Solution 1 to problem l1o35
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Expressions
The solution is given through the following expressions:
b75=0
b74=0
b73=0
25 2 7 5 10
--------*a19*a2 *a3 *a7*b2 + ---------*a3 *a7*b2
279936 2519424
b72=---------------------------------------------------
2 9 1 7 3 1 5 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
25 2 6 5 9
-------*a19*a2 *a3 *a7*b2 + --------*a3 *a7*b2
15552 139968
b71=------------------------------------------------
2 8 1 6 3 1 4 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
b70=0
5 2 6 35 9
------*a19*a2 *a3 *a7*b2 + ---------*a3 *a7*b2
5184 1679616
b69=------------------------------------------------
2 8 1 6 3 1 4 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
5 2 5 35 8
-----*a19*a2 *a3 *a7*b2 + --------*a3 *a7*b2
864 279936
b68=----------------------------------------------
2 7 1 5 3 1 3 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
5 2 5 25 8
------*a19*a2 *a3 *a7*b2 + --------*a3 *a7*b2
1296 279936
b67=-----------------------------------------------
2 7 1 5 3 1 3 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
b66=0
b65=0
5 2 5 35 8
-----*a19*a2 *a3 *a7*b2 + --------*a3 *a7*b2
864 279936
b64=----------------------------------------------
2 7 1 5 3 1 3 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
b63=0
5 2 5 5 8
------*a19*a2 *a3 *a7*b2 + --------*a3 *a7*b2
3888 186624
b62=-----------------------------------------------
2 7 1 5 3 1 3 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
5 2 4 5 7
-----*a19*a2 *a3 *a7*b2 + -------*a3 *a7*b2
648 31104
b61=----------------------------------------------
2 6 1 4 3 1 2 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
5 2 4 25 7
-----*a19*a2 *a3 *a7*b2 + -------*a3 *a7*b2
432 93312
b60=----------------------------------------------
2 6 1 4 3 1 2 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
b59=0
b58=0
b57=0
b56=0
25 2 2 5 5 8
- ------*a19 *a2 *a3 *b2 - -------*a19*a3 *b2
7776 69984
b55=------------------------------------------------
2 7 1 5 3 1 3 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
5 2 4 4 5 2 7 5 10
- -----*a19 *a2 *a3 *b2 - ------*a19*a2 *a3 *b2 - --------*a3 *b2
144 3888 419904
b54=---------------------------------------------------------------------
2 8 1 6 3 1 4 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
85 2 4 4 5 2 7 5 10
- -----*a19 *a2 *a3 *b2 - ------*a19*a2 *a3 *b2 - --------*a3 *b2
648 1458 419904
b53=---------------------------------------------------------------------
2 8 1 6 3 1 4 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
5 2 4 3 5 2 6 5 9
- ----*a19 *a2 *a3 *b2 - -----*a19*a2 *a3 *b2 - -------*a3 *b2
12 324 34992
b52=-----------------------------------------------------------------
2 7 1 5 3 1 3 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
5 2 4 3 5 2 6 5 9
- ---*a19 *a2 *a3 *b2 - -----*a19*a2 *a3 *b2 - -------*a3 *b2
4 108 11664
b51=----------------------------------------------------------------
2 7 1 5 3 1 3 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
