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{
"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
}