add jupyter notebook
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"%matplotlib inline\n",
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"%load_ext pycodestyle_magic\n",
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"\n",
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"\n",
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"# display full output, not only last result, except ended with semicolon\n",
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"from IPython.core.interactiveshell import InteractiveShell\n",
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"InteractiveShell.ast_node_interactivity = 'all';\n",
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"from IPython.display import Image, SVG\n",
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"\n",
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"\n",
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"# magic functions that do not work in current ipython --version\n",
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"# \n",
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"# auto check each cell, E703 - \"statement ends with a semicolon\"\n",
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"# %flake8_on --ignore E703\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"import importlib\n",
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"\n",
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"def import_sage(module_name):\n",
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" \n",
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" importlib.invalidate_caches() \n",
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" sage_name = module_name + \".sage\"\n",
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" python_name = module_name + \".sage.py\"\n",
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"\n",
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" if os.path.isfile(sage_name):\n",
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" os.system('sage --preparse {}'.format(sage_name));\n",
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" os.system('mv {} {}.py'.format(python_name, module_name))\n",
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" if module_name in sys.modules:\n",
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" return importlib.reload(sys.modules[module_name]) \n",
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" return importlib.import_module(module_name, package=None)\n",
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"\n",
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"cs = import_sage('cable_signature')\n",
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"# sig = import_sage('signature')"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Cables with 8 direct summands "
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"formula_1 = \"[[k[0], k[5], k[3]], \" + \\\n",
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" \"[-k[1], -k[3]], \" + \\\n",
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" \"[k[2], k[3]], \" + \\\n",
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" \"[-k[0], -k[2], -k[3]]]\"\n",
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"formula_2 = \"[[k[4], k[1], k[7]], \" + \\\n",
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" \"[-k[5], -k[7]], \" + \\\n",
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" \"[k[6], k[7]], \" + \\\n",
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" \"[-k[4], -k[6], -k[7]]]\"\n",
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"\n",
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"\n",
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"\n",
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"cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n",
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"cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n",
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"cable_template = cable_template_1 + cable_template_2"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Relatively small cables "
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"q_vector = (5, 13, 19, 41,\\\n",
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" 7, 17, 23, 43)\n",
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"cable_template.fill_q_vector(q_vector=q_vector)\n",
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"cable = cable_template.cable\n",
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"print(cable.knot_description)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"scrolled": true
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},
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"outputs": [],
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"source": [
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"# cable.is_signature_big_for_all_metabolizers()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"q_vector_small = (3, 7, 13, 19,\\\n",
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" 5, 11, 17, 23)\n",
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"cable_template.fill_q_vector(q_vector=q_vector)\n",
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"cable = cable_template.cable\n",
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"print(cable.knot_description)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# cable.is_signature_big_for_all_metabolizers()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Slice candidate"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"\n",
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"cable_template.fill_q_vector()\n",
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"# print(cable_template.q_vector)\n",
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"# print(cable_template.knot_formula)\n",
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"\n",
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"slice_canidate = cable_template.cable\n",
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"print(slice_canidate.knot_description)\n",
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"sf = slice_canidate(4,4,4,4,0,0,0,0)\n",
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"sf = slice_canidate(4,1,1,4,0,0,0,0)\n",
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"\n",
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"\n",
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"# cable.is_signature_big_for_all_metabolizers()\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Other cables"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"\n",
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"\n",
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"# knot_formula = \"[[k[0], k[1], k[4]], [-k[1], -k[3]],\\\n",
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"# [k[2], k[3]], [-k[0], -k[2], -k[4]]]\"\n",
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"\n",
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"# knot_formula = \"[[k[3]], [-k[3]],\\\n",
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"# [k[3]], [-k[3]] ]\"\n",
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"\n",
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"# knot_formula = \"[[k[3], k[2], k[0]], [-k[2], -k[0]],\\\n",
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"# [k[1], k[0]], [-k[3], -k[1], -k[0]]]\"\n",
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"\n",
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"# knot_formula = \"[[k[0], k[1], k[2]], [k[3], k[4]],\\\n",
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"# [-k[0], -k[3], -k[4]], [-k[1], -k[2]]]\"\n",
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"\n",
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"# knot_formula = \"[[k[0], k[1], k[2]], [k[3]],\\\n",
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"# [-k[0], -k[1], -k[3]], [-k[2]]]\""
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"scrolled": true
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},
