## G6PQ.txt   20221111
# refer to G6Nmemo.txt for notation.

# Svalues
S123np:=r*(-1+r)*(r-2)*(-r+e6)*(-r+e5)*(-r+e4):                         
S123pn:=r*(-1+r)*(r+1)*(-r-1+e6)*(-r-1+e5)*(-r-1+e4):                         
S456np:=-r*(-1+r)*(r-2)*(-r+e3)*(-r+e2)*(-r+e1):                         
S456pn:=-r*(-1+r)*(r+1)*(-r-1+e3)*(-r+e2-1)*(-r+e1-1):                         
S16n79p:=r*(-1+r)*(r+1)*(e8-1)*(e7-1)*(e9-1):
S16p79n:=r*e7*e8*e9*(-1+r)*(r-2):                         
S123n789p:=r^2*e9*e8*e7*(r+1)*(r-2)*(r-1)^2*(r+1-e3)*(r-e2+1)*(r-e1+1):

# shift operators 
P123n:=(-1+x)*dx-r:                         
Q123n:=(-1+x)*dx+3-r:                         
P456n:=x*dx-r:                         
Q456n:=3-r+x*dx:                         
P16n79p:=dx:                         
Q16n79p:=dx:                         

# shift operators
# P123p, P456p, P16p79n, P123n789p, P123p789n, P123p, P456p, P16p79n,
# are listed below

# for the decomposition of P123p as
# P123p= P123p0 +a0*P123pa0 +a1*P123pa1 +a2*P123pa2 +a3*P123pa3
#          +a4*P123pa4 +a5*P123pa5 +a6*P123pa6,
# P123p0, P123pa0, P123pa1, P123pa2, P123pa3, P123pa4, P123pa5, P123pa6
# are listed below.
# similarly for decompositions for P456p, P16p79n, P123p, P456p, P16p79n.

P123p:=x^3*(-1+x)^5*dx^5+x^2*(-1+x)^4*(11*x+e7*x+x*e9+e8*x-2*r*x+e1-9+e2+e3)*dx^4+1/3*x*(-1+x)^3*(57+3*r*x*e7+2*x*e1*e8-3*r*x*e1-147*x+3*r*x*e9+x*e5*e6+3*e1*e2+3*e1*e3+3*e2*e3-15*e1-15*e2-15*e3-21*e7*x-e7*x*e9+x*e1^2-3*r*x*e3+93*x^2+x*e3^2+x*e7^2+21*x^2*e9+21*e7*x^2-21*e8*x+36*r*x-39*r*x^2+15*e2*x+x*e8^2+15*x*e1+3*r^2*x^2-x*e4^2-x*e6^2+21*e8*x^2+2*e8*x*e2+2*x*e9*e1-3*r*x*e2-e7*x*e8-6*r*e7*x^2-6*r*e8*x^2-6*r*x^2*e9+3*e7*e8*x^2+3*e7*x^2*e9+3*e8*x^2*e9-21*x*e9+x*e9^2+x*e2^2+15*x*e3-x*e5^2+3*r*x*e8-e8*x*e9-x*e1*e2-x*e1*e3+x*e4*e5-e2*x*e3+x*e4*e6+2*x*e1*e7+2*e2*x*e7+2*e2*x*e9+2*x*e3*e7+2*x*e3*e8+2*x*e3*e9)*dx^3+1/54*(-1+x)^2*(-432+3*x*e5*e6^2-3*x^2*e1^2*e3+90*e3*x^2*e8+6*x^2*e3^2*e9+9*x*e1^2*e3-216*r*x*e7+6*e2*x*e8^2-126*x*e1*e8+216*e7*x^3*e9-6*x^2*e4^2*e8-18*r*x^2*e9^2+18*r*x*e2^2-54*x*a1*e1^2+3*x^2*e5*e6^2-18*r*x^2*e8^2-54*x*a6*e8^3+90*e2*x^2*e7+6*x^2*e1^2*e9+108*r*x*e1+9*e8*x^2*e9^2+18*r*x*e7^2+6*x*e1*e9^2-54*x*a2*e6^2-6*e2*x*e4^2+54*x^2*a2*e5^2-6*x^2*e4^2*e9-54*r^2*e8*x^2+9*x^2*e8^2*e9+234*e2*x^2-54*r^2*x^2*e9+9*e7*x^2*e9^2+54*x^2*a3*e7^2+1863*x+3*x^2*e4*e6^2-216*r*x*e9+18*r*x*e3^2+90*e2*x^2*e8-63*x*e5*e6+18*r*x*e5*e6-324*x*a4*e1*e2*e3-54*x*a2*e5^2-54*x*a0-54*x*a3*e9^2-108*e1*e2-108*e1*e3-108*e2*e3+216*e1+216*e2+216*e3+54*e1*e2*e3+558*e7*x+6*x^2*e3^2*e7-54*x*a4*e2^3+2*x^2*e3^3+63*e7*x*e9-18*r*x^2*e4*e5-324*x*a5*e4*e5*e6-45*x^2*e6^2-18*r*x^2*e7^2-63*x*e1^2+45*x^2*e8^2+6*x^2*e1^2*e8+108*r*x*e3+36*r*x*e1*e7-54*x*a3*e8^2-6*x*e1*e6^2-2673*x^2+1188*x^3+18*e1*x^2*e8*e9-81*x^2*a5*e5^2*e6-18*r*e7*e8*x-18*r*x*e1*e2+18*e8*x*e2*e3+81*x*a5*e4^2*e6+81*x*a6*e8^2*e7-918*r*x^3+540*x^3*e9+234*e1*x^2+234*e3*x^2+540*e8*x^3+540*e7*x^3+90*e1*x^2*e8-63*x*e3^2-63*x*e7^2-45*x^2*e4^2-1044*x^2*e9-1044*e7*x^2+558*e8*x-2*x*e6^3-702*r*x+1620*r*x^2-396*e2*x-2*x^2*e5^3-63*x*e8^2+45*x^2*e7^2-2*x*e5^3-396*x*e1+2*x*e7^3+45*x^2*e9^2-162*r^2*x^2+2*x*e9^3-2*x*e4^3+63*x*e4^2+63*x*e6^2+162*r^2*x^3-1044*e8*x^2+45*x^2*e3^2-6*e2*x^2*e7*e3-54*x*a1*e2^2-54*x*a2*e4^2-126*e8*x*e2-126*x*e9*e1+108*r*x*e2+63*e7*x*e8+594*r*e7*x^2-108*r*e1*x^2-108*r*e2*x^2+594*r*e8*x^2+594*r*x^2*e9-315*e7*e8*x^2-315*e7*x^2*e9-315*e8*x^2*e9-54*r^2*e7*x^2-378*r*e7*x^3-378*r*e8*x^3-378*r*x^3*e9+216*e7*e8*x^3+216*e8*x^3*e9+54*r^2*e7*x^3+54*r^2*e8*x^3+54*r^2*x^3*e9+558*x*e9-63*x*e9^2-2*x^2*e6^3+45*x^2*e2^2-63*x*e2^2-45*x^2*e5^2-396*x*e3+54*x^2*a0+63*x*e5^2-2*x^2*e4^3+45*x^2*e1^2+2*x^2*e2^3+2*x*e8^3+18*x*e9*e1*e2-18*r*x*e2*e3-18*r*x*e7*e9+12*e7*x*e8*e9+126*r*e7*e8*x^2+126*r*e7*x^2*e9+81*x*a4*e1^2*e3+18*r*x*e4*e5-18*r*x*e1*e3+18*r*e1*x^2*e3+36*r*x*e3*e9+6*e2*x*e5*e6+126*r*e8*x^2*e9-54*e7*e8*x^2*e9-108*r*e7*e8*x^3-108*r*e7*x^3*e9-108*r*e8*x^3*e9+54*e7*e8*x^3*e9+54*x*a3*e7*e8+54*x*a3*e8*e9+81*x*a5*e5^2*e4-18*r*x*e8*e9-6*x*e1*e8*e9+54*x*a2*e4*e6-54*x^2*a2*e4*e5+81*x*a5*e4^2*e5+36*r*x*e2*e8-18*r*x*e4^2-216*r*x*e8-54*x*a3*e7^2-3*x*e7^2*e9+2*x^2*e1^3-6*e1*x^2*e8*e3+81*x*a5*e5^2*e6-81*x^2*a6*e9^2*e8-36*r*x^2*e3*e8+54*x*a3*e7*e9+18*r*x*e4*e6+36*r*x*e1*e8+36*r*x*e1*e9+36*r*x*e2*e7+36*r*x*e2*e9+36*r*x*e3*e7+36*r*x*e3*e8+63*e8*x*e9-3*e1*x^2*e2^2+117*x*e1*e2+117*x*e1*e3-63*x*e4*e5+117*e2*x*e3-63*x*e4*e6-126*x*e1*e7-126*e2*x*e7+54*x^2*a2*e4^2-126*e2*x*e9-126*x*e3*e7-126*x*e3*e8-126*x*e3*e9+18*r*x*e1^2-18*r*x*e5^2-18*r*x*e6^2+18*r*x*e8^2+18*r*x*e9^2-108*r*x^2*e3-45*e1*x^2*e2-45*e1*x^2*e3+45*x^2*e4*e5-45*e2*x^2*e3+45*x^2*e4*e6+45*x^2*e5*e6+90*e1*x^2*e7+90*e1*x^2*e9+90*e2*x^2*e9+90*e3*x^2*e7+90*e3*x^2*e9+9*x*e2^2*e3-3*e7*x*e9^2+324*x^2*a4*e1*e2*e3-54*x*a4*e3^3+9*x*e1*e2^2-3*x*e8^2*e9+3*x*e4^2*e5+3*x*e4^2*e6+3*x*e4*e5^2+3*x*e5^2*e6+3*x*e4*e6^2+9*x*e1^2*e2+9*x*e1*e3^2+9*e2*x*e3^2-3*x*e7^2*e8-3*e7*x*e8^2-3*e8*x*e9^2-54*x*a1*e3^2-54*x*a4*e1^3-54*x*a5*e4^3-54*x*a5*e5^3-54*x*a5*e6^3-54*x*a6*e7^3-54*x*a6*e9^3-6*x^2*e6^2*e7+18*x*e1*e7*e3+54*x*a2*e5*e6+81*x*a6*e7^2*e8+81*x*a4*e1^2*e2+18*x*e1*e7*e2-6*x*e3*e8*e9+54*x*a2*e4*e5+54*x*a1*e1*e3-54*x*e1*e2*e3-12*x*e4*e5*e6+54*x*a1*e1*e2+81*x*a5*e6^2*e4+81*x*a5*e6^2*e5+81*x*a4*e2^2*e1+81*x*a4*e2^2*e3+81*x*a4*e3^2*e1+81*x*a4*e3^2*e2+18*e2*x*e7*e3+18*x*e1*e8*e2+18*x*e1*e8*e3+18*x*e9*e1*e3+18*e2*x*e9*e3-6*x*e1*e7*e8-6*x*e1*e7*e9-6*e2*x*e7*e8-6*e2*x*e7*e9-6*e8*x*e2*e9-6*x*e3*e7*e8-6*x*e3*e7*e9+81*x*a6*e7^2*e9+81*x*a6*e8^2*e9+81*x*a6*e9^2*e7+81*x*a6*e9^2*e8+54*x*a1*e2*e3+6*x^2*e2^2*e9-6*x^2*e5^2*e7+54*x^2*a5*e6^3-6*x^2*e4^2*e7-18*r*x^2*e2^2+9*e7*x^2*e8^2+3*x^2*e5^2*e6+54*x^2*a4*e1^3+18*r*x^2*e5^2+54*x^2*a6*e7^3+6*x^2*e3^2*e8-6*x^2*e5^2*e9+54*x^2*a5*e4^3+6*x^2*e2^2*e8-6*x^2*e6^2*e8+54*x^2*a4*e3^3+3*x^2*e4^2*e6+54*x^2*a1*e3^2+54*x^2*a6*e8^3-3*e1*x^2*e3^2-18*r*x^2*e3^2+54*x^2*a3*e9^2+54*x^2*a3*e8^2+3*x^2*e4*e5^2+9*x^2*e7^2*e9-6*x^2*e5^2*e8+6*x^2*e1^2*e7+3*x^2*e4^2*e5+54*x^2*a2*e6^2+9*x^2*e7^2*e8+6*x^2*e2^2*e7+18*r*x^2*e4^2+54*x^2*a6*e9^3-6*x^2*e6^2*e9-18*r*x^2*e1^2-3*e2*x^2*e3^2+54*x^2*a1*e1^2+54*x^2*a5*e5^3+18*r*x^2*e6^2-3*x^2*e1^2*e2+54*x^2*a4*e2^3-3*x^2*e2^2*e3+54*x^2*a1*e2^2-324*e7*x*e8*e9*a6+18*r*e1*x^2*e2+18*r*e2*x^2*e3-18*r*x^2*e4*e6-18*r*x^2*e5*e6-36*r*e1*x^2*e7-36*r*e1*x^2*e8-36*r*e1*x^2*e9-36*r*e2*x^2*e7-36*r*e2*x^2*e8-36*r*e2*x^2*e9-36*r*x^2*e3*e7-36*r*x^2*e3*e9+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  

