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Computer Algebra System
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software Mathematical software is software used to mathematical model, model, analyze or calculate numeric, symbolic or geometric data. It is a type of application software which is used for solving mathematical problems or mathematical study. There are v ... with the ability to manipulate mathematical expressions In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed formula, well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constant (mathematics ... in a way similar to the traditional manual computations of mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained ( ...s and scienti ...
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Mathematical Software
Mathematical software is software Software is a collection of instructions Instruction or instructions may refer to: Computing * Instruction, one operation of a processor within a computer architecture instruction set * Computer program, a collection of instructions Music * I ... used to model In general, a model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. ..., analyze or calculate numeric, symbolic or geometric data. Evolution of mathematical software 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). Numerical analysis ... and symbolic computation In mathematics Mathematics (from Ancie ...
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Memory Management
Memory management is a form of resource management In organizational studies Organizational studies is "the examination of how individuals construct organizational structures, processes, and practices and how these, in turn, shape social relations and create institutions that ultimately influence p ... applied to computer memory In computing Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes and development of both computer hardware , hardware and soft .... The essential requirement of memory management is to provide ways to dynamically allocate portions of memory to programs at their request, and free it for reuse when no longer needed. This is critical to any advanced computer system where more than a single process A process is a series or set of activities that interact to produce a result; it may occur once-only or be recurrent or periodic. Things ca ...
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Martinus Veltman
Martinus Justinus Godefriedus "Tini" Veltman (; 27 June 1931 – 4 January 2021) was a Dutch theoretical physicist Theoretical physics is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, i .... He shared the 1999 Nobel Prize in physics The Nobel Prize in Physics is a yearly award given by the Royal Swedish Academy of Sciences for those who have made the most outstanding contributions for mankind in the field of physics. It is one of the five Nobel Prizes established by the will ... with his former PhD student Gerardus 't Hooft Gerardus (Gerard) 't Hooft (; born July 5, 1946) is a Dutch theoretical physicist and professor at Utrecht University Utrecht University (UU; nl, Universiteit Utrecht, formerly ''Rijksuniversiteit Utrecht'') is a public In public relat ... for their work on particle t ...
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Artificial Intelligence
Artificial intelligence (AI) is intelligence Intelligence has been defined in many ways: the capacity for abstraction Abstraction in its main sense is a conceptual process where general rules and concept Concepts are defined as abstract ideas or general notions that occur in the mind, ... demonstrated by machine A machine is any physical system with ordered structural and functional properties. It may represent human-made or naturally occurring device molecular machine A molecular machine, nanite, or nanomachine is a molecular component that produce ...s, unlike the natural intelligence displayed by humans and animals Animals (also called Metazoa) are multicellular Multicellular organisms are organism In biology, an organism (from Ancient Greek, Greek: ὀργανισμός, ''organismos'') is any individual contiguous system that embodies the L ..., which involves consciousness and emotionality. The distinction between the former and the la ...
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Computer Algebra System
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software Mathematical software is software used to mathematical model, model, analyze or calculate numeric, symbolic or geometric data. It is a type of application software which is used for solving mathematical problems or mathematical study. There are v ... with the ability to manipulate mathematical expressions In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed formula, well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constant (mathematics ... in a way similar to the traditional manual computations of mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained ( ...s and scienti ...
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SageMath
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 Mathematical software is software used to mathematical model, model, analyze or calculate numeric, symbolic or geometric data. It is a type of applica ... (CAS) with features covering many aspects of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ..., including algebra Algebra (from ar, الجبر, lit=reunion of broken parts, bonesetting, translit=al-jabr) is one of the areas of mathematics, broad areas of mathematics, together with number theory, geometry and mathematical analysis, analysis. In its most ge ..., combinatorics Combinatorics is an area ...
