fianl_draft.ipynb

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   "source": [
    "### Toric and Semitoric Packing Capacities project program"
   ]
  },
  {
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   "source": [
    "import numpy as np\n",
    "from fractions import Fraction\n",
    "import numpy.linalg as la\n",
    "from itertools import combinations\n",
    "from sympy import Point, Polygon \n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Polygon as polygon\n",
    "\n",
    "\n",
    "\n",
    "def checkConvex(vertices):\n",
    "  polygon = Polygon(*map(Point, vertices))\n",
    "  return polygon.is_convex()\n",
    "\n",
    "\n",
    "#version 1 (work but optimization needed)\n",
    "def scale(vertices):\n",
    "  demoni = np.array([], dtype = int) #array for all denominator in Fraction form of corridinates\n",
    "  nomi = np.array([], dtype=int) #arr for all nominator of corridiate after removing Fraction form\n",
    "  for vertice in vertices: #add all denominator in the demoni np array\n",
    "    for cor in vertice:\n",
    "      cor = Fraction(cor)\n",
    "      demoni = np.append(demoni, int(cor.denominator))\n",
    "      \n",
    "  lcm = np.lcm.reduce(demoni) #calculate the lcm for all demoni\n",
    "\n",
    "  for vertice in vertices: #multiply corridinate with lcm to remove the Fraction form\n",
    "    vertice *= lcm\n",
    "  vertices = vertices.astype(int)\n",
    "  for i in range(len(vertices)): # use floor division to convert \n",
    "    for j in range(len(vertices[i])):\n",
    "      vertices[i][j] = int(vertices[i][j]) // 1\n",
    "\n",
    "  return vertices\n",
    "\n",
    "#To do: figure out how to show image with in a function (may save in local first and display at the end of program)\n",
    "def show_graph(Vertices, sl2_length, first, tittle=\"\"): \n",
    "  Vertices = Vertices.tolist()\n",
    "  Vertices.append(Vertices[0]) #repeat the first point to create a 'closed loop'\n",
    "  xs, ys = zip(*Vertices) #create lists of x and y values\n",
    "\n",
    "  #first = max_list[0]\n",
    "  for i in range(len(first)):\n",
    "    if (first[i] != 0):\n",
    "      packing = [Vertices[i]]\n",
    "\n",
    "      forward = i + 1 if i + 1 < len(first) else 0\n",
    "      backward = i - 1 if i - 1 >= 0 else len(first) - 1\n",
    "      \n",
    "      forward_vertex = np.array(Vertices[i]) + (first[i] / sl2_length[i]) * np.array([Vertices[forward][0] - Vertices[i][0], Vertices[forward][1] - Vertices[i][1]])\n",
    "      backward_vertex = np.array(Vertices[i]) + (first[i] / sl2_length[backward]) * np.array([Vertices[backward][0] - Vertices[i][0], Vertices[backward][1] - Vertices[i][1]])\n",
    "      packing.append(forward_vertex)\n",
    "      packing.append(backward_vertex)\n",
    "      axes = plt.gca()\n",
    "      axes.add_patch(polygon(packing, closed=True, facecolor='orange'))\n",
    "\n",
    "  #     print(\"value of i: {}\\n forward:{}\\n backward:{}\\n packing vertices: {}\".format(i, forward, backward, packing))\n",
    "  #     print(\"forward vertices: {}\".format(forward_vertex))\n",
    "  #     print(\"backward vertices: {}\\n\".format(backward_vertex))\n",
    "  # print(\"Vertices: {}\\nsl2: {}\\n\".format(Vertices, sl2_length))\n",
    "  plt.axis(\"equal\")\n",
    "  plt.plot(xs,ys) \n",
    "  plt.title(tittle)\n",
    "  plt.show()\n",
    "\n",
    "\n",
    "\n",
    "#Delzan Section\n",
    "#This function verifies the Delzant determinant condition for two edges (three vertices), returning true if the condition is met and false otherwise\n",
    "def verifyDelzant(vert, nA, nB):\n",
    "  # This breaks if vert == nA or vert == nB as gcd will output zero.\n",
    "  # we can check for this, but it may be a waste of time\n",
    "\n",
    "  # compute the edges to compair\n",
    "  edgeA = nA - vert\n",
    "  edgeB = vert - nB\n",
    "\n",
    "  # find the primitive direction vector of the edges\n",
    "  a = np.gcd(edgeA[0], edgeA[1])\n",
    "  edgeA = edgeA / a\n",
    "\n",
    "  b = np.gcd(edgeB[0], edgeB[1])\n",
    "  edgeB = edgeB / b\n",
    "\n",
