u[n_,ep_]:=If[n==0,0,If[n==1,1,u[n-1,ep]+(ep-2)*u[n,ep]]];

u[1,1]

Length[K8]

uk8[n_,ep_]:=u[n,ep]/(Sum[u[k,ep]^2,{k,1,128}]);

uk8[1,1]

Plot[u[128,K8[[ep]]],{ep,1,128}]

ufin:={};

For[k=1,k<129,k++,AppendTo[ufin,u[128,K8[[k]]]]];

RSolve[{v[n+1]==-v[n-1]+(2-1)*v[n],v[0]==0,v[1]==1},v[n],n]

RSolve[{v[n+1]==-v[n-1]+(2-ep)*v[n],v[0]==0,v[1]==1},v[n],n]

vep[n_,ep_]:=-N[(((2^(-n)) ((((2-(Sqrt[-4+ep]) (Sqrt[ep])-ep))^n)-(((2+(Sqrt[-4+ep]) (Sqrt[ep])-ep))^n)))/((Sqrt[-4+ep]) (Sqrt[ep])))];

norms:={};

For[k=2,k<129,k++,AppendTo[norms,{Sum[vep[n,K8[[k]]]^2,{n,1,128}]}]];

Length[norms]

vepnorm[n_,ep_]:=If[ep==1,1,vep[n,K8[[ep]]]/norms[[ep-1]][[1]]];

Plot[Abs[vepnorm[n,6]],{n,1,128}]

psi[k_,t_]:=Sum[k^(-2)*vepnorm[k,ep]*Exp[-I*K8[[ep]]*t],{ep,1,128}];

Deltav2[t_]:=Sum[n^2*Abs[psi[n,t]]^2,{n,1,128}];

Deltav2[1]

vepnorm[1,3]

psi[1,1]

norms[[2]][[1]]

Plot[Sqrt[Deltav2[t]],{t,1,100}]

pow[ep_,k_]:=ep^k;

Array[pow,{2,2}]

p = Array[pow,{2,2}]

p[[2,2]]

Length[K8]

K7 = cantor[7];

Length[K7]

64

pow2[k_,ep_]:=If[k==1,1,N[K7[[ep]]^(k-1)]];

mat7:=Array[pow2,{64,64}];

inv7 = Inverse[mat7];

inv7.mat7

t = {{1,2},{3,4}}

t.t

K6 = cantor[6];

Length[K6]

pow6[k_,ep_]:=If[k==1,1,N[K6[[ep]]^(k-1)]];

mat6 = Array[pow6,{32,32}];

inv6 = Inverse[mat6];

Length[K5]

pow5[k_,ep_]:=If[k==1,1,N[K5[[ep]]^(k-1)]];

Length[K7]

64
hkth:={};

hkthv13[4,7]

deltath[t_]:=Sum[n^2*Sum[Sum[coefd[[j,n]]*coefd[[jj,n]]*hkthv13[j,t]*Conjugate[hkthv13[jj,t]],{jj,1,64}],{j,1,64}],{n,1,65}];

deltath[2]

hkth[[1,1]]:=3;

hkth

deltathv2[t_]:=Sum[n^2*Abs[Sum[coefd[[j,n]]*t^(-j-a)*Sum[N[t^(-2*I*Pi*m/Log[3])]*rm[m]*Gamma[j+a+2*I*Pi*m/Log[3]]*Exp[0.5*I*Pi*(j+a+2*I*Pi*m/Log[3])],{m,-40,-34}],{j,1,n}]]^2,{n,1,10}];

Plot[Sqrt[deltathv2[t]],{t,1,10}]

deltav2:={};

For[l=1,l<100,l++,AppendTo[deltav2,deltathv2[l/10]]];

deltav2[[3]]

ListLinePlot[deltav3]

test:={1,2,3,4};

deltav2

deltav4:={};

For[ll=1,ll<1000,ll++,AppendTo[deltav4,deltathv2[150+ll/10]]];

ListLinePlot[deltav5]

deltav4

deltav5:=10^(-610)*deltav4;

deltav6:={};

For[m=1,m<1000,m++,AppendTo[deltav6,deltathv2[150+m/10]]];

deltav7:=10^(-610)*deltav6;

ListLinePlot[deltav7]

deltav8:={};

For[mm=1,mm<1000,mm++,AppendTo[deltav8,deltathv2[150+mm/10]]];

ListLinePlot[deltav8]

ListLogLogPlot[deltav8]

For[h=1,h<1000,h++,AppendTo[deltav8,deltathv2[250+h/10]]];

ListLinePlot[deltav8]

ListLinePlot[Sqrt[deltav8]]

ListLogLogPlot[Sqrt[deltav8]]

tsc:={};

