Programs like Mathematica or Wolfram Alpha are able to calculate very complex limits with apparent ease. I'm trying to make my own program to compute limits. I've searched all over, but haven't found anything about how they do it. What algorithm can I use to compute limits?

  • $\begingroup$ Think simple: The ε-δ definition of the limit $\endgroup$ – bolzano Jun 14 '16 at 16:49
  • $\begingroup$ I presume you mean performing algebraic manipulations rather than generating numerical approximations, right? That cannot be a simple task and will probably require lots of programming and development. $\endgroup$ – String Jun 14 '16 at 17:54

Unfortunately, there is no rigourous answer. They "cheat" by simply doing some basic reduction, and then looking up in a large database of general forms.

A generalized algorithm is undecidable, due to being equivalent to the zero-recognition problem.

  • $\begingroup$ For exp–log functions, zero recognition is at the very least semi-decidable. Moreover, given that you can decide zero recognition, determining the limit of an exp–log function is comparatively easy – cf. the sources I gave in my question here: mathematica.stackexchange.com/questions/134802/… $\endgroup$ – Manuel Eberl Dec 5 '18 at 16:32
  • $\begingroup$ Admittedly, if you have an expression involving rounding or sin etc., things become much more difficult and I have no idea what Mathematica, Maple, etc. do there – probably some heuristics. But the exp–log case is already very powerful, and it can be treated systematically. $\endgroup$ – Manuel Eberl Dec 5 '18 at 16:33

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