    "  # find the determinant \n",
    "  return abs((edgeA[0] * edgeB[1]) - (edgeB[0] * edgeA[1])) == 1\n",
    "\n",
    "#This function will comput the  SL2(ℤ)  lengths of any two vertices of integer coordinates\n",
    "def getSL(vert, nVert):\n",
    "# Again, this code breaks if vert == nVert,\n",
    "# but this may not be worth checking\n",
    "# If vert is the origin\n",
    "  if not np.any(vert):\n",
    "    return np.gcd(nVert[0], nVert[1])\n",
    "  # If nVert is the origin\n",
    "  elif not np.any(nVert):\n",
    "    return np.gcd(vert[0], vert[1])\n",
    "  # Otherwise\n",
    "  else:\n",
    "    return np.gcd(nVert[0] - vert[0] , nVert[1] - vert[1])\n",
    "\n",
    "\n",
    "#This function will take in an array of vertices, create a temporary edge, and send that edge to a function that will verify it's Delzant proproties and another that will obtain the  SL2(ℤ)  length, returning a numpy array of these lengths\n",
    "def get_edges(vertices):\n",
    "  len = np.int(vertices.size / 2)\n",
    "  sl2ZLengths = np.zeros(len)\n",
    "  for i in range(len):\n",
    "    vert = vertices[i]\n",
    "    if i + 1 >= len:\n",
    "      nA = vertices[0]\n",
    "      nB = vertices[i - 1]\n",
    "    elif i - 1 < 0:\n",
    "      nA = vertices[i + 1]\n",
    "      nB = vertices[i - 1] # this conditional is the same as the next one, don't we want [n-1] instead of [i-1] ??\n",
    "    else:\n",
    "      nA = vertices[i + 1]\n",
    "      nB = vertices[i - 1]\n",
    "    if (not verifyDelzant(vert, nA, nB)):\n",
    "      return False, sl2ZLengths\n",
    "    else:\n",
    "      sl2ZLengths[i] = getSL(vert, nA)\n",
    "  \n",
    "  return True, sl2ZLengths\n",
    "    \n",
    "\n",
    "\n",
    "#SL_length is the array contains the SL2 length\n",
    "#ieq_idx contains the information for inequality. 2d array, each row represent one inequality\n",
    "#ie: [i,j,idx] lamda_i + lamda_j ≤ SL2_idx \n",
    "# k is the number of equalities we take each time to compute candidate\n",
    "def get_candidate(SL_length, k):\n",
    "  result = set()\n",
    "  n = len(SL_length)\n",
    "  #print(\"value of n: {}\".format(n))\n",
    "  lamdas = list(combinations([i for i in range(n)], k))\n",
    "  zeros = list(combinations([i for i in range(n)], n-k))\n",
    "  for possible in lamdas:\n",
    "    row_idx = 0\n",
    "    A = np.zeros((n,n))\n",
    "    b = np.zeros(n)\n",
    "    for i in possible:\n",
    "      idx1 = i\n",
    "      idx2 = i + 1 if (i+1) < (n) else 0\n",
    "      #print(\"value of idx123: {} {} {}\".format(idx1, idx2, idx1))\n",
    "      A[row_idx][idx1] = 1.0\n",
    "      A[row_idx][idx2] = 1.0\n",
    "      b[row_idx] = SL_length[idx1]\n",
    "      row_idx += 1\n",
    "\n",
    "    if (len(zeros) != 0):\n",
    "      for poss in zeros:\n",
    "        z_idx = row_idx\n",
    "        AA = A.copy()\n",
    "        for z in poss:\n",
    "          AA[z_idx][z] = 1\n",
    "          z_idx += 1\n",
    "        \n",
    "        candidate = np.zeros_like(b)\n",
    "        candidate[0] = -10;\n",
    "        try:\n",
    "          candidate = la.solve(AA,b)\n",
    "        except:\n",
    "          pass\n",
    "        if (np.any(candidate < 0)):\n",
    "          pass\n",
    "        else:\n",
    "          result.add(tuple(np.abs(candidate)))\n",
    "  return result\n",
    "\n",
    "#wrap function for all possibilities for once\n",
    "def get_vertex(SL_length):\n",
    "  final = list()\n",
    "  final.append(tuple(np.zeros(len(SL_length))))\n",
    "  for i in range(1, len(SL_length) + 1):\n",
    "    tmp = get_candidate(SL_length, i)\n",
    "    for t in tmp:\n",
    "      if t not in final:\n",
    "        final.append(t)\n",
    "  \n",
    "  return sorted(final, key=magnitude,reverse=True)\n",
    "\n",
    "def magnitude(Vertex):\n",
    "  sum = 0\n",
    "  for v in Vertex:\n",
    "    sum += v**2\n",
    "  sum /= 2\n",
    "  return sum\n",
    "\n",
    "def filter(vertex, SL2):\n",
    "  for i in range(len(vertex)):\n",
    "    later = i + 1 if (i+1) < len(vertex) else 0\n",
