Definition:Content of Polynomial/GCD Domain

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Definition

Let $D$ be a GCD domain.

Let $K$ be the field of quotients of $D$.

Let $f \in K \sqbrk X$ be a polynomial.

Let $a \in D$ be such that $a f \in D \sqbrk X$.

Let $d$ be the greatest common divisor of the coefficients of $a f$.

Then we define the content of $f$ to be:

$\cont f := \dfrac d a$

Also denoted as

The content of a polynomial $f$ can be seen in the literature variously denoted as:

$\cont f$ (currently used on $\mathsf{Pr} \infty \mathsf{fWiki}$)

$c_f$

$\left\langle \! \left\langle {f} \right\rangle \! \right\rangle$

Also see

• Results about Content of Polynomial can be found here.