In[]:=
ClearAll["Global`*"]
In[]:=
ver4={X41,X42,X43,X44};B4=(+2s++2tX41+4sX41+2X41++2st+-2sX42-2X42-2stX41X42-2X41X42+-2sX43-2X43-2stX41X43-2X41X43+4stX42X43+2X42X43++2(s+t)(s(t-X41)+t(t+X41-X42-X43))X44++(++2t(X41+X44))+(++2t(X41+X44))+2(-t(t+X41-2X43+X44)(t+X41-X42-X43+X44)-s(+2(t-X41)X44+)-(++2t(X41+X44)))-2(t(t+X41-2X42+X44)(t+X41-X42-X43+X44)+s(++2t(X41+X44))));
1
16
2
s
2
t
3
t
4
t
2
s
2
t
3
t
2
s
2
X41
2
X41
2
t
2
X41
2
t
3
t
2
t
2
t
2
X42
2
t
3
t
2
t
2
t
2
t
2
X43
2
(s+t)
2
X44
4
m1
2
t
2
(X41-X44)
4
m2
2
t
2
(X41-X44)
2
m1
2
(t+X41)
2
X44
2
m2
2
t
2
(X41-X44)
2
m2
2
t
2
(X41-X44)
In[]:=
ureg4=Product[ver4[[i]]^rho4[i],{i,1,4}]*B4^((d-5)/2)
Out[]=
5-d
4
rho4[1]
X41
rho4[2]
X42
rho4[3]
X43
rho4[4]
X44
1
2
(+2s++2tX41+4sX41+2X41++2st+-2sX42-2X42-2stX41X42-2X41X42+-2sX43-2X43-2stX41X43-2X41X43+4stX42X43+2X42X43++2(s+t)(s(t-X41)+t(t+X41-X42-X43))X44++(++2t(X41+X44))+(++2t(X41+X44))+2(-t(t+X41-2X43+X44)(t+X41-X42-X43+X44)-s(+2(t-X41)X44+)-(++2t(X41+X44)))-2(t(t+X41-2X42+X44)(t+X41-X42-X43+X44)+s(++2t(X41+X44))))
2
s
2
t
3
t
4
t
2
s
2
t
3
t
2
s
2
X41
2
X41
2
t
2
X41
2
t
3
t
2
t
2
t
2
X42
2
t
3
t
2
t
2
t
2
t
2
X43
2
(s+t)
2
X44
4
m1
2
t
2
(X41-X44)
4
m2
2
t
2
(X41-X44)
2
m1
2
(t+X41)
2
X44
2
m2
2
t
2
(X41-X44)
2
m2
2
t
2
(X41-X44)
In[]:=
uregnum4=ureg4/.{s:>17,t:>23,m1:>37,m2:>43,d:>1/97,rho[1]:>1/113,rho[2]:>1/149,rho[3]:>1/173,rho[4]:>1/197};
In[]:=
dlist4=Table[FullSimplify[D[Log[uregnum4],ver4[[i]]]],{i,1,4}];
In[]:=
EQSu=Table[dlist4[[i]]==0,{i,1,4}];
In[]:=
SOL=Solve[EQSu,ver4];
Out[]=
Solve[EQSu,{X41,X42,X43,X44}]
In[]:=
lenSOL=Length[SOL]
7
In[]:=
subsets4=Subsets[ver4]
Out[]=
{{},{X41},{X42},{X43},{X44},{X41,X42},{X41,X43},{X41,X44},{X42,X43},{X42,X44},{X43,X44},{X41,X42,X43},{X41,X42,X44},{X41,X43,X44},{X42,X43,X44},{X41,X42,X43,X44}}
{{},{X41},{X42},{X43},{X44},{X41,X42},{X41,X43},{X41,X44},{X42,X43},{X42,X44},{X43,X44},{X41,X42,X43},{X41,X42,X44},{X41,X43,X44},{X42,X43,X44},{X41,X42,X43,X44}}
In[]:=
Do[currentvars4=subsets4[[k]];remvars4=Join[Complement[ver4,currentvars4],{s,t,d,m1,m2,rho4[1],rho4[2],rho4[3],rho4[4]}];numrules4=Table[remvars4[[i]]->1/Prime[23+45*i],{i,Length[remvars4]}];dlistdo4=Table[Simplify[D[Log[ureg4/.numrules4],currentvars4[[j]]]],{j,1,Length[currentvars4]}];SOLdo4=Solve[dlistdo4==0,currentvars4];lenSOLdo4=Length[SOLdo4];Print[k,"/",Length[subsets4]," ",currentvars4," ",lenSOLdo4];,{k,2,Length[subsets4]}];
