> # ``classicalR3Z3braidform.mws'' > # This program computes the cocycle invariant for R_3 > # with Z_3 coefficients for a given closed braid. > # A 2-cocy is specified below by specific values and solutions. > # Output: > # The color vector at the s-th braid generator, the coefficient matrix > # acting on the cocycle, the cocycle value at the crossing, the coeff times > # the cocycle value (state-sum contribution), and the last line is the cocycle > # invariant (a family of vectors). > > > clear: > with(LinearAlgebra): > > # Forming vectors. > f:=array(0..2,0..2,1..3): > > # Quandle cocycle conditions. > for i from 0 to 2 do > for k from 1 to 3 do > f[i,i,k]:=0 : > od: od: > > f[1,2,1]:=2: > f[1,2,2]:=2: > f[1,2,3]:=0: > f[1,0,1]:=0: > f[1,0,2]:=2: > f[1,0,3]:=0: > f[2,1,2]:=0: > > h:=array(0..2,0..2): > for i from 0 to 2 do > for j from 0 to 2 do > h[i,j]:=Vector([f[i,j,1],f[i,j,2],f[i,j,3]]): > od: od: > > # Defining matrices, 1 = (2 3), 2 = (1 3), 0 = (1 2). > M[1]:=<<1,0,0>|<0,0,1>|<0,1,0>>: > M[2]:=<<0,0,1>|<0,1,0>|<1,0,0>>: > M[0]:=<<0,1,0>|<1,0,0>|<0,0,1>>: > > # Defining quandle operation. > for i from 0 to 2 do > for j from 0 to 2 do > g[i,j]:=2*j-i mod 3 : > od: od: > > # Defining 2-cocy equations. > for x from 0 to 2 do > for y from 0 to 2 do > for z from 0 to 2 do > E[x,y,z]:= M[z].h[x,y] + h[g[x,y],z] + M[g[g[x,y],z]].h[y,z] > - h[y,z] - M[g[y,z]].h[x,z] - h[g[x,z],g[y,z]]: > od: od: od: > > # Defining the set of equations. > EQ:=[]: > for x from 0 to 2 do > for y from 0 to 2 do > for z from 0 to 2 do > for w from 1 to 3 do > EQ:=[ op(EQ), E[x,y,z][w]=0 ] : > od: od: od: od: > Eq:=convert(EQ, set): # Converting the list EQ to a set Eq. > > # Solving the cocycle conditions: > Sol:=msolve(Eq, Var, 3); > > ## The following prints the cocycle values, if necessary. > #for i from 0 to 2 do > #for j from 0 to 2 do > #print(subs(Sol, h[i,j])); > #od: od: > > Sol := {f[0, 2, 3] = 0, f[0, 2, 1] = 0, f[2, 0, 3] = 0, f[0, 1, 1] = 1, f[0, 1, 2] = 2, f[2, 1, 3] = 1, f[2, 0, 1] = 1, f[2, 1, 1] = 1, f[0, 1, 3] = 1, f[2, 0, 2] = 0, f[0, 2, 2] = 2} > # Input a braid word and the braid index, brind, here: > bw[1]:= [1,1,2,3,3,-1,2,-3,2]: brind[1]:=4: > # This is 7_4 as an example. > > for KT from 1 to 1 do # Add bw[j] above for j=2,3,..., and can do all at once. > > print(Knot, KT); # When you do more than one, this will print the number. > > # Setting up the state-sum terms. > SST:= [ ] : > > # Defining Burau rep for R_3, acting from the right to row vectors. > Burau:=linalg[matrix](2,2,[0,-1,1,2]): > Burinv:=linalg[matrix](2,2,[2,1,-1,0]): > > for j0 from 1 to brind[KT]-1 do # Copying the Burau matrix into bigger ones. > B[j0]:=array(1..brind[KT],1..brind[KT]): > B[-j0]:=array(1..brind[KT],1..brind[KT]): > od: > ID:=Matrix(1..brind[KT],1..brind[KT],shape=identity); > for j1 from 1 to brind[KT]-1 do > for j2 from 1 to brind[KT] do > for j3 from 1 to brind[KT] do > B[j1][j2,j3]:=linalg[copyinto](Burau, ID, j1,j1)[j2,j3]: > B[-j1][j2,j3]:=linalg[copyinto](Burinv, ID, j1,j1)[j2,j3]: > od: od: od: > > # Color vectors. > for jj3 from 1 to (nops(bw[KT])+1) do > Color[jj3]:=array(1..brind[KT]): > od: > > # Producing all color vectors. > num:=3^(brind[KT]) : > for