Reciprocal Polynomial

In the mathematical area of algebra, given a polynomial p with coefficients from an arbitrary field such as:

we define the reciprocal polynomial, p*by:

Essentially, the coefficients are written in reverse order.

In the special case that the polynomial p has complex coefficients, that is,

the conjugate reciprocal polynomial, p* given by,

where denotes the complex conjugate of, is called the reciprocal polynomial when no confusion can arise.

A polynomial is called self-reciprocal if .

The coefficients of a self-reciprocal polynomial satisfy ai = ani, and in this case p is also called a palindromic polynomial. In the conjugate reciprocal case, the coefficients must be real to satisfy the condition.

Read more about Reciprocal Polynomial:  Properties, Properties of Conjugate Reciprocal Polynomials, Application in Coding Theory

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