{ "cells": [ { "cell_type": "code", "execution_count": 4, "id": "7f57f279-07a0-4757-828d-3957562a4767", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle (1,13)(2,12)(3,11)(4,10)(5,9)(6,8)(14,16)(17,20)(18,19)(21,22)\\)" ], "text/latex": [ "$\\displaystyle (1,13)(2,12)(3,11)(4,10)(5,9)(6,8)(14,16)(17,20)(18,19)(21,22)$" ], "text/plain": [ "(1,13)(2,12)(3,11)(4,10)(5,9)(6,8)(14,16)(17,20)(18,19)(21,22)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.display import Math\n", "import numpy as np\n", "import pandas as pd\n", "from IPython.display import HTML\n", "from collections import Counter\n", "from sage.modules.free_module_integer import IntegerLattice\n", "\n", "H = IntegralLattice(\"H\")\n", "E8 = IntegralLattice(\"E8\").twist(-1)\n", "E82 = E8.twist(2)\n", "H2 = H.twist(2)\n", "\n", "def namestr(obj):\n", " namespace = globals()\n", " return [name for name in namespace if namespace[name] is obj][0]\n", "\n", "S22 = SymmetricGroup(22)\n", "rho = S22(\"(5, 9, 13, 1)(6, 10, 14, 2)(7, 11, 15, 3)(8, 12, 16, 4)(18, 19, 20, 17)(21, 22)\")\n", "s = S22(\"(1, 9)(2, 8)(3, 7)(4, 6)(10, 16)(11, 15)(12, 14)(17, 19)\")\n", "r = rho * rho\n", "d = s\n", "h = rho * s\n", "v = s * rho\n", "display(v)" ] }, { "cell_type": "code", "execution_count": 5, "id": "b7f9f00e-bbc7-4ae7-bce7-923026bd6d30", "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle V_{1}=(0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle V_{2}=(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle V_{3}=(0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ 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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle W_{2}^*=(1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle W_{3}^*=(0, 0, 0, 0, -4, -5, -7, -10, -8, -6, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle W_{4}^*=(0, 0, 0, 0, -5, -8, -10, -15, -12, -9, -6, -3, 0, 0, 0, 0, 0, 0, 0, 0)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle W_{5}^*=(0, 0, 0, 0, -7, -10, -14, -20, -16, -12, -8, -4, 0, 0, 0, 0, 0, 0, 0, 0)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle W_{6}^*=(0, 0, 0, 0, -10, -15, -20, -30, -24, -18, -12, -6, 0, 0, 0, 0, 0, 0, 0, 0)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle W_{7}^*=(0, 0, 0, 0, -8, -12, -16, -24, -20, -15, -10, -5, 0, 0, 0, 0, 0, 0, 0, 0)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle W_{8}^*=(0, 0, 0, 0, -6, -9, -12, -18, -15, -12, -8, -4, 0, 0, 0, 0, 0, 0, 0, 0)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle W_{9}^*=(0, 0, 0, 0, -4, -6, -8, -12, -10, -8, -6, -3, 0, 0, 0, 0, 0, 0, 0, 0)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle W_{10}^*=(0, 0, 0, 0, -2, -3, -4, -6, -5, -4, -3, -2, 0, 0, 0, 0, 0, 0, 0, 0)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle W_{11}^*=(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -5, -7, -10, -8, -6, -4, -2)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle W_{12}^*=(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -5, -8, -10, -15, -12, -9, -6, -3)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle W_{13}^*=(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, -10, -14, -20, -16, -12, -8, -4)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle W_{14}^*=(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, -15, -20, -30, -24, -18, -12, -6)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle W_{15}^*=(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -12, -16, -24, -20, -15, -10, -5)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle W_{16}^*=(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -9, -12, -18, -15, -12, -8, -4)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle W_{17}^*=(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -6, -8, -12, -10, -8, -6, -3)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle W_{18}^*=(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -3, -4, -6, -5, -4, -3, -2)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Build (20, 2, 0) = U+U(2)+E_8+E_8, which contains (18, 2, 0) = U + E_8 + E_8 for the square Coxeter diagram\n", "\n", "L_20_2_0 = H.direct_sum(H2).direct_sum(E8).direct_sum(E8)\n", "\n", "dot = lambda x,y : x * L_20_2_0.gram_matrix() * y\n", "nm = lambda x: dot(x, x)\n", "\n", "Gram_L_20_2_0 = L_20_2_0.gram_matrix()\n", "Gram_L_20_2_0.subdivide([2, 4, 12], [2, 4, 12])\n", "L_20_2_0_dual_changeofbasis = Gram_L_20_2_0.inverse()\n", "L_20_2_0_dual_changeofbasis.subdivide([2, 4, 12], [2, 4, 12])\n", "\n", "e,f ,ep,fp, a1,a2,a3,a4,a5,a6,a7,a8, a1t,a2t,a3t,a4t,a5t,a6t,a7t,a8t = L_20_2_0.basis()\n", "eb,fb, epb,fpb, w1,w2,w3,w4,w5,w6,w7,w8, w1t,w2t,w3t,w4t,w5t,w6t,w7t,w8t = L_20_2_0_dual_changeofbasis.columns()\n", "\n", "# display(Math(\"$(18, 2, 0)=\"), Gram_L_20_2_0)\n", "# display(Math(\"$(18, 2, 0)^{\\\\vee} =$\"), L_20_2_0_dual_changeofbasis)\n", "\n", "# The primes are the image of the diagonal embedding from E_8(2)\n", "a1p = a1 + a1t\n", "a2p = a2 + a2t\n", "a3p = a3 + a3t\n", "a4p = a4 + a4t \n", "a5p = a5 + a5t\n", "a6p = a6 + a6t\n", "a7p = a7 + a7t\n", "a8p = a8 + a8t\n", "\n", "w1p = w1 + w1t\n", "w2p = w2 + w2t\n", "w3p = w3 + w3t\n", "w4p = w4 + w4t\n", "w5p = w5 + w5t\n", "w6p = w6 + w6t\n", "w7p = w7 + w7t\n", "w8p = w8 + w8t\n", "\n", "MS = [e,f, ep,fp, a1,a2,a3,a4,a5,a6,a7,a8, a1t,a2t,a3t,a4t,a5t,a6t,a7t,a8t]\n", "MS_dual = [eb,fb, epb,fpb, w1,w2,w3,w4,w5,w6,w7,w8, w1t,w2t,w3t,w4t,w5t,w6t,w7t,w8t]\n", "\n", "VS = [ep,fp, a1,a2,a3,a4,a5,a6,a7,a8, a1t,a2t,a3t,a4t,a5t,a6t,a7t,a8t]\n", "VS_dual = [epb,fpb, w1,w2,w3,w4,w5,w6,w7,w8, w1t,w2t,w3t,w4t,w5t,w6t,w7t,w8t]\n", "\n", "WS = [e,f, a1,a2,a3,a4,a5,a6,a7,a8, a1t,a2t,a3t,a4t,a5t,a6t,a7t,a8t]\n", "WS_dual = [eb,fb, w1,w2,w3,w4,w5,w6,w7,w8, w1t,w2t,w3t,w4t,w5t,w6t,w7t,w8t]\n", "\n", "for i, v in enumerate(VS):\n", " display(Math(f'V_{{{i+1}}}=' + str(v)))\n", "for i, v in enumerate(VS_dual):\n", " display(Math(f'V_{{{i+1}}}^*=' + str(v)))\n", "\n", "for i, v in enumerate(WS):\n", " display(Math(f'W_{{{i+1}}}=' + str(v)))\n", "for i, v in enumerate(WS_dual):\n", " display(Math(f'W_{{{i+1}}}^*=' + str(v)))" ] }, { "cell_type": "code", "execution_count": 6, "id": "1d6eaaa2-39a6-4be3-90ec-4041ca4e890b", "metadata": {}, "outputs": [], "source": [ "## Build (18, 0, 0) = U+E_8+E_8.\n", "\n", "# L_18_0_0 = H.direct_sum(E8).direct_sum(E8)\n", "# dot_w = lambda x,y : x * L_18_0_0.gram_matrix() * y\n", "# nm_2 = lambda x: dot(x, x)\n", "\n", "\n", "# Gram_L_18_0_0 = L_18_0_0.gram_matrix()\n", "# Gram_L_18_0_0.subdivide([2, 10], [2, 10])\n", "\n", "# display(Math(\"$(18, 0, 0)=$\"), Gram_L_18_0_0)\n", "# e_w,f_w,a1_w,a2_w,a3_w,a4_w,a5_w,a6_w,a7_w,a8_w,a1p_w,a2p_w,a3p_w,a4p_w,a5p_w,a6p_w,a7p_w,a8p_w = L_18_0_0.basis()\n", "# WS = [e_w,f_w,a1_w,a2_w,a3_w,a4_w,a5_w,a6_w,a7_w,a8_w,a1p_w,a2p_w,a3p_w,a4p_w,a5p_w,a6p_w,a7p_w,a8p_w]\n", "\n", "# L_18_0_0_dual_changeofbasis = Gram_L_18_0_0.inverse()\n", "# L_18_0_0_dual_changeofbasis.subdivide([2, 10], [2, 10])\n", "\n", "# display(Math(\"$(18, 0, 0)^{\\\\vee}=$\"), L_18_0_0_dual_changeofbasis)\n", "\n", "# eb_1800, fb_1800, w1_1800, w2_1800, w3_1800, w4_1800, w5_1800, w6_1800, w7_1800, w8_1800, w1_t_1800, w2_t_1800, w3_t_1800, w4_t_1800, w5_t_1800, w6_t_1800, w7_t_1800, w8_t_1800 = L_18_0_0_dual_changeofbasis.columns()\n", "# WS_dual = [eb_1800, fb_1800, w1_1800, w2_1800, w3_1800, w4_1800, w5_1800, w6_1800, w7_1800, w8_1800, w1_t_1800, w2_t_1800, w3_t_1800, w4_t_1800, w5_t_1800, w6_t_1800, w7_t_1800, w8_t_1800]\n", "\n", "\n", "# for i, w in enumerate(WS):\n", "# display(Math(f'$W_{{{i+1}}}=' + str(w)))\n", " \n", "# for i, w in enumerate(WS_dual):\n", "# display(Math(f'$\\\\overline W_{{{i+1}}}=' + str(w)))" ] }, { "cell_type": "code", "execution_count": 7, "id": "bccdcb46-d936-4ab4-866c-54bfedfb4dc4", "metadata": {}, "outputs": [], "source": [ "# Starting new indexing\n", "# l = [(i+1, i) for i in range(22) ]\n", "# d = dict(l)\n", "# H = PermutationGroup([[d[i] for i in g.tuple()] for g in S22.gens()], domain=d.values() )\n", "# rho = H(\"(4,8,12,0)(5,9,13,1)(6,10,14,2)(7,11,15,3)(17,18,19,16)(20,21)\")\n", "# s = H(\"(0, 8)(1, 7)(2, 6)(3, 5)(9, 15)(10, 14)(11, 13)(16, 18)\")\n", "# r = rho * rho\n", "# d = s\n", "# h = rho * s\n", "# v = s * rho" ] }, { "cell_type": "code", "execution_count": 8, "id": "4e6602e0-eaa0-4e5f-a30f-30ea151202a5", "metadata": {}, "outputs": [], "source": [ "# Checking lattice invariants:\n", "\n", "# Check lattice invariants\n", "# LS2 = IntegralLattice(MS3)\n", "# LS2p = IntegerLattice(MS3)\n", "\n", "# display(\"Lattice L^+ for Sterk 3:\")\n", "# display( \"Signature: \" + str( LS2.signature_pair()) )\n", "# display( \"Is an even lattice? \" + str( LS2.is_even() ) )\n", "# display( \"Is unimodular? \" + str(LS2p.is_unimodular() ) )\n", "\n", "# invs = lattice_invariants( LS2 )\n", "# display( \"Attempt to compute lattice invariants for L^+:\" ) \n", "# display(Math( \"L^+\" + \": (r,a,\\\\delta) = \" + latex(invs[\"RAD\"]) ))\n", "# display(invs)\n", "\n", "# LS2.discriminant_group()" ] }, { "cell_type": "code", "execution_count": 9, "id": "61fb9db5-c354-4947-a50f-65fe5a66bca1", "metadata": {}, "outputs": [], "source": [ "# Build a Coxeter diagram from a Coxeter matrix\n", "\n", "def Coxeter_Diagram(M):\n", " nverts = M.ncols()\n", " # print(str(nverts) + \" vertices\")\n", " G = Graph()\n", " vertex_labels = dict();\n", "# plot_coxeter_diagram(G)\n", " \n", " vertex_colors = {\n", " '#F8F9FE': [], # white\n", " '#BFC9CA': [], # black\n", " }\n", " \n", " for i in range(nverts):\n", " for j in range(nverts):\n", " mij = M[i, j]\n", " if i == j: \n", " if mij == -2:\n", " vertex_colors[\"#F8F9FE\"].append(i) # white\n", " continue\n", " if mij == -4:\n", " vertex_colors[\"#BFC9CA\"].append(i) # black\n", " continue\n", " continue\n", " if mij > 0:\n", " G.add_edge(i, j, str(mij) )\n", " continue\n", " assert len( vertex_colors[\"#F8F9FE\"]) + len( vertex_colors[\"#BFC9CA\"]) == nverts\n", " G.vertex_colors = vertex_colors \n", " return G\n", "\n", "def plot_coxeter_diagram(G, v_labels, pos={}):\n", " n = len( G.vertices() )\n", " vlabs = {v: k for v, k in enumerate(v_labels)}\n", " if pos == {}:\n", " display(G.plot(\n", " edge_labels=True, \n", " vertex_labels = vlabs,\n", " vertex_size=200,\n", " vertex_colors = G.vertex_colors\n", " ))\n", " else:\n", " display(G.plot(\n", " edge_labels=True, \n", " vertex_labels = vlabs,\n", " vertex_size=200,\n", " vertex_colors = G.vertex_colors,\n", " pos = pos\n", " ))\n", " \n", "def root_intersection_matrix(vectors, labels, bil_form):\n", " n = len(vectors)\n", " M = zero_matrix(ZZ, n)\n", " nums = Set(range(n))\n", " for i in range(n):\n", " for j in range(n):\n", " M[i, j] = bil_form( vectors[i], vectors[j] )\n", "\n", " print(\"Diagonal entries/square norms: \")\n", " display(M.diagonal())\n", "\n", " # Labels!\n", " \n", " \n", " df = pd.DataFrame(M, columns=labels, index=labels)\n", " display(HTML(df.to_html()))\n", " \n", " # Must be symmetric\n", " assert M.is_symmetric()\n", " \n", " # Must have -2 or -4 on the diagonal\n", " s = Set( M.diagonal() )\n", " assert s in Subsets( Set( [-2, -4] ) )\n", "\n", " # Diagonals should be square norms of vectors\n", " for i in range(n):\n", " assert M[i, i] == bil_form(vectors[i], vectors[i])\n", "\n", " \n", "\n", " return M\n", "\n", "def lattice_invariants(L):\n", " G = L.gram_matrix()\n", " A = L.discriminant_group()\n", " Q = A.gram_matrix_quadratic()\n", " D,U,V = Q.smith_form()\n", " \n", " if len(list(set(Q.diagonal()) - set([1]) )) >= 2:\n", " print(\"Not a p-elementary lattice. Multiple distinct elementary divisors: \", Q.diagonal())\n", " \n", " diagonal_all_integers = reduce(lambda x,y : x and y, [s.is_integer() for s in Q.diagonal()] )\n", " delta = 0 if diagonal_all_integers else 1 \n", " \n", " return {\n", " \"RAD\": (L.rank(), len(Q.elementary_divisors()), delta),\n", " \"elementary divisors\": Q.elementary_divisors(),\n", " \"SNF\": D, \n", " \"discriminant form\": Q, \n", " \"discriminant group\": A\n", " }\n", "\n", " \n", "# Counter( MS3.elementary_divisors() )\n", "# D,U,V = MS3.smith_form()\n", "# display(D)\n", "# display(MS3.elementary_divisors() )\n", "# from collections import Counter\n", "# Counter(MS3.elementary_divisors() )\n", "# Test\n", "#M = Matrix(ZZ, 4, [ [-2, 1, 0, 0], [1, -2, 1, 0], [0, 1, -2, 2], [0, 0, 2, -4] ])\n", "#display(M)\n", "#G = Coxeter_Diagram(M)\n", "#plot_coxeter_diagram(G, v_labels = [f\"$r_{ {i + 1} }$\" for i in range( 4 )] )" ] }, { "cell_type": "code", "execution_count": 10, "id": "3c3604e1-6aab-45f6-9fc7-1ae0e0b83d4c", "metadata": {}, "outputs": [], "source": [ "# display( lattice_invariants(H.direct_sum(H.twist(2)).direct_sum(E8).direct_sum(E8) ) )\n", "# display( lattice_invariants(H.direct_sum(H.twist(2)).direct_sum(E8.twist(2)) ) )" ] }, { "attachments": { "8d1b270c-a19e-43de-ab7d-aa208ab82743.png": { "image/png": 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" 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$v_{21}$00000000000000002020-44
$v_{22}$000000000000000002024-4
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Root vectors for (18, 2, 0), roots taken from above, v_i are according to numerical labeling above\n", "\n", "v1 = a8t\n", "v2 = ep + fp + w1 + w8t\n", "v3 = a1 \n", "v4 = a3\n", "v5 = a4\n", "v6 = a5\n", "v7 = a6\n", "v8 = a7\n", "v9 = a8\n", "v10 = ep + fp + w8 + w1t\n", "v11 = a1t\n", "v12 = a3t\n", "v13 = a4t\n", "v14 = a5t\n", "v15 = a6t\n", "v16 = a7t\n", "\n", "v17 = ep + w8t\n", "v18 = a2\n", "v19 = ep + w8\n", "v20 = a2t\n", "\n", "v21 = fp - ep\n", "v22 = 5 ep + 3 fp + 2 w2 + 2 w2t\n", "\n", "V = [v1, v2, v3, v4, v5, v6, v7, v8, v9, v10, v11, v12, v13, v14, v15, v16, v17, v18, v19, v20, v21, v22]\n", "MV = root_intersection_matrix(V, labels = [f\"$v_{ {r + 1} }$\" for r in range( len(V) )], bil_form=dot)\n", "# for v in V:\n", "# display(v)" ] }, { "cell_type": "code", "execution_count": 13, "id": "50540b5d-8be9-472f-8e60-c7882ba82f25", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle -4\\)" ], "text/latex": [ "$\\displaystyle -4$" ], "text/plain": [ "-4" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dot(v22, v22)" ] }, { "cell_type": "code", "execution_count": 12, "id": "6791265f-7d69-47a1-b787-446d14ffe378", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 73 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "G = Coxeter_Diagram(MV)\n", "plot_coxeter_diagram(\n", " G, \n", " v_labels = [f\"$v_{ {i + 1} }$\" for i in range( 22 )],\n", " pos = {\n", " 0: [0, 0],\n", " 1: [4, 0],\n", " 2: [8, 0],\n", " 3: [12, 0],\n", " 4: [16, 0],\n", " 5: [16, -4],\n", " 6: [16, -8],\n", " 7: [16, -12],\n", " 8: [16, -16],\n", " 9: [12, -16],\n", " 10: [8, -16],\n", " 11: [4, -16],\n", " 12: [0, -16],\n", " 13: [0, -12],\n", " 14: [0, -8],\n", " 15: [0, -4],\n", " 16: [4, -4],\n", " 17: [12, -4],\n", " 18: [12, -12],\n", " 19: [4, -12],\n", " 20: [8, -10],\n", " 21: [8, -6],\n", " }\n", ")" ] }, { "cell_type": "markdown", "id": "86fc644c-431f-426d-8cf1-dc02fbaf64b3", "metadata": {}, "source": [ "# Coxeter diagram and roots for $(18, 0, 0)_1 = U + E_8^2$, coming from $U + E_8^2 + A_1$" ] }, { "attachments": { "8871bac3-d409-466c-a281-e113d731e084.png": { "image/png": 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" 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", "text/plain": [ "Graphics object consisting of 56 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Root vectors for (18, 0, 0), roots taken from above, w_i are according to numerical labeling above\n", "\n", "w1 = a1\n", "w2 = a3\n", "w3 = a4\n", "w4 = a5\n", "w5 = a6\n", "w6 = a7\n", "w7 = a8\n", "w8 = w8 + e\n", "w9 = f- e\n", "w10 = w8t + e\n", "w11 = a8t\n", "w12 = a7t\n", "w13 = a6t\n", "w14 = a5t\n", "w15 = a4t\n", "w16 = a3t\n", "w17 = a1t\n", "w18 = a2\n", "w19 = a2t\n", "\n", "W = [w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15, w16, w17, w18, w19]\n", "MW = root_intersection_matrix(W, labels = [f\"$w_{ {r + 1} }$\" for r in range( len(W) )], bil_form=dot)\n", "\n", "\n", "G = Coxeter_Diagram(MW)\n", "plot_coxeter_diagram(\n", " G, \n", " v_labels = [f\"$w_{ {i + 1} }$\" for i in range( 19 )],\n", " pos = {\n", " 0: [-4, 0],\n", " 1: [-8, 0],\n", " 2: [-12, 0],\n", " 3: [-10, 4],\n", " 4: [-8, 8],\n", " 5: [-6, 12],\n", " 6: [-4, 16],\n", " 7: [-2, 20],\n", " 8: [0, 24],\n", " 9: [2, 20],\n", " 10: [4, 16],\n", " 11: [6, 12],\n", " 12: [8, 8],\n", " 13: [10, 4],\n", " 14: [12, 0],\n", " 15: [8, 0],\n", " 16: [4, 0],\n", " 17: [-4, 4],\n", " 18: [4, 4]\n", " }\n", ")" ] }, { "attachments": { "13297f30-0fa4-4961-b6f0-3d3b99ab32d9.png": { "image/png": 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" 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"text/plain": [ "Graphics object consisting of 39 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sterk 1\n", "\n", "display(r.cycle_tuples(singletons=True))\n", "\n", "s1_1 = v3 + v11\n", "s1_2 = v4 + v12\n", "s1_3 = v5 + v13\n", "s1_4 = v6 + v14\n", "s1_5 = v7 + v15\n", "s1_6 = v8 + v16\n", "s1_7 = v9 + v1\n", "s1_8 = v10 + v2\n", "s1_9 = v17 + v19\n", "s1_10 = v21\n", "s1_11 = v22\n", "s1_12 = v18 + v20\n", "\n", "S1 = [s1_1, s1_2, s1_3, s1_4, s1_5, s1_6, s1_7, s1_8, s1_9, s1_10, s1_11, s1_12]\n", "MS1 = root_intersection_matrix(S1, labels = [f\"$s^1_{ {r + 1} }$\" for r in range( len(S1) )], bil_form=dot)\n", "\n", "G = Coxeter_Diagram(MS1)\n", "plot_coxeter_diagram(\n", " G, \n", " v_labels = [f\"$s^1_{ {i + 1} }$\" for i in range( 22 )],\n", " pos = {\n", " 0: [0, 0],\n", " 1: [4, 0],\n", " 2: [8, 0],\n", " 3: [8, -4],\n", " 4: [8, -8],\n", " 5: [4, -8],\n", " 6: [0, -8],\n", " 7: [0, -4],\n", " 8: [0, -8],\n", " 9: [2, -6],\n", " 10: [4, -4],\n", " 11: [6, -2]\n", " }\n", ")" ] }, { "cell_type": "code", "execution_count": 32, "id": "872fc304-704b-4b15-a1f1-e9848fc6770f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Diagonal entries/square norms: \n" ] }, { "data": { "text/html": [ "\\(\\displaystyle \\left[-4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4\\right]\\)" ], "text/latex": [ "$\\displaystyle \\left[-4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4\\right]$" ], "text/plain": [ "[-4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " 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$S^1_{1}$$S^1_{2}$$S^1_{3}$$S^1_{4}$$S^1_{5}$$S^1_{6}$$S^1_{7}$$S^1_{8}$$S^1_{9}$$S^1_{10}$$S^1_{11}$$S^1_{12}$
$S^1_{1}$-402000000020
$S^1_{2}$0-40200000004
$S^1_{3}$20-4200000000
$S^1_{4}$022-420000000
$S^1_{5}$0002-42000000
$S^1_{6}$00002-4200000
$S^1_{7}$000002-420000
