1 2 2 1 2 2 1 2 2
b42=( - ----*a1 *a2*a4*a6 *b1 + -----*a1 *a2*a4*a6 *b24 + ----*a1*a2 *a4 *a6*b1
32 128 64
1 2 2 1 3 3 1 3 3 6
- -----*a1*a2 *a4 *a6*b24 - -----*a2 *a4 *b1 + ------*a2 *a4 *b24)/a1
256 512 2048
1 2 2 1 2 2 1 2
b41=( - ----*a1 *a2*a6 *b1 + ----*a1 *a2*a6 *b24 - ----*a1*a2 *a4*a6*b1
16 64 32
1 2 3 3 2 3 3 2 5
+ -----*a1*a2 *a4*a6*b24 + -----*a2 *a4 *b1 - ------*a2 *a4 *b24)/a1
128 256 1024
3 3 3 2 2
b40=( - ---*a1*a2*a4*a6*b1 + ----*a1*a2*a4*a6*b24 + ----*a2 *a4 *b1
8 16 32
3 2 2 4
- ----*a2 *a4 *b24)/a1
64
3 2 2 3 3 2 2
----*a1 *a6 *b24 - ----*a1*a2*a4*a6*b24 + -----*a2 *a4 *b24
16 32 256
b39=-------------------------------------------------------------
4
a1
1 2 1 2
- ---*a2 *a6*b1 + ----*a2 *a6*b24
8 32
b38=------------------------------------
3
a1
1 1 3 2
- ---*a1*a2*a6*b1 + ---*a1*a2*a6*b24 - ----*a2 *a4*b1
4 4 16
b37=--------------------------------------------------------
3
a1
3 3 2
---*a1*a2*a6*b24 - ----*a2 *a4*b24
8 32
b36=------------------------------------
3
a1
1 1 3 2
- ---*a1*a2*a6*b1 + ----*a1*a2*a6*b24 + ----*a2 *a4*b24
4 16 64
b35=----------------------------------------------------------
3
a1
1 1
- ---*a2*a4*b1 + ---*a2*a4*b24
4 4
b34=---------------------------------
2
a1
3 1 5
---*a1*a6*b24 - ---*a2*a4*b1 - ----*a2*a4*b24
4 4 16
b33=-----------------------------------------------
2
a1
3 3
---*a1*a6*b24 - ---*a2*a4*b24
2 8
b32=-------------------------------
2
a1
3 3
---*a1*a6*b24 - ----*a2*a4*b24
4 16
b31=--------------------------------
2
a1
1 3 1 3
- ----*a2 *b1 + ----*a2 *b24
16 64
b30=-------------------------------
3
a1
3 2
----*a2 *b24
16
b29=--------------
2
a1
3 2 3 2
- ---*a2 *b1 + ----*a2 *b24
8 16
b28=------------------------------
2
a1
3
---*a2*b24
4
b27=------------
a1
3
---*a2*b24
4
b26=------------
a1
1 1
- ---*a2*b1 + ---*a2*b24
4 4
b25=---------------------------
a1
1 3 3 1 3 3 3 2 2 2
b23=(----*a1 *a4*a6 *b1 - ----*a1 *a4*a6 *b24 - ----*a1 *a2*a4 *a6 *b1
16 64 64
3 2 2 2 3 2 3
+ -----*a1 *a2*a4 *a6 *b24 + -----*a1*a2 *a4 *a6*b1
256 256
3 2 3 1 3 4 1 3 4 7
- ------*a1*a2 *a4 *a6*b24 - ------*a2 *a4 *b1 + ------*a2 *a4 *b24)/a1
1024 1024 4096
1 3 3 1 3 3 1 2 2
b22=(---*a1 *a6 *b1 - ----*a1 *a6 *b24 + ----*a1 *a2*a4*a6 *b1
8 32 32
1 2 2 5 2 2
