# Definition:Content of Polynomial/Rational

< Definition:Content of Polynomial(Redirected from Definition:Content of Rational Polynomial)

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## Contents

## 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 $61$