On 5/23/2012 1:04 AM, Soegtrop, Michael wrote:
> I agree. I wouldn't expect that 0*inf is 0 or inf-inf is 0.
> Can someone explain what is the rationale behind this?
Yes. If you know nothing about inf, and treat it like an indeterminate
(x,y,z) then 0*inf=0 just as 0*x=0.
You can add a few pieces of information so that it can be used by limit
as part of the input and output
of that program, and maybe a few others like integrate and sum. But not
get it all right, because
that is hard; maybe impossible unless ... see below...
> Is there an option to change this behaviour?
Rewriting a lot of code, removing "optimizations", creating a
satisfactory model of the extended
field of complex numbers (including real signed and complex infinity and
undefined).
>
> Best regards,
>
> Michael
>
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Evgeniy Maevskiy
> Sent: Wednesday, May 23, 2012 8:31 AM
> To: maxima at math.utexas.edu
> Subject: Re: [Maxima] erf(inf)
>
> Not only this. We have also
>
> limit(1/zeroa-1/zeroa) => 0
>
> I.e. zeroa is the certain infinitesimal while usually in mathematics
> o(1) is equivalence class of infinitesimals.
>
> I think that erf(inf)=1 and atan(inf)=%pi/2, but 0*inf is 0*inf and not 0. Similarly, inf-inf is inf-inf, not 0.
>
> Another question whether we should assume that inf-inf=inf+minf. I think that is(inf-inf=inf+minf)=>false, but is(equal(inf-inf,inf+minf))=>true.
>
> I'm sorry that interfered.
>
>
> 23.05.2012 7:46, Raymond Toy ?????:
>> As mentioned a few days ago, maxima automatically simplifies erf(inf)
>> to 1. And also atan(inf) to %pi/2. This seems intentional, but can
>> lead to interesting things like
>>
>> (atan(inf)-%pi/2)*inf => 0
>> but
>> limit(atan(x)-%pi/2)*x,x,inf) => -1
>>
>> as Stavros mentioned.
>>
>> Therefore, I think we should change this behavior so that erf(inf) is
>> erf(inf) and not 1.
>>
>> But since this seems intentional, I'm soliciting opinions on this.
>> This also affects erfc, erfi, gamma_incomplete, fresnel_s and fresnel_c.
>> There might be others as well.
>>
>> Ray
> _______________________________________________
> Maxima mailing list
> Maxima at math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima
> _______________________________________________
> Maxima mailing list
> Maxima at math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima