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Foriegn variable names in the outputs of computing a Lie bracket commutation

Nomsa Ledwaba

Posted 2 days ago

Hello. I'm computing a Lie bracket commutation `[Xi, Xj] = C_{i,j}^{k} X_{k} = - [Xi, Xj]`, i,j = 1, ... , 6 and i<j. For example the following are some of the outputs: For [X1,X5] = For [X1,X6] = For [X2,X5] = u (-((E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3])) - (t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/ Sqrt[3]) (-1 + E^(( 2 t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/Sqrt[ 3])) (3 Sqrt[3] x Sqrt[\[Kappa]] + 2 Sqrt[3] \[Theta] Sqrt[\[Kappa]] - 3 x Sqrt[8 \[Theta] + 3 \[Kappa]]))/(16 x^( 3/2) \[Theta] Sqrt[\[Kappa]] Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])) + 1/(4 Sqrt[x] \[Theta] Sqrt[\[Kappa]]) E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3])) (-3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] - Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]) c$48559[2, 5, 1] + 1/(4 Sqrt[x] \[Theta] Sqrt[\[Kappa]]) E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3]))) (-3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] + Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]) c$48559[2, 5, 2]) + (-(( E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(2 Sqrt[3])) u)/(2 Sqrt[x])) + ( 3 E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(2 Sqrt[3])) u Sqrt[x])/(4 \[Theta]) + ( Sqrt[3] E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3])) u Sqrt[x] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 4 \[Theta] Sqrt[\[Kappa]])) f$48559[ 1] + (-(( E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3]))) u)/(2 Sqrt[x])) + ( 3 E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3]))) u Sqrt[x])/(4 \[Theta]) - 1/(4 \[Theta] Sqrt[\[Kappa]]) Sqrt[3] E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3]))) u Sqrt[x] Sqrt[8 \[Theta] + 3 \[Kappa]]) f$48559[ 2] For [X2,X6] = u (-((3 E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3])) - (t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/ Sqrt[3]) (-1 + E^(( t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/Sqrt[ 3]))^2 (3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] - Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]))/(16 x^( 3/2) \[Theta] \[Kappa]^(3/2) (8 \[Theta] + 3 \[Kappa]))) + 1/(4 Sqrt[x] \[Theta] Sqrt[\[Kappa]]) E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3])) (-3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] - Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]) c$52039[2, 6, 1] + 1/(4 Sqrt[x] \[Theta] Sqrt[\[Kappa]]) E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3]))) (-3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] + Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]) c$52039[2, 6, 2]) + (-(( E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(2 Sqrt[3])) u)/(2 Sqrt[x])) + ( 3 E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(2 Sqrt[3])) u Sqrt[x])/(4 \[Theta]) + ( Sqrt[3] E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3])) u Sqrt[x] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 4 \[Theta] Sqrt[\[Kappa]])) f$52039[ 1] + (-(( E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3]))) u)/(2 Sqrt[x])) + ( 3 E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3]))) u Sqrt[x])/(4 \[Theta]) - ( Sqrt[3] E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3]))) u Sqrt[x] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 4 \[Theta] Sqrt[\[Kappa]])) f$52039[2] For [X5, X6] = -u ((3 E^(-((t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/Sqrt[ 3])) (-1 + E^((t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/ Sqrt[3])) (8 Sqrt[3] \[Theta] + 8 Sqrt[3] E^((t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/ Sqrt[3]) \[Theta] + 3 Sqrt[3] \[Kappa] + 3 Sqrt[3] E^((t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/ Sqrt[3]) \[Kappa] - 3 Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])] + 3 E^((t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/Sqrt[3]) Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])]))/(8 \[Theta] \[Kappa] (8 \[Theta] + 3 \[Kappa]) Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])]) + 1/(4 Sqrt[x] \[Theta] Sqrt[\[Kappa]]) E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3])) (-3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] - Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]) c$54648[5, 6, 1] + 1/(4 Sqrt[x] \[Theta] Sqrt[\[Kappa]]) E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3]))) (-3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] + Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]) c$54648[5, 6, 2]) - (-(( E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(2 Sqrt[3])) u)/(2 Sqrt[x])) + ( 3 E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(2 Sqrt[3])) u Sqrt[x])/(4 \[Theta]) + ( Sqrt[3] E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3])) u Sqrt[x] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 4 \[Theta] Sqrt[\[Kappa]])) f$54648[ 1] - (-(( E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3]))) u)/(2 Sqrt[x])) + ( 3 E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3]))) u Sqrt[x])/(4 \[Theta]) - ( Sqrt[3] E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 2 Sqrt[3]))) u Sqrt[x] Sqrt[8 \[Theta] + 3 \[Kappa]])/( 4 \[Theta] Sqrt[\[Kappa]])) f$54648[2] Why am I getting them as part of the outputs. I want to see numbers or mathematical expressions. I humbly request your assistance. Please help.

