3 3 3 3 3 2 3 3 2
b42=( - ----*a14 *a4 *b24 + ----*a14 *a4 *a5*b24 + ----*a14 *a4*a5 *b24
64 64 64
3 3 3 6
- ----*a14 *a5 *b24)/a12
64
3 2 3
b41=(---*a12*a14*a15*a4 *b24 - ---*a12*a14*a15*a4*a5*b24
8 4
3 2 3 3 2 3 3 2 5
+ ---*a12*a14*a15*a5 *b24 - ----*a14 *a4 *b24 + ----*a14 *a5 *b24)/a12
8 16 16
3 2 2 3 2 3 2 2
- ---*a14 *a4 *b24 - ---*a14 *a4*a5*b24 + ---*a14 *a5 *b24
8 8 4
b40=-------------------------------------------------------------
4
a12
3 2 2 3 2 3 2 2
----*a14 *a4 *b24 - ---*a14 *a4*a5*b24 + ----*a14 *a5 *b24
16 8 16
b39=------------------------------------------------------------
4
a12
3 3 3 3
b38=(---*a12*a14*a15*a4*b24 - ---*a12*a14*a15*a5*b24 - ----*a14 *a4*b24
2 2 16
3 3 4
- ----*a14 *a5*b24)/a12
16
b37
3 3 3 2 9 2
---*a12*a15*a4*b24 - ---*a12*a15*a5*b24 - ---*a14 *a4*b24 - ---*a14 *a5*b24
2 2 8 8
=-----------------------------------------------------------------------------
3
a12
3 2 3 2
---*a14 *a4*b24 - ---*a14 *a5*b24
4 4
b36=-----------------------------------
3
a12
3 3 3 2
---*a12*a15*a4*b24 - ---*a12*a15*a5*b24 - ---*a14 *a5*b24
2 2 8
b35=-----------------------------------------------------------
3
a12
3
- ---*a14*a5*b24
4
b34=-------------------
2
a12
3
- ---*a14*a5*b24
4
b33=-------------------
2
a12
3 3
---*a14*a4*b24 - ---*a14*a5*b24
2 2
b32=---------------------------------
2
a12
3 3
---*a14*a4*b24 - ---*a14*a5*b24
4 4
b31=---------------------------------
2
a12
3
---*a14*a15*b24
2
b30=-----------------
2
a12
3 2
---*a14 *b24
4
b29=--------------
2
a12
9 3 2
---*a12*a15*b24 + ---*a14 *b24
2 8
b28=--------------------------------
2
a12
3
---*a14*b24
2
b27=-------------
a12
3
---*a14*b24
2
b26=-------------
a12
3 3 2
---*a12*a15*b24 + ---*a14 *b24
2 8
b25=--------------------------------
a12*a14
3 3 4 3 3 3 3 3 3
b23=(----*a14 *a4 *b24 - ----*a14 *a4 *a5*b24 + ----*a14 *a4*a5 *b24
64 32 32
3 3 4 7
- ----*a14 *a5 *b24)/a12
64
3 3 9 2
b22=( - ---*a12*a14*a15*a4 *b24 + ---*a12*a14*a15*a4 *a5*b24
8 8
9 2 3 3 3 3 3
- ---*a12*a14*a15*a4*a5 *b24 + ---*a12*a14*a15*a5 *b24 + ----*a14 *a4 *b24
8 8 16
3 3 2 3 3 2 3 3 3 6
- ----*a14 *a4 *a5*b24 - ----*a14 *a4*a5 *b24 + ----*a14 *a5 *b24)/a12
16 16 16
