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{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "05f8d418",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pseudowalls import *\n",
    "%display latex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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 0x7f4aeb415ab0>"
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = Chern_Char(3, 2, -2)\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": 3,
     "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": 4,
   "id": "edf2389e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle 16\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle 16$"
      ],
      "text/plain": [
       "16"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v.Q_tilt()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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}$"
      ],
      "text/plain": [
       "<pseudowalls.chern_character.Twisted_Chern_Char object at 0x7f4ae3797d60>"
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v.twist(beta_min)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "aa77740a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html>\\(\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 1 \\\\ \\mathrm{ch}_{1} = 0 \\ell^{1} \\\\ \\mathrm{ch}_{2} = 0 \\ell^{2} \\end{array}\\)</html>"
      ],
      "text/latex": [
       "$\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 1 \\\\ \\mathrm{ch}_{1} = 0 \\ell^{1} \\\\ \\mathrm{ch}_{2} = 0 \\ell^{2} \\end{array}$"
      ],
      "text/plain": [
       "<pseudowalls.chern_character.Chern_Char object at 0x7f4ae37c8310>"
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u = Chern_Char(1,0,0)\n",
    "u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c711b1ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 5 graphics primitives"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha = stability.Tilt().alpha\n",
    "beta = stability.Tilt().beta\n",
    "\n",
    "mu = stability.Mumford().slope\n",
    "\n",
    "pr = 5\n",
    "\n",
    "coords_range = (beta, -5, 5), (alpha, 0, 5)\n",
    "\n",
    "p = (\n",
    "    implicit_plot(stability.Tilt().degree(u), *coords_range , rgbcolor = \"red\")\n",
    "    + implicit_plot(stability.Tilt().degree(v), *coords_range )\n",
    "    + line([(mu(v),0),(mu(v),5)], linestyle = \"dashed\", legend_label = r\"$(3,2\\ell,-4\\ell^2/2)$\")\n",
    "    + line([(mu(u),0),(mu(u),5)], rgbcolor = \"red\", linestyle = \"dashed\", legend_label = r\"$(1,0,0)$\")\n",
    "    + implicit_plot(stability.Tilt().wall_eqn(u,v)/alpha, *coords_range , rgbcolor = \"black\")\n",
    ")\n",
    "p.xmax(1)\n",
    "p.xmin(-2)\n",
    "p.ymax(1.5)\n",
    "p.axes_labels([r\"$\\beta$\", r\"$\\alpha$\"])\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "2887e82d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 9 graphics primitives"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = Chern_Char(3, 2, -2)\n",
    "\n",
    "p = (\n",
    "    implicit_plot(stability.Tilt().degree(v), *coords_range )\n",
    "    + line([(mu(v),0),(mu(v),5)], linestyle = \"dashed\")\n",
    "    + text(r\"$ch_2^{\\alpha, \\beta}(v)=0$\",[3.5, 2], rotation=45, fontsize=\"large\")\n",
    "    + text(r\"$ch_1^{\\alpha, \\beta}(v)=0$\", [0.45, 1.5], rotation=90, fontsize=\"large\")\n",
    "    + text(r\"$ch_2^{\\alpha, \\beta}(v)=0$\", [-2, 2], rotation=-45, fontsize=\"large\")\n",
    "    + text(r\"$\\nu_{\\alpha, \\beta}(v)>0$\", [-3, 1], rgbcolor=\"black\", fontsize=\"large\")\n",
    "    + text(r\"$\\nu_{\\alpha, \\beta}(v)<0$\", [-1, 3], rgbcolor=\"black\", fontsize=\"large\")\n",
    "    + text(r\"$\\nu_{\\alpha, \\beta}(-v)>0$\", [2, 3], rgbcolor=\"black\", fontsize=\"large\")\n",
    "    + text(r\"$\\nu_{\\alpha, \\beta}(-v)<0$\", [4, 1], rgbcolor=\"black\", fontsize=\"large\")\n",
    "    \n",
    ")\n",
    "p.xmax(5)\n",
    "p.xmin(-4)\n",
    "p.ymax(4)\n",
    "p.axes_labels([r\"$\\beta$\", r\"$\\alpha$\"])\n",
    "p.tick_label_color(\"white\")\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "a25ad0e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "Graphics object consisting of 9 graphics primitives"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = Chern_Char(3, 2, 2/3)\n",
    "\n",
    "p = (\n",
    "    implicit_plot(stability.Tilt().degree(v), *coords_range )\n",
    "    + line([(mu(v),0),(mu(v),5)], linestyle = \"dashed\")\n",
    "    + text(r\"$ch_2^{\\alpha, \\beta}(v)=0$\",[3, 1.5], rotation=45)\n",
    "    + text(r\"$ch_1^{\\alpha, \\beta}(v)=0$\", [0.45, 1.5], rotation=90)\n",
    "    + text(r\"$ch_2^{\\alpha, \\beta}(v)=0$\", [-2, 2], rotation=-45)\n",
    "    + text(r\"$\\nu_{\\alpha, \\beta}(v)>0$\", [-3, 1], rgbcolor=\"black\", fontsize=\"large\")\n",
    "    + text(r\"$\\nu_{\\alpha, \\beta}(v)<0$\", [-1, 3], rgbcolor=\"black\", fontsize=\"large\")\n",
    "    + text(r\"$\\nu_{\\alpha, \\beta}(-v)>0$\", [2, 3], rgbcolor=\"black\", fontsize=\"large\")\n",
    "    + text(r\"$\\nu_{\\alpha, \\beta}(-v)<0$\", [4, 1], rgbcolor=\"black\", fontsize=\"large\")\n",
    "    \n",
    ")\n",
    "p.xmax(5)\n",
    "p.xmin(-4)\n",
    "p.ymax(4)\n",
    "p.axes_labels([r\"$\\beta$\", r\"$\\alpha$\"])\n",
    "p.tick_label_color(\"white\")\n",
    "p"
   ]
  }
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