signature_function/main.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "%load_ext pycodestyle_magic\n",
    "\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",
    "\n",
    "\n",
    "# magic functions that do not work in current ipython --version\n",
    "# \n",
    "# auto check each cell, E703 - \"statement ends with a semicolon\"\n",
    "# %flake8_on --ignore E703\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import importlib\n",
    "\n",
    "def import_sage(module_name):\n",
    "    \n",
    "    importlib.invalidate_caches() \n",
    "    sage_name = module_name + \".sage\"\n",
    "    python_name = module_name + \".sage.py\"\n",
    "\n",
    "    if os.path.isfile(sage_name):\n",
    "        os.system('sage --preparse {}'.format(sage_name));\n",
    "        os.system('mv {} {}.py'.format(python_name, module_name))\n",
    "    if module_name in sys.modules:\n",
    "        return importlib.reload(sys.modules[module_name])  \n",
    "    return importlib.import_module(module_name, package=None)\n",
    "\n",
    "cs = import_sage('cable_signature')\n",
    "# sig = import_sage('signature')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cables with 8 direct summands "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": "markdown",
   "metadata": {},
   "source": [
    "# Relatively small cables "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T(2, 5; 2, 17; 2, 41) # -T(2, 13; 2, 41) # T(2, 19; 2, 41) # -T(2, 5; 2, 19; 2, 41) # T(2, 7; 2, 13; 2, 43) # -T(2, 17; 2, 43) # T(2, 23; 2, 43) # -T(2, 7; 2, 23; 2, 43)\n"
     ]
    }
   ],
   "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# cable.is_signature_big_for_all_metabolizers()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T(2, 5; 2, 17; 2, 41) # -T(2, 13; 2, 41) # T(2, 19; 2, 41) # -T(2, 5; 2, 19; 2, 41) # T(2, 7; 2, 13; 2, 43) # -T(2, 17; 2, 43) # T(2, 23; 2, 43) # -T(2, 7; 2, 23; 2, 43)\n"
     ]
    }
   ],
   "source": [
    "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": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# cable.is_signature_big_for_all_metabolizers()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Slice candidate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T(2, 5; 2, 71; 2, 347) # -T(2, 67; 2, 347) # T(2, 61; 2, 347) # -T(2, 5; 2, 61; 2, 347) # T(2, 11; 2, 67; 2, 367) # -T(2, 71; 2, 367) # T(2, 79; 2, 367) # -T(2, 11; 2, 79; 2, 367)\n"
     ]
    }
   ],
   "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": "markdown",
   "metadata": {},
   "source": [
    "# Other cables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": 10,
   "metadata": {
    "scrolled": true
   },
   "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)\n",
    "cable = template.cable\n",
