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...

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

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...

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...

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

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...

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...

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...

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

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

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...

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...

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...

contained in K {\displaystyle K} . An algebraic integer is a root of a monic polynomial with integer coefficients: x n + c n − 1 x n − 1 + ⋯ + c 0 {\displaystyle...

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

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...

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...

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...

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...

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

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

of the same kind. For example, 3 × 5 is an integer factorization of 15, and (x – 2)(x + 2) is a polynomial factorization of x2 – 4. Factorization is not...

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