This might be a question people already asked or is obvious to experts, or is not appropriate for this forum, if so, I apologize. I am trying to calculate things like $z/(e^z-1)$, or find the inverse of $x=z+ 2z+5z^2+\cdots$, expand as power series. What is the best (or favorite) software package you use to do stuff like this?
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- 7$\begingroup$ Sage can do it: sagemath.org. (Search hint: finding the inverse function of a power series is called "Lagrange inversion", or sometimes "reversion".) $\endgroup$Tom Leinster– Tom Leinster2012-11-03 20:04:10 +00:00Commented Nov 3, 2012 at 20:04
- 1$\begingroup$ Pari/GP's serreverse(). $\endgroup$Pasha Zusmanovich– Pasha Zusmanovich2012-11-06 16:47:48 +00:00Commented Nov 6, 2012 at 16:47
- 1$\begingroup$ In flint library (flintlib.org) there's a bunch of functions for computing inverse series in different fields. For example, fmpz_poly_inv_series $\endgroup$Anton– Anton2013-04-03 02:16:47 +00:00Commented Apr 3, 2013 at 2:16
- 1$\begingroup$ Assuming you mean the compositional inverse, fmpz_poly_revert_series. flint is a good choice if you want say 10000 terms. $\endgroup$Fredrik Johansson– Fredrik Johansson2013-04-03 22:57:45 +00:00Commented Apr 3, 2013 at 22:57
- 2$\begingroup$ You don't say what kind of answer you're looking for. Would you be happy with a list of numerical values for a finite part of the list of coefficients or are you looking for something in a symbolic form where possible? $\endgroup$Dan Piponi– Dan Piponi2013-05-25 14:54:09 +00:00Commented May 25, 2013 at 14:54
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3 Answers
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Okay, I've gathered the answers from the comments in alphabetical order.
flint has the fmpz_poly_revert_series command (A web search revealed a reference pdf, but no web page). Some benchmarks seem to indicate that flint is unusually fast.
Mathematica has the InverseSeries command.
Pari/GP has the serreverse function.
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0 For the TI-nspire CAS calculator: http://www.ticalc.org/archives/files/fileinfo/424/42499.html.
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Maple produces it. See http://www.maplesoft.com/support/help/Maple/view.aspx?path=powseries , especially the command http://www.maplesoft.com/support/help/Maple/view.aspx?path=powseries%2freversion for info.
