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

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...

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...

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...

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

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

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

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...

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

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...

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

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...

integer program. Then it was shown in 2018 that integer programming can be solved in strongly polynomial and fixed-parameter tractable time parameterized...

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

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...

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...

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...

{\displaystyle P(G,x)} is a monic polynomial of degree exactly n, with integer coefficients. The chromatic polynomial includes at least as much information...

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

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

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

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

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...

arithmetic Square-free Square-free integer Square-free polynomial Square number Power of two Integer-valued polynomial Rational number Unit fraction Irreducible...

In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander...

Can integer factorization be solved in polynomial time on a classical computer? (more unsolved problems in computer science) In mathematics, integer factorization...

strongly polynomial time and weakly polynomial time algorithms. These two concepts are only relevant if the inputs to the algorithms consist of integers. The...

subset has sum zero is a verifier. Clearly, summing the integers of a subset can be done in polynomial time, and the subset sum problem is therefore in NP...

is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, for which only integer solutions are of interest. A...