From a5ae08a800679993a05c0e07d9badbd5ca715db8 Mon Sep 17 00:00:00 2001
From: Luke Naylor <l.naylor@sms.ed.ac.uk>
Date: Fri, 26 May 2023 13:10:49 +0100
Subject: [PATCH] notebook work towards loose bounds graphic
---
plot_playground.ipynb | 154 ++++++++++++++++++++++++++++++++++++++++++
1 file changed, 154 insertions(+)
create mode 100644 plot_playground.ipynb
diff --git a/plot_playground.ipynb b/plot_playground.ipynb
new file mode 100644
index 0000000..36aa023
--- /dev/null
+++ b/plot_playground.ipynb
@@ -0,0 +1,154 @@
+{
+ "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
+}
--
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