{ "cells": [ { "cell_type": "code", "execution_count": 2, "id": "d5b177c7-4f7f-4ff1-b669-e7c15fc9b9f0", "metadata": {}, "outputs": [], "source": [ "from collections import defaultdict" ] }, { "cell_type": "code", "execution_count": 3, "id": "20559cf0-376a-474a-aaf5-4595c6e7e13c", "metadata": {}, "outputs": [], "source": [ "def is_valid_line(line):\n", " # Split the line by spaces and check if it contains exactly three elements\n", " elements = line.strip().split()\n", " if len(elements) != 3:\n", " return False\n", " \n", " # Check if each element is a valid integer\n", " for element in elements:\n", " if not element.isdigit():\n", " return False\n", " \n", " return True\n", " \n", "class CoxeterDiagram:\n", "\n", " def __init__(self):\n", " print(\"Created empty Coxeter diagram.\")\n", " self.coxiter_file_path = \"\"\n", " self.coxiter_data = []\n", " self.graph_loopless = Graph()\n", " self.graph = Graph(loops=True)\n", " self.vertex_positions = {}\n", " self.matrix = []\n", " self.subgraphs = []\n", "\n", " def init_from_tuples(self, tuples):\n", " self.coxiter_data = tuples\n", " self.build_graph()\n", " self.matrix = self.graph.weighted_adjacency_matrix()\n", "\n", " \n", " def init_from_coxiter_file(self, coxiter_file_path):\n", " self.coxiter_file_path = coxiter_file_path\n", " filename = self.coxiter_file_path\n", " valid_lines = []\n", " try:\n", " with open(filename, 'r') as file:\n", " for line in file:\n", " if is_valid_line(line):\n", " vertex_edge_tuple = tuple(map(int, line.strip().split()))\n", " valid_lines.append(vertex_edge_tuple)\n", " self.init_from_tuples(valid_lines)\n", " except FileNotFoundError:\n", " print(\"File not found!\")\n", "\n", " def compute_subgraphs(self):\n", " S = Subsets(self.graph.vertex_iterator())\n", " for s in S:\n", " Hi = self.graph.subgraph(list(s))\n", " self.subgraphs.append(Hi)\n", " \n", " def color_nodes(self, ls):\n", " if len(ls) != self.graph.num_verts():\n", " raise ValueError(\"List incorrect length: expected \" + str( self.graph.num_edges() ) + \" entries.\")\n", " else:\n", " for i, l in enumerate(ls):\n", " vert = i+1\n", " weight = l\n", " self.graph.add_edge(vert, vert, weight)\n", " self.matrix = self.graph.weighted_adjacency_matrix()\n", " self.compute_subgraphs()\n", "\n", " def plot(self):\n", " return self.graph.plot(\n", " # talk = True,\n", " edge_labels = True,\n", " edge_thickness = 0.5, \n", " edge_color = 'blue', \n", " edge_style = 'solid', \n", " vertex_size = 20\n", " )\n", "\n", " def set_vertex_positions(self, positions):\n", " self.graph.set_pos(positions)\n", " \n", " def build_graph(self):\n", " for e in self.coxiter_data:\n", " self.graph.add_edge(e)\n", " self.graph_loopless = Graph(self.graph)\n", " self.graph_loopless.allow_loops(False)" ] }, { "cell_type": "code", "execution_count": 4, "id": "f7fa37b8-20f8-4827-a6ba-7ddb7dec6ce0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Created empty Coxeter diagram.\n" ] }, { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 44 graphics primitives" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G991 = CoxeterDiagram()\n", "G991.init_from_coxiter_file(\"/home/dzack/dissertation/Research_Files/9-9-1_1.coxiter\")\n", "G991.color_nodes([-2, -2, -2, -2, -2, -2, -2, -2, -4])\n", "G991_positions = {\n", " 1: (0, 0),\n", " 2: (2, 1),\n", " 3: (1, 0),\n", " 4: (2, 0),\n", " 5: (3, 0),\n", " 6: (4, 0),\n", " 7: (5, 0),\n", " 8: (6, 0),\n", " 9: (7, 0)\n", "}\n", "G991.set_vertex_positions(G991_positions)\n", "G991.plot()" ] }, { "cell_type": "code", "execution_count": 5, "id": "c3384f38-3f7e-4238-a7c4-4661d790c82a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[-2 0 3 0 0 0 0 0 0]\n", "[ 0 -2 0 3 0 0 0 0 0]\n", "[ 3 0 -2 3 0 0 0 0 0]\n", "[ 0 3 3 -2 3 0 0 0 0]\n", "[ 0 0 0 3 -2 3 0 0 0]\n", "[ 0 0 0 0 3 -2 3 0 0]\n", "[ 0 0 0 0 0 3 -2 3 0]\n", "[ 0 0 0 0 0 0 3 -2 4]\n", "[ 0 0 0 0 0 0 0 4 -4]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\\(\\displaystyle \\left(\\begin{array}{rrrrrrrrr}\n", "-2 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 2 \\\\\n", "2 & -2 & 2 & 3 & 2 & 2 & 2 & 2 & 2 \\\\\n", "3 & 2 & -2 & 3 & 2 & 2 & 2 & 2 & 2 \\\\\n", "2 & 3 & 3 & -2 & 3 & 2 & 2 & 2 & 2 \\\\\n", "2 & 2 & 2 & 3 & -2 & 3 & 2 & 2 & 2 \\\\\n", "2 & 2 & 2 & 2 & 3 & -2 & 3 & 2 & 2 \\\\\n", "2 & 2 & 2 & 2 & 2 & 3 & -2 & 3 & 2 \\\\\n", "2 & 2 & 2 & 2 & 2 & 2 & 3 & -2 & 4 \\\\\n", "2 & 2 & 2 & 2 & 2 & 2 & 2 & 4 & -4\n", "\\end{array}\\right)\\)" ], "text/latex": [ "$\\displaystyle \\left(\\begin{array}{rrrrrrrrr}\n", "-2 & 2 & 3 & 2 & 2 & 2 & 2 & 2 & 2 \\\\\n", "2 & -2 & 2 & 3 & 2 & 2 & 2 & 2 & 2 \\\\\n", "3 & 2 & -2 & 3 & 2 & 2 & 2 & 2 & 2 \\\\\n", "2 & 3 & 3 & -2 & 3 & 2 & 2 & 2 & 2 \\\\\n", "2 & 2 & 2 & 3 & -2 & 3 & 2 & 2 & 2 \\\\\n", "2 & 2 & 2 & 2 & 3 & -2 & 3 & 2 & 2 \\\\\n", "2 & 2 & 2 & 2 & 2 & 3 & -2 & 3 & 2 \\\\\n", "2 & 2 & 2 & 2 & 2 & 2 & 3 & -2 & 4 \\\\\n", "2 & 2 & 2 & 2 & 2 & 2 & 2 & 4 & -4\n", "\\end{array}\\right)$" ], "text/plain": [ "[-2 2 3 2 2 2 2 2 2]\n", "[ 2 -2 2 3 2 2 2 2 2]\n", "[ 3 2 -2 3 2 2 2 2 2]\n", "[ 2 3 3 -2 3 2 2 2 2]\n", "[ 2 2 2 3 -2 3 2 2 2]\n", "[ 2 2 2 2 3 -2 3 2 2]\n", "[ 2 2 2 2 2 3 -2 3 2]\n", "[ 2 2 2 2 2 2 3 -2 4]\n", "[ 2 2 2 2 2 2 2 4 -4]" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "M2 = Matrix(ZZ, G991.matrix)\n", "for i in range( G991.matrix.nrows() ):\n", " for j in range ( G991.matrix.ncols() ):\n", " if G991.matrix[i, j] == 0:\n", " M2[i, j] = 2\n", "display( G991.matrix )\n", "show( M2 )" ] }, { "cell_type": "code", "execution_count": 