15 2 3 9 2 2 27 2 2
b21=(----*a14 *a4 *b24 - ----*a14 *a4 *a5*b24 - ----*a14 *a4*a5 *b24
16 16 16
21 2 3 5
+ ----*a14 *a5 *b24)/a12
16
3 2
b20=( - ---*a12*a14*a15*a4 *b24 + 3*a12*a14*a15*a4*a5*b24
2
3 2 3 3 2 3 3 2 5
- ---*a12*a14*a15*a5 *b24 + ----*a14 *a4 *b24 - ----*a14 *a5 *b24)/a12
2 16 16
9 2 9 2
b19=( - ---*a12*a15*a4 *b24 + 9*a12*a15*a4*a5*b24 - ---*a12*a15*a5 *b24
2 2
15 2 2 3 2 21 2 2 4
+ ----*a14 *a4 *b24 + ---*a14 *a4*a5*b24 - ----*a14 *a5 *b24)/a12
8 4 8
9 2 9 9 2
b18=( - ---*a12*a15*a4 *b24 + ---*a12*a15*a4*a5*b24 - ---*a12*a15*a5 *b24
4 2 4
9 2 2 9 2 2 4
+ ----*a14 *a4 *b24 - ----*a14 *a5 *b24)/a12
16 16
3 2 3 2
---*a14*a4 *b24 + ---*a14*a4*a5*b24 - 3*a14*a5 *b24
2 2
b17=-----------------------------------------------------
3
a12
3 2 3 9 2
---*a14*a4 *b24 + ---*a14*a4*a5*b24 - ---*a14*a5 *b24
4 2 4
b16=-------------------------------------------------------
3
a12
3 2 3 2
---*a14*a4 *b24 - ---*a14*a5 *b24
2 2
b15=-----------------------------------
3
a12
3 3
- ---*a14*a15*a4*b24 + ---*a14*a15*a5*b24
2 2
b14=--------------------------------------------
3
a12
3 2 3 2
- 6*a12*a15*a4*b24 + 6*a12*a15*a5*b24 + ---*a14 *a4*b24 + ---*a14 *a5*b24
4 4
b13=----------------------------------------------------------------------------
3
a12
21 21 9 2
b12=( - ----*a12*a15*a4*b24 + ----*a12*a15*a5*b24 + ---*a14 *a4*b24
2 2 8
3 2 3
+ ---*a14 *a5*b24)/a12
8
3 2 9 2
- 3*a12*a15*a4*b24 + 3*a12*a15*a5*b24 + ---*a14 *a4*b24 + ---*a14 *a5*b24
4 4
b11=----------------------------------------------------------------------------
2
a12 *a14
9 2 3 2
- 3*a12*a15*a4*b24 + 3*a12*a15*a5*b24 + ---*a14 *a4*b24 + ---*a14 *a5*b24
4 4
b10=----------------------------------------------------------------------------
2
a12 *a14
9 2 9 2
- 9*a12*a15*a4*b24 + 9*a12*a15*a5*b24 + ---*a14 *a4*b24 + ---*a14 *a5*b24
4 4
b9=----------------------------------------------------------------------------
2
a12 *a14
b8=
9 9 3 2 3 2
- ---*a12*a15*a4*b24 + ---*a12*a15*a5*b24 + ---*a14 *a4*b24 + ---*a14 *a5*b24
2 2 8 8
--------------------------------------------------------------------------------
2
a12 *a14
3
---*a5*b24
2
b7=------------
a12
3
3*a4*b24 + ---*a5*b24
2
