> restart; > with(LinearAlgebra): > with(Involutive): > pol:=proc(a,n) > t^n+add((-1)^i*a[i]*t^(n-i),i=1..n); > end proc: > > REL:=proc(a,n,b,m,c)local A,B,C; > A:=CompanionMatrix(pol(a,n),t); > B:=CompanionMatrix(pol(b,m),t); > C:=Matrix(convert(Matrix(n,n,(i,j)->A[i,j]*B),listlist)); > map(i->coeff(CharacteristicPolynomial(C,t)-pol(c,n*m),t,n*m-i),[$1..n* > m]); > end proc: > > # Preparation for Det=1: > L:=REL(a,3,b,3,c); L := [-a[1] b[1] + c[1], 2 2 -2 a[2] b[2] + b[1] a[2] + a[1] b[2] - c[2], -3 a[3] b[3] 3 + 3 b[2] a[3] b[1] + 3 a[1] a[2] b[3] - b[1] a[3] 3 2 - b[1] a[2] a[1] b[2] - a[1] b[3] + c[3], -2 b[2] a[3] a[1] 2 - 2 a[2] b[3] b[1] - a[1] b[3] a[3] b[1] 2 2 2 2 + b[1] a[3] a[1] b[2] + b[1] a[2] a[1] b[3] + a[2] b[2] 2 - c[4], b[2] a[3] a[2] b[3] - a[3] b[2] a[2] b[1] 2 2 + 2 a[3] b[2] a[1] b[3] + 2 a[2] b[3] b[1] a[3] 2 2 2 - a[2] b[3] a[1] b[2] - a[3] b[1] a[1] b[3] + c[5], 2 2 -3 b[2] a[3] b[3] b[1] - 3 a[1] b[3] a[3] a[2] 2 2 2 3 3 2 + 3 a[3] b[3] + a[3] b[2] + a[2] b[3] + a[3] b[2] a[1] b[3] a[2] b[1] - c[6], 2 2 2 2 2 a[1] b[3] a[3] b[1] - a[3] b[2] b[3] a[1] 2 2 2 2 - a[2] b[3] a[3] b[1] + c[7], b[2] a[3] b[3] a[2] - c[8], 3 3 -a[3] b[3] + c[9]] > sL:=solve({op(L)},map(i->c[i],{$1..9})): > L1:=subs([c[9]=1,b[3]=1,a[3]=1],L)[1..-2]; L1 := [-a[1] b[1] + c[1], 2 2 -2 a[2] b[2] + b[1] a[2] + a[1] b[2] - c[2], -3 3 + 3 b[2] b[1] + 3 a[1] a[2] - b[1] - b[1] a[2] a[1] b[2] 3 2 2 - a[1] + c[3], -2 b[2] a[1] - 2 a[2] b[1] - a[1] b[1] 2 2 2 2 + b[1] a[1] b[2] + b[1] a[2] a[1] + a[2] b[2] - c[4], 2 2 2 a[2] b[2] - b[2] a[2] b[1] + 2 a[1] b[2] + 2 b[1] a[2] 2 2 2 - a[2] a[1] b[2] - b[1] a[1] + c[5], -3 b[2] b[1] 3 3 - 3 a[1] a[2] + 3 + b[2] + a[2] + b[1] a[2] a[1] b[2] 2 2 - c[6], 2 a[1] b[1] - b[2] a[1] - a[2] b[1] + c[7], a[2] b[2] - c[8]] > sL1:=solve({op(L1)},map(i->c[i],{$1..8})): > v := [c[8]=16, c[7] = 14, c[6] = 12, c[5] = 10, c[4] = 8, c[3] = 6, > c[2] = 4, c[1] = 2, b[2]=2,b[1]=1,a[2]=2,a[1]=1]; v := [c[8] = 16, c[7] = 14, c[6] = 12, c[5] = 10, c[4] = 8, c[3] = 6, c[2] = 4, c[1] = 2, b[2] = 2, b[1] = 1, a[2] = 2, a[1] = 1] > Verf:=proc(v,gg,d) > local an1,an2,aa,vv,i; > global J; > aa:=map(i->lhs(v[i]),d); > vv:=v; > for i from 1 to nops(d) do vv:=subsop(d[i]=(aa[i]=gg),vv) end do; > J:=InvolutiveBasisGINV(J,vv): > an1:=nops(map(r->if not has(r,aa) then r end if,J)); > an2:=nops(map(r->if not has(LeadingMonomial(r,vv),aa) then r end > if,J)); > return(an1,an2,gg,nops(J)); > end proc: > > J:=copy(L1): > nops(v); 12 # sequence of degrees for a[1]: 1,5,10,15 > > Verf(v,1,[12]); 1, 8, 1, 8 > Verf(v,5,[12]); 55, 57, 5, 132 > Verf(v,10,[12]); 55, 57, 10, 132 > Verf(v,15,[12]); 84, 84, 15, 167 > J:=select(r->not has(r,[a[1]]),J): > nops(J); 84 > v := [c[8] = 16, c[7] = 14, c[6] = 12, c[5] = 10, c[4] = 8, c[3] = 6, > c[2] = 4, c[1] = 2, b[2] = 2,b[1] = 1, a[2] = 2]; v := [c[8] = 16, c[7] = 14, c[6] = 12, c[5] = 10, c[4] = 8, c[3] = 6, c[2] = 4, c[1] = 2, b[2] = 2, b[1] = 1, a[2] = 2] > nops(v); 11 # sequence of degrees for b[1]: 2,5,10,15 > > Verf(v,2,[10]); 3, 39, 2, 74 > Verf(v,5,[10]); Warning, resulting involutive basis is big; reading it may take a while... 43, 81, 5, 502 > Verf(v,10,[10]); Warning, resulting involutive basis is big; reading it may take a while... 47, 72, 10, 481 > Verf(v,15,[10]); Warning, resulting involutive basis is big; reading it may take a while... 62, 62, 15, 283 > J:=select(r->not has(r,b[1]),J): > nops(J); 62 > indets(J); {a[2], b[2], c[1], c[2], c[3], c[4], c[5], c[6], c[7], c[8]} > v := [c[8] = 16, c[7] = 14, c[6] = 12, c[5] = 10, c[4] = 8, c[3] = 6, > c[2] = 4, c[1] = 2, b[2] = 2, a[2] = 2]; v := [c[8] = 16, c[7] = 14, c[6] = 12, c[5] = 10, c[4] = 8, c[3] = 6, c[2] = 4, c[1] = 2, b[2] = 2, a[2] = 2] > nops(v); 10 > # the following is too slow: > Verf(v,2,[10]); 0, 30, 2, 52 > Verf(v,5,[10]); Error, (in Involutive/ginvBasis) error during call of Python or interruption. > v := [c[8] = 2, c[7] = 3, c[6] = 4, c[5] = 5, c[4] = 4, c[3] = 3, c[2] > = 2, c[1] = 1,b[2] = 2,a[2] = 2]; v := [c[8] = 2, c[7] = 3, c[6] = 4, c[5] = 5, c[4] = 4, c[3] = 3, c[2] = 2, c[1] = 1, b[2] = 2, a[2] = 2] > nops(v); 10 > Verf(v,2,[10]); Warning, resulting involutive basis is big; reading it may take a while... 44, 84, 2, 216 > Verf(v,4,[10]); Warning, resulting involutive basis is big; reading it may take a while... 49, 116, 4, 462 > Verf(v,8,[10]); Warning, resulting involutive basis is big; reading it may take a while... 133, 158, 8, 751 > Verf(v,12,[10]); Warning, resulting involutive basis is big; reading it may take a while... 184, 184, 12, 886 > J:=select(r->not has(r,a[2]),J): > nops(J); 184 > v := [c[8] = 2, c[7] = 3, c[6] = 4, c[5] = 5, c[4] = 4, c[3] = 3, c[2] > = 2, c[1] = 1, b[2] = 2]; v := [c[8] = 2, c[7] = 3, c[6] = 4, c[5] = 5, c[4] = 4, c[3] = 3, c[2] = 2, c[1] = 1, b[2] = 2] > nops(v); 9 > Verf(v,3,[9]); Warning, resulting involutive basis is big; reading it may take a while... 44, 44, 3, 81 > J:=select(r->not has(r,b[2]),J): > v := [c[8] = 2, c[7] = 3, c[6] = 4, c[5] = 5, c[4] = 4, c[3] = 3, c[2] > = 2, c[1] = 1]; v := [c[8] = 2, c[7] = 3, c[6] = 4, c[5] = 5, c[4] = 4, c[3] = 3, c[2] = 2, c[1] = 1] > Jmin:=J: > Verf(v,6,[4]); 19, 26, 6, 46 > v := [c[8] = 2, c[7] = 3, c[6] = 6, c[5] = 5, c[4] = 4, c[3] = 3, c[2] > = 2, c[1] = 1]; v := [c[8] = 2, c[7] = 3, c[6] = 6, c[5] = 5, c[4] = 4, c[3] = 3, c[2] = 2, c[1] = 1] > Verf(v,7,[2]); 22, 22, 7, 36 > v := [c[8] = 2, c[7] = 7, c[6] = 6, c[5] = 5, c[4] = 4, c[3] = 3, c[2] > = 2, c[1] = 1]; v := [c[8] = 2, c[7] = 7, c[6] = 6, c[5] = 5, c[4] = 4, c[3] = 3, c[2] = 2, c[1] = 1] > indets(J); {c[1], c[2], c[3], c[4], c[5], c[6], c[7], c[8]} > nops(J);map(nops,J); 36 [12, 10, 29, 32, 33, 6, 54, 56, 55, 58, 19, 69, 14, 36, 35, 112, 8, 117, 137, 138, 150, 56, 73, 19, 252, 99, 199, 258, 254, 249, 119, 302, 173, 8, 584, 839] > Jmin:=J: > > Verf(v,4,[1]); > Verf(v,6,[1]); > Verf(v,8,[1]); > Warning, resulting involutive basis is big; reading it may take a while... 1, 67, 4, 135 Warning, resulting involutive basis is big; reading it may take a while... 1, 118, 6, 177 Warning, resulting involutive basis is big; reading it may take a while... 1, 122, 8, 171 # until here. Result complete. > > L1[-1]; a[2] b[2] - c[8] > U:=InvolutiveBasis([a[2]*b[2]-c[8],a[2]+b[2]-s],[a[2],b[2]],1); 2 U := [b[2] - b[2] s + c[8], a[2] + b[2] - s] > PolTabVar(); 2 2 [b[2] - b[2] s + c[8], [*, b[2]], b[2] ] [a[2] + b[2] - s, [a[2], b[2]], a[2]] > X:=map(PolInvReduce,J,U,[a[2],b[2]],1): > indets(X); {s, b[2], c[1], c[2], c[3], c[4], c[5], c[6], c[7], c[8]} > map(r->if degree(r,b[2])>0 then r end if,X); 2 2 3 [(6 c[2] + 3 c[5] + 12 c[8] - 3 c[1] - c[1] c[8] - s c[8] 2 2 + c[6] c[8] + 3 s c[8] ) b[2], -3 c[5] c[8] - 12 c[8] 2 3 2 - c[6] c[8] - 3 s c[8] - 6 c[2] c[8] + 3 c[1] c[8] 3 3 2 2 2 2 + c[1] c[8] + s c[8] + (3 s c[8] - c[1] s c[8] 2 4 + 3 c[5] s + 6 c[2] s - 3 c[1] s + c[6] c[8] s - s c[8] 3 + 12 s c[8]) b[2], (-3 c[1] + 3 c[5] c[1] + 6 c[2] c[1] 2 2 3 - c[1] c[8] - c[1] s c[8] + c[6] c[1] c[8] + 12 c[1] c[8] 2 3 + 3 c[1] s c[8] ) b[2], -3 c[5] c[1] c[8] - 3 c[1] s c[8] 3 2 2 2 + c[1] s c[8] - c[6] c[1] c[8] - 12 c[1] c[8] 2 3 3 - 6 c[2] c[1] c[8] + c[1] c[8] + 3 c[1] c[8] + ( 2 2 12 c[1] s c[8] + 3 c[1] s c[8] + c[6] c[1] c[8] s 3 2 2 4 + 3 c[5] c[1] s - 3 c[1] s - c[1] s c[8] - c[1] s c[8] 3 + 6 c[2] c[1] s) b[2], (-c[3] s c[8] + 3 c[5] c[3] 2 2 + 6 c[3] c[2] - 3 c[3] c[1] + 3 c[3] s c[8] 2 + c[6] c[3] c[8] - c[3] c[1] c[8] + 12 c[3] c[8]) b[2], ( 2 2 2 2 2 -3 c[3] c[1] + 12 c[3] c[8] + 3 c[3] s c[8] 2 3 2 2 - c[3] s c[8] + c[6] c[3] c[8] + 3 c[5] c[3] 2 2 2 2 3 + 6 c[3] c[2] - c[3] c[1] c[8] ) b[2], (-3/8 c[3] c[1] s + 9/8 c[4] c[1] + 36 c[2] + 18 c[5] + 81 c[8] 2 2 + 9/8 c[4] c[3] c[1] + 9/4 c[4] + 9/4 c[2] c[1] 3 5 2 + 9/4 c[2] c[1] - 9/8 c[1] - 63/4 c[1] 2 3 2 + 9/8 c[3] c[1] s c[8] - 18 c[5] s c[8] - 2 c[1] s c[8] 2 2 + 3/8 c[6] c[3] c[1] - 9/2 c[4] c[8] + 93/4 c[2] c[1] c[8] 2 2 - 9 c[2] s c[8] + 63/8 c[1] s c[8] - 9/8 c[3] c[1] c[8] 2 3 + 6 c[5] c[1] c[8] - 9/8 c[6] c[1] + 6 c[1] s c[8] 2 3 2 3 + 3/8 c[1] c[8] - 3/8 c[3] c[1] c[8] + 1/8 c[1] c[8] 3 2 2 4 2 + 6 s c[8] - 18 s c[8] - 9/8 c[4] c[1] c[8] + 6 s c[8] 6 2 3 4 - s c[8] + c[6] c[8] + 9/8 c[5] c[1] + 9/4 c[8] 2 3 3 3 3 - 9 s c[8] + 6 c[5] s - 75/8 c[1] c[8] + 3 c[2] s 2 3 - 21/8 c[1] s ) b[2]] > evala(subs(sL1,J[6])); 0 > map(r->degree(r,s),X); [0, 3, 3, 3, -infinity, 3, 3, 3, 3, 4, 3, 3, 0, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 6, 3, 6, 3, 3, 3, 6, 6, 3, 3, 3, 3, 6, 6, 6, 6, 3, 3, 3, 6, 6, 6, 3, 3, 6, 6, 6, 3, 3, 6, 6, 6, 9, 3, 6, 6 ] > v := [c[8] = 16, c[7] = 14, c[6] = 12, c[5] = 10, c[4] = 8, c[3] = 6, > c[2] = 4, c[1] = 2, s = 2]; v := [c[8] = 16, c[7] = 14, c[6] = 12, c[5] = 10, c[4] = 8, c[3] = 6, c[2] = 4, c[1] = 2, s = 2] > X[1]; 2 2 4 2 -2 c[2] c[1] + 2 c[2] + c[5] c[2] + 1/2 c[1] - 1/2 c[5] c[1] 2 2 3 - 2 c[8] - c[1] c[8] + 1/2 c[1] c[8] - c[5] c[8] 2 - c[3] c[8] + 3 c[2] c[8] + 1/2 c[4] c[1] c[8] > J:=X: > v:=[c[8] = 2, c[7] = 3, c[6] = 4, c[5] = 4, c[4] = 4, c[3] = 4, c[2] = > 3, c[1] = 2,s=2]; v := [c[8] = 2, c[7] = 3, c[6] = 4, c[5] = 4, c[4] = 4, c[3] = 4, c[2] = 3, c[1] = 2, s = 2] > nops(v); 9 > Verf(v,3,[9]); 69, 69, 3, 128 > J:=select(r->not has(r,s),J): > nops(J); 69 > v := [c[8] = 2, c[7] = 3, c[6] = 4, c[5] = 4, c[4] = 4, c[3] = 3, c[2] > = 2, c[1] = 1]; v := [c[8] = 2, c[7] = 3, c[6] = 4, c[5] = 4, c[4] = 4, c[3] = 3, c[2] = 2, c[1] = 1] > Verf(v,4,[4]); 1, 14, 4, 23 > Verf(v,5,[4]); 1, 28, 5, 44 > v := [c[8] = 2, c[7] = 3, c[6] = 4, c[5] = 5, c[4] = 4, c[3] = 3, c[2] > = 2, c[1] = 1]; v := [c[8] = 2, c[7] = 3, c[6] = 4, c[5] = 5, c[4] = 4, c[3] = 3, c[2] = 2, c[1] = 1] > Verf(v,6,[3]); 13, 14, 6, 26 > v := [c[8] = 2, c[7] = 3, c[6] = 6, c[5] = 5, c[4] = 4, c[3] = 3, c[2] > = 2, c[1] = 1]; v := [c[8] = 2, c[7] = 3, c[6] = 6, c[5] = 5, c[4] = 4, c[3] = 3, c[2] = 2, c[1] = 1] > Verf(v,6,[2]); 22, 22, 6, 36 > Verf(v,7,[2]); 22, 22, 7, 36 > v := [c[8] = 2, c[7] = 7, c[6] = 6, c[5] = 5, c[4] = 4, c[3] = 3, c[2] > = 2, c[1] = 1]; v := [c[8] = 2, c[7] = 7, c[6] = 6, c[5] = 5, c[4] = 4, c[3] = 3, c[2] = 2, c[1] = 1] > Verf(v,4,[1]); Warning, resulting involutive basis is big; reading it may take a while... 