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Scientific area at the interface between computer science and mathematics
In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to
Computer_algebra
Mathematical software
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions
Computer_algebra_system
comparison of computer algebra systems (CAS). A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects,
List of computer algebra systems
List_of_computer_algebra_systems
Algebraic manipulation of "true" and "false"
mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables
Boolean_algebra
Computer algebra system
computer algebra system. It consists of an interpreter environment, a compiler and a library, which defines a strongly typed hierarchy. Two computer algebra
Axiom (computer algebra system)
Axiom_(computer_algebra_system)
Branch of mathematics
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems
Algebra
Computer system for solving algebra problems
is a computer algebra system designed to solve problems in algebra, number theory, geometry and combinatorics. It is named after the algebraic structure
Magma (computer algebra system)
Magma_(computer_algebra_system)
computer algebra system (CAS) is a software product designed for manipulation of mathematical formulae. The principal objective of a computer algebra
List of open-source software for mathematics
List_of_open-source_software_for_mathematics
Computer algebra system
Fermat (named after Pierre de Fermat) is a computer algebra system developed by Prof. Robert H. Lewis of Fordham University. It can work on integers (of
Fermat (computer algebra system)
Fermat_(computer_algebra_system)
Computer algebra system
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
Derive (computer algebra system)
Derive_(computer_algebra_system)
Computer algebra system
algorithms and programming) is an open-source computer algebra system for computational discrete algebra with particular emphasis on computational group
GAP_(computer_algebra_system)
Field of mathematics
Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which
Numerical_linear_algebra
REDUCE is a general-purpose computer algebra system originally geared towards applications in physics. The development of REDUCE was started in 1963 by
Reduce (computer algebra system)
Reduce_(computer_algebra_system)
also includes a programming language and computer algebra abilities. PARI/GP is a widely used computer algebra system designed for fast computations in
List of numerical-analysis software
List_of_numerical-analysis_software
Technique to solve differential equations
designed for the computer era with the goal of "computing with functions instead of numbers." In conjunction with a computer algebra system such as Mathematica
Homotopy_analysis_method
Area of mathematics
complexity, numerical methods and computer algebra. Computational mathematics refers also to the use of computers for mathematics itself. This includes
Computational_mathematics
Branch of mathematics
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems
Algebraic_geometry
Application of mathematical methods to other fields
the mathematics of computation (for example, theoretical computer science, computer algebra, numerical analysis). Statistics is probably the most widespread
Applied_mathematics
Specialist field of computer science
include: Computer algebra, including symbolic computation in fields such as statistics, equation solving, algebra, calculus, geometry, linear algebra, tensor
Computational_science
Approach to teaching mathematics that emphasizes the use of computers
manage homework assignments. Computer algebra - computer algebra systems, list of computer algebra systems, free computer algebra software. Computational geometry
Computer-based mathematics education
Computer-based_mathematics_education
Computer algebra system
for Algebra and Geometry Experimentation") is a computer algebra system (CAS) with features covering many aspects of mathematics, including algebra, combinatorics
SageMath
Series of Casio graphing calculators
The Casio Algebra FX series was a line of graphing calculators manufactured by Japanese electronics company Casio Computer Co., Ltd from 1999 to 2003.
