A2-9*g1+75*x^2+45*x*u-40*x*A2+42*x*g1+18*x*g4+x*A3^2-8*x^2*A2*g1+6*x^2*g1*g4-8*x^2*A2*g4+3*x^2*g1^2+5*x^2*A2^2-x^2*A3^2+3*x^2*g4^2-16*x^2*A2*u-54*x^2*u-x*A1^2-6*x*u*g4-15*x*g1*u+14*x*A2*u+12*x*A2*g1-6*x*g1*g4+4*x*A2*g4+10*x^2*u^2+12*x^2*g1*u+12*x^2*u*g4-A0^2-5*x*A2^2-6*x*g1^2-8*x*u^2+44*x^2*A2-33*x^2*g1-33*x^2*g4+x*A0^2)*dx^3-1/2*x*(-2*g1^3-40*x^2*u*A2^2+60*x^2*A2*u^2-36*x^2*u*g1^2-54*x^2*g1*u^2-36*x^2*u^2*g4-12*x^2*u*g4^2-81*x-6*x^2*g1^3+6*x^2*A2^3-20*x^2*A2^2*g1-12*x^2*g1^2*g4+20*x^2*g1^2*A2-6*x^2*g1*g4^2+2*x^2*A3^2*g4+4*x^2*g1*A3^2+8*x^2*u*A3^2-6*x^2*A2*A3^2-230*x^3+2*x^2*A0^2*g1+4*x^2*u*A0^2-2*x^2*A0^2*A2+2*A0^2*g1-2*A2^2*g1+4*g1^2*A2+24*x^2*A2*g1*g4+36*x^3*u^2*g4+36*x^3*g1*u^2-48*x^3*A2*u^2+14*x^3*A3^2+2*x^2*A1^2*A2-2*x^2*A1^2*g4-4*x^2*A1^2*u+2*x^2*A0^2*g4+295*x^2+100*x*u-92*x*A2+100*x*g1+38*x*g4+186*x^3*g4+186*x^3*g1+298*x^3*u-248*x^3*A2+5*x*A3^2+30*x^3*u*A2^2+18*x^3*u*g1^2+36*x^3*g1*u*g4+18*x^3*u*g4^2-48*x^3*A2*u*g4-48*x^3*u*A2*g1+2*x*A1^2*g1-9*x^2*A0^2-2*x^2*A1^2*g1-132*x^3*u^2+20*x^3*u^3-188*x^2*A2*g1+114*x^2*g1*g4-116*x^2*A2*g4-48*x^2*g1*u*g4+48*x^2*A2*u*g4+80*x^2*u*A2*g1+84*x^2*g1^2+95*x^2*A2^2-19*x^2*A3^2+30*x^2*g4^2+12*x*u*A2^2-16*x*A2*u^2+18*x*u*g1^2+18*x*g1*u^2+2*x*A2^2*g4+12*x*A2^2*g1+6*x*g1^2*g4-16*x*g1^2*A2+6*x*u^2*g4-2*x*g1*A3^2-2*x*u*A3^2+2*x*A2*A3^2-24*x^2*u^3-6*x^3*u*A3^2+2*x*A1^2*u-162*x^3*g1*u+2*x^3*g1^3+216*x^3*A2*u-4*x^3*A2^3-16*x^3*A2*g1*g4+2*x^3*g4^3-2*x^3*g1*A3^2+4*x^3*A2*A3^2-2*x^3*A3^2*g4+6*x^3*g1*g4^2+10*x^3*A2^2*g1-8*x^3*g1^2*A2+6*x^3*g1^2*g4+10*x^3*A2^2*g4-162*x^3*u*g4-8*x^3*g4^2*A2-276*x^2*A2*u+112*x^3*A2*g1-374*x^2*u-5*x*A1^2+112*x^3*A2*g4-84*x^3*g1*g4+12*x*g1*u*g4-8*x*A2*u*g4-8*x*A2*g1*g4-32*x*u*A2*g1-30*x*u*g4-84*x*g1*u+76*x*A2*u+76*x*A2*g1-30*x*g1*g4+20*x*A2*g4+162*x^2*u^2+246*x^2*g1*u-2*x*A0^2*g4+168*x^2*u*g4-2*x*A2^3+6*x*g1^3+6*x*u^3-4*x*u*A0^2-4*x*A0^2*g1+2*x*A0^2*A2-29*x*A2^2+4*x^2*g4^2*A2-10*x^2*A2^2*g4-70*x^3*A2^2-42*x^3*g1^2-42*x*g1^2-42*x*u^2-42*x^3*g4^2+324*x^2*A2-286*x^2*g1-200*x^2*g4-2*x*A1^2*A2+9*x*A0^2+9*x^2*A1^2)*dx^2+1/2*(u-2)*(2*g1^3-20*x^2*u*A2^2+20*x^2*A2*u^2-18*x^2*u*g1^2-18*x^2*g1*u^2-12*x^2*u^2*g4-6*x^2*u*g4^2-6*x^2*g1^3+6*x^2*A2^3-20*x^2*A2^2*g1-12*x^2*g1^2*g4+20*x^2*g1^2*A2-6*x^2*g1*g4^2+2*x^2*A3^2*g4+4*x^2*g1*A3^2+4*x^2*u*A3^2-6*x^2*A2*A3^2-46*x^3+2*x^2*A0^2*g1+2*x^2*u*A0^2-2*x^2*A0^2*A2-2*A0^2*g1+2*A2^2*g1-4*g1^2*A2+24*x^2*A2*g1*g4+24*x^3*u^2*g4+24*x^3*g1*u^2-32*x^3*A2*u^2+10*x^3*A3^2+2*x^2*A1^2*A2-2*x^2*A1^2*g4-2*x^2*A1^2*u+2*x^2*A0^2*g4+31*x^2+66*x^3*g4+66*x^3*g1+80*x^3*u-88*x^3*A2+30*x^3*u*A2^2+18*x^3*u*g1^2+36*x^3*g1*u*g4+18*x^3*u*g4^2-48*x^3*A2*u*g4-48*x^3*u*A2*g1-3*x^2*A0^2-2*x^2*A1^2*g1-48*x^3*u^2+10*x^3*u^3-68*x^2*A2*g1+42*x^2*g1*g4-44*x^2*A2*g4-24*x^2*g1*u*g4+24*x^2*A2*u*g4+40*x^2*u*A2*g1+30*x^2*g1^2+35*x^2*A2^2-7*x^2*A3^2+12*x^2*g4^2-6*x^2*u^3-6*x^3*u*A3^2-78*x^3*g1*u+4*x^3*g1^3+104*x^3*A2*u-8*x^3*A2^3-32*x^3*A2*g1*g4+4*x^3*g4^3-4*x^3*g1*A3^2+8*x^3*A2*A3^2-4*x^3*A3^2*g4+12*x^3*g1*g4^2+20*x^3*A2^2*g1-16*x^3*g1^2*A2+12*x^3*g1^2*g4+20*x^3*A2^2*g4-78*x^3*u*g4-16*x^3*g4^2*A2-68*x^2*A2*u+80*x^3*A2*g1-52*x^2*u+80*x^3*A2*g4-60*x^3*g1*g4+30*x^2*u^2+60*x^2*g1*u+42*x^2*u*g4+4*x^2*g4^2*A2-10*x^2*A2^2*g4-50*x^3*A2^2-30*x^3*g1^2-30*x^3*g4^2+60*x^2*A2-52*x^2*g1-38*x^2*g4+3*x^2*A1^2)*dx-(u-1)*x^2*(-A3-A2-1+g1+g4+u)*(-2*A2-1+g1+g4+u)*(-A2-1+A3+g1+g4+u)*(u-2): 