notebook work towards loose bounds graphic

a5ae08a8 · Luke Naylor · ba9fdd97 · a5ae08a8
Commit a5ae08a8 authored 1 year ago by Luke Naylor
--- a/plot_playground.ipynb
+++ b/plot_playground.ipynb
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "05f8d418",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from pseudowalls import *\n",
+    "%display latex"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "b46f8a6a",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<html>\\(\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 3 \\\\ \\mathrm{ch}_{1} = 2 \\ell^{1} \\\\ \\mathrm{ch}_{2} = -2 \\ell^{2} \\end{array}\\)</html>"
+      ],
+      "text/latex": [
+       "$\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 3 \\\\ \\mathrm{ch}_{1} = 2 \\ell^{1} \\\\ \\mathrm{ch}_{2} = -2 \\ell^{2} \\end{array}$"
+      ],
+      "text/plain": [
+       "<pseudowalls.chern_character.Chern_Char object at 0x7f0034ca7310>"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "v = Chern_Char(3, 2, -2)\n",
+    "v"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "8ed6de82",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<html>\\(\\displaystyle -\\frac{2}{3}\\)</html>"
+      ],
+      "text/latex": [
+       "$\\displaystyle -\\frac{2}{3}$"
+      ],
+      "text/plain": [
+       "-2/3"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "beta_min = stability.Tilt(alpha=0).degree(v).roots()[0][0]\n",
+    "beta_min"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "edf2389e",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<html>\\(\\displaystyle 16\\)</html>"
+      ],
+      "text/latex": [
+       "$\\displaystyle 16$"
+      ],
+      "text/plain": [
+       "16"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "v.Q_tilt()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "1dcae94c",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<html>\\(\\displaystyle \\text{ Twisted Chern Character for $\\beta={ -\\frac{2}{3} }$ } \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 3 \\\\ \\mathrm{ch}_{1} = 4 \\ell^{1} \\\\ \\mathrm{ch}_{2} = 0 \\ell^{2} \\end{array}\\)</html>"
+      ],
+      "text/latex": [
+       "$\\displaystyle \\text{ Twisted Chern Character for $\\beta={ -\\frac{2}{3} }$ } \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 3 \\\\ \\mathrm{ch}_{1} = 4 \\ell^{1} \\\\ \\mathrm{ch}_{2} = 0 \\ell^{2} \\end{array}$"
+      ],
+      "text/plain": [
+       "<pseudowalls.chern_character.Twisted_Chern_Char object at 0x7f002672b710>"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "v.twist(beta_min)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "aa77740a",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "SageMath 9.8",
+   "language": "sage",
+   "name": "sagemath"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
+%% Cell type:code id:05f8d418 tags:
+``` sage
+from pseudowalls import *
+%display latex
+```
+%% Cell type:code id:b46f8a6a tags:
+``` sage
+v = Chern_Char(3, 2, -2)
+v
+```
+%% Output
+    $\displaystyle \text{Chern Character:} \\ \begin{array}{l} \mathrm{ch}_{0} = 3 \\ \mathrm{ch}_{1} = 2 \ell^{1} \\ \mathrm{ch}_{2} = -2 \ell^{2} \end{array}$
+    <pseudowalls.chern_character.Chern_Char object at 0x7f0034ca7310>
+%% Cell type:code id:8ed6de82 tags:
+``` sage
+beta_min = stability.Tilt(alpha=0).degree(v).roots()[0][0]
+beta_min
+```
+%% Output
+    $\displaystyle -\frac{2}{3}$
+    -2/3
+%% Cell type:code id:edf2389e tags:
+``` sage
+v.Q_tilt()
+```
+%% Output
+    $\displaystyle 16$
+    16
+%% Cell type:code id:1dcae94c tags:
+``` sage
+v.twist(beta_min)
+```
+%% Output
+    $\displaystyle \text{ Twisted Chern Character for $\beta={ -\frac{2}{3} }$ } \\ \begin{array}{l} \mathrm{ch}_{0} = 3 \\ \mathrm{ch}_{1} = 4 \ell^{1} \\ \mathrm{ch}_{2} = 0 \ell^{2} \end{array}$
+    <pseudowalls.chern_character.Twisted_Chern_Char object at 0x7f002672b710>
+%% Cell type:code id:aa77740a tags:
+``` sage
+```