The approach taken by Mathematica is that they hope to
provide, for any expression that can be evaluated numerically,
a method for evaluating it to arbitrary precision. That is,
N[ ...., d] evaluates to "Accuracy" d.
Sometimes not, but that's the intent.
There is a subtle argument to be made that no one needs
certain functions to super-high accuracy.. why bother.
The key to doing numerical evaluation in maxima is perhaps
not ideal. Sin(1.2) is changed to a number, but sin(12/10) is
not. ev(%,numer) is kind of broken, leaving things like %i and %e
around sometimes.
Maybe we need an analog of n(...,d), as a separate function, doing
something more careful than just
than
n(h,d):=block([fpprec:d],bfloat(h)); ... this does computation in
d digits, but doesn't necessarily provide an answer that is right to d digits.
RJF
Robert Dodier wrote:
> --- Raymond Toy wrote:
>
>
>>The other issue is what to do about the mathematical properites of
>>such functions. If we implemented, say, an incomplete gamma
>>function, it would be nice if maxima actually knew something about
>
> the
>
>>incomplete gamma function. Things like derivatives, integrals,
>>limits, special values, etc.
>
>
> Agreed entirely, but I think the numerical stuff is useful
> independently of the symbolic stuff. So I guess I would
> suggest let's go ahead with some numerical functions and
> let the symbolic properties catch up on their own schedule.
>
> Thanks for your interest in this topic -- I appreciate it.
>
> Robert Dodier
>
>
>
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