Let $({\overline{L}},s)$ be a metrized toric line bundle with a toric section as in the theorem above. Then the roof function associated to $({\overline{L}},s)$ is the concave function $\vartheta_{{\overline{L}},s}\colon\Delta_{\Psi}\to\mathbb{R}$ defined as

$$\vartheta_{{\overline{L}},s}=f_{{\overline{L}},s}^{\vee}=\lambda_{K}\psi_{{\overline{L}},s}^{\vee}.$$

The concave function $\psi_{{\overline{L}},s}^{\vee}$ will be called the rational roof function. When the toric section $s$ is clear form the context, we will denote $f_{{\overline{L}},s}$ and $\vartheta_{{\overline{L}},s}$ by $f_{\|\cdot\|}$ and $\vartheta_{\|\cdot\|}$ respectively.