65 2 4 3 35 2 6 5 9
- ----*a19 *a2 *a3 *b2 - ------*a19*a2 *a3 *b2 - -------*a3 *b2
72 1296 31104
b50=------------------------------------------------------------------
2 7 1 5 3 1 3 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
65 2 4 3 35 2 6 5 9
- -----*a19 *a2 *a3 *b2 - ------*a19*a2 *a3 *b2 - -------*a3 *b2
108 1944 46656
b49=-------------------------------------------------------------------
2 7 1 5 3 1 3 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
5 2 4 2 5 2 5 5 8
- ---*a19 *a2 *a3 *b2 - ----*a19*a2 *a3 *b2 - ------*a3 *b2
2 54 5832
b48=--------------------------------------------------------------
2 6 1 4 3 1 2 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
15 2 4 2 5 2 5 5 8
- ----*a19 *a2 *a3 *b2 - ----*a19*a2 *a3 *b2 - ------*a3 *b2
2 18 1944
b47=---------------------------------------------------------------
2 6 1 4 3 1 2 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
15 2 4 2 5 2 5 5 8
- ----*a19 *a2 *a3 *b2 - ----*a19*a2 *a3 *b2 - ------*a3 *b2
4 36 3888
b46=---------------------------------------------------------------
2 6 1 4 3 1 2 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
2 4 2 5 2 5 5 8
- 5*a19 *a2 *a3 *b2 - ----*a19*a2 *a3 *b2 - ------*a3 *b2
27 2916
b45=------------------------------------------------------------
2 6 1 4 3 1 2 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
55 2 4 2 65 2 5 35 8
- ----*a19 *a2 *a3 *b2 - -----*a19*a2 *a3 *b2 - -------*a3 *b2
18 648 46656
b44=-----------------------------------------------------------------
2 6 1 4 3 1 2 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
55 2 4 2 65 2 5 35 8
- ----*a19 *a2 *a3 *b2 - ------*a19*a2 *a3 *b2 - -------*a3 *b2
36 1296 93312
b43=------------------------------------------------------------------
2 6 1 4 3 1 2 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
15 2 4 5 2 4 5 7
- ----*a19 *a2 *a3*b2 - ----*a19*a2 *a3 *b2 - ------*a3 *b2
2 18 1944
b42=--------------------------------------------------------------
2 5 1 3 3 1 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2*a3
72 5184
2 4 5 2 4 5 7
- 15*a19 *a2 *a3*b2 - ---*a19*a2 *a3 *b2 - -----*a3 *b2
9 972
b41=----------------------------------------------------------
2 5 1 3 3 1 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2*a3
72 5184
2 4 5 2 4 5 7
- 15*a19 *a2 *a3*b2 - ---*a19*a2 *a3 *b2 - -----*a3 *b2
9 972
b40=----------------------------------------------------------
2 5 1 3 3 1 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2*a3
72 5184
15 2 4 5 2 4 5 7
- ----*a19 *a2 *a3*b2 - ----*a19*a2 *a3 *b2 - ------*a3 *b2
2 18 1944
b39=--------------------------------------------------------------
2 5 1 3 3 1 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2*a3
72 5184
5 2 4 25 2 4 5 7
- ---*a19 *a2 *a3*b2 - -----*a19*a2 *a3 *b2 - -------*a3 *b2
3 432 10368
b38=---------------------------------------------------------------
2 5 1 3 3 1 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2*a3
72 5184
2 4 1 2 3 1 6
- 9*a19 *a2 *b2 - ---*a19*a2 *a3 *b2 - -----*a3 *b2
