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luke naylor latex documents
research
Max Destabilizer Rank
Commits
2636c4d3
Commit
2636c4d3
authored
1 year ago
by
Luke Naylor
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Adjust rank 0 charact curve diagram
parent
4d2777ab
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rank_zero_case.ipynb
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rank_zero_case.ipynb
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2636c4d3
...
...
@@ -90,14 +90,14 @@
}
],
"source": [
"alpha_range = alpha, 0, 2\n",
"alpha_range = alpha, 0,
1.
2\n",
"beta_range = beta, -1, 1\n",
"black_text_args = {\"fontsize\":\"xx-large\", \"clip\":True, \"rgbcolor\":\"black\"}\n",
"\n",
"Theta_v_plot = implicit_plot(stability.Tilt().degree(v), beta_range, alpha_range)\n",
"Theta_v_plot += text(r\"$\\nu_{\\alpha,\\beta}(v)
<
0$\",
(0.5,
1
),
**black_text_args
)\
n
",
"
Theta_v_plot
+=
text
(
r
\"$\\
nu_
{\\
alpha
,\\
beta
}(
v
)
>
0$\", (-0.5,
1
), **black_text_args)\n",
"Theta_v_plot += text(r\"$\\Theta_v$\", (-0.
1
,
1
.5), rotation=90, fontsize=\"xx-large\")\n",
"Theta_v_plot += text(r\"$\\nu_{\\alpha,\\beta}(v)
<
0$\",
(0.5,
0.6
),
**black_text_args
)\
n
",
"
Theta_v_plot
+=
text
(
r
\"$\\
nu_
{\\
alpha
,\\
beta
}(
v
)
>
0$\", (-0.5,
0.6
), **black_text_args)\n",
"Theta_v_plot += text(r\"$\\Theta_v$\", (-0.
05
,
0
.5), rotation=90, fontsize=\"xx-large\")\n",
"Theta_v_plot.axes_labels([r\"$\\beta$\", r\"$\\alpha$\"])\n",
"Theta_v_plot"
]
...
...
%% Cell type:code id:7402c3b8 tags:
```
sage
from pseudowalls import *
%display latex
alpha = stability.Tilt().alpha
beta = stability.Tilt().beta
```
%% Cell type:code id:30570b37 tags:
```
sage
var("C D r c d", domain="real")
```
%% Output
$\displaystyle \left(C, D, r, c, d\right)$
(C, D, r, c, d)
%% Cell type:code id:1eb8a0c7 tags:
```
sage
v = Chern_Char(0,1,0)
v
```
%% Output
$\displaystyle \text{Chern Character:} \\ \begin{array}{l} \mathrm{ch}_{0} = 0 \\ \mathrm{ch}_{1} = 1 \ell^{1} \\ \mathrm{ch}_{2} = 0 \ell^{2} \end{array}$
<pseudowalls.chern_character.Chern_Char object at 0x7f2735ae0ee0>
%% Cell type:code id:c0e0ff38 tags:
```
sage
alpha_range = alpha, 0, 2
alpha_range = alpha, 0,
1.
2
beta_range = beta, -1, 1
black_text_args = {"fontsize":"xx-large", "clip":True, "rgbcolor":"black"}
Theta_v_plot = implicit_plot(stability.Tilt().degree(v), beta_range, alpha_range)
Theta_v_plot += text(r"$\nu_{\alpha,\beta}(v) < 0$", (0.5,
1
), **black_text_args)
Theta_v_plot += text(r"$\nu_{\alpha,\beta}(v) > 0$", (-0.5,
1
), **black_text_args)
Theta_v_plot += text(r"$\Theta_v$", (-0.
1
,
1
.5), rotation=90, fontsize="xx-large")
Theta_v_plot += text(r"$\nu_{\alpha,\beta}(v) < 0$", (0.5,
0.6
), **black_text_args)
Theta_v_plot += text(r"$\nu_{\alpha,\beta}(v) > 0$", (-0.5,
0.6
), **black_text_args)
Theta_v_plot += text(r"$\Theta_v$", (-0.
05
,
0
.5), rotation=90, fontsize="xx-large")
Theta_v_plot.axes_labels([r"$\beta$", r"$\alpha$"])
Theta_v_plot
```
%% Output
Graphics object consisting of 4 graphics primitives
%% Cell type:code id:5bf18ed0 tags:
```
sage
alpha_range = alpha, 0, 2
beta_range = beta, -2, 2
u_1 = Chern_Char(1,2,1.8)
u_1
```
%% Output
$\displaystyle \text{Chern Character:} \\ \begin{array}{l} \mathrm{ch}_{0} = 1 \\ \mathrm{ch}_{1} = 2 \ell^{1} \\ \mathrm{ch}_{2} = 1.80000000000000 \ell^{2} \end{array}$
<pseudowalls.chern_character.Chern_Char object at 0x7f9ed152cc10>
%% Cell type:code id:26d52f14 tags:
```
sage
u_2 = Chern_Char(1,-2,1.8)
u_2
```
%% Output
$\displaystyle \text{Chern Character:} \\ \begin{array}{l} \mathrm{ch}_{0} = 1 \\ \mathrm{ch}_{1} = -2 \ell^{1} \\ \mathrm{ch}_{2} = 1.80000000000000 \ell^{2} \end{array}$
<pseudowalls.chern_character.Chern_Char object at 0x7f9ed1547dd0>
%% Cell type:code id:be444fa0 tags:
```
sage
implicit_plot(stability.Tilt().wall_eqn(u_1, v)/alpha, beta_range, alpha_range) \
+ implicit_plot(stability.Tilt().degree(u_1), beta_range, alpha_range) \
+ Theta_v_plot
```
%% Output
Graphics object consisting of 3 graphics primitives
%% Cell type:code id:2452201f tags:
```
sage
implicit_plot(stability.Tilt().wall_eqn(u_2, v)/alpha, beta_range, alpha_range) \
+ implicit_plot(stability.Tilt().degree(u_2), beta_range, alpha_range) \
+ Theta_v_plot
```
%% Output
Graphics object consisting of 3 graphics primitives
...
...
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