Paramodular_calculations -- Sage

Lemma 5.1

I'm going to start by proving Lemma 5.1 with just a direct calculation. I did this once before kind of brute force, so now I want to use some of the new commands and methods I'll try to use to show our paramodular version. I want to try to work them out in a case I know they work first.

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

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

Q2.inverse()

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

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

Here we create a matrix $D$ automatically rather than typing all the variables out. Not sure how I didn't bother to figure this out earlier. We start with $D$ because it is the easier matrix to find in the calculations because of the $(h,1)$.

a = var(s); D = matrix(SR,N,N,a); D

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

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)$

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

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

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 can now create our general element in $P_8(F)$.

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,h01], [h10,h11]]);H2=matrix([[h02,h03],[h12,h13]]);H3=matrix([[h20,h21],[h30,h31]]);H4=matrix([[h22,h23],[h32,h33]]);H1;H2;H3;H4

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

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

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

We now have constructed all the matrices we need. We want to show that if $Q_2^{-1} p Q_2 (h,1)$ is in $\Gamma_4(\varpi)$, then $h \in \Gamma_2(\varpi)$. We look at $Q_2^{-1} p Q_2 (h,1)$ and assume this is congruent to $1_{8}$ modulo $\varpi$. We could just subtract it from $1_8$ and then say this is $0_8$ modulo $\varpi$, but I'm not sure how easily that will generalize to our case so I don't do it here. One warning is the matrix entries have SAGE labels that start at 0, so the upper left entry is the $(0,0)$ entry and not the $(1,1)$ entry so one has to be careful when picking out the entries.

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

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

Working modulo $\varpi$ now, we have anything off the diagonal of $Z$ must be 0 modulo $\varpi$. For instance, we see below that the $(1,4)$ entry of $Z$ is $-x_{03}$, so $x_{03} = 0$.

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

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

Z=Z.substitute(x12==0).substitute(x13==0).substitute(x22==0).substitute(x23==0).substitute(x32==0).substitute(x33==0).substitute(x02==0).substitute(x03==0);Z

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

Modulo $\varpi$, the diagonal entries need to be 1 and the off-diagonal need to be 0.

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

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

Z=Z.substitute(d22==1).substitute(d33==1).substitute(d23==0).substitute(d32==0).substitute(d02==0).substitute(d03==0).substitute(d12==0).substitute(d13==0);Z

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

Z=Z.substitute(x21==0).substitute(x30==0).substitute(d01==0).substitute(d10==0);Z

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

One now must solve the equations in each row to simplify things further. For instance, we set $z_{7,8} = 0$ and solve for $x_{2,1}$ and substitute this back into $Z$.

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());Z

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

Z=Z.substitute(d21==0).substitute(d11==(Z[5,7]==0).solve(d11)[0].right()).substitute(d31==0);Z

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

Z=(Z.substitute(d11==(Z[7,7]==1).solve(d11)[0].right())).simplify_full();Z

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

Z=(Z.substitute(d31==(Z[1,7]==0).solve(d31)[0].right()).substitute(x20==0).substitute(x10==0).substitute(d30==0)).simplify_full();Z

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

Z=(Z.substitute(d00==1).substitute(x00==(Z[0,6]==0).solve(x00)[0].right())).simplify_full();Z

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

Z=Z.substitute(d20==0);Z

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

Observe we have shown that if $Q_2^{-1} p Q_2 (h,1) \in \Gamma_4(\varpi)$, then modulo $\varpi$ we have $Q_2^{-1} p Q_2 (h,1) = (h,1)$. Thus, reading the this last matrix modulo $\varpi$ gives that $h \in \Gamma_2(\varpi)$ as claimed in Lemma 5.1.

Paramodular Level

Below I will try to follow the same process for the section for the paramodular level. We want to show that if $h \in \textrm{Sp}_4(F)$ satisfies $Q_2 (h,1) = PQ_2 (h_1,k_1)$ with $P \in \textrm{Sp}_(F)$ and $h_1, k_1 \in \Gamma_2[\varpi]$, then necessarily $h \in \Gamma_2[\varpi]$. In other words, we want to use that $(h_1, k_1) = Q_2^{-1} P^{-1} Q_2 (h,1)$ to show $h \in \Gamma_2[\varpi]$. Since $P^{-1}$ is also in the parabolic subgroup, we just rewrite it as $P$.

 $\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)$

It seems one needs to build the paramodular matrices somewhat by hand to take into account the location of the $p$ and $p^{-1}$ terms. We can build the $P$ matrices as before though.

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

var(s);

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

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]]);H1;H2;H3;H4

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

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

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

HI1=matrix([[H00,p*H01], [H10,H11]]);HI2=matrix([[H02,H03],[H12,H13/p]]);HI3=matrix([[H20,p*H21],[p*H30,p*H31]]);HI4=matrix([[H22,H23],[p*H32,H33]]);

HI=block_matrix(4,4,[HI1,O2,-HI2,O2,O2,I2,O2,O2,-HI3,O2,HI4,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 working on 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)$

Next is the 7th column.

