moRe: Base change notation

[Marc LeBrun]

 >=franktaw at netscape.net
 > Apparently, nobody but Marc and myself cares about this.

Sorry, a few last things I forgot to add, so I can forevermore hold my peace:

Just to be clear: my long response to Frank's original proposal was 
intended to supply the background for the existing notation, and 
shouldn't be construed as a debate.  That would have to come later, if ever.

Even so, I want to confess one last hidden agenda I forgot to state, 
which was to encourage the adoption of writing [n] as a natural 
degenerate notation for any "generic" indexed objects that support 
some object-oriented arithmetic (aka "numbrals").  Of course this 
goes far afield of rebasing.  One motivation was a need in OEIS 
entries to ASCIIfy Conway & Guy's "nimbers", which are printed in red 
in their "Book of Numbers" (prompting Knuth to joke that [.] should 
be called the "red-shift" operator).  The idea was to start with 
things like Z2[n](x), simplify to Z2[n], and finally just [n] with 
the affixes supplied by context.  Uncluttering Z2[n](4) led to 2[n]4 
and the rest followed.  But all this is grandiose and tangential to 
burden simple rebasing with, and I'm quite happy to forego entangling 
the two concepts/notations, and retire to a private corner to diddle 
with my numbrals.

Moreover, I'll be delighted just to have ANY standard notation for 
rebasing!  Originally I felt there was a significant void that needed 
filling.  I tried hard to come up with something reasonably good, but 
if there's something everyone likes even better, which will encourage 
wider adoption, I'm all for it!

For that matter--completely aside from notation--in my view merely 
adopting and standardizing the concept and terminology of rebasing 
constitutes progress, and can help clear up a lot of the confusion 
that had begun to creep into certain OEIS entries.

Anyway the applications and connections are what's really interesting 
to me.  I'll be happy with ANY notation because it gives us an 
operator that is very handy in such diverse and previously apparently 
disconnected contexts as digit reversal, polynomial arithmetic, 
Fibonacci expansions, etc etc.

On the bright side: if a new notation is adopted then I can fancy 
myself as Newton to Frank's Leibniz!  (Hey, by long OEIS precedent I 
believe we amateurs are obligated to indulge in a certain amount of 
crankish megalomania!<;-)