Ptolemy
Geogebra sheet
Coq statement
Lemma Ptolemy: forall A B C D O:point, forall x4 x5 x6:R,
X A = 0 -> Y A = 0 ->
equaldistance O A O B ->
equaldistance O A O C ->
equaldistance O A O D ->
(distance2 A B) * (distance2 C D) = x4^2 ->
(distance2 B C) * (distance2 A D) = x5^2 ->
(distance2 B D) * (distance2 A C) = x6^2 ->
(x4 + x5 - x6) * (x4 + x5 + x6) * (x4 - (x5 - x6)) * (x4 - (x5 + x6)) = 0
\/ ((X C - X A)^2 + (Y C - Y A)^2)^2 = 0
\/ Y B = 0
\/ ((X B - X A)^2 + (Y B - Y A)^2)^2 = 0
\/ (Y B * X C - X B * Y C)^2 = 0.
Proof.
geo_begin.
tzRpv 0%Z (Y B::X B::X C::Y C::Y D::nil)
(Y O::X O::X D::x4::x5::x6::nil).
Qed.
Algebraic version
p:= ((u1^7+u1^3*u2^4+2*u1^5*u2^2)*u3^6+(u1*u2^6+2*u1^3*u2^4+u1^5*u2^2)*u4^6+(((-2)*u1^2*u2^5+(-4)*u1^4*u2^3+(-2)*u1^6*u2)*u3)*u4^5+((u1^7+2*u1*u2^6+5*u1^3*u2^4+4*u1^5*u2^2)*u3^2)*u4^4+(((-4)*u1^2*u2^5+(-8)*u1^4*u2^3+(-4)*u1^6*u2)*u3^3)*u4^3+((2*u1^7+u1*u2^6+4*u1^3*u2^4+5*u1^5*u2^2)*u3^4)*u4^2+(((-2)*u1^2*u2^5+(-4)*u1^4*u2^3+(-2)*u1^6*u2)*u3^5)*u4) *i^4 + (((-2)*u1^7+(-2)*u1^3*u2^4+(-4)*u1^5*u2^2)*u3^6+((-2)*u1*u2^6+(-4)*u1^3*u2^4+(-2)*u1^5*u2^2)*u4^6+((4*u1^2*u2^5+8*u1^4*u2^3+4*u1^6*u2)*u3)*u4^5+(((-2)*u1^7+(-4)*u1*u2^6+(-10)*u1^3*u2^4+(-8)*u1^5*u2^2)*u3^2)*u4^4+((8*u1^2*u2^5+16*u1^4*u2^3+8*u1^6*u2)*u3^3)*u4^3+(((-4)*u1^7+(-2)*u1*u2^6+(-8)*u1^3*u2^4+(-10)*u1^5*u2^2)*u3^4)*u4^2+((4*u1^2*u2^5+8*u1^4*u2^3+4*u1^6*u2)*u3^5)*u4) *i^2*j^2 + ((u1^7+u1^3*u2^4+2*u1^5*u2^2)*u3^6+(u1*u2^6+2*u1^3*u2^4+u1^5*u2^2)*u4^6+(((-2)*u1^2*u2^5+(-4)*u1^4*u2^3+(-2)*u1^6*u2)*u3)*u4^5+((u1^7+2*u1*u2^6+5*u1^3*u2^4+4*u1^5*u2^2)*u3^2)*u4^4+(((-4)*u1^2*u2^5+(-8)*u1^4*u2^3+(-4)*u1^6*u2)*u3^3)*u4^3+((2*u1^7+u1*u2^6+4*u1^3*u2^4+5*u1^5*u2^2)*u3^4)*u4^2+(((-2)*u1^2*u2^5+(-4)*u1^4*u2^3+(-2)*u1^6*u2)*u3^5)*u4) *j^4 + (((-2)*u1^7+(-2)*u1^3*u2^4+(-4)*u1^5*u2^2)*u3^6+((-2)*u1*u2^6+(-4)*u1^3*u2^4+(-2)*u1^5*u2^2)*u4^6+((4*u1^2*u2^5+8*u1^4*u2^3+4*u1^6*u2)*u3)*u4^5+(((-2)*u1^7+(-4)*u1*u2^6+(-10)*u1^3*u2^4+(-8)*u1^5*u2^2)*u3^2)*u4^4+((8*u1^2*u2^5+16*u1^4*u2^3+8*u1^6*u2)*u3^3)*u4^3+(((-4)*u1^7+(-2)*u1*u2^6+(-8)*u1^3*u2^4+(-10)*u1^5*u2^2)*u3^4)*u4^2+((4*u1^2*u2^5+8*u1^4*u2^3+4*u1^6*u2)*u3^5)*u4) *i^2*k^2 + (((-2)*u1^7+(-2)*u1^3*u2^4+(-4)*u1^5*u2^2)*u3^6+((-2)*u1*u2^6+(-4)*u1^3*u2^4+(-2)*u1^5*u2^2)*u4^6+((4*u1^2*u2^5+8*u1^4*u2^3+4*u1^6*u2)*u3)*u4^5+(((-2)*u1^7+(-4)*u1*u2^6+(-10)*u1^3*u2^4+(-8)*u1^5*u2^2)*u3^2)*u4^4+((8*u1^2*u2^5+16*u1^4*u2^3+8*u1^6*u2)*u3^3)*u4^3+(((-4)*u1^7+(-2)*u1*u2^6+(-8)*u1^3*u2^4+(-10)*u1^5*u2^2)*u3^4)*u4^2+((4*u1^2*u2^5+8*u1^4*u2^3+4*u1^6*u2)*u3^5)*u4) *j^2*k^2 + ((u1^7+u1^3*u2^4+2*u1^5*u2^2)*u3^6+(u1*u2^6+2*u1^3*u2^4+u1^5*u2^2)*u4^6+(((-2)*u1^2*u2^5+(-4)*u1^4*u2^3+(-2)*u1^6*u2)*u3)*u4^5+((u1^7+2*u1*u2^6+5*u1^3*u2^4+4*u1^5*u2^2)*u3^2)*u4^4+(((-4)*u1^2*u2^5+(-8)*u1^4*u2^3+(-4)*u1^6*u2)*u3^3)*u4^3+((2*u1^7+u1*u2^6+4*u1^3*u2^4+5*u1^5*u2^2)*u3^4)*u4^2+(((-2)*u1^2*u2^5+(-4)*u1^4*u2^3+(-2)*u1^6*u2)*u3^5)*u4) *k^4
F:= [
(2*u1) *f + (2*u2) *g + ((-1)*u1^2+(-1)*u2^2) ;
(2*u4) *f + (2*u3) *g + ((-1)*u3^2+(-1)*u4^2) ;
(2) *g*h + ((-1)) *h^2 + (2*u5) *f + ((-1)*u5^2) ;
(u1^2+u2^2) *h^2 + ((-1)) *i^2 + (((-2)*u1^2+(-2)*u2^2)*u3) *h + ((u1^2+u2^2)*u3^2+(u1^2+u2^2)*u4^2+(u1^2+u2^2)*u5^2+(((-2)*u1^2+(-2)*u2^2)*u4)*u5) ;
(u1^2+u2^2+u3^2+(-2)*u2*u3+u4^2+(-2)*u1*u4) *h^2 + ((-1)) *j^2 + ((u1^2+u2^2+u3^2+(-2)*u2*u3+u4^2+(-2)*u1*u4)*u5^2) ;
(u3^2+u4^2) *h^2 + ((-1)) *k^2 + ((-2)*u2*u3^2+(-2)*u2*u4^2) *h + ((u1^2+u2^2)*u3^2+(u1^2+u2^2)*u4^2+(u3^2+u4^2)*u5^2+((-2)*u1*u3^2+(-2)*u1*u4^2)*u5) ;
];
Certificate
CR:=[
(((-4)*u1^6+(-4)*u1^4*u2^2)*u3^3+(4*u1*u2^5+4*u1^3*u2^3)*u4^3+(((-12)*u1^2*u2^4+(-12)*u1^4*u2^2)*u3)*u4^2+((12*u1^3*u2^3+12*u1^5*u2)*u3^2)*u4) *k^2 + ((8*u1^4*u2^3+8*u1^6*u2)*u3^6+(4*u1^8+(-12)*u1^4*u2^4+(-8)*u1^6*u2^2)*u3^5+(8*u1^2*u2^5+8*u1^4*u2^3)*u4^6+(4*u1*u2^7+(-8)*u1^3*u2^5+(-12)*u1^5*u2^3+((-16)*u1^3*u2^4+(-16)*u1^5*u2^2)*u3)*u4^5+((16*u1^2*u2^5+24*u1^4*u2^3+8*u1^6*u2)*u3^2+((-20)*u1^2*u2^6+8*u1^4*u2^4+28*u1^6*u2^2)*u3)*u4^4+(((-32)*u1^3*u2^4+(-32)*u1^5*u2^2)*u3^3+(4*u1*u2^7+20*u1^3*u2^5+(-4)*u1^5*u2^3+(-20)*u1^7*u2)*u3^2)*u4^3+((8*u1^2*u2^5+24*u1^4*u2^3+16*u1^6*u2)*u3^4+(4*u1^8+(-20)*u1^2*u2^6+(-4)*u1^4*u2^4+20*u1^6*u2^2)*u3^3)*u4^2+(((-16)*u1^3*u2^4+(-16)*u1^5*u2^2)*u3^5+(28*u1^3*u2^5+8*u1^5*u2^3+(-20)*u1^7*u2)*u3^4)*u4+(((-8)*u1^3*u2^3+(-8)*u1^5*u2)*u3^6+((-4)*u1^7+12*u1^3*u2^4+8*u1^5*u2^2)*u3^5+((-8)*u1*u2^5+(-8)*u1^3*u2^3)*u4^6+((-4)*u2^7+8*u1^2*u2^5+12*u1^4*u2^3+(16*u1^2*u2^4+16*u1^4*u2^2)*u3)*u4^5+(((-16)*u1*u2^5+(-24)*u1^3*u2^3+(-8)*u1^5*u2)*u3^2+(20*u1*u2^6+(-8)*u1^3*u2^4+(-28)*u1^5*u2^2)*u3)*u4^4+((32*u1^2*u2^4+32*u1^4*u2^2)*u3^3+((-4)*u2^7+(-20)*u1^2*u2^5+4*u1^4*u2^3+20*u1^6*u2)*u3^2)*u4^3+(((-8)*u1*u2^5+(-24)*u1^3*u2^3+(-16)*u1^5*u2)*u3^4+((-4)*u1^7+20*u1*u2^6+4*u1^3*u2^4+(-20)*u1^5*u2^2)*u3^3)*u4^2+((16*u1^2*u2^4+16*u1^4*u2^2)*u3^5+((-28)*u1^2*u2^5+(-8)*u1^4*u2^3+20*u1^6*u2)*u3^4)*u4)*u5) ; (((-4)*u1^6+(-4)*u1^4*u2^2)*u3^6+(8*u1^4*u2^3+8*u1^6*u2)*u3^5+((-4)*u1^2*u2^4+(-4)*u1^4*u2^2)*u4^6+((-4)*u1*u2^6+4*u1^5*u2^2+(8*u1^3*u2^3+8*u1^5*u2)*u3)*u4^5+(((-4)*u1^6+(-8)*u1^2*u2^4+(-12)*u1^4*u2^2)*u3^2+(16*u1^2*u2^5+8*u1^4*u2^3+(-8)*u1^6*u2)*u3)*u4^4+((16*u1^3*u2^3+16*u1^5*u2)*u3^3+(4*u1^7+(-4)*u1*u2^6+(-20)*u1^3*u2^4+(-12)*u1^5*u2^2)*u3^2)*u4^3+(((-8)*u1^6+(-4)*u1^2*u2^4+(-12)*u1^4*u2^2)*u3^4+(16*u1^2*u2^5+16*u1^4*u2^3)*u3^3)*u4^2+((8*u1^3*u2^3+8*u1^5*u2)*u3^5+(4*u1^7+(-20)*u1^3*u2^4+(-16)*u1^5*u2^2)*u3^4)*u4+(((-4)*u1^3*u2^3+(-4)*u1^5*u2)*u3^5+(4*u2^6+4*u1^2*u2^4)*u4^5+(((-12)*u1*u2^5+(-12)*u1^3*u2^3)*u3)*u4^4+((4*u2^6+16*u1^2*u2^4+12*u1^4*u2^2)*u3^2)*u4^3+(((-12)*u1*u2^5+(-16)*u1^3*u2^3+(-4)*u1^5*u2)*u3^3)*u4^2+((12*u1^2*u2^4+12*u1^4*u2^2)*u3^4)*u4)*u5) ; ((4*u1^10+4*u1^4*u2^6+12*u1^6*u2^4+12*u1^8*u2^2)*u3^8+((-8)*u1^4*u2^7+(-24)*u1^6*u2^5+(-24)*u1^8*u2^3+(-8)*u1^10*u2)*u3^7+(4*u1^2*u2^8+12*u1^4*u2^6+12*u1^6*u2^4+4*u1^8*u2^2)*u4^8+(4*u1*u2^10+8*u1^3*u2^8+(-8)*u1^7*u2^4+(-4)*u1^9*u2^2+((-8)*u1^3*u2^7+(-24)*u1^5*u2^5+(-24)*u1^7*u2^3+(-8)*u1^9*u2)*u3)*u4^7+((4*u1^10+12*u1^2*u2^8+40*u1^4*u2^6+48*u1^6*u2^4+24*u1^8*u2^2)*u3^2+((-16)*u1^2*u2^9+(-40)*u1^4*u2^7+(-24)*u1^6*u2^5+8*u1^8*u2^3+8*u1^10*u2)*u3)*u4^6+(((-24)*u1^3*u2^7+(-72)*u1^5*u2^5+(-72)*u1^7*u2^3+(-24)*u1^9*u2)*u3^3+((-4)*u1^11+8*u1*u2^10+36*u1^3*u2^8+56*u1^5*u2^6+32*u1^7*u2^4)*u3^2)*u4^5+((12*u1^10+12*u1^2*u2^8+48*u1^4*u2^6+72*u1^6*u2^4+48*u1^8*u2^2)*u3^4+((-32)*u1^2*u2^9+(-88)*u1^4*u2^7+(-72)*u1^6*u2^5+(-8)*u1^8*u2^3+8*u1^10*u2)*u3^3)*u4^4+(((-24)*u1^3*u2^7+(-72)*u1^5*u2^5+(-72)*u1^7*u2^3+(-24)*u1^9*u2)*u3^5+((-8)*u1^11+4*u1*u2^10+48*u1^3