Casio_Algebra_FX_Series
Mathematical computing environment
capacity for symbolic computing include those of a general-purpose computer algebra system. For instance, it can manipulate mathematical expressions and
Maple_(software)
Computer algebra system
Cadabra is a computer algebra system designed specifically for the solution of problems encountered in classical field theory, quantum field theory and
Cadabra_(computer_program)
Algebra based on a vector space with a quadratic form
mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure
Clifford_algebra
Algebraic structure designed for geometry
geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is
Geometric_algebra
Basic concepts of algebra
{b^{2}-4ac}}}{2a}}}}}} Elementary algebra, also known as high school algebra or college algebra, encompasses the basic concepts of algebra. It is often contrasted
Elementary_algebra
Branch of mathematics
Linear algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b
Linear_algebra
Software used in mathematical applications
mathematical suites are computer algebra systems that use symbolic mathematics. They are designed to solve classical algebra equations and problems in
Mathematical_software
Computer algebra system
is a computer algebra system for polynomial computations with special emphasis on the needs of commutative and non-commutative algebra, algebraic geometry
Singular_(software)
Algebraic structure with a binary operation
In abstract algebra, a magma, binar, or, rarely, groupoid is a basic kind of algebraic structure. Specifically, a magma consists of a set equipped with
Magma_(algebra)
British-American scientist (born 1959)
29 August 1959) is a British-American computer scientist, physicist, and businessman. He works in computer algebra and theoretical physics. In 2012, he
Stephen_Wolfram
Computer algebra system
is a free and open source software software package for performing computer algebra calculations in mathematics and the physical sciences. It is written
Maxima_(software)
symbolic computation In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area
Glossary_of_computer_science
Predecessor of computer algebra program Mathematica
Symbolic Manipulation Program (SMP) was a computer algebra system designed by Chris A. Cole and Stephen Wolfram at Caltech circa 1979. It was initially
SMP_(computer_algebra_system)
Subfield of computer science and mathematics
number theory and algebra. Work in this field is often distinguished by its emphasis on mathematical technique and rigor. Theoretical computer science is closely
Theoretical_computer_science
Computer algebra system
Macaulay2 is a free computer algebra system created by Daniel Grayson (from the University of Illinois at Urbana–Champaign) and Michael Stillman (from
Macaulay2
Overview of and topical guide to computer science
complexity, probability, algebra, and number theory to invent and break codes, and analyze the security of cryptographic protocols. Computer architecture – The
Outline_of_computer_science
Computer algebra system (CAS)
MuPAD is a computer algebra system (CAS). Originally developed by the MuPAD research group at the University of Paderborn, Germany, development was taken
MuPAD
Canadian mathematician (born 1947)
of Toronto. Geddes is probably best known for co-founding the Maple computer algebra system, now in widespread academic use around the world. He is also
Keith_Geddes
Algorithm in computer algebra
FGLM is one of the main algorithms in computer algebra, named after its designers, Faugère, Gianni, Lazard and Mora. They introduced their algorithm in
FGLM_algorithm
British computer scientist
September 1953) is a British computer scientist who works in computer algebra. Having done his PhD and early research at the Computer Laboratory, University
James_H._Davenport
Educational programs combining academic and technical skills for workforce preparation
learning, computer vision, list of artificial intelligence projects, comparison of deep learning software. Computer algebra - computer algebra systems,
Career and technical education
Career_and_technical_education
American mathematician
for being one of the creators (with Daniel Grayson) of the Macaulay2 computer algebra system. Michael Stillman completed his PhD at Harvard University in
Michael_Stillman
Unix-like systems. KCalc, Linux based scientific calculator Maxima: a computer algebra system which bignum integers are directly inherited from its implementation
List of arbitrary-precision arithmetic software
List_of_arbitrary-precision_arithmetic_software
Computer Scientist, Entrepreneur
Uruguayan Canadian and Swiss computer scientist and entrepreneur. He is best known for his contributions to the Maple computer algebra system and the creation
Gaston_Gonnet
Topics referred to by the same term
Axioms (album), a 1999 album by Asia Axiom (computer algebra system), a free, general-purpose computer algebra system AXIOM (camera), a professional grade
Axiom_(disambiguation)
Python library for symbolic computation
an open-source Python library for symbolic computation. It provides computer algebra capabilities either as a standalone application, as a library to other
SymPy
Programming language which first appeared in 1990
It is the successor of A# as the extension language of the Axiom computer algebra system. Aldor combines imperative, functional, and object-oriented
Aldor
Computer algebra system
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
PARI/GP
Topics referred to by the same term