b6=-----------------------
a12
b5=0
3 2
- 9*a12*a15*b24 + ---*a14 *b24
4
b4=---------------------------------
2
a12
3 2
- 9*a12*a15*b24 + ---*a14 *b24
4
b3=---------------------------------
a12*a14
3 2
- 9*a12*a15*b24 + ---*a14 *b24
4
b2=---------------------------------
a12*a14
1 2
- 3*a12*a15*b24 + ---*a14 *b24
4
b1=---------------------------------
2
a14
1 2 2 1 2 2
- ----*a14 *a4 + ----*a14 *a5
16 16
a19=----------------------------------
3
a12
1 1 1 2 1 2
---*a12*a15*a4 - ---*a12*a15*a5 - ---*a14 *a4 - ---*a14 *a5
2 2 8 8
a18=-------------------------------------------------------------
2
a12
1
- ---*a14*a5
2
a17=---------------
a12
1 1
---*a14*a4 - ---*a14*a5
2 2
a16=-------------------------
a12
1 2
a12*a15 + ---*a14
4
a13=--------------------
a14
1 2 3 1 2 2 1 2 2 1 2 3
----*a14 *a4 - ----*a14 *a4 *a5 - ----*a14 *a4*a5 + ----*a14 *a5
16 16 16 16
a11=---------------------------------------------------------------------
4
a12
1 2 1 2 1 2 2
a10=( - ---*a12*a15*a4 + a12*a15*a4*a5 - ---*a12*a15*a5 + ---*a14 *a4
2 2 8
1 2 2 3
- ---*a14 *a5 )/a12
8
1 2 1 2
---*a14*a4 + ---*a14*a4*a5 - a14*a5
2 2
a9=---------------------------------------
2
a12
- a15*a4 + a15*a5
a8=--------------------
a12
1 2 1 2
- 2*a12*a15*a4 + 2*a12*a15*a5 + ---*a14 *a4 + ---*a14 *a5
2 2
a7=------------------------------------------------------------
a12*a14
1 2
- 2*a12*a15*a4 + 2*a12*a15*a5 + ---*a14 *a4
2
a6=----------------------------------------------
a12*a14
a3=0
2
- 4*a12*a15 + a14
a2=---------------------
a14
2 1 2
- 2*a12 *a15 + ---*a12*a14
2
a1=------------------------------
2
a14
b24,a5,a4,a15,a14,a12
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
6 1 5 2 4
df(u,t)=( - 2*u *a12 *a15 + ---*u *a12 *a14 - 2*u *f(v,v)*a12 *a14*a15*a4
2x 2 2x x
4 1 3 3
+ 2*u *f(v,v)*a12 *a14*a15*a5 + ---*u *f(v,v)*a12 *a14 *a4
x 2 x
5 4 3 4 2
- 4*u *a12 *a14*a15*u + u *a12 *a14 *u + f(v ,v )*a12 *a14 *a4
x x x x
4 2 1 2 3 2
+ f(v,v )*a12 *a14 *a5 + ---*f(v,v )*f(v,v)*a12 *a14 *a4
2x 2 x
1 2 3 2 3 2
+ ---*f(v,v )*f(v,v)*a12 *a14 *a4*a5 - f(v,v )*f(v,v)*a12 *a14 *a5
2 x x
4 4
- 2*f(v,v )*a12 *a14*a15*a4*u + 2*f(v,v )*a12 *a14*a15*a5*u
x x
1 3 3 1 3 3
