Solution 13 to problem l1o35
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Expressions
The solution is given through the following expressions:
b75=0
b74=0
b73=0
b72=(2/27*a16*b27)/(sqrt(5)*a2 - 5/3*a2)
b71= - b27
b70=0
b69= - 1/3*sqrt(5)*b27 - 4/3*b27
b68=(7/2*sqrt(5)*a2*b27 - 5/2*a2*b27)/a16
b67=(sqrt(5)*a2*b27 - 5*a2*b27)/a16
b66=0
b65=0
b64=(7/2*sqrt(5)*a2*b27 - 5/2*a2*b27)/a16
b63=0
b62=(sqrt(5)*a2*b27)/a16
b61=(15/2*sqrt(5)*a2**2*b27 - 45/2*a2**2*b27)/a16**2
b60=(15*sqrt(5)*a2**2*b27 - 30*a2**2*b27)/a16**2
b59=0
b58=0
b57=0
b56=0
b55=( - 1/42525*sqrt(5)*a16**4*b27 - 1/42525*a16**4*b27)/(sqrt(5)*a2**3*a22 - 47
/21*a2**3*a22)
b54=( - 1/486*sqrt(5)*a16**3*b27 - 1/486*a16**3*b27)/(sqrt(5)*a2**2*a22 - 20/9*
a2**2*a22)
b53=( - 1/243*sqrt(5)*a16**3*b27 - 1/243*a16**3*b27)/(sqrt(5)*a2**2*a22 - 20/9*
a2**2*a22)
b52=( - 2/27*sqrt(5)*a16**2*b27 - 2/27*a16**2*b27)/(sqrt(5)*a2*a22 - 7/3*a2*a22)
b51=( - 2/9*sqrt(5)*a16**2*b27 - 2/9*a16**2*b27)/(sqrt(5)*a2*a22 - 7/3*a2*a22)
b50=( - 1/9*sqrt(5)*a16**2*b27 - 1/9*a16**2*b27)/(sqrt(5)*a2*a22 - 7/3*a2*a22)
b49=( - 2/27*sqrt(5)*a16**2*b27 - 2/27*a16**2*b27)/(sqrt(5)*a2*a22 - 7/3*a2*a22)
b48=( - 10/9*sqrt(5)*a16*b27 - 10/9*a16*b27)/(sqrt(5)*a22 - 5/3*a22)
b47=( - 10/3*sqrt(5)*a16*b27 - 10/3*a16*b27)/(sqrt(5)*a22 - 5/3*a22)
b46=( - 5/3*sqrt(5)*a16*b27 - 5/3*a16*b27)/(sqrt(5)*a22 - 5/3*a22)
b45=( - 20/9*sqrt(5)*a16*b27 - 20/9*a16*b27)/(sqrt(5)*a22 - 5/3*a22)
b44=( - 10/9*sqrt(5)*a16*b27 - 10/9*a16*b27)/(sqrt(5)*a22 - 5/3*a22)
b43=( - 5/9*sqrt(5)*a16*b27 - 5/9*a16*b27)/(sqrt(5)*a22 - 5/3*a22)
b42=(5/2*sqrt(5)*a2*b27 + 5/2*a2*b27)/a22
b41=(5*sqrt(5)*a2*b27 + 5*a2*b27)/a22
b40=(5*sqrt(5)*a2*b27 + 5*a2*b27)/a22
b39=(5/2*sqrt(5)*a2*b27 + 5/2*a2*b27)/a22
b38=(1/2*sqrt(5)*a2*b27 + 1/2*a2*b27)/a22
b37=(3/2*sqrt(5)*a2**2*b27 - 15/2*a2**2*b27)/(a16*a22)
b36=0
b35=0
b34=0
b33=0
b32=0
b31=0
b30=0
b29=0
b28=2/3*b27
b26=( - 9/2*sqrt(5)*a2*b27 + 15/2*a2*b27)/a16
b25=( - 9/2*sqrt(5)*a2*b27 + 15/2*a2*b27)/a16
b24=( - 16*sqrt(5)*a2*b27 + 20*a2*b27)/a16
b23=( - 7/2*sqrt(5)*a2*b27 + 5/2*a2*b27)/a16
b22=( - 7/2*sqrt(5)*a2*b27 + 5/2*a2*b27)/a16
