Solution 4 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
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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*r353
r26=---------
a11
r27=0
r28=0
r210=0
r212=0
r213=0
r214=0
r215=0
r216=0
r217=0
r218=0
r219=0
m3*r455
r30=---------
a11
r31=0
m3*r455
r32=---------
a11
r33=0
r34=0
r35=0
r36=0
m3*r455
r37=---------
a11
r38=0
r39=0
a11*r312 + c33*r353
r310=---------------------
a11
r311=0
r313=0
r314=0
r315=r312
a11*r327 + b33*r353 + m3*r4114
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
r333=r353
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
r354=0
r355=0
c33*r455
r40=----------
a11
r41=0
c33*r455
r42=----------
a11
r43=0
r44=0
r45=0
r46=0
r47=0
r48=0
c33*r455
r49=----------
a11
r410=0
r411=0
r412=0
r413=0
b33*r455
r415=----------
a11
r416=0
b33*r455
r417=----------
a11
r418=0
r419=0
r420=0
r421=0
b33*r455
r422=----------
a11
r423=0
r424=0
a11*r430 - a11*r455 + c33*r4114
r425=---------------------------------
a11
r426=0
r427=r430
r428=0
r429=0
a11*r452 + b33*r4114
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= - 2*r455
r447=0
r448=0
r449=0
r450=0
r451=0
r453=0
r454=0
r456=0
r458=0
r459=0
r460=r455
r461=0
r462=0
r463=0
r464=r4114
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= - 2*r455
r484=0
r485=0
r486=0
r487=0
r488=r452
r489=0
r490=0
r491=0
r492=0
r493=0
r494= - 2*r455
r495=0
r496=0
r497=0
r498=0
r499=0
r4100=0
r4101=0
r4102=0
r4103=0
r4104=0
r4105=r455
r4106=0
r4107=r455
r4108=0
r4109=0
r4111=0
r4112=0
r4113=0
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
b22=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, r430, r312, r455, r353, r327, r452,
r4114, m3, c33, n3, b33, a33, 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.
{a11,a33,a11 - a33,b33}
Relevance for the application:
The system of equations related to the Hamiltonian HAM:
2 2 2 2
HAM=u1 *a11 + u2 *a11 + 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 3 2 2 2
FI=u1 *u3 *a11 + u2 *u3 *a11 + u3 *v3*b33 + u3 *v3 *c33 + u3 *v3*m3
{HAM,FI} = 0
2 2 3
FI=u1*u3 *v1 + u2*u3 *v2 + u3 *v3
{HAM,FI} = 0
2
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 2
FI=u1 *v2 *a11 + u1 *v3 *a11 - 2*u1*u2*v1*v2*a11 - 2*u1*u3*v1*v3*a11
2 2 2 2 2 2
+ u2 *v1 *a11 + u2 *v3 *a11 - 2*u2*u3*v2*v3*a11 - u3 *v3 *a11
2 2 3 2 2 2
+ u3*v1 *v3*b33 + u3*v2 *v3*b33 + u3*v3 *b33 + v1 *v3 *c33 + v1 *v3*m3
2 2 2 4 3
+ v2 *v3 *c33 + v2 *v3*m3 + v3 *c33 + 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**2*a33 + 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*v3**2*c33 + u3**2*v3
*m3$
FI=u1*u3**2*v1 + u2*u3**2*v2 + u3**3*v3$
FI=u1*u3*v1 + u2*u3*v2 + u3**2*v3$
FI=u1**2*u3*a11 + u2**2*u3*a11 + u3**2*v3*b33 + u3*v3**2*c33 + u3*v3*m3$
FI=u1**2*v2**2*a11 + u1**2*v3**2*a11 - 2*u1*u2*v1*v2*a11 - 2*u1*u3*v1*v3*a11 +
u2**2*v1**2*a11 + u2**2*v3**2*a11 - 2*u2*u3*v2*v3*a11 - u3**2*v3**2*a11 + u3*v1
**2*v3*b33 + u3*v2**2*v3*b33 + u3*v3**3*b33 + v1**2*v3**2*c33 + v1**2*v3*m3 + v2
**2*v3**2*c33 + v2**2*v3*m3 + v3**4*c33 + v3**3*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$