3 324
b37=------------------------------------------------------
2 4 1 2 3 1 6
a19 *a2 + ----*a19*a2 *a3 - ------*a3
72 5184
b36=0
b35=0
b34=0
b33=0
b32=0
b31=0
b30=0
b29=0
25 2 6 5 9
- -------*a19*a2 *a3 *a7*b2 - --------*a3 *a7*b2
23328 209952
b28=---------------------------------------------------
2 8 1 6 3 1 4 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
25 2 6 5 9
- -------*a19*a2 *a3 *a7*b2 - --------*a3 *a7*b2
15552 139968
b27=---------------------------------------------------
2 8 1 6 3 1 4 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
25 2 5 5 8
- ------*a19*a2 *a3 *a7*b2 - -------*a3 *a7*b2
2592 23328
b26=-------------------------------------------------
2 7 1 5 3 1 3 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
25 2 5 5 8
- ------*a19*a2 *a3 *a7*b2 - -------*a3 *a7*b2
2592 23328
b25=-------------------------------------------------
2 7 1 5 3 1 3 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
5 2 5 95 8
- -----*a19*a2 *a3 *a7*b2 - --------*a3 *a7*b2
162 139968
b24=-------------------------------------------------
2 7 1 5 3 1 3 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
5 2 5 35 8
- -----*a19*a2 *a3 *a7*b2 - --------*a3 *a7*b2
864 279936
b23=-------------------------------------------------
2 7 1 5 3 1 3 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
5 2 5 35 8
- -----*a19*a2 *a3 *a7*b2 - --------*a3 *a7*b2
864 279936
b22=-------------------------------------------------
2 7 1 5 3 1 3 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
5 2 4 35 7
- -----*a19*a2 *a3 *a7*b2 - -------*a3 *a7*b2
144 46656
b21=------------------------------------------------
2 6 1 4 3 1 2 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
35 2 4 85 7
- -----*a19*a2 *a3 *a7*b2 - -------*a3 *a7*b2
432 46656
b20=------------------------------------------------
2 6 1 4 3 1 2 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
5 2 4 35 7
- ----*a19*a2 *a3 *a7*b2 - -------*a3 *a7*b2
72 23328
b19=-----------------------------------------------
2 6 1 4 3 1 2 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
25 2 4 5 7
- -----*a19*a2 *a3 *a7*b2 - ------*a3 *a7*b2
432 3888
b18=-----------------------------------------------
2 6 1 4 3 1 2 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
65 2 4 25 7
- ------*a19*a2 *a3 *a7*b2 - -------*a3 *a7*b2
1296 23328
b17=-------------------------------------------------
2 6 1 4 3 1 2 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
5 2 4 5 7
- -----*a19*a2 *a3 *a7*b2 - -------*a3 *a7*b2
648 31104
b16=------------------------------------------------
2 6 1 4 3 1 2 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3
72 5184
5 2 3 5 6
- -----*a19*a2 *a3 *a7*b2 - ------*a3 *a7*b2
108 5184
b15=-----------------------------------------------
2 5 1 3 3 1 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2*a3
72 5184
25 2 3 5 6
- -----*a19*a2 *a3 *a7*b2 - ------*a3 *a7*b2
216 1944
b14=-----------------------------------------------
2 5 1 3 3 1 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2*a3
