Paramodular_Lemma_5.1 -- Sage

Q2=matrix([[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1],[0,0,0,0,1,0,1,0],[0,0,0,0,0,1,0,1],[1,0,-1,0,0,0,0,0],[0,1,0,-1,0,0,0,0]]);Q2

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 \\ 1 & 0 & -1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & -1 & 0 & 0 & 0 & 0 \end{array}\right)$

N=4;s=[]; for (i,j) in cartesian_product([range(N),range(N)]): s.append('d%d%d' %(i,j)) a = var(s); D = matrix(SR,N,N,a); D

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} d_{00} & d_{01} & d_{02} & d_{03} \\ d_{10} & d_{11} & d_{12} & d_{13} \\ d_{20} & d_{21} & d_{22} & d_{23} \\ d_{30} & d_{31} & d_{32} & d_{33} \end{array}\right)$

N=4;s=[]; for (i,j) in cartesian_product([range(N),range(N)]): s.append('x%d%d' %(i,j)) a = var(s); X = matrix(SR,N,N,a); X

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} x_{00} & x_{01} & x_{02} & x_{03} \\ x_{10} & x_{11} & x_{12} & x_{13} \\ x_{20} & x_{21} & x_{22} & x_{23} \\ x_{30} & x_{31} & x_{32} & x_{33} \end{array}\right)$

As our matrices will be in $\textrm{Sp}_4(F)$, we can take the parabolic element to be of the form $\begin{pmatrix} ^{t}D^{-1} & X \\ 0 & D \end{pmatrix}$.

A=(D.det()*D.transpose().inverse()).simplify_full();A

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} -{\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} + {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} - {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} & {\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} & -{\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{30} + {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{31} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} d_{33} & {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{30} - {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{31} + {\left(d_{11} d_{20} - d_{10} d_{21}\right)} d_{32} \\ {\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} & -{\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} + {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} - {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} & {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{31} + {\left(d_{01} d_{20} - d_{00} d_{21}\right)} d_{33} & -{\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{30} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{31} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} d_{32} \\ -{\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} + {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} - {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} & {\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} & -{\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{30} + {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{31} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{33} & {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{30} - {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{31} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{32} \\ {\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} & -{\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} + {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} - {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} & {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{21} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{23} & -{\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{20} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{21} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{22} \end{array}\right)$

O4=matrix(4);O4;O2=matrix(2);O2;I2=matrix.identity(2);I2

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr} 0 & 0 \\ 0 & 0 \end{array}\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr} 1 & 0 \\ 0 & 1 \end{array}\right)$

We now create our element $P \in P_8(F) \subset \textrm{Sp}_8(F)$.

P=block_matrix(2,2,[A,X,O4,D]);P;

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr|rrrr} -{\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} + {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} - {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} & {\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} & -{\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{30} + {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{31} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} d_{33} & {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{30} - {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{31} + {\left(d_{11} d_{20} - d_{10} d_{21}\right)} d_{32} & x_{00} & x_{01} & x_{02} & x_{03} \\ {\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} & -{\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} + {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} - {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} & {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{31} + {\left(d_{01} d_{20} - d_{00} d_{21}\right)} d_{33} & -{\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{30} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{31} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} d_{32} & x_{10} & x_{11} & x_{12} & x_{13} \\ -{\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} + {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} - {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} & {\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} & -{\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{30} + {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{31} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{33} & {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{30} - {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{31} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{32} & x_{20} & x_{21} & x_{22} & x_{23} \\ {\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} & -{\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} + {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} - {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} & {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{21} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{23} & -{\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{20} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{21} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{22} & x_{30} & x_{31} & x_{32} & x_{33} \\ \hline 0 & 0 & 0 & 0 & d_{00} & d_{01} & d_{02} & d_{03} \\ 0 & 0 & 0 & 0 & d_{10} & d_{11} & d_{12} & d_{13} \\ 0 & 0 & 0 & 0 & d_{20} & d_{21} & d_{22} & d_{23} \\ 0 & 0 & 0 & 0 & d_{30} & d_{31} & d_{32} & d_{33} \end{array}\right)$

N=4;s=[]; for (i,j) in cartesian_product([range(N),range(N)]): s.append('h%d%d' %(i,j)) var(s);

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(h_{00}, h_{01}, h_{02}, h_{03}, h_{10}, h_{11}, h_{12}, h_{13}, h_{20}, h_{21}, h_{22}, h_{23}, h_{30}, h_{31}, h_{32}, h_{33}\right)$

h1=matrix([[h00,p*h01], [h10,h11]]);h2=matrix([[h02,h03],[h12,h13/p]]);h3=matrix([[h20,p*h21],[p*h30,p*h31]]);h4=matrix([[h22,h23],[p*h32,h33]]);

N=4;s=[]; for (i,j) in cartesian_product([range(N),range(N)]): s.append('k%d%d' %(i,j)) var(s);

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(k_{00}, k_{01}, k_{02}, k_{03}, k_{10}, k_{11}, k_{12}, k_{13}, k_{20}, k_{21}, k_{22}, k_{23}, k_{30}, k_{31}, k_{32}, k_{33}\right)$

k1=matrix([[k00,p*k01], [k10,k11]]);k2=matrix([[k02,k03],[k12,k13/p]]);k3=matrix([[k20,p*k21],[p*k30,p*k31]]);k4=matrix([[k22,k23],[p*k32,k33]]);

HK=block_matrix(4,4,[h1,O2,-h2,O2,O2,k1,O2,k2,-h3,O2,h4,O2,O2,k3,O2,k4]);HK

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr|rr|rr|rr} h_{00} & h_{01} p & 0 & 0 & -h_{02} & -h_{03} & 0 & 0 \\ h_{10} & h_{11} & 0 & 0 & -h_{12} & -\frac{h_{13}}{p} & 0 & 0 \\ \hline 0 & 0 & k_{00} & k_{01} p & 0 & 0 & k_{02} & k_{03} \\ 0 & 0 & k_{10} & k_{11} & 0 & 0 & k_{12} & \frac{k_{13}}{p} \\ \hline -h_{20} & -h_{21} p & 0 & 0 & h_{22} & h_{23} & 0 & 0 \\ -h_{30} p & -h_{31} p & 0 & 0 & h_{32} p & h_{33} & 0 & 0 \\ \hline 0 & 0 & k_{20} & k_{21} p & 0 & 0 & k_{22} & k_{23} \\ 0 & 0 & k_{30} p & k_{31} p & 0 & 0 & k_{32} p & k_{33} \end{array}\right)$

N=4;s=[]; for (i,j) in cartesian_product([range(N),range(N)]): s.append('H%d%d' %(i,j)) var(s); var('p');

 $\newcommand{\Bold}[1]{\mathbf{#1}}p$

H1=matrix([[H00,p*H01], [H10,H11]]);H2=matrix([[H02,H03],[H12,H13/p]]);H3=matrix([[H20,p*H21],[p*H30,p*H31]]);H4=matrix([[H22,H23],[p*H32,H33]]);

HI=block_matrix(4,4,[H1,O2,-H2,O2,O2,I2,O2,O2,-H3,O2,H4,O2,O2,O2,O2,I2]);HI

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr|rr|rr|rr} H_{00} & H_{01} p & 0 & 0 & -H_{02} & -H_{03} & 0 & 0 \\ H_{10} & H_{11} & 0 & 0 & -H_{12} & -\frac{H_{13}}{p} & 0 & 0 \\ \hline 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ \hline -H_{20} & -H_{21} p & 0 & 0 & H_{22} & H_{23} & 0 & 0 \\ -H_{30} p & -H_{31} p & 0 & 0 & H_{32} p & H_{33} & 0 & 0 \\ \hline 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \end{array}\right)$

We set $Z = (h_1,k_1) = Q_2^{-1}P Q_2 (H,1)$ and use that this is in $\Gamma_2[\varpi] \times \Gamma_2[\varpi]$ to try and deduce $H \in \Gamma_2[\varpi]$.

Z=Q2.inverse()*P*Q2*HI;Z

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} -H_{30} p x_{01} - {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} - x_{02}\right)} H_{00} + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} + x_{03}\right)} H_{10} - H_{20} x_{00} & -{\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} - x_{02}\right)} H_{01} p - H_{21} p x_{00} - H_{31} p x_{01} + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} + x_{03}\right)} H_{11} & -x_{02} & -x_{03} & H_{32} p x_{01} + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} - x_{02}\right)} H_{02} - {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} + x_{03}\right)} H_{12} + H_{22} x_{00} & {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} - x_{02}\right)} H_{03} + H_{23} x_{00} + H_{33} x_{01} - \frac{{\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} + x_{03}\right)} H_{13}}{p} & -{\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{30} + {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{31} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} d_{33} + x_{00} & {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{30} - {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{31} + {\left(d_{11} d_{20} - d_{10} d_{21}\right)} d_{32} + x_{01} \\ -H_{30} p x_{11} + {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} + x_{12}\right)} H_{00} - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} - x_{13}\right)} H_{10} - H_{20} x_{10} & {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} + x_{12}\right)} H_{01} p - H_{21} p x_{10} - H_{31} p x_{11} - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} - x_{13}\right)} H_{11} & -x_{12} & -x_{13} & H_{32} p x_{11} - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} + x_{12}\right)} H_{02} + {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} - x_{13}\right)} H_{12} + H_{22} x_{10} & -{\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} + x_{12}\right)} H_{03} + H_{23} x_{10} + H_{33} x_{11} + \frac{{\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} - x_{13}\right)} H_{13}}{p} & {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{31} + {\left(d_{01} d_{20} - d_{00} d_{21}\right)} d_{33} + x_{10} & -{\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{30} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{31} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} d_{32} + x_{11} \\ H_{30} {\left(d_{21} - x_{01}\right)} p - {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} + d_{22} - x_{02}\right)} H_{00} + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} - d_{23} + x_{03}\right)} H_{10} + H_{20} {\left(d_{20} - x_{00}\right)} & -{\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} + d_{22} - x_{02}\right)} H_{01} p + H_{21} {\left(d_{20} - x_{00}\right)} p + H_{31} {\left(d_{21} - x_{01}\right)} p + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} - d_{23} + x_{03}\right)} H_{11} & d_{22} - x_{02} & d_{23} - x_{03} & -H_{32} {\left(d_{21} - x_{01}\right)} p + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} + d_{22} - x_{02}\right)} H_{02} - {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} - d_{23} + x_{03}\right)} H_{12} - H_{22} {\left(d_{20} - x_{00}\right)} & {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} + d_{22} - x_{02}\right)} H_{03} - H_{23} {\left(d_{20} - x_{00}\right)} - H_{33} {\left(d_{21} - x_{01}\right)} - \frac{{\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} - d_{23} + x_{03}\right)} H_{13}}{p} & -{\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{30} + {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{31} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} d_{33} - d_{20} + x_{00} & {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{30} - {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{31} + {\left(d_{11} d_{20} - d_{10} d_{21}\right)} d_{32} - d_{21} + x_{01} \\ H_{30} {\left(d_{31} - x_{11}\right)} p + {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} - d_{32} + x_{12}\right)} H_{00} - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} + d_{33} - x_{13}\right)} H_{10} + H_{20} {\left(d_{30} - x_{10}\right)} & {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} - d_{32} + x_{12}\right)} H_{01} p + H_{21} {\left(d_{30} - x_{10}\right)} p + H_{31} {\left(d_{31} - x_{11}\right)} p - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} + d_{33} - x_{13}\right)} H_{11} & d_{32} - x_{12} & d_{33} - x_{13} & -H_{32} {\left(d_{31} - x_{11}\right)} p - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} - d_{32} + x_{12}\right)} H_{02} + {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} + d_{33} - x_{13}\right)} H_{12} - H_{22} {\left(d_{30} - x_{10}\right)} & -{\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} - d_{32} + x_{12}\right)} H_{03} - H_{23} {\left(d_{30} - x_{10}\right)} - H_{33} {\left(d_{31} - x_{11}\right)} + \frac{{\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} + d_{33} - x_{13}\right)} H_{13}}{p} & {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{31} + {\left(d_{01} d_{20} - d_{00} d_{21}\right)} d_{33} - d_{30} + x_{10} & -{\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{30} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{31} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} d_{32} - d_{31} + x_{11} \\ -H_{30} {\left(d_{01} - x_{21}\right)} p + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} + d_{02} - x_{22}\right)} H_{00} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} - d_{03} + x_{23}\right)} H_{10} - H_{20} {\left(d_{00} - x_{20}\right)} & {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} + d_{02} - x_{22}\right)} H_{01} p - H_{21} {\left(d_{00} - x_{20}\right)} p - H_{31} {\left(d_{01} - x_{21}\right)} p - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} - d_{03} + x_{23}\right)} H_{11} & -d_{02} + x_{22} & -d_{03} + x_{23} & H_{32} {\left(d_{01} - x_{21}\right)} p - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} + d_{02} - x_{22}\right)} H_{02} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} - d_{03} + x_{23}\right)} H_{12} + H_{22} {\left(d_{00} - x_{20}\right)} & -{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} + d_{02} - x_{22}\right)} H_{03} + H_{23} {\left(d_{00} - x_{20}\right)} + H_{33} {\left(d_{01} - x_{21}\right)} + \frac{{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} - d_{03} + x_{23}\right)} H_{13}}{p} & {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{31} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{33} + d_{00} - x_{20} & -{\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{30} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{31} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{32} + d_{01} - x_{21} \\ -H_{30} {\left(d_{11} - x_{31}\right)} p - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} - d_{12} + x_{32}\right)} H_{00} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} + d_{13} - x_{33}\right)} H_{10} - H_{20} {\left(d_{10} - x_{30}\right)} & -{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} - d_{12} + x_{32}\right)} H_{01} p - H_{21} {\left(d_{10} - x_{30}\right)} p - H_{31} {\left(d_{11} - x_{31}\right)} p + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} + d_{13} - x_{33}\right)} H_{11} & -d_{12} + x_{32} & -d_{13} + x_{33} & H_{32} {\left(d_{11} - x_{31}\right)} p + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} - d_{12} + x_{32}\right)} H_{02} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} + d_{13} - x_{33}\right)} H_{12} + H_{22} {\left(d_{10} - x_{30}\right)} & {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} - d_{12} + x_{32}\right)} H_{03} + H_{23} {\left(d_{10} - x_{30}\right)} + H_{33} {\left(d_{11} - x_{31}\right)} - \frac{{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} + d_{13} - x_{33}\right)} H_{13}}{p} & -{\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{20} + {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{21} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{23} + d_{10} - x_{30} & {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{20} - {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{21} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{22} + d_{11} - x_{31} \\ -H_{30} p x_{21} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} - x_{22}\right)} H_{00} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} + x_{23}\right)} H_{10} - H_{20} x_{20} & -{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} - x_{22}\right)} H_{01} p - H_{21} p x_{20} - H_{31} p x_{21} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} + x_{23}\right)} H_{11} & -x_{22} & -x_{23} & H_{32} p x_{21} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} - x_{22}\right)} H_{02} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} + x_{23}\right)} H_{12} + H_{22} x_{20} & {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} - x_{22}\right)} H_{03} + H_{23} x_{20} + H_{33} x_{21} - \frac{{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} + x_{23}\right)} H_{13}}{p} & -{\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{30} + {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{31} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{33} + x_{20} & {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{30} - {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{31} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{32} + x_{21} \\ -H_{30} p x_{31} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} + x_{32}\right)} H_{00} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} - x_{33}\right)} H_{10} - H_{20} x_{30} & {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} + x_{32}\right)} H_{01} p - H_{21} p x_{30} - H_{31} p x_{31} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} - x_{33}\right)} H_{11} & -x_{32} & -x_{33} & H_{32} p x_{31} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} + x_{32}\right)} H_{02} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} - x_{33}\right)} H_{12} + H_{22} x_{30} & -{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} + x_{32}\right)} H_{03} + H_{23} x_{30} + H_{33} x_{31} + \frac{{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} - x_{33}\right)} H_{13}}{p} & {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{21} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{23} + x_{30} & -{\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{20} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{21} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{22} + x_{31} \end{array}\right)$

We start by simplifying the third and fourth columns.

(HK[0,2],Z[0,2]);(HK[0,3], Z[0,3]);(HK[1,2],Z[1,2]);(HK[1,3],Z[1,3]);

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(0, -x_{02}\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(0, -x_{03}\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(0, -x_{12}\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(0, -x_{13}\right)$

Z=Z.substitute(x02==0).substitute(x03==0).substitute(x12==0).substitute(x13==0);Z;