P16p79n:=x^3*(-1+x)^3*dx^5+x^2*(-1+x)^2*(e8*x+e7*x+12*x-3*r*x+x*e9+e1-9+e2+e3)*dx^4+1/3*x*(-1+x)*(57+3*r*x*e7+2*x*e1*e8-6*r*x*e1-165*x+3*r*x*e9+x*e5*e6+3*e1*e2+3*e1*e3+3*e2*e3-15*e1-15*e2-15*e3-21*e7*x-e7*x*e9+x*e1^2-6*r*x*e3+111*x^2+x*e3^2+x*e7^2+24*x^2*e9+24*e7*x^2-21*e8*x+54*r*x-63*r*x^2+18*e2*x+x*e8^2+18*x*e1+9*r^2*x^2-x*e4^2-x*e6^2+24*e8*x^2+2*e8*x*e2+2*x*e9*e1-6*r*x*e2-e7*x*e8-9*r*e7*x^2-9*r*e8*x^2-9*r*x^2*e9+3*e7*e8*x^2+3*e7*x^2*e9+3*e8*x^2*e9-21*x*e9+x*e9^2+x*e2^2+18*x*e3-x*e5^2+3*r*x*e8-e8*x*e9-x*e1*e2-x*e1*e3+x*e4*e5-e2*x*e3+x*e4*e6+2*x*e1*e7+2*e2*x*e7+2*e2*x*e9+2*x*e3*e7+2*x*e3*e8+2*x*e3*e9)*dx^3+(-8+1/18*x*e5*e6^2-1/18*x^2*e1^2*e3+7/3*e3*x^2*e8+1/9*x^2*e3^2*e9+1/6*x*e1^2*e3-4*r*x*e7+1/9*e2*x*e8^2-7/3*x*e1*e8+5*e7*x^3*e9-1/9*x^2*e4^2*e8-2/3*r*x^2*e9^2+1/3*r*x*e2^2-x*a1*e1^2+1/18*x^2*e5*e6^2-2/3*r*x^2*e8^2-x*a6*e8^3+r^2*e1*x^2+7/3*e2*x^2*e7+1/9*x^2*e1^2*e9+5*r*x*e1+1/6*e8*x^2*e9^2+1/3*r*x*e7^2+1/9*x*e1*e9^2-x*a2*e6^2-1/9*e2*x*e4^2+x^2*a2*e5^2-1/9*x^2*e4^2*e9-2*r^2*e8*x^2+1/6*x^2*e8^2*e9+19/3*e2*x^2-2*r^2*x^2*e9+1/6*e7*x^2*e9^2+x^2*a3*e7^2+83/2*x+1/18*x^2*e4*e6^2-4*r*x*e9+1/3*r*x*e3^2+7/3*e2*x^2*e8-7/6*x*e5*e6+1/3*r*x*e5*e6-6*x*a4*e1*e2*e3-x*a2*e5^2-x*a0-x*a3*e9^2-2*e1*e2-2*e1*e3-2*e2*e3+4*e1+4*e2+4*e3+e1*e2*e3+31/3*e7*x+1/9*x^2*e3^2*e7-x*a4*e2^3+1/27*x^2*e3^3+7/6*e7*x*e9-2/3*r*x^2*e4*e5-6*x*a5*e4*e5*e6-7/6*x^2*e6^2-2/3*r*x^2*e7^2-7/6*x*e1^2+7/6*x^2*e8^2+1/9*x^2*e1^2*e8+5*r*x*e3+2/3*r*x*e1*e7-x*a3*e8^2-1/9*x*e1*e6^2-125/2*x^2+29*x^3+1/3*e1*x^2*e8*e9-3/2*x^2*a5*e5^2*e6-1/3*r*e7*e8*x-4/3*r*x*e1*e2+1/3*e8*x*e2*e3+3/2*x*a5*e4^2*e6+3/2*x*a6*e8^2*e7-29*r*x^3+13*x^3*e9+19/3*e1*x^2+19/3*e3*x^2+13*e8*x^3+13*e7*x^3+7/3*e1*x^2*e8-7/6*x*e3^2-7/6*x*e7^2-7/6*x^2*e4^2-70/3*x^2*e9-70/3*e7*x^2+31/3*e8*x-1/27*x*e6^3-20*r*x+49*r*x^2-31/3*e2*x-1/27*x^2*e5^3-7/6*x*e8^2+7/6*x^2*e7^2-1/27*x*e5^3-31/3*x*e1+1/27*x*e7^3+7/6*x^2*e9^2-9*r^2*x^2-r^3*x^3+1/27*x*e9^3-1/27*x*e4^3+7/6*x*e4^2+7/6*x*e6^2+9*r^2*x^3-70/3*e8*x^2+7/6*x^2*e3^2-1/9*e2*x^2*e7*e3-x*a1*e2^2-x*a2*e4^2-7/3*e8*x*e2-7/3*x*e9*e1+5*r*x*e2+7/6*e7*x*e8+16*r*e7*x^2-5*r*e1*x^2-5*r*e2*x^2+16*r*e8*x^2+16*r*x^2*e9-37/6*e7*e8*x^2-37/6*e7*x^2*e9-37/6*e8*x^2*e9-2*r^2*e7*x^2-12*r*e7*x^3-12*r*e8*x^3-12*r*x^3*e9+5*e7*e8*x^3+5*e8*x^3*e9+3*r^2*e7*x^3+3*r^2*e8*x^3+3*r^2*x^3*e9+31/3*x*e9-7/6*x*e9^2-1/27*x^2*e6^3+7/6*x^2*e2^2-7/6*x*e2^2-7/6*x^2*e5^2-31/3*x*e3+x^2*a0+7/6*x*e5^2-1/27*x^2*e4^3+7/6*x^2*e1^2+1/27*x^2*e2^3+1/27*x*e8^3+1/3*x*e9*e1*e2-4/3*r*x*e2*e3-1/3*r*x*e7*e9+2/9*e7*x*e8*e9+8/3*r*e7*e8*x^2+8/3*r*e7*x^2*e9+3/2*x*a4*e1^2*e3+1/3*r*x*e4*e5-4/3*r*x*e1*e3+2/3*r*e1*x^2*e3+2/3*r*x*e3*e9+1/9*e2*x*e5*e6+8/3*r*e8*x^2*e9-e7*e8*x^2*e9-3*r*e7*e8*x^3-3*r*e7*x^3*e9-3*r*e8*x^3*e9+e7*e8*x^3*e9+x*a3*e7*e8+x*a3*e8*e9+3/2*x*a5*e5^2*e4-1/3*r*x*e8*e9-1/9*x*e1*e8*e9+x*a2*e4*e6-x^2*a2*e4*e5+3/2*x*a5*e4^2*e5+2/3*r*x*e2*e8-1/3*r*x*e4^2-4*r*x*e8-x*a3*e7^2-1/18*x*e7^2*e9+1/27*x^2*e1^3-1/9*e1*x^2*e8*e3+3/2*x*a5*e5^2*e6-3/2*x^2*a6*e9^2*e8-4/3*r*x^2*e3*e8+x*a3*e7*e9+1/3*r*x*e4*e6+2/3*r*x*e1*e8+2/3*r*x*e1*e9+2/3*r*x*e2*e7+2/3*r*x*e2*e9+2/3*r*x*e3*e7+2/3*r*x*e3*e8+7/6*e8*x*e9-1/18*e1*x^2*e2^2+19/6*x*e1*e2+19/6*x*e1*e3-7/6*x*e4*e5+19/6*e2*x*e3-7/6*x*e4*e6-7/3*x*e1*e7-7/3*e2*x*e7+x^2*a2*e4^2-7/3*e2*x*e9-7/3*x*e3*e7-7/3*x*e3*e8-7/3*x*e3*e9+1/3*r*x*e1^2-1/3*r*x*e5^2-1/3*r*x*e6^2+1/3*r*x*e8^2+1/3*r*x*e9^2-5*r*x^2*e3-7/6*e1*x^2*e2-7/6*e1*x^2*e3+7/6*x^2*e4*e5-7/6*e2*x^2*e3+7/6*x^2*e4*e6+7/6*x^2*e5*e6+7/3*e1*x^2*e7+7/3*e1*x^2*e9+7/3*e2*x^2*e9+7/3*e3*x^2*e7+7/3*e3*x^2*e9+1/6*x*e2^2*e3-1/18*e7*x*e9^2+6*x^2*a4*e1*e2*e3-x*a4*e3^3+1/6*x*e1*e2^2-1/18*x*e8^2*e9+1/18*x*e4^2*e5+1/18*x*e4^2*e6+1/18*x*e4*e5^2+1/18*x*e5^2*e6+1/18*x*e4*e6^2+1/6*x*e1^2*e2+1/6*x*e1*e3^2+1/6*e2*x*e3^2-1/18*x*e7^2*e8-1/18*e7*x*e8^2-1/18*e8*x*e9^2-x*a1*e3^2-x*a4*e1^3-x*a5*e4^3-x*a5*e5^3-x*a5*e6^3-x*a6*e7^3-x*a6*e9^3-1/9*x^2*e6^2*e7+1/3*x*e1*e7*e3+x*a2*e5*e6+3/2*x*a6*e7^2*e8+3/2*x*a4*e1^2*e2+1/3*x*e1*e7*e2-1/9*x*e3*e8*e9+x*a2*e4*e5+x*a1*e1*e3-x*e1*e2*e3-2/9*x*e4*e5*e6+x*a1*e1*e2+3/2*x*a5*e6^2*e4+3/2*x*a5*e6^2*e5+3/2*x*a4*e2^2*e1+3/2*x*a4*e2^2*e3+3/2*x*a4*e3^2*e1+3/2*x*a4*e3^2*e2+1/3*e2*x*e7*e3+1/3*x*e1*e8*e2+1/3*x*e1*e8*e3+1/3*x*e9*e1*e3+1/3*e2*x*e9*e3-1/9*x*e1*e7*e8-1/9*x*e1*e7*e9-1/9*e2*x*e7*e8-1/9*e2*x*e7*e9-1/9*e8*x*e2*e9-1/9*x*e3*e7*e8-1/9*x*e3*e7*e9+3/2*x*a6*e7^2*e9+3/2*x*a6*e8^2*e9+3/2*x*a6*e9^2*e7+3/2*x*a6*e9^2*e8+x*a1*e2*e3+1/9*x^2*e2^2*e9-1/9*x^2*e5^2*e7+x^2*a5*e6^3-1/9*x^2*e4^2*e7-2/3*r*x^2*e2^2+1/6*e7*x^2*e8^2+1/18*x^2*e5^2*e6+x^2*a4*e1^3+2/3*r*x^2*e5^2+x^2*a6*e7^3+1/9*x^2*e3^2*e8-1/9*x^2*e5^2*e9+x^2*a5*e4^3+1/9*x^2*e2^2*e8-1/9*x^2*e6^2*e8+x^2*a4*e3^3+1/18*x^2*e4^2*e6+x^2*a1*e3^2+r^2*e2*x^2+x^2*a6*e8^3-1/18*e1*x^2*e3^2-2/3*r*x^2*e3^2+x^2*a3*e9^2+x^2*a3*e8^2+1/18*x^2*e4*e5^2+1/6*x^2*e7^2*e9-1/9*x^2*e5^2*e8+1/9*x^2*e1^2*e7+1/18*x^2*e4^2*e5+x^2*a2*e6^2+1/6*x^2*e7^2*e8+1/9*x^2*e2^2*e7+2/3*r*x^2*e4^2+x^2*a6*e9^3-1/9*x^2*e6^2*e9-2/3*r*x^2*e1^2-1/18*e2*x^2*e3^2+x^2*a1*e1^2+r^2*e3*x^2+x^2*a5*e5^3+2/3*r*x^2*e6^2-1/18*x^2*e1^2*e2+x^2*a4*e2^3-1/18*x^2*e2^2*e3+x^2*a1*e2^2-6*e7*x*e8*e9*a6+2/3*r*e1*x^2*e2+2/3*r*e2*x^2*e3-2/3*r*x^2*e4*e6-2/3*r*x^2*e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  

