Solution 6 to problem over

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

Expressions

The solution is given through the following expressions:


      1
     ---*a33*n3*r26
      2
r10=----------------
             2
          a23


r11=0


r12=0


r13=0


r14=0


r15=0


         1     2
      - ---*a33 *r26
         2
r20=-----------------
             2
          a23


     a33*r26
r21=---------
       a23


r22=0


r23=0


r24=0


     a33*r26
r27=---------
       a23


r28=0


r29=0


r210=0


r211=r26


r212=0


r214=0


r215=0


r216=0


r217=r26


r218=0


r219=0


m3=n3


c33= - a33


c23=a23


b33=0


b12=0


b22=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:

 r00, r26, n3, a33, 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,r26,a33}

Relevance for the application:

The system of equations related to the Hamiltonian HAM:

                                  2
HAM=2*u2*u3*a23 + 2*u2*v3*a23 + u3 *a33 + 2*u3*v2*a23 + u3*n3 + 2*v2*v3*a23

         2
     - v3 *a33 + v3*n3

has apart from the Hamiltonian and Casimirs the following 2 first integrals: 

            2            2                            2
FI=u1*v1*a23  + u2*v2*a23  + u3*v2*a23*a33 + u3*v3*a23  + v2*v3*a23*a33

       1    2    2    1
    - ---*v3 *a33  + ---*v3*a33*n3
       2              2

                                    1
  = a product of the elements of: {---,
                                    2

              2              2                                2
   2*u1*v1*a23  + 2*u2*v2*a23  + 2*u3*v2*a23*a33 + 2*u3*v3*a23

                          2    2
    + 2*v2*v3*a23*a33 - v3 *a33  + v3*a33*n3}

{HAM,FI} = 0



FI=1

which the program can not factorize further.

{HAM,FI} = 0





And again in machine readable form:



HAM=2*u2*u3*a23 + 2*u2*v3*a23 + u3**2*a33 + 2*u3*v2*a23 + u3*n3 + 2*v2*v3*a23 - 
v3**2*a33 + v3*n3$

FI=u1*v1*a23**2 + u2*v2*a23**2 + u3*v2*a23*a33 + u3*v3*a23**2 + v2*v3*a23*a33 - 
1/2*v3**2*a33**2 + 1/2*v3*a33*n3$

FI=1$