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Re: how to explain this weird effect? Integrate

• To: mathgroup at smc.vnet.net
• Subject: [mg46411] Re: how to explain this weird effect? Integrate
• From: nma124 at hotmail.com (steve_H)
• Date: Tue, 17 Feb 2004 07:05:44 -0500 (EST)
• References: <c0qjgq$ka6$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Bill Rowe <readnewsciv at earthlink.net> wrote in message news:<c0qjgq$ka6$1 at smc.vnet.net>...

> On 2/14/04 at 10:19 PM, nma124 at hotmail.com (steve_H) wrote:
> 
> >Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote in message
> >news:<c0kr0g$fo8$1 at smc.vnet.net>...
>
  
> >>Quite apart from that, the order of evaluation is a key issue in
> >>functional programming languages and there are lots of cases where
> >>Mathematica will produce different answers if you change the order
> >>of evaluation even if "mathematically" you are computing the same
> >>thing.
>
  
> >Ok, that is my main point then. All what I was saying is that we
> >are looking at results that are artifacts of artificial programming
> >side-effects, and are not results due to mathematics proper.
> 

hi Bill and Andzej;

thanks both for your inputs. Bill said:

> But these effect you label "artificial side-effects", are no 
> different that what a human might achieve. That is if you don't 
> see a way to re-arrange things or do things in a different order 
> you likely to get the same results as Mathematica does.
> 

Correct. This is IF you (a human) do not see a way to re-arrange 
things.  But I expect a computer program to see a way to re-arrange 
things. After all, it is supposed to be much better at doing these
things. 

> Take the example you used when you started this thread. If you 
> gave the results of the integral with the same denominator, 
> m^2 - n^2, a human, they either have the same problem with 
> division by zero when m = n or must take the appropriate limit. 
> Taking the appropriate limit is an additional step. It is no 
> different when using Mathematica.

But that is exactly my point. I wanted Mathematica to act as if it was a
human. (A very smart human at that).

All what I am saying is that Mathematica should have taken that extra step
without me having to tell. 

The way I look at it, is that when I tell a computer algebra program
to solve X, then I expect the program to do what it can and apply
any number of different steps and 'tricks' to solve X.

I do not have to tell it to do step 1 first, then step 2, then if it
can't do step 2, then try this trick first, and then do step 2, etc...

All what iam saying is that taking the limit in this case is NOT an
additional step becuase it would have lead to the solution I wanted.

I guess it is a design issue. Some folks here do not seem to agree 
with this, but I think this is how a computer algebra system should 
work. So, may be we should drop this subject and leave it at that. 
We agree to diagree.

regards,
Steve

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