# P123p= P123p0 +a0*P123pa0 +a1*P123pa1 +a2*P123pa2 +a3*P123pa3
#          +a4*P123pa4 +a5*P123pa5 +a6*P123pa6
#
P123p0:=x^3*(-1+x)^5*dx^5+x^2*(-1+x)^4*(11*x+e7*x+x*e9+e8*x-2*r*x+e1-9+e2+e3)*dx^4+1/3*x*(-1+x)^3*(57+3*r*x*e7+2*x*e1*e8-3*r*x*e1-147*x+3*r*x*e9+x*e5*e6+3*e1*e2+3*e1*e3+3*e2*e3-15*e1-15*e2-15*e3-21*e7*x-e7*x*e9+x*e1^2-3*r*x*e3+93*x^2+x*e3^2+x*e7^2+21*x^2*e9+21*e7*x^2-21*e8*x+36*r*x-39*r*x^2+15*e2*x+x*e8^2+15*x*e1+3*r^2*x^2-x*e4^2-x*e6^2+21*e8*x^2+2*e8*x*e2+2*x*e9*e1-3*r*x*e2-e7*x*e8-6*r*e7*x^2-6*r*e8*x^2-6*r*x^2*e9+3*e7*e8*x^2+3*e7*x^2*e9+3*e8*x^2*e9-21*x*e9+x*e9^2+x*e2^2+15*x*e3-x*e5^2+3*r*x*e8-e8*x*e9-x*e1*e2-x*e1*e3+x*e4*e5-e2*x*e3+x*e4*e6+2*x*e1*e7+2*e2*x*e7+2*e2*x*e9+2*x*e3*e7+2*x*e3*e8+2*x*e3*e9)*dx^3+1/54*(-1+x)^2*(-432+3*x*e5*e6^2-3*x^2*e1^2*e3+90*e3*x^2*e8+6*x^2*e3^2*e9+9*x*e1^2*e3-216*r*x*e7+6*e2*x*e8^2-126*x*e1*e8+216*e7*x^3*e9-6*x^2*e4^2*e8-18*r*x^2*e9^2+18*r*x*e2^2+3*x^2*e5*e6^2-18*r*x^2*e8^2+90*e2*x^2*e7+6*x^2*e1^2*e9+108*r*x*e1+9*e8*x^2*e9^2+18*r*x*e7^2+6*x*e1*e9^2-6*e2*x*e4^2-6*x^2*e4^2*e9-54*r^2*e8*x^2+9*x^2*e8^2*e9+234*e2*x^2-54*r^2*x^2*e9+9*e7*x^2*e9^2+1863*x+3*x^2*e4*e6^2-216*r*x*e9+18*r*x*e3^2+90*e2*x^2*e8-63*x*e5*e6+18*r*x*e5*e6-108*e1*e2-108*e1*e3-108*e2*e3+216*e1+216*e2+216*e3+54*e1*e2*e3+558*e7*x+6*x^2*e3^2*e7+2*x^2*e3^3+63*e7*x*e9-18*r*x^2*e4*e5-45*x^2*e6^2-18*r*x^2*e7^2-63*x*e1^2+45*x^2*e8^2+6*x^2*e1^2*e8+108*r*x*e3+36*r*x*e1*e7-6*x*e1*e6^2-2673*x^2+1188*x^3+18*e1*x^2*e8*e9-18*r*e7*e8*x-18*r*x*e1*e2+18*e8*x*e2*e3-918*r*x^3+540*x^3*e9+234*e1*x^2+234*e3*x^2+540*e8*x^3+540*e7*x^3+90*e1*x^2*e8-63*x*e3^2-63*x*e7^2-45*x^2*e4^2-1044*x^2*e9-1044*e7*x^2+558*e8*x-2*x*e6^3-702*r*x+1620*r*x^2-396*e2*x-2*x^2*e5^3-63*x*e8^2+45*x^2*e7^2-2*x*e5^3-396*x*e1+2*x*e7^3+45*x^2*e9^2-162*r^2*x^2+2*x*e9^3-2*x*e4^3+63*x*e4^2+63*x*e6^2+162*r^2*x^3-1044*e8*x^2+45*x^2*e3^2-6*e2*x^2*e7*e3-126*e8*x*e2-126*x*e9*e1+108*r*x*e2+63*e7*x*e8+594*r*e7*x^2-108*r*e1*x^2-108*r*e2*x^2+594*r*e8*x^2+594*r*x^2*e9-315*e7*e8*x^2-315*e7*x^2*e9-315*e8*x^2*e9-54*r^2*e7*x^2-378*r*e7*x^3-378*r*e8*x^3-378*r*x^3*e9+216*e7*e8*x^3+216*e8*x^3*e9+54*r^2*e7*x^3+54*r^2*e8*x^3+54*r^2*x^3*e9+558*x*e9-63*x*e9^2-2*x^2*e6^3+45*x^2*e2^2-63*x*e2^2-45*x^2*e5^2-396*x*e3+63*x*e5^2-2*x^2*e4^3+45*x^2*e1^2+2*x^2*e2^3+2*x*e8^3+18*x*e9*e1*e2-18*r*x*e2*e3-18*r*x*e7*e9+12*e7*x*e8*e9+126*r*e7*e8*x^2+126*r*e7*x^2*e9+18*r*x*e4*e5-18*r*x*e1*e3+18*r*e1*x^2*e3+36*r*x*e3*e9+6*e2*x*e5*e6+126*r*e8*x^2*e9-54*e7*e8*x^2*e9-108*r*e7*e8*x^3-108*r*e7*x^3*e9-108*r*e8*x^3*e9+54*e7*e8*x^3*e9-18*r*x*e8*e9-6*x*e1*e8*e9+36*r*x*e2*e8-18*r*x*e4^2-216*r*x*e8-3*x*e7^2*e9+2*x^2*e1^3-6*e1*x^2*e8*e3-36*r*x^2*e3*e8+18*r*x*e4*e6+36*r*x*e1*e8+36*r*x*e1*e9+36*r*x*e2*e7+36*r*x*e2*e9+36*r*x*e3*e7+36*r*x*e3*e8+63*e8*x*e9-3*e1*x^2*e2^2+117*x*e1*e2+117*x*e1*e3-63*x*e4*e5+117*e2*x*e3-63*x*e4*e6-126*x*e1*e7-126*e2*x*e7-126*e2*x*e9-126*x*e3*e7-126*x*e3*e8-126*x*e3*e9+18*r*x*e1^2-18*r*x*e5^2-18*r*x*e6^2+18*r*x*e8^2+18*r*x*e9^2-108*r*x^2*e3-45*e1*x^2*e2-45*e1*x^2*e3+45*x^2*e4*e5-45*e2*x^2*e3+45*x^2*e4*e6+45*x^2*e5*e6+90*e1*x^2*e7+90*e1*x^2*e9+90*e2*x^2*e9+90*e3*x^2*e7+90*e3*x^2*e9+9*x*e2^2*e3-3*e7*x*e9^2+9*x*e1*e2^2-3*x*e8^2*e9+3*x*e4^2*e5+3*x*e4^2*e6+3*x*e4*e5^2+3*x*e5^2*e6+3*x*e4*e6^2+9*x*e1^2*e2+9*x*e1*e3^2+9*e2*x*e3^2-3*x*e7^2*e8-3*e7*x*e8^2-3*e8*x*e9^2-6*x^2*e6^2*e7+18*x*e1*e7*e3+18*x*e1*e7*e2-6*x*e3*e8*e9-54*x*e1*e2*e3-12*x*e4*e5*e6+18*e2*x*e7*e3+18*x*e1*e8*e2+18*x*e1*e8*e3+18*x*e9*e1*e3+18*e2*x*e9*e3-6*x*e1*e7*e8-6*x*e1*e7*e9-6*e2*x*e7*e8-6*e2*x*e7*e9-6*e8*x*e2*e9-6*x*e3*e7*e8-6*x*e3*e7*e9+6*x^2*e2^2*e9-6*x^2*e5^2*e7-6*x^2*e4^2*e7-18*r*x^2*e2^2+9*e7*x^2*e8^2+3*x^2*e5^2*e6+18*r*x^2*e5^2+6*x^2*e3^2*e8-6*x^2*e5^2*e9+6*x^2*e2^2*e8-6*x^2*e6^2*e8+3*x^2*e4^2*e6-3*e1*x^2*e3^2-18*r*x^2*e3^2+3*x^2*e4*e5^2+9*x^2*e7^2*e9-6*x^2*e5^2*e8+6*x^2*e1^2*e7+3*x^2*e4^2*e5+9*x^2*e7^2*e8+6*x^2*e2^2*e7+18*r*x^2*e4^2-6*x^2*e6^2*e9-18*r*x^2*e1^2-3*e2*x^2*e3^2+18*r*x^2*e6^2-3*x^2*e1^2*e2-3*x^2*e2^2*e3+18*r*e1*x^2*e2+18*r*e2*x^2*e3-18*r*x^2*e4*e6-18*r*x^2*e5*e6-36*r*e1*x^2*e7-36*r*e1*x^2*e8-36*r*e1*x^2*e9-36*r*e2*x^2*e7-36*r*e2*x^2*e8-36*r*e2*x^2*e9-36*r*x^2*e3*e7-36*r*x^2*e3*e9+6*x^2*e9*e4*e5+6*e7*x^2*e4*e5-6*e1*x^2*e9*e2-6*e1*x^2*e7*e3+6*e8*x^2*e4*e6+6*e8*x^2*e4*e5-6*e1*x^2*e7*e2+18*e3*x^2*e8*e9+12*e1*x^2*e2*e3-12*x^2*e4*e5*e6-6*e1*x^2*e8*e2-6*e2*x^2*e8*e3-6*e1*x^2*e9*e3-6*e2*x^2*e9*e3+6*e7*x^2*e4*e6+6*e7*x^2*e5*e6+6*e8*x^2*e5*e6+6*x^2*e9*e4*e6+6*x^2*e9*e5*e6+18*e1*x^2*e7*e8+18*e1*x^2*e7*e9+18*e2*x^2*e7*e8+18*e2*x^2*e7*e9+18*e2*x^2*e8*e9+18*e3*x^2*e7*e8+18*e3*x^2*e7*e9+6*x*e3*e7^2-6*x*e3*e4^2-6*x*e1*e5^2+6*x*e1*e7^2-6*e2*x*e5^2-6*e2*x*e6^2-6*x*e3*e5^2-6*x*e3*e6^2+6*x*e1*e8^2+6*e2*x*e7^2+6*e2*x*e9^2+6*x*e3*e8^2+6*x*e3*e9^2-6*x*e1*e4^2+6*x*e1*e4*e6+6*e2*x*e4*e5+6*e2*x*e4*e6+6*x*e1*e5*e6+6*x*e1*e4*e5+6*x*e3*e4*e6+6*x*e3*e4*e5+6*x*e3*e5*e6)*dx^2-1/54*(-1+r)*(-1+x)*(-27-6*x*e5*e6^2-3*x^2*e1^2*e3-6*e2*e4*e5+18*e3*x^2*e8-12*x*e3^2*e9-18*e9*e1*e2+6*x^2*e3^2*e9-12*x*e1^2*e8-6*e2*e4*e6+6*x*e1^2*e3-54*r*x*e7-36*x*e1*e8+108*e7*x^3*e9-6*x^2*e4^2*e8-6*e1*e5*e6-6*e1*e4*e5-6*e3*e4*e6+3*x^2*e5*e6^2+12*x*e4^2*e8-18*e7*e1*e3-6*e1*e4*e6+18*e2*x^2*e7+6*x^2*e1^2*e9+9*e8*x^2*e9^2-6*x^2*e4^2*e9-6*e3*e5*e6+9*x^2*e8^2*e9+18*e2*x^2+9*e7*x^2*e9^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e1*e4^2+3*e1*e7^2+81*e7*x*e8*e9-81*e7*e8*x^2*e9+27*e7*e8*x^3*e9)*(-1+r):   