    "    if ((vertex[i]+vertex[later]) > SL2[i]):\n",
    "      return False;\n",
    "  return True;\n",
    "\n",
    "\n",
    "def parse(SL2_lengths):\n",
    "  candidate = get_vertex(SL2_lengths)\n",
    "  num = 1\n",
    "  tmp = []\n",
    "  result = []\n",
    "  for i in candidate:\n",
    "    if(filter(i, SL2_lengths)):\n",
    "      print(\"{}th:\\t Vertex Coordinate: {}\\t Magnitude: {}\".format(num, i, magnitude(i)))\n",
    "      num += 1\n",
    "      tmp.append(i)\n",
    "\n",
    "  maximum = magnitude(tmp[0])\n",
    "  for i in tmp:\n",
    "    if (magnitude(i) == maximum):\n",
    "      result.append(i)\n",
    "  \n",
    "  return result\n",
    "\n",
    "def show_info(Vertices):\n",
    "  if (not checkConvex(Vertices)):\n",
    "    print(\"Convex Polygon, Please check your input vertices\")\n",
    "    return;\n",
    "\n",
    "  Vertices = scale(Vertices);\n",
    "  # show_graph(Vertices)\n",
    "  print(\"The 2D graph of polygon shows above\\n\")\n",
    "  valid, sl2_length = get_edges(Vertices)\n",
    "  if (not valid):\n",
    "    print(\"Not Delzant, Please check your input vertices\")\n",
    "    return;\n",
    "\n",
    "  print(\"This is the array of SL2 length: \\n{} \\n\\nFollowing shows the Packing vertices & its magnitude: \".format(sl2_length))\n",
    "  Coordinates = parse(sl2_length)\n",
    "  for i in Coordinates:\n",
    "    show_graph(Vertices,sl2_length, i)\n"
   ]
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   "source": [
    "#Data structure: \n",
    "Vertices: size of np array (x,y)\n",
    "x,y are objects of fraction module. eg:x = fraction(a,b) = a/b\n",
    "\n",
    "Array of vertex: 2d np array containg the per vertice per row\n",
    "\n",
    "[[x,y],\n",
    "\n",
    "[x,y]]\n",
    "\n",
    "Input requirement: Counterclock wise vertices order"
   ]
  },
  {
   "cell_type": "code",
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    "executionInfo": {
     "elapsed": 537,
     "status": "ok",
     "timestamp": 1636507574894,
     "user": {
      "displayName": "Zheyu Zhang",
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   "outputs": [
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The 2D graph of polygon shows above\n",
      "\n",
      "This is the array of SL2 length: \n",
      "[13. 17.  1.  2.  8.  7.] \n",
      "\n",
      "Following shows the Packing vertices & its magnitude: \n",
      "1th:\t Vertex Coordinate: (0.0, 13.0, 1.0, 0.0, 1.0, 7.0)\t Magnitude: 110.0\n",
      "2th:\t Vertex Coordinate: (0.0, 13.0, 0.0, 1.0, 1.0, 7.0)\t Magnitude: 110.0\n",
      "3th:\t Vertex Coordinate: (0.0, 13.0, 1.0, 0.0, 0.0, 7.0)\t Magnitude: 109.5\n",
      "4th:\t Vertex Coordinate: (0.0, 13.0, 0.0, 1.0, 0.0, 7.0)\t Magnitude: 109.5\n",
      "5th:\t Vertex Coordinate: (0.0, 13.0, 0.0, 0.0, 1.0, 7.0)\t Magnitude: 109.5\n",
      "6th:\t Vertex Coordinate: (0.0, 13.0, 0.0, 0.0, 0.0, 7.0)\t Magnitude: 109.0\n",
      "7th:\t Vertex Coordinate: (0.0, 13.0, 1.0, 0.0, 2.0, 6.0)\t Magnitude: 105.0\n",
      "8th:\t Vertex Coordinate: (0.0, 13.0, 0.0, 0.0, 2.0, 6.0)\t Magnitude: 104.5\n",
      "9th:\t Vertex Coordinate: (1.0, 12.0, 1.0, 0.0, 2.0, 6.0)\t Magnitude: 93.0\n",
      "10th:\t Vertex Coordinate: (1.0, 12.0, 0.0, 0.0, 2.0, 6.0)\t Magnitude: 92.5\n",
      "11th:\t Vertex Coordinate: (0.0, 13.0, 1.0, 0.0, 2.0, 0.0)\t Magnitude: 87.0\n",
      "12th:\t Vertex Coordinate: (0.0, 13.0, 0.0, 0.0, 2.0, 0.0)\t Magnitude: 86.5\n",
      "13th:\t Vertex Coordinate: (0.0, 13.0, 0.0, 1.0, 1.0, 0.0)\t Magnitude: 85.5\n",
      "14th:\t Vertex Coordinate: (0.0, 13.0, 0.0, 1.0, 0.0, 0.0)\t Magnitude: 85.0\n",
      "15th:\t Vertex Coordinate: (0.0, 13.0, 1.0, 0.0, 0.0, 0.0)\t Magnitude: 85.0\n",
      "16th:\t Vertex Coordinate: (0.0, 13.0, 0.0, 0.0, 0.0, 0.0)\t Magnitude: 84.5\n",
      "17th:\t Vertex Coordinate: (7.0, 6.0, 1.0, 0.0, 2.0, 0.0)\t Magnitude: 45.0\n",
      "18th:\t Vertex Coordinate: (7.0, 6.0, 0.0, 0.0, 2.0, 0.0)\t Magnitude: 44.5\n",
      "19th:\t Vertex Coordinate: (7.0, 6.0, 0.0, 1.0, 1.0, 0.0)\t Magnitude: 43.5\n",
      "20th:\t Vertex Coordinate: (7.0, 6.0, 0.0, 1.0, 0.0, 0.0)\t Magnitude: 43.0\n",
