[Maxima] laplace transform
eric.reyssat at math.unicaen.fr
eric.reyssat at math.unicaen.fr
Thu Feb 26 15:21:43 CST 2009
Andrej,
thank you for the "rectform(u), logexpand=all" command.
Dieter,
for sin(t)/t^2, the integral is really divergent, so returning a noun form
or an error message (divergent integral) seems ok.
Eric
> Am Donnerstag, den 26.02.2009, 18:19 +0100 schrieb Andrej Vodopivec:
>> On Thu, Feb 26, 2009 at 6:13 PM, Raymond Toy
>> <raymond.toy at stericsson.com> wrote:
>> > eric.reyssat at math.unicaen.fr wrote:
>> >> Yes, the answer given by specint (all in lowercase) is true, thank
>> you.
>> >>
>> >> But
>> >>
>> >> 1/ I still don't understand the error message given by laplace
>> >
>> > Sounds like a bug in laplace
>> >>
>> >> 2/ when laplace is unable to compute the answer, it could (should ?)
>> call
>> >> specint
>> >
>> > I think this has been discussed before. But AFAIK, no one has
>> actually
>> > done anything about it.
>>
>> Laplace calls defint with wrong arguments:
>>
>> (%i4) trace(defint)$
>> (%i5) laplace(sin(2*t)/t,t,s);
>> 1 Enter defint[2/(s10^2+4),s11,s,inf]
>> Integral is divergent
>> -- an error. To debug this try debugmode(true);
>>
>> I guess s11 should be s10
>
> I had a look into the code. The error is due to a change of the code of
> the function createname with the following revision:
>
> Mon Apr 30 16:35:28 2007 UTC (21 months, 4 weeks ago) by are_muc
> Branch: MAIN
> Changes since 1.7: +3 -3 lines
> Diff to previous 1.7
> replaced compilcated implode/explode with gentemp and format.
>
>
> This is the old code:
>
> (implode (nconc (explodec head) (explodec tail)))
>
> And this the new code which does not work:
>
> (gentemp (format nil "~S~S" head tail)))
>
> If we insert the old code we get
>
> (%i6) laplace (sin(t)/t,t,s);
> (%o6) %pi/2-atan(s)
>
> That is equivalent to atan(2/s) and correct. So laplace is able to find
> a solution for sin(t)/t.
>
> The reason is that gentemp does more than the algorithm expected.
> gentemp produce for every call a new symbol. But the function createname
> should return the same symbol when the arguments head and tail have not
> changed.
>
> But there are more problems. sin(t)/t works, but with sin(t)/t^2 we get
> a endlessly loop. For sin(t)/t^2 specint fails too, but returns a noun
> form.
>
> Perhaps this is a very old problem. Perhaps there are more changes of
> the code which have changed the algorithm.
>
> Dieter Kaiser
>
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