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 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.