      "21th:\t Vertex Coordinate: (7.0, 6.0, 1.0, 0.0, 0.0, 0.0)\t Magnitude: 43.0\n",
      "22th:\t Vertex Coordinate: (7.0, 6.0, 0.0, 0.0, 0.0, 0.0)\t Magnitude: 42.5\n",
      "23th:\t Vertex Coordinate: (7.0, 0.0, 1.0, 0.0, 2.0, 0.0)\t Magnitude: 27.0\n",
      "24th:\t Vertex Coordinate: (7.0, 0.0, 0.0, 0.0, 2.0, 0.0)\t Magnitude: 26.5\n",
      "25th:\t Vertex Coordinate: (0.0, 0.0, 0.0, 1.0, 1.0, 7.0)\t Magnitude: 25.5\n",
      "26th:\t Vertex Coordinate: (7.0, 0.0, 0.0, 1.0, 1.0, 0.0)\t Magnitude: 25.5\n",
      "27th:\t Vertex Coordinate: (0.0, 0.0, 1.0, 0.0, 1.0, 7.0)\t Magnitude: 25.5\n",
      "28th:\t Vertex Coordinate: (0.0, 0.0, 0.0, 1.0, 0.0, 7.0)\t Magnitude: 25.0\n",
      "29th:\t Vertex Coordinate: (7.0, 0.0, 0.0, 1.0, 0.0, 0.0)\t Magnitude: 25.0\n",
      "30th:\t Vertex Coordinate: (0.0, 0.0, 1.0, 0.0, 0.0, 7.0)\t Magnitude: 25.0\n",
      "31th:\t Vertex Coordinate: (0.0, 0.0, 0.0, 0.0, 1.0, 7.0)\t Magnitude: 25.0\n",
      "32th:\t Vertex Coordinate: (7.0, 0.0, 1.0, 0.0, 0.0, 0.0)\t Magnitude: 25.0\n",
      "33th:\t Vertex Coordinate: (0.0, 0.0, 0.0, 0.0, 0.0, 7.0)\t Magnitude: 24.5\n",
      "34th:\t Vertex Coordinate: (7.0, 0.0, 0.0, 0.0, 0.0, 0.0)\t Magnitude: 24.5\n",
      "35th:\t Vertex Coordinate: (1.0, 0.0, 1.0, 0.0, 2.0, 6.0)\t Magnitude: 21.0\n",
      "36th:\t Vertex Coordinate: (0.0, 0.0, 1.0, 0.0, 2.0, 6.0)\t Magnitude: 20.5\n",
      "37th:\t Vertex Coordinate: (1.0, 0.0, 0.0, 0.0, 2.0, 6.0)\t Magnitude: 20.5\n",
      "38th:\t Vertex Coordinate: (0.0, 0.0, 0.0, 0.0, 2.0, 6.0)\t Magnitude: 20.0\n",
      "39th:\t Vertex Coordinate: (0.0, 0.0, 1.0, 0.0, 2.0, 0.0)\t Magnitude: 2.5\n",
      "40th:\t Vertex Coordinate: (0.0, 0.0, 0.0, 0.0, 2.0, 0.0)\t Magnitude: 2.0\n",
      "41th:\t Vertex Coordinate: (0.0, 0.0, 0.0, 1.0, 1.0, 0.0)\t Magnitude: 1.0\n",
      "42th:\t Vertex Coordinate: (0.0, 0.0, 1.0, 0.0, 0.0, 0.0)\t Magnitude: 0.5\n",
      "43th:\t Vertex Coordinate: (0.0, 0.0, 0.0, 1.0, 0.0, 0.0)\t Magnitude: 0.5\n",
      "44th:\t Vertex Coordinate: (0.0, 0.0, 0.0, 0.0, 0.0, 0.0)\t Magnitude: 0.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test = np.array([[0,0],\n",
    "                 [13,-13],\n",
    "                 [13,4],\n",
    "                 [12,5],\n",
    "                 [8,7],\n",
    "                 [0,7]\n",
    "                 ]\n",
    "                     )\n",
    "show_info(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "executionInfo": {
     "elapsed": 788,
     "status": "ok",
     "timestamp": 1636507588345,
     "user": {
      "displayName": "Zheyu Zhang",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
      "userId": "15713465514849060191"
     },
     "user_tz": 360
    },
    "id": "5R5KCufY-rv-",
    "outputId": "ba1caca3-99c7-4377-ffe1-5d7636fb288f"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The 2D graph of polygon shows above\n",
      "\n",
      "This is the array of SL2 length: \n",
      "[6. 1. 3. 1.] \n",
      "\n",
      "Following shows the Packing vertices & its magnitude: \n",
      "1th:\t Vertex Coordinate: (1.0, 0.0, 1.0, 0.0)\t Magnitude: 1.0\n",
      "2th:\t Vertex Coordinate: (1.0, 1.0, 0.0, 0.0)\t Magnitude: 1.0\n",
      "3th:\t Vertex Coordinate: (0.0, 0.0, 1.0, 1.0)\t Magnitude: 1.0\n",
      "4th:\t Vertex Coordinate: (0.0, 1.0, 0.0, 1.0)\t Magnitude: 1.0\n",
      "5th:\t Vertex Coordinate: (1.0, 0.0, 0.0, 0.0)\t Magnitude: 0.5\n",
      "6th:\t Vertex Coordinate: (0.0, 0.0, 0.0, 1.0)\t Magnitude: 0.5\n",
      "7th:\t Vertex Coordinate: (0.0, 0.0, 1.0, 0.0)\t Magnitude: 0.5\n",
      "8th:\t Vertex Coordinate: (0.0, 1.0, 0.0, 0.0)\t Magnitude: 0.5\n",
      "9th:\t Vertex Coordinate: (0.0, 0.0, 0.0, 0.0)\t Magnitude: 0.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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W6kt3STpQ4khN0bZn5LP4uqTFkvaM/xvW3oj4w3JHap2IGLP9BUlPSeqS9GhE7C95rDLdIemzkv7X9ovV1/40Ip4ocSa0jz+WtLt60vOapD8oeZ7C8Sv6AJBcyksrAICrCDkAJEfIASA5Qg4AyRFyAEiOkANAcoQcAJL7f0HPotoUA2GSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+i68Di4FdE3+G2Z2Zf1DvSO2TmeMR8QXgMaAPeCAz99U8Vp1uAT4L/Dginpl87U8y85EaZ1Ln+CPgwcmLnheB3695nsr5K/qSVLgib61Iks4z5JJUOEMuSYUz5JJUOEMuSYUz5JJUOEMuSYX7f1CCPeLaj/coAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GxIGSxyrTvZI+L+l/bb9Sfe+PI+KZEmdC+/hDSburFz2HJf1uyfMUjl/RB4DkUt5aAQBcQ8gBIDlCDgDJEXIASI6QA0ByhBwAkiPkAJDc/wPPfaOJ4VkrIwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test = np.array([[1,0],\n",