For[b=1,b<2001,b++,AppendTo[tsc,150+b/10]];

Length[tsc2]

Length[deltav8]

tsc2:={};

For[bb=1,bb<1999,bb++,AppendTo[tsc2,150+bb/10]];

ListLinePlot[tsc2,deltav8]

dv10:={};

For[bwbbb=1,bwbbb<1999,bwbbb++,AppendTo[dv10,{tsc2[[bwbbb]],Sqrt[deltav8[[bwbbb]]]}]];

ListPlot[dv10]

ListLogLogPlot[dv10]

deltathv2[t_]:=Sum[n^2*Abs[Sum[coefd[[j,n]]*t^(-j-a)*Sum[N[t^(-2*I*Pi*m/Log[3])]*rm[m]*Gamma[j+a+2*I*Pi*m/Log[3]]*Exp[0.5*I*Pi*(j+a+2*I*Pi*m/Log[3])],{m,-40,-34}],{j,1,n}]]^2,{n,1,10}];

Det[mat6]

test2:={{1,2},{3,4}}

test2

Cofactor[test2,{1,1}]

Needs["Combinatorica`"]

coefc:={};

Cofactor[mat6,{1,1}]

d6:=Det[mat6]

d6

For[z=1,z<65,z++,AppendTo[coefc,d6^(-1)*Sum[Cofactor[mat6,{r,z}]*2^(r-1),{r,1,64}]]];

Length[coefc]

coefc

Export["coefc.txt",coefc]

N[Sum[N[Cofactor[mat6,{r,2}]*2^(r-1)],{r,1,64}]]

cof := {};
For[r1=1,r1<65,r1++,For[rr1=1,rr1<65,rr1++,AppendTo[cof,Cofactor[mat6,{r1,rr1}]]]];

coefcv2:={};

cof[[1]]

cof

Cofactor[mat6,{14,1}]

te3:={1,2};

te4:={3,4};

t5={te3,te4}

t5[[2,2]]

c1:={};

c2:={};c3:={};

c4:={};c5:={};c6:={};c7:={};c8:={};c9:={};c10:={};c11:={};c12:={};c13:={};c14:={};c15:={};c16:={};c17:={};c18:={};c19:={};c20:={};c21:={};c22:={};c23:={};c24:={};c25:={};c26:={};c27:={};c28:={};c29:={};c30:={};c31:={};c32:={};c33:={};c34:={};c35:={};c36:={};c37:={};c38:={};c39:={};c40:={};c41:={};c42:={};c43:={};c44:={};c45:={};c46:={};c47:={};c48:={};c49:={};c50:={};c51:={};c52:={};c53:={};c54:={};c55:={};c56:={};c57:={};c58:={};c59:={};c60:={};c61:={};c62:={};c63:={};c64:={};

For[k1=1,k1<65,k1++,AppendTo[c1,Cofactor[mat6,{k1,1}]]];

For[k2=1,k2<65,k2++,AppendTo[c2,Cofactor[mat6,{k2,2}]]];

For[k3=1,k3<65,k3++,AppendTo[c3,Cofactor[mat6,{k3,3}]]];For[k4=1,k4<65,k4++,AppendTo[c4,Cofactor[mat6,{k4,4}]]];For[k5=1,k5<65,k5++,AppendTo[c5,Cofactor[mat6,{k5,5}]]];For[k6=1,k6<65,k6++,AppendTo[c6,Cofactor[mat6,{k6,6}]]];For[k7=1,k7<65,k7++,AppendTo[c7,Cofactor[mat6,{k7,7}]]];For[k8=1,k8<65,k8++,AppendTo[c8,Cofactor[mat6,{k8,8}]]];For[k9=1,k9<65,k9++,AppendTo[c9,Cofactor[mat6,{k9,9}]]];For[k10=1,k10<65,k10++,AppendTo[c10,Cofactor[mat6,{k10,10}]]];For[k11=1,k11<65,k11++,AppendTo[c11,Cofactor[mat6,{k11,11}]]];For[k12=1,k12<65,k12++,AppendTo[c12,Cofactor[mat6,{k12,12}]]];For[k13=1,k13<65,k13++,AppendTo[c13,Cofactor[mat6,{k13,13}]]];For[k14=1,k14<65,k14++,AppendTo[c14,Cofactor[mat6,{k14,14}]]];For[k15=1,k15<65,k15++,AppendTo[c15,Cofactor[mat6,{k15,15}]]];For[k16=1,k16<65,k16++,AppendTo[c16,Cofactor[mat6,{k16,16}]]];For[k17=1,k17<65,k17++,AppendTo[c17,Cofactor[mat6,{k17,17}]]];For[k18=1,k18<65,k18++,AppendTo[c18,Cofactor[mat6,{k18,18}]]];For[k19=1,k19<65,k19++,AppendTo[c19,Cofactor[mat6,{k19,19}]]];For[k20=1,k20<65,k20++,AppendTo[c20,Cofactor[mat6,{k20,20}]]];For[k21=1,k21<65,k21++,AppendTo[c21,Cofactor[mat6,{k21,21}]]];For[k22=1,k22<65,k22++,AppendTo[c22,Cofactor[mat6,{k22,22}]]];For[k23=1,k23<65,k23++,AppendTo[c23,Cofactor[mat6,{k23,23}]]];For[k24=1,k24<65,k24++,AppendTo[c24,Cofactor[mat6,{k24,24}]]];For[k25=1,k25<65,k25++,AppendTo[c25,Cofactor[mat6,{k25,25}]]];For[k26=1,k26<65,k26++,AppendTo[c26,Cofactor[mat6,{k26,26}]]];For[k27=1,k27<65,k27++,AppendTo[c27,Cofactor[mat6,{k27,27}]]];For[k28=1,k28<65,k28++,AppendTo[c28,Cofactor[mat6,{k28,28}]]];For[k29=1,k29<65,k29++,AppendTo[c29,Cofactor[mat6,{k29,29}]]];For[k30=1,k30<65,k30++,AppendTo[c30,Cofactor[mat6,{k30,30}]]];