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} -H_{30} p x_{01} - {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33}\right)} H_{00} + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33}\right)} H_{10} - H_{20} x_{00} & -{\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33}\right)} H_{01} p - H_{21} p x_{00} - H_{31} p x_{01} + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33}\right)} H_{11} & 0 & 0 & H_{32} p x_{01} + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33}\right)} H_{02} - {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33}\right)} H_{12} + H_{22} x_{00} & {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33}\right)} H_{03} + H_{23} x_{00} + H_{33} x_{01} - \frac{{\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33}\right)} H_{13}}{p} & -{\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{30} + {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{31} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} d_{33} + x_{00} & {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{30} - {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{31} + {\left(d_{11} d_{20} - d_{10} d_{21}\right)} d_{32} + x_{01} \\ -H_{30} p x_{11} + {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33}\right)} H_{00} - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33}\right)} H_{10} - H_{20} x_{10} & {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33}\right)} H_{01} p - H_{21} p x_{10} - H_{31} p x_{11} - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33}\right)} H_{11} & 0 & 0 & H_{32} p x_{11} - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33}\right)} H_{02} + {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33}\right)} H_{12} + H_{22} x_{10} & -{\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33}\right)} H_{03} + H_{23} x_{10} + H_{33} x_{11} + \frac{{\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33}\right)} H_{13}}{p} & {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{31} + {\left(d_{01} d_{20} - d_{00} d_{21}\right)} d_{33} + x_{10} & -{\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{30} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{31} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} d_{32} + x_{11} \\ H_{30} {\left(d_{21} - x_{01}\right)} p - {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} + d_{22}\right)} H_{00} + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} - d_{23}\right)} H_{10} + H_{20} {\left(d_{20} - x_{00}\right)} & -{\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} + d_{22}\right)} H_{01} p + H_{21} {\left(d_{20} - x_{00}\right)} p + H_{31} {\left(d_{21} - x_{01}\right)} p + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} - d_{23}\right)} H_{11} & d_{22} & d_{23} & -H_{32} {\left(d_{21} - x_{01}\right)} p + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} + d_{22}\right)} H_{02} - {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} - d_{23}\right)} H_{12} - H_{22} {\left(d_{20} - x_{00}\right)} & {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} + d_{22}\right)} H_{03} - H_{23} {\left(d_{20} - x_{00}\right)} - H_{33} {\left(d_{21} - x_{01}\right)} - \frac{{\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} - d_{23}\right)} H_{13}}{p} & -{\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{30} + {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{31} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} d_{33} - d_{20} + x_{00} & {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{30} - {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{31} + {\left(d_{11} d_{20} - d_{10} d_{21}\right)} d_{32} - d_{21} + x_{01} \\ H_{30} {\left(d_{31} - x_{11}\right)} p + {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} - d_{32}\right)} H_{00} - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} + d_{33}\right)} H_{10} + H_{20} {\left(d_{30} - x_{10}\right)} & {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} - d_{32}\right)} H_{01} p + H_{21} {\left(d_{30} - x_{10}\right)} p + H_{31} {\left(d_{31} - x_{11}\right)} p - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} + d_{33}\right)} H_{11} & d_{32} & d_{33} & -H_{32} {\left(d_{31} - x_{11}\right)} p - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} - d_{32}\right)} H_{02} + {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} + d_{33}\right)} H_{12} - H_{22} {\left(d_{30} - x_{10}\right)} & -{\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} - d_{32}\right)} H_{03} - H_{23} {\left(d_{30} - x_{10}\right)} - H_{33} {\left(d_{31} - x_{11}\right)} + \frac{{\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} + d_{33}\right)} H_{13}}{p} & {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{31} + {\left(d_{01} d_{20} - d_{00} d_{21}\right)} d_{33} - d_{30} + x_{10} & -{\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{30} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{31} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} d_{32} - d_{31} + x_{11} \\ -H_{30} {\left(d_{01} - x_{21}\right)} p + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} + d_{02} - x_{22}\right)} H_{00} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} - d_{03} + x_{23}\right)} H_{10} - H_{20} {\left(d_{00} - x_{20}\right)} & {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} + d_{02} - x_{22}\right)} H_{01} p - H_{21} {\left(d_{00} - x_{20}\right)} p - H_{31} {\left(d_{01} - x_{21}\right)} p - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} - d_{03} + x_{23}\right)} H_{11} & -d_{02} + x_{22} & -d_{03} + x_{23} & H_{32} {\left(d_{01} - x_{21}\right)} p - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} + d_{02} - x_{22}\right)} H_{02} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} - d_{03} + x_{23}\right)} H_{12} + H_{22} {\left(d_{00} - x_{20}\right)} & -{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} + d_{02} - x_{22}\right)} H_{03} + H_{23} {\left(d_{00} - x_{20}\right)} + H_{33} {\left(d_{01} - x_{21}\right)} + \frac{{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} - d_{03} + x_{23}\right)} H_{13}}{p} & {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{31} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{33} + d_{00} - x_{20} & -{\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{30} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{31} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{32} + d_{01} - x_{21} \\ -H_{30} {\left(d_{11} - x_{31}\right)} p - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} - d_{12} + x_{32}\right)} H_{00} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} + d_{13} - x_{33}\right)} H_{10} - H_{20} {\left(d_{10} - x_{30}\right)} & -{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} - d_{12} + x_{32}\right)} H_{01} p - H_{21} {\left(d_{10} - x_{30}\right)} p - H_{31} {\left(d_{11} - x_{31}\right)} p + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} + d_{13} - x_{33}\right)} H_{11} & -d_{12} + x_{32} & -d_{13} + x_{33} & H_{32} {\left(d_{11} - x_{31}\right)} p + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} - d_{12} + x_{32}\right)} H_{02} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} + d_{13} - x_{33}\right)} H_{12} + H_{22} {\left(d_{10} - x_{30}\right)} & {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} - d_{12} + x_{32}\right)} H_{03} + H_{23} {\left(d_{10} - x_{30}\right)} + H_{33} {\left(d_{11} - x_{31}\right)} - \frac{{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} + d_{13} - x_{33}\right)} H_{13}}{p} & -{\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{20} + {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{21} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{23} + d_{10} - x_{30} & {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{20} - {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{21} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{22} + d_{11} - x_{31} \\ -H_{30} p x_{21} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} - x_{22}\right)} H_{00} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} + x_{23}\right)} H_{10} - H_{20} x_{20} & -{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} - x_{22}\right)} H_{01} p - H_{21} p x_{20} - H_{31} p x_{21} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} + x_{23}\right)} H_{11} & -x_{22} & -x_{23} & H_{32} p x_{21} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} - x_{22}\right)} H_{02} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} + x_{23}\right)} H_{12} + H_{22} x_{20} & {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} - x_{22}\right)} H_{03} + H_{23} x_{20} + H_{33} x_{21} - \frac{{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} + x_{23}\right)} H_{13}}{p} & -{\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{30} + {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{31} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{33} + x_{20} & {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{30} - {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{31} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{32} + x_{21} \\ -H_{30} p x_{31} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} + x_{32}\right)} H_{00} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} - x_{33}\right)} H_{10} - H_{20} x_{30} & {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} + x_{32}\right)} H_{01} p - H_{21} p x_{30} - H_{31} p x_{31} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} - x_{33}\right)} H_{11} & -x_{32} & -x_{33} & H_{32} p x_{31} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} + x_{32}\right)} H_{02} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} - x_{33}\right)} H_{12} + H_{22} x_{30} & -{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} + x_{32}\right)} H_{03} + H_{23} x_{30} + H_{33} x_{31} + \frac{{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} - x_{33}\right)} H_{13}}{p} & {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{21} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{23} + x_{30} & -{\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{20} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{21} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{22} + x_{31} \end{array}\right)$

(HK[4,2],Z[4,2]);(HK[4,3], Z[4,3]);(HK[5,2],Z[5,2]);(HK[5,3],Z[5,3]);

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(0, -d_{02} + x_{22}\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(0, -d_{03} + x_{23}\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(0, -d_{12} + x_{32}\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(0, -d_{13} + x_{33}\right)$

Z=Z.substitute(x22==d02).substitute(x23==d03).substitute(x32==d12).substitute(x33==d13);Z;

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} -H_{30} p x_{01} - {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33}\right)} H_{00} + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33}\right)} H_{10} - H_{20} x_{00} & -{\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33}\right)} H_{01} p - H_{21} p x_{00} - H_{31} p x_{01} + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33}\right)} H_{11} & 0 & 0 & H_{32} p x_{01} + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33}\right)} H_{02} - {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33}\right)} H_{12} + H_{22} x_{00} & {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33}\right)} H_{03} + H_{23} x_{00} + H_{33} x_{01} - \frac{{\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33}\right)} H_{13}}{p} & -{\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{30} + {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{31} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} d_{33} + x_{00} & {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{30} - {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{31} + {\left(d_{11} d_{20} - d_{10} d_{21}\right)} d_{32} + x_{01} \\ -H_{30} p x_{11} + {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33}\right)} H_{00} - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33}\right)} H_{10} - H_{20} x_{10} & {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33}\right)} H_{01} p - H_{21} p x_{10} - H_{31} p x_{11} - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33}\right)} H_{11} & 0 & 0 & H_{32} p x_{11} - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33}\right)} H_{02} + {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33}\right)} H_{12} + H_{22} x_{10} & -{\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33}\right)} H_{03} + H_{23} x_{10} + H_{33} x_{11} + \frac{{\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33}\right)} H_{13}}{p} & {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{31} + {\left(d_{01} d_{20} - d_{00} d_{21}\right)} d_{33} + x_{10} & -{\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{30} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{31} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} d_{32} + x_{11} \\ H_{30} {\left(d_{21} - x_{01}\right)} p - {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} + d_{22}\right)} H_{00} + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} - d_{23}\right)} H_{10} + H_{20} {\left(d_{20} - x_{00}\right)} & -{\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} + d_{22}\right)} H_{01} p + H_{21} {\left(d_{20} - x_{00}\right)} p + H_{31} {\left(d_{21} - x_{01}\right)} p + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} - d_{23}\right)} H_{11} & d_{22} & d_{23} & -H_{32} {\left(d_{21} - x_{01}\right)} p + {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} + d_{22}\right)} H_{02} - {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} - d_{23}\right)} H_{12} - H_{22} {\left(d_{20} - x_{00}\right)} & {\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{31} - {\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{32} + {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{33} + d_{22}\right)} H_{03} - H_{23} {\left(d_{20} - x_{00}\right)} - H_{33} {\left(d_{21} - x_{01}\right)} - \frac{{\left({\left(d_{13} d_{22} - d_{12} d_{23}\right)} d_{30} - {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{32} + {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{33} - d_{23}\right)} H_{13}}{p} & -{\left(d_{13} d_{21} - d_{11} d_{23}\right)} d_{30} + {\left(d_{13} d_{20} - d_{10} d_{23}\right)} d_{31} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} d_{33} - d_{20} + x_{00} & {\left(d_{12} d_{21} - d_{11} d_{22}\right)} d_{30} - {\left(d_{12} d_{20} - d_{10} d_{22}\right)} d_{31} + {\left(d_{11} d_{20} - d_{10} d_{21}\right)} d_{32} - d_{21} + x_{01} \\ H_{30} {\left(d_{31} - x_{11}\right)} p + {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} - d_{32}\right)} H_{00} - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} + d_{33}\right)} H_{10} + H_{20} {\left(d_{30} - x_{10}\right)} & {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} - d_{32}\right)} H_{01} p + H_{21} {\left(d_{30} - x_{10}\right)} p + H_{31} {\left(d_{31} - x_{11}\right)} p - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} + d_{33}\right)} H_{11} & d_{32} & d_{33} & -H_{32} {\left(d_{31} - x_{11}\right)} p - {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} - d_{32}\right)} H_{02} + {\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} + d_{33}\right)} H_{12} - H_{22} {\left(d_{30} - x_{10}\right)} & -{\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{31} - {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{32} + {\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{33} - d_{32}\right)} H_{03} - H_{23} {\left(d_{30} - x_{10}\right)} - H_{33} {\left(d_{31} - x_{11}\right)} + \frac{{\left({\left(d_{03} d_{22} - d_{02} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{32} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{33} + d_{33}\right)} H_{13}}{p} & {\left(d_{03} d_{21} - d_{01} d_{23}\right)} d_{30} - {\left(d_{03} d_{20} - d_{00} d_{23}\right)} d_{31} + {\left(d_{01} d_{20} - d_{00} d_{21}\right)} d_{33} - d_{30} + x_{10} & -{\left(d_{02} d_{21} - d_{01} d_{22}\right)} d_{30} + {\left(d_{02} d_{20} - d_{00} d_{22}\right)} d_{31} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} d_{32} - d_{31} + x_{11} \\ -H_{30} {\left(d_{01} - x_{21}\right)} p + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33}\right)} H_{00} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33}\right)} H_{10} - H_{20} {\left(d_{00} - x_{20}\right)} & {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33}\right)} H_{01} p - H_{21} {\left(d_{00} - x_{20}\right)} p - H_{31} {\left(d_{01} - x_{21}\right)} p - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33}\right)} H_{11} & 0 & 0 & H_{32} {\left(d_{01} - x_{21}\right)} p - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33}\right)} H_{02} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33}\right)} H_{12} + H_{22} {\left(d_{00} - x_{20}\right)} & -{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33}\right)} H_{03} + H_{23} {\left(d_{00} - x_{20}\right)} + H_{33} {\left(d_{01} - x_{21}\right)} + \frac{{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33}\right)} H_{13}}{p} & {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{31} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{33} + d_{00} - x_{20} & -{\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{30} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{31} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{32} + d_{01} - x_{21} \\ -H_{30} {\left(d_{11} - x_{31}\right)} p - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23}\right)} H_{00} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23}\right)} H_{10} - H_{20} {\left(d_{10} - x_{30}\right)} & -{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23}\right)} H_{01} p - H_{21} {\left(d_{10} - x_{30}\right)} p - H_{31} {\left(d_{11} - x_{31}\right)} p + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23}\right)} H_{11} & 0 & 0 & H_{32} {\left(d_{11} - x_{31}\right)} p + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23}\right)} H_{02} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23}\right)} H_{12} + H_{22} {\left(d_{10} - x_{30}\right)} & {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23}\right)} H_{03} + H_{23} {\left(d_{10} - x_{30}\right)} + H_{33} {\left(d_{11} - x_{31}\right)} - \frac{{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23}\right)} H_{13}}{p} & -{\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{20} + {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{21} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{23} + d_{10} - x_{30} & {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{20} - {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{21} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{22} + d_{11} - x_{31} \\ -H_{30} p x_{21} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} - d_{02}\right)} H_{00} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} + d_{03}\right)} H_{10} - H_{20} x_{20} & -{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} - d_{02}\right)} H_{01} p - H_{21} p x_{20} - H_{31} p x_{21} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} + d_{03}\right)} H_{11} & -d_{02} & -d_{03} & H_{32} p x_{21} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} - d_{02}\right)} H_{02} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} + d_{03}\right)} H_{12} + H_{22} x_{20} & {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{31} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{32} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{33} - d_{02}\right)} H_{03} + H_{23} x_{20} + H_{33} x_{21} - \frac{{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{30} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{32} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{33} + d_{03}\right)} H_{13}}{p} & -{\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{30} + {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{31} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{33} + x_{20} & {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{30} - {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{31} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{32} + x_{21} \\ -H_{30} p x_{31} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} + d_{12}\right)} H_{00} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} - d_{13}\right)} H_{10} - H_{20} x_{30} & {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} + d_{12}\right)} H_{01} p - H_{21} p x_{30} - H_{31} p x_{31} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} - d_{13}\right)} H_{11} & -d_{12} & -d_{13} & H_{32} p x_{31} - {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} + d_{12}\right)} H_{02} + {\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} - d_{13}\right)} H_{12} + H_{22} x_{30} & -{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{21} - {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{22} + {\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{23} + d_{12}\right)} H_{03} + H_{23} x_{30} + H_{33} x_{31} + \frac{{\left({\left(d_{03} d_{12} - d_{02} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{22} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{23} - d_{13}\right)} H_{13}}{p} & {\left(d_{03} d_{11} - d_{01} d_{13}\right)} d_{20} - {\left(d_{03} d_{10} - d_{00} d_{13}\right)} d_{21} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{23} + x_{30} & -{\left(d_{02} d_{11} - d_{01} d_{12}\right)} d_{20} + {\left(d_{02} d_{10} - d_{00} d_{12}\right)} d_{21} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} d_{22} + x_{31} \end{array}\right)$

Z=Z.substitute(d22==k00).substitute(d23==p*k01).substitute(d32==k10).substitute(d33==k11).substitute(d02==-k20).substitute(d03==-p*k21).substitute(d12==-p*k30).substitute(d02==-p*k31).substitute(d13==-p*k31);Z;

