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[book] decomposition.md: avoid introducing `m` when we already have `range`. 

Signed-off-by: Daira Hopwood <daira@jacaranda.org>
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Daira Hopwood 2021-07-27 17:06:36 +01:00
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book/src/design/circuit/gadgets/decomposition.md
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@ -73,4 +73,4 @@ $$q_\mathit{lookup} \cdot \left(q_\mathit{running} \cdot (z_i - 2^K \cdot z_{i+1
where $z_i$ and $\textsf{word}$ are the same cell (but distinguished here for clarity of usage).
## Short range decomposition
For a short range (for instance, $[0, m)$ where $m \leq 8$), we can range-constrain each word using a degree-$m$ polynomial constraint instead of a lookup: $$\texttt{range\_check(word, range)} = \texttt{word} \cdot (1 - \texttt{word}) \cdots (\texttt{range} - 1 - \texttt{word}).$$
For a short range (for instance, $[0, \texttt{range})$ where $\texttt{range} \leq 8$), we can range-constrain each word using a degree-$\texttt{range}$ polynomial constraint instead of a lookup: $$\texttt{range\_check(word, range)} = \texttt{word} \cdot (1 - \texttt{word}) \cdots (\texttt{range} - 1 - \texttt{word}).$$