2 3 3 2
a14 *a18 *b24 - a18 *a2 *b24
b42=------------------------------------------
5 4 3 2 2 3
a14 - 3*a14 *a2 + 3*a14 *a2 - a14 *a2
3 2 2 3 2 2
---*a14 *a18 *b24 - ---*a18 *a2 *b24
2 2
b41=----------------------------------------
3 2 2
a12*a14 - 2*a12*a14 *a2 + a12*a14*a2
2 2 2 2
6*a14 *a18 *b24 - 6*a18 *a2 *b24
b40=----------------------------------
4 3 2 2
a14 - 2*a14 *a2 + a14 *a2
2
3*a18 *b24
b39=-----------------------
2 2
a14 - 2*a14*a2 + a2
3 3
---*a14*a18*b24 + ---*a18*a2*b24
4 4
b38=----------------------------------
2
a12
3*a14*a18*b24 + 3*a18*a2*b24
b37=------------------------------
a12*a14
3*a14*a18*b24
b36=------------------
a12*a14 - a12*a2
3 3
---*a14*a18*b24 + ---*a18*a2*b24
2 2
b35=----------------------------------
a12*a14
b34=0
b33=0
6*a18*b24
b32=-----------
a14
3*a18*b24
b31=-----------
a14 - a2
1 3 1 2
---*a14 *b24 - ---*a14*a2 *b24
8 8
b30=--------------------------------
3
a12
3 2
---*a14 *b24
4
b29=--------------
2
a12
3 2 3 2
---*a14 *b24 - ---*a2 *b24
4 4
b28=----------------------------
2
a12
3
---*a14*b24
2
b27=-------------
a12
3 3
---*a14*b24 - ---*a2*b24
2 2
b26=--------------------------
a12
b25=0
2 4 4 2
- 4*a12*a14 *a18 *b24 + 4*a12*a18 *a2 *b24
b23=-------------------------------------------------------
7 6 5 2 4 3 3 4
a14 - 4*a14 *a2 + 6*a14 *a2 - 4*a14 *a2 + a14 *a2
2 3 3 2
- 6*a14 *a18 *b24 + 6*a18 *a2 *b24
b22=------------------------------------------
5 4 3 2 2 3
a14 - 3*a14 *a2 + 3*a14 *a2 - a14 *a2
3 3
- 36*a12*a14*a18 *b24 - 36*a12*a18 *a2*b24
b21=---------------------------------------------
5 4 3 2
a14 - 2*a14 *a2 + a14 *a2
2 2
- 3*a14*a18 *b24 - 3*a18 *a2*b24
b20=-----------------------------------
2
a12*a14 - a12*a14*a2
2 2
- 24*a14*a18 *b24 - 24*a18 *a2*b24
b19=-------------------------------------
3 2
a14 - a14 *a2
2 2 2 2
- 6*a14 *a18 *b24 + 9*a18 *a2 *b24
b18=-------------------------------------
4 3 2 2
a14 - 2*a14 *a2 + a14 *a2
2
- 24*a12*a18 *b24
b17=----------------------------
3 2 2
a14 - 2*a14 *a2 + a14*a2
2 2
- 12*a12*a14*a18 *b24 - 12*a12*a18 *a2*b24
b16=---------------------------------------------
4 3 2 2
a14 - 2*a14 *a2 + a14 *a2
2
- 12*a12*a18 *a2*b24
b15=-----------------------------
4 3 2 2
a14 - 2*a14 *a2 + a14 *a2
1 1
- ---*a14*a18*b24 - ---*a18*a2*b24
2 2
b14=-------------------------------------
2
a12
- 3*a14*a18*b24 - 3*a18*a2*b24
b13=---------------------------------
a12*a14
2 2
- 3*a14 *a18*b24 + 6*a18*a2 *b24
b12=-----------------------------------
2