category of sets Regular chains in computer algebra Regular element (disambiguation), certain kinds of elements of an algebraic structure Regular extension of
Regular
Multivalued function in mathematics
physics. Prompted by this, Rob Corless and developers of the Maple computer algebra system realized that "the Lambert W function has been widely used in
Lambert_W_function
Topics referred to by the same term
environment A Sharp (Axiom), a programming language for the Axiom computer algebra system A♯1 Roller Rager, 2009 song by CKY This disambiguation page
A-sharp
Associative algebra together with a Lie bracket that satisfies Leibniz's law
In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz's law; that is, the bracket is also
Poisson_algebra
Branch of physics
interaction or decay (computer algebra) and event generators (stochastic methods). Computer algebra: Many of the computer algebra languages were developed
Computational particle physics
Computational_particle_physics
mathematics and computational mathematics, with one major exception in computer algebra. Closed-form formulas for polynomial roots exist only when the degree
Polynomial_root-finding
Branch of mathematics
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations
Abstract_algebra
Russian mathematician and professor (1947–2021)
of Algebraic and Quantum Computations. His research interests were concentrated in computer algebra, symbolic and algebraic computations, algebraic and
Vladimir_Gerdt
Sequence of operations for a task
In mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ ) is a finite sequence of mathematically rigorous instructions, typically used to solve
Algorithm
Dutch mathematician and computer scientist
(born 1971) is a Dutch mathematician and computer scientist, specializing in algebraic analysis and computer algebra. He is the primary developer of GNU TeXmacs
Joris_van_der_Hoeven
Method for evaluating indefinite integrals
computer algebra systems to find antiderivatives. It is named after the American mathematician Robert Henry Risch, a specialist in computer algebra who
Risch_algorithm
Study of Lie groups, Lie algebras and differential equations
subgroups generate the Lie algebra. The structure of a Lie group is implicit in its algebra, and the structure of the Lie algebra is expressed by root systems
Lie_theory
Mathematical construct in computer algebra
mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular
Gröbner_basis
electrical substations, and Lightning List of computer algebra systems - Computer algebra system List of computer simulation software List of discrete event
List of computer-aided engineering software
List_of_computer-aided_engineering_software
In computer algebra, a regular semi-algebraic system is a particular kind of triangular system of multivariate polynomials over a real closed field. Regular
Regular_semi-algebraic_system
Branch of functional analysis
In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with
Operator_algebra
Study of discrete mathematical structures
closely related to computability. Petri nets and process algebras are used to model computer systems, and methods from discrete mathematics are used in
Discrete_mathematics
Computer algebra system
free computer algebra system released under the GNU General Public License. The name is a recursive acronym for "GiNaC is Not a CAS" (Computer Algebra System)
GiNaC
Algorithms for computing Gröbner bases
In computer algebra, the Faugère F4 algorithm, by Jean-Charles Faugère, computes the Gröbner basis of an ideal of a multivariate polynomial ring. The algorithm
Faugère's F4 and F5 algorithms
Faugère's_F4_and_F5_algorithms
compilable with Windows. The Unix and Linux versions do not contain a computer algebra subsystem. Euler Math Toolbox originated in 1988 as a program for Atari
Euler_Mathematical_Toolbox
Device used for calculations
statistical calculations. Some calculators even have the ability to do computer algebra. Graphing calculators can be used to graph functions defined on the
Calculator
abstract algebra. Algebraic computation An older name of computer algebra. Algebraic geometry a branch that combines techniques from abstract algebra with
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Topics referred to by the same term
Erable, a computer algebra system integrated into the HP 40/49/50 series of Hewlett-Packard scientific calculators Xcas/Giac, a computer algebra system integrated
HP_CAS
Hidden subgroup problem: framework for quantum algorithms based on hidden algebraic structure Non-local quantum computation: quantum-information task involving
List_of_algorithms
Schoonschip was one of the first computer algebra systems, developed in 1963 by Martinus J. G. Veltman, for use in particle physics. "Schoonschip" refers
Schoonschip
Statement in mathematical combinatorics
achieved using a combination of Boolean satisfiability (SAT) solving and computer algebra systems (CAS). The proof was generated automatically using the SAT+CAS
Ramsey's_theorem
Software projects developed at universities
(Wisconsin–Madison) Macaulay2 – computer algebra system for algebraic geometry and commutative algebra (Illinois and Cornell) Macsyma – computer algebra system (MIT) Magma
List of software developed at universities
List_of_software_developed_at_universities
Computer algebra system
Xcas is a user interface to Giac, which is an open source computer algebra system (CAS) for Windows, macOS and Linux among many other platforms. Giac can
Xcas
