Complete details for Section 12.3 
based on Sections 14.1 and 14.2  
(with m = 2 and n = 2)

Input from Section 14.1

$Version

m=2;

u[s_,p1_,p2_,r_]:=Floor[(1/(p1+p2+r))*(s-Sum[(p1+p2+k)*e[s,p1,p2,k],{k,r+1,s-p1-p2}]-Sum[(p1+i2+k)*e[s,p1,i2,k],{i2,p2+1,m},{k,0,s-p1-i2}]-Sum[(i1+i2+k)*e[s,i1,i2,k],{i1,p1+1,m},{i2,i1,m},{k,0,s-i1-i2}])]

nM[s_]:=Module[{counter,seq},counter=0;
seq=Apply[Sequence,Reverse[Flatten[Table[{e[s,i1,i2,k],0,u[s,i1,i2,k]},{i1,0,m},{i2,Max[1,i1],m},{k,0,s-i1-i2}],2]]];
Do[If[(Sum[(i1+i2+k)*e[s,i1,i2,k],{i1,0,m},{i2,Max[1,i1],m},{k,0,s-i1-i2}])==s,(counter=counter+1;monM[s,counter]=Product[D[w[i1,i2][z],{z,k}]^e[s,i1,i2,k],{i1,0,m},{i2,Max[1,i1],m},{k,0,s-i1-i2}]),counter=counter],Evaluate[seq]];counter]

printM[s_]:=Do[Print["monM[",s,",",j,"] = ",monM[s,j]],{j,1,nM[s]}]

wPolynomial[s_]:=Sum[x[s,j]*monM[s,j],{j,1,nM[s]}]

sub[s_]:=Flatten[Table[D[w[i1,i2][z],{z,k}]->D[c[i1,i2][z],{z,k}],{i1,0,m},{i2,Max[1,i1],m},{k,0,s-i1-i2}]]

cPoly[s_]:=wPolynomial[s]/.sub[s]

c[0,0][z_]=1;

c[i1_,i2_][z_]:=Apply[c,Sort[{i1,i2}]][z]/;{i1,i2}≠Sort[{i1,i2}]

cOneStar[i1_,i2_][z_]:=Sum[Binomial[m-j1,i1-j1]*Binomial[m-j2,i2-j2]*(D[rho[z],{z,i1-j1}]/rho[z])*(D[rho[z],{z,i2-j2}]/rho[z])*c[j1,j2][z],{j1,0,i1},{j2,0,i2}]

sub1[s_]:=Flatten[Table[D[w[i1,i2][z],{z,k}]->D[cOneStar[i1,i2][z],{z,k}],{i1,0,m},{i2,Max[1,i1],m},{k,0,s-i1-i2}]]

cOneStarPoly[s_]:=wPolynomial[s]/.sub1[s]

alpha[0,j_][zet_]=1;

alpha[i_,j_][zet_]:=Sum[D[alpha[i-1,k][zet],zet]-(i-1+k)(f''[zet]/f'[zet])alpha[i-1,k][zet],{k,1,j}]/;i≥1

cTwoStar[i1_,i2_][zet_]:=Sum[f'[zet]^(j1+j2)*alpha[i1-j1,m-i1][zet]*alpha[i2-j2,m-i2][zet]*c[j1,j2][f[zet]],{j1,0,i1},{j2,0,i2}]

sub2[s_]:=Flatten[Table[D[w[i1,i2][z],{z,k}]->D[cTwoStar[i1,i2][zet],{zet,k}],{i1,0,m},{i2,Max[1,i1],m},{k,0,s-i1-i2}]]

cTwoStarPoly[s_]:=wPolynomial[s]/.sub2[s]

firstCondition[s_]:=firstCondition[s]=Expand[rho[z]^s*(cOneStarPoly[s]-cPoly[s])]

secondCondition[s_]:=secondCondition[s]=Expand[f'[zet]^s*(cTwoStarPoly[s]-f'[zet]^s*(cPoly[s]/.z->f[zet]))]

v[s_,p1_]:=Floor[(1/p1)*(s-Sum[(i1+i2+k)*e[s,i1,i2,k],{i1,0,m},{i2,Max[1,i1],m},{k,0,s-i1-i2}]-Sum[t*h[s,t],{t,p1+1,s}])]

nA[s_]:=Module[{counter,seq1,seq2},counter=0;
seq1=Apply[Sequence,Reverse[Flatten[Table[{e[s,i1,i2,k],0,u[s,i1,i2,k]},{i1,0,m},{i2,Max[1,i1],m},{k,0,s-i1-i2}],2]]];
seq2=Apply[Sequence,Reverse[Table[{h[s,t],0,v[s,t]},{t,1,s}]]];
Do[If[(Sum[(i1+i2+k)*e[s,i1,i2,k],{i1,0,m},{i2,Max[1,i1],m},{k,0,s-i1-i2}]+Sum[t*h[s,t],{t,1,s}])==s,(counter=counter+1;
monA[s,counter]=Product[D[c[i1,i2][z],{z,k}]^e[s,i1,i2,k],{i1,0,m},{i2,Max[1,i1],m},{k,0,s-i1-i2}]*rho[z]^(s-Sum[h[s,t],{t,1,s}])*Product[D[rho[z],{z,t}]^h[s,t],{t,1,s}]),counter=counter],Evaluate[seq1],Evaluate[seq2]];counter]

