Awesome-FLOSS-CAS

A curated list of outstanding Free, Libre, and Open Source Software (FLOSS) Computer Algebra Systems (CAS) for mathematicians, educators, and researchers.

Introduction
CAS List
Comparison Table
Helps Needed
How to Contribute
License

Introduction

This repository gathers and documents the best open-source computer algebra systems available. These tools are invaluable for various mathematical computations, symbolic manipulations, and educational purposes.

CAS List

Maxima

Description: Maxima is a system for manipulating symbolic and numerical expressions, including differentiation, integration, and more.
Platform: Cross-platform
License: GPL
Website: Visit Maxima

Sympy

Description: Sympy is a Python library for symbolic mathematics, aiming to become a full-featured CAS.
Platform: Cross-platform
License: BSD
Website: Visit Sympy

SageMath

Description: Integrates many existing open-source mathematics software packages (including Symy, Maxima, and GiNaC) into a common interface.
Platform: Cross-platform
License: GPL
Website: Visit SageMath

Yacas

Description: Yacas (Yet Another Computer Algebra System) is designed for easy extensibility, featuring a small core and its own programming language.
Platform: Cross-platform
License: LGPL
Website: Visit Yacas

PanAxiom

Description: PanAxiom includes several forks of the Axiom computer algebra system, focusing on different aspects of symbolic computation.
- Axiom: Visit Axiom
- FriCAS: Visit FriCAS
- OpenAxiom: Visit OpenAxiom
Platform: Cross-platform
License: BSD, GPL

FORM

Description: FORM is a tool for large-scale algebraic calculations, specialized for computations in high-energy physics.
Platform: Cross-platform
License: GPLv3
Website: Visit FORM

Macaulay2

Description: Macaulay2 is a software system devoted to supporting research in algebraic geometry and commutative algebra.
Platform: Cross-platform
License: GPL
Website: Visit Macaulay2

Magnus

Description: Magnus is a computer algebra system that focuses on computations in group theory, particularly for infinite groups.
Platform: Unix
License: Custom free software license
Website: Visit Magnus

Mathomatic

Description: Mathomatic is a portable, lightweight computer algebra system capable of symbolic calculation and manipulation.
Platform: Cross-platform
License: LGPL
Website: Visit Mathomatic

REDUCE

Description: REDUCE is one of the oldest and most comprehensive general-purpose computer algebra systems used in various scientific fields.
Platform: Cross-platform
License: BSD
Website: Visit REDUCE

Euler Math Toolbox (EMT)

Description: Euler Math Toolbox combines numerical and symbolic tools and is noted for integrating a powerful numerical engine with Maxima for symbolic operations.
Platform: Windows, Linux
License: GPL
Website: Visit EMT

Mathics

Description: Mathics is a free, open-source alternative to Mathematica that supports many of its standard library functions.
Platform: Cross-platform
License: AGPL
Website: Visit Mathics

Cantor

Description: Cantor integrates different mathematical software into a consistent KDE-integrated interface, providing a user-friendly environment.
Platform: Cross-platform
License: GPL
Website: Visit Cantor

MathAction

Description: MathAction provides a web interface to the Axiom/FriCAS computer algebra systems, facilitating collaborative mathematical work.
Platform: Web
License: BSD
Website: Visit MathAction

SymbolicC++

Description: SymbolicC++ brings symbolic manipulation capabilities directly into the C++ language, enabling symbolic computations in a standard programming environment.
Platform: Cross-platform
License: LGPL
Website: Visit SymbolicC++

SymEngine

Description: SymEngine is a fast symbolic manipulation library designed for use in larger systems like Python's SymPy.
Platform: Cross-platform
License: BSD
Website: Visit SymEngine

GiNaC

Description: GiNaC is an open framework for symbolic computation within the C++ programming language that does not require external libraries.
Platform: Cross-platform
License: GPL
Website: Visit GiNaC

Piranha

Description: Piranha is a C++ library for symbolic mathematics, particularly focusing on multivariate polynomials and series manipulations.
Platform: Cross-platform
License: MPL
Website: Visit Piranha

