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Formal power series inversion fails on power law type functions #26039

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@stefanhiemer

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Happy new year to everyone,

I inverted a power law type equation via the Lagrange inversion theorem analytically
analytical_calculation.pdf
and tried to implement the inversion (for checking) and evaluation with the Formal Power Series module. Unfortunately it does not convert equation 3 into a formal power series and inversion then obviously does not work.
sympy_issue_fps.txt
I thought, maybe it is some problem of the specific function and then tried the same other power law functions e. g. (1+x)**3.5 , but the result was the same. My impression is that the FPS module does not work on power laws, but I have found no hint in the module regarding that. I also found the behaviour quite weired to throw the analytical function just back at me without any warning, error, etc. My questions now as an inexperienced sympy user: Have I done an obvious mistake here or is this the intended sympy behaviour? If this is the case is there a better way to evaluate the inverted function (equation 0.7 in the pdf)? If fps fails to derive a formal power series, I'd find it more intuitive to raise an error or supply a success flag to make it immediately apparent if something does not work or the user did something wrong.

Thanks.

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