​

wt6

In[]:=
wt6[{a1_,a2_,a3_,a4_,a5_,a6_},n_]:=x0^(n-a6)x1^(a6-a5)x2^(a5-a4)x3^(a4-a3)x4^(a3-a2)x5^(a2-a1)x6^a1;

chainWeight


helper functions to split Min conditions


makeWeightSymols


weight of chains


check

NonNegativeLatticeSum[monomial_,constraints_]:=Module[{vars},​​vars=Union@@Map[Variables,Cases[monomial,Power[_,s_]:>s,{0,Infinity}]];​​ResourceFunction["LatticeSum"][monomial,constraints&&And@@Thread[vars>=0]]​​];

​

In[]:=
ss=Names["tw*"]
Out[]=
{tw01,tw02,tw03even,tw03old,tw04even,tw04old,tw05even,tw05old,tw06even,tw06odd,tw07even,tw07odd,tw08even,tw08odd,tw09even,tw09odd,tw10,tw11,twc0,twc11,twc12,twc2,twd0,twd1,twd2,twe00,twe01,twe02,twe03,twe101,twe102,twe103,twe111,twe112,twe12,twe13,twe20,twe21,twe22,twe23,twe24,twe25,twf11,twf12,twf2,twf30,twf31,twf32,twf41,twf421,twf422,twf50,twf51,twf52,twf53,twf541,twf542,twf61,twf62,twf63,twf64,twr00,twr01,twr02,twr03,twr101,twr102,twr103,twr111,twr112,twr12,twr13,twr20,twr21,twr22,twr23,twr24,twr25,tws11,tws12,tws2,tws31,tws32,tws33,tws34,tws41,tws42,tws50,tws511,tws512,tws521,tws522,tws523,tws53,tws54,tws61,tws62,tws63,tws64,twu0,twu1,twx11,twx12,twx2,twz11,twz12,twz13,twz2}
In[]:=
Length[ss]
Out[]=
108
In[]:=
allconds1=Flatten[Table[Table[sp[v],{v,List@@Symbol[ss[[ii]]]}],{ii,1,Length[ss]}],2];
In[]:=
Length[allconds1]
Out[]=
2935
In[]:=
allconds2=Select[allconds1,#[[2]]=!=False&];
In[]:=
Length[allconds2]
Out[]=
2324
In[]:=
terms=Table[Check[NonNegativeLatticeSum[PowerExpand[allconds2[[ij,1]]],allconds2[[ij,2]]],Print[ij]],{ij,1,Length[allconds2]}];
In[]:=
res=Plus@@terms-1/((1-x0)(1-x1)(1-x2)(1-x3)(1-x4)(1-x5)(1-x6));
In[]:=
res/.Thread[{x0,x1,x2,x3,x4,x5,x6}->Table[1/Prime[i],{i,1,7}]]
Out[]=
0