indx from 0 to (num-1) do # One color at a time. > > for jj5 from 1 to brind[KT] do > Color[1][jj5]:=iquo(indx,3^(jj5-1)) mod 3: > od: > > # Computing all color vectors. > for jj6 from 1 to nops(bw[KT]) do > Newcolorvec[jj6]:=evalm(Color[jj6] &* B[bw[KT][jj6]]): > for jj8 from 1 to brind[KT] do > Color[jj6+1][jj8]:=map( z -> z mod 3, Newcolorvec[jj6][jj8]): > od: > od: > > SSTcontri:=Vector([0,0,0]): > # State-sum contributions. > > # Finding if the colors match. > ColorDiff0:=evalm(Color[1]-Color[nops(bw[KT])+1]); > ColDiffMatch0:=sum(abs(ColorDiff0[jj]),jj=1..brind[KT]); > # This is zero iff the top color vec matches the bottom. > > > if ColDiffMatch0 =0 then > > > for s from 1 to nops(bw[KT]) do > > # Computing the weight in front of the cocycle. > > WT[0]:=Matrix(1..3,1..3,shape=identity): > WT[1]:=M[Color[s][brind[KT]]]: > # WT[1] is the weight for the crossing of \sigma_{n-2}. The target region is > # to the right of the crossing. > for k7 from 1 to (brind[KT]-1) do > WT[k7+1]:=MatrixMatrixMultiply( WT[k7], M[Color[s][brind[KT]-k7]] ) : > od: > > # The weight WGT[1] for the \signa_1 is WT[n-2], > # and WGT[2]=WT[n-3], ... , WGT[n-2]=WT[1]. > > if brind[KT]>2 then > for k77 from 1 to (brind[KT]-2) do > WGT[k77]:=WT[brind[KT]-k77-1]: > od: > WGT[brind[KT]-1]:=WT[0]: > else > WGT[1]:=WT[0]: > fi: > > if (bw[KT][s])>0 then > > SSTcontri:=evalm( SSTcontri + > MatrixVectorMultiply(WGT[abs(bw[KT][s])], > h[Color[s][abs(bw[KT][s])], Color[s][abs(bw[KT][s])+1] ] ) ): > > # Printing details. > # The color vector at the s-th braid generator, the coefficient matrix > # acting on the cocycle, and the cocycle value at the crossing, coeff times > # the cocycle value. > > print(PrintingColors, s, Color[s], WeightCoeff, WGT[abs(bw[KT][s])], StateSumContribution, map(z -> z mod 3, subs(Sol, > h[Color[s][abs(bw[KT][s])], Color[s][abs(bw[KT][s])+1] ] )), > map(z -> z mod 3, subs(Sol, > MatrixVectorMultiply(WGT[abs(bw[KT][s])], > h[Color[s][abs(bw[KT][s])], Color[s][abs(bw[KT][s])+1] ] ) ) )); > > else > > SSTcontri:=evalm( SSTcontri - > MatrixVectorMultiply(WGT[abs(bw[KT][s])], > h[Color[s+1][abs(bw[KT][s])], Color[s][abs(bw[KT][s])] ] ) ): > > # Printing details. > > print(PrintingColors, s, Color[s], WeightCoeff, WGT[abs(bw[KT][s])], StateSumContribution, map(z -> z mod 3, subs(Sol, > h[Color[s+1][abs(bw[KT][s])], Color[s][abs(bw[KT][s])] ] )), > map(z -> z mod 3, subs(Sol, > MatrixVectorMultiply(WGT[abs(bw[KT][s])], > h[Color[s+1][abs(bw[KT][s])], Color[s][abs(bw[KT][s])] ] ) ) ) ); > > fi: > > > od: # Closing the state-sum term, for s. > > SST:=[ op(SST), map(z -> z mod 3, subs(Sol, evalm(SSTcontri) ) ) ]: > > fi: # Closing the case when it colors. > > > od: # Closing one color here at a time, for indx. > > > print(SST); > > od: # Closing KT. > Knot, 1 [1 0 0] [ ] PrintingColors, 1, [0, 0, 0, 0], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 2, [0, 0, 0, 0], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [0 1 0] [ ] PrintingColors, 3, [0, 0, 0, 0], WeightCoeff, [1 0 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 4, [0, 0, 0, 0], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 5, [0, 0, 0, 0], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 