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Pg4n:=x^3*(x-1)^4*dx^5-x^2*(x-1)^3*(-4*x*A2-16*x+3*x*g1+3*x*g4+5*x*u+9+2*A2-3*g1-3*u)*dx^4+x*(x-1)^2*(19-15*u-85*x+3*u^2+6*g1*u+3*g1^2-4*A2*u-4*A2*g1+A2^2+10*A2-15*g1+75*x^2+63*x*u-48*x*A2+48*x*g1+24*x*g4+x*A3^2-8*x^2*A2*g1+6*x^2*g1*g4-8*x^2*A2*g4+3*x^2*g1^2+5*x^2*A2^2-x^2*A3^2+3*x^2*g4^2-16*x^2*A2*u-54*x^2*u-x*A1^2-9*x*u*g4-18*x*g1*u+18*x*A2*u+12*x*A2*g1-6*x*g1*g4+4*x*A2*g4+10*x^2*u^2+12*x^2*g1*u+12*x^2*u*g4-A0^2-5*x*A2^2-6*x*g1^2-12*x*u^2+44*x^2*A2-33*x^2*g1-33*x^2*g4+x*A0^2)*dx^3-1/2*(x-1)*(-2*g1^3-2*u^3-50*x^2*u*A2^2+84*x^2*A2*u^2-42*x^2*u*g1^2-72*x^2*g1*u^2-54*x^2*u^2*g4-18*x^2*u*g4^2+16-24*u-181*x-6*x^2*g1^3+6*x^2*A2^3-20*x^2*A2^2*g1-12*x^2*g1^2*g4+20*x^2*g1^2*A2-6*x^2*g1*g4^2+2*x^2*A3^2*g4+4*x^2*g1*A3^2+10*x^2*u*A3^2-6*x^2*A2*A3^2-230*x^3+2*x^2*A0^2*g1+4*x^2*u*A0^2+2*u*A0^2-2*u*A2^2+4*A2*u^2-6*u*g1^2-6*g1*u^2+12*u^2+24*g1*u+12*g1^2-16*A2*u-16*A2*g1+4*A2^2-2*x^2*A0^2*A2+2*A0^2*g1-2*A2^2*g1+4*g1^2*A2+24*x^2*A2*g1*g4+36*x^3*u^2*g4+36*x^3*g1*u^2-48*x^3*A2*u^2+14*x^3*A3^2+2*x^2*A1^2*A2-2*x^2*A1^2*g4-4*x^2*A1^2*u+16*A2-24*g1+2*x^2*A0^2*g4+395*x^2+246*x*u-188*x*A2+196*x*g1+86*x*g4+186*x^3*g4+186*x^3*g1+298*x^3*u-248*x^3*A2+9*x*A3^2+30*x^3*u*A2^2+18*x^3*u*g1^2+36*x^3*g1*u*g4+18*x^3*u*g4^2-48*x^3*A2*u*g4-48*x^3*u*A2*g1+2*x*A1^2*g1-9*x^2*A0^2-2*x^2*A1^2*g1-132*x^3*u^2+20*x^3*u^3-220*x^2*A2*g1+138*x^2*g1*g4-148*x^2*A2*g4-60*x^2*g1*u*g4+64*x^2*A2*u*g4+96*x^2*u*A2*g1+96*x^2*g1^2+115*x^2*A2^2-23*x^2*A3^2+42*x^2*g4^2+22*x*u*A2^2-40*x*A2*u^2+30*x*u*g1^2+42*x*g1*u^2+2*x*A2^2*g4+12*x*A2^2*g1+6*x*g1^2*g4-16*x*g1^2*A2+18*x*u^2*g4-2*x*g1*A3^2-4*x*u*A3^2+2*x*A2*A3^2-36*x^2*u^3-6*x^3*u*A3^2+4*x*A1^2*u-162*x^3*g1*u+2*x^3*g1^3+216*x^3*A2*u-4*x^3*A2^3-16*x^3*A2*g1*g4+2*x^3*g4^3-2*x^3*g1*A3^2+4*x^3*A2*A3^2-2*x^3*A3^2*g4+6*x^3*g1*g4^2+10*x^3*A2^2*g1-8*x^3*g1^2*A2+6*x^3*g1^2*g4+10*x^3*A2^2*g4-162*x^3*u*g4-8*x^3*g4^2*A2-372*x^2*A2*u+112*x^3*A2*g1-520*x^2*u-9*x*A1^2+112*x^3*A2*g4-84*x^3*g1*g4+24*x*g1*u*g4-16*x*A2*u*g4-8*x*A2*g1*g4-56*x*u*A2*g1-78*x*u*g4-180*x*g1*u+172*x*A2*u+124*x*A2*g1-54*x*g1*g4+36*x*A2*g4+8*u*A2*g1+234*x^2*u^2+318*x^2*g1*u-2*x*A0^2*g4+240*x^2*u*g4-4*A0^2-2*x*A2^3+6*x*g1^3+18*x*u^3-6*x*u*A0^2-4*x*A0^2*g1+2*x*A0^2*A2-49*x*A2^2+4*x^2*g4^2*A2-10*x^2*A2^2*g4-70*x^3*A2^2-42*x^3*g1^2-66*x*g1^2-114*x*u^2-42*x^3*g4^2+420*x^2*A2-358*x^2*g1-272*x^2*g4-2*x*A1^2*A2+13*x*A0^2+9*x^2*A1^2)*dx^2+1/2*(u-2)*(-12*g1*u*g4+2*A2^3-4*g1^3-4*u^3-70*x^2*u*A2^2+76*x^2*A2*u^2-48*x^2*u*g1^2-60*x^2*g1*u^2-54*x^2*u^2*g4-36*x^2*u*g4^2+15-28*u-76*x-12*x^2*g1^3+18*x^2*A2^3-50*x^2*A2^2*g1-30*x^2*g1^2*g4+44*x^2*g1^2*A2-24*x^2*g1*g4^2+8*x^2*A3^2*g4+10*x^2*g1*A3^2+14*x^2*u*A3^2-18*x^2*A2*A3^2-2*A1^2*u-2*A1^2*g1+2*A1^2*A2-46*x^3+2*x^2*A0^2*g1+2*x^2*u*A0^2+18*u*g4+2*u*A0^2-10*u*A2^2+12*A2*u^2-12*u*g1^2-12*g1*u^2+18*u^2+36*g1*u+18*g1^2-36*A2*u-36*A2*g1+15*A2^2-2*x^2*A0^2*A2+2*A0^2*g4+2*A0^2*g1+18*g1*g4-12*A2*g4-2*A2^2*g4-10*A2^2*g1-6*g1^2*g4+12*g1^2*A2-6*u^2*g4+72*x^2*A2*g1*g4+24*x^3*u^2*g4+24*x^3*g1*u^2-32*x^3*A2*u^2+10*x^3*A3^2+2*x^2*A1^2*A2-2*x^2*A1^2*g4-2*x^2*A1^2*u+2*g1*A3^2+2*u*A3^2-2*A2*A3^2+28*A2-28*g1-14*g4+2*x^2*A0^2*g4+3*A1^2+107*x^2+136*x*u-144*x*A2+122*x*g1+94*x*g4-6*x^2*g4^3+66*x^3*g4+66*x^3*g1+80