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Among octave, R or python with or without numpy, which has the simplist coding for solving algebraic equations?

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Well, everything depends on what is your task. I believe that easiest of them is the Python with SymPY package. Additionally it has more capabilities than Yacas (R is using it) and Octave (which does not have infinite precision arithmetic and does not offer Number Theory capabilities).

Therefore I would suggest you to use Python out of these 3. What's more - you will learn really useful programming language, that can benefit you in future. In case you are looking for something really powerful, then use the Wolfram Alpha or the best out of all CAS - Mathematica.

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