possibly related to http://trac.sagemath.org/ticket/12588 ?
Regards, CH
Am 2014-11-13 um 06:19 schrieb Ondřej Čertík:
> Hi,
>
> With Sage 6.3, I am getting:
>
> sage: abs(x).diff(x)
> x/abs(x)
> sage: abs(I*x).diff(x)
> -x/abs(I*x)
>
> But abs(I*x) == abs(x). So also abs(x).diff(x) and abs(I*x).diff(x)
> must be the same. But in the first case we get x/abs(x), and in the
> second we got -x/abs(x).
>
> In SymPy, the answer is:
>
> In [1]: abs(x).diff(x)
> Out[1]:
> d d
> re(x)⋅──(re(x)) + im(x)⋅──(im(x))
> dx dx
> ─────────────────────────────────
> │x│
>
>
> In [2]: x = Symbol("x", real=True)
>
> In [3]: abs(x).diff(x)
> Out[3]: sign(x)
>
> In [4]: abs(I*x).diff(x)
> Out[4]: sign(x)
>
> In [26]: var("x")
> Out[26]: x
>
> Which seems all correct --- in the complex case [1] we get a little
> messy expression, but a correct one. For a real case, we get the
> correct answer.
>
> In Wolfram Alpha, the answer of abs(I*x).diff(x) is x/abs(x):
>
> http://www.wolframalpha.com/input/?i=Diff%5BAbs%5Bi*x%5D%2C+x%5D
>
> Which is only correct for real "x", but at least it is correct for
> this special case.
>
> The Sage result seems wrong for any "x".
>
> Ondrej
>
--
Univ.-Prof. Dr. Clemens Heuberger Alpen-Adria-Universität Klagenfurt
Institut für Mathematik, Universitätsstraße 65-67, 9020 Klagenfurt, Austria
Tel: +43 463 2700 3121 Fax: +43 463 2700 99 3121
clemens.heuber...@aau.at http://wwwu.aau.at/cheuberg
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