{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Basic Tutorial: Reeb graph class" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook, we'll walk through the basic functionality of the `cereeberus.ReebGraph` class. See [here](../modules/reeb/reebgraph.rst) for full documentation." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import networkx as nx\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "# The main class for the Reeb Graph\n", "from cereeberus import ReebGraph\n", "\n", "# Some built in example graphs\n", "import cereeberus.data.ex_reebgraphs as ex_rg" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A Reeb graph consists of a graph $G$ with a function $f:G \\to \\mathbb{R}$ which is monotone on the edges. For our encoding purposes, we are going to assume that the function is defined by providing the function value on the vertices\n", "$$\n", "f:V(G) \\to \\mathbb{R}\n", "$$\n", "with the property that for any edge $e = (u,v)$, $f(u) \\neq f(v)$. \n", "\n", "In this tutorial, we go over the basic structure of the `cereeberus.ReebGraph` class. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Basic operations on a Reeb graph\n", "\n", "We're going to start with an empty Reeb graph." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ReebGraph with 0 nodes and 0 edges.\n" ] } ], "source": [ "R = ReebGraph()\n", "print(R)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's add some vertices. Of course, we have to be sure to specify the function value at the same time. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ReebGraph with 5 nodes and 0 edges.\n" ] } ], "source": [ "R.add_node('A', f_vertex = 3.2)\n", "R.add_node('B', f_vertex = 1.7)\n", "R.add_node('C', f_vertex = 0)\n", "R.add_node('D', f_vertex = -2)\n", "R.add_node('E', f_vertex = np.pi)\n", "\n", "print(R)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also add some edges to our Reeb graph. Note that the Reeb graph allows for multiple edges between two vertices." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ReebGraph with 5 nodes and 6 edges.\n" ] } ], "source": [ "R.add_edge('A','B')\n", "R.add_edge('B','C')\n", "R.add_edge('A','D')\n", "R.add_edge('D','E')\n", "R.add_edge('D','B')\n", "R.add_edge('D','B')\n", "\n", "\n", "print(R)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function values are stored in the dictionary `R.f`. Below we can see function values for some of the vertices we just added. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "f(A) = 3.2\n", "f(B) = 1.7\n", "f(E) = 3.141592653589793\n" ] } ], "source": [ "print(f\"f(A) = {R.f['A']}\")\n", "print(f\"f(B) = {R.f['B']}\")\n", "print(f\"f(E) = {R.f['E']}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can take a look at the Reeb graph using the built in drawing function. The `cpx` input controls loopiness for the drawing. The `R.set_pos_from_f` randomly sets the drawing positions. In this case, we picked `seed = 2` to make a reasonable graph, however, this command is unnecessary unless you want more control over drawing locations. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "R.set_pos_from_f(seed = 2)\n", "R.draw(cpx = 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can manually control the drawing locations for the vertices if you want to. The drawing locations are held in the dictionary `R.pos_f`. So I can just move vertex `A` over a bit to the left to make my drawing a touch nicer. The second coordinate is always the function value `R.f['A']`, but we can change the first coordinate. Note that later when adding vertices and edges, this will likely be reset so you won't likely want to use this tweaking much. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Drawing location for A: (0.14133460941762915, 3.2)\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "print(f'Drawing location for A: {R.pos_f[\"A\"]}')\n", "R.pos_f['A'] = (-.5,R.f['A'])\n", "R.draw(cpx=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also subdivde edges. Note that in a Reeb graph, because we think of an edge as being a copy of the unit interval, the result is considered the same Reeb graph. So, we can add a vertex to an edge $(u,v)$ at any function value $f(u) < a< f(b)$." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "R.subdivide_edge('A','D','F',1)\n", "R.subdivide_edge('B','D','G',0)\n", "\n", "# Just for drawing purposes\n", "R.set_pos_from_f(seed = 42)\n", "R.draw(cpx=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These so-called regular vertices can also be removed. Either by using the command `R.remove_regular_vertex(v)` (note the difference between removing a regular vertex and the `R.remove_node` command which deletes a vertex and all adjacent edges from the Reeb graph), or by removing all at once as follows. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "R.remove_all_regular_vertices()\n", "\n", "R.set_pos_from_f(seed = 1)\n", "R.draw(cpx=3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that if you add an edge between two vertices at the same function value, the Reeb graph will actually merge the two vertices into one. First I'm going to put back in an extra vertex on the edge $(D,E)$ at the same function value as $C$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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EREQ4f/481dXVREZGMnz48ECH02lKRHzMFyMioJ4iIiLi5pmWyczMJCwsLMDRdJ4SER/zxYgIfN9T5PLlyxQVFXn12iIi0jP09GkZUCLic74aEYmKirK+6VS0KiLSO128eJGKigrCw8MZOXJkoMPpEiUiPuRyuXyWiIB6ioiI9Hae0ZCRI0cSHh4e4Gi6RomID9XU1Fj1G93tqtqapj1Fjh8/7vXri4hI8AqFaRlQIuJTTetDfNFu12azMXHiREDTMyIivc3ly5cpKyvDbreTmZkZ6HC6TImIDzVt7+4rnumZEydOqKeIiEgv4lktM2LECCIjIwMcTdcpEfEhb7d3b01ycjLp6emYpsnhw4d9dh8REQkuoTAtA0pEfMpXS3evp54iIiK9S1lZGSUlJdhsNrKysgIdTrcoEfEhX66YaWrcuHGEhYVRUlLCxYsXfXovEREJPM+0zLBhw4iOjg5wNN2jRMSH/DUiEhUVxejRowEVrYqI9AahMi0DSkR8yl8jIqCeIiIivUV5eTkXL17EMAzrl9CeTImID/mjWNVj+PDhxMfHU1tbS0FBgc/vJyIigeEZDcnIyPBJjyp/UyLiI6Zp+mX5rod6ioiI9A6hNC0DSkR8pqamBpfLBfgnEYHvV88UFBRYSZCIiISOqqoqCgsLASUi0g5PIhATE4PdbvfLPZOTkxk0aJB6ioiIhCjPaEh6ejoJCQkBjsY7lIj4iD/rQ5ryjIrk5OSop4iISIgJtWkZUCLiM4FKRMaNG4fdbqekpIRLly759d4iIuI7165d4+zZs4ASEekAfxaqNhUdHa2eIiIiISg/Px/TNBk4cCB9+vQJdDheo0TER/zVzKw1np4ihw8fxul0+v3+IiLifZ5uqqE0GgJKRHzGn83MrjdixAji4uKora3l+PHjfr+/iIh4V21tLadPnwaUiEgHBapGBJr3FDl48KDf7y8iIt51/PhxXC4X/fv3Jzk5OdDheJUSER8JVI2IR9OeIteuXQtIDCIi4h2huFrGQ4mID5imGdAREYD+/fszaNAgXC6XeoqIiPRg9fX1nDhxAoCxY8cGOBrvUyLiA3V1dVaRaKBGROD7olWtnhER6bkKCgpwOp307duXlJSUQIfjdUpEfMAzGhIdHU1YWFjA4hg/fjx2u53i4mL1FBER6aGaTssYhhHgaLxPiYgPBLo+xCM6OpqsrCxAoyIiIj1RY2OjtaN6KNaHgI8Tkeeff56bb76Z+Ph4UlJSWLJkCfn5+b68ZVAIdH1IU56iVfUUERHpeU6ePEljYyOJiYmkpaUFOhyf8GkismvXLp5++mn27t3L9u3bcTgczJ8/P+RXcQRTIuLpKVJTU2Nl1SIi0jOE+rQMgE8LGD788MNmf16/fj0pKSl888033HHHHb68dUAFy9QMuHuKTJgwgS+//JKDBw9a7d9FRCS4ORwOaxYhVKdlwM81IhUVFQD07du31eP19fVUVlY2e/VEwTQiAt9Pzxw/fjzkR6NERELF6dOnqa+vJy4ujsGDBwc6HJ/xWyJimiY//elPue222xg/fnyr5zz//PMkJiZar576Fx9MIyIAKSkppKWl4XK5OHLkSKDDERGRDvDsLTN69OiQnZYBPyYiq1at4tChQ7z22ms3POe5556joqLCehUWFvorPK8KthERUE8REZGexOVyWdMyodjErCm/JCLPPPMM7733Hjt37iQ9Pf2G50VGRpKQkNDs1dMEQ1fV1owfPx6bzcalS5coLi4OdDgiItKGM2fOUFtbS3R0NEOGDAl0OD7l00TENE1WrVrFO++8wyeffMKwYcN8ebugUF9fj8PhAIJnagYgJiZGPUVERHoIz2qZ0aNHY7OFdssvn351Tz/9NL///e959dVXiY+P59KlS1y6dIna2lpf3jagPPUhkZGRhIeHBzia5tRTREQk+JmmybFjx4DQXi3j4dNEZM2aNVRUVDB79mwGDhxovd544w1f3jaggnFaxmPEiBHExsZy7do1awMlEREJLoWFhVRXVxMZGcnw4cMDHY7P+bSPiGmavrx8UGhwNXKiqpAT1YVcrC3lUmkxZ0dewxkTy/GqswyPTSfMZg90mADY7XYmTJjA3r17OXjwoDVVIyIiwcOzWiYrKwu7PTieH74UuB3ZergLtSVsKfqcjy7tpdZZj4GBzbBhmi7MQSbFxjm++fYXxIfFct/AWdyXNovkyD6BDpvJkyezd+9e8vPzqampISYmJtAhiYjId3rbtAxo07tOc7icvHp2K3/89c/ZfOFzap31AJiYOE0nLkxMG/Ddku8qxzU2FG7nx1//Pe8XfYbLdAUueCA1NZWBAweqp4iISBAqKiqioqKC8PBwRowYEehw/EKJSCdUNFTx029/wX+d3YoLExcdSypcmDS4Gllz4i1+dniNlbwEinqKiIgEJ8+0TGZmZtAtePAVJSIdVNl4jb84+CtOXyvq1nUOlh/nfx/+NXXOBi9F1nkTJkzAZrNx8eJF9RQREQkSpmk22+Sut1Ai0gGmafKPR1/mYm1ph0dBbsSFSX7lGdaefMtL0XVeTEwMmZmZABw8eDBgcYiIyPeKi4u5evUqYWFhjBo1KtDh+I2KVTvgo0t7+bY8v9Vj57ce5dA/fNzsvYjEKOKG9WPY8imk3tqyiZsLk48u7eW25ClM7RuYrHfy5MkcO3aMQ4cOMW/evJBvmCMiEuw8oyEjRowgIiIiwNH4j54+7ah3NvDbU5vaPW/i/5rHzF8vY+ZLDzH+z+dg2Ay+ee59ir843er5BgZrTmwI2BLnkSNHEhMTo54iIiJBojdOy4ASkXZ9fvlbrjnb7wQbN6wvfcYNoM/4gQy4YwTT/mEhtgg7RTuOt3q+icnFulIOlRd4O+QOsdvtTJw4EdD0jIhIoJWWlnL58mVsNluv6/GkRKQd2y59iUHnt1+2Rdixhdmwhd34r9hu2NhevLc74XWLZ/VMfn5+SLfdFxEJdp7VMsOHDycqKirA0fiXEpE2OE0XBVXnMOnA9InLxOVw4XI4qS2p5ujqz3HUOUibl9nm9XMrTnox4s4ZMGAAAwYMwOl0qqeIiEgA9dZpGVCxapsu1BTTaDo6dO6elRua/dkWYWfcn9xJ/1va3r65pP4q1Y4a4sIC0+F00qRJXLp0iZycHG6++eaAxCAi0ptdvXqVS5cuYRhGr5uWASUibbraUNXhcyf95d3EDnG3cG+sqOPS5yfJ/ddPMV0uhj4wqc3PVjRWBywRmTBhAtu3b6eoqIiSkhJSUlICEoeISG/lGQ0ZMmQIsbGxAY7G/zQ10wZXR6ZkvhM7pA9Jo1NJGp1K/+lDmPDnc0i+OYNj/7aHxqq2O6m6Arg5YGxsrLVeXUWrIiL+50lExo4dG+BIAkOJSBviwqK79fmE4cm46h1cO3+1zfNiu3mf7po8eTIAhw4dwuUK7F44IiK9SWVlJefPnwdg9OjRAY4mMJSItCEjZkCXVsx4VJ64DEBE0o0TjfiwGPqEx3f5Ht4watQoYmJiqK6u5uTJwBXPioj0Np7RkMGDBxMfH9hnQaCoRqQNkfYIBsekcq7mUrvnVp++gul0T7E0VtZy6bNTlO4vJPX24cQMTGz1MwYGWfFDMYyuJzveYLfbmTBhAl999RUHDx7sVa2FRUQCqTevlvFQItKOu1Km8bszW9pdwtu0zXtYXAQxAxIY8/RtZCyZeMPPmJjcmTLVa7F2x+TJk/nqq684duwYtbW1REcHdrpIRCTUVVdXc/bsWUCJiLRh/oCZvHL2gxu2Yk+/dwzp93btGyg2LJrb+k/uRnTeM2DAAFJTUykuLubIkSNayisi4mPHjh0DIC0tjaSkpMAGE0CqEWlHUkQ8iwfN7latyI38ICObCFu416/bVZ5Oq1o9IyLie5qWcVMi0gGPDbmP1Ki+2LyUjNiwMTp+KIsG3emV63nLxIkTsdlsXLhwgcuXLwc6HBGRkFVbW8uZM2cAJSJKRDog0h7BX479ERG28G4nIzbDRkJ4DP9jzA+xGcH116+eIiIi/pGfn4/L5SIlJYV+/foFOpyACq4nYRAbEZfOzyeuIsoeib2Lf22GCUnhcfy/SX9CalRwfuN5pmfUU0RExHc0LfM9JSKdMDphKC9O/Z+MTRwB0PG6ke/qXJMuR/CHzjmkx6T6KMLuy8zMJDo6mqqqKk6dOhXocEREQk59fb3Vs6m3dlNtSolIJ6VG9eP5iav4adajDIkd6H7ThOtX99qwWYlKXGUYow7HMyo3nr2ffEFdXZ1/g+4ET08R0PSMiIgvHD9+HKfTSb9+/ejfv3+gwwk4JSJdYBgGc1Nv4cWb/ifPj1lF+qkY+lwOJz0qhQFR/RgSM5Db+0/hj4Yv5qWp/4u5F0fTpzQCAJfLxauvvhrgr6BtnpbvR48eDeqkSUSkJ2o6LRPohpbBQH1EusEwDOKrw0k7F01S0kD+5KE/afW8xYsX82//9m/WnwsLCzl27FjQ7iswYMAAUlJSKCkp4ciRI0ybNi3QIYmIhISGhgYKCgoATct4aESkm4qKigB3Q5obSU1NZeDAgc3e27hxY9AWgxqGoZ4iIiI+cOLECRwOB0lJSQwYMCDQ4QQFJSLddPHiRYB2v6EWL17c7M8NDQ1s2rTJV2F128SJEzEMg/Pnz1NaWhrocEREQoKmZVpSItJNnkSkrRERaD4q4vnmO3z4MMXFxb4NsIvi4uLUU0RExIscDgfHjx8HtGy3KSUi3VBXV8eVK1cAWky9tGbp0qUAmKaJzeb+q3/ttdd8F2A3NZ2eCdZpJBGRnuLUqVM0NDQQHx9Penp6oMMJGkpEuuHSpUsAJCYmEhMT0+75/fv3Z9CgQc3eq6io4LPPPvNJfN2VmZlJVFQUVVVVnD59OtDhiIj0aJ5pmdGjR2tapgklIt3gmZbpyGiIx5IlSwD3Mt7Y2FgAdu3aRU1Njdfj666wsDD1FBER8QKn02nttqvVMs0pEemGriQiycnJ1pCcp0dHMPcWUU8REZHuO3PmDHV1dcTExJCRkRHocIKKEpFu6EoiAt/XijidTqvI9cKFC+Tl5Xk3QC8YOHAg/fv3x+FwkJubG+hwRER6pKbTMp4aQXHT30YXNTQ0WMtaO5uI9O3b18qIi4uLrSmad999N+iKQtVTRESke1wulzUto9UyLSkR6SJPoWp8fDxxcXGd/nzTUZEhQ4YAwdtbxNNTpLCwkLKyskCHIyLSo5w7d45r164RFRXFsGHDAh1O0FEi0kVdnZbxSEpKYujQoQDk5+eTmZkJBGdvkfj4eEaOHAloVEREpLM80zJZWVnY7fYARxN8lIh0UXcTEWg+KhIbG0tYmHvrn2DsLaKeIiIinWeaZrNuqtKSEpEu8kYikpCQwIgRIwD3Az47Oxtw9xbZvXt394P0oqysLKKioqisrOTMmTOBDkdEpEe4cOECVVVVREREWP/eS3NKRLqgsbGRy5cvA+23dm9P074i58+fJzU1FYCdO3cG1XLZsLAwxo8fD0BOTk5ggxER6SE8qyEzMzOtUW9pTolIFxQXF2OaJrGxsV0qVG3q+j1dHnroIQzDwOVyBd0UTdOeIvX19YENRkQkyGlapmOUiHRBUVER4B4N8Uab3iVLlmAYBqZpsmvXLmbMmAG4K60LCgq6fX1vSUtLIzk5WT1FREQ64NKlS5SXlxMWFmYV/EtLSkS6wFMfMmDAAK9cLyYmhtGjRwOQm5vLbbfdZu1d88477wRNcahhGNaoiFbPiIi0zTMaMnLkSCIiIgIcTfBSItIFnkSku/UhTS1atMgaFdm8eTPLly8H3G3gt2zZ4rX7dJenp8i5c+esnYdFRKQlTct0jBKRTnI4HFahandWzFwvKirKKgbNz8+nb9++VoX1gQMHguahHx8fb8WlolURkdZdvnyZ0tJSbDab1SdKWqdEpJOKi4txuVzExMSQkJDg1WsvWLAAm82GaZps2rSJhx9+2Gp+E0yb4nl6ihw6dAjTNAMcjYhI8PGslhkxYgRRUVEBjia4KRHppKb9Q7xRqNpURESEVYNx8uRJ6urqmD9/PgBlZWXs37/fq/frqtGjRxMZGUlFRYV6ioiItELTMh2nRKSTvNHIrC333nuvNQqyceNGbrnlFvr27QvAtm3bcDgcPrlvZ6iniIjIjV25coXi4mIMwyArKyvQ4QQ9JSKd5OtEJCwsjGnTpgFw5swZrly5wooVKwB3fcqGDRt8ct/OUk8REZHWeaZlhg0bZq2AlBtTItIJTqeTkpISwHeJCMD8+fOtDnzvvPMOycnJVl3G8ePHuXDhgs/u3VGDBg2iX79+NDY2Wj90IiKiaZnOUiLSCSUlJTidTqKiokhKSvLZfWw2GzNnzgTc+xQUFxezaNEiax36G2+84bN7d5R6ioiItFRRUWE1vfT0h5K2KRHpBF8Wql5v9uzZhIeHA7Bp0yZsNhuLFy8GoKqqil27dvn0/h3h6Sly9uzZoFleLCISSJ7RkIyMjG5vAdJbKBHpBE+W68tpGQ+bzcYdd9wBuNsEnz9/nrFjx1r3/uyzz6ipqfF5HG1JSEhg+PDhgEZFRERA0zJd4dNE5LPPPmPhwoXWniybNm3y5e187tKlS4B/EhGAW2+9lcjISADr7+4HP/iBtSne66+/7pc42uKpXTl48KB6iohIr1ZdXc25c+cAJSKd4dNE5Nq1a0yaNIkXX3zRl7fxC6fT6fdExGazMXfuXMDdR+TUqVPExcVZ9SOFhYUB3xSvaU+Rs2fPBjQWEZFA8oyGDBo0iMTExABH03P4NBG59957+fu//3seeOABX97GL0pLS3E6nURGRlp9Pfzh5ptvtpZ/bd68GYC5c+cGzaZ44eHhjBs3DlBPERHp3TQt0zVBVSNSX19PZWVls1ew8NSHDBgwwOeFqtfLzs4GoLy8nKNHj2Kz2Vi2bBng3hTvww8/9Gs81/OsnsnLy6OhoSGgsYiIBEJNTY3VaVqJSOcEVSLy/PPPk5iYaL0GDx4c6JAsvm5k1pYJEyYQHx8PwAcffADA0KFDGTp0KAD79++noqLC73F5pKen07dvX/UUEZFe69ixY5imSWpqql9HzUNBUCUizz33HBUVFdarsLAw0CFZApmIANx///2AuxjKMwWyfPlya5O81157LSBxgXqKiIh4pmXGjh0b4Eh6nqBKRCIjI0lISGj2CgYul8sqVE1LSwtIDFlZWfTp0weAjz76CICoqCjuuusuwL0r8OHDhwMSG7h7ioC7Lf3Vq1cDFoeIiL/V1dVx6tQpQNMyXRFUiUiwKi0txeFwEB4eHtAht0WLFgFQW1vLl19+CcBtt91mJWzvv/9+wApXExMT1VNERHql48eP43K5SE5Opn///oEOp8fxaSLimUbwTCWcPn2anJwca511T9F0WsZmC1zuNnToUFJSUgD49NNPraRj+fLlADQ0NPDuu+8GLD71FBGR3kirZbrHp0/V/fv3M2XKFKZMmQLAT3/6U6ZMmcLPfvYzX97W6zyJyIABAwIcCSxZsgRwJx2ffvop4J4u8mw1fejQIcrKygIS25gxY4iIiKC8vLzHJZsiIl3R0NDAiRMnANWHdJVPE5HZs2djmmaL18svv+zL23qdJxEJVH1IUwMHDmTQoEEA7NmzxxoVeeihh7Db7QABK1xVTxER6W0KCgpwOBz06dOH1NTUQIfTI6lGpB2mafq9o2p7HnzwQcDd7XXr1q0AhIWFcc899wDuLqwHDhwISGye1TO5ubnqKSIiIa/ptIy/e0yFCiUi7SgrK6OhoYGwsDCSk5MDHQ4Affr0sQpDDxw4YD3wb775ZquYduvWrTgcDr/HNnjwYKuniOcHVEQkFDkcDmubDdWHdJ0SkXY0rQ8JZKHq9ZYuXQq4lxZ7Wr/D94WrDoeDjRs3+j0uwzCsolVNz4hIKDt58iQNDQ0kJCRYU+bSecHzZA1SgW5kdiNxcXFWBp6bm0tNTQ0AKSkpVp1GXl4eJSUlfo/Nk4icOXOG8vJyv99fRMQfPJ2kR48erWmZblAi0o5gTUTA3VfE01m16ejHkiVLCAsLA+D111/3e1yJiYkMGzYMUE8REQlNTqeT/Px8QKtlukuJSBtM0wzqRCQqKsoqDj1x4oQ1+hAWFsa9994LwNWrV/n666/9Hpt6iohIKDt9+jT19fXExsYG1b5oPZESkTZcvXqV+vp67HZ70HbLu/fee61lu2+//bb1/k033US/fv0Ad0t4fxeuenqKXL16VT1FRCTkNJ2WCab6wZ5If3ttKCoqAiA1NdV62AebsLAwZs6cCcD58+etERyARx55BHAXrjZNUvwhIiLCGq7U9IyIhBKXy6VpGS9SItKGYJ6Waequu+4iIiICoFmtSHJyMhMmTADcW1QXFxf7NS71FBGRUHT27FlqamqIjo5myJAhgQ6nx1Mi0oaekojYbDZrF97Lly9z+vRp69iiRYsIDw8H/F+4mpGRQZ8+fWhoaODYsWN+vbeIiK94eiRlZWUF7Wh5T6JE5AaaFqoGQ2v39syYMYPo6GiAZhvfhYWFcd999wFQXl7Ovn37/BaTeoqISKgxTVOb3HmZEpEbKC8vp66uDpvNFrSFqtfzrJSpqKjgyJEj1vuTJ0+2usL6u3DVk4icPn2aiooKv91XRMQXzp8/T3V1NZGRkVaHa+keJSI34BkNSU1NtXpyBLsJEyaQmJgIYO1B4+EpXHU6nX4tXE1KSmLo0KGAilZFpOfzrJbJzMzsMc+GYKdE5AaatnbvSRYtWgRATU0Ne/futd7v169fwApXPUWr6ikiIj2ZpmV8Q4nIDfSk+pCmhg8fbk0l7dy5E5fLZR1rWrj6xhtv+C2mMWPGEB4ezpUrVygsLPTbfUVEvOnixYtUVFQQHh7OyJEjAx1OyFAi0opg76jangcffBCAhoYGPvnkE+v96zuu7t+/3y/xREREWPvfqGhVRHoqz7TMyJEjrV/qpPuUiLSisrKSmpoaDMMgNTU10OF0WmpqKunp6QDs3bu3WXHqlClTrI6r27Zt81vhqqdoNS8vj8bGRr/cU0TEWzQt4ztKRFrhGQ1JSUnpscVIDz30EOAuTt2yZUuzY8uXLwfcHVebNkDzpSFDhpCUlER9fb16iohIj1NSUsKVK1ew2+1kZmYGOpyQokSkFT15WsYjMTHR+mE5ePAgNTU11rH+/ftbbYnz8vK4fPmyz+NRTxER6ck8oyEjRowgMjIywNGEFiUirQiFRARg6dKlGIaBaZotRj6WLl1qjfb4q3DVk4icOnVKPUVEpEfRtIzvKBFpRagkIlFRUdbS2RMnTnD16lXrWFhYGPPnzwegrKzML6MUffr0sfZlOHTokM/vJyLiDWVlZZSUlGCz2cjKygp0OCFHich1qqqqqK6uxjCMHtdDpDX33XeftRfCW2+91ezYzTffTFJSEgAffPBBs6W+vqKeIiLS03hWywwbNszaSkO8R4nIdTyjIcnJySGxPCssLIxZs2YBUFRUxIULF5odf/jhhwFobGxk8+bNPo9n7NixhIeHU1ZWxvnz531+PxGR7tK0jG8pEblOUVER0POnZZq68847reKq62tFBg4caBW15uTkNJu+8YWIiAirUFZFqyIS7MrLy7l48SKGYTB69OhAhxOSlIhc59KlS0BoJSI2m61ZPcj1y2cffPBBa/rGH4WrnqLV3Nxc9RQRkaDmGQ3JyMggNjY2wNGEJiUi1wnFERGAm266ifj4eIAWfUUiIiK46667ACguLrbmQ31l6NChJCYmUl9fT35+vk/vJSLSHZ5/DzUt4ztKRJqorq6mqqoK6Hmb3XXEwoULAffXuW/fvmbHZs2aZSUq7733nk8LV9VTRER6gsrKSquWTYmI7ygRacJTqNqvX7+QbFgzatQokpOTAdixY0eLZMPTjbW+vp5t27b5NJamPUUqKyt9ei8Rka7wTGOnp6eTkJAQ4GhClxKRJnrqjrud8cADDwDuDfF27NjR7FhGRgZDhw4F4Ouvv6a6utpncfTt25eMjAxM01RPEREJSlot4x9KRJrwJCKhOC3jMXDgQAYPHgy4N8RraGhodnzZsmXYbDZM0+TNN9/0aSzqKSIiweratWucPXsWUCLia0pEmugNIyLw/RSMy+Vq0TskJiaGmTNnAlBYWMjp06d9Foenp0hpaWmL/iYiIoF07NgxTNNk4MCB9OnTJ9DhhDQlIt+pqamx9j8J5RERgISEBCvDz83NbTEFM2fOHKt74DvvvOOzOCIjI604VLQqIsFE0zL+o0TkO57RkL59+xIVFRXgaHxvyZIl1hTM9a3fbTYbixcvBtwrbD777DOfxeEpWj1y5AgOh8Nn9xER6aja2lprNFiJiO8pEflOqGx011ERERHcfPPNAJw9e5bi4uJmx7OysqyRoV27drWoJfGWYcOGkZCQQH19fYtGayIigXD8+HFcLhf9+/e3VhqK7ygR+U5vS0QA5s+fb+2n8/bbb7c4/sgjjwDuWpLrR028pWlPkYMHD/rkHiIinaFpGf9SIvKd3piI2Gw25syZA8Dly5cpKChodjwxMdFa2VJQUNBi1MRbPPc4efKk1VBORCQQ6uvrOXHiBIC1L5b4lhIR3POBns3eelMiAjBjxgxr/4T33nuvxfGFCxdaoya+Ws7bt29fBg8erJ4iIhJwBQUFOJ1O+vbtS0pKSqDD6RWUiPD9RndJSUnWapHepGnr96+//rrZMZvNRnZ2NgBXrlzh22+/9UkMnlGRnJwc9RQRkYBpOi1jGEaAo+kdlIgQuhvddVRWVpZVkPXxxx+3aP1+0003Wevot27d6pN9aMaOHUtYWBilpaXWfw8REX9qbGy0pqhVH+I/SkT4fkSktyYi0Lz1+8cff9zi+LJlywD3D+r777/v9ftHRUWpp4iIBNSJEydobGwkMTEx5BtbBhMlImhEBNxf+5AhQwD46quvWizXHThwICNHjgTciYIvNqpTTxERCSRNywRGr09E6uvruXLlCtC7ExFwt343DAOXy8WmTZtaHH/wwQetJmhvvPGG1+/v6SlSV1dHfn6+168vInIjDoeD48ePA5qW8bden4h4lu0mJCRYq0d6q7i4OMaNGwe4fzPwtLz3iIqKYtasWYB7FOnkyZNevb/NZmPixImAeoqIiH+dPn2a+vp64uLirI1BxT+UiPSSje46avHixdjtdgA2bNjQ4vjs2bOtlUUbN270+v09q2dOnDihniIi4jd5eXkAjB49WtMyfqZE5LtEJNQ3uuuosLAwbr31VgAuXLhAYWFhs+M2m42lS5cC7m2yvb0PTb9+/ayeIocPH/bqtUVEWuNyuazpYDUx87+wQAfgL9fqGviy4Bx5F4rJL7pMdV0DdptBRXERMQ3hzIiIxTRNZcK4Rz2+/vpr6urqeOedd/iTP/mTZsdHjRrFgAEDuHTpEp999hkzZswgIiLCa/efNGkShYWF5OTkMHPmTP03EZFuq6lvYG9BIbnni8m/eJmq2nrsNoOBSQmkRtspqq5nYGy0VbQv/hPyiUhhWTn/uesAm/bnUtfowG6z4XK58LTMMjAxieLbdz5n1J6jPHb7FBZPG4vd1nsHizxNzDZt2kR5eTmHDx9mwoQJzc5Zvnw5v/rVr3A6nWzcuJHly5d77f7jxo3jww8/5PLly1y8eFHTZiLSZReuVPCfnx3gnX1HWn0G2G0GLpeJSRwpRjgjvs5lybRxhNl77zPA30L2b9rlMnnl8wMs+qffseGrQ9Q1upeDOpt8AwKYGID7N+4TxaX8bMN2/mD165wqueL/oIPIpEmTSEpKAuCDDz5o0cQsKSnJSk6OHTtGaWmp1+4dFRXF6NGjAfUUEZGucblMXvsih0X/9J+88eXBGz4DnC7T+vPlmkb+9q2PWbH6NU5c8t6/adK2kExE6hodrHr5Xf7fe7todDpxujrWMtzTWfxoUQkP/vIVPs075cMog5+nFqSuro5du3a1OL5o0SLCwtyDat5ezuspWlVPERHprAaHg5/8bjM/37STekcnngHf/e/xi5d56F//i48Pn/BdkGIJuUSk0enkJ//5HruPnenyNZwuE4fTxZ908zo9XUZGBoMGDQLgiy++aJEQhIWFMXfuXABKS0utqnNvGDZsGPHx8dTW1lpr+0VE2uNwuvjpK1vY2Y1fJJ0uE6fTxU9feZ9P87zbpkBaCrlE5Dc79vFF/llc3dw4zQRcpsmf/f59SiqqvRNcD+Rp7e50OlttcjZjxgwSEhIA2Lx5s9f2oVFPERHpiv/4dD+f5p3q9uaZJmCaJn/xX1u5WK5WAr4UUsWqxy6UsPbjr2jv26/uchFl+3dxrfAkjmuVGDYbEX36kzh6CkkTphMW7W5sZpruaZ6/eWs7v/6jJb1y9UZiYiJjx44lLy+P3Nxc5s+fbyUeHg8++CDr16+nrq6OHTt2cPfdd3vl3pMnT+aLL76goKCA6upq4uLivHJdEQlNBZdKeemjPTc8nvvPP233Gv1nzidllnvHcRP3NM//fvMj/v3HD/TKZ4A/hFQi8qsPv8AwoK1M5MqhL7n48dtE9kkh+ea7iOyXiulyUltcyJWDe6gpOkPGkj+yzne6TD4/doZvzxRx07BBvv8igtDixYs5duwYLpeLDRs28KMf/ajZ8YyMDAYPHkxhYSF79+7l9ttvJyoqqtv3TU5OJj09nfPnz3P48GFmzpzZ7WuKSOha/eGNkxCAYT94ttX3TZeLC1tfxVFdQdzw5u3dnS6TvQXn2HeykOkjM7wWq3wvZKZmLlypYPexM20WJdUUneHi9reJy8hk+GM/pe+UWcRmjCRuaBb9p89j5B/9L5LG39Lic3abwet7eu/0QEREhJUEnD9/nvPnz7c45+GHH7b2qXnrrbe8dm/PRng5OTndHmoVkdB1qbyKT/NOtfkMiEkb2uqrMj+HxoorDJjzADEDW/YRsdsMXuvFzwBf80si8utf/5phw4YRFRXF1KlT+fzzz71+j605+e0Om13e+zEYkDZ/GbawloNBNnsYCSPHt3jf6TL56FAB9Y29d/XGnDlziIyMBODtt99ucTwuLo4pU6YAcPLkSYqLi71y33HjxmG32ykpKeHSpUteuaaIhJ4PD3atqL08dz9Xvt1N0oTp9J3U+qir02XyyZGT1NQ3tHpcusfnicgbb7zBT37yE/7qr/6Kb7/9lttvv517772Xc+fOefU+h8+1/ZAyXS6unTtBdGo64Ql9On19h8vF8Yu9d125zWbj3nvvBaC8vLzVAtL777+f8PBwoPV9aroiOjpaPUVEpF1HCi/R2QqO2uLzFG3fQPSAwQyc+2Cb57pMk2NFl7seoNyQzxORX/7yl/zoRz/iySefZMyYMfzrv/4rgwcPZs2aNV69z+HC4jZXyjhrr2E6GghP7Nflexy9UNLlz4aCpk3Otm7d2mKFjM1mY/78+QCUlZV5ba8YT0+Rw4cP43Q6vXJNEQkthwsv4ezE9K2jpprCd9djC49k8KLHWx0lb8ow9AzwFZ8mIg0NDXzzzTfWw8lj/vz57NnTsqiovr6eysrKZq+Oqqyt63a8bbHbbJTX+PYePcGDD7p/a6ivr+eTTz5pcXzatGkkJiYCsGXLFq8s5x0+fLh6iohImyo68e+z6XJx/v1XaKyqYPDCxzo0Sm439AzwFZ8mIqWlpTidTlJTU5u9n5qa2up8//PPP09iYqL1Gjx4cIfv1d6qKnt0LEZYBI0VZR2+ZnNmu/foDdLT063/Ll9++SUNDS3nTJsmKx9//HG372mz2ax28uopIiKtMToxMVO8azPXzhWQescCYjNGdeIe4gt+KVa9voj0RrvcPvfcc1RUVFiv67egb0tSTHTbMdhsxA0ZRW3xeRqryjt8XQ+ny6RPbNv36C0eeugha4XMxo0bWxwfPHgwGRnuZW5fffUVdXXd/y3CMz1TUFDAtWvXun09EQktHf33ueLoAcq+2UVC1mSSb57d4es7XS49A3zEp4lIcnIydru9xehHSUlJi1ESgMjISBISEpq9Omr84AHY2hmySJ4+F0wo2vYmLmfLFTCm00nVydwbfn7MoJQOxxPKEhISGD/evbro2LFjXLnScoPAZcuWeXU5b//+/Rk0aBAul8trtSciEjomZAzAbmv7GVB3uYgL294kMnkAg+7p3I7hJnoG+IpPE5GIiAimTp3K9u3bm72/fft2br31Vq/ea2LGgHbPiUkbysC7H6T63HFOvfJLrnz7BdcKT1B99jil+z7hxPr/x9XDX7X62XC7jVEDul7oGmoWLVqE3W4HWl8hExcXx0033QR4bzlv054iIiJNTcgY0PaChboazm36D0yng+Rb5lBXepGaojMtXg3lra+ODLPZyErr76vwezWfd1b96U9/ymOPPca0adOYOXMmv/nNbzh37hx//Md/7NX73DdlNP/ywe52z+s7cSYxAzIo++YzSvd9gqOmEsNmd7d4H3MTfafc1uIzdpvBfVNGE9FOVXVvEhYWxp133sknn3zCpUuXOHnyJCNGjGh2zn333cehQ4dobGxkw4YNrFq1qlv3HD9+PNu2baO4uJhLly4xYED7yaeI9A7ZEzP5p827brhypq6kiMYK9+jthQ9eveF1ksbdzKB7VzR7z24zuGdSJtER4d4LWCw+f7IuX76csrIy/s//+T9cvHiR8ePH88EHHzBkSMvudd2RmhjHnHEj2Jl3st0tn6NSBrX4RmuL02XyyK2TuhtiyLn99tvZu3cvNTU1bNq0iT/7sz9rdtyznHfLli2UlZVx5MgRa0qnK6Kjo8nKyiIvL4+cnByys7O7+yWISIioLC1mWLTByWsuzFbKSmMzRjLuz3/ZpWs7XSbLZ07sbohyA34pVv3v//2/c+bMGerr6/nmm2+44447fHKfZ++d5fVNiew2g3smZjJhsH77bs2iRYsAqK6u5ssvv2xxfNq0aVatjzeW86qniIg0VVpaymuvvcYrr7zCKLPC6ytb7DaDOeNGMGVompevLB4hs9cMwPCUvjybPctr17MZBrGREfz1A3O8ds1Qk5WVRf/+7nnTTz75BIejZRGwZzlvXV0dO3fu7Nb9RowYQVxcHDU1NRQUFHTrWiLSc9XW1rJ161bWrFnD8ePHsdlszJ15Cz+517vPgOiIcH724FztvOtDIZWIAPzwjpu4Z2Jmt3t+2AwDu81g9eOLtGSrHcuWLQPA4XCwZcuWFsczMjJIT08HYM+ePa32Huko9RQR6d2cTid79+7lhRdeYN++fbhcLjIzM1m5ciXZ2dk8PvsW7p8yutsjI4YBNpvBr364kOT4WK/ELq0LuUTEbrPxDz/I5r7J7v1JuvLNaLcZRIaHsfbHDzB1eLp3AwxB/fv3Z9Qod1OggwcPUl1d3eKcpst533nnnW7dzzM9c/z4cfUUEeklTNMkPz+fNWvWsG3bNurq6khJSeGxxx5jxYoVJCcnA+7k4efL72HxtLFAN54BYWGs+aMlTB+Z4cWvQloTcokIQLjdzj+syObny+cTHRHebn8RD895N48YzHt//ofcMqLjnV17uwceeACbzYZpmq0u501ISLBGMvLz8ykr62qHW0hJSSEtLU09RUR6ieLiYl555RVef/11ysrKiI2NZcGCBTz11FMMHz68xflhdhv/9+H5/MOKbGIiIzr9DJgydBDv/vkfMjPTu4sqpHUhux7VMAwWTxvHrZlDeG3PQd748hAVNXXYDAPDcFdBG4Z7/wDHdwWUU4cP4g9mTWHu+BGaD+ykqKgoZsyYwZ49ezh37hyFhYUtWvQvXLiQvLw8HA4HGzZs6NYS7kmTJlFUVMTBgweZMWNGd8MXkSBUXV3Nzp07+fbbbzFNE7vdzowZM7j99tuJjIxs87OGYbDgpjHMGJXB6989A65eq23zGTBlaBp/cNtk7p4wSs8APzJMsxPbFfpZZWUliYmJVFRUdKrLamsaHU6+PVtE3vkS8osuc62+gTC7jdTEOMalpzJpyEAG90vyTuC9lMvl4h//8R+pr68nMTGRn/zkJy3O2bNnj9Xg7gc/+IE1pdNZNTU1/PKXv8TpdPLUU0+pp4hICHE4HOzdu5fPP//cqikbO3Ys8+bNo0+f9jeoa02j00nOmYvknS8m/+Jlquvcz4CUhDjGpqcweUgaGclJXvwqerfOPL97TSIi/nH48GGrBmThwoVWd9WmfvGLX1BdXU1MTAx/8Rd/0eV7vfnmmxw9epQZM2Zwzz33dPk6IhIcTNMkLy+Pjz/+mPLycgDS0tK45557rP2rpGfozPM7JGtEJHAmTJhA3759Afjwww9b7RuyePFiwD2q8cUXX3T5Xp6i1UOHDqmniEgPd+HCBV5++WXeeustysvLiY+PZ8mSJTz55JNKQkKcEhHxuoceegiAxsZGPvzwwxbHR44caW16+Omnn7bae6QjRowYQWxsLDU1NZw4caLrAYtIwFRWVrJx40bWrVvHuXPnCA8P584772TVqlVMmjRJtRq9gBIR8bqBAwcybNgwAPbv309NTU2Lc5r2Hnn//fe7dB+73c7Eie62y+opItKzNDQ08Omnn7J69WoOHToEuIvQV61axezZs4mIiAhwhOIvSkTEJx566CEMw7jhct5+/fqRlZUFuKdWWus90hGeHXnz8/NbTXhEJLiYpsnBgwd58cUX2bVrFw6Hg8GDB/Pkk0+yZMkS1QP2QkpExCdiYmK4+eabAThz5gxFRUUtzmmv90hHpKamMnDgQPUUEekBzp07x7p169i0aRNVVVUkJSXx0EMP8cQTTzBo0KBAhycBokREfOaee+6xhldbSzQiIiKsHiDnzp3jwoULXbqPZ1RE0zMiwenq1ats2LCB9evXU1RUREREBHPnzuXpp59m3LhxqgPp5ZSIiM/YbDbuvfdeAMrLy/n2229bnDN37lyrMdHbb7/dpftMmDABm83GxYsXKS4u7nrAIuJV9fX1bN++nZdeeom8vDwMw+Cmm27imWee4bbbbiMsLGR7akonKBERn5o8ebLVgKi15bw2m43s7GzA/VtTV6ZXYmJirHoTjYqIBJ7L5eKbb77hhRdeYM+ePTidToYPH85TTz3FwoULiYuLC3SIEkSUiIjPeVbINDQ0tLqcd/LkySQmJgLwwQcftNp7pD2e6Rn1FBEJrFOnTrF27Vref/99ampq6NevHytWrODRRx+1lu2LNKVERHxu4MCB1sZU+/fvb3WFzAMPPABAXV0dn376aafvMXLkSGJiYrh27RonT57sVrwi0nmlpaW89tprvPLKK5SUlBAVFUV2djYrV64kMzNTdSByQ0pExC+WLVtmrZB56623WhzPyMiwqua/+OILa3+JjlJPEZHAqK2tZevWraxZs4bjx49js9mYPn06zz77LNOnT8dutwc6RAlySkTEL6Kiopg+fToAZ8+epbCwsMU5Dz/8MOCeX37vvfc6fQ9Py3f1FBHxPafTyd69e3nhhRfYt28fLpeLzMxMVq5cSXZ2NtHR0YEOUXoIJSLiN/PmzWtzhUxCQgLjxo0DIDc3l4qKik5dPzU1lQEDBuB0Ojly5Ej3AxaRFkzTJD8/nzVr1rBt2zbq6upISUnhscceY8WKFSQnJwc6ROlhlIiI39hsNu6//34AKioq+Prrr1ucs2jRImw297dlV5qcqaeIiO8UFxfzyiuv8Prrr1NWVkZsbCwLFizgqaeesurARDpLiYj41YQJE+jXrx8AH330UYsVMhEREcyaNQtw78bZ2hROe9e32WwUFRVRUlLinaBFernq6mo2b97M2rVrOX36NHa7nVmzZvHMM88wdepU65cHka7Qd4/4nacWxOFwsHnz5hbHZ8+eTVRUFADvvPNOp64dGxtLZmYmoFERke5yOBzs3r2b1atXc+DAAUzTZOzYsTz99NPNplpFukOJiPhdSkqKlSzk5OS0qAVp2uSsvLy8003OmvYU6UpPEpHezjRNcnNzeemll9ixYwcNDQ2kpaXxxBNPsGzZMqtJoYg3KBGRgHjwwQet4dw333yzxfFJkyaRlJQEdL7J2ahRo4iJiaG6ulo9RUQ66cKFC7z88su89dZblJeXEx8fz5IlS3jyySfJyMgIdHgSgpSISEBERERw++23A1BUVMSJEydanLN06VLA3eRs165dHb623W5nwoQJgHvERUTaV1lZycaNG1m3bh3nzp0jPDycO++8k1WrVjFp0iQ1JBOfUSIiATN79mxiYmIA2LhxY4vjGRkZpKWlAe4mZw6Ho8PXbtpTpLa2tvvBioSohoYGPv30U1avXs2hQ4cA94jkqlWrmD17trWDtoivKBGRgFqyZAkANTU1fPbZZy2Oe/apcTqdnWpyNmDAAFJTU9VTROQGTNPk4MGDvPjii+zatQuHw0FGRgY//vGPWbJkCQkJCYEOUXoJJSISUKNGjWLgwIEA7Nq1q0Vr96SkJEaPHg3AkSNHWt2n5kbUU0SkdefOnWPdunVs2rSJqqoqkpKSWLZsGY8//rg1CiniL0pEJOCWL18OuFu7t9ZxdenSpW3uU3MjEydOxGazceHCBS5fvuy1eEV6qqtXr7JhwwbWr19PUVERERERzJ07l6effpqxY8eqDkQCQomIBFxiYqI1enH8+HGKi4ubHY+IiOCWW24B3PvUXH/8RmJjYxk1ahSgolXp3err69m+fTsvvfQSeXl5GIbBTTfdxDPPPMNtt91GWFhYoEOUXkyJiASFRYsWER4eDrTe2v3uu++2iuY6MyriSXAOHz6sniLS67hcLvbv388LL7zAnj17cDqdDB8+nKeeeoqFCxcSFxcX6BBFlIhIcLDZbMyfPx+AsrKyFnUdNpuNuXPnAlBaWkp+fn6HrpuZmUl0dDRVVVWcOnXKu0GLBLGTJ0+ydu1atmzZQk1NDf369WPFihU8+uijpKamBjo8EYsSEQka06ZNa7OJ2S233GL9Bvf+++936JrqKSK9TWlpKa+99hq///3vKSkpISoqiuzsbFauXElmZqbqQCToKBGRoOLZh6ahoYEtW7a0OL5o0SLAvQnXV1991aFrenqKHDt2TD1FJGTV1taydetW1qxZw/Hjx7HZbEyfPp1nn32W6dOnY7fbAx2iSKuUiEhQGThwICNGjADg22+/pbKystnxUaNGkZycDMCOHTs6VPcxYMAAUlJScDqd5Obmej9okQByOp3s3buXF154gX379uFyucjMzGTlypVkZ2cTHR0d6BBF2qRERILOQw89ZC3XfeONN1o9DtDY2Mj27dvbvZ5hGOopIiHHNE3y8/NZs2YN27Zto66ujpSUFB577DFWrFhhJewiwU6JiASdqKgobrvtNqD1fWhSU1MZMmQIAPv27WvRBK01EydOxDAMzp8/T2lpqfeDFvGj4uJiXnnlFV5//XXKysqIjY1lwYIFPPXUUwwfPjzQ4Yl0ihIRCUp33nlnm/vQPPDAAxiGgcvl4t133233enFxceopIj1edXU1mzdvZu3atZw+fRq73c6sWbN45plnmDp1qrWjtUhPou9aCUo2m83afbempoadO3c2O56QkMDYsWMByMvLa1FL0hrP9MyhQ4fUU0R6FIfDwe7du1m9ejUHDhzANE3Gjh3L008/zbx584iMjAx0iCJdpkREgtbIkSOtfS92795NXV1ds+OLFi2yfgNsrTX89Zr2FDl9+rT3AxbxMtM0yc3N5aWXXmLHjh00NDSQlpbGE088wbJly+jTp0+gQxTpNiUiEtSWL19uTcFc33E1IiKC6dOnA+5NvNpr/R4WFsb48eMBTc9I8Ltw4QLr16/nrbfeory8nPj4eJYsWcKTTz5JRkZGoMMT8RolIhLUEhISuOmmmwA4deoU58+fb3Z83rx5nWr93rSnyPUjLCLBoLKyko0bN7Ju3ToKCwsJDw/nzjvvZNWqVUyaNEkNySTkKBGRoHffffdZycb1oyLXt34vKCho81oDBw6kf//+OBwO9RSRoNLQ0MCnn37K6tWrOXToEOCua1q1ahWzZ8+2fgZEQo0SEQl6NpuNBQsWAO7fFvfu3dvs+C233EJsbCwAmzdvbvNahmFYoyLqKSLBwDRNDh48yIsvvsiuXbtwOBxkZGTw4x//mCVLlpCQkBDoEEV8SomI9AgTJkywGjR9/PHHOByOZsfvv/9+AKqqqjhw4EC71zIMg8LCQsrKynwTsEgHnD17lnXr1rFp0yaqqqpISkpi2bJlPP7441ahtkioUyIiPcYjjzwCuFtav/POO82OjRkzhr59+wLw0Ucftbk8Nz4+npEjRwIqWpXAuHr1Khs2bODll1+mqKiIiIgI5s2bx9NPP83YsWNVByK9ihIR6TH69etnrXo5evQoJSUlzY57+o7U19eza9euNq+lniISCPX19Wzfvp2XXnqJvLw8DMPgpptu4plnnmHWrFmEhYUFOkQRv1MiIj3K4sWLrX+s33zzzWbH0tPTreHsL774osX0TVNZWVlERUVRWVnJmTNnfBavCIDL5WL//v288MIL7NmzB6fTyfDhw3nqqadYuHAhcXFxgQ5RJGCUiEiPEhYWxj333ANAWVlZi3oQz4Z4TqeTDz74oM3rqKeI+MPJkydZu3YtW7Zsoaamhn79+rFixQoeffRRUlNTAx2eSMApEZEeZ9q0aVZHyQ8//LDZ1EqfPn2a1X+01SvEs3rm6NGj6ikiXldaWsqrr77K73//e0pKSoiKiiI7O5uVK1eSmZmpOhCR7ygRkR5p+fLlADQ2NrbY9G7p0qUYhoFpmq1umOeRlpZGcnIyDoeDvLw8n8YrvUdNTQ1bt25lzZo1FBQUYLPZmD59Os8++yzTp0/HbrcHOkSRoKJERHqk1NRUsrKyAHfB6ZUrV6xjMTExTJw4EYDjx49TUVHR6jWa9hTR9Ix0l9PpZO/evaxevZp9+/bhcrnIzMxk5cqVZGdnEx0dHegQRYKSEhHpsR544AHrt8vXX3+92bEFCxZYx9raEG/ixIlWT5GmyYxIR5mmSX5+PmvWrGHbtm3U1dWRkpLCY489xooVK6z+NyLSOp8mIj//+c+59dZbiYmJISkpyZe3kl7I03sB4PLlyxw+fNg6FhYWxowZMwAoLCzk4sWLrV4jPj6eESNGABoVkc4rLi7mlVde4fXXX6esrIzY2FgWLFjAU089xfDhwwMdnkiP4NNEpKGhgWXLlrFy5Upf3kZ6sRkzZpCYmAjA+++/36xwdc6cOdb+HG3Vinh6ihw8eBDTNH0YrYSK6upqNm/ezNq1azl9+jR2u51Zs2bxzDPPMHXqVGw2DTaLdJRPf1r+7u/+jj/90z9lwoQJvryN9HIPP/ww4E58m+41Y7PZmDNnDuAeMTl16lSrnx89ejSRkZFUVlZy+vRp3wcsPZbD4WD37t2sXr2aAwcOYJomY8eO5emnn2bevHlERkYGOkSRHieo0vb6+noqKyubvUTak5aW1mzJ7tWrV61j06dPJyYmBqDF6hqPpj1FtBGetMY0TXJzc3nppZfYsWMHDQ0NpKWl8cQTT7Bs2TJrObmIdF5QJSLPP/88iYmJ1mvw4MGBDkl6iGXLlt2wcPW+++4D3Dv3Nq0jacqzeiYvL4/6+nrfBSo9zoULF1i/fj1vvfUW5eXlxMfHs2TJEp588kkyMjICHZ5Ij9fpRORv//ZvMQyjzdf+/fu7FMxzzz1HRUWF9SosLOzSdaT3iYiIsKZhSkpKmiUc48aNs+pItm7d2urnBw0aRL9+/dRTRCyVlZVs3LiRdevWUVhYSHh4OHfeeSerVq1i0qRJakgm4iWd3mFp1apV1i6oNzJ06NAuBRMZGak5VumyW2+9la+++orKykref/99xo0bZxUNLl68mN/97nfU1tby5ZdfMnPmzGaf9fQU2bFjBzk5OUyZMiUQX4IEgYaGBr744gv27Nlj7Vc0adIk5syZQ0JCQoCjEwk9nU5EkpOTtS5egtby5cv593//d6twdfHixQAMGzaMlJQUSkpK2LlzJ9OnT2+xsmHixIl88sknnDt3jitXrtC3b99AfAkSIKZpcujQIXbs2EFVVRUAGRkZ3HPPPdZmiiLifT6tETl37hw5OTmcO3cOp9NJTk4OOTk5VFdX+/K20ou1Vbj6wAMPAO628Dt37mzx2YSEBKv3g4pWe5ezZ8+ybt06Nm3aRFVVFUlJSSxbtozHH39cSYiIj/k0EfnZz37GlClT+Ju/+Ruqq6uZMmUKU6ZM6XINiUhH3KhwNTU1lfT0dAC+/PJLa9i9KfUU6V2uXr3Khg0bePnllykqKrKa5D399NOMHTtWdSAifuDTROTll1/GNM0Wr9mzZ/vyttLLRUREMHfuXKBl4eqDDz4IuPcF+eCDD1p81tNTpKKigjNnzvglXvG/+vp6tm/fzksvvUReXh6GYTB16lSeffZZZs2aRVhYp2etRaSLgmr5roi3zJw501ops3nzZqvjalJSUrOpm7q6umafCw8PZ9y4cYCmZ0KRy+Vi//79vPDCC+zZswen08nw4cN56qmnWLBgAbGxsYEOUaTXUSIiIWv58uWAuyZk06ZN1vtLly7FMAxM0+S9995r8bmmPUUaGhr8Ear4wcmTJ1m7di1btmyhpqaGfv36sWLFCh599FFSU1MDHZ5Ir6VERELWwIEDycrKAuDw4cOUlZUBEBMTY416HD16tEXxdHp6On379qWxsVE9RUJAaWkpr776Kr///e8pKSkhKiqK7OxsVq5cSWZmpupARAJMiYiEtAceeMAqXH3ttdes9xcuXGgt333nnXeafcbTUwS0I29PVlNTw9atW1mzZg0FBQXYbDamT5/Os88+y/Tp063vCxEJLCUiEtIiIiKYP38+AGVlZRw4cMB6f+rUqQCcPn2aK1euNPvcxIkTAfeyzqZLgCX4OZ1O9u7dy+rVq9m3bx8ul4vMzExWrlxJdnY20dHRgQ5RRJpQIiIh75ZbbrE2Jdu6dau1bDc7O9v6rfj6UZHExET1FOlhTNMkPz+fNWvWsG3bNurq6khJSeGxxx5jxYoVasQoEqSUiEiv4ClcdTgcbNy4EQCbzcatt94KuDc2u3jxYrPPeKZn1FMk+BUXF/PKK6/w+uuvU1ZWRmxsLAsWLOCpp56yEkoRCU5KRKRXSE1NtQpU8/LyKC4uBmD27NlEREQANFtZA+6eIhEREZSXl3P27Fm/xisdU11dzebNm1m7di2nT5/Gbrcza9YsnnnmGaZOndqijb+IBB/9lEqvsWTJEsLDw4HvO67abDbuuusuwN38rGkTM/UUCV4Oh4Pdu3ezevVqDhw4gGmajBs3jqeffpp58+Zp80yRHkSJiPQaYWFh3HfffQCUl5ezd+9eAGbMmGEVMF7fV8QzPZObm6ueIkHANE1yc3N56aWX2LFjBw0NDaSlpfHEE0/w0EMPWbVAItJzKBGRXmXy5MlW0eLHH39sJReelTVXr14lPz/fOn/w4MFWT5GjR4/6P2CxXLhwgfXr1/PWW29RXl5OfHw8S5Ys4cknnyQjIyPQ4YlIFykRkV7nBz/4AeBe5vnmm28C7gQlLi4OgC1btljnGoZhbYSnniKBUVlZycaNG1m3bh2FhYWEh4dz5513smrVKiZNmqSGZCI9nBIR6XX69OnDlClTAHfb78LCQgDuv/9+AKqqqprVhHgSkTNnzlBeXu7fYHuxhoYGdu7cyerVqzl06BDg/m+xatWqZkXGItKzKRGRXmnBggVWQaNnVGT06NEkJSUBsG3bNuvcxMREhg0bBqho1R9M0yQnJ4cXX3yRzz77DIfDQUZGBj/+8Y9ZsmQJCQkJgQ5RRLxIiYj0SjabjcWLFwPuJaA7d+4EYNGiRQDU1tayb98+63z1FPGPs2fPsm7dOt59912qqqpISkpi2bJlPP7446SlpQU6PBHxgbBAByASKGPGjCEtLY2ioiJ2797N9OnTGTZsGMnJyZSWlvLJJ58wbdo0bDab1VPk6tWrnDt3jiFDhgQ6/JBy9epVPv74Y2uTwYiICO644w6mT59OWJj+mRIJZRoRkV5txYoVGIaBy+WyNsVbsmQJAPX19XzxxReA+8E4duxYQEWr3lRXV8f27dt56aWXyMvLwzAMpk6dyrPPPsusWbOUhIj0AkpEpFeLi4uz2ryfP3+e/Px8Bg0axIABAwD4/PPPcblcwPfTM3l5eeop0k0ul4v9+/ezevVq9uzZg9PpZPjw4Tz11FMsWLCA2NjYQIcoIn6iRER6vTlz5hATEwO427y7XC5rVKSxsdGqH8nIyKBPnz40NDSop0g3nDx5krVr17JlyxZqamro168fK1as4NFHHyU1NTXQ4YmInykRkV7PZrOxbNkywD1VsGXLFlJTU0lPTwfgyy+/xOVyNespotUznVdaWsqrr77K73//e0pKSoiKiiI7O5uVK1eSmZmpfiAivZQSERFg6NCh1i6tBw4c4OrVqzzwwAOAu/HZhx9+CHzfU+T06dPqKdJBNTU1bN26lTVr1lBQUIDNZmP69Ok8++yzTJ8+HbvdHugQRSSAlIiIfGf58uXWQ/HVV1+lT58+DB06FIBvvvkGh8NBUlKS9Z6nyZa0zul0snfvXlavXs2+fftwuVxkZmaycuVKsrOzrf19RKR3UyIi8p2IiAjmzZsHuKcRDhw4wNKlSwF3ceUHH3wAqKdIe0zTJD8/n1//+tds27aNuro6UlNTeeyxx1ixYoW114+ICCgREWlmxowZ1g6uW7duJSYmhpEjRwLuxKOhoYExY8YQERHBlStXrPbw4lZcXMwrr7zC66+/zpUrV4iNjWXBggX8t//236ypLxGRppSIiFxnxYoVADgcDt566y2WLl1q9RrZvHmzeoq0orq6ms2bN7N27VpOnz6N3W5n1qxZPPPMM0ydOhWbTf/UiEjr9K+DyHX69+/PxIkTAcjPz+fKlStkZWUBkJubS11dnVW0mpubS2NjY8BiDTSHw8Hu3btZvXo1Bw4cwDRNxo0bx9NPP828efOs/XxERG5EiYhIKxYvXmzt7vrGG2+wePFiDMPANE3effddhgwZQlJSUq/tKWKaJkeOHOHFF19kx44dNDQ0kJaWxhNPPMFDDz1kTW+JiLRHiYhIK2w2m9XUrLq6mj179jBu3DjAPUpSW1vba3uKXLhwgfXr1/P2229TUVFBfHw8S5cu5cknnyQjIyPQ4YlID6NEROQGxowZw6BBgwDYvXs3c+bMwWazYZomGzdutBKRU6dOUVFREchQ/aKyspKNGzeybt06CgsLCQ8P584772TVqlVMnDhRDclEpEuUiIi04ZFHHrGmZDZs2GAlHydOnMBut1u78IZyT5GGhgZ27tzJ6tWrra9z0qRJrFq1itmzZ1tTWCIiXaFERKQNcXFx3H777QBcvHiRIUOGWCtA3n33XaunSE5OTsj1FDFNk5ycHF588UU+++wzHA4HGRkZ/PjHP2bJkiUkJCQEOkQRCQHaY1ukHXfddRfffvstVVVVfPDBB0yePJkDBw5w6tQpsrOzCQ8P58qVK5w/f57BgwcHOlyvOHv2LNu2bePixYsAJCUlcffddzNmzBhNwYiIVykREemA5cuXs27dOhoaGqivr8dut+N0OtmyZQtjx47l4MGD5OTk9PhE5OrVq3z88cfk5eUB7m6zd9xxB9OnTycsTP9ciIj3aWpGpAMGDRrE6NGjAXfvEE9Ds7Nnz1odQ3tyT5G6ujq2b9/OSy+9RF5eHoZhMHXqVJ599llmzZqlJEREfEb/uoh00IMPPsg//uM/0tjYyLlz56xRkf3795OYmEhFRQXHjh1jwoQJgQ61w1wuFwcOHGDnzp3U1NQAMHz4cObPn09qamqAoxOR3kAjIiIdFBYWxv333w9ARUWFtbS3sLCQUaNGAT2rp8jJkydZu3YtW7Zsoaamhn79+rFixQoeffRRJSEi4jcaERHphEmTJrF3714uXbpEYWGhNSpy/vx5wN1TpLKyMqhXlJSWlvLRRx9RUFAAQHR0NHfeeSfTpk3DbrcHODoR6W00IiLSSStWrLB6i8TExABw6dIlBgwYgGmaQdtTpKamhq1bt7JmzRoKCgqw2WxMnz6dZ555hunTpysJEZGA0IiISCclJCQwa9Ysdu/eTVVVlTUqUldXB7h7isyaNStolrk6nU6+/vprdu3aZcWYmZnJ3XffTXJycoCjE5HeTomISBfMnTuXnJwcqqurrffKy8ux2+2UlZVx4cIF0tPTAxihuyHZ8ePH+eijj7hy5QoAqampzJ8/31rpIyISaEpERLpo+fLl/Pa3v8XpdFpTNeHh4TidTnJycgKaiBQXF7Nt2zZOnz4NQGxsLHfddRdTpkyxOsOKiAQDJSIiXZSens7o0aM5duyY1d7dM/Vx5MgRsrOz/d5/o7q6mp07d/Ltt99imiZ2u50ZM2Zw++23ExkZ6ddYREQ6QomISDc07S3iYbPZqK+v59ixY4wfP94vcTgcDvbu3cvnn39OQ0MDAOPGjWPu3Ln06dPHLzGIiHSFEhGRbggLC2PhwoW888471nsulwtw9xTxdSJimia5ubl8/PHHVFRUAJCWlsY999xDRkaGT+8tIuINSkREumnChAl8+eWX1gZxHidPnuTcifNczC/m9OFz1FbXYQ+zk5KRzKipwxkyNp2w8K7/CF64cIFt27ZRWFgIQHx8PPPmzWPChAlBs2JHRKQ9hhnEe5dXVlZarbODuUGUSHV1Nf/yL/+Cy+XC5XBxObeCi1+VUX3RXTNis9uw2QxMwNnoBCA6Por7fjSXBSvvIX3UwA7fq7Kykh07dlj9SsLDw5k1axa33nor4eHhXv/aREQ6qzPPbyUiIl6ya9cu3v3PLRzfeJ76ikYwgHZ+umx2G6bLZNmfL+KHf/cwEVERNzy3oaGBL774gj179uBwOAB3p9c5c+bo50NEgkpnnt+amhHxAtM0OfPJJQ6/fNqdgEC7SQiAy+muJ9nwi/fY8+4+nv/wrxkwNKXFtQ8ePMgnn3xCVVUVABkZGdxzzz2kpaV588sQEfE7JSIi3WSaJr/5i1d465ebv3ujC9dwmRSdKuZPZv01L+z5OalD+gNw9uxZtm3bZtWfJCUlcffddzNmzBjVgYhISFAiItJN29bv/D4J6QaXw0XF5Qr+6v7/j+d3/CU7d+3k6NGjAERERHDHHXcwffp0v/cmERHxJdWIiHRDSWEpPxr7E+qu1bc4VmSeIY/91p9t2AgjnFgS6EsqgxhKhBHV8qIGZNyRSsbs/hiGwU033cRdd91FbGysL78UERGvUY2IiJ/8x1++SmN9Y5vnjGUascTjwkUD9ZRTylnyOcdxxpvT6WekNv+ACec+K+bmxRNZumIxqamprV9YRCQEaNMJkS66WlLBp2/swelwtXleHAkkGv3oY/Qn1Ugny5jMDO7Ghp1DfEm9WdfiM4ZhEFkWryREREKezxKRM2fO8KMf/Yhhw4YRHR3NiBEj+Ju/+Rur/bRIT/fJf31udVHtrCgjhkwm4cTBBU61OG66TLb85mOCeOZURMQrfDY1c+zYMVwuF2vXrmXkyJEcOXKEH//4x1y7do1//ud/9tVtRfwmd8+xjrQKuaFkBmBgUE5pq8crLldSfPZyi+W8IiKhxGeJSHZ2NtnZ2dafhw8fTn5+PmvWrFEiIiHh6N4CXK6uj1jYjTDCzQjqqb3hOQXfnFIiIiIhza/FqhUVFfTt2/eGx+vr66mv/371QWVlpT/CEumSqyUVPr2+YTMovXDFp/cQEQk0vxWrnjx5ktWrV/PHf/zHNzzn+eefJzEx0XoNHjzYX+GJdJrp7Fp9iIfTdNBIA5FEt3rcMAyr86qISKjqdCLyt3/7txiG0eZr//79zT5TVFREdnY2y5Yt48knn7zhtZ977jkqKiqsl2dXUZFgFBXbSg+QTijlIiYmSfRv9bjL6SImofUkRUQkVHR6ambVqlU88sgjbZ4zdOhQ6/8vKirirrvuYubMmfzmN79p83ORkZFERkZ2NiSRgBg+aQhHdh/r0mfrzBqOc4gwwklneBv3GNrF6EREeoZOJyLJyckkJyd36NwLFy5w1113MXXqVNavX4/NprYlEjpG3zKKo3sLcDqcbZ5XTSWmaWJi0kA9V7nMRc5iYDCRmUQYrSff9jAbwyZk+CJ0EZGg4bNi1aKiImbPnk1GRgb//M//zOXLl61jAwYM8NVtRfzm9odmdGiPGU+bdwMb4YQTQzxDyGIQw9pMQmYsmEZEZLhXYxYRCTY+S0Q++ugjTpw4wYkTJ0hPT292TE2aJBSMmT6KYRMyOHOksNXv6TRjKGkM7dK1nQ4Xi57Obv9EEZEezmdzJY8//rh7OLqVl0goMAyDH/7dcq9/T9vCbIyZMYopc8Z79boiIsFIRRsi3TBryS3c+fCt2Oze+1Gy2Wz8j/98BsMwvHZNEZFgpUREpJue/fWTDBiWgj3MOz9Of7r2KdJHDfTKtUREgp0SEZFuSugbzy92/i0DhqV2eWTEZjPAgGdfepL5P5zt3QBFRIKYEhERL0ge1I8Xv3qeuX9wO+Buz95RNruNPgOS+H/b/jcLV97jqxBFRIKSEhERL4lLiuV/vLyKn2/5S0ZPHwW4k4zWkhJ7uB2A2MQYlv3ZQn6b96/cNG+iX+MVEQkGhhnEy1gqKytJTEykoqKChISEQIcj0imnDp1lz7tfc3z/SQq+PUXdtXrsdhspQ/oz+pZRjL9tNLctvYWIqIhAhyoi4lWdeX77dfddkd5k+MQhDJ84JNBhiIgENU3NiIiISMAoEREREZGACeqpGU/5SmVlZYAjERERkY7yPLc7UoYa1IlIVVUVAIMHDw5wJCIiItJZVVVVJCYmtnlOUK+acblcFBUVER8fr3bXIiIiPYRpmlRVVZGWlobN1nYVSFAnIiIiIhLaVKwqIiIiAaNERERERAJGiYiIiIgEjBIRERERCRglIiIiIhIwSkREREQkYJSIiIiISMD8/0isWaKtn9aiAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "R.subdivide_edge('D','E','Z',R.f['C'])\n", "R.draw()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then if I try to add the edge $(Z,C)$, it will merge the two endpoints, keeping the name as the first vertex I passed in. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "R.add_edge('Z','C')\n", "R.draw(cpx = 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Subgraphs and slices of the Reeb graph\n", "Let's get a new Reeb graph to work with. In this case, we're going to use one of the example Reeb graphs provided in `cereeberus.data.ex_reebgraphs`. I'm also going to add a few edges for fun. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "R = ex_rg.dancing_man()\n", "R.add_node(8,4)\n", "R.add_edges_from(((6,0), (6,0),(7,1), (5,1), (8,2)))\n", "R.set_pos_from_f(seed = 0)\n", "R.draw(cpx = 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "We can get the induced sub-Reeb-graph by providing a collection of vertices. This returns the portion of the Reeb graph with vertices from the set, and edges are included only if both endpoints are in the set. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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Kjhw5QlJSEgUFBepxNzc3IiIi6NGjh9ljF0LYFklGRJ3cuXOHdevWqb9Be3l58corr9jsXJmG7JdFrlqtlkGDBjF8+PBKi1zLHD9+nLi4uHK9SlxdXQkLC6Nfv35mjFoIYUskGRG1tn//fmJjY9W/BwUFERERYcGIRE3cv3+fqKiockWuw4cPZ+DAgdVO+z137hxRUVHk5uaqx1xcXAgNDSUgIMCscQshGj9JRkSNKYrChg0b1LbkdnZ2vPTSS3JbxsqUdXLNyMgAjEWuYWFh9OjRo9Ii1zKXL19m9+7dZGdnq8ecnZ0JCQlh4MCBZo1bCNF4STIiaiQ7O5tVq1apy/Wenp4sWLBAbstYKUVROHnyJPHx8WpjurZt2xIREYGvr2+111+/fp2dO3fy8OFD9VjZduLAwECzxS2EaJwkGRHVOn/+PJGRkWovin79+jFp0iQLRyVMobi4WO3kWlbk2qNHD8LCwvDw8Kj2+rS0NHbu3ElmZqZ6zNHRkREjRhAUFGS2uIUQjYskI6JKu3fv5siRI4A0MWvMHj9+THx8PCdOnABqV+QKcOvWLbZv3672NwFjUjJy5EhZKRFCVEuSEVEhvV7PmjVruHv3LmCsC1iwYEGNflsW1uv+/ftER0dz9epVoHZFrmDcZfWvf/2rXFLi5ORESEgIgwYNMlvcQgjrJsmIeEpWVhZffvml2mOiTZs2zJ8/v0YfRqJx+GWRa/PmzQkPD69RkSsYO/L+61//Knf7xsnJidDQUCl0FUI8RZIRUU5qaipbtmxR60MGDRrE2LFjLRyVsARFUTh16hRxcXHlilxHjRpV4xbxN2/eZPv27eWSEhcXFyIiIujbt69Z4hZCWB9JRoQqKSmJ+Ph4wDhaftq0afTs2dPCUQlLKy4uJjk5mQMHDqhFrt27dyc8PLzGt+1u3rzJDz/8UG73jaurK2PHjpWOrkIISUaE8TfgLVu2kJqaChgLD1999VW8vLwsHJloSMqKXE+ePInBYECr1TJw4ECGDx+Oi4tLjZ7j2rVrbN++nUePHqnHmjVrxvjx4+nSpYuZIhdCNHSSjNi44uJiVq5cqS6je3h48Prrr0v/EFGpjIwMoqOjuXLlCmBMXocPH86gQYNqXFeUmprKrl27ynV09fDwYNKkSTIlWAgbJMmIDcvJyeGLL75QC1W7du3Kiy++iFartXBkwhpcvXqV6Oho7t+/DxiLXMPCwujZs2eNilzB2GZ+z549ak0KgLe3N1OmTMHb29sscQshGh5JRmzUrVu3WLt2LaWlpQAMGzaMsLAwC0clrE1ZkWt8fDyPHz8GjLuvIiIiarXCcfz4caKjoyksLFSP+fr6MnXqVJo3b27qsIUQDYwkIzbozJkzfP/99xgMBjQaDZMmTZKdDeKZVFbkGhYWhqenZ42f58CBAyQmJqrPAdC5c2emTJlS47oUIYT1kWTExuzbt4+4uDgAdDod8+bNq9EsEiFqIi8vT+3kWlbkOmDAAEaMGFHjZEJRFOLi4jh06JC6cqfRaOjTpw/jx4+XfjdCNEKSjNiQ7du3c/z4ccDYgOrNN9+U/07CLDIyMoiJieHy5cuAscg1ODiYwYMH1ziZ0Ov17Nq1S929A8YEOjAwkNDQUKltEqIRkWTEBiiKwsaNG9UW325ubvz617/GwcHBwpGJxu7atWtERUWpRa5ubm6EhYXRq1evGhe5FhYW8v3333Pp0iX1mIODA2FhYdJiXohGQpKRRk5RFFauXMm9e/cA8PHx4bXXXpPfKkW9URSF06dPExcXpxa5+vj4EBERQfv27Wv8PDk5OWzdupXbt2+rx1xdXZk4caL0KBHCykky0ojp9Xr++c9/kp2dDYC/vz8zZ860cFTCVpWUlKhFrsXFxQB069aN8PDwWhW5pqen891335VrMd+yZUumTZsm24GFsFJmS0bu3LnDhx9+yO7duykoKKBr166sWrWKgICACs9PSEggJCTkqeMXLlygW7duNXpNSUZ+UlhYyLJly9T+Dc899xwTJkywcFRCGItcExISOH78eJ2LXMHYOG379u08efJEPebn58cLL7wgO2+EsDJmSUays7Pp378/ISEhvPnmm3h5eXH16lU6dOhAp06dKrymLBlJTU0tF0jLli3R6XQm/WYau7y8PJYtW6b2bAgODiY0NNTCUQlR3oMHD4iOjn6mIleAQ4cOERcXp24H1mg09OvXj/Hjx8vtSCGshFmSkX//93/nwIED7Nu3r8aBlCUj2dnZdW5yJMmI8b76P//5T3UZfPTo0QQGBlo4KiEqd+3aNaKjo9W6proUuSqKwt69e0lJSVEnTtvZ2REWFiY//0JYAbMkIz169GD06NHcvn2bxMRE2rRpw69//Wtef/31Sq8pS0Y6dOhAYWEhPXr04A9/+EOFt27KFBUVUVRUVO6b8fX1tdlkJCsri+XLl6u/IU6YMIHnnnvOwlEJUT2DwcDp06eJjY19piLXwsJCIiMj1bk5YCxynTx5cqWrskIIyzNLMlI2ZO39999n+vTpHDlyhHfffZcvvviCuXPnVnhNamoqSUlJBAQEUFRUxPr161m+fDkJCQkMHz68wmv+9Kc/8ec///mp47aYjDx48IAVK1ag1+sBmDZtGr169bJwVELUTklJCYcOHWL//v3q6p6/vz/h4eG0aNGixs/z4MEDvv32Wx48eKAea9WqFTNmzMDd3d3kcQshno1ZkhEHBwcGDBjAwYMH1WOLFi3i6NGjJCcn1zi4CRMmoNFo+OGHHyr8uqyMGD148IAvvviC0tJSNBoNM2bMqHHRrxAN0S+LXDUajVrk2qRJkxo/T2pqKj/88AP5+fnqsV69ejFp0iTp5CpEA1LTZKRWVWCtW7emR48e5Y51796dmzdv1iq4wMBAtbitIo6OjjRr1qzcw9ZkZmaWS0RmzZoliYiweq6urowfP54333yTrl27YjAYOHr0KJ9++in79+8vN7umKv7+/vz2t78lJCRELYQ/e/Ysf/3rX2v1i5EQomGoVTIydOhQUlNTyx27dOlSre79Apw4cYLWrVvX6hpbUlEiIs2fRGPSsmVLZs2axdy5c2nVqhVFRUXExsaybNkyTp8+TU0XbIcPH87vfvc7unfvDhh78ERFRfH3v/+dtLQ0M34HQghTqtVtmqNHjzJkyBD+/Oc/M2PGDI4cOcLrr7/OihUrmD17NgCLFy/mzp07rFu3DoClS5fSoUMHevbsSXFxMRs2bOC//uu/iIyMZOrUqTV6XVvaTfPo0SOWLVuGXq+XRETYhLIi17i4OHJzcwHjKmxERAQdOnSo8fM8fPiQLVu2kJGRoR5r164dL774ovQnEcJCzNb0bMeOHSxevJjLly/j5+fH+++/X243zfz580lLSyMhIQGA//7v/2bFihXcuXMHZ2dnevbsyeLFixk3bpzJvxlrl5eXx6effqoW+L300kuSiAibYaoi1wsXLvDDDz+o/Xg0Gg2BgYGEh4dLfxIh6pm0g7cy+fn5fPrpp+ob6PTp05+qzxHCFjx58oSEhASOHTumFrkGBAQwcuTIGhe5KopCTEwMhw4dUm/5ODk5MXnyZPz9/c0ZvhDiZyQZsSLFxcX8z//8j7ozYNKkSfTr18+yQQlhYZmZmcTExKh1ag4ODgwbNozAwEDs7e1r9Bz5+fl888035YrsW7duzcyZMxvle4kQDY0kI1ZCURQ+++wzdejdmDFjGDx4sIWjEqLhSEtLIyoqivT0dACaNWtGaGgoffr0qXEn17S0NCIjI9WZThqNhkGDBhERESG3boQwI0lGrMSKFSvUN9nhw4dX2ZlWCFtlMBg4c+YMsbGx5YpcR40ahZ+fX42fJyEhgX379qmt5Z2dnZk6dSqdO3c2S9xC2DpJRqzAxo0b1X4r/fv3Z+LEiRaOSIiGraSkhMOHD7Nv3z61yLVr166Eh4fTsmXLGj1Hfn4+W7Zs4caNG+oxX19fZs6cKbtuhDAxSUYauN27d3PkyBEAunTpwksvvWThiISwHk+ePCExMZGUlJQ6F7leu3aNyMhItVZLq9UycuRIgoODzRm6EDZFkpEG7OjRo+zatQswztVYuHChhSMSwjo9a5GroijExsaSnJys7rpxc3Nj1qxZeHt7mzV2IWyBJCMN1OXLl9m4cSNgbI39zjvvyCwNIZ5RWloa0dHR3L17F6h9kWtubi6bNm3i3r176rGePXsydepUKXAV4hlIMtIAZWVlsWzZMhRFwd7ennfffVfuUQthIgaDgbNnzxIbG0tOTg5gXHmMiIiocZHrqVOn2Llzpzojx8HBgalTp0pvEiHqSJKRBqa4uJh//OMfFBYWotVqWbhwIV5eXpYOS4hGR6/Xq0WuZdO/u3TpwqhRo2pU5KrX6/nuu++4cOGCeqx9+/bMnDkTJycns8UtRGMkyUgD889//pMHDx4A0l1ViPpQVuR67NgxFEVBo9Hw3HPPMXLkSFxdXau9/vbt22zevJknT54AoNPpGD16NAMHDjR36EI0GpKMNCCRkZGcPXsWgODgYEJDQy0ckRC2IzMzk9jYWC5evAgYb70MHTqUoKCgaotcFUUhKiqKw4cPq8datmzJnDlzrPK9SIj6JslIA3Hs2DF27NgBQKdOnZgzZ46FIxLCNt24cYOoqCi1yLVp06ZqkWt1RapZWVl8/fXXZGVlAcYOriEhIbINWIhqSDLSANy/f58vvvgCg8FA06ZNeffdd6UyXwgLqqzIddSoUXTs2LHa6w8cOEBcXJzawdXDw4OXX36Z5s2bmzNsIayWJCMWVlxczN///neKiorQ6XQsWrTIamIXorGrrMg1PDy82sLyvLw8NmzYwP379wHjKklwcLCMchCiApKMWNiXX37JnTt3AHjppZfo0qWLhSMSQvxSfn6+2sm1rMi1f//+hISEVFvkevToUfbs2aOukri7uzN37lxZJRHiZyQZsaCkpCTi4+MBCAoKIiIiwsIRCSGq8vDhQ2JjY9XtvPb29mqRq4ODQ6XX5efns2HDBnXYpUajYeTIkQwfPrxe4haioZNkxELS09NZsWIFYKy6//Wvf23hiIQQNVVRkWtISAh9+/atst4rJSWF3bt3q6sknp6ezJ07t8G/XwlhbpKMWICiKHz00UcUFhZiZ2fHb37zG2mSJISVMRgMnDt3jpiYGLXI1dvbm4iIiCqLXPPz81m3bp1aS6LVaomIiGDw4MH1ErcQDZEkIxawceNGLl++DMDs2bPp3LmzhSMSQtSVXq/nyJEjJCUlqUWunTt3ZtSoUVUWuR46dIjo6Gh1lcTHx4eXX35ZfjERNkmSkXp2/vx5vv32WwB69+7N1KlTLRyREMIU8vPzSUpK4ujRo+WKXEeOHEnTpk0rvCY3N5e1a9eqfUns7OyYMmWKdF4WNkeSkXpUWFjI3/72N0pLS3F1deW9996TfiJCNDJ1KXKNjY1l//796t+7dOnCzJkz5f1B2AxJRurRqlWruH37NgBvvvmmDMATohG7efMmUVFR6tZ9V1dXQkNDKy1yvX//PuvXr1dn3Dg7O/Pyyy/TunXreo1bCEuQZKSenDp1im3btgEwZMgQRo0aZdmAhBBmV1bkGhsby6NHjwDw8vIiIiKCTp06PXW+oih8//336owqkDlVwjZIMlIPiouL+eijj9Dr9TRr1oz33nvP0iEJIepRWZHrvn37KCwsBIwzqEaNGoW3t/dT56emprJ161b0ej0ALVq04JVXXsHFxaVe4xaivkgyUg/Wr1/PtWvXALk9I4Qtq6jItV+/foSEhDxV5FpYWMi6devURmk6nY7p06fj7+9vidCFMCtJRswsLS2NtWvXAhAQEMD48eMtHJEQwtKysrKIjY3l/PnzgLHIdciQIQwZMuSpItf9+/cTFxdH2Vtw3759mThxohS3ikZFkhEzUhSFjz/+mPz8fJycnPjtb38rbyBCCNWtW7eIiopSC9tdXV0JCQmhX79+5d4r7t+/z9q1aykoKADAzc2NV199tUG8zwlhCpKMmFFUVBTJycmADMETQlTMYDBw/vx5YmJiyhW5jho1qlxDREVR2LhxI1evXgWMnVunTJlCr169LBG2ECYlyYiZFBYW8tFHH6EoCu3ateOVV16xaDxCiIZNr9dz9OhRkpKSqixyPXbsGDt37lRv2/Tp04dJkybJqquwapKMmElZ0apGo+H999+vdsy4EEIAFBQUkJSUxJEjR9RW8f369SM0NFQtcn348CGrV68mPz8fAHd3d1599VV5nxFWS5IRM/j5RN6BAwcybtw4i8UihLBOFRW5BgUFMXToUBwcHJ66baPT6XjxxRfldrCwSpKMmMGyZcvIzMzEwcGBDz/8UJZPhRB1VlGR68iRI+nfvz9arZZDhw4RFRWl3rYZOnQo4eHhlgxZiFqTZMTELl++zMaNGwEYN24cAwcOtEgcQojGw2AwcOHCBWJiYsjOzgaMRa7h4eF07tyZjIwM1qxZo04Nbtu2LfPmzcPOzs6SYQtRY5KMmNjf//53Hj9+TJMmTfjggw8sEoMQonHS6/WkpKSQmJioFrl27NiRUaNG4eHhwZo1a7h37x5gnG3z2muv4enpacmQhagRSUZM6MyZM3z33XcATJ8+XcaACyHMoqCggH379nHkyBFKS0sB1E6u+/fv5+jRo4Bx+++0adPkvUg0eDX9/JaihxqIiooCjA2J5B+/EMJcnJ2diYiI4K233qJnz54AnDx5kk8//RRnZ2cmT56MVqtFURS+/fZb9b1JCGsnKyPVOH/+PN9++y0AM2fOlPkRQoh6c/v2baKiorh16xYATZo0YdCgQSQnJ6u3c9q1a8e8efNqVVBfoC/m0uN0Lube4VHxEwyAm70LXZu2xt/NB1c7J3N8O8IGyW0aE/nHP/5Bbm6uTOUVQlhERUWunp6eKIqi/t3V1ZWFCxdW2Y/EYDBw6tENvr1xiLj7Zyk1KGjQoNNoAFAMBhQMaNAwrKU/09sHMdizM5ofvy5EXUgyYgI/H4b3wgsvqMumQghR30pLS9VOrmWzbFxdXcnLywPAzs6O+fPn06ZNm6euzSx6zH+d20ZSxgV0Gi2lBqXK19JpNJQaDPR378B/9H6BNi4epv+GhE2QmhET2LNnD2C8jyuJiBDCknQ6HYGBgfzbv/0bQUFB6HQ6NREB446cVatWcerUqXLXpTy8yox9f+fAg1SAahMR4znG31FPP7rJzP1Lib931oTfiRBPk2SkEtnZ2dy/fx+AoKAgC0cjhBBGPy9y/eUwPYPBwLZt29TC1iMPr7AoZQ1P9MU1SkJ+qdSgUKzo+feTm4hOP22S+IWoiHTOqcTevXsB428jQ4cOtXA0QghRnru7O9OmTWPw4MFER0dz8+ZN9WvJyclcz07na/drlBoMGKj73XgDoMHAf5zeQvsmLenarLUJoheiPElGKqAoCpcvXwage/fu0vZdCNFgtW3blvnz53Px4kWioqJ49OgRBgxs4xJFpQYMldSfluYXcXfTAfKv3if/6n30uQX4zB5GmznBT51r+PF///fpLawf8jZ2Wp05vyVhg+RTtgKHDh1Sp2qOGjXKwtEIIUTVNBoN3bt35+233yYiIoIMT3joVnkiAqB/XMCD3ScxlJTSfEjXal+j1GDgat59tt0+asLIhTCSZKQChw8fBqBFixYWHcwnhBC1odPpCAoKQh/QGk01d2YcvNzo