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[?] Solve a symmetric equation system with three variables?

Posted 5 years ago

Hey all, I've been trying to use Mathematica to solve a symmetric equation system with three variables(as attached pictureenter image description here), The results so far I get always looks like as below. I have no idea about what Out[0] or ClearAll means shown in result. If anyone knows about it , pls help explain. Thanks so much!

{{Subscript[\[Tau]p, 1] -> 0.0348564 + 1.76546 Out[0], 
  Subscript[\[Tau]p, 2] -> -0.0231215 + 0.37882 Out[0], 
  Subscript[\[Tau]p, 3] -> -0.00951187 + 0.130589 Out[0]}}

or

{Subscript[\[Tau]p, 1] -> 0.0348564 + 1.76546 ClearAll, 
 Subscript[\[Tau]p, 2] -> -0.0231215 + 0.37882 ClearAll, 
 Subscript[\[Tau]p, 3] -> -0.00951187 + 0.130589 ClearAll}
POSTED BY: Qian Che
5 Replies

Please post your code in plaintext form and/or upload a worksheet. Nobody feels like retyping your code. Most people wouldn't want to Answer a Question if they couldn't test that Answer in Mathematica.

POSTED BY: Mariusz Iwaniuk
Posted 5 years ago

Here is the code

Solve[{Subscript[\[Tau]p, 1] == (-((3 a b 
\!\(\*SubsuperscriptBox[\(c\), \(2\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(c\), \(3\), \(2\)]\))/(-b Subscript[c, 1]
            Subscript[c, 2] - b Subscript[c, 1] Subscript[c, 3] - 
          b Subscript[c, 2] Subscript[c, 3] - 
          3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2) - (
       3 a Subscript[c, 1] 
\!\(\*SubsuperscriptBox[\(c\), \(2\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(c\), \(3\), \(2\)]\))/(-b Subscript[c, 1]
           Subscript[c, 2] - b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2 - (
       a Subscript[c, 2] Subscript[c, 
        3])/(-b Subscript[c, 1] Subscript[c, 2] - 
        b Subscript[c, 1] Subscript[c, 3] - 
        b Subscript[c, 2] Subscript[c, 3] - 
        3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 
         3]) + (((-1 - (
             b Subscript[c, 2] Subscript[c, 
              3])/(-b Subscript[c, 1] Subscript[c, 2] - 
              b Subscript[c, 1] Subscript[c, 3] - 
              b Subscript[c, 2] Subscript[c, 3] - 