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"outputs": [],
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"source": [
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"knot_formula = \"[[k[0], k[1], k[3]],\" + \\\n",
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" \" [-k[1], -k[3]],\" + \\\n",
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" \" [k[2], k[3]],\" + \\\n",
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" \" [-k[0], -k[2], -k[3]]]\"\n",
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"# q_vector = (3, 5, 7, 13)\n",
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"q_vector = (3, 5, 7, 11)\n",
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"\n",
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"template = cs.CableTemplate(knot_formula, q_vector=q_vector)\n",
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"cable = template.cable\n",
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"cable.plot_all_summands()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"cable.plot_sum_for_theta_vector([0,4,0,4], save_to_dir=True)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"formula_1 = \"[[k[0], k[5], k[3]], \" + \\\n",
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" \"[-k[1], -k[3]], \" + \\\n",
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" \"[k[2], k[3]], \" + \\\n",
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" \"[-k[0], -k[2], -k[3]]]\"\n",
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"formula_2 = \"[[k[4], k[1], k[7]], \" + \\\n",
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" \"[-k[5], -k[7]], \" + \\\n",
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" \"[k[6], k[7]], \" + \\\n",
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" \"[-k[4], -k[6], -k[7]]]\"\n",
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"\n",
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"\n",
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"\n",
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"cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n",
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"cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n",
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"cable_template = cable_template_1 + cable_template_2\n",
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"\n",
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"cable_template.fill_q_vector()\n",
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"# print(cable_template.q_vector)\n",
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"# print(cable_template.knot_formula)\n",
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"\n",
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"slice_canidate = cable_template.cable\n",
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"print(slice_canidate.knot_description)\n",
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"sf = slice_canidate(4,4,4,4,0,0,0,0)\n",
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"sf = slice_canidate(4,1,1,4,0,0,0,0)\n",
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"\n",
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"\n",
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"slice_canidate.q_order\n",
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"# slice_canidate.is_signature_big_for_all_metabolizers()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"formula_1 = \"[[k[0], k[5], k[3]], \" + \\\n",
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" \"[-k[5], -k[3]], \" + \\\n",
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" \"[k[2], k[3]], \" + \\\n",
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" \"[-k[4], -k[2], -k[3]]]\"\n",
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"formula_2 = \"[[k[4], k[1], k[7]], \" + \\\n",
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" \"[-k[1], -k[7]], \" + \\\n",
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" \"[k[6], k[7]], \" + \\\n",
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" \"[-k[0], -k[6], -k[7]]]\"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n",
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"cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n",
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"cable_template = cable_template_1 + cable_template_2\n",
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"cable_template.fill_q_vector()\n",
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"\n",
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"slice_canidate = cable_template.cable\n",
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"print(slice_canidate.knot_description)\n",
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"\n",
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"slice_canidate.q_order\n",
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"slice_canidate.is_signature_big_for_all_metabolizers()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"\n",
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"\n",
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"\n",
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"\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"scrolled": false
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},
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"outputs": [],
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"source": [
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"formula_1 = \"[[k[0], k[5], k[3]], \" + \\\n",
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" \"[-k[5], -k[3]], \" + \\\n",
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" \"[k[2], k[3]], \" + \\\n",
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" \"[-k[4], -k[6], -k[3]]]\"\n",
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"formula_2 = \"[[k[4], k[1], k[7]], \" + \\\n",
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" \"[-k[1], -k[7]], \" + \\\n",
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" \"[k[6], k[7]], \" + \\\n",
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" \"[-k[0], -k[2], -k[7]]]\"\n",
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"\n",
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"\n",
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"\n",
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"\n",
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"cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n",
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"cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n",
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"cable_template = cable_template_1 + cable_template_2\n",
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"\n",
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"cable_template.fill_q_vector()\n",
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"# print(cable_template.q_vector)\n",
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"# print(cable_template.knot_formula)\n",
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"\n",
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"slice_canidate = cable_template.cable\n",
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"print(slice_canidate.knot_description)\n",
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"sf = slice_canidate(4,4,4,4,0,0,0,0)\n",
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"sf = slice_canidate(4,1,1,4,0,0,0,0)\n",
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"slice_canidate.q_order\n",
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"# slice_canidate.is_signature_big_for_all_metabolizers()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "SageMath 9.0",
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"language": "sage",
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"name": "sagemath"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 4
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}
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