/+17dPtoDm3nj6zR82uAb9IOYgWbMIWVqXUycufOHebMmYOnpycuLi7069ePY8eOVXlNYmIiAQEBODk50bFjR5YvX17ngM0tJyeH3NxcAIYNG2bhaIQQonbu5GdxMudGlasiYFxNqW0PEQNwIz+Tszm36h6gEBWoVTKSnZ3N0KFDsbe3Z/fu3Zw/f56PP/6Y5s2bV3rN9evXGTduHMHBwZw4cYLf//73LFq0iMjIyGeN3Szi4+MB428YvXv3tnA0QghRO2ce3az+pGegRWP21xC2p1YFrH/961/x9fVlzZo16rEOHTpUec3y5ctp164dS5cuBYwFoSkpKfztb39j2rRptQ7Y3C5evAgYvy8pXBVCWJuLuXex02jR12Erb01oNHAh545ZnlvYrlp92v7www8MGDCA6dOn4+XlRf/+/Vm5cmWV1yQnJxMREVHu2OjRo0lJSaGkpKTCa4qKisjNzS33qA/p6ekUFRUBMHLkyHp5TSGEMKUHhTkoZqzpKDUYuF+YY7bnF7apVsnItWvX+Pzzz+nSpQt79+7ljTfeYNGiRaxbt67Sa+7du4e3t3e5Y97e3uj1ejIzMyu8ZsmSJbi5uakPX1/f2oRZZwcOHADAwcGBtm3b1strCiGEKRn7ipj7Ncyz6iJsV62SEUVReO655/jP//xP+vfvz8KFC3n99df5/PPPq7zul0VSZZXYlRVPLV68mJycHPVRNrHS3K5evQoYp2AKIYQ1amLniNaMw+00IFN9hcnVKhlp3bo1PXr0KHese/fu5Tr//VKrVq24d+9euWMZGRnY2dnh6elZ4TWOjo40a9as3MPcHj16pI7kHjJkiNlfTwghzKFr09ZmvU2j1Wjxly6swsRqVcA6dOhQUlNTyx27dOkS7du3r/SaoKAgtm/fXu5YVFQUAwYMwN7evjYvb1ZHjhwBjLto/Pz8LByNEELUTTe3NjVu//7o6FWUwhJKC4oBKLiZSdY+YxG/28BO6Jyefo8uNSh0a/b0ZGAhnkWtkpH33nuPIUOG8J//+Z/MmDGDI0eOsGLFClasWKGes3jxYu7cuaPWkbzxxht89tlnvP/++7z++uskJyezatUqNm3aZNrv5BldunQJgJYtW1o4EiGEqLuebm3xcHAlqziv2nNvfLaX4oyfilGz910k+8dkpM9Xb6Jzav7UNU5aewa36GKyeIWAWiYjAwcO5Pvvv2fx4sX8n//zf/Dz82Pp0qXMnj1bPSc9Pb3cbRs/Pz927drFe++9x7Jly/Dx8eGTTz5pUNt6FUUhKysL4KnbUEIIYU3stDqmtwtk5ZVYlGpWSPqu/XWtnlun0TKhbQBN7ByfJUQhnqIxWEFf39zcXNzc3MjJyTFL/UhaWhpr164F4Le//S0uLi4mfw0hhKgvj4qfMC3pY/L0hSbdWeOgteObYe/SxsXDhM8qGrOafn5LVy/g9OnTgHFLryQiQghr19yhCYt7TTH5Ft/5PkMlERFmIckIcOPGDUDqRYQQjUd4q95MaTvQNE9mAO8sDRnbj6ktEIQwJUlGMA7HA+jYsaOFIxFCCNP5Xc9JjG/z3DM/z5AWXZlS0pmS4hK+/vprjh8/boLohPiJzScjeXl5lJaWAsaeKUII0VjoNFr+2Gsav+sxEUetHTpNzd/yNQbQKOB/S8fUok7Mnf0yffr0wWAwsH37dmJjY7GCkkNhJWq1m6YxKuubotFoaN1aGvkIIRoXjUbDC+0CCWrRlRVXYohOP02pQUGr0T7V1l2n0aoJRrBXN5yS72L3sJD4u3G4ujRh8uTJNG/enKSkJPbv38+jR4+YNGkSdnY2/1EinpHN/wRdv34dAGdnZwtHIoQQ5tPGxYM/95nBe92eJ+beGc49us3ZnJs8Ks7HgIFm9s70dPOlh1tbwlv1pqVTMwp7FvLJJ59QUFDA9u3badq0KSEhIbi7u7N9+3bOnj1Lbm4uL774ohT/i2di81t7ly9fzv379/Hx8eH111836XMLIYS1y8vL45NPPqGkpAStVsuCBQto3bo1165dY8uWLRQVFeHh4cHs2bPx8JCdNqI82dpbQ7m5uQB4eXlZOBIhhGh4XF1def3119FqtSiKwurVq8nNzaVjx468+uqruLm5kZWVxapVq+ptqKlofGw+GSkbjtemjcxaEEKIirRs2ZKXX34ZAL1ez/LlyykuLsbLy4sFCxbg4+NDfn4+a9eu5dy5cxaOVlgjm05GiouL1WItX19fC0cjhBANV4cOHZg8eTIABQUFrFy5EkVRcHV1Zd68efj7+1NaWsrWrVs5cOCA7LQRtWLTyci9e/fUP0vDMyGEqFrfvn0JDg4GIDMzk2+++QYwdq+eMWMGgwYNAiAmJoadO3eiKEqlzyXEz9l0MnL//n0AtFotWq1N/6cQQogaCQ0Nxd/fHzBOO4+NjQWM76Njx45l9OjRABw7dozNmzdTVFRksViF9bDpT+CySb329vYWjkQIIazHjBkz1NXk/fv3c/HiRfVrgYGBvPjii9jZ2XH58mW++uordaOAEJWx6WQkLy8PkGRECCFqo2yLr5OTEwDffvut+ssdQLdu3Zg/fz5NmjTh3r17rFq1Sl2JFqIiNp2M5OfnA8b7nUIIIWrOwcGB1157DY1Gg6IofPnll+j1evXrbdq04bXXXqNFixbk5uayevVqrly5YsGIRUNm08lIQUEBAI6OjhaORAghrE+LFi2YNm0aYHw/Xbt2bbmvu7u78+qrr9KhQweKi4vZuHEjx44ds0SoooGz6WSkbECe3KYRQoi66dmzp7qL5vbt28THx5f7urOzM3PmzFGH7O3YsUOG7ImnSDICMuRJCCGewdixY/H29gYgKSmJtLS0cl/X6XRMnjyZESNGAMai18jIyHK3dYRtk2QE4z8UIYQQdffqq6+qq8wbN26kuLi43Nc1Gg0jR45k0qRJaLVazp07x7p169TaPWHbbDoZKVsmlB4jQgjxbBwcHJg7dy4AJSUlfPXVVxWe169fP+bMmYOjoyO3bt1i1apV5XbiCNtk05/CGo0GQLoECiGECbRt25Zhw4YBkJ6eTlJSUoXn+fn58dprr8mQPaGy6WSkbEVEkhEhhDCNsLAwdQp6fHx8pf1FWrZsKUP2hMqmk5GylZGy2hEhhBDPbt68eWot3vr16yv9hU+G7IkyNp2MlDU7+2WhlRBCiLpzcXFh6tSpADx58oTt27dXeq4M2RNg48lIWbMzSUaEEMK0evToQadOnQA4efIkN2/erPTciobsbdq0SYbs2RBJRpBkRAghzGHmzJnqCvTmzZurXe34+ZC9K1eusGbNGhmyZyNsOhlp2rQpIMmIEEKYg52dHTNmzACM7eJ37NhR7TU/H7J3//59vvzyS+7du2fuUIWF2XQy4u7uDhj3xAshhDC9Tp06qbdrTpw4UaPpvT8fsvf48WPWrFkjQ/YaOZtORjw9PQHZTSOEEOY0c+ZMdezGpk2banSNDNmzLTadjLRu3Vr9s9yXFEII87Czs2PixIkA5OTkcPDgwRpdV9GQvZiYGNn62wjZdDLSrFkz9c83btywYCRCCNG49e7dW22GFhcXV+NavV8O2Ttw4IAM2WuEbDoZgZ96jdy9e9fCkQghROM2a9YswHhr/Ntvv63xdTJkr/Gz+WTExcUFoEZFVUIIIequefPm9O/fH4ArV66QkZFRq+tlyF7jZfPJSIsWLQB4+PChhSMRQojGb/z48djb2wPUanWkzC+H7H355ZcyZK8RsPlkxNfXFzC2LBZCCGFeWq2WsLAwADIzM0lNTa31c/x8yF5BQYEM2WsEbD4Z6dKlC2C8hyn3H4UQwvwGDx6Mq6srQJVza6oiQ/YaF5tPRry9vdXpvWfOnLFwNEIIYRsmTZoEGFeljx8/XqfnKBuyN3jwYECG7Fkzm09GtFqtmqFfvnzZwtEIIYRt6Ny5Mx4eHoAxiagrrVbLmDFjZMielbP5ZASgVatWgOyoEUKI+lS2OlJQUMChQ4ee6blkyJ51k2QE42AmgLy8PGmkI4QQ9aRdu3a0bNkSgKSkpGd+PhmyZ70kGQH69Omj/lkqsoUQov6MHz8eMK6OnDp16pmfr02bNixYsECG7FkZSUYwzk0oqxuRIlYhhKg/7dq1o3nz5gDExsaa5DmbN2/Oa6+9JkP2rIgkIz8q6zdy584dC0cihBC2ZcyYMQA8fvyYa9eumeQ5nZycmDNnDn379pUhe1ZAkpEfDRw4EIDCwkKys7MtHI0QQtgOf39/dTRHdHS0yZ5Xp9MxadIkGbJnBSQZ+ZGfnx86nQ6A5ORkC0cjhBC2paxXyL1790y6C6ZsyN7kyZNlyF4DVqtk5E9/+hMajabco2xbbEUSEhKeOl+j0XDx4sVnDtwcWrduDVCn9sRCCCHqbtiwYeovhHv27DH58/ft2/epIXsyk6zhqPXKSM+ePUlPT1cfNSn4TE1NLXdNWQv2hmbAgAEA5ObmkpeXZ+FohBDCdmi1Wvz9/QG4dOmSWbqo/nLI3qpVq7h586bJX0fUXq2TETs7O1q1aqU+yvaIV8XLy6vcNWXZb0PTu3dvtFrjf5LExEQLRyOEELYlPDwcMM4KO336tFle45dD9tatWyctHRqAWicjly9fxsfHBz8/P2bOnFmjyuf+/fvTunVrwsLCiI+Pr/b8oqIicnNzyz3qg1arpW3btgCcP3++Xl5TCCGEkbu7u7rN98CBA2Z7HVdXV+bPn19uyN7+/ftlp40F1SoZGTx4MOvWrWPv3r2sXLmSe/fuMWTIkErvu7Vu3ZoVK1YQGRnJd999h7+/P2FhYdV22luyZAlubm7qo2zbbX0YNmwYAPn5+aSnp9fb6wohhIBBgwYBkJmZSWFhodlex97evtyQvdjYWHbs2CFD9ixEY3iGVPDJkyd06tSJ3/3ud7z//vs1umbChAloNBp++OGHSs8pKioqN+QoNzcXX19fcnJyaNasWV3DrbElS5ZQXFxMp06dmDNnjtlfTwghhJGiKPzlL3/BYDAwbNgwwsLCzP6ahw8fVotmO3fuzAsvvICjo6PZX9cW5Obm4ubmVu3n9zNt7W3SpAm9e/eu1bTbwMDAas93dHSkWbNm5R71qUePHgBcv35dsmQhhKhHWq1W3aVprrqRXxo8eLAM2bOwZ0pGioqKuHDhgroltiZOnDhRq/MtoSwTVxSFgwcPWjgaIYSwLWW3TnJzc+utH4gM2bOsWiUjH3zwAYmJiVy/fp3Dhw/zwgsvkJuby7x58wBYvHgxc+fOVc9funQp27Zt4/Lly5w7d47FixcTGRnJ22+/bdrvwsRcXV3x8vICeOax1kIIIWqnd+/eaDQaoH7fg2XInuXUKhm5ffs2s2bNwt/fn6lTp+Lg4MChQ4do3749AOnp6eX2bBcXF/PBBx/Qp08fgoOD2b9/Pzt37mTq1Kmm/S7MYNSoUYCxLsZUsxKEEEJUT6vVqm0j6ntnY9mQPT8/PxmyV4+eqYC1vtS0AMbUPvroI/Lz8/H29uaNN96ot9cVQghbd+DAAWJiYgD44x//qPaAqi+lpaVs376dU6dOATB06FDCwsLUFRtRM/VSwNrYBQUFAXD//n0ePHhg4WiEEMJ2lA0vBbhw4UK9v37ZkL2RI0cCMmTP3CQZqcKQIUOwt7cHYPv27RaORgghbIeDg4M6ybdsdaK+aTQaRowYIUP26oEkI1XQarXqvJpbt27JVi8hhKhHZR2x79y5Y9E4ZMie+UkyUo3w8HB1ls73339v4WiEEMJ29O7dGzB2xLb07ZGyIXvNmzeXIXtmIMlINbRaLQEBAQCkpaWRlZVl4YiEEMI2dOvWTf3zpUuXLBiJUcuWLXnttdfKDdk7e/aspcNqFCQZqYHRo0fL6ogQQtQzOzs7nJycAMsUsVakbMhet27dKC0tJTIyUobsmYAkIzWg1WrVnTW3b9+WAXpCCFFPyvqN3L1718KR/MTe3p7p06fLkD0TkmSkhkJCQnBwcABg69atFo5GCCFsQ9nU9oa2gUCr1TJmzBjGjBmDRqPh+PHjbNy4sdyQV1FzkozUkFarJSIiAoCsrCzOnTtn4YiEEKLx69y5MwB6vd7iRawVKRuyZ29vz9WrV2XIXh1JMlILAQEBagc5WZITQgjzKxs3AnD16lULRlI5f39/GbL3jCQZqaUpU6YAUFhYSHR0tIWjEUKIxk2r1arNJ2/dumXhaCrn4+PDggULaNmypTpk7/Lly5YOy2pIMlJLHTp0UDP1w4cPk5eXZ+GIhBCicSvrxJqRkWHhSKrWvHlzXn31VXXI3qZNm0hJSbF0WFZBkpE6mDFjBlqtFoPBwKZNmywdjhBCNGplt8ezs7MtHEn1nJycmD17Nn379sVgMLBz506io6Nl6281JBmpAxcXF4YOHQoYt5tJMasQQpiPp6cnAE+ePLFwJDXzyyF7Bw8eZOvWrQ2yALehkGSkjkJDQ2natCkA//rXv+SHTAghzMTd3R2AkpISC0dSc78csnf+/HkZslcFSUaewaxZswDjP5Bvv/3WwtEIIUTjVLYyYo2/9PXt25eXX34ZJycnGbJXBUlGnkHr1q3p06cPYJybcOXKFQtHJIQQjU9ZF1awzoSkQ4cOvPrqqzJkrwqSjDyjSZMmqbMTvv32W6v8hyKEEA1Z8+bN1T8/fvzYcoE8g7Ihe23atJEhexWQZOQZabVaZs+eDaBu5RJCCGE6ZaM4wHqTETAO2Zs3b54M2auAJCMm0LZtW/r37w/AtWvXOHPmjIUjEkKIxsnaezuVDdkLDAwEfhqyV1paauHILEuSERMZP348rq6uAGzbts3q/8EIIURDotFoAGP3a2un1WoZPXp0uSF7mzZtsukhe5KMmIhWq2X+/PloNBoUReGrr76ydEhCCNFolCUjjWkmmAzZ+4kkIybk6empTvZ9+PAhu3fvtnBEQgjRuDSmZAR+GrLn6upq00P2JBkxscDAQHx9fQE4cuSIbPcVQggTamzJCBiH7L322ms2PWRPkhEzmDt3Lo6OjgBs3rxZOu4JIYSJ/HxnTWNi60P2JBkxAzs7O+bNm4dGo6G0tJQvv/yyUWbzQghRX8q2vzbWZAR+GrLXr18/mxuyJ8mImbRu3VqtH8nOzua7776zcERCCGG9yj6Q7e3tLRyJeel0OiZOnPjUkD1rmstTF5KMmFFgYCCdO3cG4Ny5cxw6dMjCEQkhhPX5+cpys2bNLBhJ/SgbsjdlypRyQ/asZWpxXUgyYmazZs3Czc0NgL1798o8AiGEqKWfb3ctm+BrC/r06aMO2bt9+3ajHrInyYiZabVafvWrX2FnZwfA+vXrpSGaEELUwqNHj9Q/l80CsxU/H7KXnZ3daIfsSTJSD1xcXJg7dy5gnDj5xRdfyEA9IYSooczMTOCnxme2xhaG7EkyUk98fX0ZP348YJytsHr1agtHJIQQ1uHBgwdA495JU53GPmRPkpF6FBAQwKBBgwBIT08nMjLSwhEJIUTDl52dDdjeLZpfqmjI3vbt2xvFkD1JRurZ2LFj6dChAwBnz54lPj7esgEJIUQDl5OTA6AOI7VlZUP2xo4di0aj4cSJE41iyJ4kIxbw8ssv4+HhAUBSUhLHjx+3cERCCNFwPX78GDDWTgijQYMGlRuyt3r1ajVps0aSjFiAVqtl4cKFuLi4ALB9+3abm0MghBA1VVhYCECbNm0sHEnD8vMhexkZGaxatcpqh+xJMmIhDg4OvPnmm2o3wU2bNnHnzh0LRyWEEA1LXl6eWqTp5+dn4WganroO2dOXKly6/YB/HTzH8h3JLPvXAVbvOULi6as8yKn/9hMagxWU4ubm5uLm5kZOTk6j67734MEDli9fjqIo6HQ6Fi5cKEuRQgjxo5SUFHbu3IlGo+E//uM/LB1Og1VYWMiWLVu4fv06Go2GcePGMWDAgKfOu/XgEVuTTvP9/jPkFRYDYKfVgsbYcr9UMaYE/m1bMjOkP6MH+OPkYFfnuGr6+S0rIxbWsmVL5s+frw7VW7FihVXf9xNCCFO6du0agHpbW1SsuiF7xSV6lv3rAFP+91d8HXdcTUQA9IqCvlRRExGAy3ce8Of1UUz50xqOpt4ye/ySjDQAvr6+zJo1CzA2Rfv888+lS6sQQoBaA9GiRQsLR9LwlQ3ZCwkJAX4asnc7I5uXlnzN6j1HUAwGFKX6GyJlpzx49ISFS7fy6Tbz9jSRZKSB6NKlC1OnTgWgqKiIZcuWkZ+fb+GohBDCsspWitu1a2fhSKyDRqNh+PDh6pC9Y2cuMOsva7lxP5u6pBLKjwnImr1H+e9v4s2WkEgy0oD07t2b559/HjDe//vss8/UKnIhhLA1GRkZ6sTefv36WTYYK9OnTx9mvTSbI4+akF9S/hZMXX2TeIpvk06bILqn1b0qRZjFgAEDUBSF3bt3U1BQwKeffso777xj022QhRC26dSpU4Dx9kNZbyZRcwmXHvCopOI1h/zMO6Qf2UVBVjr6gjy0dvY4NveiZc+heHR9uvC1zD8iExnaswNtWriZNFZZGWmABg0aREREBAD5+fn8z//8j6yQCCFsztWrVwEkEamDzJwnrNhxqNKvlxYVYO/aHJ9B4+g07nXah76EQ1MPbsRt5N6x6Eqv05cqLP1un8njlWSkgQoKCiI8