SageMath#Features

{{Infobox software

| name = SageMath

| title =

| logo = 250px

| logo caption =

| screenshot = File:Sagemath-jupyter-screenshot.png

| caption = Sagemath document (Jupyter Notebook) inside a web browser

| collapsible =

| author =

| developer =

| released = {{Start date and age|2005|02|24|df=yes}}

| discontinued =

| latest release version = {{LSR/wikidata}}

| latest preview version = 10.6.beta8

| latest preview date = {{Start date and age|2025|03|01|df=yes}}

| programming language = Python, Cython

| operating system = Linux, macOS, Microsoft Windows, Solaris, Android, iOS

| platform = {{Plainlist|

Personal computers and web platform
IA-32, x86-64, ARM, SPARC (and before Itanium)

}}

| size = Approx. 112–3319 MB

| language =

| language count =

| language footnote =

| genre = Computer algebra system

| license = GPLv3{{cite web|url=https://git.sagemath.org/sage.git/tree/COPYING.txt|title=COPYING.txt – sage.git|publisher=The Sage Repository|access-date=4 April 2017|archive-date=14 March 2017|archive-url=https://web.archive.org/web/20170314063622/https://git.sagemath.org/sage.git/tree/COPYING.txt|url-status=dead}}

| website = {{URL|https://www.sagemath.org/}}

}}

SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation"{{cite web|last=Stein|first=William|title=SAGE: A Computer System for Algebra and Geometry Experimentation|url=http://wstein.org/sage.html|access-date=30 March 2012}}) 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".{{cite web| last=Stein | first= William | url= https://www.sagemath.org/why/stein-sd4.pdf | title=Sage Days 4 | date=12 June 2007 | access-date=2 August 2007 |archive-url = https://web.archive.org/web/20070627235122/https://www.sagemath.org/why/stein-sd4.pdf |archive-date = 27 June 2007}} 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,{{cite book | url=https://drive.google.com/open?id=0B_q6VhhkczIYMy1jaDlGTGhPS00 | title=Numerical Analysis Using Sage | publisher=Springer | last1=Anastassiou | first1=George A. | last2=Mezei | first2=Razvan A. | year=2015 | location=New York | pages=x1 and 1 | isbn=9783319167381}} supporting procedural, functional, and object-oriented constructs.

Development

File:William A. Stein.png

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.{{cite web|url=http://wiki.sagemath.org/days7|title=Sage Days 7: Combinatorics|date=14 November 2008|website=SageWiki|access-date=9 December 2013}}

SageMath uses both students and professionals for development. The development of SageMath is supported by both volunteer work and grants.{{cite web|url=https://www.sagemath.org/development-ack.html|title=Sage – Acknowledgement to Supporters|access-date=6 January 2017}} However, it was not until 2016 that the first full-time Sage developer was hired (funded by an EU grant).William Stein: [http://wstein.org/talks/2016-06-sage-bp/bp.pdf The origins of SageMath – creating a viable open source alternative to Magma, Maple, Mathematica, and Matlab] (presentation, 11 June 2016) 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.

Achievements

2007: first prize in the scientific software division of Les Trophées du Libre, an international competition for free software.{{cite web|url=https://www.sciencedaily.com/releases/2007/12/071206145213.htm|title=Free Software Brings Affordability, Transparency To Mathematics|date=7 December 2007|publisher=Science Daily|access-date=6 January 2017}}
2012: one of the projects selected for the Google Summer of Code.{{cite web|url=https://www.google-melange.com/archive/gsoc/2012/orgs/sage|title=Sage Mathematical Software System|website=Google Summer of Code / Code-in Archive|access-date=6 January 2017}}
2013: ACM/SIGSAM Jenks Prize.{{cite web|url=http://www.sigsam.org/awards/jenks/awardees/2013/|title=Richard Dimick Jenks Memorial Prize 2013 Award|website=Association for Computing Machinery – SIGSAM|access-date=6 January 2017}}

Performance

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.{{cite web|url=http://sagemath.blogspot.com/2010/11/cython-sage-and-need-for-speed.html|title=Cython, Sage, and the Need for Speed|last=Stein|first=William|date=3 November 2010|access-date=6 January 2017}}

Licensing and availability

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

;Windows

SageMath 10.0 (May 2023) requires Windows Subsystem for Linux in version 2,{{cite web|url=https://doc.sagemath.org/html/en/installation/index.html|title=Welcome to Sage Installation Guide|date=1 May 2023|access-date=28 July 2023}} which in turn requires Windows to run as a Hyper-V client. SageMath 8.0 (July 2017), with development funded by the OpenDreamKit project, successfully built on Cygwin, and a binary installer for 64-bit versions of Windows was available.{{cite web|url=https://groups.google.com/d/msg/sage-announce/lznROhGi-2U/CPRsY7zZAwAJ|title=SageMath 8.0 installer for Windows|last=Lelievre|first=Samuel|date=18 August 2017|access-date=28 August 2017}} 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.{{cite web|url=https://groups.google.com/d/topic/sage-devel/LTWgQ_24cPs/discussion|title=Re: Question about Sage|last=Stein|first=William|date=16 March 2012|access-date=6 January 2017}}