    "# cable.plot_all_summands()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T(2, 5; 2, 71; 2, 347) # -T(2, 67; 2, 347) # T(2, 61; 2, 347) # -T(2, 5; 2, 61; 2, 347) # T(2, 11; 2, 67; 2, 367) # -T(2, 71; 2, 367) # T(2, 79; 2, 367) # -T(2, 11; 2, 79; 2, 367)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "127349"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T(2, 11; 2, 53; 2, 347) # -T(2, 53; 2, 347) # T(2, 61; 2, 347) # -T(2, 7; 2, 61; 2, 347) # T(2, 7; 2, 71; 2, 367) # -T(2, 71; 2, 367) # T(2, 79; 2, 367) # -T(2, 11; 2, 79; 2, 367)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "127349"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T(2, 11; 2, 71; 2, 313) # -T(2, 61; 2, 313) # T(2, 313) # -T(2, 7; 2, 67; 2, 313) # T(2, 7; 2, 61; 2, 347) # -T(2, 347) # T(2, 67; 2, 347) # -T(2, 11; 2, 71; 2, 347)\n"
     ]
    }
   ],
   "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": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T(2, 43; 2, 191) # -T(2, 37; 2, 191) # T(2, 191) # -T(2, 5; 2, 41; 2, 191) # T(2, 5; 2, 37; 2, 211) # -T(2, 211) # T(2, 41; 2, 211) # -T(2, 43; 2, 211)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "40301"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "sf = slice_canidate()\n",
    "sf = sf[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sf.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83) # T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "8549"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "**********\n",
      "[0, 0, 1, 1, 0, 0, 0, 0] 2\n",
      "[0, 0, 2, 2, 0, 0, 0, 0] 2\n",
      "[0, 0, 3, 3, 0, 0, 0, 0] 2\n",
      "[0, 0, 4, 4, 0, 0, 0, 0] 6\n",
      "[0, 0, 5, 5, 0, 0, 0, 0] 6\n",
      "[0, 0, 6, 6, 0, 0, 0, 0] 6\n",
      "[0, 0, 7, 7, 0, 0, 0, 0] 8\n",
      "**********\n",
      "[0, 1, 1, 0, 0, 0, 0, 0] 2\n",
      "[0, 2, 2, 0, 0, 0, 0, 0] 2\n",
      "[0, 3, 3, 0, 0, 0, 0, 0] 2\n",
      "[0, 4, 4, 0, 0, 0, 0, 0] 6\n",
      "[0, 5, 5, 0, 0, 0, 0, 0] 6\n",
      "[0, 6, 6, 0, 0, 0, 0, 0] 6\n",
      "[0, 7, 7, 0, 0, 0, 0, 0] 6\n",
      "[0, 8, 8, 0, 0, 0, 0, 0] 8\n",
      "**********\n",
      "[0, 2, 2, 0, 0, 0, 0, 0] 2\n",
      "[0, 4, 4, 0, 0, 0, 0, 0] 6\n",
      "[0, 6, 6, 0, 0, 0, 0, 0] 6\n",
      "[0, 8, 8, 0, 0, 0, 0, 0] 8\n",
      "**********\n",
      "[0, 3, 3, 0, 0, 0, 0, 0] 2\n",
      "[0, 6, 6, 0, 0, 0, 0, 0] 6\n",
      "[0, 9, 9, 0, 0, 0, 0, 0] 8\n",
      "**********\n",
      "[0, 4, 4, 0, 0, 0, 0, 0] -6\n",
      "[0, 8, 8, 0, 0, 0, 0, 0] 8\n",
      "**********\n",
      "[0, 5, 5, 0, 0, 0, 0, 0] -6\n",
      "[0, 10, 10, 0, 0, 0, 0, 0] 8\n",
      "**********\n",
      "[0, 6, 6, 0, 0, 0, 0, 0] -6\n",
      "[0, 12, 12, 0, 0, 0, 0, 0] 10\n",
      "**********\n",
      "[0, 7, 7, 0, 0, 0, 0, 0] -6\n",
      "[0, 14, 14, 0, 0, 0, 0, 0] 10\n",
      "**********\n",
