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

Don Morrison dfm at ringing.org
Thu Oct 16 18:41:08 UTC 2014

```I don't think I've ever actually seen an explicit definition of what
we mean by "rotation" of a method. Is it something like the following
(which would certainly need to be tidied up), or something else?

- It applies only to method candidatess the rows of which are
generated by an explicit sequence of place notation, broken into 1 or
more divisions (plain leads) that are all generated by exactly the
same sequence. Rotation is undefined for things like Dixonoids and
most other rule based methods. (While reversals get tricky with jump
changes, I think jump changes don't make things any more complicated
for rotations.) What it may or may not mean for cylindrical and
related constructs I don't even want to begin thinking about!

- 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.

Is that right?

A method candidate is a trivial rotation of itself, right?

If a method candidate has lead length (that is, the length of the
sequence of place notation) N, there are at most N distinct
rotations, including the trivial one, possible for it, though
there may in practice be fewer. Right?

If a division of a method candidate is not the shortest repeating
subunit, rotating the corresponding method candidate based on just
that shortest subunit M ticks is equivlent to rotating the bigger
method candidate M ticks, right?

Including the null change does not complicate things in any way, right?

"Is a rotation of" is an equivalence relation, right?

Rotation potentially mucks up symmetries, or rather moves them

If a method candidate has exactly N hunt bells, any rotation also has exactly
N hunt bells, though they will typically be different specific bells. Right?

More generally, the set of cycles of hunt (cycle length 1) and working
(cycle length > 1) bells is invariant under rotation, though which
specific bells are in which cycles changes. Right?

If using the current CCCBR taxonomy of methods, if a method candidate
is a method, its classification cannot change under rotation, right?

Note that if one (a) allows methods with one lead coures, and (b)
disallows more than N consecutive blows in a place for some N, then
rotation *can* sometimes make an "illegal" method into a "legal" one,
and vice-versa.

Are there any subtlties that I'm missing?

--
Don Morrison <dfm at ringing.org>
"The problem with being consistent is that there are lots of ways to
be consistent, and they're all inconsistent with each other."
-- Larry Wall, the Perl 6 mailing list

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