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==k23).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_{23} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{23} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{10} + {\left(k_{02} k_{13} k_{21} - {\left({\left(k_{02} - k_{03}\right)} k_{11} + k_{01} k_{13}\right)} k_{23} - {\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_{23} - {\left(k_{03} k_{12} k_{20} + {\left({\left(k_{02} - k_{03}\right)} 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_{23} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{23} + {\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} - {\left({\left(k_{02} - k_{03}\right)} k_{11} + k_{01} k_{13}\right)} k_{23}\right)} p\right)} H_{21} - {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{23} - {\left(k_{03} k_{12} k_{20} + {\left({\left(k_{02} - k_{03}\right)} 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_{23} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{23} + {\left(k_{02} k_{10} - k_{00} k_{12}\right)} k_{21}\right)} p\right)} H_{12} - {\left(k_{02} k_{13} k_{21} - {\left({\left(k_{02} - k_{03}\right)} k_{11} + k_{01} k_{13}\right)} k_{23} - {\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_{23} - {\left(k_{03} k_{12} k_{20} + {\left({\left(k_{02} - k_{03}\right)} 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_{23} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{23} + {\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} - {\left({\left(k_{02} - k_{03}\right)} k_{11} + k_{01} k_{13}\right)} k_{23}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{23} - {\left(k_{03} k_{12} k_{20} + {\left({\left(k_{02} - k_{03}\right)} 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_{23} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{23} + {\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} - {\left({\left(k_{02} - k_{03}\right)} k_{11} + k_{01} k_{13}\right)} k_{23} - {\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_{23} - {\left(k_{03} k_{12} k_{20} + {\left({\left(k_{02} - k_{03}\right)} 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_{23} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{23} + {\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} - {\left({\left(k_{02} - k_{03}\right)} k_{11} + k_{01} k_{13}\right)} k_{23} - k_{12}\right)} p\right)} H_{21} - {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{23} - {\left(k_{03} k_{12} k_{20} + {\left({\left(k_{02} - k_{03}\right)} 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_{23} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{23} + {\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} - {\left({\left(k_{02} - k_{03}\right)} k_{11} + k_{01} k_{13}\right)} k_{23} - {\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_{23} - {\left(k_{03} k_{12} k_{20} + {\left({\left(k_{02} - k_{03}\right)} 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_{23} - {\left(k_{01} k_{12} k_{20} - k_{01} k_{10} k_{23} + {\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} - {\left({\left(k_{02} - k_{03}\right)} k_{11} + k_{01} k_{13}\right)} k_{23} - k_{12}\right)} p\right)} H_{23} + {\left(k_{02} k_{13} k_{20} - k_{00} k_{13} k_{23} - {\left(k_{03} k_{12} k_{20} + {\left({\left(k_{02} - k_{03}\right)} 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_{23} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{23}\right)} k_{31}\right)} p\right)} H_{10} + {\left(k_{13} k_{23} k_{31} - k_{11} k_{23} 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_{23} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{23}\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_{23} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{23}\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_{23} k_{31} - k_{11} k_{23} 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_{23} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{23}\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_{23} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{23}\right)} k_{31}\right)} p\right)} H_{12} - {\left(k_{13} k_{23} k_{31} - k_{11} k_{23} 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_{23} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{23}\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_{23} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{23}\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_{23} k_{31} - k_{11} k_{23} 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_{23} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{23}\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_{23}\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{23}\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_{02} - k_{03}\right)} k_{23} k_{31} - {\left(k_{02} k_{21} - k_{01} k_{23}\right)} k_{33}\right)} p\right)} H_{20} + {\left({\left(k_{02} k_{20} - k_{00} k_{23}\right)} k_{33} p - {\left({\left(k_{02} - k_{03}\right)} k_{23} 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_{23}\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{23}\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_{02} - k_{03}\right)} k_{23} k_{31} - {\left(k_{02} k_{21} - k_{01} k_{23}\right)} k_{33}\right)} p^{2}\right)} H_{21} + {\left({\left(k_{02} k_{20} - k_{00} k_{23}\right)} k_{33} p - {\left({\left(k_{02} - k_{03}\right)} k_{23} 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_{23}\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{23}\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_{02} - k_{03}\right)} k_{23} k_{31} - {\left(k_{02} k_{21} - k_{01} k_{23}\right)} k_{33}\right)} p\right)} H_{22} - {\left({\left(k_{02} k_{20} - k_{00} k_{23}\right)} k_{33} p - {\left({\left(k_{02} - k_{03}\right)} k_{23} 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_{23}\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{23}\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_{02} - k_{03}\right)} k_{23} k_{31} - {\left(k_{02} k_{21} - k_{01} k_{23}\right)} k_{33}\right)} p\right)} H_{23} - {\left({\left(k_{02} k_{20} - k_{00} k_{23}\right)} k_{33} - {\left({\left(k_{02} - k_{03}\right)} k_{23} 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_{23} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{23}\right)} k_{31} - k_{21}\right)} p\right)} H_{10} - {\left(k_{13} k_{23} k_{31} - k_{11} k_{23} 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_{23}\right)} H_{20} - {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{23} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{23}\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_{23} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{23}\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_{23} k_{31} - k_{11} k_{23} k_{33} + k_{23}\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_{23} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{23}\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_{23} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{23}\right)} k_{31} - k_{21}\right)} p\right)} H_{12} + {\left(k_{13} k_{23} k_{31} - k_{11} k_{23} 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_{23}\right)} H_{22} + {\left({\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p^{2} - {\left(k_{13} k_{23} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{23}\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_{23} k_{30} - k_{11} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{23}\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_{23} k_{31} - k_{11} k_{23} 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_{23}\right)} H_{23} - {\left(k_{13} k_{23} k_{30} - k_{13} k_{20} k_{32} + {\left(k_{12} k_{20} - k_{10} k_{23}\right)} k_{33} - {\left(k_{12} k_{23} k_{30} - k_{10} k_{23} k_{32}\right)} p - k_{23}\right)} H_{33} & k_{23} & 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_{23} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{23}\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_{02} - k_{03}\right)} k_{23} k_{31} - {\left(k_{02} k_{21} - k_{01} k_{23}\right)} k_{33} + k_{32}\right)} p\right)} H_{20} - {\left({\left(k_{02} k_{20} - k_{00} k_{23} + 1\right)} k_{33} p - {\left({\left(k_{02} - k_{03}\right)} k_{23} 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_{23} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{23}\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_{02} - k_{03}\right)} k_{23} k_{31} - {\left(k_{02} k_{21} - k_{01} k_{23}\right)} k_{33} + k_{32}\right)} p^{2}\right)} H_{21} - {\left({\left(k_{02} k_{20} - k_{00} k_{23} + 1\right)} k_{33} p - {\left({\left(k_{02} - k_{03}\right)} k_{23} 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_{23} + 1\right)} k_{31} p - {\left({\left(k_{02} k_{21} - k_{01} k_{23}\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_{02} - k_{03}\right)} k_{23} k_{31} - {\left(k_{02} k_{21} - k_{01} k_{23}\right)} k_{33} + k_{32}\right)} p\right)} H_{22} + {\left({\left(k_{02} k_{20} - k_{00} k_{23} + 1\right)} k_{33} p - {\left({\left(k_{02} - k_{03}\right)} k_{23} 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_{23} + 1\right)} k_{31} - {\left({\left(k_{02} k_{21} - k_{01} k_{23}\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_{02} - k_{03}\right)} k_{23} k_{31} - {\left(k_{02} k_{21} - k_{01} k_{23}\right)} k_{33} + k_{32}\right)} p\right)} H_{23} + {\left({\left(k_{02} k_{20} - k_{00} k_{23} + 1\right)} k_{33} - {\left({\left(k_{02} - k_{03}\right)} k_{23} 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)$