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} -H_{30} p x_{01} - {\left({\left(k_{01} k_{30} p^{2} - k_{00} k_{31} p\right)} d_{31} + {\left(d_{11} k_{01} p + d_{21} k_{31} p\right)} k_{10} - {\left(d_{21} k_{30} p + d_{11} k_{00}\right)} k_{11}\right)} H_{00} + {\left({\left(k_{01} k_{30} p^{2} - k_{00} k_{31} p\right)} d_{30} + {\left(d_{10} k_{01} p + d_{20} k_{31} p\right)} k_{10} - {\left(d_{20} k_{30} p + d_{10} k_{00}\right)} k_{11}\right)} H_{10} - H_{20} x_{00} & -{\left({\left(k_{01} k_{30} p^{2} - k_{00} k_{31} p\right)} d_{31} + {\left(d_{11} k_{01} p + d_{21} k_{31} p\right)} k_{10} - {\left(d_{21} k_{30} p + d_{11} k_{00}\right)} k_{11}\right)} H_{01} p - H_{21} p x_{00} - H_{31} p x_{01} + {\left({\left(k_{01} k_{30} p^{2} - k_{00} k_{31} p\right)} d_{30} + {\left(d_{10} k_{01} p + d_{20} k_{31} p\right)} k_{10} - {\left(d_{20} k_{30} p + d_{10} k_{00}\right)} k_{11}\right)} H_{11} & 0 & 0 & H_{32} p x_{01} + {\left({\left(k_{01} k_{30} p^{2} - k_{00} k_{31} p\right)} d_{31} + {\left(d_{11} k_{01} p + d_{21} k_{31} p\right)} k_{10} - {\left(d_{21} k_{30} p + d_{11} k_{00}\right)} k_{11}\right)} H_{02} - {\left({\left(k_{01} k_{30} p^{2} - k_{00} k_{31} p\right)} d_{30} + {\left(d_{10} k_{01} p + d_{20} k_{31} p\right)} k_{10} - {\left(d_{20} k_{30} p + d_{10} k_{00}\right)} k_{11}\right)} H_{12} + H_{22} x_{00} & {\left({\left(k_{01} k_{30} p^{2} - k_{00} k_{31} p\right)} d_{31} + {\left(d_{11} k_{01} p + d_{21} k_{31} p\right)} k_{10} - {\left(d_{21} k_{30} p + d_{11} k_{00}\right)} k_{11}\right)} H_{03} + H_{23} x_{00} + H_{33} x_{01} - \frac{{\left({\left(k_{01} k_{30} p^{2} - k_{00} k_{31} p\right)} d_{30} + {\left(d_{10} k_{01} p + d_{20} k_{31} p\right)} k_{10} - {\left(d_{20} k_{30} p + d_{10} k_{00}\right)} k_{11}\right)} H_{13}}{p} & {\left(d_{11} k_{01} p + d_{21} k_{31} p\right)} d_{30} - {\left(d_{10} k_{01} p + d_{20} k_{31} p\right)} d_{31} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{11} + x_{00} & -{\left(d_{21} k_{30} p + d_{11} k_{00}\right)} d_{30} + {\left(d_{20} k_{30} p + d_{10} k_{00}\right)} d_{31} + {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{10} + x_{01} \\ -H_{30} p x_{11} + {\left({\left(k_{01} k_{20} p - k_{00} k_{21} p\right)} d_{31} + {\left(d_{01} k_{01} p + d_{21} k_{21} p\right)} k_{10} - {\left(d_{01} k_{00} + d_{21} k_{20}\right)} k_{11}\right)} H_{00} - {\left({\left(k_{01} k_{20} p - k_{00} k_{21} p\right)} d_{30} + {\left(d_{00} k_{01} p + d_{20} k_{21} p\right)} k_{10} - {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{11}\right)} H_{10} - H_{20} x_{10} & {\left({\left(k_{01} k_{20} p - k_{00} k_{21} p\right)} d_{31} + {\left(d_{01} k_{01} p + d_{21} k_{21} p\right)} k_{10} - {\left(d_{01} k_{00} + d_{21} k_{20}\right)} k_{11}\right)} H_{01} p - H_{21} p x_{10} - H_{31} p x_{11} - {\left({\left(k_{01} k_{20} p - k_{00} k_{21} p\right)} d_{30} + {\left(d_{00} k_{01} p + d_{20} k_{21} p\right)} k_{10} - {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{11}\right)} H_{11} & 0 & 0 & H_{32} p x_{11} - {\left({\left(k_{01} k_{20} p - k_{00} k_{21} p\right)} d_{31} + {\left(d_{01} k_{01} p + d_{21} k_{21} p\right)} k_{10} - {\left(d_{01} k_{00} + d_{21} k_{20}\right)} k_{11}\right)} H_{02} + {\left({\left(k_{01} k_{20} p - k_{00} k_{21} p\right)} d_{30} + {\left(d_{00} k_{01} p + d_{20} k_{21} p\right)} k_{10} - {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{11}\right)} H_{12} + H_{22} x_{10} & -{\left({\left(k_{01} k_{20} p - k_{00} k_{21} p\right)} d_{31} + {\left(d_{01} k_{01} p + d_{21} k_{21} p\right)} k_{10} - {\left(d_{01} k_{00} + d_{21} k_{20}\right)} k_{11}\right)} H_{03} + H_{23} x_{10} + H_{33} x_{11} + \frac{{\left({\left(k_{01} k_{20} p - k_{00} k_{21} p\right)} d_{30} + {\left(d_{00} k_{01} p + d_{20} k_{21} p\right)} k_{10} - {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{11}\right)} H_{13}}{p} & -{\left(d_{01} k_{01} p + d_{21} k_{21} p\right)} d_{30} + {\left(d_{00} k_{01} p + d_{20} k_{21} p\right)} d_{31} + {\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{11} + x_{10} & {\left(d_{01} k_{00} + d_{21} k_{20}\right)} d_{30} - {\left(d_{00} k_{00} + d_{20} k_{20}\right)} d_{31} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{10} + x_{11} \\ H_{30} {\left(d_{21} - x_{01}\right)} p - {\left({\left(k_{01} k_{30} p^{2} - k_{00} k_{31} p\right)} d_{31} + {\left(d_{11} k_{01} p + d_{21} k_{31} p\right)} k_{10} - {\left(d_{21} k_{30} p + d_{11} k_{00}\right)} k_{11} + k_{00}\right)} H_{00} + {\left({\left(k_{01} k_{30} p^{2} - k_{00} k_{31} p\right)} d_{30} + {\left(d_{10} k_{01} p + d_{20} k_{31} p\right)} k_{10} - {\left(d_{20} k_{30} p + d_{10} k_{00}\right)} k_{11} - k_{01} p\right)} H_{10} + H_{20} {\left(d_{20} - x_{00}\right)} & -{\left({\left(k_{01} k_{30} p^{2} - k_{00} k_{31} p\right)} d_{31} + {\left(d_{11} k_{01} p + d_{21} k_{31} p\right)} k_{10} - {\left(d_{21} k_{30} p + d_{11} k_{00}\right)} k_{11} + k_{00}\right)} H_{01} p + H_{21} {\left(d_{20} - x_{00}\right)} p + H_{31} {\left(d_{21} - x_{01}\right)} p + {\left({\left(k_{01} k_{30} p^{2} - k_{00} k_{31} p\right)} d_{30} + {\left(d_{10} k_{01} p + d_{20} k_{31} p\right)} k_{10} - {\left(d_{20} k_{30} p + d_{10} k_{00}\right)} k_{11} - k_{01} p\right)} H_{11} & k_{00} & k_{01} p & -H_{32} {\left(d_{21} - x_{01}\right)} p + {\left({\left(k_{01} k_{30} p^{2} - k_{00} k_{31} p\right)} d_{31} + {\left(d_{11} k_{01} p + d_{21} k_{31} p\right)} k_{10} - {\left(d_{21} k_{30} p + d_{11} k_{00}\right)} k_{11} + k_{00}\right)} H_{02} - {\left({\left(k_{01} k_{30} p^{2} - k_{00} k_{31} p\right)} d_{30} + {\left(d_{10} k_{01} p + d_{20} k_{31} p\right)} k_{10} - {\left(d_{20} k_{30} p + d_{10} k_{00}\right)} k_{11} - k_{01} p\right)} H_{12} - H_{22} {\left(d_{20} - x_{00}\right)} & {\left({\left(k_{01} k_{30} p^{2} - k_{00} k_{31} p\right)} d_{31} + {\left(d_{11} k_{01} p + d_{21} k_{31} p\right)} k_{10} - {\left(d_{21} k_{30} p + d_{11} k_{00}\right)} k_{11} + k_{00}\right)} H_{03} - H_{23} {\left(d_{20} - x_{00}\right)} - H_{33} {\left(d_{21} - x_{01}\right)} - \frac{{\left({\left(k_{01} k_{30} p^{2} - k_{00} k_{31} p\right)} d_{30} + {\left(d_{10} k_{01} p + d_{20} k_{31} p\right)} k_{10} - {\left(d_{20} k_{30} p + d_{10} k_{00}\right)} k_{11} - k_{01} p\right)} H_{13}}{p} & {\left(d_{11} k_{01} p + d_{21} k_{31} p\right)} d_{30} - {\left(d_{10} k_{01} p + d_{20} k_{31} p\right)} d_{31} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{11} - d_{20} + x_{00} & -{\left(d_{21} k_{30} p + d_{11} k_{00}\right)} d_{30} + {\left(d_{20} k_{30} p + d_{10} k_{00}\right)} d_{31} + {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{10} - d_{21} + x_{01} \\ H_{30} {\left(d_{31} - x_{11}\right)} p + {\left({\left(k_{01} k_{20} p - k_{00} k_{21} p\right)} d_{31} + {\left(d_{01} k_{01} p + d_{21} k_{21} p\right)} k_{10} - {\left(d_{01} k_{00} + d_{21} k_{20}\right)} k_{11} - k_{10}\right)} H_{00} - {\left({\left(k_{01} k_{20} p - k_{00} k_{21} p\right)} d_{30} + {\left(d_{00} k_{01} p + d_{20} k_{21} p\right)} k_{10} - {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{11} + k_{11}\right)} H_{10} + H_{20} {\left(d_{30} - x_{10}\right)} & {\left({\left(k_{01} k_{20} p - k_{00} k_{21} p\right)} d_{31} + {\left(d_{01} k_{01} p + d_{21} k_{21} p\right)} k_{10} - {\left(d_{01} k_{00} + d_{21} k_{20}\right)} k_{11} - k_{10}\right)} H_{01} p + H_{21} {\left(d_{30} - x_{10}\right)} p + H_{31} {\left(d_{31} - x_{11}\right)} p - {\left({\left(k_{01} k_{20} p - k_{00} k_{21} p\right)} d_{30} + {\left(d_{00} k_{01} p + d_{20} k_{21} p\right)} k_{10} - {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{11} + k_{11}\right)} H_{11} & k_{10} & k_{11} & -H_{32} {\left(d_{31} - x_{11}\right)} p - {\left({\left(k_{01} k_{20} p - k_{00} k_{21} p\right)} d_{31} + {\left(d_{01} k_{01} p + d_{21} k_{21} p\right)} k_{10} - {\left(d_{01} k_{00} + d_{21} k_{20}\right)} k_{11} - k_{10}\right)} H_{02} + {\left({\left(k_{01} k_{20} p - k_{00} k_{21} p\right)} d_{30} + {\left(d_{00} k_{01} p + d_{20} k_{21} p\right)} k_{10} - {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{11} + k_{11}\right)} H_{12} - H_{22} {\left(d_{30} - x_{10}\right)} & -{\left({\left(k_{01} k_{20} p - k_{00} k_{21} p\right)} d_{31} + {\left(d_{01} k_{01} p + d_{21} k_{21} p\right)} k_{10} - {\left(d_{01} k_{00} + d_{21} k_{20}\right)} k_{11} - k_{10}\right)} H_{03} - H_{23} {\left(d_{30} - x_{10}\right)} - H_{33} {\left(d_{31} - x_{11}\right)} + \frac{{\left({\left(k_{01} k_{20} p - k_{00} k_{21} p\right)} d_{30} + {\left(d_{00} k_{01} p + d_{20} k_{21} p\right)} k_{10} - {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{11} + k_{11}\right)} H_{13}}{p} & -{\left(d_{01} k_{01} p + d_{21} k_{21} p\right)} d_{30} + {\left(d_{00} k_{01} p + d_{20} k_{21} p\right)} d_{31} + {\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{11} - d_{30} + x_{10} & {\left(d_{01} k_{00} + d_{21} k_{20}\right)} d_{30} - {\left(d_{00} k_{00} + d_{20} k_{20}\right)} d_{31} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{10} - d_{31} + x_{11} \\ -H_{30} {\left(d_{01} - x_{21}\right)} p + {\left({\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{31} + {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} k_{10} + {\left(d_{01} k_{30} p - d_{11} k_{20}\right)} k_{11}\right)} H_{00} - {\left({\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{30} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} k_{10} + {\left(d_{00} k_{30} p - d_{10} k_{20}\right)} k_{11}\right)} H_{10} - H_{20} {\left(d_{00} - x_{20}\right)} & {\left({\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{31} + {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} k_{10} + {\left(d_{01} k_{30} p - d_{11} k_{20}\right)} k_{11}\right)} H_{01} p - H_{21} {\left(d_{00} - x_{20}\right)} p - H_{31} {\left(d_{01} - x_{21}\right)} p - {\left({\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{30} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} k_{10} + {\left(d_{00} k_{30} p - d_{10} k_{20}\right)} k_{11}\right)} H_{11} & 0 & 0 & H_{32} {\left(d_{01} - x_{21}\right)} p - {\left({\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{31} + {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} k_{10} + {\left(d_{01} k_{30} p - d_{11} k_{20}\right)} k_{11}\right)} H_{02} + {\left({\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{30} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} k_{10} + {\left(d_{00} k_{30} p - d_{10} k_{20}\right)} k_{11}\right)} H_{12} + H_{22} {\left(d_{00} - x_{20}\right)} & -{\left({\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{31} + {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} k_{10} + {\left(d_{01} k_{30} p - d_{11} k_{20}\right)} k_{11}\right)} H_{03} + H_{23} {\left(d_{00} - x_{20}\right)} + H_{33} {\left(d_{01} - x_{21}\right)} + \frac{{\left({\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{30} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} k_{10} + {\left(d_{00} k_{30} p - d_{10} k_{20}\right)} k_{11}\right)} H_{13}}{p} & -{\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} d_{30} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} d_{31} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{11} + d_{00} - x_{20} & -{\left(d_{01} k_{30} p - d_{11} k_{20}\right)} d_{30} + {\left(d_{00} k_{30} p - d_{10} k_{20}\right)} d_{31} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{10} + d_{01} - x_{21} \\ -H_{30} {\left(d_{11} - x_{31}\right)} p - {\left({\left(d_{01} k_{30} p - d_{11} k_{20}\right)} k_{01} p + {\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{21} + {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} k_{00}\right)} H_{00} + {\left({\left(d_{00} k_{30} p - d_{10} k_{20}\right)} k_{01} p + {\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{20} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} k_{00}\right)} H_{10} - H_{20} {\left(d_{10} - x_{30}\right)} & -{\left({\left(d_{01} k_{30} p - d_{11} k_{20}\right)} k_{01} p + {\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{21} + {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} k_{00}\right)} H_{01} p - H_{21} {\left(d_{10} - x_{30}\right)} p - H_{31} {\left(d_{11} - x_{31}\right)} p + {\left({\left(d_{00} k_{30} p - d_{10} k_{20}\right)} k_{01} p + {\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{20} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} k_{00}\right)} H_{11} & 0 & 0 & H_{32} {\left(d_{11} - x_{31}\right)} p + {\left({\left(d_{01} k_{30} p - d_{11} k_{20}\right)} k_{01} p + {\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{21} + {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} k_{00}\right)} H_{02} - {\left({\left(d_{00} k_{30} p - d_{10} k_{20}\right)} k_{01} p + {\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{20} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} k_{00}\right)} H_{12} + H_{22} {\left(d_{10} - x_{30}\right)} & {\left({\left(d_{01} k_{30} p - d_{11} k_{20}\right)} k_{01} p + {\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{21} + {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} k_{00}\right)} H_{03} + H_{23} {\left(d_{10} - x_{30}\right)} + H_{33} {\left(d_{11} - x_{31}\right)} - \frac{{\left({\left(d_{00} k_{30} p - d_{10} k_{20}\right)} k_{01} p + {\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{20} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} k_{00}\right)} H_{13}}{p} & -{\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{01} p + {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} d_{20} - {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} d_{21} + d_{10} - x_{30} & {\left(d_{01} k_{30} p - d_{11} k_{20}\right)} d_{20} - {\left(d_{00} k_{30} p - d_{10} k_{20}\right)} d_{21} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{00} + d_{11} - x_{31} \\ -H_{30} p x_{21} - {\left({\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{31} + {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} k_{10} + {\left(d_{01} k_{30} p - d_{11} k_{20}\right)} k_{11} + k_{20}\right)} H_{00} + {\left({\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{30} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} k_{10} + {\left(d_{00} k_{30} p - d_{10} k_{20}\right)} k_{11} - k_{21} p\right)} H_{10} - H_{20} x_{20} & -{\left({\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{31} + {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} k_{10} + {\left(d_{01} k_{30} p - d_{11} k_{20}\right)} k_{11} + k_{20}\right)} H_{01} p - H_{21} p x_{20} - H_{31} p x_{21} + {\left({\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{30} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} k_{10} + {\left(d_{00} k_{30} p - d_{10} k_{20}\right)} k_{11} - k_{21} p\right)} H_{11} & k_{20} & k_{21} p & H_{32} p x_{21} + {\left({\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{31} + {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} k_{10} + {\left(d_{01} k_{30} p - d_{11} k_{20}\right)} k_{11} + k_{20}\right)} H_{02} - {\left({\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{30} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} k_{10} + {\left(d_{00} k_{30} p - d_{10} k_{20}\right)} k_{11} - k_{21} p\right)} H_{12} + H_{22} x_{20} & {\left({\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{31} + {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} k_{10} + {\left(d_{01} k_{30} p - d_{11} k_{20}\right)} k_{11} + k_{20}\right)} H_{03} + H_{23} x_{20} + H_{33} x_{21} - \frac{{\left({\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{30} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} k_{10} + {\left(d_{00} k_{30} p - d_{10} k_{20}\right)} k_{11} - k_{21} p\right)} H_{13}}{p} & {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} d_{30} - {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} d_{31} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{11} + x_{20} & {\left(d_{01} k_{30} p - d_{11} k_{20}\right)} d_{30} - {\left(d_{00} k_{30} p - d_{10} k_{20}\right)} d_{31} + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{10} + x_{21} \\ -H_{30} p x_{31} + {\left({\left(d_{01} k_{30} p - d_{11} k_{20}\right)} k_{01} p + {\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{21} + {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} k_{00} - k_{30} p\right)} H_{00} - {\left({\left(d_{00} k_{30} p - d_{10} k_{20}\right)} k_{01} p + {\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{20} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} k_{00} + k_{31} p\right)} H_{10} - H_{20} x_{30} & {\left({\left(d_{01} k_{30} p - d_{11} k_{20}\right)} k_{01} p + {\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{21} + {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} k_{00} - k_{30} p\right)} H_{01} p - H_{21} p x_{30} - H_{31} p x_{31} - {\left({\left(d_{00} k_{30} p - d_{10} k_{20}\right)} k_{01} p + {\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{20} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} k_{00} + k_{31} p\right)} H_{11} & k_{30} p & k_{31} p & H_{32} p x_{31} - {\left({\left(d_{01} k_{30} p - d_{11} k_{20}\right)} k_{01} p + {\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{21} + {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} k_{00} - k_{30} p\right)} H_{02} + {\left({\left(d_{00} k_{30} p - d_{10} k_{20}\right)} k_{01} p + {\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{20} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} k_{00} + k_{31} p\right)} H_{12} + H_{22} x_{30} & -{\left({\left(d_{01} k_{30} p - d_{11} k_{20}\right)} k_{01} p + {\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{21} + {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} k_{00} - k_{30} p\right)} H_{03} + H_{23} x_{30} + H_{33} x_{31} + \frac{{\left({\left(d_{00} k_{30} p - d_{10} k_{20}\right)} k_{01} p + {\left(k_{21} k_{30} p^{2} - k_{20} k_{31} p\right)} d_{20} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} k_{00} + k_{31} p\right)} H_{13}}{p} & {\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{01} p - {\left(d_{11} k_{21} p - d_{01} k_{31} p\right)} d_{20} + {\left(d_{10} k_{21} p - d_{00} k_{31} p\right)} d_{21} + x_{30} & -{\left(d_{01} k_{30} p - d_{11} k_{20}\right)} d_{20} + {\left(d_{00} k_{30} p - d_{10} k_{20}\right)} d_{21} - {\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{00} + x_{31} \end{array}\right)$

Now the 8th column.

Z=(Z.substitute(x31==(Z[5,7]==0).solve(x31)[0].right()).substitute(x11==(Z[1,7]==0).solve(x11)[0].right()).substitute(x01==(Z[0,7]==0).solve(x01)[0].right()).substitute(x21==(Z[4,7]==0).solve(x21)[0].right())).simplify_full();Z

