demo1_root_structures.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Demo 1: Search for 2pc-equivalent root structures\n",
    "\n",
    "* Author: Mauricio Fernández\n",
    "* Last update: 2020-06-17\n",
    "\n",
    "Table of contents\n",
    "\n",
    "* [1. Examples in 1D](#1.-Examples-in-1D)\n",
    "* [2. Examples in 2D](#2.-Examples-in-2D)\n",
    "* [3. Example in 3D](#3.-Example-in-3D)\n",
    "* [4. Save and load root structures](#4.-Save-and-load-root-structures)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Description\n",
    "The present notebook demonstrates how 2pc-equivalent root structures with 2 and 3 phases can be searched for in 1D, 2D and 3D. At the end of the notebook, found root structures are saved for future generation of 2pc-equivalent child structures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import src.eq2pc as e2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Examples in 1D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a 1D-structure with 12 positions and 5 events in phase 1 (and 12-5=7 events in phase 2), search for existing 2pc-equivalent structure sets. Set `info=True` for more information on current computation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "...Generating indicator arrays\n",
      "...Computing correlations\n",
      "...Searching for cases\n",
      "...Number of structure sets: 1\n",
      "[array([[1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2],\n",
      "       [1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2]])]\n"
     ]
    }
   ],
   "source": [
    "sets = e2.Ceq_search([12], [5], info=False)\n",
    "print(sets)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extract structures and visualize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S1 = sets[0][0]\n",
    "S2 = sets[0][1]\n",
    "e2.plot_S(S1)\n",
    "e2.plot_S(S2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Are the structures related by translation, reflection or phase inversion?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e2.rel(S1,S2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Are the structures 2pc-equivalent?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e2.Ceq(S1,S2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a 1D-structure with 12 positions with (2,3,12-2-3) events for phases 1,2,3 search for existing 2pc-equivalent structure sets and visualize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "...Generating indicator arrays\n",
      "...Computing correlations\n",
      "...Searching for cases\n",
      "...Number of structure sets: 1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAxsAAAB+CAYAAABMDwy9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+j8jraAAAK1klEQVR4nO3dXYhV5RoH8GdyZ+dQmoQzNTWKiZHbmWq+ygKJTCYtxMARUSbQVAaii0K66KropiSQtA+CQELsHIVuMvqYC5UILJE5TsVgiZADziQ1g0r5hTrtc3E4gsePRs96Z223vx94sRcve/31YQ/z3+tdy6pSqVQKAACAjN2QdwAAAKAyKRsAAEASygYAAJCEsgEAACShbAAAAEkoGwAAQBKFvAMAAACjb968eTE0NHTesYkTJ0ZXV1dm51A2AADgOjQ0NBTd3d3nHWttbc30HLZRAQAASSgbAABAEsoGAACQhLIBAAAkoWwAAABJKBsAAEASygYAAJBEWZeNrq6uuPfee2PatGmxZs2avOOQkYMHD8bs2bOjWCxGfX19rF+/Pu9IZGx4eDiamppi/vz5eUchQ0ePHo1FixbF9OnTo1gsxrfffpt3JDLy1ltvRX19fTQ0NMTSpUvj1KlTeUfiKq1YsSJqamqioaHh3LHDhw9HW1tb3HPPPdHW1hZHjhzJMSHXm7ItG8PDw/H888/Hl19+GXv37o3NmzfH3r17845FBgqFQqxduzZ+/PHH2LVrV7z33ntmW2HWr18fxWIx7xhk7IUXXoh58+bFTz/9FN9//70ZV4iBgYF4++23o7u7O3p7e2N4eDi2bNmSdyyu0vLlyy/435/XrFkTc+bMif3798ecOXN8gcuoKtuysXv37pg2bVpMnTo1xo4dG0uWLImtW7fmHYsM1NbWRnNzc0REjBs3LorFYgwMDOSciqz09/fH559/HqtWrco7Chn6/fff4+uvv46VK1dGRMTYsWNjwoQJOaciK2fPno2TJ0/G2bNn48SJE3HnnXfmHYmr9Oijj8Ztt9123rGtW7fGsmXLIiJi2bJl8cknn+QRjetU2ZaNgYGBmDRp0rnXdXV1fiGtQH19fdHT0xMzZ87MOwoZefHFF+PNN9+MG24o2x8vXIWff/45qqur49lnn42mpqZYtWpVHD9+PO9YZOCuu+6Kl156KSZPnhy1tbVx6623xhNPPJF3LDL066+/Rm1tbUT85wu/3377LedEXE/K9reBUql0wbGqqqockpDKsWPHor29PdatWxfjx4/POw4Z+Oyzz6KmpiZaWlryjkLGzp49G3v27Innnnsuenp64uabb7YVo0IcOXIktm7dGgcOHIhffvkljh8/Hh999FHesYAKUbZlo66uLg4ePHjudX9/v8u6FeTMmTPR3t4eHR0dsXDhwrzjkJGdO3fGp59+GlOmTIklS5bEjh074plnnsk7Fhmoq6uLurq6c1chFy1aFHv