- -----*a1 *a2*a4*a6 *b24 - -----*a1*a2 *a4 *a6*b1
128 128
5 2 2 3 3 3 3 3 3 6
+ -----*a1*a2 *a4 *a6*b24 + -----*a2 *a4 *b1 - ------*a2 *a4 *b24)/a1
512 512 2048
3 2 2 9 2 2 3 2
b21=(---*a1 *a4*a6 *b1 - ----*a1 *a4*a6 *b24 - ---*a1*a2*a4 *a6*b1
2 16 4
9 2 3 2 3 9 2 3 5
+ ----*a1*a2*a4 *a6*b24 + ----*a2 *a4 *b1 - -----*a2 *a4 *b24)/a1
32 32 256
b20=
1 2 1 2 1 2 1 2
---*a1*a2*a6 *b1 - ----*a1*a2*a6 *b24 - ----*a2 *a4*a6*b1 + ----*a2 *a4*a6*b24
4 16 16 64
--------------------------------------------------------------------------------
4
a1
3 2 2 3 2 2 3 9 2 2
b19=(---*a1 *a6 *b1 - ---*a1 *a6 *b24 + ---*a1*a2*a4*a6*b1 - ----*a2 *a4 *b1
2 4 4 32
3 2 2 4
+ ----*a2 *a4 *b24)/a1
64
3 2 2 3 3 2 2 3 2 2
---*a1 *a6 *b1 - ----*a1*a2*a4*a6*b24 - ----*a2 *a4 *b1 + ----*a2 *a4 *b24
4 16 64 64
b18=----------------------------------------------------------------------------
4
a1
3 3 2 3 2
3*a1*a4*a6*b1 - ---*a1*a4*a6*b24 - ---*a2*a4 *b1 + ---*a2*a4 *b24
2 4 8
b17=-------------------------------------------------------------------
3
a1
5 1 2 5 2
2*a1*a4*a6*b1 - ---*a1*a4*a6*b24 - ---*a2*a4 *b1 + ----*a2*a4 *b24
4 2 16
b16=--------------------------------------------------------------------
3
a1
1 1 2 1 2
2*a1*a4*a6*b1 - ---*a1*a4*a6*b24 - ---*a2*a4 *b1 + ---*a2*a4 *b24
2 2 8
b15=-------------------------------------------------------------------
3
a1
1 2 1 2 1 3 1 3
---*a1*a2 *a6*b1 - ----*a1*a2 *a6*b24 - ----*a2 *a4*b1 + -----*a2 *a4*b24
8 32 32 128
b14=---------------------------------------------------------------------------
4
a1
1
a2*a6*b1 - ---*a2*a6*b24
4
b13=--------------------------
2
a1
7 1 3 2
---*a1*a2*a6*b1 - ---*a1*a2*a6*b24 - ----*a2 *a4*b1
4 4 16
b12=-----------------------------------------------------
3
a1
3
a1*a6*b1 - a1*a6*b24 + ---*a2*a4*b1
4
b11=-------------------------------------
2
a1
1 3 3
a1*a6*b1 + ---*a1*a6*b24 + ---*a2*a4*b1 - ---*a2*a4*b24
2 4 8
b10=---------------------------------------------------------
2
a1
3 3
3*a1*a6*b1 + ---*a2*a4*b1 - ---*a2*a4*b24
4 4
b9=-------------------------------------------
2
a1
3 1 1
---*a1*a6*b1 - ---*a2*a4*b1 - ---*a2*a4*b24
2 8 4
b8=---------------------------------------------
2
a1
a4*b1 - a4*b24
b7=----------------
a1
3*a4*b1
b6=---------
a1
b5=0
3 2
---*a2 *b1
4
b4=------------
2
a1
3
