Solution 7 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
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Expressions
The solution is given through the following expressions:
r40=0
r41=0
r42=0
r43=0
r44=0
r45=0
r46=0
r47=0
r48=0
r49=0
r410=0
r411=0
r412=0
r413=0
r418=0
r421=0
r423=0
r424=0
r427=0
r429=0
r430=r460
r432=0
r433=0
r434=0
r435=0
r436=0
r437=0
r438=0
r439=0
r440=0
r441=0
r442=0
r443=0
r444=0
r447=0
r449=0
r450=0
r452=0
- 4*a33*r460
r453=---------------
b12
r454=0
r455=0
r456=0
r457=0
r458=0
r459=0
r462=0
r463=0
2
4*a33 *r460
r464=-------------
2
b12
r465=0
r466=0
- 4*a33*r460
r467=---------------
b12
r468=0
2
4*a33 *r460
r469=-------------
2
b12
r470=0
r471=0
r472=0
r473=0
r474=0
r475=0
r476=0
r477=0
r479=0
r482=0
r484=0
r485=0
r487=0
r488=0
r489=0
r490=0
r491=0
r492=0
r493=0
r494=0
r495=0
r497=0
r498=0
r499=0
r4100=0
r4101=0
r4102=0
r4103=0
r4104=0
r4105=0
r4106=0
r4108=0
r4109=0
r4110=r460
r4112=0
r4113=0
r4114=0
r4115=0
r4116=0
- 4*a33*r460
r4117=---------------
b12
r4118=0
2
4*a33 *r460
r4119=-------------
2
b12
r4120=0
r4121=0
r4122=0
r4123=0
r4124=0
r4125=0
a23=0
a22=2*a33
a13=0
2 1 2
a33 - ---*b12 *kap
4
a11=---------------------
a33
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:
r460, a33, 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.
2 2
{a33,b12,r460,4*a33 + b12 *kap}
Relevance for the application:
The system of equations related to the Hamiltonian HAM:
2 2 1 2 2 2
HAM=(u1 *(a33 - ---*b12 *kap) + u1*v2*a33*b12 + 2*u2 *a33 - u2*v1*a33*b12
4
2 2
+ u3 *a33 )/a33
has apart from the Hamiltonian and Casimirs only the following first integral:
2 2 2 2 2 2 2 4 2
FI=4*u1 *u2 *a33 - 4*u1 *u2*v1*a33*b12 + u1 *v1 *b12 + 4*u2 *a33
3 2 2 2 2 2 2 2
- 4*u2 *v1*a33*b12 + 4*u2 *u3 *a33 + u2 *v1 *b12 - 4*u2*u3 *v1*a33*b12
2 2 2
+ u3 *v1 *b12
2 2 2 2 3 3
{HAM,FI} = 8*u1*u2 *u3*v1*a33 *b12 - 8*u1*u2*u3*v1 *a33*b12 + 2*u1*u3*v1 *b12
3 2 2 2 2
+ 8*u2 *u3*v2*a33 *b12 + 8*u2 *u3 *v3*a33 *b12
2 2 2 2
- 8*u2 *u3*v1*v2*a33*b12 - 8*u2*u3 *v1*v3*a33*b12
2 3 2 2 3
+ 2*u2*u3*v1 *v2*b12 + 2*u3 *v1 *v3*b12
And again in machine readable form:
HAM=(u1**2*(a33**2 - 1/4*b12**2*kap) + u1*v2*a33*b12 + 2*u2**2*a33**2 - u2*v1*
a33*b12 + u3**2*a33**2)/a33$
FI=4*u1**2*u2**2*a33**2 - 4*u1**2*u2*v1*a33*b12 + u1**2*v1**2*b12**2 + 4*u2**4*
a33**2 - 4*u2**3*v1*a33*b12 + 4*u2**2*u3**2*a33**2 + u2**2*v1**2*b12**2 - 4*u2*
u3**2*v1*a33*b12 + u3**2*v1**2*b12**2$