      "[1, 0, 0, 1, 0, 0, 0, 0] 4\n",
      "[2, 0, 0, 2, 0, 0, 0, 0] 4\n",
      "[3, 0, 0, 3, 0, 0, 0, 0] 8\n",
      "**********\n",
      "[1, 1, 0, 0, 0, 0, 0, 0] 4\n",
      "[2, 2, 0, 0, 0, 0, 0, 0] 4\n",
      "[3, 3, 0, 0, 0, 0, 0, 0] 8\n",
      "**********\n",
      "[1, 1, 1, 1, 0, 0, 0, 0] 6\n",
      "[2, 2, 2, 2, 0, 0, 0, 0] 6\n",
      "[3, 3, 3, 3, 0, 0, 0, 0] 10\n",
      "**********\n",
      "[1, 2, 2, 1, 0, 0, 0, 0] 6\n",
      "[2, 4, 4, 2, 0, 0, 0, 0] 10\n",
      "**********\n",
      "[1, 3, 3, 1, 0, 0, 0, 0] 6\n",
      "[2, 6, 6, 2, 0, 0, 0, 0] 10\n",
      "**********\n",
      "[2, 2, 0, 0, 0, 0, 0, 0] 4\n",
      "[4, 4, 0, 0, 0, 0, 0, 0] 4\n",
      "[6, 6, 0, 0, 0, 0, 0, 0] 4\n",
      "[8, 8, 0, 0, 0, 0, 0, 0] 8\n",
      "**********\n",
      "[2, 2, 1, 1, 0, 0, 0, 0] 6\n",
      "[4, 4, 2, 2, 0, 0, 0, 0] 6\n",
      "[6, 6, 3, 3, 0, 0, 0, 0] 6\n",
      "[8, 8, 4, 4, 0, 0, 0, 0] 6\n",
      "[10, 10, 5, 5, 0, 0, 0, 0] 6\n",
      "[12, 12, 6, 6, 0, 0, 0, 0] 8\n",
      "[14, 14, 7, 7, 0, 0, 0, 0] 8\n",
      "[16, 16, 8, 8, 0, 0, 0, 0] 6\n",
      "[18, 18, 9, 9, 0, 0, 0, 0] 10\n",
      "**********\n",
      "[4, 4, 0, 0, 0, 0, 0, 0] 4\n",
      "[8, 8, 0, 0, 0, 0, 0, 0] 8\n",
      "**********\n",
      "[4, 4, 1, 1, 0, 0, 0, 0] 6\n",
      "[8, 8, 2, 2, 0, 0, 0, 0] 8\n",
      "[12, 12, 3, 3, 0, 0, 0, 0] 6\n",
      "[16, 16, 4, 4, 0, 0, 0, 0] 8\n",
      "[20, 20, 5, 5, 0, 0, 0, 0] 8\n",
      "[24, 24, 6, 6, 0, 0, 0, 0] 10\n",
      "**********\n",
      "[5, 5, 0, 0, 0, 0, 0, 0] -4\n",
      "[10, 10, 0, 0, 0, 0, 0, 0] 8\n",
      "**********\n",
      "[5, 5, 1, 1, 0, 0, 0, 0] 4\n",
      "[10, 10, 2, 2, 0, 0, 0, 0] 8\n",
      "[15, 15, 3, 3, 0, 0, 0, 0] 10\n",
      "**********\n",
      "[6, 6, 0, 0, 0, 0, 0, 0] -4\n",
      "[12, 12, 0, 0, 0, 0, 0, 0] 4\n",
      "[18, 18, 0, 0, 0, 0, 0, 0] 8\n",
      "**********\n",
      "[6, 6, 1, 1, 0, 0, 0, 0] -4\n",
      "[12, 12, 2, 2, 0, 0, 0, 0] 6\n",
      "[18, 18, 3, 3, 0, 0, 0, 0] 10\n",
      "**********\n",
      "[7, 7, 0, 0, 0, 0, 0, 0] -4\n",
      "[14, 14, 0, 0, 0, 0, 0, 0] 8\n",
      "**********\n",
      "[7, 7, 1, 1, 0, 0, 0, 0] -6\n",
      "[14, 14, 2, 2, 0, 0, 0, 0] 10\n",
      "**********\n",
      "[8, 8, 1, 1, 0, 0, 0, 0] 8\n",
      "[16, 16, 2, 2, 0, 0, 0, 0] 10\n",
      "**********\n",
      "[12, 12, 0, 0, 0, 0, 0, 0] -4\n",
      "[24, 24, 0, 0, 0, 0, 0, 0] 8\n",
      "**********\n",
      "[12, 12, 1, 1, 0, 0, 0, 0] -6\n",
      "[24, 24, 2, 2, 0, 0, 0, 0] 10\n",
      "**********\n",
      "[26, 29, 0, 1, 0, 0, 0, 0] -8\n",
      "[52, 58, 0, 2, 0, 0, 0, 0] 10\n",
      "\n",
      "OK\n",
      "**********\n",
      "[0, 0, 0, 0, 0, 0, 1, 1] -4\n",
      "[0, 0, 0, 0, 0, 0, 2, 2] 4\n",
      "[0, 0, 0, 0, 0, 0, 3, 3] 4\n",
      "[0, 0, 0, 0, 0, 0, 4, 4] 4\n",
