Which environment to choose Matlab vs Mathematica vs Maple vs python?

Question

Python

I decided for my selfish purposes to adopt some kind of software for solving mathematical problems, modeling, building other things.
But that problem arose because there is a wide choice, but I don’t know what I need:
1) Mathematica - I only know that you can do a lot of things in it, but everyone swears at the language
2) Matlab is a very strong thing for working with data (read on bourgeois forum)
3) Maple - I know a little more than nothing
4) Python - familiar but I have no idea how it can replace the first 3, although maybe I don’t know this snake
Help

Answer 1

Matlab Home - $135
Mathematica Home - $255
Maple 2015 Student Edition - $124
Python + SciPy - free
GNU Octave - free

Answer 2

Mathematica is a convenient and powerful language, a huge standard library, and a wonderful interface. Cons - the price and complexity of the initial entry. For modeling dynamic systems, there is a separate implementation of the Modelica language (SystemModeler), but only for Windows and I have not heard that anyone would use it.
Matlab - good for numerical calculations, weak in symbolic ones. For simulation, there is a Simulink package, which was highly praised by friends. The same costs money.
Python is popular and simple, lots of prebuilt packages, nice ipython interface (deflated from Mathematica). But as a weak language - generalized algorithms are hard to write in it, high efficiency is ensured only with the help of libraries in C.
Octave: a free, relatively decent clone of Matlab. I have not heard about modeling systems for him.
SciLab: A free but kinky and half-baked clone of Matlab. For that, it has a relatively decent Xcos modeling system.
R: Handy language for data processing and statistics. Huge and well organized external library.
Julia: Combines the best features of Matlab, R and python (and some of Lisp as well). But the developers have not yet announced a stable version. If stability is not critical for you, I highly recommend it.
I don't know anything about the rest.

Answer 3

I would advise you to go to professional forums and see how various tasks are solved by different means. See what suits you best.
From my purely biased point of view (I work as a developer at WRI), Mathematica will outperform most other tools, for a wide class of mathematical problems. I say this both as a programmer and as a person who was engaged in science in the past (Phd, theoretical physics, quantum field theory).
Visit our forum:
mathematica.stackexchange.com
We have a strong, professional and friendly community. Look at what tasks are solved and how, how the code looks, etc. Look also at other communities for other tools, and decide what is closer to your tasks.
And do not listen to those who talk about "stoned language" - this is a superficial and ignorant point of view. Here is what the creator of the Clojure language (one of the most modern and elegant programming languages) Rich Hickey said about Mathematica: "Every developer should buy a copy of Mathematica, because it will expand their mind".

Answer 4

I won’t tell you anything for the first 3 points, but for the 4th:
bender.astro.sunysb.edu/classes/python-science
www.astro.cornell.edu/staff/loredo/statpy
python itself is popular in this area not because it is python, but because of the existing tools that python already lies on, with all that for which it is loved and disliked

Answer 5

Each system has its pros/cons. Let's talk about Maple.
On Maple, it is convenient to do complex analytical transformations - integrals, derivatives, translations to different coordinate systems, vector fields, analytically solve diffuses, etc. Also, the results of transformations can be immediately translated into C text and inserted into your program. I use constantly in scientific work.
In terms of syntax, it is close to programming languages ​​- unlike Matkad, for example.
Matlab - there is another idea, one of the pluses - the Matlab libraries can be used, for example, in Borland C ++.
I won’t say anything about Mathematics - but friends from Moscow State University also love it for its analytics.