PBwwJiSffPKJ1JAIIWxK2YC8Ll26WDgS67PtwFm13qMiTdt0pt3w6Xh0HUDTNl1wa98Tv/CXcfFqR+aF5EqvK1UMxJ+8woNHpt1kUatk5E9/+hMajabco1WrVlVek5iYSEBAAE5OTnTs2JHly5c/U8C2ZOjQoeoKSUFBAZ999pkkJEIIm5CWlqbWiwwePNjC0VifrftOV5mMVMbOyRWNpvrUYPuh83UJq1K1Xhnp2bMn6enp6uPMmTOVnnv9+nXGjRtHcHAwJ06c4Pe//z2LFi2SabW1EBQUxNixYwFjQvLJJ5+Qm5tr4aiEEMK8UlJSAHB0dGx0zS7N7UFOHhk1XLkwGBQMSiklBXk8OHuA3NsX8e4fWvU1GDh19a4pQlXVuoDVzs6u2tWQMsuXL6ddu3YsXboUgO7du5OSksLf/vY3pk2bVtuXtlmDBg1Cq9Wyc+dOioqK+Oyzz1i4cCGenp6WDk0IIcyirNmZr6+vhSOxPhduZtT43Fv7Inl43nhbRqPV0XboFFr0GFLlNQYDnE0z7QycWq+MXL58GR8fH/z8/Jg5c6b6A1OR5ORk9TZDmdGjR5OSkkJJSUml1xUVFZGbm1vuYesGDBig9iEpKSnh888/Jz093cJRCSGE6T18+JCCggIAhgyp+oNRPK2mqyIArfqH4z/1PTqOXYBnt8Hc3v8d90/GV3tddl6BSXuO1CoZGTx4MOvWrWPv3r2sXLmSe/fuMWTIEB4+fFjh+ffu3cPb27vcMW9vb/R6PZmZmZW+zpIlS3Bzc1Mfkhkb9e7dm5kzZ6qt47/88kvS0tIsHZYQQpjU/v37AeNKvAzHqz1FMaCp4bkOTd1x8fLFrX0PfIe/QIvuQdw9spOSguoTGlP0LilTq2Rk7NixTJs2jd69exMeHs7OnTsBWLt2baXXaDTl/5OUZVK/PP5zixcvJicnR33cumX+vvjWwt/fn7lz56LValEUhXXr1nH27FlLhyWEECaTmpoKQNu2bS0ciXVydXaoU7dVABevdqAoFOdWvMhQxt5Oh53OdBtyn+mZmjRpQu/evSsdV9yqVSt1rkCZjIwM7Ozsqqx3KCtY+vlD/KRDhw4sWLAAOzs7DAYDkZGRJCdXvhVLCCGsRXp6unqLZsSIERaOxjp1aVP3ye+P714BjQaHZlXXJHZpY9pZQc+UjBQVFXHhwgVat25d4deDgoKIji7fPCUqKooBAwZgb2//LC9t81q3bs3bb7+Nk5MTYPzvunfvXgtHJYQQzyY+3liv4OjoSIcOHSwbjJXya+WBvZ2uynNuJm7hTvIPZF85yeO7V3h07RTXo9eRfSkFrz4jsXd2rfRanVZLrw4128hSU7VKRj744AMSExO5fv06hw8f5oUXXiA3N5d58+YBxtsrc+fOVc9/4403uHHjBu+//z4XLlxg9erVrFq1ig8++MCk34StcnNz45133qFp06YAHDp0iM2bN1s4KiGEqBtFUdRNEV27drVwNNbLTqcltF8ndNrKyyGaeHfgScZNbu+P5MqO5dxM2II+/zHtQ1+iTdCEKp+/VFEY9Zxp//+p1dbe27dvM2vWLDIzM2nZsiWBgYEcOnSI9u3bA8bltZs3b6rn+/n5sWvXLt577z2WLVuGj48Pn3zyiWzrNSEnJycWLVrEypUrycjIIDU1leXLl6u3cYQQwlocO3aM0tJSAMLCwiwcjfV6/PgxbeyeVFlg6tltEJ7dBtX6uTWAr1dznuvS5hkirOB5DeaaB2xCubm5uLm5kZOTI/UjlVAUhc2bN6v1O66urrz55pu4uLhYODIhhKiZpUuXkpOTg6enJ2+//balw7E6hYWFHDx4kOTkZEpK9BzIciGrxK7OxayVWfLaOEYP8K/RuTX9/JbZNI2EVqvlpZdeIjAwEIC8vDyWLl0qvUiEEFbhwYMH5OTkABAcHGzhaKyLXq/n0KFDfPLJJ+zbtw+9Xk+7dr7854LxONhXXTtSGzqthpF9OxERYPpbaLKO38iMHj0aDw8Pdu3aRUlJCStXrmTq1Kn06tXL0qEJIUSlylpF2Nvb07dvXwtHYx0MBgNnz54lLi6OR48eAdCiRQvCwsLw9/dHo9Hwv1/W8PvVu5/5tXRaDd7uTfnDS+FVtuaoK0lGGqGBAwfSokULvv76a0pLS4mMjCQjI4PQ0KrnDQghhCXk5+dz48YNAPr372/haKzD1atXiYmJUdtnuLq6MnLkSPr3749W+9NNjzEDu1FYouf/bohGg6ZOw/O0PyYiK9+fjkcz89z6l2SkkfLz8+Ptt99mxYoVFBQUsG/fPtLT05k1a1a5H1QhhLC0PXv2AMZmmKNGjbJwNA1beno6MTEx6q4jR0dHhg4dyuDBg3FwcKjwmslDetG2hRt//GovDx7l1Tgh0WqMycuo57ry4YshNHd1Ntn38UtSwNrIFRcX8+WXX/LgwQMAmjdvzuuvvy6FrUKIBkGv17NkyRIURcHf35+ZM2daOqQGKTs7m7i4OLXjtlarZeDAgQwfPrzG7+f5hcWs2XuUb5NOkZtfhJ1Oi75UKXeORmNMQkoVAz3be7Ng3GBG9OlU57hr+vktyYgNUBSFyMhIzp8/Dxjvyc6dO1daLQshLG7Hjh0cO3YMgN/85je4ulbebMsWPXnyhKSkJFJSUlAUY+LQu3dvQkJCcHd3r9NzFpfoSTh9lRNX7nLmejp3H+ZSqig4O9jj37YlPdp7M6JvJ7r5ej1z/JKMiKccOnSoXJfWcePGMXDgQAtGJISwZT9fFenUqRNz5syxdEgNRnFxMYcOHeLAgQMUFxcD0KlTJ8LCwirtet4Q1fTzW2pGbEhgYCA+Pj6sX78evV7Prl27uHHjBlOnTpU6EiFEvduzZ4/62/7EiRMtHE3DoCgKx48fJzExkbw84+TcVq1aMWrUKDp27Gjh6MxHkhEb065dO9555x1WrlxJbm4u586d4+7duyxYsEDqSIQQ9aa4uJgTJ04A0LFjR5tf9TYYDFy8eJHY2FgePjROzG3evDmhoaH06tXLLNtpGxK5TWOjftmx1c7OjtmzZ8tgKiFEvdiyZQsXLlxAo9Hw/vvv23StyM2bN4mOjub27dsAuLi4MHz4cAICAqx+rIfcphFVKuvYmpycTFRUFHq9nrVr1zJ8+HBCQkIsHZ4QohHLzc3lwoULAPTs2dNmE5EHDx4QExPDpUuXAOPmgsDAQIYOHYqjo6OFo6tfkozYuKCgIHx9fVm3bh0lJSUkJSVx7do15s2bZ/UZuRCiYdqyZQtg/KVowoSqJ8Q2Rrm5ucTHx3Pq1CkMBgMajYbnnnuOESNGqFPYbY3cphGAccDSV199xf379wFjI5158+ZZVdW2EKLhu379OuvWrQOMM2hsqTN0YWEh+/fv5/Dhw+j1egC6detGWFgYLVq0sHB05iFbe0Wd7Nmzh8OHD6t/HzVqFEOGDLFgREKIxuTjjz8mLy8PZ2dnPvjgA5vYyafX6zl69Cj79u2joKAAMG4mCA8Px9fX18LRmZfUjIg6GTNmDJ07d2bz5s2UlpYSHR3NxYsXmTt3rty2EUI8k6SkJHW76sSJExt9IqIoCmfOnCE+Pl6dSNyyZUvCwsLo2rVro98hUxuyMiIqlJ+fz+rVq9UtZo6OjsyZM0e6tgoh6iQ/P5+PP/4YRVFo1aoVCxcutHRIZmMwGNRBdmW3vps2bUpISAh9+/Zt9EnYz8ltGmESu3fv5siRI+rfbe0erxDCNFavXs2tW7fQaDS8++67jfa9/O7du0RHR5OWlgYYf5EbNmwYgwcPxt7e3rLBWYDcphEmMXbsWPz9/dm8eTMlJSXs27eP1NRU5s2bJ03ShBA1cuHCBW7dugUYd/A1xkQkKyuLuLg4zp07B4BOp2PQoEEMGzZM3itrQFZGRI0UFxezZs0a7t27Bxj/oU2dOpUePXpYODIhREOm1+v57//+b0pKSmjSpAnvv/9+o7pN8eTJExITEzl27Jja2r5Pnz6EhITQvHlzywbXAMhtGmEWSUlJJCQkUPZj061bN6ZPn96o3lyEEKazYcMGrl69CsCvfvWrRtMuoLi4mOTkZA4ePKgOsuvcuTNhYWG0atXKwtE1HJKMCLPJyMhg7dq15OfnA8bWxXPmzGk0bzJCCNNITU1l8+bNAPTv379RDMMrLS1VB9k9efIEAB8fH8LDw/Hz87NwdA2PJCPCrBRFITIykvPnz6vHgoKCiIiIsGBUQoiGori4mI8++gi9Xo+Liwu/+c1vrHoF1WAwcOHCBWJjY8nKygLA3d2dsLAwevToIdt0KyEFrMKstFot06dPJzU1la1bt6LX60lOTubChQvMnz8fNzc3S4cohLCg9evXq11G58yZY9WJSFpaGjExMdy5cwcwrgaPGDGCgIAAdDqdhaNrHGRlRDyz4uJiNmzYoFbLazQaRo0aRVBQkIUjE0JYwtGjR9m1axdg3Sum9+/fJzY2Vp1ubm9vT1BQEEOGDLG5QXZ1JbdpRL1LSUlh9+7dakW5t7c3c+bMsdmJnELYoqysLD777DMMBgMeHh7827/9m6VDqrWcnBwSEhI4efIkYPwFKyAggBEjRsj7WS1JMiIsIi8vj7Vr15KZmQkYb+eMGTOGgQMHWjgyIYS5KYrCP/7xD/Ly8tBqtbzzzjtW9Z5dUFCgDrIrLS0FoEePHoSGhuLp6Wnh6KyTJCPCon65Bbh169bMmTNHmv8I0Yh98803XLx4EYCpU6fSu3dvC0dUMyUlJRw5coT9+/dTWFgIQPv27QkPD5cRGM9IkhFhcY8ePWL9+vVq5bmskgjReB0/fpzt27cDxtWE6dOnWzii6imKwunTp4mPjyc3NxcALy8vwsPD6dy5s+yQMQFJRkSDERcXx/79+9VVklatWjF79my59ypEI3H//n2++OILDAYDTZs25d13323Qu2cMBgOXL18mNjaWjIwMAJo1a0ZISAh9+vRp0LFbG0lGRIOSnZ3Nhg0byq2ShIWFMWTIEAtHJoR4Fnq9no8//pjCwkJ0Oh2LFi1q0O/Tt2/fJiYmhhs3bgDg5OREcHAwgwYNws5Oul2YmiQjokH6ZS1JixYtmD17tsxwEMJKrVixgvT0dABmzpyJv7+/hSOq2MOHD4mLi1MbNep0OgYPHsywYcNwdna2cHSNlyQjosHKzc1lw4YNPHjwADBumwsKCmLUqFEWjkwIURs//PADJ06cABpuP5G8vDx1kF3Zx12/fv0YOXKkNGesB5KMiAbv0KFDREdHq31JXF1deemll2TGjRBWICUlhZ07dwLQrl07XnnlFQtHVF5RUREHDx4kOTmZkpISALp27UpYWBheXl4Wjs52SDIirEJhYSEbN25Uu7cC9OrViylTpkgRmRAN1K1bt1i9ejVAgytYLS0t5dixYyQmJqrDPNu0aUN4eDgdOnSwbHA2SJIRYVXOnz/Ptm3b1N9gHBwcmDRpEj169LBwZEKIn8vJyeHTTz+ltLQUOzs73nnnnQaxM85gMHDu3Dni4uLIzs4GwMPDg7CwMLp37y7bdC1EkhFhdfR6PZGRkWrTJDCO5p41a1aDeLMTwtYVFxezdOlSCgoK0Gg0vPLKK/j6+lo6LK5fv05MTAx3794FoEmTJowcOZL+/fvLIDsLk2REWK07d+7wzTff8PjxY8BY4BocHExISIiFIxPCdimKwrJly9Tt+Q2hw+q9e/eIjY3lypUrgHFFdciQIQQFBeHg4GDR2ISRJCPC6sXHx7Nv3z61Ar5p06bMmDFD2jMLYQFfffWV2ptjxIgRjBw50mKxPHr0iPj4eE6fPg0Y+xYNGDCA4cOH06RJE4vFJZ4myYhoFPLy8ti0aZO6/ArQqVMnZsyYIb/5CFFPtm7dyrlz5wBjgfm0adMsEkd+fj779u3j6NGj6iC7nj17EhoaioeHh0ViElWTZEQ0KufPn+eHH36gqKgIMDYsCgsLIygoyMKRCdG47d27l0OHDgGW28JbUlLC4cOH2b9/v/oe4OfnR3h4OD4+PvUej6g5SUZEo6MoCjt37uT48ePqMTc3N2bMmCFvSEKYwYEDB4iJiQGM3ZLffPPNet3CqygKJ0+eJCEhQa0h8/b2Jjw8nE6dOskOGSsgyYhotB49esSmTZvUAVcAnTt3Zvr06XLrRggT+XlTs6ZNm7Jo0aJ6m91iMBi4dOkSsbGxaqdmNzc3QkND6d27tyQhVkSSEdHonTp1il27dlFcXAwYi9hGjBjB8OHDLRyZENbtzJkzfPfddwA4OzuzaNEinJyc6uW1b926RUxMDDdv3lRfPzg4mIEDB8ogOyskyYiwCWW3bk6cOKHuunF1dWXatGnSbVGIOkhNTWXz5s0AODo6smjRIlxcXMz+upmZmcTGxqp9huzs7NRBdvWVCAnTk2RE2JScnBy++eYbdXooQNu2bZk+fbr8zAhRQ5cvX2bTpk0YDAbs7e15++23zf7v5/HjxyQkJKi/UGg0GnWQnfzbtX41/fx+pkqkJUuWoNFoePfddys9JyEhAY1G89Tj5102hXhWbm5u/OpXv2LmzJnqOPDbt2+zdOlSfvjhB3UYnxCiYj9PROzs7HjjjTfMmgwUFhYSFxfHJ598wvHjxzEYDPj7+/Pmm28yceJESURsTJ1vwB09epQVK1bQp0+fGp2fmppa7oerZcuWdX1pISrl7+/PBx98QEJCAgcOHEBRFE6cOMHZs2cZPXo0AQEBlg5RiAanokTEXH079Ho9KSkpJCUlUVBQABhXMUeNGkW7du3M8pqi4atTMpKXl8fs2bNZuXIlf/nLX2p0jZeXF82bN6/LywlRK1qtltDQUIYMGUJkZCRXrlyhpKSEHTt2sG/fPqZNm9Yg5mkI0RCkpqbyzTffqInIwoUL8fT0NPnrGAwGzp49S1xcHI8ePQLA09OT8PBw/P39ZYeMjatTMvLWW2/x/PPPEx4eXuNkpH///hQWFtKjRw/+8Ic/VDlnpKioSG1sA8Z7TkLUlpOTE7Nnz+b+/ft8++23PHz4kJycHFavXi31JEIA586dY+vWrYCxkeDChQtp0aKFyV/n6tWrxMTEcO/ePcBYZF42yK4++5aIhqvWycjmzZs5fvw4R48erdH5rVu3ZsWKFQQEBFBUVMT69esJCwsjISGh0i2YS5Ys4c9//nNtQxOiQt7e3rz99tucOXOGXbt2UVhYqNaT9OrVi4kTJ8qWQWFzTp06xbZt2wDUFRFTJyLp6enExMRw7do1wDjIbujQoQQGBkpPIFFOrXbT3Lp1iwEDBhAVFUXfvn0BGDlyJP369WPp0qU1ftEJEyag0Wj44YcfKvx6RSsjvr6+sptGPDNFUYiPj+fgwYNqUatOp2PEiBEEBwdbODoh6sfRo0fZtWsXYEwQ3nzzTZPeRs/OziY+Pp4zZ84AxlunAwcOZPjw4fWyTVg0HGbZ2rtt2zamTJmCTqdTj5WWlqLRaNBqtRQVFZX7WmX+3//7f2zYsIELFy7U6HVla68wteLiYr7//vtyu7qcnZ15/vnn6dmzpwUjE8K8EhMTSUhIAIx9RH7961+b7H31yZMn6iC7smS/d+/ehISE4O7ubpLXENbFLMnI48eP1RHSZV555RW6devGhx9+SK9evWr0PC+88AJZWVnExcXV6HxJRoS5ZGVl8e2336r3sgHc3d2ZNm0abdq0sWBkQpjerl271FvsLi4uvPXWWyZZqSguLubQoUMcOHBA7YjcsWNHwsPDad269TM/v7BeNf38rtWN8qZNmz6VcDRp0gRPT0/1+OLFi7lz5w7r1q0DYOnSpXTo0IGePXtSXFzMhg0biIyMJDIysrbfkxAm5+HhwcKFC0lLS2Pbtm3k5OSQnZ3Nl19+Sdu2bXnhhRdwc3OzdJhCPLOtW7dy7tw5wNiX59e//vUz122UbZ1PSEggLy8PgFatWqmD7ISoKZNX7aWnp6szBcCYMX/wwQfcuXMHZ2dnevbsyc6dOxk3bpypX1qIOuvQoQPvvvsuJ06cYO/evRQVFalFrv7+/kyePFlaUgurpCgKa9euVd+Xvby8WLhw4TPtYjEYDFy8eJHY2FgePnwIQPPmzQkNDaVXr16yTVfUmrSDF+IXFEUhISGBgwcPUlpaCoBGo6F///6MHTtWdt4Iq1FcXMwXX3xBVlYWAO3atWPevHnPlIjcvHmT6Ohobt++DRhrrYYPH86AAQPk34Z4isymEeIZ6fV6duzYwenTp9UhfDqdjqFDhzJixAjpjyAatLy8PD7//HPy8/MBYyHp1KlT6/x8Dx48IDY2ltTUVMC4HTgoKIghQ4bIqqGolCQjQphIfn4+33//PVeuXFGPOTo6EhYWxsCBAy0YmRAVu3//PqtWraKkpASA4OBgQkND6/Rcubm5JCQkcPLkSXWQXf/+/Rk5ciRNmzY1ZdiiEZJkRAgTy87OZuvWrdy9e1c95uLiwtixY2u8k0wIc7t48SJbtmxRV/PGjx9fp5lMhYWF7N+/n8OHD6PX6wHo1q0bYWFhZunSKhonSUaEMJM7d+6wbds2MjMz1WNubm5MmDBBdhAIizpw4AAxMTGAsdHYSy+9VOufSb1ez9GjR9m3b586yM7X15dRo0bJTCdRa5KMCGFmV69eZfv27eTk5KjHPD09mTx5Mm3btrVgZMIWff/995