*x^3*u-88*x^3*A2+16*x*A3^2+30*x^3*u*A2^2+18*x^3*u*g1^2+36*x^3*g1*u*g4+18*x^3*u*g4^2-48*x^3*A2*u*g4-48*x^3*u*A2*g1+4*x*A1^2*g1-3*x^2*A0^2-2*x^2*A1^2*g1-48*x^3*u^2+10*x^3*u^3-196*x^2*A2*g1+138*x^2*g1*g4-172*x^2*A2*g4-84*x^2*g1*u*g4+104*x^2*A2*u*g4+120*x^2*u*A2*g1+78*x^2*g1^2+115*x^2*A2^2-23*x^2*A3^2+60*x^2*g4^2+50*x*u*A2^2-56*x*A2*u^2+42*x*u*g1^2+48*x*g1*u^2-8*x*g4^2*A2+20*x*A2^2*g4+40*x*A2^2*g1+24*x*g1^2*g4-40*x*g1^2*A2+36*x*u^2*g4+12*x*g1*g4^2-4*x*A3^2*g4-8*x*g1*A3^2-10*x*u*A3^2+12*x*A2*A3^2+18*x*u*g4^2-24*x^2*u^3+4*x*A1^2*g4-6*x^3*u*A3^2+4*x*A1^2*u-78*x^3*g1*u+4*x^3*g1^3+104*x^3*A2*u-8*x^3*A2^3-32*x^3*A2*g1*g4+4*x^3*g4^3-4*x^3*g1*A3^2+8*x^3*A2*A3^2-4*x^3*A3^2*g4+12*x^3*g1*g4^2+20*x^3*A2^2*g1-16*x^3*g1^2*A2+12*x^3*g1^2*g4+20*x^3*A2^2*g4-78*x^3*u*g4-16*x^3*g4^2*A2-244*x^2*A2*u+80*x^3*A2*g1+8*A2*u*g4+8*A2*g1*g4-188*x^2*u-6*x*A1^2-3*A3^2+80*x^3*A2*g4-60*x^3*g1*g4+60*x*g1*u*g4-64*x*A2*u*g4-48*x*A2*g1*g4-96*x*u*A2*g1-114*x*u*g4-150*x*g1*u+176*x*A2*u+152*x*A2*g1-96*x*g1*g4+104*x*A2*g4+24*u*A2*g1+114*x^2*u^2+192*x^2*g1*u-4*x*A0^2*g4+174*x^2*u*g4-3*A0^2-30*x*g4^2-2*A0^2*A2-12*x*A2^3+12*x*g1^3+18*x*u^3-4*x*u*A0^2-4*x*A0^2*g1+4*x*A0^2*A2-80*x*A2^2+28*x^2*g4^2*A2-40*x^2*A2^2*g4-50*x^3*A2^2-30*x^3*g1^2-66*x*g1^2-84*x*u^2-30*x^3*g4^2+204*x^2*A2-160*x^2*g1-146*x^2*g4-4*x*A1^2*A2+6*x*A0^2+3*x^2*A1^2)*dx-(u-1)*(-A3-A2-1+g1+g4+u)*(-2*A2-1+g1+g4+u)*(-A2-1+A3+g1+g4+u)*(x-1)^2*(u-2): 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+186*x*u*g4+186*x*g1*u-248*x*A2*u-192*x*A2*g1+144*x*g1*g4-192*x*A2*g4-148*u*A2*g1-16*x*g4^3+2*u*A0^2*g4+3*A0^2+8*A2*u^2*g4+12*u*g1^2*A2+2*u*A0^2*g1+24*u*g4^2-6*u*g1^2*g4+72*x*g4^2-2*u*A0^2*A2+6*A0^2*A2-2*g4^3+32*x*A2^3-16*x*g1^3-64*x*u^3-12*g1*u^2*g4+2*u*g1*A3^2-2*u*A2*A3^2+120*x*A2^2+72*x*g1^2+116*x*u^2): ### ## coeff(PA0n,dx,5)=coeff(QA0n,dx,5) Pn5:= x^3*(x-1)^3*(-A0^2*x+4*A0*A2*x-2*A0*g1*x-2*A0*g4*x+A1^2*x-3*A2^2*x+2*A2*g1*x+2*A2*g4*x-A3^2*x+2*A0^2-4*A0*A2+2*A0*g1-2*A0*u+2*A2^2-2*A2*g1+2*A2*u-2*A2*x+2*g1*x+2*g4*x-2*g1+2*u+x-2): ## in the following, denom of coeff(*,dx,5) is to be multiplied to the operator 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1*g4*u^3+12*A3^2*g1^2*g4*u-96*A3^2*g1*g4^2*x+4*A3^2*g1*g4*u^2-152*A3^2*g4^2*u*x-144*g1*g4^3*u*x-288*g1*g4*u^3*x-108*A0*A1^2*g4*u-808*A0*A2*g4^2*u+108*A0*A3^2*g4*u+576*A0*g1*g4^2*u+12*A1^2*A2*g4*u-20*A1^2*g1*g4*u-12*A2*A3^2*g4*u-368*A2*g1*g4^2*u+20*A3^2*g1*g4*u+280*A2*g4^2*u-128*A3^2*g4*u-240*g1*g4^2*u)/(A0-1): ## Pp5=coeff(Pp,dx,5)=coeff(Qp,dx,5) Pp5:=x^3*(x-1)^3*(-A0^2*x-4*A0*A2*x+2*A0*g1*x+2*A0*g4*x+A1^2*x-3*A2^2*x+2*A2*g1*x+2*A2*g4*x-A3^2*x+2*A0^2+4*A0*A2-2*A0*g1+2*A0*u+2*A2^2-2*A2*g1+2*A2*u-2*A2*x+2*g1*x+2*g4*x-2*g1+2*u+x-2): PA0p:=x^3*(x-1)^3*(-A0^2*x-4*A0*A2*x+2*A0*g1*x+2*A0*g4*x+A1^2*x-3*A2^2*x+2*A2*g1*x+2*A2*g4*x-A3^2*x+2*A0^2+4*A0*A2-2*A0*g1+2*A0*u+2*A2^2-2*A2*g1+2*A2*u-2*A2*x+2*g1*x+2*g4*x-2*g1+2*u+x-2)*dx^5-x^2*(x-1)^2*(-14+9*A0^2*g1*x-17*A2^2*g1*x^2+2*A1^2*A2*x+6*A0*g4^2*x^2-17*A2^2*g4*x^2-4*A1^2*A2*x^2-24*A0*A2^2*x+5*A1^2*u*x^2+3*A1^2*g1*x^2-3*A3^2*g1*x^2-10*A2*u*x^2+10*A0*u^2*x-5*A0^2*u*x^2+18*u+39*x-12*g1+4*A0-22*A2*g1-43*A0^2*x+7*A1^2*x-7*A3^2*x-61*A2^2*x+12*A0*u+16*A2*u-8*A2*x+41*g1*x+8*g4*x+18*A2^2+18*A0^2-18*A0*g1+36*A0*A2-100*A0*A2*x+50*A0*g1*x+14*A0*g4*x+68*A2*g1*x+18*A2*g4*x+