              3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 
               3])) Subscript[e, 1])/Subscript[c, 1] - (
          b Subscript[c, 3] Subscript[e, 
           2])/(-b Subscript[c, 1] Subscript[c, 2] - 
           b Subscript[c, 1] Subscript[c, 3] - 
           b Subscript[c, 2] Subscript[c, 3] - 
           3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3]) - (
          b Subscript[c, 2] Subscript[e, 
           3])/(-b Subscript[c, 1] Subscript[c, 2] - 
           b Subscript[c, 1] Subscript[c, 3] - 
           b Subscript[c, 2] Subscript[c, 3] - 
           3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 
            3])) Subscript[\[Delta], 1] - (b^2 Subscript[c, 2] 
\!\(\*SubsuperscriptBox[\(c\), \(3\), \(2\)]\) Subscript[\[Tau]p, 
        2])/(-b Subscript[c, 1] Subscript[c, 2] - 
         b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2 - (
       b Subscript[c, 1] Subscript[c, 2] 
\!\(\*SubsuperscriptBox[\(c\), \(3\), \(2\)]\) Subscript[\[Tau]p, 
        2])/(-b Subscript[c, 1] Subscript[c, 2] - 
         b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2 - (b^2 
\!\(\*SubsuperscriptBox[\(c\), \(2\), \(2\)]\) Subscript[c, 3]
         Subscript[\[Tau]p, 
        3])/(-b Subscript[c, 1] Subscript[c, 2] - 
         b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2 - (
       b Subscript[c, 1] 
\!\(\*SubsuperscriptBox[\(c\), \(2\), \(2\)]\) Subscript[c, 3]
         Subscript[\[Tau]p, 
        3])/(-b Subscript[c, 1] Subscript[c, 2] - 
         b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2)/((b 
\!\(\*SubsuperscriptBox[\(c\), \(2\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(c\), \(3\), \(2\)]\))/(-b Subscript[c, 1]
           Subscript[c, 2] - b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2 + (b^2 
\!\(\*SubsuperscriptBox[\(c\), \(2\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(c\), \(3\), \(2\)]\))/(
       Subscript[c, 
        1] (-b Subscript[c, 1] Subscript[c, 2] - 
          b Subscript[c, 1] Subscript[c, 3] - 
          b Subscript[c, 2] Subscript[c, 3] - 
          3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2) + (
       b Subscript[c, 2] Subscript[c, 3])/(
       Subscript[c, 
        1] (-b Subscript[c, 1] Subscript[c, 2] - 
          b Subscript[c, 1] Subscript[c, 3] - 
          b Subscript[c, 2] Subscript[c, 3] - 
          3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 
           3])) + (-1 - (
        b Subscript[c, 2] Subscript[c, 
         3])/(-b Subscript[c, 1] Subscript[c, 2] - 
         b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3]))/
       Subscript[c, 1]) /. {Subscript[c, 1] -> 1.7, 
    Subscript[c, 2] -> 8.1, Subscript[c, 3] -> 4.3, 
    Subscript[e, 1] -> 0.3852, Subscript[e, 2] -> 0.26388, 
    Subscript[e, 3] -> 0.20196, Subscript[\[Delta], 1] -> 5 %, 
    Subscript[\[Delta], 2] -> 1.5 %, Subscript[\[Delta], 3] -> 0.5 %, 
    a -> 1, b -> 0.5},
  Subscript[\[Tau]p, 2] == (-((3 a b 
\!\(\*SubsuperscriptBox[\(c\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(c\), \(3\), \(2\)]\))/(-b Subscript[c, 1]
            Subscript[c, 2] - b Subscript[c, 1] Subscript[c, 3] - 
          b Subscript[c, 2] Subscript[c, 3] - 
          3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2) - (3 a 
\!\(\*SubsuperscriptBox[\(c\), \(1\), \(2\)]\) Subscript[c, 2] 
\!\(\*SubsuperscriptBox[\(c\), \(3\), \(2\)]\))/(-b Subscript[c, 1]
           Subscript[c, 2] - b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2 - (
       a Subscript[c, 1] Subscript[c, 
        3])/(-b Subscript[c, 1] Subscript[c, 2] - 
        b Subscript[c, 1] Subscript[c, 3] - 
        b Subscript[c, 2] Subscript[c, 3] - 
        3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 
         3]) + (-((
           b Subscript[c, 3] Subscript[e, 