Pushing ahead with column 5.. Yikes!

Z[0,5].simplify_full();

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

Z=(Z.substitute(k03==(Z[2,5]==0).solve(k03)[0].right())).simplify_full();Z

WARNING: Output truncated!  
full_output.txt



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

WARNING: Output truncated!  
full_output.txt

full_output.txt

This is still a bit of a disaster. We may need to use that $K$ is a symplectic matrix to simplify all of these $k$ terms out.

K=block_matrix(2,2,[K1,K2,K3,K4]);K; J2=block_matrix(2,2,[O2, I2, -I2, O2]);J2

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

U=K.transpose()*J2*K

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

W=(W.substitute(k00==(U[1,0]==0).solve(k00)[0].right())).simplify_full();W

WARNING: Output truncated!  
full_output.txt



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

WARNING: Output truncated!  
full_output.txt

full_output.txt

Section is well-defined

The following matrix is $(h_3,k_3)$ for $h_3, k_3 \in \Gamma_4[p]$.

H=matrix([[h11,p*h12, 0,0,-h13,-h14,0,0],[h21,h22,0,0,-h23, -h24/p,0,0],[0,0,k11,p*k12,0,0,k13,k14],[0,0,k21,k22,0,0,k23,k24/p],[-h31,-p*h32,0,0,h33,h34,0,0],[-p*h41,-p*h42, 0,0,p*h43,h44,0,0],[0,0,k31, p*k32,0,0,k33,k34],[0,0,p*k41,p*k42,0,0,p*k43,k44]]);latex(H)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} h_{11} & h_{12} p & 0 & 0 & -h_{13} & -h_{14} & 0 & 0 \\ h_{21} & h_{22} & 0 & 0 & -h_{23} & -\frac{h_{24}}{p} & 0 & 0 \\ 0 & 0 & k_{11} & k_{12} p & 0 & 0 & k_{13} & k_{14} \\ 0 & 0 & k_{21} & k_{22} & 0 & 0 & k_{23} & \frac{k_{24}}{p} \\ -h_{31} & -h_{32} p & 0 & 0 & h_{33} & h_{34} & 0 & 0 \\ -h_{41} p & -h_{42} p & 0 & 0 & h_{43} p & h_{44} & 0 & 0 \\ 0 & 0 & k_{31} & k_{32} p & 0 & 0 & k_{33} & k_{34} \\ 0 & 0 & k_{41} p & k_{42} p & 0 & 0 & k_{43} p & k_{44} \end{array}\right)$

The following matrix is $p_1^{-1} p_2$ for the well-defined calculation, so it must be that this lies in the Siegel parabolic subgroup.

Q2*H*(Q2.inverse());latex(Q2*H*Q2.inverse())

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} h_{11} & h_{12} p & h_{13} & h_{14} & -h_{13} & -h_{14} & 0 & 0 \\ h_{21} & h_{22} & h_{23} & \frac{h_{24}}{p} & -h_{23} & -\frac{h_{24}}{p} & 0 & 0 \\ k_{31} & k_{32} p & k_{33} & k_{34} & 0 & 0 & -k_{31} & -k_{32} p \\ k_{41} p & k_{42} p & k_{43} p & k_{44} & 0 & 0 & -k_{41} p & -k_{42} p \\ -h_{31} + k_{31} & -h_{32} p + k_{32} p & -h_{33} + k_{33} & -h_{34} + k_{34} & h_{33} & h_{34} & -k_{31} & -k_{32} p \\ -h_{41} p + k_{41} p & -h_{42} p + k_{42} p & -h_{43} p + k_{43} p & -h_{44} + k_{44} & h_{43} p & h_{44} & -k_{41} p & -k_{42} p \\ h_{11} - k_{11} & h_{12} p - k_{12} p & h_{13} - k_{13} & h_{14} - k_{14} & -h_{13} & -h_{14} & k_{11} & k_{12} p \\ h_{21} - k_{21} & h_{22} - k_{22} & h_{23} - k_{23} & \frac{h_{24}}{p} - \frac{k_{24}}{p} & -h_{23} & -\frac{h_{24}}{p} & k_{21} & k_{22} \end{array}\right)$ 
 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} h_{11} & h_{12} p & h_{13} & h_{14} & -h_{13} & -h_{14} & 0 & 0 \\ h_{21} & h_{22} & h_{23} & \frac{h_{24}}{p} & -h_{23} & -\frac{h_{24}}{p} & 0 & 0 \\ k_{31} & k_{32} p & k_{33} & k_{34} & 0 & 0 & -k_{31} & -k_{32} p \\ k_{41} p & k_{42} p & k_{43} p & k_{44} & 0 & 0 & -k_{41} p & -k_{42} p \\ -h_{31} + k_{31} & -h_{32} p + k_{32} p & -h_{33} + k_{33} & -h_{34} + k_{34} & h_{33} & h_{34} & -k_{31} & -k_{32} p \\ -h_{41} p + k_{41} p & -h_{42} p + k_{42} p & -h_{43} p + k_{43} p & -h_{44} + k_{44} & h_{43} p & h_{44} & -k_{41} p & -k_{42} p \\ h_{11} - k_{11} & h_{12} p - k_{12} p & h_{13} - k_{13} & h_{14} - k_{14} & -h_{13} & -h_{14} & k_{11} & k_{12} p \\ h_{21} - k_{21} & h_{22} - k_{22} & h_{23} - k_{23} & \frac{h_{24}}{p} - \frac{k_{24}}{p} & -h_{23} & -\frac{h_{24}}{p} & k_{21} & k_{22} \end{array}\right)$