*u2^8+112*u1^5*u2^6+88*u1^7*u2^4+12*u1^9*u2^2)*u3^4)*u4^3+((12*u1^10+4*u1^2*u2^8+24*u1^4*u2^6+48*u1^6*u2^4+40*u1^8*u2^2)*u3^6+((-16)*u1^2*u2^9+(-56)*u1^4*u2^7+(-72)*u1^6*u2^5+(-40)*u1^8*u2^3+(-8)*u1^10*u2)*u3^5)*u4^2+(((-8)*u1^3*u2^7+(-24)*u1^5*u2^5+(-24)*u1^7*u2^3+(-8)*u1^9*u2)*u3^7+((-4)*u1^11+20*u1^3*u2^8+56*u1^5*u2^6+48*u1^7*u2^4+8*u1^9*u2^2)*u3^6)*u4+((4*u1^8+(-4)*u1^2*u2^6+(-4)*u1^4*u2^4+4*u1^6*u2^2)*u3^8+(4*u1^2*u2^7+(-4)*u1^4*u2^5+(-20)*u1^6*u2^3+(-12)*u1^8*u2)*u3^7+((-4)*u2^8+(-4)*u1^2*u2^6+4*u1^4*u2^4+4*u1^6*u2^2)*u4^8+(12*u1*u2^8+20*u1^3*u2^6+4*u1^5*u2^4+(-4)*u1^7*u2^2+(8*u1*u2^7+8*u1^3*u2^5+(-8)*u1^5*u2^3+(-8)*u1^7*u2)*u3)*u4^7+((4*u1^8+(-12)*u2^8+(-16)*u1^2*u2^6+8*u1^4*u2^4+16*u1^6*u2^2)*u3^2+(4*u2^9+(-28)*u1^2*u2^7+(-60)*u1^4*u2^5+(-20)*u1^6*u2^3+8*u1^8*u2)*u3)*u4^6+((24*u1*u2^7+24*u1^3*u2^5+(-24)*u1^5*u2^3+(-24)*u1^7*u2)*u3^3+((-4)*u1^9+16*u1*u2^8+60*u1^3*u2^6+68*u1^5*u2^4+20*u1^7*u2^2)*u3^2)*u4^5+((12*u1^8+(-12)*u2^8+(-24)*u1^2*u2^6+24*u1^6*u2^2)*u3^4+(8*u2^9+(-52)*u1^2*u2^7+(-124)*u1^4*u2^5+(-60)*u1^6*u2^3+4*u1^8*u2)*u3^3)*u4^4+((24*u1*u2^7+24*u1^3*u2^5+(-24)*u1^5*u2^3+(-24)*u1^7*u2)*u3^5+((-8)*u1^9+(-4)*u1*u2^8+60*u1^3*u2^6+124*u1^5*u2^4+52*u1^7*u2^2)*u3^4)*u4^3+((12*u1^8+(-4)*u2^8+(-16)*u1^2*u2^6+(-8)*u1^4*u2^4+16*u1^6*u2^2)*u3^6+(4*u2^9+(-20)*u1^2*u2^7+(-68)*u1^4*u2^5+(-60)*u1^6*u2^3+(-16)*u1^8*u2)*u3^5)*u4^2+((8*u1*u2^7+8*u1^3*u2^5+(-8)*u1^5*u2^3+(-8)*u1^7*u2)*u3^7+((-4)*u1^9+(-8)*u1*u2^8+20*u1^3*u2^6+60*u1^5*u2^4+28*u1^7*u2^2)*u3^6)*u4)*u5^2+(((-8)*u1^9+(-8)*u1^5*u2^4+(-16)*u1^7*u2^2)*u3^8+(4*u1^3*u2^7+28*u1^5*u2^5+44*u1^7*u2^3+20*u1^9*u2)*u3^7+((-8)*u1^3*u2^6+(-16)*u1^5*u2^4+(-8)*u1^7*u2^2)*u4^8+((-4)*u2^10+(-20)*u1^2*u2^8+(-20)*u1^4*u2^6+4*u1^6*u2^4+8*u1^8*u2^2+(16*u1^4*u2^5+32*u1^6*u2^3+16*u1^8*u2)*u3)*u4^7+(((-8)*u1^9+(-24)*u1^3*u2^6+(-56)*u1^5*u2^4+(-40)*u1^7*u2^2)*u3^2+(12*u1*u2^9+68*u1^3*u2^7+84*u1^5*u2^5+12*u1^7*u2^3+(-16)*u1^9*u2)*u3)*u4^6+((48*u1^4*u2^5+96*u1^6*u2^3+48*u1^8*u2)*u3^3+(8*u1^10+(-8)*u2^10+(-52)*u1^2*u2^8+(-116)*u1^4*u2^6+(-100)*u1^6*u2^4+(-20)*u1^8*u2^2)*u3^2)*u4^5+(((-24)*u1^9+(-24)*u1^3*u2^6+(-72)*u1^5*u2^4+(-72)*u1^7*u2^2)*u3^4+(24*u1*u2^9+140*u1^3*u2^7+196*u1^5*u2^5+68*u1^7*u2^3+(-12)*u1^9*u2)*u3^3)*u4^4+((48*u1^4*u2^5+96*u1^6*u2^3+48*u1^8*u2)*u3^5+(16*u1^10+(-4)*u2^10+(-44)*u1^2*u2^8+(-172)*u1^4*u2^6+(-212)*u1^6*u2^4+(-64)*u1^8*u2^2)*u3^4)*u4^3+(((-24)*u1^9+(-8)*u1^3*u2^6+(-40)*u1^5*u2^4+(-56)*u1^7*u2^2)*u3^6+(12*u1*u2^9+76*u1^3*u2^7+140*u1^5*u2^5+100*u1^7*u2^3+24*u1^9*u2)*u3^5)*u4^2+((16*u1^4*u2^5+32*u1^6*u2^3+16*u1^8*u2)*u3^7+(8*u1^10+(-12)*u1^2*u2^8+(-76)*u1^4*u2^6+(-108)*u1^6*u2^4+(-36)*u1^8*u2^2)*u3^6)*u4)*u5) ; (((4*u1^4*u2^3+4*u1^6*u2)*u3^6+(4*u2^7+4*u1^2*u2^5)*u4^6+(((-16)*u1*u2^6+(-16)*u1^3*u2^4)*u3)*u4^5+((4*u2^7+28*u1^2*u2^5+24*u1^4*u2^3)*u3^2)*u4^4+(((-16)*u1*u2^6+(-32)*u1^3*u2^4+(-16)*u1^5*u2^2)*u3^3)*u4^3+((24*u1^2*u2^5+28*u1^4*u2^3+4*u1^6*u2)*u3^4)*u4^2+(((-16)*u1^3*u2^4+(-16)*u1^5*u2^2)*u3^5)*u4)*u5) ; (((-1)*u1^7+(-1)*u1^3*u2^4+(-2)*u1^5*u2^2)*u3^4+((-1)*u1*u2^6+(-2)*u1^3*u2^4+(-1)*u1^5*u2^2)*u4^4+((2*u1^2*u2^5+4*u1^4*u2^3+2*u1^6*u2)*u3)*u4^3+(((-1)*u1^7+(-1)*u1*u2^6+(-3)*u1^3*u2^4+(-3)*u1^5*u2^2)*u3^2)*u4^2+((2*u1^2*u2^5+4*u1^4*u2^3+2*u1^6*u2)*u3^3)*u4) *i^2 + ((4*u1^7+4*u1^3*u2^4+8*u1^5*u2^2)*u3^4+((-4)*u1^3*u2^5+(-8)*u1^5*u2^3+(-4)*u1^7*u2)*u3^3+(u1^9+u1^3*u2^6+3*u1^5*u2^4+3*u1^7*u2^2)*u3^2+(4*u1*u2^6+8*u1^3*u2^4+4*u1^5*u2^2)*u4^4+((-4)*u1^2*u2^6+(-8)*u1^4*u2^4+(-4)*u1^6*u2^2+((-8)*u1^2*u2^5+(-16)*u1^4*u2^3+(-8)*u1^6*u2)*u3)*u4^3+(u1*u2^8+3*u1^3*u2^6+3*u1^5*u2^4+u1^7*u2^2+(4*u1^7+4*u1*u2^6+12*u1^3*u2^4+12*u1^5*u2^2)*u3^2+((-4)*u1*u2^7+12*u1^5*u2^3+8*u1^7*u2)*u3)*u4^2+(((-8)*u1^2*u2^5+(-16)*u1^4*u2^3+(-8)*u1^6*u2)*u3^3+((-4)*u1^8+8*u1^2*u2^6+12*u1^4*u2^4)*u3^2+((-2)*u1^2*u2^7+(-6)*u1^4*u2^5+(-6)*u1^6*u2^3+(-2)*u1^8*u2)*u3)*u4) *k^2 + ((4*u1^3*u2^5+8*u1^5*u2^3+4*u1^7*u2)*u3^6+(2*u1^9+(-6)*u1^3*u2^6+(-10)*u1^5*u2^4+(-2)*u1^7*u2^2)*u3^5+(2*u1^3*u2^7+6*u1^5*u2^5+6*u1^7*u2^3+2*u1^9*u2)*u3^4+(4*u1*u2^7+8*u1^3*u2^5+4*u1^5*u2^3)*u4^6+((-8)*u1^2*u2^7+(-16)*u1^4*u2^5+(-8)*u1^6*u2^3+((-8)*u1^2*u2^6+(-16)*u1^4*u2^4+(-8)*u1^6*u2^2)*u3)*u4^5+(2*u1*u2^9+6*u1^3*u2^7+6*u1^5*u2^5+2*u1^7*u2^3+(8*u1*u2^7+20*u1^3*u2^5+16*u1^5*u2^3+4*u1^7*u2)*u3^2+((-6)*u1*u2^8+6*u1^3*u2^6+30*u1^5*u2^4+18*u1^7*u2^2)*u3)*u4^4+(((-16)*u1^2*u2^6+(-32)*u1^4*u2^4+(-16)*u1^6*u2^2)*u3^3+(4*u1^2*u2^7+(-4)*u1^4*u2^5+(-20)*u1^6*u2^3+(-12)*u1^8*u2)*u3^2+((-4)*u1^2*u2^8+(-12)*u1^4*u2^6+(-12)*u1^6*u2^4+(-4)*u1^8*u2^2)*u3)*u4^3+((4*u1*u2^7+16*u1^3*u2^5+20*u1^5*u2^3+8*u1^7*u2)*u3^4+(2*u1^9+(-6)*u1*u2^8+20*u1^5*u2^4+16*u1^7*u2^2)*u3^3+(2*u1*u2^9+8*u1^3*u2^7+12*u1^5*u2^5+8*u1^7*u2^3+2*u1^9*u2)*u3^2)*u4^2+(((-8)*u1^2*u2^6+(-16)*u1^4*u2^4+(-8)*u1^6*u2^2)*u3^5+(12*u1^2*u2^7+12*u1^4*u2^5+(-12)*u1^6*u2^3+(-12)*u1^8*u2)*u3^4+((-4)*u1^2*u2^8+(-12)*u1^4*u2^6+(-12)*u1^6*u2^4+(-4)*u1^8*u2^2)*u3^3)*u4) *h + (((-4)*u1^3*u2^4+(-4)*u1^5*u2^2)*u3^8+(8*u1^3*u2^5+(-8)*u1^7*u2)*u3^7+((-7)*u1^9+(-7)*u1^3*u2^6+(-5)*u1^5*u2^4+(-5)*u1^7*u2^2)*u3^6+(4*u1^3*u2^7+12*u1^5*u2^5+12*u1^7*u2^3+4*u1^9*u2)*u3^5+((-1)*u1^11+(-1)*u1^3*u2^8+(-4)*u1^5*u2^6+(-6)*u1^7*u2^4+(-4)*u1^9*u2^2)*u3^4+((-4)*u1*u2^6+(-4)*u1^3*u2^4)*u4^8+(16*u1^2*u2^6+16*u1^4*u2^4+(8*u1^2*u2^5+8*u1^4*u2^3)*u3)*u4^7+((-3)*u1*u2^8+(-25)*u1^3*u2^6+(-25)*u1^5*u2^4+(-3)*u1^7*u2^2+((-12)*u1*u2^6+(-16)*u1^3*u2^4+(-4)*u1^5*u2^2)*u3^2+(8*u1*u2^7+(-32)*u1^3*u2^5+(-40)*u1^5*u2^3)*u3)*u4^6+(4*u1^2*u2^8+12*u1^4*u2^6+12*u1^6*u2^4+4*u1^8*u2^2+(24*u1^2*u2^5+24*u1^4*u2^3)*u3^3+(16*u1^2*u2^6+48*u1^4*u2^4+32*u1^6*u2^2)*u3^2+((-10)*u1^2*u2^7+50*u1^4*u2^5+66*u1^6*u2^3+6*u1^8*u2)*u3)*u4^5+((-1)*u1*u2^10+(-4)*u1^3*u2^8+(-6)*u1^5*u2^6+(-4)*u1^7*u2^4+(-1)*u1^9*u2^2+((-12)*u1*u2^6+(-24)*u1^3*u2^4+(-12)*u1^5*u2^2)*u3^4+(16*u1*u2^7+(-56)*u1^3*u2^5+(-80)*u1^5*u2^3+(-8)*u1^7*u2)*u3^3+((-3)*u1^9+(-10)*u1*u2^8+(-1)*u1^3*u2^6+(-55)*u1^5*u2^4+(-67)*u1^7*u2^2)*u3^2+(4*u1*u2^9+4*u1^3*u2^7+(-12)*u1^5*u2^5+(-20)*u1^7*u2^3+(-8)*u1^9*u2)*u3)*u4^4+((24*u1^2*u2^5+24*u1^4*u2^3)*u3^5+((-16)*u1^2*u2^6+48*u1^4*u2^4+64*u1^6*u2^2)*u3^4+(4*u1^2*u2^7+44*u1^4*u2^5+76*u1^6*u2^3+36*u1^8*u2)*u3^3+(4*u1^10+(-4)*u1^2*u2^8+(-8)*u1^4*u2^6+8*u1^8*u2^2)*u3^2+(2*u1^2*u2^9+8*u1^4*u2^7+12*u1^6*u2^5+8*u1^8*u2^3+2*u1^10*u2)*u3)*u4^3+(((-4)*u1*u2^6+(-16)*u1^3*u2^4+(-12)*u1^5*u2^2)*u3^6+(8*u1*u2^7+(-16)*u1^3*u2^5+(-40)*u1^5*u2^3+(-16)*u1^7*u2)*u3^5+((-10)*u1^9+(-7)*u1*u2^8+17*u1^3*u2^6+(-35)*u1^5*u2^4+(-69)*u1^7*u2^2)*u3^4+(4*u1*u2^9+8*u1^3*u2^7+(-8)*u1^7*u2^3+(-4)*u1^9*u2)*u3^3+((-1)*u1^11+(-1)*u1*u2^10+(-5)*u1^