;Linux

SageMath is available as a package in some Linux distributions, including Arch Linux, Debian, Ubuntu and NixOS. In Gentoo, it is available via layman in the "sage-on-gentoo"{{cite web|url=https://github.com/cschwan/sage-on-gentoo/wiki|title=sage-on-gentoo Wiki|website=GitHub |access-date=6 January 2017}} overlay. The package used by NixOS is available for use on other distributions, due to the distribution-agnostic nature of its package manager, Nix.

;Other operating systems

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.

class="wikitable plainrowheaders" ! {{rh2}} rowspan="12" \| Mathematics packages contained in SageMath{{cite web\|url=http://doc.sagemath.org/html/en/installation/standard_packages.html\|title=Standard Packages\|website=doc.sagemath.org\|access-date=6 January 2017}} ! scope="row" \| Algebra \| GAP, Singular, FLINT
scope="row" \| Algebraic geometry \| Singular
scope="row" \| Arbitrary-precision arithmetic \| GMP, MPFR, MPFI, NTL, mpmath, Arb
scope="row" \| Arithmetic geometry \| PARI/GP, NTL, mwrank, ECM
scope="row" \| Calculus \| Maxima, SymPy, GiNaC, Giac, FriCAS
scope="row" \| Combinatorics \| Symmetrica, Sage-Combinat
scope="row" \| Linear algebra \| ATLAS, BLAS, LAPACK, NumPy, LinBox, IML, GSL
scope="row" \| Graph theory \| NetworkX
scope="row" \| Group theory \| GAP
scope="row" \| Numerical computation \| GSL, SciPy, NumPy, ATLAS
scope="row" \| Number theory \| PARI/GP, FLINT, NTL
scope="row" \| Statistical computing \| R, SciPy
{{rh2}} rowspan="6" \| Other packages contained in SageMath ! scope="row" \| Command-line shell \| IPython
scope="row" \| Database \| ZODB, SQLite
scope="row" \| Graphical interface \| SageMath Notebook, MathJax{{cite web \| url=https://doc.sagemath.org/html/en/reference/spkg/ \| title=External Packages — External Packages }} (formerly jsMath)
scope="row" \| Graphics \| matplotlib, Tachyon, GD, Jmol
scope="row" \| Interactive programming language \| Python
scope="row" \| Networking \| Twisted
{{rh2}} \| Other Mathematics package available for SageMath ! scope="row" \| Differential geometry and tensor calculus \| Sage Manifolds

class="wikitable plainrowheaders"

! {{rh2}} rowspan="12" | Mathematics packages
contained in SageMath{{cite web|url=http://doc.sagemath.org/html/en/installation/standard_packages.html|title=Standard Packages|website=doc.sagemath.org|access-date=6 January 2017}}

! scope="row" | Algebra

| GAP, Singular, FLINT

scope="row" | Algebraic geometry

| Singular

scope="row" | Arbitrary-precision arithmetic

| GMP, MPFR, MPFI, NTL, mpmath, Arb

scope="row" | Arithmetic geometry

| PARI/GP, NTL, mwrank, ECM

scope="row" | Calculus

| Maxima, SymPy, GiNaC, Giac, FriCAS

scope="row" | Combinatorics

| Symmetrica, Sage-Combinat

scope="row" | Linear algebra

| ATLAS, BLAS, LAPACK, NumPy, LinBox, IML, GSL

scope="row" | Graph theory

| NetworkX

scope="row" | Group theory

| GAP

scope="row" | Numerical computation

| GSL, SciPy, NumPy, ATLAS

scope="row" | Number theory

| PARI/GP, FLINT, NTL

scope="row" | Statistical computing

| R, SciPy

{{rh2}} rowspan="6" | Other packages
contained in SageMath

! scope="row" | Command-line shell

| IPython

scope="row" | Database

| ZODB, SQLite

scope="row" | Graphical interface

| SageMath Notebook, MathJax{{cite web | url=https://doc.sagemath.org/html/en/reference/spkg/ | title=External Packages — External Packages }} (formerly jsMath)

scope="row" | Graphics

| matplotlib, Tachyon, GD, Jmol

scope="row" | Interactive programming language

| Python

scope="row" | Networking

| Twisted

{{rh2}} | Other Mathematics package
available for SageMath

! scope="row" | Differential geometry and tensor calculus

| Sage Manifolds