printA[s_]:=Do[Print["monA[",s,", ",j,"] = ",monA[s,j]],{j,1,nA[s]}]

nB[s_]:=Module[{counter,seq1,seq2},counter=0;
seq1=Apply[Sequence,Reverse[Flatten[Table[{e[s,i1,i2,k],0,u[s,i1,i2,k]},{i1,0,m},{i2,Max[1,i1],m},{k,0,s-i1-i2}],2]]];
seq2=Apply[Sequence,Reverse[Table[{h[s,t],0,v[s,t]},{t,1,s}]]];
Do[If[(Sum[(i1+i2+k)*e[s,i1,i2,k],{i1,0,m},{i2,Max[1,i1],m},{k,0,s-i1-i2}]+Sum[t*h[s,t],{t,1,s}])==s,(counter=counter+1;
monB[s,counter]=Product[(D[c[i1,i2][z],{z,k}]/.z->f[zet])^e[s,i1,i2,k],{i1,0,m},{i2,Max[1,i1],m},{k,0,s-i1-i2}]*f'[zet]^(2s-Sum[(t+1)*h[s,t],{t,1,s}])*Product[D[f[zet],{zet,t+1}]^h[s,t],{t,1,s}]),counter=counter],Evaluate[seq1],Evaluate[seq2]];counter]

printB[s_]:=Do[Print["monB[",s,", ",j,"] = ",monB[s,j]],{j,1,nB[s]}]

firstCoefficients[s_]:=Do[a[s,i]=Coefficient[firstCondition[s],monA[s,i]],{i,1,nA[s]}]

firstZeroCheck[s_]:=Expand[firstCondition[s]-Sum[a[s,i]*monA[s,i],{i,1,nA[s]}]]

secondCoefficients[s_]:=Do[b[s,j]=Coefficient[secondCondition[s],monB[s,j]],{j,1,nB[s]}]

secondZeroCheck[s_]:=Expand[secondCondition[s]-Sum[b[s,j]*monB[s,j],{j,1,nB[s]}]]

eqs[s_]:=Join[Table[a[s,i]==0,{i,1,nA[s]}],Table[b[s,j]==0,{j,1,nB[s]}]]

rules[s_]:=If[TrueQ[$VersionNumber<7.5],Flatten[Solve[eqs[s],Table[x[s,j],{j,1,nM[s]}]]],Flatten[Solve[eqs[s],Table[x[s,nM[s]+1-j],{j,1,nM[s]}]]]]

invariants[s_]:=Module[{expansion,counter},counter=0;
Print["   "];
Print["   Computation of invariants[",s,"]"];
Print["Number of Monic Monomials = ",nM[s]];
Print["Number of firstCondition Terms = ",nA[s]];
Print["Number of secondCondition Terms = ",nB[s]];
firstCondition[s];firstCoefficients[s];
Print["firstZeroCheck[",s,"] = ",firstZeroCheck[s]];
secondCondition[s];secondCoefficients[s];
Print["secondZeroCheck[",s,"] = ",secondZeroCheck[s]];
expansion=Expand[(Sum[x[s,j]*monM[s,j],{j,1,nM[s]}])/.rules[s]];
Do[If[Length[Coefficient[expansion,x[s,j]]]≠0,(counter=counter+1;
inv[s,counter]=Coefficient[expansion,x[s,j]];
Print["inv[",s,", ",counter,"] = ",inv[s,counter]]),counter=counter],{j,1,nM[s]}];
d[s]=counter;
Print["The vector space for weight ",s," has dimension d[",s,"] = ",d[s],"."]]

Input from Section 14.2

aFirstKind[m_,2][z_]:=(1/Binomial[m+1,3])(w[0,2][z]-((m-1)/2)D[w[0,1][z],z]-((m-1)/(2m))w[0,1][z]^2)

B[h_,i_,j_][z_]:=0/;i≤-1

B[h_,0,j_][z_]:=1

B[h_,i_,j_][z_]:=Sum[D[B[h,i-1,k][z],z]-k(2h+k-1)aFirstKind[m,2][z]*B[h,i-2,k-1][z],{k,i-1,j-1}]/;i≥1

Ce[p_,q_,r_,mu_]:=(-1)^mu*Binomial[r,mu]*Binomial[2q+r-1,mu]/Binomial[2p+mu-1,mu]

A[p_,q_,r_,s_,t_][z_]:=Sum[Ce[p,q,r,t+k]*B[p,k,t+k][z]*B[q,s-k,r-t-k][z],{k,0,s}]

weight[iso_]:=Module[{h,seq,t1,t2,t3,t4,t5,t6,t7},t1=Expand[iso];
t2=If[Head[t1]===Plus,w[0,0][z]*t1[[1]],Expand[w[0,0][z]*t1]];
t3=Apply[List,t2];
seq={w[i1_,i2_][z]->h[i1,i2,0,1],Power[w[i1_,i2_][z],k_]->h[i1,i2,0,k],Derivative[j_][w[i1_,i2_]][z]->h[i1,i2,j,1],Power[Derivative[j_][w[i1_,i2_]][z],k_]->h[i1,i2,j,k]};t4=t3/.seq;
t5=Cases[t4,h[i1_,i2_,j_,k_]];
t6=t5/.h[i1_,i2_,j_,k_]->(i1+i2+j)k;
t7=Apply[Plus,t6]]