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} -{\left(d_{31} k_{01} k_{30} p^{2} - d_{11} k_{00} k_{11} + {\left(d_{11} k_{01} k_{10} - d_{21} k_{11} k_{30} - {\left(d_{31} k_{00} - d_{21} k_{10}\right)} k_{31}\right)} p\right)} H_{00} + {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31}\right)} p\right)} H_{10} - {\left({\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{30} p^{2} + {\left({\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{00} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{10}\right)} p\right)} H_{30} - H_{20} x_{00} & -H_{21} p x_{00} - {\left(d_{31} k_{01} k_{30} p^{3} - d_{11} k_{00} k_{11} p + {\left(d_{11} k_{01} k_{10} - d_{21} k_{11} k_{30} - {\left(d_{31} k_{00} - d_{21} k_{10}\right)} k_{31}\right)} p^{2}\right)} H_{01} + {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31}\right)} p\right)} H_{11} - {\left({\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{30} p^{2} + {\left({\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{00} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{10}\right)} p\right)} H_{31} & 0 & 0 & {\left(d_{31} k_{01} k_{30} p^{2} - d_{11} k_{00} k_{11} + {\left(d_{11} k_{01} k_{10} - d_{21} k_{11} k_{30} - {\left(d_{31} k_{00} - d_{21} k_{10}\right)} k_{31}\right)} p\right)} H_{02} - {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31}\right)} p\right)} H_{12} + {\left({\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{30} p^{2} + {\left({\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{00} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{10}\right)} p\right)} H_{32} + H_{22} x_{00} & \frac{H_{23} p x_{00} + {\left(d_{31} k_{01} k_{30} p^{3} - d_{11} k_{00} k_{11} p + {\left(d_{11} k_{01} k_{10} - d_{21} k_{11} k_{30} - {\left(d_{31} k_{00} - d_{21} k_{10}\right)} k_{31}\right)} p^{2}\right)} H_{03} - {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31}\right)} p\right)} H_{13} + {\left({\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{30} p^{2} + {\left({\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{00} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{10}\right)} p\right)} H_{33}}{p} & -{\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{11} + {\left({\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{01} + {\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{31}\right)} p + x_{00} & 0 \\ {\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{00} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{10} + {\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{20}\right)} H_{30} p - {\left(d_{01} k_{00} k_{11} + d_{21} k_{11} k_{20} - {\left(d_{01} k_{01} k_{10} + d_{31} k_{01} k_{20} - {\left(d_{31} k_{00} - d_{21} k_{10}\right)} k_{21}\right)} p\right)} H_{00} + {\left(d_{00} k_{00} k_{11} + d_{20} k_{11} k_{20} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{10} - H_{20} x_{10} & {\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{00} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{10} + {\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{20}\right)} H_{31} p - H_{21} p x_{10} + {\left({\left(d_{01} k_{01} k_{10} + d_{31} k_{01} k_{20} - {\left(d_{31} k_{00} - d_{21} k_{10}\right)} k_{21}\right)} p^{2} - {\left(d_{01} k_{00} k_{11} + d_{21} k_{11} k_{20}\right)} p\right)} H_{01} + {\left(d_{00} k_{00} k_{11} + d_{20} k_{11} k_{20} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{11} & 0 & 0 & -{\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{00} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{10} + {\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{20}\right)} H_{32} p + {\left(d_{01} k_{00} k_{11} + d_{21} k_{11} k_{20} - {\left(d_{01} k_{01} k_{10} + d_{31} k_{01} k_{20} - {\left(d_{31} k_{00} - d_{21} k_{10}\right)} k_{21}\right)} p\right)} H_{02} - {\left(d_{00} k_{00} k_{11} + d_{20} k_{11} k_{20} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{12} + H_{22} x_{10} & -\frac{{\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{00} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{10} + {\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{20}\right)} H_{33} p - H_{23} p x_{10} + {\left({\left(d_{01} k_{01} k_{10} + d_{31} k_{01} k_{20} - {\left(d_{31} k_{00} - d_{21} k_{10}\right)} k_{21}\right)} p^{2} - {\left(d_{01} k_{00} k_{11} + d_{21} k_{11} k_{20}\right)} p\right)} H_{03} + {\left(d_{00} k_{00} k_{11} + d_{20} k_{11} k_{20} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{13}}{p} & {\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{11} - {\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{01} + {\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{21}\right)} p + x_{10} & 0 \\ -{\left(d_{31} k_{01} k_{30} p^{2} - d_{11} k_{00} k_{11} + {\left(d_{11} k_{01} k_{10} - d_{21} k_{11} k_{30} - {\left(d_{31} k_{00} - d_{21} k_{10}\right)} k_{31}\right)} p + k_{00}\right)} H_{00} + {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31} - k_{01}\right)} p\right)} H_{10} - {\left({\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{30} p^{2} + {\left({\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{00} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{10} - d_{21}\right)} p\right)} H_{30} + H_{20} {\left(d_{20} - x_{00}\right)} & -{\left(d_{31} k_{01} k_{30} p^{3} + {\left(d_{11} k_{01} k_{10} - d_{21} k_{11} k_{30} - {\left(d_{31} k_{00} - d_{21} k_{10}\right)} k_{31}\right)} p^{2} - {\left(d_{11} k_{00} k_{11} - k_{00}\right)} p\right)} H_{01} + {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31} - k_{01}\right)} p\right)} H_{11} + {\left(d_{20} p - p x_{00}\right)} H_{21} - {\left({\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{30} p^{2} + {\left({\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{00} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{10} - d_{21}\right)} p\right)} H_{31} & k_{00} & k_{01} p & {\left(d_{31} k_{01} k_{30} p^{2} - d_{11} k_{00} k_{11} + {\left(d_{11} k_{01} k_{10} - d_{21} k_{11} k_{30} - {\left(d_{31} k_{00} - d_{21} k_{10}\right)} k_{31}\right)} p + k_{00}\right)} H_{02} - {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31} - k_{01}\right)} p\right)} H_{12} + {\left({\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{30} p^{2} + {\left({\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{00} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{10} - d_{21}\right)} p\right)} H_{32} - H_{22} {\left(d_{20} - x_{00}\right)} & \frac{{\left(d_{31} k_{01} k_{30} p^{3} + {\left(d_{11} k_{01} k_{10} - d_{21} k_{11} k_{30} - {\left(d_{31} k_{00} - d_{21} k_{10}\right)} k_{31}\right)} p^{2} - {\left(d_{11} k_{00} k_{11} - k_{00}\right)} p\right)} H_{03} - {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31} - k_{01}\right)} p\right)} H_{13} - {\left(d_{20} p - p x_{00}\right)} H_{23} + {\left({\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{30} p^{2} + {\left({\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{00} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{10} - d_{21}\right)} p\right)} H_{33}}{p} & -{\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{11} + {\left({\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{01} + {\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{31}\right)} p - d_{20} + x_{00} & -d_{21} \\ {\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{00} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{10} + {\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{20} + d_{31}\right)} H_{30} p - {\left(d_{01} k_{00} k_{11} + d_{21} k_{11} k_{20} - {\left(d_{01} k_{01} k_{10} + d_{31} k_{01} k_{20} - {\left(d_{31} k_{00} - d_{21} k_{10}\right)} k_{21}\right)} p + k_{10}\right)} H_{00} + {\left(d_{20} k_{11} k_{20} + {\left(d_{00} k_{00} - 1\right)} k_{11} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{10} + H_{20} {\left(d_{30} - x_{10}\right)} & {\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{00} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{10} + {\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{20} + d_{31}\right)} H_{31} p + {\left({\left(d_{01} k_{01} k_{10} + d_{31} k_{01} k_{20} - {\left(d_{31} k_{00} - d_{21} k_{10}\right)} k_{21}\right)} p^{2} - {\left(d_{01} k_{00} k_{11} + d_{21} k_{11} k_{20} + k_{10}\right)} p\right)} H_{01} + {\left(d_{20} k_{11} k_{20} + {\left(d_{00} k_{00} - 1\right)} k_{11} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{11} + {\left(d_{30} p - p x_{10}\right)} H_{21} & k_{10} & k_{11} & -{\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{00} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{10} + {\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{20} + d_{31}\right)} H_{32} p + {\left(d_{01} k_{00} k_{11} + d_{21} k_{11} k_{20} - {\left(d_{01} k_{01} k_{10} + d_{31} k_{01} k_{20} - {\left(d_{31} k_{00} - d_{21} k_{10}\right)} k_{21}\right)} p + k_{10}\right)} H_{02} - {\left(d_{20} k_{11} k_{20} + {\left(d_{00} k_{00} - 1\right)} k_{11} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{12} - H_{22} {\left(d_{30} - x_{10}\right)} & -\frac{{\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{00} - {\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{10} + {\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{20} + d_{31}\right)} H_{33} p + {\left({\left(d_{01} k_{01} k_{10} + d_{31} k_{01} k_{20} - {\left(d_{31} k_{00} - d_{21} k_{10}\right)} k_{21}\right)} p^{2} - {\left(d_{01} k_{00} k_{11} + d_{21} k_{11} k_{20} + k_{10}\right)} p\right)} H_{03} + {\left(d_{20} k_{11} k_{20} + {\left(d_{00} k_{00} - 1\right)} k_{11} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{13} + {\left(d_{30} p - p x_{10}\right)} H_{23}}{p} & {\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{11} - {\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{01} + {\left(d_{21} d_{30} - d_{20} d_{31}\right)} k_{21}\right)} p - d_{30} + x_{10} & -d_{31} \\ {\left(d_{31} k_{21} k_{30} p^{2} - d_{11} k_{11} k_{20} + {\left(d_{11} k_{10} k_{21} + d_{01} k_{11} k_{30} - {\left(d_{01} k_{10} + d_{31} k_{20}\right)} k_{31}\right)} p\right)} H_{00} - {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{10} k_{10} k_{21} + d_{00} k_{11} k_{30} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{10} - {\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{30} p^{2} + {\left({\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{10} - {\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{20}\right)} p\right)} H_{30} - H_{20} {\left(d_{00} - x_{20}\right)} & {\left(d_{31} k_{21} k_{30} p^{3} - d_{11} k_{11} k_{20} p + {\left(d_{11} k_{10} k_{21} + d_{01} k_{11} k_{30} - {\left(d_{01} k_{10} + d_{31} k_{20}\right)} k_{31}\right)} p^{2}\right)} H_{01} - {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{10} k_{10} k_{21} + d_{00} k_{11} k_{30} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{11} - {\left(d_{00} p - p x_{20}\right)} H_{21} - {\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{30} p^{2} + {\left({\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{10} - {\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{20}\right)} p\right)} H_{31} & 0 & 0 & -{\left(d_{31} k_{21} k_{30} p^{2} - d_{11} k_{11} k_{20} + {\left(d_{11} k_{10} k_{21} + d_{01} k_{11} k_{30} - {\left(d_{01} k_{10} + d_{31} k_{20}\right)} k_{31}\right)} p\right)} H_{02} + {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{10} k_{10} k_{21} + d_{00} k_{11} k_{30} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{12} + {\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{30} p^{2} + {\left({\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{10} - {\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{20}\right)} p\right)} H_{32} + H_{22} {\left(d_{00} - x_{20}\right)} & -\frac{{\left(d_{31} k_{21} k_{30} p^{3} - d_{11} k_{11} k_{20} p + {\left(d_{11} k_{10} k_{21} + d_{01} k_{11} k_{30} - {\left(d_{01} k_{10} + d_{31} k_{20}\right)} k_{31}\right)} p^{2}\right)} H_{03} - {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{10} k_{10} k_{21} + d_{00} k_{11} k_{30} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{13} - {\left(d_{00} p - p x_{20}\right)} H_{23} - {\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{30} p^{2} + {\left({\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{10} - {\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{20}\right)} p\right)} H_{33}}{p} & {\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{11} - {\left({\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{21} - {\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{31}\right)} p + d_{00} - x_{20} & 0 \\ -{\left({\left(d_{01} k_{01} + d_{21} k_{21}\right)} k_{30} p^{2} - {\left(d_{11} k_{01} k_{20} - d_{11} k_{00} k_{21} + {\left(d_{01} k_{00} + d_{21} k_{20}\right)} k_{31}\right)} p\right)} H_{00} + {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{31}\right)} p\right)} H_{10} + {\left({\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{30} p^{2} + {\left({\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{00} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{20}\right)} p\right)} H_{30} - H_{20} {\left(d_{10} - x_{30}\right)} & -{\left({\left(d_{01} k_{01} + d_{21} k_{21}\right)} k_{30} p^{3} - {\left(d_{11} k_{01} k_{20} - d_{11} k_{00} k_{21} + {\left(d_{01} k_{00} + d_{21} k_{20}\right)} k_{31}\right)} p^{2}\right)} H_{01} + {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{31}\right)} p\right)} H_{11} - {\left(d_{10} p - p x_{30}\right)} H_{21} + {\left({\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{30} p^{2} + {\left({\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{00} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{20}\right)} p\right)} H_{31} & 0 & 0 & {\left({\left(d_{01} k_{01} + d_{21} k_{21}\right)} k_{30} p^{2} - {\left(d_{11} k_{01} k_{20} - d_{11} k_{00} k_{21} + {\left(d_{01} k_{00} + d_{21} k_{20}\right)} k_{31}\right)} p\right)} H_{02} - {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{31}\right)} p\right)} H_{12} - {\left({\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{30} p^{2} + {\left({\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{00} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{20}\right)} p\right)} H_{32} + H_{22} {\left(d_{10} - x_{30}\right)} & {\left({\left(d_{01} k_{01} + d_{21} k_{21}\right)} k_{30} p^{2} - {\left(d_{11} k_{01} k_{20} - d_{11} k_{00} k_{21} + {\left(d_{01} k_{00} + d_{21} k_{20}\right)} k_{31}\right)} p\right)} H_{03} + {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} - {\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p + {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{31}\right)} H_{13} - {\left({\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{30} p + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{00} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{20}\right)} H_{33} + H_{23} {\left(d_{10} - x_{30}\right)} & -{\left({\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{01} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{21} + {\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{31}\right)} p + d_{10} - x_{30} & 0 \\ -{\left(d_{31} k_{21} k_{30} p^{2} - {\left(d_{11} k_{11} - 1\right)} k_{20} + {\left(d_{11} k_{10} k_{21} + d_{01} k_{11} k_{30} - {\left(d_{01} k_{10} + d_{31} k_{20}\right)} k_{31}\right)} p\right)} H_{00} + {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{00} k_{11} k_{30} + {\left(d_{10} k_{10} - 1\right)} k_{21} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{10} + {\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{30} p^{2} + {\left({\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{10} - {\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{20} - d_{01}\right)} p\right)} H_{30} - H_{20} x_{20} & -H_{21} p x_{20} - {\left(d_{31} k_{21} k_{30} p^{3} - {\left(d_{11} k_{11} - 1\right)} k_{20} p + {\left(d_{11} k_{10} k_{21} + d_{01} k_{11} k_{30} - {\left(d_{01} k_{10} + d_{31} k_{20}\right)} k_{31}\right)} p^{2}\right)} H_{01} + {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{00} k_{11} k_{30} + {\left(d_{10} k_{10} - 1\right)} k_{21} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{11} + {\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{30} p^{2} + {\left({\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{10} - {\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{20} - d_{01}\right)} p\right)} H_{31} & k_{20} & k_{21} p & {\left(d_{31} k_{21} k_{30} p^{2} - {\left(d_{11} k_{11} - 1\right)} k_{20} + {\left(d_{11} k_{10} k_{21} + d_{01} k_{11} k_{30} - {\left(d_{01} k_{10} + d_{31} k_{20}\right)} k_{31}\right)} p\right)} H_{02} - {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{00} k_{11} k_{30} + {\left(d_{10} k_{10} - 1\right)} k_{21} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{12} - {\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{30} p^{2} + {\left({\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{10} - {\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{20} - d_{01}\right)} p\right)} H_{32} + H_{22} x_{20} & \frac{H_{23} p x_{20} + {\left(d_{31} k_{21} k_{30} p^{3} - {\left(d_{11} k_{11} - 1\right)} k_{20} p + {\left(d_{11} k_{10} k_{21} + d_{01} k_{11} k_{30} - {\left(d_{01} k_{10} + d_{31} k_{20}\right)} k_{31}\right)} p^{2}\right)} H_{03} - {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{00} k_{11} k_{30} + {\left(d_{10} k_{10} - 1\right)} k_{21} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{13} - {\left({\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{30} p^{2} + {\left({\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{10} - {\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{20} - d_{01}\right)} p\right)} H_{33}}{p} & -{\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{11} + {\left({\left(d_{11} d_{30} - d_{10} d_{31}\right)} k_{21} - {\left(d_{01} d_{30} - d_{00} d_{31}\right)} k_{31}\right)} p + x_{20} & d_{01} \\ {\left({\left(d_{01} k_{01} + d_{21} k_{21}\right)} k_{30} p^{2} - {\left(d_{11} k_{01} k_{20} - d_{11} k_{00} k_{21} + {\left(d_{01} k_{00} + d_{21} k_{20}\right)} k_{31} + k_{30}\right)} p\right)} H_{00} - {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20} - 1\right)} k_{31}\right)} p\right)} H_{10} - {\left({\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{30} p^{2} + {\left({\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{00} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{20} + d_{11}\right)} p\right)} H_{30} - H_{20} x_{30} & -H_{21} p x_{30} + {\left({\left(d_{01} k_{01} + d_{21} k_{21}\right)} k_{30} p^{3} - {\left(d_{11} k_{01} k_{20} - d_{11} k_{00} k_{21} + {\left(d_{01} k_{00} + d_{21} k_{20}\right)} k_{31} + k_{30}\right)} p^{2}\right)} H_{01} - {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20} - 1\right)} k_{31}\right)} p\right)} H_{11} - {\left({\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{30} p^{2} + {\left({\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{00} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{20} + d_{11}\right)} p\right)} H_{31} & k_{30} p & k_{31} p & -{\left({\left(d_{01} k_{01} + d_{21} k_{21}\right)} k_{30} p^{2} - {\left(d_{11} k_{01} k_{20} - d_{11} k_{00} k_{21} + {\left(d_{01} k_{00} + d_{21} k_{20}\right)} k_{31} + k_{30}\right)} p\right)} H_{02} + {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20} - 1\right)} k_{31}\right)} p\right)} H_{12} + {\left({\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{30} p^{2} + {\left({\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{00} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{20} + d_{11}\right)} p\right)} H_{32} + H_{22} x_{30} & -{\left({\left(d_{01} k_{01} + d_{21} k_{21}\right)} k_{30} p^{2} - {\left(d_{11} k_{01} k_{20} - d_{11} k_{00} k_{21} + {\left(d_{01} k_{00} + d_{21} k_{20}\right)} k_{31} + k_{30}\right)} p\right)} H_{03} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} - {\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p + {\left(d_{00} k_{00} + d_{20} k_{20} - 1\right)} k_{31}\right)} H_{13} + {\left({\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{30} p + {\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{00} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{20} + d_{11}\right)} H_{33} + H_{23} x_{30} & {\left({\left(d_{01} d_{10} - d_{00} d_{11}\right)} k_{01} - {\left(d_{11} d_{20} - d_{10} d_{21}\right)} k_{21} + {\left(d_{01} d_{20} - d_{00} d_{21}\right)} k_{31}\right)} p + x_{30} & d_{11} \end{array}\right)$

Z=Z.substitute(d21==-k03).substitute(d31==-k13/p).substitute(d01==k23).substitute(d11==k33);Z;

