Computer algebra

Computer Algebra: Concepts and Techniques
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The project was started in the labs of the MIT in the 60s and continues to thrive still today due to its widespread popularity and notoriously powerful feature sets. The system is designed to tackle symbolic and numerical expressions including differentiation, integration, Taylor series, Laplace transforms, differential equations, systems of linear equations alongside polynomials, sets, lists, vectors, matrices, and tensors.

Computer Algebra Software

Get Maxima. SymPy is an opensource Python library for manipulating symbolic mathematics. Users can use it either as a standalone application, live on the web, or as a library inside other programs. Due to its BSD license, SymPy is arguably among the best computer algebra systems for opensource enthusiasts or mathematicians looking for free computer algebra systems. SymPy is maintained regularly, and new updates are rolled out very often, making it a suitable choice for both professional analysts and academians.

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In computational mathematics, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and. A computer algebra system (CAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual.

Get SymPy. SINGULAR is arguably among the best computer algebra systems for handling polynomial problems like commutative algebra, algebraic geometry, and singularity theory.

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It comes with the fastest algorithmic implementations for computing Groebner resp. SINGULAR also provides features such as polynomial factorization, Syzygy, and free-resolution computations, characteristic set, resultant, and many more.

Symbolic computing of mathematical expressions

Maple is one of the major Linux computer algebra systems used by corporations around the world. It is developed and marketed by Maplesoft who designed it with emphasis on symbolic and numeric computing. It also offers a high-level programming language to aid in advanced computing tasks. Maple also comes equipped with an extensive range of tools to make scientific computation effortless and accessible to a broader range of public. Get Maple.

Macaulay2 is one of the most prominent computer algebra systems for researchers dealing in algebraic geometry and commutative algebra. It is a fairly modern CAS with a plethora of built-in features that aid in the development of new solutions to traditional and futuristic mathematical research problems. It implements its own high-level programming language to tackle numeric and symbolic algebra and is released under the opensource GNU GPL license.

Get Macaulay2. It is a modern symbolic computer algebra system CAS aimed at field theory researchers and provides an extensive set of functionalities for aiding its purpose.

SIGSAM: Computer Algebra Software

Cadabra handles tensor polynomial simplifications very effectively by utilizing Bianchi and Schouten identities and can also be used for fermions and anti-commuting variables, Clifford algebras, Fierz transformations, and many other problems. Get Cadabra. Wolfram Mathematica is a modern-day computer algebra system that encompasses most areas of technical computing including geometry, data science , visualizations, neural networks, image processing, and such. It is used very widely by both researchers and professionals for a broad spectrum of tasks.

Although very powerful, Wolfram Mathematica is not free and requires a paid license before you start using it for your research.

General purpose commercial systems

It supports thousands of mathematical functions, real-time data, natural language input, and many more exciting features. Features of Wolfram Mathematica. Get Wolfram Mathematica. Magma is a robust computer algebra system that combines advanced numerical computing features seamlessly with an easy to use yet effective user interface.


It has widespread usage in the fields of pure mathematics and is featured extensively in research. Magma can handle several types of problems associated with the areas of algebra, number theory, algebraic geometry, and algebraic combinatorics. It is distributed by the University of Sydney and comes with a non-commercial proprietary license. Get Magma. Reduce is a robust computer algebra system aimed at physics researchers.

It offers an extensive list of features that make it a suitable choice for anyone handling complex physics problems. It comes under the BSD license, which enables developers to extend the software any way they like and distribute it. Reduce has been under development since the 60s and is used in physics labs around the world. However, the growth seems to slow down, and the last stable release saw light eight years back. Get Reduce. Number theory plays a significant role in modern computing, and there are numerous applications of this growing field. It comes with a broad set of advanced function implementations alongside the more traditional ones and can be used extensively by both number theory researchers and computer scientists alike.

GAP is a powerful opensource system for solving computational discrete algebra problems. It is an exciting platform which combines features from the best computer algebra systems with a high-level, intuitive, and convenient programming language. GAP can tackle different types of discrete mathematical problems but emphasizes heavily on computational Group theory.

The default library is quite extensive and features more than thousands of function implementations right out of the box. Get GAP. SMath Studio is a free, cross-platform computer algebra system for Linux. It is written using the C programming language and supports almost every major operating system. It also has added support for the Android and iOS smartphone platform alongside some handheld devices. Get SMath Studio. Axiom is a general-purpose computer algebra system that has widespread usage in different types of computational tasks. It can be used for either academic research purposes or for developing complex, modern-day mathematical algorithms.

Axiom emphasizes on a strongly typed, mathematically correct type hierarchy that ensures maximum optimization boost for your algorithms. Axiom features a modified BSD license that enables researchers to extend the software for meeting customized demands. Get Axiom. It is a lightweight interactive system that offers a number of powerful features for making commutative algebra computations easier than ever.

Get CoCoA. Yacas, short for Yet Another Computer Algebra System , is a general-purpose computer algebra system that can perform a wide range of numeric and symbolic mathematical calculations effectively. It comes pre-equipped with its own programming language which provides a high-level abstraction of the underlying complex mathematical expressions.

It can compute arbitrary-precision numerical computations with exact results and offers powerful plotting capabilities for efficient data visualization and analysis. Get Yacas. FriCAS is an advanced computer algebra system built on top of Axiom. It offers a self-contained toolbox which can be used in a number of different mathematical computation ranging from traditional calculus to geometric algebra. It comes with a robust integrated help system that provides helpful documentation for new users. The system is entirely opensource and can be easily extended using the SPAD programming language.

Get FriCAS. Linux offers some of the best computer algebra systems mathematicians can get their hands on. Consequently, the large number and variant of these options tend to confuse many users. To help them find the perfect CAS system for their everyday computing, our editors have compiled this informative guide outlining the 20 best computer algebra systems for Linux. Comment your thoughts on our picks below and stay tuned for more exciting Linux software guides.

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Nice article. However, it would reallty be nice to have a table at the end with a summary of the features for each software for easier side-by-side comparisons. Save my name, email, and website in this browser for the next time I comment.

Computer algebra system

Sign in. Log into your account. Privacy Policy. Password recovery. Forgot your password? Get help. Best Computer Algebra Systems for Linux 1. SageMath 2. Scilab 4. Octave 5.

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At the simplest level one can generate assignment statements for the target language. One may note that an important efficiency aspect may be whether a program is run interpreted i. Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problems Yaroslav D. The outputs should ideally be [75, 0. Axiom use a strong type scheme; then parametrized data types can take advantage of an object-oriented design. Farina Busto L Some new cosmological results of quadratic Lagrangians. In contrast to numerical computations, which can suffer from floating-point errors, symbolic computations are carried out exactly.