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Solve this equation set in Wolfram|Alpha?

How long can I type in the input window in wolframalpha? The equation set below is too long.How can i solve it?

    solve (C1=Ca+Cb+Cc,
C1*L2*C2+C1*L3*C3=Ca*Lc*Cc+Ca*Lb*Cb+Cb*Lc*Cc+Cb*La*Ca+Cc*La*Ca+Cc*Lb*Cb,
C1*C2*C3*L2*L3=Ca*Cb*Cc*Lb*Lc+Ca*Cb*Cc*La*Lc+Ca*Cb*Cc*La*Lb,
C1*L1+C2*L2+C1*L3+C2*L2+C3*L3=Ca*La+Cb*Lb+Cc*Lc,
C1*C2*L1*L2+C1*C2*L2*L3+C1*C3*L1*L3+C1*C3*L2*L3+C2*C3*L2*L3=Ca*Cb*La*Lb+Ca*Cc*La*Lc+Cb*Cc*Lb*Lc,
C1*C2*C3*L1*L2*L3=Ca*Cb*Cc*La*Lb*Lc,
{Ca,Cb,Cc,La,Lb,Lc})
Attachments:
POSTED BY: ? ??
6 Replies
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You can use NSolve and approximate computing. In such case the code is:

c1 = c2 = c3 = l1 = l2 = l3 = 1.;
NSolve[{
  ca + cb + cc == c1,
  ca lc cc + ca lb cb + cb lc cc + cb la ca + cc la ca + cc lb cb == 
   c1 l2 c2 + c1 l3 c3,
  ca cb cc lb lc + ca cb cc la lc + ca cb cc la lb == c1 c2 c3 l2 l3,
  ca la + cb  lb + cc lc == c1 l1 + c1 l2 + c1 l3 + c2 l2 + c3 l3,
  ca cb la lb + ca cc la lc + cb cc lb lc == c2 c3 l2 l3,
  ca cb cc la lb lc == c1 c2 c3 l1 l2 l3}, {ca, cb, cc, la, lb, lc}]

{{ca -> 0.177312 + 0.16778 I, cb -> 0.645259 - 9.19986*10^-6 I, 
  cc -> 0.177341 - 0.167806 I, la -> 1.50331 + 1.10002 I, 
  lb -> 7.49442 - 0.0000188153 I, 
  lc -> 1.50317 - 1.09989 I}, {ca -> 0.177343 - 0.167799 I, 
  cb -> 0.177334 + 0.167793 I, cc -> 0.64527 + 7.69554*10^-7 I, 
  la -> 1.50309 - 1.09987 I, lb -> 1.50327 + 1.09995 I, 
  lc -> 7.49426 + 0.0000573922 I}, {ca -> 0.177339 + 0.167798 I, 
  cb -> 0.177357 - 0.167798 I, cc -> 0.645273 - 0.00004873 I, 
  la -> 1.50322 + 1.09995 I, lb -> 1.50296 - 1.09988 I, 
  lc -> 7.49425 + 0.00060717 I}, {ca -> 0.645294 - 0.0000468883 I, 
  cb -> 0.177355 - 0.16779 I, cc -> 0.177339 + 0.167809 I, 
  la -> 7.49423 + 0.000272327 I, lb -> 1.50303 - 1.09989 I, 
  lc -> 1.50316 + 1.09983 I}, {ca -> 0.645299 - 0.0000183038 I, 
  cb -> 0.17733 + 0.167802 I, cc -> 0.177352 - 0.167804 I, 
  la -> 7.49422 - 0.0000507398 I, lb -> 1.50317 + 1.09986 I, 
  lc -> 1.50307 - 1.09984 I}, {ca -> 0.177331 - 0.167788 I, 
  cb -> 0.645295 - 0.000013715 I, cc -> 0.177317 + 0.167793 I, 
  la -> 1.50324 - 1.09994 I, lb -> 7.49403 + 0.000151404 I, 
  lc -> 1.50336 + 1.0999 I}}

And the code with Manipulate:

Manipulate[NSolve[{
   ca + cb + cc == c1,
   ca lc cc + ca lb cb + cb lc cc + cb la ca + cc la ca + cc lb cb == 
    c1 l2 c2 + c1 l3 c3,
   ca cb cc lb lc + ca cb cc la lc + ca cb cc la lb == c1 c2 c3 l2 l3,
   ca la + cb  lb + cc lc == c1 l1 + c1 l2 + c1 l3 + c2 l2 + c3 l3,
   ca cb la lb + ca cc la lc + cb cc lb lc == c2 c3 l2 l3,
   ca cb cc la lb lc == c1 c2 c3 l1 l2 l3}, {ca, cb, cc, la, lb, lc}],
 {{c1, 1., "\!\(\*SubscriptBox[\(c\), \(1\)]\)"}, -10, 10, 1, 
  Appearance -> "Labeled", ImageSize -> Tiny},
 {{c2, 1., "\!\(\*SubscriptBox[\(c\), \(2\)]\)"}, -10, 10, 1, 
  Appearance -> "Labeled", ImageSize -> Tiny},
 {{c3, 1., "\!\(\*SubscriptBox[\(c\), \(3\)]\)"}, -10, 10, 1, 
  Appearance -> "Labeled", ImageSize -> Tiny},
 {{l1, 1., "\!\(\*SubscriptBox[\(l\), \(1\)]\)"}, -10, 10, 1, 
  Appearance -> "Labeled", ImageSize -> Tiny},
 {{l2, 1., "\!\(\*SubscriptBox[\(l\), \(2\)]\)"}, -10, 10, 1, 
  Appearance -> "Labeled", ImageSize -> Tiny},
 {{l3, 1., "\!\(\*SubscriptBox[\(l\), \(3\)]\)"}, -10, 10, 1, 
  Appearance -> "Labeled", ImageSize -> Tiny}
 ]
Attachments:
POSTED BY: Valeriu Ungureanu

