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MathGroup Archive 2007

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Re: Trouble with a system of equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg77722] Re: Trouble with a system of equations
  • From: Yaroslav Bulatov <yaroslavvb at gmail.com>
  • Date: Fri, 15 Jun 2007 04:44:10 -0400 (EDT)
  • References: <f4lb44$fvv$1@smc.vnet.net><200706131142.HAA07187@smc.vnet.net>

As Ray Koopman and some others pointed out, the system of equations
becomes linear with a proper choice of variables. But now getting the
original variables is problematic.

In particular, if I replace all terms of the form Exp[a+b+c]/1+Exp[a+b
+c..] with single variables, I will have to solve the following to get
a,b,c..back

mapping[k_] := Module[{mm, params, tuples},
  mm = KroneckerProduct @@ Table[{{1, 1}, {1, 0}}, {i, 1, k}];
  params = (Subscript[t, #1] & ) /@ Range[1, 2^k];
  tuples = (Plus @@ (params*#1) & ) /@ mm /. a_Plus :> Times @@ a;
  terms = (#1/(#1 + 1) & ) /@ tuples;
  {MapIndexed[#1 == Subscript[m, #2[[1]]] & , terms], params}]


Inverting it for 2 variables works
Solve @@ mapping[2]

But for 3 variables it takes too long
Solve @@ mapping[3]

Making equations polynomial and solving them gives solution in terms
of "InverseFunction" for 3 variables and takes too long for 4



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