Solution 5 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Expressions
The solution is given through the following expressions:
r10=0
r11=0
r12=0
r14=0
r15=0
r20=0
r21=0
r22=0
r23=0
r24=0
m3*r333
r26=---------
a11
r27=0
r28=0
r210=0
r212=0
r213=0
r214=0
r215=0
r216=0
r217=0
r218=0
r219=0
1
- ---*m3*r483
2
r30=----------------
a11
r31=0
1
- ---*m3*r483
2
r32=----------------
a11
r33=0
r34=0
r35=0
r36=0
1
- ---*m3*r483
2
r37=----------------
a11
r38=0
r39=0
a11*r315 + c33*r333
r310=---------------------
a11
r311=0
r312=r315
r313=0
r314=0
a11*r327 + b33*r333 + m3*r464
r316=-------------------------------
a11
r317=0
r318=0
r320=0
r321=0
r322=0
r323=0
r324=0
r325=0
r326=0
r328=0
r329=0
r330=0
r331=0
r332=0
r334=0
r335=0
r336=0
r337=0
r338=0
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=r333
r354=0
r355=0
1
- ---*c33*r483
2
r40=-----------------
a11
r41=0
1
- ---*c33*r483
2
r42=-----------------
a11
r43=0
r44=0
r45=0
r46=0
r47=0
r48=0
1
- ---*c33*r483
2
r49=-----------------
a11
r410=0
r411=0
r412=0
r413=0
1
- ---*b33*r483
2
r415=-----------------
a11
r416=0
1
- ---*b33*r483
2
r417=-----------------
a11
r418=0
r419=0
r420=0
r421=0
1
- ---*b33*r483
2
r422=-----------------
a11
r423=0
r424=0
r426=0
1
a11*r425 - ---*a11*r483 - c33*r464
2
r427=------------------------------------
a11
r428=0
r429=0
1
a11*r425 - ---*a11*r483 - c33*r464
2
r430=------------------------------------
a11
a11*r488 + b33*r464
r431=---------------------
a11
r432=0
r433=0
r435=0
r436=0
r437=0
r438=0
r439=0
r440=0
r441=0
r442=0
r444=0
r445=0
r446=r483
r447=0
r448=0
r449=0
r450=0
r451=0
r452=r488
r453=0
r454=0
1
r455= - ---*r483
2
r456=0
r458=0
r459=0
1
r460= - ---*r483
2
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
r484=0
r485=0
r486=0
r487=0
r489=0
r490=0
r491=0
r492=0
r493=0
r494=r483
r495=0
r496=0
r497=0
r498=0
r499=0
r4100=0
r4101=0
r4102=0
r4103=0
r4104=0
1
r4105= - ---*r483
2
r4106=0
1
r4107= - ---*r483
2
r4108=0
r4109=0
r4111=0
r4112=0
r4113=0
r4114=r464
r4115=0
r4117=0
r4118=0
r4119=0
r4120=0
r4121=0
r4122=0
r4123=0
r4124=0
m2=0
m1=0
n2=0
n1=0
c23=0
c22=0
c13=0
c12=0
b32=0
b31=0
b11=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:
r434, r319, r29, r13, r425, r315, r333, r488, r327, r483,
r464, m3, c33, n3, b33, a11
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.
{{n3,m3},a11,b33}
Relevance for the application:
The system of equations related to the Hamiltonian HAM:
2 2 2
HAM=u1 *a11 + u2 *a11 + 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 3 2 2 2 2
FI=u1 *u3 *a11 + u2 *u3 *a11 + u3 *v3*b33 - u3 *v1 *c33 - u3 *v2 *c33
2
+ u3 *v3*m3
{HAM,FI} = 0
1 2 2 1 2 2
FI= - ---*u1 *v2 *a11 - ---*u1 *v3 *a11 + u1*u2*v1*v2*a11 + u1*u3*v1*v3*a11
2 2
1 2 2 1 2 2 1 2 2
- ---*u2 *v1 *a11 - ---*u2 *v3 *a11 + u2*u3*v2*v3*a11 - ---*u3 *v1 *a11
2 2 2
1 2 2 1 2 1 2 1 3
- ---*u3 *v2 *a11 - ---*u3*v1 *v3*b33 - ---*u3*v2 *v3*b33 - ---*u3*v3 *b33
2 2 2 2
1 2 2 1 2 1 2 2 1 2
- ---*v1 *v3 *c33 - ---*v1 *v3*m3 - ---*v2 *v3 *c33 - ---*v2 *v3*m3
2 2 2 2
1 4 1 3
- ---*v3 *c33 - ---*v3 *m3
2 2
{HAM,FI} = 0
2
FI=u1*u3*v1 + u2*u3*v2 + u3 *v3
{HAM,FI} = 0
2 2 3
FI=u1*u3 *v1 + u2*u3 *v2 + u3 *v3
{HAM,FI} = 0
2 2 2 2
FI=u1 *u3*a11 + u2 *u3*a11 + u3 *v3*b33 + u3*v3 *c33 + u3*v3*m3
{HAM,FI} = 0
2 2 2
FI=u3*v1 + u3*v2 + u3*v3
{HAM,FI} = 0
2 2 2 2 2 2
FI=u3 *v1 + u3 *v2 + u3 *v3
{HAM,FI} = 0
FI=u3
{HAM,FI} = 0
2
FI=u3
{HAM,FI} = 0
3
FI=u3
{HAM,FI} = 0
4
FI=u3
{HAM,FI} = 0
And again in machine readable form:
HAM=u1**2*a11 + u2**2*a11 + u3*v3*b33 + u3*n3 + v3**2*c33 + v3*m3$
FI=u1**2*u3**2*a11 + u2**2*u3**2*a11 + u3**3*v3*b33 - u3**2*v1**2*c33 - u3**2*v2
**2*c33 + u3**2*v3*m3$
FI= - 1/2*u1**2*v2**2*a11 - 1/2*u1**2*v3**2*a11 + u1*u2*v1*v2*a11 + u1*u3*v1*v3*
a11 - 1/2*u2**2*v1**2*a11 - 1/2*u2**2*v3**2*a11 + u2*u3*v2*v3*a11 - 1/2*u3**2*v1
**2*a11 - 1/2*u3**2*v2**2*a11 - 1/2*u3*v1**2*v3*b33 - 1/2*u3*v2**2*v3*b33 - 1/2*
u3*v3**3*b33 - 1/2*v1**2*v3**2*c33 - 1/2*v1**2*v3*m3 - 1/2*v2**2*v3**2*c33 - 1/2
*v2**2*v3*m3 - 1/2*v3**4*c33 - 1/2*v3**3*m3$
FI=u1*u3*v1 + u2*u3*v2 + u3**2*v3$
FI=u1*u3**2*v1 + u2*u3**2*v2 + u3**3*v3$
FI=u1**2*u3*a11 + u2**2*u3*a11 + u3**2*v3*b33 + u3*v3**2*c33 + u3*v3*m3$
FI=u3*v1**2 + u3*v2**2 + u3*v3**2$
FI=u3**2*v1**2 + u3**2*v2**2 + u3**2*v3**2$
FI=u3$
FI=u3**2$
FI=u3**3$
FI=u3**4$