4*A2^3+6*g1^2-4*u^2-16*x^2-20*A0*A2*g1*x^2-16*A1^2*x^2-14*A2^3*x+56*A2^2*x^2+16*A3^2*x^2+6*g1^2*x^2+4*A0^2*A2-6*A0^2*g1-6*A0^2*u+8*A0*A2^2+6*A0*g1^2-4*A0*u^2-10*A2^2*g1-2*A2^2*u+6*A2*g1^2-4*A2*u^2+28*A2*x^2-12*g1^2*x-29*g1*x^2-29*g4*x^2+10*u^2*x+5*u*x^2-4*A0*x-44*u*x-20*A0*A2*g4*x^2-20*A0*A2*u*x^2+12*A0*g1*g4*x^2+10*A0*g1*u*x^2+10*A0*g4*u*x^2+12*A2*g1*g4*x^2+10*A2*g1*u*x^2+10*A2*g4*u*x^2+36*A0*A2*g1*x+16*A0*A2*g4*x+24*A0*A2*u*x-12*A0*g1*g4*x-10*A0*g1*u*x+2*A0*g4*u*x-12*A2*g1*g4*x-10*A2*g1*u*x+2*A2*g4*u*x+16*A0^2*x^2+12*A2^3*x^2-3*A0^2*g4*x^2+16*A0*A2^2*x^2+6*A0*g1^2*x^2+3*A1^2*g4*x^2-15*A2^2*u*x^2+4*A2*A3^2*x^2+6*A2*g1^2*x^2+6*A2*g4^2*x^2-3*A3^2*g4*x^2-5*A3^2*u*x^2-10*A0^2*A2*x+6*A0^2*g4*x+14*A0^2*u*x+64*A0*A2*x^2-12*A0*g1^2*x-32*A0*g1*x^2-32*A0*g4*x^2-3*A1^2*g1*x-2*A1^2*u*x+27*A2^2*g1*x+10*A2^2*g4*x+10*A2^2*u*x-2*A2*A3^2*x-12*A2*g1^2*x-46*A2*g1*x^2-46*A2*g4*x^2+10*A2*u^2*x+3*A3^2*g1*x+2*A3^2*u*x+12*g1*g4*x^2+10*g1*u*x^2+10*g4*u*x^2-16*A0*A2*g1+6*g4^2*x^2+4*A0^2*A2*x^2-3*A0^2*g1*x^2-8*A0*A2*u-30*A0*u*x-34*A2*u*x-12*g1*g4*x-10*g1*u*x+2*g4*u*x)*dx^4+(-18-2*A2^2*A3^2*x^3+20*A2*u^3*x^2-20*A0*A2^3*x^3+6*A2*g1^3*x^3+31*A3^2*g4*x^3+113*A0^2*g1*x-432*A2^2*g1*x^2-36*g1^2*g4*x^2+6*A1^2*A2*x+92*A2*u*x^3+12*A0^2*g1^2*x^2-25*A2^2*g4^2*x^3-88*A2*g4^2*x^3+54*A0^2*u*x^3+36*A0*g4^2*x^2-230*A2^2*g4*x^2+14*A2^2*g4^2*x^2+3*A1^2*g1^2*x^3-25*A2^2*g1^2*x^3-38*A1^2*A2*x^2+18*g1^2*g4*x^3+34*A2^3*g1*x^3-232*A0*A2^2*x-3*A0^2*g4^2*x^3-33*A1^2*g1*x^3-4*A0^3*A2*x^2+2*A2*g1*u^2+296*A2*g1*x^3+45*A1^2*u*x^2-10*A0^2*u^2*x^3+36*A0^2*u^2*x^2+10*A2^3*g4*x-18*A2*g1^3*x^2-6*A0^2*A2*g1-3*A0^2*g1^2*x^3-42*A2*A3^2*x^3+40*A1^2*g1*x^2+34*A2^3*g4*x^3+114*A0*u*x^2-300*A0*A2*x^3-38*A3^2*g1*x^2-10*A0^2*A2*u+158*A2*u*x^2-53*A2^2*g1^2*x+10*A1^2*u^2*x^3-54*g1^2*u*x^2+80*A0*u^2*x+8*A0^3*A2*x-189*A0^2*u*x^2-33*A1^2*g4*x^3+64*A2^2*g1^2*x^2+30*u+139*x-16*g1+4*A2+16*A0-58*A2*g1-198*A0^2*x+11*A1^2*x-11*A3^2*x-238*A2^2*x+6*A0*u+22*A2*u+12*A2*x+111*g1*x-18*g4*x+18*A0*g1^3*x+40*A2^2+36*A0^2-46*A0*g1+76*A0*A2-432*A0*A2*x+228*A0*g1*x+30*A0*g4*x+334*A2*g1*x+34*A2*g4*x+20*A2^3+24*g1^2-14*u^2-215*x^2+2*A2^4+A0^2*A3^2*x^3-A0^4*x^2-A1^2*A3^2*x^3-A1^2*A2^2*x+A1^2*u^2*x+A2^2*A3^2*x-A2^2*u^2*x-A3^2*u^2*x-A3^4*x^2+A3^4*x^3-A1^4*x^2-6*g1^3-2*A0^4+2*u^3+75*x^3-508*A0*A2*g1*x^2-66*A1^2*x^2-124*A2^3*x+466*A2^2*x^2+68*A3^2*x^2+150*g1^2*x^2+20*A0^2*A2-28*A0^2*g1-26*A0^2*u+40*A0*A2^2+30*A0*g1^2-10*A0*u^2-52*A2^2*g1-14*A2^2*u+38*A2*g1^2-14*A2*u^2+42*A2*x^2-111*g1^2*x-212*g1*x^2-46*g4*x^2+107*u^2*x+303*u*x^2-56*A0*x-226*u*x-15*A2^4*x^3+25*A2^4*x^2-142*A2^3*x^3+6*g1^3*x^3+6*g4^3*x^3+3*A0^4*x-75*A0^2*x^3+75*A1^2*x^3-308*A0*A2*g4*x^2-388*A0*A2*u*x^2+198*A0*g1*g4*x^2+174*A0*g1*u*x^2+30*A0*g4*u*x^2+258*A2*g1*g4*x^2+256*A2*g1*u*x^2+54*A2*g4*u*x^2+368*A0*A2*g1*x+108*A0*A2*g4*x+232*A0*A2*u*x-66*A0*g1*g4*x-78*A0*g1*u*x+18*A0*g4*u*x-82*A2*g1*g4*x-104*A2*g1*u*x+22*A2*g4*u*x+8*A0^2*A2*g1*x^3+8*A0^2*A2*g4*x^3+16*A0^2*A2*u*x^3-6*A0^2*g1*g4*x^3-12*A0^2*g1*u*x^3-12*A0^2*g4*u*x^3+42*A0*A2^2*g1*x^3+42*A0*A2^2*g4*x^3+64*A0*A2^2*u*x^3+4*A0*A2*A3^2*x^3-28*A0*A2*g1^2*x^3-28*A0*A2*g4^2*x^3-40*A0*A2*u^2*x^3-2*A0*A3^2*g1*x^3-2*A0*A3^2*g4*x^3+18*A0*g1^2*g4*x^3+24*A0*g1^2*u*x^3+18*A0*g1*g4^2*x^3+20*A0*g1*u^2*x^3+24*A0*g4^2*u*x^3+20*A0*g4*u^2*x^3-8*A1^2*A2*g1*x^3-8*A1^2*A2