From 0271ae547ce0f9618379704b90a8305aff5cc0a3 Mon Sep 17 00:00:00 2001
From: Luke Naylor <l.naylor@sms.ed.ac.uk>
Date: Wed, 10 May 2023 23:30:58 +0100
Subject: [PATCH] Add figures for example bounds on d in term of r for diff
q-vals
---
main.tex | 50 +++++++++++++++++++++++++++++++++++++++++++++-----
1 file changed, 45 insertions(+), 5 deletions(-)
diff --git a/main.tex b/main.tex
index a2e6ffe..fb0f6fc 100644
--- a/main.tex
+++ b/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
--
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