This seems to indicate that we must have $h_3 = k_3$ in order to have an equality of the form $p_1 Q_2 (h_1, k_1) = p_2 Q_2 (h_2, k_2)$ with $p_{i}$ in the Siegel parabolic and $h_{i}, k_{i} \in \Gamma_2[p]$ and we have set $(h_3, k_3) = (h_1, k_1)(h_2^{-1},k_2^{-1})$. We use this to adjust the embedded matrices:

K=matrix([[h11,p*h12, 0,0,-h13,-h14,0,0],[h21,h22,0,0,-h23, -h24/p,0,0],[0,0,h11,p*h12,0,0,h13,h14],[0,0,h21,h22,0,0,h23,h24/p],[-h31,-p*h32,0,0,h33,h34,0,0],[-p*h41,-p*h42, 0,0,p*h43,h44,0,0],[0,0,h31, p*h32,0,0,h33,h34],[0,0,p*h41,p*h42,0,0,p*h43,h44]]);latex(K)

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} h_{11} & h_{12} p & 0 & 0 & -h_{13} & -h_{14} & 0 & 0 \\ h_{21} & h_{22} & 0 & 0 & -h_{23} & -\frac{h_{24}}{p} & 0 & 0 \\ 0 & 0 & h_{11} & h_{12} p & 0 & 0 & h_{13} & h_{14} \\ 0 & 0 & h_{21} & h_{22} & 0 & 0 & h_{23} & \frac{h_{24}}{p} \\ -h_{31} & -h_{32} p & 0 & 0 & h_{33} & h_{34} & 0 & 0 \\ -h_{41} p & -h_{42} p & 0 & 0 & h_{43} p & h_{44} & 0 & 0 \\ 0 & 0 & h_{31} & h_{32} p & 0 & 0 & h_{33} & h_{34} \\ 0 & 0 & h_{41} p & h_{42} p & 0 & 0 & h_{43} p & h_{44} \end{array}\right)$

Taking this into account we have the following form for $p_1^{-1} p_2$:

latex(Q2*K*(Q2.inverse()))

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} h_{11} & h_{12} p & h_{13} & h_{14} & -h_{13} & -h_{14} & 0 & 0 \\ h_{21} & h_{22} & h_{23} & \frac{h_{24}}{p} & -h_{23} & -\frac{h_{24}}{p} & 0 & 0 \\ h_{31} & h_{32} p & h_{33} & h_{34} & 0 & 0 & -h_{31} & -h_{32} p \\ h_{41} p & h_{42} p & h_{43} p & h_{44} & 0 & 0 & -h_{41} p & -h_{42} p \\ 0 & 0 & 0 & 0 & h_{33} & h_{34} & -h_{31} & -h_{32} p \\ 0 & 0 & 0 & 0 & h_{43} p & h_{44} & -h_{41} p & -h_{42} p \\ 0 & 0 & 0 & 0 & -h_{13} & -h_{14} & h_{11} & h_{12} p \\ 0 & 0 & 0 & 0 & -h_{23} & -\frac{h_{24}}{p} & h_{21} & h_{22} \end{array}\right)$

This gives our matrix $A$ as:

A = matrix([[h11, p*h12, h13, h14], [h21,h22, h23, h24/p],[h31,p*h32,h33,h34],[p*h41, p*h42,p*h43, h44]]);A

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrr} h_{11} & h_{12} p & h_{13} & h_{14} \\ h_{21} & h_{22} & h_{23} & \frac{h_{24}}{p} \\ h_{31} & h_{32} p & h_{33} & h_{34} \\ h_{41} p & h_{42} p & h_{43} p & h_{44} \end{array}\right)$

Note this $A$ is equal to the matrix $h_3$. That means that $A \in \textrm{Sp}_{2n}(F)$, and so it must have determinant $\pm 1$. That should be enough to give the same result as in the paper about it being well-defined. Can ignore the stuff below.

Since all of the $h_{ij}$ are integral, we see the determinant of $A$ is still integral but I am not sure how to see it is a unit.. hmmm..

We now want to show if $Q_2 (h,1)$ is in $P_4(F) Q_2 (\Gamma_4[\varpi] \times \Gamma_4[\varpi])$, then $h \in \Gamma_4[\varpi]$.