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Mathematica
Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning Machine learning (ML) is the study of computer algorithms that can improve automatically through experience and by the use of data. It is seen as a part of artificial intelligence. Machine learning algorithms build a model based on sample data ..., statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more technical sens ..., symbolic computation In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ..., manipulating matrices Matrix or MATRIX may refer to: Science ...
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Maple (software)
Maple is a symbolic and numeric computing environment as well as a multi-paradigm programming language Programming paradigms are a way to classify programming languages based on their features. Languages can be classified into multiple paradigms. Some paradigms are concerned mainly with implications for the execution model of the language, suc .... It covers several areas of technical computing, such as symbolic mathematics, numerical analysis, data processing, visualization, and others. A toolbox, MapleSim MapleSim is a Modelica Modelica is an object-oriented, declarative, multi-domain modeling language for Component-based software engineering, component-oriented modeling of complex systems, e.g., systems containing mechanical, electrical, elect ..., adds functionality for multidomain physical modeling and code generation. Maple's capacity for symbolic computing include those of a general-purpose computer algebra system A computer algebra system (CAS) or symboli ...
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Magma (computer Algebra System)
Magma is a computer algebra system A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software Mathematical software is software used to mathematical model, model, analyze or calculate numeric, symbolic or geometric data. It is a type of applica ... designed to solve problems in algebra Algebra (from ar, الجبر, lit=reunion of broken parts, bonesetting, translit=al-jabr) is one of the areas of mathematics, broad areas of mathematics, together with number theory, geometry and mathematical analysis, analysis. In its most ge ..., number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of devoted primarily to the study of the s and . German mathematician (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen ..., geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerne ...
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Maxima (software)
Maxima () is a computer algebra system A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software Mathematical software is software used to mathematical model, model, analyze or calculate numeric, symbolic or geometric data. It is a type of applica ... (CAS) based on a 1982 version of Macsyma Macsyma (; "Project MAC's SYmbolic MAnipulator") is one of the oldest general-purpose computer algebra systems still in wide use. It was originally developed from 1968 to 1982 at MIT's Project MAC. In 1982, Macsyma was licensed to Symbolics and be .... It is written in Common Lisp Common Lisp (CL) is a dialect of the Lisp programming language Lisp (historically LISP) is a family of programming language A programming language is a formal language In mathematics Mathematics (from Ancient Greek, Greek: ) incl ... and runs on all POSIX The Portable Operating System Interface (POSIX) is a family of standard Standard may refer to: ...
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Axiom (computer Algebra System)
Axiom is a free software, free, general-purpose computer algebra system. It consists of an interpreter environment, a compiler and a library, which defines a strongly typed hierarchy. History Two computer algebra systems named Scratchpad were developed by IBM. The first one was started in 1965 by James Griesmeat the request of Ralph E. Gomory, Ralph Gomory, and written in Fortran. The development of this software was stopped before any public release. The second Scratchpad, originally named Scratchpad II, was developed from 1977 on, at Thomas J. Watson Research Center, under the direction of Richard Dimick Jenks. The design is principally due to Richard D. Jenks (IBM Research), James H. Davenport (University of Bath), Barry M. Trager (IBM Research), David Y.Y. Yun (Southern Methodist University) and Victor S. Miller (IBM Research). Early consultants on the project were David Barton (University of California, Berkeley) and James W. Thatcher (IBM Research). Implementation include ...
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Polynomial Greatest Common Divisor
In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factorization, factor of both the two original polynomials. This concept is analogous to the greatest common divisor of two integers. In the important case of univariate polynomials over a field (mathematics), field the polynomial GCD may be computed, like for the integer GCD, by the Euclidean algorithm using polynomial long division, long division. The polynomial GCD is defined only up to the multiplication by an invertible constant. The similarity between the integer GCD and the polynomial GCD allows extending to univariate polynomials all the properties that may be deduced from the Euclidean algorithm and Euclidean division. Moreover, the polynomial GCD has specific properties that make it a fundamental notion in various areas of algebra. Typically, the root of a function, roots of the GCD of two polynomials are the common roots ...
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