Created
March 16, 2021 12:17
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{ | |
"cells": [ | |
{ | |
"cell_type": "code", | |
"execution_count": 38, | |
"id": "verbal-newton", | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"(-1.0998221190617903,\n", | |
" 1.099991529479133,\n", | |
" -1.087778931006891,\n", | |
" 0.8446397060849049)" | |
] | |
}, | |
"execution_count": 38, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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\n", | |
"text/plain": [ | |
"<Figure size 432x288 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"image/png": { | |
"height": 248, | |
"width": 386 | |
}, | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"from clifford import Cl,MVArray\n", | |
"from pylab import * \n", | |
"\n", | |
"\n", | |
"\n", | |
"theta = linspace(0,2,101)\n", | |
"\n", | |
"for ratio in [1,2,.5]:\n", | |
" l, b = Cl(sig=[sqrt(ratio),1/sqrt(ratio)])\n", | |
" locals().update(b)\n", | |
"\n", | |
" z = [e**(x*e12)*e1*~e**(x*e12) for x in theta]\n", | |
" plot ([k[e1] for k in z],\n", | |
" [k[e2] for k in z]label=) \n", | |
"\n", | |
"\n", | |
"\n", | |
"axis('equal')" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": null, | |
"id": "familiar-spray", | |
"metadata": {}, | |
"outputs": [], | |
"source": [] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.7.7" | |
}, | |
"toc": { | |
"nav_menu": {}, | |
"number_sections": true, | |
"sideBar": true, | |
"skip_h1_title": false, | |
"toc_cell": false, | |
"toc_position": {}, | |
"toc_section_display": "block", | |
"toc_window_display": false | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 5 | |
} |
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