A = Q2.inverse()*P*Q2*H;A

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rrrrrrrr} -b_{12} h_{41} p + {\left(a_{11} + b_{13}\right)} h_{11} + {\left(a_{12} + b_{14}\right)} h_{21} - b_{11} h_{31} & {\left(a_{11} + b_{13}\right)} h_{12} p - b_{11} h_{32} p - b_{12} h_{42} p + {\left(a_{12} + b_{14}\right)} h_{22} & {\left(a_{14} + b_{12}\right)} k_{41} p - b_{13} k_{11} - b_{14} k_{21} + {\left(a_{13} + b_{11}\right)} k_{31} & -b_{13} k_{12} p + {\left(a_{13} + b_{11}\right)} k_{32} p + {\left(a_{14} + b_{12}\right)} k_{42} p - b_{14} k_{22} & b_{12} h_{43} p - {\left(a_{11} + b_{13}\right)} h_{13} - {\left(a_{12} + b_{14}\right)} h_{23} + b_{11} h_{33} & -{\left(a_{11} + b_{13}\right)} h_{14} + b_{11} h_{34} + b_{12} h_{44} - \frac{{\left(a_{12} + b_{14}\right)} h_{24}}{p} & {\left(a_{14} + b_{12}\right)} k_{43} p - b_{13} k_{13} - b_{14} k_{23} + {\left(a_{13} + b_{11}\right)} k_{33} & -b_{13} k_{14} + {\left(a_{13} + b_{11}\right)} k_{34} + {\left(a_{14} + b_{12}\right)} k_{44} - \frac{b_{14} k_{24}}{p} \\ -b_{22} h_{41} p + {\left(a_{21} + b_{23}\right)} h_{11} + {\left(a_{22} + b_{24}\right)} h_{21} - b_{21} h_{31} & {\left(a_{21} + b_{23}\right)} h_{12} p - b_{21} h_{32} p - b_{22} h_{42} p + {\left(a_{22} + b_{24}\right)} h_{22} & {\left(a_{23} + b_{22}\right)} k_{41} p - b_{23} k_{11} - b_{24} k_{21} + {\left(a_{23} + b_{21}\right)} k_{31} & -b_{23} k_{12} p + {\left(a_{23} + b_{21}\right)} k_{32} p + {\left(a_{23} + b_{22}\right)} k_{42} p - b_{24} k_{22} & b_{22} h_{43} p - {\left(a_{21} + b_{23}\right)} h_{13} - {\left(a_{22} + b_{24}\right)} h_{23} + b_{21} h_{33} & -{\left(a_{21} + b_{23}\right)} h_{14} + b_{21} h_{34} + b_{22} h_{44} - \frac{{\left(a_{22} + b_{24}\right)} h_{24}}{p} & {\left(a_{23} + b_{22}\right)} k_{43} p - b_{23} k_{13} - b_{24} k_{23} + {\left(a_{23} + b_{21}\right)} k_{33} & -b_{23} k_{14} + {\left(a_{23} + b_{21}\right)} k_{34} + {\left(a_{23} + b_{22}\right)} k_{44} - \frac{b_{24} k_{24}}{p} \\ -{\left(b_{12} - d_{32}\right)} h_{41} p + {\left(a_{11} + b_{13} - d_{33}\right)} h_{11} + {\left(a_{12} + b_{14} - d_{34}\right)} h_{21} - {\left(b_{11} - d_{31}\right)} h_{31} & {\left(a_{11} + b_{13} - d_{33}\right)} h_{12} p - {\left(b_{11} - d_{31}\right)} h_{32} p - {\left(b_{12} - d_{32}\right)} h_{42} p + {\left(a_{12} + b_{14} - d_{34}\right)} h_{22} & {\left(a_{14} + b_{12} - d_{32}\right)} k_{41} p - {\left(b_{13} - d_{33}\right)} k_{11} - {\left(b_{14} - d_{34}\right)} k_{21} + {\left(a_{13} + b_{11} - d_{31}\right)} k_{31} & -{\left(b_{13} - d_{33}\right)} k_{12} p + {\left(a_{13} + b_{11} - d_{31}\right)} k_{32} p + {\left(a_{14} + b_{12} - d_{32}\right)} k_{42} p - {\left(b_{14} - d_{34}\right)} k_{22} & {\left(b_{12} - d_{32}\right)} h_{43} p - {\left(a_{11} + b_{13} - d_{33}\right)} h_{13} - {\left(a_{12} + b_{14} - d_{34}\right)} h_{23} + {\left(b_{11} - d_{31}\right)} h_{33} & -{\left(a_{11} + b_{13} - d_{33}\right)} h_{14} + {\left(b_{11} - d_{31}\right)} h_{34} + {\left(b_{12} - d_{32}\right)} h_{44} - \frac{{\left(a_{12} + b_{14} - d_{34}\right)} h_{24}}{p} & {\left(a_{14} + b_{12} - d_{32}\right)} k_{43} p - {\left(b_{13} - d_{33}\right)} k_{13} - {\left(b_{14} - d_{34}\right)} k_{23} + {\left(a_{13} + b_{11} - d_{31}\right)} k_{33} & -{\left(b_{13} - d_{33}\right)} k_{14} + {\left(a_{13} + b_{11} - d_{31}\right)} k_{34} + {\left(a_{14} + b_{12} - d_{32}\right)} k_{44} - \frac{{\left(b_{14} - d_{34}\right)} k_{24}}{p} \\ -{\left(b_{22} - d_{42}\right)} h_{41} p + {\left(a_{21} + b_{23} - d_{43}\right)} h_{11} + {\left(a_{22} + b_{24} - d_{44}\right)} h_{21} - {\left(b_{21} - d_{41}\right)} h_{31} & {\left(a_{21} + b_{23} - d_{43}\right)} h_{12} p - {\left(b_{21} - d_{41}\right)} h_{32} p - {\left(b_{22} - d_{42}\right)} h_{42} p + {\left(a_{22} + b_{24} - d_{44}\right)} h_{22} & {\left(a_{23} + b_{22} - d_{42}\right)} k_{41} p - {\left(b_{23} - d_{43}\right)} k_{11} - {\left(b_{24} - d_{44}\right)} k_{21} + {\left(a_{23} + b_{21} - d_{41}\right)} k_{31} & -{\left(b_{23} - d_{43}\right)} k_{12} p + {\left(a_{23} + b_{21} - d_{41}\right)} k_{32} p + {\left(a_{23} + b_{22} - d_{42}\right)} k_{42} p - {\left(b_{24} - d_{44}\right)} k_{22} & {\left(b_{22} - d_{42}\right)} h_{43} p - {\left(a_{21} + b_{23} - d_{43}\right)} h_{13} - {\left(a_{22} + b_{24} - d_{44}\right)} h_{23} + {\left(b_{21} - d_{41}\right)} h_{33} & -{\left(a_{21} + b_{23} - d_{43}\right)} h_{14} + {\left(b_{21} - d_{41}\right)} h_{34} + {\left(b_{22} - d_{42}\right)} h_{44} - \frac{{\left(a_{22} + b_{24} - d_{44}\right)} h_{24}}{p} & {\left(a_{23} + b_{22} - d_{42}\right)} k_{43} p - {\left(b_{23} - d_{43}\right)} k_{13} - {\left(b_{24} - d_{44}\right)} k_{23} + {\left(a_{23} + b_{21} - d_{41}\right)} k_{33} & -{\left(b_{23} - d_{43}\right)} k_{14} + {\left(a_{23} + b_{21} - d_{41}\right)} k_{34} + {\left(a_{23} + b_{22} - d_{42}\right)} k_{44} - \frac{{\left(b_{24} - d_{44}\right)} k_{24}}{p} \\ {\left(b_{32} - d_{12}\right)} h_{41} p - {\left(a_{31} + b_{33} - d_{13}\right)} h_{11} - {\left(a_{32} + b_{34} - d_{14}\right)} h_{21} + {\left(b_{31} - d_{11}\right)} h_{31} & -{\left(a_{31} + b_{33} - d_{13}\right)} h_{12} p + {\left(b_{31} - d_{11}\right)} h_{32} p + {\left(b_{32} - d_{12}\right)} h_{42} p - {\left(a_{32} + b_{34} - d_{14}\right)} h_{22} & -{\left(a_{34} + b_{32} - d_{12}\right)} k_{41} p + {\left(b_{33} - d_{13}\right)} k_{11} + {\left(b_{34} - d_{14}\right)} k_{21} - {\left(a_{33} + b_{31} - d_{11}\right)} k_{31} & {\left(b_{33} - d_{13}\right)} k_{12} p - {\left(a_{33} + b_{31} - d_{11}\right)} k_{32} p - {\left(a_{34} + b_{32} - d_{12}\right)} k_{42} p + {\left(b_{34} - d_{14}\right)} k_{22} & -{\left(b_{32} - d_{12}\right)} h_{43} p + {\left(a_{31} + b_{33} - d_{13}\right)} h_{13} + {\left(a_{32} + b_{34} - d_{14}\right)} h_{23} - {\left(b_{31} - d_{11}\right)} h_{33} & {\left(a_{31} + b_{33} - d_{13}\right)} h_{14} - {\left(b_{31} - d_{11}\right)} h_{34} - {\left(b_{32} - d_{12}\right)} h_{44} + \frac{{\left(a_{32} + b_{34} - d_{14}\right)} h_{24}}{p} & -{\left(a_{34} + b_{32} - d_{12}\right)} k_{43} p + {\left(b_{33} - d_{13}\right)} k_{13} + {\left(b_{34} - d_{14}\right)} k_{23} - {\left(a_{33} + b_{31} - d_{11}\right)} k_{33} & {\left(b_{33} - d_{13}\right)} k_{14} - {\left(a_{33} + b_{31} - d_{11}\right)} k_{34} - {\left(a_{34} + b_{32} - d_{12}\right)} k_{44} + \frac{{\left(b_{34} - d_{14}\right)} k_{24}}{p} \\ {\left(b_{42} - d_{22}\right)} h_{41} p - {\left(a_{41} + b_{43} - d_{23}\right)} h_{11} - {\left(a_{42} + b_{44} - d_{24}\right)} h_{21} + {\left(b_{41} - d_{21}\right)} h_{31} & -{\left(a_{41} + b_{43} - d_{23}\right)} h_{12} p + {\left(b_{41} - d_{21}\right)} h_{32} p + {\left(b_{42} - d_{22}\right)} h_{42} p - {\left(a_{42} + b_{44} - d_{24}\right)} h_{22} & -{\left(a_{44} + b_{42} - d_{22}\right)} k_{41} p + {\left(b_{43} - d_{23}\right)} k_{11} + {\left(b_{44} - d_{24}\right)} k_{21} - {\left(a_{43} + b_{41} - d_{21}\right)} k_{31} & {\left(b_{43} - d_{23}\right)} k_{12} p - {\left(a_{43} + b_{41} - d_{21}\right)} k_{32} p - {\left(a_{44} + b_{42} - d_{22}\right)} k_{42} p + {\left(b_{44} - d_{24}\right)} k_{22} & -{\left(b_{42} - d_{22}\right)} h_{43} p + {\left(a_{41} + b_{43} - d_{23}\right)} h_{13} + {\left(a_{42} + b_{44} - d_{24}\right)} h_{23} - {\left(b_{41} - d_{21}\right)} h_{33} & {\left(a_{41} + b_{43} - d_{23}\right)} h_{14} - {\left(b_{41} - d_{21}\right)} h_{34} - {\left(b_{42} - d_{22}\right)} h_{44} + \frac{{\left(a_{42} + b_{44} - d_{24}\right)} h_{24}}{p} & -{\left(a_{44} + b_{42} - d_{22}\right)} k_{43} p + {\left(b_{43} - d_{23}\right)} k_{13} + {\left(b_{44} - d_{24}\right)} k_{23} - {\left(a_{43} + b_{41} - d_{21}\right)} k_{33} & {\left(b_{43} - d_{23}\right)} k_{14} - {\left(a_{43} + b_{41} - d_{21}\right)} k_{34} - {\left(a_{44} + b_{42} - d_{22}\right)} k_{44} + \frac{{\left(b_{44} - d_{24}\right)} k_{24}}{p} \\ -b_{32} h_{41} p + {\left(a_{31} + b_{33}\right)} h_{11} + {\left(a_{32} + b_{34}\right)} h_{21} - b_{31} h_{31} & {\left(a_{31} + b_{33}\right)} h_{12} p - b_{31} h_{32} p - b_{32} h_{42} p + {\left(a_{32} + b_{34}\right)} h_{22} & {\left(a_{34} + b_{32}\right)} k_{41} p - b_{33} k_{11} - b_{34} k_{21} + {\left(a_{33} + b_{31}\right)} k_{31} & -b_{33} k_{12} p + {\left(a_{33} + b_{31}\right)} k_{32} p + {\left(a_{34} + b_{32}\right)} k_{42} p - b_{34} k_{22} & b_{32} h_{43} p - {\left(a_{31} + b_{33}\right)} h_{13} - {\left(a_{32} + b_{34}\right)} h_{23} + b_{31} h_{33} & -{\left(a_{31} + b_{33}\right)} h_{14} + b_{31} h_{34} + b_{32} h_{44} - \frac{{\left(a_{32} + b_{34}\right)} h_{24}}{p} & {\left(a_{34} + b_{32}\right)} k_{43} p - b_{33} k_{13} - b_{34} k_{23} + {\left(a_{33} + b_{31}\right)} k_{33} & -b_{33} k_{14} + {\left(a_{33} + b_{31}\right)} k_{34} + {\left(a_{34} + b_{32}\right)} k_{44} - \frac{b_{34} k_{24}}{p} \\ -b_{42} h_{41} p + {\left(a_{41} + b_{43}\right)} h_{11} + {\left(a_{42} + b_{44}\right)} h_{21} - b_{41} h_{31} & {\left(a_{41} + b_{43}\right)} h_{12} p - b_{41} h_{32} p - b_{42} h_{42} p + {\left(a_{42} + b_{44}\right)} h_{22} & {\left(a_{44} + b_{42}\right)} k_{41} p - b_{43} k_{11} - b_{44} k_{21} + {\left(a_{43} + b_{41}\right)} k_{31} & -b_{43} k_{12} p + {\left(a_{43} + b_{41}\right)} k_{32} p + {\left(a_{44} + b_{42}\right)} k_{42} p - b_{44} k_{22} & b_{42} h_{43} p - {\left(a_{41} + b_{43}\right)} h_{13} - {\left(a_{42} + b_{44}\right)} h_{23} + b_{41} h_{33} & -{\left(a_{41} + b_{43}\right)} h_{14} + b_{41} h_{34} + b_{42} h_{44} - \frac{{\left(a_{42} + b_{44}\right)} h_{24}}{p} & {\left(a_{44} + b_{42}\right)} k_{43} p - b_{43} k_{13} - b_{44} k_{23} + {\left(a_{43} + b_{41}\right)} k_{33} & -b_{43} k_{14} + {\left(a_{43} + b_{41}\right)} k_{34} + {\left(a_{44} + b_{42}\right)} k_{44} - \frac{b_{44} k_{24}}{p} \end{array}\right)$

