For less elementary aspects of the subject, see Polynomial ring.
In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example of a polynomial of a single indeterminate x is x2 − 4x + 7. An example with three indeterminates is x3 + 2xyz2 − yz + 1.
Polynomials appear in many areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; and they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, which are central concepts in algebra and algebraic geometry.
In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the...
In numerical analysis, the Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a...
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The...
Quasi-polynomial time algorithms are algorithms whose running time exhibits quasi-polynomial growth, a type of behavior that may be slower than polynomial time...
The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)} and...
precisely, it is a polynomial function of the coefficients of the original polynomial. The discriminant is widely used in polynomial factoring, number...
In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues...
In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable...
systems get a short check value attached, based on the remainder of a polynomial division of their contents. On retrieval, the calculation is repeated...
of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more...
an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials. The property of...
algorithm that solves the task and runs in polynomial time exists, meaning the task completion time varies as a polynomial function on the size of the input to...
numerical analysis, a Bernstein polynomial is a polynomial expressed as a linear combination of Bernstein basis polynomials. The idea is named after mathematician...
In numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes...
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...
Newton polynomial, named after its inventor Isaac Newton, is an interpolation polynomial for a given set of data points. The Newton polynomial is sometimes...
In mathematics, a homogeneous polynomial, sometimes called quantic in older texts, is a polynomial whose nonzero terms all have the same degree. For example...
symmetric polynomial is a polynomial P(X1, X2, ..., Xn) in n variables, such that if any of the variables are interchanged, one obtains the same polynomial. Formally...
mathematics, the order of a polynomial may refer to: the degree of a polynomial, that is, the largest exponent (for a univariate polynomial) or the largest sum...
mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a vast number of...
In machine learning, the polynomial kernel is a kernel function commonly used with support vector machines (SVMs) and other kernelized models, that represents...
In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version...
A polynomial P is annihilating or called an annihilating polynomial in linear algebra and operator theory if the polynomial considered as a function of...
In algebra, a monic polynomial is a non-zero univariate polynomial (that is, a polynomial in a single variable) in which the leading coefficient (the...
In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence. The polynomials arise in: signal processing as Hermitian wavelets...
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...
In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander...
Global Information