Solution 2 to problem over
Remaining equations |
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Equations
The following unsolved equations remain:
1 4 2 2 2 2 1 2 2 2
0=---*a11 *n1 + a11 *a13 *n1 + ---*a11 *b12 *kap*n1
4 4
Expressions
The solution is given through the following expressions:
r10=0
1
- ---*m3*n1*n2*r494
2
r11=----------------------
2
a13*b12
1 2
- ---*m3*n1 *r494
2
r12=--------------------
2
a13*b12
1 2 3 1 2 2
---*a11 *n1 *r494 - ---*a13 *kap*m3 *n1*r494
8 2
r13=----------------------------------------------
3 2
a13 *b12
1 2
- ---*a11*n1 *n2*r494
4
r14=------------------------
2 2
a13 *b12
1 3
- ---*a11*n1 *r494
4
r15=---------------------
2 2
a13 *b12
r20=0
r21=0
r22=0
r23=0
r24=0
1 2
- a13*m3*n2*r494 + ---*b12*n1 *r494
2
r27=--------------------------------------
2
a13*b12
1
- 2*a13*m3*n1*r494 - ---*b12*n1*n2*r494
2
r28=------------------------------------------
2
a13*b12
r29
1 2 2 1 2 2 2 2 1 2 2
---*a11 *n1 *r494 - ---*a13 *kap*m3 *r494 + a13 *n1 *r494 + ---*a13 *n2 *r494
8 2 2
=-------------------------------------------------------------------------------
2 2
a13 *b12
1 2
- ---*n1 *r494
2
r210=-----------------
a13*b12
- a11*m3*n1*r494
r211=-------------------
2
a13*b12
r212=0
1
---*a11*n1*n2*r494
2
r213=--------------------
2
a13*b12
2
n1 *r494
r214=----------
2
b12
1
---*n1*n2*r494
2
r215=----------------
a13*b12
- a11*m3*n1*r494
r217=-------------------
2
a13*b12
r218=0
- n1*n2*r494
r219=---------------
2
b12
1 2 1 2
---*n1 *r494 + ---*n2 *r494
2 2
r220=-----------------------------
2
b12
r30=0
r31=0
r32=0
r33=0
r34=0
r35=0
r36=0
r37=0
r38=0
r39=0
1
---*n1*r494
2
r312=-------------
a13
r314=0
1
---*n1*r494
2
r315=-------------
a13
2*n1*r494
r317=-----------
b12
- 2*a13*m3*r494 - b12*n2*r494
r318=--------------------------------
2
b12
1 2 1 2
- ---*a11 *n1*r494 - ---*b12 *kap*n1*r494
2 2
r319=--------------------------------------------
2
a13*b12
r320=0
1
- ---*n1*r494
2
r321=----------------
a13
r322=0
r323=0
r324=0
r325=0
- a11*m3*r494
r327=----------------
2
b12
- a11*n1*r494
r328=----------------
a13*b12
a11*n2*r494
r329=-------------
2
b12
r330=0
2*n1*r494
r331=-----------
b12
r332=0
2 2 1 2