3*u2^8+(-10)*u1^5*u2^6+(-10)*u1^7*u2^4+(-5)*u1^9*u2^2)*u3^2)*u4^2+((8*u1^2*u2^5+8*u1^4*u2^3)*u3^7+((-16)*u1^2*u2^6+16*u1^4*u2^4+32*u1^6*u2^2)*u3^6+(14*u1^2*u2^7+(-6)*u1^4*u2^5+10*u1^6*u2^3+30*u1^8*u2)*u3^5+(4*u1^10+(-8)*u1^2*u2^8+(-20)*u1^4*u2^6+(-12)*u1^6*u2^4+4*u1^8*u2^2)*u3^4+(2*u1^2*u2^9+8*u1^4*u2^7+12*u1^6*u2^5+8*u1^8*u2^3+2*u1^10*u2)*u3^3)*u4+((4*u1^4*u2^3+4*u1^6*u2)*u3^7+(4*u1^8+(-4)*u1^4*u2^4)*u3^6+((-8)*u1^4*u2^5+(-16)*u1^6*u2^3+(-8)*u1^8*u2)*u3^5+(2*u1^10+2*u1^4*u2^6+6*u1^6*u2^4+6*u1^8*u2^2)*u3^4+((-4)*u1*u2^6+(-4)*u1^3*u2^4)*u4^7+((-4)*u2^8+4*u1^2*u2^6+12*u1^4*u2^4+4*u1^6*u2^2+(12*u1^2*u2^5+12*u1^4*u2^3)*u3)*u4^6+(2*u1*u2^8+(-2)*u1^3*u2^6+(-10)*u1^5*u2^4+(-6)*u1^7*u2^2+((-8)*u1*u2^6+(-20)*u1^3*u2^4+(-12)*u1^5*u2^2)*u3^2+(20*u1*u2^7+(-28)*u1^5*u2^3+(-8)*u1^7*u2)*u3)*u4^5+(2*u1^2*u2^8+6*u1^4*u2^6+6*u1^6*u2^4+2*u1^8*u2^2+(24*u1^2*u2^5+28*u1^4*u2^3+4*u1^6*u2)*u3^3+(4*u1^8+(-4)*u2^8+(-28)*u1^2*u2^6+28*u1^6*u2^2)*u3^2+((-12)*u1^2*u2^7+(-12)*u1^4*u2^5+12*u1^6*u2^3+12*u1^8*u2)*u3)*u4^4+(((-4)*u1*u2^6+(-28)*u1^3*u2^4+(-24)*u1^5*u2^2)*u3^4+(20*u1*u2^7+20*u1^3*u2^5+(-20)*u1^5*u2^3+(-20)*u1^7*u2)*u3^3+((-6)*u1^9+2*u1*u2^8+16*u1^3*u2^6+20*u1^5*u2^4)*u3^2+((-4)*u1^3*u2^7+(-12)*u1^5*u2^5+(-12)*u1^7*u2^3+(-4)*u1^9*u2)*u3)*u4^3+((12*u1^2*u2^5+20*u1^4*u2^3+8*u1^6*u2)*u3^5+(8*u1^8+(-32)*u1^2*u2^6+(-16)*u1^4*u2^4+24*u1^6*u2^2)*u3^4+((-12)*u1^2*u2^7+(-20)*u1^4*u2^5+(-4)*u1^6*u2^3+4*u1^8*u2)*u3^3+(2*u1^10+2*u1^2*u2^8+8*u1^4*u2^6+12*u1^6*u2^4+8*u1^8*u2^2)*u3^2)*u4^2+(((-12)*u1^3*u2^4+(-12)*u1^5*u2^2)*u3^6+(20*u1^3*u2^5+8*u1^5*u2^3+(-12)*u1^7*u2)*u3^5+((-6)*u1^9+18*u1^3*u2^6+30*u1^5*u2^4+6*u1^7*u2^2)*u3^4+((-4)*u1^3*u2^7+(-12)*u1^5*u2^5+(-12)*u1^7*u2^3+(-4)*u1^9*u2)*u3^3)*u4)*u5) ; ((2*u1^7+2*u1^3*u2^4+4*u1^5*u2^2)*u3^4+(2*u1*u2^6+4*u1^3*u2^4+2*u1^5*u2^2)*u4^4+(((-4)*u1^2*u2^5+(-8)*u1^4*u2^3+(-4)*u1^6*u2)*u3)*u4^3+((2*u1^7+2*u1*u2^6+6*u1^3*u2^4+6*u1^5*u2^2)*u3^2)*u4^2+(((-4)*u1^2*u2^5+(-8)*u1^4*u2^3+(-4)*u1^6*u2)*u3^3)*u4) *i^2 + (((-1)*u1^7+(-1)*u1^3*u2^4+(-2)*u1^5*u2^2)*u3^4+((-1)*u1*u2^6+(-2)*u1^3*u2^4+(-1)*u1^5*u2^2)*u4^4+((2*u1^2*u2^5+4*u1^4*u2^3+2*u1^6*u2)*u3)*u4^3+(((-1)*u1^7+(-1)*u1*u2^6+(-3)*u1^3*u2^4+(-3)*u1^5*u2^2)*u3^2)*u4^2+((2*u1^2*u2^5+4*u1^4*u2^3+2*u1^6*u2)*u3^3)*u4) *j^2 + ((u1^7+u1^3*u2^4+2*u1^5*u2^2)*u3^4+(2*u1^3*u2^5+4*u1^5*u2^3+2*u1^7*u2)*u3^3+((-1)*u1^9+(-1)*u1^3*u2^6+(-3)*u1^5*u2^4+(-3)*u1^7*u2^2)*u3^2+(u1*u2^6+2*u1^3*u2^4+u1^5*u2^2)*u4^4+(2*u1^2*u2^6+4*u1^4*u2^4+2*u1^6*u2^2+((-2)*u1^2*u2^5+(-4)*u1^4*u2^3+(-2)*u1^6*u2)*u3)*u4^3+((-1)*u1*u2^8+(-3)*u1^3*u2^6+(-3)*u1^5*u2^4+(-1)*u1^7*u2^2+(u1^7+u1*u2^6+3*u1^3*u2^4+3*u1^5*u2^2)*u3^2+(2*u1*u2^7+(-6)*u1^5*u2^3+(-4)*u1^7*u2)*u3)*u4^2+(((-2)*u1^2*u2^5+(-4)*u1^4*u2^3+(-2)*u1^6*u2)*u3^3+(2*u1^8+(-4)*u1^2*u2^6+(-6)*u1^4*u2^4)*u3^2+(2*u1^2*u2^7+6*u1^4*u2^5+6*u1^6*u2^3+2*u1^8*u2)*u3)*u4) *k^2 + (((-2)*u1^3*u2^5+(-4)*u1^5*u2^3+(-2)*u1^7*u2)*u3^6+(4*u1^3*u2^6+8*u1^5*u2^4+4*u1^7*u2^2)*u3^5+((-2)*u1^3*u2^7+(-6)*u1^5*u2^5+(-6)*u1^7*u2^3+(-2)*u1^9*u2)*u3^4+((-2)*u1*u2^7+(-4)*u1^3*u2^5+(-2)*u1^5*u2^3)*u4^6+(4*u1^2*u2^7+8*u1^4*u2^5+4*u1^6*u2^3+(4*u1^2*u2^6+8*u1^4*u2^4+4*u1^6*u2^2)*u3)*u4^5+((-2)*u1*u2^9+(-6)*u1^3*u2^7+(-6)*u1^5*u2^5+(-2)*u1^7*u2^3+((-4)*u1*u2^7+(-10)*u1^3*u2^5+(-8)*u1^5*u2^3+(-2)*u1^7*u2)*u3^2+(4*u1*u2^8+(-12)*u1^5*u2^4+(-8)*u1^7*u2^2)*u3)*u4^4+((8*u1^2*u2^6+16*u1^4*u2^4+8*u1^6*u2^2)*u3^3+((-4)*u1^2*u2^7+(-4)*u1^4*u2^5+4*u1^6*u2^3+4*u1^8*u2)*u3^2+(4*u1^2*u2^8+12*u1^4*u2^6+12*u1^6*u2^4+4*u1^8*u2^2)*u3)*u4^3+(((-2)*u1*u2^7+(-8)*u1^3*u2^5+(-10)*u1^5*u2^3+(-4)*u1^7*u2)*u3^4+(4*u1*u2^8+4*u1^3*u2^6+(-4)*u1^5*u2^4+(-4)*u1^7*u2^2)*u3^3+((-2)*u1*u2^9+(-8)*u1^3*u2^7+(-12)*u1^5*u2^5+(-8)*u1^7*u2^3+(-2)*u1^9*u2)*u3^2)*u4^2+((4*u1^2*u2^6+8*u1^4*u2^4+4*u1^6*u2^2)*u3^5+((-8)*u1^2*u2^7+(-12)*u1^4*u2^5+4*u1^8*u2)*u3^4+(4*u1^2*u2^8+12*u1^4*u2^6+12*u1^6*u2^4+4*u1^8*u2^2)*u3^3)*u4) *h + ((u1^9+u1^3*u2^6+3*u1^5*u2^4+3*u1^7*u2^2)*u3^6+((-2)*u1^3*u2^7+(-6)*u1^5*u2^5+(-6)*u1^7*u2^3+(-2)*u1^9*u2)*u3^5+(u1^11+u1^3*u2^8+4*u1^5*u2^6+6*u1^7*u2^4+4*u1^9*u2^2)*u3^4+(u1*u2^8+3*u1^3*u2^6+3*u1^5*u2^4+u1^7*u2^2)*u4^6+((-2)*u1^2*u2^8+(-6)*u1^4*u2^6+(-6)*u1^6*u2^4+(-2)*u1^8*u2^2+((-2)*u1^2*u2^7+(-6)*u1^4*u2^5+(-6)*u1^6*u2^3+(-2)*u1^8*u2)*u3)*u4^5+(u1*u2^10+4*u1^3*u2^8+6*u1^5*u2^6+4*u1^7*u2^4+u1^9*u2^2+(u1^9+2*u1*u2^8+7*u1^3*u2^6+9*u1^5*u2^4+5*u1^7*u2^2)*u3^2+((-2)*u1*u2^9+(-2)*u1^3*u2^7+6*u1^5*u2^5+10*u1^7*u2^3+4*u1^9*u2)*u3)*u4^4+(((-4)*u1^2*u2^7+(-12)*u1^4*u2^5+(-12)*u1^6*u2^3+(-4)*u1^8*u2)*u3^3+((-2)*u1^10+2*u1^2*u2^8+4*u1^4*u2^6+(-4)*u1^8*u2^2)*u3^2+((-2)*u1^2*u2^9+(-8)*u1^4*u2^7+(-12)*u1^6*u2^5+(-8)*u1^8*u2^3+(-2)*u1^10*u2)*u3)*u4^3+((2*u1^9+u1*u2^8+5*u1^3*u2^6+9*u1^5*u2^4+7*u1^7*u2^2)*u3^4+((-2)*u1*u2^9+(-4)*u1^3*u2^7+4*u1^7*u2^3+2*u1^9*u2)*u3^3+(u1^11+u1*u2^10+5*u1^3*u2^8+10*u1^5*u2^6+10*u1^7*u2^4+5*u1^9*u2^2)*u3^2)*u4^2+(((-2)*u1^2*u2^7+(-6)*u1^4*u2^5+(-6)*u1^6*u2^3+(-2)*u1^8*u2)*u3^5+((-2)*u1^10+4*u1^2*u2^8+10*u1^4*u2^6+6*u1^6*u2^4+(-2)*u1^8*u2^2)*u3^4+((-2)*u1^2*u2^9+(-8)*u1^4*u2^7+(-12)*u1^6*u2^5+(-8)*u1^8*u2^3+(-2)*u1^10*u2)*u3^3)*u4+(((-2)*u1^8+(-2)*u1^4*u2^4+(-4)*u1^6*u2^2)*u3^6+(4*u1^4*u2^5+8*u1^6*u2^3+4*u1^8*u2)*u3^5+((-2)*u1^10+(-2)*u1^4*u2^6+(-6)*u1^6*u2^4+(-6)*u1^8*u2^2)*u3^4+((-2)*u1^2*u2^6+(-4)*u1^4*u2^4+(-2)*u1^6*u2^2)*u4^6+(4*u1^3*u2^6+8*u1^5*u2^4+4*u1^7*u2^2+(4*u1^3*u2^5+8*u1^5*u2^3+4*u1^7*u2)*u3)*u4^5+((-2)*u1^2*u2^8+(-6)*u1^4*u2^6+(-6)*u1^6*u2^4+(-2)*u1^8*u2^2+((-2)*u1^8+(-4)*u1^2*u2^6+(-10)*u1^4*u2^4+(-8)*u1^6*u2^2)*u3^2+(4*u1^2*u2^7+(-12)*u1^6*u2^3+(-8)*u1^8*u2)*u3)*u4^4+((8*u1^3*u2^5+16*u1^5*u2^3+8*u1^7*u2)*u3^3+(4*u1^9+(-4)*u1^3*u2^6+(-4)*u1^5*u2^4+4*u1^7*u2^2)*u3^2+(4*u1^3*u2^7+12*u1^5*u2^5+12*u1^7*u2^3+4*u1^9*u2)*u3)*u4^3+(((-4)*u1^8+(-2)*u1^2*u2^6+(-8)*u1^4*u2^4+(-10)*u1^6*u2^2)*u3^4+(4*u1^2*u2^7+4*u1^4*u2^5+(-4)*u1^6*u2^3+(-4)*u1^8*u2)*u3^3+((-2)*u1^10+(-2)*u1^2*u2^8+(-8)*u1^4*u2^6+(-12)*u1^6*u2^4+(-8)*u1^8*u2^2)*u3^2)*u4^2+((4*u1^3*u2^5+8*u1^5*u2^3+4*u1^7*u2)*u3^5+(4*u1^9+(-8)*u1^3*u2^6+(-12)*u1^5*u2^4)*u3^4+(4*u1^3*u2^7+12*u1^5*u2^5+12*u1^7*u2^3+4*u1^9*u2)*u3^3)*u4)*u5) ; 0; 