sec-bit · KyrinCode · May 23, 2024
diff --git a/.gitignore b/.gitignore
@@ -1 +1,2 @@
 .DS_Store
+.vscode
diff --git a/plonk-intro-cn/2-plonk-lagrange-basis.md b/plonk-intro-cn/2-plonk-lagrange-basis.md
@@ -227,10 +227,10 @@ $$
 还拿 $\mathbb{F}_{13}$ 为例，我们取 $H=(1,5,12,8)$，并且乘法群的生成元 $g=2$。于是我们可以得到下面两个 Coset：
 
 $$
-\begin{split}
-H_1 &= g\cdot H  = (g, g\omega, g\omega^2, g\omega^3) &= (2,10,11,3) \\
-H_2 &= g^2\cdot H = (g^2, g^2\omega, g^2\omega^2, g^2\omega^3) &= (4,7,9,6) \\
-\end{split}
+\begin{aligned}
+H_1 &= g\cdot H = (g, g\omega, g\omega^2, g\omega^3) = (2,10,11,3) \\
+H_2 &= g^2\cdot H = (g^2, g^2\omega, g^2\omega^2, g^2\omega^3) = (4,7,9,6) \\
+\end{aligned}
 $$
 
 可以看到 $\mathbb{F}^*_{13}=H\cup H_1 \cup H_2$，并且它们交集为空，没有任何重叠。并且它们的 Vanishing Polynomial 也可以快速计算：

diff --git a/plonk-intro-cn/3-plonk-permutation.md b/plonk-intro-cn/3-plonk-permutation.md
@@ -113,9 +113,9 @@ $$
 \begin{array}{c|c|c}
 q_i & r_i & q_i\cdot r_i \\
 \hline
-q_0 & 1  & r_0\\
-q_1 & r_0 & r_1\\
-q_2 & r_1 & r_2\\
+q_0 & r_0=1  & r_1\\
+q_1 & r_1 & r_2\\
+q_2 & r_2 & r_3\\
 \vdots & \vdots & \vdots\\
 q_{n-2} & r_{n-2} & r_{n-1}\\
 q_{n-1}=\frac{1}{p} & r_{n-1} & 1 \\