{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%load_ext pycodestyle_magic\n",
    "\n",
    "# display full output, not only last result, except ended with semicolon\n",
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = 'all';\n",
    "from IPython.display import Image, SVG\n",
    "import logging\n",
    "logging.basicConfig(level=logging.INFO)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import path\n",
    "from gaknot import import_sage\n",
    "cs = import_sage('cable_signature', package='gaknot', path=path.module_path)\n",
    "sg = import_sage('signature', package='gaknot', path=path.module_path)\n",
    "m = import_sage('main', package='gaknot', path=path.module_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "m.prove_lemma(verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Other cables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# knot_formula = \"[[k[0], k[1], k[3]],\" + \\\n",
    "#                \" [-k[1], -k[3]],\" + \\\n",
    "#                \" [k[2], k[3]],\" + \\\n",
    "#                \" [-k[0], -k[2], -k[3]]]\"\n",
    "# # q_vector = (3, 5, 7, 13)\n",
    "# q_vector = (3, 5, 7, 11)\n",
    "\n",
    "# template = cs.CableTemplate(knot_formula, q_vector=q_vector, verbose=True)\n",
    "# cable = template.cable\n",
    "# # cable.plot_all_summands()\n",
    "# cable.is_function_big_for_all_metabolizers(invariant=cs.SIGMA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cables with 8 direct summands "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "formula_1 = \"[[k[0], k[5], k[3]], \" + \\\n",
    "                  \"[-k[1], -k[3]], \" + \\\n",
    "                   \"[k[2], k[3]], \" + \\\n",
    "           \"[-k[0], -k[2], -k[3]]]\"\n",
    "formula_2 = \"[[k[4], k[1], k[7]], \" + \\\n",
    "                  \"[-k[5], -k[7]], \" + \\\n",
    "                   \"[k[6], k[7]], \" + \\\n",
    "           \"[-k[4], -k[6], -k[7]]]\"\n",
    "\n",
    "\n",
    "\n",
    "# cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n",
    "# cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n",
    "# cable_template = cable_template_1 + cable_template_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# cable_template.knot_formula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Relatively small cables "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# q_vector = (5, 13, 19, 41,\\\n",
    "#             7, 17, 23, 43)\n",
    "# cable_template.fill_q_vector(q_vector=q_vector)\n",
    "# cable = cable_template.cable\n",
    "# print(cable.knot_description)\n",
    "\n",
    "# q_vector_small = (3, 7, 13, 19,\\\n",
    "#                   5, 11, 17, 23)\n",
    "# cable_template.fill_q_vector(q_vector=q_vector)\n",
    "# cable = cable_template.cable\n",
    "# print(cable.knot_description)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# cable.is_signature_big_for_all_metabolizers()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Slice candidate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# cable_template.fill_q_vector()\n",
    "# # print(cable_template.q_vector)\n",
    "# # print(cable_template.knot_formula)\n",
    "\n",
    "# slice_canidate = cable_template.cable\n",
    "# print(slice_canidate.knot_description)\n",
    "# sf = slice_canidate(4,4,4,4,0,0,0,0)\n",
    "# sf = slice_canidate(4,1,1,4,0,0,0,0)\n",
    "\n",
    "\n",
    "# cable.is_signature_big_for_all_metabolizers()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "# knot_formula = \"[[k[0], k[1], k[4]], [-k[1], -k[3]],\\\n",
    "#                  [k[2], k[3]], [-k[0], -k[2], -k[4]]]\"\n",
    "\n",
    "# knot_formula = \"[[k[3]], [-k[3]],\\\n",
    "#                 [k[3]], [-k[3]] ]\"\n",
    "\n",
    "# knot_formula = \"[[k[3], k[2], k[0]], [-k[2], -k[0]],\\\n",
    "#                  [k[1], k[0]], [-k[3], -k[1], -k[0]]]\"\n",
    "\n",
    "# knot_formula = \"[[k[0], k[1], k[2]], [k[3], k[4]],\\\n",
    "#                  [-k[0], -k[3], -k[4]], [-k[1], -k[2]]]\"\n",
    "\n",
    "# knot_formula = \"[[k[0], k[1], k[2]], [k[3]],\\\n",
    "#                  [-k[0], -k[1], -k[3]], [-k[2]]]\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "formula_1 = \"[[k[0], k[5], k[3]], \" + \\\n",
    "                  \"[-k[1], -k[3]], \" + \\\n",
    "                   \"[k[2], k[3]], \" + \\\n",
    "           \"[-k[0], -k[2], -k[3]]]\"\n",
    "formula_2 = \"[[k[4], k[1], k[7]], \" + \\\n",
    "                  \"[-k[5], -k[7]], \" + \\\n",
    "                   \"[k[6], k[7]], \" + \\\n",
    "           \"[-k[4], -k[6], -k[7]]]\"\n",
    "\n",
    "\n",
    "\n",
    "# cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n",
    "# cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n",
    "# cable_template = cable_template_1 + cable_template_2\n",
    "\n",
    "# cable_template.fill_q_vector()\n",
    "# # print(cable_template.q_vector)\n",
    "# # print(cable_template.knot_formula)\n",
    "\n",
    "# slice_canidate = cable_template.cable\n",
    "# print(slice_canidate.knot_description)\n",
    "# sf = slice_canidate(4,4,4,4,0,0,0,0)\n",
