Adjust rank 0 charact curve diagram

2636c4d3 · Luke Naylor · 4d2777ab · 2636c4d3
Commit 2636c4d3 authored 1 year ago by Luke Naylor
--- a/rank_zero_case.ipynb
+++ b/rank_zero_case.ipynb
@@ -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