H[2,1];

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

d31=(A[2,1]==0).solve(d31)[0].right();d31;

 $\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{{\left(a_{12} + b_{14} - d_{34}\right)} h_{22} + {\left({\left(a_{11} + b_{13} - d_{33}\right)} h_{12} - b_{11} h_{32} - {\left(b_{12} - d_{32}\right)} h_{42}\right)} p}{h_{32} p}$

Z[7,3]

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

W=matrix([[Z[6,6],Z[6,7]],[Z[7,6],Z[4,7]]]);W

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr} -d_{01} d_{10} + d_{00} d_{11} + {\left(d_{01} - d_{11}\right)} d_{30} - {\left(d_{00} - d_{10}\right)} d_{31} + x_{20} & -{\left(d_{01} - d_{11}\right)} d_{30} + {\left(d_{00} - d_{10}\right)} d_{31} + x_{21} \\ -{\left(d_{01} - d_{11}\right)} d_{20} + {\left(d_{00} - d_{10}\right)} d_{21} + x_{30} & {\left(d_{01} - d_{11}\right)} d_{30} - {\left(d_{00} - d_{10}\right)} d_{31} + d_{01} - x_{21} \end{array}\right)$

(W[0,1]==0).solve(x21)[0]

 $\newcommand{\Bold}[1]{\mathbf{#1}}x_{21} = {\left(d_{01} - d_{11}\right)} d_{30} - {\left(d_{00} - d_{10}\right)} d_{31}$

W.substitute(x21==(W[0,1]==0).solve(x21)[0].right());

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr} -d_{01} d_{10} + d_{00} d_{11} + {\left(d_{01} - d_{11}\right)} d_{30} - {\left(d_{00} - d_{10}\right)} d_{31} + x_{20} & 0 \\ -{\left(d_{01} - d_{11}\right)} d_{20} + {\left(d_{00} - d_{10}\right)} d_{21} + x_{30} & d_{01} \end{array}\right)$

d32=(A[2,0]==0).solve(d32)[0].right();d32;

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{b_{12} h_{41} p - {\left(a_{11} + b_{13} - d_{33}\right)} h_{11} - {\left(a_{12} + b_{14} - d_{34}\right)} h_{21} + {\left(b_{11} - d_{31}\right)} h_{31}}{h_{41} p}$

Traceback (click to the left of this block for traceback)
...
IndexError: list index out of range