    "# sf = slice_canidate(4,1,1,4,0,0,0,0)\n",
    "\n",
    "\n",
    "# slice_canidate.q_order\n",
    "# # slice_canidate.is_signature_big_for_all_metabolizers()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "formula_1 = \"[[k[0], k[5], k[3]], \" + \\\n",
    "                  \"[-k[5], -k[3]], \" + \\\n",
    "                   \"[k[2], k[3]], \" + \\\n",
    "            \"[-k[4], -k[2], -k[3]]]\"\n",
    "formula_2 = \"[[k[4], k[1], k[7]], \" + \\\n",
    "                  \"[-k[1], -k[7]], \" + \\\n",
    "                   \"[k[6], k[7]], \" + \\\n",
    "            \"[-k[0], -k[6], -k[7]]]\"\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n",
    "# cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n",
    "# cable_template = cable_template_1 + cable_template_2\n",
    "# cable_template.fill_q_vector()\n",
    "\n",
    "# slice_canidate = cable_template.cable\n",
    "# print(slice_canidate.knot_description)\n",
    "\n",
    "# slice_canidate.q_order\n",
    "# # slice_canidate.is_signature_big_for_all_metabolizers()\n",
    "# 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, 9, 9, 9, 0,0,0,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "formula_1 = \"[[k[0], k[5], k[3]], \" + \\\n",
    "                  \"[-k[1], -k[3]], \" + \\\n",
    "                         \"[ k[3]], \" + \\\n",
    "            \"[-k[4], -k[6], -k[3]]]\"\n",
    "\n",
    "formula_2 = \"[[k[4], k[1], k[7]], \" + \\\n",
    "                       \"[ -k[7]], \" + \\\n",
    "                   \"[k[6], k[7]], \" + \\\n",
    "            \"[-k[0], -k[5], -k[7]]]\"\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n",
    "# cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n",
    "# cable_template = cable_template_1 + cable_template_2\n",
    "\n",
    "# cable_template.fill_q_vector()\n",
    "# # print(cable_template.q_vector)\n",
    "# # print(cable_template.knot_formula)\n",
    "\n",
    "# slice_canidate = cable_template.cable\n",
    "# print(slice_canidate.knot_description)\n",
    "# sf = slice_canidate(4,4,4,4,0,0,0,0)\n",
    "# sf = slice_canidate(4,1,1,4,0,0,0,0)\n",
    "# slice_canidate.is_signature_big_for_all_metabolizers()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "formula_1 = \"       [ [k[5],  k[3]], \" + \\\n",
    "            \"       [ -k[1], -k[3]], \" + \\\n",
    "                   \"       [  k[3]], \" + \\\n",
    "            \"[-k[4],  -k[6], -k[3]]]\"\n",
    "\n",
    "formula_2 = \"[[k[4],   k[1],  k[7]], \" + \\\n",
    "                       \"[    -k[7]], \" + \\\n",
    "                     \"[k[6],  k[7]], \" + \\\n",
    "                    \"[-k[5], -k[7]]]\"\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n",
    "# cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n",
    "# cable_template = cable_template_1 + cable_template_2\n",
    "\n",
    "# cable_template.fill_q_vector()\n",
    "# # print(cable_template.q_vector)\n",
    "# # print(cable_template.knot_formula)\n",
    "\n",
    "# slice_canidate = cable_template.cable\n",
    "# print(slice_canidate.knot_description)\n",
    "# sf = slice_canidate(4,4,4,4,0,0,0,0)\n",
    "# sf = slice_canidate(4,1,1,4,0,0,0,0)\n",
    "# slice_canidate.q_order\n",
    "# # slice_canidate.is_signature_big_for_all_metabolizers()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sf = slice_canidate()\n",
    "# sf = sf[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sf.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "formula_1 = \"[ [k[5],  k[3]], \" + \\\n",
    "            \"[ -k[1], -k[3]], \" + \\\n",
    "            \"[         k[3]], \" + \\\n",
    "            \"[ -k[6], -k[3]]]\"\n",
    "\n",
    "formula_2 = \"[[ k[1],   k[7]], \" + \\\n",
    "             \"[        -k[7]], \" + \\\n",
    "             \"[  k[6],  k[7]], \" + \\\n",
    "             \"[ -k[5], -k[7]]]\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n",
    "# cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n",
    "# cable_template = cable_template_1 + cable_template_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# cable_template.knot_formula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# cable_template.fill_q_vector()\n",
    "# print(cable_template.q_vector)\n",
    "# print(cable_template.knot_formula)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# cable_template.fill_q_vector()\n",
    "# print(cable_template.q_vector)\n",
    "# print(cable_template.knot_formula)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# slice_canidate = cable_template.cable\n",
    "# print(slice_canidate.knot_description)\n",
    "# sf = slice_canidate(4,4,4,4,0,0,0,0)\n",
    "# sf = slice_canidate(4,1,1,4,0,0,0,0)\n",
    "# slice_canidate.q_order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# slice_canidate.is_sigma_big_for_all_metabolizers()\n",
    "# slice_canidate.is_signature_big_for_all_metabolizers()\n",
    "# slice_canidate.is_function_big_for_all_metabolizers()"
   ]
  },
  {
   "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": []
  }
 ],
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