
 
The particle is gs and it's mass is mxy
      2
 - mxy =0

and then mix matrix is =

                     2
mat((( - 4*cos(theta) *gm(r1,r1)*gm(v,va)

                     2
       + 4*cos(theta) *gm(r1,v)*gm(r1,va)

                            2  2   2               2
       + gm(v,va)*sin(theta) *g *v0 )/(8*cos(theta) ),

                              2   2
       - gm(v,va)*sin(theta)*g *v0
     -------------------------------),
              8*cos(theta)

                              2   2
       - gm(v,va)*sin(theta)*g *v0
    (-------------------------------,( - 4*gm(r1,r1)*gm(v,va)
              8*cos(theta)

                                            2   2
         + 4*gm(r1,v)*gm(r1,va) + gm(v,va)*g *v0 )/8))


 

 
The particle is p and it's mass is 0
0=0

 
The particle is z and it's mass is zm
                2   2    2   2
  - 4*cos(theta) *zm  + g *v0
-------------------------------=0
                     2
         4*cos(theta)

                    - gm(r1,r1)*gm(v,va) + gm(r1,v)*gm(r1,va)
The mass list is={--------------------------------------------,
                                       2

                   2
   ( - 4*cos(theta) *gm(r1,r1)*gm(v,va)

                   2                                2   2
     + 4*cos(theta) *gm(r1,v)*gm(r1,va) + gm(v,va)*g *v0 )/(8

                 2
      *cos(theta) )}

 

 
The particle is h0 and it's mass is hm
           2              2
3*c(0,5)*v0  + c(0,1) + hm =0

 
The particle is nue and it's mass is 0
0=0

The coefficient of progaptor should be 1 = - l(1)

 

 
The particle is numu and it's mass is 0
0=0

The coefficient of progaptor should be 1 = - l(1)

 

 
The particle is nut and it's mass is 0
0=0

The coefficient of progaptor should be 1 = - l(1)

 

 
The particle is qd and it's mass is fmd
  - sqrt(2)*fmd + v0*wangm1
----------------------------=0
          sqrt(2)

The coefficient of progaptor should be 1 =-1

 

 
The particle is qs and it's mass is fms
  - sqrt(2)*fms + v0*wangm2
----------------------------=0
          sqrt(2)

The coefficient of progaptor should be 1 =-1

 

 
The particle is qb and it's mass is fmb
  - sqrt(2)*fmb + v0*wangm3
----------------------------=0
          sqrt(2)

The coefficient of progaptor should be 1 =-1

 

 
The particle is ef and it's mass is fme
  - sqrt(2)*fme + v0*wangm4
----------------------------=0
          sqrt(2)

The coefficient of progaptor should be 1 =-1

 

 
The particle is mu and it's mass is fmmu
  - sqrt(2)*fmmu + v0*wangm5
-----------------------------=0
           sqrt(2)

The coefficient of progaptor should be 1 =-1

 

 
The particle is tau and it's mass is fmtau
  - sqrt(2)*fmtau + v0*wangm6
------------------------------=0
           sqrt(2)

The coefficient of progaptor should be 1 =-1

 

 
The particle is qu and it's mass is fmu
  - sqrt(2)*fmu + v0*wangm7
----------------------------=0
          sqrt(2)

The coefficient of progaptor should be 1 =-1

 

 
The particle is qc and it's mass is fmc
  - sqrt(2)*fmc + v0*wangm8
----------------------------=0
          sqrt(2)

The coefficient of progaptor should be 1 =-1

 

 
The particle is qt and it's mass is fmt
  - sqrt(2)*fmt + v0*wangm9
----------------------------=0
          sqrt(2)

The coefficient of progaptor should be 1 =-1

 

 
The particle is w and it's mass is wm
  2   2       2
 g *v0  - 4*wm
----------------=0
       4

