Conformal-Maps: Code for interactive conformal mapping with SymPy

[Zoufiné Lauer-Baré]

Hello together,

 I work a as simulation engineer and studied math, inclusively phd in applied math. I teach Python for Data Science students as external lecturer.

Recently I gave a talk about conformal mappings with SymPy on th 20. Scipy:

https://twitter.com/SymPy/status/1419090293450711040?s=20

https://conference.scipy.org/proceedings/scipy2021/lauer_bare_gaertig.html

Based on that work, I joined a community project which helped me to visualize my research:

https://github.com/im-AMS/Conformal-Maps

This project permits to interactively transform circles, annuli, rectangles, squares to corresponding domains, when function of a comlpex variable are applied on them, see attachement. This project is based on SymPy, NumPy, Plotly and Jupyter Notebook.

It would great, if this project (https://github.com/im-AMS/Conformal-Maps) could be listed on the SymPy  webpage.

In my opinion, this is one of the best codes to interactively see how functions of a complex variable change geometries, also compared to Maple and Mathematica.

I am looking forward to hearing feedback from the SymPy commuity on this project.

Regards,

Zoufiné Lauer-Baré

[Aaron Meurer]

I saw your SciPy talk. It was a very nice use of SymPy.

By the way, I wonder if SymPy shouldn't have some convenience
functions somewhere for working with conformal mappings and Mobius
functions. I've noticed that dealing with complex infinity in
particular can be a little annoying. For instance, simply substituting
zoo in an expression for a mobius transformation doesn't give you the
correct value.

Aaron Meurer

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[Zoufiné Lauer-Baré]

Hello Aaron,

Thank you for the reply and the feedback on my Scipy talk.

1.) In what part of sympy could conformal mappings be implemented in sympy?

2.) I did not understand the moebius mapping problem you mentioned, is there already an issue in github on that?

3.) I think, that for the usage of conformal mappings with sympy a separation of real and imaginary parts of more complicated functions as artan(z) or artan2(z) should be supported, I may write an issue on this topic, if there is none already.

Regards!

Zoufiné

> Am 08.09.2021 um 21:02 schrieb Aaron Meurer <asme...@gmail.com>:
>
> I saw your SciPy talk. It was a very nice use of SymPy.

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