[BMS08, Def. 2.9] Given an ideal ${\mathfrak{a}}$ in ${\mathcal{O}}_{X}$ and $\lambda\in\mathbb{R}_{\geq 0}$ one defines the test ideal of ${\mathfrak{a}}$ of exponent $\lambda$ to be

$$\tau({\mathfrak{a}}^{\lambda}):=\bigcup_{e\in\mathbb{N}_{>0}}\Bigl({\mathfrak{a}}^{\lceil\lambda p^{e}\rceil}\Bigr)^{[1/p^{e}]}$$

where given $r\in\mathbb{R}$ we write $\lceil r\rceil$ for the smallest integer $\geq r$.