$S^1_{8}$0000002-40220
$S^1_{9}$00000000-4404
$S^1_{10}$000000024-400
$S^1_{11}$2000000200-40
$S^1_{12}$04000000400-4
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", "text/plain": [ "Graphics object consisting of 39 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "S1roots = [\n", " a1p, #1\n", " a2p, #2\n", " a3p, #3\n", " a4p, #4\n", " a5p, #5\n", " a6p, #6\n", " a7p, #7\n", " a8p, #8\n", " fp-ep, #9\n", " w8p + 2ep, #10\n", " 2ep + 2fp + w1p + w8p, #11\n", " 5ep + 3fp + 2w2p #12\n", "]\n", "\n", "labs = [f\"$S^1_{ {r + 1} }$\" for r in range( len(S1roots) )]\n", "\n", "plot_coxeter_diagram(\n", " Coxeter_Diagram(\n", " root_intersection_matrix(\n", " S1roots, \n", " labels = labs, \n", " bil_form=dot\n", " )\n", " ), \n", " v_labels = labs,\n", " pos = {\n", " 0: [0, 0],\n", " 1: [-4, -8],\n", " 2: [-4, -4],\n", " 3: [-8, -8],\n", " 4: [-4, -12],\n", " 5: [0, -16],\n", " 6: [4, -12],\n", " 7: [8, -8],\n", " 8: [2, -8],\n", " 9: [5, -8],\n", " 10: [4, -4],\n", " 11: [-1, -8]\n", "}\n", ")" ] }, { "attachments": { "10817378-d9c6-4e77-bfa3-4c8dc63ace71.png": { "image/png": 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" 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$s^2_{1}$$s^2_{2}$$s^2_{3}$$s^2_{4}$$s^2_{5}$$s^2_{6}$$s^2_{7}$$s^2_{8}$$s^2_{9}$$s^2_{10}$
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"text/plain": [ "Graphics object consisting of 29 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sterk 2\n", "\n", "s2_1 = w1 + w17\n", "s2_2 = w2 + w16\n", "s2_3 = w3 + w15\n", "s2_4 = w4 + w14\n", "s2_5 = w5 + w13\n", "s2_6 = w6 + w12\n", "s2_7 = w7 + w11\n", "s2_8 = w8 + w10\n", "s2_9 = w9\n", "s2_10 = w18 + w19\n", "\n", "S2 = [s2_1, s2_2, s2_3, s2_4, s2_5, s2_6, s2_7, s2_8, s2_9, s2_10]\n", "MS2 = root_intersection_matrix(S2, labels = [f\"$s^2_{ {r + 1} }$\" for r in range( len(S2) )], bil_form=dot )\n", "\n", "G = Coxeter_Diagram(MS2)\n", "plot_coxeter_diagram(\n", " G, \n", " v_labels = [f\"$s^2_{ {i + 1} }$\" for i in range( 22 )],\n", " pos = {\n", " 0: [0, 0],\n", " 1: [-4, 0],\n", " 2: [-8, 0],\n", " 3: [-7, 4],\n", " 4: [-6, 8],\n", " 5: [-5, 12],\n", " 6: [-4, 16],\n", " 7: [-3, 20],\n", " 8: [-2, 24],\n", " 9: [-2, 6]\n", " }\n", ")" ] }, { "cell_type": "code", "execution_count": 34, "id": "3e2a620f-84f4-4764-b7b3-78d3bd11c77b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Diagonal entries/square norms: \n" ] }, { "data": { "text/html": [ "\\(\\displaystyle \\left[-4, -4, -4, -4, -4, -4, -4, -4, -4, -2\\right]\\)" ], "text/latex": [ "$\\displaystyle \\left[-4, -4, -4, -4, -4, -4, -4, -4, -4, -2\\right]$" ], "text/plain": [ "[-4, -4, -4, -4, -4, -4, -4, -4, -4, -2]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", 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$S^2_{1}$$S^2_{2}$$S^2_{3}$$S^2_{4}$$S^2_{5}$$S^2_{6}$$S^2_{7}$$S^2_{8}$$S^2_{9}$$S^2_{10}$
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$S^2_{5}$0002-420000
$S^2_{6}$00002-42000
$S^2_{7}$000002-4200
$S^2_{8}$0000002-420
$S^2_{9}$00000002-42
$S^2_{10}$000000002-2
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", "text/plain": [ "Graphics object consisting of 29 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sterk's own basis for Sterk 2\n", "S2roots = [\n", " a1p, #1\n", " a2p, #2\n", " a3p, #3\n", " a4p, #4\n", " a5p, #5\n", " a6p, #6\n", " a7p, #7\n", " a8p, #8\n", " w8p + 2f, #9\n", " e-f, #10\n", "]\n", "\n", "labs = [f\"$S^2_{ {r + 1} }$\" for r in range( len(S2roots) )]\n", "\n", "plot_coxeter_diagram(\n", " Coxeter_Diagram(\n", " root_intersection_matrix(\n", " S2roots, \n", " labels = labs, \n", " bil_form=dot\n", " )\n", " ), \n", " v_labels = labs,\n", " pos = {\n", " 0: [0, 0],\n", " 1: [8, -4],\n", " 2: [4, 0],\n", " 3: [8, 0],\n", " 4: [12, 0],\n", " 5: [16, 0],\n", " 6: [20, 0],\n", " 7: [24, 0],\n", " 8: [28, 0],\n", " 9: [32, 0]\n", "}\n", ")" ] }, { "attachments": { "841e0fa1-0c65-440e-9317-6b4db0c8131d.png": { "image/png": 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" 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"text/plain": [ "Graphics object consisting of 37 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sterk 3\n", "\n", "display(d.cycle_tuples(singletons=True))\n", "\n", "wa = lambda x: x + (1/2)*dot(v22, x) * v22\n", "I = lambda x: x + wa(x)\n", "\n", "s3_1 = v13\n", "s3_2 = v14 + v12\n", "s3_3 = v15 + v11\n", "s3_4 = v16 + v10\n", "s3_5 = v1 + v9\n", "s3_6 = v2 + v8\n", "s3_7 = v3 + v7\n", "s3_8 = v4 + v6\n", "s3_9 = v5\n", "s3_10 = v17 + v19\n", "s3_11 = I(v20) #v22 + 2*v20\n", "s3_12 = I(v18) #v22 + 2*v18\n", "\n", "S3 = [s3_1, s3_2, s3_3, s3_4, s3_5, s3_6, s3_7, s3_8, s3_9, s3_10, s3_11, s3_12]\n", "MS3 = root_intersection_matrix(S3, labels = [f\"$s^2_{ {r + 1} }$\" for r in range( len(S3) )], bil_form=dot )\n", "\n", "G = Coxeter_Diagram(MS3)\n", "pos_dict = {\n", " 0: [0, -4],\n", " 1: [0, 4],\n", " 2: [0, 8],\n", " 3: [0, 12],\n", " 4: [0, 16],\n", " 5: [4, 16],\n", " 6: [8, 16],\n", " 7: [12, 16],\n", " 8: [20, 16],\n", " 9: [4, 12],\n", " 10: [6, 2],\n", " 11: [14, 10],\n", " }\n", "plot_coxeter_diagram(\n", " G, \n", " v_labels = [f\"$s^3_{ {i + 1} }$\" for i in range( len(S3) )],\n", " pos = pos_dict\n", ")\n", "\n", "#pos_dict" ] }, { "cell_type": "code", "execution_count": 36, "id": "e77cb412-f598-4cad-9f2e-49d6c823ccb4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Diagonal entries/square norms: \n" ] }, { "data": { "text/html": [ "\\(\\displaystyle \\left[-4, -4, -4, -4, -2, -4, -4, -2, -4, -4, -4, -4\\right]\\)" ], "text/latex": [ "$\\displaystyle \\left[-4, -4, -4, -4, -2, -4, -4, -2, -4, -4, -4, -4\\right]$" ], "text/plain": [ "[-4, -4, -4, -4, -2, -4, -4, -2, -4, -4, -4, -4]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", 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$S^3_{1}$$S^3_{2}$$S^3_{3}$$S^3_{4}$$S^3_{5}$$S^3_{6}$$S^3_{7}$$S^3_{8}$$S^3_{9}$$S^3_{10}$$S^3_{11}$$S^3_{12}$
$S^3_{1}$-420000000022
$S^3_{2}$2-42000000000
$S^3_{3}$02-4200000000
$S^3_{4}$002-420000000
$S^3_{5}$0002-22000000
$S^3_{6}$00002-4400000
$S^3_{7}$000004-420000
$S^3_{8}$0000002-22000
$S^3_{9}$00000002-4200
$S^3_{10}$000000002-420
$S^3_{11}$2000000002-40
$S^3_{12}$20000000000-4
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", "text/plain": [ "Graphics object consisting of 37 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# # Sterk's own basis for Sterk 3\n", "sa1 = a1p\n", "sa2 = a2p\n", "sa3 = a3p\n", "sa4 = a4p\n", "sa5 = a5p\n", "sa6 = a6p\n", "sa7 = a7p\n", "# alpha_8 is not on this diagram\n", "sa9 = f-e\n", "sa10 = 2fp + w8p\n", "sa11 = 2e - 2fp - w8p\n", "sa12 = 2e + w1p - w8p\n", "sa13 = e + f + a8p - fp\n", "\n", "S3roots = [\n", " sa4, #1\n", " sa3, #2\n", " sa1, #3\n", " sa12, #4\n", " sa9, #5\n", " sa11, #6\n", " sa10, #7\n", " sa13, #8\n", " sa7, #9\n", " sa6, #10\n", " sa5, #11\n", " sa2 #12\n", "]\n", "\n", "labs = [f\"$S^3_{ {r + 1} }$\" for r in range( len(S3roots) )]\n", "\n", "plot_coxeter_diagram(\n", " Coxeter_Diagram(\n", " root_intersection_matrix(\n", " S3roots, \n", " labels = labs, \n", " bil_form=dot\n", " )\n", " ), \n", " v_labels = labs,\n", " pos = {\n", " 0: [0, 0],\n", " 1: [-4, -4],\n", " 2: [-8, -8],\n", " 3: [-12, -12],\n", " 4: [-8, -16],\n", " 5: [-4, -20],\n", " 6: [4, -20],\n", " 7: [8, -16],\n", " 8: [12, -12],\n", " 9: [8, -8],\n", " 10: [4, -4],\n", " 11: [0, -4]\n", " }\n", ")" ] }, { "attachments": { "0f46319d-315a-42dd-a8bc-3e3cb0f7970f.png": { "image/png": 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" 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7qwCqq6t9WhZXuD55HH5i48aNCQkJ9686xsTEjBgxQqVS3bhx4913342Ojv7ss8+4LtN33nnnndDQ0FGjRt2dkICAgMTExNmzZ3/55ZdcV8cBnU6XlJTUI9FHjRoVHh5eXl7OdXUcMJlM8+bNGzNmTPeXZnQbMWJEWFjYCy+8wHV1vtPU1DRmzJg333yzq6srJycnPj7+/m8+iomJGTly5K9//Wuuy/QdrEnyzrFjx7766qtz586dOHFi1qxZkydPTk5OXrZsWfe9Bw4cUKvV//znP2fNmsVtnT5z5syZuro6o9F46tSp4cOHT506NSkp6YknnvDbr7Vrb28/dOhQY2Pj6dOnf/jhh5SUlKSkpOnTpzM/AIc8hw4dam5urqura21tnT179vjx40ePHr1gwQKu6/KR8+fPL1myZO3atWvXru3+ySeffNLc3Hz27Nnq6uq0tLSpU6eOGzfOfyaEwudtfBYQ8PPPjh/GGwD05sFgu19vbYR4OL9NeJ599lmKoh5//HHEG4Cfcx9s/gzZJkiINwBAsLmBbBMqxBuAP0OwuYdsEzDEG4B/QrD1CdkmbIg3AH+DYGMC2SZ4iDcA/4FgYwjZRgLEG4A/QLAxh2wjBOINgGwItn5BtpED8QZAKgRbfyHbiIJ4AyAPgs0DyDbSIN4ASIJg8wyyjUCINwAyINg8hmwjE+INQOgQbAOBbCMW4g1AuBBsA4RsIxniDUCIEGwDh2wjHOINQFgQbF6BbCMf4g1AKBBs3oJs8wuINwD+Q7B5EbLNXyDeAPgMweZdyDY/gngD4CcEm9ch2/wL4g2AbxBsbEC2+R3EGwB/INhYgmzzR4g3AD5AsLEH2eanEG8A3EKwsQrZ5r8QbwBcQbCxDdnm1xBvAL6HYPMBZJu/Q7wB+BKCzTeQbYB4A/ARBJvPINuAohBvAOxDsPkSsg1uQ7wBsAfB5mPINrgH8QbABgSb7yHb4CcQbwDehWDjBLINekK8AXgLgo0ryDb4GYg3gIFDsHEI2QY/D/EGMBAINm4h26BXiDcAzyDYOIdsA3cQbwD9hWDjA2Qb9AHxBsAcgo0nkG3QN8QbABMINv5AtgEjiDcA9xBsvIJsA6YQbwC9QbDxDbIN+gHxBvAgBBsPIdugfxBvAPdDsPETsg36DfEG0A3BxlvINvAE4g0AwcZnyDbwEOIN/BmCjeeQbeA5xBv4JwQb/yHbYEAQb+BvEGyCgGyDgUK8gf9AsAkFsg28APEG/gDBJiDINvAOwcdbJ/4afE5Qc45gE5ZArgsAcjz77LO7du16/PHHP//8c65r6adOc/HTKbknuS7DrwhqzhFsgoNsA28SaLwZS3K31didLq7r8CcCmnMEmxAJZ0UABEJwi5POM0UVtFIprue6ED8ioDlHsAkU9tvA+4S099ZRW3REqlou5boOfyKcOUewCReyDVghkHiz697Wy1crJVi/8B3BzDmCTdB4//oCweL/4qT1UJFxrjpHTFGdXJfiN4Qy5wg2oUO2AYt4HW8XSovblOqlNNd1+BOBzDmCjQDINmAXb+PNaXU4Wss1m8opiqI6jTqrTVySn386VbVeKYAPgoRJEHOOYCNDQFdXF9c1wM8LCCDn2Tlw4IBareYy3jrMtTW1jVYqUqZQzpH23HFwlmYOz4+rNO1N46Q4QglwzskLNpLaSL/