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} {\left(k_{01} k_{13} k_{30} p + k_{00} k_{11} k_{33} - {\left(k_{03} k_{11} k_{30} + k_{01} k_{10} k_{33} - {\left(k_{03} k_{10} - \frac{k_{00} k_{13}}{p}\right)} k_{31}\right)} p\right)} H_{00} + {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31}\right)} p\right)} H_{10} + {\left({\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{30} p^{2} - {\left({\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{00} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{10}\right)} p\right)} H_{30} - H_{20} x_{00} & -H_{21} p x_{00} + {\left(k_{01} k_{13} k_{30} p^{2} + k_{00} k_{11} k_{33} p - {\left(k_{03} k_{11} k_{30} + k_{01} k_{10} k_{33} - {\left(k_{03} k_{10} - \frac{k_{00} k_{13}}{p}\right)} k_{31}\right)} p^{2}\right)} H_{01} + {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31}\right)} p\right)} H_{11} + {\left({\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{30} p^{2} - {\left({\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{00} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{10}\right)} p\right)} H_{31} & 0 & 0 & -{\left(k_{01} k_{13} k_{30} p + k_{00} k_{11} k_{33} - {\left(k_{03} k_{11} k_{30} + k_{01} k_{10} k_{33} - {\left(k_{03} k_{10} - \frac{k_{00} k_{13}}{p}\right)} k_{31}\right)} p\right)} H_{02} - {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31}\right)} p\right)} H_{12} - {\left({\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{30} p^{2} - {\left({\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{00} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{10}\right)} p\right)} H_{32} + H_{22} x_{00} & \frac{H_{23} p x_{00} - {\left(k_{01} k_{13} k_{30} p^{2} + k_{00} k_{11} k_{33} p - {\left(k_{03} k_{11} k_{30} + k_{01} k_{10} k_{33} - {\left(k_{03} k_{10} - \frac{k_{00} k_{13}}{p}\right)} k_{31}\right)} p^{2}\right)} H_{03} - {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31}\right)} p\right)} H_{13} - {\left({\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{30} p^{2} - {\left({\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{00} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{10}\right)} p\right)} H_{33}}{p} & -{\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{11} + {\left({\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{01} - {\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{31}\right)} p + x_{00} & 0 \\ {\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{00} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{10} - {\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{20}\right)} H_{30} p + {\left(k_{03} k_{11} k_{20} - k_{00} k_{11} k_{23} + {\left(k_{01} k_{10} k_{23} - {\left(k_{03} k_{10} - \frac{k_{00} k_{13}}{p}\right)} k_{21} - \frac{k_{01} k_{13} k_{20}}{p}\right)} p\right)} H_{00} + {\left(d_{00} k_{00} k_{11} + d_{20} k_{11} k_{20} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{10} - H_{20} x_{10} & {\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{00} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{10} - {\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{20}\right)} H_{31} p - H_{21} p x_{10} + {\left({\left(k_{01} k_{10} k_{23} - {\left(k_{03} k_{10} - \frac{k_{00} k_{13}}{p}\right)} k_{21} - \frac{k_{01} k_{13} k_{20}}{p}\right)} p^{2} + {\left(k_{03} k_{11} k_{20} - k_{00} k_{11} k_{23}\right)} p\right)} H_{01} + {\left(d_{00} k_{00} k_{11} + d_{20} k_{11} k_{20} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{11} & 0 & 0 & -{\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{00} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{10} - {\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{20}\right)} H_{32} p - {\left(k_{03} k_{11} k_{20} - k_{00} k_{11} k_{23} + {\left(k_{01} k_{10} k_{23} - {\left(k_{03} k_{10} - \frac{k_{00} k_{13}}{p}\right)} k_{21} - \frac{k_{01} k_{13} k_{20}}{p}\right)} p\right)} H_{02} - {\left(d_{00} k_{00} k_{11} + d_{20} k_{11} k_{20} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{12} + H_{22} x_{10} & -\frac{{\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{00} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{10} - {\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{20}\right)} H_{33} p - H_{23} p x_{10} + {\left({\left(k_{01} k_{10} k_{23} - {\left(k_{03} k_{10} - \frac{k_{00} k_{13}}{p}\right)} k_{21} - \frac{k_{01} k_{13} k_{20}}{p}\right)} p^{2} + {\left(k_{03} k_{11} k_{20} - k_{00} k_{11} k_{23}\right)} p\right)} H_{03} + {\left(d_{00} k_{00} k_{11} + d_{20} k_{11} k_{20} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{13}}{p} & {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{11} - {\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{01} - {\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{21}\right)} p + x_{10} & 0 \\ {\left(k_{01} k_{13} k_{30} p + k_{00} k_{11} k_{33} - {\left(k_{03} k_{11} k_{30} + k_{01} k_{10} k_{33} - {\left(k_{03} k_{10} - \frac{k_{00} k_{13}}{p}\right)} k_{31}\right)} p - k_{00}\right)} H_{00} + {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31} - k_{01}\right)} p\right)} H_{10} + {\left({\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{30} p^{2} - {\left({\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{00} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{10} + k_{03}\right)} p\right)} H_{30} + H_{20} {\left(d_{20} - x_{00}\right)} & {\left(k_{01} k_{13} k_{30} p^{2} - {\left(k_{03} k_{11} k_{30} + k_{01} k_{10} k_{33} - {\left(k_{03} k_{10} - \frac{k_{00} k_{13}}{p}\right)} k_{31}\right)} p^{2} + {\left(k_{00} k_{11} k_{33} - k_{00}\right)} p\right)} H_{01} + {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31} - k_{01}\right)} p\right)} H_{11} + {\left(d_{20} p - p x_{00}\right)} H_{21} + {\left({\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{30} p^{2} - {\left({\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{00} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{10} + k_{03}\right)} p\right)} H_{31} & k_{00} & k_{01} p & -{\left(k_{01} k_{13} k_{30} p + k_{00} k_{11} k_{33} - {\left(k_{03} k_{11} k_{30} + k_{01} k_{10} k_{33} - {\left(k_{03} k_{10} - \frac{k_{00} k_{13}}{p}\right)} k_{31}\right)} p - k_{00}\right)} H_{02} - {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31} - k_{01}\right)} p\right)} H_{12} - {\left({\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{30} p^{2} - {\left({\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{00} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{10} + k_{03}\right)} p\right)} H_{32} - H_{22} {\left(d_{20} - x_{00}\right)} & -\frac{{\left(k_{01} k_{13} k_{30} p^{2} - {\left(k_{03} k_{11} k_{30} + k_{01} k_{10} k_{33} - {\left(k_{03} k_{10} - \frac{k_{00} k_{13}}{p}\right)} k_{31}\right)} p^{2} + {\left(k_{00} k_{11} k_{33} - k_{00}\right)} p\right)} H_{03} + {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31} - k_{01}\right)} p\right)} H_{13} + {\left(d_{20} p - p x_{00}\right)} H_{23} + {\left({\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{30} p^{2} - {\left({\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{00} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{10} + k_{03}\right)} p\right)} H_{33}}{p} & -{\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{11} + {\left({\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{01} - {\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{31}\right)} p - d_{20} + x_{00} & k_{03} \\ {\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{00} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{10} - {\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{20} - \frac{k_{13}}{p}\right)} H_{30} p + {\left(k_{03} k_{11} k_{20} - k_{00} k_{11} k_{23} + {\left(k_{01} k_{10} k_{23} - {\left(k_{03} k_{10} - \frac{k_{00} k_{13}}{p}\right)} k_{21} - \frac{k_{01} k_{13} k_{20}}{p}\right)} p - k_{10}\right)} H_{00} + {\left(d_{20} k_{11} k_{20} + {\left(d_{00} k_{00} - 1\right)} k_{11} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{10} + H_{20} {\left(d_{30} - x_{10}\right)} & {\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{00} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{10} - {\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{20} - \frac{k_{13}}{p}\right)} H_{31} p + {\left({\left(k_{01} k_{10} k_{23} - {\left(k_{03} k_{10} - \frac{k_{00} k_{13}}{p}\right)} k_{21} - \frac{k_{01} k_{13} k_{20}}{p}\right)} p^{2} + {\left(k_{03} k_{11} k_{20} - k_{00} k_{11} k_{23} - k_{10}\right)} p\right)} H_{01} + {\left(d_{20} k_{11} k_{20} + {\left(d_{00} k_{00} - 1\right)} k_{11} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{11} + {\left(d_{30} p - p x_{10}\right)} H_{21} & k_{10} & k_{11} & -{\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{00} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{10} - {\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{20} - \frac{k_{13}}{p}\right)} H_{32} p - {\left(k_{03} k_{11} k_{20} - k_{00} k_{11} k_{23} + {\left(k_{01} k_{10} k_{23} - {\left(k_{03} k_{10} - \frac{k_{00} k_{13}}{p}\right)} k_{21} - \frac{k_{01} k_{13} k_{20}}{p}\right)} p - k_{10}\right)} H_{02} - {\left(d_{20} k_{11} k_{20} + {\left(d_{00} k_{00} - 1\right)} k_{11} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{12} - H_{22} {\left(d_{30} - x_{10}\right)} & -\frac{{\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{00} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{10} - {\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{20} - \frac{k_{13}}{p}\right)} H_{33} p + {\left({\left(k_{01} k_{10} k_{23} - {\left(k_{03} k_{10} - \frac{k_{00} k_{13}}{p}\right)} k_{21} - \frac{k_{01} k_{13} k_{20}}{p}\right)} p^{2} + {\left(k_{03} k_{11} k_{20} - k_{00} k_{11} k_{23} - k_{10}\right)} p\right)} H_{03} + {\left(d_{20} k_{11} k_{20} + {\left(d_{00} k_{00} - 1\right)} k_{11} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{13} + {\left(d_{30} p - p x_{10}\right)} H_{23}}{p} & {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{11} - {\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{01} - {\left(d_{30} k_{03} - \frac{d_{20} k_{13}}{p}\right)} k_{21}\right)} p - d_{30} + x_{10} & \frac{k_{13}}{p} \\ -{\left(k_{13} k_{21} k_{30} p + k_{11} k_{20} k_{33} - {\left(k_{11} k_{23} k_{30} + k_{10} k_{21} k_{33} - {\left(k_{10} k_{23} - \frac{k_{13} k_{20}}{p}\right)} k_{31}\right)} p\right)} H_{00} - {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{10} k_{10} k_{21} + d_{00} k_{11} k_{30} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{10} - {\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{30} p^{2} + {\left({\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{10} - {\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{20}\right)} p\right)} H_{30} - H_{20} {\left(d_{00} - x_{20}\right)} & -{\left(k_{13} k_{21} k_{30} p^{2} + k_{11} k_{20} k_{33} p - {\left(k_{11} k_{23} k_{30} + k_{10} k_{21} k_{33} - {\left(k_{10} k_{23} - \frac{k_{13} k_{20}}{p}\right)} k_{31}\right)} p^{2}\right)} H_{01} - {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{10} k_{10} k_{21} + d_{00} k_{11} k_{30} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{11} - {\left(d_{00} p - p x_{20}\right)} H_{21} - {\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{30} p^{2} + {\left({\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{10} - {\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{20}\right)} p\right)} H_{31} & 0 & 0 & {\left(k_{13} k_{21} k_{30} p + k_{11} k_{20} k_{33} - {\left(k_{11} k_{23} k_{30} + k_{10} k_{21} k_{33} - {\left(k_{10} k_{23} - \frac{k_{13} k_{20}}{p}\right)} k_{31}\right)} p\right)} H_{02} + {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{10} k_{10} k_{21} + d_{00} k_{11} k_{30} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{12} + {\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{30} p^{2} + {\left({\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{10} - {\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{20}\right)} p\right)} H_{32} + H_{22} {\left(d_{00} - x_{20}\right)} & \frac{{\left(k_{13} k_{21} k_{30} p^{2} + k_{11} k_{20} k_{33} p - {\left(k_{11} k_{23} k_{30} + k_{10} k_{21} k_{33} - {\left(k_{10} k_{23} - \frac{k_{13} k_{20}}{p}\right)} k_{31}\right)} p^{2}\right)} H_{03} + {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{10} k_{10} k_{21} + d_{00} k_{11} k_{30} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{13} + {\left(d_{00} p - p x_{20}\right)} H_{23} + {\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{30} p^{2} + {\left({\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{10} - {\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{20}\right)} p\right)} H_{33}}{p} & {\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{11} - {\left({\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{21} - {\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{31}\right)} p + d_{00} - x_{20} & 0 \\ {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} + {\left(k_{01} k_{20} k_{33} - k_{00} k_{21} k_{33} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31}\right)} p\right)} H_{00} + {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{31}\right)} p\right)} H_{10} + {\left({\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{30} p^{2} + {\left({\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{00} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{20}\right)} p\right)} H_{30} - H_{20} {\left(d_{10} - x_{30}\right)} & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{3} + {\left(k_{01} k_{20} k_{33} - k_{00} k_{21} k_{33} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31}\right)} p^{2}\right)} H_{01} + {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{31}\right)} p\right)} H_{11} - {\left(d_{10} p - p x_{30}\right)} H_{21} + {\left({\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{30} p^{2} + {\left({\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{00} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{20}\right)} p\right)} H_{31} & 0 & 0 & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} + {\left(k_{01} k_{20} k_{33} - k_{00} k_{21} k_{33} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31}\right)} p\right)} H_{02} - {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{31}\right)} p\right)} H_{12} - {\left({\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{30} p^{2} + {\left({\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{00} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{20}\right)} p\right)} H_{32} + H_{22} {\left(d_{10} - x_{30}\right)} & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} + {\left(k_{01} k_{20} k_{33} - k_{00} k_{21} k_{33} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31}\right)} p\right)} H_{03} + {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} - {\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p + {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{31}\right)} H_{13} - {\left({\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{30} p + {\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{00} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{20}\right)} H_{33} + H_{23} {\left(d_{10} - x_{30}\right)} & -{\left({\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{01} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{21} + {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{31}\right)} p + d_{10} - x_{30} & 0 \\ {\left(k_{13} k_{21} k_{30} p + {\left(k_{11} k_{33} - 1\right)} k_{20} - {\left(k_{11} k_{23} k_{30} + k_{10} k_{21} k_{33} - {\left(k_{10} k_{23} - \frac{k_{13} k_{20}}{p}\right)} k_{31}\right)} p\right)} H_{00} + {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{00} k_{11} k_{30} + {\left(d_{10} k_{10} - 1\right)} k_{21} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{10} + {\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{30} p^{2} + {\left({\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{10} - {\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{20} - k_{23}\right)} p\right)} H_{30} - H_{20} x_{20} & -H_{21} p x_{20} + {\left(k_{13} k_{21} k_{30} p^{2} + {\left(k_{11} k_{33} - 1\right)} k_{20} p - {\left(k_{11} k_{23} k_{30} + k_{10} k_{21} k_{33} - {\left(k_{10} k_{23} - \frac{k_{13} k_{20}}{p}\right)} k_{31}\right)} p^{2}\right)} H_{01} + {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{00} k_{11} k_{30} + {\left(d_{10} k_{10} - 1\right)} k_{21} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{11} + {\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{30} p^{2} + {\left({\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{10} - {\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{20} - k_{23}\right)} p\right)} H_{31} & k_{20} & k_{21} p & -{\left(k_{13} k_{21} k_{30} p + {\left(k_{11} k_{33} - 1\right)} k_{20} - {\left(k_{11} k_{23} k_{30} + k_{10} k_{21} k_{33} - {\left(k_{10} k_{23} - \frac{k_{13} k_{20}}{p}\right)} k_{31}\right)} p\right)} H_{02} - {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{00} k_{11} k_{30} + {\left(d_{10} k_{10} - 1\right)} k_{21} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{12} - {\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{30} p^{2} + {\left({\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{10} - {\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{20} - k_{23}\right)} p\right)} H_{32} + H_{22} x_{20} & \frac{H_{23} p x_{20} - {\left(k_{13} k_{21} k_{30} p^{2} + {\left(k_{11} k_{33} - 1\right)} k_{20} p - {\left(k_{11} k_{23} k_{30} + k_{10} k_{21} k_{33} - {\left(k_{10} k_{23} - \frac{k_{13} k_{20}}{p}\right)} k_{31}\right)} p^{2}\right)} H_{03} - {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{00} k_{11} k_{30} + {\left(d_{10} k_{10} - 1\right)} k_{21} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{13} - {\left({\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{30} p^{2} + {\left({\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{10} - {\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{20} - k_{23}\right)} p\right)} H_{33}}{p} & -{\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{11} + {\left({\left(d_{30} k_{33} + \frac{d_{10} k_{13}}{p}\right)} k_{21} - {\left(d_{30} k_{23} + \frac{d_{00} k_{13}}{p}\right)} k_{31}\right)} p + x_{20} & k_{23} \\ -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} + {\left(k_{01} k_{20} k_{33} - k_{00} k_{21} k_{33} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} + k_{30}\right)} p\right)} H_{00} - {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20} - 1\right)} k_{31}\right)} p\right)} H_{10} - {\left({\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{30} p^{2} + {\left({\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{00} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{20} + k_{33}\right)} p\right)} H_{30} - H_{20} x_{30} & -H_{21} p x_{30} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{3} + {\left(k_{01} k_{20} k_{33} - k_{00} k_{21} k_{33} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} + k_{30}\right)} p^{2}\right)} H_{01} - {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20} - 1\right)} k_{31}\right)} p\right)} H_{11} - {\left({\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{30} p^{2} + {\left({\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{00} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{20} + k_{33}\right)} p\right)} H_{31} & k_{30} p & k_{31} p & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} + {\left(k_{01} k_{20} k_{33} - k_{00} k_{21} k_{33} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} + k_{30}\right)} p\right)} H_{02} + {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20} - 1\right)} k_{31}\right)} p\right)} H_{12} + {\left({\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{30} p^{2} + {\left({\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{00} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{20} + k_{33}\right)} p\right)} H_{32} + H_{22} x_{30} & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} + {\left(k_{01} k_{20} k_{33} - k_{00} k_{21} k_{33} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} + k_{30}\right)} p\right)} H_{03} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} - {\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p + {\left(d_{00} k_{00} + d_{20} k_{20} - 1\right)} k_{31}\right)} H_{13} + {\left({\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{30} p + {\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{00} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{20} + k_{33}\right)} H_{33} + H_{23} x_{30} & {\left({\left(d_{10} k_{23} - d_{00} k_{33}\right)} k_{01} - {\left(d_{10} k_{03} + d_{20} k_{33}\right)} k_{21} + {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{31}\right)} p + x_{30} & k_{33} \end{array}\right)$

On to column 7.

Z=(Z.substitute(x00==(Z[0,6]==0).solve(x00)[0].right()).substitute(x10==(Z[1,6]==0).solve(x10)[0].right()).substitute(x20==(Z[4,6]==0).solve(x20)[0].right()).substitute(x30==(Z[5,6]==0).solve(x30)[0].right())).simplify_full();Z

