I understand the definition of Seshadri constant $$\epsilon_{D}(E)=\sup\{k \in \mathbb{R}_{\geq 0}|E-kD\text{ is nef}\}.$$ I am not sure how to apply this definition to practice calculation, or maybe there an alternative way to do the specific calculation.
For an easy example, let $X=\mathbb{P}^{2}$, blow it up at $n$ points $P_{1},\ldots,P_{n}$ and then obtain $\tilde{X}$ with exceptional divisors $E_{1},\ldots,E_{n}$. Let $\pi$ be the blow up map $\pi:\tilde{X} \to X$. Let $l$ be a line in $X$. Now I want to calculate $$\epsilon_{E_{i}}(m\pi^{*}l-E_{1}-\cdots-E_{n})$$ for some integer $m$. Intuitively, I believe the answer should be $m-n$, but how do I do it rigorously?