*g4*x^3-16*A1^2*A2*u*x^3+6*A1^2*g1*g4*x^3+12*A1^2*g1*u*x^3+12*A1^2*g4*u*x^3-50*A2^2*g1*g4*x^3-68*A2^2*g1*u*x^3-68*A2^2*g4*u*x^3+6*A2*A3^2*g1*x^3+6*A2*A3^2*g4*x^3+16*A2*A3^2*u*x^3+18*A2*g1^2*g4*x^3+24*A2*g1^2*u*x^3+18*A2*g1*g4^2*x^3+20*A2*g1*u^2*x^3+24*A2*g4^2*u*x^3+20*A2*g4*u^2*x^3-6*A3^2*g1*g4*x^3-12*A3^2*g1*u*x^3-12*A3^2*g4*u*x^3-26*A0^2*A2*g1*x^2-18*A0^2*A2*g4*x^2-54*A0^2*A2*u*x^2+18*A0^2*g1*g4*x^2+45*A0^2*g1*u*x^2+36*A0^2*g4*u*x^2+4*A0*A1^2*A2*x^2-2*A0*A1^2*g1*x^2-2*A0*A1^2*g4*x^2-100*A0*A2^2*g1*x^2-58*A0*A2^2*g4*x^2-126*A0*A2^2*u*x^2-8*A0*A2*A3^2*x^2+76*A0*A2*g1^2*x^2+220*A0*A2*g1*x^3+20*A0*A2*g4^2*x^2+220*A0*A2*g4*x^3+56*A0*A2*u^2*x^2+216*A0*A2*u*x^3+4*A0*A3^2*g1*x^2+256*A0^2*x^2+234*A2^3*x^2-94*A0^2*g4*x^2+368*A0*A2^2*x^2+18*g1^2*g4*x+162*A0*g1^2*x^2+16*A1^2*g4*x^2-217*A2^2*u*x^2+38*A2*A3^2*x^2+214*A2*g1^2*x^2+44*A2*g4^2*x^2-16*A3^2*g4*x^2-47*A3^2*u*x^2-108*A0^2*A2*x+46*A0^2*g4*x+146*A0^2*u*x+656*A0*A2*x^2-126*A0*g1^2*x-332*A0*g1*x^2-142*A0*g4*x^2-7*A1^2*g1*x-8*A1^2*u*x+271*A2^2*g1*x+62*A2^2*g4*x+82*A2^2*u*x-6*A2*A3^2*x-164*A2*g1^2*x-572*A2*g1*x^2-238*A2*g4*x^2+106*A2*u^2*x+7*A3^2*g1*x+8*A3^2*u*x+180*g1*g4*x^2+129*g1*u*x^2-6*g4*u*x^2-80*A0*A2*g1+30*g4^2*x^2+142*A0^2*A2*x^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2*x+160*A2^2*g1*g4*u^3*x+16*A2*A3^2*g1^2*u^2*x-72*A2*A3^2*g1^2*u*x^2+16*A2*A3^2*g1*g4*u^2*x-144*A2*A3^2*g1*g4*u*x^2+8*A2*A3^2*g1*u^3*x-72*A2*A3^2*g4^2*u*x^2-8*A2*A3^2*g4*u^3*x-40*A2*g1^3*u^3*x-24*A2*g1^2*u^4*x+8*A2*g1*u^5*x-200*A2*g1*u^4*x^2-72*A2*g4^4*u*x^2+8*A2*g4^3*u^3*x+24*A2*g4^2*u^4*x+24*A2*g4*u^5*x+36*A3^2*g4^3*u*x^2+32*g1^3*g4*u^2*x^2+48*g1^2*g4^2*u^2*x^2+72*g1^2*g4*u^3*x^2+32*g1*g4^3*u^2*x^2+72*g1*g4^2*u^3*x^2+48*g1*g4*u^4*x^2-42*A0^4*A2*g1*u-192*A0^4*A2*g1*x-8*A0^4*A2*g4*u-192*A0^4*A2*g4*x-8*A0^4*g1*g4*u+128*A0^4*g1*g4*x-16*A0^3*A1^2*A2*u-64*A0^3*A1^2*A2*x+16*A0^3*A1^2*g1*u+64*A0^3*A1^2*g1*x+28*A0^3*A1^2*g4*u+64*A0^3*A1^2*g4*x+104*A0^3*A1^2*u*x+284*A0^3*A2^2*g1*u+208*A0^3*A2^2*g4*u+96*A0^3*A2*A3^2*u-276*A0^3*A2*g1^2*u-600*A0^3*A2*g1*u^2-104*A0^3*A2*g4^2*u-412*A0^3*A2*g4*u^2-56*A0^3*A3^2*g1*u-28*A0^3*A3^2*g4*u+180*A0^3*g1^2*g4*u+96*A0^3*g1*g4^2*u+340*A0^3*g1*g4*u^2-44*A0^2*A1^2*A2^2*u-128*A0^2*A1^2*A2^2*x+54*A0^2*A1^2*A2*u^2-48*A2*g1^3*g4*u^2*x-48*A2*g1^2*g4^2*u^2*x-72*A2*g1^2*g4*u^3*x-16*A2*g1*g4^3*u^2*x-24*A2*g1*g4^2*u^3*x+192*A0^2*A1^2*A2*g1*x+56*A0^2*A1^2*A2*g4*u+192*A0^2*A1^2*A2*g4*x+6*A0^2*A1^2*A3^2*u-34*A0^2*A1^2*g1^2*u-64*A0^2*A1^2*g1^2*x-38*A0^2*A1^2*g1*u^2-64*A0^2*A1^2*g4^2*x+644*A0^2*A2^3*g1*u+328*A0^2*A2^3*g4*u+180*A0^2*A2^2*A3^2*u-786*A0^2*A2^2*g1^2*u-1314*A0^2*A2^2*g1*u^2-136*A0^2*A2^2*g4^2*u-644*A0^2*A2^2*g4*u^2-106*A0^2*A2*A3^2*u^2+400*A0^2*A2*g1^3*u+948*A0^2*A2*g1^2*u^2+616*A0^2*A2*g1*u^3+136*A0^2*A2*g4^2*u^2+208*A0^2*A2*g4*u^3+62*A0^2*A3^2*g1^2*u+66*A0^2*A3^2*g1*u^2+64*A0^2*A3^2*g4^2*x-144*A0^2*g1^3*g4*u-72*A0^2*g1^2*g4^2*u-276*A0^2*g1^2*g4*u^2-64*A0^2*g1*g4^2*u^2-80*A0^2*g1*g4*u^3-6*A0*A1^4*A2*u+32*A0*A1^4*A2*x+6*A0*A1^4*g1*u-32*A0*A1^4*g1*x-32*A0*A1^4*g4*x-52*A0*A1^4*u*x-16*A0*A1^2*A2^3*u+30*A0*A1^2*A2^2*u^2-4*A0*A1^2*A2*u^3-2*A0*A1^2*A3^2*u^2+12*A0*A1^2*g1^3*u-96*A0*A1^2*g1^3*x+24*A0*A1^2*g1^2*u^2+12*A0*A1^2*g1*u^3-40*A0^2*A1^2*g1*g4*u-128*A0^2*A1^2*g1*g4*x-824*A0^2*A2^2*g1*g4*u-56*A0^2*A2*A3^2*g4*u+624*A0^2*A2