72 5184
5 2 3 25 6
- ----*a19*a2 *a3 *a7*b2 - -------*a3 *a7*b2
72 15552
b13=-----------------------------------------------
2 5 1 3 3 1 6
a19 *a2 + ----*a19*a2 *a3 - ------*a2*a3
72 5184
b12=0
5 4
----*a3 *b2
81
b11=-------------
4
a2
10 3
----*a3 *b2
9
b10=-------------
3
a2
10 3
----*a3 *b2
27
b9=-------------
3
a2
5 2
---*a3 *b2
3
b8=------------
2
a2
50 2
----*a3 *b2
9
b7=-------------
2
a2
10 2
----*a3 *b2
9
b6=-------------
2
a2
10
----*a3*b2
3
b5=------------
a2
5*a3*b2
b4=---------
a2
5
---*a3*b2
3
b3=-----------
a2
b2=b2
1 2
- ----*a3 *a7
36
a22=----------------
2
a2
1
- ---*a3*a7
6
a21=--------------
a2
a20=0
a19=a19
2 1 3
18*a19*a2 + ---*a3
3
a18=----------------------
a2*a3
2 1 3
18*a19*a2 + ---*a3
6
a17=----------------------
a2*a3
2 3
108*a19*a2 + 2*a3
a16=---------------------
2
a3
2 3
108*a19*a2 + 2*a3
a15=---------------------
2
a3
2 1 3
36*a19*a2 + ---*a3
2
a14=----------------------
2
a3
3 3
216*a19*a2 + 4*a2*a3
a13=------------------------
3
a3
a12=0
a11=0
1
---*a3*a7
3
a10=-----------
a2
1
---*a3*a7
6
a9=-----------
a2
a8=a7
a6=0
1 2
---*a3
3
a5=---------
a2
a4=a3
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:
b2,a19,a7,a3,a2
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
2 2 1 1 2 2
df(u,t)=(u *a2 + u *a2*a3*u + u *a2*a3 + ---*u *f(v,v)*a3*a7 + ---*u *a3 *u
3x 2x x 6 x 3 x
1
+ f(v ,v )*a2*a7 + f(v,v )*a2*a7 + ---*f(v,v )*a3*a7*u)/a2
x x 2x 3 x
4 1 2 4 4
df(v,t)=(36*u *a19*a2 *a3*v + ---*u *a2 *a3 *v + 108*u *v *a19*a2 *a3
2x 2 2x x x
2 4 3 2 1 5
+ 2*u *v *a2 *a3 + 18*u *a19*a2 *a3 *u*v + ---*u *a2*a3 *u*v
x x x 6 x
5 3 3 4
+ 216*v *a19*a2 + 4*v *a2 *a3 + 108*v *a19*a2 *a3*u
3x 3x 2x
2 4 3 2 2 1 5 2
+ 2*v *a2 *a3 *u + 18*v *a19*a2 *a3 *u + ---*v *a2*a3 *u
2x x 3 x
1 4 1 5 2 3 3
- ---*f(v,v )*a2*a3 *a7*v - ----*f(v,v)*a3 *a7*u*v + a19*a2 *a3 *u *v)
6 x 36
2 3
/(a2 *a3 )
2 8 1 6 3 1 4 6
df(u,s)=(u *a19 *a2 *b2 + ----*u *a19*a2 *a3 *b2 - ------*u *a2 *a3 *b2
5x 72 5x 5184 5x
5 2 7 5 5 4
+ ---*u *a19 *a2 *a3*b2*u + -----*u *a19*a2 *a3 *b2*u
3 4x 216 4x
5 3 7 2 7
- -------*u *a2 *a3 *b2*u + 5*u *u *a19 *a2 *a3*b2
15552 4x 3x x
5 5 4 5 3 7
+ ----*u *u *a19*a2 *a3 *b2 - ------*u *u *a2 *a3 *b2
72 3x x 5184 3x x
5 4 4
- -----*u *f(v,v)*a19*a2 *a3 *a7*b2
648 3x
5 2 7 10 2 6 2 2
- -------*u *f(v,v)*a2 *a3 *a7*b2 + ----*u *a19 *a2 *a3 *b2*u
31104 3x 9 3x
5 4 5 2 5 2 8 2
+ -----*u *a19*a2 *a3 *b2*u - -------*u *a2 *a3 *b2*u
324 3x 23328 3x
10 2 2 7 5 2 5 4
+ ----*u *a19 *a2 *a3*b2 + -----*u *a19*a2 *a3 *b2
3 2x 108 2x
5 2 3 7 50 2 6 2
- ------*u *a2 *a3 *b2 + ----*u *u *a19 *a2 *a3 *b2*u
7776 2x 9 2x x
25 4 5 25 2 8
+ -----*u *u *a19*a2 *a3 *b2*u - -------*u *u *a2 *a3 *b2*u
324 2x x 23328 2x x
65 4 4
- ------*u *f(v,v )*a19*a2 *a3 *a7*b2
1296 2x x
25 2 7
- -------*u *f(v,v )*a2 *a3 *a7*b2
23328 2x x
5 3 5
- -----*u *f(v,v)*a19*a2 *a3 *a7*b2*u
864 2x
35 8 10 2 5 3 3
- --------*u *f(v,v)*a2*a3 *a7*b2*u + ----*u *a19 *a2 *a3 *b2*u
279936 2x 27 2x
5 3 6 3 5 9 3
+ -----*u *a19*a2 *a3 *b2*u - -------*u *a2*a3 *b2*u
972 2x 69984 2x