1, 67, 4, 135 > Verf(v,5,[1]); Error, (in Involutive/ginvBasis) error during call of Python or interruption. > > > > > > > read "/home/plesken/CharlesMatrix.d/paper.d/Neun.d/ErzNeunDet1": > vv; [c[8] = 2, c[7] = 3, c[6] = 4, c[5] = 4, c[4] = 4, c[3] = 4, c[2] = 3, c[1] = 2] > nops(JEx); 57 > evala(subs(sL1,JEx[-1])); 0 > JEx[2]; 2 2 c[4] c[1] - c[7] c[4] + c[6] c[1] + c[2] c[1] c[8] + c[1] c[8] 3 2 2 2 - c[1] c[8] + 2 c[1] - 3 c[7] c[1] + c[8] c[7] - 2 c[7] > algsubs(t^3=z[3],algsubs(t^9=c[9],(numer(subs(map(i->c[i]=c[i]/t^i,[$1 > ..8]),JEx[2]))))); 2 2 2 2 z[3] c[2] c[1] c[8] c[9] + c[1] z[3] c[8] + c[1] z[3] c[6] c[9] 2 2 2 - 3 c[1] z[3] c[7] c[9] + 2 z[3] c[1] c[9] 2 3 - z[3] c[7] c[4] c[9] - 2 c[7] c[9] - z[3] c[1] c[8] c[9] 2 2 + c[4] c[1] c[9] + c[8] c[7] > v; [c[8] = 16, c[7] = 14, c[6] = 12, c[5] = 10, c[4] = 8, c[3] = 6, c[2] = 4, c[1] = 2, s = 2] > algsubs(t^3=z[3],algsubs(t^9=c[9],(numer(subs(map(i->c[i]=c[i]/t^i,[$1 > ..8]),JEx[1]))))); 3 2 2 -2 c[8] c[7] c[9] - z[3] c[1] c[9] + 2 z[3] c[2] c[1] c[9] 2 3 - z[3] c[4] c[8] c[9] + c[5] c[1] c[9] + c[8] > resultant(algsubs(t^3=z[3],algsubs(t^9=c[9],(numer(subs(map(i->c[i]=c[ > i]/t^i,[$1..8]),JEx[1]))))),algsubs(t^3=z[3],algsubs(t^9=c[9],(numer(s > ubs(map(i->c[i]=c[i]/t^i,[$1..8]),JEx[2])))))); Error, (in resultant) invalid arguments > algsubs(t^3=z[3],algsubs(t^9=c[9],(numer(subs(map(i->c[i]=c[i]/t^i,[$1 > ..8]),JEx[1]))))); 3 2 2 -2 c[8] c[7] c[9] - z[3] c[1] c[9] + 2 z[3] c[2] c[1] c[9] 2 3 - z[3] c[4] c[8] c[9] + c[5] c[1] c[9] + c[8] > algsubs(t^3=z[3],algsubs(t^9=c[9],(numer(subs(map(i->c[i]=c[i]/t^i,[$1 > ..8]),JEx[1]))))); 3 2 2 -2 c[8] c[7] c[9] - z[3] c[1] c[9] + 2 z[3] c[2] c[1] c[9] 2 3 - z[3] c[4] c[8] c[9] + c[5] c[1] c[9] + c[8] > hom:=proc(r) > algsubs(t^3=z[3],algsubs(t^9=c[9],(numer(subs(map(i->c[i]=c[i]/t^i,[$1 > ..8]),r))))); > end proc: > hom(-2*c[8]*c[7]*c[9]-z[3]*c[1]^3*c[9]^2+2*z[3]*c[2]*c[1]*c[9]^2-z[3]* > c[4]*c[8]*c[9]+c[5]*c[1]*c[9]^2+c[8]^3); 2 2 3 4 2 4 -2 c[8] c[7] c[9] - z[3] c[1] c[9] + 2 z[3] c[2] c[1] c[9] 2 2 4 3 - z[3] c[4] c[8] c[9] + c[5] c[1] c[9] + c[8] > JExhom:=map(hom,JEx): > JExhom[-1]; 2 2 3 8 2 2 3 4 c[1] c[4] c[7] c[8] - 15 c[9] c[1] - 2 c[7] c[9] c[1] 4 3 2 3 + 71 c[4] c[1] c[9] - 148 c[4] c[1] c[9] c[2] 2 2 2 2 + 94 c[4] c[1] c[9] c[8] + 4 c[7] c[9] c[2] c[1] 2 2 3 - 14 c[7] c[9] c[4] c[8] - 37 c[8] c[7] c[1] c[9] 4 2 2 2 + 50 c[5] c[1] c[8] c[9] + 202 c[1] c[8] c[7] c[9] 3 3 4 3 2 - 115 c[1] c[9] c[5] - 125 c[1] c[9] c[2] 2 3 3 2 2 + 50 c[1] c[9] c[2] - 42 c[8] c[4] c[2] c[1] c[9] 2 2 2 + c[7] c[5] c[4] c[1] c[9] - 77 c[8] c[5] c[2] c[1] c[9] 2 2 2 6 2 + 15 z[3] c[8] c[7] c[1] - 38 z[3] c[1] c[8] c[9] 5 3 2 + 179 z[3] c[1] c[9] - 6 z[3] c[1] c[8] c[4] c[2] c[9] 3 3 2 2 - 504 z[3] c[1] c[9] c[2] + 39 z[3] c[5] c[1] c[8] c[9] 2 - 2 z[3] c[4] c[5] c[7] c[9] 3 - 20 z[3] c[8] c[7] c[5] c[1] c[9] 2 - 90 z[3] c[7] c[1] c[8] c[9] 3 2 - 37 z[3] c[4] c[1] c[8] c[9] 4 2 + 112 z[3] c[2] c[1] c[8] c[9] 2 2 + 42 z[3] c[7] c[5] c[1] c[9] 2 + 20 z[3] c[7] c[4] c[2] c[1] c[9] 2 2 + 216 z[3] c[4] c[1] c[8] c[9] 2 2 2 3 2 2 - 71 z[3] c[2] c[1] c[8] c[9] - 40 c[1] z[3] c[8] c[9] 4 2 2 4 2 2 - 20 c[1] z[3] c[7] c[9] + 46 c[1] z[3] c[8] c[9] 2 2 2 + 27 c[1] z[3] c[8] c[5] c[9] 2 2 2 - 118 c[1] z[3] c[2] c[8] c[9] 3 2 + 30 c[1] z[3] c[8] c[2] c[7] c[9] 2 2 2 2 - 35 c[1] z[3] c[5] c[2] c[9] 2 + 118 c[1] z[3] c[4] c[8] c[7] c[9] 2 2 2 - 76 c[1] z[3] c[5] c[4] c[9] 2 2 2 - 6 c[1] z[3] c[7] c[2] c[9] 2 2 - 37 c[1] z[3] c[5] c[8] c[7] 2 2 2 + 23 c[8] c[1] c[4] c[5] c[9] - 150 c[1] c[8] c[9] 2 2 2 + 3 c[8] c[5] c[2] c[9] + 20 c[8] c[5] c[4] c[9] 2 2 2 + 42 c[8] c[2] c[7] c[9] - 14 c[7] c[4] c[2] c[9] 3 2 + 6 c[1] c[9] c[5] c[2] + 18 z[3] c[5] c[2] c[8] c[9] 2 3 2 + 60 z[3] c[8] c[7] c[9] + 288 z[3] c[1] c[9] c[2] 2 - 144 z[3] c[4] c[2] c[8] c[9] 2 - 30 z[3] c[5] c[1] c[8] c[9] 2 + 12 z[3] c[4] c[8] c[7] c[9] 3 2 - 7 z[3] c[7] c[4] c[1] c[9] 2 2 2 2 - 7 z[3] c[5] c[4] c[1] c[9] - 121 z[3] c[4] c[8] c[9] 2 2 2 2 2 2 - 25 z[3] c[5] c[1] c[9] - 45 z[3] c[2] c[8] c[9] 2 2 2 2 2 3 2 + 96 z[3] c[7] c[2] c[9] + 21 z[3] c[4] c[1] c[9] 2 2 2 - 6 z[3] c[8] c[7] c[4] c[1] 2 + 48 z[3] c[7] c[5] c[8] c[9] 2 2 + 150 z[3] c[2] c[1] c[8] c[9] 2 2 - 6 z[3] c[5] c[4] c[2] c[9] 2 2 + 2 z[3] c[4] c[2] c[7] c[9] 2 2 - 2 z[3] c[8] c[5] c[2] c[9] 2 2 + 10 z[3] c[1] c[8] c[2] c[7] c[9] 2 5 - 10 z[3] c[1] c[7] c[8] c[9] 2 2 2 2 2 + z[3] c[7] c[4] c[1] c[9] - 4 c[5] c[8] c[9] 2 2 2 2 - 10 c[8] c[7] c[2] c[1] c[9] - 4 c[7] c[5] c[9] 3 2 3 2 + 89 c[8] c[4] c[2] c[1] c[9] + 7 c[9] c[4] c[2] 3 5 3 6 + 3 c[9] c[3] c[1] + 80 c[9] c[2] c[1] 3 2 3 3 + 6 c[9] c[3] c[2] c[1] - 9 c[9] c[3] c[2] c[1] 3 2 3 2 - z[3] c[8] c[5] c[9] + 5 z[3] c[2] c[1] c[8] c[9] + 8 z[3] c[8] c[6] c[5] c[4] c[9] 2 2 - 3 z[3] c[5] c[3] c[1] c[9] 2 2 2 - 20 z[3] c[5] c[2] c[1] c[9] 2 2 - 3 z[3] c[5] c[3] c[2] c[1] c[9] 2 2 2 - 48 z[3] c[4] c[2] c[1] c[9] 2 + 17 z[3] c[8] c[5] c[4] c[2] c[1] c[9] 2 4 2 2 + 20 z[3] c[5] c[2] c[1] c[9] + 4 c[4] c[6] c[8] c[9] 2 2 2 3 - 19 c[4] c[1] c[8] c[9] - 2 c[1] c[4] c[7] c[9] 2 2 2 4 + 12 c[8] c[4] c[2] c[9] + 5 c[8] c[7] c[1] c[9] 2 + 2 c[1] c[7] c[8] c[4] c[5] c[9] 2 2 + 5 c[8] c[5] c[2] c[1] c[9] 2 2 2 2 - 10 c[5] c[1] c[8] c[7] c[9] - c[4] c[2] c[1] c[8] c[9] 3 2 3 2 + 2 c[5] c[4] c[9] + c[5] c[2] c[9] 3 2 2 2 2 + 4 c[5] c[1] c[9] - c[5] c[4] c[2] c[1] c[9] 2 2 2 2 2 - c[5] c[4] c[3] c[9] + 8 c[7] c[4] c[1] c[9] 5 2 4 - 29 c[8] c[4] c[1] c[9] - z[3] c[4] c[7] 2 2 2 2 + z[3] c[5] c[6] c[8] - 4 z[3] c[8] c[4] c[6] 2 4 2 3 2 + 15 z[3] c[5] c[1] c[9] - 4 z[3] c[4] c[2] c[9] 3 2 2 2 - z[3] c[4] c[1] c[9] + 4 z[3] c[4] c[6] c[8] c[7] 2 - 6 z[3] c[4] c[5] c[8] c[7] 3 2 3 - 10 z[3] c[2] c[1] c[8] c[9] + z[3] c[1] c[5] c[7] c[9] 2 2 2 + 2 z[3] c[1] c[4] c[7] c[9] - 2 z[3] c[7] c[6] c[5] c[9] 2 + 6 z[3] c[8] c[7] c[4] c[2] c[1] c[9] - 2 z[3] c[7] c[6] c[5] c[4] c[1] c[9] 2 + 2 z[3] c[8] c[7] c[4] c[2] c[9] 2 + 3 z[3] c[8] c[5] c[4] c[1] c[9] 3 2 + 20 z[3] c[7] c[2] c[1] c[9] 2 3 2 - 20 z[3] c[7] c[2] c[1] c[9] 5 2 + 5 z[3] c[7] c[2] c[1] c[9] 2 + 3 z[3] c[5] c[4] c[3] c[2] c[9] 3 2 2 4 - 4 z[3] c[5] c[4] c[2] c[1] c[9] - z[3] c[5] c[9] 2 3 2 2 2 2 2 + z[3] c[1] c[8] c[5] - 2 z[3] c[8] c[5] c[4] 2 3 2 6 2 + 24 z[3] c[8] c[4] c[9] - 5 z[3] c[5] c[1] c[9] 2 2 2 + 5 z[3] c[4] c[3] c[2] c[1] c[9] 2 2 2 + 5 z[3] c[8] c[7] c[5] c[1] 2 2 2 - 2 z[3] c[8] c[5] c[2] c[1] 2 2 - 2 z[3] c[8] c[7] c[4] c[2] c[1] 2 2 3 - 2 z[3] c[7] c[5] c[1] c[9] 2 2 - 6 z[3] c[7] c[5] c[4] c[9] 2 2 2 - 2 z[3] c[8] c[4] c[2] c[9] 2 2 2 2 2 + z[3] c[6] c[4] c[2] c[9] + 3 z[3] c[6] c[5] c[4] c[9] 2 3 - 17 z[3] c[5] c[8] c[1] c[4] c[9] 2 2 - z[3] c[6] c[5] c[3] c[1] c[9] 2 2 2 + 8 z[3] c[8] c[4] c[2] c[1] c[9] 2 3 2 + 8 z[3] c[4] c[2] c[1] c[9] 2 2 2 - 2 z[3] c[4] c[3] c[2] c[9] 2 2 3 2 - 16 z[3] c[4] c[2] c[1] c[9] 2 4 2 - 2 z[3] c[4] c[3] c[1] c[9] 2 5 2 + 6 z[3] c[4] c[2] c[1] c[9] > v; [c[8] = 16, c[7] = 14, c[6] = 12, c[5] = 10, c[4] = 8, c[3] = 6, c[2] = 4, c[1] = 2, s = 2] > vneu:=map(i->c[10-i]=10-i,[$1..9]); > vneu := [c[9] = 9, c[8] = 8, c[7] = 7, c[6] = 6, c[5] = 5, c[4] = 4, c[3] = 3, c[2] = 2, c[1] = 1] > vneu := [c[9] = 9, c[8] = 8, c[7] = 7, c[6] = 6, c[5] = 5, c[4] = 4, > c[3] = 3, c[2] = 2, c[1] = 1,z[3]=3]; vneu := [c[9] = 9, c[8] = 8, c[7] = 7, c[6] = 6, c[5] = 5, c[4] = 4, c[3] = 3, c[2] = 2, c[1] = 1, z[3] = 3] > vneu := [c[9] = 9, c[8] = 8, c[7] = 7, c[6] = 6, c[5] = 5, c[4] = 4, > c[3] = 3, c[2] = 2, c[1] = 1, z[3] = 3]; vneu := [c[9] = 9, c[8] = 8, c[7] = 7, c[6] = 6, c[5] = 5, c[4] = 4, c[3] = 3, c[2] = 2, c[1] = 1, z[3] = 3] > Jneu:=InvolutiveBasisGINV([op(JExhom),nn,c[9]-z[3]^2],vneu,"time"=20): Warning, resulting involutive basis is big; reading it may take a while... Warning, computation of involutive basis stopped due to time restriction. > nops(Jneu); 373 > DEG:=proc(a) > degree(subs([z[3]=t^3,op(map(i->c[i]=t^i,[$1..9]))],LeadingMonomial(a, > vneu))); > end proc: > map(DEG,Jneu[1..40]); [9, 15, 18, 19, 21, 21, 22, 22, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25] > Jneu:=algsubs(z[3]^3=c[9],Jneu): > collect(Jneu[4],z[3]);; 2 (c[7] c[5] c[1] - 3 c[4] c[1] c[8] + c[5] c[8] + c[3] c[1] c[8] 2 2 2 2 - 3 c[2] c[8] + c[1] c[8]) z[3] + (2 c[8] - 2 c[2] c[9] 2 4 2 - c[6] c[1] c[8] - c[1] c[9] + 2 c[2] c[1] c[9]) z[3] 2 - c[5] c[2] c[9] + c[3] c[8] - c[4] c[2] c[1] c[9] 2 + 3 c[5] c[1] c[9] > collect(Jneu[2],z[3]); > nn:=evala(Jneu[2]/z[3]); 2 (-2 c[4] c[8] + c[7] c[5] + c[3] c[1] c[8] - c[2] c[1] c[9]) z[3] + (c[8] c[7] + 2 c[5] c[1] c[9] - c[4] c[2] c[9] - c[6] c[1] c[8]) z[3] nn := -2 z[3] c[4] c[8] + z[3] c[7] c[5] + z[3] c[1] c[3] c[8] - z[3] c[1] c[2] c[9] + c[8] c[7] + 2 c[5] c[1] c[9] - c[4] c[2] c[9] - c[6] c[1] c[8] > Jneu[3]; c[8] c[7] + z[3] c[7] c[5] - 2 z[3] c[4] c[8] - c[6] c[1] c[8] 2 2 + z[3] c[1] c[3] c[8] - z[3] c[4] c[2] + 2 z[3] c[5] c[1] 3 - z[3] c[2] c[1] > > > nops(Jx); 1 > read "/home/plesken/CharlesMatrix.d/paper.d/Neun.d/ResDet1.m"; > nops(J); 171 > v := [c[8] = 8, c[7] = 7, c[6] = 6, c[5] = 5, c[4] = 4, c[3] = 3, c[2] > = 2, c[1] = 1]; v := [c[8] = 8, c[7] = 7, c[6] = 6, c[5] = 5, c[4] = 4, c[3] = 3, c[2] = 2, c[1] = 1] > hom(J[1]); 3 6 3 -c[2] c[9] + c[1] c[9] - c[4] c[2] c[1] c[8] + c[4] c[1] c[8] 2 - c[3] c[1] c[8] + c[4] c[3] c[8] + c[3] c[2] c[1] c[9] + 2 z[3] c[4] c[8] - c[5] c[1] c[9] + c[4] c[2] c[9] - 3 z[3] c[1] c[3] c[8] + 2 z[3] c[1] c[2] c[9] 2 2 4 3 + 4 c[2] c[1] c[9] - 4 c[2] c[1] c[9] + c[3] c[1] c[9] 2 - 2 c[4] c[1] c[9] - z[3] c[7] c[4] c[1] 2 + 3 z[3] c[2] c[1] c[8] + z[3] c[7] c[3] c[2] 2 4 2 - 2 z[3] c[2] c[8] - z[3] c[1] c[8] + z[3] c[2] c[3] c[4] 2 2 - z[3] c[5] c[3] c[1] - z[3] c[6] c[2] c[1] 2 2 2 3 + 2 z[3] c[5] c[2] c[1] + z[3] c[6] c[1] 2 2 4 2 2 + z[3] c[5] c[4] - z[3] c[5] c[1] - z[3] c[5] c[2] 2 2 2 2 - z[3] c[4] c[1] + z[3] c[7] c[2] - 2 z[3] c[8] c[1] > DEG(%); 15 > Jh:=map(hom,J): > DEG(Jh[1]); 15 > map(DEG,Jh); [15, 15, 16, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 29, 29, 29, 29, 29, 29, 29, 29, 30, 30, 30, 30, 30, 31, 31, 31, 31, 31, 32, 32, 32, 33, 33, 33, 33, 34, 34, 34, 35, 35, 35, 36, 36, 36, 37, 37, 38, 39, 41] > Jh[1];Jh[2]; 3 6 3 -c[2] c[9] + c[1] c[9] - c[4] c[2] c[1] c[8] + c[4] c[1] c[8] 2 - c[3] c[1] c[8] + c[4] c[3] c[8] + c[3] c[2] c[1] c[9] + 2 z[3] c[4] c[8] - c[5] c[1] c[9] + c[4] c[2] c[9] - 3 z[3] c[1] c[3] c[8] + 2 z[3] c[1] c[2] c[9] 2 2 4 3 + 4 c[2] c[1] c[9] - 4 c[2] c[1] c[9] + c[3] c[1] c[9] 2 - 2 c[4] c[1] c[9] - z[3] c[7] c[4] c[1] 2 + 3 z[3] c[2] c[1] c[8] + z[3] c[7] c[3] c[2] 2 4 2 - 2 z[3] c[2] c[8] - z[3] c[1] c[8] + z[3] c[2] c[3] c[4] 2 2 - z[3] c[5] c[3] c[1] - z[3] c[6] c[2] c[1] 2 2 2 3 + 2 z[3] c[5] c[2] c[1] + z[3] c[6] c[1] 2 2 4 2 2 + z[3] c[5] c[4] - z[3] c[5] c[1] - z[3] c[5] c[2] 2 2 2 2 - z[3] c[4] c[1] + z[3] c[7] c[2] - 2 z[3] c[8] c[1] -2 z[3] c[4] c[8] + z[3] c[7] c[5] + z[3] c[1] c[3] c[8] - z[3] c[1] c[2] c[9] + c[8] c[7] + 2 c[5] c[1] c[9] - c[4] c[2] c[9] - c[6] c[1] c[8] > map(degree,Jh,z[3]); [2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] > map(i->if degree(Jh[i],z[3])=1 then i end if,[$1..171]);; [2, 95] > vneu := [z[3] = 3, c[9] = 9, c[8] = 8, c[7] = 7, c[6] = 6, c[5] = 5, > c[4] = 4, c[3] = 3, c[2] = 2, c[1] = 1]; vneu := [z[3] = 3, c[9] = 9, c[8] = 8, c[7] = 7, c[6] = 6, c[5] = 5, c[4] = 4, c[3] = 3, c[2] = 2, c[1] = 1] > Jhneu:=InvolutiveBasisGINV([op(Jh),c[9]-z[3]^3],vneu): Warning, resulting involutive basis is big; reading it may take a while... > Jhneu[2]; 3 6 -1/2 c[2] c[9] + 1/2 c[1] c[9] - 1/2 c[4] c[2] c[1] c[8] 3 2 + 1/2 c[4] c[1] c[8] - 1/2 c[3] c[1] c[8] + 1/2 c[4] c[3] c[8] + 1/2 c[3] c[2] c[1] c[9] + z[3] c[4] c[8] - 1/2 c[5] c[1] c[9] + 1/2 c[4] c[2] c[9] - 3/2 z[3] c[1] c[3] c[8] + z[3] c[1] c[2] c[9] 2 2 4 + 2 c[2] c[1] c[9] - 2 c[2] c[1] c[9] 3 2 + 1/2 c[3] c[1] c[9] - c[4] c[1] c[9] 2 - 1/2 z[3] c[7] c[4] c[1] + 3/2 z[3] c[2] c[1] c[8] 2 + 1/2 z[3] c[7] c[3] c[2] - z[3] c[2] c[8] 4 2 - 1/2 z[3] c[1] c[8] + 1/2 z[3] c[2] c[3] c[4] 2 2 - 1/2 z[3] c[5] c[3] c[1] - 1/2 z[3] c[6] c[2] c[1] 2 2 2 3 + z[3] c[5] c[2] c[1] + 1/2 z[3] c[6] c[1] 2 2 4 + 1/2 z[3] c[5] c[4] - 1/2 z[3] c[5] c[1] 2 2 2 2 - 1/2 z[3] c[5] c[2] - 1/2 z[3] c[4] c[1] 2 2 + 1/2 z[3] c[7] c[2] - z[3] c[8] c[1] > map(degree,Jhneu,z[3]); [3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2] > map(DEG,Jhneu); [9, 15, 15, 16, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 28, 28, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 31, 31, 31, 31, 31, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 35, 35, 35, 36, 36, 36, 36, 36, 37, 37, 37, 38, 38, 39, 39, 39, 40, 40, 41, 42, 43] > map(nops,Jhneu); [2, 32, 33, 24, 42, 72, 81, 67, 102, 90, 93, 130, 114, 101, 156, 151, 152, 169, 154, 198, 203, 200, 199, 221, 215, 218, 274, 257, 275, 272, 269, 275, 284, 279, 284, 291, 433, 445, 359, 372, 374, 312, 536, 539, 537, 333, 347, 548, 578, 583, 580, 395, 582, 582, 566, 585, 361, 453, 404, 625, 580, 711, 710, 715, 732, 741, 741, 632, 744, 636, 728, 710, 449, 843, 791, 837, 810, 766, 870, 863, 881, 861, 878, 890, 867, 870, 883, 1070, 910, 1082, 833, 724, 984, 1018, 1084, 1122, 1130, 1124, 957, 1115, 929, 926, 1120, 1123, 1119, 1150, 1145, 1224, 1097, 961, 1260, 1299, 1310, 1309, 1318, 1459, 1482, 1403, 1442, 1373, 1644, 1614, 1652, 1614, 1711, 1818, 1777, 1822, 1831, 1643, 1691, 1811, 1782, 1899, 1921, 1927, 1904, 1839, 1927, 1927, 2147, 2142, 2091, 2164, 2205, 2281, 2278, 2281, 2270, 2257, 2502, 2490, 2462, 2591, 2513, 2545, 