P123pa0:=x*(-1+x)^3*dx^2-(-1+r)*(-1+x)^3*dx:                         
P123pa1:=(-1+x)^3*x*(-e1*e2+e1^2-e2*e3+e3^2+e2^2-e1*e3)*dx^2-(-1+r)*(-1+x)^3*(-e1*e2+e1^2-e2*e3+e3^2+e2^2-e1*e3)*dx:  
P123pa2:=(-1+x)^3*x*(e5^2-e4*e5-e5*e6+e6^2+e4^2-e4*e6)*dx^2-(-1+r)*(-1+x)^3*(e5^2-e4*e5-e5*e6+e6^2+e4^2-e4*e6)*dx:                         
P123pa3:=(-1+x)^3*x*(e8^2+e9^2+e7^2-e7*e8-e7*e9-e8*e9)*dx^2-(-1+r)*(-1+x)^3*(e8^2+e9^2+e7^2-e7*e8-e7*e9-e8*e9)*dx:  

P123pa4:=1/2*(-1+x)^3*x*(-2*e2+e1+e3)*(e2+e1-2*e3)*(-e2+2*e1-e3)*dx^2-1/2*(-1+r)*(-1+x)^3*(-2*e2+e1+e3)*(e2+e1-2*e3)*(-e2+2*e1-e3)*dx:  
P123pa5 =1/2*(-1+x)^3*x*(e5+e4-2*e6)*(e4-2*e5+e6)*(-e5+2*e4-e6)*dx^2-1/2*(-1+r)*(-1+x)^3*(e5+e4-2*e6)*(e4-2*e5+e6)*(-e5+2*e4-e6)*dx: 
P123pa6:=1/2*(-1+x)^3*x*(-2*e8+e7+e9)*(e8+e7-2*e9)*(2*e7-e8-e9)*dx^2-1/2*(-1+r)*(-1+x)^3*(-2*e8+e7+e9)*(e8+e7-2*e9)*(2*e7-e8-e9)*dx: 