Your system is not so simple to solve symbolically. So, you can try to solve it for various numerical values of parameters: c1, c2, c3, l1, l2, l3. You will understand what is the complexity of solutions you search for.

For convenience, I attach the file with the code and a variant of the code that use the function Manipulate.

E.g. for c1=c2=c3=l1=l2=l3=1 the solutions are:

c1 = c2 = c3 = l1 = l2 = l3 = 1;
Solve[{
  ca + cb + cc == c1,
  ca lc cc + ca lb cb + cb lc cc + cb la ca + cc la ca + cc lb cb == 
   c1 l2 c2 + c1 l3 c3,
  ca cb cc lb lc + ca cb cc la lc + ca cb cc la lb == c1 c2 c3 l2 l3,
  ca la + cb  lb + cc lc == c1 l1 + c1 l2 + c1 l3 + c2 l2 + c3 l3,
  ca cb la lb + ca cc la lc + cb cc lb lc == c2 c3 l2 l3,
  ca cb cc la lb lc == c1 c2 c3 l1 l2 l3}, {ca, cb, cc, la, lb, lc}]

{{ca -> 1/3 + 1/624 (31096 - 3432 Sqrt[78])^(1/3) + (
    I (31096 - 3432 Sqrt[78])^(1/3))/(
    208 Sqrt[3]) + (299 + 33 Sqrt[78])^(1/3)/(24 13^(2/3)) - (
    I (299 + 33 Sqrt[78])^(1/3))/(8 Sqrt[3] 13^(2/3)) + 
    1/104 \[Sqrt]((-52 + 
          52 (1/3 - 
             1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
              1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
             12 13^(2/3))))^2 - 
        208 (15 - 
           52 (1/3 - 
              1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
               1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
              12 13^(2/3))) + 

