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If $A$ is an algebra and $D_1, D_2\in A$ we can define the commutator $$[D_1, D_2]:=D_1\circ D_2-D_2\circ D_1.$$

I'd like to create an analogous notation to sum up things like these:

$$D_1\circ D-D\circ D_2.$$

It must be a notation which makes sense in general.

It seems something silly, but I am going to use this in another context where expressions like this are huge and very frequent so it would be very useful to have such a notation.

Thanks.

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    Look at the definition of _free algebra_. Perhaps this helps. – 2017-01-28
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    Ok, I'll check it. – 2017-01-28

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