Question: Symbolic differentiation complex conjugates

I am looking at some asymptotic expansions of a PDE and need to do some differentiating with complex conjugates.  Specifically, I have a number of functions that are functions of both z and conjugate(z), they may look something like:


S -> (z,conjugate(z),xi)

I would like to take the conjugate(z) derivative,

S[conjugate(z)]  = diff(S(z,conjugate(z),xi),conjugate(z)),

but I get:

D1S(z,conjugate(z),xi) + D2S(z,conjugate(z),xi)(-\frac{conjugate(z)}{z} - \frac{abs(1,z)}{signum(z)}

How do I get maple to recognize z and conjugate(z) are complex while still getting symbolic derivatives.


Also, how can I check compatibility conditions?  Say I have two expressions,

S[xi] := phi(z,conjugate(z),xi,S[z],S[conjugate(z)]),

u := S[z]*S[conjugate(z)]


How can I find the xi derivative of u, u[xi], via the first expression?




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