---*a2*b1
2
b3=-----------
a1
3
---*a2*b1
2
b2=-----------
a1
1 1 2 2
- ----*a1*a2*a4*a6 + ----*a2 *a4
16 64
a19=------------------------------------
3
a1
1 1 2
- ---*a1*a2*a6 - ----*a2 *a4
8 32
a18=-------------------------------
2
a1
1
- ---*a2*a4
4
a17=--------------
a1
a16=0
1 2
- ---*a2
8
a15=------------
a1
a14=0
1
a13= - ---*a2
4
a12=0
1 2 2 1 2 1 2 3
---*a1 *a4*a6 - ----*a1*a2*a4 *a6 + -----*a2 *a4
8 16 128
a11=----------------------------------------------------
4
a1
1 2 2 1 2 2
---*a1 *a6 - ----*a2 *a4
4 64
a10=----------------------------
3
a1
3 3 2
---*a1*a4*a6 - ---*a2*a4
2 8
a9=---------------------------
2
a1
1 1 2
---*a1*a2*a6 - ----*a2 *a4
4 16
a8=----------------------------
2
a1
1
a1*a6 + ---*a2*a4
4
a7=-------------------
a1
a5=a4
a3=0
b24,b1,a6,a4,a2,a1
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
5 4 4 4
df(u,t)=(u *a1 + u *f(v,v)*a1 *a6 + u *a1 *a2*u + f(v ,v )*a1 *a4
2x x x x x
4 3 3
+ f(v,v )*a1 *a4 + ---*f(v,v )*f(v,v)*a1 *a4*a6
2x 2 x
3 2 2 4
- ---*f(v,v )*f(v,v)*a1 *a2*a4 + f(v,v )*a1 *a6*u
8 x x
1 3 1 3 2 2
+ ---*f(v,v )*a1 *a2*a4*u + ---*f(v,v) *a1 *a4*a6
4 x 8
1 3 2 1 3 2 3
- ----*f(v,v) *a1*a2*a4 *a6 + -----*f(v,v) *a2 *a4
16 128
1 2 3 2 1 2 2 2
+ ---*f(v,v) *a1 *a6 *u - ----*f(v,v) *a1*a2 *a4 *u
4 64
1 3 2 1 2 2 2 4
+ ---*f(v,v)*a1 *a2*a6*u - ----*f(v,v)*a1 *a2 *a4*u )/a1
4 16
1 3 1 2
df(v,t)=( - ---*u *a1 *a2*v - ---*f(v,v )*a1 *a2*a4*v
4 x 4 x
1 2 1 2 2 2
- ----*f(v,v) *a1*a2*a4*a6*v + ----*f(v,v) *a2 *a4 *v
16 64
1 2 1 2
- ---*f(v,v)*a1 *a2*a6*u*v - ----*f(v,v)*a1*a2 *a4*u*v
8 32
1 2 2 2 3
- ---*a1 *a2 *u *v)/a1
8
7 3 6 1 5
df(u,s)=(u *a1 *b1 + ---*u *f(v,v)*a1 *a6*b1 - ---*u *f(v,v)*a1 *a2*a4*b1
3x 2 2x 8 2x
1 5 3 6
- ---*u *f(v,v)*a1 *a2*a4*b24 + ---*u *a1 *a2*b1*u
4 2x 2 2x
3 2 6 6
+ ---*u *a1 *a2*b1 + 3*u *f(v,v )*a1 *a6*b1
2 x x x
3 5 3 5
+ ---*u *f(v,v )*a1 *a2*a4*b1 - ---*u *f(v,v )*a1 *a2*a4*b24
4 x x 4 x x
3 2 5 2 3 2 4
+ ---*u *f(v,v) *a1 *a6 *b1 - ----*u *f(v,v) *a1 *a2*a4*a6*b24
4 x 16 x
3 2 3 2 2 3 2 3 2 2
- ----*u *f(v,v) *a1 *a2 *a4 *b1 + ----*u *f(v,v) *a1 *a2 *a4 *b24
64 x 64 x
7 5 1 5
+ ---*u *f(v,v)*a1 *a2*a6*b1*u - ---*u *f(v,v)*a1 *a2*a6*b24*u
4 x 4 x
3 4 2 3 5 2 2
- ----*u *f(v,v)*a1 *a2 *a4*b1*u + ---*u *a1 *a2 *b1*u
16 x 4 x
6 5
