In[]:=
EliminateIP-T-V,T
2
c
me0-1+
1
1-
2
β
,{T}
Out[]=
2IP-2
2
c
me0+2V+
2
c
me0
-((-1+β)(1+β))
1-β
+
2
c
me0
-((-1+β)(1+β))
1+β
0&&-1+β≠0&&1+β≠0
In[]:=
EliminateV-
2
e
Z
4πrϵ0
,r
a0
me0
Amp
+
1-
2
β
Z
,IP-T-V,T
2
c
me0-1+
1
1-
2
β
,{T}
Out[]=
4πV-
2
e
Z
rϵ0
&&2IP-2
2
c
me0+2V+
2
c
me0
-((-1+β)(1+β))
1-β
+
2
c
me0
-((-1+β)(1+β))
1+β
0&&a0-1+
2
me0
2
A
2
mp
+
2
β
-rZ
me0
Amp
-
-((-1+β)(1+β))
0&&-rZ+a0
me0
Amp
+
-((-1+β)(1+β))
0&&a0-
2
A
2
mp
+
2
me0
1-β
-
2
A
2
mp
β-
AmprZme0-Amp
-((-1+β)(1+β))

1-β
0&&a0-
2
A
2
mp
+
2
A
2
mp
β+
2
me0
1+β
-
AmprZme0-Amp
-((-1+β)(1+β))

1+β
0&&A≠0&&mp≠0&&r≠0&&Z≠0&&-1+β≠0&&1+β≠0&&ϵ0≠0
In[]:=
Eliminateβ
Zα
1+
me0
2Amp
,IP-T-V,T
2
c
me0-1+
1
1-
2
β
,{T}
Out[]=
2AmpZα(me0+2Amp)β&&-1+
me0
me0+2Amp
Zα-β&&2IP-2
2
c
me0+2V+
2
c
me0
-((-1+β)(1+β))
1-β
+
2
c
me0
-((-1+β)(1+β))
1+β
0&&me0+2Amp≠0&&-1+β≠0&&1+β≠0
In[]:=
Eliminateβ
Zα
1+
me0
2Amp
,r
a0
me0
Amp
+
1-
2
β
Z
,IP-T-V,T
2
c
me0-1+
1
1-
2
β
,{T}
Out[]=
2α
2+
me0
Amp
β
Z
&&2IP-2
2
c
me0+2V+
2
c
me0
-((-1+β)(1+β))
1-β
+
2
c
me0
-((-1+β)(1+β))
1+β
0&&r-
a0
me0
Amp
+
-((-1+β)(1+β))
Z
0&&A≠0&&mp≠0&&me0+2Amp≠0&&Z≠0&&-1+β≠0&&1+β≠0
In[]:=
EliminateV-
2
e
Z
4πrϵ0
,β
Zα
1+
me0
2Amp
,IP-T-V,T
2
c
me0-1+
1
1-
2
β
,{T}
Out[]=
4πV-
2
e
Z
rϵ0
&&2AmpZα(me0+2Amp)β&&-1+
me0
me0+2Amp
Zα-β&&2IP-2
2
c
me0+2V+
2
c
me0
-((-1+β)(1+β))
1-β
+
2
c
me0
-((-1+β)(1+β))
1+β
0&&me0+2Amp≠0&&r≠0&&-1+β≠0&&1+β≠0&&ϵ0≠0
In[]:=
EliminateV-
2
e
Z
4πrϵ0
,β
Zα
1+
me0
2Amp
,r
a0
me0
Amp
+
1-
2
β
Z
,IP-T-V,T
2
c
me0-1+
1
1-
2
β
,{T}
Out[]=
$Aborted