[r-t] What IS a rotation of a method?

[Matthew Frye]

On 16 Oct 2014, at 19:41, Don Morrison <dfm at ringing.org> wrote:

> I don't think I've ever actually seen an explicit definition of what
> we mean by "rotation" of a method.

> - Two such method candidates are rotations of one another if that
> sequence of place notations for one is the same as for the other,
> albeit typically starting with a different change and wrapping back to
> include the stuff elided before the starting point.

I might wish to phrase it more along the lines of "a rotation of an N change round block can be formed by ringing changes M to N followed by changes 1 to (M-1)" to be totally explicit about it, but I think we're saying the same thing.

> Is that right?

Yes, I think I agree with all your points. Including a null change will mean that two rotations will contain the same rows, but that's more or less an incidental property, I think. I'm not certain about the "equivalence relation" statement if it has special mathematical meaning, but it's probably true anyway. The final observation about allowed/non-allowed methods in rotations is an interesting albeit probably useless one.

Anyway, this all seems fairly common-sense to me (yes, yes I know that's very dangerous) and I seem to have lost exactly what the point of bringing up/formalising rotations was (we seem to have got somewhat sucked into the usual Grandsire/New Grandsire argument). Would you mind re-stating what exactly you were hoping to discuss/achieve here please?

MF