On the other hand, not making this assumption about symbols (and expressions
containing unevaluated symbols) would mean that the simplifier is not
allowed to simplify 0*x, for instance, seriously reducing its practical
utility. So in a sense, you have to draw the line somewhere, sacrificing
mathematical purity for the sake of constructing a practical CAS.
But, I think that this does not justify allowing the simplifier to produce
results that are known to be incorrect when indeterminate symbols are
explicitly present in an expression. I see a difference between simplifying
0*x to 0 (by quietly assuming that x is finite and determinate) vs.
simplifying 0*inf to 0.
Hmmm, perhaps one possibility is to consider introducing a dreaded global
flag, or perhaps better, a property that would allow us to tell the
simplifier to treat symbols (or a specific symbol) as possibly
indeterminate/infinite? Sorry, just thinking aloud here, about a wheel that
may have been invented elsewhere already.
Viktor
-----Original Message-----
From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu]
On Behalf Of Richard Fateman
Sent: Monday, September 13, 2010 9:53 AM
To: maxima at math.utexas.edu
Subject: Re: [Maxima] Extended real arithmetic (was Re: inf - inf = 0 ??)
On 9/13/2010 5:52 AM, Stavros Macrakis wrote:
> Exactly.
>
> On 2010-09-13, Viktor T. Toth<vttoth at vttoth.com> wrote:
>> Correct me if I am mistaken but I think a basic assumption behind
>> simplification is that any unevaluated symbol represents a finite,
>> determinate quantity.
You could make this assumption, and perhaps the simplifier implicitly
makes this assumption, but
it is an incorrect assumption. For example, assume you allow the
expression x*tan(x).
Now let x=pi/2. You have finite * (+- infinity).
If you make the assumption that any expression (not just symbols) cannot
be indeterminate or infinite,
then the simplifier probably "works".
That is, however, like curing world hunger by assuming everyone has
enough food to eat.
RJF
>> Hence, you're allowed to simplify 0*x as 0, even
>> though 0*inf is definitely not 0, because the value of x, whatever it
might
>> be (real number, complex number, vector, matrix, operator, quaternion,
>> etc.), is not infinite or indeterminate.
>>
>>
>> Viktor
>>
>>
>>
...
_______________________________________________
Maxima mailing list
Maxima at math.utexas.edu
http://www.math.utexas.edu/mailman/listinfo/maxima