5 3 2 6 2 5 3 4 5
+ ---*u *a19 *a2 *a3 *b2 + -----*u *a19*a2 *a3 *b2
3 x 216 x
5 3 2 8 5 2 3 5
- -------*u *a2 *a3 *b2 - -----*u *f(v,v)*a19*a2 *a3 *a7*b2
15552 x 864 x
35 2 8 10 2 2 5 3 2
- --------*u *f(v,v)*a2*a3 *a7*b2 + ----*u *a19 *a2 *a3 *b2*u
279936 x 9 x
5 2 3 6 2 5 2 9 2
+ -----*u *a19*a2 *a3 *b2*u - -------*u *a2*a3 *b2*u
324 x 23328 x
25 4 4
- -----*u *f(v ,v )*a19*a2 *a3 *a7*b2
432 x x x
5 2 7
- ------*u *f(v ,v )*a2 *a3 *a7*b2
3888 x x x
5 4 4
- ----*u *f(v,v )*a19*a2 *a3 *a7*b2
72 x 2x
35 2 7
- -------*u *f(v,v )*a2 *a3 *a7*b2
23328 x 2x
5 3 5
- -----*u *f(v,v )*a19*a2 *a3 *a7*b2*u
162 x x
95 8
- --------*u *f(v,v )*a2*a3 *a7*b2*u
139968 x x
25 2 6 2
- -------*u *f(v,v)*a19*a2 *a3 *a7*b2*u
15552 x
5 9 2 5 2 4 4 4
- --------*u *f(v,v)*a3 *a7*b2*u + ----*u *a19 *a2 *a3 *b2*u
139968 x 81 x
5 2 7 4 5 10 4
+ ------*u *a19*a2 *a3 *b2*u - --------*u *a3 *b2*u
5832 x 419904 x
5 5 3 25 3 6
- ----*f(v ,v )*a19*a2 *a3 *a7*b2 - -------*f(v ,v )*a2 *a3 *a7*b2
72 2x 2x 15552 2x 2x
25 5 3 5 3 6
- -----*f(v ,v )*a19*a2 *a3 *a7*b2 - ------*f(v ,v )*a2 *a3 *a7*b2
216 x 3x 1944 x 3x
35 4 4
- -----*f(v ,v )*a19*a2 *a3 *a7*b2*u
432 x 2x
85 2 7
- -------*f(v ,v )*a2 *a3 *a7*b2*u
46656 x 2x
25 3 5 2
- ------*f(v ,v )*a19*a2 *a3 *a7*b2*u
2592 x x
5 8 2 5 5 3
- -------*f(v ,v )*a2*a3 *a7*b2*u - -----*f(v,v )*a19*a2 *a3 *a7*b2
23328 x x 108 4x
5 3 6 5 4 4
- ------*f(v,v )*a2 *a3 *a7*b2 - -----*f(v,v )*a19*a2 *a3 *a7*b2*u
5184 4x 144 3x
35 2 7
- -------*f(v,v )*a2 *a3 *a7*b2*u
46656 3x
25 3 5 2
- ------*f(v,v )*a19*a2 *a3 *a7*b2*u
2592 2x
5 8 2
- -------*f(v,v )*a2*a3 *a7*b2*u
23328 2x
25 2 6 3 5 9 3
- -------*f(v,v )*a19*a2 *a3 *a7*b2*u - --------*f(v,v )*a3 *a7*b2*u
23328 x 209952 x
2 8 1 6 3 1 4 6
)/(a19 *a2 + ----*a19*a2 *a3 - ------*a2 *a3 )
72 5184
5 2 8 25 6 4
df(v,s)=( - ---*u *a19 *a2 *a3*b2*v - -----*u *a19*a2 *a3 *b2*v
3 4x 432 4x
5 4 7 15 2 8
- -------*u *a2 *a3 *b2*v - ----*u *v *a19 *a2 *a3*b2
10368 4x 2 3x x
5 6 4 5 4 7
- ----*u *v *a19*a2 *a3 *b2 - ------*u *v *a2 *a3 *b2
18 3x x 1944 3x x
55 2 7 2 65 5 5
- ----*u *a19 *a2 *a3 *b2*u*v - ------*u *a19*a2 *a3 *b2*u*v
36 3x 1296 3x
35 3 8 55 2 7 2
- -------*u *a2 *a3 *b2*u*v - ----*u *u *a19 *a2 *a3 *b2*v
93312 3x 18 2x x
65 5 5 35 3 8
- -----*u *u *a19*a2 *a3 *b2*v - -------*u *u *a2 *a3 *b2*v
648 2x x 46656 2x x
2 8 5 6 4
- 15*u *v *a19 *a2 *a3*b2 - ---*u *v *a19*a2 *a3 *b2
2x 2x 9 2x 2x
5 4 7 2 7 2
- -----*u *v *a2 *a3 *b2 - 5*u *v *a19 *a2 *a3 *b2*u
972 2x 2x 2x x
5 5 5 5 3 8
- ----*u *v *a19*a2 *a3 *b2*u - ------*u *v *a2 *a3 *b2*u
27 2x x 2916 2x x
5 4 5
+ ------*u *f(v,v)*a19*a2 *a3 *a7*b2*v
3888 2x
5 2 8 65 2 6 3 2
+ --------*u *f(v,v)*a2 *a3 *a7*b2*v - -----*u *a19 *a2 *a3 *b2*u *v
186624 2x 108 2x
35 4 6 2 5 2 9 2
- ------*u *a19*a2 *a3 *b2*u *v - -------*u *a2 *a3 *b2*u *v
1944 2x 46656 2x
15 2 2 7 2 5 2 5 5
- ----*u *v *a19 *a2 *a3 *b2 - ----*u *v *a19*a2 *a3 *b2
4 x x 36 x x
5 2 3 8 65 2 2 6 3
- ------*u *v *a2 *a3 *b2 - ----*u *a19 *a2 *a3 *b2*u*v
3888 x x 72 x
35 2 4 6 5 2 2 9
- ------*u *a19*a2 *a3 *b2*u*v - -------*u *a2 *a3 *b2*u*v
