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

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