2585, 2601, 2989, 3006, 2942, 2925, 2914, 2872, 3105, 3107, 2989, 2719, 3106, 3101, 3110, 3136, 3319, 3473, 3475, 3479, 3606, 4061, 4034, 4009, 4074, 4443, 4457, 4092, 4165, 4590, 4597, 4597, 4596, 5265, 5261, 5263, 5822, 5828, 5829, 6557, 6674, 6676, 6676, 6674, 7342, 7340, 7343, 8330, 8303, 9178, 9178, 9178, 10248, 10247, 11186, 12511, 13573] > AssertInvBasis(Jhneu,vneu): > sf:=SubmoduleBasis(vneu); 2 z[3] c[7] c[6] c[4] c[3] 2 sf := ------------------------------------------- + z[3] c[4] (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[9] /((1 - c[9]) (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 2 c[6] c[5] c[4] c[9] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 c[7] c[5] c[2] z[3] c[7] c[6] c[4] c[2] + --------------------- + -------------------------------- (1 - c[2]) (1 - c[1]) (1 - c[6]) (1 - c[2]) (1 - c[1]) 2 3 c[5] c[4] c[3] + ------------------------------------------- (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 3 z[3] c[7] c[4] c[3] + ------------------------------------------- + c[8] c[7]/( (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 2 c[8] c[6] c[5] c[4] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[7] c[4] c[9] + ------------------------------------------------------ + (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 z[3] c[7] c[9]/((1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 2 2 z[3] c[4] c[2] c[9] + ------------------------------------------------------ (1 - c[9]) (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[7] c[2] c[9] + ------------------------------------------------------ (1 - c[9]) (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[6] c[5] c[4] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 3 z[3] c[6] c[4] c[3] c[9] + ------------------------------------------------------ + (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 z[3] c[5] c[4] c[9] /((1 - c[9]) (1 - c[6]) (1 - c[4]) 2 (1 - c[3]) (1 - c[2]) (1 - c[1])) + z[3] c[4] c[8] c[9] /( (1 - c[9]) (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) 2 3 c[6] c[5] c[3] (1 - c[1])) + ------------------------------------------- (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 3 2 c[4] c[9] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 2 c[6] c[5] c[4] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 z[3] c[7] c[6] c[4] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[5] c[4] c[9] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[8] c[6] c[4] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) z[3] c[4] c[8] c[9] + ------------------------------------------------------ + (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[5] c[4] c[9] /((1 - c[9]) (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 2 c[4] c[8] c[9] + ------------------------------------------------------ + (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 3 c[6] c[5] c[9]/((1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 3 c[6] c[5] c[4] + ------------------------------------------- (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 5 c[5] + ------------------------------------------------------ (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[5] c[4] c[9] + ------------------------------------------- (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) c[8] c[6] c[5] c[4] + ------------------------------------------- (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) z[3] c[7] c[4] c[9] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) z[3] c[7] c[5] c[4] 2 + ------------------------------------------- + c[7] c[5]/( (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) 2 (1 - c[1])) + z[3] c[5] c[8]/((1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) + z[3] c[7] c[5] 2 c[9] /((1 - c[9]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) 2 (1 - c[2]) (1 - c[1])) + c[9] c[8] c[7]/((1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 2 z[3] c[4] c[8] c[9] + ------------------------------------------------------ + (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 c[8] c[6] c[5] /((1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) 2 (1 - c[2]) (1 - c[1])) + c[7] c[5] c[9] /((1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) + 2 z[3] c[8] c[7] c[9]/((1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 2 c[7] c[6] c[5] c[4] c[3] c[2] 2 2 + ------------------------------------------- + z[3] c[5] (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) c[9]/((1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) + z[3] c[5] c[8] c[9]/((1 - c[6]) (1 - c[5]) 2 (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) + c[8] c[9]/( (1 - c[8]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 2 2 z[3] c[7] c[6] c[2] + -------------------------------- (1 - c[6]) (1 - c[2]) (1 - c[1]) 2 z[3] c[7] c[6] c[3] c[2] + ------------------------------------------- (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[4] c[2] c[9] + ------------------------------------------------------ (1 - c[9]) (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[7] c[5] c[3] 3 + -------------------------------- + z[3] c[6] c[5] /( (1 - c[3]) (1 - c[2]) (1 - c[1]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 4 z[3] c[5] + ------------------------------------------------------ + (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[7] c[6] c[5] /((1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) c[6] c[5] c[4] c[2] c[9] (1 - c[2]) (1 - c[1])) + -------------------------------- + (1 - c[6]) (1 - c[2]) (1 - c[1]) 2 c[7] c[9]/((1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) 2 (1 - c[3]) (1 - c[2]) (1 - c[1])) + c[8] c[7]/((1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) 2 2 2 (1 - c[1])) + z[3] c[9] c[5] /((1 - c[9]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) + 2 z[3] c[9] c[8] c[5]/((1 - c[9]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 3 c[5] c[9] + ------------------------------------------------------ (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 z[3] c[4] c[3] c[9] + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 z[3] c[4] c[3] c[9] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[7] c[6] c[4] c[3] + ------------------------------------------- (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 z[3] c[6] c[5] c[4] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[5] c[8] + ------------------------------------------------------ (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[7] c[4] c[9] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 4 c[6] c[5] + ------------------------------------------------------ + (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 3 z[3] c[6] c[5] /((1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) 2 (1 - c[2]) (1 - c[1])) + z[3] c[7] c[6] c[5]/((1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 2 c[5] c[4] c[9] + ------------------------------------------- (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[8] c[6] c[4] + ------------------------------------------- (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 3 z[3] c[5] c[4] + ------------------------------------------- (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 3 c[7] c[5] + ------------------------------------------------------ (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[5] c[9] + ------------------------------------------------------ (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 z[3] c[6] c[4] c[3] c[9] 2 2 + ------------------------------------------- + z[3] c[4] (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[9] /((1 - c[9]) (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) 2 (1 - c[1])) + z[3] c[7] c[4] c[9] /((1 - c[9]) (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) + z[3] c[5] c[8] /((1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) 2 2 z[3] c[7] c[2] (1 - c[1])) + --------------------- (1 - c[2]) (1 - c[1]) 2 z[3] c[2] c[3] c[4] c[9] 2 + ------------------------------------------- + z[3] c[8] /( (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) (1 - c[8]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) 3 z[3] c[5] c[2] (1 - c[3]) (1 - c[2]) (1 - c[1])) + --------------------- (1 - c[2]) (1 - c[1]) 2 z[3] c[7] c[4] c[3] 2 + -------------------------------- + z[3] c[7] /((1 - c[7]) (1 - c[3]) (1 - c[2]) (1 - c[1]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) c[8] c[5] c[3] c[2] (1 - c[1])) + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[7] c[3] c[2] + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 z[3] c[5] c[2] 2 2 + -------------------------------- + c[9] c[8] /((1 - c[8]) (1 - c[3]) (1 - c[2]) (1 - c[1]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) 3 2 (1 - c[2]) (1 - c[1])) + c[9] c[4] /((1 - c[9]) (1 - c[6]) 2 (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) + z[3] c[7] 2 c[4] c[9] /((1 - c[9]) (1 - c[6]) (1 - c[4]) (1 - c[3]) 2 (1 - c[2]) (1 - c[1])) + z[3] c[7] c[5] c[9]/((1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) c[5] c[4] c[3] c[9] + -------------------------------- + c[5] c[8] c[9]/( (1 - c[3]) (1 - c[2]) (1 - c[1]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) 2 4 (1 - c[1])) + c[6] c[5] /((1 - c[6]) (1 - c[5]) (1 - c[4]) 2 2 (1 - c[3]) (1 - c[2]) (1 - c[1])) + c[7] c[9] /((1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) 2 2 (1 - c[1])) + z[3] c[7] c[9] /((1 - c[9]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 3 c[9] c[7] c[2] + ------------------------------------------------------ + (1 - c[9]) (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 3 c[9] c[5] c[4]/((1 - c[9]) (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 2 c[4] c[2] c[9] + ------------------------------------------- (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 z[3] c[6] c[5] c[2] + ------------------------------------------- (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[7] c[2] c[9] + ------------------------------------------- (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 2 c[5] c[4] c[3] + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[6] c[4] c[3] c[2] c[9] + -------------------------------- + z[3] c[8] c[7] c[9]/( (1 - c[6]) (1 - c[2]) (1 - c[1]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) 2 2 c[4] c[2] c[9] (1 - c[2]) (1 - c[1])) + -------------------------------- + (1 - c[6]) (1 - c[2]) (1 - c[1]) 2 2 z[3] c[4] c[8] c[9] /((1 - c[9]) (1 - c[6]) (1 - c[4]) 2 2 (1 - c[3]) (1 - c[2]) (1 - c[1])) + z[3] c[7] c[5] c[9] /( (1 - c[9]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) 2 (1 - c[2]) (1 - c[1])) + z[3] c[8] c[7] c[9] /((1 - c[9]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) 2 2 c[6] c[5] c[4] c[2] (1 - c[2]) (1 - c[1])) + -------------------------------- (1 - c[6]) (1 - c[2]) (1 - c[1]) 2 z[3] c[7] c[6] c[4] c[2] + -------------------------------- (1 - c[6]) (1 - c[2]) (1 - c[1]) 2 3 c[6] c[5] c[4] + ------------------------------------------------------ + (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 3 2 c[9] c[5] /((1 - c[9]) (1 - c[6]) (1 - c[5]) (1 - c[4]) 2 2 (1 - c[3]) (1 - c[2]) (1 - c[1])) + z[3] c[9] c[8] c[5]/( (1 - c[9]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 3 c[9] c[4] c[2] + ------------------------------------------------------ (1 - c[9]) (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[5] c[4] c[3] + ------------------------------------------- (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) c[8] c[5] c[4] c[3] + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[7] c[4] c[3] + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) c[8] c[6] c[4] c[3] + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) 3 