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

$c_i:\mathbb{F}\to \mathbb{F}$, such that

$c_j(i)={\mathbb{T}}_{ij}\mathrm{\forall }i\in \mathbb{H},\mathrm{\forall }j\in \{1,\dots ,m\}$.