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Automatic differentiation

In mathematics and computer algebra, automatic differentiation (AD), also called algorithmic differentiation, computational differentiation, auto-differentiation, or simply autodiff, is a set of techn

Factorization of polynomials

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

Dimension of an algebraic variety

In mathematics and specifically in algebraic geometry, the dimension of an algebraic variety may be defined in various equivalent ways. Some of these definitions are of geometric nature, while some ot

Elementary function

In mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots and compositions of finitely many polynomial, rati

Regular semi-algebraic system

In computer algebra, a regular semi-algebraic system is a particular kind of triangular system of multivariate polynomials over a real closed field.

Janet basis

In mathematics, a Janet basis is a normal form for systems of linear homogeneous partial differential equations (PDEs) that removes the inherent arbitrariness of any such system. It was introduced in

Journal of Symbolic Computation

The Journal of Symbolic Computation is a peer-reviewed monthly scientific journal covering all aspects of symbolic computation published by Academic Press and then by Elsevier. It is targeted to both

Elimination theory

In commutative algebra and algebraic geometry, elimination theory is the classical name for algorithmic approaches to eliminating some variables between polynomials of several variables, in order to s

Gröbner fan

In computer algebra, the Gröbner fan of an ideal in the ring of polynomials is a concept in the theory of Gröbner bases. It is defined to be a fan consisting of cones that correspond to different mono

International Symposium on Symbolic and Algebraic Computation

ISSAC, the International Symposium on Symbolic and Algebraic Computation, is an academic conference in the field of computer algebra. ISSAC has been organized annually since 1988, typically in July. T

Abramov's algorithm

In mathematics, particularly in computer algebra, Abramov's algorithm computes all rational solutions of a linear recurrence equation with polynomial coefficients. The algorithm was published by Serge

Polynomial long division

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

Conway polynomial (finite fields)

In mathematics, the Conway polynomial Cp,n for the finite field Fpn is a particular irreducible polynomial of degree n over Fp that can be used to define a standard representation of Fpn as a splittin

Cantor–Zassenhaus algorithm

In computational algebra, the Cantor–Zassenhaus algorithm is a method for factoring polynomials over finite fields (also called Galois fields). The algorithm consists mainly of exponentiation and poly

Polynomial decomposition

In mathematics, a polynomial decomposition expresses a polynomial f as the functional composition of polynomials g and h, where g and h have degree greater than 1; it is an algebraic functional decomp

Binary expression tree

A binary expression tree is a specific kind of a binary tree used to represent expressions. Two common types of expressions that a binary expression tree can represent are algebraic and boolean. These

Symbolic integration

In calculus, symbolic integration is the problem of finding a formula for the antiderivative, or indefinite integral, of a given function f(x), i.e. to find a differentiable function F(x) such that Th

Resultant

In mathematics, the resultant of two polynomials is a polynomial expression of their coefficients, which is equal to zero if and only if the polynomials have a common root (possibly in a field extensi

Synthetic division

In algebra, synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division. It is mostly taught for division by l

Polynomial identity testing

In mathematics, polynomial identity testing (PIT) is the problem of efficiently determining whether two multivariate polynomials are identical. More formally, a PIT algorithm is given an arithmetic ci

Wu's method of characteristic set

Wenjun Wu's method is an algorithm for solving multivariate polynomial equations introduced in the late 1970s by the Chinese mathematician Wen-Tsun Wu. This method is based on the mathematical concept

System of polynomial equations

A system of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over

Gosper's algorithm

In mathematics, Gosper's algorithm, due to Bill Gosper, is a procedure for finding sums of hypergeometric terms that are themselves hypergeometric terms. That is: suppose one has a(1) + ... + a(n) = S

Symbolic-numeric computation

In mathematics and computer science, symbolic-numeric computation is the use of software that combines symbolic and numeric methods to solve problems.

Liouvillian function

In mathematics, the Liouvillian functions comprise a set of functions including the elementary functions and their repeated integrals. Liouvillian functions can be recursively defined as integrals of

Risch algorithm

In symbolic computation, the Risch algorithm is a method of indefinite integration used in some computer algebra systems to find antiderivatives. It is named after the American mathematician Robert He

Berlekamp's algorithm

In mathematics, particularly computational algebra, Berlekamp's algorithm is a well-known method for factoring polynomials over finite fields (also known as Galois fields). The algorithm consists main

Pollard's kangaroo algorithm

In computational number theory and computational algebra, Pollard's kangaroo algorithm (also Pollard's lambda algorithm, see below) is an algorithm for solving the discrete logarithm problem. The algo

FGLM algorithm

FGLM is one of the main algorithms in computer algebra, named after its designers, Faugère, Gianni, Lazard and Mora. They introduced their algorithm in 1993. The input of the algorithm is a Gröbner ba

Schwartz–Zippel lemma

In mathematics, the Schwartz–Zippel lemma (also called the DeMillo-Lipton-Schwartz–Zippel lemma) is a tool commonly used in probabilistic polynomial identity testing, i.e. in the problem of determinin

Bareiss algorithm

In mathematics, the Bareiss algorithm, named after , is an algorithm to calculate the determinant or the echelon form of a matrix with integer entries using only integer arithmetic; any divisions that

Landau's algorithm

No description available.

Square-free polynomial

In mathematics, a square-free polynomial is a polynomial defined over a field (or more generally, an integral domain) that does not have as a divisor any square of a non-constant polynomial. A univari

Buchberger's algorithm

In the theory of multivariate polynomials, 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 c

Factorization of polynomials over finite fields

In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for p

Sum of radicals

In computational complexity theory, there is an open problem of whether some information about a sum of radicals may be computed in polynomial time depending on the input size, i.e., in the number of

Symbolic regression

Symbolic regression (SR) is a type of regression analysis that searches the space of mathematical expressions to find the model that best fits a given dataset, both in terms of accuracy and simplicity

Sturm's theorem

In mathematics, the Sturm sequence of a univariate polynomial p is a sequence of polynomials associated with p and its derivative by a variant of Euclid's algorithm for polynomials. Sturm's theorem ex

Berlekamp–Zassenhaus algorithm

In mathematics, in particular in computational algebra, the Berlekamp–Zassenhaus algorithm is an algorithm for factoring polynomials over the integers, named after Elwyn Berlekamp and Hans Zassenhaus.

Computer algebra

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 softwa

Faugère's F4 and F5 algorithms

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 uses the same mathematical principles as

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 factor of both the two original polynomials. This

Regular chain

In computer algebra, a regular chain is a particular kind of triangular set in a multivariate polynomial ring over a field. It enhances the notion of characteristic set.

Gröbner basis

In mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal i

Kronecker substitution

Kronecker substitution is a technique named after Leopold Kronecker for determining the coefficients of an unknown polynomial by evaluating it at a single value. If p(x) is a polynomial with integer c

Triangular decomposition

In computer algebra, a triangular decomposition of a polynomial system S is a set of simpler polynomial systems S1, ..., Se such that a point is a solution of S if and only if it is a solution of one

Real-root isolation

In mathematics, and, more specifically in numerical analysis and computer algebra, real-root isolation of a polynomial consist of producing disjoint intervals of the real line, which contain each one

Ore 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 differential and/or recurrence operators. Th

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