            1])/(-b Subscript[c, 1] Subscript[c, 2] - 
            b Subscript[c, 1] Subscript[c, 3] - 
            b Subscript[c, 2] Subscript[c, 3] - 
            3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 
             3])) + ((-1 - (
             b Subscript[c, 1] Subscript[c, 
              3])/(-b Subscript[c, 1] Subscript[c, 2] - 
              b Subscript[c, 1] Subscript[c, 3] - 
              b Subscript[c, 2] Subscript[c, 3] - 
              3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 
               3])) Subscript[e, 2])/Subscript[c, 2] - (
          b Subscript[c, 1] Subscript[e, 
           3])/(-b Subscript[c, 1] Subscript[c, 2] - 
           b Subscript[c, 1] Subscript[c, 3] - 
           b Subscript[c, 2] Subscript[c, 3] - 
           3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 
            3])) Subscript[\[Delta], 2] - (b^2 Subscript[c, 1] 
\!\(\*SubsuperscriptBox[\(c\), \(3\), \(2\)]\) Subscript[\[Tau]p, 
        1])/(-b Subscript[c, 1] Subscript[c, 2] - 
         b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2 - (
       b Subscript[c, 1] Subscript[c, 2] 
\!\(\*SubsuperscriptBox[\(c\), \(3\), \(2\)]\) Subscript[\[Tau]p, 
        1])/(-b Subscript[c, 1] Subscript[c, 2] - 
         b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2 - (b^2 
\!\(\*SubsuperscriptBox[\(c\), \(1\), \(2\)]\) Subscript[c, 3]
         Subscript[\[Tau]p, 
        3])/(-b Subscript[c, 1] Subscript[c, 2] - 
         b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2 - (b 
\!\(\*SubsuperscriptBox[\(c\), \(1\), \(2\)]\) Subscript[c, 2]
         Subscript[c, 3] Subscript[\[Tau]p, 
        3])/(-b Subscript[c, 1] Subscript[c, 2] - 
         b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2)/((b 
\!\(\*SubsuperscriptBox[\(c\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(c\), \(3\), \(2\)]\))/(-b Subscript[c, 1]
           Subscript[c, 2] - b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2 + (b^2 
\!\(\*SubsuperscriptBox[\(c\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(c\), \(3\), \(2\)]\))/(
       Subscript[c, 
        2] (-b Subscript[c, 1] Subscript[c, 2] - 
          b Subscript[c, 1] Subscript[c, 3] - 
          b Subscript[c, 2] Subscript[c, 3] - 
          3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2) + (
       b Subscript[c, 1] Subscript[c, 3])/(
       Subscript[c, 
        2] (-b Subscript[c, 1] Subscript[c, 2] - 
          b Subscript[c, 1] Subscript[c, 3] - 
          b Subscript[c, 2] Subscript[c, 3] - 
          3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 
           3])) + (-1 - (
        b Subscript[c, 1] Subscript[c, 
         3])/(-b Subscript[c, 1] Subscript[c, 2] - 
         b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3]))/
       Subscript[c, 2]) /. {Subscript[c, 1] -> 1.7, 
    Subscript[c, 2] -> 8.1, Subscript[c, 3] -> 4.3, 
    Subscript[e, 1] -> 0.3852, Subscript[e, 2] -> 0.26388, 
    Subscript[e, 3] -> 0.20196, Subscript[\[Delta], 1] -> 5 %, 
    Subscript[\[Delta], 2] -> 1.5 %, Subscript[\[Delta], 3] -> 0.5 %, 
    a -> 1, b -> 0.5},
  Subscript[\[Tau]p, 3] == (-((3 a b 
\!\(\*SubsuperscriptBox[\(c\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(c\), \(2\), \(2\)]\))/(-b Subscript[c, 1]
            Subscript[c, 2] - b Subscript[c, 1] Subscript[c, 3] - 
          b Subscript[c, 2] Subscript[c, 3] - 
          3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2) - (3 a 
\!\(\*SubsuperscriptBox[\(c\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(c\), \(2\), \(2\)]\) Subscript[c, 
        3])/(-b Subscript[c, 1] Subscript[c, 2] - 
         b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2 - (
       a Subscript[c, 1] Subscript[c, 
        2])/(-b Subscript[c, 1] Subscript[c, 2] - 
        b Subscript[c, 1] Subscript[c, 3] - 