For[k31=1,k31<65,k31++,AppendTo[c31,Cofactor[mat6,{k31,31}]]];For[k32=1,k32<65,k32++,AppendTo[c32,Cofactor[mat6,{k32,32}]]];For[k33=1,k33<65,k33++,AppendTo[c33,Cofactor[mat6,{k33,33}]]];For[k34=1,k34<65,k34++,AppendTo[c34,Cofactor[mat6,{k34,34}]]];For[k35=1,k35<65,k35++,AppendTo[c35,Cofactor[mat6,{k35,35}]]];For[k36=1,k36<65,k36++,AppendTo[c36,Cofactor[mat6,{k36,36}]]];For[k37=1,k37<65,k37++,AppendTo[c37,Cofactor[mat6,{k37,37}]]];For[k38=1,k38<65,k38++,AppendTo[c38,Cofactor[mat6,{k38,38}]]];For[k39=1,k39<65,k39++,AppendTo[c39,Cofactor[mat6,{k39,39}]]];For[k40=1,k40<65,k40++,AppendTo[c40,Cofactor[mat6,{k40,40}]]];For[k41=1,k41<65,k41++,AppendTo[c41,Cofactor[mat6,{k41,41}]]];For[k42=1,k42<65,k42++,AppendTo[c42,Cofactor[mat6,{k42,42}]]];For[k43=1,k43<65,k43++,AppendTo[c43,Cofactor[mat6,{k43,43}]]];For[k44=1,k44<65,k44++,AppendTo[c44,Cofactor[mat6,{k44,44}]]];For[k45=1,k45<65,k45++,AppendTo[c45,Cofactor[mat6,{k45,45}]]];For[k46=1,k46<65,k46++,AppendTo[c46,Cofactor[mat6,{k46,46}]]];For[k47=1,k47<65,k47++,AppendTo[c47,Cofactor[mat6,{k47,47}]]];For[k48=1,k48<65,k48++,AppendTo[c48,Cofactor[mat6,{k48,48}]]];For[k49=1,k49<65,k49++,AppendTo[c49,Cofactor[mat6,{k49,49}]]];For[k50=1,k50<65,k50++,AppendTo[c50,Cofactor[mat6,{k50,50}]]];For[k51=1,k51<65,k51++,AppendTo[c51,Cofactor[mat6,{k51,51}]]];For[k52=1,k52<65,k52++,AppendTo[c52,Cofactor[mat6,{k52,52}]]];For[k53=1,k53<65,k53++,AppendTo[c53,Cofactor[mat6,{k53,53}]]];For[k54=1,k54<65,k54++,AppendTo[c54,Cofactor[mat6,{k54,54}]]];For[k55=1,k55<65,k55++,AppendTo[c55,Cofactor[mat6,{k55,55}]]];For[k56=1,k56<65,k56++,AppendTo[c56,Cofactor[mat6,{k56,56}]]];For[k57=1,k57<65,k57++,AppendTo[c57,Cofactor[mat6,{k57,57}]]];For[k58=1,k58<65,k58++,AppendTo[c58,Cofactor[mat6,{k58,58}]]];For[k59=1,k59<65,k59++,AppendTo[c59,Cofactor[mat6,{k59,59}]]];For[k60=1,k60<65,k60++,AppendTo[c60,Cofactor[mat6,{k60,60}]]];For[k61=1,k61<65,k61++,AppendTo[c61,Cofactor[mat6,{k61,61}]]];For[k62=1,k62<65,k62++,AppendTo[c62,Cofactor[mat6,{k62,62}]]];For[k63=1,k63<65,k63++,AppendTo[c63,Cofactor[mat6,{k63,63}]]];For[k64=1,k64<65,k64++,AppendTo[c64,Cofactor[mat6,{k64,64}]]];

coefc1b:=N[Sum[N[c1b[[w1]]]*2^(w1-1),{w1,1,64}]]

