Polynomials

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 exponentiation to nonnegative integer powers, and has a finite number of terms. An example of a polynomial of a single indeterminate x is x^2 - 4x + 7. An example with three indeterminates is x^3 + 2xyz^2 - yz + 1.

In mathematics, a coefficient is a multiplicative factor involved in some term of a polynomial, a series, or any other type of expression. It may be a number without units, in which case it is known as a numerical factor. It may also be a constant with units of measurement, in which it is known as a constant multiplier. In general, coefficients may be any expression (including variables such as , and ). When the combination of variables and constants is not necessarily involved in a product, it may be called a parameter. For example, the polynomial 2x^2-x+3 has coefficients 2, −1, and 3, and

polynomial with two terms

a polynomial equation in a single variable where the highest exponent of the variable is 3.

In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the roots without computing them. More precisely, it is a polynomial function of the coefficients of the original polynomial. The discriminant is widely used in polynomial factoring, number theory, and algebraic geometry.

equation of the form of equality of two polynomials

relations between the coefficients and the roots of a polynomial

type of hash function used to detect errors in data storage or transmission

complex number whose positive integer power equals one

function that can be defined as the root of a polynomial equation

solutions to Legendre's differential equation

polynomial equation of degree four

algorithm for polynomial evaluation

polynomial sequence

method for solving quadratic equations

highest power of the variables occurring in a monomial in a given polynomial

polynomial with roots that are the eigenvalues of a given matrix

polynomials used for interpolation

ring of polynomials (with one or several variables) with coefficients in a given ring

two sequences of polynomials

dividing polynomials similar to long division for regular numbers

polynomial sequence

type of polynomial used in Numerical Analysis

thumb|upright=2|Layers of Pascal's pyramid derived from [[coefficients in an upside-down ternary plot of the terms in the expansions of the powers of a trinomial ]] In elementary algebra, a trinomial is a polynomial consisting of three terms or monomials.

univariate polynomial in which the leading coefficient is equal to 1

In mathematics, the resultant of two polynomials is a polynomial expression of their coefficients that is equal to zero if and only if the polynomials have a common root (possibly in a field extension), or, equivalently, a common factor (over their field of coefficients). In some older texts, the resultant is also called the eliminant.

irreducible element in the ring of polynomials; a non-constant polynomial that is not the product of two non-constant polynomials

minimal polynomial of a matrix

Theorem: polynomials without common complex zeros generate the unit ideal

polynomial where any interchange in variables results in the same polynomial

polynomial sequence

theorem

given an element α of a field extension E/F, the unique monic polynomial p∈F[x] of minimal degree such that p(α) = 0

irreducible polynomial of integer coefficients whose roots are nth roots of unity

interpolation of a given data set by the polynomial of lowest possible degree that passes through the points of the dataset

polynomial equation of degree six

mathematical function

Polynomial division computation method

Mathematic test in control system theory

mathematical equation

square matrix associated to two univariate polynomials with coefficients in a field or a commutative ring

computational method

mathematical expression

concept in mathematics

function used as a performance test problem for optimization algorithms

mathematical term; type of polynomial transformation

one case when solving a cubic equation

historical term in mathematics

polynomial sequence

Study of polynomial equations

knot invariant

term in an algebraic expression which does not contain any variables

polynomial sequence considered as a generalization of Fibbonacci numbers

(of a real number a) unique real root of the polynomial x^5+x+a

conjecture asserting that, over a characteristic-zero field K, given a polynomial map f: Kⁿ → Kⁿ, if its Jacobian determinant J: Kⁿ → K is a nonzero constant map, then f admits a polynomial inverse g: Kⁿ → Kⁿ

mathematical invariant of a knot or link

polynomial in the logarithm of n

triangular array of polynomials in combinatorial mathematics

expression whose number of distinct roots is equal to its degree

algebra of all possible symmetric tensors over a vector space or ring module