Solution 2 to problem l21o24
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem l21o24
Expressions
The solution is given through the following expressions:
b28=0
b27=0
a3*b19
b26=--------
a1
a3*b19
b25=--------
a1
b24=0
b23=0
b22=0
b21=0
b20=0
b18=0
b17=0
b16=0
b15=0
2
- a3 *b19
b14=------------
2
a1
2
- a3 *b19
b13=------------
2
a1
b12=0
b11=0
b10=0
b9=0
- a3*b19
b8=-----------
a1
a3*b19
b7=--------
a8
4*a3*b19
b6=----------
a8
3*a3*b19
b5=----------
a8
b4=0
b3=0
b2=0
a1*b19
b1=--------
a8
1
---*a3*a8
2
a9=-----------
a1
a7=0
1 2
- ---*a3 *a8
2
a6=---------------
2
a1
- a3*a8
a5=----------
a1
a4=a3
a2=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:
b19, a3, a1, 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.
{a8,
b19,
a1,
a1*g0009 + a3*g0010,
a1*g0017 + a3*g0018,
a3,
2 2
2*a1 *g0012 + 2*a1 *g0013 - 2*a1*a8*g0015 - a3*a8*g0014,
a5,
a1*g0038 + a3*g0044 + a3*g0045,
3 2 2 2
a1 *g0020 + 3*a1 *a3*g0024 + 4*a1 *a3*g0025 + a1 *a3*g0026 - a1*a3*a8*g0027
2 2
- a3 *a8*g0032 - a3 *a8*g0033}
Relevance for the application:
/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
3 2 2 1 2 2
df(u,t)=(u *a1 + f(v ,v )*a1 *a3 + f(v,v )*a1 *a3 - ---*f(v,v) *a3 *a8
2x x x 2x 2
2
- f(v,v)*a1*a3*a8*u)/a1
1
---*f(v,v)*a3*a8*v + a1*a8*u*v
2
df(v,t)=--------------------------------
a1
3 2
df(u,s)=(u *a1 *b19 - u *f(v,v)*a1*a3*a8*b19 + 3*f(v ,v )*a1 *a3*b19
4x 2x 2x 2x
2 2
+ 4*f(v ,v )*a1 *a3*b19 - f(v ,v )*f(v,v)*a3 *a8*b19
x 3x x x
2 2 2
+ f(v,v )*a1 *a3*b19 - f(v,v )*f(v,v)*a3 *a8*b19)/(a1 *a8)
4x 2x
u *a1*b19*v + f(v ,v )*a3*b19*v + f(v,v )*a3*b19*v
2x x x 2x
df(v,s)=------------------------------------------------------
a1