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Fermat

Computer algebra system

Fermat (named after Pierre de Fermat) is a freeware program developed by Prof. Robert H. Lewis of Fordham University. It is a computer algebra system, in which items being computed can be integers (of arbitrary size), rational numbers, real numbers, complex numbers, modular numbers, finite field elements, multivariable polynomials, rational functions, or polynomials modulo other polynomials. The main areas of application are multivariate rational function arithmetic and matrix algebra over rings of multivariate polynomials or rational functions. Fermat does not do simplification of transcendental functions or symbolic integration.
A session with Fermat usually starts by choosing rational or modular "mode" to establish the ground field (or ground ring) F as \mathbb{Z} or \mathbb{Z}/n. On top of this may be attached any number of symbolic variables t_1, t_2, \dots, t_n, thereby creating the polynomial ring F and its quotient field. Further, some polynomials p, q, \dots involving some of the t_i can be chosen to mod out with, creating the quotient ring F(t_1, t_2, \dots)/(p, q, \dots). Finally, it is possible to allow Laurent polynomials, those with negative as well as positive exponents. Once the computational ring is established in this way, all computations are of elements of this ring. The computational ring can be changed later in the session.
The polynomial gcd procedures, which call each other in a highly recursive manner, are about 7000 lines of code.
Fermat has extensive built-in primitives for array and matrix manipulations, such as submatrix, sparse matrix, determinant, normalize, column reduce, row echelon, Smith normal form, and matrix inverse. It is consistently faster than some well known computer algebra systems, especially in multivariate polynomial gcd. It is also space efficient.
The basic data item in Fermat is a multivariate rational function or quolynomial. The numerator and denominator are polynomials with no common factor. Polynomials are implemented recursively as general linked lists, unlike some systems that implement polynomials as lists of monomials. To implement (most) finite fields, the user finds an irreducible monic polynomial in a symbolic variable, say p(t_1), and commands Fermat to mod out by it. This may be continued recursively, q(t_2, t_1), etc. Low level data structures are set up to facilitate arithmetic and gcd over this newly created ground field. Two special fields, GF(2^{8}) and GF(2^{16}), are more efficiently implemented at the bit level.
To help implement the Dixon resultant technique, special features have been added to the determinant function. These provide a dramatic increase in the speed of resultant calculations with systems of polynomial equations that exhibit symmetry.
Fermat provides a complete programming language. Programs and data can be saved to an ordinary text file that can be examined as such, read during a later session, or read by some other software system.

Latest version of Fermat is 6.17 and it was released on 2017-07-12.

Developed by Robert H. Lewis

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    Tags: Computer Algebra System Software For Linux, Computer Algebra System Software For Macos, Computer Algebra System Software For Windows, Crossplatform Free Software, Free Computer Algebra Systems, Computer Algebra Systems
  • PARIGP by Henri Cohen, Karim Belabas, et al., at the Université Bordeaux 1

    PARI/GP is a computer algebra system with the main aim of facilitating number theory computations. Versions 2.1.0 and higher are distributed under the GNU General Public License. It runs on most...

    Latest version of PARI/GP is 2.9.2 and it was released on 2017-03-22.

    Tags: 1985 Software, C Libraries, Commandline Software, Computer Algebra System Software For Linux, Crossplatform Free Software, Free Computer Algebra Systems, Free Software Programmed In C, Portable Software
  • Macaulay

    Macaulay is a computer algebra system for doing polynomial computations, particularly Gröbner basis calculations. Macaulay is designed for solving problems in commutative algebra and algebraic...

    Tags: Computer Algebra System Software For Linux, Computer Algebra Systems, Free Software Programmed In C
  • MapleSim by Maplesoft

    MapleSim is a Modelica-based, multi-domain modeling and simulation tool developed by Maplesoft. MapleSim generates model equations, runs simulations, and performs analyses using the symbolic and...

    Tags: Maplesoft, Plotting Software, Mathematical Optimization Software, Computer Algebra System Software For Linux, Computer Algebra System Software For Windows, Computer Algebra System Software For Macos, Crossplatform Software, Simulation Software
  • Mathomatic by George Gesslein II

    Mathomatic is a free, portable, general-purpose computer algebra system (CAS) that can symbolically solve, simplify, combine, and compare algebraic equations, and can perform complex number,...

    Latest version of Mathomatic is 16.0.5 and it was released on 2012-10-21.

    Tags: 1987 Software, Android Software, C Libraries, Commandline Software, Computer Algebra System Software For Linux, Computer Algebra System Software For Macos, Computer Algebra System Software For Windows, Crossplatform Free Software, Embedded Linux, Free Computer Algebra Systems, Free Educational Software, Free Software Programmed In C, Ios Software, Nintendo Ds Homebrew, Portable Software
  • Xcas by Bernard Parisse

    Xcas is a user interface to Giac, a free, basic Computer Algebra System (CAS) for Windows, macOS and Linux/Unix. Giac can be used directly inside software written in C++. Xcas and Giac are...

