Solution 25 to problem over

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

Expressions

The solution is given through the following expressions:


r11=0


r12=0


r14=0


r15=0


r21=0


r22=0


r23=0


r24=0


r27=0


r28=0


r210=0


r212=0


r213=0


r214=0


r215=0


r216=0


r217=0


r218=0


r219=0


r220=0


r31=0


r33=0


r34=0


r35=0


r36=0


r37=r32


r38=0


r39=0


r311=0


r312=r315


r313=0


r314=0


r317=0


r318=0


r320=0


r322=0


r323=0


r324=0


r325=0


r326=0


r328=0


r329=0


r330=0


r331=0


r332=0


r333=0


r334=0


r335=0


r336=0


r337=0


r338=r321


r339=0


r340=0


r341=0


r342=0


r343=r327


r344=0


r345=0


r346=0


r347=0


r348=0


r349=0


r350=0


r351=0


r352=0


r353=0


r354=0


r355=0


r41=0


r43=0


r44=0


r45=0


r46=0


r47=0


r48=0


r49=r42


r410=0


r411=0


r412=0


r413=0


r416=0


r417=r422


r418=0


r419=0


r420=0


r421=0


r423=0


r424=0


r426=0


r427=0


r428=0


r429=0


r432=0


r433=0


r435=0


r436=r474


r437=0


r438=0


r439=0


r440=0


r441=0


r442=0


r444=0


r445=0


r447=0


r448=0


r449=0


r450=0


r451=0


r453=0


r454=0


r455=0


r456=0


r458=0


r459=0


r460=0


r461=0


r462=0


r463=0


r464=0


r465=0


r466=0


r467=0


r468=0


r469=0


r470=0


r471=0


r472=0


r473=0


r475=0


r476=0


r477=0


r478=0


r479=0


r480=0


r481=0


r482=0


r483=r446


r484=0


r485=0


r486=0


r487=0


r488=0


r489=0


r490=0


r491=0


r492=0


r493=0


r494=0


r495=0


r496=0


r497=0


r498=0


r499=0


r4100=0


r4101=0


r4102=0


r4103=0


r4104=0


r4105=0


r4106=0


r4107=0


r4108=0


r4109=0


r4110=0


r4111=0


r4112=0


r4113=0


r4114=0


r4115=0


r4116=0


r4117=0


r4118=0


r4119=0


r4120=0


r4121=0


r4122=0


r4123=0


r4124=0


r4125=0


m2=0


m1=0


n2=0


n1=0


c23=0


c22=0


c13=0


c12=0


c11=0


b32=0


b31=0


b23=0


b22=0


b21=0


b13=0


b12=0


b11=0


a23=0


a22=0


a13=0


a12=0


a11=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:

 r40, r30, r20, r10, r42, r319, r32, r13, r315, r425, 
r415, r316, r310, r26, r321, r422, r474, r327, r446, r431, 
c33, m3, n3, b33, a33

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.

 
{a33}

Relevance for the application:

The new Hamiltonian in form of a list of vanishing expressions: 

{a11,
a12,
a13,
a22,
a23,
b11,
b12,
b13,
b21,
b22,
b23,
b31,
b32,
c11,
c12,
c13,
c22,
c23,
n1,
n2,
m1,
m2}$

The system of equations related to the Hamiltonian HAM:

      2                             2
HAM=u3 *a33 + u3*v3*b33 + u3*n3 + v3 *c33 + v3*m3

has apart from the Hamiltonian and Casimirs the following 20 first integrals: 

     3
FI=u3 *v3

  = a product of the elements of: {u3,u3,u3,v3}

{HAM,FI} = 0



FI=u1*u3*v1*v3 + u2*u3*v2*v3

  = a product of the elements of: {v3,u3,u1*v1 + u2*v2}

{HAM,FI} = 0



FI=u1*u3*v1 + u2*u3*v2

  = a product of the elements of: {u3,u1*v1 + u2*v2}

{HAM,FI} = 0



           2           2
FI=u1*v1*v3  + u2*v2*v3

  = a product of the elements of: {v3,v3,u1*v1 + u2*v2}

{HAM,FI} = 0



        2           2
FI=u3*v1 *v3 + u3*v2 *v3

  = a product of the elements of: {v3,

   v1 - i*v2,

   v1 + i*v2,

   u3}

{HAM,FI} = 0



FI=u1*v1*v3 + u2*v2*v3

  = a product of the elements of: {v3,u1*v1 + u2*v2}

{HAM,FI} = 0



FI=u3*v3

  = a product of the elements of: {v3,u3}

{HAM,FI} = 0



        2
FI=u3*v3

  = a product of the elements of: {v3,v3,u3}

{HAM,FI} = 0



     2
FI=u3 *v3

  = a product of the elements of: {u3,u3,v3}

{HAM,FI} = 0



        3
FI=u3*v3

  = a product of the elements of: {v3,v3,v3,u3}

{HAM,FI} = 0



     2   2
FI=u3 *v3

  = a product of the elements of: {v3,v3,u3,u3}

{HAM,FI} = 0



        2        2
FI=u3*v1  + u3*v2

  = a product of the elements of: {v1 - i*v2,v1 + i*v2,u3}

{HAM,FI} = 0



FI=u3

which the program can not factorize further.

{HAM,FI} = 0



     2        2
FI=v1 *v3 + v2 *v3

  = a product of the elements of: {v3,v1 - i*v2,v1 + i*v2}

{HAM,FI} = 0



     3
FI=u3

  = a product of the elements of: {u3,u3,u3}

{HAM,FI} = 0



     2   2     2   2
FI=v1 *v3  + v2 *v3

  = a product of the elements of: {v3,

   v3,

   v1 - i*v2,

   v1 + i*v2}

{HAM,FI} = 0



FI=v3

which the program can not factorize further.

{HAM,FI} = 0



     2
FI=v3

  = a product of the elements of: {v3,v3}

{HAM,FI} = 0



     3
FI=v3

  = a product of the elements of: {v3,v3,v3}

{HAM,FI} = 0



     4
FI=v3

  = a product of the elements of: {v3,v3,v3,v3}

{HAM,FI} = 0





And again in machine readable form:



HAM=u3**2*a33 + u3*v3*b33 + u3*n3 + v3**2*c33 + v3*m3$

FI=u3**3*v3$

FI=u1*u3*v1*v3 + u2*u3*v2*v3$

FI=u1*u3*v1 + u2*u3*v2$

FI=u1*v1*v3**2 + u2*v2*v3**2$

FI=u3*v1**2*v3 + u3*v2**2*v3$

FI=u1*v1*v3 + u2*v2*v3$

FI=u3*v3$

FI=u3*v3**2$

FI=u3**2*v3$

FI=u3*v3**3$

FI=u3**2*v3**2$

FI=u3*v1**2 + u3*v2**2$

FI=u3$

FI=v1**2*v3 + v2**2*v3$

FI=u3**3$

FI=v1**2*v3**2 + v2**2*v3**2$

FI=v3$

FI=v3**2$

FI=v3**3$

FI=v3**4$