a11 *n1*r494 + 4*a13 *n1*r494 + ---*b12 *kap*n1*r494
2
r333=------------------------------------------------------
2
a13*b12
r334=0
r335=0
r336=0
r337=0
r339=0
r340=0
a11*n1*r494
r342=-------------
a13*b12
- a11*m3*r494
r343=----------------
2
b12
2*a11*n1*r494
r344=---------------
2
b12
r345=0
- n2*r494
r346=------------
b12
2*n1*r494
r347=-----------
b12
- 2*a13*n2*r494
r348=------------------
2
b12
r349=0
r350=0
r351=0
- n2*r494
r352=------------
b12
2 2 1 2
a11 *n1*r494 + 2*a13 *n1*r494 + ---*b12 *kap*n1*r494
2
r353=------------------------------------------------------
2
a13*b12
r354=0
r355=0
r40=0
r41=0
r42=0
r43=0
r44=0
r45=0
r46=0
r47=0
r48=0
r49=0
r410=0
r411=0
r412=0
r413=0
r418=0
r421=0
r423=0
r424=0
1
r427=---*r494
2
r429=0
1
r430=---*r494
2
2*a13*r494
r432=------------
b12
r433=0
2 2 2
- a11 *r494 - 2*a13 *r494 - b12 *kap*r494
r434=--------------------------------------------
2
b12
r435=0
r436=0
r437=0
r438=0
r439=0
r440=0
r441=0
r442=0
r443=0
r444=0
r447=0
r449=0
r450=0
r452=0
- a11*r494
r453=-------------
b12
r454=0
r455=0
r456=0
1
r457=---*r494
2
r458=0
r459=0
r460=0
2*a13*r494
r462=------------
b12
r463=0
2 2 1 2
a11 *r494 + 4*a13 *r494 + ---*b12 *kap*r494
2
r464=---------------------------------------------
2
b12
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
r479=0
r482=0
r484=0
r485=0
a11*r494
r487=----------
b12
r488=0
2*a11*a13*r494
r489=----------------
2
b12
r490=0
r491=0
r492=0
r493=0
r495=0
r497=0
2*a13*r494
r498=------------
b12
r499=0
r4100=0
r4101=0
r4102=0
r4103=0
r4104=0
r4105=0
r4106=0
r4108=0
r4109=0
1
r4110=---*r494
2
r4112=0
r4113=0
2 2 1 2
a11 *r494 + 2*a13 *r494 + ---*b12 *kap*r494
2
r4114=---------------------------------------------
2
b12
r4115=0
r4116=0
r4117=0
r4118=0
r4119=0
r4120=0
r4121=0
r4122=0
r4123=0
r4124=0
r4125=0
m2=0
m1=0
a33=0
a23=0
a22=a11
1
- ---*a11*n1
2
n3=---------------
a13
1
- ---*n1*r494
2
r338=----------------
a13
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:
r494, a13, m3, a11, n2, n1, b12
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.
{b12,n1,r338}
Relevance for the application:
Modulo the following equation:
1 4 2 2 2 2 1 2 2 2
0=---*a11 *n1 + a11 *a13 *n1 + ---*a11 *b12 *kap*n1
