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luke naylor latex documents
Presentations
Stabilities - Hodge Club
Commits
9c838f68
Commit
9c838f68
authored
2 years ago
by
Luke Naylor
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Have first sage plot working
parent
765a9152
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#24618
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2 years ago
Stage: build
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.gitignore
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.gitignore
Makefile
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Makefile
main.tex
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main.tex
sagetexscripts/fig1.sage
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sagetexscripts/fig1.sage
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.gitignore
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9c838f68
main*
!main.tex
sage-plots-for-main.tex/*
**/__pycache__/
sagetexscripts/*.py
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Makefile
0 → 100644
+
37
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0
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9c838f68
# 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
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main.tex
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−
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9c838f68
...
...
@@ -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
}
...
...
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sagetexscripts/fig1.sage
0 → 100644
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#!/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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