    Latest version of Xcas is 1.2.3 and it was released on {{release date|2017|01|df=yes}}.

    Tags: C Libraries, Computer Algebra System Software For Linux, Computer Algebra System Software For Macos, Computer Algebra System Software For Windows, Free Computer Algebra Systems, Free Mathematics Software, Free Software Programmed In C, Mathematical Software
  • SymPy by Independent group of people

    SymPy is a Python library for symbolic computation. It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live...

    Latest version of SymPy is 1.1.1 and it was released on 2017-07-22.

    Tags: Articles With Example Python Code, Computer Algebra System Software For Linux, Computer Algebra System Software For Macos, Computer Algebra System Software For Windows, Free Computer Algebra Systems, Free Mathematics Software, Free Software Programmed In Python, Python Scientific Libraries
  • SageMath

    SageMath (previously Sage or SAGE, "System for Algebra and Geometry Experimentation") is mathematical software with features covering many aspects of mathematics, including algebra, combinatorics,...

    Latest version of SageMath is 8.0 and it was released on 2017-07-21.

    Tags: Articles With Example Python Code, Computer Algebra System Software For Linux, Computer Algebra System Software For Macos, Computer Algebra System Software For Windows, Free And Opensource Android Software, Free Computer Algebra Systems, Free Educational Software, Free Mathematics Software, Free Software Programmed In Python, Mathematical Software, Python Scientific Libraries
  • Maxima by Macsyma group at Project MAC and volunteer contributors

    Maxima is a computer algebra system (CAS) based on a 1982 version of Macsyma. It is written in Common Lisp and runs on all POSIX platforms such as macOS, Unix, BSD, and Linux, as well as under...

    Latest version of Maxima is 5.40.0 and it was released on 2017-05-30.

    Tags: Common Lisp Software, Computer Algebra System Software For Linux, Computer Algebra System Software For Macos, Computer Algebra System Software For Windows, Crossplatform Free Software, Free Computer Algebra Systems, Free Educational Software, Free Software Programmed In Lisp, Software That Uses Wxwidgets
  • Cantor by KDE Education Project

    Cantor is a free software mathematics application for scientific statistics and analysis. It is part of the KDE Software Compilation 4, and was introduced with the 4.4 release as part of the KDE...

    Latest version of Cantor is 17.08.0 and it was released on 2017-08-17.

    Tags: Computational Notebook, Computer Algebra System Software For Linux, Computer Algebra System Software For Macos, Computer Algebra System Software For Windows, Educational Math Software, Free Computer Algebra Systems, Free Educational Software, Kde Education Project, Science Software That Uses Qt
  • Wolfram Mathematica by Wolfram Research

    Wolfram Mathematica (usually termed Mathematica, Mathematica software suite) is a mathematical symbolic computation program, sometimes termed a computer algebra system or program, used in many...

    Tags: 1988 Software, Astronomical Databases, Computational Notebook, Computer Algebra System Software For Linux, Computer Algebra System Software For Macos, Computer Algebra System Software For Windows, Computer Algebra Systems, Crossplatform Software, Data Mining And Machine Learning Software, Earth Sciences Graphics Software, Econometrics Software, Formula Editors, Interactive Geometry Software, Mathematical Optimization Software, Mathematical Software, Numerical Analysis Software For Linux, Numerical Analysis Software For Macos, Numerical Analysis Software For Windows, Numerical Programming Languages, Numerical Software, Physics Software, Pirelated Software, Plotting Software, Proprietary Commercial Software For Linux, Proprietary Crossplatform Software, Regression And Curve Fitting Software, Simulation Programming Languages, Software That Uses Qt, Statistical Programming Languages, Theorem Proving Software Systems, Time Series Software, Wolfram Research
  • Speakeasy by Speakeasy Computing Corporation

    Speakeasy is a numerical computing interactive environment also featuring an interpreted programming language. It was initially developed for internal use at the Physics Division of Argonne National...

    Latest version of Speakeasy is IV Iota and it was released on 2006.

    Tags: Data Analysis Software, Mathematical Software, Physics Software, Proprietary Crossplatform Software, Numerical Analysis Software For Linux, Numerical Analysis Software For Macos, Numerical Analysis Software For Windows, Computer Algebra System Software For Windows, Computer Algebra System Software For Macos, Computer Algebra System Software For Linux, Array Programming Languages, Numerical Programming Languages, Numerical Linear Algebra, Statistical Programming Languages, Simulation Programming Languages, Programming Languages Created In 1964
  • GAMS by GAMS Development Corporation

    The General Algebraic Modeling System (GAMS) is a high-level modeling system for mathematical optimization. GAMS is designed for modeling and solving linear, nonlinear, and mixed-integer...

