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I want to use MapleSoft for small project (few days) and want don't to buy it. Since, it doesn't provide any free trial period, I am looking for some alternative. I am planning to use Maple to solve some sequence and series that it seems solves seamlessly.

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    https://en.wikipedia.org/wiki/List_of_computer_algebra_systems, for example: SAGE, Maximia and others...2017-02-03

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  • Mathematica has a free trial that you could take a look at (and in my opinion is the most powerful CAS)
  • Sage is also pretty good, but may be more difficult to get work on all platforms
  • Personally, I think the easiest one to use for quick stuff is SymPy; it has virtually no learning curve if you already know Python.

Also check out this question.