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_172.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("QS5zdWJzdGl0dXRlKGQzMj0oQVsyLDBdPT0wKS5zb2x2ZShkMzIpWzBdLnJpZ2h0KCkpOw=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpREmFrz/___code___.py", line 3, in <module>
    exec compile(u'A.substitute(d32=(A[_sage_const_2 ,_sage_const_0 ]==_sage_const_0 ).solve(d32)[_sage_const_0 ].right());
  File "", line 1, in <module>
    
  File "/usr/local/sage-6.10/local/lib/python2.7/site-packages/sage/structure/sequence.py", line 531, in __getitem__
    return list.__getitem__(self,n)
IndexError: list index out of range

a33=eq.solve(a33)[0].right();a33

 $\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{{\left(a_{34} + b_{32}\right)} k_{43} p - b_{33} k_{13} - b_{34} k_{23} + b_{31} k_{33}}{k_{33}}$

d32.s

Traceback (click to the left of this block for traceback)
...
SyntaxError: keyword can't be an expression

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_138.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("ZXEuc3Vic3RpdHV0ZShBWzcsN109MCk7"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpsFx9GE/___code___.py", line 3
    eq.substitute(A[_sage_const_7 ,_sage_const_7 ]=_sage_const_0 );
SyntaxError: keyword can't be an expression

Delta=a*b-c*d;

var('a,b,c,d');

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(a, b, c, d\right)$

B=matrix([[a,b],[c,d]]);B

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

(B.det()).substitute(d=0);

 $\newcommand{\Bold}[1]{\mathbf{#1}}-b c$

a=0;a

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

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr} a & b \\ c & d \end{array}\right)$

B=B.substitute(a=B[0,1]);B

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

B=matrix([[s11,s12],[s21,s22]]);

D=matrix([[t11,t12],[t21,t22]]);D

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr} t_{11} & t_{12} \\ t_{21} & t_{22} \end{array}\right)$

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

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr} t_{22} & -t_{21} \\ -t_{12} & t_{11} \end{array}\right)$

s=[]

N=4

for (i,j) in cartesian_product([range(N),range(N)]): s.append('y%d%d' %(i,j))

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left[\verb|y00|, \verb|y01|, \verb|y02|, \verb|y03|, \verb|y10|, \verb|y11|, \verb|y12|, \verb|y13|, \verb|y20|, \verb|y21|, \verb|y22|, \verb|y23|, \verb|y30|, \verb|y31|, \verb|y32|, \verb|y33|, \verb|y00|, \verb|y01|, \verb|y02|, \verb|y03|, \verb|y10|, \verb|y11|, \verb|y12|, \verb|y13|, \verb|y20|, \verb|y21|, \verb|y22|, \verb|y23|, \verb|y30|, \verb|y31|, \verb|y32|, \verb|y33|\right]$

a = var(s);

y00=0;

s.substitute(y00==0);s;

Traceback (click to the left of this block for traceback)
...
AttributeError: 'list' object has no attribute 'substitute'

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_387.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("cy5zdWJzdGl0dXRlKHkwMD09MCk7czs="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmp5oFAMx/___code___.py", line 3, in <module>
    exec compile(u's.substitute(y00==_sage_const_0 );s;
  File "", line 1, in <module>
    
AttributeError: 'list' object has no attribute 'substitute'

A = matrix(SR,N,N,a); A

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

A.substitute(y01==0).substitute(y02==0);A

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

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

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

F[0,0]

 $\newcommand{\Bold}[1]{\mathbf{#1}}-{\left(y_{13} y_{22} - y_{12} y_{23}\right)} y_{31} + {\left(y_{13} y_{21} - y_{11} y_{23}\right)} y_{32} - {\left(y_{12} y_{21} - y_{11} y_{22}\right)} y_{33}$

F[0,1]*det(A).simplify_full()

 $\newcommand{\Bold}[1]{\mathbf{#1}}y_{12} y_{20} - y_{10} y_{22}$

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr} s_{11} & s_{12} \\ s_{21} & s_{22} \end{array}\right)$

block_matrix(2,2,[B,B,B,B]);

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr|rr} s_{11} & s_{12} & s_{11} & s_{12} \\ s_{21} & s_{22} & s_{21} & s_{22} \\ \hline s_{11} & s_{12} & s_{11} & s_{12} \\ s_{21} & s_{22} & s_{21} & s_{22} \end{array}\right)$

F.substitute(D.det()==1).simplify_full();

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr} -\frac{t_{22}}{t_{12} t_{21} - t_{11} t_{22}} & \frac{t_{21}}{t_{12} t_{21} - t_{11} t_{22}} \\ \frac{t_{12}}{t_{12} t_{21} - t_{11} t_{22}} & -\frac{t_{11}}{t_{12} t_{21} - t_{11} t_{22}} \end{array}\right)$

s11=F[0,0];

s11;

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{t_{11}} - \frac{t_{12} t_{21}}{t_{11}^{2} {\left(\frac{t_{12} t_{21}}{t_{11}} - t_{22}\right)}}$

s12=F[0,1];s21=F[1,0]; s22=F[1,1];

for i in [0..1]: for j in [0..1]: B[i,j]=F[i,j].simplify_full()

 $\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr} t_{22} & -t_{21} \\ -t_{12} & \frac{t_{12} t_{21} + 1}{t_{22}} \end{array}\right)$

t11=(t12*t21+1)/t22;t11

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{t_{12} t_{21} + 1}{t_{22}}$

B=matrix([[s11,s12],[s21,s22]])

B[0,0]

 $\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{t_{11}} - \frac{t_{12} t_{21}}{t_{11}^{2} {\left(\frac{t_{12} t_{21}}{t_{11}} - t_{22}\right)}}$

B[0,0].simplify_full()

 $\newcommand{\Bold}[1]{\mathbf{#1}}t_{22}$

Paramodular_calculations

1758 days ago by jimlb