Com[r_,P_,Q_]:=Module[{p,q},p=weight[P];q=weight[Q];
Sum[A[p,q,r,s,t][z]*D[P,{z,t}]*D[Q,{z,r-s-t}],{s,0,r},{t,0,r-s}]]

Verification for Section 12.3
(where m = 2 and n = 2)

$Version

Do[invariants[s],{s,2,5}]

f[2,1]=inv[2,1];

f[3,1]=inv[3,1];

f[4,1]=f[2,1]^2;

f[4,2]=inv[4,2];

f[5,1]=f[2,1]*f[3,1];

Expand[ inv[5,1] - f[5,1] ]

invariants[6]

f[6,1]=f[2,1]^3;

f[6,2]=f[3,1]^2;

f[6,3]=f[2,1]*f[4,2];

f[6,4]=Com[1,f[2,1],f[3,1]];

f[6,5]=Com[2,f[2,1],f[2,1]];

Do[expr[6,i]=(inv[6,i]-Sum[c[6,i,j]*f[6,j],{j,1,d[6]}]),{i,1,d[6]}]

nM[6]

So that the later computations are not too complicated, we shall use 76 in place of  nM[s]  for  s  greater than 6.

Do[y[6,i,k]=Coefficient[expr[6,i],monM[6,k]],{k,1,76},{i,1,d[6]}]

sol[6,i_]:=Solve[Table[y[6,i,k]==0,{k,1,76}],Table[c[6,i,j],{j,1,d[6]}]]

sol[6,1]

Expand[ inv[6,1] - f[6,1] ]

sol[6,2]

Expand[ inv[6,2] - (1/2)f[6,5] ]

sol[6,3]

Expand[ inv[6,3] - f[6,2] ]

sol[6,4]

Expand[ inv[6,4] - (f[6,4] + (1/8)f[6,5]) ]

sol[6,5]

Expand[ inv[6,5] - (f[6,3] + (1/3)f[6,4] + (1/40)f[6,5]) ]

invariants[7]

f[7,1] = f[2,1]^2*f[3,1];

f[7,2] = f[3,1]*f[4,2];

f[7,3] = Com[1, f[2,1], f[4,2]];

f[7,4] = Com[2,f[2,1], f[3,1]];

Do[expr[7,i]=(inv[7,i]-Sum[c[7,i,j]*f[7,j],{j,1,d[7]}]),{i,1,d[7]}]

Do[y[7,i,k]=Coefficient[expr[7,i],monM[7,k]],{k,1,76},{i,1,d[7]}]

sol[7,i_]:=Solve[Table[y[7,i,k]==0,{k,1,76}],Table[c[7,i,j],{j,1,d[7]}]]

sol[7,1]

Expand[ inv[7,1] - f[7,1] ]

sol[7,2]

Expand[ inv[7,2] - f[7,4] ]

sol[7,3]

Expand[ inv[7,3] - f[7,2] ]

sol[7,4]

Expand[ inv[7,4] - (f[7,3] + (1/3)f[7,4]) ]

invariants[8]

f[8,1] = f[2,1]^4;

f[8,2] = f[2,1]*f[3,1]^2;

f[8,3] = f[2,1]^2*f[4,2];

f[8,4] = f[4,2]^2;

f[8,5] = f[2,1]*Com[1, f[2,1], f[3,1]];

f[8,6] = f[2,1]*Com[2,f[2,1], f[2,1]];

f[8,7] = Com[1, f[3,1], f[4,2]];

f[8,8] = Com[2, f[3,1], f[3,1]];

f[8,9] = Com[2, f[2,1], f[4,2]];

f[8,10] = Com[3, f[2,1], f[3,1]];

f[8,11] = Com[4, f[2,1], f[2,1]];

Do[expr[8,i]=(inv[8,i]-Sum[c[8,i,j]*f[8,j],{j,1,d[8]}]),{i,1,d[8]}]

Do[y[8,i,k]=Coefficient[expr[8,i],monM[8,k]],{k,1,100},{i,1,d[8]}]

sol[8,i_]:=Solve[Table[y[8,i,k]==0,{k,1,100}],Table[c[8,i,j],{j,1,d[8]}]]

sol[8,1]

Expand[ inv[8,1] - f[8,1]  ]

sol[8,2]

Expand[ inv[8,2] - (1/2)f[8,6] ]

sol[8,3]

Expand[ inv[8,3] - (1/2)f[8,11] ]

sol[8,4]

Expand[ inv[8,4] - f[8,2] ]

sol[8,5]

Expand[ inv[8,5] - (f[8,5]+(1/8)f[8,6]) ]

sol[8,6]

Expand[ inv[8,6] - (1/2)f[8,8] ]

sol[8,7]

Expand[ inv[8,7] - (f[8,10] + (1/8)f[8,11]) ]

sol[8,8]

Expand[ inv[8,8] - (f[8,3] +(1/3)f[8,5] + (1/40)f[8,6]) ]

sol[8,9]

Expand[ inv[8,9] - f[8,4] ]

sol[8,10]