gWBLwBW4PLXGe3pW9qtgyMj1zhVLuqsj/X539vnuNH27Lf0VbH2TTF+bmF+qsvq+PREKcc/KCza91AV+R9+y8++670dHRn332mU8f1WXIm6rQGG/fatyjlIzNqXb5tAS/I8A5b2pqGjNmzJtvvsl1IV5GXhthCJ+3ge9w89lbS5WuxZ7SaqeSxRRFRSam5+7ISMULn1VCm3PssRGI63CFXpH67Ph6781WnpVAURQtma7MWr+3utVHD+vXBDXnpO6xdSO1jfTJT39tQSD4RenjeHOc0+atTJcn0BRFUZIM7f2t1mFrrCrISss53HPFzGbYl6d+VVOwPU+9vuAwv7szD3ky570+FywiO9i6iG4j7vnpry0IZL8ofRRvLpul1XbnhsNUqVaIaeU+y+3b9VrN9r3lb6mk4VnlP+2npr9mKF6udnTfaN6rnJ2nd7BbKTk8mnM3zwV7iA+2LtLbiBt++msLAvEvSvbjzaJdLqbCM7R3O21XY8EciarypzFVlycT/7Sfugx5kySqqru3TQVzJBmlti7om6dz7v7nLPCHYOvygzbSG5wDAJxh/8QAm9kuU+3IVYrv/KChSidak7O4r+titOlrL8RJR969HSeNs9fXGtgpkjCezrlv4eAR4vH40CXwAywfOSnL2ZipqdFXHXFIaae5Qa8zRqoP5Mn7fNVfsVgomr7XjWmKpixWq5Oi+NWh+cjTOfchBJs/4NMrjkidmOM+sBpv4jR1wVy7tcVs7qAVK9KzopllU6ezxw9oiqY6KWQbEx7Oua8g2LyJx/2Nr3WRodNc/HSm8RVDwRyuK+E3dvfegsSSZLmkX/8lPJKmKOe9C9U7nZ1OOlzMrybNZx7MuU8g2LyJ3/0Nn7exyFiSu63G7nRxXYcQ8Ov73hJlMtpqsdy9bbdcoWSTH7giIggKgs27eN7fkG1scZ4pqqCV9z5Rh75wGW+dP/06sfD07KWU8Yz59s0OQ705NfNJma+rIltnL1/h1tvPBwbB5l38729Yk2RHR23REalqHa15zcMNuFwuiqIcDodIJPJmYfzmfnGyvr5+xIgRsbGxXnu8lopdBwyWpipLkL3olXxDtDRzg0oeTlGUWLljv35Vbr4kN3uyQ/9WEbVpb85Yrz2sX+ttznt9LvrhypUrbW1tU6dO7fFzvw227jbicrmCg4O9ud0B9zdf4PokBCLZqncUVNu6ulzVOYnSHF3//vPatWsnTJhAUVRsbOzgwYMnT56sVqu/++47dkrlox7nve3fv/8Xv/hFcHDwsGHDhg4dOmrUqBdffNEn1zRxWOr11Tp942X2HwoGwGg0Pvfcc/Hx8aGhodHR0SKRaMGCBVu2bOm+10/OY+th7dq1Mpmsu41QFCWTydauXeulbQ+ov/kMss37LJWavbWOrq5+P/d1dXVxcXGJiYk93n9IJJJhw4b5+vL5nOqOt08//XTevHmjRo168D0ZTdPvvfce12UC97Zv3y4SiWJiYnq8QhISEqZPn67X6/0t2Orq6iQSyciRI3tMSHx8/OjRoxsaGga4fY/7m48h27zNrNW8Zbh9DYb+PPe7d+/ucyd79+7dLFbOM9u3b3c/G8HBwampqVyXCVxatGhRWFiY+9fJ1q1buS7Td1hvI572N9/z069k9ZoHvlnY+VmxpvLOMQidxopCnXh5TvrkVNV6pbT3zdTW1qampjJ5QL1er1AovFA570kkkm+//db9mODg4Ly8vM2bN/umJOCVioqKZ555pvsjJTekUqnJZPJNSdzyfhvxUn/jBtfhKmCOuoKsFXnl9RZbu82kK1Bvre55wUGHNiOc0fsa5nGVkpLCyi/DM2vWrImPj2cyISEhIQaDget6wde+/PLLPvfYug0ZMmTDhg1c1+sLzM8NnTFjRp9b82J/4wTOAfBUZ73md+UTXtNkTJWIw8XOBp32QIXhvmOXjR9uy39FWx9k0xfm5hfqrL1vyWQynTt3juHDNjc319fXD6hyIThy5MjFixeZjIyIiGA+e0CM06dPi8WMjkC/fv16WVkZ2/VwzmQyNTQ0MBz81Vdf9bEv673+xhWcA+Cpvr5ZWLY8T7Oc0rzV95ZMJlNISAjDh71165bBYJDL5Z7ULBAOh+Obb75hOPi7775DtvmhpqYmhu9+KIpqbW0l/nQak8kUFMS0nwcGBppMptGjR/c6wnv9jSvYb/OURCYVG4sejYubsSR7Q1GjXK1+0sPrVnz99dfff/89w8E3b96srq726HEEw2QyhYf348ym2tpa9ooBfqqrq2M+WCQSNTc3s1cMH3z99dft7e0MB3d0dDQ2Nrob4b3+xhVkm6fEGcVHtHkrU+OsutKda345I7O0zcMtBQYGDho0iPl4L5+GyT+BgYEBAQHMxzN/uwrE6NeTHhAQEBhIeK/rVxsJCAjoY63Ie/2NK4Q/32zptFvb7PSkLM2BakOrzVSpVjirtEfurDk7jRU783M35a55ITPz2W0VTT0vKt9DcnLy4MGDGT5yVFTUggULBlI7/40dO/bGjRvMxz/yyCPsFQP81K9rat+8eTMpKYm9YvggOTk5IiKC4eAhQ4YkJyf3erf7/kbZ68uKdhUWFRXu2rZpW+kZ+0BLZwnXB7MIkftvFraUr1eXt3b/3NG4RymOVu5vdre5trY25i9KkUhkNBrZ+914YtKkSQwnRCKR/OMf/+C6XvA1rVb74FUOejN+/Hiu62VdW1sb85X8sLCwtra2XrbUxzenm/bl5OnufIu6w5C3OKuclxfuwX6bB9x+s3CHTvuOVnus+z0OLfudStmpK/7I6GZz8fHxS5YsYfjYjz32mLs3XKRYuXKluw+67xMUFPT444+zXQ/wzRNPPNHF7NzcYcOGrVu3ju16OBcfH8/8D0GpVPZ+jo37b0631x7T39tTo2WpCVYjD4+SpCicu+0Je80uTQ2VopDf/WbhrNfU6be/rspatbPYvlSdlUxTFEU5K7Ljss2bDPr1fVxFPjQ09NatW+7HiESifi3WCdq0adPq6+vdvz5pmj5+/PjMmTN9VhXwx6lTp+bOndvnX41SqTx8+LBvSuKcV9qI2/5GGV9PTdntzH6tQLM6XdxUpNpBa/6qkvLwI2+O9xuFy2WzGA36ukbTZYebUbYPsiTRyv2tfW9Pr9f3+WR193r/MWzYMDcHzoSGhvrJObnQm82bNw8ZMsTNn4xIJOK6Rp/yWhtx099cJu3LCkkQJU6WK1bsbXTX/7iEbGOTWZsxSaE+2vN0/t5cu3Zt8eLFY8aM6fFaHDVq1MMPP3zx4kVWi+Wn1atXP7h4MmrUqODg4Orqaq6rA+6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$s^4_{1}$$s^4_{2}$$s^4_{3}$$s^4_{4}$$s^4_{5}$$s^4_{6}$$s^4_{7}$$s^4_{8}$$s^4_{9}$$s^4_{10}$$s^4_{11}$
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"text/plain": [ "Graphics object consisting of 32 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sterk 4\n", "\n", "# display(v.cycle_tuples(singletons=True))\n", "\n", "s4_1 = v15\n", "s4_2 = v16 + v14\n", "s4_3 = v1 + v13\n", "s4_4 = v2 + v12\n", "s4_5 = v3 + v11\n", "s4_6 = v4 + v10\n", "s4_7 = v5 + v9\n", "s4_8 = v6 + v8\n", "s4_9 = v7\n", "s4_10 = v17 + v20\n", "s4_11 = v18 + v19\n", "s4_12 = v22 + v21\n", "\n", "# Although s412 is an invariant vector, it is not a root:\n", "# Math('(s^4_{12})^2=' + str( nm(s4_12)))\n", "\n", "S4 = [s4_1, s4_2, s4_3, s4_4, s4_5, s4_6, s4_7, s4_8, s4_9, s4_10, s4_11]\n", "MS4 = root_intersection_matrix(S4, labels = [f\"$s^4_{ {r + 1} }$\" for r in range( len(S4) )], bil_form=dot)\n", "\n", "G = Coxeter_Diagram(MS4)\n", "plot_coxeter_diagram(\n", " G, \n", " v_labels = [f\"$s^4_{ {i + 1} }$\" for i in range( 11 )],\n", " pos = {\n", " 0: [0, 0],\n", " 1: [0, 4],\n", " 2: [0, 8],\n", " 3: [4, 8],\n", " 4: [8, 8],\n", " 5: [12, 8],\n", " 6: [16, 8],\n", " 7: [16, 4],\n", " 8: [16, 0],\n", " 9: [4, 4],\n", " 10: [12, 4] \n", "}\n", ")" ] }, { "cell_type": "code", "execution_count": 38, "id": "511a2f36-79bf-4ac0-b0cb-e88d269b36f5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Diagonal entries/square norms: \n" ] }, { "data": { "text/html": [ "\\(\\displaystyle \\left[-2, -4, -4, -4, -4, -4, -4, -4, -2, -4, -4\\right]\\)" ], "text/latex": [ "$\\displaystyle \\left[-2, -4, -4, -4, -4, -4, -4, -4, -2, -4, -4\\right]$" ], "text/plain": [ "[-2, -4, -4, -4, -4, -4, -4, -4, -2, -4, -4]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " 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$S^4_{1}$$S^4_{2}$$S^4_{3}$$S^4_{4}$$S^4_{5}$$S^4_{6}$$S^4_{7}$$S^4_{8}$$S^4_{9}$$S^4_{10}$$S^4_{11}$
$S^4_{1}$-22000000000
$S^4_{2}$2-4200000000
$S^4_{3}$02-420000020
$S^4_{4}$002-42000000
$S^4_{5}$0002-4200000
$S^4_{6}$00002-420000
$S^4_{7}$000002-42002
$S^4_{8}$0000002-4200
$S^4_{9}$00000002-200
$S^4_{10}$002000000-40
$S^4_{11}$0000002000-4
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", "text/plain": [ "Graphics object consisting of 32 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sterk's own roots for Sterk 4\n", "\n", "# sa1 = a1p no alpha_1 on this diagram\n", "sa2 = a2p\n", "sa3 = a3p\n", "sa4 = a4p\n", "sa5 = a5p\n", "sa6 = a6p\n", "sa7 = a7p\n", "sa8 = a8p\n", "sa9 = f-e\n", "sa10 = w8p + 2ep\n", "sa11 = e + f + a1p - ep\n", "sa12 = 2e - 2ep + w8p - w1p\n", "\n", "S4roots = [\n", " sa11, #1\n", " sa3, #2\n", " sa4, #3\n", " sa5, #4\n", " sa6, #5\n", " sa7, #6\n", " sa8, #7\n", " sa12, #8\n", " sa9, #9\n", " sa2, #10\n", " sa10, #11\n", "]\n", "\n", "labs = [f\"$S^4_{ {r + 1} }$\" for r in range( len(S4roots) )]\n", "\n", "plot_coxeter_diagram(\n", " Coxeter_Diagram(\n", " root_intersection_matrix(\n", " S4roots, \n", " labels = labs, \n", " bil_form=dot\n", " )\n", " ), \n", " v_labels = labs,\n", " pos = {\n", " 0: [0, 0],\n", " 1: [4, 0],\n", " 2: [8, 0],\n", " 3: [12, 0],\n", " 4: [16, 0],\n", " 5: [20, 0],\n", " 6: [24, 0],\n", " 7: [28, 0],\n", " 8: [32, 0],\n", " 9: [8, -4],\n", " 10: [24, -4]\n", " }\n", ")" ] }, { "attachments": { "5b32ddd7-135d-452b-98c1-b2be375ce219.png": { "image/png": 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" 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", "text/plain": [ "Graphics object consisting of 49 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sterk 5\n", "\n", "s5_1 = v16 + 2v1 + v2\n", "s5_2 = v2 + 2v3 + v4\n", "s5_3 = v4 + 2v5 + v6\n", "s5_4 = v6 + 2v7 + v8\n", "s5_5 = v8 + 2v9 + v10\n", "s5_6 = v10 + 2v11 + v12\n", "s5_7 = v12 + 2v13 + v14\n", "s5_8 = v14 + 2v15 + v16\n", "s5_9 = v17\n", "s5_10 = v18\n", "s5_11 = v19\n", "s5_12 = v20\n", "s5_13 = v21\n", "s5_14 = v22\n", "\n", "S5 = [s5_1, s5_2, s5_3, s5_4, s5_5, s5_6, s5_7, s5_8, s5_9, s5_10, s5_11, s5_12, s5_13, s5_14]\n", "MS5 = root_intersection_matrix(S5, labels = [f\"$s^5_{ {r + 1} }$\" for r in range( len(S5) )], bil_form=dot)\n", "\n", "G = Coxeter_Diagram(MS5)\n", "plot_coxeter_diagram(\n", " G, \n", " v_labels = [f\"$s^5_{ {i + 1} }$\" for i in range( 14 )],\n", " pos = {\n", " 0: [0, 0],\n", " 1: [10, 0],\n", " 2: [20, 0],\n", " 3: [20, -10],\n", " 4: [20, -20],\n", " 5: [10, -20],\n", " 6: [0, -20],\n", " 7: [0, -10],\n", " 8: [4, -4],\n", " 9: [16, -4],\n", " 10: [16, -16],\n", " 11: [4, -16],\n", " 12: [8, -8],\n", " 13: [8, -12]\n", "}\n", ")" ] }, { "cell_type": "code", "execution_count": 40, "id": "65024948-9105-463f-9c75-7005fb377bfa", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\verb|dot|\\verb| |\\verb|with|\\verb| |\\verb|a1|\\verb| |\\verb|tilde|\\verb| |\\verb|bar|\\)" ], "text/latex": [ "$\\displaystyle \\verb|dot|\\verb| |\\verb|with|\\verb| |\\verb|a1|\\verb| |\\verb|tilde|\\verb| |\\verb|bar|$" ], "text/plain": [ "'dot with a1 tilde bar'" ] }, "metadata": {}, "output_type": "display_data" }, { "ename": "NameError", "evalue": "name 's_a1_tilde_bar' 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 4\u001b[0m\n\u001b[1;32m 2\u001b[0m s_a1_tildebar \u001b[38;5;241m=\u001b[39m epb \u001b[38;5;241m-\u001b[39m fpb\n\u001b[1;32m 3\u001b[0m display(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mdot with a1 tilde bar\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m----> 4\u001b[0m show( dot(s_a1_tilde, \u001b[43ms_a1_tilde_bar\u001b[49m) )\n\u001b[1;32m 5\u001b[0m \u001b[38;5;66;03m# show( dot(s_a2_tilde, s_a2_tilde_bar) )\u001b[39;00m\n\u001b[1;32m 6\u001b[0m \u001b[38;5;66;03m# show( dot(s_a3_tilde, s_a3_tilde_bar) )\u001b[39;00m\n\u001b[1;32m 7\u001b[0m \u001b[38;5;66;03m# show( dot(s_a6_tilde, s_a6_tilde_bar) )\u001b[39;00m\n\u001b[1;32m 8\u001b[0m \u001b[38;5;66;03m# show( dot(s_a8_tilde, s_a8_tilde_bar) )\u001b[39;00m\n\u001b[1;32m 