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Commit 9aed81df authored by Luke Naylor's avatar Luke Naylor
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Add notebook for creating figures with sage

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%% Cell type:code id:ae7688ac tags:
``` sage
from pseudowalls import *
```
%% Cell type:code id:cc0d5079 tags:
``` sage
O = Chern_Char(1,0)
O
```
%% Output
Chern Character:\begin{array}{l} \mathrm{ch}_{0} = 1 \\ \mathrm{ch}_{1} = 0 \ell^{1} \end{array}
<pseudowalls.chern_character.Chern_Char object at 0x7f1b13fac400>
%% Cell type:code id:2a351730 tags:
``` sage
O1 = exponential_chern(1,1)
O1
```
%% Output
Chern Character:\begin{array}{l} \mathrm{ch}_{0} = 1 \\ \mathrm{ch}_{1} = 1 \ell^{1} \end{array}
<pseudowalls.chern_character.Chern_Char object at 0x7f1b14057400>
%% Cell type:code id:feb674aa tags:
``` sage
O1inv = exponential_chern(-1,1)
O1inv
```
%% Output
Chern Character:\begin{array}{l} \mathrm{ch}_{0} = 1 \\ \mathrm{ch}_{1} = -1 \ell^{1} \end{array}
<pseudowalls.chern_character.Chern_Char object at 0x7f1b140577c0>
%% Cell type:code id:ec14fd95 tags:
``` sage
O2 = O1 * O1
O2
```
%% Output
Chern Character:\begin{array}{l} \mathrm{ch}_{0} = 1 \\ \mathrm{ch}_{1} = 2 \ell^{1} \end{array}
<pseudowalls.chern_character.Chern_Char object at 0x7f1b14054f40>
%% Cell type:code id:45fcb764 tags:
``` sage
O_x = Chern_Char(0,1)
O_x
```
%% Output
Chern Character:\begin{array}{l} \mathrm{ch}_{0} = 0 \\ \mathrm{ch}_{1} = 1 \ell^{1} \end{array}
<pseudowalls.chern_character.Chern_Char object at 0x7f1b0bb9bfa0>
%% Cell type:code id:a0847d59 tags:
``` sage
def plot_central_charge(chern, name):
Z = stability.Mumford().central_charge(chern)
x = Z.real()
y = Z.imag()
argument = arctan(y/x) if x != 0 else pi
if argument <= 0:
argument += 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((pi-argument/2)/pi),
(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"$\mathcal{I}$"])
p.show()
```
%% Output
%% Cell type:code id:011017ec tags:
``` sage
z = 1 + I
arctan(1)
```
%% Output
1/4*pi
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