> I read that this is sometimes called "the alternating tensor of third
> order", or, "psuedotensor". Which is one thing that made me suspicious
> to start with... As far as I can tell the difference between choosing
> the symmetry properties:
> A_{ijk} = A_{ikj}, and A_{ijk} = A_{kij}
> ie, last two, or first two indices are symmetric, is wholly a matter of
> convention.
I see. There is of course the totally antisymmetric tensor eps_{ijk}, but
that's something entirely different.
As I said, if you're interested, feel free to implement whatever you think
makes sense. The easier route would probably be to just use a
Tensor<3,dim> and set its elements in such a way that it has the desired
symmetry.
> Yes, first-order = second-order * third-order. By that I meant a
> contraction over outer indices (or a double contraction).
>
> Example ->
> X_{ij} = \sum_k A_{ijk} B_{jk}
> X_i = \sum_{jk} A_{ijk} B_{jk}
I have no objections to adding more contract() functions to tensor.h.
Best
W.
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Wolfgang Bangerth email: [email protected]
www: http://www.math.tamu.edu/~bangerth/
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