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When I run Reduce[expr, vars] in which one of the variables has a subscript, Mathematica gives me an output after some minutes (the system has 10 equations), but if I change the variable with the subscript for a variable without it, Mathematica freezes after some time and does not give any answer.

I have tried to solve other systems with lesser dimensions, trying with some variables subscripted or trying with all variables non-subscripted, but the output is the same.

I don't know what is happening. I need the results but I don't know if I can trust them when I have a variable with a subscript. The system is

q = 1 - m^2/2 - 2 v^2 - w^2 + z^2 + Σ^2;
fx = x (q - 1 - 2 Σ) - 2 s p Subscript[ξ, j];
fy = y (Σ + q - 1) - Subscript[ξ, j] (p^2 + s^2 + w^2);
fw = w (Subscript[ξ, j] y + q - Σ) + Sqrt[2] Subscript[ξ, j] s z;
fz = z (q - 2) - w Subscript[ξ, j] (α v + Sqrt[2] s);
fv = v (q + 1) + α Subscript[ξ, j] w z;
fr = r (q - 1);
fm = m (q - 1/2);
fp = p (q - 1 + Σ+y ξ) +s x Subscript[ξ, j] ;
fs = s (2 y Subscript[ξ, j] - 2 Σ + q - 1);
fΣ = Σ (q - 2) - (p^2 - s^2) + w^2 - y^2 + x^2;
Subscript[fξ, j] = Subscript[ξ, j] (1 - Subscript[ξ, j] y + Σ);     

And the function

Reduce[
  {fx == 0, fy == 0, fw == 0, fz == 0, fv == 0, fm == 0, fp == 0, fs == 0, 
   fΣ == 0, Subscript[fξ, j] == 0}, 
  {x, y, w, z, v, m, p, s, Σ, Subscript[ξ, j]}];

I have Mathematica 10.2.

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    $\begingroup$ Please include code, otherwise we would not be able to give you specific answers. If you just need to check the accuracy of the results, you should be able to just substitute the results back into the original equation and see if it is satisfied. $\endgroup$ – MarcoB May 5 at 22:41
  • $\begingroup$ @MarcoB makes a good suggestion for checking the results. Even simpler is to substitute numbers for some or all of your variables e.g result /. x->5 (see ReplaceAll in the help). $\endgroup$ – mikado May 5 at 22:53
  • $\begingroup$ Subscript[fξ, j] == 0 looks suspicious. Shouldn't it be Subscriptfξ, j] == 0 $\endgroup$ – m_goldberg May 6 at 2:31
  • $\begingroup$ I don't understand the reason behind removing the "[" in your suggestion @m_goldberg. $\endgroup$ – Miguel Angel Alvarez Ballester May 6 at 16:32
  • $\begingroup$ Sorry, reviewing your code makes me think I read it wrong the 1st time. I see no problem on rereading. $\endgroup$ – m_goldberg May 6 at 16:53

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