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} -{\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p\right)} H_{00} + {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31}\right)} p\right)} H_{10} - {\left(d_{10} k_{03} k_{11} - d_{10} k_{01} k_{13} - d_{20} k_{13} k_{31} + d_{20} k_{11} k_{33} + {\left(d_{30} k_{03} k_{31} - d_{30} k_{01} k_{33}\right)} p\right)} H_{20} + {\left(d_{30} k_{03} k_{30} p^{2} - d_{10} k_{00} k_{13} + {\left(d_{10} k_{03} k_{10} - d_{20} k_{13} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{33}\right)} p\right)} H_{30} & {\left({\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p^{2} - {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33}\right)} p\right)} H_{01} + {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31}\right)} p\right)} H_{11} - {\left({\left(d_{30} k_{03} k_{31} - d_{30} k_{01} k_{33}\right)} p^{2} + {\left(d_{10} k_{03} k_{11} - d_{10} k_{01} k_{13} - d_{20} k_{13} k_{31} + d_{20} k_{11} k_{33}\right)} p\right)} H_{21} + {\left(d_{30} k_{03} k_{30} p^{2} - d_{10} k_{00} k_{13} + {\left(d_{10} k_{03} k_{10} - d_{20} k_{13} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{33}\right)} p\right)} H_{31} & 0 & 0 & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p\right)} H_{02} - {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31}\right)} p\right)} H_{12} + {\left(d_{10} k_{03} k_{11} - d_{10} k_{01} k_{13} - d_{20} k_{13} k_{31} + d_{20} k_{11} k_{33} + {\left(d_{30} k_{03} k_{31} - d_{30} k_{01} k_{33}\right)} p\right)} H_{22} - {\left(d_{30} k_{03} k_{30} p^{2} - d_{10} k_{00} k_{13} + {\left(d_{10} k_{03} k_{10} - d_{20} k_{13} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{33}\right)} p\right)} H_{32} & -\frac{{\left({\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p^{2} - {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33}\right)} p\right)} H_{03} + {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31}\right)} p\right)} H_{13} - {\left({\left(d_{30} k_{03} k_{31} - d_{30} k_{01} k_{33}\right)} p^{2} + {\left(d_{10} k_{03} k_{11} - d_{10} k_{01} k_{13} - d_{20} k_{13} k_{31} + d_{20} k_{11} k_{33}\right)} p\right)} H_{23} + {\left(d_{30} k_{03} k_{30} p^{2} - d_{10} k_{00} k_{13} + {\left(d_{10} k_{03} k_{10} - d_{20} k_{13} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{33}\right)} p\right)} H_{33}}{p} & 0 & 0 \\ {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p\right)} H_{00} + {\left(d_{00} k_{00} k_{11} + d_{20} k_{11} k_{20} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{10} + {\left(d_{00} k_{03} k_{11} - d_{00} k_{01} k_{13} - d_{20} k_{13} k_{21} + d_{20} k_{11} k_{23} + {\left(d_{30} k_{03} k_{21} - d_{30} k_{01} k_{23}\right)} p\right)} H_{20} + {\left(d_{00} k_{00} k_{13} + d_{20} k_{13} k_{20} - {\left(d_{00} k_{03} k_{10} + d_{30} k_{03} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{23}\right)} p\right)} H_{30} & -{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20}\right)} p\right)} H_{01} + {\left(d_{00} k_{00} k_{11} + d_{20} k_{11} k_{20} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{11} + {\left({\left(d_{30} k_{03} k_{21} - d_{30} k_{01} k_{23}\right)} p^{2} + {\left(d_{00} k_{03} k_{11} - d_{00} k_{01} k_{13} - d_{20} k_{13} k_{21} + d_{20} k_{11} k_{23}\right)} p\right)} H_{21} + {\left(d_{00} k_{00} k_{13} + d_{20} k_{13} k_{20} - {\left(d_{00} k_{03} k_{10} + d_{30} k_{03} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{23}\right)} p\right)} H_{31} & 0 & 0 & -{\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p\right)} H_{02} - {\left(d_{00} k_{00} k_{11} + d_{20} k_{11} k_{20} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{12} - {\left(d_{00} k_{03} k_{11} - d_{00} k_{01} k_{13} - d_{20} k_{13} k_{21} + d_{20} k_{11} k_{23} + {\left(d_{30} k_{03} k_{21} - d_{30} k_{01} k_{23}\right)} p\right)} H_{22} - {\left(d_{00} k_{00} k_{13} + d_{20} k_{13} k_{20} - {\left(d_{00} k_{03} k_{10} + d_{30} k_{03} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{23}\right)} p\right)} H_{32} & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20}\right)} p\right)} H_{03} - {\left(d_{00} k_{00} k_{11} + d_{20} k_{11} k_{20} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{13} - {\left({\left(d_{30} k_{03} k_{21} - d_{30} k_{01} k_{23}\right)} p^{2} + {\left(d_{00} k_{03} k_{11} - d_{00} k_{01} k_{13} - d_{20} k_{13} k_{21} + d_{20} k_{11} k_{23}\right)} p\right)} H_{23} - {\left(d_{00} k_{00} k_{13} + d_{20} k_{13} k_{20} - {\left(d_{00} k_{03} k_{10} + d_{30} k_{03} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{23}\right)} p\right)} H_{33}}{p} & 0 & 0 \\ -{\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{00} + {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31} - k_{01}\right)} p\right)} H_{10} - {\left(d_{10} k_{03} k_{11} - d_{10} k_{01} k_{13} - d_{20} k_{13} k_{31} + d_{20} k_{11} k_{33} + {\left(d_{30} k_{03} k_{31} - d_{30} k_{01} k_{33}\right)} p - d_{20}\right)} H_{20} + {\left(d_{30} k_{03} k_{30} p^{2} - d_{10} k_{00} k_{13} + {\left(d_{10} k_{03} k_{10} - d_{20} k_{13} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{33} - k_{03}\right)} p\right)} H_{30} & {\left({\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p^{2} - {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} + k_{00}\right)} p\right)} H_{01} + {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31} - k_{01}\right)} p\right)} H_{11} - {\left({\left(d_{30} k_{03} k_{31} - d_{30} k_{01} k_{33}\right)} p^{2} + {\left(d_{10} k_{03} k_{11} - d_{10} k_{01} k_{13} - d_{20} k_{13} k_{31} + d_{20} k_{11} k_{33} - d_{20}\right)} p\right)} H_{21} + {\left(d_{30} k_{03} k_{30} p^{2} - d_{10} k_{00} k_{13} + {\left(d_{10} k_{03} k_{10} - d_{20} k_{13} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{33} - k_{03}\right)} p\right)} H_{31} & k_{00} & k_{01} p & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{02} - {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31} - k_{01}\right)} p\right)} H_{12} + {\left(d_{10} k_{03} k_{11} - d_{10} k_{01} k_{13} - d_{20} k_{13} k_{31} + d_{20} k_{11} k_{33} + {\left(d_{30} k_{03} k_{31} - d_{30} k_{01} k_{33}\right)} p - d_{20}\right)} H_{22} - {\left(d_{30} k_{03} k_{30} p^{2} - d_{10} k_{00} k_{13} + {\left(d_{10} k_{03} k_{10} - d_{20} k_{13} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{33} - k_{03}\right)} p\right)} H_{32} & -\frac{{\left({\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p^{2} - {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} + k_{00}\right)} p\right)} H_{03} + {\left(d_{30} k_{01} k_{30} p^{2} - d_{10} k_{00} k_{11} + {\left(d_{10} k_{01} k_{10} - d_{20} k_{11} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{31} - k_{01}\right)} p\right)} H_{13} - {\left({\left(d_{30} k_{03} k_{31} - d_{30} k_{01} k_{33}\right)} p^{2} + {\left(d_{10} k_{03} k_{11} - d_{10} k_{01} k_{13} - d_{20} k_{13} k_{31} + d_{20} k_{11} k_{33} - d_{20}\right)} p\right)} H_{23} + {\left(d_{30} k_{03} k_{30} p^{2} - d_{10} k_{00} k_{13} + {\left(d_{10} k_{03} k_{10} - d_{20} k_{13} k_{30} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{33} - k_{03}\right)} p\right)} H_{33}}{p} & -d_{20} & k_{03} \\ {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p - k_{10}\right)} H_{00} + {\left(d_{20} k_{11} k_{20} + {\left(d_{00} k_{00} - 1\right)} k_{11} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{10} + {\left(d_{00} k_{03} k_{11} - d_{00} k_{01} k_{13} - d_{20} k_{13} k_{21} + d_{20} k_{11} k_{23} + {\left(d_{30} k_{03} k_{21} - d_{30} k_{01} k_{23}\right)} p + d_{30}\right)} H_{20} + {\left(d_{20} k_{13} k_{20} + {\left(d_{00} k_{00} - 1\right)} k_{13} - {\left(d_{00} k_{03} k_{10} + d_{30} k_{03} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{23}\right)} p\right)} H_{30} & -{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - k_{10}\right)} p\right)} H_{01} + {\left(d_{20} k_{11} k_{20} + {\left(d_{00} k_{00} - 1\right)} k_{11} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{11} + {\left({\left(d_{30} k_{03} k_{21} - d_{30} k_{01} k_{23}\right)} p^{2} + {\left(d_{00} k_{03} k_{11} - d_{00} k_{01} k_{13} - d_{20} k_{13} k_{21} + d_{20} k_{11} k_{23} + d_{30}\right)} p\right)} H_{21} + {\left(d_{20} k_{13} k_{20} + {\left(d_{00} k_{00} - 1\right)} k_{13} - {\left(d_{00} k_{03} k_{10} + d_{30} k_{03} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{23}\right)} p\right)} H_{31} & k_{10} & k_{11} & -{\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p - k_{10}\right)} H_{02} - {\left(d_{20} k_{11} k_{20} + {\left(d_{00} k_{00} - 1\right)} k_{11} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{12} - {\left(d_{00} k_{03} k_{11} - d_{00} k_{01} k_{13} - d_{20} k_{13} k_{21} + d_{20} k_{11} k_{23} + {\left(d_{30} k_{03} k_{21} - d_{30} k_{01} k_{23}\right)} p + d_{30}\right)} H_{22} - {\left(d_{20} k_{13} k_{20} + {\left(d_{00} k_{00} - 1\right)} k_{13} - {\left(d_{00} k_{03} k_{10} + d_{30} k_{03} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{23}\right)} p\right)} H_{32} & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - k_{10}\right)} p\right)} H_{03} - {\left(d_{20} k_{11} k_{20} + {\left(d_{00} k_{00} - 1\right)} k_{11} - {\left(d_{00} k_{01} k_{10} + d_{30} k_{01} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{21}\right)} p\right)} H_{13} - {\left({\left(d_{30} k_{03} k_{21} - d_{30} k_{01} k_{23}\right)} p^{2} + {\left(d_{00} k_{03} k_{11} - d_{00} k_{01} k_{13} - d_{20} k_{13} k_{21} + d_{20} k_{11} k_{23} + d_{30}\right)} p\right)} H_{23} - {\left(d_{20} k_{13} k_{20} + {\left(d_{00} k_{00} - 1\right)} k_{13} - {\left(d_{00} k_{03} k_{10} + d_{30} k_{03} k_{20} - {\left(d_{30} k_{00} - d_{20} k_{10}\right)} k_{23}\right)} p\right)} H_{33}}{p} & -d_{30} & \frac{k_{13}}{p} \\ {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{00} - {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{10} k_{10} k_{21} + d_{00} k_{11} k_{30} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{10} - {\left(d_{10} k_{13} k_{21} - d_{10} k_{11} k_{23} - d_{00} k_{13} k_{31} + d_{00} k_{11} k_{33} - {\left(d_{30} k_{23} k_{31} - d_{30} k_{21} k_{33}\right)} p\right)} H_{20} - {\left(d_{30} k_{23} k_{30} p^{2} - d_{10} k_{13} k_{20} + {\left(d_{10} k_{10} k_{23} + d_{00} k_{13} k_{30} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{33}\right)} p\right)} H_{30} & -{\left({\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p^{2} - {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33}\right)} p\right)} H_{01} - {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{10} k_{10} k_{21} + d_{00} k_{11} k_{30} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{11} + {\left({\left(d_{30} k_{23} k_{31} - d_{30} k_{21} k_{33}\right)} p^{2} - {\left(d_{10} k_{13} k_{21} - d_{10} k_{11} k_{23} - d_{00} k_{13} k_{31} + d_{00} k_{11} k_{33}\right)} p\right)} H_{21} - {\left(d_{30} k_{23} k_{30} p^{2} - d_{10} k_{13} k_{20} + {\left(d_{10} k_{10} k_{23} + d_{00} k_{13} k_{30} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{33}\right)} p\right)} H_{31} & 0 & 0 & -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{02} + {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{10} k_{10} k_{21} + d_{00} k_{11} k_{30} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{12} + {\left(d_{10} k_{13} k_{21} - d_{10} k_{11} k_{23} - d_{00} k_{13} k_{31} + d_{00} k_{11} k_{33} - {\left(d_{30} k_{23} k_{31} - d_{30} k_{21} k_{33}\right)} p\right)} H_{22} + {\left(d_{30} k_{23} k_{30} p^{2} - d_{10} k_{13} k_{20} + {\left(d_{10} k_{10} k_{23} + d_{00} k_{13} k_{30} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{33}\right)} p\right)} H_{32} & \frac{{\left({\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p^{2} - {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33}\right)} p\right)} H_{03} + {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{10} k_{10} k_{21} + d_{00} k_{11} k_{30} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{13} - {\left({\left(d_{30} k_{23} k_{31} - d_{30} k_{21} k_{33}\right)} p^{2} - {\left(d_{10} k_{13} k_{21} - d_{10} k_{11} k_{23} - d_{00} k_{13} k_{31} + d_{00} k_{11} k_{33}\right)} p\right)} H_{23} + {\left(d_{30} k_{23} k_{30} p^{2} - d_{10} k_{13} k_{20} + {\left(d_{10} k_{10} k_{23} + d_{00} k_{13} k_{30} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{33}\right)} p\right)} H_{33}}{p} & 0 & 0 \\ {\left(d_{10} k_{03} k_{21} - d_{10} k_{01} k_{23} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{31} + {\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{33}\right)} H_{20} p + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{00} + {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{31}\right)} p\right)} H_{10} + {\left({\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{30} p^{2} - {\left(d_{10} k_{03} k_{20} - d_{10} k_{00} k_{23} + {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{33}\right)} p\right)} H_{30} & {\left(d_{10} k_{03} k_{21} - d_{10} k_{01} k_{23} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{31} + {\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{33}\right)} H_{21} p^{2} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{3} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p^{2}\right)} H_{01} + {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{31}\right)} p\right)} H_{11} + {\left({\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{30} p^{2} - {\left(d_{10} k_{03} k_{20} - d_{10} k_{00} k_{23} + {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{33}\right)} p\right)} H_{31} & 0 & 0 & -{\left(d_{10} k_{03} k_{21} - d_{10} k_{01} k_{23} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{31} + {\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{33}\right)} H_{22} p - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{02} - {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{31}\right)} p\right)} H_{12} - {\left({\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{30} p^{2} - {\left(d_{10} k_{03} k_{20} - d_{10} k_{00} k_{23} + {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{33}\right)} p\right)} H_{32} & -{\left(d_{10} k_{03} k_{21} - d_{10} k_{01} k_{23} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{31} + {\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{33}\right)} H_{23} p - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{03} + {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} - {\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p + {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{31}\right)} H_{13} + {\left(d_{10} k_{03} k_{20} - d_{10} k_{00} k_{23} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{30} p + {\left(d_{00} k_{00} + d_{20} k_{20}\right)} k_{33}\right)} H_{33} & 0 & 0 \\ -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{00} + {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{00} k_{11} k_{30} + {\left(d_{10} k_{10} - 1\right)} k_{21} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{10} + {\left(d_{10} k_{13} k_{21} - d_{10} k_{11} k_{23} - d_{00} k_{13} k_{31} + d_{00} k_{11} k_{33} - {\left(d_{30} k_{23} k_{31} - d_{30} k_{21} k_{33}\right)} p - d_{00}\right)} H_{20} + {\left(d_{30} k_{23} k_{30} p^{2} - d_{10} k_{13} k_{20} + {\left(d_{00} k_{13} k_{30} + {\left(d_{10} k_{10} - 1\right)} k_{23} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{33}\right)} p\right)} H_{30} & {\left({\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p^{2} - {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} + k_{20}\right)} p\right)} H_{01} + {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{00} k_{11} k_{30} + {\left(d_{10} k_{10} - 1\right)} k_{21} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{11} - {\left({\left(d_{30} k_{23} k_{31} - d_{30} k_{21} k_{33}\right)} p^{2} - {\left(d_{10} k_{13} k_{21} - d_{10} k_{11} k_{23} - d_{00} k_{13} k_{31} + d_{00} k_{11} k_{33} - d_{00}\right)} p\right)} H_{21} + {\left(d_{30} k_{23} k_{30} p^{2} - d_{10} k_{13} k_{20} + {\left(d_{00} k_{13} k_{30} + {\left(d_{10} k_{10} - 1\right)} k_{23} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{33}\right)} p\right)} H_{31} & k_{20} & k_{21} p & {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{02} - {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{00} k_{11} k_{30} + {\left(d_{10} k_{10} - 1\right)} k_{21} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{12} - {\left(d_{10} k_{13} k_{21} - d_{10} k_{11} k_{23} - d_{00} k_{13} k_{31} + d_{00} k_{11} k_{33} - {\left(d_{30} k_{23} k_{31} - d_{30} k_{21} k_{33}\right)} p - d_{00}\right)} H_{22} - {\left(d_{30} k_{23} k_{30} p^{2} - d_{10} k_{13} k_{20} + {\left(d_{00} k_{13} k_{30} + {\left(d_{10} k_{10} - 1\right)} k_{23} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{33}\right)} p\right)} H_{32} & -\frac{{\left({\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p^{2} - {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} + k_{20}\right)} p\right)} H_{03} + {\left(d_{30} k_{21} k_{30} p^{2} - d_{10} k_{11} k_{20} + {\left(d_{00} k_{11} k_{30} + {\left(d_{10} k_{10} - 1\right)} k_{21} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{31}\right)} p\right)} H_{13} - {\left({\left(d_{30} k_{23} k_{31} - d_{30} k_{21} k_{33}\right)} p^{2} - {\left(d_{10} k_{13} k_{21} - d_{10} k_{11} k_{23} - d_{00} k_{13} k_{31} + d_{00} k_{11} k_{33} - d_{00}\right)} p\right)} H_{23} + {\left(d_{30} k_{23} k_{30} p^{2} - d_{10} k_{13} k_{20} + {\left(d_{00} k_{13} k_{30} + {\left(d_{10} k_{10} - 1\right)} k_{23} - {\left(d_{00} k_{10} + d_{30} k_{20}\right)} k_{33}\right)} p\right)} H_{33}}{p} & d_{00} & k_{23} \\ -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{00} - {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20} - 1\right)} k_{31}\right)} p\right)} H_{10} - {\left({\left(d_{10} k_{03} k_{21} - d_{10} k_{01} k_{23} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{31} + {\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{33}\right)} p + d_{10}\right)} H_{20} - {\left({\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{30} p^{2} - {\left(d_{10} k_{03} k_{20} - d_{10} k_{00} k_{23} + {\left(d_{00} k_{00} + d_{20} k_{20} - 1\right)} k_{33}\right)} p\right)} H_{30} & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{3} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p^{2}\right)} H_{01} - {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20} - 1\right)} k_{31}\right)} p\right)} H_{11} - {\left({\left(d_{10} k_{03} k_{21} - d_{10} k_{01} k_{23} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{31} + {\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{33}\right)} p^{2} + d_{10} p\right)} H_{21} - {\left({\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{30} p^{2} - {\left(d_{10} k_{03} k_{20} - d_{10} k_{00} k_{23} + {\left(d_{00} k_{00} + d_{20} k_{20} - 1\right)} k_{33}\right)} p\right)} H_{31} & k_{30} p & k_{31} p & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{02} + {\left({\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p^{2} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} + {\left(d_{00} k_{00} + d_{20} k_{20} - 1\right)} k_{31}\right)} p\right)} H_{12} + {\left({\left(d_{10} k_{03} k_{21} - d_{10} k_{01} k_{23} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{31} + {\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{33}\right)} p + d_{10}\right)} H_{22} + {\left({\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{30} p^{2} - {\left(d_{10} k_{03} k_{20} - d_{10} k_{00} k_{23} + {\left(d_{00} k_{00} + d_{20} k_{20} - 1\right)} k_{33}\right)} p\right)} H_{32} & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{03} - {\left(d_{10} k_{01} k_{20} - d_{10} k_{00} k_{21} - {\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{30} p + {\left(d_{00} k_{00} + d_{20} k_{20} - 1\right)} k_{31}\right)} H_{13} + {\left({\left(d_{10} k_{03} k_{21} - d_{10} k_{01} k_{23} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{31} + {\left(d_{00} k_{01} + d_{20} k_{21}\right)} k_{33}\right)} p + d_{10}\right)} H_{23} - {\left(d_{10} k_{03} k_{20} - d_{10} k_{00} k_{23} - {\left(d_{00} k_{03} + d_{20} k_{23}\right)} k_{30} p + {\left(d_{00} k_{00} + d_{20} k_{20} - 1\right)} k_{33}\right)} H_{33} & d_{10} & k_{33} \end{array}\right)$

Z=(Z.substitute(d20==-k02).substitute(d30==-k12).substitute(d00==k22).substitute(d10==p*k32)).simplify_full();Z;

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} -{\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p\right)} H_{00} - {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31}\right)} p\right)} H_{10} - {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p\right)} H_{20} - {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33}\right)} p\right)} H_{30} & {\left({\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p^{2} - {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33}\right)} p\right)} H_{01} - {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31}\right)} p\right)} H_{11} + {\left({\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33}\right)} p\right)} H_{21} - {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33}\right)} p\right)} H_{31} & 0 & 0 & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p\right)} H_{02} + {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31}\right)} p\right)} H_{12} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p\right)} H_{22} + {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33}\right)} p\right)} H_{32} & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p\right)} H_{03} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - {\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p\right)} H_{13} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p\right)} H_{23} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - {\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p\right)} H_{00} - {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{10} + {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - {\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p\right)} H_{20} - {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{30} & -{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20}\right)} p\right)} H_{01} - {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{11} - {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22}\right)} p\right)} H_{21} - {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{31} & 0 & 0 & -{\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p\right)} H_{02} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{12} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - {\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p\right)} H_{22} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{32} & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20}\right)} p\right)} H_{03} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{13} + {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{33}}{p} & 0 & 0 \\ -{\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{00} - {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - k_{01}\right)} p\right)} H_{10} - {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p + k_{02}\right)} H_{20} - {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - k_{03}\right)} p\right)} H_{30} & {\left({\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p^{2} - {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} + k_{00}\right)} p\right)} H_{01} - {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - k_{01}\right)} p\right)} H_{11} + {\left({\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} + k_{02}\right)} p\right)} H_{21} - {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - k_{03}\right)} p\right)} H_{31} & k_{00} & k_{01} p & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{02} + {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - k_{01}\right)} p\right)} H_{12} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p + k_{02}\right)} H_{22} + {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - k_{03}\right)} p\right)} H_{32} & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{03} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - {\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p - k_{01}\right)} H_{13} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p + k_{02}\right)} H_{23} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - {\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p - k_{03}\right)} H_{33} & k_{02} & k_{03} \\ {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p - k_{10}\right)} H_{00} - {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{10} + {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - {\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p - k_{12}\right)} H_{20} - {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{30} & -{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - k_{10}\right)} p\right)} H_{01} - {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{11} - {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - k_{12}\right)} p\right)} H_{21} - {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{31} & k_{10} & k_{11} & -{\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p - k_{10}\right)} H_{02} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{12} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - {\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p - k_{12}\right)} H_{22} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{32} & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - k_{10}\right)} p\right)} H_{03} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{13} + {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - k_{12}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{33}}{p} & k_{12} & \frac{k_{13}}{p} \\ {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{00} + {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31}\right)} p\right)} H_{10} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p\right)} H_{20} + {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33}\right)} p\right)} H_{30} & -{\left({\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p^{2} - {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33}\right)} p\right)} H_{01} + {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31}\right)} p\right)} H_{11} - {\left({\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33}\right)} p\right)} H_{21} + {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33}\right)} p\right)} H_{31} & 0 & 0 & -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{02} - {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31}\right)} p\right)} H_{12} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p\right)} H_{22} - {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33}\right)} p\right)} H_{32} & -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{03} + {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - {\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p\right)} H_{13} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p\right)} H_{23} + {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{00} + {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{10} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p\right)} H_{20} + {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{30} & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{3} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p^{2}\right)} H_{01} + {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{11} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{3} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p^{2}\right)} H_{21} + {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{31} & 0 & 0 & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{02} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{12} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p\right)} H_{22} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{32} & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{03} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p\right)} H_{13} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p\right)} H_{23} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{00} - {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - k_{21}\right)} p\right)} H_{10} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{20} - {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - k_{23}\right)} p\right)} H_{30} & {\left({\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p^{2} - {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} + k_{20}\right)} p\right)} H_{01} - {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - k_{21}\right)} p\right)} H_{11} + {\left({\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} + k_{22}\right)} p\right)} H_{21} - {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - k_{23}\right)} p\right)} H_{31} & k_{20} & k_{21} p & {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{02} + {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - k_{21}\right)} p\right)} H_{12} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{22} + {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - k_{23}\right)} p\right)} H_{32} & {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{03} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - {\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p - k_{21}\right)} H_{13} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{23} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p - k_{23}\right)} H_{33} & k_{22} & k_{23} \\ -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{00} - {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{10} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{20} - {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{30} & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{3} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p^{2}\right)} H_{01} - {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{11} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{3} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p^{2}\right)} H_{21} - {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{31} & k_{30} p & k_{31} p & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{02} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{12} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{22} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{32} & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{03} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p\right)} H_{13} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{23} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p\right)} H_{33} & k_{32} p & k_{33} \end{array}\right)$

Recall we have that $Z[2,0]=Z[3,0]=Z[6,0]=Z[7,0]=0$.

