In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects. Although computer algebra could be considered a subfield of scientific computing, they are generally considered as distinct fields because scientific computing is usually based on numerical computation with approximate floating point numbers, while symbolic computation emphasizes exact computation with expressions containing variables that have no given value and are manipulated as symbols.
Facts
Disputed
Origin YearNo single founding moment is agreed for the field; McCarthy's 1960 symbolic-computation work in Lisp is the most commonly cited starting point. Core ConcernDeveloping algorithms and software that manipulate mathematical expressions symbolically and exactly, rather than through approximate numerical computation. 1 Computer Algebra
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Associated With
Computer algebra is defined by Wikipedia as the study and development of algorithms for manipulating mathematical expressions, placing it alongside the atlas's algorithms and complexity theory field.
Source Computer Algebra (Wikipedia)
Field-to-field association; both are standard neighbouring areas of computing
Includes
Source Wikipedia: Abramov's algorithm
Source Wikipedia: Anthony C. Hearn
Source Wikipedia: Berlekamp's algorithm
Source Wikipedia: Berlekamp-Zassenhaus algorithm
Source Bruno Buchberger (Wikipedia)
Source Wikipedia: Buchberger's algorithm
Source Wikipedia: Cantor-Zassenhaus algorithm
Source Wikipedia: Coreset
Source Wikipedia: Cylindrical algebraic decomposition
Source Wikipedia: Factorization of polynomials
Source Factorization of polynomials over finite fields (Wikipedia)
Source Wikipedia: Faugère's F4 and F5 algorithms
Source Wikipedia: FGLM algorithm
Source Wikipedia: Gaston Gonnet
Source Wikipedia: Gosper's algorithm
Source Wikipedia: Polynomial greatest common divisor
Source Wikipedia: Polynomial long division
Source Richard Fateman (Wikipedia)
Source Risch algorithm (Wikipedia)
Source Robert Henry Risch (Wikipedia)
Source Wikipedia: Stephen Wolfram
Source Symbolic integration (Wikipedia)
Source Wikipedia: Wu's method of characteristic set
Source Wikipedia: Zassenhaus algorithm
Sources
1. Computer Algebra (Wikipedia)
Wikimedia FoundationHistory, Foundations and early applications section, first sentence
In 1960, John McCarthy explored an extension of primitive recursive functions for computing symbolic expressions through the Lisp programming language while at the Massachusetts Institute of Technology.
Lead paragraph, first sentence
In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects.
Associated With: Algorithms and Complexity Theory, Lead section
In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects.
View the Source Robert Henry Risch (Wikipedia)
Includes: Robert Henry Risch, Lead sectionQuote, Includes: Robert Henry Risch, Lead section
is known for his work on symbolic integration, specifically the Risch algorithm
Computer algebra system (Wikipedia)
In Group: Graphics, Imaging and Symbolic Computation, lead sectionView the Source Bruno Buchberger (Wikipedia)
Includes: Bruno Buchberger, Article textQuote, Includes: Bruno Buchberger, Article text
In his 1965 Ph.D. thesis, he created the theory of Gröbner bases
Risch algorithm (Wikipedia)
Includes: Risch Algorithm, Lead sentenceQuote, Includes: Risch Algorithm, Lead sentence
Risch algorithm is a method of indefinite integration used in some computer algebra systems to find antiderivatives.
Wikipedia: Berlekamp's algorithm
Includes: Berlekamp's algorithm, Lead sentenceQuote, Includes: Berlekamp's algorithm, Lead sentence
Berlekamp's algorithm is a well-known method for factoring polynomials over finite fields (also known as Galois fields).
Wikipedia: Buchberger's algorithm
Includes: Buchberger's algorithm, Lead sentenceQuote, Includes: Buchberger's algorithm, Lead sentence
Buchberger's algorithm is a method for transforming a given set of polynomials into a Gröbner basis, which is another set of polynomials that have the same common zeros and are more convenient for extracting information on these common zeros.
Wikipedia: Cantor-Zassenhaus algorithm
Includes: Cantor-Zassenhaus Algorithm, Lead sentenceQuote, Includes: Cantor-Zassenhaus Algorithm, Lead sentence
Cantor-Zassenhaus algorithm is a method for factoring polynomials over finite fields (also called Galois fields).