    "                     [7,0],\n",
    "                 [1,1],\n",
    "                     [-2,1]]\n",
    "                  \n",
    "                     )\n",
    "show_info(test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "a6myueqwbUME"
   },
   "source": [
    "#test field"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 265
    },
    "executionInfo": {
     "elapsed": 299,
     "status": "ok",
     "timestamp": 1636421522459,
     "user": {
      "displayName": "Zheyu Zhang",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
      "userId": "15713465514849060191"
     },
     "user_tz": 360
    },
    "id": "iB-1yk1ee5ty",
    "outputId": "ab89061c-4609-4cec-a0cd-da9d05ff73e2"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test = np.array([[1,0],\n",
    "                     [7,0],\n",
    "                 [1,1],\n",
    "                     [-2,1]]\n",
    "                     )\n",
    "max_list = [\n",
    "            (1.0, 0.0, 1.0, 0.0),\n",
    "            (1.0, 1.0, 0.0, 0.0),\n",
    "            (0.0, 0.0, 1.0, 1.0),\n",
    "            (0.0, 1.0, 0.0, 1.0)\n",
    "]\n",
    "sl2_length = [6.0, 1.0, 3.0, 1.0] \n",
    "\n",
    "def show_graph2(Vertices, sl2_length, max_list, tittle=\"\"): \n",
    "  Vertices = Vertices.tolist()\n",
    "  Vertices.append(Vertices[0]) #repeat the first point to create a 'closed loop'\n",
    "  xs, ys = zip(*Vertices) #create lists of x and y values\n",
    "\n",
    "  first = max_list[3]\n",
    "  for i in range(len(first)):\n",
    "    if (first[i] != 0):\n",
    "      packing = [Vertices[i]]\n",
    "\n",
    "      forward = i + 1 if i + 1 < len(first) else 0\n",
    "      backward = i - 1 if i - 1 >= 0 else len(first) - 1\n",
    "      \n",
    "      forward_vertex = np.array(Vertices[i]) + (first[i] / sl2_length[i]) * np.array([Vertices[forward][0] - Vertices[i][0], Vertices[forward][1] - Vertices[i][1]])\n",
    "      backward_vertex = np.array(Vertices[i]) + (first[i] / sl2_length[backward]) * np.array([Vertices[backward][0] - Vertices[i][0], Vertices[backward][1] - Vertices[i][1]])\n",
    "      packing.append(forward_vertex)\n",
    "      packing.append(backward_vertex)\n",
    "      axes = plt.gca()\n",
    "      axes.add_patch(polygon(packing, closed=True, facecolor='orange'))\n",
    "\n",
    "  #     print(\"value of i: {}\\n forward:{}\\n backward:{}\\n packing vertices: {}\".format(i, forward, backward, packing))\n",
    "  #     print(\"forward vertices: {}\".format(forward_vertex))\n",
    "  #     print(\"backward vertices: {}\\n\".format(backward_vertex))\n",
    "  # print(\"Vertices: {}\\nsl2: {}\\n\".format(Vertices, sl2_length))\n",
    "\n",
    "  plt.plot(xs,ys) \n",
    "  plt.title(tittle)\n",
    "  plt.show()\n",
    "\n",
    "show_graph2(test,sl2_length, max_list)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 435
    },
    "executionInfo": {
     "elapsed": 271,
     "status": "ok",
     "timestamp": 1636419318096,
     "user": {
      "displayName": "Zheyu Zhang",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
      "userId": "15713465514849060191"
     },
     "user_tz": 360
    },
    "id": "NrGeOGSWMSiA",
    "outputId": "5afac7a1-9128-481f-f234-b94e9a0faa20"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4 3]\n",
      " [4 0]\n",
      " [1 0]\n",
      " [0 1]\n",
      " [0 3]]\n",
      "[[ 3  2]\n",
      " [ 3 -1]\n",
      " [ 0 -1]\n",
      " [-1  0]\n",
      " [-1  2]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.patches import Polygon\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def show_graph2(Vertices, tittle=\"\"): \n",
    "  print(Vertices)\n",
    "  print(Vertices-1)\n",
    "  Vertices1 = Vertices.tolist()\n",