1296 x 31104 x
2 8 5 6 4
- 15*u *v *a19 *a2 *a3*b2 - ---*u *v *a19*a2 *a3 *b2
x 3x 9 x 3x
5 4 7 15 2 7 2
- -----*u *v *a2 *a3 *b2 - ----*u *v *a19 *a2 *a3 *b2*u
972 x 3x 2 x 2x
5 5 5 5 3 8
- ----*u *v *a19*a2 *a3 *b2*u - ------*u *v *a2 *a3 *b2*u
18 x 2x 1944 x 2x
5 2 6 3 2 5 4 6 2
- ---*u *v *a19 *a2 *a3 *b2*u - -----*u *v *a19*a2 *a3 *b2*u
4 x x 108 x x
5 2 9 2 5 4 5
- -------*u *v *a2 *a3 *b2*u + -----*u *f(v,v )*a19*a2 *a3 *a7*b2*v
11664 x x 864 x x
35 2 8
+ --------*u *f(v,v )*a2 *a3 *a7*b2*v
279936 x x
5 3 6
+ ------*u *f(v,v)*a19*a2 *a3 *a7*b2*u*v
5184 x
35 9 85 2 5 4 3
+ ---------*u *f(v,v)*a2*a3 *a7*b2*u*v - -----*u *a19 *a2 *a3 *b2*u *v
1679616 x 648 x
5 3 7 3 5 10 3
- ------*u *a19*a2 *a3 *b2*u *v - --------*u *a2*a3 *b2*u *v
1458 x 419904 x
2 9 1 7 3 1 5 6
- 9*v *a19 *a2 *b2 - ---*v *a19*a2 *a3 *b2 - -----*v *a2 *a3 *b2
5x 3 5x 324 5x
15 2 8 5 6 4
- ----*v *a19 *a2 *a3*b2*u - ----*v *a19*a2 *a3 *b2*u
2 4x 18 4x
5 4 7 5 2 7 2 2
- ------*v *a2 *a3 *b2*u - ---*v *a19 *a2 *a3 *b2*u
1944 4x 2 3x
5 5 5 2 5 3 8 2
- ----*v *a19*a2 *a3 *b2*u - ------*v *a2 *a3 *b2*u
54 3x 5832 3x
5 2 6 3 3 5 4 6 3
- ----*v *a19 *a2 *a3 *b2*u - -----*v *a19*a2 *a3 *b2*u
12 2x 324 2x
5 2 9 3 5 2 5 4 4
- -------*v *a2 *a3 *b2*u - -----*v *a19 *a2 *a3 *b2*u
34992 2x 144 x
5 3 7 4 5 10 4
- ------*v *a19*a2 *a3 *b2*u - --------*v *a2*a3 *b2*u
3888 x 419904 x
5 5 4
+ -----*f(v ,v )*a19*a2 *a3 *a7*b2*v
432 x 2x
25 3 7
+ -------*f(v ,v )*a2 *a3 *a7*b2*v
93312 x 2x
5 4 5
+ ------*f(v ,v )*a19*a2 *a3 *a7*b2*u*v
1296 x x
25 2 8
+ --------*f(v ,v )*a2 *a3 *a7*b2*u*v
279936 x x
5 5 4
+ -----*f(v,v )*a19*a2 *a3 *a7*b2*v
648 3x
5 3 7
+ -------*f(v,v )*a2 *a3 *a7*b2*v
31104 3x
5 4 5
+ -----*f(v,v )*a19*a2 *a3 *a7*b2*u*v
864 2x
35 2 8
+ --------*f(v,v )*a2 *a3 *a7*b2*u*v
279936 2x
25 3 6 2
+ -------*f(v,v )*a19*a2 *a3 *a7*b2*u *v
15552 x
5 9 2
+ --------*f(v,v )*a2*a3 *a7*b2*u *v
139968 x
25 2 7 3
+ --------*f(v,v)*a19*a2 *a3 *a7*b2*u *v
279936
5 10 3 25 2 4 5 5
+ ---------*f(v,v)*a3 *a7*b2*u *v - ------*a19 *a2 *a3 *b2*u *v
2519424 7776
5 2 8 5 2 9 1 7 3
- -------*a19*a2 *a3 *b2*u *v)/(a19 *a2 + ----*a19*a2 *a3
69984 72
1 5 6
- ------*a2 *a3 )
5184
df(u,t)=(df(u,x,3)*a2**2 + df(u,x,2)*a2*a3*u + df(u,x)**2*a2*a3 + 1/6*df(u,x)*f(
v,v)*a3*a7 + 1/3*df(u,x)*a3**2*u**2 + f(df(v,x),df(v,x))*a2*a7 + f(v,df(v,x,2))*
a2*a7 + 1/3*f(v,df(v,x))*a3*a7*u)/a2$
df(v,t)=(36*df(u,x,2)*a19*a2**4*a3*v + 1/2*df(u,x,2)*a2**2*a3**4*v + 108*df(u,x)
*df(v,x)*a19*a2**4*a3 + 2*df(u,x)*df(v,x)*a2**2*a3**4 + 18*df(u,x)*a19*a2**3*a3
**2*u*v + 1/6*df(u,x)*a2*a3**5*u*v + 216*df(v,x,3)*a19*a2**5 + 4*df(v,x,3)*a2**3
*a3**3 + 108*df(v,x,2)*a19*a2**4*a3*u + 2*df(v,x,2)*a2**2*a3**4*u + 18*df(v,x)*
a19*a2**3*a3**2*u**2 + 1/3*df(v,x)*a2*a3**5*u**2 - 1/6*f(v,df(v,x))*a2*a3**4*a7*
v - 1/36*f(v,v)*a3**5*a7*u*v + a19*a2**2*a3**3*u**3*v)/(a2**2*a3**3)$
df(u,s)=(df(u,x,5)*a19**2*a2**8*b2 + 1/72*df(u,x,5)*a19*a2**6*a3**3*b2 - 1/5184*
df(u,x,5)*a2**4*a3**6*b2 + 5/3*df(u,x,4)*a19**2*a2**7*a3*b2*u + 5/216*df(u,x,4)*