27Mk5FVnYtm1b3H333VFdXR033nhjLFy4ML755pu8Y5Gh22+/PQ4dOhQREYcOHYqampqcE3E9Kduy8eCDD8b+/fvjwIEDcfr06diyZUssWLAg71hkoFQqxcqVK6NYLMbq1avzjkOG3njjjejv74++vr7YsmVLPP74474hrRB33HFHTJo0Kfbt2xcREdu3b48ZM2bknIosTJ48OXbt2hUnTpyIUqkU27dvd/N/hVmwYEFs3LgxIiI2btwYTz/9dM6JuJadOnUqHnrooXjggQeivr4+Xn311cuuL4xSritWKBTi3Xffjblz58bw8HCsWLEi6uvr845FBnbu3BmbNm2K++67LxobGyMi4vXXX4+nnnoq52TA5bzzzjvR0dERp0+fjqlTp8aHH36YdyQyMHPmzFi0aFE0NzdHoVCIpqam6OzszDsWV2np0qXx1VdfxdDQUNTV1cVrr70WL7/8cixevDg2bNgQkydPjo8//jjvmFzDbrrpptixY0fccsstcebMmZg1a1Y8+eST8fDDD190fVXpYjdHAAAAFa21tTW6u7v/8tilnDhxImbNmhXvv//+JR/2U7bbqAAAgPIzPDwcjY2NUVNTE21tbZd9qqiyAQAARETE4OBgtLa2nvvzwQcfXLBmzJgx8d1330V/f3/s3r07ent7L/l+ZXvPBgAAMLqqq6tHvI1qwoQJ8dhjj0VXV1c0NDRcdI0rGwAAwIgMDg7G0aNHIyLi5MmTsW3btpg+ffol17uyAQAAjMihQ4di2bJlMTw8HH/++WcsXrw45s+ff8n1ZX9l42L7xKgc5lu5zLZymW3lMtvKZbZk5f7774+enp744Ycfore3N1555ZXLrlc2yJX5Vi6zrVxmW7nMtnKZLXkp+7IBAABcm67ono2qqqpRbyeliBhTVTXKZ/2PpttyOW0+7m7J5bT/fbwalSe32R741+ifMy8+t2TM53Z09Bwe/XPm9ftUU0s+P6fy0NfXF0NDQ3nHKDtXVDZuiIi/JQpSjrrn5Z1gFP1jZI84g7LXkc+XE7nwuaVSXE+f24i4+Z95Jxg9I32EaiXwJczF2UYFAAAkoWwAAABJKBsAAEASygYAAJCEsgEAACShbAAAAEkoGwAAQBLKBgAAkISyAQAAJKFsAAAASRTyDgAAAOTgwL8iOqr+52BLpqdwZQMAAEhC2QAAAJJQNgAAgCSUDQAAIAllAwAASELZAAAAklA2AACAJJQNAAAgCWUDAABIQtkAAACSUDYAAIAklA0AACAJZQMAAEhC2QAAAEbk4MGDMXv27CgWi1FfXx/r16+/7PrCKOUCAACucYVCIdauXRvNzc3xxx9/REtLS7S1tcWMGTMuut6VDQAAYERqa2ujubk5IiLGjRsXxWIxBgYGLrle2QAAAK5YX19f9PT0xMyZMy+5xjYqAAAgIiIGBwejtbX13OvOzs7o7Oy8YN2xY8eivb091q1bF+PHj7/k+ykbAABARERUV1dHd3f3ZdecOXMm2tvbo6OjIxYuXHjZtbZRAQAAI1IqlWLlypVRLBZj9erVf7le2QAAAEZk586dsWnTptixY0c0NjZGY2NjfPHFF5dcbxsVAAAwIrNmzYpSqTTi9a5sAAAASSgbAABAEsoGAACQhLIBAAAkoWwAAABJKBsAAEASygYAAJCEsgEAACShbAAAAEkoGwAAQBLKBgAAkISyAQAAJKFsAAAASSgbAABAEoW8AwAAAKOv53DELf88/9j0lmzP4coGAACQhLIBAAAkoWwAAABJKBsAAEASygYAAJCEsgEAACShbAAAAEkoGwAAQBLKBgAAkISyAQAAJFFVKpVKI108ceLEmDJlSsI4FxocHIzq6upRPSejx3wrl9lWLrOtXGZbucw2vb6+vhgaGso7xhUZU1UVf/+fY9NbWqK7uzuzcxSuZHEe/4Ctra2Z/oUpL+Zbucy2cplt5TLbymW25MU2KgAAIAllAwAAGJEVK1ZETU1NNDQ0jGh92ZeNzs7OvCOQkPlWLrOtXGZbucy2cpktWVm+fHl0dXWNeP0V3SAOAABUhqu9Qbyvry/mz58fvb29f3mOsr+yAQAAXJuu6GlUAABA5RocHIzW1tZzrzs7O/+vbXjKBgAAEBER1dXVmT4m2TYqAAAgCWUDAAAYkaVLl8YjjzwS+/bti7q6utiwYcNl19tGBQAAjMjmzZuvaL0rGwAAQBLKBgAAkISyAQAAJKFsAAAASSgbAABAEsoGAACQhLIBAAAkoWwAAABJKBsAAEASygYAAJCEsgEAACShbAAAAEkoGwAAQBLKBgAAkEQh7wAAAMDoa5s7N4aGhs47NnHixEzPUVUqlUqZviMAAEDYRgUAACSibAAAAEkoGwAAQBLKBgAAkISyAQAAJPFvZgiiHRsK4Y0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1152x144 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sets = e2.Ceq_search([12], [2, 3])\n",
    "for S in sets[0]: e2.plot_S(S)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Examples in 2D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a 2D-structure with dimensions (4,3) and (5,12-5) events for phases 1 and 2, search for 2pc-equivalent structure sets, visualize, check relations and 2pc-equivalence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "...Generating indicator arrays\n",
      "...Computing correlations\n",
      "...Searching for cases\n",
      "...Number of structure sets: 1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x384 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x384 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "sets = e2.Ceq_search([4, 3], [5])\n",
    "S1, S2 = sets[0]\n",
    "e2.plot_S(S1)\n",
    "e2.plot_S(S2)\n",
    "print(e2.rel(S1, S2))\n",
    "print(e2.Ceq(S1, S2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a 2D-structure with dimensions (4,3) and (3,2,12-3-2) events in phases 1,2,3 search and visualize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "...Generating indicator arrays\n",
      "...Computing correlations\n",
      "...Searching for cases\n",
      "...Number of structure sets: 1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x384 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x384 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sets = e2.Ceq_search([4, 3], [3, 2])\n",
