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Theano has an interesting description of the lay of the land as they see it, where they position themselves as a hybrid of numpy/MATLAB type numerical-computational tools and sympy/Mathematica-style CAS tools: http://deeplearning.net/software/theano/introduction.html#wh...


From the link, they mention this:

The closest Python package to Theano is sympy. Theano focuses more on tensor expressions than Sympy, and has more machinery for compilation. Sympy has more sophisticated algebra rules and can handle a wider variety of mathematical operations (such as series, limits, and integrals).




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