Definition:Content of Polynomial/Rational

Definition

Let $f \in \Q \sqbrk X$ be a polynomial with rational coefficients.

The content of $f$ is defined as:

$\cont f := \dfrac {\cont {n f} } n$

where $n \in \N$ is such that $n f \in \Z \sqbrk X$.

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.

Sources

• 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $6$: Polynomials and Euclidean Rings: $\S 31$. Polynomials with Integer Coefficients: Theorem $61$