0; ((4*u1^3*u2^4+4*u1^5*u2^2)*u3^10+((-8)*u1^3*u2^5+8*u1^7*u2)*u3^9+(4*u1^9+4*u1^3*u2^6+(-4)*u1^5*u2^4+(-4)*u1^7*u2^2)*u3^8+(4*u1*u2^6+4*u1^3*u2^4)*u4^10+((-16)*u1^2*u2^6+(-16)*u1^4*u2^4+((-8)*u1^2*u2^5+(-8)*u1^4*u2^3)*u3)*u4^9+(16*u1^3*u2^6+16*u1^5*u2^4+(16*u1*u2^6+20*u1^3*u2^4+4*u1^5*u2^2)*u3^2+((-8)*u1*u2^7+32*u1^3*u2^5+40*u1^5*u2^3)*u3)*u4^8+(((-32)*u1^2*u2^5+(-32)*u1^4*u2^3)*u3^3+((-32)*u1^2*u2^6+(-64)*u1^4*u2^4+(-32)*u1^6*u2^2)*u3^2+(16*u1^2*u2^7+(-32)*u1^4*u2^5+(-48)*u1^6*u2^3)*u3)*u4^7+((24*u1*u2^6+40*u1^3*u2^4+16*u1^5*u2^2)*u3^4+((-24)*u1*u2^7+88*u1^3*u2^5+120*u1^5*u2^3+8*u1^7*u2)*u3^3+(4*u1*u2^8+(-4)*u1^3*u2^6+44*u1^5*u2^4+52*u1^7*u2^2)*u3^2)*u4^6+(((-48)*u1^2*u2^5+(-48)*u1^4*u2^3)*u3^5+((-96)*u1^4*u2^4+(-96)*u1^6*u2^2)*u3^4+(24*u1^2*u2^7+(-40)*u1^4*u2^5+(-88)*u1^6*u2^3+(-24)*u1^8*u2)*u3^3)*u4^5+((16*u1*u2^6+40*u1^3*u2^4+24*u1^5*u2^2)*u3^6+((-24)*u1*u2^7+72*u1^3*u2^5+120*u1^5*u2^3+24*u1^7*u2)*u3^5+(4*u1^9+8*u1*u2^8+(-52)*u1^3*u2^6+36*u1^5*u2^4+100*u1^7*u2^2)*u3^4)*u4^4+(((-32)*u1^2*u2^5+(-32)*u1^4*u2^3)*u3^7+(32*u1^2*u2^6+(-64)*u1^4*u2^4+(-96)*u1^6*u2^2)*u3^6+(16*u1^4*u2^5+(-32)*u1^6*u2^3+(-48)*u1^8*u2)*u3^5)*u4^3+((4*u1*u2^6+20*u1^3*u2^4+16*u1^5*u2^2)*u3^8+((-8)*u1*u2^7+8*u1^3*u2^5+40*u1^5*u2^3+24*u1^7*u2)*u3^7+(8*u1^9+4*u1*u2^8+(-28)*u1^3*u2^6+4*u1^5*u2^4+44*u1^7*u2^2)*u3^6)*u4^2+(((-8)*u1^2*u2^5+(-8)*u1^4*u2^3)*u3^9+(16*u1^2*u2^6+(-16)*u1^4*u2^4+(-32)*u1^6*u2^2)*u3^8+((-8)*u1^2*u2^7+24*u1^4*u2^5+8*u1^6*u2^3+(-24)*u1^8*u2)*u3^7)*u4+(((-4)*u1^4*u2^3+(-4)*u1^6*u2)*u3^9+(8*u1^4*u2^4+8*u1^6*u2^2)*u3^8+(4*u1*u2^6+4*u1^3*u2^4)*u4^9+(4*u2^8+(-4)*u1^4*u2^4+((-12)*u1^2*u2^5+(-12)*u1^4*u2^3)*u3)*u4^8+((12*u1*u2^6+24*u1^3*u2^4+12*u1^5*u2^2)*u3^2+((-20)*u1*u2^7+(-8)*u1^3*u2^5+12*u1^5*u2^3)*u3)*u4^7+(((-36)*u1^2*u2^5+(-40)*u1^4*u2^3+(-4)*u1^6*u2)*u3^3+(8*u2^8+36*u1^2*u2^6+16*u1^4*u2^4+(-12)*u1^6*u2^2)*u3^2)*u4^6+((12*u1*u2^6+48*u1^3*u2^4+36*u1^5*u2^2)*u3^4+((-40)*u1*u2^7+(-44)*u1^3*u2^5+4*u1^7*u2)*u3^3)*u4^5+(((-36)*u1^2*u2^5+(-48)*u1^4*u2^3+(-12)*u1^6*u2)*u3^5+(4*u2^8+72*u1^2*u2^6+52*u1^4*u2^4+(-16)*u1^6*u2^2)*u3^4)*u4^4+((4*u1*u2^6+40*u1^3*u2^4+36*u1^5*u2^2)*u3^6+((-20)*u1*u2^7+(-64)*u1^3*u2^5+(-36)*u1^5*u2^3+8*u1^7*u2)*u3^5)*u4^3+(((-12)*u1^2*u2^5+(-24)*u1^4*u2^3+(-12)*u1^6*u2)*u3^7+(36*u1^2*u2^6+40*u1^4*u2^4+4*u1^6*u2^2)*u3^6)*u4^2+((12*u1^3*u2^4+12*u1^5*u2^2)*u3^8+((-28)*u1^3*u2^5+(-24)*u1^5*u2^3+4*u1^7*u2)*u3^7)*u4)*u5) ; ((8*u1^5*u2^5+16*u1^7*u2^3+8*u1^9*u2)*u3^9+((-16)*u1^5*u2^6+(-32)*u1^7*u2^4+(-16)*u1^9*u2^2)*u3^8+((-8)*u1^2*u2^8+(-16)*u1^4*u2^6+(-8)*u1^6*u2^4)*u4^9+((-8)*u1*u2^10+(-8)*u1^3*u2^8+8*u1^5*u2^6+8*u1^7*u2^4+(24*u1^3*u2^7+48*u1^5*u2^5+24*u1^7*u2^3)*u3)*u4^8+(((-24)*u1^2*u2^8+(-72)*u1^4*u2^6+(-72)*u1^6*u2^4+(-24)*u1^8*u2^2)*u3^2+(40*u1^2*u2^9+56*u1^4*u2^7+(-8)*u1^6*u2^5+(-24)*u1^8*u2^3)*u3)*u4^7+((72*u1^3*u2^7+152*u1^5*u2^5+88*u1^7*u2^3+8*u1^9*u2)*u3^3+((-16)*u1*u2^10+(-88)*u1^3*u2^8+(-104)*u1^5*u2^6+(-8)*u1^7*u2^4+24*u1^9*u2^2)*u3^2)*u4^6+(((-24)*u1^2*u2^8+(-120)*u1^4*u2^6+(-168)*u1^6*u2^4+(-72)*u1^8*u2^2)*u3^4+(80*u1^2*u2^9+168*u1^4*u2^7+88*u1^6*u2^5+(-8)*u1^8*u2^3+(-8)*u1^10*u2)*u3^3)*u4^5+((72*u1^3*u2^7+168*u1^5*u2^5+120*u1^7*u2^3+24*u1^9*u2)*u3^5+((-8)*u1*u2^10+(-152)*u1^3*u2^8+(-248)*u1^5*u2^6+(-72)*u1^7*u2^4+32*u1^9*u2^2)*u3^4)*u4^4+(((-8)*u1^2*u2^8+(-88)*u1^4*u2^6+(-152)*u1^6*u2^4+(-72)*u1^8*u2^2)*u3^6+(40*u1^2*u2^9+168*u1^4*u2^7+200*u1^6*u2^5+56*u1^8*u2^3+(-16)*u1^10*u2)*u3^5)*u4^3+((24*u1^3*u2^7+72*u1^5*u2^5+72*u1^7*u2^3+24*u1^9*u2)*u3^7+((-72)*u1^3*u2^8+(-152)*u1^5*u2^6+(-88)*u1^7*u2^4+(-8)*u1^9*u2^2)*u3^6)*u4^2+(((-24)*u1^4*u2^6+(-48)*u1^6*u2^4+(-24)*u1^8*u2^2)*u3^8+(56*u1^4*u2^7+104*u1^6*u2^5+40*u1^8*u2^3+(-8)*u1^10*u2)*u3^7)*u4+(((-4)*u1^4*u2^5+(-8)*u1^6*u2^3+(-4)*u1^8*u2)*u3^9+(8*u1^4*u2^6+16*u1^6*u2^4+8*u1^8*u2^2)*u3^8+(4*u1*u2^8+8*u1^3*u2^6+4*u1^5*u2^4)*u4^9+(4*u2^10+4*u1^2*u2^8+(-4)*u1^4*u2^6+(-4)*u1^6*u2^4+((-12)*u1^2*u2^7+(-24)*u1^4*u2^5+(-12)*u1^6*u2^3)*u3)*u4^8+((12*u1*u2^8+36*u1^3*u2^6+36*u1^5*u2^4+12*u1^7*u2^2)*u3^2+((-20)*u1*u2^9+(-28)*u1^3*u2^7+4*u1^5*u2^5+12*u1^7*u2^3)*u3)*u4^7+(((-36)*u1^2*u2^7+(-76)*u1^4*u2^5+(-44)*u1^6*u2^3+(-4)*u1^8*u2)*u3^3+(8*u2^10+44*u1^2*u2^8+52*u1^4*u2^6+4*u1^6*u2^4+(-12)*u1^8*u2^2)*u3^2)*u4^6+((12*u1*u2^8+60*u1^3*u2^6+84*u1^5*u2^4+36*u1^7*u2^2)*u3^4+((-40)*u1*u2^9+(-84)*u1^3*u2^7+(-44)*u1^5*u2^5+4*u1^7*u2^3+4*u1^9*u2)*u3^3)*u4^5+(((-36)*u1^2*u2^7+(-84)*u1^4*u2^5+(-60)*u1^6*u2^3+(-12)*u1^8*u2)*u3^5+(4*u2^10+76*u1^2*u2^8+124*u1^4*u2^6+36*u1^6*u2^4+(-16)*u1^8*u2^2)*u3^4)*u4^4+((4*u1*u2^8+44*u1^3*u2^6+76*u1^5*u2^4+36*u1^7*u2^2)*u3^6+((-20)*u1*u2^9+(-84)*u1^3*u2^7+(-100)*u1^5*u2^5+(-28)*u1^7*u2^3+8*u1^9*u2)*u3^5)*u4^3+(((-12)*u1^2*u2^7+(-36)*u1^4*u2^5+(-36)*u1^6*u2^3+(-12)*u1^8*u2)*u3^7+(36*u1^2*u2^8+76*u1^4*u2^6+44*u1^6*u2^4+4*u1^8*u2^2)*u3^6)*u4^2+((12*u1^3*u2^6+24*u1^5*u2^4+12*u1^7*u2^2)*u3^8+((-28)*u1^3*u2^7+(-52)*u1^5*u2^5+(-20)*u1^7*u2^3+4*u1^9*u2)*u3^7)*u4)*u5) ; 0; ((((-4)*u1^8+(-4)*u1^4*u2^4+(-8)*u1^6*u2^2)*u3^6+((-4)*u2^8+(-8)*u1^2*u2^6+(-4)*u1^4*u2^4)*u4^6+((16*u1*u2^7+32*u1^3*u2^5+16*u1^5*u2^3)*u3)*u4^5+(((-4)*u2^8+(-32)*u1^2*u2^6+(-52)*u1^4*u2^4+(-24)*u1^6*u2^2)*u3^2)*u4^4+((16*u1*u2^7+48*u1^3*u2^5+48*u1^5*u2^3+16*u1^7*u2)*u3^3)*u4^3+(((-4)*u1^8+(-24)*u1^2*u2^6+(-52)*u1^4*u2^4+(-32)*u1^6*u2^2)*u3^4)*u4^2+((16*u1^3*u2^5+32*u1^5*u2^3+16*u1^7*u2)*u3^5)*u4)*u5) *k^2 + (((4*u1^8+4*u1^4*u2^4+8*u1^6*u2^2)*u3^9+((-8)*u1^4*u2^5+(-16)*u1^6*u2^3+(-8)*u1^8*u2)*u3^8+((-4)*u1*u2^7+(-8)*u1^3*u2^5+(-4)*u1^5*u2^3)*u4^9+((-4)*u2^9+(-4)*u1^2*u2^7+4*u1^4*u2^5+4*u1^6*u2^3+(12*u1^2*u2^6+24*u1^4*u2^4+12*u1^6*u2^2)*u3)*u4^8+(((-12)*u1*u2^7+(-36)*u1^3*u2^5+(-36)*u1^5*u2^3+(-12)*u1^7*u2)*u3^2+(20*u1*u2^8+28*u1^3*u2^6+(-4)*u1^5*u2^4+(-12)*u1^7*u2^2)*u3)*u4^7+((4*u1^8+36*u1^2*u2^6+76*u1^4*u2^4+44*u1^6*u2^2)*u3^3+((-8)*u2^9+(-44)*u1^2*u2^7+(-52)*u1^4*u2^5+(-4)*u1^6*u2^3+12*u1^8*u2)*u3^2)*u4^6+(((-12)*u1*u2^7+(-60)*u1^3*u2^5+(-84)*u1^5*u2^3+(-36)*u1^7*u2)*u3^4+((-4)*u1^9+40*u1*u2^8+84*u1^3*u2^6+44*u1^5*u2^4+(-4)*u1^7*u2^2)*u3^3)*u4^5+((12*u1^8+36*u1^2*u2^6+84*u1^4*u2^4+60*u1^6*u2^2)*u3^5+((-4)*u2^9+(-76)*u1^2*u2^7+(-124)*u1^4*u2^5+(-36)*u1^6*u2^3+16*u1^8*u2)*u3^4)*u4^4+(((-4)*u1*u2^7+(-44)*u1^3*u2^5+(-76)*u1^5*u2^3+(-36)*u1^7*u2)*u3^6+((-8)*u1^9+20*u1*u2^8+84*u1^3*u2^6+100*u1^5*u2^4+28*u1^7*u2^2)*u3^5)*u4^3+((12*u1^8+12*u1^2*u2^6+36*u1^4*u2^4+36*u1^6*u2^2)*u3^7+((-36)*u1^2*u2^7+(-76)*u1^4*u2^5+(-44)*u1^6*u2^3+(-4)*u1^8*u2)*u3^6)*u4^2+(((-12)*u1^3*u2^5+(-24)*u1^5*u2^3+(-12)*u1^7*u2)*u3^8+((-4)*u1^9+28*u1^3*u2^6+52*u1^5*u2^4+20*u1^7*u2^2)*u3^7)*u4)*u5) *h + ((((-4)*u1^3*u2^5+(-8)*u1^5*u2^3+(-4)*u1^7*u2)*u3^9+((-4)*u1^9+4*u1^3*u2^6+4*u1^5*u2^4+(-4)*u1^7*u2^2)*u3^8+(4*u2^8+8*u1^2*u2^6+4*u1^4*u2^4)*u4^9+((-8)*u1*u2^8+(-16)*u1^3*u2^6+(-8)*u1^5*u2^4+((-12)*u1*u2^7+(-24)*u1^3*u2^5+(-12)*u1^5*u2^3)*u3)*u4^8+((12*u2^8+36*u1^2*u2^6+36*u1^4*u2^4+12*u1^6*u2^2)*u3^2+((-4)*u2^9+20*u1^2*u2^7+52*u1^4*u2^5+28*u1^6*u2^3)*u3)*u4^7+(((-36)*u1*u2^7+(-76)*u1^3*u2^5+(-44)*u1^5*u2^3+(-4)*u1^7*u2)*u3^3+((-4)*u1*u2^8+(-44)*u1^3*u2^6+(-76)*u1^5*u2^4+(-36)*u1^7*u2^2)*u3^2)*u4^6+((12*u2^8+60*u1^2*u2^6+84*u1^4*u2^4+36*u1^6*u2^2)*u3^4+((-8)*u2^9+28*u1^2*u2^7+100*u1^4*u2^5+84*u1^6*u2^3+20*u1^8*u2)*u3^3)*u4^5+(((-36)*u1*u2^7+(-84)*u1^3*u2^5+(-60)*u1^5*u2^3+(-12)*u1^7*u2)*u3^5+((-4)*u1^9+16*u1*u2^8+(-36)*u1^3*u2^6+(-124)*u1^5*u2^4+(-76)*u1^7*u2^2)*u3^4)*u4^4+((4*u2^8+44*u1^2*u2^6+76*u1^4*u2^4+36*u1^6*u2^2)*u3^6+((-4)*u2^9+(-4)*u1^2*u2^7+44*u1^4*u2^5+84*u1^6*u2^3+40*u1^8*u2)*u3^5)*u4^3+(((-12)*u1*u2^7+(-36)*u1^3*u2^5+(-36)*u1^5*u2^3+(-12)*u1^7*u2)*u3^7+((-8)*u1^9+12*u1*u2^8+(-4)*u1^3*u2^6+(-52)*u1^5*u2^4+(-44)*u1^7*u2^2)*u3^6)*u4^2+((12*u1^2*u2^6+24*u1^4*u2^4+12*u1^6*u2^2)*u3^8+((-12)*u1^2*u2^7+(-4)*u1^4*u2^5+28*u1^6*u2^3+20*u1^8*u2)*u3^7)*u4)*u5^2+((4*u1^10+4*u1^4*u2^6+12*u1^6*u2^4+12*u1^8*u2^2)*u3^8+(4*u2^10+12*u1^2*u2^8+12*u1^4*u2^6+4*u1^6*u2^4)*u4^8+(((-16)*u1*u2^9+(-48)*u1^3*u2^7+(-48)*u1^5*u2^5+(-16)*u1^7*u2^3)*u3)*u4^7+((8*u2^10+48*u1^2*u2^8+96*u1^4*u2^6+80*u1^6*u2^4+24*u1^8*u2^2)*u3^2)*u4^6+(((-32)*u1*u2^9+(-112)*u1^3*u2^7+(-144)*u1^5*u2^5+(-80)*u1^7*u2^3+(-16)*u1^9*u2)*u3^3)*u4^5+((4*u1^10+4*u2^10+60*u1^2*u2^8+160*u1^4*u2^6+160*u1^6*u2^4+60*u1^8*u2^2)*u3^4)*u4^4+(((-16)*u1*u2^9+(-80)*u1^3*u2^7+(-144)*u1^5*u2^5+(-112)*u1^7*u2^3+(-32)*u1^9*u2)*u3^5)*u4^3+((8*u1^10+24*u1^2*u2^8+80*u1^4*u2^6+96*u1^6*u2^4+48*u1^8*u2^2)*u3^6)*u4^2+(((-16)*u1^3*u2^7+(-48)*u1^5*u2^5+(-48)*u1^7*u2^3+(-16)*u1^9*u2)*u3^7)*u4)*u5) ; ];
C:=[
[
(((-4)*u1^6+(-4)*u1^4*u2^2)*u3^3+(4*u1*u2^5+4*u1^3*u2^3)*u4^3+(((-12)*u1^2*u2^4+(-12)*u1^4*u2^2)*u3)*u4^2+((12*u1^3*u2^3+12*u1^5*u2)*u3^2)*u4) *k^2 + ((8*u1^4*u2^3+8*u1^6*u2)*u3^6+(4*u1^8+(-12)*u1^4*u2^4+(-8)*u1^6*u2^2)*u3^5+(8*u1^2*u2^5+8*u1^4*u2^3)*u4^6+(4*u1*u2^7+(-8)*u1^3*u2^5+(-12)*u1^5*u2^3+((-16)*u1^3*u2^4+(-16)*u1^5*u2^2)*u3)*u4^5+((16*u1^2*u2^5+24*u1^4*u2^3+8*u1^6*u2)*u3^2+((-20)*u1^2*u2^6+8*u1^4*u2^4+28*u1^6*u2^2)*u3)*u4^4+(((-32)*u1^3*u2^4+(-32)*u1^5*u2^2)*u3^3+(4*u1*u2^7+20*u1^3*u2^5+(-4)*u1^5*u2^3+(-20)*u1^7*u2)*u3^2)*u4^3+((8*u1^2*u2^5+24*u1^4*u2^3+16*u1^6*u2)*u3^4+(4*u1^8+(-20)*u1^2*u2^6+(-4)*u1^4*u2^4+20*u1^6*u2^2)*u3^3)*u4^2+(((-16)*u1^3*u2^4+(-16)*u1^5*u2^2)*u3^5+(28*u1^3*u2^5+8*u1^5*u2^3+(-20)*u1^7*u2)*u3^4)*u4+(((-8)*u1^3*u2^3+(-8)*u1^5*u2)*u3^6+((-4)*u1^7+12*u1^3*u2^4+8*u1^5*u2^2)*u3^5+((-8)*u1*u2^5+(-8)*u1^3*u2^3)*u4^6+((-4)*u2^7+8*u1^2*u2^5+12*u1^4*u2^3+(16*u1^2*u2^4+16*u1^4*u2^2)*u3)*u4^5+(((-16)*u1*u2^5+(-24)*u1^3*u2^3+(-8)*u1^5*u2)*u3^2+(20*u1*u2^6+(-8)*u1^3*u2^4+(-28)*u1^5*u2^2)*u3)*u4^4+((32*u1^2*u2^4+32*u1^4*u2^2)*u3^3+((-4)*u2^7+(-20)*u1^2*u2^5+4*u1^4*u2^3+20*u1^6*u2)*u3^2)*u4^3+(((-8)*u1*u2^5+(-24)*u1^3*u2^3+(-16)*u1^5*u2)*u3^4+((-4)*u1^7+20*u1*u2^6+4*u1^3*u2^4+(-20)*u1^5*u2^2)*u3^3)*u4^2+((16*u1^2*u2^4+16*u1^4*u2^2)*u3^5+((-28)*u1^2*u2^5+(-8)*u1^4*u2^3+20*u1^6*u2)*u3^4)*u4)*u5) ; (((-4)*u1^6+(-4)*u1^4*u2^2)*u3^6+(8*u1^4*u2^3+8*u1^6*u2)*u3^5+((-4)*u1^2*u2^4+(-4)*u1^4*u2^2)*u4^6+((-4)*u1*u2^6+4*u1^5*u2^2+(8*u1^3*u2^3+8*u1^5*u2)*u3)*u4^5+(((-4)*u1^6+(-8)*u1^2*u2^4+(-12)*u1^4*u2^2)*u3^2+(16*u1^2*u2^5+8*u1^4*u2^3+(-8)*u1^6*u2)*u3)*u4^4+((16*u1^3*u2^3+16*u1^5*u2)*u3^3+(4*u1^7+(-4)*u1*u2^6+(-20)*u1^3*u2^4+(-12)*u1^5*u2^2)*u3^2)*u4^3+(((-8)*u1^6+(-4)*u1^2*u2^4+(-12)*u1^4*u2^2)*u3^4+(16*u1^2*u2^5+16*u1^4*u2^3)*u3^3)*u4^2+((8*u1^3*u2^3+8*u1^5*u2)*u3^5+(4*u1^7+(-20)*u1^3*u2^4+(-16)*u1^5*u2^2)*u3^4)*u4+(((-4)*u1^3*u2^3+(-4)*u1^5*u2)*u3^5+(4*u2^6+4*u1^2*u2^4)*u4^5+(((-12)*u1*u2^5+(-12)*u1^3*u2^3)*u3)*u4^4+((4*u2^6+16*u1^2*u2^4+12*u1^4*u2^2)*u3^2)*u4^3+(((-12)*u1*u2^5+(-16)*u1^3*u2^3+(-4)*u1^5*u2)*u3^3)*u4^2+((12*u1^2*u2^4+12*u1^4*u2^2)*u3^4)*u4)*u5) ; ((4*u1^10+4*u1^4*u2^6+12*u1^6*u2^4+12*u1^8*u2^2)*u3^8+((-8)*u1^4*u2^7+(-24)*u1^6*u2^5+(-24)*u1^8*u2^3+(-8)*u1^10*u2)*u3^7+(4*u1^2*u2^8+12*u1^4*u2^6+12*u1^6*u2^4+4*u1^8*u2^2)*u4^8+(4*u1*u2^10+8*u1^3*u2^8+(-8)*u1^7*u2^4+(-4)*u1^9*u2^2+((-8)*u1^3*u2^7+(-24)*u1^5*u2^5+(-24)*u1^7*u2^3+(-8)*u1^9*u2)*u3)*u4^7+((4*u1^10+12*u1^2*u2^8+40*u1^4*u2^6+48*u1^6*u2^4+24*u1^8*u2^2)*u3^2+((-16)*u1^2*u2^9+(-40)*u1^4*u2^7+(-24)*u1^6*u2^5+8*u1^8*u2^3+8*u1^10*u2)*u3)*u4^6+(((-24)*u1^3*u2^7+(-72)*u1^5*u2^5+(-72)*u1^7*u2^3+(-24)*u1^9*u2)*u3^3+((-4)*u1^11+8*u1*u2^10+36*u1^3*u2^8+56*u1^5*u2^6+32*u1^7*u2^4)*u3^2)*u4^5+((12*u1^10+12*u1^2*u2^8+48*u1^4*u2^6+72*u1^6*u2^4+48*u1^8*u2^2)*u3^4+((-32)*u1^2*u2^9+(-88)*u1^4*u2^7+(-72)*u1^6*u2^5+(-8)*u1^8*u2^3+8*u1^10*u2)*u3^3)*u4^4+(((-24)*u1^3*u2^7+(-72)*u1^5*u2^5+(-72)*u1^7*u2^3+(-24)*u1^9*u2)*u3^5+((-8)*u1^11+4*u1*u2^10+48*u1^3*u2^8+112*u1^5*u2^6+88*u1^7*u2^4+12*u1^9*u2^2)*u3^4)*u4^3+((12*u1^10+4*u1^2*u2^8+24*u1^4*u2^6+48*u1^6*u2^4+40*u1^8*u2^2)*u3^6+((-16)*u1^2*u2^9+(-56)*u1^4*u2^7+(-72)*u1^6*u2^5+(-40)*u1^8*u2^3+(-8)*u1^10*u2)*u3^5)*u4^2+(((-8)*u1^3*u2^7+(-24)*u1^5*u2^5+(-24)*u1^7*u2^3+(-8)*u1^9*u2)*u3^7+((-4)*u1^11+20*u1^3*u2^8+56*u1^5*u2^6+48*u1^7*u2^4+8*u1^9*u2^2)*u3^6)*u4+((4*u1^8+(-4)*u1^2*u2^6+(-4)*u1^4*u2^4+4*u1^6*u2^2)*u3^8+(4*u1^2*u2^7+(-4)*u1^4*u2^5+(-20)*u1^6*u2^3+(-12)*u1^8*u2)*u3^7+((-4)*u2^8+(-4)*u1^2*u2^6+4*u1^4*u2^4+4*u1^6*u2^2)*u4^8+(12*u1*u2^8+20*u1^3*u2^6+4*u1^5*u2^4+(-4)*u1^7*u2^2+(8*u1*u2^7+8*u1^3*u2^5+(-8)*u1^5*u2^3+(-8)*u1^7*u2)*u3)*u4^7+((4*u1^8+(-12)*u2^8+(-16)*u1^2*u2^6+8*u1^4*u2^4+16*u1^6*u2^2)*u3^2+(4*u2^9+(-28)*u1^2*u2^7+(-60)*u1^4*u2^5+(-20)*u1^6*u2^3+8*u1^8*u2)*u3)*u4^6+((24*u1*u2^7+24*u1^3*u2^5+(-24)*u1^5*u2^3+(-24)*u1^7*u2)*u3^3+((-4)*u1^9+16*u1*u2^8+60*u1^3*u2^6+68*u1^5*u2^4+20*u1^7*u2^2)*u3^2)*u4^5+((12*u1^8+(-12)*u2^8+(-24)*u1^2*u2^6+24*u1^6*u2^2)*u3^4+(8*u2^9+(-52)*u1^2*u2^7+(-124)*u1^4*u2^5+(-60)*u1^6*u2^3+4*u1^8*u2)*u3^3)*u4^4+((24*u1*u2^7+24*u1^3*u2^5+(-24)*u1^5*u2^3+(-24)*u1^7*u2)*u3^5+((-8)*u1^9+(-4)*u1*u2^8+60*u1^3*u2^6+124*u1^5*u2^4+52*u1^7*u2^2)*u3^4)*u4^3+((12*u1^8+(-4)*u2^8+(-16)*u1^2*u2^6+(-8)*u1^4*u2^4+16*u1^6*u2^2)*u3^6+(4*u2^9+(-20)*u1^2*u2^7+(-68)*u1^4*u2^5+(-60)*u1^6*u2^3+(-16)*u1^8*u2)*u3^5)*u4^2+((8*u1*u2^7+8*u1^3*u2^5+(-8)*u1^5*u2^3+(-8)*u1^7*u2)*u3^7+((-4)*u1^9+(-8)*u1*u2^8+20*u1^3*u2^6+60*u1^5*u2^4+28*u1^7*u2^2)*u3^6)*u4)*u5^2+(((-8)*u1^9+(-8)*u1^5*u2^4+(-16)*u1^7*u2^2)*u3^8+(4*u1^3*u2^7+28*u1^5*u2^5+44*u1^7*u2^3+20*u1^9*u2)*u3^7+((-8)*u1^3*u2^6+(-16)*u1^5*u2^4+(-8)*u1^7*u2^2)*u4^8+((-4)*u2^10+(-20)*u1^2*u2^8+(-20)*u1^4*u2^6+4*u1^6*u2^4+8*u1^8*u2^2+(16*u1^4*u2^5+32*u1^6*u2^3+16*u1^8*u2)*u3)*u4^7+(((-8)*u1^9+(-24)*u1^3*u2^6+(-56)*u1^5*u2^4+(-40)*u1^7*u2^2)*u3^2+(12*u1*u2^9+68*u1^3*u2^7+84*u1^5*u2^5+12*u1^7*u2^3+(-16)*u1^9*u2)*u3)*u4^6+((48*u1^4*u2^5+96*u1^6*u2^3+48*u1^8*u2)*u3^3+(8*u1^10+(-8)*u2^10+(-52)*u1^2*u2^8+(-116)*u1^4*u2^6+(-100)*u1^6*u2^4+(-20)*u1^8*u2^2)*u3^2)*u4^5+(((-24)*u