Plot for characteristic curves

main.tex

@@ -29,6 +29,16 @@
 
 \begin{document}
 
+\begin{sagesilent}
+# Requires extra package:
+#! sage -pip install "pseudowalls==0.0.3" --extra-index-url https://gitlab.com/api/v4/projects/43962374/packages/pypi/simple
+
+from pseudowalls import *
+
+Δ = lambda v: v.Q_tilt()
+mu = stability.Mumford().slope
+\end{sagesilent}
+
 \title{Explicit Formulae for Bounds on the Ranks of Tilt Destabilizers and
 Practical Methods for Finding Pseudowalls}
 
@@ -85,6 +95,41 @@ bounds on $\chern_0(E)$ of potential destabilizers $E$ of $F$.
 \section{Characteristic Curves of Stability Conditions Associated to Chern
 Characters}
 
+\begin{sagesilent}
+v = Chern_Char(3, 2, -2)
+u = Chern_Char(1, 0, 0)
+
+alpha = stability.Tilt().alpha
+beta = stability.Tilt().beta
+
+coords_range = (beta, -5, 5), (alpha, 0, 5)
+
+charact_curve_plot = (
+	implicit_plot(stability.Tilt().degree(u), *coords_range , rgbcolor = "red")
+	+ implicit_plot(stability.Tilt().degree(v), *coords_range )
+	+ line([(mu(v),0),(mu(v),5)], linestyle = "dashed", legend_label =
+	r"$(3,2\ell,-4\ell^2/2)$")
+	+ line([(mu(u),0),(mu(u),5)], rgbcolor = "red", linestyle =
+	"dashed", legend_label = r"$(1,0,0)$")
+	+ implicit_plot(stability.Tilt().wall_eqn(u,v)/alpha,
+	*coords_range , rgbcolor = "black")
+)
+charact_curve_plot.xmax(1)
+charact_curve_plot.xmin(-2)
+charact_curve_plot.ymax(1.5)
+charact_curve_plot.axes_labels([r"$\beta$", r"$\alpha$"])
+\end{sagesilent}
+
+\begin{figure}
+  \centering
+	\sageplot[width=\linewidth]{charact_curve_plot}
+	\caption{}
+  \label{fig:characteristic-curves-example}
+\end{figure}
+
+Talk about figure \ref{fig:characteristic-curves-example}.
+
+
 \section{Loose Bounds on $\chern_0(E)$ for Semistabilizers Along Fixed
 $\beta\in\QQ$}