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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: 1,398
Registered: 12/7/04
Re: Applying Mathematica to practical problems
Posted: Jun 3, 2013 3:24 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, 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
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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