# Thread: Commutator notation extension - [A,B,C]

1. ## Commutator notation extension - [A,B,C]

While some extensions to the notation have been proposed in the past, this is a common group of algorithms and the notation is already somewhat being used.

I propose that [A,B,C] = [A,B] [B,C].

After expanding, a cancellation in the middle gives A B A' C B' C'.

For example, [l', RUR'U', r] is a common 4x4x4 last layer algorithm.

This notation can be extended further -

[A,B,C,D] = [A,B] [B,C] [C,D] = A B A' C B' D C' D'

but I am yet to find a use for it :)

Finally, just as [A,B]' = [B,A], [A,B,C]' = [C,B,A].

2. Nice, this will make it easier to write some stuff (probably, I don't know much about commutators).

It reminds me of the chain rule.

3. I like it. Probably wouldn't use it too often but being able to avoid typing out an entire cyclic shift is good enough for me

[F R', U2, R' F]

4. Originally Posted by riffz
I like it. Probably wouldn't use it too often but being able to avoid typing out an entire cyclic shift is good enough for me

[F R', U2, R' F]
Ooh, that is a good use for this. I never thought of it before. I've only used it for 2*3 cycles and 5 cycles

5. btw

[R, U, U2, R]

6. I haven't seen that many algorithms that contain a product of two (or more) non-conjugated (or non shifted) commutators. Moreover, I have seen that algorithms for 2 3-cycle cases are just as brief (or even briefer) if handled with one commutator instead of 2. I think it would be much more useful to establish a notation extension that illustrates cyclic shifts rather than a product of two commutators.

7. Originally Posted by Kirjava
btw

[R, U, U2, R]
I though it was super duper complex!

8. Originally Posted by cmowla
I haven't seen that many algorithms that contain a product of two (or more) non-conjugated (or non shifted) commutators.
Are you sure? K4 makes heavy use of them.

Originally Posted by cmowla
Moreover, I have seen that algorithms for 2 3-cycle cases are just as brief (or even briefer) if handled with one commutator instead of 2.

Originally Posted by cmowla
I think it would be much more useful to establish a notation extension that illustrates cyclic shifts rather than a product of two commutators.
I mentioned this yesterday, but didn't see much use in it. Can you elaborate?

Do you have anything in mind? I think a single delimiter to denote the location of the shift could be a solution.

9. Originally Posted by Kirjava
I mentioned this yesterday, but didn't see much use in it. Can you elaborate?
Well, the only real use I would see is showing the decomposition of an algorithm more effectively (even permutation or odd permutation). (Sure there are most likely move cancellations with these, but is it not so with the product of commutators? If the two commutators affect only one piece type each and there are no move cancellations between them, then they should be seen as two different algorithms, not one. Of course, I'm not saying you ever said this, but just for sake of argument).

Originally Posted by Kirjava
Do you have anything in mind? I think a single delimiter to denote the location of the shift could be a solution.
I think a single delimiter is great too. No I don't have anything in mind to suggest, because honestly, I can't recall a single time when my suggestions were considered. I just like to post my opinion which usually gives people in the thread something to oppose...in doing so, "the people find direction." If you all do decide to do this (which I highly doubt, because the notations which are currently standard "shall not be modified" ), then I'm sure you all will agree on some symbol to use as a delimiter (I'm not going to waste my time...again).

10. When you intend to use it, just write that "|" (or whatever) denotes a cyclic shift. Maybe it'll catch on.

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