SageMath is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more.
SageMath vs Mathematica opinions
Sage supports symbolic maths through Maxima
It can calculate many things symbolically and combines many other software packages.
Sage needs programming language skills, it doesn't support well symbolic math.
Its free and sounds capable
Octave is a computer program for performing numerical computations which is mostly compatible with MATLAB. It is part of the GNU Project. It is free software under the terms of the GNU General Public License.
GNU Octave vs Mathematica opinions
Octave needs programming language skills, it doesn't support well symbolic math.
The Jupyter Notebook is a web application that allows you to create and share documents that contain live code, equations, visualizations and explanatory text. Uses include: data cleaning and transformation, numerical simulation, statistical modeling, machine learning and much...
Jupyter vs Mathematica opinions
It can run python inline and do markup work all in one system. Can be worked via network and connected to via browser (including through phone) and set up to run distributed computing systems easily. Additionally it's open source and server side runs on most major operating systems.
R is a free software environment for statistical computing and graphics. It is a GNU project which is similar to the S language and environment which was developed at Bell Laboratories (formerly AT&T, now Lucent Technologies) by John Chambers and colleagues. R can be consider.
R (programming language) vs Mathematica opinions
R is really only useful for statistics, and not even mathematical statistics.
Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors.
Maxima vs Mathematica opinions
It's free. It is also smaller, so starts up fast. Runs on Android devices as well. Lot's of functionality, including symbolic and numerical operations. Symbolic operations are not as extensive as Mathematica, but adequate for many operations. Numeric operations are considerably slower than Mathematica, and numerically oriented apps such as R, Matlab or Octave.
It does support Symbolic math, but Matlab or Octave not
I'm a theoretical physicist and I can do almost al the math I need with Mxima
Julia is a high-level, high-performance dynamic programming language for technical computing, with syntax that is familiar to users of other technical computing environments. It provides a sophisticated compiler, distributed parallel execution, numerical accuracy, and an...
Julia vs Mathematica opinions
It's an easy, powerful, really fast language which feels like a mix of Python and Ruby but runs like C. It comes with many mathematical functions, has a good stack of libraries for graphs (including Matplotlib as PyPlot) and can be used with the Jupyter Notebook. Still not at version 1.0, but already a great tool!
Scilab is a scientific software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. Scilab is an open source software and includes hundreds of mathematical functions with the possibility to add...This app doesn't have any features at the moment.
Spyder (previously known as Pydee) is a free open-source Python development environment providing MATLAB-like features in a simple and light-weighted software, available for Windows XP/Vista/7, GNU/Linux and Mac OS X.
Spyder vs Mathematica opinions
It is a development environment for Python, not a symbolic math language/software.
wxMaxima is a document based interface for the computer algebra system Maxima. wxMaxima uses wxWidgets and runs natively on Windows, X11 and Mac OS X. wxMaxima provides menus and dialogs for many common maxima commands, autocompletion, inline plots and simple animations.
SymPy is a Python library for symbolic computation. The stated goals of the library are to become a full-featured computer algebra system and to keep a simple code base to promote extensibility and comprehensibility.
SymPy vs Mathematica opinions