functional decomposition. Algorithms are known for decomposing univariate polynomials in polynomial time. Polynomials which are decomposable in this way...

fraction decomposition, and a characterization of the coefficients. The above partial fraction decomposition implies, for each 1 ≤ i ≤ r, a polynomial expansion...

nilpotent. The two parts are polynomials in the operator, which makes them behave nicely in algebraic manipulations. The decomposition has a short description...

Monomial Polynomial long division Synthetic division Polynomial factorization Rational function Partial fraction Partial fraction decomposition over R Vieta's...

larger than 1. A polynomial that cannot be decomposed is indecomposable. Ritt's polynomial decomposition theorem asserts that if f = g 1 ∘ g 2 ∘ ⋯ ∘...

common divisor of the polynomial and its derivative. A square-free decomposition or square-free factorization of a polynomial is a factorization into...

Polynomial Matrix Spectral Factorization or Matrix Fejer–Riesz Theorem is a tool used to study the matrix decomposition of polynomial matrices. Polynomial...

Quasi-polynomial time algorithms are algorithms whose running time exhibits quasi-polynomial growth, a type of behavior that may be slower than polynomial time...

Overview of the Research on Decomposition". A Survey of Literature on Function Decomposition. Version IV. Functional Decomposition Group, Department of Electrical...

primary decomposition form of the structure theorem for finitely generated modules over a principal ideal domain, and for the special case of polynomial rings...

factorized is a normal or real symmetric matrix, the decomposition is called "spectral decomposition", derived from the spectral theorem. A (nonzero) vector...

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

In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike...

discipline of linear algebra, the Schur decomposition or Schur triangulation, named after Issai Schur, is a matrix decomposition. It allows one to write an arbitrary...

field of a polynomial with coefficients in a field is the smallest field extension of that field over which the polynomial splits, i.e., decomposes into linear...

{\displaystyle (x^{3})^{2}-9(x^{3})+8=0} (this is a simple case of a polynomial decomposition). Thus the equation may be simplified by defining a new variable...

In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the...

homogeneous polynomials of degree d form a vector space (or a module), commonly denoted R d . {\displaystyle R_{d}.} The above unique decomposition means that...

elementary symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed...

mathematics, Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers...

product of irreducible polynomials (those that are not the product of two non-constant polynomials). Moreover, this decomposition is unique up to multiplication...

of a Taylor series is a polynomial of degree n that is called the nth Taylor polynomial of the function. Taylor polynomials are approximations of a function...

algebraic geometry. Given a set S of polynomials in Rn, a cylindrical algebraic decomposition is a decomposition of Rn into connected semialgebraic sets...

one generally considers the "LUP decomposition" having a permutation matrix as its third factor. See Matrix decomposition for the most common types of matrix...

of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in...

mathematics, more precisely in measure theory, the Lebesgue decomposition theorem provides a way to decompose a measure into two distinct parts based on their relationship...

an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials. The property of...

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

an invertible matrix with polynomial coefficients as a product of three matrices. The Birkhoff - von Neumann decomposition, introduced by Garrett Birkhoff...

linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃəˈlɛski/ shə-LES-kee) is a decomposition of a Hermitian, positive-definite...