Solution 1 to problem
Remaining equations |
Expressions |
Parameters |
Inequalities |
Relevance |
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Equations
The following unsolved equations remain:
2 2
0=a11 + b12 *kap
Expressions
The solution is given through the following expressions:
r30=0
r31=0
r32=0
r33=0
r34=0
r35=0
r36=0
r37=0
r38=0
r39=0
r311=0
r312=r310
r313=0
r314=0
r315=r310
r316=r327
r317=0
r318=0
r320=0
r321=0
r322=0
r323=0
r324=0
r325=0
r326=0
r329=0
r330=0
r331=0
r332=0
- a11*r328 + b12*kap*r310
r333=----------------------------
b12
r334=0
r335=0
r336=0
r337=0
r338=0
r339=0
r340=0
r341=0
r342= - r328
r343=r327
r344=0
r345=0
r346=0
r347=0
r348=0
r349=0
r350=0
r351=0
r352=0
- a11*r328 + b12*kap*r310
r353=----------------------------
b12
r354=0
r355=0
a33= - a11
a23=0
a22=a11
a13=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:
r319, r310, r328, r327, a11, b12
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.
{b12,a11}
Relevance for the application:
Modulo the following equation:
2 2
0=a11 + b12 *kap
the system of equations related to the Hamiltonian HAM:
2 2 2
HAM=u1 *a11 + u1*v2*b12 + u2 *a11 - u2*v1*b12 - u3 *a11
has apart from the Hamiltonian and Casimirs the following 4 first integrals:
2
FI=u1*u3*v1 + u2*u3*v2 + u3 *v3
= a product of the elements of: {u3,u1*v1 + u2*v2 + u3*v3}
{HAM,FI} = 0
2 2
FI= - u1 *u3*a11 - u1*u3*v2*b12 - u2 *u3*a11 + u2*u3*v1*b12
2 2
= a product of the elements of: { - u3,u1 *a11 + u1*v2*b12 + u2 *a11
- u2*v1*b12}
{HAM,FI} = 0
2 2 2 2 2
FI=u1 *u3*kap + u2 *u3*kap + u3*v1 + u3*v2 + u3*v3
2 2 2 2 2
= a product of the elements of: {u3,u1 *kap + u2 *kap + v1 + v2 + v3 }
{HAM,FI} = 0
3
FI=u3
= a product of the elements of: {u3,u3,u3}
{HAM,FI} = 0
And again in machine readable form:
HAM=u1**2*a11 + u1*v2*b12 + u2**2*a11 - u2*v1*b12 - u3**2*a11$
FI=u1*u3*v1 + u2*u3*v2 + u3**2*v3$
FI= - u1**2*u3*a11 - u1*u3*v2*b12 - u2**2*u3*a11 + u2*u3*v1*b12$
FI=u1**2*u3*kap + u2**2*u3*kap + u3*v1**2 + u3*v2**2 + u3*v3**2$
FI=u3**3$