Definition:Depends Relation (Matroid)

Definition
Let $M = \struct{S, \mathscr I}$ be a matroid.

Let $\rho : \powerset S \to \Z$ be the rank function of $M$. For $x \in S$ and $A \subseteq S$, $x$ is said to depend on $A$, denoted as $x \sim A$, :
 * $\map \rho {A \cup \set x} = \map \rho A$