1^9+(-24)*u1^3*u2^6+(-72)*u1^5*u2^4+(-72)*u1^7*u2^2)*u3^4+(24*u1*u2^9+140*u1^3*u2^7+196*u1^5*u2^5+68*u1^7*u2^3+(-12)*u1^9*u2)*u3^3)*u4^4+((48*u1^4*u2^5+96*u1^6*u2^3+48*u1^8*u2)*u3^5+(16*u1^10+(-4)*u2^10+(-44)*u1^2*u2^8+(-172)*u1^4*u2^6+(-212)*u1^6*u2^4+(-64)*u1^8*u2^2)*u3^4)*u4^3+(((-24)*u1^9+(-8)*u1^3*u2^6+(-40)*u1^5*u2^4+(-56)*u1^7*u2^2)*u3^6+(12*u1*u2^9+76*u1^3*u2^7+140*u1^5*u2^5+100*u1^7*u2^3+24*u1^9*u2)*u3^5)*u4^2+((16*u1^4*u2^5+32*u1^6*u2^3+16*u1^8*u2)*u3^7+(8*u1^10+(-12)*u1^2*u2^8+(-76)*u1^4*u2^6+(-108)*u1^6*u2^4+(-36)*u1^8*u2^2)*u3^6)*u4)*u5) ; (((4*u1^4*u2^3+4*u1^6*u2)*u3^6+(4*u2^7+4*u1^2*u2^5)*u4^6+(((-16)*u1*u2^6+(-16)*u1^3*u2^4)*u3)*u4^5+((4*u2^7+28*u1^2*u2^5+24*u1^4*u2^3)*u3^2)*u4^4+(((-16)*u1*u2^6+(-32)*u1^3*u2^4+(-16)*u1^5*u2^2)*u3^3)*u4^3+((24*u1^2*u2^5+28*u1^4*u2^3+4*u1^6*u2)*u3^4)*u4^2+(((-16)*u1^3*u2^4+(-16)*u1^5*u2^2)*u3^5)*u4)*u5) ; (((-1)*u1^7+(-1)*u1^3*u2^4+(-2)*u1^5*u2^2)*u3^4+((-1)*u1*u2^6+(-2)*u1^3*u2^4+(-1)*u1^5*u2^2)*u4^4+((2*u1^2*u2^5+4*u1^4*u2^3+2*u1^6*u2)*u3)*u4^3+(((-1)*u1^7+(-1)*u1*u2^6+(-3)*u1^3*u2^4+(-3)*u1^5*u2^2)*u3^2)*u4^2+((2*u1^2*u2^5+4*u1^4*u2^3+2*u1^6*u2)*u3^3)*u4) *i^2 + ((4*u1^7+4*u1^3*u2^4+8*u1^5*u2^2)*u3^4+((-4)*u1^3*u2^5+(-8)*u1^5*u2^3+(-4)*u1^7*u2)*u3^3+(u1^9+u1^3*u2^6+3*u1^5*u2^4+3*u1^7*u2^2)*u3^2+(4*u1*u2^6+8*u1^3*u2^4+4*u1^5*u2^2)*u4^4+((-4)*u1^2*u2^6+(-8)*u1^4*u2^4+(-4)*u1^6*u2^2+((-8)*u1^2*u2^5+(-16)*u1^4*u2^3+(-8)*u1^6*u2)*u3)*u4^3+(u1*u2^8+3*u1^3*u2^6+3*u1^5*u2^4+u1^7*u2^2+(4*u1^7+4*u1*u2^6+12*u1^3*u2^4+12*u1^5*u2^2)*u3^2+((-4)*u1*u2^7+12*u1^5*u2^3+8*u1^7*u2)*u3)*u4^2+(((-8)*u1^2*u2^5+(-16)*u1^4*u2^3+(-8)*u1^6*u2)*u3^3+((-4)*u1^8+8*u1^2*u2^6+12*u1^4*u2^4)*u3^2+((-2)*u1^2*u2^7+(-6)*u1^4*u2^5+(-6)*u1^6*u2^3+(-2)*u1^8*u2)*u3)*u4) *k^2 + ((4*u1^3*u2^5+8*u1^5*u2^3+4*u1^7*u2)*u3^6+(2*u1^9+(-6)*u1^3*u2^6+(-10)*u1^5*u2^4+(-2)*u1^7*u2^2)*u3^5+(2*u1^3*u2^7+6*u1^5*u2^5+6*u1^7*u2^3+2*u1^9*u2)*u3^4+(4*u1*u2^7+8*u1^3*u2^5+4*u1^5*u2^3)*u4^6+((-8)*u1^2*u2^7+(-16)*u1^4*u2^5+(-8)*u1^6*u2^3+((-8)*u1^2*u2^6+(-16)*u1^4*u2^4+(-8)*u1^6*u2^2)*u3)*u4^5+(2*u1*u2^9+6*u1^3*u2^7+6*u1^5*u2^5+2*u1^7*u2^3+(8*u1*u2^7+20*u1^3*u2^5+16*u1^5*u2^3+4*u1^7*u2)*u3^2+((-6)*u1*u2^8+6*u1^3*u2^6+30*u1^5*u2^4+18*u1^7*u2^2)*u3)*u4^4+(((-16)*u1^2*u2^6+(-32)*u1^4*u2^4+(-16)*u1^6*u2^2)*u3^3+(4*u1^2*u2^7+(-4)*u1^4*u2^5+(-20)*u1^6*u2^3+(-12)*u1^8*u2)*u3^2+((-4)*u1^2*u2^8+(-12)*u1^4*u2^6+(-12)*u1^6*u2^4+(-4)*u1^8*u2^2)*u3)*u4^3+((4*u1*u2^7+16*u1^3*u2^5+20*u1^5*u2^3+8*u1^7*u2)*u3^4+(2*u1^9+(-6)*u1*u2^8+20*u1^5*u2^4+16*u1^7*u2^2)*u3^3+(2*u1*u2^9+8*u1^3*u2^7+12*u1^5*u2^5+8*u1^7*u2^3+2*u1^9*u2)*u3^2)*u4^2+(((-8)*u1^2*u2^6+(-16)*u1^4*u2^4+(-8)*u1^6*u2^2)*u3^5+(12*u1^2*u2^7+12*u1^4*u2^5+(-12)*u1^6*u2^3+(-12)*u1^8*u2)*u3^4+((-4)*u1^2*u2^8+(-12)*u1^4*u2^6+(-12)*u1^6*u2^4+(-4)*u1^8*u2^2)*u3^3)*u4) *h + (((-4)*u1^3*u2^4+(-4)*u1^5*u2^2)*u3^8+(8*u1^3*u2^5+(-8)*u1^7*u2)*u3^7+((-7)*u1^9+(-7)*u1^3*u2^6+(-5)*u1^5*u2^4+(-5)*u1^7*u2^2)*u3^6+(4*u1^3*u2^7+12*u1^5*u2^5+12*u1^7*u2^3+4*u1^9*u2)*u3^5+((-1)*u1^11+(-1)*u1^3*u2^8+(-4)*u1^5*u2^6+(-6)*u1^7*u2^4+(-4)*u1^9*u2^2)*u3^4+((-4)*u1*u2^6+(-4)*u1^3*u2^4)*u4^8+(16*u1^2*u2^6+16*u1^4*u2^4+(8*u1^2*u2^5+8*u1^4*u2^3)*u3)*u4^7+((-3)*u1*u2^8+(-25)*u1^3*u2^6+(-25)*u1^5*u2^4+(-3)*u1^7*u2^2+((-12)*u1*u2^6+(-16)*u1^3*u2^4+(-4)*u1^5*u2^2)*u3^2+(8*u1*u2^7+(-32)*u1^3*u2^5+(-40)*u1^5*u2^3)*u3)*u4^6+(4*u1^2*u2^8+12*u1^4*u2^6+12*u1^6*u2^4+4*u1^8*u2^2+(24*u1^2*u2^5+24*u1^4*u2^3)*u3^3+(16*u1^2*u2^6+48*u1^4*u2^4+32*u1^6*u2^2)*u3^2+((-10)*u1^2*u2^7+50*u1^4*u2^5+66*u1^6*u2^3+6*u1^8*u2)*u3)*u4^5+((-1)*u1*u2^10+(-4)*u1^3*u2^8+(-6)*u1^5*u2^6+(-4)*u1^7*u2^4+(-1)*u1^9*u2^2+((-12)*u1*u2^6+(-24)*u1^3*u2^4+(-12)*u1^5*u2^2)*u3^4+(16*u1*u2^7+(-56)*u1^3*u2^5+(-80)*u1^5*u2^3+(-8)*u1^7*u2)*u3^3+((-3)*u1^9+(-10)*u1*u2^8+(-1)*u1^3*u2^6+(-55)*u1^5*u2^4+(-67)*u1^7*u2^2)*u3^2+(4*u1*u2^9+4*u1^3*u2^7+(-12)*u1^5*u2^5+(-20)*u1^7*u2^3+(-8)*u1^9*u2)*u3)*u4^4+((24*u1^2*u2^5+24*u1^4*u2^3)*u3^5+((-16)*u1^2*u2^6+48*u1^4*u2^4+64*u1^6*u2^2)*u3^4+(4*u1^2*u2^7+44*u1^4*u2^5+76*u1^6*u2^3+36*u1^8*u2)*u3^3+(4*u1^10+(-4)*u1^2*u2^8+(-8)*u1^4*u2^6+8*u1^8*u2^2)*u3^2+(2*u1^2*u2^9+8*u1^4*u2^7+12*u1^6*u2^5+8*u1^8*u2^3+2*u1^10*u2)*u3)*u4^3+(((-4)*u1*u2^6+(-16)*u1^3*u2^4+(-12)*u1^5*u2^2)*u3^6+(8*u1*u2^7+(-16)*u1^3*u2^5+(-40)*u1^5*u2^3+(-16)*u1^7*u2)*u3^5+((-10)*u1^9+(-7)*u1*u2^8+17*u1^3*u2^6+(-35)*u1^5*u2^4+(-69)*u1^7*u2^2)*u3^4+(4*u1*u2^9+8*u1^3*u2^7+(-8)*u1^7*u2^3+(-4)*u1^9*u2)*u3^3+((-1)*u1^11+(-1)*u1*u2^10+(-5)*u1^3*u2^8+(-10)*u1^5*u2^6+(-10)*u1^7*u2^4+(-5)*u1^9*u2^2)*u3^2)*u4^2+((8*u1^2*u2^5+8*u1^4*u2^3)*u3^7+((-16)*u1^2*u2^6+16*u1^4*u2^4+32*u1^6*u2^2)*u3^6+(14*u1^2*u2^7+(-6)*u1^4*u2^5+10*u1^6*u2^3+30*u1^8*u2)*u3^5+(4*u1^10+(-8)*u1^2*u2^8+(-20)*u1^4*u2^6+(-12)*u1^6*u2^4+4*u1^8*u2^2)*u3^4+(2*u1^2*u2^9+8*u1^4*u2^7+12*u1^6*u2^5+8*u1^8*u2^3+2*u1^10*u2)*u3^3)*u4+((4*u1^4*u2^3+4*u1^6*u2)*u3^7+(4*u1^8+(-4)*u1^4*u2^4)*u3^6+((-8)*u1^4*u2^5+(-16)*u1^6*u2^3+(-8)*u1^8*u2)*u3^5+(2*u1^10+2*u1^4*u2^6+6*u1^6*u2^4+6*u1^8*u2^2)*u3^4+((-4)*u1*u2^6+(-4)*u1^3*u2^4)*u4^7+((-4)*u2^8+4*u1^2*u2^6+12*u1^4*u2^4+4*u1^6*u2^2+(12*u1^2*u2^5+12*u1^4*u2^3)*u3)*u4^6+(2*u1*u2^8+(-2)*u1^3*u2^6+(-10)*u1^5*u2^4+(-6)*u1^7*u2^2+((-8)*u1*u2^6+(-20)*u1^3*u2^4+(-12)*u1^5*u2^2)*u3^2+(20*u1*u2^7+(-28)*u1^5*u2^3+(-8)*u1^7*u2)*u3)*u4^5+(2*u1^2*u2^8+6*u1^4*u2^6+6*u1^6*u2^4+2*u1^8*u2^2+(24*u1^2*u2^5+28*u1^4*u2^3+4*u1^6*u2)*u3^3+(4*u1^8+(-4)*u2^8+(-28)*u1^2*u2^6+28*u1^6*u2^2)*u3^2+((-12)*u1^2*u2^7+(-12)*u1^4*u2^5+12*u1^6*u2^3+12*u1^8*u2)*u3)*u4^4+(((-4)*u1*u2^6+(-28)*u1^3*u2^4+(-24)*u1^5*u2^2)*u3^4+(20*u1*u2^7+20*u1^3*u2^5+(-20)*u1^5*u2^3+(-20)*u1^7*u2)*u3^3+((-6)*u1^9+2*u1*u2^8+16*u1^3*u2^6+20*u1^5*u2^4)*u3^2+((-4)*u1^3*u2^7+(-12)*u1^5*u2^5+(-12)*u1^7*u2^3+(-4)*u1^9*u2)*u3)*u4^3+((12*u1^2*u2^5+20*u1^4*u2^3+8*u1^6*u2)*u3^5+(8*u1^8+(-32)*u1^2*u2^6+(-16)*u1^4*u2^4+24*u1^6*u2^2)*u3^4+((-12)*u1^2*u2^7+(-20)*u1^4*u2^5+(-4)*u1^6*u2^3+4*u1^8*u2)*u3^3+(2*u1^10+2*u1^2*u2^8+8*u1^4*u2^6+12*u1^6*u2^4+8*u1^8*u2^2)*u3^2)*u4^2+(((-12)*u1^3*u2^4+(-12)*u1^5*u2^2)*u3^6+(20*u1^3*u2^5+8*u1^5*u2^3+(-12)*u1^7*u2)*u3^5+((-6)*u1^9+18*u1^3*u2^6+30*u1^5*u2^4+6*u1^7*u2^2)*u3^4+((-4)*u1^3*u2^7+(-12)*u1^5*u2^5+(-12)*u1^7*u2^3+(-4)*u1^9*u2)*u3^3)*u4)*u5) ; ((2*u1^7+2*u1^3*u2^4+4*u1^5*u2^2)*u3^4+(2*u1*u2^6+4*u1^3*u2^4+2*u1^5*u2^2)*u4^4+(((-4)*u1^2*u2^5+(-8)*u1^4*u2^3+(-4)*u1^6*u2)*u3)*u4^3+((2*u1^7+2*u1*u2^6+6*u1^3*u2^4+6*u1^5*u2^2)*u3^2)*u4^2+(((-4)*u1^2*u2^5+(-8)*u1^4*u2^3+(-4)*u1^6*u2)*u3^3)*u4) *i^2 + (((-1)*u1^7+(-1)*u1^3*u2^4+(-2)*u1^5*u2^2)*u3^4+((-1)*u1*u2^6+(-2)*u1^3*u2^4+(-1)*u1^5*u2^2)*u4^4+((2*u1^2*u2^5+4*u1^4*u2^3+2*u1^6*u2)*u3)*u4^3+(((-1)*u1^7+(-1)*u1*u2^6+(-3)*u1^3*u2^4+(-3)*u1^5*u2^2)*u3^2)*u4^2+((2*u1^2*u2^5+4*u1^4*u2^3+2*u1^6*u2)*u3^3)*u4) *j^2 + ((u1^7+u1^3*u2^4+2*u1^5*u2^2)*u3^4+(2*u1^3*u2^5+4*u1^5*u2^3+2*u1^7*u2)*u3^3+((-1)*u1^9+(-1)*u1^3*u2^6+(-3)*u1^5*u2^4+(-3)*u1^7*u2^2)*u3^2+(u1*u2^6+2*u1^3*u2^4+u1^5*u2^2)*u4^4+(2*u1^2*u2^6+4*u1^4*u2^4+2*u1^6*u2^2+((-2)*u1^2*u2^5+(-4)*u1^4*u2^3+(-2)*u1^6*u2)*u3)*u4^3+((-1)*u1*u2^8+(-3)*u1^3*u2^6+(-3)*u1^5*u2^4+(-1)*u1^7*u2^2+(u1^7+u1*u2^6+3*u1^3*u2^4+3*u1^5*u2^2)*u3^2+(2*u1*u2^7+(-6)*u1^5*u2^3+(-4)*u1^7*u2)*u3)*u4^2+(((-2)*u1^2*u2^5+(-4)*u1^4*u2^3+(-2)*u1^6*u2)*u3^3+(2*u1^8+(-4)*u1^2*u2^6+(-6)*u1^4*u2^4)*u3^2+(2*u1^2*u2^7+6*u1^4*u2^5+6*u1^6*u2^3+2*u1^8*u2)*u3)*u4) *k^2 + (((-2)*u1^3*u2^5+(-4)*u1^5*u2^3+(-2)*u1^7*u2)*u3^6+(4*u1^3*u2^6+8*u1^5*u2^4+4*u1^7*u2^2)*u3^5+((-2)*u1^3*u2^7+(-6)*u1^5*u2^5+(-6)*u1^7*u2^3+(-2)*u1^9*u2)*u3^4+((-2)*u1*u2^7+(-4)*u1^3*u2^5+(-2)*u1^5*u2^3)*u4^6+(4*u1^2*u2^7+8*u1^4*u2^5+4*u1^6*u2^3+(4*u1^2*u2^6+8*u1^4*u2^4+4*u1^6*u2^2)*u3)*u4^5+((-2)*u1*u2^9+(-6)*u1^3*u2^7+(-6)*u1^5*u2^5+(-2)*u1^7*u2^3+((-4)*u1*u2^7+(-10)*u1^3*u2^5+(-8)*u1^5*u2^3+(-2)*u1^7*u2)*u3^2+(4*u1*u2^8+(-12)*u1^5*u2^4+(-8)*u1^7*u2^2)*u3)*u4^4+((8*u1^2*u2^6+16*u1^4*u2^4+8*u1^6*u2^2)*u3^3+((-4)*u1^2*u2^7+(-4)*u1^4*u2^5+4*u1^6*u2^3+4*u1^8*u2)*u3^2+(4*u1^2*u2^8+12*u1^4*u2^6+12*u1^6*u2^4+4*u1^8*u2^2)*u3)*u4^3+(((-2)*u1*u2^7+(-8)*u1^3*u2^5+(-10)*u1^5*u2^3+(-4)*u1^7*u2)*u3^4+(4*u1*u2^8+4*u1^3*u2^6+(-4)*u1^5*u2^4+(-4)*u1^7*u2^2)*u3^3+((-2)*u1*u2^9+(-8)*u1^3*u2^7+(-12)*u1^5*u2^5+(-8)*u1^7*u2^3+(-2)*u1^9*u2)*u3^2)*u4^2+((4*u1^2*u2^6+8*u1^4*u2^4+4*u1^6*u2^2)*u3^5+((-8)*u1^2*u2^7+(-12)*u1^4*u2^5+4*u1^8*u2)*u3^4+(4*u1^2*u2^8+12*u1^4*u2^6+12*u1^6*u2^4+4*u1^8*u2^2)*u3^3)*u4) *h + ((u1^9+u1^3*u2^6+3*u1^5*u2^4+3*u1^7*u2^2)*u3^6+((-2)*u1^3*u2^7+(-6)*u1^5*u2^5+(-6)*u1^7*u2^3+(-2)*u1^9*u2)*u3^5+(u1^11+u1^3*u2^8+4*u1^5*u2^6+6*u1^7*u2^4+4*u1^9*u2^2)*u3^4+(u1*u2^8+3*u1^3*u2^6+3*u1^5*u2^4+u1^7*u2^2)*u4^6+((-2)*u1^2*u2^8+(-6)*u1^4*u2^6+(-6)*u1^6*u2^4+(-2)*u1^8*u2^2+((-2)*u1^2*u2^7+(-6)*u1^4*u2^5+(-6)*u1^6*u2^3+(-2)*u1^8*u2)*u3)*u4^5+(u1*u2^10+4*u1^3*u2^8+6*u1^5*u2^6+4*u1^7*u2^4+u1^9*u2^2+(u1^9+2*u1*u2^8+7*u1^3*u2^6+9*u1^5*u2^4+5*u1^7*u2^2)*u3^2+((-2)*u1*u2^9+(-2)*u1^3*u2^7+6*u1^5*u2^5+10*u1^7*u2^3+4*u1^9*u2)*u3)*u4^4+(((-4)*u1^2*u2^7+(-12)*u1^4*u2^5+(-12)*u1^6*u2^3+(-4)*u1^8*u2)*u3^3+((-2)*u1^10+2*u1^2*u2^8+4*u1^4*u2^6+(-4)*u1^8*u2^2)*u3^2+((-2)*u1^2*u2^9+(-8)*u1^4*u2^7+(-12)*u1^6*u2^5+(-8)*u1^8*u2^3+(-2)*u1^10*u2)*u3)*u4^3+((2*u1^9+u1*u2^8+5*u1^3*u2^6+9*u1^5*u2^4+7*u1^7*u2^2)*u3^4+((-2)*u1*u2^9+(-4)*u1^3*u2^7+4*u1^7*u2^3+2*u1^9*u2)*u3^3+(u1^11+u1*u2^10+5*u1^3*u2^8+10*u1^5*u2^6+10*u1^7*u2^4+5*u1^9*u2^2)*u3^2)*u4^2+(((-2)*u1^2*u2^7+(-6)*u1^4*u2^5+(-6)*u1^6*u2^3+(-2)*u1^8*u2)*u3^5+((-2)*u1^10+4*u1^2*u2^8+10*u1^4*u2^6+6*u1^6*u2^4+(-2)*u1^8*u2^2)*u3^4+((-2)*u1^2*u2^9+(-8)*u1^4*u2^7+(-12)*u1^6*u2^5+(-8)*u1^8*u2^3+(-2)*u1^10*u2)*u3^3)*u4+(((-2)*u1^8+(-2)*u1^4*u2^4+(-4)*u1^6*u2^2)*u3^6+(4*u1^4*u2^5+8*u1^6*u2^3+4*u1^8*u2)*u3^5+((-2)*u1^10+(-2)*u1^4*u2^6+(-6)*u1^6*u2^4+(-6)*u1^8*u2^2)*u3^4+((-2)*u1^2*u2^6+(-4)*u1^4*u2^4+(-2)*u1^6*u2^2)*u4^6+(4*u1^3*u2^6+8*u1^5*u2^4+4*u1^7*u2^2+(4*u1^3*u2^5+8*u1^5*u2^3+4*u1^7*u2)*u3)*u4^5+((-2)*u1^2*u2^8+(-6)*u1^4*u2^6+(-6)*u1^6*u2^4+(-2)*u1^8*u2^2+((-2)*u1^8+(-4)*u1^2*u2^6+(-10)*u1^4*u2^4+(-8)*u1^6*u2^2)*u3^2+(4*u1^2*u2^7+(-12)*u1^6*u2^3+(-8)*u1^8*u2)*u3)*u4^4+((8*u1^3*u2^5+16*u1^5*u2^3+8*u1^7*u2)*u3^3+(4*u1^9+(-4)*u1^3*u2^6+(-4)*u1^5*u2^4+4*u1^7*u2^2)*u3^2+(4*u1^3*u2^7+12*u1^5*u2^5+12*u1^7*u2^3+4*u1^9*u2)*u3)*u4^3+(((-4)*u1^8+(-2)*u1^2*u2^6+(-8)*u1^4*u2^4+(-10)*u1^6*u2^2)*u3^4+(4*u1^2*u2^7+4*u1^4*u2^5+(-4)*u1^6*u2^3+(-4)*u1^8*u2)*u3^3+((-2)*u1^10+(-2)*u1^2*u2^8+(-8)*u1^4*u2^6+(-12)*u1^6*u2^4+(-8)*u1^8*u2^2)*u3^2)*u4^2+((4*u1^3*u2^5+8*u1^5*u2^3+4*u1^7*u2)*u3^5+(4*u1^9+(-8)*u1^3*u2^6+(-12)*u1^5*u2^4)*u3^4+(4*u1^3*u2^7+12*u1^5*u2^5+12*u1^7*u2^3+4*u1^9*u2)*u3^3)*u4)*u5) ; 0; 0; ((4*u1^3*u2^4+4*u1^5*u2^2)*u3^10+((-8)*u1^3*u2^5+8*u1^7*u2)*u3^9+(4*u1^9+4*u1^3*u2^6+(-4)*u1^5*u2^4+(-4)*u1^7*u2^2)*u3^8+(4*u1*u2^6+4*u1^3*u2^4)*u4^10+((-16)*u1^2*u2^6+(-16)*u1^4*u2^4+((-8)*u1^2*u2^5+(-8)*u1^4*u2^3)*u3)*u4^9+(16*u1^3*u2^6+16*u1^5*u2^4+(16*u1*u2^6+20*u1^3*u2^4+4*u1^5*u2^2)*u3^2+((-8)*u1*u2^7+32*u1^3*u2^5+40*u1^5*u2^3)*u3)*u4^8+(((-32)*u1^2*u2^5+(-32)*u1^4*u2^3)*u3^3+((-32)*u1^2*u2^6+(-64)*u1^4*u2^4+(-32)*u1^6*u2^2)*u3^2+(16*u1^2*u2^7+(-32)*u1^4*u2^5+(-48)*u1^6*u2^3)*u3)*u4^7+((24*u1*u2^6+40*u1^3*u2^4+16*u1^5*u2^2)*u3^4+((-24)*u1*u2^7+88*u1^3*u2^5+120*u1^5*u2^3+8*u1^7*u2)*u3^3+(4*u1*u2^8+(-4)*u1^3*u2^6+44*u1^5*u2^4+52*u1^7*u2^2)*u3^2)*u4^6+(((-48)*u1^2*u2^5+(-48)*u1^4*u2^3)*u3^5+((-96)*u1^4*u2^4+(-96)*u1^6*u2^2)*u3^4+(24*u1^2*u2^7+(-40)*u1^4*u2^5+(-88)*u1^6*u2^3+(-24)*u1^8*u2)*u3^3)*u4^5+((16*u1*u2^6+40*u1^3*u2^4+24*u1^5*u2^2)*u3^6+((-24)*u1*u2^7+72*u1^3*u2^5+120*u1^5*u2^3+24*u1^7*u2)*u3^5+(4*u1^9+8*u1*u2^8+(-52)*u1^3*u2^6+36*u1^5*u2^4+100*u1^7*u2^2)*u3^4)*u4^4+(((-32)*u1^2*u2^5+(-32)*u1^4*u2^3)*u3^7+(32*u1^2*u2^6+(-64)*u1^4*u2^4+(-96)*u1^6*u2^2)*u3^6+(16*u1^4*u2^5+(-32)*u1^6*u2^3+(-48)*u1^8*u2)*u3^5)*u4^3+((4*u1*u2^6+20*u1^3*u2^4+16*u1^5*u2^2)*u3^8+((-8)*u1*u2^7+8*u1^3*u2^5+40*u1^5*u2^3+24*u1^7*u2)*u3^7+(8*u1^9+4*u1*u2^8+(-28)*u1^3*u2^6+4*u1^5*u2^4+44*u1^7*u2^2)*u3^6)*u4^2+(((-8)*u1^2*u2^5+(-8)*u1^4*u2^3)*u3^9+(16*u1^2*u2^6+(-16)*u1^4*u2^4+(-32)*u1^6*u2^2)*u3^8+((-8)*u1^2*u2^7+24*u1^4*u2^5+8*u1^6*u2^3+(-24)*u1^8*u2)*u3^7)*u4+(((-4)*u1^4*u2^3+(-4)*u1^6*u2)*u3^9+(8*u1^4*u2^4+8*u1^6*u2^2)*u3^8+(4*u1*u2^6+4*u1^3*u2^4)*u4^9+(4*u2^8+(-4)*u1^4*u2^4+((-12)*u1^2*u2^5+(-12)*u1^4*u2^3)*u3)*u4^8+((12*u1*u2^6+24*u1^3*u2^4+12*u1^5*u2^2)*u3^2+((-20)*u1*u2^7+(-8)*u1^3*u2^5+12*u1^5*u2^3)*u3)*u4^7+(((-36)*u1^2*u2^5+(-40)*u1^4*u2^3+(-4)*u1^6*u2)*u3^3+(8*u2^8+36*u1^2*u2^6+16*u1^4*u2^4+(-12)*u1^6*u2^2)*u3^2)*u4^6+((12*u1*u2^6+48*u1^3*u2^4+36*u1^5*u2^2)*u3^4+((-40)*u1*u2^7+(-44)*u1^3*u2^5+4*u1^7*u2)*u3^3)*u4^5+(((-36)*u1^2*u2^5+(-48)*u1^4*u2^3+(-12)*u1^6*u2)*u3^5+(4*u2^8+72*u1^2*u2^6+52*u1^4*u2^4+(-16)*u1^6*u2^2)*u3^4)*u4^4+((4*u1*u2^6+40*u1^3*u2^4+36*u1^5*u2^2)*u3^6+((-20)*u1*u2^7+(-64)*u1^3*u2^5+(-36)*u1^5*u2^3+8*u1^7*u2)*u3^5)*u4^3+(((-12)*u1^2*u2^5+(-24)*u1^4*u2^3+(-12)*u1^6*u2)*u3^7+(36*u1^2*u2^6+40*u1^4*u2^4+4*u1^6*u2^2)*u3^6)*u4^2+((12*u1^3*u2^4+12*u1^5*u2^2)*u3^8+((-28)*u1^3*u2^5+(-24)*u1^5*u2^3+4*u1^7*u2)*u3^7)*u4)*u5) ; ((8*u1^5*u2^5+16*u1^7*u2^3+8*u1^9*u2)*u3^9+((-16)*u1^5*u2^6+(-32)*u1^7*u2^4+(-16)*u1^9*u2^2)*u3^8+((-8)*u1^2*u2^8+(-16)*u1^4*u2^6+(-8)*u1^6*u2^4)*u4^9+((-8)*u1*u2