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