Solution 29 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
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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
r213=0
r215=0
r216= - r212
r217=0
r218=0
r219=0
r220=r214
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
r324=0
r325=0
r326=0
r328= - r342
r329=0
r330=r350
r331=0
r332=0
r333=r353
r334=0
r335=0
r336= - r323
r337=0
r338=r321
r339=0
r340=0
r341=0
r343=r327
r344=0
r345=0
r346=0
r347=0
r348=0
r349=0
r351=0
r352=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= - r471
r440=0
r442=0
r444=r441
r445=0
r447=0
r449=0
r450=0
r451=0
r454=0
r456=0
r458=0
r459=r495
- r494
r460=---------
2
r461=r4111
r462=0
r463=0
r465=0
r466=r4116
r467=r4117
r468=0
r4119
r469=-------
2
r470=0
r472=0
r473= - r441
r475=0
r476=0
r477=0
r478= - r441
r479=0
r480=0
r481= - r448
r482=0
r483=r446
r484=0
r485=0
r486=0
r487= - r453
r488=0
r489=0
r490=0
r491=0
r492= - r495
r493=0
r496=0
r497=0
r498=0
r499=0
r4100=0
r4101= - r4117
r4102=r4116
r4103=0
r4104=0
r4105=r455
r4106=0
- r494
r4107=---------
2
r4108=0
r4109= - r495
r4110=0
r4112=0
r4113=0
r4114=r464
r4115=0
r4118=0
r4120=0
r4121= - r4117
r4122=r4116
r4123=0
r4124=0
r4119
r4125=-------
2
m3=0
m2=0
m1=0
n2=0
n1=0
c33=0
c23=0
c22=0
c13=0
c12=0
c11=0
b33=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, r214, r13, r455,
r212, r315, r350, r431, r425, r415, r316, r310, r26, r323,
r471, r4119, r441, r321, r353, r422, r474, r342, r453,
r327, r495, r4117, r4111, r4116, r448, r494, r446, r464,
n3, 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,
b33,
c11,
c12,
c13,
c22,
c23,
c33,
n1,
n2,
m1,
m2,
m3}$
The system of equations related to the Hamiltonian HAM:
2
HAM=u3 *a33 + u3*n3
has apart from the Hamiltonian and Casimirs the following 38 first integrals:
2 2 2 2
FI=u1 *u3 + u2 *u3
= a product of the elements of: {u3,
u3,
u1 - i*u2,
u1 + i*u2}
{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
2 2 2 2
FI= - u1 *v2 + 2*u1*u2*v1*v2 - u2 *v1
= a product of the elements of: { - u1*v2 + u2*v1,u1*v2 - u2*v1}
{HAM,FI} = 0
FI= - u1*u3*v2*v3 + u2*u3*v1*v3
= a product of the elements of: { - v3,u3,u1*v2 - u2*v1}
{HAM,FI} = 0
3 2 2 3
FI=u1 *v1 + u1 *u2*v2 + u1*u2 *v1 + u2 *v2
= a product of the elements of: {u1 - i*u2,
u1 + i*u2,
u1*v1 + u2*v2}
{HAM,FI} = 0
2 2
FI=u1 *u3*v3 + u2 *u3*v3
= a product of the elements of: {v3,
u3,
u1 - i*u2,
u1 + i*u2}
{HAM,FI} = 0
3 2 2 3
FI= - u1 *v2 + u1 *u2*v1 - u1*u2 *v2 + u2 *v1
= a product of the elements of: { - u1 + i*u2,
u1 + i*u2,
u1*v2 - u2*v1}
{HAM,FI} = 0
2 2 2 2
