RCCOUT_20060922_0827.mw

 > Delta:=evalm((R-B)/2):A:=evalm((R+B)/2): `R`=matrans(R);`B`=matrans(B);

 > print("pi=",pi);

AA is (numerical) Asup2. Use A2 for two-out subgraph corresponding to the coloring

 > eau:=evalm(AA&*uu);idx:={}:for i to NN do if (eau[i]<1) then idx:=idx union {i} fi od:print("not crossed",idx);

 > unassign('t'):map(evalf,eigenvalues(A));map(abs,map(evalf,[eigenvalues(A)]));   map(abs,map(evalf,[eigenvalues(AA)]));

 > A2:=evalm((1/2)*(R2+B2)):a2:=evalm(AA+Del2):iszero(A2-a2),"det",det(evalm(J2-AA)),"synced?",det(J2-A2);

 > map(abs,map(evalf,[eigenvalues(A2)]));

 > print(P,Q);

 > rdd:=read2(Del2):for i to nops(rdd[1]) do print(convert(choose(n,2)[i],set),i,rdd[1][i],"               ",rdd[2][i]) od;

 > unassign('x'):pi2:=evalm(1/x[1]*(linsolve(transpose(J2-A2),vector(NN,0),'r',x)));u2:=evalm((1/x[1]*linsolve(J2-A2,vector(NN,0),'r',x)));

 > k:=2:print(seq({i,choose(n,k)[i]},i=1..binomial(n,k)));

 > NN:=binomial(n,2):J2:=IdentityMatrix(binomial(n,2)):unassign('e','x'):e:=vector(n):ee:=vector(n,1):ee:=evalm(e):phi:=diag(seq(ee[q],q=1..n)):deta:=multiply(phi,Delta):psi:=sympow(phi,2):

 > APART:=ecliffe(evalm(symult(A,J)+symult(deta,J)));

 > A2:=evalm(AA+D2):#"xA2",xtend(A2);

 > J2A2:=evalm(J2-A2):evalm(J2A2);

DJ2 is the determinant with e's

 > dt2:=det(J2-AA):"FROM det Asup2",dt2;DJ2:=ecliffit(det(J2A2));gamma:=zcliffsubsmat(DJ2,vector(n,0)):"LOOKING FOR",gamma;

 > evalf(dt2),"gamma",evalf(gamma),evalf(dt2-gamma);

 > "PI-SIDE",matvec(ecliffe(map(simplify,evalm((linsolve(transpose(J2-AA-Del2),vector(NN,0),'r',x))))));

 > "U-SIDE",matvec(ecliffe(map(simplify,evalm((linsolve((J2-AA-Del2),vector(NN,0),'r',x))))));

 > V2:=transpose(linsolve(transpose(J2-AA),transpose(Del2),'r',a));

 > #####################################################################################

 > #################### !!!!!!!!!!!!!!!!!! START RUNS HERE !!!!!!!!!!!!! ######################################

 > #####################################################################################

 > print(matrans(R),matrans(B));

 > "rank Delta"=rank(Delta);"rank A"=rank(A);"min-poly",factor(minpoly(Delta,x));unassign('phi','ee','e');print("pi",pi);

 > d:=rank(Delta);n:=rowdim(A):zeta:=vector(n,0):ND:=nullspace(Delta);P:=concat(seq(ND[k],k=1..nops(ND)),seq(zeta,j=1..d)):nullspace(J-P);

DETTA DEFINED HERE

 > ee:=[1,1,1,1,1,1,1,1,1,1,1, 1,1, 1]:phi:=diag(seq(ee[q],q=1..n)):Detta:=evalm(phi&*Delta):R:=evalm(A+Detta):B:=evalm(A-Detta):matrans(R),matrans(B);factor(minpoly(R,s)),factor(minpoly(B,s));nullspace(transpose(Detta));minpoly(Detta,x),factor(minpoly(Detta,x));D2:=sympow(Detta,2):psi:=sympow(phi,2):"MORPHISM CHECK",iszero(evalm(psi&*Del2-D2));A2:=evalm(AA+D2);

 > map(abs,map(evalf,[eigenvalues(AA)]));map(abs,map(evalf,[eigenvalues(A2)]));

PLOT OF det(I-Asup2-t times Del2)

 > unassign('t'):dp:=simplify(det(J2-AA-t*D2));subs(t=0,dp),subs(t=1,dp);plot(dp,t=-0.1..1.1);

 > trace(D2);V2:=multiply(D2,inverse(J2-AA)):trace(V2)*(-1);

FULLY SYMMETRIC ARE COMING HERE

 > AS2:=sym2(A):RS2:=sym2(R):BS2:=sym2(B):as2:=evalm(1/2*(RS2+BS2)):

 > print("A-sup-2",AA,"A",A,"A-SYM2",AS2);

 > JX:=IdentityMatrix(NN+n):unassign('t'):factor(det(JX-t*AS2));

 > "pi for ASYM2",nullspace(transpose(JX-AS2));

 > print("RS2",RS2,"BS2",BS2,"as2 combines RS2 and BS2",as2);

 > unassign('x'):psi2:=evalm((linsolve(transpose(JX-as2),vector(n+NN,0),'r',x)));us2:=evalm((linsolve(JX-as2,vector(n+NN,0),'r',x)));

HERE THE ABSORBING STATE HAS BEEN EXTENDED TO n STATES

 > abas2:=abel(as2);

LEVEL TWO HERE

 > R2:=sympow(R,2):B2:=sympow(B,2):

 > N2:=binomial(n,2):J2:=evalm(IdentityMatrix(N2)):UJ:=matrix(n,n,1):

 > nx:=evalm(linsolve(Omega,vector(n,0),'r',x));

 > unassign('x'):pi2:=evalm(1/x[1]*linsolve(J2-transpose(A2),vector(N2,0),'r',x)):u2:=evalm(1/x[1]*linsolve(J2-A2,vector(N2,0),'r',x)):

 > print("pi2",pi2);print("u2",evalm(u2));uu:=vector(N2,1):

 > pssi2:=subs({x[1]=1,x[2]=0},evalm(psi2));uss2:=subs({x[1]=2,x[2]=3},evalm(us2));

 > rank(abas2);