+ ---*f(v,v )*a12 *a14 *a4*u + ---*f(v,v )*a12 *a14 *a5*u
2 x 2 x
1 3 4 3 1 3 4 2
+ ----*f(v,v) *a14 *a4 - ----*f(v,v) *a14 *a4 *a5
16 16
1 3 4 2 1 3 4 3
- ----*f(v,v) *a14 *a4*a5 + ----*f(v,v) *a14 *a5
16 16
1 2 2 2 2 2 2 2
- ---*f(v,v) *a12 *a14 *a15*a4 *u + f(v,v) *a12 *a14 *a15*a4*a5*u
2
1 2 2 2 2 1 2 4 2
- ---*f(v,v) *a12 *a14 *a15*a5 *u + ---*f(v,v) *a12*a14 *a4 *u
2 8
1 2 4 2 3 2 2
- ---*f(v,v) *a12*a14 *a5 *u - f(v,v)*a12 *a14 *a15*a4*u
8
3 2 2 4 2
+ f(v,v)*a12 *a14 *a15*a5*u )/(a12 *a14 )
4 1 3 2 4
df(v,t)=(u *a12 *a15*v + ---*u *a12 *a14 *v + v *a12 *a14
x 4 x 2x
1 2 2 1 2 2
+ ---*v *f(v,v)*a12 *a14 *a4 - ---*v *f(v,v)*a12 *a14 *a5
2 x 2 x
3 2 1 2 2
+ v *a12 *a14 *u - ---*f(v,v )*a12 *a14 *a5*v
x 2 x
1 2 3 2 1 2 3 2
- ----*f(v,v) *a14 *a4 *v + ----*f(v,v) *a14 *a5 *v
16 16
1 2 1 2
+ ---*f(v,v)*a12 *a14*a15*a4*u*v - ---*f(v,v)*a12 *a14*a15*a5*u*v
2 2
1 3 1 3
- ---*f(v,v)*a12*a14 *a4*u*v - ---*f(v,v)*a12*a14 *a5*u*v
8 8
3 2 3
+ a12 *a14*a15*u *v)/(a12 *a14)
8 1 7 2
df(u,s)=( - 3*u *a12 *a15*b24 + ---*u *a12 *a14 *b24
3x 4 3x
9 6
- ---*u *f(v,v)*a12 *a14*a15*a4*b24
2 2x
9 6 3 5 3
+ ---*u *f(v,v)*a12 *a14*a15*a5*b24 + ---*u *f(v,v)*a12 *a14 *a4*b24
2 2x 8 2x
3 5 3 7
+ ---*u *f(v,v)*a12 *a14 *a5*b24 - 9*u *a12 *a14*a15*b24*u
8 2x 2x
3 6 3 2 7
+ ---*u *a12 *a14 *b24*u - 9*u *a12 *a14*a15*b24
4 2x x
3 2 6 3 6
+ ---*u *a12 *a14 *b24 - 9*u *f(v,v )*a12 *a14*a15*a4*b24
4 x x x
6 9 5 3
+ 9*u *f(v,v )*a12 *a14*a15*a5*b24 + ---*u *f(v,v )*a12 *a14 *a4*b24
x x 4 x x
9 5 3
+ ---*u *f(v,v )*a12 *a14 *a5*b24
4 x x
9 2 4 2 2
- ---*u *f(v,v) *a12 *a14 *a15*a4 *b24
4 x
9 2 4 2
+ ---*u *f(v,v) *a12 *a14 *a15*a4*a5*b24
2 x
9 2 4 2 2
- ---*u *f(v,v) *a12 *a14 *a15*a5 *b24
4 x
9 2 3 4 2
+ ----*u *f(v,v) *a12 *a14 *a4 *b24
16 x
9 2 3 4 2
- ----*u *f(v,v) *a12 *a14 *a5 *b24
16 x
21 5 2
- ----*u *f(v,v)*a12 *a14 *a15*a4*b24*u
2 x
21 5 2
+ ----*u *f(v,v)*a12 *a14 *a15*a5*b24*u
2 x
9 4 4 3 4 4
+ ---*u *f(v,v)*a12 *a14 *a4*b24*u + ---*u *f(v,v)*a12 *a14 *a5*b24*u
8 x 8 x
6 2 2 3 5 4 2
- 9*u *a12 *a14 *a15*b24*u + ---*u *a12 *a14 *b24*u
x 4 x
6 2 3 6 2
+ 3*f(v ,v )*a12 *a14 *a4*b24 + ---*f(v ,v )*a12 *a14 *a5*b24
x 2x 2 x 2x
3 4 3 2
+ ---*f(v ,v )*f(v,v)*a12 *a14 *a4 *b24
