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...

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

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

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...

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...

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...

{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...

+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 (...

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...

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

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...

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...

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...

an equation that requires the sum of the reciprocals of two positive integers a and b to equal the reciprocal of a third positive integer c: 1 a + 1 b...

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

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...

with the left fraction. Simplifying the fraction and substituting the reciprocal b / a = 1 / φ {\displaystyle b/a=1/\varphi } , a + b a = a a + b a = 1...

solution. The power sum symmetric polynomial is a building block for symmetric polynomials. The sum of the reciprocals of all perfect powers including duplicates...

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

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...

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

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...

_{a\in \mathrm {GF} (p)}(X-a)} for polynomials over GF(p). More generally, every element in GF(pn) satisfies the polynomial equation xpn − x = 0. Any finite...

description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely...

every point, which is its Taylor series of order 1. So just having a polynomial expansion at singular points is not enough, and the Taylor series must...

a.} Because of the reciprocal relation between r {\displaystyle r} and φ {\displaystyle \varphi } it is also called a reciprocal spiral. The same relation...