z[3] c[5] c[3] + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) c[7] c[2] c[9] + ------------------------------------------- (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[8] c[5] c[6] + ------------------------------------------------------ + (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[7] c[6] c[5]/((1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 2 c[6] c[5] c[4] c[9] + ------------------------------------------------------ + (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[6] c[5] c[9]/((1 - c[6]) (1 - c[5]) (1 - c[4]) 2 2 (1 - c[3]) (1 - c[2]) (1 - c[1])) + z[3] c[9] c[8] /( (1 - c[9]) (1 - c[8]) (1 - c[7]) (1 - c[6]) (1 - c[5]) 2 (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) + c[6] c[8] /( (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) 2 c[8] c[5] c[4] (1 - c[1])) + ------------------------------------------- + (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 3 c[9] c[7] c[4]/((1 - c[9]) (1 - c[6]) (1 - c[4]) (1 - c[3]) 2 2 z[3] c[7] c[4] c[3] (1 - c[2]) (1 - c[1])) + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) 3 c[6] c[5] c[3] 2 2 2 + -------------------------------- + z[3] c[7] c[9] /( (1 - c[3]) (1 - c[2]) (1 - c[1]) (1 - c[9]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) 3 (1 - c[3]) (1 - c[2]) (1 - c[1])) + c[9] c[4] c[8]/( (1 - c[9]) (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) 2 2 (1 - c[1])) + z[3] c[8] /((1 - c[8]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 2 z[3] c[7] c[6] c[3] c[2] + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[6] c[5] c[2] c[9] + ------------------------------------------- (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[8] c[6] c[5] c[2] + ------------------------------------------- (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[7] c[2] c[9] + ------------------------------------------- (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 3 c[7] c[5] c[4] c[3] 3 + ------------------------------------------- + c[9] c[7] (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) c[5]/((1 - c[9]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) + z[3] c[7] c[5] c[9]/((1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 3 2 2 2 c[5] c[3] c[2] c[5] c[4] c[3] c[2] + -------------------------------- + --------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) (1 - c[2]) (1 - c[1]) 3 + c[7] /((1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) 3 (1 - c[3]) (1 - c[2]) (1 - c[1])) + z[3] /((1 - z[3]) (1 - c[9]) (1 - c[8]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) z[3] c[4] c[8] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 z[3] c[7] c[4] + ------------------------------------------- (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[7] c[5] c[4] + ------------------------------------------- (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 2 z[3] c[5] c[4] + ------------------------------------------- (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 4 c[5] c[4] 2 + ------------------------------------------- + z[3] c[8] (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) c[7]/((1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) 2 3 z[3] c[7] c[3] c[2] (1 - c[2]) (1 - c[1])) + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 c[5] c[4] c[3] c[2] + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) z[3] c[5] c[4] c[9] + ------------------------------------------- (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) c[4] c[8] c[9] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 3 z[3] c[5] + ------------------------------------------------------ (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 z[3] c[7] c[2] c[9] + ------------------------------------------------------ (1 - c[9]) (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 3 c[7] c[6] c[5] c[4] c[3] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) z[3] c[7] c[6] c[5] + ------------------------------------------------------ + (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) c[7] c[5] c[9]/((1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 3 z[3] c[4] c[3] c[9] + ------------------------------------------- (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) c[6] c[5] c[4] c[3] c[9] + ------------------------------------------- (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 z[3] c[7] c[6] c[4] + ------------------------------------------------------ + (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 z[3] c[9] c[8] c[7]/((1 - c[9]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) + 3 c[9] c[8] c[5]/((1 - c[9]) (1 - c[6]) (1 - c[5]) (1 - c[4]) 2 2 2 (1 - c[3]) (1 - c[2]) (1 - c[1])) + z[3] c[9] c[8] /( (1 - c[9]) (1 - c[8]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 4 2 2 c[5] c[2] z[3] c[5] c[4] c[2] 2 + --------------------- + --------------------- + c[5] (1 - c[2]) (1 - c[1]) (1 - c[2]) (1 - c[1]) 2 c[9] /((1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) 2 c[2] c[8] (1 - c[1])) + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) z[3] c[7] c[5] c[3] + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[7] c[4] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[4] c[8] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) z[3] c[6] c[5] c[4] c[9] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[5] c[4] c[9] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[8] c[5] + ------------------------------------------------------ (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[7] c[5] + ------------------------------------------------------ + (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) z[3] c[8] c[7]/((1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) 2 (1 - c[3]) (1 - c[2]) (1 - c[1])) + z[3] c[5] c[8] c[9]/( (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) 2 (1 - c[1])) + z[3] c[8] c[9]/((1 - c[8]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) c[7] c[4] c[9] + ------------------------------------------------------ (1 - c[6]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 c[4] c[8] + ------------------------------------------- (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[7] c[5] + ------------------------------------------------------ (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 2 c[5] c[4] c[3] c[2] z[3] c[7] c[4] c[3] c[2] + --------------------- + ------------------------- (1 - c[2]) (1 - c[1]) (1 - c[2]) (1 - c[1]) 2 c[6] c[5] c[4] c[3] + ------------------------------------------- (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 z[3] c[5] c[4] c[3] 3 2 + -------------------------------- + c[9] c[7] /((1 - c[9]) (1 - c[3]) (1 - c[2]) (1 - c[1]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 2 c[7] c[6] c[5] c[4] c[3] c[2] + ------------------------------------------- (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[6] c[4] c[3] c[2] c[9] 2 + ------------------------------------------- + z[3] c[7] (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) c[9]/((1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) 2 2 (1 - c[2]) (1 - c[1])) + z[3] c[5] c[9] /((1 - c[9]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) 2 (1 - c[1])) + c[5] c[8] c[9] /((1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 2 2 c[4] c[3] c[9] + ------------------------------------------- (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 2 c[6] c[5] c[4] c[3] 3 + ------------------------------------------- + c[9] c[8] (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) c[7]/((1 - c[9]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) 3 2 (1 - c[3]) (1 - c[2]) (1 - c[1])) + c[9] c[8] /((1 - c[9]) (1 - c[8]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) + c[8] c[7] c[9]/( (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) 3 (1 - c[2]) (1 - c[1])) + c[8] /((1 - c[8]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) 2 c[7] c[5] c[4] c[3] c[2] (1 - c[1])) + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[4] c[3] c[2] c[9] + ------------------------- (1 - c[2]) (1 - c[1]) z[3] c[7] c[6] c[4] c[3] + ------------------------------------------- (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 4 c[5] c[3] 2 2 + -------------------------------- + z[3] c[7] /((1 - c[7]) (1 - c[3]) (1 - c[2]) (1 - c[1]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) 3 c[5] c[4] c[2] (1 - c[1])) + --------------------- (1 - c[2]) (1 - c[1]) 2 c[5] c[2] c[9] + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) 3 2 c[5] c[4] + ------------------------------------------- (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[7] c[5] c[2] z[3] c[7] c[4] c[3] c[2] + --------------------- + ------------------------ (1 - c[2]) (1 - c[1]) (1 - c[2]) (1 - c[1]) 2 c[5] c[8] c[4] c[2] z[3] c[7] c[4] c[2] 2 + --------------------- + --------------------- + z[3] (1 - c[2]) (1 - c[1]) (1 - c[2]) (1 - c[1]) 2 c[8] c[9]/((1 - c[8]) (1 - c[7]) (1 - c[6]) (1 - c[5]) (1 - c[4]) (1 - c[3]) (1 - c[2]) (1 - c[1])) 3 c[5] c[4] c[3] + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) c[8] c[2] c[5] c[6] + -------------------------------- (1 - c[3]) (1 - c[2]) (1 - c[1]) 2 z[3] c[7] c[6] c[2] + ------------------------------------------- (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) z[3] c[7] c[2] c[9] + ------------------------------------------- (1 - c[6]) (1 - c[3]) (1 - c[2]) (1 - c[1]) > sft:=evala(subs(map(r->lhs(r)=t^rhs(r),vneu),sf)); 9 9 8 7 6 29 19 25 sft := t (1 + 9 t + 2 t + t + 2 t - 45 t - 12 t + 45 t 15 24 30 23 33 27 - 23 t + 48 t - 65 t + 52 t - 14 t - 6 t 31 26 20 32 17 21 - 43 t + 16 t + 7 t - 41 t - 33 t + 27 t 22 34 37 28 36 18 + 41 t + 4 t + 46 t - 38 t + 39 t - 21 t 16 35 39 40 38 42 - 27 t + 31 t + 15 t + 6 t + 37 t - 15 t 43 41 14 12 11 10 45 - 23 t - 13 t - 9 t + 8 t + 6 t + 8 t - 19 t 51 49 50 54 47 48 13 + 2 t + 6 t + 9 t - 2 t - t + 15 t - 9 t 46 56 59 58 44 / 3 2 - 4 t - 4 t + 2 t - t - 16 t ) / ((-1 + t ) / 9 8 7 6 5 4 (-1 + t ) (-1 + t ) (-1 + t ) (-1 + t ) (-1 + t ) (-1 + t ) 2 (-1 + t ) (-1 + t)) > taylor(sft,t=0,40); 9 10 11 12 13 14 15 16 17 t + t + 2 t + 4 t + 6 t + 9 t + 17 t + 24 t + 38 t 18 19 20 21 22 23 + 66 t + 99 t + 149 t + 235 t + 328 t + 472 t + 24 25 26 27 28 29 663 t + 895 t + 1195 t + 1602 t + 2061 t + 2663 t 30 31 32 33 34 + 3407 t + 4280 t + 5346 t + 6667 t + 8169 t + 35 36 37 38 39 10002 t + 12178 t + 14683 t + 17637 t + 21135 t + 40 O(t ) > map(DEG,map(numer,[op(sf)])); [36, 38, 24, 24, 24, 24, 24, 24, 24, 39, 39, 39, 24, 40, 40, 41, 24, 24, 24, 24, 24, 42, 43, 24, 25, 25, 36, 37, 37, 36, 35, 36, 36, 37, 38, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 28, 28, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 31, 31, 31, 31, 31, 32, 32, 32, 32, 32, 33, 33, 9, 15, 15, 16, 17, 17, 18, 33, 33, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 33, 33, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 22, 21, 21, 21, 21, 21, 21, 21, 33, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 33, 34, 34, 34, 23, 35, 23, 23, 24, 24, 24, 35, 24, 24, 26, 26, 30] > select(r->r=1,map(numer,[op(sf)])); [] > nops(Jhneu); 213 > LJhneu:=map(LeadingMonomial,Jhneu,vneu): > Nummer:=proc(r) > op(map(i->if r=LeadingMonomial(LJhneu[i],vneu) then i end > if,[$1..213])); > end proc: > Nummer(c[8]^2*c[7]); 86 > save > vneu,Jhneu,"/home/plesken/CharlesMatrix.d/paper.d/acht.d/NeunMitz3.m"; > read "/home/plesken/CharlesMatrix.d/paper.d/acht.d/NeunMitz3.m"; > nops(Jhneu); 213 > vneu; [z[3] = 3, c[9] = 9, c[8] = 8, c[7] = 7, c[6] = 6, c[5] = 5, c[4] = 4, c[3] = 3, c[2] = 2, c[1] = 1] > nops(sf); 213 > BB:=map(r->[DEG(numer(r)),LeadingMonomial(numer(r),vneu),indets(denom( > r)) ],[op(sf)]); 2 BB := [[29, z[3] c[7] c[6] c[4] c[3], %1], 2 2 2 [29, z[3] c[4] c[9] , %13], [29, c[6] c[5] c[4] c[9], %11], 2 [19, c[7] c[5] c[2], {c[1], c[2]}], 2 [25, z[3] c[7] c[6] c[4] c[2], %14], 2 3 3 [25, c[5] c[4] c[3], %4], [25, z[3] c[7] c[4] c[3], %4], 2 [15, c[8] c[7], %5], [29, c[8] c[6] c[5] c[4], %11], 2 2 2 [29, c[7] c[4] c[9] , %11], [29, z[3] c[7] c[9], %5], 2 2 [30, z[3] c[4] c[2] c[9] , %12], 2 [30, z[3] c[7] c[2] c[9] , %12], 2 [23, z[3] c[6] c[5] c[4], %11], 3 [33, z[3] c[6] c[4] c[3] c[9], %11], 2 2 [33, z[3] c[5] c[4] c[9] , %13], 2 2 3 [33, z[3] c[4] c[8] c[9] , %13], [30, c[6] c[5] c[3], %1], 3 2 2 2 2 [30, c[4] c[9] , %11], [30, c[6] c[5] c[4] , %11], 2 2 [30, z[3] c[7] c[6] c[4] , %11], 2 2 [24, z[3] c[5] c[4] c[9], %11], [24, c[8] c[6] c[4], %11], [24, z[3] c[4] c[8] c[9], %11], 2 2 [30, z[3] c[5] c[4] c[9] , %13], [30, c[4] c[8] c[9] , %11], 3 3 [30, c[6] c[5] c[9], %8], [25, c[6] c[5] c[4], %4], 5 2 [25, c[5] , %10], [23, c[5] c[4] c[9], %4], [23, c[8] c[6] c[5] c[4], %4], [23, z[3] c[7] c[4] c[9], %11], 2 [19, z[3] c[7] c[5] c[4], %4], [19, c[7] c[5], %8], 2 2 [19, z[3] c[5] c[8], %8], [33, z[3] c[7] c[5] c[9] , %9], 2 2 [33, c[9] c[8] c[7], %5], [27, z[3] c[4] c[8] c[9], %11], 2 2 2 [30, c[8] c[6] c[5] , %8], [30, c[7] c[5] c[9] , %8], 2 [30, z[3] c[8] c[7] c[9], %5], 2 [31, c[7] c[6] c[5] c[4] c[3] c[2], %1], 2 2 [25, z[3] c[5] c[9], %8], [25, z[3] c[5] c[8] c[9], %8], 2 2 2 [25, c[8] c[9], %3], [26, z[3] c[7] c[6] c[2] , %14], 2 [27, z[3] c[7] c[6] c[3] c[2], %1], 2 2 [27, z[3] c[4] c[2] c[9] , %12], [20, c[7] c[5] c[3], %2], 3 4 [24, z[3] c[6] c[5] , %8], [23, z[3] c[5] , %10], 2 [23, c[7] c[6] c[5] , %8], 2 [26, c[6] c[5] c[4] c[2] c[9], %14], [23, c[7] c[9], %5], 2 2 2 2 [23, c[8] c[7], %5], [34, z[3] c[9] c[5] , %9], 2 3 [34, z[3] c[9] c[8] c[5], %9], [24, c[5] c[9], %10], 2 2 [26, z[3] c[4] c[3] c[9], %2], 2 2 [26, z[3] c[4] c[3] c[9], %11], 2 [26, z[3] c[7] c[6] c[4] c[3], %1], 2 2 2 [26, z[3] c[6] c[5] c[4], %11], [21, c[5] c[8] , %10], 2 4 [26, z[3] c[7] c[4] c[9], %11], [26, c[6] c[5] , %10], 2 3 2 [27, z[3] c[6] c[5] , %8], [27, z[3] c[7] c[6] c[5], %8], 2 2 [22, c[5] c[4] c[9], %4], [22, c[8] c[6] c[4] , %4], 3 3 [22, z[3] c[5] c[4], %4], [22, c[7] c[5] , %10], 2 [22, z[3] c[5] c[9], %10], 2 2 [32, z[3] c[6] c[4] c[3] c[9], %1], 2 2 2 2 [32, z[3] c[4] c[9] , %13], [32, z[3] c[7] c[4] c[9] , %13], [16, z[3] c[5] c[8], %8], 2 2 [17, z[3] c[7] c[2] , {c[1], c[2]}], 2 2 [24, z[3] c[2] c[3] c[4] c[9], %1], [19, z[3] c[8] , %3], 3 [20, z[3] c[5] c[2], {c[1], c[2]}], 2 2 [20, z[3] c[7] c[4] c[3] , %2], [17, z[3] c[7] , %5], 2 [18, c[8] c[5] c[3] c[2], %2], [18, z[3] c[7] c[3] c[2], %2], 2 2 2 2 [18, z[3] c[5] c[2], %2], [34, c[9] c[8] , %3], 3 2 2 2 [35, c[9] c[4] , %13], [35, z[3] c[7] c[4] c[9] , %13], 2 [27, z[3] c[7] c[5] c[9], %8], [21, c[5] c[4] c[3] c[9], %2], 2 4 [22, c[5] c[8] c[9], %8], [32, c[6] c[5] , %8], 2 2 2 2 [32, c[7] c[9] , %5], [35, z[3] c[7] c[9] , %7], 3 3 [36, c[9] c[7] c[2], %12], [36, c[9] c[5] c[4], %13], 2 2 2 [24, c[4] c[2] c[9] , %1], [24, z[3] c[6] c[5] c[2], %1], 2 2 2 2 [24, z[3] c[7] c[2] c[9], %1], [24, c[5] c[4] c[3] , %2], 2 [31, z[3] c[6] c[4] c[3] c[2] c[9], %14], 2 2 [27, z[3] c[8] c[7] c[9], %5], [28, c[4] c[2] c[9] , %14], 2 2 [36, z[3] c[4] c[8] c[9] , %13], 2 2 [36, z[3] c[7] c[5] c[9] , %9], 2 [36, z[3] c[8] c[7] c[9] , %7], 2 2 [28, c[6] c[5] c[4] c[2], %14], 2 [28, z[3] c[7] c[6] c[4] c[2], %14], 2 3 3 2 [31, c[6] c[5] c[4], %11], [37, c[9] c[5] , %9], 2 2 3 [37, z[3] c[9] c[8] c[5], %9], [33, c[9] c[4] c[2], %12], 2 [20, z[3] c[5] c[4] c[3], %4], [20, c[8] c[5] c[4] c[3], %2], 2 [20, z[3] c[7] c[4] c[3], %2], [21, c[8] c[6] c[4] c[3], %2], 3 [21, z[3] c[5] c[3], %2], [18, c[7] c[2] c[9], %1], 2 2 [24, c[8] c[5] c[6], %10], [24, z[3] c[7] c[6] c[5], %8], 2 [28, c[6] c[5] c[4] c[9], %11], 2 2 2 [28, z[3] c[6] c[5] c[9], %8], [37, z[3] c[9] c[8] , %6], 2 2 [22, c[6] c[8] , %8], [21, c[8] c[5] c[4] , %4], 3 2 2 [38, c[9] c[7] c[4], %13], [24, z[3] c[7] c[4] c[3] , %2], 3 2 2 2 [24, c[6] c[5] c[3], %2], [38, z[3] c[7] c[9] , %7], 3 2 2 [39, c[9] c[4] c[8], %13], [22, z[3] c[8] , %3], 2 [23, z[3] c[7] c[6] c[3] c[2] , %2], 2 [27, c[6] c[5] c[2] c[9], %1], 2 2 [27, c[8] c[6] c[5] c[2], %1], [27, c[7] c[2] c[9] , %1], 3 3 [27, c[7] c[5] c[4] c[3], %4], [39, c[9] c[7] c[5], %9], 3 2 [24, z[3] c[7] c[5] c[9], %8], [23, c[5] c[3] c[2], %2], 2 2 3 [23, c[5] c[4] c[3] c[2], {c[1], c[2]}], [21, c[7] , %5], [ 3 9, z[3] , {c[1], c[2], c[3], c[4], c[5], c[6], c[7], c[8], c[9], z[3]}] 2 2 , [15, z[3] c[4] c[8], %11], [21, z[3] c[7] c[4] , %4], 2 2 2 2 [21, c[7] c[5] c[4], %4], [24, z[3] c[5] c[4] , %4], 4 2 [24, c[5] c[4], %4], [21, z[3] c[8] c[7], %5], 2 3 [22, z[3] c[7] c[3] c[2] , %2], 2 2 [22, c[5] c[4] c[3] c[2], %2], [21, z[3] c[5] c[4] c[9], %4], [21, c[4] c[8] c[9], %11], 2 3 2 2 [21, z[3] c[5] , %10], [33, z[3] c[7] c[2] c[9] , %12], 3 [33, c[7] c[6] c[5] c[4] c[3], %11], [21, z[3] c[7] c[6] c[5], %10], [21, c[7] c[5] c[9], %8], 3 [27, z[3] c[4] c[3] c[9], %4], [27, c[6] c[5] c[4] c[3] c[9], %1], 2 2 [27, z[3] c[7] c[6] c[4] , %11], 2 2 3 [39, z[3] c[9] c[8] c[7], %7], [40, c[9] c[8] c[5], %9], 2 2 2 4 [40, z[3] c[9] c[8] , %6], [22, c[5] c[2], {c[1], c[2]}], 2 2 [22, z[3] c[5] c[4] c[2], {c[1], c[2]}], 2 2 2 [28, c[5] c[9] , %8], [18, c[2] c[8] , %2], 2 [18, z[3] c[7] c[5] c[3], %2], [18, c[7] c[4], %11], 2 [18, z[3] c[4] c[8], %11], [27, z[3] c[6] c[5] c[4] c[9], %11], 2 2 [27, c[5] c[4] c[9] , %11], [18, c[8] c[5] , %10], 2 [18, z[3] c[7] c[5], %10], [18, z[3] c[8] c[7], %5], 2 2 [28, z[3] c[5] c[8] c[9], %8], [28, z[3] c[8] c[9], %3], 2 [20, c[7] c[4] c[9], %11], [20, c[4] c[8] , %4], 2 [20, z[3] c[7] c[5] , %10], 2 2 [21, c[5] c[4] c[3] c[2] , {c[1], c[2]}], 2 [23, z[3] c[7] c[4] c[3] c[2], {c[1], c[2]}], 2 [23, c[6] c[5] c[4] c[3], %4], 2 2 3 2 [23, z[3] c[5] c[4] c[3], %2], [41, c[9] c[7] , %7], 2 [29, c[7] c[6] c[5] c[4] c[3] c[2] , %1], 2 [29, z[3] c[6] c[4] c[3] c[2] c[9], %1], 2 2 2 [26, z[3] c[7] c[9], %5], [31, z[3] c[5] c[9] , %9], 2 2 2 [31, c[5] c[8] c[9] , %8], [29, c[4] c[3] c[9] , %1], 2 2 3 [29, c[6] c[5] c[4] c[3], %1], [42, c[9] c[8] c[7], %7], 3 2 [43, c[9] c[8] , %6], [24, c[8] c[7] c[9], %5], 3 2 [24, c[8] , %3], [25, c[7] c[5] c[4] c[3] c[2], %2], 2 [25, z[3] c[4] c[3] c[2] c[9], {c[1], c[2]}], 4 [23, z[3] c[7] c[6] c[4] c[3], %4], [23, c[5] c[3], %2], 2 2 3 [20, z[3] c[7] , %5], [21, c[5] c[4] c[2], {c[1], c[2]}], 2 3 2 [21, c[5] c[2] c[9], %2], [23, c[5] c[4] , %4], 2 [19, z[3] c[7] c[5] c[2] , {c[1], c[2]}], [19, z[3] c[7] c[4] c[3] c[2], {c[1], c[2]}], [19, c[5] c[8] c[4] c[2], {c[1], c[2]}], 2 [19, z[3] c[7] c[4] c[2], {c[1], c[2]}], 2 2 3 [31, z[3] c[8] c[9], %3], [22, c[5] c[4] c[3], %2], 2 [21, c[8] c[2] c[5] c[6], %2], [21, z[3] c[7] c[6] c[2], %1], [21, z[3] c[7] c[2] c[9], %1]] %1 := {c[1], c[2], c[3], c[6]} %2 := {c[1], c[2], c[3]} %3 := {c[1], c[2], c[3], c[4], c[5], c[6], c[7], c[8]} %4 := {c[1], c[2], c[3], c[4]} %5 := {c[1], c[2], c[3], c[4], c[5], c[6], c[7]} %6 := {c[1], c[2], c[3], c[4], c[5], c[6], c[7], c[8], c[9]} %7 := {c[1], c[2], c[3], c[4], c[5], c[6], c[7], c[9]} %8 := {c[1], c[2], c[3], c[4], c[5], c[6]} %9 := {c[1], c[2], c[3], c[4], c[5], c[6], c[9]} %10 := {c[1], c[2], c[3], c[4], c[5]} %11 := {c[1], c[2], c[3], c[4], c[6]} %12 := {c[1], c[2], c[3], c[6], c[9]} %13 := {c[1], c[2], c[3], c[4], c[6], c[9]} %14 := {c[1], c[2], c[6]} > with(combinat, partition); [partition] > partition(5,3); [[1, 1, 1, 1, 1], [1, 1, 1, 2], [1, 2, 2], [1, 1, 3], [2, 3]] > select(r->r[1]<15,BB); 3 [[9, z[3] , {c[1], c[2], c[3], c[4], c[5], c[6], c[7], c[8], c[9], z[3]}] ] > mul(1/(1-t^i),i=1..9)/(1-t^3); 2 3 2 4 5 6 7 1/((1 - t) (1 - t ) (1 - t ) (1 - t ) (1 - t ) (1 - t ) (1 - t ) 8 9 (1 - t ) (1 - t )) > taylor(sft-t^9*mul(1/(1-t^i),i=1..9)/(1-t^3),t=0,40); 15 16 17 18 19 20 21 2 t + 3 t + 7 t + 21 t + 37 t + 64 t + 117 t + 172 22 23 24 25 26 27 t + 264 t + 388 t + 538 t + 735 t + 1009 t + 1311 28 29 30 31 32 33 t + 1715 t + 2216 t + 2798 t + 3511 t + 4400 t + 34 35 36 37 38 5396 t + 6618 t + 8066 t + 9716 t + 11661 t + 13963 39 40 t + O(t ) > BBc:=map(r->if not has(r[3],z[3]) then [r[1],r[2],{$1..9} minus > map(DEG,r[3])] end if,BB): > select(r->r[1]=15,BB); [[15, c[8] c[7], {c[1], c[2], c[3], c[4], c[5], c[6], c[7]}], [15, z[3] c[4] c[8], {c[1], c[2], c[3], c[4], c[6]}]] [[15, z[3] c[4] c[8], {c[1], c[2], c[3], c[4], c[6]}], [15, c[8] c[7], {c[1], c[2], c[3], c[4], c[5], c[6], c[7]}]] > coeffs(expand(coeff(u[1]*Jhneu[Nummer(z[3]*c[4]*c[8])]+u[2]*Jhneu[Numm > er(c[8]*c[7])],z[3],1)),map(i->c[i],[$1..9])); 3/2 u[1] + 3 u[2], -3/2 u[1] - 2 u[2], -u[2] - 1/2 u[1], -u[1] - 2 u[2], u[1], 1/2 u[1] + u[2], -u[2] - 1/2 u[1], u[2], u[2] + u[1] # Test Grad 20: > > Bbc:=map(i->select(r->r[1]=i,BBc),[$15..35]): > Bbc[1]; [[15, c[8] c[7], {8, 9}], [15, z[3] c[4] c[8], {5, 7, 8, 9}]] > map(nops,Bbc); [2, 1, 2, 11, 9, 10, 20, 13, 17, 19, 10, 9, 16, 8, 10, 12, 6, 5, 8, 3, 3] [2, 1, 2, 11, 9, 10, 20, 13, 17, 19, 10, 9, 16, 8, 10, 12, 6, 5, 8, 3, 3] > PO:=proc(b,p) > if b[3] intersect {op(p)} = {} then return mul(c[p[i]],i=1..nops(p)) > end if; > end proc: > PO([15, z[3]*c[4]*c[8], {5, 7, 8, 9}],[5]); > map(i->nops(partition(i,i)),[$1..5]); [1, 2, 3, 5, 7] > nops(Bbc[1]); 2 > map(r->PO(Bbc[1][2],r),partition(5,5)); 5 3 2 2 [c[1] , c[2] c[1] , c[2] c[1], c[3] c[1] , c[3] c[2], c[4] c[1], c[5]] > F20:=map(V->map(K->map(r->PO(K,r),partition(20-K[1],20-K[1])),V),Bbc[1 > ..5]); 5 3 2 2 F20 := [[[c[1] , c[1] c[2], c[1] c[2] , c[1] c[3], c[2] c[3], 5 3 2 2 c[1] c[4], c[5]], [c[1] , c[1] c[2], c[1] c[2] , c[1] c[3], c[2] c[3], c[1] c[4]]], 4 2 2 [[c[1] , c[1] c[2], c[2] , c[1] c[3], c[4]]], 3 3 [[c[1] , c[1] c[2]], [c[1] , c[1] c[2], c[3]]], [%1, %1, %1, %1, %1, %1, %1, %1, %1, %1, %1], [[c[1]], [c[1]], [c[1]], [c[1]], [c[1]], [c[1]], [c[1]], [c[1]], [c[1]]]] 2 %1 := [c[1] , c[2]] 5 3 2 2 F20 := [[[c[1] , c[2] c[1] , c[2] c[1], c[3] c[1] , c[3] c[2], 5 3 2 2 c[4] c[1]], [c[1] , c[2] c[1] , c[2] c[1], c[3] c[1] , c[3] c[2], c[4] c[1], c[5]]], 4 2 2 [[c[1] , c[2] c[1] , c[2] , c[3] c[1], c[4]]], 3 3 [[c[1] , c[2] c[1]], [c[1] , c[2] c[1], c[3]]], [%1, %1, %1, %1, %1, %1, %1, %1, %1, %1, %1], [[c[1]], [c[1]], [c[1]], [c[1]], [c[1]], [c[1]], [c[1]], [c[1]], [c[1]]]] 2 %1 := [c[1] , c[2]] > nops(map(op,map(op,F20))); 54 > nops(F20); 5 > Bbc[1][1]; [15, z[3] c[4] c[8], {5, 7, 8, 9}] > H20:=map(op,zip((i,j)->zip((k,l)->[k,l],i,j),F20,Bbc)); 5 3 2 2 H20 := [[[c[1] , c[2] c[1] , c[2] c[1], c[3] c[1] , c[3] c[2], 5 c[4] c[1]], [15, z[3] c[4] c[8], {5, 7, 8, 9}]], [[c[1] , 3 2 2 c[2] c[1] , c[2] c[1], c[3] c[1] , c[3] c[2], c[4] c[1], c[5]], [15, c[8] c[7], {8, 9}]], [ 4 2 2 [c[1] , c[2] c[1] , c[2] , c[3] c[1], c[4]], [16, z[3] c[5] c[8], {7, 8, 9}]], 3 2 2 [[c[1] , c[2] c[1]], [17, z[3] c[7] c[2] , %1]], 3 2 [[c[1] , c[2] c[1], c[3]], [17, z[3] c[7] , {8, 9}]], [%2, [18, c[8] c[5] c[3] c[2], {4, 5, 6, 7, 8, 9}]], 2 [%2, [18, z[3] c[7] c[3] c[2], {4, 5, 6, 7, 8, 9}]], 2 [%2, [18, c[2] c[8] , {4, 5, 6, 7, 8, 9}]], 2 2 [%2, [18, z[3] c[5] c[2], {4, 5, 6, 7, 8, 9}]], [%2, [18, c[7] c[2] c[9], {4, 5, 7, 8, 9}]], [%2, [18, z[3] c[7] c[5] c[3], {4, 5, 6, 7, 8, 9}]], 2 [%2, [18, c[7] c[4], {5, 7, 8, 9}]], 2 [%2, [18, z[3] c[4] c[8], {5, 7, 8, 9}]], 2 [%2, [18, c[8] c[5] , {6, 7, 8, 9}]], 2 [%2, [18, z[3] c[7] c[5], {6, 7, 8, 9}]], [%2, [18, z[3] c[8] c[7], {8, 9}]], 2 [[c[1]], [19, z[3] c[7] c[5] c[2] , %1]], [[c[1]], [19, z[3] c[7] c[4] c[3] c[2], %1]], [[c[1]], [19, c[5] c[8] c[4] c[2], %1]], 2 [[c[1]], [19, z[3] c[7] c[4] c[2], %1]], 2 [[c[1]], [19, c[7] c[5] c[2], %1]], [[c[1]], [19, z[3] c[7] c[5] c[4], {5, 6, 7, 8, 9}]], 2 [[c[1]], [19, c[7] c[5], {7, 8, 9}]], 2 [[c[1]], [19, z[3] c[8] , {9}]], 2 [[c[1]], [19, z[3] c[5] c[8], {7, 8, 9}]]] %1 := {3, 4, 5, 6, 7, 8, 9} 2 %2 := [c[1] , c[2]] > H20:=map(r->[r[1],Nummer(r[2][2])],H20); 5 3 2 2 H20 := [[[c[1] , c[2] c[1] , c[2] c[1], c[3] c[1] , c[3] c[2], 5 3 2 2 c[4] c[1]], 