Z[0,0]=Z[0,0]-Z[2,0];

Z[2,0]=0;Z[1,0]=Z[1,0]-Z[3,0];Z.simplify_full()

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} H_{10} k_{01} p + H_{30} k_{03} p + H_{00} k_{00} + H_{20} k_{02} & {\left({\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p^{2} - {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33}\right)} p\right)} H_{01} - {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31}\right)} p\right)} H_{11} + {\left({\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33}\right)} p\right)} H_{21} - {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33}\right)} p\right)} H_{31} & 0 & 0 & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p\right)} H_{02} + {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31}\right)} p\right)} H_{12} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p\right)} H_{22} + {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33}\right)} p\right)} H_{32} & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p\right)} H_{03} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - {\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p\right)} H_{13} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p\right)} H_{23} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - {\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ H_{00} k_{10} + H_{10} k_{11} + H_{20} k_{12} + H_{30} k_{13} & -{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20}\right)} p\right)} H_{01} - {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{11} - {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22}\right)} p\right)} H_{21} - {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{31} & 0 & 0 & -{\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p\right)} H_{02} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{12} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - {\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p\right)} H_{22} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{32} & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20}\right)} p\right)} H_{03} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{13} + {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{33}}{p} & 0 & 0 \\ 0 & {\left({\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p^{2} - {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} + k_{00}\right)} p\right)} H_{01} - {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - k_{01}\right)} p\right)} H_{11} + {\left({\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} + k_{02}\right)} p\right)} H_{21} - {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - k_{03}\right)} p\right)} H_{31} & k_{00} & k_{01} p & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{02} + {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - k_{01}\right)} p\right)} H_{12} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p + k_{02}\right)} H_{22} + {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - k_{03}\right)} p\right)} H_{32} & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{03} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - {\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p - k_{01}\right)} H_{13} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p + k_{02}\right)} H_{23} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - {\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p - k_{03}\right)} H_{33} & k_{02} & k_{03} \\ {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p - k_{10}\right)} H_{00} - {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{10} + {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - {\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p - k_{12}\right)} H_{20} - {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{30} & -{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - k_{10}\right)} p\right)} H_{01} - {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{11} - {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - k_{12}\right)} p\right)} H_{21} - {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{31} & k_{10} & k_{11} & -{\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p - k_{10}\right)} H_{02} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{12} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - {\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p - k_{12}\right)} H_{22} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{32} & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - k_{10}\right)} p\right)} H_{03} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{13} + {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - k_{12}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{33}}{p} & k_{12} & \frac{k_{13}}{p} \\ {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{00} + {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31}\right)} p\right)} H_{10} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p\right)} H_{20} + {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33}\right)} p\right)} H_{30} & -{\left({\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p^{2} - {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33}\right)} p\right)} H_{01} + {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31}\right)} p\right)} H_{11} - {\left({\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33}\right)} p\right)} H_{21} + {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33}\right)} p\right)} H_{31} & 0 & 0 & -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{02} - {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31}\right)} p\right)} H_{12} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p\right)} H_{22} - {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33}\right)} p\right)} H_{32} & -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{03} + {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - {\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p\right)} H_{13} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p\right)} H_{23} + {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{00} + {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{10} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p\right)} H_{20} + {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{30} & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{3} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p^{2}\right)} H_{01} + {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{11} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{3} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p^{2}\right)} H_{21} + {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{31} & 0 & 0 & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{02} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{12} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p\right)} H_{22} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{32} & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{03} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p\right)} H_{13} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p\right)} H_{23} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{00} - {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - k_{21}\right)} p\right)} H_{10} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{20} - {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - k_{23}\right)} p\right)} H_{30} & {\left({\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p^{2} - {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} + k_{20}\right)} p\right)} H_{01} - {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - k_{21}\right)} p\right)} H_{11} + {\left({\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} + k_{22}\right)} p\right)} H_{21} - {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - k_{23}\right)} p\right)} H_{31} & k_{20} & k_{21} p & {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{02} + {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - k_{21}\right)} p\right)} H_{12} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{22} + {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - k_{23}\right)} p\right)} H_{32} & {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{03} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - {\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p - k_{21}\right)} H_{13} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{23} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p - k_{23}\right)} H_{33} & k_{22} & k_{23} \\ -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{00} - {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{10} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{20} - {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{30} & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{3} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p^{2}\right)} H_{01} - {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{11} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{3} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p^{2}\right)} H_{21} - {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{31} & k_{30} p & k_{31} p & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{02} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{12} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{22} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{32} & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{03} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p\right)} H_{13} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{23} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p\right)} H_{33} & k_{32} p & k_{33} \end{array}\right)$

Z[3,0]=0;Z[4,0]=Z[4,0]+Z[6,0];Z[5,0]=Z[5,0]+Z[7,0];Z.simplify_full()

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} H_{10} k_{01} p + H_{30} k_{03} p + H_{00} k_{00} + H_{20} k_{02} & {\left({\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p^{2} - {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33}\right)} p\right)} H_{01} - {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31}\right)} p\right)} H_{11} + {\left({\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33}\right)} p\right)} H_{21} - {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33}\right)} p\right)} H_{31} & 0 & 0 & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p\right)} H_{02} + {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31}\right)} p\right)} H_{12} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p\right)} H_{22} + {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33}\right)} p\right)} H_{32} & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p\right)} H_{03} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - {\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p\right)} H_{13} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p\right)} H_{23} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - {\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ H_{00} k_{10} + H_{10} k_{11} + H_{20} k_{12} + H_{30} k_{13} & -{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20}\right)} p\right)} H_{01} - {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{11} - {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22}\right)} p\right)} H_{21} - {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{31} & 0 & 0 & -{\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p\right)} H_{02} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{12} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - {\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p\right)} H_{22} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{32} & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20}\right)} p\right)} H_{03} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{13} + {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{33}}{p} & 0 & 0 \\ 0 & {\left({\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p^{2} - {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} + k_{00}\right)} p\right)} H_{01} - {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - k_{01}\right)} p\right)} H_{11} + {\left({\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} + k_{02}\right)} p\right)} H_{21} - {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - k_{03}\right)} p\right)} H_{31} & k_{00} & k_{01} p & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{02} + {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - k_{01}\right)} p\right)} H_{12} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p + k_{02}\right)} H_{22} + {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - k_{03}\right)} p\right)} H_{32} & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{03} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - {\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p - k_{01}\right)} H_{13} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p + k_{02}\right)} H_{23} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - {\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p - k_{03}\right)} H_{33} & k_{02} & k_{03} \\ 0 & -{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - k_{10}\right)} p\right)} H_{01} - {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{11} - {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - k_{12}\right)} p\right)} H_{21} - {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{31} & k_{10} & k_{11} & -{\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p - k_{10}\right)} H_{02} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{12} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - {\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p - k_{12}\right)} H_{22} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{32} & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - k_{10}\right)} p\right)} H_{03} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{13} + {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - k_{12}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{33}}{p} & k_{12} & \frac{k_{13}}{p} \\ -H_{10} k_{21} p - H_{30} k_{23} p - H_{00} k_{20} - H_{20} k_{22} & -{\left({\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p^{2} - {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33}\right)} p\right)} H_{01} + {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31}\right)} p\right)} H_{11} - {\left({\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33}\right)} p\right)} H_{21} + {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33}\right)} p\right)} H_{31} & 0 & 0 & -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{02} - {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31}\right)} p\right)} H_{12} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p\right)} H_{22} - {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33}\right)} p\right)} H_{32} & -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{03} + {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - {\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p\right)} H_{13} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p\right)} H_{23} + {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ -H_{00} k_{30} p - H_{10} k_{31} p - H_{20} k_{32} p - H_{30} k_{33} p & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{3} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p^{2}\right)} H_{01} + {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{11} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{3} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p^{2}\right)} H_{21} + {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{31} & 0 & 0 & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{02} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{12} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p\right)} H_{22} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{32} & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{03} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p\right)} H_{13} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p\right)} H_{23} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{00} - {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - k_{21}\right)} p\right)} H_{10} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{20} - {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - k_{23}\right)} p\right)} H_{30} & {\left({\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p^{2} - {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} + k_{20}\right)} p\right)} H_{01} - {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - k_{21}\right)} p\right)} H_{11} + {\left({\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} + k_{22}\right)} p\right)} H_{21} - {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - k_{23}\right)} p\right)} H_{31} & k_{20} & k_{21} p & {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{02} + {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - k_{21}\right)} p\right)} H_{12} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{22} + {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - k_{23}\right)} p\right)} H_{32} & {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{03} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - {\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p - k_{21}\right)} H_{13} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{23} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p - k_{23}\right)} H_{33} & k_{22} & k_{23} \\ -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{00} - {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{10} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{20} - {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{30} & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{3} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p^{2}\right)} H_{01} - {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{11} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{3} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p^{2}\right)} H_{21} - {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{31} & k_{30} p & k_{31} p & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{02} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{12} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{22} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{32} & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{03} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p\right)} H_{13} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{23} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p\right)} H_{33} & k_{32} p & k_{33} \end{array}\right)$

Z[6,0]=0;Z[7,0]=0;

Z.simplify_full();

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} H_{10} k_{01} p + H_{30} k_{03} p + H_{00} k_{00} + H_{20} k_{02} & {\left({\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p^{2} - {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33}\right)} p\right)} H_{01} - {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31}\right)} p\right)} H_{11} + {\left({\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33}\right)} p\right)} H_{21} - {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33}\right)} p\right)} H_{31} & 0 & 0 & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p\right)} H_{02} + {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31}\right)} p\right)} H_{12} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p\right)} H_{22} + {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33}\right)} p\right)} H_{32} & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p\right)} H_{03} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - {\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p\right)} H_{13} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p\right)} H_{23} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - {\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ H_{00} k_{10} + H_{10} k_{11} + H_{20} k_{12} + H_{30} k_{13} & -{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20}\right)} p\right)} H_{01} - {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{11} - {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22}\right)} p\right)} H_{21} - {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{31} & 0 & 0 & -{\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p\right)} H_{02} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{12} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - {\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p\right)} H_{22} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{32} & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20}\right)} p\right)} H_{03} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{13} + {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{33}}{p} & 0 & 0 \\ 0 & {\left({\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p^{2} - {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} + k_{00}\right)} p\right)} H_{01} - {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - k_{01}\right)} p\right)} H_{11} + {\left({\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} + k_{02}\right)} p\right)} H_{21} - {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - k_{03}\right)} p\right)} H_{31} & k_{00} & k_{01} p & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{02} + {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - k_{01}\right)} p\right)} H_{12} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p + k_{02}\right)} H_{22} + {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - k_{03}\right)} p\right)} H_{32} & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{03} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - {\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p - k_{01}\right)} H_{13} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p + k_{02}\right)} H_{23} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - {\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p - k_{03}\right)} H_{33} & k_{02} & k_{03} \\ 0 & -{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - k_{10}\right)} p\right)} H_{01} - {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{11} - {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - k_{12}\right)} p\right)} H_{21} - {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{31} & k_{10} & k_{11} & -{\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p - k_{10}\right)} H_{02} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{12} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - {\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p - k_{12}\right)} H_{22} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{32} & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - k_{10}\right)} p\right)} H_{03} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{13} + {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - k_{12}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{33}}{p} & k_{12} & \frac{k_{13}}{p} \\ -H_{10} k_{21} p - H_{30} k_{23} p - H_{00} k_{20} - H_{20} k_{22} & -{\left({\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p^{2} - {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33}\right)} p\right)} H_{01} + {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31}\right)} p\right)} H_{11} - {\left({\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33}\right)} p\right)} H_{21} + {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33}\right)} p\right)} H_{31} & 0 & 0 & -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{02} - {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31}\right)} p\right)} H_{12} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p\right)} H_{22} - {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33}\right)} p\right)} H_{32} & -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{03} + {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - {\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p\right)} H_{13} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p\right)} H_{23} + {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ -H_{00} k_{30} p - H_{10} k_{31} p - H_{20} k_{32} p - H_{30} k_{33} p & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{3} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p^{2}\right)} H_{01} + {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{11} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{3} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p^{2}\right)} H_{21} + {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{31} & 0 & 0 & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{02} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{12} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p\right)} H_{22} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{32} & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{03} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p\right)} H_{13} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p\right)} H_{23} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ 0 & {\left({\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p^{2} - {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} + k_{20}\right)} p\right)} H_{01} - {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - k_{21}\right)} p\right)} H_{11} + {\left({\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} + k_{22}\right)} p\right)} H_{21} - {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - k_{23}\right)} p\right)} H_{31} & k_{20} & k_{21} p & {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{02} + {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - k_{21}\right)} p\right)} H_{12} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{22} + {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - k_{23}\right)} p\right)} H_{32} & {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{03} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - {\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p - k_{21}\right)} H_{13} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{23} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p - k_{23}\right)} H_{33} & k_{22} & k_{23} \\ 0 & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{3} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p^{2}\right)} H_{01} - {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{11} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{3} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p^{2}\right)} H_{21} - {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{31} & k_{30} p & k_{31} p & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{02} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{12} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{22} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{32} & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{03} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p\right)} H_{13} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{23} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p\right)} H_{33} & k_{32} p & k_{33} \end{array}\right)$

Now we make use of the fact that $Z[2,1]=Z[3,1]=Z[6,1]=Z[7,1]=0$.

Z[0,1]=Z[0,1]-Z[2,1];Z[1,1]=Z[1,1]-Z[3,1];Z[4,1]=Z[4,1]+Z[6,1];Z[5,1]=Z[5,1]+Z[7,1];Z.simplify_full()

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} H_{10} k_{01} p + H_{30} k_{03} p + H_{00} k_{00} + H_{20} k_{02} & H_{01} k_{00} p + H_{11} k_{01} p + H_{21} k_{02} p + H_{31} k_{03} p & 0 & 0 & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p\right)} H_{02} + {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31}\right)} p\right)} H_{12} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p\right)} H_{22} + {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33}\right)} p\right)} H_{32} & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p\right)} H_{03} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - {\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p\right)} H_{13} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p\right)} H_{23} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - {\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ H_{00} k_{10} + H_{10} k_{11} + H_{20} k_{12} + H_{30} k_{13} & H_{01} k_{10} p + H_{21} k_{12} p + H_{11} k_{11} + H_{31} k_{13} & 0 & 0 & -{\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p\right)} H_{02} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{12} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - {\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p\right)} H_{22} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{32} & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20}\right)} p\right)} H_{03} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{13} + {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{33}}{p} & 0 & 0 \\ 0 & {\left({\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p^{2} - {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} + k_{00}\right)} p\right)} H_{01} - {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - k_{01}\right)} p\right)} H_{11} + {\left({\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} + k_{02}\right)} p\right)} H_{21} - {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - k_{03}\right)} p\right)} H_{31} & k_{00} & k_{01} p & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{02} + {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - k_{01}\right)} p\right)} H_{12} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p + k_{02}\right)} H_{22} + {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - k_{03}\right)} p\right)} H_{32} & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{03} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - {\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p - k_{01}\right)} H_{13} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p + k_{02}\right)} H_{23} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - {\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p - k_{03}\right)} H_{33} & k_{02} & k_{03} \\ 0 & -{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - k_{10}\right)} p\right)} H_{01} - {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{11} - {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - k_{12}\right)} p\right)} H_{21} - {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{31} & k_{10} & k_{11} & -{\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p - k_{10}\right)} H_{02} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{12} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - {\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p - k_{12}\right)} H_{22} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{32} & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - k_{10}\right)} p\right)} H_{03} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{13} + {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - k_{12}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{33}}{p} & k_{12} & \frac{k_{13}}{p} \\ -H_{10} k_{21} p - H_{30} k_{23} p - H_{00} k_{20} - H_{20} k_{22} & -H_{01} k_{20} p - H_{11} k_{21} p - H_{21} k_{22} p - H_{31} k_{23} p & 0 & 0 & -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{02} - {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31}\right)} p\right)} H_{12} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p\right)} H_{22} - {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33}\right)} p\right)} H_{32} & -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{03} + {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - {\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p\right)} H_{13} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p\right)} H_{23} + {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ -H_{00} k_{30} p - H_{10} k_{31} p - H_{20} k_{32} p - H_{30} k_{33} p & -H_{01} k_{30} p^{2} - H_{21} k_{32} p^{2} - H_{11} k_{31} p - H_{31} k_{33} p & 0 & 0 & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{02} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{12} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p\right)} H_{22} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{32} & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{03} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p\right)} H_{13} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p\right)} H_{23} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ 0 & {\left({\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p^{2} - {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} + k_{20}\right)} p\right)} H_{01} - {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - k_{21}\right)} p\right)} H_{11} + {\left({\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} + k_{22}\right)} p\right)} H_{21} - {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - k_{23}\right)} p\right)} H_{31} & k_{20} & k_{21} p & {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{02} + {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - k_{21}\right)} p\right)} H_{12} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{22} + {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - k_{23}\right)} p\right)} H_{32} & {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{03} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - {\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p - k_{21}\right)} H_{13} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{23} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p - k_{23}\right)} H_{33} & k_{22} & k_{23} \\ 0 & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{3} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p^{2}\right)} H_{01} - {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{11} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{3} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p^{2}\right)} H_{21} - {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{31} & k_{30} p & k_{31} p & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{02} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{12} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{22} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{32} & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{03} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p\right)} H_{13} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{23} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p\right)} H_{33} & k_{32} p & k_{33} \end{array}\right)$

Z[2,1]=0; Z[3,1]=0;Z[6,1]=0;Z[7,1]=0;Z.simplify_full()

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} H_{10} k_{01} p + H_{30} k_{03} p + H_{00} k_{00} + H_{20} k_{02} & H_{01} k_{00} p + H_{11} k_{01} p + H_{21} k_{02} p + H_{31} k_{03} p & 0 & 0 & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p\right)} H_{02} + {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31}\right)} p\right)} H_{12} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p\right)} H_{22} + {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33}\right)} p\right)} H_{32} & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p\right)} H_{03} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - {\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p\right)} H_{13} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p\right)} H_{23} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - {\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ H_{00} k_{10} + H_{10} k_{11} + H_{20} k_{12} + H_{30} k_{13} & H_{01} k_{10} p + H_{21} k_{12} p + H_{11} k_{11} + H_{31} k_{13} & 0 & 0 & -{\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p\right)} H_{02} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{12} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - {\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p\right)} H_{22} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{32} & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20}\right)} p\right)} H_{03} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{13} + {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{33}}{p} & 0 & 0 \\ 0 & 0 & k_{00} & k_{01} p & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{02} + {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - k_{01}\right)} p\right)} H_{12} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p + k_{02}\right)} H_{22} + {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - k_{03}\right)} p\right)} H_{32} & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{03} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - {\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p - k_{01}\right)} H_{13} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p + k_{02}\right)} H_{23} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - {\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p - k_{03}\right)} H_{33} & k_{02} & k_{03} \\ 0 & 0 & k_{10} & k_{11} & -{\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p - k_{10}\right)} H_{02} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{12} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - {\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p - k_{12}\right)} H_{22} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{32} & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - k_{10}\right)} p\right)} H_{03} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{13} + {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - k_{12}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{33}}{p} & k_{12} & \frac{k_{13}}{p} \\ -H_{10} k_{21} p - H_{30} k_{23} p - H_{00} k_{20} - H_{20} k_{22} & -H_{01} k_{20} p - H_{11} k_{21} p - H_{21} k_{22} p - H_{31} k_{23} p & 0 & 0 & -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{02} - {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31}\right)} p\right)} H_{12} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p\right)} H_{22} - {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33}\right)} p\right)} H_{32} & -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{03} + {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - {\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p\right)} H_{13} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p\right)} H_{23} + {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ -H_{00} k_{30} p - H_{10} k_{31} p - H_{20} k_{32} p - H_{30} k_{33} p & -H_{01} k_{30} p^{2} - H_{21} k_{32} p^{2} - H_{11} k_{31} p - H_{31} k_{33} p & 0 & 0 & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{02} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{12} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p\right)} H_{22} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{32} & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{03} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p\right)} H_{13} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p\right)} H_{23} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ 0 & 0 & k_{20} & k_{21} p & {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{02} + {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - k_{21}\right)} p\right)} H_{12} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{22} + {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - k_{23}\right)} p\right)} H_{32} & {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{03} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - {\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p - k_{21}\right)} H_{13} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{23} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p - k_{23}\right)} H_{33} & k_{22} & k_{23} \\ 0 & 0 & k_{30} p & k_{31} p & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{02} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{12} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{22} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{32} & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{03} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p\right)} H_{13} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{23} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p\right)} H_{33} & k_{32} p & k_{33} \end{array}\right)$

We now use that $Z[2,4]=Z[3,4]=Z[6,4]=Z[7,4]=0$.

