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Topic: Work on Basic Mathematica Stephen!
Replies: 81   Last Post: Jun 4, 2013 5:59 AM

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Richard Fateman

Posts: 1,400
Registered: 12/7/04
Re: Applying Mathematica to practical problems
Posted: Jun 3, 2013 3:25 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 6/1/2013 9:23 PM, Mark McClure wrote:
....

>
> 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.


OK. Introductory courses on Mathematica that don't even mention
extended floats and significance arithmetic are perhaps not exploring
a major part of the system that goes beyond what is available in
ordinary numeric systems (whose names may not be mentioned here).
That is, using Mathematica to execute machine-hardware arithmetic
only is fairly safe, but also unremarkable.
>
> 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.


If you are able to entirely shield your users from a mistaken transition
to extended precision, that might be good. However a serious
user, not under the protective umbrella of your introductory course,
might stumble into the pit. I think we can hope that students in
classes will have appropriate corrective influences surrounding them. It
is the people trying to break new ground (maybe graduate students and
above) who can get into mysterious difficulties.


> 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.


I can imagine. However, how many Mathematica users would find it
puzzling? How many people reading this note right now on mathgroup
would find it puzzling?

>
> 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.


Actually the "other side" of the debate is that it is hazardous
to do numerical work with Mathematica' non-machine floats. And if
you are just using ordinary machine floats, the justification for
using Mathematica because somewhat less cogent.
>
> Mark McClure
>






Date Subject Author
5/12/13
Read Work on Basic Mathematica Stephen!
David Park
5/13/13
Read Re: Work on Basic Mathematica Stephen!
psycho_dad
5/13/13
Read Re: Work on Basic Mathematica Stephen!
psycho_dad
5/14/13
Read Re: Work on Basic Mathematica Stephen!
Nasser Abbasi
5/15/13
Read Re: Work on Basic Mathematica Stephen!
szhorvat@gmail.com
5/16/13
Read Re: Work on Basic Mathematica Stephen!
szhorvat@gmail.com
5/16/13
Read Re: Work on Basic Mathematica Stephen!
Dr. Peter Klamser
5/17/13
Read Re: Work on Basic Mathematica Stephen!
Andrzej Kozlowski
5/17/13
Read Re: Work on Basic Mathematica Stephen!
Murray Eisenberg
5/17/13
Read Re: Work on Basic Mathematica Stephen!
Dr. Peter Klamser
5/18/13
Read Re: Work on Basic Mathematica Stephen!
Dr. Peter Klamser
5/19/13
Read Re: Work on Basic Mathematica Stephen!
Murray Eisenberg
5/19/13
Read Re: Work on Basic Mathematica Stephen!
paulmchale7@gmail.com
5/19/13
Read Re: Work on Basic Mathematica Stephen!
paulmchale7@gmail.com
5/23/13
Read Re: Work on Basic Mathematica Stephen!
szhorvat@gmail.com
5/24/13
Read Re: Work on Basic Mathematica Stephen!
David Park
5/20/13
Read Re: Work on Basic Mathematica Stephen!
Ingolf Dahl
5/20/13
Read Re: Work on Basic Mathematica Stephen!
David Annetts
5/22/13
Read Re: Work on Basic Mathematica Stephen!
mathgroup
5/23/13
Read expanding the use of symbolic computation in engineering .. was Re:
Richard Fateman
5/24/13
Read Re: expanding the use of symbolic computation in engineering .. was Re:
W. Craig Carter
5/23/13
Read Re: Work on Basic Mathematica Stephen!
David Park
5/23/13
Read Re: Work on Basic Mathematica Stephen!
mathgroup
5/24/13
Read Re: Work on Basic Mathematica Stephen!
Richard Fateman
5/25/13
Read Re: Work on Basic Mathematica Stephen!
David Park
5/25/13
Read Re: Work on Basic Mathematica Stephen!
Richard Fateman
5/25/13
Read Re: Work on Basic Mathematica Stephen!
David Park
5/28/13
Read Re: Work on Basic Mathematica Stephen!
Alexei Boulbitch
5/28/13
Read Re: Work on Basic Mathematica Stephen!
Alexei Boulbitch
6/4/13
Read Re: Work on Basic Mathematica Stephen!
Bill Rowe
5/24/13
Read Re: Work on Basic Mathematica Stephen!
David Park
5/27/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
Noqsi
5/28/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
Richard Fateman
5/31/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
David Bailey
6/1/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
Richard Fateman
6/2/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
David Bailey
6/3/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
Richard Fateman
6/3/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
David Bailey
6/4/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
Andrzej Kozlowski
5/29/13
Read Re: Warsaw Univ. course, was Re: Work on Basic Mathematica Stephen!
fd
5/30/13
Read Applying Mathematica to practical problems
Noqsi
5/31/13
Read Re: Applying Mathematica to practical problems
Richard Fateman
5/31/13
Read Re: Applying Mathematica to practical problems
Kevin J. McCann
5/31/13
Read Re: Applying Mathematica to practical problems
Andrzej Kozlowski
6/1/13
Read Re: Applying Mathematica to practical problems
Richard Fateman
6/1/13
Read Re: Applying Mathematica to practical problems
Richard Fateman
6/2/13
Read Re: Applying Mathematica to practical problems
Andrzej Kozlowski
6/3/13
Read Re: Applying Mathematica to practical problems
Richard Fateman
6/3/13
Read Re: Applying Mathematica to practical problems
Andrzej Kozlowski
6/1/13
Read Mathematica numerics and... Re: Applying Mathematica to practical problems
Daniel Lichtblau
6/2/13
Read Interval vs default, was Re: Mathematica numerics and... Re: Applying
Richard Fateman
6/2/13
Read Re: Applying Mathematica to practical problems
James Stein
6/3/13
Read Re: Applying Mathematica to practical problems
waku
6/3/13
Read Re: Interval vs default, was Re: Mathematica numerics and... Re: Applying
Daniel Lichtblau
5/27/13
Read Re: Work on Basic Mathematica Stephen!
Noqsi
6/2/13
Read Re: Work on Basic Mathematica Stephen!
David Bailey
5/28/13
Read Re: Work on Basic Mathematica Stephen!
fd
5/31/13
Read Re: Work on Basic Mathematica Stephen!
David Bailey
5/28/13
Read Re: Work on Basic Mathematica Stephen!
fd
6/2/13
Read Re: Applying Mathematica to practical problems
Mark McClure
6/3/13
Read Re: Applying Mathematica to practical problems
Richard Fateman
6/3/13
Read Re: Applying Mathematica to practical problems
Joseph Gwinn
6/3/13
Read Re: Warsaw Univ. course, was Re: Work on Basic
lshifr@gmail.com
6/3/13
Read Re: Warsaw Univ. course, was Re: Work on Basic
lshifr@gmail.com

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