2], [[c[1] , c[2] c[1] , c[2] c[1], c[3] c[1] , c[3] c[2], c[4] c[1], c[5]], 3], 4 2 2 [[c[1] , c[2] c[1] , c[2] , c[3] c[1], c[4]], 4], 3 3 [[c[1] , c[2] c[1]], 5], [[c[1] , c[2] c[1], c[3]], 6], [%1, 7], [%1, 8], [%1, 11], [%1, 9], [%1, 10], [%1, 12], [%1, 13], [%1, 14], [%1, 15], [%1, 16], [%1, 17], [[c[1]], 18], [[c[1]], 19], [[c[1]], 20], [[c[1]], 21], [[c[1]], 22], [[c[1]], 23], [[c[1]], 24], [[c[1]], 26], [[c[1]], 25]] 2 %1 := [c[1] , c[2]] > BH20:=map(r->op(map(u->u*Jhneu[r[2]],r[1])),H20): > nops(BH20); 54 > map(r->Nummer(r[2]),Bbc[6]); [27, 28, 29, 30, 31, 32, 33, 34, 35, 36] > BH20:=[op(BH20),op(map(i->Jhneu[i],%))]: > nops(BH20); 64 > L20:=coeffs(expand(coeff(add(u[i]*BH20[i],i=1..64),z[3],1)),map(i->c[i > ],[$1..9])): > L20[1]; -1/2 u[61] + 5/2 u[64] > solve({L20},map(i->u[i],{$1..64})); {u[1] = 0, u[2] = 0, u[9] = 0, u[3] = 0, u[4] = 0, u[5] = 0, u[7] = 0, u[8] = 0, u[15] = 0, u[17] = 0, u[19] = 0, u[20] = 0, u[10] = 0, u[11] = 0, u[12] = 0, u[13] = 0, u[14] = 0, u[24] = 0, u[25] = 0, u[26] = 0, u[27] = 0, u[28] = 0, u[29] = 0, u[30] = 0, u[31] = 0, u[32] = 0, u[46] = 0, u[47] = 0, u[48] = 0, u[16] = 0, u[49] = 0, u[50] = 0, u[39] = 0, u[40] = 0, u[41] = 0, u[42] = 0, u[43] = 0, u[33] = 0, u[34] = 0, u[35] = 0, u[36] = 0, u[37] = 0, u[38] = 0, u[58] = 0, u[59] = 0, u[60] = 0, u[61] = 0, u[62] = 0, u[51] = 0, u[52] = 0, u[54] = 0, u[56] = 0, u[63] = 0, u[64] = 0, u[6] = 0, u[21] = 0, u[22] = 0, u[18] = 0, u[45] = 0, u[44] = 0, u[23] = 0, u[57] = 0, u[53] = 0, u[55] = 0} > F26:=map(V->map(K->map(r->PO(K,r),partition(26-K[1],min(26-K[1],9))),V > ),Bbc[1..11]); 11 9 2 7 5 3 3 4 F26 := [[[c[1] , c[2] c[1] , c[2] c[1] , c[1] c[2] , c[1] c[2] , 5 8 6 2 4 c[2] c[1], c[3] c[1] , c[3] c[2] c[1] , c[3] c[2] c[1] , 2 3 4 2 5 2 3 c[1] c[2] c[3], c[2] c[3], c[3] c[1] , c[3] c[2] c[1] , 2 2 2 3 3 7 c[3] c[2] c[1], c[1] c[3] , c[3] c[2], c[1] c[4], 5 2 3 3 c[4] c[2] c[1] , c[4] c[2] c[1] , c[4] c[2] c[1], 4 2 2 c[4] c[3] c[1] , c[4] c[3] c[2] c[1] , c[4] c[3] c[2] , 2 2 3 2 2 c[4] c[3] c[1], c[4] c[1] , c[4] c[2] c[1], c[4] c[3], 5 3 2 2 c[6] c[1] , c[6] c[2] c[1] , c[6] c[2] c[1], c[6] c[3] c[1] , 11 9 c[6] c[3] c[2], c[6] c[4] c[1]], [c[1] , c[2] c[1] , 2 7 5 3 3 4 5 8 c[2] c[1] , c[1] c[2] , c[1] c[2] , c[2] c[1], c[3] c[1] , 6 2 4 2 3 c[3] c[2] c[1] , c[3] c[2] c[1] , c[1] c[2] c[3], 4 2 5 2 3 2 2 c[2] c[3], c[3] c[1] , c[3] c[2] c[1] , c[3] c[2] c[1], 2 3 3 7 5 c[1] c[3] , c[3] c[2], c[1] c[4], c[4] c[2] c[1] , 2 3 3 4 c[4] c[2] c[1] , c[4] c[2] c[1], c[4] c[3] c[1] , 2 2 2 c[4] c[3] c[2] c[1] , c[4] c[3] c[2] , c[4] c[3] c[1], 2 3 2 2 6 c[4] c[1] , c[4] c[2] c[1], c[4] c[3], c[5] c[1] , 4 2 2 3 c[5] c[2] c[1] , c[5] c[2] c[1] , c[5] c[2] , 3 2 c[5] c[3] c[1] , c[5] c[3] c[2] c[1], c[5] c[3] , 2 2 5 c[5] c[4] c[1] , c[5] c[4] c[2], c[5] c[1], c[6] c[1] , 3 2 2 c[6] c[2] c[1] , c[6] c[2] c[1], c[6] c[3] c[1] , 4 c[6] c[3] c[2], c[6] c[4] c[1], c[6] c[5], c[7] c[1] , 2 2 c[7] c[2] c[1] , c[7] c[2] , c[7] c[3] c[1], c[7] c[4]]], [[ 10 8 2 6 4 3 4 2 c[1] , c[2] c[1] , c[2] c[1] , c[1] c[2] , c[2] c[1] , 5 7 5 2 3 c[2] , c[3] c[1] , c[3] c[2] c[1] , c[3] c[2] c[1] , 3 2 4 2 2 2 2 c[1] c[2] c[3], c[3] c[1] , c[3] c[2] c[1] , c[3] c[2] , 3 6 4 2 2 c[1] c[3] , c[4] c[1] , c[4] c[2] c[1] , c[4] c[2] c[1] , 3 3 2 c[4] c[2] , c[4] c[3] c[1] , c[1] c[2] c[3] c[4], c[4] c[3] , 2 2 2 5 3 c[4] c[1] , c[4] c[2], c[5] c[1] , c[5] c[2] c[1] , 2 2 c[5] c[2] c[1], c[5] c[3] c[1] , c[5] c[3] c[2], 2 4 2 c[5] c[4] c[1], c[5] , c[6] c[1] , c[6] c[2] c[1] , 2 c[6] c[2] , c[6] c[3] c[1], c[6] c[4]]], [ 9 7 2 5 3 3 4 [c[1] , c[2] c[1] , c[2] c[1] , c[2] c[1] , c[2] c[1]], [ 9 7 2 5 3 3 4 c[1] , c[2] c[1] , c[2] c[1] , c[2] c[1] , c[2] c[1], 6 4 2 2 3 c[3] c[1] , c[3] c[2] c[1] , c[3] c[2] c[1] , c[3] c[2] , 2 3 2 3 5 c[3] c[1] , c[3] c[2] c[1], c[3] , c[4] c[1] , 3 2 2 c[4] c[2] c[1] , c[4] c[2] c[1], c[4] c[3] c[1] , 2 4 2 c[2] c[3] c[4], c[4] c[1], c[5] c[1] , c[5] c[2] c[1] , 2 3 c[5] c[2] , c[5] c[3] c[1], c[5] c[4], c[6] c[1] , 2 c[6] c[2] c[1], c[6] c[3], c[7] c[1] , c[7] c[2]]], [%22, %22, 8 6 4 5 %22, %22, [c[1] , c[2] c[1] , %21, %20, c[2] , c[3] c[1] , 2 2 %19, %18, %17, c[3] c[2], c[6] c[1] , c[6] c[2]], %22, [ 8 6 4 5 c[1] , c[2] c[1] , %21, %20, c[2] , c[3] c[1] , %19, %18, %17, 2 4 2 2 c[3] c[2], c[4] c[1] , %16, c[4] c[2] , %15, c[4] , 2 8 6 4 c[6] c[1] , c[6] c[2]], [c[1] , c[2] c[1] , %21, %20, c[2] , 5 2 4 c[3] c[1] , %19, %18, %17, c[3] c[2], c[4] c[1] , %16, 2 2 2 8 c[4] c[2] , %15, c[4] , c[6] c[1] , c[6] c[2]], [c[1] , 6 4 5 c[2] c[1] , %21, %20, c[2] , c[3] c[1] , %19, %18, %17, 2 4 2 2 c[3] c[2], c[4] c[1] , %16, c[4] c[2] , %15, c[4] , 3 8 6 c[5] c[1] , c[5] c[2] c[1], c[5] c[3]], [c[1] , c[2] c[1] , 4 5 2 %21, %20, c[2] , c[3] c[1] , %19, %18, %17, c[3] c[2], 4 2 2 3 c[4] c[1] , %16, c[4] c[2] , %15, c[4] , c[5] c[1] , 8 6 c[5] c[2] c[1], c[5] c[3]], [c[1] , c[2] c[1] , %21, %20, 4 5 2 4 c[2] , c[3] c[1] , %19, %18, %17, c[3] c[2], c[4] c[1] , %16, 2 2 3 c[4] c[2] , %15, c[4] , c[5] c[1] , c[5] c[2] c[1], c[5] c[3], 2 c[6] c[1] , c[6] c[2], c[7] c[1]]], [%14, %14, %14, %14, %14, 7 5 3 4 [c[1] , c[2] c[1] , %13, c[2] c[1], c[3] c[1] , %12, 2 2 3 7 c[3] c[2] , c[3] c[1], c[4] c[1] , %11, c[4] c[3]], [c[1] , 5 3 4 2 c[2] c[1] , %13, c[2] c[1], c[3] c[1] , %12, c[3] c[2] , 2 3 2 c[3] c[1], c[4] c[1] , %11, c[4] c[3], c[5] c[1] , c[5] c[2], 7 5 3 4 c[6] c[1]], [c[1] , c[2] c[1] , %13, c[2] c[1], c[3] c[1] , 2 2 3 %12, c[3] c[2] , c[3] c[1], c[4] c[1] , %11, c[4] c[3], 2 7 5 c[5] c[1] , c[5] c[2], c[6] c[1], c[7]], [c[1] , c[2] c[1] , 3 4 2 2 %13, c[2] c[1], c[3] c[1] , %12, c[3] c[2] , c[3] c[1], 3 2 c[4] c[1] , %11, c[4] c[3], c[5] c[1] , c[5] c[2], c[6] c[1]] 6 4 3 6 4 ], [[c[1] , c[2] c[1] , %9, c[2] ], %10, [c[1] , c[2] c[1] , 3 3 2 2 %9, c[2] , c[3] c[1] , %8, c[3] , c[4] c[1] , c[4] c[2]], %10, 6 4 3 3 %10, %10, [c[1] , c[2] c[1] , %9, c[2] , c[3] c[1] , %8, 2 2 6 4 c[3] , c[4] c[1] , c[4] c[2], c[6]], [c[1] , c[2] c[1] , %9, 3 3 2 2 6 c[2] , c[3] c[1] , %8, c[3] , c[4] c[1] , c[4] c[2]], [c[1] , 4 3 3 2 2 c[2] c[1] , %9, c[2] , c[3] c[1] , %8, c[3] , c[4] c[1] , 6 4 3 c[4] c[2], c[5] c[1]], [c[1] , c[2] c[1] , %9, c[2] , 3 2 2 c[3] c[1] , %8, c[3] , c[4] c[1] , c[4] c[2], c[5] c[1], c[6] 5 3 2 ]], [[c[1] , c[2] c[1] , c[2] c[1]], 5 3 2 [c[1] , c[2] c[1] , c[2] c[1]], %7, %7, %7, %7, %7, %7, %7, %6, %6, %6, %6, %6, %5, %5, %5, %5, %5, %5], [ 4 2 2 [c[1] , c[2] c[1] , c[2] ], %4, %4, 4 2 2 [c[1] , c[2] c[1] , c[2] ], %4, %3, %3, %3, %3, %3, %3, %3, 3 3 %3], [%2, %2, [c[1] , c[2] c[1]], [c[1] , c[2] c[1]], %2, %2, %2, %2, %2, %2, %2, %2, %2, %2, %2, %2, %2], [%1, %1, %1, %1, %1, %1, %1, %1, %1, %1, %1, %1, %1, %1, %1, %1, %1, %1, %1], [[c[1]], [c[1]], [c[1]], [c[1]], [c[1]], [c[1]], [c[1]], [c[1]], [c[1]], [c[1]]]] 2 %1 := [c[1] , c[2]] 3 %2 := [c[1] , c[2] c[1], c[3]] 4 2 2 %3 := [c[1] , c[2] c[1] , c[2] , c[3] c[1], c[4]] 4 2 2 %4 := [c[1] , c[2] c[1] , c[2] , c[3] c[1]] 5 3 2 2 %5 := [c[1] , c[2] c[1] , c[2] c[1], c[3] c[1] , c[3] c[2], c[4] c[1], c[5]] 5 3 2 2 %6 := [c[1] , c[2] c[1] , c[2] c[1], c[3] c[1] , c[3] c[2], c[4] c[1]] 5 3 2 2 %7 := [c[1] , c[2] c[1] , c[2] c[1], c[3] c[1] , c[3] c[2]] %8 := c[3] c[2] c[1] 2 2 %9 := c[2] c[1] 6 4 3 3 2 %10 := [c[1] , c[2] c[1] , %9, c[2] , c[3] c[1] , %8, c[3] ] %11 := c[4] c[2] c[1] 2 %12 := c[3] c[2] c[1] 2 3 %13 := c[2] c[1] 7 5 3 %14 := [c[1] , c[2] c[1] , %13, c[2] c[1]] %15 := c[4] c[3] c[1] 2 %16 := c[4] c[2] c[1] 2 2 %17 := c[3] c[1] 2 %18 := c[3] c[2] c[1] 3 %19 := c[3] c[2] c[1] 3 2 %20 := c[2] c[1] 2 4 %21 := c[2] c[1] 8 6 4 5 %22 := [c[1] , c[2] c[1] , %21, %20, c[2] , c[3] c[1] , %19, %18, 2 %17, c[3] c[2]] > nops(map(op,map(op,F26))); 726 > nops(Bbc[12]); 9 > H26:=map(op,zip((i,j)->zip((k,l)->[k,l],i,j),F26,Bbc)): > H26:=map(r->[r[1],Nummer(r[2][2])],H26): > BH26:=map(r->op(map(u->u*Jhneu[r[2]],r[1])),H26): > nops(BH26); 726 > map(r->Nummer(r[2]),Bbc[12]); [116, 118, 119, 120, 121, 122, 124, 117, 123] > BH26:=[op(BH26),op(map(i->Jhneu[i],%))]: > nops(BH26); 735 > L26:=coeffs(expand(coeff(add(u[i]*BH26[i],i=1..735),z[3],1)),map(i->c[ > i],[$1..9])): > M26:=coeffs(expand(coeff(add(u[i]*BH26[i],i=1..735),z[3],2)),map(i->c[ > i],[$1..9])): > solve({L26,M26},map(i->u[i],{$1..735})); {u[424] = 0, u[425] = 0, u[421] = 0, u[432] = 0, u[435] = 0, u[436] = 0, u[437] = 0, u[433] = 0, u[428] = 0, u[426] = 0, u[429] = 0, u[430] = 0, u[431] = 0, u[427] = 0, u[422] = 0, u[440] = 0, u[388] = 0, u[35] = 0, u[575] = 0, u[1] = 0, u[2] = 0, u[9] = 0, u[3] = 0, u[4] = 0, u[5] = 0, u[603] = 0, u[25] = 0, u[655] = 0, u[656] = 0, u[658] = 0, u[654] = 0, u[657] = 0, u[665] = 0, u[667] = 0, u[668] = 0, u[670] = 0, u[666] = 0, u[663] = 0, u[659] = 0, u[661] = 0, u[662] = 0, u[664] = 0, u[675] = 0, u[671] = 0, u[673] = 0, u[674] = 0, u[676] = 0, u[672] = 0, u[669] = 0, u[677] = 0, u[679] = 0, u[680] = 0, u[682] = 0, u[678] = 0, u[687] = 0, u[683] = 0, u[685] = 0, u[686] = 0, u[688] = 0, u[684] = 0, u[681] = 0, u[689] = 0, u[692] = 0, u[693] = 0, u[358] = 0, u[117] = 0, u[411] = 0, u[412] = 0, u[409] = 0, u[407] = 0, u[402] = 0, u[404] = 0, u[405] = 0, u[406] = 0, u[403] = 0, u[417] = 0, u[418] = 0, u[419] = 0, u[415] = 0, u[416] = 0, u[420] = 0, u[423] = 0, u[392] = 0, u[348] = 0, u[329] = 0, u[628] = 0, u[226] = 0, u[64] = 0, u[12] = 0, u[478] = 0, u[480] = 0, u[476] = 0, u[471] = 0, u[499] = 0, u[502] = 0, u[503] = 0, u[504] = 0, u[500] = 0, u[495] = 0, u[493] = 0, u[496] = 0, u[497] = 0, u[498] = 0, u[494] = 0, u[489] = 0, u[487] = 0, u[490] = 0, u[491] = 0, u[492] = 0, u[488] = 0, u[507] = 0, u[505] = 0, u[508] = 0, u[509] = 0, u[511] = 0, u[506] = 0, u[479] = 0, u[695] = 0, u[152] = 0, u[150] = 0, u[153] = 0, u[154] = 0, u[155] = 0, u[151] = 0, u[146] = 0, u[144] = 0, u[147] = 0, u[148] = 0, u[149] = 0, u[145] = 0, u[158] = 0, u[168] = 0, u[171] = 0, u[172] = 0, u[173] = 0, u[169] = 0, u[164] = 0, u[162] = 0, u[165] = 0, u[166] = 0, u[167] = 0, u[163] = 0, u[170] = 0, u[176] = 0, u[174] = 0, u[177] = 0, u[178] = 0, u[179] = 0, u[175] = 0, u[194] = 0, u[196] = 0, u[197] = 0, u[198] = 0, u[195] = 0, u[193] = 0, u[190] = 0, u[191] = 0, u[192] = 0, u[189] = 0, u[187] = 0, u[185] = 0, u[182] = 0, u[180] = 0, u[183] = 0, u[184] = 0, u[186] = 0, u[181] = 0, u[200] = 0, u[202] = 0, u[203] = 0, u[204] = 0, u[201] = 0, u[199] = 0, u[206] = 0, u[208] = 0, u[209] = 0, u[210] = 0, u[207] = 0, u[205] = 0, u[224] = 0, u[227] = 0, u[414] = 0, u[468] = 0, u[326] = 0, u[694] = 0, u[701] = 0, u[704] = 0, u[705] = 0, u[706] = 0, u[703] = 0, u[696] = 0, u[698] = 0, u[699] = 0, u[700] = 0, u[697] = 0, u[691] = 0, u[708] = 0, u[707] = 0, u[710] = 0, u[711] = 0, u[712] = 0, u[709] = 0, u[702] = 0, u[713] = 0, u[716] = 0, u[717] = 0, u[718] = 0, u[715] = 0, u[714] = 0, u[719] = 0, u[722] = 0, u[723] = 0, u[724] = 0, u[721] = 0, u[720] = 0, u[731] = 0, u[734] = 0, u[735] = 0, u[733] = 0, u[726] = 0, u[725] = 0, u[728] = 0, u[729] = 0, u[727] = 0, u[732] = 0, u[690] = 0, u[472] = 0, u[473] = 0, u[474] = 0, u[470] = 0, u[465] = 0, u[463] = 0, u[466] = 0, u[467] = 0, u[464] = 0, u[461] = 0, u[458] = 0, u[456] = 0, u[459] = 0, u[460] = 0, u[462] = 0, u[457] = 0, u[483] = 0, u[481] = 0, u[484] = 0, u[485] = 0, u[486] = 0, u[482] = 0, u[477] = 0, u[475] = 0, u[452] = 0, u[77] = 0, u[660] = 0, u[51] = 0, u[52] = 0, u[53] = 0, u[54] = 0, u[55] = 0, u[56] = 0, u[63] = 0, u[103] = 0, u[100] = 0, u[104] = 0, u[105] = 0, u[106] = 0, u[102] = 0, u[101] = 0, u[114] = 0, u[116] = 0, u[118] = 0, u[115] = 0, u[113] = 0, u[108] = 0, u[110] = 0, u[111] = 0, u[112] = 0, u[590] = 0, u[581] = 0, u[579] = 0, u[582] = 0, u[583] = 0, u[584] = 0, u[580] = 0, u[573] = 0, u[576] = 0, u[577] = 0, u[578] = 0, u[574] = 0, u[569] = 0, u[602] = 0, u[599] = 0, u[597] = 0, u[600] = 0, u[601] = 0, u[598] = 0, u[604] = 0, u[606] = 0, u[607] = 