a12*a14 - a12*a14*a2
- 6*a14*a18*b24 - 6*a18*a2*b24
b11=---------------------------------
2
a14 - a14*a2
- 6*a18*a2*b24
b10=-----------------
2
a14 - a14*a2
- 6*a14*a18*b24 - 6*a18*a2*b24
b9=---------------------------------
2
a14 - a14*a2
- 3*a18*a2*b24
b8=-----------------
2
a14 - a14*a2
b7=0
12*a12*a18*b24
b6=----------------
2
a14 - a14*a2
b5=0
3 2
---*a2 *b24
4
b4=-------------
2
a12
3
- ---*a2*b24
2
b3=---------------
a12
3
- ---*a2*b24
2
b2=---------------
a12
b1=b24
2
a12*a18
a19=---------------
2
a14 - a14*a2
4*a12*a18
a17=-----------
a14
2*a12*a18
a16=-----------
a14 - a2
1 2 1
---*a14 - ---*a14*a2
4 4
a15=-----------------------
a12
a13=a14 - a2
2 3
- 4*a12 *a18
a11=-----------------------------
4 3 2 2
a14 - 2*a14 *a2 + a14 *a2
2
- 4*a12*a18
a10=---------------
2
a14 - a14*a2
2 2
- 24*a12 *a18
a9=-----------------
3 2
a14 - a14 *a2
a8= - a18
- 4*a12*a18
a7=--------------
a14
- 4*a12*a14*a18 + 6*a12*a18*a2
a6=---------------------------------
2
a14 - a14*a2
2
- 8*a12 *a18
a5=---------------
2
a14 - a14*a2
2
- 4*a12 *a18
a4=---------------
2
a14 - a14*a2
a3=0
a1= - a12
b24,a2,a18,a14,a12
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
4 3 2 2
df(u,t)=( - u *a12*a14 + 2*u *a12*a14 *a2 - u *a12*a14 *a2
2x 2x 2x
3 2
- 4*u *f(v,v)*a12*a14 *a18 + 10*u *f(v,v)*a12*a14 *a18*a2
x x
2 4 3 2
- 6*u *f(v,v)*a12*a14*a18*a2 + u *a14 *a2*u - 2*u *a14 *a2 *u
x x x
2 3 2 2
+ u *a14 *a2 *u - 4*f(v ,v )*a12 *a14 *a18
x x x
2 2 2
+ 4*f(v ,v )*a12 *a14*a18*a2 - 8*f(v,v )*a12 *a14 *a18
x x 2x
2 2 2
+ 8*f(v,v )*a12 *a14*a18*a2 - 24*f(v,v )*f(v,v)*a12 *a14*a18
2x x
2 2 3
+ 24*f(v,v )*f(v,v)*a12 *a18 *a2 - 4*f(v,v )*a12*a14 *a18*u
x x
2 2
+ 8*f(v,v )*a12*a14 *a18*a2*u - 4*f(v,v )*a12*a14*a18*a2 *u
x x
3 2 3 2 2 2
- 4*f(v,v) *a12 *a18 - 4*f(v,v) *a12*a14 *a18 *u
2 2 4 2
+ 4*f(v,v) *a12*a14*a18 *a2*u - f(v,v)*a14 *a18*u
3 2 2 2 2 4 3
+ 2*f(v,v)*a14 *a18*a2*u - f(v,v)*a14 *a18*a2 *u )/(a14 - 2*a14 *a2
2 2
+ a14 *a2 )
3 2 2 2 2
df(v,t)=(u *a12*a14 *v - 2*u *a12*a14 *a2*v + u *a12*a14*a2 *v + v *a12 *a14
x x x 2x
2 2 3
- v *a12 *a14*a2 + 2*v *f(v,v)*a12 *a14*a18 + v *a12*a14 *u
2x x x
2 2
- v *a12*a14 *a2*u + 4*f(v,v )*a12 *a14*a18*v
x x
2 2 2 2
- 4*f(v,v )*a12 *a18*a2*v + f(v,v) *a12 *a18 *v
x
2 1 4 2
+ f(v,v)*a12*a14 *a18*u*v - f(v,v)*a12*a14*a18*a2*u*v + ---*a14 *u *v
4
1 3 2 1 2 2 2 2
- ---*a14 *a2*u *v + ---*a14 *a2 *u *v)/(a12*a14 - a12*a14*a2)
2 4
2 6 2 5 2 4 2
df(u,s)=(u *a12 *a14 *b24 - 3*u *a12 *a14 *a2*b24 + 3*u *a12 *a14 *a2 *b24