# P456p= P456p0 +a0*P456pa0 +a1*P456pa1 +a2*P456pa2 +a3*P456pa3
#          +a4*P456pa4 +a5*P456pa5 +a6*P456pa6
# 
P456p0:=x^5*(-1+x)^3*dx^5+x^4*(-1+x)^2*(11*x+e7*x+x*e9+e8*x-2*r*x-r-8+e1+e2+e3)*dx^4+1/3*x^3*(-1+x)*(39+2*x*e1*e8-3*r*x*e1-129*x+x*e5*e6+3*e1*e2+3*e1*e3+3*e2*e3-12*e1-12*e2-12*e3+15*r-18*e7*x-e7*x*e9-3*r*e1-3*r*e2-3*r*e3+3*r^2+x*e1^2-3*r*x*e3+93*x^2+x*e3^2+x*e7^2+3*r^2*x+21*x^2*e9+21*e7*x^2-18*e8*x+15*r*x-39*r*x^2+15*e2*x+x*e8^2+15*x*e1+3*r^2*x^2-x*e4^2-x*e6^2+21*e8*x^2+2*e8*x*e2+2*x*e9*e1-3*r*x*e2-e7*x*e8-6*r*e7*x^2-6*r*e8*x^2-6*r*x^2*e9+3*e7*e8*x^2+3*e7*x^2*e9+3*e8*x^2*e9-18*x*e9+x*e9^2+x*e2^2+15*x*e3-x*e5^2-e8*x*e9-x*e1*e2-x*e1*e3+x*e4*e5-e2*x*e3+x*e4*e6+2*x*e1*e7+2*e2*x*e7+2*e2*x*e9+2*x*e3*e7+2*x*e3*e8+2*x*e3*e9)*dx^3+1/54*x^2*(-54+3*x*e5*e6^2-3*x^2*e1^2*e3+90*e3*x^2*e8+6*x^2*e3^2*e9+9*x*e1^2*e3-54*r*e2*e3+6*e2*x*e8^2-90*x*e1*e8+216*e7*x^3*e9-6*x^2*e4^2*e8-18*r*x^2*e9^2+3*x^2*e5*e6^2-18*r*x^2*e8^2+90*e2*x^2*e7+6*x^2*e1^2*e9+9*e8*x^2*e9^2+6*x*e1*e9^2-54*r*e1*e2-6*e2*x*e4^2-6*x^2*e4^2*e9+9*x^2*e8^2*e9-54*r*e1*e3+234*e2*x^2+9*e7*x^2*e9^2+1161*x+3*x^2*e4*e6^2+90*e2*x^2*e8-45*x*e5*e6-54*e1*e2-54*e1*e3-54*e2*e3+54*e1+54*e2+54*e3-162*r+54*e1*e2*e3+342*e7*x+6*x^2*e3^2*e7+2*x^2*e3^3+45*e7*x*e9-18*r*x^2*e4*e5+108*r*e1+108*r*e2+108*r*e3-162*r^2-45*x^2*e6^2+54*r^2*e1+54*r^2*e2+54*r^2*e3-18*r*x^2*e7^2-45*x*e1^2+45*x^2*e8^2+6*x^2*e1^2*e8-6*x*e1*e6^2-2295*x^2+1188*x^3+18*e1*x^2*e8*e9+18*e8*x*e2*e3-918*r*x^3+540*x^3*e9+234*e1*x^2+234*e3*x^2+540*e8*x^3+540*e7*x^3+90*e1*x^2*e8-45*x*e3^2-45*x*e7^2-45*x^2*e4^2-882*x^2*e9-882*e7*x^2+342*e8*x-2*x*e6^3+1080*r*x^2-288*e2*x-2*x^2*e5^3-45*x*e8^2+45*x^2*e7^2-2*x*e5^3-288*x*e1+2*x*e7^3+45*x^2*e9^2+2*x*e9^3-2*x*e4^3+45*x*e4^2+45*x*e6^2+162*r^2*x^3-882*e8*x^2+45*x^2*e3^2-6*e2*x^2*e7*e3-90*e8*x*e2-90*x*e9*e1+45*e7*x*e8+378*r*e7*x^2-108*r*e1*x^2-108*r*e2*x^2+378*r*e8*x^2+378*r*x^2*e9-261*e7*e8*x^2-261*e7*x^2*e9-261*e8*x^2*e9-378*r*e7*x^3-378*r*e8*x^3-378*r*x^3*e9+216*e7*e8*x^3+216*e8*x^3*e9+54*r^2*e7*x^3+54*r^2*e8*x^3+54*r^2*x^3*e9+342*x*e9-45*x*e9^2-2*x^2*e6^3+45*x^2*e2^2-45*x*e2^2-45*x^2*e5^2-288*x*e3+45*x*e5^2-2*x^2*e4^3+45*x^2*e1^2+2*x^2*e2^3+2*x*e8^3+18*x*e9*e1*e2+12*e7*x*e8*e9+72*r*e7*e8*x^2+72*r*e7*x^2*e9+18*r*e1*x^2*e3+6*e2*x*e5*e6+72*r*e8*x^2*e9-54*e7*e8*x^2*e9-108*r*e7*e8*x^3-108*r*e7*x^3*e9-108*r*e8*x^3*e9+54*e7*e8*x^3*e9-6*x*e1*e8*e9-54*r^3-3*x*e7^2*e9+2*x^2*e1^3-6*e1*x^2*e8*e3-36*r*x^2*e3*e8+45*e8*x*e9-3*e1*x^2*e2^2+99*x*e1*e2+99*x*e1*e3-45*x*e4*e5+99*e2*x*e3-45*x*e4*e6-90*x*e1*e7-90*e2*x*e7-90*e2*x*e9-90*x*e3*e7-90*x*e3*e8-90*x*e3*e9-108*r*x^2*e3-45*e1*x^2*e2-45*e1*x^2*e3+45*x^2*e4*e5-45*e2*x^2*e3+45*x^2*e4*e6+45*x^2*e5*e6+90*e1*x^2*e7+90*e1*x^2*e9+90*e2*x^2*e9+90*e3*x^2*e7+90*e3*x^2*e9+9*x*e2^2*e3-3*e7*x*e9^2+9*x*e1*e2^2-3*x*e8^2*e9+3*x*e4^2*e5+3*x*e4^2*e6+3*x*e4*e5^2+3*x*e5^2*e6+3*x*e4*e6^2+9*x*e1^2*e2+9*x*e1*e3^2+9*e2*x*e3^2-3*x*e7^2*e8-3*e7*x*e8^2-3*e8*x*e9^2-6*x^2*e6^2*e7+18*x*e1*e7*e3+18*x*e1*e7*e2-6*x*e3*e8*e9-54*x*e1*e2*e3-12*x*e4*e5*e6+18*e2*x*e7*e3+18*x*e1*e8*e2+18*x*e1*e8*e3+18*x*e9*e1*e3+18*e2*x*e9*e3-6*x*e1*e7*e8-6*x*e1*e7*e9-6*e2*x*e7*e8-6*e2*x*e7*e9-6*e8*x*e2*e9-6*x*e3*e7*e8-6*x*e3*e7*e9+6*x^2*e2^2*e9-6*x^2*e5^2*e7-6*x^2*e4^2*e7-18*r*x^2*e2^2+9*e7*x^2*e8^2+3*x^2*e5^2*e6+18*r*x^2*e5^2+6*x^2*e3^2*e8-6*x^2*e5^2*e9+6*x^2*e2^2*e8-6*x^2*e6^2*e8+3*x^2*e4^2*e6-3*e1*x^2*e3^2-18*r*x^2*e3^2+3*x^2*e4*e5^2+9*x^2*e7^2*e9-6*x^2*e5^2*e8+6*x^2*e1^2*e7+3*x^2*e4^2*e5+9*x^2*e7^2*e8+6*x^2*e2^2*e7+18*r*x^2*e4^2-6*x^2*e6^2*e9-18*r*x^2*e1^2-3*e2*x^2*e3^2+18*r*x^2*e6^2-3*x^2*e1^2*e2-3*x^2*e2^2*e3+18*r*e1*x^2*e2+18*r*e2*x^2*e3-18*r*x^2*e4*e6-18*r*x^2*e5*e6-36*r*e1*x^2*e7-36*r*e1*x^2*e8-36*r*e1*x^2*e9-36*r*e2*x^2*e7-36*r*e2*x^2*e8-36*r*e2*x^2*e9-36*r*x^2*e3*e7-36*r*x^2*e3*e9+6*x^2*e9*e4*e5+6*e7*x^2*e4*e5-6*e1*x^2*e9*e2-6*e1*x^2*e7*e3+6*e8*x^2*e4*e6+6*e8*x^2*e4*e5-6*e1*x^2*e7*e2+18*e3*x^2*e8*e9+12*e1*x^2*e2*e3-12*x^2*e4*e5*e6-6*e1*x^2*e8*e2-6*e2*x^2*e8*e3-6*e1*x^2*e9*e3-6*e2*x^2*e9*e3+6*e7*x^2*e4*e6+6*e7*x^2*e5*e6+6*e8*x^2*e5*e6+6*x^2*e9*e4*e6+6*x^2*e9*e5*e6+18*e1*x^2*e7*e8+18*e1*x^2*e7*e9+18*e2*x^2*e7*e8+18*e2*x^2*e7*e9+18*e2*x^2*e8*e9+18*e3*x^2*e7*e8+18*e3*x^2*e7*e9+6*x*e3*e7^2-6*x*e3*e4^2-6*x*e1*e5^2+6*x*e1*e7^2-6*e2*x*e5^2-6*e2*x*e6^2-6*x*e3*e5^2-6*x*e3*e6^2+6*x*e1*e8^2+6*e2*x*e7^2+6*e2*x*e9^2+6*x*e3*e8^2+6*x*e3*e9^2-6*x*e1*e4^2+6*x*e1*e4*e6+6*e2*x*e4*e5+6*e2*x*e4*e6+6*x*e1*e5*e6+6*x*e1*e4*e5+6*x*e3*e4*e6+6*x*e3*e4*e5+6*x*e3*e5*e6)*dx^2-1/54*x*(-1+r)*(54-3*x^2*e1^2*e3+18*e3*x^2*e8+6*x^2*e3^2*e9+54*r*e2*e3+108*e7*x^3*e9-6*x^2*e4^2*e8+3*x^2*e5*e6^2+18*e2*x^2*e7+6*x^2*e1^2*e9+9*e8*x^2*e9^2+54*r*e1*e2-6*x^2*e4^2*e9+9*x^2*e8^2*e9+54*r*e1*e3+18*e2*x^2+9*e7*x^2*e9^2+3*x^2*e4*e6^2+18*e2*x^2*e8+54*e1*e2+54*e1*e3+54*e2*e3-54*e1-54*e2-54*e3+162*r-54*e1*e2*e3+6*x^2*e3^2*e7+2*x^2*e3^3-108*r*e1-108*r*e2-108*r*e3+162*r^2-9*x^2*e6^2-54*r^2*e1-54*r^2*e2-54*r^2*e3+9*x^2*e8^2+6*x^2*e1^2*e8-135*x^2+108*x^3+18*e1*x^2*e8*e9-54*r*x^3+108*x^3*e9+18*e1*x^2+18*e3*x^2+108*e8*x^3+108*e7*x^3+18*e1*x^2*e8-9*x^2*e4^2-126*x^2*e9-126*e7*x^2-2*x^2*e5^3+9*x^2*e7^2+9*x^2*e9^2-126*e8*x^2+9*x^2*e3^2-6*e2*x^2*e7*e3-117*e7*e8*x^2-117*e7*x^2*e9-117*e8*x^2*e9-54*r*e7*x^3-54*r*e8*x^3-54*r*x^3*e9+108*e7*e8*x^3+108*e8*x^3*e9-2*x^2*e6^3+9*x^2*e2^2-9*x^2*e5^2-2*x^2*e4^3+9*x^2*e1^2+2*x^2*e2^3-54*e7*e8*x^2*e9-54*r*e7*e8*x^3-54*r*e7*x^3*e9-54*r*e8*x^3*e9+108*e7*e8*x^3*e9+54*r^3+2*x^2*e1^3-6*e1*x^2*e8*e3-3*e1*x^2*e2^2-9*e1*x^2*e2-9*e1*x^2*e3+9*x^2*e4*e5-9*e2*x^2*e3+9*x^2*e4*e6+9*x^2*e5*e6+18*e1*x^2*e7+18*e1*x^2*e9+18*e2*x^2*e9+18*e3*x^2*e7+18*e3*x^2*e9-6*x^2*e6^2*e7+6*x^2*e2^2*e9-6*x^2*e5^2*e7-6*x^2*e4^2*e7+9*e7*x^2*e8^2+3*x^2*e5^2*e6+6*x^2*e3^2*e8-6*x^2*e5^2*e9+6*x^2*e2^2*e8-6*x^2*e6^2*e8+3*x^2*e4^2*e6-3*e1*x^2*e3^2+3*x^2*e4*e5^2+9*x^2*e7^2*e9-6*x^2*e5^2*e8+6*x^2*e1^2*e7+3*x^2*e4^2*e5+9*x^2*e7^2*e8+6*x^2*e2^2*e7-6*x^2*e6^2*e9-3*e2*x^2*e3^2-3*x^2*e1^2*e2-3*x^2*e2^2*e3+6*x^2*e9*e4*e5+6*e7*x^2*e4*e5-6*e1*x^2*e9*e2-6*e1*x^2*e7*e3+6*e8*x^2*e4*e6+6*e8*x^2*e4*e5-6*e1*x^2*e7*e2+18*e3*x^2*e8*e9+12*e1*x^2*e2*e3-12*x^2*e4*e5*e6-6*e1*x^2*e8*e2-6*e2*x^2*e8*e3-6*e1*x^2*e9*e3-6*e2*x^2*e9*e3+6*e7*x^2*e4*e6+6*e7*x^2*e5*e6+6*e8*x^2*e5*e6+6*x^2*e9*e4*e6+6*x^2*e9*e5*e6+18*e1*x^2*e7*e8+18*e1*x^2*e7*e9+18*e2*x^2*e7*e8+18*e2*x^2*e7*e9+18*e2*x^2*e8*e9+18*e3*x^2*e7*e8+18*e3*x^2*e7*e9)*dx+r*(-1+r)*(-r^3+r^2*e1-3*r^2+r^2*e3+r^2*e2+2*r*e1-r*e2*e3-r*e1*e3-r*e1*e2+2*r*e2+2*r*e3-3*r+e1*e2*e3+e7*e8*x^3*e9-1+e1+e2+e3-e2*e3-e1*e3-e1*e2): 

