Solution 2 to problem over

Expressions | Parameters | Inequalities | Relevance | Back to problem over

Expressions

The solution is given through the following expressions:


     b32*r10
r11=---------
       b33


r13=0


r14=0


r15=0


c22=0


c11=0


     b31*r10
r12=---------
       b33

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:

 r10, b33, b32, a33, b31, a23

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.

 
{a23}

Relevance for the application:

The system of equations related to the Hamiltonian HAM:

                    2
HAM=2*u2*u3*a23 + u3 *a33 + u3*v1*b31 + u3*v2*b32 + u3*v3*b33

has apart from the Hamiltonian and Casimirs only the following first integral: 

FI=v1*b31 + v2*b32 + v3*b33

which the program can not factorize further.

{HAM,FI} = 0





And again in machine readable form:



HAM=2*u2*u3*a23 + u3**2*a33 + u3*v1*b31 + u3*v2*b32 + u3*v3*b33$

FI=v1*b31 + v2*b32 + v3*b33$