4 4
the system of equations related to the Hamiltonian HAM:
2 2 2
HAM=(u1 *a11*a13 + 2*u1*u3*a13 + u1*v2*a13*b12 + u1*a13*n1 + u2 *a11*a13
1
- u2*v1*a13*b12 + u2*a13*n2 - ---*u3*a11*n1 + v3*a13*m3)/a13
2
has apart from the Hamiltonian and Casimirs only the following first integral:
2 2 2 3 5 1 3 2
FI=u1 *u3 *(a11 *a13 + 2*a13 + ---*a13 *b12 *kap)
2
2 2 2 4 1 2 2
+ u1 *u3*(a11 *a13 *n1 + 2*a13 *n1 + ---*a13 *b12 *kap*n1)
2
1 2 2 3 2 2 3
+ ---*u1 *v1 *a13 *b12 - u1 *v1*a13 *b12*n2
2
2 1 3 2 1 3 2 4
+ u1 *(---*a13 *n1 + ---*a13 *n2 ) + 2*u1*u2*u3*v1*a13 *b12
2 2
4 3 2 3
- 2*u1*u2*u3*a13 *n2 + u1*u2*v1*v2*a13 *b12 + 2*u1*u2*v1*a13 *b12*n1
3 3 3 4
- u1*u2*v2*a13 *b12*n2 - u1*u2*a13 *n1*n2 + 2*u1*u3 *a11*a13
2 3 2 3 3
+ u1*u3 *v2*a11*a13 *b12 + 2*u1*u3 *a11*a13 *n1 - u1*u3*v1*a11*a13 *m3
2 1 2 2
+ u1*u3*v2*a11*a13 *b12*n1 - ---*u1*v1*v3*a13 *b12 *n1
2
2 1 2 1 3
- u1*v1*a11*a13 *m3*n1 + ---*u1*v3*a13 *b12*n1*n2 - ---*u1*a11*a13*n1
2 4
2 2 2 3 5 1 3 2 2 4
+ u2 *u3 *(a11 *a13 + 4*a13 + ---*a13 *b12 *kap) + 2*u2 *u3*v2*a13 *b12
2
2 2 2 4 1 2 2
+ u2 *u3*(a11 *a13 *n1 + 4*a13 *n1 + ---*a13 *b12 *kap*n1)
2
1 2 2 3 2 2 3 2 3 2
+ ---*u2 *v2 *a13 *b12 + 2*u2 *v2*a13 *b12*n1 + u2 *a13 *n1
2
2 3 2 3 2
- u2*u3 *v1*a11*a13 *b12 + u2*u3 *a11*a13 *n2 - u2*u3*v1*a11*a13 *b12*n1
3 1 2
- u2*u3*v2*a11*a13 *m3 + ---*u2*u3*a11*a13 *n1*n2
2
1 2 2 2 1 2 2
- ---*u2*v2*v3*a13 *b12 *n1 - u2*v2*a11*a13 *m3*n1 - ---*u2*v3*a13 *b12*n1
2 2
1 2 4 2 3 5 3 2
- ---*u2*a11*a13*n1 *n2 + u3 *( - a11 *a13 - 2*a13 - a13 *b12 *kap)
4
3 4 3 1 2 2 1 2 2
+ 2*u3 *v2*a13 *b12 + u3 *( - ---*a11 *a13 *n1 - ---*a13 *b12 *kap*n1)
2 2
1 2 2 3 2 2 4 3
+ ---*u3 *v1 *a13 *b12 + u3 *v1*( - 2*a13 *m3 - a13 *b12*n2)
2
1 2 2 3 2 2 3
+ ---*u3 *v2 *a13 *b12 + 2*u3 *v2*a13 *b12*n1
2
2 1 2 2 1 3 2 3 2 1 3 2
+ u3 *(---*a11 *a13*n1 - ---*a13 *kap*m3 + a13 *n1 + ---*a13 *n2 )
8 2 2
1 2 2 2 3 1 2
+ ---*u3*v1 *a13 *b12 *n1 + u3*v1*( - 2*a13 *m3*n1 - ---*a13 *b12*n1*n2)
2 2
1 2 2 2 3 1 2 2
+ ---*u3*v2 *a13 *b12 *n1 + u3*v2*( - a13 *m3*n2 + ---*a13 *b12*n1 )
2 2
1 2 3 1 2 2 1 2 2
+ u3*(---*a11 *n1 - ---*a13 *kap*m3 *n1) - ---*v1*a13 *m3*n1
8 2 2
1 2
- ---*v2*a13 *m3*n1*n2
2
3 5 3 3