Reasoning about equations with free variables
and algebraic description of models appropriate for the study of various logics (in the form of classes of algebras that constitute the algebraic semantics
Algebraic_logic
Mathematical software
myexpr = 8*x^3; FORM was started in 1984 as a successor to Schoonschip, an algebra engine developed by M. Veltman. It was initially coded in FORTRAN 77, but
FORM (symbolic manipulation system)
FORM_(symbolic_manipulation_system)
Calculator designed to calculate problems in science, engineering, and mathematics
as by numerical computing, computer algebra, statistical, and spreadsheet software packages running on personal computers. Both desktop and mobile software
Scientific_calculator
Computer algebra system
SymbolicC++ is a general purpose computer algebra system written in the programming language C++. It is free software released under the terms of the GNU
SymbolicC++
Computational software program
Fourth-generation programming language Functional programming List of computer algebra systems List of computer simulation software List of information graphics software
Wolfram_Mathematica
List of notable software written in or for the C++ programming language
library General Polygon Clipper — polygon clipping library GiNaC — computer algebra system that uses Class Library for Numbers for implementing arbitrary-precision
List of C++ software and tools
List_of_C++_software_and_tools
Type of functional equation (mathematics)
The Computer Algebra Program Maxima - a Tutorial (in Maxima documentation on SourceForge). Archived from the original on 2022-10-04. "Basic Algebra and
Differential_equation
Decomposing n-space into cells in which each of a set of polynomials has constant sign
cylindrical algebraic decomposition (CAD) is a notion, along with an algorithm to compute it, that is fundamental for computer algebra and real algebraic geometry
Cylindrical algebraic decomposition
Cylindrical_algebraic_decomposition
Concept in computer algebra
In computer algebra, an Ore algebra is a special kind of iterated Ore extension that can be used to represent linear functional operators, including linear
Ore_algebra
Operation in mathematical calculus
this purpose. With the spread of computers, many professionals, educators, and students have turned to computer algebra systems that are specifically designed
Integral
Electronic calculator capable of plotting graphs
have a computer algebra system (CAS), which means that they are capable of producing symbolic results. These calculators can manipulate algebraic expressions
Graphing_calculator
Computer algebra system
Normaliz is a free computer algebra system developed by Winfried Bruns, Robert Koch (1998–2002), Bogdam Ichim (2007/08) and Christof Soeger (2009–2016)
Normaliz
Types of special mathematical functions
\end{aligned}}} The incomplete gamma functions are available in various of the computer algebra systems. Even if unavailable directly, however, incomplete function
Incomplete_gamma_function
Measure of a mathematical object studied in the field of algebraic geometry
are purely algebraic and rely on commutative algebra. Some are restricted to algebraic varieties while others apply also to any algebraic set. Some are
Dimension of an algebraic variety
Dimension_of_an_algebraic_variety
Computer algebra system
Cambridge Algebra System (CAMAL) is a computer algebra system written in Cambridge University by David Barton, Steve Bourne, and John Fitch. It was initially
Cambridge_Algebra_System
Integer
George (1992). "Chapter 2: Algebra of Polynomials, Rational Functions, and Power Series". Algorithms for Computer Algebra (1st ed.). Boston: Kluwer Academic
−1
Branch of elementary mathematics
Selected Papers. Springer. ISBN 978-3-319-49463-0. Cohen, Joel S. (2003). Computer Algebra and Symbolic Computation: Mathematical Methods. CRC Press. ISBN 978-1-4398-6370-1
Arithmetic
Algorithms for zeros of functions
specifically, the study of root-finding algorithms belongs to computer algebra, since algebraic properties of polynomials are fundamental for the most efficient
Root-finding_algorithm
Part of algebraic geometry devoted to the elimination of variables between polynomials
polynomial equations, such as Gröbner bases, which were needed for computer algebra. The field of elimination theory was motivated by the need of methods
Elimination_theory
Programming language
Pyrex. Cython was forked from Pyrex in 2007 by developers of the Sage computer algebra package, because they were unhappy with Pyrex's limitations and could
Cython
Programming tool blending code and documents
are widely used for statistics, data science, machine learning, and computer algebra. At the notebook core is the idea of literate programming tools which
Notebook_interface
Topics referred to by the same term
using previous values of the function Reduce (computer algebra system), a general-purpose computer algebra system geared towards applications in physics
Reduction
COMPUTER ALGEBRA
COMPUTER ALGEBRA
Boy/Male
Muslim
Compiler of Hadith
Boy/Male
Irish
From an Irish name meaning “â€one who aids or assists.â€â€ It is usually translated as Terence and Terry, two names that have become strongly associated with Ireland. Turlough O’Carolan was a 17th century blind harpist and composer who wrote one of the most haunting pieces of Irish music, “â€O’Carolan’s Concerto.â€â€
Male
German
Middle High German byname HEIDEN means "heathen." The composer Josef Haydn's surname was a respelling of this name.