           52 (1/3 - 
              1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
               1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
              12 13^(2/3)))^2)), 
  cb -> 1/104 (52 - 
      52 (1/3 - 
         1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
          1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
         12 13^(2/3))) - \[Sqrt]((-52 + 
           52 (1/3 - 
              1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
               1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
              12 13^(2/3))))^2 - 
         208 (15 - 
            52 (1/3 - 
               1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))) + 
            52 (1/3 - 
               1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3)))^2))), 
  cc -> 1/3 - 
    1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
     1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(12 13^(2/3)),
   la -> 1/11 (364/9 + 13/72 (31096 - 3432 Sqrt[78])^(1/3) - (
      5 I (31096 - 3432 Sqrt[78])^(1/3))/(24 Sqrt[3]) + 
      1/4 I Sqrt[3] (31096 - 3432 Sqrt[78])^(1/3) + (
      5 (31096 - 3432 Sqrt[78])^(2/3))/3744 - (
      5 I (31096 - 3432 Sqrt[78])^(2/3))/(1248 Sqrt[3]) + (
      5 (299 + 33 Sqrt[78])^(2/3))/(72 13^(1/3)) + (
      5 I (299 + 33 Sqrt[78])^(2/3))/(24 Sqrt[3] 13^(1/3)) + 
      13/36 (13 (299 + 33 Sqrt[78]))^(1/3) + (
      5 I (13 (299 + 33 Sqrt[78]))^(1/3))/(12 Sqrt[3]) - 
      1/2 I Sqrt[3] (13 (299 + 33 Sqrt[78]))^(1/3) - (
      5 ((31096 - 3432 Sqrt[78]) (299 + 33 Sqrt[78]))^(1/3))/(
      36 13^(2/3)) + 
      13/12 \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 
          208 (15 - 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2)) + (1/1248)
      5 (31096 - 3432 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 
          208 (15 - 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2)) + (1/(416 Sqrt[3]))
      5 I (31096 - 3432 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 
          208 (15 - 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2)) + (1/(48 13^(2/3)))
      5 (299 + 33 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 
          208 (15 - 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2)) - (1/(16 Sqrt[3] 13^(2/3)))
      5 I (299 + 33 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 
          208 (15 - 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2))), 
  lb -> 1/11 (-26 + 
      130 (1/3 - 
         1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
          1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
         12 13^(2/3))) - 
      130 (1/3 - 
         1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
          1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
         12 13^(2/3)))^2 + 
      3/2 (52 - 
         52 (1/3 - 
            1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
             1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
            12 13^(2/3))) - \[Sqrt]((-52 + 
              52 (1/3 - 
                 1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                  1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                 12 13^(2/3))))^2 - 
            208 (15 - 
               52 (1/3 - 
                  1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                   1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(
                   1/3))/(12 13^(2/3))) + 
               52 (1/3 - 
                  1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                   1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(
                   1/3))/(12 13^(2/3)))^2))) - 
      5/4 (1/3 - 
         1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
          1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
         12 13^(2/3))) (52 - 
         52 (1/3 - 
            1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
             1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
            12 13^(2/3))) - \[Sqrt]((-52 + 
              52 (1/3 - 
                 1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                  1/3) - ((1 - I Sqrt[3]) (299 + 33 S/3))/(
                 12 13^(2/3))))^2 - 
            208 (15 - 
               52 (1/3 - 
                  1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                   1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(
                   1/3))/(12 13^(2/3))) + 
               52 (1/3 - 
                  1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                   1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(
                   1/3))/(12 13^(2/3)))^2)))), 
  lc -> (1/5148)
   I (-18018 I + 338 I (13 (299 - 33 Sqrt[78]))^(1/3) - 
      338 Sqrt[3] (13 (299 - 33 Sqrt[78]))^(1/3) + 
      5 I (13 (299 - 33 Sqrt[78]))^(2/3) + 
      5 Sqrt[3] (13 (299 - 33 Sqrt[78]))^(2/3) + 
      338 I (13 (299 + 33 Sqrt[78]))^(1/3) + 
      338 Sqrt[3] (13 (299 + 33 Sqrt[78]))^(1/3) + 
      5 I (13 (299 + 33 Sqrt[78]))^(2/3) - 
      5 Sqrt[3] (13 (299 + 33 Sqrt[78]))^(2/3))}, {ca -> 
   1/3 + 1/624 (31096 - 3432 Sqrt[78])^(1/3) + (
    I (31096 - 3432 Sqrt[78])^(1/3))/(
    208 Sqrt[3]) + (299 + 33 Sqrt[78])^(1/3)/(24 13^(2/3)) - (
    I (299 + 33 Sqrt[78])^(1/3))/(8 Sqrt[3] 13^(2/3)) - 
    1/104 \[Sqrt]((-52 + 
          52 (1/3 - 
             1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
              1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
             12 13^(2/3))))^2 - 
        208 (15 - 
           52 (1/3 - 
              1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
               1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
              12 13^(2/3))) + 
           52 (1/3 - 
              1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
               1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
              12 13^(2/3)))^2)), 
  cb -> 1/104 (52 - 
      52 (1/3 - 
         1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
          1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
         12 13^(2/3))) + \[Sqrt]((-52 + 
           52 (1/3 - 
              1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
               1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
              12 13^(2/3))))^2 - 
         208 (15 - 
            52 (1/3 - 

