Correct me if I am mistaken but I think a basic assumption behind
simplification is that any unevaluated symbol represents a finite,
determinate quantity. 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
-----Original Message-----
From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu]
On Behalf Of Stavros Macrakis
Sent: Sunday, September 12, 2010 6:52 PM
To: Richard Hennessy; maxima at math.utexas.edu
Subject: Re: [Maxima] Extended real arithmetic (was Re: inf - inf = 0 ??)
As Fateman has pointed out on this discussion before, Maxima often
assumes the general case, even when there are special cases which are
incorrect. For example, Maxima simplifies x/x => 1 without the caveat
that x # 0.
As for 'limit', it tries to be careful about cases like this, and it
does assume (sensibly I think) that independent parameters are finite.
You make it sound very simplistic. Certainly it has bugs and
limitations, but they're (mostly!) not quite as trivial as you're
implying.
-s
On 2010-09-12, Richard Hennessy <rich.hennessy at verizon.net> wrote:
> I get using real number mathematics that 0*x = 0 for all x. I get from
> extended real arithmetic that und*0 # 0 or inf*0
> # 0. So I can prove that the answer is both zero and nonzero at the same
> time depending on the approach. So extended
> real arithmetic is not self consistent.
>
> FWIW.
>
> --------------------------------------------------
> From: "Richard Hennessy" <rich.hennessy at verizon.net>
> Sent: Saturday, September 11, 2010 11:16 PM
> To: "Richard Fateman" <fateman at cs.berkeley.edu>
> Cc: "Maxima List" <maxima at math.utexas.edu>
> Subject: Re: [Maxima] Extended real arithmetic (was Re: inf - inf = 0 ??)
>
>> Rich,
>>
>> I have been reading your paper, there is more to this than I thought. I
>> have not finished reading the paper yet, it
>> is a lot to digest. I would have been satisfied with not allowing
>> arithmetic on inf, minf, und or ind. I suppose that
>> is not good enough.
>>
>> Rich
>>
>>
>> --------------------------------------------------
>> From: "Richard Fateman" <fateman at cs.berkeley.edu>
>> Sent: Saturday, September 11, 2010 10:07 AM
>> To: "Leo Butler" <l.butler at ed.ac.uk>
>> Cc: <maxima at math.utexas.edu>; "Andreas Eder" <andreas_eder at gmx.net>
>> Subject: Re: [Maxima] Extended real arithmetic (was Re: inf - inf = 0 ??)
>>
>>> At the risk of repeating myself, I can refer you to a paper that
>>> suggests this fits within
>>> a framework of interval arithmetic.
>>> e.g. interval(-inf, inf) means --- there is a real number but we
>>> don't know anything about its value.
>>> this is perhaps indefinite (IND)
>>>
>>> an empty interval (we can choose one to be canonical) that has nothing
>>> in its interior means
>>> --- there is no number that this could be, which is perhaps undefined
>>> (UND)
>>>
>>> http://www.cs.berkeley.edu/~fateman/papers/interval.pdf
>>>
>>> There are what I consider misuses of intervals regarding limits that are
>>> present in Mathematica and Maple,
>>> eg..
>>>
>>> limit(sin(x),x,inf) ?=? interval(-1,1).
>>>
>>> This leads to either erroneous answers to limit problems and things
>>> related to limits, or to a substantially
>>> overloaded notion of "equality". Like any interval that contains 0 is
>>> equal to 0.
>>>
>>> Whether this can be put together in a computer algebra system to be more
>>> consistent is possible, but
>>> consistency in general is tough, and certainly not achieved now.
>>> There are many examples in which, for some procedure f,
>>>
>>> f(a) is different from subst(a,x, simplify(f(x)) )
>>> where x is some arbitrary symbol and a is some particular value.
>>>
>>>
>>> RJF
>>>
>>>
>>>
>>> _______________________________________________
>>> Maxima mailing list
>>> Maxima at math.utexas.edu
>>> http://www.math.utexas.edu/mailman/listinfo/maxima
>>>
>>
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