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:
“Parenting is a profoundly reciprocal process: we, the shapers of our children’s lives, are also being shaped. As we struggle to be parents, we are forced to encounter ourselves; and if we are willing to look at what is happening between us and our children, we may learn how we came to be who we are.”
—Augustus Y. Napier (20th century)