b21=( - 75/2*sqrt(5)*a2**2*b27 + 195/2*a2**2*b27)/a16**2
b20=( - 195/2*sqrt(5)*a2**2*b27 + 435/2*a2**2*b27)/a16**2
b19=( - 75*sqrt(5)*a2**2*b27 + 195*a2**2*b27)/a16**2
b18=( - 135/2*sqrt(5)*a2**2*b27 + 315/2*a2**2*b27)/a16**2
b17=( - 105/2*sqrt(5)*a2**2*b27 + 285/2*a2**2*b27)/a16**2
b16=( - 15/2*sqrt(5)*a2**2*b27 + 45/2*a2**2*b27)/a16**2
b15=( - 315/2*sqrt(5)*a2**3*b27 + 675/2*a2**3*b27)/a16**3
b14=( - 405*sqrt(5)*a2**3*b27 + 900*a2**3*b27)/a16**3
b13=( - 495/2*sqrt(5)*a2**3*b27 + 1125/2*a2**3*b27)/a16**3
b12=0
b11=0
b10=0
b9=0
b8=0
b7=0
b6=0
b5=0
b4=0
b3=0
b2=0
a21=( - 9/2*sqrt(5)*a2*a22 + 15/2*a2*a22)/a16
a20=0
a19=(1/810*sqrt(5)*a16**3 + 1/810*a16**3)/(sqrt(5)*a2**2 - 20/9*a2**2)
a18=( - 2/9*a16**2)/(sqrt(5)*a2 - 5/3*a2)
a17=(1/15*sqrt(5)*a16**2 - 1/45*a16**2)/(sqrt(5)*a2 - 7/3*a2)
a15=a16
a14=(1/3*sqrt(5)*a16 - 1/3*a16)/(sqrt(5) - 5/3)
a13= - 3/2*sqrt(5)*a2 + 5/2*a2
a12=0
a11=0
a10=(9*sqrt(5)*a2*a22 - 15*a2*a22)/a16
a9=(9/2*sqrt(5)*a2*a22 - 15/2*a2*a22)/a16
a8=(135/2*sqrt(5)*a2**2*a22 - 315/2*a2**2*a22)/a16**2
a7=(135/2*sqrt(5)*a2**2*a22 - 315/2*a2**2*a22)/a16**2
a6=0
a5=( - 8/45*a16**2)/(sqrt(5)*a2 - 7/3*a2)
a4=( - 4/3*a16)/(sqrt(5) - 5/3)
a3=( - 4/3*a16)/(sqrt(5) - 5/3)
Parameters
Apart from the condition that they must not vanish to give
a non-trivial solution and a non-singular solution with
non-vanishing denominators, the following parameters are free:
b27,a22,a16,a2
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\$
2 2 20 2 2 1 3
df(u,t)=(sqrt(5)*u *a16 *a2 - ----*u *a16 *a2 + ---*sqrt(5)*u *a16 *a2*u
3x 9 3x 3 2x
7 3 1 2 3 7 2 3
- ---*u *a16 *a2*u + ---*sqrt(5)*u *a16 *a2 - ---*u *a16 *a2
9 2x 3 x 9 x
35 2 2 4 2
- ----*sqrt(5)*u *f(v,v)*a16*a2 *a22 + ----*sqrt(5)*u *a16 *u
2 x 45 x
235 2 2 4 2
+ -----*u *f(v,v)*a16*a2 *a22 - ----*u *a16 *u
6 x 27 x
615 3 615 3
- -----*sqrt(5)*f(v ,v )*a2 *a22 - -----*sqrt(5)*f(v,v )*a2 *a22
2 x x 2 2x
2 1375 3
- 35*sqrt(5)*f(v,v )*a16*a2 *a22*u + ------*f(v ,v )*a2 *a22
x 2 x x
1375 3 235 2
+ ------*f(v,v )*a2 *a22 + -----*f(v,v )*a16*a2 *a22*u)/(
2 2x 3 x
2 20 2
sqrt(5)*a16 *a2 - ----*a16 *a2)
9
199 2 2 89 2 2
