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 de ...

(CAS) with features covering many aspects of

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, including

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

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

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...

differentiable manifolds In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One may ...

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

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

calculus Calculus 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 generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...

, and

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

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

free and open-source software Free and open-source software (FOSS) is software available under a license that grants users the right to use, modify, and distribute the software modified or not to everyone free of charge. FOSS is an inclusive umbrella term encompassing free ...

under the terms of the

GNU General Public License The GNU General Public Licenses (GNU GPL or simply GPL) are a series of widely used free software licenses, or ''copyleft'' licenses, that guarantee end users the freedom to run, study, share, or modify the software. The GPL was the first ...

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 (sometimes colloquially but incorrectly referred to as ''lava'') is found beneath the surface of the Earth, and evidence of magmatism has also ...

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

Mathematica Wolfram (previously known as Mathematica and Wolfram Mathematica) is a software system with built-in libraries for several areas of technical computing that allows machine learning, statistics, symbolic computation, data manipulation, network ...

, 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, mathematical structure, structure, space, Mathematica ...

at the

University of Washington The University of Washington (UW and informally U-Dub or U Dub) is a public research university in Seattle, Washington, United States. Founded in 1861, the University of Washington is one of the oldest universities on the West Coast of the Uni ...

. 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, and

object-oriented Object-oriented programming (OOP) is a programming paradigm based on the concept of '' objects''. Objects can contain data (called fields, attributes or properties) and have actions they can perform (called procedures or methods and impleme ...

constructs.

Development

Stein realized when designing Sage that there were many

open-source Open source is source code that is made freely available for possible modification and redistribution. Products include permission to use and view the source code, design documents, or content of the product. The open source model is a decentrali ...

mathematics software packages already written in different

languages Language is a structured system of communication that consists of grammar and vocabulary. It is the primary means by which humans convey meaning, both in spoken and signed forms, and may also be conveyed through writing. Human language is ch ...

, namely C, C++,

Common Lisp Common Lisp (CL) is a dialect of the Lisp programming language, published in American National Standards Institute (ANSI) standard document ''ANSI INCITS 226-1994 (S2018)'' (formerly ''X3.226-1994 (R1999)''). The Common Lisp HyperSpec, a hyperli ...

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

Cython Cython () is a superset of the programming language Python, which allows developers to write Python code (with optional, C-inspired syntax extensions) that yields performance comparable to that of C. Cython is a compiled language that is ty ...

) 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 In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for communication through a communicati ...

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. 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. * 2013: ACM/ SIGSAM 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 files ...

and

source code In computing, source code, or simply code or source, is a plain text computer program written in a programming language. A programmer writes the human readable source code to control the behavior of a computer. Since a computer, at base, only ...

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

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. Historically, flint was widely used to make stone tools and start ...

, 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.

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

Licensing and availability

SageMath is

free software Free software, libre software, libreware sometimes known as freedom-respecting software is computer software distributed open-source license, under terms that allow users to run the software for any purpose as well as to study, change, distribut ...

, distributed under the terms of the

version 3. ;Windows SageMath 10.0 (May 2023) requires Windows Subsystem for Linux in version 2, 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. Although Microsoft was sponsoring a Windows version of SageMath, prior to 2016 users of Windows had to use

virtualization In computing, virtualization (abbreviated v12n) is a series of technologies that allows dividing of physical computing resources into a series of virtual machines, operating systems, processes or containers. Virtualization began in the 1960s wit ...

technology such as

VirtualBox Oracle VirtualBox (formerly Sun VirtualBox, Sun xVM VirtualBox and InnoTek VirtualBox) is a hosted hypervisor for x86 virtualization developed by Oracle Corporation. VirtualBox was originally created by InnoTek Systemberatung GmbH, which was ac ...

to run SageMath. ;Linux SageMath is available as a package in some

Linux distribution A Linux distribution, often abbreviated as distro, is an operating system that includes the Linux kernel for its kernel functionality. Although the name does not imply product distribution per se, a distro—if distributed on its own—is oft ...

s, including Arch Linux,

Debian Debian () is a free and open-source software, free and open source Linux distribution, developed by the Debian Project, which was established by Ian Murdock in August 1993. Debian is one of the oldest operating systems based on the Linux kerne ...

Ubuntu Ubuntu ( ) is a Linux distribution based on Debian and composed primarily of free and open-source software. Developed by the British company Canonical (company), Canonical and a community of contributors under a Meritocracy, meritocratic gover ...

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. ;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 A library is a collection of Book, books, and possibly other Document, materials and Media (communication), media, that is accessible for use by its members and members of allied institutions. Libraries provide physical (hard copies) or electron ...

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