6, [0, 0, 0, 0], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [0 1 0] [ ] PrintingColors, 7, [0, 0, 0, 0], WeightCoeff, [1 0 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 8, [0, 0, 0, 0], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [0 1 0] [ ] PrintingColors, 9, [0, 0, 0, 0], WeightCoeff, [1 0 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [0 0 1] [ ] PrintingColors, 1, [0, 1, 1, 0], WeightCoeff, [1 0 0], [ ] [0 1 0] [1] [1] [ ] [ ] StateSumContribution, [2], [1] [ ] [ ] [1] [2] [0 0 1] [ ] PrintingColors, 2, [1, 2, 1, 0], WeightCoeff, [1 0 0], [ ] [0 1 0] [2] [0] [ ] [ ] StateSumContribution, [2], [2] [ ] [ ] [0] [2] [0 1 0] [ ] PrintingColors, 3, [2, 0, 1, 0], WeightCoeff, [1 0 0], [ ] [0 0 1] [1] [2] [ ] [ ] StateSumContribution, [2], [1] [ ] [ ] [1] [1] [1 0 0] [ ] PrintingColors, 4, [2, 1, 2, 0], WeightCoeff, [0 1 0], [ ] [0 0 1] [1] [1] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 5, [2, 1, 0, 1], WeightCoeff, [0 1 0], [ ] [0 0 1] [1] [1] [ ] [ ] StateSumContribution, [2], [2] [ ] [ ] [1] [1] [0 1 0] [ ] PrintingColors, 6, [2, 1, 1, 2], WeightCoeff, [0 0 1], [ ] [1 0 0] [0] [2] [ ] [ ] StateSumContribution, [2], [0] [ ] [ ] [0] [0] [0 0 1] [ ] PrintingColors, 7, [0, 2, 1, 2], WeightCoeff, [0 1 0], [ ] [1 0 0] [1] [1] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [1] [1] [1 0 0] [ ] PrintingColors, 8, [0, 1, 0, 2], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [2], [2] [ ] [ ] [0] [0] [0 1 0] [ ] PrintingColors, 9, [0, 1, 1, 0], WeightCoeff, [1 0 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [0 1 0] [ ] PrintingColors, 1, [0, 2, 2, 0], WeightCoeff, [0 0 1], [ ] [1 0 0] [0] [2] [ ] [ ] StateSumContribution, [2], [0] [ ] [ ] [0] [0] [0 1 0] [ ] PrintingColors, 2, [2, 1, 2, 0], WeightCoeff, [0 0 1], [ ] [1 0 0] [1] [0] [ ] [ ] StateSumContribution, [0], [1] [ ] [ ] [1] [1] [0 1 0] [ ] PrintingColors, 3, [1, 0, 2, 0], WeightCoeff, [1 0 0], [ ] [0 0 1] [0] [2] [ ] [ ] StateSumContribution, [2], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 4, [1, 2, 1, 0], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [2], [2] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 5, [1, 2, 0, 2], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [2], [2] [ ] [ ] [0] [0] [0 0 1] [ ] PrintingColors, 6, [1, 2, 2, 1], WeightCoeff, [1 0 0], [ ] [0 1 0] [1] [1] [ ] [ ] StateSumContribution, [2], [1] [ ] [ ] [1] [2] [1 0 0] [ ] PrintingColors, 7, [0, 1, 2, 1], WeightCoeff, [0 0 1], [ ] [0 1 0] [2] [2] [ ] [ ] StateSumContribution, [2], [0] [ ] [ ] [0] [2] [1 0 0] [ ] PrintingColors, 8, [0, 2, 0, 1], WeightCoeff, [0 1 0], [ ] [0 0 1] [1] [1] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [0 1 0] [ ] PrintingColors, 9, [0, 2, 2, 0], WeightCoeff, [1 0 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [0 1 0] [ ] PrintingColors, 1, [1, 0, 0, 1], WeightCoeff, [0 0 1], [ ] [1 0 0] [0] [2] [ ] [ ] StateSumContribution, [2], [0] [ ] [ ] [0] [0] [0 1 0] [ ] PrintingColors, 2, [0, 2, 0, 1], WeightCoeff, [0 0 1], [ ] [1 0 0] [0] [2] [ ] [ ] StateSumContribution, [2], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 3, [2, 1, 0, 1], WeightCoeff, [0 0 1], [ ] [0 1 0] [0] [0] [ ] [ ] StateSumContribution, [2], [0] [ ] [ ] [0] [2] [1 0 0] [ ] PrintingColors, 4, [2, 0, 2, 1], WeightCoeff, [0 1 0], [ ] [0 0 1] [1] [1] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [1] [1] [1 0 0] [ ] PrintingColors, 5, [2, 0, 1, 0], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [2], [2] [ ] [ ] [0] [0] [0 0 1] [ ] PrintingColors, 6, [2, 0, 0, 2], WeightCoeff, [1 0 0], [ ] [0 1 0] [2] [0] [ ] [ ] StateSumContribution, [2], [2] [ ] [ ] [0] [2] [0 0 1] [ ] PrintingColors, 7, [1, 2, 0, 2], WeightCoeff, [0 1 0], [ ] [1 0 0] [1] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [1] [1 0 0] [ ] PrintingColors, 8, [1, 0, 1, 2], WeightCoeff, [0 1 0], [ ] [0 0 1] [1] [1] [ ] [ ] StateSumContribution, [2], [2] [ ] [ ] [1] [1] [1 0 0] [ ] PrintingColors, 9, [1, 0, 0, 1], WeightCoeff, [0 0 1], [ ] [0 1 0] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 1, [1, 1, 1, 1], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 2, [1, 1, 1, 1], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 3, [1, 1, 1, 1], WeightCoeff, [0 0 1], [ ] [0 1 0] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 4, [1, 1, 1, 1], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 5, [1, 1, 1, 1], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 6, [1, 1, 1, 1], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 7, [1, 1, 1, 1], WeightCoeff, [0 0 1], [ ] [0 1 0] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 8, [1, 1, 1, 1], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 9, [1, 1, 1, 1], WeightCoeff, [0 0 1], [ ] [0 1 0] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [0 0 1] [ ] PrintingColors, 1, [1, 2, 2, 1], WeightCoeff, [1 0 0], [ ] [0 1 0] [2] [0] [ ] [ ] StateSumContribution, [2], [2] [ ] [ ] [0] [2] [0 0 1] [ ] PrintingColors, 2, [2, 0, 2, 1], WeightCoeff, [1 0 0], [ ] [0 1 0] [1] [0] [ ] [ ] StateSumContribution, [0], [1] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 3, [0, 1, 2, 1], WeightCoeff, [0 0 1], [ ] [0 1 0] [2] [2] [ ] [ ] StateSumContribution, [2], [0] [ ] [ ] [0] [2] [1 0 0] [ ] PrintingColors, 4, [0, 2, 0, 1], WeightCoeff, [0 1 0], [ ] [0 0 1] [1] [1] [ ] [ ] StateSumContribution, [2], [2] [ ] [ ] [1] [1] [1 0 0] [ ] PrintingColors, 5, [0, 2, 1, 2], WeightCoeff, [0 1 0], [ ] [0 0 1] [2] [2] [ ] [ ] StateSumContribution, [2], [2] [ ] [ ] [0] [0] [0 1 0] [ ] PrintingColors, 6, [0, 2, 2, 0], WeightCoeff, [0 0 1], [ ] [1 0 0] [0] [2] [ ] [ ] StateSumContribution, [2], [0] [ ] [ ] [0] [0] [0 1 0] [ ] PrintingColors, 7, [1, 0, 2, 0], WeightCoeff, [1 0 0], [ ] [0 0 1] [0] [2] [ ] [ ] StateSumContribution, [2], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 8, [1, 2, 1, 0], WeightCoeff, [0 1 0], [ ] [0 0 1] [1] [1] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [1] [1] [1 0 0] [ ] PrintingColors, 9, [1, 2, 2, 1], WeightCoeff, [0 0 1], [ ] [0 1 0] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [0 0 1] [ ] PrintingColors, 1, [2, 0, 0, 2], WeightCoeff, [1 0 0], [ ] [0 1 0] [1] [0] [ ] [ ] StateSumContribution, [0], [1] [ ] [ ] [0] [0] [0 0 1] [ ] PrintingColors, 2, [0, 1, 0, 2], WeightCoeff, [1 0 0], [ ] [0 1 0] [1] [1] [ ] [ ] StateSumContribution, [2], [1] [ ] [ ] [1] [2] [0 0 1] [ ] PrintingColors, 3, [1, 2, 0, 2], WeightCoeff, [0 1 0], [ ] [1 0 0] [1] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [1] [1 0 0] [ ] PrintingColors, 4, [1, 0, 1, 2], WeightCoeff, [0 1 0], [ ] [0 0 1] [2] [2] [ ] [ ] StateSumContribution, [2], [2] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 5, [1, 0, 2, 0], WeightCoeff, [0 1 0], [ ] [0 0 1] [1] [1] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [0 1 0] [ ] PrintingColors, 6, [1, 0, 0, 1], WeightCoeff, [0 0 1], [ ] [1 0 0] [1] [0] [ ] [ ] StateSumContribution, [0], [1] [ ] [ ] [1] [1] [1 0 0] [ ] PrintingColors, 7, [2, 1, 0, 1], WeightCoeff, [0 0 1], [ ] [0 1 0] [0] [0] [ ] [ ] StateSumContribution, [2], [0] [ ] [ ] [0] [2] [1 0 0] [ ] PrintingColors, 8, [2, 0, 2, 1], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [2], [2] [ ] [ ] [0] [0] [0 0 1] [ ] PrintingColors, 9, [2, 0, 0, 2], WeightCoeff, [0 1 0], [ ] [1 0 0] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [0 1 0] [ ] PrintingColors, 1, [2, 1, 1, 2], WeightCoeff, [0 0 1], [ ] [1 0 0] [1] [0] [ ] [ ] StateSumContribution, [0], [1] [ ] [ ] [1] [1] [0 1 0] [ ] PrintingColors, 2, [1, 0, 1, 2], WeightCoeff, [0 0 1], [ ] [1 0 0] [0] [2] [ ] [ ] StateSumContribution, [2], [0] [ ] [ ] [0] [0] [0 0 1] [ ] PrintingColors, 3, [0, 2, 1, 2], WeightCoeff, [0 1 0], [ ] [1 0 0] [1] [1] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [1] [1] [1 0 0] [ ] PrintingColors, 4, [0, 1, 0, 2], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [2], [2] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 5, [0, 1, 2, 1], WeightCoeff, [0 1 0], [ ] [0 0 1] [1] [1] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [1] [1] [0 0 1] [ ] PrintingColors, 6, [0, 1, 1, 0], WeightCoeff, [1 0 0], [ ] [0 1 0] [1] [0] [ ] [ ] StateSumContribution, [0], [1] [ ] [ ] [0] [0] [0 1 0] [ ] PrintingColors, 7, [2, 0, 1, 0], WeightCoeff, [1 0 0], [ ] [0 0 1] [1] [2] [ ] [ ] StateSumContribution, [2], [1] [ ] [ ] [1] [1] [1 0 0] [ ] PrintingColors, 8, [2, 1, 2, 0], WeightCoeff, [0 1 0], [ ] [0 0 1] [2] [2] [ ] [ ] StateSumContribution, [2], [2] [ ] [ ] [0] [0] [0 0 1] [ ] PrintingColors, 9, [2, 1, 1, 2], WeightCoeff, [0 1 0], [ ] [1 0 0] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 1, [2, 2, 2, 2], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 2, [2, 2, 2, 2], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [0 0 1] [ ] PrintingColors, 3, [2, 2, 2, 2], WeightCoeff, [0 1 0], [ ] [1 0 0] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 4, [2, 2, 2, 2], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 5, [2, 2, 2, 2], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 6, [2, 2, 2, 2], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [0 0 1] [ ] PrintingColors, 7, [2, 2, 2, 2], WeightCoeff, [0 1 0], [ ] [1 0 0] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [1 0 0] [ ] PrintingColors, 8, [2, 2, 2, 2], WeightCoeff, [0 1 0], [ ] [0 0 1] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [0 0 1] [ ] PrintingColors, 9, [2, 2, 2, 2], WeightCoeff, [0 1 0], [ ] [1 0 0] [0] [0] [ ] [ ] StateSumContribution, [0], [0] [ ] [ ] [0] [0] [[0, 0, 0], [1, 1, 1], [1, 1, 1], [1, 1, 1], [0, 0, 0], [1, 1, 1], [1, 1, 1], [1, 1, 1], [0, 0, 0]] > >