      "[0, 0, 0, 0, 0, 0, 5, 5] 4\n",
      "[0, 0, 0, 0, 0, 0, 6, 6] 4\n",
      "[0, 0, 0, 0, 0, 0, 7, 7] 4\n",
      "[0, 0, 0, 0, 0, 0, 8, 8] 4\n",
      "[0, 0, 0, 0, 0, 0, 9, 9] 4\n",
      "[0, 0, 0, 0, 0, 0, 10, 10] 8\n",
      "**********\n",
      "[0, 0, 0, 0, 0, 1, 1, 0] -2\n",
      "[0, 0, 0, 0, 0, 2, 2, 0] 2\n",
      "[0, 0, 0, 0, 0, 3, 3, 0] 2\n",
      "[0, 0, 0, 0, 0, 4, 4, 0] 6\n",
      "[0, 0, 0, 0, 0, 5, 5, 0] 6\n",
      "[0, 0, 0, 0, 0, 6, 6, 0] 6\n",
      "[0, 0, 0, 0, 0, 7, 7, 0] 6\n",
      "[0, 0, 0, 0, 0, 8, 8, 0] 8\n",
      "**********\n",
      "[0, 0, 0, 0, 0, 2, 2, 0] -2\n",
      "[0, 0, 0, 0, 0, 4, 4, 0] 6\n",
      "[0, 0, 0, 0, 0, 6, 6, 0] 6\n",
      "[0, 0, 0, 0, 0, 8, 8, 0] 8\n",
      "**********\n",
      "[0, 0, 0, 0, 0, 3, 3, 0] -2\n",
      "[0, 0, 0, 0, 0, 6, 6, 0] 6\n",
      "[0, 0, 0, 0, 0, 9, 9, 0] 8\n",
      "**********\n",
      "[0, 0, 0, 0, 0, 4, 4, 0] 6\n",
      "[0, 0, 0, 0, 0, 8, 8, 0] 8\n",
      "**********\n",
      "[0, 0, 0, 0, 0, 5, 5, 0] 6\n",
      "[0, 0, 0, 0, 0, 10, 10, 0] 8\n",
      "**********\n",
      "[0, 0, 0, 0, 0, 6, 6, 0] 6\n",
      "[0, 0, 0, 0, 0, 12, 12, 0] 10\n",
      "**********\n",
      "[0, 0, 0, 0, 0, 7, 7, 0] 6\n",
      "[0, 0, 0, 0, 0, 14, 14, 0] 10\n",
      "**********\n",
      "[0, 0, 0, 0, 0, 23, 18, 1] 8\n",
      "[0, 0, 0, 0, 0, 46, 36, 2] 10\n",
      "**********\n",
      "[0, 0, 0, 0, 1, 0, 0, 1] -4\n",
      "[0, 0, 0, 0, 2, 0, 0, 2] 4\n",
      "[0, 0, 0, 0, 3, 0, 0, 3] 4\n",
      "[0, 0, 0, 0, 4, 0, 0, 4] 8\n",
      "**********\n",
      "[0, 0, 0, 0, 1, 1, 0, 0] -2\n",
      "[0, 0, 0, 0, 2, 2, 0, 0] 2\n",
      "[0, 0, 0, 0, 3, 3, 0, 0] 2\n",
      "[0, 0, 0, 0, 4, 4, 0, 0] 2\n",
      "[0, 0, 0, 0, 5, 5, 0, 0] 6\n",
      "[0, 0, 0, 0, 6, 6, 0, 0] 6\n",
      "[0, 0, 0, 0, 7, 7, 0, 0] 6\n",
      "[0, 0, 0, 0, 8, 8, 0, 0] 6\n",
      "[0, 0, 0, 0, 9, 9, 0, 0] 6\n",
      "[0, 0, 0, 0, 10, 10, 0, 0] 8\n",
      "**********\n",
      "[0, 0, 0, 0, 1, 1, 1, 1] -6\n",
      "[0, 0, 0, 0, 2, 2, 2, 2] 6\n",
      "[0, 0, 0, 0, 3, 3, 3, 3] 6\n",
      "[0, 0, 0, 0, 4, 4, 4, 4] 6\n",
      "[0, 0, 0, 0, 5, 5, 5, 5] 10\n",
      "**********\n",
      "[0, 0, 0, 0, 1, 2, 2, 1] -6\n",
      "[0, 0, 0, 0, 2, 4, 4, 2] 10\n",
      "**********\n",
      "[0, 0, 0, 0, 1, 3, 3, 1] -6\n",
      "[0, 0, 0, 0, 2, 6, 6, 2] 10\n",
      "**********\n",
      "[0, 0, 0, 0, 1, 6, 6, 1] 8\n",
      "[0, 0, 0, 0, 2, 12, 12, 2] 10\n",
      "**********\n",
      "[0, 0, 0, 0, 1, 7, 7, 1] 8\n",
      "[0, 0, 0, 0, 2, 14, 14, 2] 10\n",
      "**********\n",
      "[0, 0, 0, 0, 1, 8, 8, 1] 8\n",
      "[0, 0, 0, 0, 2, 16, 16, 2] 12\n",
      "**********\n",
      "[0, 0, 0, 0, 1, 15, 11, 0] 6\n",
      "[0, 0, 0, 0, 2, 30, 22, 0] 10\n",
      "**********\n",
      "[0, 0, 0, 0, 2, 2, 0, 0] -2\n",
