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 = an−i, 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
Famous quotes containing the word reciprocal:
“I had no place in any coterie, or in any reciprocal self-advertising. I stood alone. I stood outside. I wanted only to learn. I wanted only to write better.”
—Ellen Glasgow (1873–1945)