Expand[ inv[8,10] - (f[8,7] + (1/6)f[8,8]) ]

sol[8,11]

Expand[ inv[8,11] - (f[8,9] + (1/3)f[8,10] + (1/40)f[8,11]) ]

invariants[9]

f[9,1] = f[2,1]^3*f[3,1];

f[9,2] = f[3,1]^3;

f[9,3] = f[2,1]*f[3,1]*f[4,2];

f[9,4] = f[3,1]*Com[1, f[2,1], f[3,1]];

f[9,5] = f[3,1]*Com[2, f[2,1], f[2,1]];

f[9,6] = f[2,1]*Com[1, f[2,1], f[4,2]];

f[9,7] = f[2,1]*Com[2, f[2,1], f[3,1]];

f[9,8] = Com[2, f[3,1], f[4,2]];

f[9,9] = Com[3, f[2,1], f[2,1]^2];

f[9,10] = Com[3,f[2,1], f[4,2]];

f[9,11] = Com[4, f[2,1], f[3,1]];

Do[expr[9,i]=(inv[9,i]-Sum[c[9,i,j]*f[9,j],{j,1,d[9]}]),{i,1,d[9]}]

Do[y[9,i,k]=Coefficient[expr[9,i],monM[9,k]],{k,1,150},{i,1,d[9]}]

sol[9,i_]:=Solve[Table[y[9,i,k]==0,{k,1,150}],Table[c[9,i,j],{j,1,d[9]}]]

sol[9,1]

Expand[ inv[9,1] - (-1/4)f[9,9] ]

sol[9,2]

Expand[ inv[9,2] - f[9,1] ]

sol[9,3]

Expand[ inv[9,3] - (1/2)f[9,5] ]

sol[9,4]

Expand[ inv[9,4] - f[9,2] ]

sol[9,5]

Expand[ inv[9,5] - (f[9,4] + (1/8)f[9,5]) ]

sol[9,6]

Expand[ inv[9,6] - ( (-21/20)f[9,5] + f[9,7] + (-1/16)f[9,9]) ]

sol[9,7]

Expand[ inv[9,7] - f[9,11] ]

sol[9,8]

Expand[ inv[9,8] - (f[9,3] + (1/3)f[9,4] + (1/40)f[9,5]) ]

sol[9,9]

Expand[ inv[9,9] - ( (-7/20)f[9,5] + f[9,6] + (1/3)f[9,7] + (-1/80)f[9,9]) ]

sol[9,10]

Expand[ inv[9,10] - f[9,8] ]

sol[9,11]

Expand[ inv[9,11] - (f[9,10] + (1/3)f[9,11]) ]

invariants[10]

f[10,1] = f[2,1]^5;

f[10,2] = f[2,1]^2*f[3,1]^2;

f[10,3] = f[2,1]^3*f[4,2];

f[10,4] = f[2,1]*f[4,2]^2;

f[10,3] = f[2,1]^3*f[4,2];

f[10,4] = f[2,1]*f[4,2]^2;

f[10,5] = f[3,1]^2*f[4,2];

f[10,6] = f[2,1]^2*Com[1, f[2,1], f[3,1]];

f[10,7] = f[2,1]^2*Com[2, f[2,1], f[2,1]];

f[10,8] = f[2,1]*Com[1, f[3,1], f[4,2]];

f[10,9] = f[2,1]*Com[2, f[3,1], f[3,1]];

f[10,10] = f[2,1]*Com[2, f[2,1], f[4,2]];

f[10,11] = f[2,1]*Com[3, f[2,1], f[3,1]];

f[10,12] = f[2,1]*Com[4, f[2,1], f[2,1]];

f[10,13] = f[3,1]*Com[1, f[2,1], f[4,2]];

f[10,14] = f[3,1]*Com[2, f[2,1], f[3,1]];

f[10,15] = f[4,2]*Com[2, f[2,1], f[2,1]];

f[10,16] = Com[3, f[2,1], f[2,1]*f[3,1]];

f[10,17] = Com[2, f[4,2], f[4,2]];

f[10,18] = Com[3, f[3,1], f[4,2]];

f[10,19] = Com[4, f[2,1], f[4,2]];

f[10,20] = Com[4, f[3,1], f[3,1]];

f[10,21] = Com[5, f[2,1], f[3,1]];

f[10,22] = Com[6, f[2,1], f[2,1]];

Do[expr[10,i]=(inv[10,i]-Sum[c[10,i,j]*f[10,j],{j,1,d[10]}]),{i,1,d[10]}]

Do[y[10,i,k]=Coefficient[expr[10,i],monM[10,k]],{k,1,1001,10},{i,1,d[10]}]

sol[10,i_]:=Solve[Table[y[10,i,k]==0,{k,1,1001,10}],Table[c[10,i,j],{j,1,d[10]}]]

sol[10,1]

Expand[ inv[10,1] - f[10,1] ]

sol[10,2]

Expand[ inv[10,2] - (1/2)f[10,7] ]

sol[10,3]

Expand[ inv[10,3] - (1/2)f[10,12] ]

sol[10,4]

Expand[ inv[10,4] - (1/2)f[10,22] ]

sol[10,5]

Expand[ inv[10,5] - f[10,2] ]

sol[10,6]

