Solution 2 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
r23=0
r24=0
r25=0
m3*r333
r26=---------
a22
r27=0
r28=0
r210=0
r212=0
r213=0
r214=0
r215=0
r216=0
r217=0
r218=0
r219=0
r30=0
r31=0
r32=0
r33=0
r34=0
r35=0
r36=0
r37=0
r38=0
r39=0
r311=0
a22*r310 - c33*r333
r312=---------------------
a22
r313=0
r314=0
a22*r310 - c33*r333
r315=---------------------
a22
b33*r333 + m3*r464
r316=--------------------
a22
r317=0
r318=0
r320=0
r323=0
r325=0
r326=0
r328=0
r329=0
r330=0
r332=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
r347=0
r348=0
r349=0
r350=0
r351=0
r352=0
r353=r333
r354=0
r355=0
r40=0
r41=0
r42=0
r43=0
r45=0
r46=0
r47=0
r48=0
r49=0
r410=0
r411=0
r412=0
r413=0
r414=0
r415=0
r416=0
r417=0
r418=0
r419=0
r420=0
r421=0
r422=0
r423=0
r424=0
r426=0
a22*r425 - c33*r464
r427=---------------------
a22
r428=0
r429=0
a22*r425 - c33*r464
r430=---------------------
a22
b33*r464
r431=----------
a22
r432=0
r433=0
r435=0
r439=0
r442=0
r444=0
r445=0
r448=0
r450=0
r451=0
r453=0
r454=0
r455=0
r458=0
r460=0
r461=0
r463=0
r465=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
r493=0
r495=0
r496=0
r498=0
r499=0
r4100=0
r4102=0
r4103=0
r4104=0
r4105=0
r4106=0
r4108=0
r4109=0
r4110=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
c11=0
b32=0
b31=0
b23=0
b22=0
b21=0
b13=0
b12=0
b11=0
a33=0
a23=0
a13=0
a12=0
a11=a22
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:
r13, r434, r319, r29, r310, r425, r333, r464, m3, c33,
n3, b33, a22
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.
{a22}
Relevance for the application:
The new Hamiltonian in form of a list of vanishing expressions:
{a11 - a22,
a12,
a13,
a23,
a33,
b11,
b12,
b13,
b21,
b22,
b23,
b31,
b32,
c11,
c12,
c13,
c22,
c23,
n1,
n2,
m1,
m2}$
The system of equations related to the Hamiltonian HAM:
2 2 2
HAM=u1 *a22 + u2 *a22 + u3*v3*b33 + u3*n3 + v3 *c33 + v3*m3
has apart from the Hamiltonian and Casimirs the following 8 first integrals:
2 2 2 2 3 2 2 2 2
FI=u1 *u3 *a22 + u2 *u3 *a22 + u3 *v3*b33 - u3 *v1 *c33 - u3 *v2 *c33
2
+ u3 *v3*m3
= a product of the elements of: {u3,
u3,
2 2 2 2
u1 *a22 + u2 *a22 + u3*v3*b33 - v1 *c33 - v2 *c33 + v3*m3}
{HAM,FI} = 0
2 2 2 2 2
FI=u1 *u3*a22 + u2 *u3*a22 + u3 *v3*b33 - u3*v1 *c33 - u3*v2 *c33 + u3*v3*m3
= a product of the elements of: {u3,
2 2 2 2
u1 *a22 + u2 *a22 + u3*v3*b33 - v1 *c33 - v2 *c33 + v3*m3}
{HAM,FI} = 0
2 2 2 2 2 2
FI=u3 *v1 + u3 *v2 + u3 *v3
2 2 2
= a product of the elements of: {u3,u3,v1 + v2 + v3 }
{HAM,FI} = 0
2 2 2
FI=u3*v1 + u3*v2 + u3*v3
2 2 2
= a product of the elements of: {v1 + v2 + v3 ,u3}
{HAM,FI} = 0
2
FI=u3
= a product of the elements of: {u3,u3}
{HAM,FI} = 0
3
FI=u3
= a product of the elements of: {u3,u3,u3}
{HAM,FI} = 0
4
FI=u3
= a product of the elements of: {u3,u3,u3,u3}
{HAM,FI} = 0
FI=u3
which the program can not factorize further.
{HAM,FI} = 0
And again in machine readable form:
HAM=u1**2*a22 + u2**2*a22 + u3*v3*b33 + u3*n3 + v3**2*c33 + v3*m3$
FI=u1**2*u3**2*a22 + u2**2*u3**2*a22 + u3**3*v3*b33 - u3**2*v1**2*c33 - u3**2*v2
**2*c33 + u3**2*v3*m3$
FI=u1**2*u3*a22 + u2**2*u3*a22 + u3**2*v3*b33 - u3*v1**2*c33 - u3*v2**2*c33 + u3
*v3*m3$
FI=u3**2*v1**2 + u3**2*v2**2 + u3**2*v3**2$
FI=u3*v1**2 + u3*v2**2 + u3*v3**2$
FI=u3**2$
FI=u3**3$
FI=u3**4$
FI=u3$