From 9c838f680020c8116637925d2c1ddd0bf73d7d01 Mon Sep 17 00:00:00 2001
From: Luke Naylor <l.naylor@sms.ed.ac.uk>
Date: Tue, 14 Mar 2023 23:53:39 +0000
Subject: [PATCH] Have first sage plot working
---
.gitignore | 3 ++
Makefile | 37 +++++++++++++++++
main.tex | 13 +++++-
sagetexscripts/fig1.sage | 89 ++++++++++++++++++++++++++++++++++++++++
4 files changed, 140 insertions(+), 2 deletions(-)
create mode 100644 Makefile
create mode 100644 sagetexscripts/fig1.sage
diff --git a/.gitignore b/.gitignore
index 3f41c5a..991411d 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,2 +1,5 @@
main*
!main.tex
+sage-plots-for-main.tex/*
+**/__pycache__/
+sagetexscripts/*.py
diff --git a/Makefile b/Makefile
new file mode 100644
index 0000000..dce39f7
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,37 @@
+# Requires GNU make, xargs, a latex distribution, sage
+# and sagetex.sty visible in TEXINPUTS
+
+MAINTEXFILE = main.tex
+TEXFILES = ${MAINTEXFILE}
+SAGESCRIPT = main.sagetex.sage
+SAGEPLOTFILES = sagetexscripts/fig1
+
+main.pdf: ${TEXFILES} main.sagetex.sout
+ latexmk
+
+main.sagetex.sout: ${SAGESCRIPT} pymodules
+ sage $?
+
+${SAGESCRIPT}: ${TEXFILES}
+ pdflatex -interaction=nonstopmode ${MAINTEXFILE}
+
+pymodules: $(addsuffix .py,${SAGEPLOTFILES})
+
+$(addsuffix .py,${SAGEPLOTFILES}): $(addsuffix .sage,${SAGEPLOTFILES})
+ # Preparse Sagemath scripts in sagetexscripts,
+ # converting them to python files of form <basename>.py
+ # (ready to be imported as python modules)
+ sage --preparse $^
+ echo ${SAGEPLOTFILES} | xargs -I % sh -c 'mv %.sage.py %.py'
+
+.PHONY: clean
+clean:
+ latexmk -C
+ rm -f main.pdf
+ rm -f *.sagetex.*
+ rm -f *.xml
+ rm -f *.sta
+ rm -f *.bbl
+ rm -rf sage-plots-for-main.tex
+ rm -f *.tmp
+
diff --git a/main.tex b/main.tex
index 409c773..00b53a7 100644
--- a/main.tex
+++ b/main.tex
@@ -7,6 +7,7 @@
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{mathtools}
+\usepackage{sagetex}
\usepackage{ulem}
\usepackage{xcolor}
@@ -16,7 +17,7 @@
\title{Bridgeland Stabilities and Finding Walls}
\subtitle{}
\author{Luke Naylor}
-\institute{University of Edinburgh}
+\institute{Hodge Club}
\date{March 2023}
\newcommand\RR{\mathbb{R}}
@@ -32,7 +33,7 @@
\titlepage
\end{frame}
-\section{Transitioning to Stab on $D^b(X)$}
+\section{Transitioning to Stab on Triangulated Categories}
\begin{frame}{Central Charge}
\begin{align*}
@@ -41,6 +42,14 @@
\end{align*}
\end{frame}
+\begin{sagesilent}
+ import sagetexscripts.fig1
+\end{sagesilent}
+
+\begin{frame}{plot}
+ \sageplot{sagetexscripts.fig1.plot()}
+\end{frame}
+
\section{Section 1}
\section{Section 2}
diff --git a/sagetexscripts/fig1.sage b/sagetexscripts/fig1.sage
new file mode 100644
index 0000000..30a5826
--- /dev/null
+++ b/sagetexscripts/fig1.sage
@@ -0,0 +1,89 @@
+#!/usr/bin/env sage
+
+from pseudowalls import *
+
+def plot():
+ O = Chern_Char(1,0)
+ O1 = exponential_chern(1,1)
+ O1inv = exponential_chern(-1,1)
+ O2 = O1 * O1
+ O_x = Chern_Char(0,1)
+
+ def plot_central_charge(chern, name, argument = None, radius = None):
+ Z = stability.Mumford().central_charge(chern)
+ x = Z.real()
+ y = Z.imag()
+
+ if not argument:
+ argument = arctan(y/x) if x != 0 else pi / 2
+ if argument <= 0:
+ argument += pi
+
+ if not radius:
+ radius = (pi-argument/2)/pi
+
+ return point(
+ Z,
+ marker = "o",
+ size = 600,
+ rgbcolor = "white",
+ #markeredgecolor = "purple",
+ zorder = 100
+ ) + point(
+ Z,
+ marker = name,
+ size = 500,
+ rgbcolor = "red",
+ zorder = 101
+ ) + line(
+ (0, Z),
+ rgbcolor = "red",
+ linestyle = "dashed",
+ zorder = 99
+ ) + disk(
+ (0,0),
+ float(radius),
+ (0, float(argument)),
+ alpha=.2,
+ fill=False,
+ thickness=1,
+ rgbcolor="purple"
+ )
+
+ p = sum(
+ plot_central_charge(chern, name)
+ for chern, name in [
+ (O1, r"$\mathcal{O}(1)$"),
+ (O, r"$\mathcal{O}_X$"),
+ (O1inv, r"$\mathcal{O}(-1)$"),
+ (O2, r"$\mathcal{O}(2)$"),
+ (O_x, r"$\mathcal{O}_p$")
+ ]
+ )
+
+ xmax = (2.5)
+ xmin = (-2.5)
+ ymin = (-0.25)
+ ymax = (1.5)
+ aspect_ratio = (1)
+
+ p += polygon(
+ [
+ (xmax + 1,0),
+ (xmin - 1,0),
+ (xmin - 1,ymax + 1),
+ (xmax + 1,ymax + 1)
+ ],
+ rgbcolor = "yellow",
+ alpha = 0.2,
+ zorder = 102
+ )
+
+ p.xmax(xmax)
+ p.xmin(xmin)
+ p.ymin(ymin)
+ p.ymax(ymax)
+ p.set_aspect_ratio(aspect_ratio)
+
+ p.axes_labels([r"$\mathcal{R}$",r"$\mathcal{I}$"])
+ return p
--
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