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Is there any information available about the implementation of the Limit command? In particular, I am interested in how Mathematica computes limits of real functions involving basic arithmetic, Log, and Exp.

The approach that I know is to compute some kind of asymptotic expansion (using multiseries or nested expansions), as detailed e.g. in Dominik Gruntz's PhD thesis, the book ‘Symbolic Asymptotics’ by John Shackell, or various papers by Salvy/Richardson/Shackell/van der Hoeven.

My guess is that Mathematica uses something like this for that class of functions, but I wonder whether there are any more details available.

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    $\begingroup$ reference.wolfram.com/language/tutorial/… says only "Limits are found from series and using other methods." $\endgroup$ – Mr.Wizard Jan 5 '17 at 13:32
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    $\begingroup$ One of those other methods is an implementation of Gruntz's algorithm. This was done by Adam Strzebonski around 2008. $\endgroup$ – Daniel Lichtblau Jan 5 '17 at 16:29
  • $\begingroup$ Very interesting! Do you have a citable source for that? I.e. that Mathematica actually uses this? $\endgroup$ – Manuel Eberl Jan 5 '17 at 21:30
  • $\begingroup$ Maybe you can poke around using Trace? But probably the function's implementation is all-internal... $\endgroup$ – masterxilo Jan 7 '17 at 21:09
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    $\begingroup$ @ManuelEberl According to his LinkedIn profile, Daniel Lichtblau has worked for Wolfram for 25 years, and is currently with the Kernel Research Group, focusing on the "development and implementation of algorithms for mathematical computation." So he himself probably qualifies as the citable source you seek. $\endgroup$ – theorist Jan 8 '17 at 8:50

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