Expand[ inv[10,6] - (f[10,6] + (1/8)f[10,7]) ]

sol[10,7]

Expand[ inv[10,7] - ( (-5/72)f[10,11] + (5/72)f[10,16]) ]

sol[10,8]

Expand[ inv[10,8] - ( (-3/7)f[10,9] + (-5/144)f[10,11] + (6/7)f[10,14] + (5/144)f[10,16]) ]

sol[10,9]

Expand[ inv[10,9] - f[10,14] ]

sol[10,10]

Expand[ inv[10,10] - ( (19/12)f[10,11] + (1/8)f[10,12] + (-7/12)f[10,16]) ]

sol[10,11]

Expand[ inv[10,11] - (1/2)f[10,20] ]

sol[10,12]

Expand[ inv[10,12] - ( f[10,21] + (1/8)f[10,22]) ]

sol[10,13]

Expand[ inv[10,13] - (  f[10,3] + (1/3)f[10,6] + (1/40)f[10,7]) ]

sol[10,14]

Expand[ inv[10,14] - ( (-5/216)f[10,11] + (1/2)f[10,15] + (5/216)f[10,16]) ]

sol[10,17]

Expand[ inv[10,17] - (f[10,4]+(-1/2)f[10,8]+(-1/21)f[10,9]+(-1/432)f[10,11]+(1/2)f[10,13]+(2/21)f[10,14]+(1/20)f[10,15]+(1/432)f[10,16]) ]

sol[10,18]

Expand[ inv[10,18] - (f[10,13] + (1/3)f[10,14]) ]

sol[10,19]

Expand[ inv[10,19] - (f[10,10] + (19/36)f[10,11]+(1/40)f[10,12]+(-9/5)f[10,15]+(-7/36)f[10,16]) ]

sol[10,20]

Expand[ inv[10,20] - (1/2)f[10,17] ]

sol[10,21]

Expand[ inv[10,21] - ( f[10,18] + (1/6)f[10,20]) ]

sol[10,22]

Expand[ inv[10,22] - (f[10,19] + (1/3)f[10,21] + (1/40)f[10,22]) ]

invariants[11]

f[11,1] = f[2,1]^4*f[3,1];

f[11,2] = f[2,1]*f[3,1]^3;

f[11,3] = f[2,1]^2*f[3,1]*f[4,2];

f[11,4] = f[3,1]*f[4,2]^2;

f[11,5] = f[2,1]*f[3,1]*Com[1, f[2,1], f[3,1]];

f[11,6] = f[2,1]*f[3,1]*Com[2, f[2,1], f[2,1]];

f[11,7] = f[2,1]^2*Com[1, f[2,1], f[4,2]];

f[11,8] = f[2,1]^2*Com[2, f[2,1], f[3,1]];

f[11,9] = f[2,1]*Com[2, f[3,1], f[4,2]];

f[11,10] = f[2,1]*Com[3, f[2,1], f[2,1]^2];

f[11,11] = f[2,1]*Com[3, f[2,1], f[4,2]];

f[11,12] = f[2,1]*Com[4, f[2,1], f[3,1]];

f[11,13] = f[3,1]*Com[1, f[3,1], f[4,2]];

f[11,14] = f[3,1]*Com[2, f[3,1], f[3,1]];

f[11,15] = f[3,1]*Com[2, f[2,1], f[4,2]];

f[11,16] = f[3,1]*Com[3, f[2,1], f[3,1]];

f[11,17] = f[3,1]*Com[4, f[2,1], f[2,1]];

f[11,18] = f[4,2]*Com[1, f[2,1], f[4,2]];

f[11,19] = f[4,2]*Com[2, f[2,1], f[3,1]];

f[11,20] = Com[6, f[2,1], f[3,1]];

f[11,21] = Com[5, f[2,1], f[4,2]];

f[11,22] = Com[5, f[2,1], f[2,1]^2];

f[11,23] = Com[4, f[3,1], f[4,2]];

f[11,24] = Com[4, f[3,1], f[2,1]^2];

f[11,25] = Com[3, f[3,1], f[2,1]*f[3,1]];

f[11,26] = Com[3, f[4,2], f[2,1]^2];

Do[expr[11,i]=(inv[11,i]-Sum[c[11,i,j]*f[11,j],{j,1,d[11]}]),{i,1,d[11]}]

nM[11]

Do[y[11,i,k]=Coefficient[expr[11,i],monM[11,k]],{k,1,1001=,10},{i,1,d[11]}]

sol[11,i_]:=Solve[Table[y[11,i,k]==0,{k,1,1001,10}],Table[c[11,i,j],{j,1,d[11]}]]

sol[11,1]

Expand[ inv[11,1] - (-1/4)f[11,10] ]

sol[11,2]

Expand[ inv[11,2] - (-7/85)f[11,22] ]

sol[11,3]

Expand[ inv[11,3] - f[11,1] ]

sol[11,4]

Expand[ inv[11,4] - (1/2)f[11,6] ]

sol[11,5]

Expand[ inv[11,5] - (1/2)f[11,17] ]

sol[11,6]

Expand[ inv[11,6] - f[11,2] ]

sol[11,7]

Expand[ inv[11,7] - ( f[11,5]+ (1/8)f[11,6]) ]

sol[11,8]

