Suppose $K=\mathbb{Q}(\alpha)$ is a fixed number field with $[K:\mathbb{Q}]=d$ and fixed basis $b_1,b_2,..,b_d$. Define $$m(\alpha) = max \{ | p_i| , |q_i| : 1 \leq i \leq d \},$$ where the max is taken over all representatives of $\alpha$ of the form $$\alpha = \frac{p_1b_1+p_2b_2+\ldots+p_db_d}{q_1b_1+q_2b_2+\ldots+q_db_d}.$$

Are there any papers which describe techniques to compute this number?