Boy/Male
Irish
From an Irish name meaning “â€one who aids or assists.â€â€ It is usually translated as Terence and Terry, two names that have become strongly associated with Ireland. Turlough O’Carolan was a 17th century blind harpist and composer who wrote one of the most haunting pieces of Irish music, “â€O’Carolan’s Concerto.â€â€
Boy/Male
Hindu, Indian, Sanskrit
Compiler of the Vedas
Boy/Male
Latin
He who loves God. Famous Bearer: late composer Wolfgang Amadeus Mozart.
Boy/Male
Indian, Sanskrit
Unattained; Cannot be Competed with
Boy/Male
Arabic, Muslim
Abu Isa Muhammad Al-tirmidhi; Compiler of the One Collection of Prophet Muhammad
Girl/Female
Muslim
To compete with pride
Boy/Male
Latin
He who loves God. Famous Bearer: late composer Wolfgang Amadeus Mozart.
Girl/Female
Arabic, Muslim
To Compete with Pride
Boy/Male
Tamil
Computer
Boy/Male
Arabic, Muslim
Compiler of Hadith
Boy/Male
Irish
From an Irish name meaning “â€one who aids or assists.â€â€ It is usually translated as Terence and Terry, two names that have become strongly associated with Ireland. Turlough O’Carolan was a 17th century blind harpist and composer who wrote one of the most haunting pieces of Irish music, “â€O’Carolan’s Concerto.â€â€
Boy/Male
Hindu
Computer
COMPUTER ALGEBRA
COMPUTER ALGEBRA
Girl/Female
Indian
Goddess Devi
Male
Egyptian
, the name of many Egyptian kings.
Girl/Female
Irish
Eimear possessed the “Six Gifts of Womanhood†– “beauty, a gentle voice, sweet words, wisdom, needlework and chastity!†She was bethrothed to the warrior Cuchulainn (read the legend) when they were children and they loved each other very deeply. But Cuchulainn had “a wandering eye†and Eimear endured this, realizing “everything new is fair,†but when he made love to Fand, wife of the sea god Manannan, Eimear confronted the lovers. After seeing the strength of Fand’s love she offered to withdraw. Touched by this display of unselfishness, Fand left Cuchulainn and returned to the sea. When Cuchulainn died Eimear spoke movingly and lovingly at his graveside.
Male
English
Man of Flatlands
Girl/Female
Sikh
One who attaines the elixir of enlightenment
Boy/Male
Tamil
Boy/Male
Indian, Sanskrit
Praise
Boy/Male
Teutonic American German
Mighty horse.
Boy/Male
Hindu, Indian
Popular
Girl/Female
Indian
Defender of men, Helper of humankind, Defender of mankind
COMPUTER ALGEBRA
COMPUTER ALGEBRA
COMPUTER ALGEBRA
COMPUTER ALGEBRA
COMPUTER ALGEBRA
n.
One who computes.
v. t.
To compute; to count.
imp. & p. p.
of Compete
n.
A composer or compiler of hymns; one versed in hymnology.
imp. & p. p.
of Compute
v. t.
To compute erroneously.
p. pr. & vb. n.
of Compete
v. t.
To compute or rate too high.
v. i.
To calculate; to compute.
imp. & p. p.
of Commute
v. i.
To contend emulously; to seek or strive for the same thing, position, or reward for which another is striving; to contend in rivalry, as for a prize or in business; as, tradesmen compete with one another.
n.
Compiler.
n.
A preparation of fruit in sirup in such a manner as to preserve its form, either whole, halved, or quartered; as, a compote of pears.
v. t.
To exchange; to put or substitute something else in place of, as a smaller penalty, obligation, or payment, for a greater, or a single thing for an aggregate; hence, to lessen; to diminish; as, to commute a sentence of death to one of imprisonment for life; to commute tithes; to commute charges for fares.
p. pr. & vb. n.
of Commute
n.
One who commutes; especially, one who commutes in traveling.
p. pr. & vb. n.
of Compute
n.
One who composes or writes a book; a composer, as distinguished from an editor, translator, or compiler.
v. i.
To pay, or arrange to pay, in gross instead of part by part; as, to commute for a year's travel over a route.
n.
A computer.