Dear all, I already mentioned this idea quite a few years ago, but I think it really would be good to have. The idea is to turn contractions of an object with something else that has a single index into one object. A new notation for the output would be necessary for this and I guess using a colon would not be bad. That way we would get A~mu~nu*v.mu*w.nu -> A:v:w. The advantages are: * More compact expressions, hence more efficient to store; * More efficient to manipulate because functions like simplify_indexed would have fewer indices to rename. Not to mention automatic dummy index renaming. * More readable output, because if the factors in the example just-given end up somewhere near the beginning of a large product, somewhere near the middle and somewhere near the end it realy isn't readable. Also a notation for the inner product would be necessary. I think something like v:w or maybe inp(v,w) would be nice. I think in the case of a contraction with a tensor I could simply add a flag to the class idx that indicates whether the index is really an index or is a contraction. The point is that we should still store the dimension in the case one is doing dimensional regularization. What do you think? Chris