df(v,t)=(-----*sqrt(5)*u *a16 *a2 *v - -----*u *a16 *a2 *v
720 2x 144 2x
2 2 161 2 2
+ sqrt(5)*u *v *a16 *a2 - -----*u *v *a16 *a2
x x 72 x x
3 3 181 3
+ ----*sqrt(5)*u *a16 *a2*u*v - ------*u *a16 *a2*u*v
80 x 2160 x
281 3 1885 3
+ -----*sqrt(5)*v *a16*a2 - ------*v *a16*a2
48 3x 144 3x
2 2 161 2 2
+ sqrt(5)*v *a16 *a2 *u - -----*v *a16 *a2 *u
2x 72 2x
41 3 2 55 3 2
+ -----*sqrt(5)*v *a16 *a2*u - -----*v *a16 *a2*u
720 x 432 x
281 3 2
+ -----*sqrt(5)*f(v,v )*a2 *a22*v + sqrt(5)*f(v,v)*a16*a2 *a22*u*v
16 x
11 4 3 1885 3
+ -------*sqrt(5)*a16 *u *v - ------*f(v,v )*a2 *a22*v
32400 48 x
161 2 1 4 3 2
- -----*f(v,v)*a16*a2 *a22*u*v - ------*a16 *u *v)/(sqrt(5)*a16*a2
72 1296
161 2
- -----*a16*a2 )
72
15 2 45 2
df(u,s)=( - ----*sqrt(5)*u *f(v,v)*a16*a2 *b27 + ----*u *f(v,v)*a16*a2 *b27
2 3x 2 3x
105 2
- -----*sqrt(5)*u *f(v,v )*a16*a2 *b27
2 2x x
7 2 285 2
- ---*sqrt(5)*u *f(v,v)*a16 *a2*b27*u + -----*u *f(v,v )*a16*a2 *b27
2 2x 2 2x x
5 2 7 2 2
+ ---*u *f(v,v)*a16 *a2*b27*u - ---*sqrt(5)*u *f(v,v)*a16 *a2*b27
2 2x 2 x
5 2 2 135 2
+ ---*u *f(v,v)*a16 *a2*b27 - -----*sqrt(5)*u *f(v ,v )*a16*a2 *b27
2 x 2 x x x
2
- 75*sqrt(5)*u *f(v,v )*a16*a2 *b27
x 2x
2 315 2
- 16*sqrt(5)*u *f(v,v )*a16 *a2*b27*u + -----*u *f(v ,v )*a16*a2 *b27
x x 2 x x x
2 2
+ 195*u *f(v,v )*a16*a2 *b27 + 20*u *f(v,v )*a16 *a2*b27*u
x 2x x x
3 2 495 3
+ u *f(v,v)*a16 *b27*u - -----*sqrt(5)*f(v ,v )*a2 *b27
x 2 2x 2x
3
- 405*sqrt(5)*f(v ,v )*a2 *b27
x 3x
195 2
- -----*sqrt(5)*f(v ,v )*a16*a2 *b27*u
2 x 2x
9 2 2 315 3
- ---*sqrt(5)*f(v ,v )*a16 *a2*b27*u - -----*sqrt(5)*f(v,v )*a2 *b27
2 x x 2 4x
75 2
- ----*sqrt(5)*f(v,v )*a16*a2 *b27*u
2 3x
9 2 2 1125 3
- ---*sqrt(5)*f(v,v )*a16 *a2*b27*u + ------*f(v ,v )*a2 *b27
2 2x 2 2x 2x
3 435 2
+ 900*f(v ,v )*a2 *b27 + -----*f(v ,v )*a16*a2 *b27*u
x 3x 2 x 2x
15 2 2 675 3
+ ----*f(v ,v )*a16 *a2*b27*u + -----*f(v,v )*a2 *b27
2 x x 2 4x
195 2 15 2 2
+ -----*f(v,v )*a16*a2 *b27*u + ----*f(v,v )*a16 *a2*b27*u
2 3x 2 2x
2 3 3 3
+ ---*f(v,v )*a16 *b27*u )/a16
3 x
4181 2 4 9349 2 4
df(v,s)=( - ------*sqrt(5)*u *a16 *a2 *b27*v + ------*u *a16 *a2 *b27*v
6765 4x 6765 4x
4181 2 4 9349 2 4