               1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))) + 
            52 (1/3 - 
               1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3)))^2))), 
  cc -> 1/3 - 
    1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
     1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(12 13^(2/3)),
   la -> 1/11 (364/9 + 13/72 (31096 - 3432 Sqrt[78])^(1/3) - (
      5 I (31096 - 3432 Sqrt[78])^(1/3))/(24 Sqrt[3]) + 
      1/4 I Sqrt[3] (31096 - 3432 Sqrt[78])^(1/3) + (
      5 (31096 - 3432 Sqrt[78])^(2/3))/3744 - (
      5 I (31096 - 3432 Sqrt[78])^(2/3))/(1248 Sqrt[3]) + (
      5 (299 + 33 Sqrt[78])^(2/3))/(72 13^(1/3)) + (
      5 I (299 + 33 Sqrt[78])^(2/3))/(24 Sqrt[3] 13^(1/3)) + 
      13/36 (13 (299 + 33 Sqrt[78]))^(1/3) + (
      5 I (13 (299 + 33 Sqrt[78]))^(1/3))/(12 Sqrt[3]) - 
      1/2 I Sqrt[3] (13 (299 + 33 Sqrt[78]))^(1/3) - (
      5 ((31096 - 3432 Sqrt[78]) (299 + 33 Sqrt[78]))^(1/3))/(
      36 13^(2/3)) - 
      13/12 \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 
          208 (15 - 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2)) - (1/1248)
      5 (31096 - 3432 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 
          208 (15 - 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2)) - (1/(416 Sqrt[3]))
      5 I (31096 - 3432 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 
          208 (15 - 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2)) - (1/(48 13^(2/3)))
      5 (299 + 33 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 
          208 (15 - 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2)) + (1/(16 Sqrt[3] 13^(2/3)))
      5 I (299 + 33 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 
          208 (15 - 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2))), 
  lb -> 1/11 (-26 + 
      130 (1/3 - 
         1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
          1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
         12 13^(2/3))) - 
      130 (1/3 - 
         1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
          1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
         12 13^(2/3)))^2 + 
      3/2 (52 - 
         52 (1/3 - 
            1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
             1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
            12 13^(2/3))) + \[Sqrt]((-52 + 
              52 (1/3 - 
                 1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                  1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                 12 13^(2/3))))^2 - 
            208 (15 - 
               52 (1/3 - 
                  1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                   1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(
                   1/3))/(12 13^(2/3))) + 
               52 (1/3 - 
                  1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                   1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(
                   1/3))/(12 13^(2/3)))^2))) - 
      5/4 (1/3 - 
         1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
          1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
         12 13^(2/3))) (52 - 
         52 (1/3 - 
            1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
             1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
            12 13^(2/3))) + \[Sqrt]((-52 + 
              52 (1/3 - 
                 1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                  1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                 12 13^(2/3))))^2 - 
            208 (15 - 
               52 (1/3 - 
                  1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                   1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(
                   1/3))/(12 13^(2/3))) + 
               52 (1/3 - 
                  1/312 (1 + I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                   1/3) - ((1 - I Sqrt[3]) (299 + 33 Sqrt[78])^(
                   1/3))/(12 13^(2/3)))^2)))), 
  lc -> (1/5148)
   I (-18018 I + 338 I (13 (299 - 33 Sqrt[78]))^(1/3) - 
      338 Sqrt[3] (13 (299 - 33 Sqrt[78]))^(1/3) + 
      5 I (13 (299 - 33 Sqrt[78]))^(2/3) + 
      5 Sqrt[3] (13 (299 - 33 Sqrt[78]))^(2/3) + 
      338 I (13 (299 + 33 Sqrt[78]))^(1/3) + 
      338 Sqrt[3] (13 (299 + 33 Sqrt[78]))^(1/3) + 
      5 I (13 (299 + 33 Sqrt[78]))^(2/3) - 
      5 Sqrt[3] (13 (299 + 33 Sqrt[78]))^(2/3))}, {ca -> 
   1/3 + 1/624 (31096 - 3432 Sqrt[78])^(1/3) - (
    I (31096 - 3432 Sqrt[78])^(1/3))/(
    208 Sqrt[3]) + (299 + 33 Sqrt[78])^(1/3)/(24 13^(2/3)) + (
    I (299 + 33 Sqrt[78])^(1/3))/(8 Sqrt[3] 13^(2/3)) + 
    1/104 \[Sqrt]((-52 + 
          52 (1/3 - 
             1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
              1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
             12 13^(2/3))))^2 - 
        208 (15 - 
           52 (1/3 - 
              1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
               1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
              12 13^(2/3))) + 
           52 (1/3 - 
              1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
               1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
              12 13^(2/3)))^2)), 
  cb -> 1/104 (52 - 
      52 (1/3 - 
         1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
          1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
         12 13^(2/3))) - \[Sqrt]((-52 + 
           52 (1/3 - 
              1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
               1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
              12 13^(2/3))))^2 - 
         208 (15 - 
            52 (1/3 - 
               1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))) + 
            52 (1/3 - 
               1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3)))^2))), 
  cc -> 1/3 - 
    1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
     1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(12 13^(2/3)),
   la -> 1/11 (364/9 + 13/72 (31096 - 3432 Sqrt[78])^(1/3) + (
      5 I (31096 - 3432 Sqrt[78])^(1/3))/(24 Sqrt[3]) - 
      1/4 I Sqrt[3] (31096 - 3432 Sqrt[78])^(1/3) + (
      5 (31096 - 3432 Sqrt[78])^(2/3))/3744 + (
      5 I (31096 - 3432 Sqrt[78])^(2/3))/(1248 Sqrt[3]) + (
      5 (299 + 33 Sqrt[78])^(2/3))/(72 13^(1/3)) - (
      5 I (299 + 33 Sqrt[78])^(2/3))/(24 Sqrt[3] 13^(1/3)) + 
      13/36 (13 (299 + 33 Sqrt[78]))^(1/3) - (
      5 I (13 (299 + 33 Sqrt[78]))^(1/3))/(12 Sqrt[3]) + 
      1/2 I Sqrt[3] (13 (299 + 33 Sqrt[78]))^(1/3) - (
      5 ((31096 - 3432 Sqrt[78]) (299 + 33 Sqrt[78]))^(1/3))/(
      36 13^(2/3)) + 
      13/12 \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 
          208 (15 - 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2)) + (1/1248)
      5 (31096 - 3432 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 
          208 (15 - 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2)) - (1/(416 Sqrt[3]))
      5 I (31096 - 3432 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 
          208 (15 - 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2)) + (1/(48 13^(2/3)))
      5 (299 + 33 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 
          208 (15 - 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2)) + (1/(16 Sqrt[3] 13^(2/3)))
      5 I (299 + 33 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 
          208 (15 - 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2))), 
  lb -> 1/11 (-26 + 
      130 (1/3 - 
         1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
          1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
         12 13^(2/3))) - 
      130 (1/3 - 
         1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
          1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
         12 13^(2/3)))^2 + 
      3/2 (52 - 
         52 (1/3 - 
            1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
             1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
            12 13^(2/3))) - \[Sqrt]((-52 + 
              52 (1/3 - 
                 1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                  1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                 12 13^(2/3))))^2 - 
            208 (15 - 
               52 (1/3 - 
                  1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                   1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(
                   1/3))/(12 13^(2/3))) + 
               52 (1/3 - 
                  1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                   1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(
                   1/3))/(12 13^(2/3)))^2))) - 
      5/4 (1/3 - 
         1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
          1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
         12 13^(2/3))) (52 - 
         52 (1/3 - 
            1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
             1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(