 
The particle is gsg and it's mass is mxy
   2
mxy =0
fmixlist:=((z ((sin theta) (p 0 r1 v)) ((cos theta) (z 0 r1
v))) (p ((cos theta) (p 0 r1 v)) ((minus (sin theta)) (z 0 
r1 v))))fmixlist:=((z ((sin theta) (p 0 r1 v)) ((cos theta)
(z 0 r1 v))) (p ((cos theta) (p 0 r1 v)) ((minus (sin theta)
) (z 0 r1 v))))fmixlist:=((z ((sin theta) (p 0 r1 v)) ((cos
theta) (z 0 r1 v))) (p ((cos theta) (p 0 r1 v)) ((minus (sin
theta)) (z 0 r1 v))))fmixlist:=((z ((sin theta) (p 0 r1 v))
((cos theta) (z 0 r1 v))) (p ((cos theta) (p 0 r1 v)) ((
minus (sin theta)) (z 0 r1 v))))fmixlist:=((z ((sin theta) (
p 0 r1 v)) ((cos theta) (z 0 r1 v))) (p ((cos theta) (p 0 r1
v)) ((minus (sin theta)) (z 0 r1 v))))fmixlist:=((z ((sin 
theta) (p 0 r1 v)) ((cos theta) (z 0 r1 v))) (p ((cos theta)
(p 0 r1 v)) ((minus (sin theta)) (z 0 r1 v))))fmixlist:=((z
((sin theta) (p 0 r1 v)) ((cos theta) (z 0 r1 v))) (p ((cos
theta) (p 0 r1 v)) ((minus (sin theta)) (z 0 r1 v))))
fmixlist:=((z ((sin theta) (p 0 r1 v)) ((cos theta) (z 0 r1
v))) (p ((cos theta) (p 0 r1 v)) ((minus (sin theta)) (z 0 
r1 v))))fmixlist:=((z ((sin theta) (p 0 r1 v)) ((cos theta)
(z 0 r1 v))) (p ((cos theta) (p 0 r1 v)) ((minus (sin theta)
) (z 0 r1 v))))fmixlist:=((z ((sin theta) (p 0 r1 v)) ((cos
theta) (z 0 r1 v))) (p ((cos theta) (p 0 r1 v)) ((minus (sin
theta)) (z 0 r1 v))))fmixlist:=((z ((sin theta) (p 0 r1 v))
((cos theta) (z 0 r1 v))) (p ((cos theta) (p 0 r1 v)) ((
minus (sin theta)) (z 0 r1 v))))fmixlist:=((z ((sin theta) (
p 0 r1 v)) ((cos theta) (z 0 r1 v))) (p ((cos theta) (p 0 r1
v)) ((minus (sin theta)) (z 0 r1 v))))fmixlist:=((z ((sin 
theta) (p 0 r1 v)) ((cos theta) (z 0 r1 v))) (p ((cos theta)
(p 0 r1 v)) ((minus (sin theta)) (z 0 r1 v))))fmixlist:=((z
((sin theta) (p 0 r1 v)) ((cos theta) (z 0 r1 v))) (p ((cos
theta) (p 0 r1 v)) ((minus (sin theta)) (z 0 r1 v))))
fmixlist:=((z ((sin theta) (p 0 r1 v)) ((cos theta) (z 0 r1
v))) (p ((cos theta) (p 0 r1 v)) ((minus (sin theta)) (z 0 
r1 v))))fmixlist:=((z ((sin theta) (p 0 r1 v)) ((cos theta)
(z 0 r1 v))) (p ((cos theta) (p 0 r1 v)) ((minus (sin theta)
) (z 0 r1 v))))fmixlist:=((z ((sin theta) (p 0 r1 v)) ((cos
theta) (z 0 r1 v))) (p ((cos theta) (p 0 r1 v)) ((minus (sin
theta)) (z 0 r1 v))))fmixlist:=((z ((sin theta) (p 0 r1 v))
((cos theta) (z 0 r1 v))) (p ((cos theta) (p 0 r1 v)) ((
minus (sin theta)) (z 0 r1 v))))fmixlist:=((z ((sin theta) (
p 0 r1 v)) ((cos theta) (z 0 r1 v))) (p ((cos theta) (p 0 r1
v)) ((minus (sin theta)) (z 0 r1 v))))fmixlist:=((z ((sin 
theta) (p 0 r1 v)) ((cos theta) (z 0 r1 v))) (p ((cos theta)
(p 0 r1 v)) ((minus (sin theta)) (z 0 r1 v))))fmixlist:=((z
((sin theta) (p 0 r1 v)) ((cos theta) (z 0 r1 v))) (p ((cos
theta) (p 0 r1 v)) ((minus (sin theta)) (z 0 r1 v))))
fmixlist:=((z ((sin theta) (p 0 r1 v)) ((cos theta) (z 0 r1
v))) (p ((cos theta) (p 0 r1 v)) ((minus (sin theta)) (z 0 
r1 v))))fmixlist:=((z ((sin theta) (p 0 r1 v)) ((cos theta)
(z 0 r1 v))) (p ((cos theta) (p 0 r1 v)) ((minus (sin theta)
) (z 0 r1 v))))fmixlist:=((z ((sin theta) (p 0 r1 v)) ((cos
theta) (z 0 r1 v))) (p ((cos theta) (p 0 r1 v)) ((minus (sin
theta)) (z 0 r1 v))))fmixlist:=((z ((sin theta) (p 0 r1 v))
((cos theta) (z 0 r1 v))) (p ((cos theta) (p 0 r1 v)) ((
minus (sin theta)) (z 0 r1 v))))fmixlist:=((z ((sin theta) (
p 0 r1 v)) ((cos theta) (z 0 r1 v))) (p ((cos theta) (p 0 r1
v)) ((minus (sin theta)) (z 0 r1 v))))fmixlist:=((z ((sin 
theta) (p 0 r1 v)) ((cos theta) (z 0 r1 v))) (p ((cos theta)
(p 0 r1 v)) ((minus (sin theta)) (z 0 r1 v))))fmixlist:=((z
((sin theta) (p 0 r1 v)) ((cos theta) (z 0 r1 v))) (p ((cos
theta) (p 0 r1 v)) ((minus (sin theta)) (z 0 r1 v))))
                  2          2
simprules={cos(~x)  + sin(~x)  - 1}