- ------*sqrt(5)*u *v *a16 *a2 *b27 + ------*u *v *a16 *a2 *b27
1353 3x x 1353 3x x
3571 3 3 1597 3 3
- -------*sqrt(5)*u *a16 *a2 *b27*u*v + ------*u *a16 *a2 *b27*u*v
20295 3x 4059 3x
7142 3 3 3194 3 3
- -------*sqrt(5)*u *u *a16 *a2 *b27*v + ------*u *u *a16 *a2 *b27*v
20295 2x x 4059 2x x
8362 2 4 18698 2 4
- ------*sqrt(5)*u *v *a16 *a2 *b27 + -------*u *v *a16 *a2 *b27
1353 2x 2x 1353 2x 2x
14284 3 3 6388 3 3
- -------*sqrt(5)*u *v *a16 *a2 *b27*u + ------*u *v *a16 *a2 *b27*u
20295 2x x 4059 2x x
15127 4
- -------*sqrt(5)*u *f(v,v)*a16*a2 *a22*b27*v
6765 2x
244 4 2 2
- -------*sqrt(5)*u *a16 *a2 *b27*u *v
12177 2x
4 248 4 2 2
+ 5*u *f(v,v)*a16*a2 *a22*b27*v + ------*u *a16 *a2 *b27*u *v
2x 5535 2x
3571 2 3 3 1597 2 3 3
- ------*sqrt(5)*u *v *a16 *a2 *b27 + ------*u *v *a16 *a2 *b27
6765 x x 1353 x x
122 2 4 2 124 2 4 2
- ------*sqrt(5)*u *a16 *a2 *b27*u*v + ------*u *a16 *a2 *b27*u*v
4059 x 1845 x
8362 2 4 18698 2 4
- ------*sqrt(5)*u *v *a16 *a2 *b27 + -------*u *v *a16 *a2 *b27
1353 x 3x 1353 x 3x
7142 3 3 3194 3 3
- ------*sqrt(5)*u *v *a16 *a2 *b27*u + ------*u *v *a16 *a2 *b27*u
6765 x 2x 1353 x 2x
244 4 2 2 248 4 2 2
- ------*sqrt(5)*u *v *a16 *a2 *b27*u + ------*u *v *a16 *a2 *b27*u
4059 x x 1845 x x
69857 4
- -------*sqrt(5)*u *f(v,v )*a16*a2 *a22*b27*v
6765 x x
11933 2 3
- -------*sqrt(5)*u *f(v,v)*a16 *a2 *a22*b27*u*v
20295 x
1042 5 3
- --------*sqrt(5)*u *a16 *a2*b27*u *v
913275 x
31241 4
+ -------*u *f(v,v )*a16*a2 *a22*b27*v
1353 x x
26683 2 3
+ -------*u *f(v,v)*a16 *a2 *a22*b27*u*v
20295 x
466 5 3 24476 5
+ --------*u *a16 *a2*b27*u *v - -------*sqrt(5)*v *a16*a2 *b27
182655 x 2255 5x
10946 5 4181 2 4
+ -------*v *a16*a2 *b27 - ------*sqrt(5)*v *a16 *a2 *b27*u
451 5x 1353 4x
9349 2 4 7142 3 3 2
+ ------*v *a16 *a2 *b27*u - -------*sqrt(5)*v *a16 *a2 *b27*u
1353 4x 20295 3x
3194 3 3 2 244 4 2 3
+ ------*v *a16 *a2 *b27*u - -------*sqrt(5)*v *a16 *a2 *b27*u
4059 3x 12177 2x
248 4 2 3 521 5 4
+ ------*v *a16 *a2 *b27*u - --------*sqrt(5)*v *a16 *a2*b27*u
5535 2x 913275 x
233 5 4 28657 5
+ --------*v *a16 *a2*b27*u - -------*sqrt(5)*f(v ,v )*a2 *a22*b27*v
182655 x 451 x 2x
48952 4
