Solution 11 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
m2*r316
r21=---------
a33
r22=0
m1*r316
r23=---------
a33
r24=0
n3*r316
r26=---------
a33
r27=0
r28=0
r210=0
r212=0
r213=0
r214=0
r215=0
r216=0
r217=0
r218=0
r219=0
r220=0
2*c23*r316 + m2*r425
r31=----------------------
a33
r33=0
2*c13*r316 + m1*r425
r34=----------------------
a33
r36=0
a33*r32 - c22*r316
r37=--------------------
a33
r38=0
r39=0
a33*r321 + b33*r316 + n3*r425
r310=-------------------------------
a33
r311=0
r312=0
r313=0
r314=0
r315=0
r317=0
r318=0
r319=0
r320=0
r322=0
r323=0
r324=0
r325=0
r326=0
r327=0
r328=0
r329=0
r330=0
r331=0
r332=0
r333=0
r334=0
r335=0
r336=0
r337=0
r338=r321
r339=0
r340=0
r341=0
r342=0
r343=0
r344=0
r345=0
r346=0
r347=0
r348=0
r349=0
r350=0
r351=0
r352=0
r353=0
r354=0
r355=0
2*c23*r425
r41=------------
a33
r43=0
r44=0
2*c13*r425
r45=------------
a33
2*c12*r425
r46=------------
a33
r47=0
r48=0
a33*r42 - c22*r425
r49=--------------------
a33
r410=0
r411=0
r412=0
r413=0
a33*r474 + b33*r425
r415=---------------------
a33
r416=0
r417=0
r418=0
r419=0
r420=0
r421=0
r422=0
r423=0
r424=0
r426=0
r427=0
r428=0
r429=0
r431=0
r432=0
r433=0
r435=0
r436=r474
r437=0
r438=0
r439=0
r440=0
r441=0
r442=0
r444=0
r445=0
r446=0
r447=0
r448=0
r449=0
r450=0
r451=0
r453=0
r454=0
r455=0
r456=0
r458=0
r459=0
r460=0
r461=0
r462=0
r463=0
r464=0
r465=0
r466=0
r467=0
r468=0
r469=0
r470=0
r471=0
r472=0
r473=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
r4105=0
r4106=0
r4107=0
r4108=0
r4109=0
r4110=0
r4111=0
r4112=0
r4113=0
r4114=0
r4115=0
r4116=0
r4117=0
r4118=0
r4119=0
r4120=0
r4121=0
r4122=0
r4123=0
r4124=0
r4125=0
n2=0
n1=0
c11=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
2*c12*r316
r35=------------
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:
r316, r40, r30, r20, r10, r42, r32, r321, r474, r425,
m1, c22, c33, m2, m3, n3, b33, c12, c23, c13, 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,
c11,
n1,
n2}$
The system of equations related to the Hamiltonian HAM:
2 2
HAM=u3 *a33 + u3*v3*b33 + u3*n3 + 2*v1*v2*c12 + 2*v1*v3*c13 + v1*m1 + v2 *c22
2
+ 2*v2*v3*c23 + v2*m2 + v3 *c33 + v3*m3
has apart from the Hamiltonian and Casimirs the following 10 first integrals:
2 2 3 2 2 2 2
FI=u3 *v3 *a33 + u3*v3 *b33 + u3*v3 *n3 - v1 *v3 *c22 + 2*v1*v2*v3 *c12
3 2 3 2
+ 2*v1*v3 *c13 + v1*v3 *m1 + 2*v2*v3 *c23 + v2*v3 *m2
= a product of the elements of: {v3,
v3,
2 2
u3 *a33 + u3*v3*b33 + u3*n3 - v1 *c22 + 2*v1*v2*c12 + 2*v1*v3*c13 + v1*m1
+ 2*v2*v3*c23 + v2*m2}
{HAM,FI} = 0
2 2 3
FI=u1*v1*v3 + u2*v2*v3 + u3*v3
= a product of the elements of: {v3,
v3,
u1*v1 + u2*v2 + u3*v3}
{HAM,FI} = 0
2
FI=u1*v1*v3 + u2*v2*v3 + u3*v3
= a product of the elements of: {v3,u1*v1 + u2*v2 + u3*v3}
{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
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
2 2 2
FI=u3 *v3*a33 + u3*v3 *b33 + u3*v3*n3 - v1 *v3*c22 + 2*v1*v2*v3*c12
2 2
+ 2*v1*v3 *c13 + v1*v3*m1 + 2*v2*v3 *c23 + v2*v3*m2
= a product of the elements of: {v3,
2 2
u3 *a33 + u3*v3*b33 + u3*n3 - v1 *c22 + 2*v1*v2*c12 + 2*v1*v3*c13 + v1*m1
+ 2*v2*v3*c23 + v2*m2}
{HAM,FI} = 0
And again in machine readable form:
HAM=u3**2*a33 + u3*v3*b33 + u3*n3 + 2*v1*v2*c12 + 2*v1*v3*c13 + v1*m1 + v2**2*
c22 + 2*v2*v3*c23 + v2*m2 + v3**2*c33 + v3*m3$
FI=u3**2*v3**2*a33 + u3*v3**3*b33 + u3*v3**2*n3 - v1**2*v3**2*c22 + 2*v1*v2*v3**
2*c12 + 2*v1*v3**3*c13 + v1*v3**2*m1 + 2*v2*v3**3*c23 + v2*v3**2*m2$
FI=u1*v1*v3**2 + u2*v2*v3**2 + u3*v3**3$
FI=u1*v1*v3 + u2*v2*v3 + u3*v3**2$
FI=v1**2*v3 + v2**2*v3$
FI=v1**2*v3**2 + v2**2*v3**2$
FI=v3$
FI=v3**2$
FI=v3**3$
FI=v3**4$
FI=u3**2*v3*a33 + u3*v3**2*b33 + u3*v3*n3 - v1**2*v3*c22 + 2*v1*v2*v3*c12 + 2*v1
*v3**2*c13 + v1*v3*m1 + 2*v2*v3**2*c23 + v2*v3*m2$