Solution 1 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
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Expressions
The solution is given through the following expressions:
r11=0
r12=0
r13=0
r14=0
r15=0
r21=0
r22=0
r23=0
r24=0
n3*r320
r26=---------
b23
r27=0
r28=0
r29=0
r210=0
r211=0
r212=0
r214=0
r215=0
r216=0
r217=0
r218=0
r219=0
r31=0
r32=r37
r33=0
r34=0
r35=0
r36=0
r38=0
r39=0
b33*r320 + n3*r435
r310=--------------------
b23
r311=0
r312=0
r313=0
r314=0
r315=0
a33*r320 + b23*r350
r316=---------------------
b23
r317=0
r318=0
r319=0
r321=0
r322=0
r323=0
r324=0
r325=0
2*a23*r320
r326=------------
b23
r327=0
r328=0
r329=0
r330=r350
r331=0
r332=0
r333=0
r334=0
r335=0
r336=0
r337=0
r338=0
r339=0
r340=0
r341=0
r342=0
r343=0
r344=0
r345=0
r346=0
r347=0
r348=0
r349=0
r351=0
r352=0
r353=0
r354=0
r355=0
r41=0
r42=r49
r43=0
r44=0
r45=0
r46=0
r47=0
r48=0
r410=0
r411=0
r412=0
r413=0
b33*r435
r415=----------
b23
r416=0
r417=0
r418=0
r419=0
r420=0
r421=0
r422=0
r423=0
r424=0
a33*r435 + b23*r4105
r425=----------------------
b23
r426=0
r427=0
r428=0
r429=0
r430=0
r431=0
r432=0
r433=0
r434=0
r436=0
r437=0
r438=0
r439=0
r440=0
r441=0
r442=0
r443=0
r444=0
2*a23*r435
r445=------------
b23
r446=0
r447=0
r448=0
r449=0
r451=0
r452=0
r453=0
r454=0
r455=r4105
r456=0
r457=0
r458=0
r459=0
r460=0
r461=0
r462=0
r463=0
r465=0
r466=0
r467=0
r468=0
r469=0
r470=0
r471=0
r472=0
r473=0
r474=0
r475=0
r476=0
r477=0
r478=0
r479=0
r480=0
r481=0
r482=0
r483=0
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
r4106=0
r4107=0
r4108=0
r4109=0
r4111=0
r4112=0
r4113=0
r4114=0
r4115=0
r4116=0
r4117=0
r4119=0
r4120=0
r4121=0
r4122=0
r4123=0
r4124=0
c23=0
b32=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, r10, r20, r30, r37, r320, r350, r40, r49, r435,
r4105, n3, a33, m3, b33, c33, a23, b23
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.
{{r40,
1 5
----*b23 *r49,
18
r49,
7 7 6
---*b23 *r4105 - 7*b23 *c33*r435,
3
r435,
7 6
----*b23 *r435,
18
1 5
----*b23 *r4105,
24
r4105},
m3,
b23,
a23}
Relevance for the application:
The system of equations related to the Hamiltonian HAM:
2 2
HAM=2*u2*u3*a23 + u2*v3*b23 + u3 *a33 + u3*v3*b33 + u3*n3 + v3 *c33 + v3*m3
has apart from the Hamiltonian and Casimirs the following 11 first integrals:
2 2 2 2 2 2
FI=u1 *v3 + u2 *v3 + u3 *v3
2 2 2
= a product of the elements of: {v3,v3,u1 + u2 + u3 }
{HAM,FI} = 0
2 3 2 2 3 2
FI=2*u2*u3*v3 *a23 + u2*v3 *b23 + u3 *v3 *a33 + u3*v3 *b33 + u3*v3 *n3
= a product of the elements of: {v3,
v3,
2
2*u2*u3*a23 + u2*v3*b23 + u3 *a33 + u3*v3*b33 + u3*n3}
{HAM,FI} = 0
2 2 2 2
FI=v1 *v3 + v2 *v3
2 2
= a product of the elements of: {v3,v3,v1 + v2 }
{HAM,FI} = 0
4
FI=v3
= a product of the elements of: {v3,v3,v3,v3}
{HAM,FI} = 0
2 2 2
FI=u1 *v3 + u2 *v3 + u3 *v3
2 2 2
= a product of the elements of: {v3,u1 + u2 + u3 }
{HAM,FI} = 0
2 2 2
FI=2*u2*u3*v3*a23 + u2*v3 *b23 + u3 *v3*a33 + u3*v3 *b33 + u3*v3*n3
= a product of the elements of: {v3,
2
2*u2*u3*a23 + u2*v3*b23 + u3 *a33 + u3*v3*b33 + u3*n3}
{HAM,FI} = 0
2 2
FI=v1 *v3 + v2 *v3
2 2
= a product of the elements of: {v3,v1 + v2 }
{HAM,FI} = 0
3
FI=v3
= a product of the elements of: {v3,v3,v3}
{HAM,FI} = 0
2
FI=v3
= a product of the elements of: {v3,v3}
{HAM,FI} = 0
FI=v3
which the program can not factorize further.
{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 + u2*v3*b23 + u3**2*a33 + u3*v3*b33 + u3*n3 + v3**2*c33 + v3*m3$
FI=u1**2*v3**2 + u2**2*v3**2 + u3**2*v3**2$
FI=2*u2*u3*v3**2*a23 + u2*v3**3*b23 + u3**2*v3**2*a33 + u3*v3**3*b33 + u3*v3**2*
n3$
FI=v1**2*v3**2 + v2**2*v3**2$
FI=v3**4$
FI=u1**2*v3 + u2**2*v3 + u3**2*v3$
FI=2*u2*u3*v3*a23 + u2*v3**2*b23 + u3**2*v3*a33 + u3*v3**2*b33 + u3*v3*n3$
FI=v1**2*v3 + v2**2*v3$
FI=v3**3$
FI=v3**2$
FI=v3$
FI=1$