            12 13^(2/3))) - \[Sqrt]((-52 + 
              52 (1/3 - 
                 1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                  1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                 12 13^(2/3))))^2 - 
            208 (15 - 
               52 (1/3 - 
                  1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                   1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(
                   1/3))/(12 13^(2/3))) + 
               52 (1/3 - 
                  1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                   1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(
                   1/3))/(12 13^(2/3)))^2)))), 
  lc -> -(1/5148)
    I (18018 I - 338 I (13 (299 - 33 Sqrt[78]))^(1/3) - 
       338 Sqrt[3] (13 (299 - 33 Sqrt[78]))^(1/3) - 
       5 I (13 (299 - 33 Sqrt[78]))^(2/3) + 
       5 Sqrt[3] (13 (299 - 33 Sqrt[78]))^(2/3) - 
       338 I (13 (299 + 33 Sqrt[78]))^(1/3) + 
       338 Sqrt[3] (13 (299 + 33 Sqrt[78]))^(1/3) - 
       5 I (13 (299 + 33 Sqrt[78]))^(2/3) - 
       5 Sqrt[3] (13 (299 + 33 Sqrt[78]))^(2/3))}, {ca -> 
   1/3 + 1/624 (31096 - 3432 Sqrt[78])^(1/3) - (
    I (31096 - 3432 Sqrt[78])^(1/3))/(
    208 Sqrt[3]) + (299 + 33 Sqrt[78])^(1/3)/(24 13^(2/3)) + (
    I (299 + 33 Sqrt[78])^(1/3))/(8 Sqrt[3] 13^(2/3)) - 
    1/104 \[Sqrt]((-52 + 
          52 (1/3 - 
             1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
              1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
             12 13^(2/3))))^2 - 
        208 (15 - 
           52 (1/3 - 
              1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
               1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
              12 13^(2/3))) + 
           52 (1/3 - 
              1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
               1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
              12 13^(2/3)))^2)), 
  cb -> 1/104 (52 - 
      52 (1/3 - 
         1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
          1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
         12 13^(2/3))) + \[Sqrt]((-52 + 
           52 (1/3 - 
              1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
               1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
              12 13^(2/3))))^2 - 
         208 (15 - 
            52 (1/3 - 
               1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))) + 
            52 (1/3 - 
               1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3)))^2))), 
  cc -> 1/3 - 
    1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
     1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(12 13^(2/3)),
   la -> 1/11 (364/9 + 13/72 (31096 - 3432 Sqrt[78])^(1/3) + (
      5 I (31096 - 3432 Sqrt[78])^(1/3))/(24 Sqrt[3]) - 
      1/4 I Sqrt[3] (31096 - 3432 Sqrt[78])^(1/3) + (
      5 (31096 - 3432 Sqrt[78])^(2/3))/3744 + (
      5 I (31096 - 3432 Sqrt[78])^(2/3))/(1248 Sqrt[3]) + (
      5 (299 + 33 Sqrt[78])^(2/3))/(72 13^(1/3)) - (
      5 I (299 + 33 Sqrt[78])^(2/3))/(24 Sqrt[3] 13^(1/3)) + 
      13/36 (13 (299 + 33 Sqrt[78]))^(1/3) - (
      5 I (13 (299 + 33 Sqrt[78]))^(1/3))/(12 Sqrt[3]) + 
      1/2 I Sqrt[3] (13 (299 + 33 Sqrt[78]))^(1/3) - (
      5 ((31096 - 3432 Sqrt[78]) (299 + 33 Sqrt[78]))^(1/3))/(
      36 13^(2/3)) - 
      13/12 \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 

          208 (15 - 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2)) - (1/1248)
      5 (31096 - 3432 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 
          208 (15 - 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2)) + (1/(416 Sqrt[3]))
      5 I (31096 - 3432 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 

          208 (15 - 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2)) - (1/(48 13^(2/3)))
      5 (299 + 33 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 
          208 (15 - 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2)) - (1/(16 Sqrt[3] 13^(2/3)))
      5 I (299 + 33 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            52 (1/3 - 
               1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
               12 13^(2/3))))^2 - 

