mathematics, a polynomial transformation consists of computing the polynomial whose roots are a given function of the roots of a polynomial. Polynomial transformations...

mathematics, a Tschirnhaus transformation, also known as Tschirnhausen transformation, is a type of mapping on polynomials developed by Ehrenfried Walther...

This is a list of polynomial topics, by Wikipedia page. See also trigonometric polynomial, list of algebraic geometry topics. Degree: The maximum exponents...

In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version...

polynomial can be found by applying a suitable Tschirnhaus transformation to the given polynomial. Let f ( x ) = x n + a 1 x n − 1 + ⋯ + a n − 1 x + a n {\displaystyle...

In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues...

this transformation to produce an instance y of problem B, giving y as the input to an algorithm for problem B, and returning its output. Polynomial-time...

pseudo-polynomial transformation is a function which maps instances of one strongly NP-complete problem into another and is computable in pseudo-polynomial time...

Finding the roots of polynomials is a long-standing problem that has been extensively studied throughout the history and substantially influenced the...

The transformation t acts on the homology and so we can consider H 1 ( X ) {\displaystyle H_{1}(X)} a module over the ring of Laurent polynomials Z [...

precisely, it is a polynomial function of the coefficients of the original polynomial. The discriminant is widely used in polynomial factoring, number...

numerical analysis, a Bernstein polynomial is a polynomial expressed as a linear combination of Bernstein basis polynomials. The idea is named after mathematician...

reversed) by a given linear transformation. More precisely, an eigenvector v {\displaystyle \mathbf {v} } of a linear transformation T {\displaystyle T} is...

little effort. It may apply either directly or after transformation of the original polynomial. This criterion is named after Gotthold Eisenstein. In...

In numerical analysis, polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through...

mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a wide number of...

Polynomial texture mapping (PTM), also known as Reflectance Transformation Imaging (RTI), is a technique of imaging and interactively displaying objects...

In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a...

an algebraic equation or polynomial equation is an equation of the form P = 0 {\displaystyle P=0} , where P is a polynomial with coefficients in some...

especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more indeterminates (traditionally...

In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are nontrivial solutions of Laguerre's differential equation: x y ″...

In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets...

georeferencing. Higher order polynomial transformations are also commonly used. For example, a Second-order polynomial transformation would be: x o u t = A x...

the ring of polynomials, of the matrix (with polynomial entries) XIn − A (the same one whose determinant defines the characteristic polynomial). Note that...

sequences of polynomials satisfy the same recurrence relation in three terms, we can develop a continued fraction for the Stieltjes transformation whose successive...

Cremona transformations. The Jacobian conjecture is quite naturally posed in that setting. The motivation for looking at rather general polynomial transformations...

applications of affine transformations Affine geometry 3D projection Homography Flat (geometry) Bent function Multilinear polynomial Berger 1987, p. 38....

preceding section about the characteristic constant of a transformation). Its characteristic polynomial is equal to det ( λ I 2 − H ) = λ 2 − tr ⁡ H λ + det...

characteristic polynomial. With diagonalization, it is often possible to translate to and from eigenbases. Most common geometric transformations that keep...

The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. It is a polynomial in two variables which plays...