[GiNaC-devel] Derivative of conjugated is conjugated of derivative.

[Luis Rivera]

Hi Richard, Vladilmir,

f(z) = conjugate(z) is non-holomorphic
(on the whole C-plane) and so, its
derivative ill-defined.

Don't you think so ?

Luis

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On 11/06/2013 03:52 AM, Vladimir V. Kisil wrote:
> 	Dear Richard,
>>>>>> On Wed, 06 Nov 2013 00:36:01 +0100, "Richard B. Kreckel"<kreckel at ginac.de>  said:
>      RK>  Still, I'm not convinced that the general transformation
>      RK>  conjugate(f)'
>      ->  conjugate(f') is generally correct. Is it correct even on branch
>      RK>  cuts? If you have a prove, please try writing it in your patch
>      RK>  so this will be clear to people reading this section later on.
>
>      Thanks, for pointing this out. Indeed, U'-I*V' is the value for both
>    conjugate(U+I*V)' and conjugate( (U+I*V)') iff we differentiate with
>    respect to a *real* variable. So, this check shall be added to the
>    patch.
>
>    For a complex variable z the correct substitution would be:
>
>    conjugate(f).diff(z) ->  conjugate(f.diff(z.conjugate()))
>
>    But there are two problems here:
>
>    * (minor) presently GiNaC does not allow diff() for anything but
>    symbols and z.conjugate() is not a symbol. Shall we allow such
>    derivatives?
>
>    *(major) presently GiNaC for
>    	e=z.conjugate();
> 	cout<<  e.diff(z)<<  endl;
>    returns D[0](conjugate)(z) and the correct answer IMHO is 0. Shall
>    this be amended?
>
>    Best wishes,
>    Vladimir