+ 3*f(v ,v )*a1 *a4*b1 + 2*f(v ,v )*f(v,v)*a1 *a4*a6*b1
x 2x x x
1 5
- ---*f(v ,v )*f(v,v)*a1 *a4*a6*b24
2 x x
1 4 2
- ---*f(v ,v )*f(v,v)*a1 *a2*a4 *b1
2 x x
1 4 2 6
+ ---*f(v ,v )*f(v,v)*a1 *a2*a4 *b24 + f(v ,v )*a1 *a6*b1*u
8 x x x x
1 6 3 5
+ ---*f(v ,v )*a1 *a6*b24*u + ---*f(v ,v )*a1 *a2*a4*b1*u
2 x x 4 x x
3 5 6
- ---*f(v ,v )*a1 *a2*a4*b24*u + f(v,v )*a1 *a4*b1
8 x x 3x
6 5
- f(v,v )*a1 *a4*b24 + 2*f(v,v )*f(v,v)*a1 *a4*a6*b1
3x 2x
5 5
- ---*f(v,v )*f(v,v)*a1 *a4*a6*b24
4 2x
1 4 2
- ---*f(v,v )*f(v,v)*a1 *a2*a4 *b1
2 2x
5 4 2 6
+ ----*f(v,v )*f(v,v)*a1 *a2*a4 *b24 + f(v,v )*a1 *a6*b1*u
16 2x 2x
6 3 5
- f(v,v )*a1 *a6*b24*u + ---*f(v,v )*a1 *a2*a4*b1*u
2x 4 2x
2 5 3 2 5
+ 3*f(v,v ) *a1 *a4*a6*b1 - ---*f(v,v ) *a1 *a4*a6*b24
x 2 x
3 2 4 2 3 2 4 2
- ---*f(v,v ) *a1 *a2*a4 *b1 + ---*f(v,v ) *a1 *a2*a4 *b24
4 x 8 x
3 2 4 2
+ ---*f(v,v )*f(v,v) *a1 *a4*a6 *b1
2 x
9 2 4 2
- ----*f(v,v )*f(v,v) *a1 *a4*a6 *b24
16 x
3 2 3 2
- ---*f(v,v )*f(v,v) *a1 *a2*a4 *a6*b1
4 x
9 2 3 2
+ ----*f(v,v )*f(v,v) *a1 *a2*a4 *a6*b24
32 x
3 2 2 2 3
+ ----*f(v,v )*f(v,v) *a1 *a2 *a4 *b1
32 x
9 2 2 2 3
- -----*f(v,v )*f(v,v) *a1 *a2 *a4 *b24
256 x
3 5 2 3 5 2
+ ---*f(v,v )*f(v,v)*a1 *a6 *b1*u - ---*f(v,v )*f(v,v)*a1 *a6 *b24*u
2 x 4 x
3 4
+ ---*f(v,v )*f(v,v)*a1 *a2*a4*a6*b1*u
4 x
9 3 2 2
- ----*f(v,v )*f(v,v)*a1 *a2 *a4 *b1*u
32 x
3 3 2 2 5 2
+ ----*f(v,v )*f(v,v)*a1 *a2 *a4 *b24*u + f(v,v )*a1 *a2*a6*b1*u
64 x x
1 5 2 1 4 3 3
- ---*f(v,v )*a1 *a2*a6*b24*u + ----*f(v,v) *a1 *a4*a6 *b1
4 x 16
1 4 3 3 3 4 2 2 2
- ----*f(v,v) *a1 *a4*a6 *b24 - ----*f(v,v) *a1 *a2*a4 *a6 *b1
64 64
3 4 2 2 2 3 4 2 3
+ -----*f(v,v) *a1 *a2*a4 *a6 *b24 + -----*f(v,v) *a1*a2 *a4 *a6*b1
256 256
3 4 2 3 1 4 3 4
- ------*f(v,v) *a1*a2 *a4 *a6*b24 - ------*f(v,v) *a2 *a4 *b1
1024 1024
1 4 3 4 1 3 4 3
+ ------*f(v,v) *a2 *a4 *b24 + ---*f(v,v) *a1 *a6 *b1*u
4096 8
1 3 4 3 1 3 3 2
- ----*f(v,v) *a1 *a6 *b24*u + ----*f(v,v) *a1 *a2*a4*a6 *b1*u
32 32
1 3 3 2
- -----*f(v,v) *a1 *a2*a4*a6 *b24*u
128
5 3 2 2 2
- -----*f(v,v) *a1 *a2 *a4 *a6*b1*u
128
5 3 2 2 2 3 3 3 3
+ -----*f(v,v) *a1 *a2 *a4 *a6*b24*u + -----*f(v,v) *a1*a2 *a4 *b1*u
512 512
3 3 3 3 1 2 4 2 2
- ------*f(v,v) *a1*a2 *a4 *b24*u + ---*f(v,v) *a1 *a2*a6 *b1*u
2048 4
1 2 4 2 2 1 2 3 2 2
- ----*f(v,v) *a1 *a2*a6 *b24*u - ----*f(v,v) *a1 *a2 *a4*a6*b1*u