FI= - u1 *v1*v2 + u1*u2*v1 - u1*u2*v2 + u2 *v1*v2
= a product of the elements of: { - u1*v2 + u2*v1,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*u3 *v2 + u2*u3 *v1
= a product of the elements of: { - u3,u3,u1*v2 - u2*v1}
{HAM,FI} = 0
FI=u1*u3*v2 - u2*u3*v1
= a product of the elements of: {u3,u1*v2 - u2*v1}
{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
2 2
FI=u1 *u3 + u2 *u3
= a product of the elements of: {u3,u1 - i*u2,u1 + i*u2}
{HAM,FI} = 0
FI=u1*v1*v3 + u2*v2*v3
= a product of the elements of: {v3,u1*v1 + u2*v2}
{HAM,FI} = 0
2 3 3 2
FI= - u1*v1 *v2 - u1*v2 + u2*v1 + u2*v1*v2
= a product of the elements of: { - v1 + i*v2,
v1 + i*v2,
u1*v2 - u2*v1}
{HAM,FI} = 0
4 2 2 4
FI=u1 + 2*u1 *u2 + u2
= a product of the elements of: {u1 - i*u2,
u1 - i*u2,
u1 + i*u2,
u1 + i*u2}
{HAM,FI} = 0
2 2
FI=u1*v2*v3 - u2*v1*v3
= a product of the elements of: {v3,v3,u1*v2 - u2*v1}
{HAM,FI} = 0
FI= - u1*v2*v3 + u2*v1*v3
= a product of the elements of: { - v3,u1*v2 - u2*v1}
{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
3
FI=u3 *v3
= a product of the elements of: {u3,u3,u3,v3}
{HAM,FI} = 0
2 2
FI=u1 *v3 + u2 *v3
= a product of the elements of: {v3,u1 - i*u2,u1 + i*u2}
{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= - u1*v2 + u2*v1
which the program can not factorize further.
{HAM,FI} = 0
2 2 2 2
FI=u1 *v3 + u2 *v3
= a product of the elements of: {v3,
v3,
u1 - i*u2,
u1 + i*u2}
{HAM,FI} = 0
FI=u3
which the program can not factorize further.
{HAM,FI} = 0
2 2
FI=u1 + u2
= a product of the elements of: {u1 - i*u2,u1 + i*u2}
{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*n3$
FI=u1**2*u3**2 + u2**2*u3**2$
FI=u1*u3*v1*v3 + u2*u3*v2*v3$
FI= - u1**2*v2**2 + 2*u1*u2*v1*v2 - u2**2*v1**2$
FI= - u1*u3*v2*v3 + u2*u3*v1*v3$
FI=u1**3*v1 + u1**2*u2*v2 + u1*u2**2*v1 + u2**3*v2$
FI=u1**2*u3*v3 + u2**2*u3*v3$
FI= - u1**3*v2 + u1**2*u2*v1 - u1*u2**2*v2 + u2**3*v1$
FI= - u1**2*v1*v2 + u1*u2*v1**2 - u1*u2*v2**2 + u2**2*v1*v2$
FI=u1*u3*v1 + u2*u3*v2$
FI= - u1*u3**2*v2 + u2*u3**2*v1$
FI=u1*u3*v2 - u2*u3*v1$
FI=u1*v1*v3**2 + u2*v2*v3**2$
FI=u3*v1**2*v3 + u3*v2**2*v3$
FI=u1**2*u3 + u2**2*u3$
FI=u1*v1*v3 + u2*v2*v3$
FI= - u1*v1**2*v2 - u1*v2**3 + u2*v1**3 + u2*v1*v2**2$
FI=u1**4 + 2*u1**2*u2**2 + u2**4$
FI=u1*v2*v3**2 - u2*v1*v3**2$
FI= - u1*v2*v3 + u2*v1*v3$
FI=u3*v3$
FI=u3*v3**2$
FI=u3**2*v3$
FI=u3*v3**3$
FI=u3**2*v3**2$
FI=u3**3*v3$
FI=u1**2*v3 + u2**2*v3$
FI=u3*v1**2 + u3*v2**2$
FI= - u1*v2 + u2*v1$
FI=u1**2*v3**2 + u2**2*v3**2$
FI=u3$
FI=u1**2 + u2**2$
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$