Be more explicit on the values and the vector lookup trick

book/src/kimchi/lookup.md

@@ -86,7 +86,13 @@ For example, the following **query** tells us that we want to check if $r_0 \opl
 | :---:    | :---:    | :---:    |
 | 1, $r_0$ | 1, $r_2$ | 2, $r_1$ |
 
-The grand product argument for the lookup consraint will look like this at this point:
+$r_0$, $r_1$ and $r_2$ will be the result of the evaluation at $g^i$ of
+respectively the wire polynomials $w_0$, $w_1$ and $w_2$.
+To perform vector lookups (i.e. lookups over a list of values, not a single
+element), we use a standard technique which consists of coining a combiner value
+$j$ and sum the individual elements of the list using powers of this coin.
+
+The grand product argument for the lookup constraint will look like this at this point:
 
 $$
 \mathsf{acc}_i = \mathsf{acc}_{i-1} \cdot \frac{(1+\beta) \cdot {\color{green}(\gamma + w_0(g^i) + j \cdot w_2(g^i) + j^2 \cdot 2 \cdot w_1(g^i))} \cdot (\gamma(1 + \beta) + t_{i-1} + \beta t_i)}{(\gamma(1+\beta) + s_{i-1} + \beta s_{i})(\gamma(1+\beta) + s_{n+i-1} + \beta s_{n+i})}