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I have tried Mathematica for small duration and in general was wowed by it. For free CAS I would recommend to give Axiom or FriCAS(more actively developed) a run. http://fricas.sourceforge.net/ https://en.wikipedia.org/wiki/Axiom_(computer_algebra_system...
Mathematica is worth learning and using since it's so far ahead of the open source alternatives (e.g. Python/Jupyter and associated libraries ) in usability/interactivity/rapid development that it comes across like future-tech. Unfortunately it's also the single tool most hampered by its licensing and silo-like ecosystem.
I'm an R and sometimes Julia user, although not Python. Can you offer some examples of how Mathematica surpasses open source alternatives in those areas you've mentioned?
Mathematica is an amazing tool, but it has one huge downside: reproducibility. It is a closed monolith, and - especially when you start to use advanced features - you derive results from it that can't be independently verified because of the closed source nature of the monolith.
I have tried Mathematica for small duration and in general was wowed by it. For free CAS I would recommend to give Axiom or FriCAS(more actively developed) a run. http://fricas.sourceforge.net/ https://en.wikipedia.org/wiki/Axiom_(computer_algebra_system...
How good is Axiom as compared to Mathematica in general? I am familiar with Mathematica, am asking to get zeroth order idea for Axiom before I would try it out myself. Thanks.
Overall it is not that polished UI wise. I think it is pretty good for algebra and symbolic computation.
Let me quote from the book/guide of FriCas:
" FriCAS provides state-of-the-art algebraic machinery to handle your most advanced symbolic problems. For example, FriCAS’s integrator gives you the answer when an answer exists. If one does not, it provides a proof that there is no answer. Integration is just one of a multitude of symbolic operations that FriCAS provides. "
You can find out more by reading the book which is available here:
If a software is used to create data that is okay like editing text files in microsoft windows. But computational software such as Wolfram being closed source bothers me a lot. There is no way to verify the science you do is correct.
Two things I miss when working with Mathematica: refactor-rename variables and a usable object-oriented programming support.
Refactor-rename is available via Eclipse-based IDE; however math typesetting is not available there (it makes a difference for large equations/expressions).
There are a lot of community-developed approaches to OOP. I tried a number of these, sticking with a particular approach, but it also leave a lot to be desired. OOP is useful in that it ties together data and functions which act on the data. Inheritance/composition are useful if you compute properties of similar objects.
I have tried Mathematica for small duration and in general was wowed by it. For free CAS I would recommend to give Axiom or FriCAS(more actively developed) a run. http://fricas.sourceforge.net/ https://en.wikipedia.org/wiki/Axiom_(computer_algebra_system...
Sage has a notebook interface, is built on Python, and incorporates many free software math packages, like Maxima, into one system.
Earlier quoted context omitted.
How good is Axiom as compared to Mathematica in general? I am familiar with Mathematica, am asking to get zeroth order idea for Axiom before I would try it out myself. Thanks.
I think Mathematica is HUGE. Axiom/FriCAS does not have every thing that Mathematica have(specially statistics). Overall it is not that polished UI wise. I think it is pretty good for algebra and symbolic computation. Let me quote from the book/guide of FriCas: " FriCAS provides state-of-the-art algebraic machinery to handle your most advanced symbolic problems. For example, FriCAS’s integrator gives you the answer w…