16 16
1 2 3 2 2 1 4 2 3
+ ----*f(v,v) *a1 *a2 *a4*a6*b24*u + ---*f(v,v)*a1 *a2 *a6*b1*u
64 8
1 4 2 3 1 3 3 3
- ----*f(v,v)*a1 *a2 *a6*b24*u - ----*f(v,v)*a1 *a2 *a4*b1*u
32 32
1 3 3 3 7
+ -----*f(v,v)*a1 *a2 *a4*b24*u )/a1
128
1 5 1 5 3 5
df(v,s)=( - ---*u *a1 *a2*b1*v + ---*u *a1 *a2*b24*v + ---*u *v *a1 *a2*b24
4 2x 4 2x 4 x x
1 4 1 4
- ---*u *f(v,v)*a1 *a2*a6*b1*v + ----*u *f(v,v)*a1 *a2*a6*b24*v
4 x 16 x
3 3 2 3 4 2
+ ----*u *f(v,v)*a1 *a2 *a4*b24*v - ---*u *a1 *a2 *b1*u*v
64 x 8 x
3 4 2 6 3 5
+ ----*u *a1 *a2 *b24*u*v + v *a1 *b24 + ---*v *f(v,v)*a1 *a6*b24
16 x 3x 4 2x
3 4 3 5
- ----*v *f(v,v)*a1 *a2*a4*b24 + ---*v *a1 *a2*b24*u
16 2x 4 2x
3 5 3 4
+ ---*v *f(v,v )*a1 *a6*b24 - ---*v *f(v,v )*a1 *a2*a4*b24
2 x x 8 x x
3 2 4 2 3 2 3
+ ----*v *f(v,v) *a1 *a6 *b24 - ----*v *f(v,v) *a1 *a2*a4*a6*b24
16 x 32 x
3 2 2 2 2 3 4
+ -----*v *f(v,v) *a1 *a2 *a4 *b24 + ---*v *f(v,v)*a1 *a2*a6*b24*u
256 x 8 x
3 3 2 3 4 2 2
- ----*v *f(v,v)*a1 *a2 *a4*b24*u + ----*v *a1 *a2 *b24*u
32 x 16 x
3 5 1 4
+ ---*f(v ,v )*a1 *a6*b24*v - ---*f(v ,v )*a1 *a2*a4*b1*v
4 x x 4 x x
5 4 1 4
- ----*f(v ,v )*a1 *a2*a4*b24*v - ---*f(v,v )*a1 *a2*a4*b1*v
16 x x 4 2x
1 4 3 3
+ ---*f(v,v )*a1 *a2*a4*b24*v - ---*f(v,v )*f(v,v)*a1 *a2*a4*a6*b1*v
4 2x 8 x
3 3
+ ----*f(v,v )*f(v,v)*a1 *a2*a4*a6*b24*v
16 x
3 2 2 2
+ ----*f(v,v )*f(v,v)*a1 *a2 *a4 *b1*v
32 x
3 2 2 2 1 4
- ----*f(v,v )*f(v,v)*a1 *a2 *a4 *b24*v - ---*f(v,v )*a1 *a2*a6*b1*u*v
64 x 4 x
1 4 3 3 2
+ ---*f(v,v )*a1 *a2*a6*b24*u*v - ----*f(v,v )*a1 *a2 *a4*b1*u*v
4 x 16 x
1 3 2 2 1 3 2 2
- ----*f(v,v) *a1 *a2*a4*a6 *b1*v + -----*f(v,v) *a1 *a2*a4*a6 *b24*v
32 128
1 3 2 2 1 3 2 2
+ ----*f(v,v) *a1*a2 *a4 *a6*b1*v - -----*f(v,v) *a1*a2 *a4 *a6*b24*v
64 256
1 3 3 3 1 3 3 3
- -----*f(v,v) *a2 *a4 *b1*v + ------*f(v,v) *a2 *a4 *b24*v
512 2048
1 2 3 2 1 2 3 2
- ----*f(v,v) *a1 *a2*a6 *b1*u*v + ----*f(v,v) *a1 *a2*a6 *b24*u*v
16 64
1 2 2 2
- ----*f(v,v) *a1 *a2 *a4*a6*b1*u*v
32
1 2 2 2
+ -----*f(v,v) *a1 *a2 *a4*a6*b24*u*v
128
3 2 3 2 3 2 3 2
+ -----*f(v,v) *a1*a2 *a4 *b1*u*v - ------*f(v,v) *a1*a2 *a4 *b24*u*v
256 1024
1 3 2 2 1 3 2 2
- ---*f(v,v)*a1 *a2 *a6*b1*u *v + ----*f(v,v)*a1 *a2 *a6*b24*u *v
8 32
1 3 3 3 1 3 3 3 6
- ----*a1 *a2 *b1*u *v + ----*a1 *a2 *b24*u *v)/a1
16 64