Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » Software » comp.soft-sys.math.mathematica

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Andrzej Kozlowski

Posts: 226
Registered: 1/29/05
Re: Applying Mathematica to practical problems
Posted: Jun 3, 2013 11:11 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


On 3 Jun 2013, at 09:34, Richard Fateman <fateman@cs.berkeley.edu> wrote:

> 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?


Yes, I was careless about this, but that was because it does not really
matter. It is O.K. to extend the real line to an algebraic and
topological sturcture which contains objects such x such that x+1=x.
Of course such objects do not have inverses, so you can't conclude that
0=1. Admittedly, in Mathematica the underlying logic is obscured by
the fact that it equality is not identity, so you do have

1`0 == 1

True

1`0 == 0

True

but

1`0 == 0

True

All this means that equality is a non-transitive relation on this
extended set of objects (but identity is). That is also logically
perfectly sound.

>
>
> 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?


This is nonsense. Faugere does not work on numerical analysis and has
not implemented a numerical Groebner basis. Other people have worked on
approximate Grobener bases using fixed precision arithmetic but (as far
as I know) there are no working implementations available.

Groebner bases with exact coefficients are an entirely different
subject, unrelated to this discussion.


>
> 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.
>


You have never demonstrated one incorrect result proved by Mathematica.

AK




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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.