    Latest version of GAMS is 24.9.1 and it was released on 2017-08-30.

    Tags: Computer Algebra Systems, Mathematical Optimization Software
  • FORM by Jos Vermaseren, et al.

    FORM is a symbolic manipulation system. It reads text files containing definitions of mathematical expressions as well as statements that tell it how to manipulate these expressions. Its original...

    Tags: Computer Algebra Systems, Free Computer Algebra Systems, Free Software Programmed In C, Mathematical Software, Physics Software, Science Software
  • Derive by Texas Instruments

    Derive was a computer algebra system, developed as a successor to muMATH by the Soft Warehouse in Honolulu, Hawaii, now owned by Texas Instruments. Derive was implemented in , also by Soft...

    Tags: 1988 Software, Computer Algebra Systems, Discontinued Software, Lisp Software, Science Software For Windows
  • Algebrator by SoftMath

    Algebrator (also called Softmath) is a computer algebra system (CAS), which was developed in the late 1990s by Neven Jurkovic of Softmath, San Antonio, Texas. This is a CAS specifically geared...

    Latest version of Algebrator is 4.2 and it was released on {{Start date and age|2009}}.

    Tags: Computer Algebra Systems, Educational Math Software
  • mXparser

    mXparser is an open-source mathematical expressions parser/evaluator providing abilities to calculate various expressions at a run time. Expressions definitions are given as plain text, then...

    Latest version of mXparser is 4.0.0 and it was released on 2017-03-27.

    Tags: Free Mathematics Software, Parsing, 2010 Software, Free Software Programmed In Java, Free Software Programmed In C Sharp, Software Using The Bsd License, Free Mobile Software, Software That Uses Mono, Free And Opensource Android Software, Net Framework Software, Computer Algebra Systems
  • WIRIS by Maths for More

    WIRIS is a set of proprietary HTML-based JavaScript tools which can author and edit mathematical formulas, execute mathematical problems and show mathematical graphics on the Cartesian coordinate...

    Tags: Interactive Geometry Software, Mathematical Software, Formula Editors, Formula Manipulation Languages, Computer Algebra Systems, Crossplatform Software
  • Analytica by Lumina Decision Systems

    Analytica is a visual software package developed by Lumina Decision Systems for creating, analyzing and communicating quantitative decision models. As a modeling environment, it is interesting in...

    Tags: Mathematical Modeling, Mathematical Optimization Software, Science Software, Statistical Programming Languages, Visual Programming Languages, Numerical Programming Languages, Numerical Software, Array Programming Languages, Science Software For Windows, Computer Algebra Systems, Operations Research, Plotting Software, Mathematical Optimization
  • Mathcad by Mathsoft,PTC

    Mathcad is computer software primarily intended for the verification, validation, documentation and re-use of engineering calculations. First introduced in 1986 on DOS, it was the first to introduce...

    Tags: Computerrelated Introductions In 1986, Computer Algebra Systems, Numerical Software, Proprietary Software, Windowsonly Software
  • Opera Mail by Opera Software

    Opera Mail (formerly known as M2) is the email and news client developed by Opera Software. It was an integrated component within the Opera web browser from version 2 through 12. With the release of...

    Tags: Freeware, Email Client Software For Linux, Macos Email Clients, Opera Software, Usenet Clients, Windows Email Clients, Proprietary Freeware For Linux
  • OptiX by Nvidia

    Nvidia OptiX (OptiX Application Acceleration Engine) is a general purpose ray tracing API for rendering, baking, collision detection, A.I. queries, etc. OptiX is not a renderer but can implement...

    Latest version of OptiX is 4.0.0 and it was released on 2016-07-25.

    Tags: Nvidia Software, Proprietary Commercial Software For Linux, Proprietary Freeware For Linux, Ray Tracing
  • PhysX by NVIDIA Corporation

    PhysX is a proprietary realtime physics engine middleware SDK. PhysX was authored at NovodeX, an ETH Zurich spin-off. In 2004, NovodeX was acquired by Ageia, and in February 2008, Ageia was acquired...

    Latest version of PhysX is 9.17.0527 and it was released on 2017-06-29.