Comparison Table

CAS	Programming Language	Typical Applications	Notable Features
Maxima (WxMaxima, Jupyter)	Lisp	General mathematics, education	Symbolic computation, numerical methods, high precision
Python-Sympy (Jupyter)	Python	General mathematics, physics, engineering	Integrates with Python, broad library support
SageMath	Python	Broad spectrum (algebra, calculus, number theory)	Integrates many CAS backends, extensive functionality
Yacas	Lisp (own language)	Algebraic manipulations, education	Easily extensible, lightweight
PanAxiom (Axiom, FriCAS, OpenAxiom)	Lisp	Algebra, research, education	Strongly typed, algebraically oriented
FORM	Own scripting language	High energy physics	Handles very large expressions efficiently
Macaulay2	Own language	Algebraic geometry, commutative algebra	Grobner bases, characteristic sets
Magnus	C++	Group theory, especially infinite groups	Specialized in computational group theory
Mathomatic	C	Algebraic equations, education	Lightweight, portable
REDUCE	Lisp	General mathematics, physics	One of the oldest CAS, versatile
Euler Math Toolbox (EMT)	C++, own scripting	Numerical analysis, symbolic computations	Numerical and symbolic capabilities
Mathics	Python	General purpose, similar to Mathematica	Mathematica-compatible syntax, lightweight
Cantor	C++ (KDE)	Educational, integrates multiple backends	User-friendly, part of KDE education project
MathAction	Web interface	Web-based access to Axiom/FriCAS	Convenient web interface for Axiom
SymbolicC++	C++	Embedded algebra in C++ applications	Symbolic manipulation in C++
SymEngine	C++	Core for symbolic computations in Sympy	Fast, efficient, used as backend for Sympy
GiNaC	C++	Symbolic computations integrated in C++	No external dependencies, robust
Piranha	C++	Polynomial arithmetic, large algebraic expressions	High-performance polynomial operations

How to Contribute

We welcome contributions from the community! Here are some ways you can contribute:

Add a new CAS: If you know of a FLOSS CAS that is not listed here, please submit a pull request with details following the format used in the CAS List.
Improve descriptions: Help us improve the descriptions for each listed CAS to provide clearer and more comprehensive information.
Report Issues: If you notice any errors or outdated information, please open an issue.

Helps Needed

I am considering adding several features and resources:

Tutorials and Examples:
- Include tutorials or example notebooks demonstrating how to use each CAS for common mathematical problems or specific applications, such as algebra, calculus, or physics.
- Provide step-by-step guides for setting up and getting started with each system.
Comparison Tables:
- Offer a more detailed comparison table highlighting each system's strengths and weaknesses, such as performance benchmarks, feature sets, and ease of use.
Integration Guides:
- Provide documentation on integrating these systems with other software tools, such as data analysis platforms, scientific computing environments, or programming languages.
Community Contributions:
- Set up a section for user-contributed scripts or modules.
User Reviews and Experiences:
- Create a space where users can share their experiences, reviews, and tips for using different CAS tools. This could help new users make informed decisions based on community feedback.
Video Demonstrations:
- Add video tutorials or demonstrations that provide visual and practical guidance on using the CAS tools effectively.
Related Resources:
- Link to external resources, such as forums, blogs, and academic papers that discuss or use the listed CAS.
License Information:
- Clearly document the licensing information for each CAS to ensure users understand how they can legally use and distribute the software.

To contribute, please fork the repository, make your changes, and submit a pull request.

License

This curated list is published under the Creative Commons License. Contributions to this repository are accepted under the same license.

Enhance Repository Categorization and Clarify CAS Definitions

Issue Description

As the repository grows and includes a broader array of FLOSS Computer Algebra Systems (CAS), valuable feedback suggests the need for better categorization and more precise definitions regarding the nature of the tools listed. This issue addresses these points by categorizing the tools into more specific groups and clarifying which tools are inherently CAS and which are libraries or languages that can perform CAS functions with additional libraries.

Proposed Categories

Domain-Specific CAS Languages:
- Example: Maxima, REDUCE
- These are standalone environments explicitly designed for symbolic mathematics.
Languages with CAS Libraries:
- General-Purpose Languages
  - Example: Python with SymPy
  - These are not CAS by nature but can perform CAS tasks through specific libraries.
- Domain-Specific Languages for Numerical and Algebraic Calculations:
  - Example: Scilab, Octave, Julia
  - These languages are specifically designed for numerical computations such as linear algebra and can perform CAS tasks through specific libraries.
CAS Libraries:
- Interpreted Libraries:
  - Example: SymPy (Python)
  - These libraries are used within an interpreted language and do not require compilation, making them accessible for rapid prototyping and use.
- Compiled Libraries:
  - Example: GiNaC (C++)
  - These require compilation and are typically used to integrate CAS capabilities into applications written in compiled languages.
User Interfaces, Editors, and IDEs for CAS:
- Example: WxMaxima, Jupyter, Spyder, MathAction
- These tools provide environments and interfaces that enhance the usability of CAS tools, either as standalone applications or as part of larger systems.

Tools Needing Clarification

Several tools have been mentioned which might require further discussion to determine if they should be included as FLOSS and/or CAS:

Scilab
Octave
SageMath
GAP
PARI/GP
Singular
CoCoA

Task List

Categorize all listed tools under the proposed categories.
Verify the FLOSS status and CAS capabilities of Scilab, Octave, SageMath, GAP, PARI/GP, Singular, and CoCoA.
Update the README with these categorizations and clarifications.
Solicit community feedback on the proposed changes.

Call for Contributions

I am excited to see contributors help with this task by researching the tools, suggesting categorizations, and updating documentation. This will help make our repository a more structured and informative resource for everyone interested in FLOSS CAS tools.

Thank you for your support and contributions!

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