# Different output to Solve command in Mathematica changing a variable for a subscripted variable

I have a system of equations that is solved with the Solve command in Mathematica 10.2, when one of the variables is changed for a subscripted variable the answer is not the same, the difference is minimal, but they still change. The system has 9 variables

q = 1 - m^2/2 - 2 v^2 - w^2 + z^2 + Σ^2 ;
fx = x (q - 1 - 2 Σ) - 2 s^3 p Subscript[ξ, j];
fy = y (Σ + q - 1) - Subscript[ξ, j] ((p s)^2 + s^4+ w^2);
fw = w (Subscript[ξ, j] y + q - Σ) +Sqrt[2] Subscript[ξ, j] s^2 z;
fz = z (q - 2) - w Subscript[ξ, j] (α v + Sqrt[2] s^2);
fv = v (q + 1) +α Subscript[ξ, j] w z;
fr = r (q - 1);
fm = m (q - 1/2);
fp = (1/2) (p (q - 1 + 4 Σ) + 2 x Subscript[ξ, j] s);
fs = (1/2) (s (2 y Subscript[ξ, j] - 2 Σ + q - 1));
fΣ = Σ (q - 2) - s^2 (p^2 - s^2) + w^2 -y^2 + x^2;
Subscript[fξ, j] =  Subscript[ξ, j] (1 - Subscript[ξ, j] y + Σ) ;


The solve command is

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


The system above is the same as in Trying to solve a system of equation with a subscripted variable with Reduce with y=0. The answer to this system is an array of 88 entries, when the subscript is removed from ξ the system has 92 entries. I don't understand if the two solutions are correct, or if a solution is more complete(in the sense of having all the possible solution) than the other. Thank you for your time.

• In general, the solution that Mathematica gives can depend on the order of the variable names. E.g. interchanging the names x and y can give a simplification to a different (but equivalent) answer. One simple way to check equivalence is to substitute numerical values of some or all variables. May 13 '19 at 19:52
• Possible duplicate of Trying to solve a system of equation with a subscripted variable with Reduce May 13 '19 at 22:32
• Should the list of variable in Solve include y? May 19 '19 at 3:30
• @bbgodfrey, the system in this page is the same as in [mathematica.stackexchange.com/questions/197768/… but making the variable y=0, this makes the system easier to resolve and Mathematica given that with 11 variables Mathematica cannot solve it. May 20 '19 at 20:01
• Please edit your question to say that y =0. May 20 '19 at 20:04