N[coefc1]

d6

2^63

ListPlot[c1b]

Length[c1b]

coefc3:=Sum[N[c1b[[w1]]]*2^(w1-1),{w1,1,32}]

coefc3

coe1:=Sum[N[c1[[w1]]]*2^(w1-1)/d6,{w1,1,32}]

coe1

coe2:=Sum[N[c2[[w1]]]*2^(w1-1)/d6,{w1,1,32}];
coe3:=Sum[N[c3[[w1]]]*2^(w1-1)/d6,{w1,1,32}];
coe4:=Sum[N[c4[[w1]]]*2^(w1-1)/d6,{w1,1,32}];
coe5:=Sum[N[c5[[w1]]]*2^(w1-1)/d6,{w1,1,32}];

coe6:=Sum[N[c6[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe7:=Sum[N[c7[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe8:=Sum[N[c8[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe9:=Sum[N[c9[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe10:=Sum[N[c10[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe11:=Sum[N[c11[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe12:=Sum[N[c12[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe13:=Sum[N[c13[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe14:=Sum[N[c14[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe15:=Sum[N[c15[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe16:=Sum[N[c16[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe17:=Sum[N[c17[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe18:=Sum[N[c18[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe19:=Sum[N[c19[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe20:=Sum[N[c20[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe21:=Sum[N[c21[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe22:=Sum[N[c22[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe23:=Sum[N[c23[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe24:=Sum[N[c24[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe25:=Sum[N[c25[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe26:=Sum[N[c26[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe27:=Sum[N[c27[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe28:=Sum[N[c28[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe29:=Sum[N[c29[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe30:=Sum[N[c30[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe31:=Sum[N[c31[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe32:=Sum[N[c32[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe33:=Sum[N[c33[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe34:=Sum[N[c34[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe35:=Sum[N[c35[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe36:=Sum[N[c36[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe37:=Sum[N[c37[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe38:=Sum[N[c38[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe39:=Sum[N[c39[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe40:=Sum[N[c40[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe41:=Sum[N[c41[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe42:=Sum[N[c42[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe43:=Sum[N[c43[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe44:=Sum[N[c44[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe45:=Sum[N[c45[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe46:=Sum[N[c46[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe47:=Sum[N[c47[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe48:=Sum[N[c48[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe49:=Sum[N[c49[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe50:=Sum[N[c50[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe51:=Sum[N[c51[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe52:=Sum[N[c52[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe53:=Sum[N[c53[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe54:=Sum[N[c54[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe55:=Sum[N[c55[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe56:=Sum[N[c56[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe57:=Sum[N[c57[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe58:=Sum[N[c58[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe59:=Sum[N[c59[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe60:=Sum[N[c60[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe61:=Sum[N[c61[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe62:=Sum[N[c62[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe63:=Sum[N[c63[[w1]]]*2^(w1-1)/d6,{w1,1,32}];coe64:=Sum[N[c64[[w1]]]*2^(w1-1)/d6,{w1,1,32}];

coe33

coe1

coelist:={};

coelist

coelist[[11]]

Length[coelist]

Export["coelist.txt",coelist]

Length[mat6]

tets:={2,3,4}

Delete[tets,2]

tets

tets3=Delete[tets,{{1},{2}}]

tets2

coelist2=Delete[coelist,{{33},{34},{35},{36},{37},{38},{39}}];

deltathv3[t_]:=Sum[n^2*Abs[Sum[coefd[[j,n]]*t^(-j-a)*Sum[N[t^(-2*I*Pi*m/Log[3])]*rm[m]*Gamma[j+a+2*I*Pi*m/Log[3]]*Exp[0.5*I*Pi*(j+a+2*I*Pi*m/Log[3])],{m,-40,-20}],{j,1,n}]]^2,{n,1,10}];

deltav9:={};

For[h4=1,h4<1000,h4++,AppendTo[deltav9,deltathv3[150+h4/10]]];

ListPlot[Sqrt[deltav9]]

ListLogLogPlot[Sqrt[deltav9]]