What is polynomial?

  • (noun): A mathematical expression that is the sum of a number of terms.
    Synonyms: multinomial
    See also — Additional definitions below

Polynomial

In mathematics, a polynomial is an expression of finite length constructed from variables (also called indeterminates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. However, the division by a constant is allowed, because the multiplicative inverse of a non zero constant is also a constant. For example, x2 − x/4 + 7 is a polynomial, but x2 − 4/x + 7x3/2 is not, because its second term involves division by the variable x (4/x), and also because its third term contains an exponent that is not a non-negative integer (3/2). The term "polynomial" can also be used as an adjective, for quantities that can be expressed as a polynomial of some parameter, as in polynomial time, which is used in computational complexity theory.

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Some articles on polynomial:

Multiplicity (mathematics) - Multiplicity of A Root of A Polynomial
... Let F be a field and p(x) be a polynomial in one variable and coefficients in F ... F is called a root of multiplicity k of p(x) if there is a polynomial s(x) such that s(a) ≠ 0 and p(x) = (x − a)ks(x) ... For instance, the polynomial p(x) = x3 + 2x2 − 7x + 4 has 1 and −4 as roots, and can be written as p(x) = (x + 4)(x − 1)2 ...
Extensions of The Concept of A Polynomial
... Polynomials can involve more than one variable, in which they are called multivariate ... Rings of polynomials in a finite number of variables are of fundamental importance in algebraic geometry which studies the simultaneous zero sets of several such ... alternatively be constructed by repeating the construction of univariate polynomials with as coefficient ring another ring of polynomials thus the ring R of polynomials in X and Y can be viewed as the ...
Schwartz–Zippel Lemma
... In mathematics, the Schwartz–Zippel lemma is a tool commonly used in probabilistic polynomial identity testing, i.e ... in the problem of determining whether a given multivariate polynomial is the 0-polynomial (or identically equal to 0) ... The input to the problem is an n-variable polynomial over a field F ...
Bessel Polynomials - Properties - Definition in Terms of Bessel Functions
... The Bessel polynomial may also be defined using Bessel functions from which the polynomial draws its name where Kn(x) is a modified Bessel function of the second kind and yn(x) is ...
Minimax Approximation Algorithm - Polynomial Approximations
... function defined on a closed interval can be uniformly approximated as closely as desired by a polynomial function ... Polynomial expansions such as the Taylor series expansion are often convenient for theoretical work but less useful for practical applications ... desirable to minimize the maximum absolute or relative error of a polynomial fit for any given number of terms in an effort to reduce computational expense of repeated evaluation ...

More definitions of "polynomial":

  • (adj): Having the character of a polynomial.
    Example: "A polynomial expression"
    Synonyms: multinomial