581 lines
15 KiB
Plaintext
581 lines
15 KiB
Plaintext
{
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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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"# 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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"import logging\n",
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"logging.basicConfig(level=logging.INFO)"
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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 path\n",
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"from gaknot import import_sage\n",
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"cs = import_sage('cable_signature', package='gaknot', path=path.module_path)\n",
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"sg = import_sage('signature', package='gaknot', path=path.module_path)\n",
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"m = import_sage('main', package='gaknot', path=path.module_path)"
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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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"m.prove_lemma(verbose=True)"
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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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"scrolled": false
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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, verbose=True)\n",
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"# cable = template.cable\n",
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"# # cable.plot_all_summands()\n",
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"# cable.is_function_big_for_all_metabolizers(invariant=cs.SIGMA)"
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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": "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_template.knot_formula"
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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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"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)\n",
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"\n",
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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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"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": "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": "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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"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()\n",
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"# sigma = slice_canidate.get_sigma_as_function_of_theta()\n",
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"# # sigma((0, 6, 6, 0, 0,0,0,0))\n",
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"# # 13450/83\n",
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"# sigma((9, 9, 9, 9, 0,0,0,0))"
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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[1], -k[3]], \" + \\\n",
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" \"[ k[3]], \" + \\\n",
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" \"[-k[4], -k[6], -k[3]]]\"\n",
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"\n",
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"formula_2 = \"[[k[4], k[1], k[7]], \" + \\\n",
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" \"[ -k[7]], \" + \\\n",
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" \"[k[6], k[7]], \" + \\\n",
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" \"[-k[0], -k[5], -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.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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"scrolled": false
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},
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"outputs": [],
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"source": [
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"formula_1 = \" [ [k[5], k[3]], \" + \\\n",
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" \" [ -k[1], -k[3]], \" + \\\n",
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" \" [ k[3]], \" + \\\n",
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" \"[-k[4], -k[6], -k[3]]]\"\n",
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"\n",
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"formula_2 = \"[[k[4], k[1], k[7]], \" + \\\n",
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" \"[ -k[7]], \" + \\\n",
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" \"[k[6], k[7]], \" + \\\n",
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" \"[-k[5], -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()\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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"# sf = slice_canidate()\n",
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"# sf = sf[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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"outputs": [],
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"source": [
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"# sf.plot()"
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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[5], k[3]], \" + \\\n",
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" \"[ -k[1], -k[3]], \" + \\\n",
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" \"[ k[3]], \" + \\\n",
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" \"[ -k[6], -k[3]]]\"\n",
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"\n",
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"formula_2 = \"[[ k[1], k[7]], \" + \\\n",
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" \"[ -k[7]], \" + \\\n",
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" \"[ k[6], k[7]], \" + \\\n",
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" \"[ -k[5], -k[7]]]\""
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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_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": "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_template.knot_formula"
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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_template.fill_q_vector()\n",
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"# print(cable_template.q_vector)\n",
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"# print(cable_template.knot_formula)"
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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_template.fill_q_vector()\n",
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"# print(cable_template.q_vector)\n",
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"# print(cable_template.knot_formula)"
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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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"# 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"
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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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"# slice_canidate.is_sigma_big_for_all_metabolizers()\n",
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"# slice_canidate.is_signature_big_for_all_metabolizers()\n",
|
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"# slice_canidate.is_function_big_for_all_metabolizers()"
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]
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},
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|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"scrolled": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# slice_canidate.is_function_big_for_all_metabolizers(invariant=cs.SIGMA)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"scrolled": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"# slice_canidate.is_function_big_for_all_metabolizers(invariant=cs.SIGNATURE)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# sigma = slice_canidate.get_sigma_as_function_of_theta()\n",
|
|
"# sigma((0, 6, 6, 0, 0,0,0,0))\n",
|
|
"# # 13450/83\n",
|
|
"# sigma((9, 0, 0, 9, 0,0,0,0))"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# _, _, sf = slice_canidate((1, 1, 0, 0, 0,0,0,0))\n",
|
|
"# sf"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# sg.SignaturePloter.plot(sf)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {
|
|
"scrolled": true
|
|
},
|
|
"outputs": [],
|
|
"source": [
|
|
"\n",
|
|
"# slice_canidate.plot_sum_for_theta_vector([0r,4r,0r,4r,0r,0r,0r,0r], save_to_dir=True)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# sf.plot()\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": [
|
|
"# help(cs.CableTemplate.get_q_vector)"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"metadata": {},
|
|
"outputs": [],
|
|
"source": []
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "SageMath 9.0",
|
|
"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": "3.8.10"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 4
|
|
}
|