P456pa0:=x^3*(-1+x)*dx^2-x^3*(-1+r)*dx:   
P456pa1:=x^3*(-e1*e2+e1^2-e2*e3+e3^2+e2^2-e1*e3)*(-1+x)*dx^2-x^3*(-1+r)*(-e1*e2+e1^2-e2*e3+e3^2+e2^2-e1*e3)*dx:  
P456pa2:=x^3*(e5^2-e4*e5-e5*e6+e6^2+e4^2-e4*e6)*(-1+x)*dx^2-x^3*(-1+r)*(e5^2-e4*e5-e5*e6+e6^2+e4^2-e4*e6)*dx:   
P456pa3:=x^3*(e8^2+e9^2+e7^2-e7*e8-e7*e9-e8*e9)*(-1+x)*dx^2-x^3*(-1+r)*(e8^2+e9^2+e7^2-e7*e8-e7*e9-e8*e9)*dx:    

P456pa4:=1/2*x^3*(-2*e2+e1+e3)*(e2+e1-2*e3)*(-e2+2*e1-e3)*(-1+x)*dx^2-1/2*x^3*(-1+r)*(-2*e2+e1+e3)*(e2+e1-2*e3)*(-e2+2*e1-e3)*dx: 
P456pa5 =1/2*x^3*(e5+e4-2*e6)*(e4-2*e5+e6)*(-e5+2*e4-e6)*(-1+x)*dx^2-1/2*x^3*(-1+r)*(e5+e4-2*e6)*(e4-2*e5+e6)*(-e5+2*e4-e6)*dx:
P456pa6:=1/2*x^3*(-2*e8+e7+e9)*(e8+e7-2*e9)*(2*e7-e8-e9)*(-1+x)*dx^2-1/2*x^3*(-1+r)*(-2*e8+e7+e9)*(e8+e7-2*e9)*(2*e7-e8-e9)*dx:  