2 x x
3 4 3 2
- ---*f(v ,v )*f(v,v)*a12 *a14 *a5 *b24
2 x x
6 6
- 3*f(v ,v )*a12 *a14*a15*a4*b24*u + 3*f(v ,v )*a12 *a14*a15*a5*b24*u
x x x x
9 5 3 3 5 3
+ ---*f(v ,v )*a12 *a14 *a4*b24*u + ---*f(v ,v )*a12 *a14 *a5*b24*u
4 x x 4 x x
3 6 2
+ ---*f(v,v )*a12 *a14 *a5*b24
2 3x
3 4 3 2
+ ---*f(v,v )*f(v,v)*a12 *a14 *a4 *b24
4 2x
3 4 3
+ ---*f(v,v )*f(v,v)*a12 *a14 *a4*a5*b24
2 2x
9 4 3 2
- ---*f(v,v )*f(v,v)*a12 *a14 *a5 *b24
4 2x
6 6
- 3*f(v,v )*a12 *a14*a15*a4*b24*u + 3*f(v,v )*a12 *a14*a15*a5*b24*u
2x 2x
3 5 3 9 5 3
+ ---*f(v,v )*a12 *a14 *a4*b24*u + ---*f(v,v )*a12 *a14 *a5*b24*u
4 2x 4 2x
3 2 4 3 2 3 2 4 3
+ ---*f(v,v ) *a12 *a14 *a4 *b24 + ---*f(v,v ) *a12 *a14 *a4*a5*b24
2 x 2 x
2 4 3 2
- 3*f(v,v ) *a12 *a14 *a5 *b24
x
15 2 2 4 3
+ ----*f(v,v )*f(v,v) *a12 *a14 *a4 *b24
16 x
9 2 2 4 2
- ----*f(v,v )*f(v,v) *a12 *a14 *a4 *a5*b24
16 x
27 2 2 4 2
- ----*f(v,v )*f(v,v) *a12 *a14 *a4*a5 *b24
16 x
21 2 2 4 3
+ ----*f(v,v )*f(v,v) *a12 *a14 *a5 *b24
16 x
9 4 2 2
- ---*f(v,v )*f(v,v)*a12 *a14 *a15*a4 *b24*u
2 x
4 2
+ 9*f(v,v )*f(v,v)*a12 *a14 *a15*a4*a5*b24*u
x
9 4 2 2
- ---*f(v,v )*f(v,v)*a12 *a14 *a15*a5 *b24*u
2 x
15 3 4 2
+ ----*f(v,v )*f(v,v)*a12 *a14 *a4 *b24*u
8 x
3 3 4
+ ---*f(v,v )*f(v,v)*a12 *a14 *a4*a5*b24*u
4 x
21 3 4 2
- ----*f(v,v )*f(v,v)*a12 *a14 *a5 *b24*u
8 x
5 2 2
- 6*f(v,v )*a12 *a14 *a15*a4*b24*u
x
5 2 2 3 4 4 2
+ 6*f(v,v )*a12 *a14 *a15*a5*b24*u + ---*f(v,v )*a12 *a14 *a4*b24*u
x 4 x
3 4 4 2 3 4 5 4
+ ---*f(v,v )*a12 *a14 *a5*b24*u + ----*f(v,v) *a14 *a4 *b24
4 x 64
3 4 5 3 3 4 5 3
- ----*f(v,v) *a14 *a4 *a5*b24 + ----*f(v,v) *a14 *a4*a5 *b24
32 32
3 4 5 4 3 3 2 3 3
- ----*f(v,v) *a14 *a5 *b24 - ---*f(v,v) *a12 *a14 *a15*a4 *b24*u
64 8
9 3 2 3 2
+ ---*f(v,v) *a12 *a14 *a15*a4 *a5*b24*u
8
9 3 2 3 2
- ---*f(v,v) *a12 *a14 *a15*a4*a5 *b24*u
8
3 3 2 3 3
+ ---*f(v,v) *a12 *a14 *a15*a5 *b24*u
8
3 3 5 3 3 3 5 2
+ ----*f(v,v) *a12*a14 *a4 *b24*u - ----*f(v,v) *a12*a14 *a4 *a5*b24*u
16 16
3 3 5 2 3 3 5 3
- ----*f(v,v) *a12*a14 *a4*a5 *b24*u + ----*f(v,v) *a12*a14 *a5 *b24*u
16 16
3 2 3 3 2 2
- ---*f(v,v) *a12 *a14 *a15*a4 *b24*u
2
2 3 3 2
+ 3*f(v,v) *a12 *a14 *a15*a4*a5*b24*u
3 2 3 3 2 2
- ---*f(v,v) *a12 *a14 *a15*a5 *b24*u