w+fRow3kZ8/fXXazXwzmAwcPr0aeLj49Wf6RYtWhAeHk7Xrl1lh4yoE0lGhKgnZ8+eZffu3WqhIBjn4UyZMgVvb28LRiZsgV6vZ9WqVWrjvubNm7Nw4cIaF5UaDAZ1kN39+/cBY0+pslEfUqgtnoUkI0LUs6NHjxIbG1turpKPjw9TpkyRe+zCLHJyclixYoWaCLdv3565c+fWOIG4e/cuMTExXL9+HTCuqAwbNozBgwdjb29vtriF7ZBkRAgLUBSF5ORkkpKS1LbYYLznPnXqVJMOIxO27dq1a2zcuFHthRMYGMjo0aNrdG3ZOI6yjqw6nY6BAwcSHBwsg+yESUkyIoQFKYpCUlISBw4cUHcigPE31ylTpkiLefFM9u3bp8720mg0TJkyhd69e1d73ZMnT0hMTOTYsWPqILs+ffoQEhIiibIwC0lGhGgAFEUhNjaWw4cPq7/BgrH9/JQpU+TnWdSKoihs2rRJ7Xljb2/PK6+8Uu0wuuLiYpKTkzl48KC6Yte5c2fCwsJo1aqV2eMWtkuSESEaEEVRiIqKIiUlpVxS4ufnx+TJk+XnWlQrLy+PlStXkpubCxh3bi1YsKDKQtXS0lKOHz9OYmIiT548AaB169aMGjUKPz+/eolb2DZJRoRogPR6PdHR0Rw7duyppGTSpEly+0ZU6Pr162zcuFG95dezZ0+mTp1aaaGqwWDgwoULxMbGqnNp3N3dCQ0NpWfPnrJNV9QbSUaEaMD0ej1RUVHl7t2D8fbNpEmT5P69UMXFxbFv3z7AWB8yduzYKscQ3Lhxg+joaO7cuQMYuwSPGDGCgIAAdDpdvcQsRBlJRoSwAmVJyfHjx8utlLRr145Jkybh4eFhweiEJen1etauXatOx3VwcGDevHn4+PhUeH5GRgYxMTFcvnwZMNaTlA2yc3R0rLe4hfg5SUaEsCJ6vZ6YmJinakratm3LxIkTadmypQWjE/UtIyODNWvWUFhYCBib6L366qs4ODg8dW5OTo46yA6MqycBAQGMGDECV1fX+gxbiKdIMiKEFSrbfXPkyJFyW4JbtWrFxIkTq901Iazf4cOH2bt3rzrobtCgQYwdO/ap8woKCtRBdmUJbI8ePQgNDa1VG3ghzEmSESGsmKIoxMfHc/jwYXUMPBhnhUyYMIF27dpZMDphDoqisGHDBrUbqk6nY/r06fj7+5c7T6/Xc/jwYfbv36+unLRv357w8HCZiSQaHElGhGgEFEVh//79HDx4sFybeXd3d8aOHUuXLl0sGJ0wlYyMDL766it1Sq67uzuvvvpqudssiqKog+zKtvd6eXkRHh5O586dZYeMaJAkGRGikTl8+DCJiYnqBxZAs2bNCA8Pr1H3TdEwHTx4kJiYGPW2TP/+/Zk4caL6dYPBwJUrV4iJiSEjIwMw/v8eEhJCnz59ZJCdaNAkGRGikTpx4gRxcXHk5eWpx5ydnRk+fDiDBg2SDycrUVxczPr169XdMjqdjhdeeIFu3bqp59y5c4fo6Ghu3LgBgJOTE8OGDWPQoEEyyE5YBUlGhGjkzp8/T1RUFDk5OeoxBwcHBg8ezMiRIyUpacDS0tLYtGmT2prd09OT+fPnq7dlHj58SFxcHOfPnweMicrgwYMZNmwYzs7OFotbiNqSZEQIG5GWlsbOnTvJzMxUj+l0Ovr160dERESF20GF5ezevZsjR46ofx88eDBjxowBjC3fExMTOX78uNoMr1+/fowcOVK68wqrJMmIEDYmPT2dHTt2cPfuXfWYRqPB39+f559/XnpOWFhOTg5fffUVjx49AoyrWLNnz6Zdu3YUFRVx8OBBkpOT1d1TXbp0ISwsDG9vbwtGLcSzkWRECBuVnZ3Njh07uHbtWrnj7du3Z/z48bRo0cJCkdmuI0eOsGfPHrVItV27dsyePRudTsexY8dISkpSB9m1adOG8PBwOnToYMGIhTANSUaEsHH5+fns3r2b8+fPl5t/4+3tzbhx46RXST34ZZGqVqtl7NixBAQEcP78eWJjY8nOzgbAw8ODsLAwunfvLtt0RaMhyYgQAvip1fyxY8fKdXVt1qwZoaGh9O3b14LRNV4XL14kMjJS/W/u7u7O/PnzefjwITExMerttCZNmjBixAiee+45GWQnGh1JRoQQ5SiKQnJyMgcOHCjXq8TJyYnBgwczfPhw2YFjAnq9ni1btqgD6wACAwPp168fMTExXLlyBTDWjAwZMoSgoCApMhaNliQjQohKnTt3jpiYGLWYEow7cHr37s3o0aNxcnKyXHBWLC0tjc2bN6vdcl1cXJg8eTJnz57l9OnTgPFWTdkguyZNmlgyXCHMTpIRIUS1bt++za5du0hPT1ePaTQa/Pz8GDdunAxcqyFFUfj+++85e/aseqxHjx40bdq03CTmnj17EhoaioeHh6VCFaJeSTIihKixnJwcdu7cyZUrV/j5W0LLli0ZPXo0nTp1smB0DdvNmzfZtGmTOrTO0dGRnj17cu7cOXWFpEOHDoSHh9OmTRtLhipEvZNkRAhRa8XFxURFRXHq1Klyxa6urq4MGzaMgQMHSl3JjypaDWnVqhWPHz9Wt+l6e3sTHh5Op06dZIeMsEmSjAgh6kxRFI4cOcL+/fvVD1YAe3t7+vXrR3h4uE0XXaalpfHNN9+oqyF2dna4uLio03Td3NzUQXaShAhbJsmIEMIkLl++TFRUVLl282V1JWPHjrWpJmp6vZ7IyEguXryoHnN2dlZ3Jzk7OxMcHMzAgQOxs7OzVJhCNBiSjAghTCozM5Ndu3aRlpZWrq7E09OTUaNG4e/vb8HozC81NZXvvvtOHW6n1WrVZnJ2dnbqIDvZiSTETyQZEUKYRWV1Jc7OzgwaNKjR9SspLi5m06ZNpKWlPfU1jUajDrKT9yYhnibJiBDCrBRF4dixY+zbt4/Hjx+rx7VaLf7+/owZM8bq/72mpKSwZ88edWvuz/n7+xMaGoqXl5cFIhPCOkgyIoSoN2lpaezdu5d79+6VO96qVStGjRpFx44dzfK6paWl3Lp4l8vHrpF+7T76Ej1OTZzo0NOXLgEdadHGo04FpDk5OXz99dc8ePDgqa+1bduW8PBw2rdvb4pvQVQg6142l49d4/qZmxTkFaKz0+HVrgVdAjrSvkdb7OylHsdaSDIihKh3eXl57NmzhwsXLpQbzufi4kJQUBBDhgwxyS2cjJsP2PFFNDu+iOZxVh4AOnsdGkBRDCilxtdu36Mtk/9tHGGzh+Hs6lzt8yqKQkxMDIcOHeKXb42enp6EhYXRrVs32SFjBsWFxSRuSWbbp7u4dMw4cVqr06LVajAApSXG1Snnpk6Mey2M8W+Opm2X1haMWNSEJCNCCItRFIX9+/dz+PBh8vPz1eM6nQ5/f39Gjx5dp3/LpfpSNv91G+v/vAWDATXpqIxGo8GAAXcvNz5Y/RaDxvav9NybN2+yZcuWcluZwdhjZeTIkfTv379R1cI0JGf2XeCvcz/l/o0HaLQaDErVH0tanRaDYmD6BxOZ9+cZODjZ7jbzhk6SESFEg3DlyhViYmK4f/9+ueNeXl6Eh4fTpUuXGj1PdkYO/2vcf3L5xDWo5btW2QfcpLfG8ObS+eWm4xYXF7NlyxauXr1a7ho7OzuCg4MJDAy06Z4q5mQwGFj3py1s+MtW4+6kapLLX9JoNbTp3Iole/5Aqw5Su9MQSTIihGhQcnNz2bt3LxcvXix3C8fZ2ZkBAwYwfPjwSntzPHqQwztD/8C96xm1/sAqRwOjXh7BB6t/jVar5fDhw0RHRz9VoDp48GCCg4NlkJ0ZGQwGVvx2PVv/vv2Znkdrp6V5Szc+Ofj/8G7f0kTRCVORZEQI0SApisLBgwc5fPgweXl56nGtVkvHjh0ZPXp0uUZqiqLwm5H/m/OHLqHonyER+ZmZf5hMnmdmuanFYBxkFxYWhru7u0leR1Ruz+o4Pl7wuUmeS2enpU2X1iw/8RH2DvYmeU5hGpKMCCEavLS0NKKjo7l792654+7u7gQHB9O3b19+WLaXZe+srvJ5Hhkyuc5FcniIQimOuNCadnTU9KjwfI0W+r/RGZeWxgZlbdu2Zdy4cbRuLQWR9SHjViav9XiXwidFlZ6Ta8jmOhfIIQs9JTjhQit8aU9XdJqnV9A0Gg0v/a+pzP8/M80ZuqglSUaEEFYjPz+f6Ohozp49W66RGnoNyR+dp7T46T4fZe4ZbnKWI3jjSyt80WFHAU8ooqDSZAQtuHVowpBf92HSpEkylbie/dfLnxD/zYFKV7ryDLkcIQYXmuJHN+xxJJsHpHERT1rRTzO0wuu0Wg3rr/8TL1/bGVHQ0NX081s2awshLM7FxYVJkyYxYcIETp48yf79+8nOzubuscwqE5FCQwEXOEZbOtJN81zNX1CBnGtPmDF+Jm07+ZjgOxA1lZ2RQ8I3B6u85XaPmygo9CEIF40rAB54UWwo5A7XKTEUY6+poKhYo2HXihjm/19ZHbE2z7RPbcmSJWg0Gt59990qz0tMTCQgIAAnJyc6duzI8uXLn+VlhRCNlFar5bnnnmPRokW89dZbPDydV+X5d7lOKaW0p/ZzcXR2Wvauia9rqKKO4r7eV66AuSLaHz+a7Chf/1H2d20lH11KqcKOFdFP9YgRDV+dk5GjR4+yYsUK+vTpU+V5169fZ9y4cQQHB3PixAl+//vfs2jRIiIjI+v60kIIG+Ds4EJO+uMqz8nmAfY4kM9jDhmiiTVEkmjYzgXDcfSGkiqvLdUrnD1wscpzhOmdO3iR6lrGtaY9dthzkePkG/LQG0p4YLjLHa7jS+cKa0bK5DzI5f6NpzvnioatTslIXl4es2fPZuXKldVWnS9fvpx27dqxdOlSunfvzoIFC3j11Vf529/+VqeAhRC24cqJ69X2EymikFL0nOYQ3vjSn2Da05V0bnCC/dX+hnz5+PVqf0sXpnXh8BWUapqaOWuaMJAQ8sjlIHtI4F+c4iCtaU9X+lb7Gpd/7OAqrEedkpG33nqL559/nvDw8GrPTU5OJiIiotyx0aNHk5KSQklJxb+5FBUVkZubW+4hhLAtD+9m1+AsAwoKfnTDT9MND40XHTT+dKYXOTwki4wqry7KL6Igr9A0AYsayb7/qNpzCgxPOMlB7HGgN4EEMILO9OYuaVzgWJXXarQaMu9kmShaUV9qnYxs3ryZ48ePs2TJkhqdf+/ePby9vcsd8/b2Rq/Xk5mZWeE1S5Yswc3NTX34+vrWNkwhhJWrSXMze4xFjB6Uf4/xpBUAj3lkktcRpmOowX/vK5yhlBKeIxhvTVvcNS3poPHHn37cJY1sQ+W3YTQajfx/aoVqlYzcunWLd955hw0bNuDk5FTj6345VKps6bSyYVOLFy8mJydHfdy6das2YQohGgGXZtUPtnPFrcqvV1eboNFqcHRxrEVU4lk5Nan+s+MxOTSh2VO1Ic0wlgXkkVPptUqpUqOfHdGw1CoZOXbsGBkZGQQEBGBnZ4ednR2JiYl88skn2NnZPdVSGYwjxH85VjwjIwM7Ozs8PT0rfB1HR0eaNWtW7iGEsC0d+7Sv9hwv2gDwkPLvMZmkA+BGxe8xZdp0boWDo3TsrE+d+nWo9hxHnMgjF71BX+54Dg9//LpLldd37Fv9a4iGpVZ9RsLCwjhz5ky5Y6+88grdunXjww8/LDd8qkxQUBDbt5efPRAVFcWAAQOwt5c3ASFExbzbt6SJmwtPcvIrPcdT04oWhtZc5wIGA7jhwWOyucZ5WtCa5prKm19p7bR0D+xqjtBFFfwHduZ88iVK9ZX3j2lHF05xkBMk0c7QBXscyeEhaaTShGa0+PE2XEV0dlr8erczR+jCjGq1MtK0aVN69epV7tGkSRM8PT3p1asXYLzFMnfuXPWaN954gxs3bvD+++9z4cIFVq9ezapVq/jggw9M+50IIRoVjUbDyBeHorOr+m2qN4H40oU7XOMk+7nNNdrRhT4EVnmdolcInlb1OcL0gl8IrDIRAWip8eE5hqPDnlROcZIDpHODNvgRwAi0mop/JnR2WgLHD5DVLitk8g6s6enp3Lx5U/27n58fu3bt4r333mPZsmX4+PjwySefMG3aNFO/tBCikZnwZgQ7V0RXeY5Oo6MLvelC71o9t6ePO4PG9X+W8EQddB/cBb/e7Ug7e6vKrdceGi888KrVc5fqFSa+NeZZQxQWILNphBAN2h8n/RdHdp8w2cTeMu99sZBxr1ffnkCY3oFtR/jT1I9M+pxaOy1dAzryycH/rHRzhKh/Nf38fqZ28EIIYW7vLl+Ik4tj9Vtjakhnp6VfSC/GLggzzROKWhs6eRAjZgxBqzPdR5BWq+XDtf8miYiVkmRECNGgebZ259/XLzJ+yDzj54xWp8WtpRu/W/u2fGhZ2KJ/LqCVn1e1NUE19e7yX9G2qww9tFaSjAghGrygCQP4XxvfRavV1vm3aa1OS3MvNz5O+DMt21a95VeYXzOPpnwc/yda+XnX/f9TrTFBXbRsAaPnh5g4QlGfJBkRQliFETOG8I99/5dWHVqi0dZ8VaPs3MDxASw//t+07dLaXCGKWmrRxpPPDi8hbHYwQK3+f9XqtLi3as5f9/6RCW+ONleIop5IAasQwqoUFRTx7d+2s+2z3eQ8yEVnr6O0pPxWUY1Gg1anoVSv0Klve2b9fhrDXwiUWzMN2JHdJ9jwl61cSL6EVqfFYDBg+MVAvbL/r5u4uTB+4Shm/X4qTZpV3QBNWFZNP78lGRFCWCV9iZ7k7cc4k3Sei4cvc/fafUr1pTg6O9CxT3u6DuhE4PgAug3qYulQRS1cO32Dg/86yqWUq1w+cY3CJ0XodFq82rek26Au9BrWjWFTBuHg5GDpUEUNSDIihBBCCIuSrb1CCCGEsAqSjAghhBDCokzeDt4cyu4k5ebmWjgSIYQQQtRU2ed2dRUhVpGMPH78GABfX18LRyKEEEKI2nr8+DFubm6Vft0qClgVReHu3bs0bdpUtuYJIYQQVsJgMPD48WN8fHzQaiuvDLGKZEQIIYQQjZcUsAohhBDCoiQZEUIIIYRFSTIihBBCCIuSZEQIIYQQFiXJiBBCCCEsSpIRIYQQQliUJCNCCCGEsKj/DyP0ZsepBxF8AAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "v_list = [0,1,8,6,3]\n", "H = R.induced_subgraph(v_list)\n", "H.draw(cpx = 3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "We can also take a slice of the Reeb graph, defined as the inverse image $f^{-1}(a,b)$ for some interval $(a,b) \\subset \\mathbb{R}$. Note that this is not the same thing as taking the induced graph of the set of vertices $\\{v \\mid f(v) \\in (a,b)\\}$ since we treat edges as being topologically equivalent to an interval. So taking the slice is done by adding spare vertices for edges that cross this interval." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "H = R.slice(4.5,6.5)\n", "H.set_pos_from_f(seed = 0)\n", "H.draw()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although the drawing doesn't make it particularly obvious, we can do things like check the number of connected components. " ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "There are 3 components in this Reeb Graph\n" ] } ], "source": [ "print(f'There are {H.number_connected_components()} components in this Reeb Graph')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or we can extract them individually:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "H_components = [H.induced_subgraph(c) for c in H.connected_components()]\n", "\n", "H_components[0].draw()" ] } ], "metadata": { "kernelspec": { "display_name": "base", "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": "3.11.5" } }, "nbformat": 4, "nbformat_minor": 2 }