    "  Vertices1.append(Vertices1[0]) #repeat the first point to create a 'closed loop'\n",
    "  xs, ys = zip(*Vertices1) #create lists of x and y values  \n",
    "\n",
    "  axes = plt.gca()\n",
    "  axes.add_patch(Polygon([(0, 0), (1, 0.2), (0.3, 0.4)], closed=True, facecolor='orange'))\n",
    "\n",
    "  plt.plot(xs,ys) \n",
    "  plt.title(tittle)\n",
    "  plt.show()\n",
    "\n",
    "\n",
    "show_graph2(vertices)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 520
    },
    "executionInfo": {
     "elapsed": 412,
     "status": "ok",
     "timestamp": 1636419261154,
     "user": {
      "displayName": "Zheyu Zhang",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
      "userId": "15713465514849060191"
     },
     "user_tz": 360
    },
    "id": "IfK8AXskfHyj",
    "outputId": "06eac965-3681-49ee-f6a4-59c79fee2e3a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The 2D graph of polygon shows above\n",
      "\n",
      "This is the array of SL2 length: \n",
      "[4. 1. 3. 1.] \n",
      "\n",
      "Following shows the Packing vertices & its magnitude: \n",
      "1th:\t Vertex Coordinate: (1.0, 0.0, 1.0, 0.0)\t Magnitude: 1.0\n",
      "2th:\t Vertex Coordinate: (1.0, 1.0, 0.0, 0.0)\t Magnitude: 1.0\n",
      "3th:\t Vertex Coordinate: (0.0, 0.0, 1.0, 1.0)\t Magnitude: 1.0\n",
      "4th:\t Vertex Coordinate: (0.0, 1.0, 0.0, 1.0)\t Magnitude: 1.0\n",
      "5th:\t Vertex Coordinate: (1.0, 0.0, 0.0, 0.0)\t Magnitude: 0.5\n",
      "6th:\t Vertex Coordinate: (0.0, 0.0, 0.0, 1.0)\t Magnitude: 0.5\n",
      "7th:\t Vertex Coordinate: (0.0, 1.0, 0.0, 0.0)\t Magnitude: 0.5\n",
      "8th:\t Vertex Coordinate: (0.0, 0.0, 1.0, 0.0)\t Magnitude: 0.5\n",
      "9th:\t Vertex Coordinate: (0.0, 0.0, 0.0, 0.0)\t Magnitude: 0.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test = np.array([[Fraction('3'),0],\n",
    "                     [7,0],\n",
    "                 [1,1],\n",
    "                     [-2,1]]\n",
    "                     )\n",
    "show_info(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 47,
     "status": "ok",
     "timestamp": 1635804203443,
     "user": {
      "displayName": "Yu Du",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiaoPdSsR5Mocl0rsr8susDD4b13wqPReUdQl3wqg=s64",
      "userId": "04381187109528044409"
     },
     "user_tz": 300
    },
    "id": "Kl4ZYC3WN0Fi",
    "outputId": "b6e602ff-cd88-4432-ebba-c964e22e8f40"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "# SIMPLE TESTCASES For Verify Delzant\n",
    "vert = np.array([2,1])\n",
    "nA = np.array([7,0])\n",
    "nB = np.array([1,1])\n",
    "\n",
    "print(verifyDelzant(vert, nA, nB) == True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 35,
     "status": "ok",
     "timestamp": 1635804203446,
     "user": {
      "displayName": "Yu Du",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14GiaoPdSsR5Mocl0rsr8susDD4b13wqPReUdQl3wqg=s64",
      "userId": "04381187109528044409"
     },
     "user_tz": 300
    },
    "id": "ITYUEBesejvm",
    "outputId": "5106f024-9da9-45bb-b156-36d1f893b624"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# SIMPLE TEST CASE For getSL\n",
    "\n",
    "vert = np.array([2,1])\n",
    "nVert = np.array([4,0])\n",
    "getSL(vert, nVert)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "DYSBcrraj2UK"
   },
   "outputs": [],
   "source": [
    "\n",
    "# TEST CASES For get_edges\n",
    "\n",
    "# THIRD MINIMAL POLYGON\n",
    "thid_min = np.array([[0,0],\n",
    "                     [7,0],\n",
    "                     [2,1],\n",
    "                     [1,1]])\n",
    "\n",
    "result = np.array([7, 1, 1, 1])\n",
    "#print(np.all(get_edges(thid_min) == result))\n",
    "\n",
    "parse(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "yb9Q_eOgicHn"
   },
   "outputs": [],
   "source": [
    "testsl = np.array([1,10,10,1,10,10])\n",
    "ineq = np.array([[1,2,1],\n",
    "                 [2,3,2],\n",
    "                 [3,4,3],\n",
    "                 [4,5,4],\n",
    "                 [5,6,5],\n",
    "                 [1,6,6],\n",
    "                 ])\n",
    "\n",
    "result = get_vertex(testsl)\n",
    "num = 1\n",