 

          2
    v.va*g
bb=---------
       4

Time: 130 ms

             2
       v.va*g
bb=---------------
                2
    8*cos(theta)

Time: 0 ms

bb=v.va*g*wm

Time: 0 ms

      v.va*g*wm
bb=---------------
                2
    2*cos(theta)

Time: 0 ms

                2               2
    v.va*vb.vc*g  - v.vb*va.vc*g
bb=-------------------------------
                  2

Time: 10 ms

                           2  2                        2  2
bb= - v.va*vb.vc*sin(theta) *g  + v.vb*va.vc*sin(theta) *g

Time: 0 ms

                                          2
bb= - 2*v.va*vb.vc*cos(theta)*sin(theta)*g

                                     2
 + v.vb*va.vc*cos(theta)*sin(theta)*g

                                     2
 + v.vc*va.vb*cos(theta)*sin(theta)*g

Time: 0 ms

                           2  2                        2  2
bb= - v.va*vb.vc*cos(theta) *g  + v.vb*va.vc*cos(theta) *g

Time: 0 ms

bb= - g(l,v)*sin(theta)*g

Time: 0 ms

bb= - g(l,v)*sin(theta)*g

Time: 0 ms

bb= - g(l,v)*sin(theta)*g

Time: 0 ms

                                       2
     - g(l,a,v)*g + 4*g(l,v)*sin(theta) *g - g(l,v)*g
bb=---------------------------------------------------
                      4*cos(theta)

Time: 0 ms

                                       2
     - g(l,a,v)*g + 4*g(l,v)*sin(theta) *g - g(l,v)*g
bb=---------------------------------------------------
                      4*cos(theta)

Time: 0 ms

                                       2
     - g(l,a,v)*g + 4*g(l,v)*sin(theta) *g - g(l,v)*g
bb=---------------------------------------------------
                      4*cos(theta)

Time: 0 ms

    sqrt(2)*g(l,a,v)*g + sqrt(2)*g(l,v)*g
bb=---------------------------------------
                      4

Time: 0 ms

    sqrt(2)*g(l,a,v)*g + sqrt(2)*g(l,v)*g
bb=---------------------------------------
                      4

Time: 0 ms

    sqrt(2)*g(l,a,v)*g + sqrt(2)*g(l,v)*g
bb=---------------------------------------
                      4

Time: 0 ms

    sqrt(2)*g(l,a,v)*g + sqrt(2)*g(l,v)*g
bb=---------------------------------------
                      4

Time: 0 ms

    sqrt(2)*g(l,a,v)*g + sqrt(2)*g(l,v)*g
bb=---------------------------------------
                      4

Time: 0 ms

    sqrt(2)*g(l,a,v)*g + sqrt(2)*g(l,v)*g
bb=---------------------------------------
                      4

Time: 0 ms

    g(l,a,v)*g + g(l,v)*g
bb=-----------------------
        4*cos(theta)

Time: 0 ms

    g(l,a,v)*g + g(l,v)*g
bb=-----------------------
        4*cos(theta)

