Even without pwdelta pw.mac can be messy. Try converting this expression to iif() and then back again. It is a lot of
work.
(%i1) load(pw)$
(%i2) x*abs(x);
(%o2) x abs(x)
(%i3) signum2abs(simpspikes(iif2sum(pulliniif(signum2iif(abs2signum(%))))));
(%o3) x abs(x)
It works though.
Rich
--------------------------------------------------
From: "Richard Hennessy" <rich.hennessy at verizon.net>
Sent: Monday, September 13, 2010 2:16 PM
To: "Viktor T. Toth" <vttoth at vttoth.com>; "'Stavros Macrakis'" <macrakis at alum.mit.edu>; <maxima at math.utexas.edu>
Subject: Re: [Maxima] Extended real arithmetic (was Re: inf - inf = 0 ??)
> Has anyone experimented with this with in code? I think that the theory is adequately understood but to see how messy
> this might get and what can be done to keep it simple you would have to try it. In pw.mac, I did not know how messy
> diff(signum(x),x) = 2*pwdelta(x) would be until I tried it and in the end I made this feature optional. You can turn
> it off and it is turned off by default. I allow the user to turn it on if they want because you cannot get correct
> results without it in certain situations. Maybe that would be the way to go. I would like to see this in code,
> perhaps an extension to Maxima like pw.mac . . .
>
> Rich
>
>
> --------------------------------------------------
> From: "Viktor T. Toth" <vttoth at vttoth.com>
> Sent: Monday, September 13, 2010 7:46 AM
> To: "'Stavros Macrakis'" <macrakis at alum.mit.edu>; "'Richard Hennessy'" <rich.hennessy at verizon.net>;
> <maxima at math.utexas.edu>
> Subject: RE: [Maxima] Extended real arithmetic (was Re: inf - inf = 0 ??)
>
>> 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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>>
>> --
>> Sent from my mobile device
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>
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