2/16 {X41} 2
3/16 {X42} 2
4/16 {X43} 2
2/16 {X41} 2
3/16 {X42} 2
4/16 {X43} 2
5/16 {X44} 2
6/16 {X41,X42} 4
7/16 {X41,X43} 4
8/16 {X41,X44} 4
9/16 {X42,X43} 4
10/16 {X42,X44} 4
11/16 {X43,X44} 4
12/16 {X41,X42,X43} 8
13/16 {X41,X42,X44} 8
14/16 {X41,X43,X44} 8
15/16 {X42,X43,X44} 8
16/16 {X41,X42,X43,X44} 7
5/16 {X44} 2
16/16 {X41,X42,X43,X44} 7
2/16 {X41} 2
3/16 {X42} 2
4/16 {X43} 2
5/16 {X44} 2
6/16 {X41,X42} 4
7/16 {X41,X43} 4
8/16 {X41,X44} 4
9/16 {X42,X43} 4
10/16 {X42,X44} 4
11/16 {X43,X44} 4
12/16 {X41,X42,X43} 8
13/16 {X41,X42,X44} 8
14/16 {X41,X43,X44} 8
15/16 {X42,X43,X44} 8
16/16 {X41,X42,X43,X44} 7
In[]:=
Do[currentvars4=Take[ver4,ii];Print["\nFor set ",currentvars4," :"];remvars4=Join[Complement[ver4,currentvars4],{s,t,d,m1,m2,rho4[1],rho4[2],rho4[3],rho4[4]}];numrules4=Table[remvars4[[i]]->1/Prime[23+45*i],{i,Length[remvars4]}];Do[currentset4=subsets4[[k]];ureg42=Product[currentset4[[i]]^rho4[i],{i,1,Length[currentset4]}]*B4^((d-5)/2);ureg42=ureg42/.numrules4;dlistdo4=Table[Simplify[D[Log[ureg42],currentvars4[[j]]]],{j,1,Length[currentvars4]}];SOLdo4=Solve[dlistdo4==0,currentvars4];lenSOLdo4=Length[SOLdo4];Print[k,"/",Length[subsets4]," ",currentset4," ",lenSOLdo4];,{k,1,Length[subsets4]}];,{ii,1,4}];
For set {X41} :
1/16 {} 1
2/16 {X41} 2
3/16 {X42} 1
4/16 {X43} 1
5/16 {X44} 1
6/16 {X41,X42} 2
7/16 {X41,X43} 2
8/16 {X41,X44} 2
9/16 {X42,X43} 1
10/16 {X42,X44} 1
11/16 {X43,X44} 1
12/16 {X41,X42,X43} 2
13/16 {X41,X42,X44} 2
14/16 {X41,X43,X44} 2
15/16 {X42,X43,X44} 1
16/16 {X41,X42,X43,X44} 2
For set {X41,X42} :
1/16 {} 1
2/16 {X41} 2
3/16 {X42} 2
4/16 {X43} 1
5/16 {X44} 1
6/16 {X41,X42} 4
7/16 {X41,X43} 2
8/16 {X41,X44} 2
9/16 {X42,X43} 2
10/16 {X42,X44} 2
11/16 {X43,X44} 1
12/16 {X41,X42,X43} 4
13/16 {X41,X42,X44} 4
14/16 {X41,X43,X44} 2
15/16 {X42,X43,X44} 2
16/16 {X41,X42,X43,X44} 4
For set {X41,X42,X43} :
1/16 {} 1
2/16 {X41} 2
3/16 {X42} 2
4/16 {X43} 2
5/16 {X44} 1
6/16 {X41,X42} 4
7/16 {X41,X43} 4