Hello. I'm computing a Lie bracket commutation [Xi, Xj] = C_{i,j}^{k} X_{k} = - [Xi, Xj], i,j = 1, ... , 6 and i<j.
For example the following are some of the outputs:

For [X1,X5] = 
For [X1,X6] =
For [X2,X5] = u (-((E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
           2 Sqrt[3])) - (t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/
          Sqrt[3]) (-1 + E^((
           2 t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/Sqrt[
           3])) (3 Sqrt[3] x Sqrt[\[Kappa]] + 
           2 Sqrt[3] \[Theta] Sqrt[\[Kappa]] - 
           3 x Sqrt[8 \[Theta] + 3 \[Kappa]]))/(16 x^(
         3/2) \[Theta] Sqrt[\[Kappa]]
          Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])) + 
    1/(4 Sqrt[x] \[Theta] Sqrt[\[Kappa]])
      E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
      2 Sqrt[3])) (-3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] - 
        Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]) c$48559[2, 5, 1] + 
    1/(4 Sqrt[x] \[Theta] Sqrt[\[Kappa]])
      E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
       2 Sqrt[3]))) (-3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] +
         Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]) c$48559[2, 5, 
       2]) + (-((
     E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(2 Sqrt[3]))
       u)/(2 Sqrt[x])) + (
    3 E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(2 Sqrt[3]))
      u Sqrt[x])/(4 \[Theta]) + (
    Sqrt[3] E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
     2 Sqrt[3])) u Sqrt[x] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
    4 \[Theta] Sqrt[\[Kappa]])) f$48559[
   1] + (-((
     E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
       2 Sqrt[3]))) u)/(2 Sqrt[x])) + (
    3 E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
      2 Sqrt[3]))) u Sqrt[x])/(4 \[Theta]) - 
    1/(4 \[Theta] Sqrt[\[Kappa]])
      Sqrt[3] E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
       2 Sqrt[3]))) u Sqrt[x] Sqrt[8 \[Theta] + 3 \[Kappa]]) f$48559[
   2]
For [X2,X6] = u (-((3 E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
           2 Sqrt[3])) - (t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/
          Sqrt[3]) (-1 + E^((
           t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/Sqrt[
           3]))^2 (3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] - 
           Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]))/(16 x^(
         3/2) \[Theta] \[Kappa]^(3/2) (8 \[Theta] + 3 \[Kappa]))) + 
    1/(4 Sqrt[x] \[Theta] Sqrt[\[Kappa]])
      E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
      2 Sqrt[3])) (-3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] - 
        Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]) c$52039[2, 6, 1] + 
    1/(4 Sqrt[x] \[Theta] Sqrt[\[Kappa]])
      E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
       2 Sqrt[3]))) (-3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] +
         Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]) c$52039[2, 6, 
       2]) + (-((
     E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(2 Sqrt[3]))
       u)/(2 Sqrt[x])) + (
    3 E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(2 Sqrt[3]))
      u Sqrt[x])/(4 \[Theta]) + (
    Sqrt[3] E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
     2 Sqrt[3])) u Sqrt[x] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
    4 \[Theta] Sqrt[\[Kappa]])) f$52039[
   1] + (-((
     E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
       2 Sqrt[3]))) u)/(2 Sqrt[x])) + (
    3 E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
      2 Sqrt[3]))) u Sqrt[x])/(4 \[Theta]) - (
    Sqrt[3] E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
      2 Sqrt[3]))) u Sqrt[x] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
    4 \[Theta] Sqrt[\[Kappa]])) f$52039[2]
For [X5, X6] = -u ((3 E^(-((t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/Sqrt[
        3])) (-1 + E^((t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/
         Sqrt[3])) (8 Sqrt[3] \[Theta] + 
         8 Sqrt[3] E^((t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/
          Sqrt[3]) \[Theta] + 3 Sqrt[3] \[Kappa] + 
         3 Sqrt[3] E^((t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/
          Sqrt[3]) \[Kappa] - 
         3 Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])] + 
         3 E^((t Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])])/Sqrt[3])
           Sqrt[\[Kappa] (8 \[Theta] + 
             3 \[Kappa])]))/(8 \[Theta] \[Kappa] (8 \[Theta] + 
         3 \[Kappa]) Sqrt[\[Kappa] (8 \[Theta] + 3 \[Kappa])]) + 
    1/(4 Sqrt[x] \[Theta] Sqrt[\[Kappa]])
      E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
      2 Sqrt[3])) (-3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] - 
        Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]) c$54648[5, 6, 1] + 
    1/(4 Sqrt[x] \[Theta] Sqrt[\[Kappa]])
      E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
       2 Sqrt[3]))) (-3 x Sqrt[\[Kappa]] + 2 \[Theta] Sqrt[\[Kappa]] +
         Sqrt[3] x Sqrt[8 \[Theta] + 3 \[Kappa]]) c$54648[5, 6, 
       2]) - (-((
     E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(2 Sqrt[3]))
       u)/(2 Sqrt[x])) + (
    3 E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(2 Sqrt[3]))
      u Sqrt[x])/(4 \[Theta]) + (
    Sqrt[3] E^((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
     2 Sqrt[3])) u Sqrt[x] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
    4 \[Theta] Sqrt[\[Kappa]])) f$54648[
   1] - (-((
     E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
       2 Sqrt[3]))) u)/(2 Sqrt[x])) + (
    3 E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
      2 Sqrt[3]))) u Sqrt[x])/(4 \[Theta]) - (
    Sqrt[3] E^(-((t Sqrt[\[Kappa]] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
      2 Sqrt[3]))) u Sqrt[x] Sqrt[8 \[Theta] + 3 \[Kappa]])/(
    4 \[Theta] Sqrt[\[Kappa]])) f$54648[2]

Why am I getting them as part of the outputs. I want to see numbers or mathematical expressions. I humbly request your assistance. Please help.

POSTED BY: Nomsa Ledwaba

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