fix: Poseidon spec's sparse-factorization w vector

content/algorithms/crypto/poseidon.md

@@ -698,14 +698,10 @@ $\overline{\underline{\Function \textsf{sparse\_factorize}(m \typecolon \Zp^{[t
  0 & m_{t - 1, 1} & \dots & m_{t - 1, t - 1}
 \end{bmatrix} \\~
 \\
-\line{3} \wb \typecolon \Zp^{[t - 1 {\times} 1]} = \hat{m}_{\ast, 0} = \begin{bmatrix}
- \hat{m}_{0, 0} \\
+\line{3} \wb \typecolon \Zp^{[t - 1 {\times} 1]} = m_{1 \dotdot, 0} = \begin{bmatrix}
+ m_{1, 0} \\
  \vdots \\
- \hat{m}_{t - 2, 0}
-\end{bmatrix} = m_{1 \dotdot, 1} = \begin{bmatrix}
- m_{1, 1} \\
- \vdots \\
- m_{t - 1, 1}
+ m_{t - 1, 0}
 \end{bmatrix} \\~
 \\
 \line{4} \hat\wb \typecolon \Zp^{[t - 1 {\times} 1]} = \hat{m}^{\neg 1} {\times} \hso \wb = \begin{bmatrix}
@@ -730,7 +726,7 @@ $\overline{\underline{\Function \textsf{sparse\_factorize}(m \typecolon \Zp^{[t
 **Algorithm Comments:**\
 **Line 1.** $\hat{m}$ is a submatrix of $m$ which excludes $m$'s first row and first column.\
 **Line 2.** $m'$ is a copy of $m$ where $m$'s first row and first column have been replaced with $[1, 0, \dots, 0]$.\
-**Line 3.** $\wb$ is a column vector which is the first column of $\hat{m}$ or the second column of $m$ excluding the first row's value.\
+**Line 3.** $\wb$ is a column vector whose values are the first column of $m$ excluding $m$'s first row.
 **Line 4.** $\hat\wb$ is the matrix-column vector product of $\hat{m}^{\neg 1}$ and $\wb$.\
 **Line 5.** $m''$ is a sparse matrix whose first row is the first row of $m$, remaining first column is $\hat\wb$, and remaining entries are the identity matrix.