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

[Vladimir V. Kisil]

	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
-- 
Vladimir V. Kisil     email: kisilv at maths.leeds.ac.uk
                        www: http://www.maths.leeds.ac.uk/~kisilv/
Book: Geometry of Mobius Transformations
http://www.worldscientific.com/worldscibooks/10.1142/p835