6, "id": "dec86ca4-9db4-4b03-8d92-c4f47defa364", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 44 graphics primitives" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G = G991.graph\n", "plot(G, edge_labels=True)" ] }, { "cell_type": "code", "execution_count": 7, "id": "f1db163e-e816-4133-ab42-d2761cb0c3bc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "512" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len( G991.subgraphs )" ] }, { "cell_type": "code", "execution_count": 8, "id": "de7aa2cf-9874-4a73-9eb6-0eff4a1493fd", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[-2 0 3 0 0 0 0 0 0]\n", "[ 0 -2 0 3 0 0 0 0 0]\n", "[ 3 0 -2 3 0 0 0 0 0]\n", "[ 0 3 3 -2 3 0 0 0 0]\n", "[ 0 0 0 3 -2 3 0 0 0]\n", "[ 0 0 0 0 3 -2 3 0 0]\n", "[ 0 0 0 0 0 3 -2 3 0]\n", "[ 0 0 0 0 0 0 3 -2 4]\n", "[ 0 0 0 0 0 0 0 4 -4]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M = G991.matrix\n", "M" ] }, { "cell_type": "code", "execution_count": 9, "id": "1b8b15f6-ded8-4172-ac00-943b9224db54", "metadata": {}, "outputs": [], "source": [ "for i in range( M.nrows() ):\n", " for j in range( M.ncols() ):\n", " if i != j and M[i, j] > 0:\n", " M[i, j] = M[i,j] - 2" ] }, { "cell_type": "code", "execution_count": 10, "id": "725a0b99-38c0-47b6-b514-6dda041b32d9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[-2 0 0 0]\n", "[ 0 -2 3 0]\n", "[ 0 3 -2 3]\n", "[ 0 0 3 -2]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M = G991.subgraphs[176].weighted_adjacency_matrix()\n", "M" ] }, { "cell_type": "code", "execution_count": 11, "id": "d6d70a92-7848-4c8b-adb0-107bb820ef00", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 17 graphics primitives" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G991.subgraphs[176].plot(edge_labels=True)" ] }, { "cell_type": "code", "execution_count": 12, "id": "aa95395d-76f0-4d16-9105-cbc6717d3bab", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.is_positive_definite()" ] }, { "cell_type": "code", "execution_count": 13, "id": "4215a737-ff53-4661-abe0-69b6f4de95a4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.is_positive_semidefinite()" ] }, { "cell_type": "code", "execution_count": 14, "id": "f14e9071-7b1e-485a-93b1-de0f1072a31a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(-M).is_positive_definite()" ] }, { "cell_type": "code", "execution_count": 15, "id": "4253b67d-dd97-490b-99fa-d376a9f5a1ad", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(-M).is_positive_semidefinite()" ] }, { "cell_type": "code", "execution_count": 16, "id": "66448431-f002-4e78-9710-ebd952cbc774", "metadata": {}, "outputs": [], "source": [ "M = Matrix(ZZ, 2, [2, 1, 1, 2])" ] }, { "cell_type": "code", "execution_count": 17, "id": "f5d4c522-036e-4424-bb7e-a044250d720e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.is_positive_definite()" ] }, { "cell_type": "code", "execution_count": 18, "id": "f71cb2f8-6114-4872-ac5c-41cd67d4f138", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Created empty Coxeter diagram.\n" ] }, { "data": { "text/plain": [ "[-2 1 1]\n", "[ 1 -2 1]\n", "[ 1 1 -2]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A2 = CoxeterDiagram()\n", "A2.init_from_tuples([\n", " (1,2,1),\n", " (2,3,1),\n", " (1,3,1)\n", "])\n", "A2.color_nodes([-2, -2, -2])\n", "A2.matrix" ] }, { "cell_type": "code", "execution_count": 19, "id": "45a87247-bc1c-4c3f-926e-819e35e28e08", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A2.plot()" ] }, { "cell_type": "code", "execution_count": 20, "id": "58acdee5-3ac2-45b4-b150-25b253d839bf", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Finite Coxeter group over Integer Ring with Coxeter matrix:\n", "[1 3 2]\n", "[3 1 3]\n", "[2 3 1]" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A2p = CoxeterGroup([\"A\",3])\n", "A2p" ] }, { "cell_type": "code", "execution_count": 21, "id": "9341769f-1e92-4198-b1d0-2c32ff463f47", "metadata": {}, "outputs": [ { "data": { "image/png": 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LokWLcP36dZw6dYpbwiHg5KIezp8/jwMHDiAxMZHFGiIuNKiH0NBQODk5YdmyZaKjKB7LRQ/cunULiYmJCAgIgI2Njeg4isdy0QNxcXHo7OzE+vXrRUcxC1xoEID7Fwx3dnaGh4cHkpKSRMcxC1xoEABg7969aGho4PNaRsTJRQAAT09P6HQ6FBUViY5iNji5CJWVlSgoKEBaWproKGaFk4vg6+uLAwcOoL6+ntc1NiJuC1Xu5s2b2LlzJ4KCglgsI2O5VC4qKgoA4OfnJziJ+eFpoYrdu3cP48ePx8KFCxETEyM6jtnh5FKxrKwsXLlyhR8+IxFOLhWbPXs2bG1tkZ+fLzqKWeIqXqW++eYbFBcXIzs7W3QUs8XJpVKrVq3C8ePHodFoeF1jifAxlwo1NTUhPT2dFwyXGMulQtu3b8fw4cPh7e0tOopZY7lURqfTYfv27VizZg2eeOIJ0XHMGsulMunp6bh+/To2bNggOorZ40JDRQwGA2bMmAEnJyfs379fdByzx1W8ihw/fhxlZWUslolwcqnI0qVLUVlZiXPnzvG6xibA32GVaGxsRHZ2NjZs2MBimQh/l1UiPDwc9vb2WLNmjegoqsFyqUBbWxuioqLg4+MDe3t70XFUg+VSgeTkZNy6dYtXLDExLjTMnMFgwNSpU+Hs7Iw9e/aIjqMqXMWbufz8fFRXVyM0NFR0FNXh5DJzixcvRkNDAyoqKnhhBRPj5DJjdXV12LdvH6KiolgsAbjQMGNhYWEYM2YMLxguCMtlpu7cuYO4uDj4+/tjxIgRouOoEstlphISEqDVahEYGCg6impxoWGG9Ho9XnnlFbz22mtIT08XHUe1uNAwQwcOHIBGo0FCQoLoKKrGyWWG3nzzTTQ3N+PkyZPcEgrEyWVmzp07h4MHDyIpKYnFEowLDTOzdetWjBs3DkuXLhUdRfVYLoXT6/UP/r2lpQU7duzA+vXrecFwGeBjLoUpKytDfHw8iouKUFVdDZ1OBxsbG0yZPBm2I0agpKQEly9fxrhx40RHVT2WSyFqa2vh7+eHIwUFeM5pLObPcIWry0Q42I1Eq7YNFZo6HDhRimvNLfCcMwdR0dFwdnYWHVvVWC4FSElJga+vL54Z44jPgn3wrscsWFn1/qTcrq5u7C08gT+GxaKpuQWxsbFYvny5gMQEsFyyl5KSgpUrV2Llm3MR/nEI7EbYPvZntO0dCNwSiuS8fCQnJ2PFihUmSEo/xnLJmEajgaurKz54YzbiN/3+wQfLfJKYhuyjx3H+0mWMsBmO2VMn4R+B3nj5py88+Fm9Xg+vzZ9j99EiVFZW8hRRAJZLxuZ6eqKxtgand4T3mFiL/sv/xLIFb2Dmqy+hq1uPv2xPwJmLDahOiepxO217B1xXBeKnLi8h/8gREf8JqsZyyVRpaSlmzJiBzE82YcmcXz7ytjdabmHcWx+iIPwzvP7a1B7fyyooxAd/+htKS0sxffp0KSPTj/B5LplKSEjA8+Oc8K7HrMfe9vbdNgDAGIdRvb632MMdzzmNRXx8vNEz0qOxXDJVXFSEeW7T+twK/juDwYDfb42Eh+tkTJn4Yq/vW1lZYp6bK04UF0uUlB6G5ZKpqupquLpMfOztgv+5DZW19Uj5P//jobdxdZmAM1VVxoxH/cAX7sqQXq+HTqeDg93IR94u5PNw7C08gaMR/8TzTmMfervR9nbQ6XTQ6/X8KGsTYrlkyMLCAjY2NmjVtvX5fYPBgJDPw7HnaBGOhG/B+GeffuTxbt/VwsbGhsUyMZZLpqZMnowKTV2f3wv65zakHjyCPZ/+FaNGjsDV75sBAKPt7DDCtvcLdis0FzF1yhRJ81JvLJdMuc+ejeyMdHR1dfdaamzP2gcA8Az6uMfX4/7y37D27V/3+FpXVze+Kq3Akt8tkzYw9cLnuWSqrKwMbm5u/Xqe61H4PJc4LJeMzfX0xCVNDSqSwvv1msIf4ys0xOIjXBmLio5GU3MLAreE9nhTZH/o9XoEbglFU3MLoqKjJUpIj8JyyZizszNiY2ORnJcPr82fQ9ve0a+f07Z3wGvz50jOy0dsbCxftCsITwsV4If3cz3t+AQ+C/HBYg/3h76fK6ewGB+HxfH9XDLAcilEbW0tPDw8cO3aNTznNBbz3Fzh6jIBo+3tcPuuFhWai/iqtAJXrt/AXE9PREZFcWIJxnIpxLfffovx48fjD3/4A7RaLU4UF+NMVdWDz9CYOmUKZrm7w8vLi1tBmeDzXArxwwXD//KXv/S4rjFf0iRf/FNRgEddMJzFki/+ySjAzp070dLSwguGKwwfc8mcwWDAtGnTMHHiRF4wXGE4uWTuyJEjqKqqwoYNG0RHoQHi5JK59957D3V1daisrOSFFRSG20IZu3jxInJychAZGcliKRBPC2Vs27ZtcHR05AXDFYrlkqm7d+8iNjYWfn5+GDny0W/3J3liuWQqMTERd+/e5fpdwbjQkCG9Xo9JkyZh2rRpyMjIEB2HBokLDRk6ePAgLly4gJiYGNFRaAg4uWTorbfewrVr13Dq1CluCRWMk0tmLly4gP379yMhIYHFUjguNGQmLCwMTk5O+PDDD0VHoSFiuWTk9u3bSEhIwLp163jBcDPAcslIXFwcdDod1q9fLzoKGQEXGjLR3d2Nl156Ce7u7khOThYdh4yACw2ZyM3NxcWLF5Gamio6ChkJJ5dMzJ8/H1qtFsW8jpbZ4OSSgaqqKnz11VdISUkRHYWMiJNLBtatW4d9+/ahoaEB1tbWouOQkXBbKFhzczOSkpKwfv16FsvMsFyCRUdHQ6/XY926daKjkJHxtFCgrq4uTJgwAfPnz0dcXJzoOGRknFwC7dmzB99++y0/fMZMcXIJ9Prrr2PYsGE4evSo6CgkAa7iBSkvL8fXX3+N3bt3i45CEuHkEsTLywv5+fmoq6uDlRX/H2eO+JhLgOvXryMlJQVBQUEslhljuQSIjIyEpaUlfH19RUchCfG00MQ6Ozvx4osv4t1330VkZKToOCQhTi4T2717N5qamrh+VwFOLhObNWsWRo0ahUOHDomOQhLjo2kTKikpQUlJCXJyckRHIRPg5DKhjz76CCUlJaipqeEVIVWAf8Im8t133yEjIwPBwcEslkrwT9lEIiIiYGtrCy8vL9FRyERYLhPo6OhAZGQk1q5di9GjR4uOQybCcplAWloabty4gZCQENFRyIS40JCYwWCAm5sbnnnmGeTm5oqOQybEySWxwsJClJeX80ljFeLkktjSpUtRVVWFs2fP8sIKKsPJJaHGxkZkZ2cjJCSExVIhlktC27Ztg729PVavXi06CgnAckmkra0N0dHR8PHxgb29veg4JADLJZHk5GTcvn0bwcHBoqOQIFxoSMBgMGDq1KlwcXFBdna26DgkCF8VL4H8/HxUV1cjNDRUdBQSiJNLAr/5zW9QX1+PiooKbglVjJPLyOrq6rB3715ERUWxWCrHhYaRhYWFwdHRER999JHoKCQYy2VEd+7cQVxcHPz9/TFixAjRcUgwlsuIEhMTodVqERgYKDoKyQAXGkai1+vx6quvwtXVFRkZGaLjkAxwoWEkeXl5qKmp4aWA6AFOLiNZtGgRbty4gW+++YZbQgLAyWUU58+fx4EDB5CYmMhi0QNcaBhBaGgonJycsGzZMtFRSEZYriG6desWEhMTERAQABsbG9FxSEZYriGKi4tDZ2cnAgICREchmeFCYwi6u7vh4uKC2bNnIzk5WXQckhkuNIZg3759qK+vR3p6uugoJEOcXEMwb948tLe3o6ioSHQUkiFOrkE6c+YM8vPzkZqaKjoKyRQn1yD5+/sjNzcXDQ0NsLa2Fh2HZIjbwkH4/vvvkZSUhMDAQBaLHorlGoTo6GgYDAb4+/uLjkIyxtPCAerq6sL48eOxYMECvkiXHomTa4Cys7Nx+fJlbNy4UXQUkjlOrgH61a9+BUtLSxQUFIiOQjLHVfwAlJWVobCwEJmZmaKjkAJwcg3A2rVrUVBQgNraWlhZ8f9L9Gh8zNVP165dQ2pqKoKCglgs6heWq58iIyNhZWUFX19f0VFIIViufujs7ERERARWrVoFR0dH0XFIIViufti1axeuXr3KS6/SgHCh0Q+/+MUv4ODggEOHDomOQgrCR+aPceLECZw8eRJ79+4VHYUUhpPrMVasWIGTJ0+ipqYGFhY8i6b+49+WR7hy5Qp27dqFkJAQFosGjH9jHiEiIgK2trbw8vISHYUUiOV6iI6ODkRGRsLLywsODg6i45ACsVwPkZqaips3byIkJER0FFIoLjT6YDAYMH36dDz77LPIzc0VHYcUipOrD19//TVOnz7N92zRkHBy9eGDDz7A2bNnUV1dzQsr0KDxSeQfuXTpErKzsxEWFsZi0ZDwtPBHtm3bhlGjRmH16tWio5DCsVz/pr29HSUlJfjrX/8KOzs70XFI4fiYi0ginFxEEmG5iCTCchFJhOUikgjLRSQR1ZUrIgKYNg1wcLj/j7s7sH+/6FRkjlS3it+7F7C0BJyd7/86MRH47DOgvByYPFlsNjIvqitXX8aMuV8wHx/RScicqPq1hd3dwK5dgFZ7//SQyJhUWa4zZ+6XqaMDsLcHsrOBSZNEpyJzo8rTws5OoLERuHULyMwEYmKAo0dZMDIuVZbrx+bPByZOBCIjRSchc6K6VXxfDAZApxOdgsyN6h5z/fnPwKJFwAsvAHfuAGlpQEEBcOCA6GRkblRXrmvXgFWrgKYmYPTo+08oHzgALFggOhmZGz7mIpIIH3MRSYTlIpIIy0UkEZaLSCIsF5FEWC4iibBcRBJhuYgkwnIRScTsy7Vp0ya8/fbb6O7uFh2FVMasy3X16lV8+umn8PT0hKWlpeg4pDJmXa7IyEhYW1vDhx+OQQKYbbk6OzsRERGB1atXw9HRUXQcUiGzLVdGRgauXbvGC4aTMGb5lhODwYCf//zncHR0xMGDB0XHIZUyyzdLnjhxAqdOncK+fftERyEVM8vJ9eGHH6K0tBQXLlyAhYXZnvmSzJnd37zLly9j9+7dCAkJYbFIKLP72xcREYGRI0di7dq1oqOQyplVudrb2xEZGQkvLy84ODiIjkMqZ1blSk1NRXNzM9fvJAtms9AwGAx47bXX8Pzzz3NLSLJgNpPr2LFjqKiowMaNG0VHIQJgRpPrt7/9Lc6fP4/q6moMGzZMdBwi83gSuaGhAV988QW2bdvGYpFsmMVp4bZt2+Dg4IBVq1aJjkL0gOLLpdVqERMTA19fX9jZ2YmOQ/SA4suVlJSE1tZWBAUFiY5C1IOiFxoGgwGTJ0/GK6+8gqysLNFxiHpQ9ELj8OHDOHfuHCIiIkRHIepF0ZPr3XffRWNjI06fPs0tIcmOYidXbW0tcnNzERMTw2KRLCl2oREaGooxY8Zg+fLloqMQ9UmR5WptbUV8fDzWrVuHESNGiI5D1CdFlishIQFtbW0IDAwUHYXooRS30NDr9Xj55Zfh5uaGtLQ00XGIHkpxC439+/ejtrYWO3bsEB2F6JEUN7nefPNNNDc34+TJk9wSkqwpanKdO3cOBw8eRFJSEotFsqeohcbWrVsxbtw4LF26VHQUosdSTLlaWlqwY8cOrF+/HjY2NqLjED2WYsoVGxuLe/fuISAgQHQUon5RxEKju7sbEydOxOuvv84tISmGIiZXTk4OLl26xA+fIUVRxOTy9PREZ2cnjh8/LjoKUb/JfhVfWVmJgoICpKeni45CNCCyn1w+Pj7Iy8tDfX09rK2tRcch6jdZP+a6efMmdu7ciaCgIBaLFEfW5YqKisKwYcPg5+cnOgrRgMn2tPDevXsYP348Fi5ciJiYGNFxiAZMtpMrKysLV65cwYYNG0RHIRoU2U6uX/7ylxg+fDiOHDkiOgrRoMhyFX/q1CkUFRUhOztbdBSiQZPl5Fq1ahUKCwtRW1sLS0tL0XGIBkV2j7muXr2K9PR0BAcHs1ikaLIr1/bt22FtbQ1vb2/RUYiGRFbl0ul02L59O9asWQNHR0fRcYiGRFblysjIwLVr13jBcDILslloGAwGzJw5E08++STy8vJExyEaMtms4ouLi1FaWorc3FzRUYiMQjaTa9myZSgvL8f58+dhYSGrs1WiQZHF3+LLly8jMzMTISEhLBaZDVn8TQ4PD8fIkSOxZs0a0VGIjEZ4udrb2xEVFQVvb284ODiIjkNkNMLLlZKSgubmZgQHB4uOQmRUQhcaBoMBP/vZz/CTn/wEe/fuFRWDSBJCJ9fRo0dRWVnJj0wjsyR0ci1ZsgQ1NTWoqqrihRXI7Ah7Erm+vh45OTkIDw9nscgsCTst3LZtGxwcHLBy5UpREYgkJaRcd+/eRUxMDPz8/GBnZyciApHkhJQrKSkJd+7cQVBQkIi7JzIJky80DAYDJk2ahEmTJiEzM9OUd01kUiZfaBw6dAjnz59HZGSkqe+ayKRMPrnefvttXLlyBeXl5dwSklkz6eTSaDT48ssvERcXx2KR2TPpQiM0NBRPPfUUli9fbsq7JRLCZOVqbW1FfHw81q1bB1tbW1PdLZEwJitXfHw8Ojo6sH79elPdJZFQJllo6PV6vPTSS5g5cyZSU1OlvjsiWTDJQuPLL79EXV0dkpOTTXF3RLJgksm1YMEC3L59GyUlJdwSkmpIPrnOnj2Lw4cPIzk5mcUiVZF8obF161Y8/fTTWLp0qdR3RSQrkparpaUFO3bswPr16zF8+HAp74pIdiQtV0xMDLq7u7Fu3Top74ZIliRbaHR1dWHixImYM2cOEhMTpbgLIlmTbHLl5OSgsbGRFwwn1ZJscr3xxhvo7u5GYWGhFIcnkj1JVvGnT5/GsWPHkJGRIcXhiRRBksnl7e2NQ4cO4eLFi7C2tjb24YkUweiPuW7cuIGUlBQEBQWxWKRqRi9XVFQUhg0bBj8/P2MfmkhRjHpaeO/ePbz44ot46623EB0dbazDEimSUSdXZmYmvvvuO67fiWDkyTV79mzY2toiPz/fWIckUiyjreK/+eYbFBcXY8+ePcY6JJGiDXpy6fX6HtcvXrlyJYqKiqDRaGBpaWm0gERK1e/JVVZWhvj4eBQXFaGquho6nQ42NjaYMnkyprm6Ij09HZ9++imLRfQvj51ctbW18Pfzw5GCAjznNBbzZ7jC1WUiHOxGolXbhgpNHQ6eLEPTzWb8ysMDcfHxcHZ2NlV+Itl6ZLlSUlLg6+uLZ8Y44rNgH7zrMQtWVr0nU1dXN/YWnsAfw2LR1NyC2NhYfjYhqd5Dy5WSkoKVK1di5ZtzEf5xCOxGPP6zBrXtHQjcEorkvHwkJydjxYoVRg9MpBR9lkuj0cDV1RUfvDEb8Zt+32Nxcaz8DP65czdKL2jQdLMZWf/4X3jvjdkPvq/X6+G1+XPsPlqEyspKniKSavX5JPI6f388+6Qjwj8O6VEsANB2dGCay3iE/j6w7wNaWCD84xA8M8YR/nwJFKlYr21haWkpjhQUIPOTTX2eCi5yn4lF7jMfeVC7EbbYEuyND/70N5SVlWH69OnGS0ykEL0mV0JCAp4f54R3PWYN6cCLPdzxnNNYxMfHD+k4RErVq1zFRUWY5zatz63gQFhZWWKemytOFBcP6ThEStWrXFXV1XB1mWiUg7u6TMCZqiqjHItIaXqUS6/XQ6fTwcFupFEOPtreDjqdDnq93ijHI1KSHuWysLCAjY0NWrVtRjn47bta2NjY9No4EqlBr23hlMmTUaGpe+gP3G1rR+3l7x78uv67qzhdU4cxDqPwk6edety2QnMRU6dMMWJcIuXoVS732bORnZGOrq7uPpcap87XYG7Qf3/w699vjQIArHlrPuI3/eHB17u6uvFVaQWW/G6ZFLmJZK/XKzTKysrg5uaGzE82YcmcXw76wFkFhfjgT39DaWkpn+ciVerz5U9zPT1xSVODiqTwfr2m8Me07R1wXRWIn7q8hPwjR4wSlEhp+tw0REVHo6m5BYFbQge86dPr9QjcEoqm5hZE8UNqSMX6LJezszNiY2ORnJcPr82fQ9ve0a+Dads74LX5cyTn5SM2NpYv2iVV6/f7ubYEe2Oxh/tD38+VU1iMj8Pi+H4uon8Z8DuR57m5wtVlAkbb2+H2XS0qNBfxVWkFrly/gbmenoiMiuLEIsIAPqDmh8/QOFFcjDNVVQ8+Q2PqlCmY5e4OLy8vbgWJ/o3RPv2JiHqS7PpcRGrH0UMkEZaLSCIsF5FEWC4iibBcRBJhuYgk8v8B0QNTOsJxRvUAAAAASUVORK5CYII=", "text/plain": [ "Graphics object consisting of 8 graphics primitives" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G = A2p.coxeter_diagram()\n", "G.plot(edge_labels=True)" ] }, { "cell_type": "code", "execution_count": 22, "id": "53f1770e-9a4b-4c00-ae2d-731bc5d54ed8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[-2 1 0]\n", "[ 1 -2 1]\n", "[ 0 1 -2]" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "-2 * A2p.bilinear_form()" ] }, { "cell_type": "code", "execution_count": 23, "id": "447e24b6-6cf9-4eb3-9eef-de5dd68e434c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0 3 0]\n", "[3 0 3]\n", "[0 3 0]" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G.weighted_adjacency_matrix()" ] }, { "cell_type": "code", "execution_count": 24, "id": "47a97780-041a-4d12-8f71-21692aac5c04", "metadata": {}, "outputs": [ { "ename": "AttributeError", "evalue": "'Graph' object has no attribute 'coxeter_diagram'", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", "Cell \u001b[0;32mIn[24], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mG\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcoxeter_diagram\u001b[49m()\u001b[38;5;241m.\u001b[39mweighted_adjacency_matrix()\n", "\u001b[0;31mAttributeError\u001b[0m: 'Graph' object has no attribute 'coxeter_diagram'" ] } ], "source": [ "G.coxeter_diagram().weighted_adjacency_matrix()" ] }, { "cell_type": "code", "execution_count": 25, "id": "7dab4bf4-4ae9-47a3-a10d-a22debdf96bc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Finite Coxeter group over Integer Ring with Coxeter matrix:\n", "[1 3 2 2 2 2 2]\n", "[3 1 3 2 2 2 2]\n", "[2 3 1 3 2 2 2]\n", "[2 2 3 1 3 2 2]\n", "[2 2 2 3 1 3 2]\n", "[2 2 2 2 3 1 3]\n", "[2 2 2 2 2 3 1]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G = CoxeterGroup([\"A\",7])\n", "G" ] }, { "cell_type": "code", "execution_count": 26, "id": "9a25c5c2-5888-4e3e-9e5b-38a23fe1938c", "metadata": {}, "outputs": [], "source": [ "Gr = G.coxeter_diagram()" ] }, { "cell_type": "code", "execution_count": 27, "id": "b937cca3-a0cc-4b23-9605-698467427cb0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(Gr)" ] }, { "cell_type": "code", "execution_count": 97, "id": "f6bde2f4-af30-46ad-b338-e08aee185a3c", "metadata": {}, "outputs": [], "source": [ "class EllipticSubgraphs:\n", " \n", " def __init__(self, max_rank=25):\n", " self.max_rank = max_rank\n", " self.A = []\n", " self.B = []\n", " self.C = []\n", " self.D = []\n", " self.E = []\n", " for i in [j + 1 for j in range(self.max_rank)]:\n", " self.A.append( CoxeterGroup([\"A\",i]) )\n", " self.B.append( CoxeterGroup([\"B\",i]) )\n", " self.C.append( CoxeterGroup([\"C\",i]) )\n", " self.D.append( CoxeterGroup([\"D\",i+1]) )\n", " self.E.append( CoxeterGroup([\"E\",6]) )\n", " self.E.append( CoxeterGroup([\"E\",7]) )\n", " self.E.append( CoxeterGroup([\"E\",8]) )\n", " self.counts = defaultdict(lambda : 0)\n", " \n", " print(\"Initialized elliptic Coxeter diagrams of rank at most \" + str(max_rank) )\n", "\n", " def iso_type(self, H):\n", " if H.num_verts == 0:\n", " return \"\"\n", " for i, a in enumerate( self.A ):\n", " if a.coxeter_diagram().is_isomorphic(H):\n", " return \"A\" + str(i+1)\n", " for i, a in enumerate( self.B ):\n", " if a.coxeter_diagram().is_isomorphic(H):\n", " return \"B\" + str(i+1)\n", " for i, a in enumerate( self.C ):\n", " if a.coxeter_diagram().is_isomorphic(H):\n", " return \"C\" + str(i+1)\n", " for i, a in enumerate( self.D ):\n", " if a.coxeter_diagram().is_isomorphic(H):\n", " return \"D\" + str(i+2)\n", " for i, a in enumerate( self.E ):\n", " if a.coxeter_diagram().is_isomorphic(H):\n", " return \"E\" + str(i+6)\n", " return \"Unknown.