2
3 2 2 5 2 2
+ ----*f(v,v) *a12 *a14 *a4 *b24*u
16
3 2 2 5 2 2
- ----*f(v,v) *a12 *a14 *a5 *b24*u
16
3 4 3 3
- ---*f(v,v)*a12 *a14 *a15*a4*b24*u
2
3 4 3 3 7 2
+ ---*f(v,v)*a12 *a14 *a15*a5*b24*u )/(a12 *a14 )
2
3 6 3 5 2
df(v,s)=(---*u *a12 *a15*b24*v + ---*u *a12 *a14 *b24*v
2 2x 8 2x
3 5 2 3 4
+ ---*u *v *a12 *a14 *b24 + ---*u *f(v,v)*a12 *a14*a15*a4*b24*v
2 x x 2 x
3 4
- ---*u *f(v,v)*a12 *a14*a15*a5*b24*v
2 x
3 3 3 9 5
- ---*u *f(v,v)*a12 *a14 *a5*b24*v + ---*u *a12 *a14*a15*b24*u*v
8 x 2 x
3 4 3 6
+ ---*u *a12 *a14 *b24*u*v + v *a12 *a14*b24
8 x 3x
3 4 2 3 4 2
+ ---*v *f(v,v)*a12 *a14 *a4*b24 - ---*v *f(v,v)*a12 *a14 *a5*b24
4 2x 4 2x
3 5 2 3 4 2
+ ---*v *a12 *a14 *b24*u + ---*v *f(v,v )*a12 *a14 *a4*b24
2 2x 2 x x
3 4 2 3 2 2 3 2
- ---*v *f(v,v )*a12 *a14 *a5*b24 + ----*v *f(v,v) *a12 *a14 *a4 *b24
2 x x 16 x
3 2 2 3
- ---*v *f(v,v) *a12 *a14 *a4*a5*b24
8 x
3 2 2 3 2 3 3 3
+ ----*v *f(v,v) *a12 *a14 *a5 *b24 + ---*v *f(v,v)*a12 *a14 *a4*b24*u
16 x 4 x
3 3 3 3 4 3 2
- ---*v *f(v,v)*a12 *a14 *a5*b24*u + ---*v *a12 *a14 *b24*u
4 x 4 x
3 4 2 3 4 2
- ---*f(v ,v )*a12 *a14 *a5*b24*v - ---*f(v,v )*a12 *a14 *a5*b24*v
4 x x 4 2x
3 2 3 2
- ---*f(v,v )*f(v,v)*a12 *a14 *a4 *b24*v
8 x
3 2 3
- ---*f(v,v )*f(v,v)*a12 *a14 *a4*a5*b24*v
8 x
3 2 3 2
+ ---*f(v,v )*f(v,v)*a12 *a14 *a5 *b24*v
4 x
3 4
+ ---*f(v,v )*a12 *a14*a15*a4*b24*u*v
2 x
3 4
- ---*f(v,v )*a12 *a14*a15*a5*b24*u*v
2 x
3 3 3 9 3 3
- ---*f(v,v )*a12 *a14 *a4*b24*u*v - ---*f(v,v )*a12 *a14 *a5*b24*u*v
8 x 8 x
3 3 4 3 3 3 4 2
- ----*f(v,v) *a14 *a4 *b24*v + ----*f(v,v) *a14 *a4 *a5*b24*v
64 64
3 3 4 2 3 3 4 3
+ ----*f(v,v) *a14 *a4*a5 *b24*v - ----*f(v,v) *a14 *a5 *b24*v
64 64
3 2 2 2 2
+ ---*f(v,v) *a12 *a14 *a15*a4 *b24*u*v
8
3 2 2 2
- ---*f(v,v) *a12 *a14 *a15*a4*a5*b24*u*v
4
3 2 2 2 2
+ ---*f(v,v) *a12 *a14 *a15*a5 *b24*u*v
8
3 2 4 2
- ----*f(v,v) *a12*a14 *a4 *b24*u*v
16
3 2 4 2
+ ----*f(v,v) *a12*a14 *a5 *b24*u*v
16
3 3 2 2
+ ---*f(v,v)*a12 *a14 *a15*a4*b24*u *v
2
3 3 2 2
- ---*f(v,v)*a12 *a14 *a15*a5*b24*u *v
2
3 2 4 2
- ----*f(v,v)*a12 *a14 *a4*b24*u *v
16
3 2 4 2 3 4 2 3
- ----*f(v,v)*a12 *a14 *a5*b24*u *v + ---*a12 *a14 *a15*b24*u *v)/(
16 2
6
a12 *a14)