{HAM,FI} = u1 *u3*v1*( - 4*a13 *b12 - a13 *b12 *kap)
3 2 3 5 3 2
+ u1 *u3*(2*a11 *a13 *n2 + 8*a13 *n2 + 2*a13 *b12 *kap*n2)
3 4 1 2 3
+ u1 *v1*( - 4*a13 *b12*n1 - ---*a13 *b12 *kap*n1)
2
3 2 2 4 2 2
+ u1 *(a11 *a13 *n1*n2 + 4*a13 *n1*n2 + a13 *b12 *kap*n1*n2)
2 2 2 4 6 4 2
+ u1 *u2*u3 *( - 4*a11 *a13 - 16*a13 - 4*a13 *b12 *kap)
2 5 3 3
+ u1 *u2*u3*v2*( - 4*a13 *b12 - a13 *b12 *kap)
2 2 3 5 3 2
+ u1 *u2*u3*( - 4*a11 *a13 *n1 - 16*a13 *n1 - 4*a13 *b12 *kap*n1)
2 4 1 2 3 2
+ u1 *u2*v2*( - 4*a13 *b12*n1 - ---*a13 *b12 *kap*n1) + u1 *u2*(
2
1 4 2 1 2 2 2 4 2
---*a11 *n1 + ---*a11 *b12 *kap*n1 - 4*a13 *n1
4 4
2 2 2 2 2 4
- a13 *b12 *kap*n1 ) + 4*u1 *u3 *v1*a11*a13 *b12
2 2 5 3 3
+ u1 *u3 *v3*( - 4*a13 *b12 - a13 *b12 *kap)
2 3 2 2 3
+ 2*u1 *u3*v1*v2*a11*a13 *b12 + 5*u1 *u3*v1*a11*a13 *b12*n1
2 4 1 2 3
+ u1 *u3*v3*( - 4*a13 *b12*n1 - ---*a13 *b12 *kap*n1)
2
2 2 2
+ u1 *v1*v2*a11*a13 *b12 *n1
2 3 2 2
+ u1 *v1*( - a11*a13 *m3*n2 + a11*a13 *b12*n1 )
2 5 3 3
+ u1*u2 *u3*v1*( - 4*a13 *b12 - a13 *b12 *kap)
2 2 3 5 3 2
+ u1*u2 *u3*(2*a11 *a13 *n2 + 8*a13 *n2 + 2*a13 *b12 *kap*n2)
2 4 1 2 3
+ u1*u2 *v1*( - 2*a13 *b12*n1 - ---*a13 *b12 *kap*n1)
2
2 2 2 4 2 2
+ u1*u2 *(a11 *a13 *n1*n2 + 4*a13 *n1*n2 + a13 *b12 *kap*n1*n2)
2 4 2 3 2
+ 4*u1*u2*u3 *v2*a11*a13 *b12 - 2*u1*u2*u3*v1 *a11*a13 *b12
4 3
+ u1*u2*u3*v1*(2*a11*a13 *m3 + 2*a11*a13 *b12*n2)
2 3 2 3
+ 2*u1*u2*u3*v2 *a11*a13 *b12 + 5*u1*u2*u3*v2*a11*a13 *b12*n1
2 2 2 3 2
- u1*u2*v1 *a11*a13 *b12 *n1 - u1*u2*v1*v3*a13 *b12 *n1
3 1 2
+ u1*u2*v1*(a11*a13 *m3*n1 + ---*a11*a13 *b12*n1*n2)
2
2 2 2
+ u1*u2*v2 *a11*a13 *b12 *n1
3 2 2
+ u1*u2*v2*( - a11*a13 *m3*n2 + a11*a13 *b12*n1 )
3 5 3 4
+ 4*u1*u3 *v1*a13 *b12 + 4*u1*u3 *v3*a11*a13 *b12
3 2 3 5 3 2
+ u1*u3 *( - 4*a11 *a13 *n2 - 16*a13 *n2 - 4*a13 *b12 *kap*n2)
2 4 2 2 4
+ 4*u1*u3 *v1*v2*a13 *b12 + 6*u1*u3 *v1*a13 *b12*n1
2 3 2 2 3
+ 2*u1*u3 *v2*v3*a11*a13 *b12 + 5*u1*u3 *v3*a11*a13 *b12*n1 + u1
2 2 2 4 2 2
*u3 *( - 2*a11 *a13 *n1*n2 - 8*a13 *n1*n2 - 2*a13 *b12 *kap*n1*n2)
3 3 3
+ u1*u3*v1 *a13 *b12
2 4 3 2
+ u1*u3*v1 *( - 2*a13 *b12*m3 - 2*a13 *b12 *n2)
2 3 3 3 2
+ u1*u3*v1*v2 *a13 *b12 + 4*u1*u3*v1*v2*a13 *b12 *n1
3 2 3 2
+ u1*u3*v1*(2*a13 *b12*n1 + a13 *b12*n2 )
2 2
+ u1*u3*v2*v3*a11*a13 *b12 *n1