- -------*sqrt(5)*f(v ,v )*a16*a2 *a22*b27*u*v
6765 x x
17711 5
- -------*sqrt(5)*f(v,v )*a2 *a22*b27*v
451 3x
69857 4
- -------*sqrt(5)*f(v,v )*a16*a2 *a22*b27*u*v
6765 2x
2 3 2
- sqrt(5)*f(v,v )*a16 *a2 *a22*b27*u *v
x
214 3 2 3
- -------*sqrt(5)*f(v,v)*a16 *a2 *a22*b27*u *v
11275
89 6 5 64079 5
- ----------*sqrt(5)*a16 *b27*u *v + -------*f(v ,v )*a2 *a22*b27*v
13699125 451 x 2x
21892 4
+ -------*f(v ,v )*a16*a2 *a22*b27*u*v
1353 x x
39603 5
+ -------*f(v,v )*a2 *a22*b27*v
451 3x
31241 4
+ -------*f(v,v )*a16*a2 *a22*b27*u*v
1353 2x
15127 2 3 2
+ -------*f(v,v )*a16 *a2 *a22*b27*u *v
6765 x
2584 3 2 3 199 6 5
+ -------*f(v,v)*a16 *a2 *a22*b27*u *v + ----------*a16 *b27*u *v)/(
60885 13699125
2 3 15127 2 3
sqrt(5)*a16 *a2 *a22 - -------*a16 *a2 *a22)
6765
df(u,t)=(sqrt(5)*df(u,x,3)*a16**2*a2**2 - 20/9*df(u,x,3)*a16**2*a2**2 + 1/3*sqrt
(5)*df(u,x,2)*a16**3*a2*u - 7/9*df(u,x,2)*a16**3*a2*u + 1/3*sqrt(5)*df(u,x)**2*
a16**3*a2 - 7/9*df(u,x)**2*a16**3*a2 - 35/2*sqrt(5)*df(u,x)*f(v,v)*a16*a2**2*a22
+ 2/45*sqrt(5)*df(u,x)*a16**4*u**2 + 235/6*df(u,x)*f(v,v)*a16*a2**2*a22 - 2/27*
df(u,x)*a16**4*u**2 - 615/2*sqrt(5)*f(df(v,x),df(v,x))*a2**3*a22 - 615/2*sqrt(5)
*f(v,df(v,x,2))*a2**3*a22 - 35*sqrt(5)*f(v,df(v,x))*a16*a2**2*a22*u + 1375/2*f(
df(v,x),df(v,x))*a2**3*a22 + 1375/2*f(v,df(v,x,2))*a2**3*a22 + 235/3*f(v,df(v,x)
)*a16*a2**2*a22*u)/(sqrt(5)*a16**2*a2 - 20/9*a16**2*a2)$
df(v,t)=(199/720*sqrt(5)*df(u,x,2)*a16**2*a2**2*v - 89/144*df(u,x,2)*a16**2*a2**
2*v + sqrt(5)*df(u,x)*df(v,x)*a16**2*a2**2 - 161/72*df(u,x)*df(v,x)*a16**2*a2**2
+ 3/80*sqrt(5)*df(u,x)*a16**3*a2*u*v - 181/2160*df(u,x)*a16**3*a2*u*v + 281/48*
sqrt(5)*df(v,x,3)*a16*a2**3 - 1885/144*df(v,x,3)*a16*a2**3 + sqrt(5)*df(v,x,2)*
a16**2*a2**2*u - 161/72*df(v,x,2)*a16**2*a2**2*u + 41/720*sqrt(5)*df(v,x)*a16**3
*a2*u**2 - 55/432*df(v,x)*a16**3*a2*u**2 + 281/16*sqrt(5)*f(v,df(v,x))*a2**3*a22
*v + sqrt(5)*f(v,v)*a16*a2**2*a22*u*v + 11/32400*sqrt(5)*a16**4*u**3*v - 1885/48
*f(v,df(v,x))*a2**3*a22*v - 161/72*f(v,v)*a16*a2**2*a22*u*v - 1/1296*a16**4*u**3
*v)/(sqrt(5)*a16*a2**2 - 161/72*a16*a2**2)$