\"\n", "\n", " def subgraph_iso_types(self, H):\n", " types = list( map( lambda hp: self.iso_type( H.subgraph(hp) ), H.connected_components(sort=True) ) )\n", " identifier_string = reduce( lambda a,b: a + \"+\" + b, types)\n", " return identifier_string\n", "\n", " def count_subgraph_types(self, G):\n", " self.counts = defaultdict(lambda : 0)\n", " subgraphs = []\n", " S = [s for s in Subsets(G.vertex_iterator()) if s.cardinality() > 0 ]\n", " for s in S:\n", " Hi = G.subgraph(list(s))\n", " if Hi.is_connected():\n", " subgraphs.append(Hi)\n", " for sg in subgraphs:\n", " id = E.subgraph_iso_types(sg)\n", " self.counts[id] += 1\n", " return dict( self.counts )\n", " " ] }, { "cell_type": "code", "execution_count": 98, "id": "c3aaf2df-4464-483b-8747-94a0cf46672b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Initialized elliptic Coxeter diagrams of rank at most 10\n" ] } ], "source": [ "E = EllipticSubgraphs(max_rank=10)" ] }, { "cell_type": "code", "execution_count": 99, "id": "123c4b9d-20d8-4504-a397-0202dc29b97d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Finite Coxeter group over Integer Ring with Coxeter matrix:\n", "[1 3 2 2]\n", "[3 1 3 2]\n", "[2 3 1 3]\n", "[2 2 3 1]" ] }, "execution_count": 99, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A4 = CoxeterGroup([\"A\",4])\n", "A4" ] }, { "cell_type": "code", "execution_count": 100, "id": "35bfb6ab-8ec5-4fd5-8ba2-60f7e1571469", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 11 graphics primitives" ] }, "execution_count": 100, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A5 = CoxeterGroup([\"A\",4])\n", "A5.coxeter_diagram().plot(edge_labels = True)" ] }, { "cell_type": "code", "execution_count": 101, "id": "5e9a3041-87b0-43cf-9e6a-20844e901cd1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[-2 3 0 0]\n", "[ 3 -2 3 0]\n", "[ 0 3 -2 3]\n", "[ 0 0 3 -2]" ] }, "execution_count": 101, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G = A5.coxeter_diagram()\n", "G.weighted_adjacency_matrix() - 2 * identity_matrix(ZZ, 4)" ] }, { "cell_type": "code", "execution_count": 102, "id": "c394000f-f352-41a5-ae74-9b90aec169db", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'A1': 6, 'A2': 5, 'A3': 5, 'A4': 4, 'D4': 1, 'D5': 2, 'A5': 1, 'E6': 1}" ] }, "execution_count": 102, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E.count_subgraph_types( CoxeterGroup([\"E\",6]).coxeter_diagram() )" ] }, { "cell_type": "code", "execution_count": 104, "id": "eb87d4e2-88e7-4d83-b487-b6f19e829979", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graph on 6 vertices" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "G = CoxeterGroup([\"E\",6]).coxeter_diagram()\n", "G" ] }, { "cell_type": "code", "execution_count": 121, "id": "51a66938-713f-429c-a4c7-8948ceef2563", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Permutation Group with generators [(1,6)(3,5)]" ] }, "execution_count": 121, "metadata": {}, "output_type": "execute_result" } ], "source": [ "AutG = G.automorphism_group()\n", "AutG" ] }, { "cell_type": "code", "execution_count": 111, "id": "1075c44b-b1a9-4511-8dbc-f288f33e3ebc", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Subgraph of (): Graph on 3 vertices" ] }, "execution_count": 111, "metadata": {}, "output_type": "execute_result" } ], "source": [ "H = G.subgraph( [1,3,4] )\n", "H" ] }, { "cell_type": "code", "execution_count": 131, "id": "2f686021-00e5-4fc2-9aa4-08b58a69ef23", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1,6)(3,5)" ] }, "execution_count": 131, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = AutG.gen()\n", "g" ] }, { "cell_type": "code", "execution_count": 134, "id": "3b567854-67a1-4246-8a6c-e624c262a620", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(1, 6), (3, 5)]" ] }, "execution_count": 134, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.cycle_tuples()" ] }, { "cell_type": "code", "execution_count": 36, "id": "763fb89d-8bd4-49a9-ba97-aa7e722200c5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A1\n" ] }, { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "-------------------------------------------\n", "A1\n" ] }, { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "-------------------------------------------\n", "A1\n" ] }, { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "-------------------------------------------\n", "A1\n" ] }, { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "-------------------------------------------\n", "A2\n" ] }, { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 5 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "-------------------------------------------\n", "A1+A1\n" ] }, { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "-------------------------------------------\n", "A1+A1\n" ] }, { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "-------------------------------------------\n", "A2\n" ] }, { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 5 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "-------------------------------------------\n", "A1+A1\n" ] }, { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "-------------------------------------------\n", "A2\n" ] }, { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 5 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "-------------------------------------------\n", "A3\n" ] }, { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 8 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "-------------------------------------------\n", "A2+A1\n" ] }, { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 6 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "-------------------------------------------\n", "A2+A1\n" ] }, { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 6 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "-------------------------------------------\n", "A3\n" ] }, { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 8 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "-------------------------------------------\n", "A4\n" ] }, { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 11 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "-------------------------------------------\n" ] } ], "source": [ "for sg in subgraphs:\n", " id = E.subgraph_iso_types(sg)\n", " print(id)\n", " show( sg.plot(edge_labels = True) )\n", " print(\"-------------------------------------------\")" ] }, { "cell_type": "code", "execution_count": 137, "id": "0cfa4059-c9b9-46b4-8ad1-021c4445eea6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1,6)(3,5)" ] }, "execution_count": 137, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S = SymmetricGroup(6)\n", "g = S( [(1,6), (3,5)])\n", "g" ] }, { "cell_type": "code", "execution_count": 152, "id": "de6b0e5a-6e9f-4fdb-a157-ab47fcb2d1d7", "metadata": {}, "outputs": [ { "ename": "TypeError", "evalue": "unsupported operand parent(s) for *: 'Symmetric group of order 6! as a permutation group' and 'Integer Ring'", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", "Cell \u001b[0;32mIn[152], line 2\u001b[0m\n\u001b[1;32m 1\u001b[0m a \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mlambda\u001b[39;00m g, x: g\u001b[38;5;241m*\u001b[39mx\n\u001b[0;32m----> 2\u001b[0m \u001b[43mPermutationGroup\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m 3\u001b[0m \u001b[43m \u001b[49m\u001b[43m[\u001b[49m\u001b[43mg\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\n\u001b[1;32m 4\u001b[0m \u001b[43m \u001b[49m\u001b[43maction\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m \u001b[49m\u001b[43ma\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;66;43;03m# needs sage.combinat\u001b[39;49;00m\n\u001b[1;32m 5\u001b[0m \u001b[43m \u001b[49m\u001b[43mdomain\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m \u001b[49m\u001b[43m(\u001b[49m\u001b[43mInteger\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43mInteger\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m3\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43mInteger\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m4\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 6\u001b[0m \u001b[43m)\u001b[49m\u001b[38;5;241m.\u001b[39morbits()\n", "File \u001b[0;32m~/gitclones/sage/src/sage/groups/perm_gps/permgroup.py:405\u001b[0m, in \u001b[0;36mPermutationGroup\u001b[0;34m(gens, *args, **kwds)\u001b[0m\n\u001b[1;32m 403\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m domain \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m 404\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124myou must specify the domain for an action\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m--> 405\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mPermutationGroup_action\u001b[49m\u001b[43m(\u001b[49m\u001b[43mgens\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maction\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdomain\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mgap_group\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mgap_group\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 406\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m args:\n\u001b[1;32m 407\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01msage\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mmisc\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01msuperseded\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m deprecation\n", "File \u001b[0;32m~/gitclones/sage/src/sage/groups/perm_gps/permgroup.py:5296\u001b[0m, in \u001b[0;36mPermutationGroup_action.__init__\u001b[0;34m(self, gens, action, domain, gap_group, category, canonicalize)\u001b[0m\n\u001b[1;32m 5294\u001b[0m gens \u001b[38;5;241m=\u001b[39m [o \u001b[38;5;28;01mfor\u001b[39;00m o \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_orbits \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(o) \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m1\u001b[39m]\n\u001b[1;32m 5295\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m-> 5296\u001b[0m g_orbits \u001b[38;5;241m=\u001b[39m \u001b[43m[\u001b[49m\u001b[43morbit_decomposition\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdomain\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mlambda\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m:\u001b[49m\u001b[43m \u001b[49m\u001b[43maction\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 5297\u001b[0m \u001b[43m \u001b[49m\u001b[38;5;28;43;01mfor\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mg\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01min\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mgens\u001b[49m\u001b[43m]\u001b[49m\n\u001b[1;32m 5298\u001b[0m gens \u001b[38;5;241m=\u001b[39m []\n\u001b[1;32m 5299\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m g_orbit \u001b[38;5;129;01min\u001b[39;00m g_orbits:\n", "File \u001b[0;32m~/gitclones/sage/src/sage/groups/perm_gps/permgroup.py:5296\u001b[0m, in \u001b[0;36m\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m 5294\u001b[0m gens \u001b[38;5;241m=\u001b[39m [o \u001b[38;5;28;01mfor\u001b[39;00m o \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_orbits \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(o) \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m1\u001b[39m]\n\u001b[1;32m 5295\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m-> 5296\u001b[0m g_orbits \u001b[38;5;241m=\u001b[39m [\u001b[43morbit_decomposition\u001b[49m\u001b[43m(\u001b[49m\u001b[43mdomain\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mlambda\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m:\u001b[49m\u001b[43m \u001b[49m\u001b[43maction\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 5297\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m g \u001b[38;5;129;01min\u001b[39;00m gens]\n\u001b[1;32m 5298\u001b[0m gens \u001b[38;5;241m=\u001b[39m []\n\u001b[1;32m 5299\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m g_orbit \u001b[38;5;129;01min\u001b[39;00m g_orbits:\n", "File \u001b[0;32m~/gitclones/sage/src/sage/combinat/cyclic_sieving_phenomenon.py:199\u001b[0m, in \u001b[0;36morbit_decomposition\u001b[0;34m(L, cyc_act)\u001b[0m\n\u001b[1;32m 197\u001b[0m obj \u001b[38;5;241m=\u001b[39m L_prime\u001b[38;5;241m.