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