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Lengthy Contraction

  1. Feb 10, 2016 #1
    Hi,

    I was wondering if there exists some software to find the following contraction in an easy way
    $$M_{ad}M^{be}M^{cf} f^d_{bc}f^a_{ef}$$

    Here the 4x4 metric M has a block diagonal form
    $$
    \begin{pmatrix}
    e^\phi & 0\\
    0 & e^{-\phi/3}N
    \end{pmatrix}$$

    With ##N## a symmetric 3x3 matrix of determinant 1.
    The ##f^a_{bc}## are structure constants of some algebra (I have to evaluate this for 13 distinct algebras).
    A lot of them are zero, most of the others are 1.

    I keep missing terms (due to antisymmetry ##f^a_{bc} = -f^a_{cb}##) when doing any but the most trivial examples by hand.

    Thanks,

    Joris
     
  2. jcsd
  3. Feb 10, 2016 #2

    jedishrfu

    Staff: Mentor

  4. Feb 10, 2016 #3
    Thanks.

    Luckily there are some easy algebras that I can use to test the code.
     
  5. Feb 12, 2016 #4
    Well I looked at the tensor capabilities but so far it proved easier to hard code the stuff using tables. (More important, a lot faster to implement than to learn and use this new part of Mathematica)

    I added a PDF showing how I did it. When I find the time I might make it more generally applicable. (more than 4 dimensions, less constraints on allowed algebras etc)
     

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