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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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