    "for i in result:\n",
    "   if (filter(i, testsl)):\n",
    "     print(\"{}th:\\t Vertex Coordinate: {}\\t sum value: {}\".format(num, i, magnitude(i)))\n",
    "     num += 1;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "gQV7HWMFimHo"
   },
   "outputs": [],
   "source": [
    "testsl = np.array([1,2,2,2,3])\n",
    "\n",
    "result = get_vertex(testsl)\n",
    "num = 1\n",
    "for i in result:\n",
    "   if (filter(i,testsl)):\n",
    "     print(\"{}th:\\t Vertex Coordinate: {}\\t sum value: {}\".format(num, i, magnitude(i)))\n",
    "     num += 1;\n",
    "# for i in result:\n",
    "#   print(i)\n",
    "# for i in result:\n",
    "#      print(\"{}th:\\t Vertex Coordinate: {}\\t sum value: {} \\t bool:{}\".format(num, i, magnitude(i),filter(i, ineq,testsl)))\n",
    "#      num += 1;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "ayTHZUfgbTOI"
   },
   "outputs": [],
   "source": [
    "testsl = np.array([1,2,3,4])\n",
    "ineq = np.array([[0,1,0],\n",
    "                 [1,2,1],\n",
    "                 [2,3,0],\n",
    "                 [0,3,2]\n",
    "                 ])\n",
    "\n",
    "result = get_vertex(testsl)\n",
    "for i in result:\n",
    "  print(i)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "h53n7L9CeXnI"
   },
   "outputs": [],
   "source": [
    "testsl = np.array([1,2,3,4])\n",
    "ineq = np.array([[1,2,0],\n",
    "                 [2,3,1],\n",
    "                 [3,4,0],\n",
    "                 [1,4,2]\n",
    "                 ])\n",
    "\n",
    "result = get_vertex(testsl)\n",
    "for i in result:\n",
    "  print(i)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "olEy86fKpzw-"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "ECjDNf1uF8ch"
   },
   "outputs": [],
   "source": [
    "# test below:\n",
    "vertices = np.array([[Fraction('0.85'), Fraction('0.3')],\n",
    "                    [Fraction('1/3'), Fraction('0')],\n",
    "                     \n",
    "                    [Fraction('0.5'), Fraction('0.5')]])\n",
    "\n",
    "print(vertices)\n",
    "result = scale(vertices)\n",
    "print(result)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "executionInfo": {
     "elapsed": 358,
     "status": "ok",
     "timestamp": 1636419038233,
     "user": {
      "displayName": "Zheyu Zhang",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
      "userId": "15713465514849060191"
     },
     "user_tz": 360
    },
    "id": "TATg1d2qHD4V",
    "outputId": "0fcfffd8-4c0d-4c59-f11c-245a77d11b5d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Value of vertice is: [4 3]\n",
      "Value of vertice is: [4 0]\n",
      "Value of vertice is: [1 0]\n",
      "Value of vertice is: [0 1]\n",
      "Value of vertice is: [0 3]\n",
      "[[4 3]\n",
      " [4 0]\n",
      " [1 0]\n",
      " [0 1]\n",
      " [0 3]]\n"
     ]
    }
   ],
   "source": [
    "def scale2(vertices):\n",
    "  demoni = np.array([], dtype = int) #array for all denominator in Fraction form of corridinates\n",
    "  nomi = np.array([], dtype=int) #arr for all nominator of corridiate after removing Fraction form\n",
    "  for vertice in vertices: #add all denominator in the demoni np array\n",
    "    print(\"Value of vertice is: {}\".format(vertice))\n",
    "    for cor in vertice:\n",
    "      cor = Fraction(cor)\n",
    "      demoni = np.append(demoni, int(cor.denominator))\n",
    "      \n",
    "  lcm = np.lcm.reduce(demoni) #calculate the lcm for all demoni\n",
    "\n",
    "  for vertice in vertices: #multiply corridinate with lcm to remove the Fraction form\n",
    "    vertice *= lcm\n",
    "\n",
    "  for i in range(len(vertices)): # use floor division to convert \n",
    "    for j in range(len(vertices[i])):\n",
    "      vertices[i][j] = vertices[i][j] // 1\n",
    "  return vertices\n",
    "\n",
    "\n",
    "#Test of show graph\n",
    "vertices = np.array([  \n",
    "                   [4, 3],\n",
    "                   [4, 0],\n",
    "                   [1, 0],\n",
    "                   [0, 1],\n",
    "                   [0, 3],\n",
    "                   ])\n",
