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My keyboard is broken. So here is fast answer (on Mathematica 9); more later... Here is your input: dim = 3; g = RandomReal[{0, 1}, {dim, dim}]; F = RandomReal[{0, 1}, {dim, dim, dim, dim}]; Now multiply four g's and the F. Use TensorProduct[g, g, g, g, F] (don't run this yet--it's slow) to generate the rank 12 tensor (unrepeated indices). Now ...



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