\u001b[39mpop()\n\u001b[1;32m 198\u001b[0m orbit \u001b[38;5;241m=\u001b[39m [obj]\n\u001b[0;32m--> 199\u001b[0m obj \u001b[38;5;241m=\u001b[39m \u001b[43mcyc_act\u001b[49m\u001b[43m(\u001b[49m\u001b[43mobj\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 200\u001b[0m \u001b[38;5;28;01mwhile\u001b[39;00m obj \u001b[38;5;129;01min\u001b[39;00m L_prime:\n\u001b[1;32m 201\u001b[0m orbit\u001b[38;5;241m.\u001b[39mappend(obj)\n", "File \u001b[0;32m~/gitclones/sage/src/sage/groups/perm_gps/permgroup.py:5296\u001b[0m, in \u001b[0;36mPermutationGroup_action.__init__..\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m 5294\u001b[0m gens \u001b[38;5;241m=\u001b[39m [o \u001b[38;5;28;01mfor\u001b[39;00m o \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_orbits \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(o) \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m1\u001b[39m]\n\u001b[1;32m 5295\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m-> 5296\u001b[0m g_orbits \u001b[38;5;241m=\u001b[39m [orbit_decomposition(domain, \u001b[38;5;28;01mlambda\u001b[39;00m x: \u001b[43maction\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m)\n\u001b[1;32m 5297\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m g \u001b[38;5;129;01min\u001b[39;00m gens]\n\u001b[1;32m 5298\u001b[0m gens \u001b[38;5;241m=\u001b[39m []\n\u001b[1;32m 5299\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m g_orbit \u001b[38;5;129;01min\u001b[39;00m g_orbits:\n", "Cell \u001b[0;32mIn[152], line 1\u001b[0m, in \u001b[0;36m\u001b[0;34m(g, x)\u001b[0m\n\u001b[0;32m----> 1\u001b[0m a \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mlambda\u001b[39;00m g, x: \u001b[43mg\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mx\u001b[49m\n\u001b[1;32m 2\u001b[0m PermutationGroup(\n\u001b[1;32m 3\u001b[0m [g], \n\u001b[1;32m 4\u001b[0m action \u001b[38;5;241m=\u001b[39m a, \u001b[38;5;66;03m# needs sage.combinat\u001b[39;00m\n\u001b[1;32m 5\u001b[0m domain \u001b[38;5;241m=\u001b[39m (Integer(\u001b[38;5;241m1\u001b[39m),Integer(\u001b[38;5;241m3\u001b[39m),Integer(\u001b[38;5;241m4\u001b[39m))\n\u001b[1;32m 6\u001b[0m )\u001b[38;5;241m.\u001b[39morbits()\n", "File \u001b[0;32m~/gitclones/sage/src/sage/groups/perm_gps/permgroup_element.pyx:1302\u001b[0m, in \u001b[0;36msage.groups.perm_gps.permgroup_element.PermutationGroupElement.__mul__\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1300\u001b[0m return prod\n\u001b[1;32m 1301\u001b[0m \n\u001b[0;32m-> 1302\u001b[0m return coercion_model.bin_op(left, right, operator.mul)\n\u001b[1;32m 1303\u001b[0m \n\u001b[1;32m 1304\u001b[0m cpdef PermutationGroupElement _transpose_left(self, j, k):\n", "File \u001b[0;32m~/gitclones/sage/src/sage/structure/coerce.pyx:1278\u001b[0m, in \u001b[0;36msage.structure.coerce.CoercionModel.bin_op\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1276\u001b[0m # We should really include the underlying error.\n\u001b[1;32m 1277\u001b[0m # This causes so much headache.\n\u001b[0;32m-> 1278\u001b[0m raise bin_op_exception(op, x, y)\n\u001b[1;32m 1279\u001b[0m \n\u001b[1;32m 1280\u001b[0m cpdef canonical_coercion(self, x, y):\n", "\u001b[0;31mTypeError\u001b[0m: unsupported operand parent(s) for *: 'Symmetric group of order 6! as a permutation group' and 'Integer Ring'" ] } ], "source": [ "a = lambda g, x: g*x\n", "PermutationGroup(\n", " [g], \n", " action = a, # needs sage.combinat\n", " domain = (1,3,4)\n", ").orbits()\n" ] }, { "cell_type": "code", "execution_count": 39, "id": "ed12a4f1-995e-4ab7-b0fb-e6b64417d382", "metadata": {}, "outputs": [ { "ename": "NameError", "evalue": "name 'H' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "Cell \u001b[0;32mIn[39], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m hp \u001b[38;5;129;01min\u001b[39;00m \u001b[43mH\u001b[49m\u001b[38;5;241m.\u001b[39mconnected_components():\n\u001b[1;32m 2\u001b[0m Hp \u001b[38;5;241m=\u001b[39m H\u001b[38;5;241m.\u001b[39msubgraph(hp)\n\u001b[1;32m 3\u001b[0m \u001b[38;5;28mprint\u001b[39m( E\u001b[38;5;241m.\u001b[39miso_type(Hp) )\n", "\u001b[0;31mNameError\u001b[0m: name 'H' is not defined" ] } ], "source": [ "for hp in H.connected_components():\n", " Hp = H.subgraph(hp)\n", " print( E.iso_type(Hp) )" ] }, { "cell_type": "code", "execution_count": 40, "id": "63b2f10a-a2b5-414b-9d2f-6056a22b9ff6", "metadata": {}, "outputs": [ { "ename": "NameError", "evalue": "name 'H' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "Cell \u001b[0;32mIn[40], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m ls \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlist\u001b[39m( \u001b[38;5;28mmap\u001b[39m( \u001b[38;5;28;01mlambda\u001b[39;00m hp: E\u001b[38;5;241m.\u001b[39miso_type( H\u001b[38;5;241m.\u001b[39msubgraph(hp) ), \u001b[43mH\u001b[49m\u001b[38;5;241m.