          208 (15 - 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3))) + 
             52 (1/3 - 
                1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                 1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                12 13^(2/3)))^2))), 
  lb -> 1/11 (-26 + 
      130 (1/3 - 
         1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
          1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
         12 13^(2/3))) - 
      130 (1/3 - 
         1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
          1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
         12 13^(2/3)))^2 + 
      3/2 (52 - 
         52 (1/3 - 
            1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
             1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
            12 13^(2/3))) + \[Sqrt]((-52 + 
              52 (1/3 - 
                 1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                  1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                 12 13^(2/3))))^2 - 
            208 (15 - 
               52 (1/3 - 
                  1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                   1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(
                   1/3))/(12 13^(2/3))) + 
               52 (1/3 - 
                  1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                   1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(
                   1/3))/(12 13^(2/3)))^2))) - 
      5/4 (1/3 - 
         1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
          1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
         12 13^(2/3))) (52 - 
         52 (1/3 - 
            1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
             1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
            12 13^(2/3))) + \[Sqrt]((-52 + 
              52 (1/3 - 
                 1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                  1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(1/3))/(
                 12 13^(2/3))))^2 - 
            208 (15 - 
               52 (1/3 - 
                  1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                   1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(
                   1/3))/(12 13^(2/3))) + 
               52 (1/3 - 
                  1/312 (1 - I Sqrt[3]) (31096 - 3432 Sqrt[78])^(
                   1/3) - ((1 + I Sqrt[3]) (299 + 33 Sqrt[78])^(
                   1/3))/(12 13^(2/3)))^2)))), 
  lc -> -(1/5148)
    I (18018 I - 338 I (13 (299 - 33 Sqrt[78]))^(1/3) - 
       338 Sqrt[3] (13 (299 - 33 Sqrt[78]))^(1/3) - 
       5 I (13 (299 - 33 Sqrt[78]))^(2/3) + 
       5 Sqrt[3] (13 (299 - 33 Sqrt[78]))^(2/3) - 
       338 I (13 (299 + 33 Sqrt[78]))^(1/3) + 
       338 Sqrt[3] (13 (299 + 33 Sqrt[78]))^(1/3) - 
       5 I (13 (299 + 33 Sqrt[78]))^(2/3) - 
       5 Sqrt[3] (13 (299 + 33 Sqrt[78]))^(2/3))}, {ca -> 
   1/312 (104 - (31096 - 3432 Sqrt[78])^(1/3) - 
      2 (13 (299 + 33 Sqrt[78]))^(1/3) + 
      3 \[Sqrt]((-52 + 
            1/3 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
               2 (13 (299 + 33 Sqrt[78]))^(1/3)))^2 - 
          208 (15 + 
             1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
                2 (13 (299 + 33 Sqrt[78]))^(1/3)) + 
             1/468 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
                2 (13 (299 + 33 Sqrt[78]))^(1/3))^2))), 
  cb -> 1/104 (52 + 
      1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
         2 (13 (299 + 33 Sqrt[78]))^(
          1/3)) - \[Sqrt]((-52 + 
           1/3 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
              2 (13 (299 + 33 Sqrt[78]))^(1/3)))^2 - 
         208 (15 + 
            1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
               2 (13 (299 + 33 Sqrt[78]))^(1/3)) + 

            1/468 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
               2 (13 (299 + 33 Sqrt[78]))^(1/3))^2))), 
  cc -> 1/156 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
      2 (13 (299 + 33 Sqrt[78]))^(1/3)), 
  la -> 1/11 (364/9 - 13/36 (31096 - 3432 Sqrt[78])^(1/3) - (
      5 (31096 - 3432 Sqrt[78])^(2/3))/1872 - (
      5 (299 + 33 Sqrt[78])^(2/3))/(36 13^(1/3)) - 
      13/18 (13 (299 + 33 Sqrt[78]))^(1/3) - (
      5 ((31096 - 3432 Sqrt[78]) (299 + 33 Sqrt[78]))^(1/3))/(
      36 13^(2/3)) + 
      13/12 \[Sqrt]((-52 + 
            1/3 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
               2 (13 (299 + 33 Sqrt[78]))^(1/3)))^2 - 
          208 (15 + 
             1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
                2 (13 (299 + 33 Sqrt[78]))^(1/3)) + 
             1/468 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
                2 (13 (299 + 33 Sqrt[78]))^(1/3))^2)) - 
      5/624 (31096 - 3432 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            1/3 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
               2 (13 (299 + 33 Sqrt[78]))^(1/3)))^2 - 
          208 (15 + 
             1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
                2 (13 (299 + 33 Sqrt[78]))^(1/3)) + 

