Add figures for example bounds on d in term of r for diff q-vals

main.tex

@@ -9,6 +9,7 @@
 \usepackage{color}
 \usepackage{sagetex}
 \usepackage{minted}
+\usepackage{subcaption}
 \usepackage[]{breqn}
 
 \newcommand{\QQ}{\mathbb{Q}}
@@ -616,7 +617,14 @@ def beta_min(chern):
 v_example = Chern_Char(3,2,-2)
 q_example = 7/3
 
-def plot_d_bound(v_example, q_example, ymax=5, ymin=-2, xmax=20):
+def plot_d_bound(
+  v_example,
+  q_example,
+  ymax=5,
+  ymin=-2,
+  xmax=20,
+  aspect_ratio=None
+):
 
   # Equations to plot imminently representing the bounds on d:
   eq1 = (
@@ -659,7 +667,6 @@ def plot_d_bound(v_example, q_example, ymax=5, ymin=-2, xmax=20):
       color='green',
 			linestyle = "dashed",
       legend_label=r"upper bound: $\Delta(G) \geq 0$",
-			title=r"$q :=\mathrm{ch}_1^{\beta_{-}}(E)=" + latex(q_example) + r"$"
     )
     + plot(
       eq2,
@@ -686,13 +693,46 @@ def plot_d_bound(v_example, q_example, ymax=5, ymin=-2, xmax=20):
   example_bounds_on_d_plot.ymin(ymin)
   example_bounds_on_d_plot.ymax(ymax)
   example_bounds_on_d_plot.axes_labels(['$r$', '$d$'])
+  if aspect_ratio:
+    example_bounds_on_d_plot.set_aspect_ratio(aspect_ratio)
   return example_bounds_on_d_plot
 
 \end{sagesilent}
 
-\sageplot{plot_d_bound(v_example, 0)}
-\sageplot{plot_d_bound(v_example, 2)}
-\sageplot{plot_d_bound(v_example, 4)}
+\begin{figure}
+\centering
+\begin{subfigure}{.5\textwidth}
+  \centering
+	\sageplot[width=\linewidth]{plot_d_bound(v_example, 0)}
+	\caption{$q = 0$}
+  \label{fig:d_bounds_xmpl_min_q}
+\end{subfigure}%
+\begin{subfigure}{.5\textwidth}
+  \centering
+	\sageplot[width=\linewidth]{plot_d_bound(v_example, 4)}
+	\caption{$q = \chern^{\beta}(F)$}
+  \label{fig:d_bounds_xmpl_max_q}
+\end{subfigure}
+\caption{
+	Bounds on $d:=\chern_2(E)$ in terms of $r:=\chern_0(E)$ for fixed, extreme,
+	values of $q:=\chern_1^{\beta}(E)$.
+	Where $\chern(F) = (3,2,-2)$.
+}
+\label{fig:d_bounds_xmpl_extrm_q}
+\end{figure}
+
+\begin{figure}
+\centering
+\sageplot[
+	width=\linewidth
+]{plot_d_bound(v_example, 2, ymax=6, ymin=-0.5, aspect_ratio=1)}
+\caption{
+	Bounds on $d:=\chern_2(E)$ in terms of $r:=\chern_0(E)$ for a fixed
+	value $\chern_1^{\beta}(F)/2$ of $q:=\chern_1^{\beta}(E)$.
+	Where $\chern(F) = (3,2,-2)$.
+}
+\label{fig:d_bounds_xmpl_gnrc_q}
+\end{figure}
 
 \egroup