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Simplification of fraction containing subscripted variables

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123108] Simplification of fraction containing subscripted variables
  • From: "guido.reichert" <guido.reichert at gmx.de>
  • Date: Wed, 23 Nov 2011 07:08:38 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Dear all:

I cannot get Mathematica 8 to simplify a fraction containing sums and
subscripted variables although in reality this should (probably?) be
quite straightforward.

Here are two definitions I am using:

Subscript[OverTilde[p], t, z] :=
  Subscript[e, t, z]/(Subscript[OverTilde[f], t]*
          Subscript[OverTilde[m], t, z]);
bed1 = Subscript[e, t, z] == Subscript[\[Lambda], t, z]*
       Sum[Subscript[OverTilde[p], t, z]*Subscript[f, t, z, i, j],
         {i, 1, Subscript[i, max]}, {j, 1, Subscript[j, max]}] (* a
condition to be met*)

Now to solve this for Lambda one simple has to substitute the first
definition into the bed1-equation and the solution is a fraction where
everything but f_t,z,i,j is exogenous (e.g. a constant). Thus the
e_t,z should easily cancel out and the product of m_t,z times f_t
should become the numerator of the fraction that builds the solution
with the double sum of the f_t,z,i,j (summed over i and j) remains in
the denominator.

Essentially very simple - BUT Mathematica does not recognizes it even
giving it some assumptions:

FullSimplify[Solve[bed1, Subscript[\[Lambda], t, z]],
   Assumptions ->
  ForAll[{t, z, i, j}, Subscript[f, t, z, i, j] >= 0] &&
       Subscript[e, t, z] > 0 && Subscript[OverTilde[f], t] > 0 &&
       Subscript[OverTilde[m], t, z] > 0 && Subscript[i, max] > 0 &&
       Subscript[j, max] > 0]

Whatever I do I cannot get things to cancel out of the Sums (e.g. the
e_t,z should "at least" cancel out). What can and should I do?

Kind regards,

Guido



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