    "vertices = scale2(vertices)\n",
    "print(vertices)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 435
    },
    "executionInfo": {
     "elapsed": 779,
     "status": "ok",
     "timestamp": 1636419302918,
     "user": {
      "displayName": "Zheyu Zhang",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
      "userId": "15713465514849060191"
     },
     "user_tz": 360
    },
    "id": "dq9_ZvjplFol",
    "outputId": "b838f478-3984-4d94-8c21-9ab932c28cf0"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4 3]\n",
      " [4 0]\n",
      " [1 0]\n",
      " [0 1]\n",
      " [0 3]]\n",
      "[[ 3  2]\n",
      " [ 3 -1]\n",
      " [ 0 -1]\n",
      " [-1  0]\n",
      " [-1  2]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 536
    },
    "executionInfo": {
     "elapsed": 471,
     "status": "ok",
     "timestamp": 1636409961468,
     "user": {
      "displayName": "Zheyu Zhang",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
      "userId": "15713465514849060191"
     },
     "user_tz": 360
    },
    "id": "o3uHW_ilomHZ",
    "outputId": "a4292526-b4e5-4ca9-df61-b65f79070b46"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The 2D graph of polygon shows above\n",
      "\n",
      "This is the array of SL2 length: \n",
      "[6. 1. 3. 1.] \n",
      "\n",
      "Following shows the Packing vertices & its magnitude: \n",
      "1th:\t Vertex Coordinate: (1.0, 0.0, 1.0, 0.0)\t Magnitude: 1.0\n",
      "2th:\t Vertex Coordinate: (1.0, 1.0, 0.0, 0.0)\t Magnitude: 1.0\n",
      "3th:\t Vertex Coordinate: (0.0, 0.0, 1.0, 1.0)\t Magnitude: 1.0\n",
      "4th:\t Vertex Coordinate: (0.0, 1.0, 0.0, 1.0)\t Magnitude: 1.0\n",
      "5th:\t Vertex Coordinate: (1.0, 0.0, 0.0, 0.0)\t Magnitude: 0.5\n",
      "6th:\t Vertex Coordinate: (0.0, 0.0, 0.0, 1.0)\t Magnitude: 0.5\n",
      "7th:\t Vertex Coordinate: (0.0, 0.0, 1.0, 0.0)\t Magnitude: 0.5\n",
      "8th:\t Vertex Coordinate: (0.0, 1.0, 0.0, 0.0)\t Magnitude: 0.5\n",
      "9th:\t Vertex Coordinate: (0.0, 0.0, 0.0, 0.0)\t Magnitude: 0.0\n"
     ]
    }
   ],
   "source": [
    "test = np.array([[0.5,0],\n",
    "                     [3.5,0],\n",
    "                 [0.5,0.5],\n",
    "                     [-1,0.5]]\n",
    "                     )\n",
    "show_info(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 371
    },
    "executionInfo": {
     "elapsed": 288,
     "status": "ok",
     "timestamp": 1636419091793,
     "user": {
      "displayName": "Zheyu Zhang",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s64",
      "userId": "15713465514849060191"
     },
     "user_tz": 360
    },
    "id": "yP8wNA-2qcYe",
    "outputId": "9391a3f8-7dca-494e-a455-6467b771cdd8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4 3]\n",
      " [4 0]\n",
      " [1 0]\n",
      " [0 1]\n",
      " [0 3]]\n",
      "<class 'matplotlib.path.Path'>\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.path import Path\n",
    "import matplotlib.patches as patches\n",
    "\n",
    "vertices = np.array([  \n",
    "                   [4, 3],\n",
    "                   [4, 0],\n",
    "                   [1, 0],\n",
    "                   [0, 1],\n",
    "                   [0, 3],\n",
    "                   ])\n",
    "print(vertices)\n",
    "verts = [\n",
    "   (0., 0.),  # left, bottom\n",
    "   (0., 1.),  # left, top\n",
    "   (1., 1.),  # right, top\n",
    "   (1., 0.),  # right, bottom\n",
    "   (0., 0.),  # ignored\n",
    "]\n",
    "codes = [\n",
    "    Path.MOVETO,\n",
    "    Path.LINETO,\n",
    "    Path.LINETO,\n",
    "    Path.LINETO,\n",
    "    Path.CLOSEPOLY,\n",
    "]\n",
    "\n",
    "path = Path(verts, codes)\n",
    "print(Path)\n",
    "fig, ax = plt.subplots()\n",
    "patch = patches.PathPatch(path, facecolor='blue', lw=1)\n",
    "ax.add_patch(patch)\n",
    "\n",
    "\n",
    "ax.set_xlim(-2, 2)\n",
    "ax.set_ylim(-2, 2)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "fianl_draft.ipynb",
   "provenance": [
    {
     "file_id": "1v8SVK9kdLuMbzASWALT8eRWmEAGoSLxC",
     "timestamp": 1635395371004
    }
   ]
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}