# P16p79n= P16p79n0 +a0*P16p79na0 +a1*P16p79na1 +a2*P16p79na2 +a3*P16p79na3
#          +a4*P16p79na4 +a5*P16p79na5 +a6*P16p79na6
#
P16p79n0:=x^3*(-1+x)^3*dx^5+x^2*(-1+x)^2*(e8*x+e7*x+12*x-3*r*x+x*e9+e1-9+e2+e3)*dx^4+1/3*x*(-1+x)*(57+3*r*x*e7+2*x*e1*e8-6*r*x*e1-165*x+3*r*x*e9+x*e5*e6+3*e1*e2+3*e1*e3+3*e2*e3-15*e1-15*e2-15*e3-21*e7*x-e7*x*e9+x*e1^2-6*r*x*e3+111*x^2+x*e3^2+x*e7^2+24*x^2*e9+24*e7*x^2-21*e8*x+54*r*x-63*r*x^2+18*e2*x+x*e8^2+18*x*e1+9*r^2*x^2-x*e4^2-x*e6^2+24*e8*x^2+2*e8*x*e2+2*x*e9*e1-6*r*x*e2-e7*x*e8-9*r*e7*x^2-9*r*e8*x^2-9*r*x^2*e9+3*e7*e8*x^2+3*e7*x^2*e9+3*e8*x^2*e9-21*x*e9+x*e9^2+x*e2^2+18*x*e3-x*e5^2+3*r*x*e8-e8*x*e9-x*e1*e2-x*e1*e3+x*e4*e5-e2*x*e3+x*e4*e6+2*x*e1*e7+2*e2*x*e7+2*e2*x*e9+2*x*e3*e7+2*x*e3*e8+2*x*e3*e9)*dx^3+(-8+1/18*x*e5*e6^2-1/18*x^2*e1^2*e3+7/3*e3*x^2*e8+1/9*x^2*e3^2*e9+1/6*x*e1^2*e3-4*r*x*e7+1/9*e2*x*e8^2-7/3*x*e1*e8+5*e7*x^3*e9-1/9*x^2*e4^2*e8-2/3*r*x^2*e9^2+1/3*r*x*e2^2+1/18*x^2*e5*e6^2-2/3*r*x^2*e8^2+r^2*e1*x^2+7/3*e2*x^2*e7+1/9*x^2*e1^2*e9+5*r*x*e1+1/6*e8*x^2*e9^2+1/3*r*x*e7^2+1/9*x*e1*e9^2-1/9*e2*x*e4^2-1/9*x^2*e4^2*e9-2*r^2*e8*x^2+1/6*x^2*e8^2*e9+19/3*e2*x^2-2*r^2*x^2*e9+1/6*e7*x^2*e9^2+83/2*x+1/18*x^2*e4*e6^2-4*r*x*e9+1/3*r*x*e3^2+7/3*e2*x^2*e8-7/6*x*e5*e6+1/3*r*x*e5*e6-2*e1*e2-2*e1*e3-2*e2*e3+4*e1+4*e2+4*e3+e1*e2*e3+31/3*e7*x+1/9*x^2*e3^2*e7+1/27*x^2*e3^3+7/6*e7*x*e9-2/3*r*x^2*e4*e5-7/6*x^2*e6^2-2/3*r*x^2*e7^2-7/6*x*e1^2+7/6*x^2*e8^2+1/9*x^2*e1^2*e8+5*r*x*e3+2/3*r*x*e1*e7-1/9*x*e1*e6^2-125/2*x^2+29*x^3+1/3*e1*x^2*e8*e9-1/3*r*e7*e8*x-4/3*r*x*e1*e2+1/3*e8*x*e2*e3-29*r*x^3+13*x^3*e9+19/3*e1*x^2+19/3*e3*x^2+13*e8*x^3+13*e7*x^3+7/3*e1*x^2*e8-7/6*x*e3^2-7/6*x*e7^2-7/6*x^2*e4^2-70/3*x^2*e9-70/3*e7*x^2+31/3*e8*x-1/27*x*e6^3-20*r*x+49*r*x^2-31/3*e2*x-1/27*x^2*e5^3-7/6*x*e8^2+7/6*x^2*e7^2-1/27*x*e5^3-31/3*x*e1+1/27*x*e7^3+7/6*x^2*e9^2-9*r^2*x^2-r^3*x^3+1/27*x*e9^3-1/27*x*e4^3+7/6*x*e4^2+7/6*x*e6^2+9*r^2*x^3-70/3*e8*x^2+7/6*x^2*e3^2-1/9*e2*x^2*e7*e3-7/3*e8*x*e2-7/3*x*e9*e1+5*r*x*e2+7/6*e7*x*e8+16*r*e7*x^2-5*r*e1*x^2-5*r*e2*x^2+16*r*e8*x^2+16*r*x^2*e9-37/6*e7*e8*x^2-37/6*e7*x^2*e9-37/6*e8*x^2*e9-2*r^2*e7*x^2-12*r*e7*x^3-12*r*e8*x^3-12*r*x^3*e9+5*e7*e8*x^3+5*e8*x^3*e9+3*r^2*e7*x^3+3*r^2*e8*x^3+3*r^2*x^3*e9+31/3*x*e9-7/6*x*e9^2-1/27*x^2*e6^3+7/6*x^2*e2^2-7/6*x*e2^2-7/6*x^2*e5^2-31/3*x*e3+7/6*x*e5^2-1/27*x^2*e4^3+7/6*x^2*e1^2+1/27*x^2*e2^3+1/27*x*e8^3+1/3*x*e9*e1*e2-4/3*r*x*e2*e3-1/3*r*x*e7*e9+2/9*e7*x*e8*e9+8/3*r*e7*e8*x^2+8/3*r*e7*x^2*e9+1/3*r*x*e4*e5-4/3*r*x*e1*e3+2/3*r*e1*x^2*e3+2/3*r*x*e3*e9+1/9*e2*x*e5*e6+8/3*r*e8*x^2*e9-e7*e8*x^2*e9-3*r*e7*e8*x^3-3*r*e7*x^3*e9-3*r*e8*x^3*e9+e7*e8*x^3*e9-1/3*r*x*e8*e9-1/9*x*e1*e8*e9+2/3*r*x*e2*e8-1/3*r*x*e4^2-4*r*x*e8-1/18*x*e7^2*e9+1/27*x^2*e1^3-1/9*e1*x^2*e8*e3-4/3*r*x^2*e3*e8+1/3*r*x*e4*e6+2/3*r*x*e1*e8+2/3*r*x*e1*e9+2/3*r*x*e2*e7+2/3*r*x*e2*e9+2/3*r*x*e3*e7+2/3*r*x*e3*e8+7/6*e8*x*e9-1/18*e1*x^2*e2^2+19/6*x*e1*e2+19/6*x*e1*e3-7/6*x*e4*e5+19/6*e2*x*e3-7/6*x*e4*e6-7/3*x*e1*e7-7/3*e2*x*e7-7/3*e2*x*e9-7/3*x*e3*e7-7/3*x*e3*e8-7/3*x*e3*e9+1/3*r*x*e1^2-1/3*r*x*e5^2-1/3*r*x*e6^2+1/3*r*x*e8^2+1/3*r*x*e9^2-5*r*x^2*e3-7/6*e1*x^2*e2-7/6*e1*x^2*e3+7/6*x^2*e4*e5-7/6*e2*x^2*e3+7/6*x^2*e4*e6+7/6*x^2*e5*e6+7/3*e1*x^2*e7+7/3*e1*x^2*e9