a19*a2**5*a3**4*b2*u - 5/15552*df(u,x,4)*a2**3*a3**7*b2*u + 5*df(u,x,3)*df(u,x)*
a19**2*a2**7*a3*b2 + 5/72*df(u,x,3)*df(u,x)*a19*a2**5*a3**4*b2 - 5/5184*df(u,x,3
)*df(u,x)*a2**3*a3**7*b2 - 5/648*df(u,x,3)*f(v,v)*a19*a2**4*a3**4*a7*b2 - 5/
31104*df(u,x,3)*f(v,v)*a2**2*a3**7*a7*b2 + 10/9*df(u,x,3)*a19**2*a2**6*a3**2*b2*
u**2 + 5/324*df(u,x,3)*a19*a2**4*a3**5*b2*u**2 - 5/23328*df(u,x,3)*a2**2*a3**8*
b2*u**2 + 10/3*df(u,x,2)**2*a19**2*a2**7*a3*b2 + 5/108*df(u,x,2)**2*a19*a2**5*a3
**4*b2 - 5/7776*df(u,x,2)**2*a2**3*a3**7*b2 + 50/9*df(u,x,2)*df(u,x)*a19**2*a2**
6*a3**2*b2*u + 25/324*df(u,x,2)*df(u,x)*a19*a2**4*a3**5*b2*u - 25/23328*df(u,x,2
)*df(u,x)*a2**2*a3**8*b2*u - 65/1296*df(u,x,2)*f(v,df(v,x))*a19*a2**4*a3**4*a7*
b2 - 25/23328*df(u,x,2)*f(v,df(v,x))*a2**2*a3**7*a7*b2 - 5/864*df(u,x,2)*f(v,v)*
a19*a2**3*a3**5*a7*b2*u - 35/279936*df(u,x,2)*f(v,v)*a2*a3**8*a7*b2*u + 10/27*df
(u,x,2)*a19**2*a2**5*a3**3*b2*u**3 + 5/972*df(u,x,2)*a19*a2**3*a3**6*b2*u**3 - 5
/69984*df(u,x,2)*a2*a3**9*b2*u**3 + 5/3*df(u,x)**3*a19**2*a2**6*a3**2*b2 + 5/216
*df(u,x)**3*a19*a2**4*a3**5*b2 - 5/15552*df(u,x)**3*a2**2*a3**8*b2 - 5/864*df(u,
x)**2*f(v,v)*a19*a2**3*a3**5*a7*b2 - 35/279936*df(u,x)**2*f(v,v)*a2*a3**8*a7*b2
+ 10/9*df(u,x)**2*a19**2*a2**5*a3**3*b2*u**2 + 5/324*df(u,x)**2*a19*a2**3*a3**6*
b2*u**2 - 5/23328*df(u,x)**2*a2*a3**9*b2*u**2 - 25/432*df(u,x)*f(df(v,x),df(v,x)
)*a19*a2**4*a3**4*a7*b2 - 5/3888*df(u,x)*f(df(v,x),df(v,x))*a2**2*a3**7*a7*b2 -
5/72*df(u,x)*f(v,df(v,x,2))*a19*a2**4*a3**4*a7*b2 - 35/23328*df(u,x)*f(v,df(v,x,
2))*a2**2*a3**7*a7*b2 - 5/162*df(u,x)*f(v,df(v,x))*a19*a2**3*a3**5*a7*b2*u - 95/
139968*df(u,x)*f(v,df(v,x))*a2*a3**8*a7*b2*u - 25/15552*df(u,x)*f(v,v)*a19*a2**2
*a3**6*a7*b2*u**2 - 5/139968*df(u,x)*f(v,v)*a3**9*a7*b2*u**2 + 5/81*df(u,x)*a19
**2*a2**4*a3**4*b2*u**4 + 5/5832*df(u,x)*a19*a2**2*a3**7*b2*u**4 - 5/419904*df(u
,x)*a3**10*b2*u**4 - 5/72*f(df(v,x,2),df(v,x,2))*a19*a2**5*a3**3*a7*b2 - 25/
15552*f(df(v,x,2),df(v,x,2))*a2**3*a3**6*a7*b2 - 25/216*f(df(v,x),df(v,x,3))*a19
*a2**5*a3**3*a7*b2 - 5/1944*f(df(v,x),df(v,x,3))*a2**3*a3**6*a7*b2 - 35/432*f(df
(v,x),df(v,x,2))*a19*a2**4*a3**4*a7*b2*u - 85/46656*f(df(v,x),df(v,x,2))*a2**2*
a3**7*a7*b2*u - 25/2592*f(df(v,x),df(v,x))*a19*a2**3*a3**5*a7*b2*u**2 - 5/23328*
f(df(v,x),df(v,x))*a2*a3**8*a7*b2*u**2 - 5/108*f(v,df(v,x,4))*a19*a2**5*a3**3*a7
*b2 - 5/5184*f(v,df(v,x,4))*a2**3*a3**6*a7*b2 - 5/144*f(v,df(v,x,3))*a19*a2**4*
a3**4*a7*b2*u - 35/46656*f(v,df(v,x,3))*a2**2*a3**7*a7*b2*u - 25/2592*f(v,df(v,x
,2))*a19*a2**3*a3**5*a7*b2*u**2 - 5/23328*f(v,df(v,x,2))*a2*a3**8*a7*b2*u**2 -
25/23328*f(v,df(v,x))*a19*a2**2*a3**6*a7*b2*u**3 - 5/209952*f(v,df(v,x))*a3**9*
a7*b2*u**3)/(a19**2*a2**8 + 1/72*a19*a2**6*a3**3 - 1/5184*a2**4*a3**6)$
df(v,s)=( - 5/3*df(u,x,4)*a19**2*a2**8*a3*b2*v - 25/432*df(u,x,4)*a19*a2**6*a3**
4*b2*v - 5/10368*df(u,x,4)*a2**4*a3**7*b2*v - 15/2*df(u,x,3)*df(v,x)*a19**2*a2**
8*a3*b2 - 5/18*df(u,x,3)*df(v,x)*a19*a2**6*a3**4*b2 - 5/1944*df(u,x,3)*df(v,x)*
a2**4*a3**7*b2 - 55/36*df(u,x,3)*a19**2*a2**7*a3**2*b2*u*v - 65/1296*df(u,x,3)*