             1/468 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
                2 (13 (299 + 33 Sqrt[78]))^(1/3))^2)) - (1/(
      24 13^(2/3)))
      5 (299 + 33 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            1/3 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
               2 (13 (299 + 33 Sqrt[78]))^(1/3)))^2 - 
          208 (15 + 
             1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
                2 (13 (299 + 33 Sqrt[78]))^(1/3)) + 
             1/468 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
                2 (13 (299 + 33 Sqrt[78]))^(1/3))^2))), 
  lb -> 1/11 (364/9 - 13/36 (31096 - 3432 Sqrt[78])^(1/3) - (
      5 (31096 - 3432 Sqrt[78])^(2/3))/1872 - (
      5 (299 + 33 Sqrt[78])^(2/3))/(36 13^(1/3)) - 
      13/18 (13 (299 + 33 Sqrt[78]))^(1/3) - (
      5 ((31096 - 3432 Sqrt[78]) (299 + 33 Sqrt[78]))^(1/3))/(
      36 13^(2/3)) - 
      13/12 \[Sqrt]((-52 + 
            1/3 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
               2 (13 (299 + 33 Sqrt[78]))^(1/3)))^2 - 
          208 (15 + 
             1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
                2 (13 (299 + 33 Sqrt[78]))^(1/3)) + 
             1/468 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
                2 (13 (299 + 33 Sqrt[78]))^(1/3))^2)) + 
      5/624 (31096 - 3432 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            1/3 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
               2 (13 (299 + 33 Sqrt[78]))^(1/3)))^2 - 
          208 (15 + 
             1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
                2 (13 (299 + 33 Sqrt[78]))^(1/3)) + 
             1/468 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
                2 (13 (299 + 33 Sqrt[78]))^(1/3))^2)) + (1/(
      24 13^(2/3)))
      5 (299 + 33 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            1/3 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
               2 (13 (299 + 33 Sqrt[78]))^(1/3)))^2 - 
          208 (15 + 
             1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
                2 (13 (299 + 33 Sqrt[78]))^(1/3)) + 
             1/468 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
                2 (13 (299 + 33 Sqrt[78]))^(1/3))^2))), 
  lc -> (9009 + 338 (13 (299 - 33 Sqrt[78]))^(1/3) + 
    5 (13 (299 - 33 Sqrt[78]))^(2/3) + 
    338 (13 (299 + 33 Sqrt[78]))^(1/3) + 
    5 (13 (299 + 33 Sqrt[78]))^(2/3))/2574}, {ca -> 
   1/312 (104 - (31096 - 3432 Sqrt[78])^(1/3) - 
      2 (13 (299 + 33 Sqrt[78]))^(1/3) - 
      3 \[Sqrt]((-52 + 
            1/3 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
               2 (13 (299 + 33 Sqrt[78]))^(1/3)))^2 - 
          208 (15 + 
             1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
                2 (13 (299 + 33 Sqrt[78]))^(1/3)) + 
             1/468 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
                2 (13 (299 + 33 Sqrt[78]))^(1/3))^2))), 
  cb -> 1/104 (52 + 
      1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
         2 (13 (299 + 33 Sqrt[78]))^(
          1/3)) + \[Sqrt]((-52 + 
           1/3 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
              2 (13 (299 + 33 Sqrt[78]))^(1/3)))^2 - 
         208 (15 + 
            1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
               2 (13 (299 + 33 Sqrt[78]))^(1/3)) + 
            1/468 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
               2 (13 (299 + 33 Sqrt[78]))^(1/3))^2))), 
  cc -> 1/156 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
      2 (13 (299 + 33 Sqrt[78]))^(1/3)), 
  la -> 1/11 (364/9 - 13/36 (31096 - 3432 Sqrt[78])^(1/3) - (
      5 (31096 - 3432 Sqrt[78])^(2/3))/1872 - (
      5 (299 + 33 Sqrt[78])^(2/3))/(36 13^(1/3)) - 
      13/18 (13 (299 + 33 Sqrt[78]))^(1/3) - (
      5 ((31096 - 3432 Sqrt[78]) (299 + 33 Sqrt[78]))^(1/3))/(
      36 13^(2/3)) - 
      13/12 \[Sqrt]((-52 + 
            1/3 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
               2 (13 (299 + 33 Sqrt[78]))^(1/3)))^2 - 
          208 (15 + 
             1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
                2 (13 (299 + 33 Sqrt[78]))^(1/3)) + 
             1/468 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
                2 (13 (299 + 33 Sqrt[78]))^(1/3))^2)) + 
      5/624 (31096 - 3432 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            1/3 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
               2 (13 (299 + 33 Sqrt[78]))^(1/3)))^2 - 
          208 (15 + 
             1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
                2 (13 (299 + 33 Sqrt[78]))^(1/3)) + 
             1/468 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
                2 (13 (299 + 33 Sqrt[78]))^(1/3))^2)) + (1/(
      24 13^(2/3)))
      5 (299 + 33 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            1/3 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
               2 (13 (299 + 33 Sqrt[78]))^(1/3)))^2 - 
          208 (15 + 
             1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
                2 (13 (299 + 33 Sqrt[78]))^(1/3)) + 
             1/468 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
                2 (13 (299 + 33 Sqrt[78]))^(1/3))^2))), 
  lb -> 1/
    11 (364/9 - 13/36 (31096 - 3432 Sqrt[78])^(1/3) - (
      5 (31096 - 3432 Sqrt[78])^(2/3))/1872 - (
      5 (299 + 33 Sqrt[78])^(2/3))/(36 13^(1/3)) - 
      13/18 (13 (299 + 33 Sqrt[78]))^(1/3) - (
      5 ((31096 - 3432 Sqrt[78]) (299 + 33 Sqrt[78]))^(1/3))/(
      36 13^(2/3)) + 
      13/12 \[Sqrt]((-52 + 
            1/3 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
               2 (13 (299 + 33 Sqrt[78]))^(1/3)))^2 - 
          208 (15 + 
             1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
                2 (13 (299 + 33 Sqrt[78]))^(1/3)) + 
             1/468 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
                2 (13 (299 + 33 Sqrt[78]))^(1/3))^2)) - 
      5/624 (31096 - 3432 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            1/3 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
               2 (13 (299 + 33 Sqrt[78]))^(1/3)))^2 - 
          208 (15 + 
             1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
                2 (13 (299 + 33 Sqrt[78]))^(1/3)) + 
             1/468 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
                2 (13 (299 + 33 Sqrt[78]))^(1/3))^2)) - (1/(
      24 13^(2/3)))
      5 (299 + 33 Sqrt[78])^(
       1/3) \[Sqrt]((-52 + 
            1/3 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
               2 (13 (299 + 33 Sqrt[78]))^(1/3)))^2 - 
          208 (15 + 
             1/3 (-52 - (31096 - 3432 Sqrt[78])^(1/3) - 
                2 (13 (299 + 33 Sqrt[78]))^(1/3)) + 
             1/468 (52 + (31096 - 3432 Sqrt[78])^(1/3) + 
                2 (13 (299 + 33 Sqrt[78]))^(1/3))^2))), 
  lc -> (9009 + 338 (13 (299 - 33 Sqrt[78]))^(1/3) + 
    5 (13 (299 - 33 Sqrt[78]))^(2/3) + 
    338 (13 (299 + 33 Sqrt[78]))^(1/3) + 
    5 (13 (299 + 33 Sqrt[78]))^(2/3))/2574}}
Attachments:
POSTED BY: Valeriu Ungureanu
POSTED BY: ? ??