3x 3x 3x
2 3 3 2 4
- u *a12 *a14 *a2 *b24 - 3*u *f(v,v)*a12 *a14 *a18*a2*b24
3x 2x
2 3 2
+ 6*u *f(v,v)*a12 *a14 *a18*a2 *b24
2x
2 2 3 3 6
- 3*u *f(v,v)*a12 *a14 *a18*a2 *b24 - ---*u *a12*a14 *a2*b24*u
2x 2 2x
9 5 2 9 4 3
+ ---*u *a12*a14 *a2 *b24*u - ---*u *a12*a14 *a2 *b24*u
2 2x 2 2x
3 3 4 3 2 6
+ ---*u *a12*a14 *a2 *b24*u - ---*u *a12*a14 *a2*b24
2 2x 2 x
9 2 5 2 9 2 4 3
+ ---*u *a12*a14 *a2 *b24 - ---*u *a12*a14 *a2 *b24
2 x 2 x
3 2 3 4 2 5
+ ---*u *a12*a14 *a2 *b24 - 6*u *f(v,v )*a12 *a14 *a18*b24
2 x x x
2 4
+ 6*u *f(v,v )*a12 *a14 *a18*a2*b24
x x
2 3 2
+ 6*u *f(v,v )*a12 *a14 *a18*a2 *b24
x x
2 2 3 2 2 4 2
- 6*u *f(v,v )*a12 *a14 *a18*a2 *b24 - 6*u *f(v,v) *a12 *a14 *a18 *b24
x x x
2 2 3 2
+ 6*u *f(v,v) *a12 *a14 *a18 *a2*b24
x
2 2 2 2 2
+ 9*u *f(v,v) *a12 *a14 *a18 *a2 *b24
x
2 2 2 3 6
- 9*u *f(v,v) *a12 *a14*a18 *a2 *b24 - 3*u *f(v,v)*a12*a14 *a18*b24*u
x x
5
+ 6*u *f(v,v)*a12*a14 *a18*a2*b24*u
x
4 2
+ 3*u *f(v,v)*a12*a14 *a18*a2 *b24*u
x
3 3
- 12*u *f(v,v)*a12*a14 *a18*a2 *b24*u
x
2 4 3 6 2 2
+ 6*u *f(v,v)*a12*a14 *a18*a2 *b24*u + ---*u *a14 *a2 *b24*u
x 4 x
9 5 3 2 9 4 4 2
- ---*u *a14 *a2 *b24*u + ---*u *a14 *a2 *b24*u
4 x 4 x
3 3 5 2 3 4
- ---*u *a14 *a2 *b24*u + 12*f(v ,v )*a12 *a14 *a18*b24
4 x x 2x
3 3
- 24*f(v ,v )*a12 *a14 *a18*a2*b24
x 2x
3 2 2
+ 12*f(v ,v )*a12 *a14 *a18*a2 *b24
x 2x
3 2 2
- 12*f(v ,v )*f(v,v)*a12 *a14 *a18 *a2*b24
x x
3 2 2
+ 12*f(v ,v )*f(v,v)*a12 *a14*a18 *a2 *b24
x x
2 4
- 6*f(v ,v )*a12 *a14 *a18*a2*b24*u
x x
2 3 2
+ 12*f(v ,v )*a12 *a14 *a18*a2 *b24*u
x x
2 2 3
- 6*f(v ,v )*a12 *a14 *a18*a2 *b24*u
x x
3 3 2
- 12*f(v,v )*f(v,v)*a12 *a14 *a18 *b24
2x
3 2 2
+ 12*f(v,v )*f(v,v)*a12 *a14*a18 *a2 *b24
2x
2 5 2 4
- 6*f(v,v )*a12 *a14 *a18*b24*u + 6*f(v,v )*a12 *a14 *a18*a2*b24*u
2x 2x
2 3 2
+ 6*f(v,v )*a12 *a14 *a18*a2 *b24*u
2x
2 2 3 2 3 3 2
- 6*f(v,v )*a12 *a14 *a18*a2 *b24*u - 24*f(v,v ) *a12 *a14 *a18 *b24
2x x
2 3 2 2
+ 24*f(v,v ) *a12 *a14 *a18 *a2*b24
x
2 3 2 3
- 36*f(v,v )*f(v,v) *a12 *a14 *a18 *b24
x
2 3 3 2
+ 36*f(v,v )*f(v,v) *a12 *a18 *a2 *b24
x
2 4 2
- 24*f(v,v )*f(v,v)*a12 *a14 *a18 *b24*u
x
2 3 2
+ 24*f(v,v )*f(v,v)*a12 *a14 *a18 *a2*b24*u
x
2 2 2 2
+ 24*f(v,v )*f(v,v)*a12 *a14 *a18 *a2 *b24*u
x
2 2 3
- 24*f(v,v )*f(v,v)*a12 *a14*a18 *a2 *b24*u
x
6 2 5 2
- 3*f(v,v )*a12*a14 *a18*b24*u + 6*f(v,v )*a12*a14 *a18*a2*b24*u
x x
3 3 2
- 6*f(v,v )*a12*a14 *a18*a2 *b24*u
x
2 4 2 4 3 4
+ 3*f(v,v )*a12*a14 *a18*a2 *b24*u - 4*f(v,v) *a12 *a14*a18 *b24
x
4 3 4 3 2 3 3