3 2 2
+ u1*u3*v3*( - a11*a13 *m3*n2 + a11*a13 *b12*n1 )
1 3 2 3
+ ---*u1*v1 *a13 *b12 *n1
2
2 3 1 2 2
+ u1*v1 *( - 2*a13 *b12*m3*n1 - ---*a13 *b12 *n1*n2)
2
1 2 2 3
+ ---*u1*v1*v2 *a13 *b12 *n1
2
3 1 2 2 2
+ u1*v1*v2*( - a13 *b12*m3*n2 + ---*a13 *b12 *n1 )
2
3 2 2 4 6 4 2
+ u2 *u3 *( - 4*a11 *a13 - 16*a13 - 4*a13 *b12 *kap)
3 5 3 3
+ u2 *u3*v2*( - 4*a13 *b12 - a13 *b12 *kap)
3 2 3 5 3 2
+ u2 *u3*( - 4*a11 *a13 *n1 - 16*a13 *n1 - 4*a13 *b12 *kap*n1)
3 4 1 2 3 3
+ u2 *v2*( - 2*a13 *b12*n1 - ---*a13 *b12 *kap*n1) + u2 *(
2
1 4 2 1 2 2 2 4 2
---*a11 *n1 + ---*a11 *b12 *kap*n1 - 4*a13 *n1
4 4
2 2 2 2 2 5 3 3
- a13 *b12 *kap*n1 ) + u2 *u3 *v3*( - 4*a13 *b12 - a13 *b12 *kap)
2 3 2
- 2*u2 *u3*v1*v2*a11*a13 *b12
2 4 3
+ u2 *u3*v2*(2*a11*a13 *m3 + 2*a11*a13 *b12*n2)
2 4 1 2 3
+ u2 *u3*v3*( - 2*a13 *b12*n1 - ---*a13 *b12 *kap*n1)
2
2 2 2 2 3 2
- u2 *v1*v2*a11*a13 *b12 *n1 - u2 *v2*v3*a13 *b12 *n1
2 3 1 2
+ u2 *v2*(a11*a13 *m3*n1 + ---*a11*a13 *b12*n1*n2)
2
4 2 4 6 4 2
+ u2*u3 *(8*a11 *a13 + 32*a13 + 8*a13 *b12 *kap)
3 5
+ 4*u2*u3 *v2*a13 *b12
3 2 3 5 3 2
+ u2*u3 *(8*a11 *a13 *n1 + 32*a13 *n1 + 8*a13 *b12 *kap*n1)
2 3 2 2 2 4 2
- 2*u2*u3 *v1*v3*a11*a13 *b12 + 4*u2*u3 *v2 *a13 *b12
2 4
+ 6*u2*u3 *v2*a13 *b12*n1
2 4 3 2
+ u2*u3 *v3*(2*a11*a13 *m3 + 2*a11*a13 *b12*n2) + u2*u3 *(
1 4 2 1 2 2 2 4 2
- ---*a11 *n1 - ---*a11 *b12 *kap*n1 + 8*a13 *n1
2 2
2 2 2 2 3 3
+ 2*a13 *b12 *kap*n1 ) + u2*u3*v1 *v2*a13 *b12
4 3 2
+ u2*u3*v1*v2*( - 2*a13 *b12*m3 - 2*a13 *b12 *n2)
2 2 3 3 3
- u2*u3*v1*v3*a11*a13 *b12 *n1 + u2*u3*v2 *a13 *b12
2 3 2
+ 4*u2*u3*v2 *a13 *b12 *n1
3 2 3 2 2 3 2
+ u2*u3*v2*(2*a13 *b12*n1 + a13 *b12*n2 ) - u2*u3*v3 *a13 *b12 *n1
3 1 2
+ u2*u3*v3*(a11*a13 *m3*n1 + ---*a11*a13 *b12*n1*n2)
2
1 2 2 3
+ ---*u2*v1 *v2*a13 *b12 *n1
2
3 1 2 2
+ u2*v1*v2*( - 2*a13 *b12*m3*n1 - ---*a13 *b12 *n1*n2)
2
1 3 2 3
+ ---*u2*v2 *a13 *b12 *n1
2
2 3 1 2 2 2 4 5
+ u2*v2 *( - a13 *b12*m3*n2 + ---*a13 *b12 *n1 ) + 4*u3 *v3*a13 *b12
2
3 4 2 3 4
+ 4*u3 *v2*v3*a13 *b12 + 6*u3 *v3*a13 *b12*n1
2 2 3 3
+ u3 *v1 *v3*a13 *b12
2 4 3 2
+ u3 *v1*v3*( - 2*a13 *b12*m3 - 2*a13 *b12 *n2)
2 2 3 3 2 3 2
+ u3 *v2 *v3*a13 *b12 + 4*u3 *v2*v3*a13 *b12 *n1
2 3 2 3 2
