SageMath


SageMath is a computer algebra system 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". 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, supporting procedural, functional and object-oriented constructs.

Development

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 integrates many specialized Computer algebra systems 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.
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. 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

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.

Licensing and availability

SageMath is free software, distributed under the terms of the GNU General Public License 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 technology such as VirtualBox to run SageMath. As of SageMath 8.0, with development funded by the OpenDreamKit project, it successfully builds on Cygwin, and a binary installer for 64-bit versions of Windows is available.
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" overlay. The package used by NixOS is available for use on other distributions, due 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		AlgebraGAP, Singular, FLINT
Mathematics
packages
contained in
SageMath		Algebraic geometrySingular
Mathematics
packages
contained in
SageMath		Arbitrary precision arithmeticMPIR, MPFR, MPFI, NTL, mpmath, Arb
Mathematics
packages
contained in
SageMath		Arithmetic geometryPARI/GP, NTL, mwrank, ECM
Mathematics
packages
contained in
SageMath		CalculusMaxima, SymPy, GiNaC, Giac, FriCAS
Mathematics
packages
contained in
SageMath		CombinatoricsSymmetrica, Sage-Combinat
Mathematics
packages
contained in
SageMath		Linear algebraATLAS, BLAS, LAPACK, NumPy, LinBox, IML, GSL
Mathematics
packages
contained in
SageMath		Graph theoryNetworkX
Mathematics
packages
contained in
SageMath		Group theoryGAP
Mathematics
packages
contained in
SageMath		Numerical computationGSL, SciPy, NumPy, ATLAS
Mathematics
packages
contained in
SageMath		Number theoryPARI/GP, FLINT, NTL
Mathematics
packages
contained in
SageMath		Statistical computingR, SciPy
Other
packages
contained in
SageMath		Command-line shellIPython
Other
packages
contained in
SageMath		DatabaseZODB, SQLite
Other
packages
contained in
SageMath		Graphical interfaceSageMath Notebook, jsMath
Other
packages
contained in
SageMath		Graphicsmatplotlib, Tachyon, GD, Jmol
Other
packages
contained in
SageMath		Interactive programming languagePython
Other
packages
contained in
SageMath		NetworkingTwisted
Other
Mathematics
package
available for
SageMath		Differential Geometry
and Tensor Calculus		Sage Manifolds