Expand[ inv[11,8] - ( (-21/20)f[11,6] + f[11,8] + (-1/16)f[11,10]) ]

sol[11,9]

Expand[inv[11,9] - ( (5/48)f[11,12] + (-13/88)f[11,17] + (-7/176)f[11,24]) ]

sol[11,10]

Expand[ inv[11,10] - (1/2)f[11,14] ]

sol[11,11]

Expand[ inv[11,11] - ( (5/192)f[11,12] + (41/48)f[11,16] + (-13/352)f[11,17] + (-7/704)f[11,24] + (7/24)f[11,25] ) ]

sol[11,12]

Expand[ inv[11,12] - (f[11,16] + (1/8)f[11,17] ) ]

sol[11,13]

Expand[ inv[11,13] - ( (-5/4)f[11,12] + (153/110)f[11,17] + (-7/340)f[11,22] + (189/220)f[11,24] ) ]

sol[11,14]

Expand[ inv[11,14] - f[11,20] ]

sol[11,15]

Expand[ inv[11,15] - (  f[11,3] +(1/3)f[11,5] + (1/40)f[11,6] ) ]

sol[11,16]

Expand[ inv[11,16] - ( (1/192)f[11,12] + (41/144)f[11,16] + (-13/1760)f[11,17] + f[11,19]+(-7/3520)f[11,24] + (7/72)f[11,25] ) ]

sol[11,17]

Expand[ inv[11,17] - f[11,4] ]

sol[11,18]

Expand[ inv[11,18] - ( (-7/20)f[11,6] + f[11,7] + (1/3)f[11,8] + (-1/80)f[11,10]) ]

sol[11,19]

Expand[ inv[11,19] - ( (1/6)f[11,11] + (5/144)f[11,12] + (-13/264)f[11,17] + (-7/528)f[11,24] + (1/6)f[11,26] ) ]

sol[11,20]

Expand[ inv[11,20] - ( f[11,13] +(1/6)f[11,14]) ]

sol[11,21]

Expand[ inv[11,21] - ( (-1/3)f[11,9] + (1/24)f[11,11] + (5/576)f[11,12] + (1/3)f[11,15] + (41/144)f[11,16] + (-13/1056)f[11,17] + (4/7)f[11,19] + (-7/2112)f[11,24] + (7/72)f[11,25] + (1/24)f[11,26] ) ]

sol[11,22]

Expand[ inv[11,22] - ( (-1/9)f[11,9] +(1/120)f[11,11] + (1/576)f[11,12] + (1/9)f[11,15] + (41/432)f[11,16] + (-13/5280)f[11,17] + f[11,18] + (11/21)f[11,19]  + (-7/10560)f[11,24] + (7/216)f[11,25] + (1/120)f[11,26] ) ]

sol[11,23]

Expand[ inv[11,23] - ( f[11,15] +(1/3)f[11,16] + (1/40)f[11,17] ) ]

sol[11,24]

Expand[ inv[11,24] - ( (-5/4)f[11,11] + (-5/12)f[11,12] + (51/110)f[11,17] + (-7/1700)f[11,22] + (63/220)f[11,24] + (-9/4)f[11,26] ) ]

sol[11,25]

Expand[ inv[11,25] - f[11,23] ]

sol[11,26]

Expand[ inv[11,26] - ( (1/3)f[11,20] + f[11,21] ) ]

MemoryInUse[]

MaxMemoryUsed[]

DateList[]

invariants[12]

DateList[]

MemoryInUse[]

MaxMemoryUsed[]

f[12,1] = f[2,1]^6;

f[12,2] = f[2,1]^4*f[4,2];

f[12,3] = f[2,1]^3*f[3,1]^2;

f[12,4] = f[2,1]^2*f[4,2]^2;

f[12,5] = f[2,1]*f[3,1]^2*f[4,2];

f[12,6] = f[3,1]^4;

f[12,7] = f[4,2]^3;

f[12,8] = f[2,1]*Com[6, f[2,1], f[2,1]];

f[12,9] = f[2,1]*Com[5, f[2,1], f[3,1]];

f[12,10] = f[2,1]*Com[4, f[2,1], f[4,2]];

f[12,11] = f[2,1]*Com[4, f[3,1], f[3,1]];

f[12,12] = f[2,1]*Com[3, f[3,1], f[4,2]];

f[12,13] = f[2,1]*Com[2, f[4,2], f[4,2]];

f[12,14] = f[2,1]*Com[3, f[2,1], f[2,1]*f[3,1]];

f[12,15] = f[2,1]^2*Com[4, f[2,1], f[2,1]];

f[12,16] = f[2,1]^2*Com[3, f[2,1], f[3,1]];

f[12,17] = f[2,1]^2*Com[2, f[2,1], f[4,2]];

f[12,18] = f[2,1]^2*Com[2, f[3,1], f[3,1]];

f[12,19] = f[2,1]^2*Com[1, f[3,1], f[4,2]];

f[12,20] = f[2,1]*f[3,1]*Com[2, f[2,1], f[3,1]];

f[12,21] = f[2,1]*f[3,1]*Com[1, f[2,1], f[4,2]];

f[12,22] = f[2,1]^3*Com[2, f[2,1], f[2,1]];

f[12,23] = f[2,1]^3*Com[1, f[2,1], f[3,1]];