a19*a2**5*a3**5*b2*u*v - 35/93312*df(u,x,3)*a2**3*a3**8*b2*u*v - 55/18*df(u,x,2)
*df(u,x)*a19**2*a2**7*a3**2*b2*v - 65/648*df(u,x,2)*df(u,x)*a19*a2**5*a3**5*b2*v
- 35/46656*df(u,x,2)*df(u,x)*a2**3*a3**8*b2*v - 15*df(u,x,2)*df(v,x,2)*a19**2*
a2**8*a3*b2 - 5/9*df(u,x,2)*df(v,x,2)*a19*a2**6*a3**4*b2 - 5/972*df(u,x,2)*df(v,
x,2)*a2**4*a3**7*b2 - 5*df(u,x,2)*df(v,x)*a19**2*a2**7*a3**2*b2*u - 5/27*df(u,x,
2)*df(v,x)*a19*a2**5*a3**5*b2*u - 5/2916*df(u,x,2)*df(v,x)*a2**3*a3**8*b2*u + 5/
3888*df(u,x,2)*f(v,v)*a19*a2**4*a3**5*a7*b2*v + 5/186624*df(u,x,2)*f(v,v)*a2**2*
a3**8*a7*b2*v - 65/108*df(u,x,2)*a19**2*a2**6*a3**3*b2*u**2*v - 35/1944*df(u,x,2
)*a19*a2**4*a3**6*b2*u**2*v - 5/46656*df(u,x,2)*a2**2*a3**9*b2*u**2*v - 15/4*df(
u,x)**2*df(v,x)*a19**2*a2**7*a3**2*b2 - 5/36*df(u,x)**2*df(v,x)*a19*a2**5*a3**5*
b2 - 5/3888*df(u,x)**2*df(v,x)*a2**3*a3**8*b2 - 65/72*df(u,x)**2*a19**2*a2**6*a3
**3*b2*u*v - 35/1296*df(u,x)**2*a19*a2**4*a3**6*b2*u*v - 5/31104*df(u,x)**2*a2**
2*a3**9*b2*u*v - 15*df(u,x)*df(v,x,3)*a19**2*a2**8*a3*b2 - 5/9*df(u,x)*df(v,x,3)
*a19*a2**6*a3**4*b2 - 5/972*df(u,x)*df(v,x,3)*a2**4*a3**7*b2 - 15/2*df(u,x)*df(v
,x,2)*a19**2*a2**7*a3**2*b2*u - 5/18*df(u,x)*df(v,x,2)*a19*a2**5*a3**5*b2*u - 5/
1944*df(u,x)*df(v,x,2)*a2**3*a3**8*b2*u - 5/4*df(u,x)*df(v,x)*a19**2*a2**6*a3**3
*b2*u**2 - 5/108*df(u,x)*df(v,x)*a19*a2**4*a3**6*b2*u**2 - 5/11664*df(u,x)*df(v,
x)*a2**2*a3**9*b2*u**2 + 5/864*df(u,x)*f(v,df(v,x))*a19*a2**4*a3**5*a7*b2*v + 35
/279936*df(u,x)*f(v,df(v,x))*a2**2*a3**8*a7*b2*v + 5/5184*df(u,x)*f(v,v)*a19*a2
**3*a3**6*a7*b2*u*v + 35/1679616*df(u,x)*f(v,v)*a2*a3**9*a7*b2*u*v - 85/648*df(u
,x)*a19**2*a2**5*a3**4*b2*u**3*v - 5/1458*df(u,x)*a19*a2**3*a3**7*b2*u**3*v - 5/
419904*df(u,x)*a2*a3**10*b2*u**3*v - 9*df(v,x,5)*a19**2*a2**9*b2 - 1/3*df(v,x,5)
*a19*a2**7*a3**3*b2 - 1/324*df(v,x,5)*a2**5*a3**6*b2 - 15/2*df(v,x,4)*a19**2*a2
**8*a3*b2*u - 5/18*df(v,x,4)*a19*a2**6*a3**4*b2*u - 5/1944*df(v,x,4)*a2**4*a3**7
*b2*u - 5/2*df(v,x,3)*a19**2*a2**7*a3**2*b2*u**2 - 5/54*df(v,x,3)*a19*a2**5*a3**
5*b2*u**2 - 5/5832*df(v,x,3)*a2**3*a3**8*b2*u**2 - 5/12*df(v,x,2)*a19**2*a2**6*
a3**3*b2*u**3 - 5/324*df(v,x,2)*a19*a2**4*a3**6*b2*u**3 - 5/34992*df(v,x,2)*a2**
2*a3**9*b2*u**3 - 5/144*df(v,x)*a19**2*a2**5*a3**4*b2*u**4 - 5/3888*df(v,x)*a19*
a2**3*a3**7*b2*u**4 - 5/419904*df(v,x)*a2*a3**10*b2*u**4 + 5/432*f(df(v,x),df(v,
x,2))*a19*a2**5*a3**4*a7*b2*v + 25/93312*f(df(v,x),df(v,x,2))*a2**3*a3**7*a7*b2*
v + 5/1296*f(df(v,x),df(v,x))*a19*a2**4*a3**5*a7*b2*u*v + 25/279936*f(df(v,x),df
(v,x))*a2**2*a3**8*a7*b2*u*v + 5/648*f(v,df(v,x,3))*a19*a2**5*a3**4*a7*b2*v + 5/
31104*f(v,df(v,x,3))*a2**3*a3**7*a7*b2*v + 5/864*f(v,df(v,x,2))*a19*a2**4*a3**5*
a7*b2*u*v + 35/279936*f(v,df(v,x,2))*a2**2*a3**8*a7*b2*u*v + 25/15552*f(v,df(v,x
))*a19*a2**3*a3**6*a7*b2*u**2*v + 5/139968*f(v,df(v,x))*a2*a3**9*a7*b2*u**2*v +
25/279936*f(v,v)*a19*a2**2*a3**7*a7*b2*u**3*v + 5/2519424*f(v,v)*a3**10*a7*b2*u
**3*v - 25/7776*a19**2*a2**4*a3**5*b2*u**5*v - 5/69984*a19*a2**2*a3**8*b2*u**5*v
)/(a19**2*a2**9 + 1/72*a19*a2**7*a3**3 - 1/5184*a2**5*a3**6)$