SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation"[3]) is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics, graph theory, numerical analysis, number theory, calculus and statistics.

The first version of SageMath was released on 24 February 2005 as free and open-source software under the terms of the GNU General Public License version 2, with the initial goals of creating an "open source alternative to Magma, Maple, Mathematica, and MATLAB".[4] The originator and leader of the SageMath project, William Stein, was a mathematician at the University of Washington.

SageMath uses a syntax resembling Python's,[5] supporting procedural, functional and object-oriented constructs.

William A. Stein

William Stein realized when designing Sage that there were many open-source mathematics software packages already written in different languages, namely C, C++, Common Lisp, Fortran and Python.

Rather than reinventing the wheel, Sage (which is written mostly in Python and Cython) integrates many specialized CAS software packages into a common interface, for which a user needs to know only Python. However, Sage contains hundreds of thousands of unique lines of code adding new functions and creating the interface between its components.[6]

SageMath uses both students and professionals for development. The development of SageMath is supported by both volunteer work and grants.[7] However, it was not until 2016 that the first full-time Sage developer was hired (funded by an EU grant).[8] The same year, Stein described his disappointment with a lack of academic funding and credentials for software development, citing it as the reason for his decision to leave his tenured academic position to work full-time on the project in a newly founded company, SageMath, Inc.[8]

2007: first prize in the scientific software division of Les Trophées du Libre, an international competition for free software.[9]
2012: one of the projects selected for the Google Summer of Code.[10]
2013: ACM/SIGSAM Jenks Prize.[11]
SageMath has been cited in a variety of publications.[12][13]


Both binaries and source code are available for SageMath from the download page. If SageMath is built from source code, many of the included libraries such as ATLAS, FLINT, and NTL will be tuned and optimized for that computer, taking into account the number of processors, the size of their caches, whether there is hardware support for SSE instructions, etc.

Cython can increase the speed of SageMath programs, as the Python code is converted into C.[14]
Licensing and availability

SageMath is free software, distributed under the terms of the GNU General Public License version 3.[1]

Although Microsoft was sponsoring a native version of SageMath for the Windows operating system, prior to 2016 there were no plans for a native port, and users of Windows had to use virtualization technology such as VirtualBox to run SageMath.[15] As of SageMath 8.0 (July 2017), with development funded by the OpenDreamKit project[8], it successfully builds on Cygwin, and a binary installer for 64-bit versions of Windows is available.[16]

Linux distributions in which SageMath is available as a package are Fedora, Arch Linux, Debian, Ubuntu and NixOS. In Gentoo, it is available via layman in the "sage-on-gentoo"[17] overlay. The package used by NixOS is available for use on other distributions, due to the distribution-agnostic nature of its package manager, Nix.

Gentoo prefix also provides Sage on other operating systems.
Software packages contained in SageMath

The philosophy of SageMath is to use existing open-source libraries wherever they exist. Therefore, it uses many libraries from other projects.

contained in
Algebra GAP, Singular, FLINT
algebraic geometry Singular
Arbitrary precision arithmetic MPIR, MPFR, MPFI, NTL, mpmath, Arb
Arithmetic geometry PARI/GP, NTL, mwrank, ECM
Calculus Maxima, SymPy, GiNaC, Giac, FriCAS
Combinatorics Symmetrica, Sage-Combinat
Linear algebra ATLAS, BLAS, LAPACK, NumPy, LinBox, IML, GSL
Graph theory NetworkX
Group theory GAP
Numerical computation GSL, SciPy, NumPy, ATLAS
Number theory PARI/GP, FLINT, NTL
Statistical computing R, SciPy
contained in
Command-line shell IPython
Database ZODB, SQLite
Graphical interface SageMath Notebook, jsMath
Graphics matplotlib, Tachyon, GD, Jmol
Interactive programming language Python
Networking Twisted
available for
Differential Geometry
and Tensor Calculus
Sage Manifolds

See also

Free and open-source software portal iconMathematics portal

List of computer algebra systems
Comparison of numerical analysis software
Comparison of statistical packages


"COPYING.txt – sage.git". The Sage Repository. Retrieved 4 April 2017.
" Site Info". Alexa Internet. Retrieved 2018-02-13.
Stein, William. "SAGE: A Computer System for Algebra and Geometry Experimentation". Retrieved 30 March 2012.
Stein, William (12 June 2007). "Sage Days 4" (PDF). Archived from the original (PDF) on 27 June 2007. Retrieved 2 August 2007.
Anastassiou, George A.; Mezei, Razvan A. (2015). Numerical Analysis Using Sage. New York: Springer. pp. x1 and 1. ISBN 9783319167381.
"Sage Days 7: Combinatorics". SageWiki. 14 November 2008. Retrieved 9 December 2013.
"Sage – Acknowledgement to Supporters". Retrieved 6 January 2017.
William Stein: The origins of SageMath – creating a viable open source alternative to Magma, Maple, Mathematica, and Matlab (presentation, 11 June 2016)
"Free Software Brings Affordability, Transparency To Mathematics". Science Daily. 7 December 2007. Retrieved 6 January 2017.
"Sage Mathematical Software System". Google Summer of Code / Code-in Archive. Retrieved 6 January 2017.
"Richard Dimick Jenks Memorial Prize 2013 Award". Association for Computing Machinery – SIGSAM. Retrieved 6 January 2017.
"Publications Citing Sage". Retrieved 6 January 2017.
"Publications Citing Sage-Combinat". Retrieved 6 January 2017.
Stein, William (3 November 2010). "Cython, Sage, and the Need for Speed". Retrieved 6 January 2017.
Stein, William (16 March 2012). "Re: Question about Sage". Retrieved 6 January 2017.
Lelievre, Samuel (18 August 2017). "SageMath 8.0 installer for Windows". Retrieved 28 August 2017.
"sage-on-gentoo Wiki". Retrieved 6 January 2017.

"Standard Packages". Retrieved 6 January 2017.

External links
Wikibooks has a book on the topic of: Sage
Wikimedia Commons has media related to Sage (mathematics software).

Official website

Undergraduate Texts in Mathematics

Graduate Texts in Mathematics

Graduate Studies in Mathematics

Mathematics Encyclopedia



Hellenica World - Scientific Library

Retrieved from ""
All text is available under the terms of the GNU Free Documentation License