Solution 1 to problem l21o24
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem l21o24
Expressions
The solution is given through the following expressions:
1 2
---*a4 *b22
4
b28=-------------
2
a7
- a4*b22
b27=-----------
a7
- a4*b22
b26=-----------
a8
- a4*b22
b25=-----------
a8
- 2*a4*b22
b24=-------------
a8
- a4*b22
b23=-----------
a8
2*a7*b22
b21=----------
a8
2*a7*b22
b20=----------
a8
a7*b22
b19=--------
a8
2
a7 *b22
b18=---------
2
a8
1 3
---*a4 *b22
4
b17=-------------
3
a7
2
- a4 *b22
b16=------------
2
a7
2
- 2*a4 *b22
b15=--------------
a7*a8
2
- 2*a4 *b22
b14=--------------
a7*a8
2
- a4 *b22
b13=------------
a7*a8
a4*b22
b12=--------
a7
2*a4*b22
b11=----------
a8
b10=0
2*a4*b22
b9=----------
a8
a4*b22
b8=--------
a8
a4*a7*b22
b7=-----------
2
a8
b6=0
b5=0
b4=0
b3=0
b2=0
b1=0
1
- ---*a4*a8
2
a9=--------------
a7
1 2
- ---*a4 *a8
2
a6=---------------
2
a7
a4*a8
a5=-------
a7
a3=0
a2=0
a1=0
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:
b22, a4, a7, a8
Inequalities
In the following not identically vanishing expressions are shown.
Any auxiliary variables g00?? are used to express that at least
one of their coefficients must not vanish, e.g. g0019*p4 + g0020*p3
means that either p4 or p3 or both are non-vanishing.
{b22,
a4*g0010 + a7*g0011,
a7,
a8,
a4*g0018 + a7*g0019,
b19,
2 2 2 2 2
a4 *a8 *g0047 - 4*a4*a7 *a8*g0042 - 8*a4*a7 *a8*g0043 - 4*a4*a7 *a8*g0044
2 2 4 3
- 4*a4*a7 *a8*g0045 - 4*a4*a7*a8 *g0046 + 4*a7 *g0037 + 4*a7 *a8*g0038
3 3 2 2
+ 8*a7 *a8*g0039 + 8*a7 *a8*g0040 + 4*a7 *a8 *g0041,
a4,
2
a4*a8*g0014 - 2*a7 *g0013 - 2*a7*a8*g0015,
a5,
2 2 2 2 2
a4 *a8 *g0036 - 4*a4*a7 *a8*g0032 - 8*a4*a7 *a8*g0033 - 8*a4*a7 *a8*g0034
2 4 3 3
- 4*a4*a7*a8 *g0035 + 4*a7 *g0026 + 4*a7 *a8*g0027 + 8*a7 *a8*g0028
3 2 2
+ 8*a7 *a8*g0030 + 4*a7 *a8 *g0031}
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
2 1 2 2
f(v,v )*a4*a7 - ---*f(v,v) *a4 *a8 + f(v,v)*a4*a7*a8*u
2x 2
df(u,t)=----------------------------------------------------------
2
a7
2 1
v *a7 - ---*f(v,v)*a4*a8*v + a7*a8*u*v
2x 2
df(v,t)=------------------------------------------
a7
3 3
df(u,s)=(u *f(v,v)*a4*a7 *a8*b22 + 2*u *f(v,v )*a4*a7 *a8*b22
2x x x
2 2 4
- f(v ,v )*f(v,v)*a4 *a7 *a8*b22 + f(v,v )*a4*a7 *b22
x x 4x
2 2 3
- 2*f(v,v )*f(v,v)*a4 *a7 *a8*b22 + 2*f(v,v )*a4*a7 *a8*b22*u
2x 2x
2 2 2 1 3 3 2
- 2*f(v,v ) *a4 *a7 *a8*b22 + ---*f(v,v) *a4 *a8 *b22
x 4
2 2 2 2 2 2 3 2
- f(v,v) *a4 *a7*a8 *b22*u + f(v,v)*a4*a7 *a8 *b22*u )/(a7 *a8 )
3 3 4
df(v,s)=(u *a7 *a8*b22*v + 2*u *v *a7 *a8*b22 + v *a7 *b22
2x x x 4x
2 3
- v *f(v,v)*a4*a7 *a8*b22 + 2*v *a7 *a8*b22*u
2x 2x
2 2
- 2*v *f(v,v )*a4*a7 *a8*b22 - f(v ,v )*a4*a7 *a8*b22*v
x x x x
2 1 2 2 2
- f(v,v )*a4*a7 *a8*b22*v + ---*f(v,v) *a4 *a8 *b22*v
2x 4
2 2 2 2 2 2
- f(v,v)*a4*a7*a8 *b22*u*v + a7 *a8 *b22*u *v)/(a7 *a8 )