Find the word definition

Crossword clues for polynomial

Longman Dictionary of Contemporary English
▪ A more sophisticated approach fits different polynomials over different but overlapping terms to maturity.
▪ Before beginning this attempted duplication we ought perhaps to remind ourselves exactly what polynomials are.
▪ Each class comprises all those polynomials with a particular constant term.
▪ In algebra they developed a concept of polynomials and pioneered an algebraic geometry that has traditionally been ascribed to Descartes.
▪ Note that the ways of adding and multiplying polynomials in this new notation are precisely those you have always used.
▪ Thus, higher polynomials can always be constructed to improve the fit when the simpler model breaks down.
▪ We do not collect prime numbers or polynomials.
The Collaborative International Dictionary

Polynomial \Pol`y*no"mi*al\, n. [Poly- + -nomial, as in monomial, binomial: cf. F. polyn[^o]me.] (Alg.) An expression composed of two or more terms, connected by the signs plus or minus; as, a^ 2 - 2ab + b^ 2.


Polynomial \Pol`y*no"mi*al\, a.

  1. Containing many names or terms; multinominal; as, the polynomial theorem.

  2. Consisting of two or more words; having names consisting of two or more words; as, a polynomial name; polynomial nomenclature.

Douglas Harper's Etymology Dictionary

1670s (n.), 1704 (adj.), irregularly formed from poly- + stem of binomial.


a. 1 (context algebra English) Able to be described or limited by a #Noun. 2 (context taxonomy English) of a polynomial name or entity n. 1 (context algebra English) An expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power, such as a_n x^n + a_{n-1}x^{n-1} + ... + a_0 x^0. 2 (context taxonomy English) A taxonomic designation (such as of a subspecies) consisting of more than two terms.

  1. adj. having the character of a polynomial; "a polynomial expression" [syn: multinomial]

  2. n. a mathematical expression that is the sum of a number of terms [syn: multinomial]


In mathematics, a polynomial is an expression consisting of variables and coefficients which only employs the operations of addition, subtraction, multiplication, and non-negative integer exponents. An example of a polynomial of a single variable is . An example in three variables is .

Polynomials appear in a wide variety of 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 problems in the sciences; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; 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, central concepts in algebra and algebraic geometry.

Polynomial (hyperelastic model)

The ' polynomial' hyperelastic material model is a phenomenological model of rubber elasticity. In this model, the strain energy density function is of the form of a polynomial in the two invariants I, I of the left Cauchy-Green deformation tensor.

The strain energy density function for the polynomial model is

W = ∑C(I − 3)(I − 3)
where C are material constants and C = 0.

For compressible materials, a dependence of volume is added

W = ∑C( − 3)( − 3) + ∑D(J − 1)

$$\begin{align} \bar{I}_1 & = J^{-2/3}~I_1 ~;~~ I_1 = \lambda_1^2 + \lambda_2 ^2+ \lambda_3 ^2 ~;~~ J = \det(\boldsymbol{F}) \\ \bar{I}_2 & = J^{-4/3}~I_2 ~;~~ I_2 = \lambda_1^2 \lambda_2^2 + \lambda_2^2 \lambda_3^2 + \lambda_3^2 \lambda_1^2 \end{align}$$

In the limit where C = C11 = 0, the polynomial model reduces to the Neo-Hookean solid model. For a compressible Mooney-Rivlin material n = 1, C = C, C = 0, C = C, m = 1 and we have

W = C ( − 3) + C ( − 3) + D (J − 1)

Usage examples of "polynomial".

Elaine is the kind of person who can write a dissertation while simultaneously finding the antiderivative of a polynomial expression.

If you arrive at a sequence of all zeros, you can reconstruct a polynomial which describes the original set of values, such that the degree of the polynomial is one less than the number of times the procedure was applied.

It called for aggressive hiring of mathematicians expert in such esoteric fields as stochastic and Markov processes, shift register, and polynomial theory.

The sylphadese were hedonist polynomials who occupied a floating river settlement in the Dealveerd sector.

For that, they needed a quantum error correcting code, which in turn required a weak Nullstellensatz ideal, a way of defeating the complexifying polynomials of decoherence, the noise that smeared encoded data to zero.

And so he worked on, trying to incorporate into the calculation skylight radiance intensities, Chandrasekhar's radiative transfer equation, chromaticity scales, aerosol chemical compositions, Le-gendre polynomials to evaluate the angular scattering intensities, Riccati-Bessel functions to evaluate the scattering cross sections, and so on-occupying the better part of the drive to Arena Glacier, concentrating hard and steadfastly ignoring the world around him and the situation in which he now found himself.

And the more complicated the data you feed the program, the more the polynomial will have to wiggle to fit your data points.

Furious, the beast writhed and wriggled its iterated integrals beneath the King's polynomial blows, collapsed into an infinite series of indeterminate terms, then got back up by raising itself to the nth power, but the King so belabored it with differentials and partial derivatives that its Fourier coefficients all canceled out (see Riemann's Lemma), and in the ensuing confusion the constructors completely lost sight of both King and beast.

Worst of all, RSA depends upon the unprovable mathematical hypothesis that there is no polynomial time bounded algorithm for factoring numbers.