Date: Jun 2, 2013 12:23 AM
Author: Mark McClure
Subject: Re: Applying Mathematica to practical problems
On Sat, Jun 1, 2013 at 6:27 AM, Richard Fateman <email@example.com> wrote:
> On 5/31/2013 12:16 AM, Andrzej Kozlowski wrote:
>> Naive users of Mathematica practically never use arbitrary
>> precision arithmetic.
> Practically never, but occasionally? Like slightly pregnant?
While I'd prefer to steer clear of the majority of this morass, I do
have one data point that might be useful. In fact, I wrote the
following on sci.math.symbolic back in 2008:
>>>> I've been teaching undergraduate students to solve numerical
>>>> problems in calculus, differential equations, linear algebra, and
>>>> more recently numerical analysis using Mathematica since version
>>>> 1.2 and I don't believe I've ever seen the types of problems you
>>>> describe arise in that setting.
Well, that was five years ago and, as I've continued to teach with
Mathematica and even developed a course *on* Mathematica, I can now
expand on that a bit. I have now seen a novice user develope some
serious confusion due to unexpected behavior surrounding significance
arithmetic - once.
Incidentally, the significance arithmetic was triggered, not by one of
RJF's standard tricks, but by a simple bug. In versions 6 and 7 of
Mathematica, entering AiryA[0.0] yielded a non-machine number with
Precision $MachinePrecision, rather than a machine number with
Precsion MachinePrecision. I was studying the structure of Julia sets
of Airy functions with an undergraduate research student and, as you
might imagine, it was, uhmm, inconvenient to iterate with
high-precision numbers. Danny can verify the bug at least, as he
Finally, the main reason I find this debate so uninteresting is that
it is just simple observation that loads of people are doing good
numerical work with Mathematica. We have better things to talk about.