% GENERATED FILE -- DO NOT EDIT BY HAND.
% Generated and byte-for-byte checked by verify_yagzhev19_sympy.py.
\section{The 11-variable map}\label{app:phi}
With coordinate order $(x,y,z,a,b,c,d,q,s,h,k)$, the components are
\begin{align*}
\Phi_{1}={}&- a c - a d z - 3 a y^{2} - 2 a z - c d^{2} + d^{2} z - d s + 7 d y^{2} + s x y + 3 x y z + 4 y^{2} + z,\\
\Phi_{2}={}&- b c - b d z - 3 b y^{2} - 2 b z - 3 c d x - d q + q x y + 12 x y^{2} + 3 x z + y,\\
\Phi_{3}={}&- h k - h x z + k x^{2} - 3 x^{2} y + 2 x,\\
\Phi_{4}={}&a - d^{2} + 2 d x y,\\
\Phi_{5}={}&b + 3 x^{2} y,\\
\Phi_{6}={}&c + x y z + 3 y^{2} + 2 z,\\
\Phi_{7}={}&d - x y,\\
\Phi_{8}={}&b z + 3 c x + q,\\
\Phi_{9}={}&a z + c d + c x y - d z + s - x y z - 7 y^{2},\\
\Phi_{10}={}&h - x^{2},\\
\Phi_{11}={}&k + x z.
\end{align*}

\section{Quadratic and cubic parts after normalization}\label{app:qc}
The nonzero components of $Q$ are
\begin{align*}
Q_{1}={}&- \frac{h k}{2},\\
Q_{2}={}&- b c - 2 b z - d q + 3 x z,\\
Q_{3}={}&- a c - 2 a z - d s + 4 y^{2},\\
Q_{4}={}&- d^{2},\\
Q_{6}={}&2 a c + 4 a z + 2 d s - 5 y^{2},\\
Q_{7}={}&- x y,\\
Q_{8}={}&b z + 3 c x,\\
Q_{9}={}&a z + c d - d z - 7 y^{2},\\
Q_{10}={}&- x^{2},\\
Q_{11}={}&x z.
\end{align*}
All omitted $Q_i$ are zero. The nonzero components of $C$ are
\begin{align*}
C_{1}={}&- \frac{h x z}{2} + \frac{k x^{2}}{2} - \frac{3 x^{2} y}{2},\\
C_{2}={}&- b d z - 3 b y^{2} - 3 c d x + q x y + 12 x y^{2},\\
C_{3}={}&- a d z - 3 a y^{2} - c d^{2} + d^{2} z + 7 d y^{2} + s x y + 3 x y z,\\
C_{4}={}&2 d x y,\\
C_{5}={}&3 x^{2} y,\\
C_{6}={}&2 a d z + 6 a y^{2} + 2 c d^{2} - 2 d^{2} z - 14 d y^{2} - 2 s x y - 5 x y z,\\
C_{9}={}&c x y - x y z.
\end{align*}

\section{The lifted collision points}\label{app:points}
The lifted points are $\widehat p_i=(p_i,-C_S(p_i),1)$. In the coordinate order
\[
(x,y,z,a,b,c,d,q,s,h,k,Y_1,Y_2,Y_3,Y_4,Y_5,Y_6,Y_9,t),
\]
they are
\begin{align*}
\widehat p_{1}={}&(0,0,- \frac{1}{4},0,0,\frac{1}{2},0,0,0,0,0,0,0,0,0,0,0,0,1),\\
\widehat p_{2}={}&(1,- \frac{3}{2},\frac{13}{2},- \frac{9}{4},\frac{9}{2},-10,- \frac{3}{2},\frac{3}{4},- \frac{153}{8},1,- \frac{13}{2},\\
&\hspace{1cm}\frac{17}{4},\frac{45}{8},- \frac{99}{16},- \frac{9}{2},\frac{9}{2},\frac{177}{8},- \frac{99}{4},1),\\
\widehat p_{3}={}&(-1,\frac{3}{2},\frac{13}{2},- \frac{9}{4},- \frac{9}{2},-10,- \frac{3}{2},- \frac{3}{4},- \frac{153}{8},1,\frac{13}{2},\\
&\hspace{1cm}- \frac{17}{4},- \frac{45}{8},- \frac{99}{16},- \frac{9}{2},- \frac{9}{2},\frac{177}{8},- \frac{99}{4},1).
\end{align*}
Their common image is
\[
(0,0,- \frac{1}{4},0,0,\frac{1}{2},0,0,0,0,0,0,0,0,0,0,0,0,1).
\]