9\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mnamestr\u001b[39m(obj):\n", "\u001b[0;31mNameError\u001b[0m: name 's_a1_tilde_bar' is not defined" ] } ], "source": [ "s_a1_tilde = ep - fp\n", "s_a1_tildebar = epb - fpb\n", "display(\"dot with a1 tilde bar\")\n", "show( dot(s_a1_tilde, s_a1_tilde_bar) )\n", "# show( dot(s_a2_tilde, s_a2_tilde_bar) )\n", "# show( dot(s_a3_tilde, s_a3_tilde_bar) )\n", "# show( dot(s_a6_tilde, s_a6_tilde_bar) )\n", "# show( dot(s_a8_tilde, s_a8_tilde_bar) )\n", "def namestr(obj):\n", " namespace = globals()\n", " return [name for name in namespace if namespace[name] is obj][1]\n", " \n", "for v in [e,f, ep,fp, a1,a2,a3,a4,a5,a6,a7,a8, a1t,a2t,a3t,a4t,a5t,a6t,a7t,a8t]:\n", " display(\"dot with \" + namestr(v) )\n", " show( dot(s_a1_tilde_bar, v) )" ] }, { "cell_type": "code", "execution_count": null, "id": "3911166e-1396-49c9-9dee-85277c09837d", "metadata": {}, "outputs": [], "source": [ "# Sterk's own roots for Sterk 5\n", "\n", "s_e_tilde = e + ep + fp - a1p\n", "s_f_tilde = f + ep + fp - a1p\n", "\n", "s_a1_tilde = ep - fp\n", "s_a2_tilde = a2p\n", "s_a3_tilde = fp + a3p\n", "s_a4_tilde = a4p\n", "s_a5_tilde = a5p\n", "s_a6_tilde = a6p\n", "s_a7_tilde = a7p\n", "s_a8_tilde = a8p\n", "\n", "s_a1_tilde_bar = epb - fpb # probablt not\n", "s_a2_tilde_bar = w2p\n", "s_a3_tilde_bar = fpb + w3p # probably not\n", "s_a4_tilde_bar = w5p\n", "s_a5_tilde_bar = w5p\n", "s_a6_tilde_bar = w6p\n", "s_a7_tilde_bar = w7p\n", "s_a8_tilde_bar = w8p\n", "\n", "\n", "sa9 = 2 s_e_tilde - s_a1_tilde\n", "sa10 = 2 s_e_tilde + s_a6_tilde_bar - s_a3_tilde_bar # probably not\n", "sa11 = s_f_tilde - s_e_tilde\n", "sa12 = s_e_tilde + s_f_tilde + s_a6_tilde_bar - s_a3_tilde_bar # probably not\n", "sa13 = s_e_tilde + s_f_tilde + s_a1_tilde_bar + s_a8_tilde_bar - s_a3_tilde_bar # probably not\n", "sa14 = s_e_tilde + s_f_tilde + s_a3_tilde\n", "\n", "\n", "S5roots = [\n", " a4p, #1\n", " a2p, #2\n", " # sa10, #3, issue\n", " s_a8_tilde_bar, #4\n", " a8p, #5\n", " a7p, #6\n", " a6p, #7\n", " a5p, #8\n", " sa14, #9\n", " s_a1_tilde, #10\n", " # sa13, #11, issue\n", " # sa12, #12, issue\n", " sa9, #13,\n", " sa11, #14\n", "]\n", "\n", "labs = [f\"$S^5_{ {r + 1} }$\" for r in range( len(S5roots) )]\n", "\n", "plot_coxeter_diagram(\n", " Coxeter_Diagram(\n", " root_intersection_matrix(\n", " S5roots, \n", " labels = labs, \n", " bil_form=dot\n", " )\n", " ), \n", " v_labels = labs,\n", " pos = {\n", " 0: [0, 0],\n", " 1: [4, 4],\n", " 2: [8, -4],\n", " 3: [12, 4],\n", " 4: [16, -4],\n", " 5: [20, 4],\n", " 6: [24, -4],\n", " 7: [28, 4],\n", " 8: [32, -4],\n", " 9: [36, 4],\n", " 10: [40,-4],\n", " 11: [44, 4], \n", " 12: [48, -4],\n", " 13: [52, 4]\n", " }\n", ")" ] }, { "cell_type": "markdown", "id": "acafb3ea-4b24-4a9c-a033-31a44ed17e7d", "metadata": {}, "source": [ "# Appendix" ] }, { "cell_type": "code", "execution_count": null, "id": "36fed8da-1154-40d3-8f74-d510c2b00f30", "metadata": {}, "outputs": [], "source": [ "for i, s in enumerate(S5roots):\n", " show(i+1, \": \", s)" ] }, { "cell_type": "code", "execution_count": null, "id": "bba91b95-fc13-4073-9a42-14af46a80404", "metadata": {}, "outputs": [], "source": [ "sa10" ] }, { "cell_type": "code", "execution_count": null, "id": "97b2bb2e-a58a-4277-b2cd-3e24d5ebb49a", "metadata": {}, "outputs": [], "source": [ "Gram_L_20_2_0" ] }, { "cell_type": "code", "execution_count": null, "id": "32450207-f930-4359-bfa4-6b6d6bdf5bd8", "metadata": {}, "outputs": [], "source": [ "cb1 = vector( [1,0,1,1,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0] )\n", "cb2 = vector( [0,1,1,1,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0] )\n", "cb5 = vector( [0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] )\n", "cb7 = vector( [0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0] )\n", "cbz = vector( [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0] )\n", "\n", "# display( cb1 * Gram_L_20_2_0 * cb1 )\n", "# display( cb2 * Gram_L_20_2_0 * cb2 )\n", "# display( cb5 * Gram_L_20_2_0 * cb5 )\n", "# display( cb7 * Gram_L_20_2_0 * cb7 )\n", "\n", "COB = identity_matrix(20)\n", "\n", "COB[:, 1] = cb1\n", "# COB[:, 2] = cb2\n", "# COB[:, 5] = cb5\n", "# COB[:, 7] = cb7\n", "\n", "det(COB)\n", "display(COB)\n", "\n", "# M = Matrix(ZZ, 20, [cb1, cb2, cbz, cbz, cb5, cbz, cb7, cbz, cbz, cbz, cbz, cbz, cbz, cbz, cbz, cbz, cbz, cbz, cbz, cbz, ])" ] }, { "cell_type": "code", "execution_count": null, "id": "330cb2fe-8ff1-4519-ac56-474eaa4910da", "metadata": {}, "outputs": [], "source": [ "v5 = L_20_2_0(2e + 2f + w1 + w1t)\n", "v5" ] }, { "cell_type": "code", "execution_count": null, "id": "5f0b7bc6-d553-408b-8d1f-76cfab6bb826", "metadata": {}, "outputs": [], "source": [ "matrix(ZZ, 2, [0, 1, 1, 0]).inverse()" ] }, { "cell_type": "code", "execution_count": null, "id": "78a7097d-4679-44fc-ac53-5d242776b84c", "metadata": {}, "outputs": [], "source": [ "dot(e, (1/2) f)" ] }, { "cell_type": "code", "execution_count": null, "id": "db66068b-6699-4dfc-88d6-e73c62aff87e", "metadata": {}, "outputs": [], "source": [ "show( eb == f )\n", "show (fb == e )\n", "show( eb - fb == f-e )" ] }, { "cell_type": "code", "execution_count": null, "id": "c6748c68-cb27-4a5a-afb0-f274956feacc", "metadata": {}, "outputs": [], "source": [ "# Lw = H.direct_sum(H2).direct_sum(E8.twist(2))\n", "# b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12 = Lw.gens()\n", "# Lw.gram_matrix()" ] }, { "cell_type": "code", "execution_count": null, "id": "23a6d776-a488-4281-a557-74f9d5147a3c", "metadata": {}, "outputs": [], "source": [ "# B = identity_matrix(12)\n", "# B[:, 0] = b1 + b3 + b4 - b5\n", "# B[:, 1] = b2 + b3 + b4 - b5\n", "# # B[:, 4] = b3 - b4\n", "# B[:, 6] = b4 + b7\n", "# B" ] }, { "cell_type": "code", "execution_count": null, "id": "4546fb46-70a9-45d8-aaa8-0ecdb41d8845", "metadata": {}, "outputs": [], "source": [ "B.det()" ] }, { "cell_type": "code", "execution_count": null, "id": "ce1950bd-2bf9-4baf-b345-18561da2dcce", "metadata": {}, "outputs": [], "source": [ "# L = H.direct_sum(H2).direct_sum(E8.twist(2))\n", "# GL = L.gram_matrix()\n", "# GL" ] }, { "cell_type": "code", "execution_count": null, "id": "a365beec-0f2a-495c-b03c-d845cbf7a09a", "metadata": {}, "outputs": [], "source": [ "e, f, ep, fp, a1, a2, a3, a4, a5, a6, a7, a8 = L.gens()" ] }, { "cell_type": "code", "execution_count": null, "id": "5aa573f2-280c-4bea-9f1a-4f3f832a0079", "metadata": {}, "outputs": [], "source": [ "# ed, fd, epd, fpd, w1, w2, w3, w4, w5, w6, w7, w8 = GL.inverse().columns()\n", "# ZS = [ed, fd, epd, fpd, w1, w2, w3, w4, w5, w6, w7, w8]\n", "# for z in ZS:\n", "# show(z)" ] }, { "cell_type": "code", "execution_count": null, "id": "72c346da-e832-4235-8a62-657cab00ceb2", "metadata": {}, "outputs": [], "source": [ "w8t" ] }, { "cell_type": "code", "execution_count": null, "id": "94bc056e-ddc7-435a-8687-adde83732aa1", "metadata": {}, "outputs": [], "source": [ "b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12 = L.gens()\n", "B = identity_matrix(ZZ, 12)\n", "B[:, 0] = b1 + b3 + b4 - b5\n", "B[:, 1] = b2 + b3 + b4 - b5\n", "B[:, 4] = b3 - b4\n", "B[:, 6] = b4 + b7" ] }, { "cell_type": "code", "execution_count": null, "id": "bfafd53d-6aae-4100-b4f0-1d9017022952", "metadata": {}, "outputs": [], "source": [ "B" ] }, { "cell_type": "code", "execution_count": null, "id": "07a8ec96-6b65-4bc0-ad85-7ec30929b3b9", "metadata": {}, "outputs": [], "source": [ "det(B)" ] }, { "cell_type": "code", "execution_count": null, "id": "f73da562-0163-415b-9c90-5e65f8cd25b1", "metadata": {}, "outputs": [], "source": [ "e_st = e + ep + fp - a1p\n", "f_st = f + ep + fp - a1p\n", "a1_st = ep - fp\n", "a2_st = a2p\n", "a3_st = fp + a3p\n", "a4_st = a4p\n", "a5_st = a5p\n", "a6_st = a6p\n", "a7_st = a7p\n", "a8_st = a8p\n", "\n", "ST = [e_st, f_st, a1_st, a2_st, a3_st, a4_st, a5_st, a6_st, a7_st, a8_st]\n", "\n", "v_intersects = [dot(v, x) for x in ST]\n", "v_intersects" ] }, { "cell_type": "markdown", "id": "ff081297-3397-4e74-ab34-280e40bbdcad", "metadata": {}, "source": [ "# M = matrix(ZZ, 10, ST)\n", "M" ] }, { "cell_type": "code", "execution_count": null, "id": "cc4077ba-835b-4460-b44e-516333d34e3c", "metadata": {}, "outputs": [], "source": [ "M.rank()" ] }, { "cell_type": "code", "execution_count": null, "id": "b2196b6a-2508-4678-8170-27a4a3af6094", "metadata": {}, "outputs": [], "source": [ "labels = [f\"$K_{ {r + 1} }$\" for r in range( len(ST) )]\n", "n = len(ST)\n", "M = zero_matrix(ZZ, n)\n", "nums = Set(range(n))\n", "for i in range(n):\n", " for j in range(n):\n", " M[i, j] = dot( ST[i], ST[j] )\n", "\n", "print(\"Diagonal entries/square norms: \")\n", "display(M.diagonal())\n", "\n", "# Labels!