f[12,24] = f[2,1]*f[4,2]*Com[2, f[2,1], f[2,1]];

f[12,25] = f[3,1]*Com[4, f[2,1], f[3,1]];

f[12,26] = f[3,1]*Com[3, f[2,1], f[2,1]^2];

f[12,27] = f[3,1]*Com[3, f[2,1], f[4,2]];

f[12,28] = f[3,1]*Com[2, f[3,1], f[4,2]];

f[12,29] = f[3,1]^2*Com[2, f[2,1], f[2,1]];

f[12,30] = f[3,1]^2*Com[1, f[2,1], f[3,1]];

f[12,31] = f[4,2]*Com[4, f[2,1],f[2,1]];

f[12,32] = f[4,2]*Com[3, f[2,1], f[3,1]];

f[12,33] = f[4,2]*Com[2, f[2,1], f[4,2]];

f[12,34] = f[4,2]*Com[2, f[3,1], f[3,1]];

f[12,35] = f[4,2]*Com[1, f[3,1], f[4,2]];

f[12,36] = Com[8, f[2,1], f[2,1]];

f[12,37] = Com[7, f[2,1], f[3,1]];

f[12,38] = Com[6, f[2,1], f[2,1]^2];

f[12,39] = Com[6, f[2,1], f[4,2]];

f[12,40] = Com[6, f[3,1], f[3,1]];

f[12,41] = Com[5, f[2,1], f[2,1]*f[3,1]];

f[12,42] = Com[5, f[3,1], f[2,1]^2];

f[12,43] = Com[5, f[3,1], f[4,2]];

f[12,44] = Com[4, f[2,1], f[2,1]^3];

f[12,45] = Com[4, f[2,1], f[3,1]^2];

f[12,46] = Com[4, f[4,2], f[2,1]^2];

f[12,47] = Com[4, f[4,2], f[4,2]];

f[12,48] = Com[3,f[2,1], f[3,1]*f[4,2]];

f[12,49] = Com[3, f[3,1], f[3,1]^2];

Expand[ inv[12,1] - f[12,1] ]

Expand[ inv[12,2] - (1/2)f[12,22] ]

Expand[ inv[12,3] - ( (35/96)f[12,15]+(-5/288)f[12,44]) ]

Expand[ inv[12,4] - ((-115/64)f[12,15]+(7/64)f[12,44]) ]

Expand[ inv[12,5] - ((157/4680)f[12,8]+(-7/2340)f[12,38]) ]

Expand[ inv[12,6] - ((-341/260)f[12,8]+(21/130)f[12,38]) ]

Expand[ inv[12,7] - (1/2)f[12,36] ]

Expand[ inv[12,8] - (-1/4)f[12,26] ]

Expand[ inv[12,9] - f[12,3] ]

Expand[ inv[12,10] - (1/2)f[12,29] ]

Expand[ inv[12,11] - f[12,6] ]

Expand[ inv[12,12] - ((1/8)f[12,22]+f[12,23]) ]

Expand[ inv[12,13] - ((5/72)f[12,14]+(35/384)f[12,15]+(-5/72)f[12,16]+(-1/8)f[12,26]+(-5/1152)f[12,44]) ]

Expand[ inv[12,14] - ((157/18720)f[12,8]+(-11/150)f[12,9]+(-7/9360)f[12,38]+(11/570)f[12,41]+(-49/2850)f[12,42]) ]

Expand[ inv[12,15] - ((1/8)f[12,29]+f[12,30]) ]

Expand[ inv[12,16] - ((5/144)f[12,14]+(35/1536)f[12,15]+(-5/144)f[12,16]+(-3/7)f[12,18]+(6/7)f[12,20]+(-1/16)f[12,26]+(-9/10)f[12,29]+(-5/4608)f[12,44]) ]

Expand[ inv[12,17] - (f[12,20]+(-3/48)f[12,26]+(-21/20)f[12,29]) ]

Expand[ inv[12,18] - ((7/135)f[12,11]+(-7/27)f[12,25]+(7/90)f[12,45]) ]

Expand[ inv[12,19] - ((-7/12)f[12,14]+(-115/256)f[12,15]+(19/12)f[12,16]+(7/20)f[12,26]+(7/256)f[12,44]) ]

Expand[ inv[12,20] - ((157/18720)f[12,8]+(41/300)f[12,9]+(-7/9360)f[12,38]+(-13/570)f[12,41]+(413/11400)f[12,42]) ]

Expand[ inv[12,21] - (-2/9)f[12,49] ]

Expand[ inv[12,22] - ((157/74880)f[12,8]+(19/1200)f[12,9]+(-7/180)f[12,11]+(-1/18)f[12,25]+(-7/37440)f[12,38]+(-1/1140)f[12,41]+(217/45600)f[12,42]+(1/15)f[12,45]) ]

Expand[ inv[12,23] - f[12,25] ]

Expand[ inv[12,24] - ((-341/1040)f[12,8]+(-59/20)f[12,9]+(21/520)f[12,38]+(17/38)f[12,41]+(-847/760)f[12,42]) ]

Expand[ inv[12,25] - (1/2)f[12,40] ]

Expand[ inv[12,26] - ((1/8)f[12,36]+f[12,37]) ]