Time: 0 ms

    g(l,a,v)*g + g(l,v)*g
bb=-----------------------
        4*cos(theta)

Time: 0 ms

bb= - r1.v*va.vb*sin(theta)*g + r1.vb*v.va*sin(theta)*g

 + r2.v*va.vb*sin(theta)*g - r2.va*v.vb*sin(theta)*g

 + r3.va*v.vb*sin(theta)*g - r3.vb*v.va*sin(theta)*g

Time: 0 ms

bb= - r1.v*va.vb*cos(theta)*g + r1.vb*v.va*cos(theta)*g

 + r2.v*va.vb*cos(theta)*g - r2.va*v.vb*cos(theta)*g

 + r3.va*v.vb*cos(theta)*g - r3.vb*v.va*cos(theta)*g

Time: 0 ms

     - g(l,v)*sin(theta)*g
bb=------------------------
              3

Time: 0 ms

     - g(l,v)*sin(theta)*g
bb=------------------------
              3

Time: 0 ms

     - g(l,v)*sin(theta)*g
bb=------------------------
              3

Time: 0 ms

                                         2
     - 3*g(l,a,v)*g + 4*g(l,v)*sin(theta) *g - 3*g(l,v)*g
bb=-------------------------------------------------------
                        12*cos(theta)

Time: 0 ms

                                         2
     - 3*g(l,a,v)*g + 4*g(l,v)*sin(theta) *g - 3*g(l,v)*g
bb=-------------------------------------------------------
                        12*cos(theta)

Time: 0 ms

                                         2
     - 3*g(l,a,v)*g + 4*g(l,v)*sin(theta) *g - 3*g(l,v)*g
bb=-------------------------------------------------------
                        12*cos(theta)

Time: 0 ms

    sqrt(2)*g(l,a,v)*g + sqrt(2)*g(l,v)*g
bb=---------------------------------------
                      4

Time: 0 ms

    sqrt(2)*g(l,a,v)*g + sqrt(2)*g(l,v)*g
bb=---------------------------------------
                      4

Time: 0 ms

    sqrt(2)*g(l,a,v)*g + sqrt(2)*g(l,v)*g
bb=---------------------------------------
                      4

Time: 0 ms

    sqrt(2)*g(l,a,v)*g + sqrt(2)*g(l,v)*g
bb=---------------------------------------
                      4

Time: 0 ms

    sqrt(2)*g(l,a,v)*g + sqrt(2)*g(l,v)*g
bb=---------------------------------------
                      4

Time: 0 ms

    sqrt(2)*g(l,a,v)*g + sqrt(2)*g(l,v)*g
bb=---------------------------------------
                      4

Time: 0 ms

    2*g(l,v)*sin(theta)*g
bb=-----------------------
              3

Time: 0 ms

    2*g(l,v)*sin(theta)*g
bb=-----------------------
              3

Time: 0 ms

    2*g(l,v)*sin(theta)*g
bb=-----------------------
              3

Time: 0 ms

                                      2
    3*g(l,a,v)*g + 8*g(l,v)*cos(theta) *g - 5*g(l,v)*g
bb=----------------------------------------------------
                      12*cos(theta)

Time: 0 ms

                                      2
    3*g(l,a,v)*g + 8*g(l,v)*cos(theta) *g - 5*g(l,v)*g
bb=----------------------------------------------------
                      12*cos(theta)

Time: 0 ms

                                      2
    3*g(l,a,v)*g + 8*g(l,v)*cos(theta) *g - 5*g(l,v)*g
bb=----------------------------------------------------
                      12*cos(theta)

Time: 0 ms

    fme*g
bb=-------
    2*wm

Time: 0 ms

    fmmu*g
bb=--------
     2*wm

Time: 0 ms

    fmtau*g
bb=---------
     2*wm

Time: 0 ms

        2   2
     - g *hm
bb=-----------
          2
     32*wm

Time: 0 ms

           2
     - g*hm
bb=----------
      4*wm

Time: 0 ms

    fmd*g
bb=-------
    2*wm

Time: 0 ms

    fms*g
bb=-------
    2*wm

Time: 10 ms

    fmb*g
bb=-------
    2*wm

Time: 0 ms

    fmu*g
bb=-------
    2*wm

Time: 0 ms

    fmc*g
bb=-------
    2*wm

Time: 0 ms

    fmt*g
bb=-------
    2*wm

Time: 0 ms
