Category:Content of Polynomial

This category contains results about Content of Polynomial.
Definitions specific to this category can be found in Definitions/Content of Polynomial.

Integer Polynomial

Let $f \in \Z \sqbrk X$ be a polynomial with integer coefficients.

Then the content of $f$, denoted $\cont f$, is the greatest common divisor of the coefficients of $f$.

Rational Polynomial

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 $n f \in \Z \sqbrk X$.

Polynomial in GCD Domain

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:

$\cont f := \dfrac d a$

Commutative Ring with Unity

Let $R$ be a commutative ring with unity.

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

The content of $f$ is the ideal generated by its coefficients.