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

[Vladimir V. Kisil]

	Dear Luis,

>>>>> On Wed, 06 Nov 2013 05:26:58 -0800, Luis Rivera <luis.rivera at laposte.net> said:

    LR> Hi Richard, Vladilmir, f(z) = conjugate(z) is non-holomorphic
    LR> (on the whole C-plane) and so, its derivative ill-defined.
    LR> Don't you think so ?

    If you mean "differentiable with respect to the complex variable z",
  then this indeed is related (but not identical) to the holomorphic
  property and f(z)=conjugate(z) is not holomorphic.

  However, GiNaC diff() seems to be like a partial derivative, then the
  common definition is

  partial_z=1/2(partial_x-I*partial_y)
  partial_conjugate(z)=1/2(partial_x+I*partial_y)

  make it well-defined for any real-differentiable function of z=(x,y).

  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