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From: Hubert Holin (Hubert.Holin_at_[hidden])
Date: 2005-08-11 09:05:11

Somewhere in the E.U., le 11/08/2005


      Peeking back after vacations are over...

In article <BAY104-DAV130A4664B11F6CDE9DB931BFD20_at_phx.gbl>,
 Daryle Walker <darylew_at_[hidden]> wrote:

> This is for the "ll" function defined for quaternions and octonions. The
> function returns the 1-norm of its argument. Does anyone know what the "ll"
> name stands for? I finally figured out that "sup" (the infinity-norm) most
> likely stands for "supremum". (BTW, "abs" is the 2-norm. The "norm"
> function isn't actually in this system, despite the name!)

it is actually the L1 (ell-one) norm (sum of the norm of the components,
the lp norm would be the sum of the p-th power of the norm of the
components, and the l-infinite norm is just the supremum of the norm of
the components). This was to be consistent with the usual mathematical
terminology (lower-case "l" for the norm of sequence spaces, upper-case
"l" for other measured spaces, though in this case we only have a
quadruple or an octuple). I agree the resemblance between the "l" and
the "1" is quite unfortunate.

      I have no special love for that notation, but fear that changing
it now would be more hassle than what it's worth. At the very least,
I'll add a note to the documentation after the 1.33 release.


         Hubert Holin

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