On Tue, 2005-03-15 at 15:13, Richard Fateman wrote:
> 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.
Back in the day when I used Mathematica, I found the behavior N[...,d]
to be completely aggravating. It always worked in trivial cases, but it
failed to do what I wanted in every single instance where I actually had
a need for it. The maddening thing was that I could never tell which
things would be evaluated to arbitrary accuracy and which would not.
> 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.
Yes.
> 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.
I would love to see this, but it's pretty hard to do in general, isn't
it?
--Jim