Merge pull request #185 from zcash/book-sinsemilla-degree

[book] sinsemilla.md: Correct constraint degrees.

book/src/design/circuit/gadgets/sinsemilla.md

@@ -138,17 +138,6 @@ The Halo 2 circuit API can automatically substitute $y_{P,i}$, $x_{R,i}$, $y_{A,
 
 Note that each term of the last constraint is multiplied by $4$ relative to the constraint program given earlier. This is a small optimization that avoids divisions by $2$.
 
-$$
-\begin{array}{|c|l|}
-\hline
-\text{Degree} & \text{Constraint} \\\hline
-2   & q_{S4} \cdot (2 \cdot y_Q - Y_{A,0}) = 0 \\\hline
-5   & q_{S1,i} \Rightarrow (m_{i+1},\, x_{P,i},\, y_{P,i}) \in \mathcal{P} \\\hline
-3   & q_{S1,i} \cdot \big(\lambda_{2,i}^2 - (x_{A,i+1} + x_{R,i} + x_{A,i})\big) \\\hline
-6   & q_{S1,i} \cdot \left(4 \cdot \lambda_{2,i} \cdot (x_{A,i} - x_{A,i+1}) - (2 \cdot Y_{A,i} + (2 - q_{S3,i}) \cdot Y_{A,i+1} + 2 \cdot q_{S3,i} \cdot y_{A,n})\right) = 0 \\\hline
-\end{array}
-$$
-
 By gating the lookup expression on $q_{S1}$, we avoid the need to fill in unused cells with dummy values to pass the lookup argument. The optimized lookup value (using a default index of $0$) is:
 
 $$
@@ -160,3 +149,14 @@ $$
 $$
 
 This increases the degree of the lookup argument to $6$.
+
+$$
+\begin{array}{|c|l|}
+\hline
+\text{Degree} & \text{Constraint} \\\hline
+4   & q_{S4} \cdot (2 \cdot y_Q - Y_{A,0}) = 0 \\\hline
+6   & q_{S1,i} \Rightarrow (m_{i+1},\, x_{P,i},\, y_{P,i}) \in \mathcal{P} \\\hline
+3   & q_{S1,i} \cdot \big(\lambda_{2,i}^2 - (x_{A,i+1} + x_{R,i} + x_{A,i})\big) \\\hline
+5   & q_{S1,i} \cdot \left(4 \cdot \lambda_{2,i} \cdot (x_{A,i} - x_{A,i+1}) - (2 \cdot Y_{A,i} + (2 - q_{S3,i}) \cdot Y_{A,i+1} + 2 \cdot q_{S3,i} \cdot y_{A,n})\right) = 0 \\\hline
+\end{array}
+$$