+ u3 *v3*(2*a13 *b12*n1 + a13 *b12*n2 )
1 2 2 3
+ ---*u3*v1 *v3*a13 *b12 *n1
2
3 1 2 2
+ u3*v1*v3*( - 2*a13 *b12*m3*n1 - ---*a13 *b12 *n1*n2)
2
1 2 2 3
+ ---*u3*v2 *v3*a13 *b12 *n1
2
3 1 2 2 2
+ u3*v2*v3*( - a13 *b12*m3*n2 + ---*a13 *b12 *n1 )
2
And again in machine readable form:
HAM=(u1**2*a11*a13 + 2*u1*u3*a13**2 + u1*v2*a13*b12 + u1*a13*n1 + u2**2*a11*a13
- u2*v1*a13*b12 + u2*a13*n2 - 1/2*u3*a11*n1 + v3*a13*m3)/a13$
FI=u1**2*u3**2*(a11**2*a13**3 + 2*a13**5 + 1/2*a13**3*b12**2*kap) + u1**2*u3*(
a11**2*a13**2*n1 + 2*a13**4*n1 + 1/2*a13**2*b12**2*kap*n1) + 1/2*u1**2*v1**2*a13
**3*b12**2 - u1**2*v1*a13**3*b12*n2 + u1**2*(1/2*a13**3*n1**2 + 1/2*a13**3*n2**2
) + 2*u1*u2*u3*v1*a13**4*b12 - 2*u1*u2*u3*a13**4*n2 + u1*u2*v1*v2*a13**3*b12**2
+ 2*u1*u2*v1*a13**3*b12*n1 - u1*u2*v2*a13**3*b12*n2 - u1*u2*a13**3*n1*n2 + 2*u1*
u3**3*a11*a13**4 + u1*u3**2*v2*a11*a13**3*b12 + 2*u1*u3**2*a11*a13**3*n1 - u1*u3
*v1*a11*a13**3*m3 + u1*u3*v2*a11*a13**2*b12*n1 - 1/2*u1*v1*v3*a13**2*b12**2*n1 -
u1*v1*a11*a13**2*m3*n1 + 1/2*u1*v3*a13**2*b12*n1*n2 - 1/4*u1*a11*a13*n1**3 + u2
**2*u3**2*(a11**2*a13**3 + 4*a13**5 + 1/2*a13**3*b12**2*kap) + 2*u2**2*u3*v2*a13
**4*b12 + u2**2*u3*(a11**2*a13**2*n1 + 4*a13**4*n1 + 1/2*a13**2*b12**2*kap*n1) +
1/2*u2**2*v2**2*a13**3*b12**2 + 2*u2**2*v2*a13**3*b12*n1 + u2**2*a13**3*n1**2 -
u2*u3**2*v1*a11*a13**3*b12 + u2*u3**2*a11*a13**3*n2 - u2*u3*v1*a11*a13**2*b12*
n1 - u2*u3*v2*a11*a13**3*m3 + 1/2*u2*u3*a11*a13**2*n1*n2 - 1/2*u2*v2*v3*a13**2*
b12**2*n1 - u2*v2*a11*a13**2*m3*n1 - 1/2*u2*v3*a13**2*b12*n1**2 - 1/4*u2*a11*a13
*n1**2*n2 + u3**4*( - a11**2*a13**3 - 2*a13**5 - a13**3*b12**2*kap) + 2*u3**3*v2
*a13**4*b12 + u3**3*( - 1/2*a11**2*a13**2*n1 - 1/2*a13**2*b12**2*kap*n1) + 1/2*
u3**2*v1**2*a13**3*b12**2 + u3**2*v1*( - 2*a13**4*m3 - a13**3*b12*n2) + 1/2*u3**
2*v2**2*a13**3*b12**2 + 2*u3**2*v2*a13**3*b12*n1 + u3**2*(1/8*a11**2*a13*n1**2 -
1/2*a13**3*kap*m3**2 + a13**3*n1**2 + 1/2*a13**3*n2**2) + 1/2*u3*v1**2*a13**2*
b12**2*n1 + u3*v1*( - 2*a13**3*m3*n1 - 1/2*a13**2*b12*n1*n2) + 1/2*u3*v2**2*a13
**2*b12**2*n1 + u3*v2*( - a13**3*m3*n2 + 1/2*a13**2*b12*n1**2) + u3*(1/8*a11**2*
n1**3 - 1/2*a13**2*kap*m3**2*n1) - 1/2*v1*a13**2*m3*n1**2 - 1/2*v2*a13**2*m3*n1*
n2$