    "for S in sets[0]: e2.plot_S(S)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Example in 3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "...Generating indicator arrays\n",
      "...Computing correlations\n",
      "...Searching for cases\n",
      "...Number of structure sets: 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sets = e2.Ceq_search([2, 3, 4], [5])\n",
    "for S in sets[0]: e2.plot_S(S)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Save and load root structures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seach and save found examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "...Generating indicator arrays\n",
      "...Computing correlations\n",
      "...Searching for cases\n",
      "...Number of structure sets: 1\n",
      "0:00:01.424002\n",
      "...Case found\n",
      "...Saving\n",
      "...Created folder\n",
      "data/roots/2d_4_3_nev_5\n"
     ]
    }
   ],
   "source": [
    "folder = e2.Ceq_search_save([4, 3], [5])\n",
    "print(folder)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x384 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x384 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Are the shown structures related?\n",
      "\tFalse\n",
      "Are the shown structures 2PC-equivalent?\n",
      "\tTrue\n"
     ]
    }
   ],
   "source": [
    "loaded = e2.root_load(folder)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[1 1 2]\n",
      "  [1 2 2]\n",
      "  [2 2 1]\n",
      "  [1 2 2]]\n",
      "\n",
      " [[1 1 2]\n",
      "  [2 2 1]\n",
      "  [2 2 1]\n",
      "  [2 2 1]]]\n"
     ]
    }
   ],
   "source": [
    "print(loaded)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Print list of currently available / saved roots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "List of currently available roots:\n",
      "\tdata/roots/2d_4_3_nev_5\n",
      "['data/roots/2d_4_3_nev_5']\n"
     ]
    }
   ],
   "source": [
    "out = e2.roots_saved()\n",
    "print(out)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Search and save more examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "*******************************\n",
      "...Generating indicator arrays\n",
      "...Computing correlations\n",
      "...Searching for cases\n",
      "...Number of structure sets: 1\n",
      "0:00:00.440981\n",
      "...Case found\n",
      "...Saving\n",
      "...Created folder\n",
      "*******************************\n",
      "...Generating indicator arrays\n",
      "...Computing correlations\n",
      "...Searching for cases\n",
      "...Number of structure sets: 1\n",
      "0:00:14.501349\n",
      "...Case found\n",
      "...Saving\n",
      "...Created folder\n",
      "*******************************\n",
      "...Generating indicator arrays\n",
      "...Computing correlations\n",
      "...Searching for cases\n",
      "...Number of structure sets: 1\n",
      "0:00:34.203193\n",
      "...Case found\n",
      "...Saving\n",
      "...Created folder\n"
     ]
    }
   ],
   "source": [
    "print('*******************************')\n",
    "out = e2.Ceq_search_save([12], [5])\n",
    "print('*******************************')\n",
    "out = e2.Ceq_search_save([4, 3], [3, 2])\n",
    "print('*******************************')\n",
    "out = e2.Ceq_search_save([2, 3, 4], [5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "List of currently available roots:\n",
      "\tdata/roots/1d_12_nev_5\n",
      "\tdata/roots/2d_4_3_nev_3_2\n",
      "\tdata/roots/2d_4_3_nev_5\n",
      "\tdata/roots/3d_2_3_4_nev_5\n"
     ]
    }
   ],
   "source": [
    "out = e2.roots_saved()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['data/roots/1d_12_nev_5', 'data/roots/2d_4_3_nev_3_2', 'data/roots/2d_4_3_nev_5', 'data/roots/3d_2_3_4_nev_5']\n"
     ]
    }
   ],
   "source": [
    "print(out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python3",
   "name": "python3"
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    "name": "ipython",
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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