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31-459: SageMath (previously Sage or SAGE , "System for Algebra and Geometry Experimentation") 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

62-531: A GNU development toolchain (including GCC and GDB ). Programmers have ported the X Window System , K Desktop Environment 3 , GNOME , Apache , and TeX . Cygwin permits installing inetd , syslogd , sshd , Apache , and other daemons as standard Windows services . Cygwin programs have full access to the Windows API and other Windows libraries. Cygwin programs are installed by running Cygwin's "setup" program, which downloads them from repositories on

93-522: A front-end to several other free and nonfree CAS). Other significant systems include Axiom , GAP , Maxima and Magma . The movement to web-based applications in the early 2000s saw the release of WolframAlpha , an online search engine and CAS which includes the capabilities of Mathematica . More recently, computer algebra systems have been implemented using artificial neural networks , though as of 2020 they are not commercially available. The symbolic manipulations supported typically include: In

124-402: A format very similar to Unix systems, except that Windows paths appear in place of devices. Filesystems can be mounted in binary mode (by default), or in text mode, which enables automatic conversion between LF and CRLF endings (which only affects programs that open files without explicitly specifying text or binary mode). Cygwin 1.7 introduced comprehensive support for POSIX locales , and

155-406: A newly founded company, SageMath, Inc. 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

186-514: A number of terminal emulators that are based on them, including mintty , rxvt /urxvt, and xterm . The version of GCC that comes with Cygwin has various extensions for creating Windows DLLs, such as specifying whether a program is a windowing or console-mode program. Support for compiling programs that do not require the POSIX compatibility layer provided by the Cygwin DLL used to be included in

217-406: A specific part of mathematics, such as number theory , group theory , or teaching of elementary mathematics . General-purpose computer algebra systems aim to be useful to a user working in any scientific field that requires manipulation of mathematical expressions. To be useful, a general-purpose computer algebra system must include various features such as: The library must not only provide for

248-565: 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 development of the computer algebra systems in the second half of the 20th century is part of the discipline of " computer algebra " or "symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials . Computer algebra systems may be divided into two classes: specialized and general-purpose. The specialized ones are devoted to

279-520: 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 . Gentoo prefix also provides Sage on other operating systems. The philosophy of SageMath is to use existing open-source libraries wherever they exist. Therefore, it uses many libraries from other projects. Computer algebra system A computer algebra system ( CAS ) or symbolic algebra system ( SAS )

310-578: Is hardware support for SSE instructions, etc. Cython can increase the speed of SageMath programs, as the Python code is converted into C . SageMath is free software , distributed under the terms of the GNU General Public License version 3. 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

341-399: 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). 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

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372-686: The ACT , the PLAN , and in some classrooms though it may be permitted on all of College Board 's calculator-permitted tests, including the SAT , some SAT Subject Tests and the AP Calculus , Chemistry , Physics , and Statistics exams. Cygwin The terminal emulator Mintty is the default command-line interface (CLI) provided to interact with the environment. The Cygwin installation directory layout mimics

403-459: The C library newlib . He thought that it would be possible to retarget GCC and produce a cross compiler generating executables that could run on Windows. A prototype was later developed. Chamberlain bootstrapped the compiler on a Windows system, to emulate Unix to let the GNU configure shell script run. Initially, Cygwin was called gnuwin32 . When Microsoft registered the trademark Win32,

434-506: 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 technology such as VirtualBox to run SageMath. Linux distributions in which SageMath is available as a package are Fedora , Arch Linux , Debian , Ubuntu and NixOS . In Gentoo , it

465-679: The UTF-8 Unicode encoding became the default. The fork system call for duplicating a process is fully implemented, but the copy-on-write optimization strategy could not be used. The Cygwin DLL contains a console driver that emulates a Unix-style terminal within the Windows console . Cygwin's default user interface is the bash shell running in the Cygwin console. The DLL also implements pseudo terminal (pty) devices. Cygwin ships with

496-616: The root file system of Unix-like systems, with directories such as /bin , /home , /etc , /usr , and /var . Cygwin is released under the GNU Lesser General Public License version 3. It was originally developed by Cygnus Solutions , which was later acquired by Red Hat (now part of IBM ), to port the GNU toolchain to Win32 , including the GNU Compiler Suite . Rather than rewrite

527-485: The "32" was dropped to simply become Cygwin . In 1999, Cygnus offered Cygwin 1.0 as a commercial product . Subsequent versions have not been released, instead relying on continued open source releases. Geoffrey Noer was the project lead from 1996 to 1999. Christopher Faylor was lead from 1999 to 2004; he left Red Hat and became co-lead with Corinna Vinschen. Corinna Vinschen has been the project lead from mid-2014 to date (as of September, 2024). From June 23, 2016,

558-418: The 1950s, while computers were mainly used for numerical computations, there were some research projects into using them for symbolic manipulation. Computer algebra systems began to appear in the 1960s and evolved out of two quite different sources—the requirements of theoretical physicists and research into artificial intelligence . A prime example for the first development was the pioneering work conducted by

