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Comment by rwmj | Hacker News Reader

Can anyone comment on how Octave compares specifically to Mathematica, in terms of features and ease of use?

Mathematica does so much more than Octave that it's not even remotely comparable. In terms of features, Octave inherited Matlab's matrix-centric mindset by having the \ operator solve linear systems whereas in Mathematica it's slightly longer (LinearSolve[m,b] or just Inverse[m].b for non-numeric ones). But Mathematica offers symbolic computing as well, and you can very easily go from "solving this equation with machine-precision numbers" to "solve this equation with arbitrary precision algebraic numbers" to "solving this equation with an unknown parameter with conditions" in a seamless way. There are whole areas of mathematics, pure and applied, that can be done in Mathematica but not in Octave. In terms of ease of use, Mathematica also excels here; both data and code share a uniform notation that is very similar to lisp, and functional programming ideas carry over very seamlessly.

I'd say if you are someone who's even remotely mathematically minded, learning to use Mathematica is an extremely useful experience. As an example that recently happened to me, while doing front end work I needed to construct certain geometric figures as an SVG polygon; I used Mathematica's built in graphics primitives combined with its plotting capabilities to find the polygon in no time. Even though the end result is a piece of JavaScript, Mathematica gives me a way to prototype the whole thing in an environment that's "batteries included" and well-polished.

Both Octave and MATLAB have had a symbolic toolbox for ages, and can export to many vector graphics formats, from .ps to .svg.

Mathematica is way more targeted to the "general public" though. It's fairly obvious that MATLAB started its life as fronted to FORTRAN.

> It's fairly obvious that MATLAB started its life as fronted to FORTRAN.

I second that and there are quite a number of scientists which use MATLAB and FORTRAN side by side.

I would extend this statement: MATLAB feels like a REPL to FORTRAN while Mathematica like a REPL/library to/for LISP.

>Mathematica is way more targeted to the "general public" though.

Actually, it's way more targeted to mathematicians. The level of symbolic computation it can do is way ahead of any symbolic toolbox you'll find. When I was in grad school, I used NumPy and my group mate used Mathematica. One day I was looking up identities in Gradshteyn and Ryzhik (a bible for identities), and he asked why I bother as Mathematica had it all. He challenged me to find any identity that Mathematica couldn't handle. I thought this would be easy as G&R has more stuff than any other identity handbook out there, but I lost the challenge.

Also, Mathematica is free if you're running Raspbian on a Raspberry Pi (or emulating one with QEMU).

So is a lot of commercial software targeted at getting youngsters to take a peek. Dyalog APL also has a free version for Raspbian

Mathematica is useful and beautiful. But solving a linear system by the antislash operator is a major feature of octave and a piece of notation that I cannot live without.

Octave and Matlab focus on numerical computing, while Mathematica focusses on symbolic computing. The first means working with arrays (and higher dimensional arrays) of (mostly) floating point numbers, while the later means working with abstract syntax trees of mathematical expressions.

Specifically, the one "equivalent" to Mathematica is Maxima [0], I remember using it for symbolic computation on my linux machine. Especialy coupled with Wx GUI [1].

[0]: http://maxima.sourceforge.net/ [1]: https://wxmaxima-developers.github.io/wxmaxima/

Both Maxima and GNU Octave are pretty old (mature?) projects with probably outdated-looking (feeling) GUIs. Just to mention some younger and more "fresh" projects: In the SciPy ecosystem, there is SymPy https://www.sympy.org which has the obvious advantage of being Python, gaining from a big (also scientific) ecosystem, such as numpy, pandas or the JupyterLab.

A large OSS player is nowadays also SageMath https://www.sagemath.org/ which is a kind-of-meta CAS which can actually proxy evaluations to Mathematica, Maxima, Octave and many others, in a more or less uniform pythonic notation.

Probably needless to say, when it comes to evaluation power (for instance for integral solving), Mathematica is unrivalled from OSS projects. However, in certain fields (such as number theory for SageMath or the overall web notebook infrastructure by the IPython and Jupyter projects), the concurrency is catching up or may already have overtaken Wolfram's products.

Wow, sympy looks amazing. Seems to solve exactly the kind of things I'd use Mathematica/Wolfram for, especially back in my university days. Will play around with it when I have some time to repeat my math knowledge, been meaning to refresh some things for a while now.

SageMath purports to also be an alternative to Mathematica: https://www.sagemath.org/

I've not used Mathematica, so my views would be as useless here. Octave can be greatly compared to MATLAB. It actually tries its best to be as compatible with MATLAB as possible.

So, one can say it is as closed to Mathematica as MATLAB is.

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