Dear Xavier,

I've been able to both generalize (as you proposed) and leverage your suggestion re tensor dimensional sums.

I'd like to give you credit, but there are too many Xavier Roys on the Web.

If you feel like please send contact info to me at my regular email marktuttle@pacbell.net

Thank you, -- Mark

Hi Mark,

I did not succeed to obtain the sum over the second dimension using Total in the way you showed. An alternative approach which doesn't make use of Transpose would be the following

Total[a2X2X2[[#, All, All]], 2] & /@ {1, 2}
Total[a2X2X2[[All, #, All]], 2] & /@ {1, 2}
Total[a2X2X2[[All, All, #]], 2] & /@ {1, 2}

It can be easily generalized to tensors of any rank and/or dimensions. For high ranks and small number of dimensions, the timings between this version and yours are more or less similar; but for small ranks and high number of dimensions, the above version is significantly slower. (See attached file for these remarks.)

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