0, u[609] = 0, u[605] = 0, u[610] = 0, u[612] = 0, u[613] = 0, u[615] = 0, u[611] = 0, u[608] = 0, u[616] = 0, u[618] = 0, u[586] = 0, u[287] = 0, u[299] = 0, u[297] = 0, u[300] = 0, u[301] = 0, u[302] = 0, u[298] = 0, u[303] = 0, u[306] = 0, u[307] = 0, u[308] = 0, u[304] = 0, u[305] = 0, u[309] = 0, u[312] = 0, u[313] = 0, u[314] = 0, u[310] = 0, u[321] = 0, u[324] = 0, u[325] = 0, u[438] = 0, u[441] = 0, u[442] = 0, u[443] = 0, u[439] = 0, u[434] = 0, u[444] = 0, u[447] = 0, u[448] = 0, u[449] = 0, u[445] = 0, u[450] = 0, u[453] = 0, u[454] = 0, u[455] = 0, u[451] = 0, u[446] = 0, u[469] = 0, u[587] = 0, u[562] = 0, u[228] = 0, u[225] = 0, u[223] = 0, u[218] = 0, u[220] = 0, u[221] = 0, u[222] = 0, u[219] = 0, u[217] = 0, u[212] = 0, u[215] = 0, u[216] = 0, u[213] = 0, u[211] = 0, u[229] = 0, u[236] = 0, u[239] = 0, u[240] = 0, u[241] = 0, u[237] = 0, u[232] = 0, u[230] = 0, u[233] = 0, u[234] = 0, u[235] = 0, u[231] = 0, u[250] = 0, u[248] = 0, u[251] = 0, u[252] = 0, u[253] = 0, u[249] = 0, u[244] = 0, u[242] = 0, u[245] = 0, u[246] = 0, u[247] = 0, u[243] = 0, u[238] = 0, u[254] = 0, u[257] = 0, u[258] = 0, u[259] = 0, u[255] = 0, u[266] = 0, u[269] = 0, u[270] = 0, u[271] = 0, u[267] = 0, u[262] = 0, u[260] = 0, u[263] = 0, u[264] = 0, u[265] = 0, u[261] = 0, u[256] = 0, u[285] = 0, u[288] = 0, u[289] = 0, u[290] = 0, u[286] = 0, u[281] = 0, u[279] = 0, u[282] = 0, u[283] = 0, u[284] = 0, u[280] = 0, u[277] = 0, u[274] = 0, u[272] = 0, u[275] = 0, u[276] = 0, u[278] = 0, u[273] = 0, u[268] = 0, u[293] = 0, u[291] = 0, u[294] = 0, u[295] = 0, u[296] = 0, u[292] = 0, u[214] = 0, u[552] = 0, u[549] = 0, u[542] = 0, u[544] = 0, u[545] = 0, u[547] = 0, u[543] = 0, u[553] = 0, u[555] = 0, u[558] = 0, u[559] = 0, u[560] = 0, u[556] = 0, u[557] = 0, u[563] = 0, u[561] = 0, u[564] = 0, u[565] = 0, u[566] = 0, u[567] = 0, u[570] = 0, u[571] = 0, u[572] = 0, u[568] = 0, u[593] = 0, u[591] = 0, u[594] = 0, u[595] = 0, u[596] = 0, u[592] = 0, u[585] = 0, u[588] = 0, u[589] = 0, u[546] = 0, u[501] = 0, u[512] = 0, u[514] = 0, u[515] = 0, u[517] = 0, u[513] = 0, u[510] = 0, u[518] = 0, u[520] = 0, u[521] = 0, u[523] = 0, u[519] = 0, u[528] = 0, u[524] = 0, u[526] = 0, u[527] = 0, u[529] = 0, u[525] = 0, u[538] = 0, u[539] = 0, u[541] = 0, u[537] = 0, u[534] = 0, u[530] = 0, u[532] = 0, u[533] = 0, u[535] = 0, u[531] = 0, u[540] = 0, u[550] = 0, u[551] = 0, u[554] = 0, u[516] = 0, u[548] = 0, u[522] = 0, u[536] = 0, u[6] = 0, u[7] = 0, u[8] = 0, u[67] = 0, u[65] = 0, u[66] = 0, u[68] = 0, u[75] = 0, u[78] = 0, u[79] = 0, u[80] = 0, u[70] = 0, u[69] = 0, u[72] = 0, u[73] = 0, u[74] = 0, u[71] = 0, u[88] = 0, u[87] = 0, u[90] = 0, u[91] = 0, u[92] = 0, u[89] = 0, u[82] = 0, u[81] = 0, u[84] = 0, u[85] = 0, u[86] = 0, u[83] = 0, u[76] = 0, u[94] = 0, u[97] = 0, u[98] = 0, u[99] = 0, u[96] = 0, u[93] = 0, u[95] = 0, u[15] = 0, u[16] = 0, u[17] = 0, u[18] = 0, u[19] = 0, u[20] = 0, u[10] = 0, u[11] = 0, u[13] = 0, u[14] = 0, u[21] = 0, u[22] = 0, u[23] = 0, u[24] = 0, u[26] = 0, u[27] = 0, u[28] = 0, u[29] = 0, u[30] = 0, u[31] = 0, u[32] = 0, u[45] = 0, u[46] = 0, u[47] = 0, u[48] = 0, u[49] = 0, u[50] = 0, u[39] = 0, u[40] = 0, u[41] = 0, u[42] = 0, u[43] = 0, u[44] = 0, u[33] = 0, u[34] = 0, u[36] = 0, u[37] = 0, u[38] = 0, u[57] = 0, u[58] = 0, u[59] = 0, u[60] = 0, u[61] = 0, u[62] = 0, u[109] = 0, u[107] = 0, u[138] = 0, u[141] = 0, u[142] = 0, u[143] = 0, u[139] = 0, u[137] = 0, u[132] = 0, u[134] = 0, u[135] = 0, u[136] = 0, u[133] = 0, u[131] = 0, u[126] = 0, u[128] = 0, u[129] = 0, u[130] = 0, u[127] = 0, u[125] = 0, u[120] = 0, u[122] = 0, u[123] = 0, u[124] = 0, u[121] = 0, u[119] = 0, u[140] = 0, u[156] = 0, u[159] = 0, u[160] = 0, u[161] = 0, u[157] = 0, u[188] = 0, u[619] = 0, u[617] = 0, u[614] = 0, u[622] = 0, u[624] = 0, u[625] = 0, u[627] = 0, u[623] = 0, u[620] = 0, u[632] = 0, u[630] = 0, u[631] = 0, u[633] = 0, u[629] = 0, u[626] = 0, u[644] = 0, u[640] = 0, u[642] = 0, u[643] = 0, u[646] = 0, u[641] = 0, u[638] = 0, u[634] = 0, u[636] = 0, u[637] = 0, u[639] = 0, u[635] = 0, u[647] = 0, u[649] = 0, u[650] = 0, u[652] = 0, u[648] = 0, u[645] = 0, u[651] = 0, u[653] = 0, u[621] = 0, u[730] = 0, u[381] = 0, u[327] = 0, u[322] = 0, u[317] = 0, u[315] = 0, u[318] = 0, u[319] = 0, u[320] = 0, u[316] = 0, u[311] = 0, u[328] = 0, u[330] = 0, u[331] = 0, u[333] = 0, u[323] = 0, u[340] = 0, u[342] = 0, u[343] = 0, u[345] = 0, u[341] = 0, u[338] = 0, u[334] = 0, u[336] = 0, u[337] = 0, u[339] = 0, u[335] = 0, u[332] = 0, u[344] = 0, u[352] = 0, u[354] = 0, u[355] = 0, u[357] = 0, u[353] = 0, u[350] = 0, u[346] = 0, u[349] = 0, u[351] = 0, u[347] = 0, u[356] = 0, u[360] = 0, u[361] = 0, u[363] = 0, u[359] = 0, u[362] = 0, u[364] = 0, u[366] = 0, u[367] = 0, u[370] = 0, u[365] = 0, u[368] = 0, u[369] = 0, u[371] = 0, u[372] = 0, u[374] = 0, u[375] = 0, u[376] = 0, u[373] = 0, u[377] = 0, u[384] = 0, u[386] = 0, u[387] = 0, u[385] = 0, u[383] = 0, u[378] = 0, u[380] = 0, u[382] = 0, u[379] = 0, u[389] = 0, u[390] = 0, u[393] = 0, u[394] = 0, u[391] = 0, u[401] = 0, u[396] = 0, u[398] = 0, u[399] = 0, u[400] = 0, u[397] = 0, u[395] = 0, u[413] = 0, u[408] = 0, u[410] = 0} > nops([L26]);nops([M26]); 761 451 > F28:=map(V->map(K->map(r->PO(K,r),partition(28-K[1],min(28-K[1],9))),V > ),Bbc[1..13]): > nops(map(op,map(op,F28))); 1303 > nops(Bbc[14]); 8 > H28:=map(op,zip((i,j)->zip((k,l)->[k,l],i,j),F28,Bbc)): > H28:=map(r->[r[1],Nummer(r[2][2])],H28): > BH28:=map(r->op(map(u->u*Jhneu[r[2]],r[1])),H28): > nops(BH28); 1303 > map(r->Nummer(r[2]),Bbc[14]); [141, 142, 143, 144, 145, 146, 147, 148] > BH28:=[op(BH28),op(map(i->Jhneu[i],%))]: > nops(BH28); 1311 > L28:=coeffs(expand(coeff(add(u[i]*BH28[i],i=1..1311),z[3],1)),map(i->c > [i],[$1..9])): > M28:=coeffs(expand(coeff(add(u[i]*BH28[i],i=1..1311),z[3],2)),map(i->c > [i],[$1..9])): > nops([L28]);nops({L28});nops({M28});nops({L28,M28}); 1144 1131 688 1814 > solve({L28,M28},map(i->u[i],{$1..1311})); {u[1] = 0, u[2] = 0, u[9] = 0, u[3] = 0, u[4] = 0, u[7] = 0, u[816] = 0, u[827] = 0, u[831] = 0, u[838] = 0, u[842] = 0, u[849] = 0, u[853] = 0, u[860] = 0, u[864] = 0, u[876] = 0, u[872] = 0, u[885] = 0, u[889] = 0, u[820] = 0, u[55] = 0, u[63] = 0, u[64] = 0, u[103] = 0, u[737] = 0, u[740] = 0, u[758] = 0, u[766] = 0, u[792] = 0, u[783] = 0, u[774] = 0, u[800] = 0, u[808] = 0, u[56] = 0, u[35] = 0, u[37] = 0, u[38] = 0, u[57] = 0, u[58] = 0, u[59] = 0, u[60] = 0, u[61] = 0, u[62] = 0, u[51] = 0, u[52] = 0, u[53] = 0, u[54] = 0, u[36] = 0, u[156] = 0, u[160] = 0, u[161] = 0, u[157] = 0, u[152] = 0, u[150] = 0, u[153] = 0, u[154] = 0, u[155] = 0, u[151] = 0, u[146] = 0, u[144] = 0, u[147] = 0, u[159] = 0, u[131] = 0, u[128] = 0, u[129] = 0, u[130] = 0, u[127] = 0, u[125] = 0, u[120] = 0, u[122] = 0, u[123] = 0, u[124] = 0, u[121] = 0, u[119] = 0, u[140] = 0, u[126] = 0, u[112] = 0, u[107] = 0, u[138] = 0, u[141] = 0, u[142] = 0, u[143] = 0, u[139] = 0, u[137] = 0, u[132] = 0, u[134] = 0, u[135] = 0, u[136] = 0, u[133] = 0, u[109] = 0, u[104] = 0, u[106] = 0, u[102] = 0, u[101] = 0, u[114] = 0, u[116] = 0, u[117] = 0, u[118] = 0, u[115] = 0, u[113] = 0, u[108] = 0, u[110] = 0, u[111] = 0, u[105] = 0, u[898] = 0, u[912] = 0, u[916] = 0, u[925] = 0, u[929] = 0, u[940] = 0, u[944] = 0, u[959] = 0, u[966] = 0, u[977] = 0, u[984] = 0, u[993] = 0, u[100] = 0, u[902] = 0, u[233] = 0, u[235] = 0, u[231] = 0, u[250] = 0, u[248] = 0, u[251] = 0, u[252] = 0, u[253] = 0, u[249] = 0, u[244] = 0, u[242] = 0, u[245] = 0, u[246] = 0, u[234] = 0, u[212] = 0, u[215] = 0, u[216] = 0, u[213] = 0, u[211] = 0, u[229] = 0, u[236] = 0, u[239] = 0, u[240] = 0, u[241] = 0, u[237] = 0, u[232] = 0, u[230] = 0, u[214] = 0, u[202] = 0, u[204] = 0, u[201] = 0, u[199] = 0, u[206] = 0, u[208] = 0, u[209] = 0, u[210] = 0, u[207] = 0, u[205] = 0, u[224] = 0, u[226] = 0, u[225] = 0, u[203] = 0, u[188] = 0, u[191] = 0, u[192] = 0, u[189] = 0, u[187] = 0, u[185] = 0, u[182] = 0, u[180] = 0, u[183] = 0, u[184] = 0, u[186] = 0, u[181] = 0, u[200] = 0, u[190] = 0, u[163] = 0, u[176] = 0, u[174] = 0, u[177] = 0, u[178] = 0, u[179] = 0, u[175] = 0, u[194] = 0, u[196] = 0, u[197] = 0, u[198] = 0, u[195] = 0, u[193] = 0, u[170] = 0, u[148] = 0, u[145] = 0, u[158] = 0, u[168] = 0, u[171] = 0, u[172] = 0, u[173] = 0, u[169] = 0, u[164] = 0, u[162] = 0, u[165] = 0, u[166] = 0, u[167] = 0, u[149] = 0, u[747] = 0, u[285] = 0, u[288] = 0, u[289] = 0, u[290] = 0, u[286] = 0, u[281] = 0, u[279] = 0, u[282] = 0, u[283] = 0, u[284] = 0, u[280] = 0, u[277] = 0, u[745] = 0, u[260] = 0, u[264] = 0, u[265] = 0, u[261] = 0, u[736] = 0, u[738] = 0, u[256] = 0, u[739] = 0, u[742] = 0, u[743] = 0, u[741] = 0, u[744] = 0, u[746] = 0, u[263] = 0, u[247] = 0, u[238] = 0, u[254] = 0, u[257] = 0, u[258] = 0, u[259] = 0, u[255] = 0, u[266] = 0, u[269] = 0, u[270] = 0, u[271] = 0, u[267] = 0, u[262] = 0, u[243] = 0, u[752] = 0, u[755] = 0, u[753] = 0, u[303] = 0, u[306] = 0, u[307] = 0, u[308] = 0, u[304] = 0, u[761] = 0, u[763] = 0, u[764] = 0, u[762] = 0, u[305] = 0, u[754] = 0, u[299] = 0, u[300] = 0, u[301] = 0, u[302] = 0, u[298] = 0, u[748] = 0, u[750] = 0, u[751] = 0, u[749] = 0, u[756] = 0, u[759] = 0, u[760] = 0, u[757] = 0, u[297] = 0, u[274] = 0, u[275] = 0, u[276] = 0, u[278] = 0, u[273] = 0, u[268] = 0, u[293] = 0, u[291] = 0, u[294] = 0, u[295] = 0, u[296] = 0, u[292] = 0, u[287] = 0, u[272] = 0, u[772] = 0, u[771] = 0, u[321] = 0, u[324] = 0, u[325] = 0, u[322] = 0, u[317] = 0, u[315] = 0, u[318] = 0, u[319] = 0, u[320] = 0, u[316] = 0, u[311] = 0, u[773] = 0, u[309] = 0, u[313] = 0, u[314] = 0, u[310] = 0, u[765] = 0, u[768] = 0, u[769] = 0, u[767] = 0, u[775] = 0, u[777] = 0, u[778] = 0, u[776] = 0, u[770] = 0, u[312] = 0, u[328] = 0, u[331] = 0, u[333] = 0, u[329] = 0, u[779] = 0, u[781] = 0, u[782] = 0, u[780] = 0, u[326] = 0, u[323] = 0, u[340] = 0, u[342] = 0, u[343] = 0, u[330] = 0, u[352] = 0, u[355] = 0, u[357] = 0, u[353] = 0, u[788] = 0, u[790] = 0, u[791] = 0, u[789] = 0, u[350] = 0, u[346] = 0, u[348] = 0, u[349] = 0, u[351] = 0, u[354] = 0, u[345] = 0, u[338] = 0, u[334] = 0, u[336] = 0, u[337] = 0, u[339] = 0, u[335] = 0, u[784] = 0, u[786] = 0, u[787] = 0, u[785] = 0, u[332] = 0, u[344] = 0, u[341] = 0, u[372] = 0, u[375] = 0, u[376] = 0, u[373] = 0, u[377] = 0, u[384] = 0, u[386] = 0, u[387] = 0, u[388] = 0, u[385] = 0, u[383] = 0, u[378] = 0, u[380] = 0, u[374] = 0, u[367] = 0, u[365] = 0, u[802] = 0, u[804] = 0, u[805] = 0, u[803] = 0, u[797] = 0, u[799] = 0, u[801] = 0, u[798] = 0, u[368] = 0, u[369] = 0, u[371] = 0, u[370] = 0, u[347] = 0, u[793] = 0, u[795] = 0, u[796] = 0, u[794] = 0, u[358] = 0, u[360] = 0, u[361] = 0, u[363] = 0, u[359] = 0, u[362] = 0, u[364] = 0, u[366] = 0, u[356] = 0, u[822] = 0, u[435] = 0, u[436] = 0, u[437] = 0, u[433] = 0, u[428] = 0, u[426] = 0, u[429] = 0, u[430] = 0, u[431] = 0, u[427] = 0, u[422] = 0, u[440] = 0, u[432] = 0, u[415] = 0, u[420] = 0, u[423] = 0, u[424] = 0, u[425] = 0, u[421] = 0, u[815] = 0, u[818] = 0, u[819] = 0, u[817] = 0, u[821] = 0, u[823] = 0, u[824] = 0, u[416] = 0, u[396] = 0, u[399] = 0, u[400] = 0, u[397] = 0, u[395] = 0, u[413] = 0, u[811] = 0, u[813] = 0, u[814] = 0, u[812] = 0, u[408] = 0, u[410] = 0, u[411] = 0, u[398] = 0, u[381] = 0, u[379] = 0, u[806] = 0, u[809] = 0, u[810] = 0, u[807] = 0, u[389] = 0, u[390] = 0, u[392] = 0, u[393] = 0, u[394] = 0, u[391] = 0, u[401] = 0, u[382] = 0, u[471] = 0, u[837] = 0, u[839] = 0, u[836] = 0, u[499] = 0, u[502] = 0, u[503] = 0, u[504] = 0, u[500] = 0, u[495] = 0, u[493] = 0, u[496] = 0, u[497] = 0, u[835] = 0, u[834] = 0, u[483] = 0, u[481] = 0, u[484] = 0, u[485] = 0, u[486] = 0, u[482] = 0, u[477] = 0, u[475] = 0, u[478] = 0, u[479] = 0, u[480] = 0, u[476] = 0, u[832] = 0, u[463] = 0, u[467] = 0, u[468] = 0, u[464] = 