coefficients from an arbitrary field, its reciprocal polynomial or reflected polynomial, denoted by p∗ or pR, is the polynomial p ∗ ( x ) = a n + a n − 1 x + ⋯...

of reciprocal polynomials, when used in CRCs, is that they have exactly the same error-detecting strength as the polynomials they are reciprocals of....

also known as a reciprocal Reciprocal polynomial, a polynomial obtained from another polynomial by reversing its coefficients Reciprocal rule, a technique...

Q Weil reciprocity law Reciprocal polynomials, the coefficients of the remainder polynomial are the bits of the CRC Reciprocal square root Reciprocity...

has a root of absolute value 1, the minimal polynomial for a Salem number must be a reciprocal polynomial. This implies that 1 / α {\displaystyle 1/\alpha...

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

and roots of a polynomial Cohn's theorem relating the roots of a self-inversive polynomial with the roots of the reciprocal polynomial of its derivative...

{1}{z}}} is twice the real part of z. In other words, Φn is a reciprocal polynomial, the polynomial R n {\displaystyle R_{n}} that has r as a root may be deduced...

multiplicity coincides. Moreover, since the characteristic polynomial of the inverse is the reciprocal polynomial of the original, the eigenvalues share the same...

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

the reciprocal polynomial of its derivative. Cohn's theorem is useful for studying the distribution of the roots of self-inversive and self-reciprocal polynomials...

+a_{n}} be a polynomial. The polynomial whose roots are the reciprocals of the roots of P as roots is its reciprocal polynomial Q ( y ) = y n P (...

The reciprocals of prime numbers have been of interest to mathematicians for various reasons. They do not have a finite sum, as Leonhard Euler proved...

factor is irreducible (but not by Eisenstein's criterion). Only the reciprocal polynomial is irreducible by Eisenstein's criterion. We have now shown that...

} The associated Narayana polynomial N n ( z ) {\displaystyle {\mathcal {N}}_{n}(z)} is defined as the reciprocal polynomial of N n ( z ) {\displaystyle...

resultant of two polynomials is a polynomial expression of their coefficients that is equal to zero if and only if the polynomials have a common root...

g(x)h^{*}(x)=x^{n}-1} , where h ∗ ( x ) {\displaystyle h^{*}(x)} denotes the reciprocal polynomial of h ( x ) {\displaystyle h(x)} . The idempotent of C {\displaystyle...

location polynomial. The roots of the error location polynomial can be found by exhaustive search. The error locators Xk are the reciprocals of those...

for higher order polynomial equations. If there are more than n + 1 constraints (n being the degree of the polynomial), the polynomial curve can still...

the problem. The Basel problem asks for the precise summation of the reciprocals of the squares of the natural numbers, i.e. the precise sum of the infinite...

mathematics, an Appell sequence, named after Paul Émile Appell, is any polynomial sequence { p n ( x ) } n = 0 , 1 , 2 , … {\displaystyle \{p_{n}(x)\}_{n=0...

quadratic polynomial, the only ways to rearrange two roots are to either leave them be or to transpose them, so solving a quadratic polynomial is simple...

golden ratio is a root of a polynomial with rational coefficients, it is an algebraic number. Its minimal polynomial, the polynomial of lowest degree with integer...

as a polynomial mod 2. This means that the coefficients of the polynomial must be 1s or 0s. This is called the feedback polynomial or reciprocal characteristic...

smallest absolute value, one can apply the method on the reciprocal polynomial (polynomial obtained by reversing the order of the coefficients), and...

complexity that is polynomial in both the size of the input and in the reciprocal of the relative error, 1/η (rather than being polynomial merely in log(1/η)...

uses of normalizing constants include making the value of a Legendre polynomial at 1 and in the orthogonality of orthonormal functions. A similar concept...

orthogonal polynomials is zero by virtue of their mutual orthogonality. Therefore, each non-zero element of its inverse is simply the reciprocal of the corresponding...

algebra, completing the square is a technique for converting a quadratic polynomial of the form ⁠ a x 2 + b x + c {\displaystyle \textstyle ax^{2}+bx+c} ⁠...

of rational numbers; a rational polynomial may be a polynomial with rational coefficients, although the term "polynomial over the rationals" is generally...