Wikipedia: Gosper's algorithm
Includes: Gosper's Algorithm, Lead sentenceQuote, Includes: Gosper's Algorithm, Lead sentence
Gosper's algorithm, due to Bill Gosper, is a procedure for finding sums of hypergeometric terms that are themselves hypergeometric terms.
Wikipedia: Zassenhaus algorithm
Includes: Zassenhaus Algorithm, Lead sentenceQuote, Includes: Zassenhaus Algorithm, Lead sentence
Zassenhaus algorithm is a method to calculate a basis for the intersection and sum of two subspaces of a vector space.
Wikipedia: Berlekamp-Zassenhaus algorithm
Includes: Berlekamp-Zassenhaus Algorithm, Lead sentenceQuote, Includes: Berlekamp-Zassenhaus Algorithm, Lead sentence
Berlekamp-Zassenhaus algorithm is an algorithm for factoring polynomials over the integers, named after Elwyn Berlekamp and Hans Zassenhaus.
Wikipedia: Cylindrical algebraic decomposition
Includes: Cylindrical Algebraic Decomposition, Lead sentenceQuote, Includes: Cylindrical Algebraic Decomposition, Lead sentence
cylindrical algebraic decomposition (CAD) is a notion, along with an algorithm to compute it, that is fundamental for computer algebra and real algebraic geometry.
Wikipedia: Coreset
Includes: Coreset, Lead sentenceQuote, Includes: Coreset, Lead sentence
coreset is a small, possibly weighted subset of an input point set that approximately preserves the value of a specified optimization problem.
Wikipedia: Wu's method of characteristic set
Includes: Wu's Method of Characteristic Set, Lead sentenceQuote, Includes: Wu's Method of Characteristic Set, Lead sentence
Wenjun Wu's method is an algorithm for solving multivariate polynomial equations introduced in the late 1970s by the Chinese mathematician Wen-Tsun Wu.
Wikipedia: Faugère's F4 and F5 algorithms
Includes: Faugère's F4 and F5 Algorithms, Lead sentenceQuote, Includes: Faugère's F4 and F5 Algorithms, Lead sentence
Faugère F4 algorithm, by Jean-Charles Faugère, computes the Gröbner basis of an ideal of a multivariate polynomial ring.
Wikipedia: Abramov's algorithm
Includes: Abramov's Algorithm, Lead sentenceQuote, Includes: Abramov's Algorithm, Lead sentence
Abramov's algorithm computes all rational solutions of a linear recurrence equation with polynomial coefficients.
Wikipedia: FGLM algorithm
Includes: FGLM Algorithm, Lead sentenceQuote, Includes: FGLM Algorithm, Lead sentence
FGLM is one of the main algorithms in computer algebra, named after its designers, Faugère, Gianni, Lazard and Mora.
Symbolic integration (Wikipedia)
Includes: Symbolic integration, Lead sentenceQuote, Includes: Symbolic integration, Lead sentence
symbolic integration is the problem of finding a formula for the antiderivative, or indefinite integral, of a given function f(x), i.e.
Wikipedia: Stephen Wolfram
Wikimedia FoundationIncludes: Stephen Wolfram, Lead paragraphView the Source Wikipedia: Gaston Gonnet
Richard Fateman (Wikipedia)
Includes: Richard Fateman, Infobox field and known_for, lead paragraphView the Source Wikipedia: Anthony C. Hearn
Wikimedia FoundationIncludes: Anthony C. Hearn, Infobox field and known_for, lead paragraphView the Source Wikipedia: Polynomial long division
Includes: Polynomial long division, LeadQuote, Includes: Polynomial long division, Lead
In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division.
Wikipedia: Polynomial greatest common divisor
Includes: Polynomial Greatest Common Divisor, LeadQuote, Includes: Polynomial Greatest Common Divisor, Lead
In algebra, the greatest common divisor (frequently abbreviated GCD or gcd) of two polynomials is a polynomial, of the highest possible degree, which is a factor of both the two original polynomials.
Wikipedia: Factorization of polynomials
Includes: Factorization of Polynomials, LeadQuote, Includes: Factorization of Polynomials, Lead
In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.
Factorization of polynomials over finite fields (Wikipedia)
Includes: Factorization of polynomials over finite fields, LeadQuote, Includes: Factorization of polynomials over finite fields, Lead
In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors.
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