*g1^2*g4*u+224*A0^2*A2*g1*g4^2*u+40*A0^2*A3^2*g1*g4*u-160*A0*A1^2*A2^2*g1*x+12*A0*A1^2*A2*A3^2*u-128*A0*A1^2*A2*A3^2*x-52*A0*A1^2*A2*g1^2*u-40*A0*A1^2*A2*g1*g4*u+256*A0*A1^2*A2*g1*g4*x-56*A0*A1^2*A2*g1*u^2-4*A0*A1^2*A2*g4*u^2-12*A0*A1^2*A3^2*g1*u+96*A0*A1^2*A3^2*g1*x+64*A0*A1^2*A3^2*g4*x+12*A0*A1^2*g1^2*g4*u-192*A0*A1^2*g1^2*g4*x-96*A0*A1^2*g1*g4^2*x+12*A0*A1^2*g1*g4*u^2-136*A0*A1^2*g4^2*u*x+346*A0*A2^4*g1*u+140*A0*A2^4*g4*u+96*A0*A2^3*A3^2*u-500*A0*A2^3*g1^2*u-776*A0*A2^3*g1*u^2-56*A0*A2^3*g4^2*u-308*A0*A2^3*g4*u^2-66*A0*A2^2*A3^2*u^2+316*A0*A2^2*g1^3*u+768*A0*A2^2*g1^2*u^2+428*A0*A2^2*g1*u^3+72*A0*A2^2*g4^2*u^2+80*A0*A2^2*g4*u^3-6*A0*A2*A3^4*u+96*A0*A2*A3^4*x-4*A0*A2*A3^2*u^3-72*A0*A2*g1^4*u-272*A0*A2*g1^3*u^2-256*A0*A2*g1^2*u^3-32*A0*A2*g1*u^4+24*A0*A2*g4^2*u^3+48*A0*A2*g4*u^4+6*A0*A3^4*g1*u-64*A0*A3^4*g1*x-32*A0*A3^4*g4*x-108*A0*A3^4*u*x-12*A0*A3^2*g1^3*u+96*A0*A3^2*g1^3*x-32*A0*A3^2*g1^2*u^2-12*A0*A3^2*g1*u^3+32*A0*g1^3*g4*u^2+16*A0*g1^2*g4^2*u^2+32*A0*g1^2*g4*u^3+6*A1^4*A2*g1*u-8*A1^4*A2*u*x+8*A1^4*g1*u*x+8*A1^4*g4*u*x-12*A1^2*A2^3*g1*u-176*A0*A2^2*A3^2*g1*u-28*A0*A2^2*A3^2*g4*u+444*A0*A2^2*g1^2*g4*u+128*A0*A2^2*g1*g4^2*u+620*A0*A2^2*g1*g4*u^2+40*A0*A2*A3^2*g1*g4*u+104*A0*A2*A3^2*g1*u^2+4*A0*A2*A3^2*g4*u^2-144*A0*A2*g1^3*g4*u-352*A0*A2*g1^2*g4*u^2-80*A0*A2*g1*g4^2*u^2-112*A0*A2*g1*g4*u^3+96*A0*A3^2*g1*g4^2*x+288*A0*g1*g4^3*u*x+672*A0*g1*g4*u^3*x+6*A1^2*A2^2*A3^2*u+6*A1^2*A2^2*g1^2*u-10*A1^2*A2^2*g1*u^2-4*A1^2*A2^2*g4*u^2-2*A1^2*A2*A3^2*u^2+12*A1^2*A2*g1^2*u^2+8*A1^2*A2*g1*u^3+6*A1^2*A3^2*g1^2*u+2*A1^2*A3^2*g1*u^2-24*A1^2*A3^2*u^2*x+24*A1^2*g1^3*u*x-4*A1^2*g1^2*g4*u^2+72*A1^2*g1*u^3*x+24*A1^2*g4^2*u^2*x+48*A1^2*g4*u^3*x-12*A2^3*A3^2*g1*u+56*A2^3*g1*g4*u^2+6*A2^2*A3^2*g1^2*u+30*A2^2*A3^2*g1*u^2+4*A2^2*A3^2*g4*u^2-52*A2^2*g1^2*g4*u^2-16*A2^2*g1*g4^2*u^2-32*A2^2*g1*g4*u^3-128*A2^2*g4^3*u*x-296*A2^2*g4*u^3*x+6*A2*A3^4*g1*u-24*A2*A3^4*u*x-20*A2*A3^2*g1^2*u^2-8*A2*A3^2*g1*u^3+16*A2*g1^3*g4*u^2-12*A1^2*A2*A3^2*g1*u+32*A1^2*A2*A3^2*u*x+8*A1^2*A2*g1*g4*u^2-24*A1^2*A3^2*g1*u*x-16*A1^2*A3^2*g4*u*x+48*A1^2*g1^2*g4*u*x+24*A1^2*g1*g4^2*u*x+96*A1^2*g1*g4*u^2*x+8*A2*g1^2*g4^2*u^2+16*A2*g1^2*g4*u^3+8*A2*g4^3*u^2*x+16*A3^4*g1*u*x+8*A3^4*g4*u*x-24*A3^2*g1^3*u*x+4*A3^2*g1^2*g4*u^2-64*A3^2*g1*u^3*x-24*A3^2*g4^2*u^2*x-56*A3^2*g4*u^3*x-48*g1^3*g4*u^2*x-48*g1^2*g4^2*u^2*x-72*g1^2*g4*u^3*x-16*g1*g4^3*u^2*x-24*g1*g4^2*u^3*x+48*A0^2*A1^2*g4*u-632*A0^2*A2*g4^2*u+144*A2*g1*g4^3*u*x+448*A2*g1*g4*u^3*x-24*A3^2*g1*g4^2*u*x-80*A3^2*g1*g4*u^2*x-48*A0^2*A3^2*g4*u+432*A0^2*g1*g4^2*u-10*A0*A1^2*A3^2*u-256*A0*A1^2*A3^2*x+160*A0*A1^2*g4^2*x+36*A0*A1^2*g4*u^2-424*A0*A2^2*g4^2*u+80*A0*A2*g4^2*u^2-88*A0*A2*g4*u^3+44*A0*A1^2*A2*g4*u-44*A0*A2*A3^2*g4*u+592*A0*A2*g1*g4^2*u-160*A0*A3^2*g4^2*x-36*A0*A3^2*g4*u^2-144*A0*g1^2*g4^2*u-80*A0*g1*g4^2*u^2-64*A0*g1*g4*u^3+28*A1^2*A2^2*g4*u+6*A1^2*A2*A3^2*u+4*A1^2*A2*g4*u^2-6*A1^2*A3^2*g1*u+64*A1^2*A3^2*g4*x+12*A1^2*g1^2*g4*u-96*A1^2*g1*g4^2*x+4*A1^2*g1*g4*u^2-152*A1^2*g4^2*u*x-28*A2^2*A3^2*g4*u+128*A2^2*g1*g4^2*u-4*A2*A3^2*g4*u^2-72*A2*g1^2*g4^2*u-48*A2*g1*g4^2*u^2-48*A2*g1*g4*u^3-12*A3^2*g1^2*g4*u+96*A3^2*g1*g4^2*x-4*A3^2*g1*g4*u^2+152*A3^2*g4^2*u*x+144*g1*g4^3*u*x+288*g1*g4*u^3*x-108*A0*A1^2*g4*u-808*A0*A2*g4^2*u+108*A0*A3^2*g4*u+576*A0*g1*g4^2*u-12*A1^2*A2*g4*u+20*A1^2*g1*g4*u+12*A2*A3^2*g4*u+368*A2*g1*g4^2*u-20*A3^2*g1*g4*u-280*A2*g4^2*u+128*A3^2*g4*u+240*g1*g4^2*u)/(A0+1): # Pn5 