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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

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# Lengthy Contraction

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