Expand[ inv[12,27] - (f[12,2]+(1/40)f[12,22]+(1/3)f[12,23]) ]

Expand[ inv[12,28] - ((5/216)f[12,14]+(7/384)f[12,15]+(-5/216)f[12,16]+(1/2)f[12,24]+(-1/24)f[12,26]+(-1/1152)f[12,44]) ]

Expand[ inv[12,29] - ((157/93600)f[12,8]+(-11/450)f[12,9]+(1/2)f[12,31]+(-7/46800)f[12,38]+(11/1710)f[12,41]+(-49/8550)f[12,42]) ]

Expand[ inv[12,30] - (f[12,5]+(1/40)f[12,29]+(1/3)f[12,30]) ]

Expand[ inv[12,31] - ((1/108)f[12,14]+(7/1536)f[12,15]+(-1/108)f[12,16]+(-1/7)f[12,18]+(-3/4)f[12,19]+(2/7)f[12,20]+(3/4)f[12,21]+(1/8)f[12,24]+(-1/60)f[12,26]+(-3/10)f[12,29]+(-1/4608)f[12,44]) ]

Expand[ inv[12,32] - (1/2)f[12,34] ]

Expand[ inv[12,33] - ((157/374400)f[12,8]+(13/18000)f[12,9]+(-7/540)f[12,11]+(-1/54)f[12,25]+(1/8)f[12,31]+f[12,32]+(-7/187200)f[12,38]+(2/4275)f[12,41]+(259/684000)f[12,42]+(1/45)f[12,45]) ]

Expand[ inv[12,34] - (f[12,4]+(1/432)f[12,14]+(7/7680)f[12,15]+(-1/432)f[12,16]+(-1/21)f[12,18]+(-1/2)f[12,19]+(2/21)f[12,20]+(1/2)f[12,21]+(1/20)f[12,24]+(-1/240)f[12,26]+(-1/10)f[12,29]+(-1/23040)f[12,44]) ]

Expand[ inv[12,35] - f[12,7] ]

Expand[ inv[12,36] - ((1/3)f[12,20]+f[12,21]+(-1/80)f[12,26]+(-7/20)f[12,29]) ]

Expand[ inv[12,37] - ((7/405)f[12,11]+(7/80)f[12,12]+(-7/81)f[12,25]+(-7/30)f[12,27]+(1/24)f[12,32]+(7/270)f[12,45]+(7/48)f[12,48]) ]

Expand[ inv[12,38] - ((1/6)f[12,34]+f[12,35]) ]

Expand[ inv[12,39] - ((7/1215)f[12,11]+(7/120)f[12,12]+(-4/9)f[12,13]+(-7/243)f[12,25]+(-7/45)f[12,27]+(1/36)f[12,32]+(8/9)f[12,33]+(7/810)f[12,45]+(7/72)f[12,48]) ]

Expand[ inv[12,40] - ((-7/36)f[12,14]+(-23/256)f[12,15]+(19/36)f[12,16]+f[12,17]+(-9/5)f[12,24]+(7/60)f[12,26]+(7/1280)f[12,44]) ]

Expand[ inv[12,41] - ((157/93600)f[12,8]+(41/900)f[12,9]+(3/44)f[12,10]+(-39/154)f[12,31]+(-7/46800)f[12,38]+(-13/1710)f[12,41]+(413/34200)f[12,42]+(-3/44)f[12,46]) ]

Expand[ inv[12,42] - (f[12,28]+(-6/7)f[12,34]+(-2/27)f[12,49]) ]

Expand[ inv[12,43] - ((157/374400)f[12,8]+(139/18000)f[12,9]+(3/176)f[12,10]+(-7/540)f[12,11]+(-7/80)f[12,12]+(-1/54)f[12,25]+(-1/10)f[12,27]+(-39/616)f[12,31]+(-3/8)f[12,32]+(-7/187200)f[12,38]+(-4/4275)f[12,41]+(1477/684000)f[12,42]+(1/45)f[12,45]+(-3/176)f[12,46]+(3/16)f[12,48]) ]

Expand[ inv[12,44] - ((157/1872000)f[12,8]+(19/18000)f[12,9]+(3/880)f[12,10]+(-7/1620)f[12,11]+(-7/240)f[12,12]+(-1/162)f[12,25]+(-1/30)f[12,27]+(19/1540)f[12,31]+(5/24)f[12,32]+f[12,33]+(-7/936000)f[12,38]+(-1/17100)f[12,41]+(217/684000)f[12,42]+(1/135)f[12,45]+(-3/880)f[12,46]+(1/16)f[12,48]) ]

Expand[ inv[12,45] - ((1/3)f[12,25]+f[12,27]) ]

Expand[ inv[12,46] - ((-341/5200)f[12,8]+(-59/60)f[12,9]+(-5/4)f[12,10]+(51/14)f[12,31]+(21/2600)f[12,38]+(17/114)f[12,41]+(-847/2280)f[12,42]+(9/4)f[12,46]) ]

Expand[ inv[12,47] - (1/2)f[12,47] ]

Expand[ inv[12,48] - ((1/6)f[12,40]+f[12,43]) ]

Expand[ inv[12,49] - ((1/40)f[12,36]+(1/3)f[12,37]+f[12,39]) ]

MaxMemoryUsed[]