A nonlinear system

*To*: mathgroup at smc.vnet.net*Subject*: [mg28671] A nonlinear system*From*: "PSi" <psino at tee.gr>*Date*: Tue, 8 May 2001 02:51:09 -0400 (EDT)*Organization*: National Technical University of Athens, Greece*Sender*: owner-wri-mathgroup at wolfram.com

I am trying to solve a system of equations using this code: bt=Table[Sum[a[k,i], {i,0,n-k}], {k,0,n}] btt=Table[If[k==2,1,0], {k,0,n}] ct=Table[(Sum[a[i,k], {i,0,n-k}])^2, {k,2,n}] ctt=Table[If[k==2,1,0], {k,2,n}] f2=Sum[a[k,i] x^k x^i, {k,0,n}, {i,0,n-k}] f3=Sum[a[k,i] f2^k x^i, {k,0,n}, {i,0,n-k}]/x f4=Sum[a[k,i] f3^k x^i, {k,0,n}, {i,0,n-k}]/f2 p1=f2 f4 x^n+x^(n^3+15) g4=Sum[a[k,i] f2^k f2^i, {k,0,n}, {i,0,n-k}] p2=f2 g4 x^n+x^(n^3+15) eqns={bt==btt, ct==ctt, Sum[a[i,0], {i,0,n}]==0, CoefficientList[p1,x]==CoefficientList[p2,x]} Union[Solve[eqns]] It is a conjecture that for any n>3 the solutions of this system are 1. a[0,2]=1, a[2,0]=1, a[1,1]=c, a[0,1]=-c, a[1,0]=-c, a[0,0]=c-1 2. a[0,2]=-1, a[2,0]=1, a[0,1]=2, a[0,0]=-1 3. a[2,2]=1 with arbitrary c, and all other a[i,j] being equal to zero. Could anybody verify this for some value of n>5 (if possible for n=10) by using the above code? For n=4, Mathematica 2.2 on my PC (40 MB ram) gives Out of memory. Thanks, PSi