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:
“Of course we will continue to work for cheaper electricity in the homes and on the farms of America; for better and cheaper transportation; for low interest rates; for sounder home financing; for better banking; for the regulation of security issues; for reciprocal trade among nations and for the wiping out of slums. And my friends, for all of these we have only begun to fight.”
—Franklin D. Roosevelt (18821945)