Definition:Content of Polynomial/GCD Domain
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This article, or a section of it, needs explaining. In particular: Several undefined concepts here: Let $K$ be the field of quotients of $D$: field of quotients by what? Let $f \in K \sqbrk X$ be a polynomial: $K \sqbrk X$ needs to be defined. Let $a \in D$ be such that $a f \in D \sqbrk X$: $D \sqbrk X$ similarly needs to be defined. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Explain}} from the code. |
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.