0, u[461] = 0, u[458] = 0, u[456] = 0, u[459] = 0, u[460] = 0, u[462] = 0, u[457] = 0, u[830] = 0, u[833] = 0, u[466] = 0, u[445] = 0, u[450] = 0, u[453] = 0, u[454] = 0, u[455] = 0, u[451] = 0, u[446] = 0, u[469] = 0, u[472] = 0, u[473] = 0, u[474] = 0, u[470] = 0, u[465] = 0, u[452] = 0, u[438] = 0, u[442] = 0, u[443] = 0, u[439] = 0, u[434] = 0, u[825] = 0, u[828] = 0, u[829] = 0, u[826] = 0, u[444] = 0, u[447] = 0, u[448] = 0, u[449] = 0, u[441] = 0, u[844] = 0, u[522] = 0, u[518] = 0, u[520] = 0, u[521] = 0, u[523] = 0, u[519] = 0, u[528] = 0, u[524] = 0, u[526] = 0, u[527] = 0, u[529] = 0, u[525] = 0, u[841] = 0, u[501] = 0, u[512] = 0, u[514] = 0, u[515] = 0, u[517] = 0, u[513] = 0, u[845] = 0, u[847] = 0, u[848] = 0, u[846] = 0, u[510] = 0, u[840] = 0, u[843] = 0, u[516] = 0, u[498] = 0, u[489] = 0, u[487] = 0, u[490] = 0, u[491] = 0, u[492] = 0, u[488] = 0, u[507] = 0, u[505] = 0, u[508] = 0, u[509] = 0, u[511] = 0, u[506] = 0, u[494] = 0, u[536] = 0, u[539] = 0, u[541] = 0, u[537] = 0, u[534] = 0, u[530] = 0, u[532] = 0, u[533] = 0, u[535] = 0, u[531] = 0, u[540] = 0, u[855] = 0, u[857] = 0, u[538] = 0, u[594] = 0, u[596] = 0, u[592] = 0, u[587] = 0, u[585] = 0, u[588] = 0, u[589] = 0, u[590] = 0, u[586] = 0, u[581] = 0, u[579] = 0, u[582] = 0, u[583] = 0, u[595] = 0, u[565] = 0, u[562] = 0, u[859] = 0, u[862] = 0, u[863] = 0, u[861] = 0, u[567] = 0, u[570] = 0, u[571] = 0, u[572] = 0, u[568] = 0, u[593] = 0, u[591] = 0, u[566] = 0, u[545] = 0, u[543] = 0, u[553] = 0, u[552] = 0, u[555] = 0, u[558] = 0, u[559] = 0, u[560] = 0, u[556] = 0, u[557] = 0, u[563] = 0, u[561] = 0, u[564] = 0, u[547] = 0, u[858] = 0, u[548] = 0, u[550] = 0, u[551] = 0, u[554] = 0, u[549] = 0, u[546] = 0, u[850] = 0, u[852] = 0, u[854] = 0, u[851] = 0, u[542] = 0, u[544] = 0, u[856] = 0, u[878] = 0, u[644] = 0, u[640] = 0, u[642] = 0, u[643] = 0, u[646] = 0, u[641] = 0, u[638] = 0, u[634] = 0, u[636] = 0, u[639] = 0, u[635] = 0, u[647] = 0, u[875] = 0, u[624] = 0, u[627] = 0, u[623] = 0, u[620] = 0, u[632] = 0, u[628] = 0, u[630] = 0, u[631] = 0, u[633] = 0, u[629] = 0, u[626] = 0, u[874] = 0, u[877] = 0, u[625] = 0, u[605] = 0, u[612] = 0, u[613] = 0, u[615] = 0, u[611] = 0, u[608] = 0, u[616] = 0, u[618] = 0, u[619] = 0, u[621] = 0, u[617] = 0, u[614] = 0, u[622] = 0, u[610] = 0, u[871] = 0, u[870] = 0, u[602] = 0, u[599] = 0, u[597] = 0, u[600] = 0, u[601] = 0, u[603] = 0, u[598] = 0, u[604] = 0, u[606] = 0, u[607] = 0, u[609] = 0, u[873] = 0, u[584] = 0, u[575] = 0, u[573] = 0, u[576] = 0, u[577] = 0, u[578] = 0, u[574] = 0, u[569] = 0, u[865] = 0, u[867] = 0, u[868] = 0, u[866] = 0, u[869] = 0, u[580] = 0, u[671] = 0, u[674] = 0, u[676] = 0, u[672] = 0, u[669] = 0, u[883] = 0, u[886] = 0, u[887] = 0, u[884] = 0, u[677] = 0, u[679] = 0, u[680] = 0, u[682] = 0, u[673] = 0, u[882] = 0, u[665] = 0, u[667] = 0, u[668] = 0, u[670] = 0, u[666] = 0, u[663] = 0, u[659] = 0, u[661] = 0, u[662] = 0, u[664] = 0, u[660] = 0, u[675] = 0, u[880] = 0, u[649] = 0, u[652] = 0, u[648] = 0, u[645] = 0, u[651] = 0, u[653] = 0, u[655] = 0, u[656] = 0, u[658] = 0, u[654] = 0, u[657] = 0, u[879] = 0, u[881] = 0, u[650] = 0, u[678] = 0, u[891] = 0, u[892] = 0, u[890] = 0, u[687] = 0, u[683] = 0, u[685] = 0, u[686] = 0, u[688] = 0, u[684] = 0, u[681] = 0, u[689] = 0, u[692] = 0, u[888] = 0, u[693] = 0, u[690] = 0, u[701] = 0, u[704] = 0, u[705] = 0, u[706] = 0, u[703] = 0, u[696] = 0, u[695] = 0, u[698] = 0, u[699] = 0, u[700] = 0, u[697] = 0, u[694] = 0, u[923] = 0, u[922] = 0, u[926] = 0, u[928] = 0, u[930] = 0, u[927] = 0, u[931] = 0, u[933] = 0, u[934] = 0, u[932] = 0, u[939] = 0, u[942] = 0, u[943] = 0, u[924] = 0, u[728] = 0, u[730] = 0, u[727] = 0, u[732] = 0, u[917] = 0, u[919] = 0, u[920] = 0, u[918] = 0, u[911] = 0, u[914] = 0, u[915] = 0, u[913] = 0, u[921] = 0, u[729] = 0, u[723] = 0, u[721] = 0, u[720] = 0, u[731] = 0, u[734] = 0, u[735] = 0, u[733] = 0, u[726] = 0, u[907] = 0, u[909] = 0, u[910] = 0, u[908] = 0, u[725] = 0, u[724] = 0, u[901] = 0, u[713] = 0, u[716] = 0, u[717] = 0, u[718] = 0, u[715] = 0, u[714] = 0, u[903] = 0, u[905] = 0, u[906] = 0, u[904] = 0, u[719] = 0, u[722] = 0, u[899] = 0, u[691] = 0, u[707] = 0, u[710] = 0, u[711] = 0, u[712] = 0, u[709] = 0, u[893] = 0, u[895] = 0, u[896] = 0, u[894] = 0, u[702] = 0, u[897] = 0, u[900] = 0, u[708] = 0, u[968] = 0, u[991] = 0, u[992] = 0, u[990] = 0, u[985] = 0, u[987] = 0, u[988] = 0, u[986] = 0, u[980] = 0, u[982] = 0, u[983] = 0, u[981] = 0, u[975] = 0, u[989] = 0, u[951] = 0, u[950] = 0, u[957] = 0, u[960] = 0, u[961] = 0, u[958] = 0, u[962] = 0, u[964] = 0, u[965] = 0, u[963] = 0, u[967] = 0, u[969] = 0, u[970] = 0, u[952] = 0, u[941] = 0, u[937] = 0, u[938] = 0, u[936] = 0, u[945] = 0, u[947] = 0, u[948] = 0, u[946] = 0, u[953] = 0, u[955] = 0, u[956] = 0, u[954] = 0, u[949] = 0, u[935] = 0, u[1011] = 0, u[1021] = 0, u[1042] = 0, u[1053] = 0, u[1007] = 0, u[1009] = 0, u[1010] = 0, u[1008] = 0, u[1003] = 0, u[1005] = 0, u[1006] = 0, u[1004] = 0, u[1000] = 0, u[1031] = 0, u[978] = 0, u[976] = 0, u[971] = 0, u[973] = 0, u[974] = 0, u[972] = 0, u[998] = 0, u[999] = 0, u[994] = 0, u[996] = 0, u[997] = 0, u[995] = 0, u[1002] = 0, u[979] = 0, u[1023] = 0, u[1022] = 0, u[1029] = 0, u[1032] = 0, u[1033] = 0, u[1030] = 0, u[1038] = 0, u[1040] = 0, u[1041] = 0, u[1039] = 0, u[1034] = 0, u[1036] = 0, u[1037] = 0, u[1024] = 0, u[1001] = 0, u[1018] = 0, u[1019] = 0, u[1017] = 0, u[1012] = 0, u[1014] = 0, u[1015] = 0, u[1013] = 0, u[1025] = 0, u[1027] = 0, u[1028] = 0, u[1026] = 0, u[1020] = 0, u[1016] = 0, u[1035] = 0, u[1058] = 0, u[1059] = 0, u[1057] = 0, u[1051] = 0, u[1054] = 0, u[1055] = 0, u[1052] = 0, u[1047] = 0, u[1049] = 0, u[1050] = 0, u[1048] = 0, u[1043] = 0, u[1056] = 0, u[1045] = 0, u[1044] = 0, u[1060] = 0, u[1062] = 0, u[1063] = 0, u[1061] = 0, u[1064] = 0, u[1066] = 0, u[1067] = 0, u[1065] = 0, u[1072] = 0, u[1074] = 0, u[1075] = 0, u[1046] = 0, u[1087] = 0, u[1088] = 0, u[1090] = 0, u[1091] = 0, u[1089] = 0, u[1092] = 0, u[1094] = 0, u[1095] = 0, u[1093] = 0, u[1096] = 0, u[1098] = 0, u[1099] = 0, u[1097] = 0, u[1085] = 0, u[1073] = 0, u[1070] = 0, u[1071] = 0, u[1069] = 0, u[1076] = 0, u[1078] = 0, u[1079] = 0, u[1080] = 0, u[1082] = 0, u[1083] = 0, u[1081] = 0, u[1084] = 0, u[1086] = 0, u[1068] = 0, u[1128] = 0, u[1131] = 0, u[1129] = 0, u[1132] = 0, u[1134] = 0, u[1135] = 0, u[1133] = 0, u[1136] = 0, u[1138] = 0, u[1139] = 0, u[1137] = 0, u[1144] = 0, u[1146] = 0, u[1130] = 0, u[1115] = 0, u[1116] = 0, u[1118] = 0, u[1119] = 0, u[1117] = 0, u[1120] = 0, u[1122] = 0, u[1123] = 0, u[1121] = 0, u[1124] = 0, u[1126] = 0, u[1127] = 0, u[1125] = 0, u[1113] = 0, u[1108] = 0, u[1111] = 0, u[1109] = 0, u[1104] = 0, u[1106] = 0, u[1107] = 0, u[1105] = 0, u[1100] = 0, u[1102] = 0, u[1103] = 0, u[1101] = 0, u[1112] = 0, u[1114] = 0, u[1110] = 0, u[1231] = 0, u[1224] = 0, u[1226] = 0, u[1227] = 0, u[1225] = 0, u[1232] = 0, u[1234] = 0, u[1235] = 0, u[1233] = 0, u[1240] = 0, u[1242] = 0, u[1243] = 0, u[1241] = 0, u[1229] = 0, u[1212] = 0, u[1215] = 0, u[1213] = 0, u[1216] = 0, u[1218] = 0, u[1219] = 0, u[1217] = 0, u[1220] = 0, u[1222] = 0, u[1223] = 0, u[1221] = 0, u[1228] = 0, u[1230] = 0, u[1214] = 0, u[1167] = 0, u[1200] = 0, u[1202] = 0, u[1203] = 0, u[1201] = 0, u[1204] = 0, u[1206] = 0, u[1207] = 0, u[1205] = 0, u[1208] = 0, u[1210] = 0, u[1211] = 0, u[1209] = 0, u[1165] = 0, u[1176] = 0, u[1179] = 0, u[1177] = 0, u[1172] = 0, u[1174] = 0, u[1175] = 0, u[1173] = 0, u[1168] = 0, u[1170] = 0, u[1171] = 0, u[1169] = 0, u[1164] = 0, u[1166] = 0, u[1178] = 0, u[1195] = 0, u[1188] = 0, u[1190] = 0, u[1191] = 0, u[1189] = 0, u[1184] = 0, u[1186] = 0, u[1187] = 0, u[1185] = 0, u[1180] = 0, u[1182] = 0, u[1183] = 0, u[1181] = 0, u[1193] = 0, u[1156] = 0, u[1159] = 0, u[1157] = 0, u[1160] = 0, u[1162] = 0, u[1163] = 0, u[1161] = 0, u[1196] = 0, u[1198] = 0, u[1199] = 0, u[1197] = 0, u[1192] = 0, u[1194] = 0, u[1158] = 0, u[1147] = 0, u[1140] = 0, u[1142] = 0, u[1143] = 0, u[1141] = 0, u[1148] = 0, u[1150] = 0, u[1151] = 0, u[1149] = 0, u[1152] = 0, u[1154] = 0, u[1155] = 0, u[1153] = 0, u[1145] = 0, u[1283] = 0, u[1284] = 0, u[1286] = 0, u[1287] = 0, u[1285] = 0, u[1288] = 0, u[1290] = 0, u[1291] = 0, u[1289] = 0, u[1292] = 0, u[1294] = 0, u[1295] = 0, u[1293] = 0, u[1281] = 0, u[1264] = 0, u[1267] = 0, u[1265] = 0, u[1272] = 0, u[1274] = 0, u[1275] = 0, u[1273] = 0, u[1276] = 0, u[1278] = 0, u[1279] = 0, u[1277] = 0, u[1280] = 0, u[1282] = 0, u[1266] = 0, u[1263] = 0, u[1256] = 0, u[1258] = 0, u[1259] = 0, u[1257] = 0, u[1252] = 0, u[1254] = 0, u[1255] = 0, u[1253] = 0, u[1268] = 0, u[1270] = 0, u[1271] = 0, u[1269] = 0, u[1261] = 0, u[1236] = 0, u[1239] = 0, u[1237] = 0, u[1244] = 0, u[1246] = 0, u[1247] = 0, u[1245] = 0, u[1248] = 0, u[1250] = 0, u[1251] = 0, u[1249] = 0, u[1260] = 0, u[1262] = 0, u[1238] = 0, u[1311] = 0, u[1309] = 0, u[1296] = 0, u[1299] = 0, u[1297] = 0, u[1304] = 0, u[1306] = 0, u[1307] = 0, u[1305] = 0, u[1300] = 0, u[1302] = 0, u[1303] = 0, u[1301] = 0, u[1308] = 0, u[1310] = 0, u[1298] = 0, u[227] = 0, u[91] = 0, u[6] = 0, u[5] = 0, u[84] = 0, u[85] = 0, u[86] = 0, u[83] = 0, u[76] = 0, u[97] = 0, u[98] = 0, u[99] = 0, u[96] = 0, u[65] = 0, u[21] = 0, u[22] = 0, u[23] = 0, u[24] = 0, u[25] = 0, u[26] = 0, u[27] = 0, u[28] = 0, u[29] = 0, u[30] = 0, u[31] = 0, u[32] = 0, u[93] = 0, u[95] = 0, u[15] = 0, u[16] = 0, u[18] = 0, u[19] = 0, u[20] = 0, u[11] = 0, u[12] = 0, u[13] = 0, u[14] = 0, u[10] = 0, u[74] = 0, u[88] = 0, u[90] = 0, u[92] = 0, u[89] = 0, u[82] = 0, u[81] = 0, u[71] = 0, u[223] = 0, u[218] = 0, u[220] = 0, u[221] = 0, u[222] = 0, u[219] = 0, u[217] = 0, u[327] = 0, u[87] = 0, u[79] = 0, u[80] = 0, u[70] = 0, u[72] = 0, u[73] = 0, u[66] = 0, u[67] = 0, u[17] = 0, u[228] = 0, u[69] = 0, u[637] = 0, u[412] = 0, u[409] = 0, u[407] = 0, u[402] = 0, u[404] = 0, u[405] = 0, u[406] = 0, u[403] = 0, u[414] = 0, u[417] = 0, u[418] = 0, u[419] = 0, u[75] = 0, u[77] = 0, u[45] = 0, u[47] = 0, u[48] = 0, u[49] = 0, u[50] = 0, u[39] = 0, u[40] = 0, u[41] = 0, u[42] = 0, u[43] = 0, u[44] = 0, u[33] = 0, u[34] = 0, u[46] = 0, u[8] = 0, u[68] = 0, u[78] = 0, u[94] = 0, u[1077] = 0} > F30:=map(V->map(K->map(r->PO(K,r),partition(30-K[1],min(30-K[1],9))),V > ),Bbc[1..15]): > nops(map(op,map(op,F30))); 2204 > nops(Bbc[16]); 12 > H30:=map(op,zip((i,j)->zip((k,l)->[k,l],i,j),F30,Bbc)): > H30:=map(r->[r[1],Nummer(r[2][2])],H30): > BH30:=map(r->op(map(u->u*Jhneu[r[2]],r[1])),H30): > nops(BH30); 2204 > map(r->Nummer(r[2]),Bbc[16]); [159, 160, 161, 162, 163, 164, 165, 166, 167, 169, 170, 168] > BH30:=[op(BH30),op(map(i->Jhneu[i],%))]: > nops(BH30); 2216 > L30:=coeffs(expand(coeff(add(u[i]*BH30[i],i=1..2216),z[3],1)),map(i->c > [i],[$1..9])): > M30:=coeffs(expand(coeff(add(u[i]*BH30[i],i=1..2216),z[3],2)),map(i->c > [i],[$1..9])): > nops({L30});nops({M30});nops({L30,M30}); 1697 1042 2733 > solve({L30,M30},map(i->u[i],{$1..2216})); > > F31:=map(V->map(K->map(r->PO(K,r),partition(31-K[1],min(31-K[1],9))),V > ),Bbc[1..16]): > nops(map(op,map(op,F31))); 2792 > nops(Bbc[17]); 6 > H31:=map(op,zip((i,j)->zip((k,l)->[k,l],i,j),F31,Bbc)): > H31:=map(r->[r[1],Nummer(r[2][2])],H31): > BH31:=map(r->op(map(u->u*Jhneu[r[2]],r[1])),H31): > nops(BH31); 2792 > map(r->Nummer(r[2]),Bbc[17]); [171, 172, 173, 174, 175, 176] > BH31:=[op(BH31),op(map(i->Jhneu[i],%))]: > nops(BH31); 2798 > L31:=coeffs(expand(coeff(add(u[i]*BH31[i],i=1..2798),z[3],1)),map(i->c > [i],[$1..9])): > M31:=coeffs(expand(coeff(add(u[i]*BH31[i],i=1..2798),z[3],2)),map(i->c > [i],[$1..9])): > LM31:={L31,M31}: > nops(LM31); 3256 > LM31:=[op(LM31)]: > MM31:=Matrix(3256,2798,(i,j)->coeff(LM31[i],u[j],1)): > save MM31,"/home/plesken/3256x2798rat.m"; > nops({L31}); 2015 > max(op(map(nops,LM31))); 1177 > 3200*2700; 8640000 >