df(u,s)=( - 15/2*sqrt(5)*df(u,x,3)*f(v,v)*a16*a2**2*b27 + 45/2*df(u,x,3)*f(v,v)*
a16*a2**2*b27 - 105/2*sqrt(5)*df(u,x,2)*f(v,df(v,x))*a16*a2**2*b27 - 7/2*sqrt(5)
*df(u,x,2)*f(v,v)*a16**2*a2*b27*u + 285/2*df(u,x,2)*f(v,df(v,x))*a16*a2**2*b27 +
5/2*df(u,x,2)*f(v,v)*a16**2*a2*b27*u - 7/2*sqrt(5)*df(u,x)**2*f(v,v)*a16**2*a2*
b27 + 5/2*df(u,x)**2*f(v,v)*a16**2*a2*b27 - 135/2*sqrt(5)*df(u,x)*f(df(v,x),df(v
,x))*a16*a2**2*b27 - 75*sqrt(5)*df(u,x)*f(v,df(v,x,2))*a16*a2**2*b27 - 16*sqrt(5
)*df(u,x)*f(v,df(v,x))*a16**2*a2*b27*u + 315/2*df(u,x)*f(df(v,x),df(v,x))*a16*a2
**2*b27 + 195*df(u,x)*f(v,df(v,x,2))*a16*a2**2*b27 + 20*df(u,x)*f(v,df(v,x))*a16
**2*a2*b27*u + df(u,x)*f(v,v)*a16**3*b27*u**2 - 495/2*sqrt(5)*f(df(v,x,2),df(v,x
,2))*a2**3*b27 - 405*sqrt(5)*f(df(v,x),df(v,x,3))*a2**3*b27 - 195/2*sqrt(5)*f(df
(v,x),df(v,x,2))*a16*a2**2*b27*u - 9/2*sqrt(5)*f(df(v,x),df(v,x))*a16**2*a2*b27*
u**2 - 315/2*sqrt(5)*f(v,df(v,x,4))*a2**3*b27 - 75/2*sqrt(5)*f(v,df(v,x,3))*a16*
a2**2*b27*u - 9/2*sqrt(5)*f(v,df(v,x,2))*a16**2*a2*b27*u**2 + 1125/2*f(df(v,x,2)
,df(v,x,2))*a2**3*b27 + 900*f(df(v,x),df(v,x,3))*a2**3*b27 + 435/2*f(df(v,x),df(
v,x,2))*a16*a2**2*b27*u + 15/2*f(df(v,x),df(v,x))*a16**2*a2*b27*u**2 + 675/2*f(v
,df(v,x,4))*a2**3*b27 + 195/2*f(v,df(v,x,3))*a16*a2**2*b27*u + 15/2*f(v,df(v,x,2
))*a16**2*a2*b27*u**2 + 2/3*f(v,df(v,x))*a16**3*b27*u**3)/a16**3$
df(v,s)=( - 4181/6765*sqrt(5)*df(u,x,4)*a16**2*a2**4*b27*v + 9349/6765*df(u,x,4)
*a16**2*a2**4*b27*v - 4181/1353*sqrt(5)*df(u,x,3)*df(v,x)*a16**2*a2**4*b27 +
9349/1353*df(u,x,3)*df(v,x)*a16**2*a2**4*b27 - 3571/20295*sqrt(5)*df(u,x,3)*a16
**3*a2**3*b27*u*v + 1597/4059*df(u,x,3)*a16**3*a2**3*b27*u*v - 7142/20295*sqrt(5
)*df(u,x,2)*df(u,x)*a16**3*a2**3*b27*v + 3194/4059*df(u,x,2)*df(u,x)*a16**3*a2**
3*b27*v - 8362/1353*sqrt(5)*df(u,x,2)*df(v,x,2)*a16**2*a2**4*b27 + 18698/1353*df
(u,x,2)*df(v,x,2)*a16**2*a2**4*b27 - 14284/20295*sqrt(5)*df(u,x,2)*df(v,x)*a16**
3*a2**3*b27*u + 6388/4059*df(u,x,2)*df(v,x)*a16**3*a2**3*b27*u - 15127/6765*sqrt
(5)*df(u,x,2)*f(v,v)*a16*a2**4*a22*b27*v - 244/12177*sqrt(5)*df(u,x,2)*a16**4*a2