coeff(PA1n,dx,5) = coeff(QA1n,dx,5)= Qn5 Pn5:=(x-1)^3*(A0^2*x-A1^2*x+4*A1*A2*x-2*A1*g1*x-2*A1*g4*x-3*A2^2*x+2*A2*g1* x+2*A2*g4*x-A3^2*x-A0^2-A1^2+2*A1*g1+2*A1*u+A2^2-2*A2*g1-2*A2*u-2*A2*x+A3^2+2* g1*x+2*g4*x+2*A2-2*g1-2*u+x+1)*x^3: Qn5:=(x-1)^3*(A0^2*x-A1^2*x+4*A1*A2*x-2*A1*g1*x-2*A1*g4*x-3*A2^2*x+2*A2*g1* x+2*A2*g4*x-A3^2*x-A0^2-A1^2+2*A1*g1+2*A1*u+A2^2-2*A2*g1-2*A2*u-2*A2*x+A3^2+2* g1*x+2*g4*x+2*A2-2*g1-2*u+x+1)*x^3: # PA1n = x^3*(x-1)^3*linear poly of x + .. PA1n:=(x-1)^3*(A0^2*x-A1^2*x+4*A1*A2*x-2*A1*g1*x-2*A1*g4*x-3*A2^2*x+2*A2*g1 *x+2*A2*g4*x-A3^2*x-A0^2-A1^2+2*A1*g1+2*A1*u+A2^2-2*A2*g1-2*A2*u-2*A2*x+A3^2+2* g1*x+2*g4*x+2*A2-2*g1-2*u+x+1)*x^3*dx^5+(x-1)^2*(4*A0^2*A2*x^2-3*A0^2*g1*x^2-3* A0^2*g4*x^2-5*A0^2*u*x^2-4*A1^2*A2*x^2+3*A1^2*g1*x^2+3*A1^2*g4*x^2+5*A1^2*u*x^2 +16*A1*A2^2*x^2-20*A1*A2*g1*x^2-20*A1*A2*g4*x^2-20*A1*A2*u*x^2+6*A1*g1^2*x^2+12 *A1*g1*g4*x^2+10*A1*g1*u*x^2+6*A1*g4^2*x^2+10*A1*g4*u*x^2-12*A2^3*x^2+17*A2^2* g1*x^2+17*A2^2*g4*x^2+15*A2^2*u*x^2-4*A2*A3^2*x^2-6*A2*g1^2*x^2-12*A2*g1*g4*x^2 -10*A2*g1*u*x^2-6*A2*g4^2*x^2-10*A2*g4*u*x^2+3*A3^2*g1*x^2+3*A3^2*g4*x^2+5*A3^2 *u*x^2-6*A0^2*A2*x+6*A0^2*g1*x+3*A0^2*g4*x+8*A0^2*u*x+16*A0^2*x^2-2*A1^2*A2*x+3 *A1^2*g4*x+4*A1^2*u*x-16*A1^2*x^2-8*A1*A2^2*x+24*A1*A2*g1*x+4*A1*A2*g4*x+16*A1* A2*u*x+64*A1*A2*x^2-12*A1*g1^2*x-12*A1*g1*g4*x-22*A1*g1*u*x-32*A1*g1*x^2-10*A1* g4*u*x-32*A1*g4*x^2-10*A1*u^2*x+10*A2^3*x-24*A2^2*g1*x-7*A2^2*g4*x-20*A2^2*u*x-\ 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*u^2*x-18336*g1*g4*u*x^2-456*g1*u^4-8376*g1*u^3*x-18632*g1*u^2*x^2-400*g4^3*u*x -1600*g4^3*x^2-64*g4^2*u^3-2504*g4^2*u^2*x-9168*g4^2*u*x^2-192*g4*u^4-5272*g4*u ^3*x-18632*g4*u^2*x^2-128*u^5-3408*u^4*x-12624*u^3*x^2+36*A0^4-72*A0^2*A1^2-524 *A0^2*A2^2+616*A0^2*A2*A3+1040*A0^2*A2*g1+576*A0^2*A2*g4+1754*A0^2*A2*u+1536*A0 ^2*A2*x+276*A0^2*A3^2-648*A0^2*A3*g1-440*A0^2*A3*g4-1082*A0^2*A3*u-96*A0^2*A3*x -396*A0^2*g1^2-520*A0^2*g1*g4-1282*A0^2*g1*u-1056*A0^2*g1*x-124*A0^2*g4^2-826* A0^2*g4*u-1056*A0^2*g4*x-970*A0^2*u^2-1816*A0^2*u*x+36*A1^4+532*A1^2*A2^2-536* A1^2*A2*A3-992*A1^2*A2*g1-528*A1^2*A2*g4-1638*A1^2*A2*u-1536*A1^2*A2*x-396*A1^2 *A3^2+584*A1^2*A3*g1+376*A1^2*A3*g4+702*A1^2*A3*u+96*A1^2*A3*x+388*A1^2*g1^2+ 504*A1^2*g1*g4+1262*A1^2*g1*u+1056*A1^2*g1*x+116*A1^2*g4^2+806*A1^2*g4*u+1056* A1^2*g4*x+926*A1^2*u^2+1816*A1^2*u*x+688*A2^4-1952*A2^3*A3-2832*A2^3*g1-976*A2^ 3*g4-3834*A2^3*u-10240*A2^3*x-1536*A2^2*A3^2+6760*A2^2*A3*g1+2472*A2^2*A3*g4+ 9726*A2^2*A3*u+15360*A2^2*A3*x+3652*A2^2*g1^2+2968*A2^2*g1*g4+10670*A2^2*g1*u+ 24032*A2^2*g1*x+324*A2^2*g4^2+3518*A2^2*g4*u+15968*A2^2*g4*x+7523*A2^2*u^2+ 42432*A2^2*u*x+18560*A2^2*x^2+800*A2*A3^3+1632*A2*A3^2*g1+672*A2*A3^2*g4-6*A2* A3^2*u+4480*A2*A3^2*x-6808*A2*A3*g1^2-5776*A2*A3*g1*g4-19576*A2*A3*g1*u-27168* A2*A3*g1*x-696*A2*A3*g4^2-6344*A2*A3*g4*u-18592*A2*A3*g4*x-14242*A2*A3*u^2-\ 61616*A2*A3*u*x-18880*A2*A3*x^2-1632*A2*g1^3-2288*A2*g1^2*g4-7580*A2*g1^2*u-\ 15936*A2*g1^2*x-656*A2*g1*g4^2-6144*A2*g1*g4*u-22720*A2*g1*g4*x-11090*A2*g1*u^2 -54856*A2*g1*u*x-21600*A2*g1*x^2-612*A2*g4^2*u-6784*A2*g4^2*x-3842*A2*g4*u^2-\ 