Order of a polynomial information

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 of exponents...

degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is...

The order polynomial is a polynomial studied in mathematics, in particular in algebraic graph theory and algebraic combinatorics. The order polynomial counts...

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...

a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of...

In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable...

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 nonzero...

In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues...

mathematics, a quadratic polynomial is a polynomial of degree two in one or more variables. A quadratic function is the polynomial function defined by a quadratic...

nth cyclotomic polynomial, for any positive integer n, is the unique irreducible polynomial with integer coefficients that is a divisor of x n − 1 {\displaystyle...

determinant of the Vandermonde matrix. The value depends on the order of the terms: it is an alternating polynomial, not a symmetric polynomial. The defining...

constant α > 1 {\displaystyle \alpha >1} is a polynomial time algorithm. The following table summarizes some classes of commonly encountered time complexities...

symmetric polynomials are one type of basic building block for symmetric polynomials, in the sense that any symmetric polynomial can be expressed as a polynomial...

digital data. Blocks of data entering these systems get a short check value attached, based on the remainder of a polynomial division of their contents. On...

a generic third-order polynomial function and its first derivative: S 1 ⁡ ( x ) = a 3 x 3 + a 2 x 2 + a 1 x + a 0 , S 1 ′ ⁡ ( x ) = 3 a 3 x 2 + 2 a 2...

mathematical field of numerical analysis, a Newton polynomial, named after its inventor Isaac Newton, is an interpolation polynomial for a given set of data points...

the field 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...

Lagrange interpolating polynomial is the unique polynomial of lowest degree that interpolates a given set of data. Given a data set of coordinate pairs (...

algorithms, such as polynomial long division, require the terms to be in a specific order. Many of the main algorithms for multivariate polynomials are related...

irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials. The property of irreducibility...

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 the algorithm...

In a finite field of order q, the polynomial Xq − X has all q elements of the finite field as roots. The non-zero elements of a finite field form a multiplicative...

precisely, it is a polynomial function of the coefficients of the original polynomial. The discriminant is widely used in polynomial factoring, number...

high order polynomials will be lumpy; they could also be smooth, but there is no guarantee of this, unlike with low order polynomial curves. A fifteenth...

polynomial, in 1923. In 1969, John Conway showed a version of this polynomial, now called the Alexander–Conway polynomial, could be computed using a skein...