\n", "\n", "\n", "df = pd.DataFrame(M, columns=labels, index=labels)\n", "display(HTML(df.to_html()))" ] }, { "cell_type": "code", "execution_count": null, "id": "266ad280-15f3-420a-8717-1e390843c9fe", "metadata": {}, "outputs": [], "source": [ "# H.direct_sum(E8.twist(2)).gram_matrix()" ] }, { "cell_type": "code", "execution_count": null, "id": "7707a371-e8fa-4556-bf8f-ba24b0a3e65f", "metadata": {}, "outputs": [], "source": [ "v = 2e + 2f + w1" ] }, { "cell_type": "code", "execution_count": null, "id": "621fc5c6-8e5d-4859-9e33-bee118f76554", "metadata": {}, "outputs": [], "source": [ "for s in ST:\n", " show(s)\n", " show( dot(v, s) )" ] }, { "cell_type": "code", "execution_count": null, "id": "2d1ba47a-9808-4c19-9b3e-5d687c175835", "metadata": {}, "outputs": [], "source": [ "Ld = L.dual_lattice()\n", "Ld.gram_matrix()" ] }, { "cell_type": "code", "execution_count": null, "id": "e40f295f-331e-478e-bc8d-1aeca372d784", "metadata": {}, "outputs": [], "source": [ "len(a1_st)" ] }, { "cell_type": "code", "execution_count": null, "id": "cfa2cb26-dfea-4f8e-a5d3-3c5a13047da8", "metadata": {}, "outputs": [], "source": [ "L_20_2_0" ] }, { "cell_type": "code", "execution_count": null, "id": "6f8a3294-73d0-4138-8dd0-5d58930d1781", "metadata": {}, "outputs": [], "source": [ "L_20_2_0_dual = L_20_2_0.dual_lattice()\n", "L_20_2_0_dual" ] }, { "cell_type": "code", "execution_count": null, "id": "edf48e03-93e1-4ad3-8c87-4f3b85aa4c18", "metadata": {}, "outputs": [], "source": [ "fpd = L_20_2_0_dual(fp)\n", "fpd" ] }, { "cell_type": "code", "execution_count": null, "id": "84078e7b-6b46-44ad-8f07-79c8d0798b2c", "metadata": {}, "outputs": [], "source": [ "fp" ] }, { "cell_type": "code", "execution_count": null, "id": "c953ed0e-1da5-4ad1-9872-fed29570903f", "metadata": {}, "outputs": [], "source": [ "dot(fp, fpd)" ] }, { "cell_type": "code", "execution_count": null, "id": "6a3a53cf-d684-492e-bdad-d7e02fe53350", "metadata": {}, "outputs": [], "source": [ "E8.gram_matrix().inverse()" ] }, { "cell_type": "code", "execution_count": null, "id": "fd31a2d7-7a8b-4334-bce7-660896825327", "metadata": {}, "outputs": [], "source": [ "v = 2e + 2e + w1p" ] }, { "cell_type": "code", "execution_count": null, "id": "3288ac72-889b-4dcc-8e4d-935d5f691b88", "metadata": {}, "outputs": [], "source": [ "v" ] }, { "cell_type": "code", "execution_count": null, "id": "8b9f0796-7482-4d93-a8fd-44ab3e817e8a", "metadata": {}, "outputs": [], "source": [ "etilde = e + ep + fp - a1p\n", "etilde" ] }, { "cell_type": "code", "execution_count": null, "id": "c09cc6af-3eeb-45c2-9456-6d3267fa8307", "metadata": {}, "outputs": [], "source": [ "dot(v, etilde)" ] }, { "cell_type": "code", "execution_count": null, "id": "ee48c20a-e8b5-4ee2-bb20-83806aecbd6a", "metadata": {}, "outputs": [], "source": [ "ftilde = f + ep + fp - a1p\n", "dot(v, ftilde)" ] }, { "cell_type": "code", "execution_count": 41, "id": "8be0fe7b-5115-4d85-9490-66613bd4e900", "metadata": {}, "outputs": [], "source": [ "def root_intersection_matrix(vectors, labels, bil_form):\n", " n = len(vectors)\n", " M = zero_matrix(ZZ, n)\n", " nums = Set(range(n))\n", " for i in range(n):\n", " for j in range(n):\n", " M[i, j] = bil_form( vectors[i], vectors[j] )\n", "\n", " # Must be symmetric\n", " assert M.is_symmetric()\n", "\n", " # Must have -2 or -4 on the diagonal\n", " s = Set( M.diagonal() )\n", " assert s in Subsets( Set( [-2, -4] ) )\n", "\n", " # Diagonals should be square norms of vectors\n", " for i in range(n):\n", " assert M[i, i] == bil_form(vectors[i], vectors[i])\n", " return M\n", " \n", "def pp_root_matrix(M, labels, bil_form):\n", " print(\"Diagonal entries/square norms: \")\n", " display(M.diagonal())\n", " \n", " df = pd.DataFrame(M, columns=labels, index=labels)\n", " display(HTML(df.to_html()))\n", " " ] }, { "cell_type": "markdown", "id": "f682b124-30cd-476d-8f1f-f57dd3d4bba6", "metadata": {}, "source": [ "## Definitions: Elliptic and Parabolic\n", "\n", "By the order of the diagram we mean the number of its nodes. By signature and rank of diagram $\\Sigma$ we mean the signature and the rank of the matrix $G(\\Sigma)$.\n", "\n", "A Coxeter diagram $\\Sigma$ is called elliptic if the matrix $G(\\Sigma)$ is positive definite. A connected Coxeter diagram $\\Sigma$ is called parabolic if the matrix $G(\\Sigma)$ is degenerate, and any subdiagram of $\\Sigma$ is elliptic. Elliptic and connected parabolic diagrams are exactly Coxeter diagrams of spherical and Euclidean Coxeter simplices respectively, they were classified by Coxeter [2]. We represent the complete list of elliptic and connected parabolic diagrams in Table $\\mathbb{1}$.\n", "\n", "A non-connected diagram is called parabolic if it is a disjoint union of connected parabolic diagrams. A diagram is called indefinite if it contains at least one connected component that is neither elliptic nor parabolic.\n", "\n", "## Alternative definition\n", "\n", "An edge corresponding to a dihedral angle of is said to be of weight m. The number of vertices in a Coxeter diagram is called the order of the diagram. A connected Coxeter diagram is called elliptic (respectively parabolic) if the corresponding Gram matrix is positive definite (respectively semidefinite and degenerate). A Coxeter diagram that consists only of elliptic (respectively parabolic) connected components is called elliptic (respectively parabolic). The rank of a Coxeter diagram is equal to the rank of the Gram matrix. The Gram matrix of a disconnected Coxeter diagram can be transformed into a block diagonal matrix via permutations of the rows and the same permutations of the columns. Therefore the rank of a disconnected Coxeter diagram is the sum of the ranks of its connected components. The rank of a connected elliptic diagram is equal to its order, while the rank of a connected parabolic diagram is one less than its order." ] }, { "cell_type": "code", "execution_count": 42, "id": "8d1fd463-b91a-483d-9859-7339ae99576b", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 51 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Ws_parab_one = [w1, w2, w3, w4, w5, w6, w7, w8, w10, w11, w12, w13, w14, w15, w16, w17, w18, w19]\n", "\n", "M_Ws_parab_one = root_intersection_matrix(Ws_parab_one, labels = [f\"$w_{ {r + 1} }$\" for r in [0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19] ], bil_form=dot)\n", "\n", "\n", "G = Coxeter_Diagram(M_Ws_parab_one)\n", "plot_coxeter_diagram(\n", " G, \n", " v_labels = [f\"$w_{ {i + 1} }$\" for i in range( 19 )],\n", " pos = {\n", " 0: [-4, 0],\n", " 1: [-8, 0],\n", " 2: [-12, 0],\n", " 3: [-10, 4],\n", " 4: [-8, 8],\n", " 5: [-6, 12],\n", " 6: [-4, 16],\n", " 7: [-2, 20],\n", " 8: [2, 20],\n", " 9: [4, 16],\n", " 10: [6, 12],\n", " 11: [8, 8],\n", " 12: [10, 4],\n", " 13: [12, 0],\n", " 14: [8, 0],\n", " 15: [4, 0],\n", " 16: [-4, 4],\n", " 17: [4, 4]\n", " }\n", ")" ] }, { "cell_type": "code", "execution_count": 48, "id": "0215fd2c-5e30-4b61-bb11-213a2b84e8bd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Subdiagram is parabolic? True\n", "Number of vertices in full diagram: 19\n", "Number of vertices in subdiagram: 18\n", "Rank of full lattice: 18\n", "Rank of lattice generated by vectors in this subdiagram: 17\n" ] } ], "source": [ "print(f\"Subdiagram is parabolic? {is_parabolic_matrix(M_Ws_parab_one)}\")\n", "\n", "print(f\"Number of vertices in full diagram: {len(W)}\")\n", "print(f\"Number of vertices in subdiagram: {len(Ws_parab_one)}\")\n", "print(f\"Rank of full lattice: {matrix(ZZ, W).rank()}\")\n", "print(f\"Rank of lattice generated by vectors in this subdiagram: {matrix(ZZ, Ws_parab_one).rank() }\")\n" ] }, { "cell_type": "code", "execution_count": 56, "id": "59a2fc72-524d-4f0f-b0b5-b194d248f443", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of subgraphs: 1160\n" ] } ], "source": [ "W = [w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15, w16, w17, w18, w19]\n", "MW = root_intersection_matrix(W, labels = [f\"$w_{ {r + 1} }$\" for r in range( len(W) )], bil_form=dot)\n", "\n", "G = Coxeter_Diagram(MW)\n", "\n", "verts = set(list( G.vertices()) )\n", "\n", "all_subs_verts = subsets(verts)\n", "\n", "small_subgraph_sample = [l for l in all_subs_verts if len(l) >= 16]\n", "\n", "print(f\"Number of subgraphs: {len(small_subgraph_sample)}\")" ] }, { "cell_type": "code", "execution_count": 57, "id": "146dba97-780a-4c1f-814e-21bc1522d591", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Test case: 1160 subgraphs.\n", "Full matrix rank = 18 and number of vertices = 19\n" ] } ], "source": [ "subgraphs = [G.subgraph(vs) for vs in small_subgraph_sample ]\n", "test_case = [H for H in subgraphs if len(H.vertices()) >= 1 ]\n", "\n", "full_rank = matrix(ZZ, W).rank()\n", "\n", "print(f\"Test case: {len(test_case)} subgraphs.\")\n", "print(f\"Full matrix rank = {full_rank} and number of vertices = {len(G.vertices()) }\")\n", "\n", "# Seems we need to reverse the convention for parabolic/elliptic to be negative (semi)definite.