I was trying to solve the equation set below in Maple?Mathematica and WolframAlpha. But i didn't get the answer. The Maple is running about 6 hours up to now.

solve(a+b+c=g,b*c*(e+f)+a*(b*(d+e)+c*(d+f))=g*(h*k+i*m),a*b*c*(e*f+d*(e+f))=g*h*i*k*m,2*h*k+i*m+g*(o+m)=a*d+b*e+c*f,h*i*k*m+g*(i*(o+k)*m+h*k*(o+m))=b*c*e*f+a*d*(b*e+c*f),1/d=1/o+1/k+1/m,{a,b,c,d,e,f})
POSTED BY: ? ??

Thank u ! I will try again !

I think there are still six equations.

One of abc(ef+d(e+f))=ghik*m and abcdef=ghijkm

shoud be added to the eqn set.
POSTED BY: ? ??
Bill Simpson
Bill Simpson
Posted 10 years ago

Your expression is 350 characters. The WolframAlpha limit seems to be about 125 characters.

By replacing all your two character variable names with one character variable names, which often seems to be more acceptable to WolframAlpha, and grouping similar expressions using ( ) it is possible to reduce the length to 208 characters.

solve(a+b+c=g,
b*c*(e+f)+a*(b*(d+e)+c*(d+f))=g*(h*k+i*m),
a*b*c*(e*f+d*(e+f))=g*h*i*k*m,
2*h*k+i*m+g*(j+m)=a*d+b*e+c*f,
h*i*k*m+g*(i*(j+k)*m+h*k*(j+m))=b*c*e*f+a*d*(b*e+c*f),
a*b*c*d*e*f=g*h*i*j*k*m,{a,b,c,d,e,f})

Now notice the similarity between

a*b*c*(e*f+d*(e+f))=g*h*i*k*m

and

a*b*c*d*e*f=g*h*i*j*k*m

Perhaps it is possible to multiply the first equation by j and thus the two equations become

(e*f+d*(e+f))*j=d*e*f

I am concerned that only five equations remain, while you wish to solve for six variables, and you should carefully check what that means. If this has not divided by zero and is valid then the system becomes

solve(a+b+c=g,
b*c*(e+f)+a*(b*(d+e)+c*(d+f))=g*(h*k+i*m),
2*h*k+i*m+g*(j+m)=a*d+b*e+c*f,
h*i*k*m+g*(i*(j+k)*m+h*k*(j+m))=b*c*e*f+a*d*(b*e+c*f),
(e*f+d*(e+f))*j=d*e*f,{a,b,c,d,e,f})

and is 177 characters.

That is half the length of your original expression, but still much larger than 125 characters. Perhaps you can use similar methods to find additional similarities in your system, notice the ghk+gim which appears in two equations, and further reduce it to see if WolframAlpha can find a solution.
POSTED BY: Bill Simpson
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