^10+(-8)*u1^3*u2^8+8*u1^5*u2^6+8*u1^7*u2^4+(24*u1^3*u2^7+48*u1^5*u2^5+24*u1^7*u2^3)*u3)*u4^8+(((-24)*u1^2*u2^8+(-72)*u1^4*u2^6+(-72)*u1^6*u2^4+(-24)*u1^8*u2^2)*u3^2+(40*u1^2*u2^9+56*u1^4*u2^7+(-8)*u1^6*u2^5+(-24)*u1^8*u2^3)*u3)*u4^7+((72*u1^3*u2^7+152*u1^5*u2^5+88*u1^7*u2^3+8*u1^9*u2)*u3^3+((-16)*u1*u2^10+(-88)*u1^3*u2^8+(-104)*u1^5*u2^6+(-8)*u1^7*u2^4+24*u1^9*u2^2)*u3^2)*u4^6+(((-24)*u1^2*u2^8+(-120)*u1^4*u2^6+(-168)*u1^6*u2^4+(-72)*u1^8*u2^2)*u3^4+(80*u1^2*u2^9+168*u1^4*u2^7+88*u1^6*u2^5+(-8)*u1^8*u2^3+(-8)*u1^10*u2)*u3^3)*u4^5+((72*u1^3*u2^7+168*u1^5*u2^5+120*u1^7*u2^3+24*u1^9*u2)*u3^5+((-8)*u1*u2^10+(-152)*u1^3*u2^8+(-248)*u1^5*u2^6+(-72)*u1^7*u2^4+32*u1^9*u2^2)*u3^4)*u4^4+(((-8)*u1^2*u2^8+(-88)*u1^4*u2^6+(-152)*u1^6*u2^4+(-72)*u1^8*u2^2)*u3^6+(40*u1^2*u2^9+168*u1^4*u2^7+200*u1^6*u2^5+56*u1^8*u2^3+(-16)*u1^10*u2)*u3^5)*u4^3+((24*u1^3*u2^7+72*u1^5*u2^5+72*u1^7*u2^3+24*u1^9*u2)*u3^7+((-72)*u1^3*u2^8+(-152)*u1^5*u2^6+(-88)*u1^7*u2^4+(-8)*u1^9*u2^2)*u3^6)*u4^2+(((-24)*u1^4*u2^6+(-48)*u1^6*u2^4+(-24)*u1^8*u2^2)*u3^8+(56*u1^4*u2^7+104*u1^6*u2^5+40*u1^8*u2^3+(-8)*u1^10*u2)*u3^7)*u4+(((-4)*u1^4*u2^5+(-8)*u1^6*u2^3+(-4)*u1^8*u2)*u3^9+(8*u1^4*u2^6+16*u1^6*u2^4+8*u1^8*u2^2)*u3^8+(4*u1*u2^8+8*u1^3*u2^6+4*u1^5*u2^4)*u4^9+(4*u2^10+4*u1^2*u2^8+(-4)*u1^4*u2^6+(-4)*u1^6*u2^4+((-12)*u1^2*u2^7+(-24)*u1^4*u2^5+(-12)*u1^6*u2^3)*u3)*u4^8+((12*u1*u2^8+36*u1^3*u2^6+36*u1^5*u2^4+12*u1^7*u2^2)*u3^2+((-20)*u1*u2^9+(-28)*u1^3*u2^7+4*u1^5*u2^5+12*u1^7*u2^3)*u3)*u4^7+(((-36)*u1^2*u2^7+(-76)*u1^4*u2^5+(-44)*u1^6*u2^3+(-4)*u1^8*u2)*u3^3+(8*u2^10+44*u1^2*u2^8+52*u1^4*u2^6+4*u1^6*u2^4+(-12)*u1^8*u2^2)*u3^2)*u4^6+((12*u1*u2^8+60*u1^3*u2^6+84*u1^5*u2^4+36*u1^7*u2^2)*u3^4+((-40)*u1*u2^9+(-84)*u1^3*u2^7+(-44)*u1^5*u2^5+4*u1^7*u2^3+4*u1^9*u2)*u3^3)*u4^5+(((-36)*u1^2*u2^7+(-84)*u1^4*u2^5+(-60)*u1^6*u2^3+(-12)*u1^8*u2)*u3^5+(4*u2^10+76*u1^2*u2^8+124*u1^4*u2^6+36*u1^6*u2^4+(-16)*u1^8*u2^2)*u3^4)*u4^4+((4*u1*u2^8+44*u1^3*u2^6+76*u1^5*u2^4+36*u1^7*u2^2)*u3^6+((-20)*u1*u2^9+(-84)*u1^3*u2^7+(-100)*u1^5*u2^5+(-28)*u1^7*u2^3+8*u1^9*u2)*u3^5)*u4^3+(((-12)*u1^2*u2^7+(-36)*u1^4*u2^5+(-36)*u1^6*u2^3+(-12)*u1^8*u2)*u3^7+(36*u1^2*u2^8+76*u1^4*u2^6+44*u1^6*u2^4+4*u1^8*u2^2)*u3^6)*u4^2+((12*u1^3*u2^6+24*u1^5*u2^4+12*u1^7*u2^2)*u3^8+((-28)*u1^3*u2^7+(-52)*u1^5*u2^5+(-20)*u1^7*u2^3+4*u1^9*u2)*u3^7)*u4)*u5) ; 0; ((((-4)*u1^8+(-4)*u1^4*u2^4+(-8)*u1^6*u2^2)*u3^6+((-4)*u2^8+(-8)*u1^2*u2^6+(-4)*u1^4*u2^4)*u4^6+((16*u1*u2^7+32*u1^3*u2^5+16*u1^5*u2^3)*u3)*u4^5+(((-4)*u2^8+(-32)*u1^2*u2^6+(-52)*u1^4*u2^4+(-24)*u1^6*u2^2)*u3^2)*u4^4+((16*u1*u2^7+48*u1^3*u2^5+48*u1^5*u2^3+16*u1^7*u2)*u3^3)*u4^3+(((-4)*u1^8+(-24)*u1^2*u2^6+(-52)*u1^4*u2^4+(-32)*u1^6*u2^2)*u3^4)*u4^2+((16*u1^3*u2^5+32*u1^5*u2^3+16*u1^7*u2)*u3^5)*u4)*u5) *k^2 + (((4*u1^8+4*u1^4*u2^4+8*u1^6*u2^2)*u3^9+((-8)*u1^4*u2^5+(-16)*u1^6*u2^3+(-8)*u1^8*u2)*u3^8+((-4)*u1*u2^7+(-8)*u1^3*u2^5+(-4)*u1^5*u2^3)*u4^9+((-4)*u2^9+(-4)*u1^2*u2^7+4*u1^4*u2^5+4*u1^6*u2^3+(12*u1^2*u2^6+24*u1^4*u2^4+12*u1^6*u2^2)*u3)*u4^8+(((-12)*u1*u2^7+(-36)*u1^3*u2^5+(-36)*u1^5*u2^3+(-12)*u1^7*u2)*u3^2+(20*u1*u2^8+28*u1^3*u2^6+(-4)*u1^5*u2^4+(-12)*u1^7*u2^2)*u3)*u4^7+((4*u1^8+36*u1^2*u2^6+76*u1^4*u2^4+44*u1^6*u2^2)*u3^3+((-8)*u2^9+(-44)*u1^2*u2^7+(-52)*u1^4*u2^5+(-4)*u1^6*u2^3+12*u1^8*u2)*u3^2)*u4^6+(((-12)*u1*u2^7+(-60)*u1^3*u2^5+(-84)*u1^5*u2^3+(-36)*u1^7*u2)*u3^4+((-4)*u1^9+40*u1*u2^8+84*u1^3*u2^6+44*u1^5*u2^4+(-4)*u1^7*u2^2)*u3^3)*u4^5+((12*u1^8+36*u1^2*u2^6+84*u1^4*u2^4+60*u1^6*u2^2)*u3^5+((-4)*u2^9+(-76)*u1^2*u2^7+(-124)*u1^4*u2^5+(-36)*u1^6*u2^3+16*u1^8*u2)*u3^4)*u4^4+(((-4)*u1*u2^7+(-44)*u1^3*u2^5+(-76)*u1^5*u2^3+(-36)*u1^7*u2)*u3^6+((-8)*u1^9+20*u1*u2^8+84*u1^3*u2^6+100*u1^5*u2^4+28*u1^7*u2^2)*u3^5)*u4^3+((12*u1^8+12*u1^2*u2^6+36*u1^4*u2^4+36*u1^6*u2^2)*u3^7+((-36)*u1^2*u2^7+(-76)*u1^4*u2^5+(-44)*u1^6*u2^3+(-4)*u1^8*u2)*u3^6)*u4^2+(((-12)*u1^3*u2^5+(-24)*u1^5*u2^3+(-12)*u1^7*u2)*u3^8+((-4)*u1^9+28*u1^3*u2^6+52*u1^5*u2^4+20*u1^7*u2^2)*u3^7)*u4)*u5) *h + ((((-4)*u1^3*u2^5+(-8)*u1^5*u2^3+(-4)*u1^7*u2)*u3^9+((-4)*u1^9+4*u1^3*u2^6+4*u1^5*u2^4+(-4)*u1^7*u2^2)*u3^8+(4*u2^8+8*u1^2*u2^6+4*u1^4*u2^4)*u4^9+((-8)*u1*u2^8+(-16)*u1^3*u2^6+(-8)*u1^5*u2^4+((-12)*u1*u2^7+(-24)*u1^3*u2^5+(-12)*u1^5*u2^3)*u3)*u4^8+((12*u2^8+36*u1^2*u2^6+36*u1^4*u2^4+12*u1^6*u2^2)*u3^2+((-4)*u2^9+20*u1^2*u2^7+52*u1^4*u2^5+28*u1^6*u2^3)*u3)*u4^7+(((-36)*u1*u2^7+(-76)*u1^3*u2^5+(-44)*u1^5*u2^3+(-4)*u1^7*u2)*u3^3+((-4)*u1*u2^8+(-44)*u1^3*u2^6+(-76)*u1^5*u2^4+(-36)*u1^7*u2^2)*u3^2)*u4^6+((12*u2^8+60*u1^2*u2^6+84*u1^4*u2^4+36*u1^6*u2^2)*u3^4+((-8)*u2^9+28*u1^2*u2^7+100*u1^4*u2^5+84*u1^6*u2^3+20*u1^8*u2)*u3^3)*u4^5+(((-36)*u1*u2^7+(-84)*u1^3*u2^5+(-60)*u1^5*u2^3+(-12)*u1^7*u2)*u3^5+((-4)*u1^9+16*u1*u2^8+(-36)*u1^3*u2^6+(-124)*u1^5*u2^4+(-76)*u1^7*u2^2)*u3^4)*u4^4+((4*u2^8+44*u1^2*u2^6+76*u1^4*u2^4+36*u1^6*u2^2)*u3^6+((-4)*u2^9+(-4)*u1^2*u2^7+44*u1^4*u2^5+84*u1^6*u2^3+40*u1^8*u2)*u3^5)*u4^3+(((-12)*u1*u2^7+(-36)*u1^3*u2^5+(-36)*u1^5*u2^3+(-12)*u1^7*u2)*u3^7+((-8)*u1^9+12*u1*u2^8+(-4)*u1^3*u2^6+(-52)*u1^5*u2^4+(-44)*u1^7*u2^2)*u3^6)*u4^2+((12*u1^2*u2^6+24*u1^4*u2^4+12*u1^6*u2^2)*u3^8+((-12)*u1^2*u2^7+(-4)*u1^4*u2^5+28*u1^6*u2^3+20*u1^8*u2)*u3^7)*u4)*u5^2+((4*u1^10+4*u1^4*u2^6+12*u1^6*u2^4+12*u1^8*u2^2)*u3^8+(4*u2^10+12*u1^2*u2^8+12*u1^4*u2^6+4*u1^6*u2^4)*u4^8+(((-16)*u1*u2^9+(-48)*u1^3*u2^7+(-48)*u1^5*u2^5+(-16)*u1^7*u2^3)*u3)*u4^7+((8*u2^10+48*u1^2*u2^8+96*u1^4*u2^6+80*u1^6*u2^4+24*u1^8*u2^2)*u3^2)*u4^6+(((-32)*u1*u2^9+(-112)*u1^3*u2^7+(-144)*u1^5*u2^5+(-80)*u1^7*u2^3+(-16)*u1^9*u2)*u3^3)*u4^5+((4*u1^10+4*u2^10+60*u1^2*u2^8+160*u1^4*u2^6+160*u1^6*u2^4+60*u1^8*u2^2)*u3^4)*u4^4+(((-16)*u1*u2^9+(-80)*u1^3*u2^7+(-144)*u1^5*u2^5+(-112)*u1^7*u2^3+(-32)*u1^9*u2)*u3^5)*u4^3+((8*u1^10+24*u1^2*u2^8+80*u1^4*u2^6+96*u1^6*u2^4+48*u1^8*u2^2)*u3^6)*u4^2+(((-16)*u1^3*u2^7+(-48)*u1^5*u2^5+(-48)*u1^7*u2^3+(-16)*u1^9*u2)*u3^7)*u4)*u5) ; ];
[
0; (((-1)*u1^2+(-1)*u2^2)*u3^2+((-1)*u1^2+(-1)*u2^2)*u4^2) *h ; 0; (u1*u3+(-1)*u2*u4) ; 0; 0; 0; ((-1)*u1*u3^3+u2*u4^3+(-1)*u1*u3*u4^2+u2*u3^2*u4) ; (((-1)*u1^3+(-1)*u1*u2^2)*u3^3+(u2^3+u1^2*u2)*u4^3+(((-1)*u1^3+(-1)*u1*u2^2)*u3)*u4^2+((u2^3+u1^2*u2)*u3^2)*u4) ; 0; 0; ];
[
(u1^2+u2^2) *k^2 ; (u1*u3+(-1)*u2*u4) ; 0; 0; 0; 0; 0; 0; 0; 0; ];
[
0; 0; 0; 0; 0; 0; 0; ((-1)*u1) ; (u4) ; ];
[
((-1)) *h ; 0; ((-2)*u1^2+(-2)*u2^2) *g ; 0; (u3^2+u4^2) *h ; ((u1^2+u2^2)*u3^2+(u1^2+u2^2)*u4^2) *h ; 0; 0; ];
[
0; ((-1)*u1^2+(-1)*u2^2) ; 0; (u3^2+u4^2) ; 0; 0; 0; ];
[
((-1)*u1^2+(-1)*u2^2+(-1)*u3^2+2*u2*u3+(-1)*u4^2+2*u1*u4) ; (u3^2+u4^2) ; 0; 0; 0; 0; ];
];
c:=
1;