\n", "\n", "def is_elliptic_matrix(M):\n", " return (-1 * M).is_positive_definite()\n", "\n", "def is_parabolic_matrix(M):\n", " return (-1 * M).is_positive_semidefinite()\n", "\n", "def is_maximal_parabolic(M):\n", " return is_parabolic_matrix(M) and true;\n", "\n", "def roots_from_subgraph(H):\n", " return [V[index] for index in H.vertices()]" ] }, { "cell_type": "code", "execution_count": 61, "id": "8bb9ad62-ce7b-4b38-83df-df0814918917", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Parabolic of rank 17 (Type II)\n", "[17, 0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]\n" ] }, { "data": { "image/png": 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"----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Parabolic of rank 17 (Type II)\n", "[17, 18, 0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15]\n" ] }, { "data": { "image/png": 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"----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Parabolic of rank 17 (Type II)\n", "[17, 18, 0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16]\n" ] }, { "data": { "image/png": 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"----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Parabolic of rank 17 (Type II)\n", "[17, 18, 0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 15, 16]\n" ] }, { "data": { "image/png": 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", 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0 \\\\\n", "0 & 0 & 0 & 0 & 1 & -2 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "1 & 0 & 0 & 0 & 0 & 1 & -2 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -2 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 & 1 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 & 1 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 & 1 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 & 0 & 0 \\\\\n", "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -2 & 0 \\\\\n", "0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -2\n", "\\end{array}\\right)$" ], "text/plain": [ "[-2 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0]\n", "[ 0 -2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]\n", "[ 0 0 -2 1 0 0 0 0 0 0 0 0 0 0 0 1 1]\n", "[ 0 0 1 -2 1 0 0 0 0 0 0 0 0 0 0 0 0]\n", "[ 0 0 0 1 -2 1 0 0 0 0 0 0 0 0 0 0 0]\n", "[ 0 0 0 0 1 -2 1 0 0 0 0 0 0 0 0 0 0]\n", "[ 1 0 0 0 0 1 -2 1 0 0 0 0 0 0 0 0 0]\n", "[ 0 0 0 0 0 0 1 -2 0 0 0 0 0 0 0 0 0]\n", "[ 0 0 0 0 0 0 0 0 -2 1 0 0 0 0 0 0 0]\n", "[ 0 1 0 0 0 0 0 0 1 -2 1 0 0 0 0 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 1 -2 1 0 0 0 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 0 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 0 0]\n", "[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -2 0]\n", "[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -2]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "Parabolic of rank 17 (Type II)\n", "[17, 18, 0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16]\n" ] }, { "data": { "image/png": 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", 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0 0 0 0 0]\n", "[ 0 -2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]\n", "[ 0 0 -2 1 0 0 0 0 0 0 0 0 0 0 0 1 1]\n", "[ 0 0 1 -2 1 0 0 0 0 0 0 0 0 0 0 0 0]\n", "[ 0 0 0 1 -2 1 0 0 0 0 0 0 0 0 0 0 0]\n", "[ 0 0 0 0 1 -2 1 0 0 0 0 0 0 0 0 0 0]\n", "[ 1 0 0 0 0 1 -2 0 0 0 0 0 0 0 0 0 0]\n", "[ 0 0 0 0 0 0 0 -2 1 0 0 0 0 0 0 0 0]\n", "[ 0 0 0 0 0 0 0 1 -2 1 0 0 0 0 0 0 0]\n", "[ 0 1 0 0 0 0 0 0 1 -2 1 0 0 0 0 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 1 -2 1 0 0 0 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 0 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 0 0]\n", "[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -2 0]\n", "[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -2]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Parabolic of rank 17 (Type II)\n", "[17, 18, 0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16]\n" ] }, { "data": { "image/png": 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parabolic found\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "Parabolic of rank 17 (Type II)\n", "[17, 18, 0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16]\n" ] }, { "data": { "image/png": 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0 0 0 0 0]\n", "[ 0 -2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]\n", "[ 0 0 -2 1 0 0 0 0 0 0 0 0 0 0 0 1 1]\n", "[ 0 0 1 -2 1 0 0 0 0 0 0 0 0 0 0 0 0]\n", "[ 0 0 0 1 -2 0 0 0 0 0 0 0 0 0 0 0 0]\n", "[ 1 0 0 0 0 -2 1 0 0 0 0 0 0 0 0 0 0]\n", "[ 0 0 0 0 0 1 -2 1 0 0 0 0 0 0 0 0 0]\n", "[ 0 0 0 0 0 0 1 -2 1 0 0 0 0 0 0 0 0]\n", "[ 0 0 0 0 0 0 0 1 -2 1 0 0 0 0 0 0 0]\n", "[ 0 1 0 0 0 0 0 0 1 -2 1 0 0 0 0 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 1 -2 1 0 0 0 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 0 1 -2 0 0 0 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 0 0 0 -2 1 0 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 0]\n", "[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 -2 0]\n", "[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -2]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Non-maximal parabolic found\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Parabolic of rank 17 (Type II)\n", "[17, 18, 0, 1, 2, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16]\n" ] }, { "data": { "image/png": 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0 0 0 0 0]\n", "[ 0 -2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0]\n", "[ 0 0 -2 1 0 0 0 0 0 0 0 0 0 0 0 1 1]\n", "[ 0 0 1 -2 1 0 0 0 0 0 0 0 0 0 0 0 0]\n", "[ 0 0 0 1 -2 0 0 0 0 0 0 0 0 0 0 0 0]\n", "[ 1 0 0 0 0 -2 1 0 0 0 0 0 0 0 0 0 0]\n", "[ 0 0 0 0 0 1 -2 1 0 0 0 0 0 0 0 0 0]\n", "[ 0 0 0 0 0 0 1 -2 1 0 0 0 0 0 0 0 0]\n", "[ 0 0 0 0 0 0 0 1 -2 1 0 0 0 0 0 0 0]\n", "[ 0 1 0 0 0 0 0 0 1 -2 1 0 0 0 0 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 1 -2 0 0 0 0 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 0 0 -2 1 0 0 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 0]\n", "[ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 0]\n", "[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 -2 0]\n", "[ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -2]" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Non-maximal parabolic found\n", "Non-maximal parabolic found\n", "Parabolic of rank 17 (Type II)\n", "[17, 18, 0, 1, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16]\n" ] }, { "data": { 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"----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "Parabolic of rank 17 (Type II)\n", "[17, 18, 0, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16]\n" ] }, { "data": { "image/png": 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", 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"----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Parabolic of rank 17 (Type II)\n", "[17, 18, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16]\n" ] }, { "data": { "image/png": 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"----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "Non-maximal parabolic found\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "----------------------------------\n", "Parabolic of rank 17 (Type II)\n", "[17, 18, 0, 1, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]\n" ] }, { "data": { "image/png": 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DiOKUdOFTt04drFpZANCtYzuOnbvA0s07WPV/7xW6f+6FjzbUMJJgUPFqVDDITcU/e+4ciXfiyMzM4tifF+g/9T95+8xathqAsa+9TMC82cwZ/RZpGRlMXeRD8sMUenbqQMiSL2ho2ECyjEW116Vz57wLn5KoVDl3vkXRpgsfhULBwYMHNT0MrVJjgoF6DSIPPvDxY9eBwzg79iY7cm+R79PR0eFTjzF86jGmwGuSZSyqq0ePHvHDDz9w6/Ztblz5i8zMLLWHyB9+G8Cr9t1p1dyMh6lpbNoXQfjxk+xZ7FXo8bTtwkehUBAUFJSzGOTpFSKiXGpEMCisBtHuyKN84OPHwJ52pc7IzE+yjEV1FB0djZ+fH0FBQTx48IAePXpw5MiRvAufXHeSknn7M29uJybT2KgBNm0t2bPYi1d6FH4ua9uFj0Kh4MGDB9y7dw9jY+OS3yBKVO2rlsbGxqJUKunbtSN16ugTff4it+8msWL2NGYv98XFqQ8B82ax47dDrN6xm6g/L5J4/wHR61bwQrvCl59mZ2fjPv9rtkQc4uTJk5JcJjTq/v37BAcH4+fnR3R0NBYWFri7uzNhwgQsLS3p7+TE1dgLxGxYWe4LH+WYKbS2bkdoWFglfIKqd+TIEXr27El0dDQvvviipoejFar9k6SiahCZm5ng9+EMAkNCcZ//NUn3H+LQtTMLphR/5SNZxqI6UKlUHDx4kHHjxmFubs706dN57rnn2LlzJ1evXsXLywtLS0sAVvv6cjspmSney8u8Ekhby6vk/m7kIXLFqdbTRLmp+FsXzMPZsbfabTKA60AnVCrwXLCEg6fO4j1tAjZt2xR6rMzMLHYeiGSOzxpuJyVLlrHQiISEBDZs2ICfnx/nzp3D0tKSjz76iHHjxmFhYVHoe6ysrPD398fNzQ2gxHLtuVLT0pnivZzAkFCCgoK06sLHzMyMBg0aSDCoQNU6GJSmBtGoQU706NSeSQuX4jLXKy+ZLHDvfqLPX+R+SioxsX8R8kcUd5KSpXWlqHLZ2dns378fX19fduzYgY6ODsOHD2f58uU4OTmVaqmnq6srKpUKDw8PDp46h/e08QzrY19kPwNtv/CRXIOKV62fGXSzs6NLCxMC5s1W265rP5htX37MG/0c1LZHn49l6eYf2bBnH3X09XmSmUm9unXo2lbBw0dp6DZoyNmzZ6vyI4ha7ObNmwQEBODv78+VK1fo1KkTnp6ejB49GjMzs3Id8+lOZwPslCit29DYyDDvwmd/VE6ns/5OTqzS4gufIUOGoK+vz48//qjpoWiFan1nUFwqfmFs21vzmedoNuzZxx/+S7Gxssy76lq8cRsfrqr5qfiiYlRWA/nMzEx2796Nr68vu3fvxsDAgJEjR+Lp6UmvXr2eeRmklZUVoWFheT2QD0dGsjl0XV4P5K5duuA8YqTW9kDOT6FQcODAAU0PQ+Mq6lyutsGgLDWIipL/F5Q/FV8bMjBF2VR2A/lLly6xZs0aAgICuH37NnZ2dqxcuRJXV1caNWpUgZ8kh62trdp4a+N5rVAoCAwMrHW5BpV1LlfbYFCWGkSloU2p+KL0Cmsg79Z3nFoD+e3fb8bHx6fMDeQzMjLYvn07fn5+7N+/n8aNG+Pm5oaHh0eVL3esjed1bq5BcnIyJiYmmh5OpavMcxmqcTAA9VT8kmoQJd1/yLU78dy6mwjA+Ws3gJzKpS1MTbQqFV+UTmU1kD9z5gx+fn6sX7+epKQk+vbty7p163BxcaFBg/LfyYqyyd/XQNuDQWWdy2pU1VRsbKyqZcuWquYmTVSPf/9ZFbpioQoo8DX2tZdV2ZF7VWs+er/Q1z+e4KZ6/PvPqpbNmqqmTZum6Y8lqkhQUJBKR0dHNWbwANXD0B2q7Mi9JX49DN2hGjN4gEpHR0cVFBSkdryUlBSVv7+/yt7eXgWomjZtqpo9e7bq3LlzGvqEIj4+XgWotm7dqumhVKqKPpeLUi1XE+VGQRMjQ24m3M3LMyivbeEHcJnrRVRUlNY/VBP/ZK279HMgYN6sQqdQFqzbxH+/W8u7I95gyczJedvzZ6fHxMRw//59fH192bhxIykpKQwcOBAPDw+GDRtG3bp1q/JjiaeoVCqMjIyYP38+77//vqaHUymKqsDw9GpKXfvBhb7ftr0V567dLFWlhWo30Zhbh8ilnwN/bvbDyU7JBz5+pKall+t4UoOo9imsgXx+R8+ex/fHPdhYWRZ4LbeBfHPjxnSzs6N79+7s3r2bmTNn8tdff7F3715cXFwkEFQDtSHXoKgKDE+79VOw2pf/f99HR0eHtfNmY25izERPzxJ/VrUKBrGxsXh4ePBK9xdJeviQdiPGExYVw407CXmp+E8yM/nPCn9s3CZj5PQ6LYeOYuxnX3ErIbHA8bQ1FV8UragG8rlSHqUx+lNvVv/fexg3NCr0GIb1DVg03YMHDx+ydOlSrly5wmeffZY3Ry2qD20OBvnPZWfH3nhNGsdwxz6F7tvC1ETta+fvkTjZKunSVoH3tPGEhYcTHR1d7M+rVsGgqCg41WVoXg2ihOT7HD9/kY/cRxG11oetC+Zx4fpNXp/zqdqxpAZR7VRS1vq0RSt4zaEHLxdR3TNXbgP52NhY9PSK7j8sNEubg0FpKjAU5k5SMj8fPML4oYOAf87lgICAYt9XbVYTFVeHqO8LXbHr0E6tBlH+VPxl779DzwnvcS0uHgszU3YeiOQDH3/iku5pZSq+KFpxDeQ3/RpO9PmLHFmzrMTjaFMDeW2mUCjYsGGDVuYaFHcuF2fd7n00bFCf4X//DS3tuVxtgkFJUfDpGkQtm5oxoNsLKK3bcDPhLjrA/61Yw+8xp7iZkMjzrZ6T8tS1UFFZ69fvJDBj8XeELP0Cg3qlm+/Xlgby2szS0pKHDx9qZa5BWSsw5ArYFcKoQf3VzvPSnMvVJhiUJgpatbJgv89Cos/HEvDTr/xx5hyb9oXz+Ekmuro6XLx5kzf69ebKrTjuZGRJIKhlistaj/ozlvjke3Rzn5a3LSsrm99OnGbF1p2kR+wqMB0kWevVn7bmGpS3AsPvJ05z/toNNnl9qLa9NOdytQkGZYmCtu2tsW1vzZPMTEb893OuxcUTttKbRoaGgNQhqq2Ky1of0O0FTgZ+p7Zt/Odf06F1K+aMHlHocwHJWq/+8gcDbVotWN4KDGt27cWugzVKa/VS/qU5l6tFMChPFHySmcnI/37B5Vtx7PdZmBcIQK7oaqv09HSea2lRaAP5hoYN6NJWobbN0MAAk0aNCmzPJVnr1Z+pqSmGhoZa+RC5LBUYAB6kpvJD6O8smj6xwLFKcy5Xi7+UZY2CuYEg9sZNfl22ANPG6oXA5Iqudjl9+jQzZsygZcuWXPrrMiF/RJGZmfVMx8xtIN/L3r6CRikqgzbnGtg7OLDvWAyZmVkc+/MCtmOnYjt2KgCzlq3GduxUPvFdn7f/pl8jUKnAdaCj2nFKey5XizsDKH0UtDAz5a0PvYg+f5Fdi/5HVnY2cYlJAJg0akjdOnXkiq4WSElJYfPmzfj5+XH48GGaNWuGh4cHvXr1Yvjw4QUayBcmbOVXRb6mbQ3ktZlCoeDy5cuaHkaFc3d3x8fHJ+9czo7cW+z+E994jYlvvFZge2nP5WpTjmL69Ols/34zl7eu5cDJ0/Sf+p8C+4x97WU+8RhNm+HjCj1G6IqF9LHpguWb43AeMZLly5dX8qhFVVKpVBw9ehQ/Pz82btxIamoqgwcPxsPDg6FDh1KnTh0AaSBfy0ybNo2IiAhOnTql6aFUuKo8l6vNncHLL79c6ihY3Gvbwg/IFZ2WSU5OJjAwED8/P06ePEmrVq2YPXs27u7uPP/88wX2X+3ri42NDVO8lxdZm6go+bPWQyRrvUZQKBSsW7dOK3MNqvJcrhaT6sHBwbi6umJoYMDs5aulDpFApVIRERHB6NGjMTc35/3338fKyoo9e/Zw+fJlPvnkk0IDAfzTQD43a72055NkrddMCoWClJQUkpKSND2UCleV57LGg0H+wnQHfRcTl3gvrw5RWUgdIu1w584dvL29ad++PY6Ojhw5coT//e9/3Lhxg61btzJ48OBSlYdwdXUlMDCQLRGHUI6ZwrbwA0U+VM7MzGJb+AGUY6awJeKQZK3XMPmXl2qjqjqXNfrMoKjyrABjBg9g5ZzpGNY34FO/DWz+NYLr8QnUrVMHu/ZWeE0eR8/OHYCcKDjFezmBIaHyH7kGysrK4pdffsHPz4+dO3eir6+Pi4sLHh4evPTSS8906y8N5LXf3bt3adq0KVu2bOHNN9/U9HAqTWWfyxoNBv2dnLh28QLeUycQdT4W2/ZWuMz1YsZIZ1bt2I25mQne0yaQmpaBuakxbVqak5aRweJN29kS+jvnNvoReeYss5b6En//Qdm6+ohSq6x8jWvXrrFmzRrWrFnD9evXsbGxwdPTEzc3N4yNjSv0Z+VvIH/q9Gm1BvK97O1rRQN5baVSqWjYsCGfffYZs2bN0vRwKl1lncsaCwZRUVF069atQOMaXfvBbPvyY7q0UTBp4VLComLU6hA1NjLkTmIy/121FtPGjUi8/wA9XV22btvG66+/romPonUqs3n8kydP2LVrF76+voSEhGBoaIirqyuenp5069atyh4ASkKidunSpQtOTk61cgVhRZ3LGltNVFJhusLqEG3eH0HG4yfo6emip6vL6y/ZM+n11xj+oRf79u2TYPCMKrPh9oULF/D392ft2rXEx8fTq1cvfH19GTlyJEZGhfcVqEwSCLSLpaWl1j4zKElFncsaCwalLc+aW4fopwN/4PrxAh7rZNLc2JjtCz+me6f2AFJquAJURsPttLQ0tm7dip+fHxERERgbG/P2228zYcIEunbtWtkfSdQiCoWC8PBwTQ+jRtPY5dHpM2dQWrct9f5OdkqOr1vJwdXfMKiXHSM/+oL4pHtATnnWU6dPV9JItV/+FV0xG1bi7Ni7yCCtr6+Hs2NvYjasxKWfA25ubgQHB6vtExMTw/Tp07GwsGDMmDHo6uoSHBzMrVu3WLJkiQQCUeFyS1JUkxzaGkkjdwblKUxnWN8Aq1YWWLWyoFeXjrR7azz+u/Yyd+y/pTDdM8htNTp6UP+8pJZP/TbwP/8gtf2amxhz++eNed8b1jcgYF7OwzoPDw86derEkSNH8PPz4+jRozRv3pzJkyczYcIEWZ0jKl3+XANTU1NND6dG0kgwKG951vxUKhUZT54AUpjuWRTVPL5zm9b8umxB3vd6hfxuc5vH/x5zmh49upOVlc2rr77K9u3bGTJkSF55CCEqW/5cAwkG5aOxZwalLUxn2rgRn6/dyLC+vTA3NSHxwQNWbv2JGwl3eat/X0BKDZdX/lajT9c90dfTo4Vpyc1CDOsbsOhdT1zmevHzzz/z2msFC2UJUdnyBwM7OzvNDqaG0lgwsHdwYPv3m/LKs+YvTDdr2WogpzDdt3Pe5fzV67js3sfd+w8wbdyQ7h3b8du3i+jcRpFXntV5xEhNfZQaq7gVXbHXb9Jy6Cjq1alDz84d+HzyONq0NC/0OLkNt/fs2SPBQGiEiYkJRkZGWlm9tKpoLBi0aNGCm/F3S1WYbuuXHxf5mpQaLr+iVnT17NyBdR9/QLtWLbmTlMznazfSe+L7nA5eVaB3BEjzeKF52tzXoKpoZJI9ODiYefPmYW5mwgfLfaUwnYYUtaLrVfvuvOnUh65Wlrzcw5afvp4PwLrdvxZ5LFnRJTRNgsGzqfJgkH/1StgKb24nJkthOg0oy4ouw/oGdG2rIPb6rSL3yb+iSwhNkGDwbKo8GEyaOBFjowYk3LuP09Q5pGVksGHv/iLLs076cim69oNZsml73rbUtHTGzl8kpYafQVlWdGU8fsy5K9cxL+aBsqzoEpomuQbPpkr/5x49epSw8HDchwzEtoMVy2dNAWDGSGe2hB1AOeYdtfKsOyIOceTseSzMcpaK5ZZntRk9iY2/hOHl5SWF6Z5B/hVd+c1e5ktE9Eku34rjjzN/8taHn/Mg9RFjX3u5yGPJii6haQqFgtTUVBITEzU9lBqpUh8gF1bwTFdXhz2RR7Hv2gmFeXMAXnqxK1PeHMqkhUtxmetFy6Zm2HfpwK9HjvP+qOEs2bSd4JAwvg7eys2EuzjZKnmU/oTbt29X5vC1Xs6Krs1kZmapPUS+mXCXUZ98yd17D2japDG9unQg0m8xrf/+93qarOgS1UH+5aVmZmaaHUwNVClVSwsreKa0bqtW8Gzf0RPcTLgLwIrZ03jnzX8BEH0+ljW7fmHDnn08ysggKytnDrpVczOG9XXA/V+vYNvemnH/W8TZ+GSOHjtW0cOvNaKjo7GzsytQObastoUfwGWuF1FRUfIgX2hMYmIiZmZm/PDDD7i4uGh6ODVOhd8ZlLXg2Ztz5zNzyXc0aWiI60AnbNtbE3I4il5dOrJ3yeeoVCravjmO90Y6M+PfznnvV1q3YdP+tRU9/FrF1tYWJ0dHPvDxZ2BPu3I33JYVXaI6MDExoWHDhvIQuZwq9JlBeQqeAdh37cToT70JDgkj6s9Yln3/IwEfzUJHR6fIB5KNjQx5/PgxTo6OXLx4sSI/Rq2y2teX20myokvUfJJr8GwqLBjExsYyYcIEXun+IkkPH9JuxHh07QezI+KQ2n7u8xehaz847wvg1t1ERg/qj+eCJWwPP0h88j1aO4+hTp/XqNPnNa7GxTN7uS+Wzm/nHed+Sip19fW5djEWGxsbNm7ciCg7aR4vtIkEg/J7pmmi/A+IT8ScICsrm9CoGMyaNOKFdm3z+hk/bXCvbqz56H0ALP41io/cRzHcsTcHT53ltxOniNnwrfr+M/7L6FcH4D7klbxtMbF/YWNtSdiKr5jivRw3NzdUKhWjRo16lo9UK7m6uqJSqfDw8ODgqXN4TxvPsD72RU7v7TwQyRyfNdxOSpae06JaUSgUhIaGanoYNVK5gkHhHbE8CzwgBvjYdz1d2iiwamWR9349XV3iEpPzvr977z6x12/yRj97vgneRv9pc7h77wHbvvyYN/o5UEdfjxYmxrRsasa0RSv48bdD3ExIxLihEev37FMrpdyjRw+5Si2HUaNG0aNHDyZ65hSdK03D7RBpHi+qmfy5BlXVQlVblDkYlOUBcd2+Q0hIvo9yzDv4fTgD14FOAIQfP4nt2Kl5++YWputv9wING9SnW8d27I0suEpo5tJVhEfF4PnGq3zqG8g7b/6Ld79ZiYWZKSvnTOfgqXNM9PQkNCysrB9LkDNlFBoWptZwe3PoOrWG284jRkrzeFFt5c81kOWlZVOmYJD7gHj0oP6snDO92NUnuQFi8YxJ7Dl0lNGfeqNSwWD77rj070vrFs25fCuOj33Xk5mVxbGA5dSrWzdnyeiVq2rHurx9PQBd3SbhOtCR9bv342SnxGvSOPZGHuPYuQu8/pI93tPG4zLXi+joaPlj9QxsbW3Vfn/SNEjUFLm5BpcvX5ZgUEal/h+eW1OopAfEAOeuXOP1Dz4BYLzXN5y/dgPnlxzwXLAEu/bWDOndky5tFQzt24vd38znwrWb/HzoCPB3wbNLVwodQ++unfh260/cSkjkuznvEhYVw4XrNxnUK6d+eW4p5YCAgLL+HkQxJBCImiJ/4pkom1L/L8/tiDXJeQhK6zZ5pSSedunGLfpOmkX71q0A+Oa9ScwbP4pF73pibmbCpIVL1fY3NzOldYtmeUXQGhsZkvH4SYHjpqalk5KWTuKDh6Q/fkznURN5deZHrJg9lT7KnDIIUkpZiNrN2NhYcg3KqVTTRPk7Yjk79i42W/WjVet4zaE73tM8WBS0hRamxgzp3RMA72kTcqZxzsdi294agMT7D7gen5BXBO1+Sir16tbJCwj/rF7x51pcPOamJnz3n3dpbd6M346fZuqiFZibmvByj5xpDaV1GzaHriv/b0QIUWNJrkH5lerOoLiOWPllZ2fz88E/aNigAQ6eMwGYsfhbFm/cxrW4ePrbvoBR/fosWLeZK7fjCI+OYdjsTzBr3Bjnfg5AzpLR3MJ0y77fgeXwsbjM9aJVs6boAKvnvsfQvr2wsWrDtLeGMWLAS3wdvDVvDFJKWYjaTYJB+ZTqzqCojlhPi0++R0paOt9u+ylv27U7Ccxatppf/ohi25cf09CwPj/+FsnO3w9jbmaCk60Nm7w+pKFhAzIzswj54xh3ku4BcD0+gTf65dQjsnrOgiYvv1lg/lpPV5fsfOWVpJSyELWbQqFg//79mh5GjVOqv5hFdcR6WnZ2zh9l11ccyY7cm/c1tE9PjBsZUd+gHrNHuaCnp0vG7z9xZft6AubNplXzpgBs3h/BnaR7BH46B4Apw4cyYeggzBo3ppGhIf1e7MocHz/Co2O4fCuOtT//woY9+3nj77sKkFLKQtR20tegfEoMBmXpiGXWpBH6enp0tHxebXsHxfNci0sA/nlA/PQ0TmpaOnOW59S3Gf2pN5CTf2A7diqf+OYsLd04fy7dO7Zj9CfedHadyML13+M1eSyTnYcA/5RS7mVvX+JYhRDaSaFQ8OjRI+7evavpodQoJU4TlaUjVt06dejesR0Xrt1Q2x577SatWzQD/nlAnH8aJzs7m8kLl5H0IIUL369Ry1bOr4WpCWs+mlXkz995IJKb8Qm4u7uXOFYhhHaytLQEcpaXNm3aVMOjqTlKNU2UvyNWyqM0Tly4xIkLOd9fvhXHiQuXuBYXD8BsNxc27/sN3x/3cPH6LXx+2Mmug4fz+hXExP5F17aKvGPnFjwLDgmlsZEh5mZFt1YsjpRSFkKA5BqUV6mCgb2DA/uOxZCZmcWxPy9gO3ZqXjmJp6dynB178+2c6XwV+AM2oyfjv2svW76YRx9ll5xpnGMn6Nm5Y14LS+WYKWyJOMTX33zDw/QMKaUshHgmTZo0oVGjRhIMyqhUq4nc3d3x8fFh14HDODv2Jjtyb7H7jx86iPFDBxXYvvNAJDcT7nLlVhyWb44rUPCsRYsWuLm5AZRY7iJXalo6U7yXExgSSlBQkBROE6KWk1yD8inVnUH+jlilrXf/tNS0dN5fsgp9fX3uZGThPGIkUVFR7A8NzfsD7urqSmBgIFsiDqEcM4Vt4QfIzMwq9HhP31lIKWUhRC4JBmVX6h7IFy9exMbGBpd+DgTMm1WmdfzZ2dm4z/+aLRGHOHnyZIlX70+XyC6plPIqKaUshMjnvffeY9++fZw6dUpyjkqp1MEAYOPGjbi5uZWqammup6dxynL1nr+U8qnTp9VKKfeyt5dSykIINbl/M3b++CM3btwgW6WiXr16dOncGXsHB/mbUYwyBQNQ72dQlo5Y/v7+zzyNI6WUhRCFKazhltK6rXrDrWM5swlOjo6s9vWV2YSnlDkYgEzjCCGqj/wXqF9Nm1Bsw61dBw7zgY9/hV2gapNyBYNcMo0jhNCksjTcypV/6jowMFD6pv/tmYLB02QaRwhRVWJjY1EqlUUualm5dReLgrZwOzGJzpatWTxjMn1fyKlbVtZFLbVBhQYDIYSoKv2dnLh28QIn1q8scEeweV8Eb3/2FSs+mEpvm86s2r4b/117ORO8muf/Lo2TmpaOcswUWlu3k77plKHTmRBCVBe5Dbe8p04odGpo8cZtjB86CI9hr9JR8TxLZk6mVbOmauX1Desb4D1tPGHh4URHR1fl8KslCQZCiBqnuIZbj588Iep8LAN7qD+vfKWnLZGnzqltk77p/5BgIISocYpruHX33gOysrJpbmKstr25sTFxSUlq26Rv+j8kGAghapzSNNzS0VH/XoUKHXQK7Ke0bsOp06crcng1kgQDIUSNUlLDLbMmjdDT0yUuMVlte3zyvQJ3CyB903NJMBBC1CglNdyqW6cOdu2t+fXocbXt+44cx75rxwL7S9/0HKUqYS2EENVJ/oZbhZnpOpy3P/uKbh2sse/akdU79nDtTnxei9z8pG96DgkGQogax97Bge3fbyYzM6vQh8gjX+5H4v0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cpts = H.connected_components()\n", " num_cpts = len( cpts)\n", " H_verts = H.vertices()\n", "\n", " H_roots = [V[index] for index in H.vertices()]\n", " M1 = root_intersection_matrix(H_roots, labels = H_verts, bil_form=dot)\n", " rk = matrix(ZZ, H_roots).rank()\n", " order = len(H.vertices())\n", " if rk < 16:\n", " continue\n", " \n", " # pp_root_matrix(M1, labels = H_verts, bil_form=dot)\n", " if is_elliptic_matrix(M1):\n", " # print(f\"Elliptic of rank {rk} (Type III)\")\n", " # print(f\"Vertices: {H_verts}\")\n", " print(\"----------------------------------\")\n", " continue\n", " elif is_parabolic_matrix(M1):\n", " if rk >= 17:\n", " print(f\"Parabolic of rank {rk} (Type II)\")\n", " print(H_verts)\n", " show(H)\n", " else:\n", " print(\"Non-maximal parabolic found\")\n", " continue\n", " else:\n", " # print(f\"Neither elliptic nor parabolic; rank {rk}\")\n", " continue\n", " show(M1)" ] }, { "cell_type": "code", "execution_count": null, "id": "1c06506b-c04f-448a-b41a-3c6d3b42dd57", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "c3d4e191-2576-4a87-8fbf-837779743b46", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 52, "id": "03de6959-adab-4698-b56a-468c627e34c9", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\\(\\displaystyle \\mathrm{True}\\)" ], "text/latex": [ "$\\displaystyle \\mathrm{True}$" ], "text/plain": [ "True" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[0,1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18] in small_subgraph_sample" ] }, { "cell_type": "code", "execution_count": null, "id": "bbacbbc4-f131-42aa-a9bf-ebffc1583bca", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 10.1", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, 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