Mathematica is described as 'Definitive technical computing system spanning machine learning and neural networks, data science, visualizations and much more' and is a very popular numerical computation software in the education & reference category. There are more than 50 alternatives to Mathematica for a variety of platforms, including Windows, Linux, Mac, Web-based and Android apps. The best Mathematica alternative is SageMath, which is both free and Open Source. Other great apps like Mathematica are R (programming language), GNU Octave, Jupyter and Maxima.
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.
It can calculate many things symbolically and combines many other software packages.
Its free and sounds capable
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 is really only useful for statistics, and not even mathematical statistics.
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...
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.
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.
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.
I'm a theoretical physicist and I can do almost al the math I need with Mxima
It does support Symbolic math, but Matlab or Octave not
High-level environment supporting numerical computation, visualization, matrix operations, algorithm development, custom interfaces, integration with external languages, symbolic and model-based simulation, and specialized toolboxes for fields like engineering.
Both are comprehensive mathematics solutions, and have very similar features, as well as even both being commercial.
Mathematica is mainly a CAS (symbolic maths), but MATLAB is more for numeric analysis
MATLAB is mainly for numerics
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...
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!
Combines advanced editing, analysis, debugging, and profiling functionalities with data exploration, execution, and visualization capabilities. Expandable using its powerful plugin system and API, providing flexibility for custom integrations.
It is a development environment for Python, not a symbolic math language/software.
Scilab is free and open source software for numerical computation providing a powerful computing environment for engineering and scientific applications. Scilab includes hundreds of mathematical functions.
Maple is a general-purpose commercial computer algebra system. Users can enter mathematics in traditional mathematical notation. Custom user interfaces can also be created. There is support for numeric computations, to arbitrary precision, as well as symbolic computation and...
Online math solver, equation editor and database, graphing calculator and science/engineering problem helper.
Wolfram Language is a symbolic language, deliberately designed with the breadth and unity needed to develop powerful programs quickly. By integrating high-level forms—like Image, GeoPolygon or Molecule—along with advanced superfunctions—such as ImageIdentify or...
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Sage supports symbolic maths through Maxima