+7/3*e2*x^2*e9+7/3*e3*x^2*e7+7/3*e3*x^2*e9+1/6*x*e2^2*e3-1/18*e7*x*e9^2+1/6*x*e1*e2^2-1/18*x*e8^2*e9+1/18*x*e4^2*e5+1/18*x*e4^2*e6+1/18*x*e4*e5^2+1/18*x*e5^2*e6+1/18*x*e4*e6^2+1/6*x*e1^2*e2+1/6*x*e1*e3^2+1/6*e2*x*e3^2-1/18*x*e7^2*e8-1/18*e7*x*e8^2-1/18*e8*x*e9^2-1/9*x^2*e6^2*e7+1/3*x*e1*e7*e3+1/3*x*e1*e7*e2-1/9*x*e3*e8*e9-x*e1*e2*e3-2/9*x*e4*e5*e6+1/3*e2*x*e7*e3+1/3*x*e1*e8*e2+1/3*x*e1*e8*e3+1/3*x*e9*e1*e3+1/3*e2*x*e9*e3-1/9*x*e1*e7*e8-1/9*x*e1*e7*e9-1/9*e2*x*e7*e8-1/9*e2*x*e7*e9-1/9*e8*x*e2*e9-1/9*x*e3*e7*e8-1/9*x*e3*e7*e9+1/9*x^2*e2^2*e9-1/9*x^2*e5^2*e7-1/9*x^2*e4^2*e7-2/3*r*x^2*e2^2+1/6*e7*x^2*e8^2+1/18*x^2*e5^2*e6+2/3*r*x^2*e5^2+1/9*x^2*e3^2*e8-1/9*x^2*e5^2*e9+1/9*x^2*e2^2*e8-1/9*x^2*e6^2*e8+1/18*x^2*e4^2*e6+r^2*e2*x^2-1/18*e1*x^2*e3^2-2/3*r*x^2*e3^2+1/18*x^2*e4*e5^2+1/6*x^2*e7^2*e9-1/9*x^2*e5^2*e8+1/9*x^2*e1^2*e7+1/18*x^2*e4^2*e5+1/6*x^2*e7^2*e8+1/9*x^2*e2^2*e7+2/3*r*x^2*e4^2-1/9*x^2*e6^2*e9-2/3*r*x^2*e1^2-1/18*e2*x^2*e3^2+r^2*e3*x^2+2/3*r*x^2*e6^2-1/18*x^2*e1^2*e2-1/18*x^2*e2^2*e3+2/3*r*e1*x^2*e2+2/3*r*e2*x^2*e3-2/3*r*x^2*e4*e6-2/3*r*x^2*e5*e6-4/3*r*e1*x^2*e7-4/3*r*e1*x^2*e8-4/3*r*e1*x^2*e9-4/3*r*e2*x^2*e7-4/3*r*e2*x^2*e8-4/3*r*e2*x^2*e9-4/3*r*x^2*e3*e7-4/3*r*x^2*e3*e9+1/9*x^2*e9*e4*e5+1/9*e7*x^2*e4*e5-1/9*e1*x^2*e9*e2-1/9*e1*x^2*e7*e3+1/9*e8*x^2*e4*e6+1/9*e8*x^2*e4*e5-1/9*e1*x^2*e7*e2+1/3*e3*x^2*e8*e9+2/9*e1*x^2*e2*e3-2/9*x^2*e4*e5*e6-1/9*e1*x^2*e8*e2-1/9*e2*x^2*e8*e3-1/9*e1*x^2*e9*e3-1/9*e2*x^2*e9*e3+1/9*e7*x^2*e4*e6+1/9*e7*x^2*e5*e6+1/9*e8*x^2*e5*e6+1/9*x^2*e9*e4*e6+1/9*x^2*e9*e5*e6+1/3*e1*x^2*e7*e8+1/3*e1*x^2*e7*e9+1/3*e2*x^2*e7*e8+1/3*e2*x^2*e7*e9+1/3*e2*x^2*e8*e9+1/3*e3*x^2*e7*e8+1/3*e3*x^2*e7*e9+1/9*x*e3*e7^2-1/9*x*e3*e4^2-1/9*x*e1*e5^2+1/9*x*e1*e7^2-1/9*e2*x*e5^2-1/9*e2*x*e6^2-1/9*x*e3*e5^2-1/9*x*e3*e6^2+1/9*x*e1*e8^2+1/9*e2*x*e7^2+1/9*e2*x*e9^2+1/9*x*e3*e8^2+1/9*x*e3*e9^2-1/9*x*e1*e4^2+1/9*x*e1*e4*e6+1/9*e2*x*e4*e5+1/9*e2*x*e4*e6+1/9*x*e1*e5*e6+1/9*x*e1*e4*e5+1/9*x*e3*e4*e6+1/9*x*e3*e4*e5+1/9*x*e3*e5*e6)*dx^2-1/54*(-1+r)*(81+6*x*e5*e6^2+6*e2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 

P16p79na0:=x*(-1+x)*dx^2-(-1+r)*(2*x-1)*dx+r*(-1+r):  
P16p79na1:=x*(-e1*e2+e1^2-e2*e3+e3^2+e2^2-e1*e3)*(-1+x)*dx^2-(-1+r)*(-e1*e2+e1^2-e2*e3+e3^2+e2^2-e1*e3)*(2*x-1)*dx+r*(-1+r)*(-e1*e2+e1^2-e2*e3+e3^2+e2^2-e1*e3): 
P16p79na2:=x*(e5^2-e4*e5-e5*e6+e6^2+e4^2-e4*e6)*(-1+x)*dx^2-(-1+r)*(e5^2-e4*e5-e5*e6+e6^2+e4^2-e4*e6)*(2*x-1)*dx+r*(-1+r)*(e5^2-e4*e5-e5*e6+e6^2+e4^2-e4*e6):
P16p79na3:=x*(e8^2+e9^2+e7^2-e7*e8-e7*e9-e8*e9)*(-1+x)*dx^2-(-1+r)*(e8^2+e9^2+e7^2-e7*e8-e7*e9-e8*e9)*(2*x-1)*dx+r*(-1+r)*(e8^2+e9^2+e7^2-e7*e8-e7*e9-e8*e9):

P16p79na4:=1/2*x*(-2*e2+e1+e3)*(e2+e1-2*e3)*(-e2+2*e1-e3)*(-1+x)*dx^2-1/2*(-1+r)*(-2*e2+e1+e3)*(e2+e1-2*e3)*(-e2+2*e1-e3)*(2*x-1)*dx+1/2*r*(-1+r)*(-2*e2+e1+e3)*(e2+e1-2*e3)*(-e2+2*e1-e3):  
P16p79na5 =1/2*x*(e5+e4-2*e6)*(e4-2*e5+e6)*(-e5+2*e4-e6)*(-1+x)*dx^2-1/2*(-1+r)*(e5+e4-2*e6)*(e4-2*e5+e6)*(-e5+2*e4-e6)*(2*x-1)*dx+1/2*r*(-1+r)*(e5+e4-2*e6)*(e4-2*e5+e6)*(-e5+2*e4-e6):  
P16p79na6:=1/2*x*(-2*e8+e7+e9)*(e8+e7-2*e9)*(2*e7-e8-e9)*(-1+x)*dx^2-1/2*(-1+r)*(-2*e8+e7+e9)*(e8+e7-2*e9)*(2*e7-e8-e9)*(2*x-1)*dx+1/2*r*(-1+r)*(-2*e8+e7+e9)*(e8+e7-2*e9)*(2*e7-e8-e9):