Z[0,4]=Z[0,4]-Z[2,4];Z[1,4]=Z[1,4]-Z[3,4];Z[4,4]=Z[4,4]+Z[6,4];Z[5,4]=Z[5,4]+Z[7,4];Z.simplify_full();

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} H_{10} k_{01} p + H_{30} k_{03} p + H_{00} k_{00} + H_{20} k_{02} & H_{01} k_{00} p + H_{11} k_{01} p + H_{21} k_{02} p + H_{31} k_{03} p & 0 & 0 & -H_{12} k_{01} p - H_{32} k_{03} p - H_{02} k_{00} - H_{22} k_{02} & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p\right)} H_{03} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - {\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p\right)} H_{13} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p\right)} H_{23} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - {\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ H_{00} k_{10} + H_{10} k_{11} + H_{20} k_{12} + H_{30} k_{13} & H_{01} k_{10} p + H_{21} k_{12} p + H_{11} k_{11} + H_{31} k_{13} & 0 & 0 & -H_{02} k_{10} - H_{12} k_{11} - H_{22} k_{12} - H_{32} k_{13} & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20}\right)} p\right)} H_{03} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{13} + {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{33}}{p} & 0 & 0 \\ 0 & 0 & k_{00} & k_{01} p & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{02} + {\left({\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - k_{01}\right)} p\right)} H_{12} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p + k_{02}\right)} H_{22} + {\left({\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p^{2} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - k_{03}\right)} p\right)} H_{32} & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{03} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - {\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p - k_{01}\right)} H_{13} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p + k_{02}\right)} H_{23} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - {\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p - k_{03}\right)} H_{33} & k_{02} & k_{03} \\ 0 & 0 & k_{10} & k_{11} & -{\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - {\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p - k_{10}\right)} H_{02} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{12} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - {\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p - k_{12}\right)} H_{22} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{32} & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - k_{10}\right)} p\right)} H_{03} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{13} + {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - k_{12}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{33}}{p} & k_{12} & \frac{k_{13}}{p} \\ -H_{10} k_{21} p - H_{30} k_{23} p - H_{00} k_{20} - H_{20} k_{22} & -H_{01} k_{20} p - H_{11} k_{21} p - H_{21} k_{22} p - H_{31} k_{23} p & 0 & 0 & H_{12} k_{21} p + H_{32} k_{23} p + H_{02} k_{20} + H_{22} k_{22} & -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{03} + {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - {\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p\right)} H_{13} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p\right)} H_{23} + {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ -H_{00} k_{30} p - H_{10} k_{31} p - H_{20} k_{32} p - H_{30} k_{33} p & -H_{01} k_{30} p^{2} - H_{21} k_{32} p^{2} - H_{11} k_{31} p - H_{31} k_{33} p & 0 & 0 & H_{02} k_{30} p + H_{12} k_{31} p + H_{22} k_{32} p + H_{32} k_{33} p & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{03} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p\right)} H_{13} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p\right)} H_{23} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ 0 & 0 & k_{20} & k_{21} p & {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{02} + {\left({\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p^{2} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - k_{21}\right)} p\right)} H_{12} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{22} + {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - k_{23}\right)} p\right)} H_{32} & {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{03} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - {\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p - k_{21}\right)} H_{13} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{23} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p - k_{23}\right)} H_{33} & k_{22} & k_{23} \\ 0 & 0 & k_{30} p & k_{31} p & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{02} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p^{2}\right)} H_{12} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{22} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} p + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p^{2}\right)} H_{32} & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{03} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p\right)} H_{13} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{23} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p\right)} H_{33} & k_{32} p & k_{33} \end{array}\right)$

Z[2,4]=0;Z[3,4]=0;Z[6,4]=0;Z[7,4]=0;Z.simplify_full()

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} H_{10} k_{01} p + H_{30} k_{03} p + H_{00} k_{00} + H_{20} k_{02} & H_{01} k_{00} p + H_{11} k_{01} p + H_{21} k_{02} p + H_{31} k_{03} p & 0 & 0 & -H_{12} k_{01} p - H_{32} k_{03} p - H_{02} k_{00} - H_{22} k_{02} & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p\right)} H_{03} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - {\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p\right)} H_{13} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p\right)} H_{23} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - {\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ H_{00} k_{10} + H_{10} k_{11} + H_{20} k_{12} + H_{30} k_{13} & H_{01} k_{10} p + H_{21} k_{12} p + H_{11} k_{11} + H_{31} k_{13} & 0 & 0 & -H_{02} k_{10} - H_{12} k_{11} - H_{22} k_{12} - H_{32} k_{13} & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20}\right)} p\right)} H_{03} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{13} + {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p\right)} H_{33}}{p} & 0 & 0 \\ 0 & 0 & k_{00} & k_{01} p & 0 & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{03} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - {\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p - k_{01}\right)} H_{13} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p + k_{02}\right)} H_{23} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - {\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p - k_{03}\right)} H_{33} & k_{02} & k_{03} \\ 0 & 0 & k_{10} & k_{11} & 0 & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - k_{10}\right)} p\right)} H_{03} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{13} + {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - k_{12}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{33}}{p} & k_{12} & \frac{k_{13}}{p} \\ -H_{10} k_{21} p - H_{30} k_{23} p - H_{00} k_{20} - H_{20} k_{22} & -H_{01} k_{20} p - H_{11} k_{21} p - H_{21} k_{22} p - H_{31} k_{23} p & 0 & 0 & H_{12} k_{21} p + H_{32} k_{23} p + H_{02} k_{20} + H_{22} k_{22} & -{\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p\right)} H_{03} + {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - {\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p\right)} H_{13} - {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p\right)} H_{23} + {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ -H_{00} k_{30} p - H_{10} k_{31} p - H_{20} k_{32} p - H_{30} k_{33} p & -H_{01} k_{30} p^{2} - H_{21} k_{32} p^{2} - H_{11} k_{31} p - H_{31} k_{33} p & 0 & 0 & H_{02} k_{30} p + H_{12} k_{31} p + H_{22} k_{32} p + H_{32} k_{33} p & -{\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33}\right)} p\right)} H_{03} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p\right)} H_{13} - {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33}\right)} p\right)} H_{23} - {\left({\left(k_{02} k_{20} - k_{00} k_{22}\right)} k_{33} + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p\right)} H_{33} & 0 & 0 \\ 0 & 0 & k_{20} & k_{21} p & 0 & {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{03} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - {\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p - k_{21}\right)} H_{13} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{23} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p - k_{23}\right)} H_{33} & k_{22} & k_{23} \\ 0 & 0 & k_{30} p & k_{31} p & 0 & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{03} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p\right)} H_{13} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{23} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p\right)} H_{33} & k_{32} p & k_{33} \end{array}\right)$

We now use that $Z[2,5]=Z[3,5]=Z[6,5]=Z[7,5]=0$.

Z[0,5]=Z[0,5]-Z[2,5];Z[1,5]=Z[1,5]-Z[3,5];Z[4,5]=Z[4,5]+Z[6,5];Z[5,5]=Z[5,5]+Z[7,5];Z.simplify_full();

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} H_{10} k_{01} p + H_{30} k_{03} p + H_{00} k_{00} + H_{20} k_{02} & H_{01} k_{00} p + H_{11} k_{01} p + H_{21} k_{02} p + H_{31} k_{03} p & 0 & 0 & -H_{12} k_{01} p - H_{32} k_{03} p - H_{02} k_{00} - H_{22} k_{02} & -H_{03} k_{00} - H_{13} k_{01} - H_{23} k_{02} - H_{33} k_{03} & 0 & 0 \\ H_{00} k_{10} + H_{10} k_{11} + H_{20} k_{12} + H_{30} k_{13} & H_{01} k_{10} p + H_{21} k_{12} p + H_{11} k_{11} + H_{31} k_{13} & 0 & 0 & -H_{02} k_{10} - H_{12} k_{11} - H_{22} k_{12} - H_{32} k_{13} & -\frac{H_{03} k_{10} p + H_{23} k_{12} p + H_{13} k_{11} + H_{33} k_{13}}{p} & 0 & 0 \\ 0 & 0 & k_{00} & k_{01} p & 0 & {\left(k_{00} k_{13} k_{31} - k_{00} k_{11} k_{33} - {\left(k_{03} k_{10} k_{31} - k_{01} k_{10} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{30}\right)} p + k_{00}\right)} H_{03} - {\left(k_{02} k_{11} k_{30} - k_{00} k_{11} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{31} - {\left(k_{01} k_{12} k_{30} - k_{01} k_{10} k_{32}\right)} p - k_{01}\right)} H_{13} + {\left(k_{02} k_{13} k_{31} - k_{02} k_{11} k_{33} - {\left(k_{03} k_{12} k_{31} - k_{01} k_{12} k_{33} - {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{32}\right)} p + k_{02}\right)} H_{23} - {\left(k_{02} k_{13} k_{30} - k_{00} k_{13} k_{32} - {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{33} - {\left(k_{03} k_{12} k_{30} - k_{03} k_{10} k_{32}\right)} p - k_{03}\right)} H_{33} & k_{02} & k_{03} \\ 0 & 0 & k_{10} & k_{11} & 0 & \frac{{\left({\left(k_{03} k_{10} k_{21} - k_{01} k_{10} k_{23}\right)} p^{2} - {\left(k_{00} k_{13} k_{21} - k_{00} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{20} - k_{10}\right)} p\right)} H_{03} + {\left(k_{02} k_{11} k_{20} - k_{00} k_{11} k_{22} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p + k_{11}\right)} H_{13} + {\left({\left(k_{03} k_{12} k_{21} - k_{01} k_{12} k_{23}\right)} p^{2} - {\left(k_{02} k_{13} k_{21} - k_{02} k_{11} k_{23} + {\left(k_{03} k_{11} - k_{01} k_{13}\right)} k_{22} - k_{12}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{22} - {\left(k_{03} k_{12} k_{20} - k_{03} k_{10} k_{22} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{23}\right)} p + k_{13}\right)} H_{33}}{p} & k_{12} & \frac{k_{13}}{p} \\ -H_{10} k_{21} p - H_{30} k_{23} p - H_{00} k_{20} - H_{20} k_{22} & -H_{01} k_{20} p - H_{11} k_{21} p - H_{21} k_{22} p - H_{31} k_{23} p & 0 & 0 & H_{12} k_{21} p + H_{32} k_{23} p + H_{02} k_{20} + H_{22} k_{22} & H_{03} k_{20} + H_{13} k_{21} + H_{23} k_{22} + H_{33} k_{23} & 0 & 0 \\ -H_{00} k_{30} p - H_{10} k_{31} p - H_{20} k_{32} p - H_{30} k_{33} p & -H_{01} k_{30} p^{2} - H_{21} k_{32} p^{2} - H_{11} k_{31} p - H_{31} k_{33} p & 0 & 0 & H_{02} k_{30} p + H_{12} k_{31} p + H_{22} k_{32} p + H_{32} k_{33} p & H_{03} k_{30} p + H_{23} k_{32} p + H_{13} k_{31} + H_{33} k_{33} & 0 & 0 \\ 0 & 0 & k_{20} & k_{21} p & 0 & {\left(k_{13} k_{20} k_{31} - k_{11} k_{20} k_{33} - {\left(k_{10} k_{23} k_{31} - k_{10} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{30}\right)} p + k_{20}\right)} H_{03} - {\left(k_{11} k_{22} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{31} - {\left(k_{12} k_{21} k_{30} - k_{10} k_{21} k_{32}\right)} p - k_{21}\right)} H_{13} + {\left(k_{13} k_{22} k_{31} - k_{11} k_{22} k_{33} - {\left(k_{12} k_{23} k_{31} - k_{12} k_{21} k_{33} + {\left(k_{13} k_{21} - k_{11} k_{23}\right)} k_{32}\right)} p + k_{22}\right)} H_{23} - {\left(k_{13} k_{22} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{22}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p - k_{23}\right)} H_{33} & k_{22} & k_{23} \\ 0 & 0 & k_{30} p & k_{31} p & 0 & {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{30} p^{2} - {\left({\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{31} - {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{33} - k_{30}\right)} p\right)} H_{03} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{30} + {\left(k_{01} k_{20} - k_{00} k_{21}\right)} k_{32}\right)} p\right)} H_{13} + {\left({\left(k_{03} k_{21} - k_{01} k_{23}\right)} k_{32} p^{2} - {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{31} + {\left(k_{02} k_{21} - k_{01} k_{22}\right)} k_{33} - k_{32}\right)} p\right)} H_{23} + {\left({\left(k_{02} k_{20} - k_{00} k_{22} + 1\right)} k_{33} + {\left({\left(k_{03} k_{22} - k_{02} k_{23}\right)} k_{30} - {\left(k_{03} k_{20} - k_{00} k_{23}\right)} k_{32}\right)} p\right)} H_{33} & k_{32} p & k_{33} \end{array}\right)$

Z[2,5]=0;Z[3,5]=0;Z[6,5]=0;Z[7,5]=0;Z.simplify_full()

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} H_{10} k_{01} p + H_{30} k_{03} p + H_{00} k_{00} + H_{20} k_{02} & H_{01} k_{00} p + H_{11} k_{01} p + H_{21} k_{02} p + H_{31} k_{03} p & 0 & 0 & -H_{12} k_{01} p - H_{32} k_{03} p - H_{02} k_{00} - H_{22} k_{02} & -H_{03} k_{00} - H_{13} k_{01} - H_{23} k_{02} - H_{33} k_{03} & 0 & 0 \\ H_{00} k_{10} + H_{10} k_{11} + H_{20} k_{12} + H_{30} k_{13} & H_{01} k_{10} p + H_{21} k_{12} p + H_{11} k_{11} + H_{31} k_{13} & 0 & 0 & -H_{02} k_{10} - H_{12} k_{11} - H_{22} k_{12} - H_{32} k_{13} & -\frac{H_{03} k_{10} p + H_{23} k_{12} p + H_{13} k_{11} + H_{33} k_{13}}{p} & 0 & 0 \\ 0 & 0 & k_{00} & k_{01} p & 0 & 0 & k_{02} & k_{03} \\ 0 & 0 & k_{10} & k_{11} & 0 & 0 & k_{12} & \frac{k_{13}}{p} \\ -H_{10} k_{21} p - H_{30} k_{23} p - H_{00} k_{20} - H_{20} k_{22} & -H_{01} k_{20} p - H_{11} k_{21} p - H_{21} k_{22} p - H_{31} k_{23} p & 0 & 0 & H_{12} k_{21} p + H_{32} k_{23} p + H_{02} k_{20} + H_{22} k_{22} & H_{03} k_{20} + H_{13} k_{21} + H_{23} k_{22} + H_{33} k_{23} & 0 & 0 \\ -H_{00} k_{30} p - H_{10} k_{31} p - H_{20} k_{32} p - H_{30} k_{33} p & -H_{01} k_{30} p^{2} - H_{21} k_{32} p^{2} - H_{11} k_{31} p - H_{31} k_{33} p & 0 & 0 & H_{02} k_{30} p + H_{12} k_{31} p + H_{22} k_{32} p + H_{32} k_{33} p & H_{03} k_{30} p + H_{23} k_{32} p + H_{13} k_{31} + H_{33} k_{33} & 0 & 0 \\ 0 & 0 & k_{20} & k_{21} p & 0 & 0 & k_{22} & k_{23} \\ 0 & 0 & k_{30} p & k_{31} p & 0 & 0 & k_{32} p & k_{33} \end{array}\right)$

Recalling this matrix is equal to our $HK$ matrix above, this gives 16 equations in the 16 unknowns $H_{00}, \dots, H_{33}$. In terms of how we defined the $H_{ij}$ earlier, we just need to show they are integers to have the result.

We can actually set this up as four separate matrix equations. The first one we want to solve is $\begin{pmatrix} k_{00} & p k_{01} & k_{02} & p k_{03} \\ k_{10}& k_{11} & k_{12} & k_{13} \\ k_{20} & p k_{21} & k_{22} & p k_{23} \\k_{30} & k _{31} & k_{32} & k_{33} \end{pmatrix}\begin{pmatrix} H_{00} \\ H_{10} \\ H_{20} \\ H_{30} \end{pmatrix} = \begin{pmatrix} h_{00} \\h_{10} \\h_{20} \\ h_{30} \end{pmatrix}$. Note the $h_{ij}$ and $k_{ij}$ are integral by how they were defined, so if we can show that the matrix with the $k_{ij}$ has determinant $\pm 1$, we have the result for $H_{00}, H_{10},H_{20}, H_{30}$.

A=matrix([[k00,p*k01,k02,p*k03],[k10,k11,k12,k13],[k20,p*k21,k22,p*k23],[k30,k31,k32,k33]]);A

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} k_{00} & k_{01} p & k_{02} & k_{03} p \\ k_{10} & k_{11} & k_{12} & k_{13} \\ k_{20} & k_{21} p & k_{22} & k_{23} p \\ k_{30} & k_{31} & k_{32} & k_{33} \end{array}\right)$

K=block_matrix(2,2,[k1,k2,k3,4]);K

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr|rr} k_{00} & k_{01} p & k_{02} & k_{03} \\ k_{10} & k_{11} & k_{12} & \frac{k_{13}}{p} \\ \hline k_{20} & k_{21} p & k_{22} & k_{23} \\ k_{30} p & k_{31} p & k_{32} p & k_{33} \end{array}\right)$

(K.determinant()- A.determinant()).simplify_full()

 $\newcommand{\Bold}[1]{\mathbf{#1}}0$

As the matrix $K \in \Gamma_{2}[\varpi]$, we know $\det(K) = \pm 1$. This gives the desired result for $H_{00}, H_{10}, H_{20} H_{30}$. Now we must check the rest by the same method.

A=matrix([[k00,k01,k02,k03],[p*k10,k11,p*k12,k13],[k20,k21,k22,k23],[p*k30,k31,p*k32,k33]]);A

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} k_{00} & k_{01} & k_{02} & k_{03} \\ k_{10} p & k_{11} & k_{12} p & k_{13} \\ k_{20} & k_{21} & k_{22} & k_{23} \\ k_{30} p & k_{31} & k_{32} p & k_{33} \end{array}\right)$

(K.determinant()- A.determinant()).simplify_full()

 $\newcommand{\Bold}[1]{\mathbf{#1}}0$

This gives that $H_{01}, H_{11}, H_{21},$ and $H_{31}$ are integral as desired.

One obtains the same matrix of coefficients for $H_{02}, H_{12}, H_{22}, H_{32}$ as $H_{00}, H_{10}, H_{20}, H_{30}$ so this case is already done. The matrix of coefficients for $H_{03}, H_{13}, H_{23}, H_{33}$ is the same as that of $H_{01}, H_{11}, H_{21}, H_{31}$ so this case is done as well. Combining all of this, we get the version of Lemma 5.1 for our paramodular section.

Paramodular_Lemma_5.1

1931 days ago by jimlb