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Re: error estimates

Sorry, I accidentally hit the send button and
the message was cut off. Oi.

Anyway, that's basically all I had to say,
at least for now. There are obviously some
very difficult questions about how to
organize the code, factor things properly,
and create directed and useful tests.

In my dreams, I would like to see a code base
that not only burps out function values on
request but also makes itself useful in
other ways. Often clients want arrays of values,
for sequences of parameters, such as 'ell' for
Legendre functions or 'nu' for Bessel functions

Such arrays are always computed using some
iterative procedure, which is essentially
the same procedure as used to compute
single values. The library already has
some "_array" functions that do some of these.

But the best possible thing is to expose the
actual recursion to the client, so that they
can manipulate it and get what they want.
This would also simplify the design of the
underlying library code, which could reuse
the same facilities.

There are similar design questions about computing
zeros of functions. Almost always needed in sets
of many, and also closely related to other problems
of interest to the client.

Maybe one day, all this stuff could be made better.

G. Jungman

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