User:Ascii/Definition:Monomial

Definition
In elementary mathematics, a monomial is a product of:


 * a number $a$ (usually from the standard number fields: $\Q$, $\R$, $\C$)

and


 * a finite number of variables $x_0, \ldots, x_n$ each with respective exponents $i_0, \ldots, i_n$ from $\N_{>0}$

resulting in an expression of the form:


 * $\displaystyle ax_0^{i_0} \ldots x_n^{i_n}$

Coefficient
In the monomial:


 * $\displaystyle ax_0^{i_0} \ldots x_n^{i_n}$

$a$ is the coefficient.

Example 1: $2x$
$2x$ is a monomial where:
 * $2$ is the coefficient

Example 2: $(7.4 - 3.12i)x^{13}yz^{7}$
$(7.4 - 3.12i)x^{13}yz^{7}$ is a monomial where:
 * Coefficient: $7.4 - 3.12i$
 * Variables: $x$, $y$, $z$
 * Total degree: $21$ such that:
 * $x$ has degree $13$
 * $y$ has degree $1$
 * $z$ has degree $7$