[r-t] Delta-based transposition representation

[Alan Burlison]

A while ago I wrote some code to expand place notation to the 
corresponding blue line numbers. One thing that I did to make my life 
easier was to describe the difference between two rows as deltas. For 
example the change between the following two rows:

A  1 2 3 4 5 6
B  2 1 4 3 6 5

would be:

+1 -1 +1 -1 +1 -1

Between the two ends of a sequence of rows:

A  2 6 4 1 5 3
:
N  5 3 6 2 1 4

+3 +1 +3 +1 -4 -4

i.e. the bell in place 1 (#2) has moved +3 places to place 4. the bell 
in place 6 (#3) has moved -4 places to place 2.

Applying a change to ma row is very simple - just add the deltas to the 
current bell positions. It's easy to create the inverse of a change by 
simply reversing the signs of the deltas, and you trivially know if a 
change is valid by summing the deltas - the result must be 0. It's also 
easy to check for other validity errors, for example the first colunm 
must be either 0 or 1 as the bell can't move off the end of the row and 
so forth.

I haven't seen changes described this way anywhere else which puzzles me 
a bit, because to me it's the blindingly obvious way of doing it, rather 
than the position-based notation I've seen used elsewhere.

-- 
Alan Burlison
--