      "[0, 0, 0, 0, 4, 4, 0, 0] 2\n",
      "[0, 0, 0, 0, 6, 6, 0, 0] 6\n",
      "[0, 0, 0, 0, 8, 8, 0, 0] 6\n",
      "[0, 0, 0, 0, 10, 10, 0, 0] 8\n",
      "**********\n",
      "[0, 0, 0, 0, 2, 2, 1, 1] -6\n",
      "[0, 0, 0, 0, 4, 4, 2, 2] 6\n",
      "[0, 0, 0, 0, 6, 6, 3, 3] 10\n",
      "**********\n",
      "[0, 0, 0, 0, 3, 3, 0, 0] -2\n",
      "[0, 0, 0, 0, 6, 6, 0, 0] 6\n",
      "[0, 0, 0, 0, 9, 9, 0, 0] 6\n",
      "[0, 0, 0, 0, 12, 12, 0, 0] 8\n",
      "**********\n",
      "[0, 0, 0, 0, 3, 3, 1, 1] -6\n",
      "[0, 0, 0, 0, 6, 6, 2, 2] 10\n",
      "**********\n",
      "[0, 0, 0, 0, 4, 4, 0, 0] -2\n",
      "[0, 0, 0, 0, 8, 8, 0, 0] 6\n",
      "[0, 0, 0, 0, 12, 12, 0, 0] 8\n",
      "**********\n",
      "[0, 0, 0, 0, 4, 4, 1, 1] -6\n",
      "[0, 0, 0, 0, 8, 8, 2, 2] 10\n",
      "**********\n",
      "[0, 0, 0, 0, 5, 5, 0, 0] 6\n",
      "[0, 0, 0, 0, 10, 10, 0, 0] 8\n",
      "**********\n",
      "[0, 0, 0, 0, 6, 6, 0, 0] 6\n",
      "[0, 0, 0, 0, 12, 12, 0, 0] 8\n",
      "**********\n",
      "[0, 0, 0, 0, 7, 7, 0, 0] 6\n",
      "[0, 0, 0, 0, 14, 14, 0, 0] 8\n",
      "**********\n",
      "[0, 0, 0, 0, 8, 8, 0, 0] 6\n",
      "[0, 0, 0, 0, 16, 16, 0, 0] 10\n",
      "**********\n",
      "[0, 0, 0, 0, 9, 9, 0, 0] 6\n",
      "[0, 0, 0, 0, 18, 18, 0, 0] 10\n",
      "**********\n",
      "[0, 0, 0, 0, 11, 15, 1, 0] 6\n",
      "[0, 0, 0, 0, 22, 30, 2, 0] 10\n",
      "\n",
      "OK\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "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]]]\"\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()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "_, _, sf = slice_canidate((1, 1, 0, 0, 0,0,0,0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T_17_83_inv_T_11_83_T_83_inv_T_13_83_T_11_103_inv_T_103_T_13_103_inv_T_17_103\n"
     ]
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 720x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 720x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 720x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 720x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 720x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 720x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 720x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 720x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 720x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 8 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'T_17_83_inv_T_11_83_T_83_inv_T_13_83_T_11_103_inv_T_103_T_13_103_inv_T_17_103'"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "slice_canidate.plot_sum_for_theta_vector([0,4,0,4,0,0,0,0], save_to_dir=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sf.plot()\n"
   ]
  },
  {
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}