mathematics, an integer-valued polynomial (also known as a numerical polynomial) P ( t ) {\displaystyle P(t)} is a polynomial whose value P ( n ) {\displaystyle...

integer-valued. In computer programming, many functions return values of integer type due to simplicity of implementation. Integer-valued polynomial Semi-continuity...

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 x2 − 4x...

formulas Integer-valued polynomial Algebraic equation Factor theorem Polynomial remainder theorem See also Theory of equations below. Polynomial ring Greatest...

takes values in R at all integers if and only if it is an R-linear combination of binomial coefficient polynomials. The integer-valued polynomial 3t(3t...

algebraic integer is a complex number that is integral over the integers. That is, an algebraic integer is a complex root of some monic polynomial (a polynomial...

integer-valued polynomials (such as 1 2 x 2 + 1 2 x + 1 {\displaystyle {\tfrac {1}{2}}x^{2}+{\tfrac {1}{2}}x+1} , which takes integer values for all integers...

number of properties that they have in common with the ring of the integers. Polynomial rings occur and are often fundamental in many parts of mathematics...

elementary symmetric polynomials. There is one elementary symmetric polynomial of degree d in n variables for each positive integer d ≤ n, and it is formed...

criterion for a polynomial f ( x ) {\displaystyle f(x)} in one variable with integer coefficients to give infinitely many prime values in the sequence...

mathematics, the nth cyclotomic polynomial, for any positive integer n, is the unique irreducible polynomial with integer coefficients that is a divisor...

algorithm runs in pseudo-polynomial time if its running time is a polynomial in the numeric value of the input (the largest integer present in the input)—but...

bracket polynomial is a Laurent polynomial in the variable A {\displaystyle A} with integer coefficients. First, we define the auxiliary polynomial (also...

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

factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of...

factorization of a positive integer Complex integer Hyperinteger Integer complexity Integer lattice Integer part Integer sequence Integer-valued function Mathematical...

divisor of two integers. In the important case of univariate polynomials over a field the polynomial GCD may be computed, like for the integer GCD, by the...

integral), and this optimal value may be found efficiently since all polynomial-size linear programs can be solved in polynomial time. One common way of proving...

surely Cahen, Paul-Jean; Chabert, Jean-Luc (3 December 1996). Integer-Valued Polynomials. Mathematical Surveys and Monographs. Vol. 48. American Mathematical...

is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division). In algebra of polynomials, the remainder...

non-negative integer. For a univariate polynomial, the degree of the polynomial is simply the highest exponent occurring in the polynomial. The term order...

Schur polynomials are associated with pairs of partitions and have similar properties to Schur polynomials. Schur polynomials are indexed by integer partitions...

algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example...

of Alexandria, who made initial studies of integer Diophantine equations. An important type of polynomial Diophantine equations takes the form: s a +...

equation is a (usually multivariate) polynomial equation with integer coefficients for which one is interested in the integer solutions. Algebraic geometry is...

a list of distinct integers AND the integers are all in S AND the integers sum to 0 THEN OUTPUT "yes" and HALT This is a polynomial-time algorithm accepting...

chromatic polynomial The flow polynomial, a polynomial whose values at integer arguments give the number of nowhere-zero flows with integer flow amounts...

The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)}...

and m are integers with 0 ≤ m ≤ ℓ, or with trivially equivalent negative values. When in addition m is even, the function is a polynomial. When m is...

difference between strongly- and weakly-polynomial time is when the inputs to the algorithms consist of integer or rational numbers. It is particularly...