    Tags: Computer Physics Engines, Nvidia Software, Macos Programming Tools, Playstation 3 Software, Playstation 4 Software, Programming Tools For Windows, Proprietary Commercial Software For Linux, Proprietary Freeware For Linux, Science Software For Macos, Science Software For Windows, Virtual Reality, Wii Software, Xbox 360 Software
  • AMD Radeon Crimson by Advanced Micro Devices

    AMD Radeon Software Crimson (formerly named ATI Catalyst and AMD Catalyst) is a device driver and utility software package for Advanced Micro Devices's graphics cards and APUs. It runs on Microsoft...

    Tags: Advanced Micro Devices Software, Ati Technologies, Device Drivers, Linux Drivers, Proprietary Freeware For Linux, Rendering Apis Available On Linux, Proprietary Software That Uses Qt, Thirdparty Linux Kernel Modules, X Window System
  • Lphant

    Lphant was a peer-to-peer file sharing client for the Microsoft Windows, Linux and Mac OS operating systems, which supports the eDonkey Network and the BitTorrent protocol. It was available in 19...

    Tags: Windowsonly Freeware, Bittorrent Clients, Proprietary Freeware For Linux, File Sharing Software For Linux, C Sharp Software
  • Comic Seer by Adam Jordan, Xylasoft

    Comic Seer (Desktop) is a Freeware sequential image viewer application for Microsoft Windows and Linux, specifically used for viewing and reading Comic Book Archive files containing image formats,...

    Latest version of Comic Seer (Desktop) is 2.51-3/4, 2.65(metro app,8.99$) and it was released on Dec 2014, Aug 2015(metro app).

    Tags: Image Viewers, 2012 Software, 2013 Software, 2014 Software, Linux Image Viewers, Proprietary Freeware For Linux, Windows Graphicsrelated Software, Graphics Software That Uses Qt
  • Skype by Skype Technologies

    Skype is an instant messaging app that provides online text message and video chat services. Users may transmit both text and video messages, and may exchange digital documents such as images, text,...

    Tags: Skype, 2003 Software, 2011 Acquisitions, Android Software, Companies In The Prism Network, Crossplatform Software, Estonian Brands, Estonian Inventions, Freeware, Instant Messaging Clients, Ios Software, Macos Instant Messaging Clients, Microsoft Acquisitions, Microsoft Divisions, Peertopeer Software, Pocket Pc Software, Portable Software, Proprietary Freeware For Linux, Proprietary Software That Uses Qt, Silver Lake Partners Companies, Symbian Software, Universal Windows Platform Apps, Videoconferencing Software For Linux, Videotelephony, Voice Over Ip Clients For Linux, Voip Companies Of The United States, Voip Services, Voip Software, Windows Instant Messaging Clients, Windows Mobile Standard Software, Windows Phone Software, Android Auto Software
  • Kerkythea by Ioannis Pantazopoulos

    Kerkythea is a standalone rendering system that supports raytracing and Metropolis light transport, uses physically accurate materials and lighting, and is distributed as freeware. Currently, the...

    Latest version of Kerkythea is Kerkythea 2008 Echo and it was released on 2008-10-18.

    Tags: 3d Rendering Software For Linux, Freeware 3d Graphics Software, Global Illumination Software, Proprietary Freeware For Linux, Rendering Systems
  • Mental Ray by Nvidia

    Mental Ray (stylized as mental ray) is a production-quality rendering application developed by Mental Images (Berlin, Germany). Mental Images was bought in December 2007 by NVIDIA. As the name...

    Tags: Global Illumination Software, Rendering Systems, 3d Rendering Software For Linux, Proprietary Freeware For Linux
  • Gelato by Nvidia Corporation

    Gelato (from Italian language: "Frozen", or "Icecream") is a hardware-accelerated, offline renderer created by graphics card manufacturer Nvidia. It was originally intended for use with its Quadro...

    Latest version of Gelato is 2.2 Release 1 and it was released on May 2008.

    Tags: 3d Rendering Software For Linux, Freeware 3d Graphics Software, Nvidia Software, Proprietary Freeware For Linux
  • Soulseek by Nir Arbel

    Soulseek is a peer-to-peer (P2P) file-sharing network and application. The term Soulseek might refer to (1) one of the two networks, or (2) one of the three official user client interfaces. Soulseek...

    Tags: File Sharing Software, 2002 Software, Windows File Sharing Software, Macos File Sharing Software, File Sharing Software For Linux, Classic Mac Os Software, Proprietary Freeware For Linux
  • Fractint by Stone Soup Group

    Fractint is a freeware computer program that can render and display many kinds of fractals. The program originated on the MS-DOS platform, but has since been ported to Linux and Microsoft Windows....

    Latest version of Fractint is 20.04p14 and it was released on 2015-08-22.

    Tags: 1988 Software, Fractal Software, Numerical Software, Cellular Automaton Software, Dos Software, Proprietary Freeware For Linux