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 <fateman@cs.berkeley.edu> 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

fixed it.

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.

Mark McClure