- 4*f(v,v) *a12 *a18 *a2*b24 - 6*f(v,v) *a12 *a14 *a18 *b24*u
3 2 3 2 2 5 2 2
+ 6*f(v,v) *a12 *a14*a18 *a2 *b24*u - 3*f(v,v) *a12*a14 *a18 *b24*u
2 4 2 2
+ 3*f(v,v) *a12*a14 *a18 *a2*b24*u
2 3 2 2 2
+ 3*f(v,v) *a12*a14 *a18 *a2 *b24*u
2 2 2 3 2 1 7 3
- 3*f(v,v) *a12*a14 *a18 *a2 *b24*u - ---*f(v,v)*a14 *a18*b24*u
2
6 3 4 3 3
+ f(v,v)*a14 *a18*a2*b24*u - f(v,v)*a14 *a18*a2 *b24*u
1 3 4 3 2 6 2 5
+ ---*f(v,v)*a14 *a18*a2 *b24*u )/(a12 *a14 - 3*a12 *a14 *a2
2
2 4 2 2 3 3
+ 3*a12 *a14 *a2 - a12 *a14 *a2 )
3 2 5 9 2 4
df(v,s)=(---*u *v *a12 *a14 *b24 - ---*u *v *a12 *a14 *a2*b24
2 x x 2 x x
9 2 3 2 3 2 2 3
+ ---*u *v *a12 *a14 *a2 *b24 - ---*u *v *a12 *a14 *a2 *b24
2 x x 2 x x
3 2 4
+ ---*u *f(v,v)*a12 *a14 *a18*b24*v
2 x
3 2 3
- ---*u *f(v,v)*a12 *a14 *a18*a2*b24*v
2 x
3 2 2 2
- ---*u *f(v,v)*a12 *a14 *a18*a2 *b24*v
2 x
3 2 3 3 6
+ ---*u *f(v,v)*a12 *a14*a18*a2 *b24*v + ---*u *a12*a14 *b24*u*v
2 x 4 x
3 5 3 3 3
- ---*u *a12*a14 *a2*b24*u*v + ---*u *a12*a14 *a2 *b24*u*v
2 x 2 x
3 2 4 3 4
- ---*u *a12*a14 *a2 *b24*u*v + v *a12 *a14 *b24
4 x 3x
3 3 3 2 2
- 2*v *a12 *a14 *a2*b24 + v *a12 *a14 *a2 *b24
3x 3x
3 3 3 2
+ 3*v *f(v,v)*a12 *a14 *a18*b24 - 3*v *f(v,v)*a12 *a14 *a18*a2*b24
2x 2x
3 2 5 2 4
+ ---*v *a12 *a14 *b24*u - 3*v *a12 *a14 *a2*b24*u
2 2x 2x
3 2 3 2 3 3
+ ---*v *a12 *a14 *a2 *b24*u + 6*v *f(v,v )*a12 *a14 *a18*b24
2 2x x x
3 2
- 12*v *f(v,v )*a12 *a14 *a18*a2*b24
x x
3 2 2 3 2 2
+ 6*v *f(v,v )*a12 *a14*a18*a2 *b24 + 3*v *f(v,v) *a12 *a14 *a18 *b24
x x x
2 4 2 3
+ 3*v *f(v,v)*a12 *a14 *a18*b24*u - 3*v *f(v,v)*a12 *a14 *a18*a2*b24*u
x x
3 6 2 3 5 2
+ ---*v *a12*a14 *b24*u - ---*v *a12*a14 *a2*b24*u
4 x 2 x
3 4 2 2 3 2 2
+ ---*v *a12*a14 *a2 *b24*u + 6*f(v,v )*f(v,v)*a12 *a14 *a18 *b24*v
4 x x
3 2 2
- 6*f(v,v )*f(v,v)*a12 *a18 *a2 *b24*v
x
2 4 2 3
+ 3*f(v,v )*a12 *a14 *a18*b24*u*v - 3*f(v,v )*a12 *a14 *a18*a2*b24*u*v
x x
2 2 2
- 3*f(v,v )*a12 *a14 *a18*a2 *b24*u*v
x
2 3 3 3 3
+ 3*f(v,v )*a12 *a14*a18*a2 *b24*u*v + f(v,v) *a12 *a14*a18 *b24*v
x
3 3 3 3 2 2 3 2
+ f(v,v) *a12 *a18 *a2*b24*v + ---*f(v,v) *a12 *a14 *a18 *b24*u*v
2
3 2 2 2 2
- ---*f(v,v) *a12 *a14*a18 *a2 *b24*u*v
2
3 5 2
+ ---*f(v,v)*a12*a14 *a18*b24*u *v
4
3 4 2
- ---*f(v,v)*a12*a14 *a18*a2*b24*u *v
4
3 3 2 2
- ---*f(v,v)*a12*a14 *a18*a2 *b24*u *v
4
3 2 3 2 1 7 3
+ ---*f(v,v)*a12*a14 *a18*a2 *b24*u *v + ---*a14 *b24*u *v
4 8
1 6 3 1 4 3 3 1 3 4 3
- ---*a14 *a2*b24*u *v + ---*a14 *a2 *b24*u *v - ---*a14 *a2 *b24*u *v
4 4 8
3 4 3 3 3 2 2
)/(a12 *a14 - 2*a12 *a14 *a2 + a12 *a14 *a2 )