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I want to compute the laplacian of some complicate function, for example $|f''(z) + f'(z)\frac{1}{1-|f|^2}|\frac{1-|z|^2}{1-|f|^2}$ assuming $f$ is smooth and then evaluate it at $0$. I wonder whether there is some computer software that can help me with this.

We know that laplacian $\Delta$ is just multiples of $\partial_{\bar z z}$, then one approach would just be that denote the conjugate of $f(x)$ by $g(y)$, and then ask wolfram alpha to compute $\partial_{y x}$, this works out fine if we only have some simple functions, when the function becomes a little bit more complex, wolfram alpha will not give you any output.

One problem with matlab is that you have to specify the function.

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I would consider looking at MatLab. I know they have a free trial that you could use to try it out. I have never tried though so I'm sorry if this doesn't help.

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  • $\begingroup$ can matlab do symbolic differentiation? I cannot find anything relevant to it online. $\endgroup$ – Keith Jul 19 '17 at 19:59
  • $\begingroup$ Does this help? I'm not very familiar with the software so I would recommend searching the documentation on their site. $\endgroup$ – B. Standage Jul 19 '17 at 20:02

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