Initial release24 February 2005; 19 years ago (2005-02-24)
Stable release
10.3[1] Edit this on Wikidata (20 March 2024; 3 months ago (20 March 2024))
Preview release
10.3.rc2 / 4 March 2024; 4 months ago (2024-03-04)
Written inPython, Cython
Operating systemLinux, macOS, Microsoft Windows, Solaris, Android, iOS
SizeApprox. 112–3319 MB
TypeComputer algebra system

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, group theory, differentiable manifolds, 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

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 interfaces among 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]



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 OpenBLAS, FLINT, GAP (computer algebra system), 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.[12]

Licensing and availability

SageMath is free software, distributed under the terms of the GNU General Public License version 3.[2]

SageMath 10.0 (May 2023) requires Windows Subsystem for Linux in version 2,[13] which in turn requires Windows to run as a Hyper-V client. SageMath 8.0 (July 2017), with development funded by the OpenDreamKit project,[8] successfully built on Cygwin, and a binary installer for 64-bit versions of Windows was available.[14] Although Microsoft was sponsoring a Windows version of SageMath, prior to 2016 users of Windows had to use virtualization technology such as VirtualBox to run SageMath.[15]

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"[16] 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.

Mathematics packages
contained in SageMath[17]
Algebra GAP, Singular, FLINT
Algebraic geometry Singular
Arbitrary-precision arithmetic GMP, 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
Other packages
contained in SageMath
Command-line shell IPython
Database ZODB, SQLite
Graphical interface SageMath Notebook, MathJax[18] (formerly jsMath)
Graphics matplotlib, Tachyon, GD, Jmol
Interactive programming language Python
Networking Twisted
Other Mathematics package
available for SageMath
Differential geometry and tensor calculus Sage Manifolds

See also


  1. ^ "Release 10.3". 20 March 2024. Retrieved 25 March 2024.
  2. ^ a b "COPYING.txt – sage.git". The Sage Repository. Archived from the original on 14 March 2017. Retrieved 4 April 2017.
  3. ^ Stein, William. "SAGE: A Computer System for Algebra and Geometry Experimentation". Retrieved 30 March 2012.
  4. ^ Stein, William (12 June 2007). "Sage Days 4" (PDF). Archived from the original (PDF) on 27 June 2007. Retrieved 2 August 2007.
  5. ^ Anastassiou, George A.; Mezei, Razvan A. (2015). Numerical Analysis Using Sage. New York: Springer. pp. x1 and 1. ISBN 9783319167381.
  6. ^ "Sage Days 7: Combinatorics". SageWiki. 14 November 2008. Retrieved 9 December 2013.
  7. ^ "Sage – Acknowledgement to Supporters". Retrieved 6 January 2017.
  8. ^ a b c William Stein: The origins of SageMath – creating a viable open source alternative to Magma, Maple, Mathematica, and Matlab (presentation, 11 June 2016)
  9. ^ "Free Software Brings Affordability, Transparency To Mathematics". Science Daily. 7 December 2007. Retrieved 6 January 2017.
  10. ^ "Sage Mathematical Software System". Google Summer of Code / Code-in Archive. Retrieved 6 January 2017.
  11. ^ "Richard Dimick Jenks Memorial Prize 2013 Award". Association for Computing Machinery – SIGSAM. Retrieved 6 January 2017.
  12. ^ Stein, William (3 November 2010). "Cython, Sage, and the Need for Speed". Retrieved 6 January 2017.
  13. ^ "Welcome to Sage Installation Guide". 1 May 2023. Retrieved 28 July 2023.
  14. ^ Lelievre, Samuel (18 August 2017). "SageMath 8.0 installer for Windows". Retrieved 28 August 2017.
  15. ^ Stein, William (16 March 2012). "Re: Question about Sage". Retrieved 6 January 2017.
  16. ^ "sage-on-gentoo Wiki". GitHub. Retrieved 6 January 2017.
  17. ^ "Standard Packages". Retrieved 6 January 2017.
  18. ^ "External Packages — External Packages".