Definition:Content of Polynomial/Rational
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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 $61$