SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation") is a

computer algebra system A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The ...

(CAS) with features covering many aspects of

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, including

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...

graph theory In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods ...

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Ma ...

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...

and

statistics Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, indust ...

. The first version of SageMath was released on 24 February 2005 as

free and open-source software Free and open-source software (FOSS) is a term used to refer to groups of software consisting of both free software and open-source software where anyone is freely licensed to use, copy, study, and change the software in any way, and the source ...

under the terms of the

GNU General Public License The GNU General Public License (GNU GPL or simply GPL) is a series of widely used free software licenses that guarantee end users the four freedoms to run, study, share, and modify the software. The license was the first copyleft for general ...

version 2, with the initial goals of creating an "open source alternative to

Magma Magma () is the molten or semi-molten natural material from which all igneous rocks are formed. Magma is found beneath the surface of the Earth, and evidence of magmatism has also been discovered on other terrestrial planets and some natura ...

Maple ''Acer'' () is a genus of trees and shrubs commonly known as maples. The genus is placed in the family Sapindaceae.Stevens, P. F. (2001 onwards). Angiosperm Phylogeny Website. Version 9, June 2008 nd more or less continuously updated since h ...

Mathematica Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning, statistics, symbolic computation, data manipulation, network analysis, time series analysis, NLP, optimiza ...

, and

MATLAB MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementat ...

". The originator and leader of the SageMath project, William Stein, was a

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

at the

University of Washington The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington. Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seatt ...

. SageMath uses a

syntax In linguistics, syntax () is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure ( constituenc ...

resembling Python's, supporting procedural,

functional Functional may refer to: * Movements in architecture: ** Functionalism (architecture) ** Form follows function * Functional group, combination of atoms within molecules * Medical conditions without currently visible organic basis: ** Functional sy ...

and

object-oriented Object-oriented programming (OOP) is a programming paradigm based on the concept of "objects", which can contain data and code. The data is in the form of fields (often known as attributes or ''properties''), and the code is in the form of ...

constructs.

Development

Stein realized when designing Sage that there were many open-source mathematics software packages already written in different languages, namely C, C++,

Common Lisp Common Lisp (CL) is a dialect of the Lisp programming language, published in ANSI standard document ''ANSI INCITS 226-1994 (S20018)'' (formerly ''X3.226-1994 (R1999)''). The Common Lisp HyperSpec, a hyperlinked HTML version, has been derived fr ...

, Fortran and Python. Rather than reinventing the wheel, Sage (which is written mostly in Python and

Cython Cython () is a programming language that aims to be a superset of the Python programming language, designed to give C-like performance with code that is written mostly in Python with optional additional C-inspired syntax. Cython is a compiled ...

) integrates many specialized

CAS Cas may refer to: * Caș, a type of cheese made in Romania * ' (1886–) Czech magazine associated with Tomáš Garrigue Masaryk * '' Čas'' (19 April 1945–February 1948), the official, daily newspaper of the Democratic Party of Slovakia * ''CA ...

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. SageMath uses both students and professionals for development. The development of SageMath is supported by both volunteer work and

grants Grant or Grants may refer to: Places *Grant County (disambiguation) Australia * Grant, Queensland, a locality in the Barcaldine Region, Queensland, Australia United Kingdom *Castle Grant United States * Grant, Alabama * Grant, Inyo County, ...

. However, it was not until 2016 that the first full-time Sage developer was hired (funded by an EU grant).William Stein
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. * 2012: one of the projects selected for the

Google Summer of Code The Google Summer of Code, often abbreviated to GSoC, is an international annual program in which Google awards stipends to contributors who successfully complete a free and open-source software coding project during the summer. , the program is ...

. * 2013: ACM/

SIGSAM SIGSAM is the ACM Special Interest Group on Symbolic and Algebraic Manipulation. It publishes the '' ACM Communications in Computer Algebra'' and often sponsors the ''International Symposium on Symbolic and Algebraic Computation'' (ISSAC). Extern ...

Jenks Prize.

Performance

Both

binaries A binary file is a computer file that is not a text file. The term "binary file" is often used as a term meaning "non-text file". Many binary file formats contain parts that can be interpreted as text; for example, some computer document fil ...

and

source code In computing, source code, or simply code, is any collection of code, with or without comments, written using a human-readable programming language, usually as plain text. The source code of a program is specially designed to facilitate the ...

are available for SageMath from the download page. If SageMath is built from source code, many of the included libraries such as

OpenBLAS In scientific computing, OpenBLAS is an open-source implementation of the BLAS (Basic Linear Algebra Subprograms) and LAPACK APIs with many hand-crafted optimizations for specific processor types. It is developed at the Lab of Parallel Software ...