**2*b27*u**2*v + 5*df(u,x,2)*f(v,v)*a16*a2**4*a22*b27*v + 248/5535*df(u,x,2)*a16
**4*a2**2*b27*u**2*v - 3571/6765*sqrt(5)*df(u,x)**2*df(v,x)*a16**3*a2**3*b27 +
1597/1353*df(u,x)**2*df(v,x)*a16**3*a2**3*b27 - 122/4059*sqrt(5)*df(u,x)**2*a16
**4*a2**2*b27*u*v + 124/1845*df(u,x)**2*a16**4*a2**2*b27*u*v - 8362/1353*sqrt(5)
*df(u,x)*df(v,x,3)*a16**2*a2**4*b27 + 18698/1353*df(u,x)*df(v,x,3)*a16**2*a2**4*
b27 - 7142/6765*sqrt(5)*df(u,x)*df(v,x,2)*a16**3*a2**3*b27*u + 3194/1353*df(u,x)
*df(v,x,2)*a16**3*a2**3*b27*u - 244/4059*sqrt(5)*df(u,x)*df(v,x)*a16**4*a2**2*
b27*u**2 + 248/1845*df(u,x)*df(v,x)*a16**4*a2**2*b27*u**2 - 69857/6765*sqrt(5)*
df(u,x)*f(v,df(v,x))*a16*a2**4*a22*b27*v - 11933/20295*sqrt(5)*df(u,x)*f(v,v)*
a16**2*a2**3*a22*b27*u*v - 1042/913275*sqrt(5)*df(u,x)*a16**5*a2*b27*u**3*v +
31241/1353*df(u,x)*f(v,df(v,x))*a16*a2**4*a22*b27*v + 26683/20295*df(u,x)*f(v,v)
*a16**2*a2**3*a22*b27*u*v + 466/182655*df(u,x)*a16**5*a2*b27*u**3*v - 24476/2255
*sqrt(5)*df(v,x,5)*a16*a2**5*b27 + 10946/451*df(v,x,5)*a16*a2**5*b27 - 4181/1353
*sqrt(5)*df(v,x,4)*a16**2*a2**4*b27*u + 9349/1353*df(v,x,4)*a16**2*a2**4*b27*u -
7142/20295*sqrt(5)*df(v,x,3)*a16**3*a2**3*b27*u**2 + 3194/4059*df(v,x,3)*a16**3
*a2**3*b27*u**2 - 244/12177*sqrt(5)*df(v,x,2)*a16**4*a2**2*b27*u**3 + 248/5535*
df(v,x,2)*a16**4*a2**2*b27*u**3 - 521/913275*sqrt(5)*df(v,x)*a16**5*a2*b27*u**4
+ 233/182655*df(v,x)*a16**5*a2*b27*u**4 - 28657/451*sqrt(5)*f(df(v,x),df(v,x,2))
*a2**5*a22*b27*v - 48952/6765*sqrt(5)*f(df(v,x),df(v,x))*a16*a2**4*a22*b27*u*v -
17711/451*sqrt(5)*f(v,df(v,x,3))*a2**5*a22*b27*v - 69857/6765*sqrt(5)*f(v,df(v,
x,2))*a16*a2**4*a22*b27*u*v - sqrt(5)*f(v,df(v,x))*a16**2*a2**3*a22*b27*u**2*v -
214/11275*sqrt(5)*f(v,v)*a16**3*a2**2*a22*b27*u**3*v - 89/13699125*sqrt(5)*a16
**6*b27*u**5*v + 64079/451*f(df(v,x),df(v,x,2))*a2**5*a22*b27*v + 21892/1353*f(
df(v,x),df(v,x))*a16*a2**4*a22*b27*u*v + 39603/451*f(v,df(v,x,3))*a2**5*a22*b27*
v + 31241/1353*f(v,df(v,x,2))*a16*a2**4*a22*b27*u*v + 15127/6765*f(v,df(v,x))*
a16**2*a2**3*a22*b27*u**2*v + 2584/60885*f(v,v)*a16**3*a2**2*a22*b27*u**3*v +
199/13699125*a16**6*b27*u**5*v)/(sqrt(5)*a16**2*a2**3*a22 - 15127/6765*a16**2*a2
**3*a22)$