        b Subscript[c, 2] Subscript[c, 3] - 
        3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 
         3]) + (-((
           b Subscript[c, 2] Subscript[e, 
            1])/(-b Subscript[c, 1] Subscript[c, 2] - 
            b Subscript[c, 1] Subscript[c, 3] - 
            b Subscript[c, 2] Subscript[c, 3] - 
            3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])) - (
          b Subscript[c, 1] Subscript[e, 
           2])/(-b Subscript[c, 1] Subscript[c, 2] - 
           b Subscript[c, 1] Subscript[c, 3] - 
           b Subscript[c, 2] Subscript[c, 3] - 
           3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 
            3]) + ((-1 - (
             b Subscript[c, 1] Subscript[c, 
              2])/(-b Subscript[c, 1] Subscript[c, 2] - 
              b Subscript[c, 1] Subscript[c, 3] - 
              b Subscript[c, 2] Subscript[c, 3] - 
              3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 
               3])) Subscript[e, 3])/Subscript[c, 
          3]) Subscript[\[Delta], 3] - (b^2 Subscript[c, 1] 
\!\(\*SubsuperscriptBox[\(c\), \(2\), \(2\)]\) Subscript[\[Tau]p, 
        1])/(-b Subscript[c, 1] Subscript[c, 2] - 
         b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2 - (
       b Subscript[c, 1] 
\!\(\*SubsuperscriptBox[\(c\), \(2\), \(2\)]\) Subscript[c, 3]
         Subscript[\[Tau]p, 
        1])/(-b Subscript[c, 1] Subscript[c, 2] - 
         b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2 - (b^2 
\!\(\*SubsuperscriptBox[\(c\), \(1\), \(2\)]\) Subscript[c, 2]
         Subscript[\[Tau]p, 
        2])/(-b Subscript[c, 1] Subscript[c, 2] - 
         b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2 - (b 
\!\(\*SubsuperscriptBox[\(c\), \(1\), \(2\)]\) Subscript[c, 2]
         Subscript[c, 3] Subscript[\[Tau]p, 
        2])/(-b Subscript[c, 1] Subscript[c, 2] - 
         b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2)/((b 
\!\(\*SubsuperscriptBox[\(c\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(c\), \(2\), \(2\)]\))/(-b Subscript[c, 1]
           Subscript[c, 2] - b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2 + (b^2 
\!\(\*SubsuperscriptBox[\(c\), \(1\), \(2\)]\) 
\!\(\*SubsuperscriptBox[\(c\), \(2\), \(2\)]\))/(
       Subscript[c, 
        3] (-b Subscript[c, 1] Subscript[c, 2] - 
          b Subscript[c, 1] Subscript[c, 3] - 
          b Subscript[c, 2] Subscript[c, 3] - 
          3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3])^2) + (
       b Subscript[c, 1] Subscript[c, 2])/(
       Subscript[c, 
        3] (-b Subscript[c, 1] Subscript[c, 2] - 
          b Subscript[c, 1] Subscript[c, 3] - 
          b Subscript[c, 2] Subscript[c, 3] - 
          3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 
           3])) + (-1 - (
        b Subscript[c, 1] Subscript[c, 
         2])/(-b Subscript[c, 1] Subscript[c, 2] - 
         b Subscript[c, 1] Subscript[c, 3] - 
         b Subscript[c, 2] Subscript[c, 3] - 
         3 Subscript[c, 1] Subscript[c, 2] Subscript[c, 3]))/
       Subscript[c, 3]) /. {Subscript[c, 1] -> 1.7, 
    Subscript[c, 2] -> 8.1, Subscript[c, 3] -> 4.3, 
    Subscript[e, 1] -> 0.3852, Subscript[e, 2] -> 0.26388, 
    Subscript[e, 3] -> 0.20196, Subscript[\[Delta], 1] -> 5 %, 
    Subscript[\[Delta], 2] -> 1.5 %, Subscript[\[Delta], 3] -> 0.5 %, 
    a -> 1, b -> 0.5}}, {Subscript[\[Tau]p, 1], Subscript[\[Tau]p, 
  2], Subscript[\[Tau]p, 3]}]
POSTED BY: Qian Che

See attached file.

Attachments:
POSTED BY: Mariusz Iwaniuk
Posted 5 years ago

Thanks a lot! May I ask which version of Mathematica you're using? It seems I have to upgrade mine to be able to view the file completely.

POSTED BY: Qian Che

Mathematica 12.0.

POSTED BY: Mariusz Iwaniuk
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