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22-638: 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 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

44-520: 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

66-407: 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

88-406: 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

110-423: Is also growing now. A useful mathematical knowledge of such as algorism which exist before the invention of electronic computer , helped to mathematical software developing. On the other hand, by the growth of computing power (such as seeing on Moore's law ), the new treatment (for example, a new kind of technique such as data assimilation which combined numerical analysis and statistics ) needing conversely

132-574: Is available in web browsers, without the need to download or install any code. Low-level mathematical libraries intended for use within other programming languages: SageMath 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

154-581: 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

176-401: 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

198-604: 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. Mathematical software Numerical analysis and symbolic computation had been in most important place of the subject, but other kind of them

220-658: The IMSL , NMath and NAG libraries ; a free alternative is the GNU Scientific Library . A different approach is taken by the Numerical Recipes library, where emphasis is placed on clear understanding of algorithms. Many computer algebra systems (listed above) can also be used for numerical computations. Music mathematics software utilizes mathematics to analyze or synthesize musical symbols and patterns. A growing number of mathematical software

242-509: 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

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264-418: 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

286-1139: 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

308-819: The diversity of mathematical software will be kept. A software calculator allows the user to perform simple mathematical operations, like addition, multiplication, exponentiation and trigonometry. Data input is typically manual, and the output is a text label. Many mathematical suites are computer algebra systems that use symbolic mathematics . They are designed to solve classical algebra equations and problems in human readable notation. Many tools are available for statistical analysis of data. See also Comparison of statistical packages . The Netlib repository contains various collections of software routines for numerical problems, mostly in Fortran and C . Commercial products implementing many different numerical algorithms include

330-822: 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

352-399: 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

374-446: 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

396-589: The progress of the mathematical science or applied mathematics . The progress of mathematical information presentation such as TeX or MathML will demand to evolution form formula manipulation language to true mathematics manipulation language (notwithstanding the problem that whether mathematical theory is inconsistent or not). And popularization of general purpose mathematical software, special purpose mathematical software so called one purpose software which used special subject will alive with adapting for environment progress at normalization of platform. So

418-816: 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

440-424: 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

462-515: 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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484-783: 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. 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

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