15 Best Free and Open Source Linux Computer Algebra Systems

A computer algebra system (CAS) is mathematical software that can manipulate mathematical formulae in a way similar to the traditional manual computations of mathematicians and scientists. This type of system supports a wide range of mathematics including linear algebra, calculus, and algebraic and ordinary differential equations.

A CAS offers a rigorous environment for defining and working with structures such as groups, rings, fields, modules, algebras, schemes, curves, graphs, designs, codes and many others.

They have been extensively used in higher education.

The main features of a CAS include:

  • Numerical Computations: The software can determine numerical approximations of solutions, derivatives, integrals, differential equations, etc. Solve, manipulate, and plot functions without needing to generate numeric data. Often problems that cannot be solved explicitly can be solved numerically, and often only a numerical answer is sufficient.
  • Data Analysis: Having data is not sufficient; we need to extract useful information from it. There are many algorithms designed for data analysis, most of which involve too much work to be done by manual computations. CAS’s put these algorithms in one place, and offer an environment where the algorithms are easy to implement.
  • Data Visualization: CAS’s can graph 2D and 3D functions in a variety of ways. They are also designed to graph vector fields and solutions to differential equations.
  • Symbolic Computations: Most of the CAS’s can perform symbolic manipulation of expressions: reducing, expanding, simplifying, derivatives, antiderivatives, etc. Unlike numerical computations, which can exhibit floating-point errors, symbolic computations are determined exactly. They can therefore provide the exact answer to an equation (as opposed to a decimal approximation), and they can express results in terms of a wide variety of previously defined functions.

A CAS automates tedious and sometimes difficult algebraic manipulation tasks. The principal difference between a CAS and a traditional calculator is the ability to deal with equations symbolically rather than numerically.

The chart below offers our rating for each software. Some of the software is very specialized, designed to fill a particular niche. This makes comparisons difficult. All of the software is free and open source goodness.

Ratings chart for the best free and open source computer algebra systems

Let’s explore the 15 algebra systems at hand. Click the links in the table below to learn more about each program.

Computer Algebra Systems
ScilabNumerical computational package
MaximaSystem for the manipulation of symbolic and numerical expressions
OctavePowerful programming language with built-in plotting and visualization tools
SageMathOpen source alternative to Magma, Maple, Mathematica and Matlab
SymPyPython library for symbolic mathematics
SINGULARComputer Algebra System for polynomial computations
Macaulay2Software system for research in algebraic geometry
CadabraSymbolic computer algebra system for field theory problems
PARI/GPWidely used algebra system designed for fast computations in number theory
GAPSystem for computational discrete algebra
FriCASFork of Axiom
CoCoASystem for doing computations in commutative algebra
MathicsGeneral-purpose CAS with Mathematica-compatible syntax and functions
FORMSymbolic Manipulation System
AxiomGeneral purpose Computer Algebra system

This article has been revamped in line with our recent announcement.

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hc speel
hc speel
5 years ago

Can you please share what tool produces the top image, with all the bullets and their relations?

4 years ago

Giac/xcas and qcas (qt front-end) should added to this list

4 years ago

Execellent one: Reduce

4 months ago

What program has symbolic solver like in TI-89 here you can just write solve(a=b*c,c) to solve c which gives c=a/b

4 months ago
Reply to  Symbolguy

Oh looks like Qalculate can do it just like TI-89