In this short note, we establish the conventions that will be used throughout the book.

The field used will be called $\mathbb{F}$. We will call our trace domain $\mathbb{H} = \{1, \omega, \omega^2, \dots, \omega^{n-1}\}$, where $\omega \in \mathbb{F}$ is the group generator, and $n$ is the trace length. We will model the trace $\mathbb{T}$ as an $n \times m$ matrix. Recall that in STARKs, for each column, a polynomial over domain $\mathbb{H}$ is interpolated from the values in that column. We will name each column polynomial explicitly: $c_0, \dots, c_{m-1}$, where $c_i: \mathbb{F} \rightarrow \mathbb{F}$, such that $c_j(i) = \mathbb{T}_{ij} \quad \forall i \in \mathbb{H}, \forall j \in \{1, \dots, m\}$.