Dear Vladimir, Yes, I see. In that context z and conjugate(z) are treated as independent variables. But then, concerning the second problem you mentioned before, should be it enough to define z.conjugate().diff(z) = 0 ? Best, Luis ----------------- On 11/06/2013 05:55 AM, Vladimir V. Kisil wrote:
Dear Luis,
On Wed, 06 Nov 2013 05:26:58 -0800, Luis Rivera<luis.rivera@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