589-521: The Cygwin library version 2.5.2 was licensed under the GNU Lesser General Public License (LGPL) version 3. Cygwin is provided in two versions: the full 64-bit version and a stripped-down 32-bit version, whose final version was released in 2022. Cygwin consists of a library that implements the POSIX system call API in terms of Windows system calls to enable the running of a large number of application programs equivalent to those on Unix systems, and

620-730: The Internet. The Cygwin API library is licensed under the GNU Lesser General Public License version 3 (or later), with an exception to allow linking to any free and open-source software whose license conforms to the Open Source Definition . Cygwin consists of two parts: Cygwin supports POSIX symbolic links , representing them as plain-text files with the system attribute set. Cygwin 1.5 represented them as Windows Explorer shortcuts , but this

651-1139: The above, the word some indicates that the operation cannot always be performed. Many also include: Some include: Some computer algebra systems focus on specialized disciplines; these are typically developed in academia and are free. They can be inefficient for numeric operations as compared to numeric systems . The expressions manipulated by the CAS typically include polynomials in multiple variables; standard functions of expressions ( sine , exponential , etc.); various special functions ( Γ , ζ , erf , Bessel functions , etc.); arbitrary functions of expressions; optimization; derivatives, integrals, simplifications, sums, and products of expressions; truncated series with expressions as coefficients, matrices of expressions, and so on. Numeric domains supported typically include floating-point representation of real numbers , integers (of unbounded size), complex (floating-point representation), interval representation of reals , rational number (exact representation) and algebraic numbers . There have been many advocates for increasing

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682-629: The default GCC, but as of 2014 , it is provided by cross-compilers contributed by the MinGW-w64 project. Cygwin's base package selection is approximately 100MB, containing the bash (interactive user) and dash (installation) shells and the core file and text manipulation utilities. Additional packages are available as optional installs from within the Cygwin "setup" program and package manager ("setup-x86_64.exe" – 64 bit). The Cygwin Ports project provided additional packages that were not available in

713-826: The first hand-held calculator CAS with the HP-28 series . Other early handheld calculators with symbolic algebra capabilities included the Texas Instruments TI-89 series and TI-92 calculator, and the Casio CFX-9970G . The first popular computer algebra systems were muMATH , Reduce , Derive (based on muMATH), and Macsyma ; a copyleft version of Macsyma is called Maxima . Reduce became free software in 2008. Commercial systems include Mathematica and Maple , which are commonly used by research mathematicians, scientists, and engineers. Freely available alternatives include SageMath (which can act as

744-399: The later Nobel Prize laureate in physics Martinus Veltman , who designed a program for symbolic mathematics, especially high-energy physics, called Schoonschip (Dutch for "clean ship") in 1963. Other early systems include FORMAC . Using Lisp as the programming basis, Carl Engelman created MATHLAB in 1964 at MITRE within an artificial-intelligence research environment. Later MATHLAB

775-446: The needs of the users, but also the needs of the simplifier. For example, the computation of polynomial greatest common divisors is systematically used for the simplification of expressions involving fractions. This large amount of required computer capabilities explains the small number of general-purpose computer algebra systems. Significant systems include Axiom , GAP , Maxima , Magma , Maple , Mathematica , and SageMath . In

806-760: 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. 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

837-500: The tools to use the Win32 runtime environment , Cygwin implemented a POSIX -compatible environment in the form of a DLL. The brand motto is " Get that Linux feeling – on Windows ", although Cygwin doesn't have Linux in it. Cygwin began in 1995 as a project of Steve Chamberlain, a Cygnus engineer who observed that Windows NT and 95 used COFF as their object file format , and that GNU already included support for x86 and COFF, and

868-822: The use of computer algebra systems in primary and secondary-school classrooms. The primary reason for such advocacy is that computer algebra systems represent real-world math more than do paper-and-pencil or hand calculator based mathematics. This push for increasing computer usage in mathematics classrooms has been supported by some boards of education. It has even been mandated in the curriculum of some regions. Computer algebra systems have been extensively used in higher education. Many universities offer either specific courses on developing their use, or they implicitly expect students to use them for their course work. The companies that develop computer algebra systems have pushed to increase their prevalence among university and college programs. CAS-equipped calculators are not permitted on

899-423: 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. SageMath uses both students and professionals for development. The development of SageMath

930-520: Was changed for reasons of performance and POSIX correctness. Cygwin also recognises NTFS junction points and symbolic links and treats them as POSIX symbolic links, but it does not create them. The POSIX API for handling access control lists (ACLs) is supported. A Cygwin-specific version of the Unix mount command allows mounting Windows paths as "filesystems" in the Unix file space. Initial mount points can be configured in /etc/fstab , which has

961-457: Was made available to users on PDP-6 and PDP-10 systems running TOPS-10 or TENEX in universities. Today it can still be used on SIMH emulations of the PDP-10. MATHLAB (" math ematical lab oratory") should not be confused with MATLAB (" mat rix lab oratory"), which is a system for numerical computation built 15 years later at the University of New Mexico . In 1987, Hewlett-Packard introduced

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