\u001b[39mconnected_components() ) )\n\u001b[1;32m 2\u001b[0m ls\n", "\u001b[0;31mNameError\u001b[0m: name 'H' is not defined" ] } ], "source": [ "ls = list( map( lambda hp: E.iso_type( H.subgraph(hp) ), H.connected_components() ) )\n", "ls" ] }, { "cell_type": "code", "execution_count": 41, "id": "0f6ffa9b-4de3-4f78-98ce-0a64d7405577", "metadata": {}, "outputs": [ { "ename": "NameError", "evalue": "name 'ls' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "Cell \u001b[0;32mIn[41], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m reduce( \u001b[38;5;28;01mlambda\u001b[39;00m a,b: a \u001b[38;5;241m+\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m+\u001b[39m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m+\u001b[39m b, \u001b[43mls\u001b[49m)\n", "\u001b[0;31mNameError\u001b[0m: name 'ls' is not defined" ] } ], "source": [ "reduce( lambda a,b: a + \"+\" + b, ls)" ] }, { "cell_type": "code", "execution_count": 60, "id": "a2f578f6-0efd-4f6a-908f-e4f1beabdd23", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 56 graphics primitives" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def build_A(n):\n", " G = Graph(loops=True)\n", " for i in range(n):\n", " G.add_vertex(i+1)\n", " G.add_edge(i+1, i+1, 2)\n", " for i in range(n-1):\n", " G.add_edge(i+1, i+2, 3)\n", " return G\n", "\n", "def build_TA(n):\n", " G = build_A(n)\n", " G.add_vertex(n+1)\n", " G.add_edge(n+1, n+1, 2)\n", " G.add_edge(1, n+1, 2)\n", " G.add_edge(n, n+1, 2)\n", " return G\n", "\n", "G = build_TA(10)\n", "G.plot(edge_labels=True, edge_thickness=0.35)" ] }, { "cell_type": "code", "execution_count": 43, "id": "e6690252-b47d-44a6-8c00-5885b4b619ca", "metadata": {}, "outputs": [ { "ename": "NameError", "evalue": "name 'CoxeterGraph' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "Cell \u001b[0;32mIn[43], line 2\u001b[0m\n\u001b[1;32m 1\u001b[0m n\u001b[38;5;241m=\u001b[39mInteger(\u001b[38;5;241m4\u001b[39m)\n\u001b[0;32m----> 2\u001b[0m G \u001b[38;5;241m=\u001b[39m \u001b[43mCoxeterGraph\u001b[49m()\n\u001b[1;32m 3\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(n):\n\u001b[1;32m 4\u001b[0m G\u001b[38;5;241m.\u001b[39madd_vertex(i\u001b[38;5;241m+\u001b[39mInteger(\u001b[38;5;241m1\u001b[39m))\n", "\u001b[0;31mNameError\u001b[0m: name 'CoxeterGraph' is not defined" ] } ], "source": [ "n=4\n", "G = CoxeterGraph()\n", "for i in range(n):\n", " G.add_vertex(i+1)\n", " G.add_edge(i+1, i+1, 2)\n", " G.vertex_color_dict[\"#FFFFFF\"].append(i+1)\n", "G.set_edge_label(n, n, 4)\n", "G.vertex_color_dict[\"#AAAAAA\"].append(n)\n", "for i in range(n-1):\n", " G.add_edge(i+1, i+2, 3)" ] }, { "cell_type": "code", "execution_count": 44, "id": "58dd8096-3d13-4c5b-950c-0962b7d45ae6", "metadata": {}, "outputs": [ { "ename": "AttributeError", "evalue": "'Graph' object has no attribute 'vertex_color_dict'", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", "Cell \u001b[0;32mIn[44], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mG\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mvertex_color_dict\u001b[49m\n", "\u001b[0;31mAttributeError\u001b[0m: 'Graph' object has no attribute 'vertex_color_dict'" ] } ], "source": [ "G.vertex_color_dict" ] }, { "cell_type": "code", "execution_count": 45, "id": "62f197fc-732f-4e00-9459-2d0f5163d300", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 56 graphics primitives" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def plot_coxeter_diagram(G):\n", " d = {\n", " '#FFFFFF': [1,2,3], \n", " '#AAAAAA': [4]\n", " }\n", " return G.plot(\n", " # talk = True,\n", " edge_labels = True,\n", " edge_thickness = 0.5, \n", " edge_color = 'blue', \n", " edge_style = 'solid', \n", " vertex_size = 200,\n", " vertex_colors=d\n", " )\n", "\n", "plot_coxeter_diagram(G)" ] }, { "cell_type": "code", "execution_count": 47, "id": "affc23fe-609e-48c2-bbea-4892fa3b6cc1", "metadata": {}, "outputs": [], "source": [ "class CoxeterGraph(Graph):\n", "\n", " \n", " def __init__(self, *args, **kwargs):\n", " self.vertex_color_dict = {\n", " '#FFFFFF': [], \n", " '#AAAAAA': []\n", " }\n", " super(CoxeterGraph, self).__init__(*args, **kwargs)\n", " Graph.allow_loops(self, True)\n", " def plot(self):\n", " return Graph.plot(\n", " self, \n", " edge_labels = True,\n", " edge_thickness = 0.5, \n", " edge_color = 'blue', \n", " edge_style = 'solid', \n", " vertex_size = 200,\n", " vertex_colors = self.vertex_color_dict\n", " )\n", " " ] }, { "cell_type": "code", "execution_count": 48, "id": "a054dee0-ad95-4d8b-b31f-d9f450734638", "metadata": {}, "outputs": [], "source": [ "G.allow_loops(True)" ] }, { "cell_type": "code", "execution_count": 49, "id": "ab473c4a-5064-4c22-8499-ea402b5af137", "metadata": {}, "outputs": [], "source": [ "def build_A(n):\n", " G = Graph(loops=True)\n", " for i in range(n):\n", " G.add_vertex(i+1)\n", " G.add_edge(i+1, i+1, 2)\n", " for i in range(n-1):\n", " G.add_edge(i+1, i+2, 3)\n", " return G\n", "\n", "def build_TA(n):\n", " G = build_A(n)\n", " G.add_vertex(n+1)\n", " G.add_edge(n+1, n+1, 2)\n", " G.add_edge(1, n+1, 2)\n", " G.add_edge(n, n+1, 2)\n", " return G" ] }, { "cell_type": "code", "execution_count": 59, "id": "ec0deae7-78d9-4881-9932-80c896d5a2f3", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 24 graphics primitives" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A3 = build_A(5)\n", "A3.plot(edge_labels=True, edge_thickness=0.35)" ] }, { "cell_type": "code", "execution_count": null, "id": "a9fab84f-6028-4dee-bfb4-f623c1c068ea", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 10.4.beta5", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.1" } }, "nbformat": 4, "nbformat_minor": 5 }