FLINT Flint, occasionally flintstone, is a sedimentary cryptocrystalline form of the mineral quartz, categorized as the variety of chert that occurs in chalk or marly limestone. Flint was widely used historically to make stone tools and start ...

GAP (computer algebra system) GAP ( Groups, Algorithms and Programming) is a computer algebra system for computational discrete algebra with particular emphasis on computational group theory. History GAP was developed at Lehrstuhl D für Mathematik (LDFM), Rheinisch-Westf ...

, and NTL will be tuned and optimized for that computer, taking into account the number of

processors A central processing unit (CPU), also called a central processor, main processor or just processor, is the electronic circuitry that executes instructions comprising a computer program. The CPU performs basic arithmetic, logic, controlling, a ...

, the size of their caches, whether there is hardware support for SSE instructions, etc.

can increase the speed of SageMath programs, as the Python code is converted into C.

Licensing and availability

SageMath is

free software Free software or libre software is computer software distributed under terms that allow users to run the software for any purpose as well as to study, change, and distribute it and any adapted versions. Free software is a matter of liberty, n ...

, distributed under the terms of the

version 3. 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 In computing, virtualization or virtualisation (sometimes abbreviated v12n, a numeronym) is the act of creating a virtual (rather than actual) version of something at the same abstraction level, including virtual computer hardware platforms, stor ...

technology such as

VirtualBox Oracle VM VirtualBox (formerly Sun VirtualBox, Sun xVM VirtualBox and Innotek VirtualBox) is a type-2 hypervisor for x86 virtualization developed by Oracle Corporation. VirtualBox was originally created by Innotek GmbH, which was acquired by S ...

to run SageMath. As of SageMath 8.0 (July 2017), with development funded by the OpenDreamKit project, it successfully builds on

Cygwin Cygwin ( ) is a POSIX-compatible programming and runtime environment that runs natively on Microsoft Windows. Under Cygwin, source code designed for Unix-like operating systems may be compiled with minimal modification and executed. The Cygwin in ...

, and a binary installer for 64-bit versions of Windows is available.

Linux distribution A Linux distribution (often abbreviated as distro) is an operating system made from a software collection that includes the Linux kernel and, often, a package management system. Linux users usually obtain their operating system by downloading one ...

s in which SageMath is available as a package are

Fedora A fedora () is a hat with a soft brim and indented crown.Kilgour, Ruth Edwards (1958). ''A Pageant of Hats Ancient and Modern''. R. M. McBride Company. It is typically creased lengthwise down the crown and "pinched" near the front on both side ...

Arch Linux Arch Linux () is an independently developed, x86-64 general-purpose Linux distribution that strives to provide the latest stable versions of most software by following a rolling-release model. The default installation is a minimal base system, ...

Debian Debian (), also known as Debian GNU/Linux, is a Linux distribution composed of free and open-source software, developed by the community-supported Debian Project, which was established by Ian Murdock on August 16, 1993. The first version of De ...

Ubuntu Ubuntu ( ) is a Linux distribution based on Debian and composed mostly of free and open-source software. Ubuntu is officially released in three editions: '' Desktop'', ''Server'', and ''Core'' for Internet of things devices and robots. All ...

and NixOS. In Gentoo, it is available via layman in the "sage-on-gentoo" overlay. The package used by NixOS is available for use on other distributions, due to the distribution-agnostic nature of its package manager,

Nix Nix or NIX may refer to: Places * Nix, Alabama, an unincorporated community, United States * Nix, Texas, a ghost town in southwestern Lampasas County, Texas, United States * Nix (moon), a moon of Pluto People * Nix (surname), listing people wit ...

. 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 A library is a collection of Document, materials, books or media that are accessible for use and not just for display purposes. A library provides physical (hard copies) or electronic media, digital access (soft copies) materials, and may be a ...

wherever they exist. Therefore, it uses many libraries from other projects.

References

External links

* {{DEFAULTSORT:SageMath (mathematics software) Computer algebra system software for Linux Computer algebra system software for macOS Computer algebra system software for Windows Free and open-source Android software Free computer algebra systems Free educational software Free mathematics software Free software programmed in Python Mathematical software Python (programming language) scientific libraries