Definition & Betydelse | Engelska ordet POLYNOMIALS

Definition av POLYNOMIALS

1. böjningsform av polynomial

Exempel på hur man kan använda POLYNOMIALS i en mening

• Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
• In mathematics, Bézout's identity (also called Bézout's lemma), named after Étienne Bézout who proved it for polynomials, is the following theorem:.
• Some of the most common mathematical functions used in engineering, science and navigation are built from logarithmic and trigonometric functions, which can be approximated by polynomials, so a difference engine can compute many useful tables.
• Typical examples of entire functions are polynomials and the exponential function, and any finite sums, products and compositions of these, such as the trigonometric functions sine and cosine and their hyperbolic counterparts sinh and cosh, as well as derivatives and integrals of entire functions such as the error function.
• The study of field extensions and their relationship to the polynomials that give rise to them via Galois groups is called Galois theory, so named in honor of Évariste Galois who first discovered them.
• In higher mathematics, "irreducible fraction" may also refer to rational fractions such that the numerator and the denominator are coprime polynomials.
• things named after Mittag-Leffler, including: Institute, distribution, function, polynomials, star, summation, theorem, condition, and glacier.
• A natural example of a preorder is the divides relation "x divides y" between integers, polynomials, or elements of a commutative ring.
• This formula follows immediately by integrating the area parallel to the two planes of vertices by Simpson's rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic function in the height.
• The rational root theorem is a special case (for a single linear factor) of Gauss's lemma on the factorization of polynomials.
• Because polynomials are among the simplest functions, and because computers can directly evaluate polynomials, this theorem has both practical and theoretical relevance, especially in polynomial interpolation.
• In coding theory, the Bose–Chaudhuri–Hocquenghem codes (BCH codes) form a class of cyclic error-correcting codes that are constructed using polynomials over a finite field (also called a Galois field).
• For a polynomial to be Hurwitz, it is necessary but not sufficient that all of its coefficients be positive (except for quadratic polynomials, which also imply sufficiency).
• He was one of the foremost mathematical analysts of his generation and made fundamental contributions to the theory of orthogonal polynomials and Toeplitz matrices building on the work of his contemporary Otto Toeplitz.
• Gaussian integers have a Euclidean division (division with remainder) similar to that of integers and polynomials.
• This includes polynomials with real coefficients, since every real number is a complex number with its imaginary part equal to zero.
• However, the cardinality of the set of functions in the closed linear span is the cardinality of the continuum, which is the same cardinality as for the set of polynomials.
• The partial sums of a power series are polynomials, the partial sums of the Taylor series of an analytic function are a sequence of converging polynomial approximations to the function at the center, and a converging power series can be seen as a kind of generalized polynomial with infinitely many terms.
• Hence, power series can be viewed as a generalization of polynomials where the number of terms is allowed to be infinite, and differ from usual power series by the absence of convergence requirements, which implies that a power series may not represent a function of its variable.
• In mathematics, specifically in abstract algebra, a prime element of a commutative ring is an object satisfying certain properties similar to the prime numbers in the integers and to irreducible polynomials.

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