elliptic curves in Schoof's algorithm. The set of division polynomials is a sequence of polynomials in Z [ x , y , A , B ] {\displaystyle \mathbb {Z}...

method). Polynomial long division is an algorithm that implements the Euclidean division of polynomials, which starting from two polynomials A (the dividend)...

polynomials over a field the polynomial GCD may be computed, like for the integer GCD, by the Euclidean algorithm using long division. The polynomial...

taught for division by linear monic polynomials (known as Ruffini's rule), but the method can be generalized to division by any polynomial. The advantages...

misconception is that the "best" CRC polynomials are derived from either irreducible polynomials or irreducible polynomials times the factor 1 + x, which adds...

Brahmagupta polynomials Caloric polynomial Charlier polynomials Chebyshev polynomials Chihara–Ismail polynomials Cyclotomic polynomials Dickson polynomial Ehrhart...

multiplication and division of polynomials. The composition of two polynomials is another polynomial. The division of one polynomial by another is not...

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)}...

In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to...

multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with...

especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more indeterminates (traditionally...

sometimes parapsychology The reciprocal Fibonacci constant, the division polynomials, and the supergolden ratio The second Chebyshev function Water potential...

quotient (integer division). In algebra of polynomials, the remainder is the polynomial "left over" after dividing one polynomial by another. The modulo...

Bernstein polynomials, restricted to the interval [0, 1], became important in the form of Bézier curves. A numerically stable way to evaluate polynomials in...

monic polynomials in a univariate polynomial ring over a commutative ring form a monoid under polynomial multiplication. Two monic polynomials are associated...

mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the...

originally restricted to integers, Euclidean division and the division theorem can be generalized to univariate polynomials over a field and to Euclidean domains...

the polynomial remainder theorem or little Bézout's theorem (named after Étienne Bézout) is an application of Euclidean division of polynomials. It states...

representation of a polynomial as a sorted list of pairs coefficient–exponent vector a canonical representation of the polynomials (that is, two polynomials are equal...

^{7}-x^{6}-x^{5}+x^{2}+x+1.\end{aligned}}} The cyclotomic polynomials are monic polynomials with integer coefficients that are irreducible over the field...

of a Taylor series is a polynomial of degree n that is called the nth Taylor polynomial of the function. Taylor polynomials are approximations of a function...

instead of using division polynomials, we are able to work with a polynomial that has lower degree than the corresponding division polynomial: O ( l ) {\displaystyle...

a polynomial. In this context other collections of specific symmetric polynomials, such as complete homogeneous, power sum, and Schur polynomials play...

O(n^{2})} and is a polynomial-time algorithm. All the basic arithmetic operations (addition, subtraction, multiplication, division, and comparison) can...

Euclidean division of polynomials, and, for hand-written computation, polynomial long division or synthetic division. One can define a division operation for...

F[x], the ring of polynomials in the variable x with coefficients in F. Given an element α of E, let Jα be the set of all polynomials f(x) in F[x] such...

ak that are non-constant are pairwise coprime square-free polynomials (here, two polynomials are said coprime is their greatest common divisor is a constant;...

polynomials and Vieta's formulas by noting that this expression is a symmetric polynomial in the roots of A. The discriminant of a linear polynomial (degree...

division of a polynomial by a binomial of the form x – r. It was described by Paolo Ruffini in 1809. The rule is a special case of synthetic division...

and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several...