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

 Messages: [ Previous | Next ]
 Richard Fateman Posts: 1,539 Registered: 12/7/04
Re: Applying Mathematica to practical problems
Posted: Jun 3, 2013 3:24 AM

On 6/1/2013 9:23 PM, Andrzej Kozlowski wrote:
> This is one of many examples of "cross purpose" arguing. I was not
> discussing implementing non-standard analysis at all. My point was
> that that there is nothing logically more dubious about a finite
> "number" x such that x+1=1 than there is about a positive "number" x
> such that nx< 1 for every positive integer n, or, alternatively,
> finite "number" x such that x/n >1 for every positive integer n.
> Mathematicians often use the word "number" when referring to objects
> belonging to some "extension" of the real line.

Oh where to start. Here's one place.

You say it is ok to have a number x such that x+1=1. I agree.
I say it is NOT ok to have a number x such that x+1=x.
You respond
It is ok to have a number x such that x+1=1.
Can you see the difference?

Here's another.

AK says DanL says he wrote programs using significance arithmetic and
they worked.

There are other places in Mathematica in which significance
arithmetic MUST NOT be used. Convergent iterations, generally.
Will naive users be led astray by this kind of situation?
Maybe.

Also is the Grobner basis program in Mathematica the fastest?
I suspect it is not, though I have not compared it to Faugere's
work, or other unnamed systems. Is it the only one using significance
arithmetic? I suspect it is. What would that prove? What
would that prove about use as a default?

Finally, I would remind AK (and others)
that proving some number of correct results
does not prove an algorithm is correct. Proving even one incorrect
result demonstrates a bug.

RJF

Date Subject Author
5/12/13 David Park
5/14/13 Nasser Abbasi
5/15/13 szhorvat@gmail.com
5/16/13 szhorvat@gmail.com
5/16/13 Dr. Peter Klamser
5/17/13 Andrzej Kozlowski
5/17/13 Murray Eisenberg
5/17/13 Dr. Peter Klamser
5/18/13 Dr. Peter Klamser
5/19/13 Murray Eisenberg
5/19/13 paulmchale7@gmail.com
5/19/13 paulmchale7@gmail.com
5/23/13 szhorvat@gmail.com
5/24/13 David Park
5/20/13 Ingolf Dahl
5/20/13 David Annetts
5/22/13 mathgroup
5/23/13 Richard Fateman
5/24/13 W. Craig Carter
5/23/13 David Park
5/23/13 mathgroup
5/24/13 Richard Fateman
5/25/13 David Park
5/25/13 Richard Fateman
5/25/13 David Park
5/28/13 Alexei Boulbitch
5/28/13 Alexei Boulbitch
6/4/13 Bill Rowe
5/24/13 David Park
5/27/13 Noqsi
5/28/13 Richard Fateman
5/31/13 David Bailey
6/1/13 Richard Fateman
6/2/13 David Bailey
6/3/13 Richard Fateman
6/3/13 David Bailey
6/4/13 Andrzej Kozlowski
5/29/13 fd
5/30/13 Noqsi
5/31/13 Richard Fateman
5/31/13 Kevin J. McCann
5/31/13 Andrzej Kozlowski
6/1/13 Richard Fateman
6/1/13 Richard Fateman
6/2/13 Andrzej Kozlowski
6/3/13 Richard Fateman
6/3/13 Andrzej Kozlowski
6/1/13 Daniel Lichtblau
6/2/13 Richard Fateman
6/2/13 James Stein
6/3/13 waku
6/3/13 Daniel Lichtblau
5/27/13 Noqsi
6/2/13 David Bailey
5/28/13 fd
5/31/13 David Bailey
5/28/13 fd
6/2/13 Mark McClure
6/3/13 Richard Fateman
6/3/13 Joseph Gwinn
6/3/13 lshifr@gmail.com
6/3/13 lshifr@gmail.com