Definition:Content of Polynomial

Definition
Let $f \in \Z[X]$ be a polynomial.

Then the content of $f$, $\operatorname{cont} \left({f}\right)$ is the greatest common divisor of the coefficients of $f$.

If $f \in \Q[X]$ then there is some $n \in \N$ such that $n f \in \Z[X]$.

Then we define the content of $f$ to be:
 * $\operatorname{cont} \left({f}\right) := \dfrac {\operatorname{cont} \left({n f}\right)} n$

Alternative notation
$\operatorname{cont} \left({f}\right)$ is also seen denoted $c_f$.

Also see

 * Primitive polynomial: A polynomial $f$ is primitive if $\operatorname{cont} \left({f}\right) = 1$.