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pageman/liee80.ipynb

Created February 24, 2025 16:15
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liee80.ipynb
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"metadata": {
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"provenance": [],
"authorship_tag": "ABX9TyOdSIOoI02jNKfsjxyKmvwa",
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},
"kernelspec": {
"name": "python3",
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"cells": [
{
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"source": [
"<a href=\"https://colab.research.google.com/gist/pageman/13f93d489d106f4b34cb8013ebfab795/liee80.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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{
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"height": 596
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"id": "AZUK9w9duYIs",
"outputId": "eb4b7f6b-dfe3-41ba-dd7c-ee016c57c2a0"
},
"outputs": [
{
"output_type": "stream",
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"text": [
"Requirement already satisfied: plotly in /usr/local/lib/python3.11/dist-packages (5.24.1)\n",
"Requirement already satisfied: tenacity>=6.2.0 in /usr/local/lib/python3.11/dist-packages (from plotly) (9.0.0)\n",
"Requirement already satisfied: packaging in /usr/local/lib/python3.11/dist-packages (from plotly) (24.2)\n"
]
},
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" \n",
"var gd = document.getElementById('d8ec61ec-f440-473c-868f-1d8801084abc');\n",
"var x = new MutationObserver(function (mutations, observer) {{\n",
" var display = window.getComputedStyle(gd).display;\n",
" if (!display || display === 'none') {{\n",
" console.log([gd, 'removed!']);\n",
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" observer.disconnect();\n",
" }}\n",
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" }) }; </script> </div>\n",
"</body>\n",
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]
},
"metadata": {}
}
],
"source": [
"# Step 1: Install required libraries\n",
"!pip install plotly\n",
"\n",
"# Step 2: Import necessary libraries\n",
"import numpy as np\n",
"import plotly.graph_objects as go\n",
"\n",
"# Step 3: Generate the E8 root system\n",
"def generate_e8_roots():\n",
" roots = []\n",
" # Generate all permutations of ±1 with an even number of -1s\n",
" for i in range(2**8):\n",
" binary = [(-1)**int(x) for x in format(i, '08b')]\n",
" if sum(1 for x in binary if x == -1) % 2 == 0:\n",
" roots.append(binary)\n",
"\n",
" # Add permutations of ±2 with one non-zero entry\n",
" for i in range(8):\n",
" for sign in [-2, 2]:\n",
" root = [0] * 8\n",
" root[i] = sign\n",
" roots.append(root)\n",
"\n",
" return np.array(roots)\n",
"\n",
"# Step 4: Project 8D roots into 3D using a random projection matrix\n",
"def project_to_3d(roots):\n",
" projection_matrix = np.random.randn(8, 3)\n",
" projected_roots = np.dot(roots, projection_matrix)\n",
" return projected_roots\n",
"\n",
"# Step 5: Generate and project the E8 roots\n",
"e8_roots = generate_e8_roots()\n",
"projected_roots = project_to_3d(e8_roots)\n",
"\n",
"# Step 6: Create an interactive 3D plot using Plotly\n",
"fig = go.Figure(data=[go.Scatter3d(\n",
" x=projected_roots[:, 0],\n",
" y=projected_roots[:, 1],\n",
" z=projected_roots[:, 2],\n",
" mode='markers',\n",
" marker=dict(\n",
" size=3,\n",
" color=np.linalg.norm(projected_roots, axis=1), # Color by magnitude\n",
" colorscale='Viridis',\n",
" opacity=0.8\n",
" )\n",
")])\n",
"\n",
"# Update layout for better visualization\n",
"fig.update_layout(\n",
" title=\"Interactive 3D Visualization of E8 Root System\",\n",
" scene=dict(\n",
" xaxis_title='X',\n",
" yaxis_title='Y',\n",
" zaxis_title='Z'\n",
" ),\n",
" margin=dict(l=0, r=0, b=0, t=40)\n",
")\n",
"\n",
"# Step 7: Show the figure\n",
"fig.show()"
]
}
]
}
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