35624*A2*g4*u*x-21600*A2*g4*x^2-5142*A2*u^3-48416*A2*u^2*x-50128*A2*u*x^2+560* A3^4-1736*A3^3*g1-776*A3^3*g4-1430*A3^3*u+372*A3^2*g1^2+408*A3^2*g1*g4+2306*A3^ 2*g1*u-3648*A3^2*g1*x+84*A3^2*g4^2+498*A3^2*g4*u-2752*A3^2*g4*x+2663*A3^2*u^2+ 5824*A3^2*u*x+1920*A3^2*x^2+1952*A3*g1^3+2816*A3*g1^2*g4+8296*A3*g1^2*u+11968* A3*g1^2*x+864*A3*g1*g4^2+6816*A3*g1*g4*u+17600*A3*g1*g4*x+11754*A3*g1*u^2+44992 *A3*g1*u*x+11360*A3*g1*x^2+624*A3*g4^2*u+5632*A3*g4^2*x+4042*A3*g4*u^2+30192*A3 *g4*u*x+11360*A3*g4*x^2+5410*A3*u^3+43048*A3*u^2*x+35048*A3*u*x^2+160*g1^4+320* g1^3*g4+1120*g1^3*u+2624*g1^3*x+160*g1^2*g4^2+1536*g1^2*g4*u+5824*g1^2*g4*x+ 2605*g1^2*u^2+13216*g1^2*u*x+5440*g1^2*x^2+416*g1*g4^2*u+3776*g1*g4^2*x+2154*g1 *g4*u^2+18336*g1*g4*u*x+10880*g1*g4*x^2+2490*g1*u^3+22616*g1*u^2*x+22288*g1*u*x ^2+576*g4^3*x+213*g4^2*u^2+5120*g4^2*u*x+5440*g4^2*x^2+938*g4*u^3+14648*g4*u^2* x+22288*g4*u*x^2+845*u^4+12624*u^3*x+23928*u^2*x^2-812*A0^2*A2+148*A0^2*A3+644* A0^2*g1+452*A0^2*g4+992*A0^2*u+480*A0^2*x+724*A1^2*A2+52*A1^2*A3-604*A1^2*g1-\ 412*A1^2*g4-824*A1^2*u-480*A1^2*x+2252*A2^3-3220*A2^2*A3-6508*A2^2*g1-2476*A2^2 *g4-9367*A2^2*u-18560*A2^2*x-1004*A2*A3^2+7096*A2*A3*g1+2808*A2*A3*g4+12974*A2* A3*u+18880*A2*A3*x+5160*A2*g1^2+4560*A2*g1*g4+15014*A2*g1*u+25504*A2*g1*x+584* A2*g4^2+5398*A2*g4*u+17696*A2*g4*x+10769*A2*u^2+50128*A2*u*x+18240*A2*x^2-92*A3 ^3+980*A3^2*g1+532*A3^2*g4-1183*A3^2*u-1920*A3^2*x-3680*A3*g1^2-3504*A3*g1*g4-\ 11726*A3*g1*u-13312*A3*g1*x-512*A3*g4^2-4326*A3*g4*u-9408*A3*g4*x-9141*A3*u^2-\ 35048*A3*u*x-11040*A3*x^2-1024*g1^3-1488*g1^2*g4-4431*g1^2*u-7424*g1^2*x-464*g1 *g4^2-3750*g1*g4*u-10880*g1*g4*x-6281*g1*u^2-26552*g1*u*x-8640*g1*x^2-383*g4^2* u-3456*g4^2*x-2297*g4*u^2-18024*g4*u*x-8640*g4*x^2-2874*u^3-23928*u^2*x-21480*u *x^2-288*A0^2+192*A1^2+3954*A2^2-3908*A2*A3-6636*A2*g1-2732*A2*g4-10709*A2*u-\ 18240*A2*x+466*A3^2+3332*A3*g1+1380*A3*g4+7333*A3*u+11040*A3*x+2298*g1^2+2180* g1*g4+6973*g1*u+10080*g1*x+314*g4^2+2709*g4*u+7200*g4*x+5169*u^2+21480*u*x+7200 *x^2+3814*A2-2318*A3-2542*g1-1102*g4-4524*u-7200*x+1500)*m3/(A3-1)/(A2-A3+1)/( A2-g1-g4-2*u+1+A3): ### sfPQA3ps1out 20221215 m2:=2*(1+A2+A3)*(A2-g1-g4-2*u+1-A3): # so that initial term is simple PA3p:= 1/2*m2*x^3*(x-1)^3*(2*A2^2*x-2*A2*g1*x-2*A2*g4*x-4*A2*u*x-2*A3^2*x-2* A3*g1*x-2*A3*g4*x-4*A3*u*x+A0^2-A1^2-A2^2+2*A2*g1+2*A2*u+4*A2*x+A3^2+2*A3*g1+2* A3*u-2*g1*x-2*g4*x-4*u*x-2*A2+2*g1+2*u+2*x-1)/(1+A2+A3)/(A2-g1-g4-2*u+1-A3)*dx^ 5+1/2*(x-1)^2*(8*A2^3*x^2-14*A2^2*g1*x^2-14*A2^2*g4*x^2-26*A2^2*u*x^2-8*A2*A3^2 *x^2-8*A2*A3*g1*x^2-8*A2*A3*g4*x^2-16*A2*A3*u*x^2+6*A2*g1^2*x^2+12*A2*g1*g4*x^2 +22*A2*g1*u*x^2+6*A2*g4^2*x^2+22*A2*g4*u*x^2+22*A2*u^2*x^2+6*A3^2*g1*x^2+6*A3^2 *g4*x^2+10*A3^2*u*x^2+6*A3*g1^2*x^2+12*A3*g1*g4*x^2+22*A3*g1*u*x^2+6*A3*g4^2*x^ 2+22*A3*g4*u*x^2+22*A3*u^2*x^2+4*A0^2*A2*x-3*A0^2*g1*x-3*A0^2*g4*x-6*A0^2*u*x-4 *A1^2*A2*x+3*A1^2*g1*x+3*A1^2*g4*x+6*A1^2*u*x-8*A2^3*x+21*A2^2*g1*x+7*A2^2*g4*x +26*A2^2*u*x+48*A2^2*x^2+8*A2*A3^2*x+12*A2*A3*g1*x+4*A2*A3*g4*x+16*A2*A3*u*x-12 *A2*g1^2*x-12*A2*g1*g4*x-34*A2*g1*u*x-52*A2*g1*x^2-10*A2*g4*u*x-52*A2*g4*x^2-22 *A2*u^2*x-106*A2*u*x^2-9*A3^2*g1*x-3*A3^2*g4*x-10*A3^2*u*x-32*A3^2*x^2-12*A3*g1 ^2*x-12*A3*g1*g4*x-34*A3*g1*u*x-32*A3*g1*x^2-10*A3*g4*u*x-32*A3*g4*x^2-22*A3*u^ 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