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