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Reduce does not solve a system of equations

Discussion in 'Mathematics' started by pau1996, Aug 2, 2020 at 2:25 AM.

  1. pau1996

    pau1996 Guest

    I am trying to solve a system of 7 equations and 7 unknowns given a set of assuptions. I am only interested in obtaining V3 as a function of the exogenous parameters.

    I am using the following code:

    Reduce[V3 == (-12 s + 4 d V1 - 3 d l V1 + 4 d V2 - 3 d l V2 +
    3 d l V4 + 2 d l V5 + 2 d l V6 + 2 d l V7 + 12 w1 + 12 w4)/(
    12 - 4 d + 3 d l) &&
    V2 == (-12 s + 4 d V1 - 3 d l V1 + 4 d V3 - 3 d l V3 + 3 d l V4 +
    2 d l V5 + 2 d l V6 + 2 d l V7 + 12 w1 + 12 w3)/(
    12 - 4 d + 3 d l) &&
    V1 == (-12 s + 4 d V2 - 3 d l V2 + 4 d V3 - 3 d l V3 + 3 d l V4 +
    2 d l V5 + 2 d l V6 + 2 d l V7 + 12 w1 + 12 w2)/(
    12 - 4 d + 3 d l) &&
    V4 == (12 s + d l V1 + d l V2 + d l V3 + 2 d l V5 + 2 d l V6 +
    2 d l V7)/(3 (4 - 4 d + 3 d l)) &&
    V5 == (-12 b + d l V1 + d l V2 + d l V3 + 3 d l V4 + 4 d V6 -
    2 d l V6 + 4 d V7 - 2 d l V7 + 12 w2)/(2 (6 - 2 d + d l)) &&
    V6 == (-12 b + d l V1 + d l V2 + d l V3 + 3 d l V4 + 4 d V5 -
    2 d l V5 + 4 d V7 - 2 d l V7 + 12 w3)/(2 (6 - 2 d + d l)) &&
    V7 == (-12 b + d l V1 + d l V2 + d l V3 + 3 d l V4 + 4 d V5 -
    2 d l V5 + 4 d V6 - 2 d l V6 + 12 w4)/(2 (6 - 2 d + d l)) &&
    w1 > s > w2 > w3 > w4 > b > 0 && w1 + w2 + w3 + w4 == 4 s &&
    0 < d < 1 && 0 < l < 1, {V3, V2, V1, V4, V5, V6, V7, s}]


    I solved similar systems using this method and I also tried to use Solve instead of Reduce without success. However, Mathematica does not return me anything in this case.

    Does anyone know a different way to solve this problem?

    Thanks in advance.

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