{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "%load_ext pycodestyle_magic\n", "\n", "# display full output, not only last result, except ended with semicolon\n", "from IPython.core.interactiveshell import InteractiveShell\n", "InteractiveShell.ast_node_interactivity = 'all';\n", "from IPython.display import Image, SVG" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import path\n", "from cagosig import import_sage\n", "cs = import_sage('cable_signature', package='cagosig', path=path.module_path)\n", "sg = import_sage('signature', package='cagosig', path=path.module_path)\n", "m = import_sage('main', package='cagosig', path=path.module_path)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Other cables" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "**********\n", "Knot sum:\n", "T(2, 3; 2, 5; 2, 11) # -T(2, 5; 2, 11) # T(2, 7; 2, 11) # -T(2, 3; 2, 7; 2, 11)\n", "[ characters ] sigma value\n", "[0, 0, 1, 1] 4\n", "[0, 0, 2, 2] 4\n", "[0, 0, 3, 3] 4\n", "[0, 0, 4, 4] 4\n", "[0, 0, 5, 5] 0\n", "[0, 0, 6, 6] 0\n", "[0, 0, 7, 7] 4\n", "[0, 0, 8, 8] 4\n", "[0, 0, 9, 9] 4\n", "[0, 0, 10, 10] 4\n" ] }, { "data": { "text/plain": [ "False" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "knot_formula = \"[[k[0], k[1], k[3]],\" + \\\n", " \" [-k[1], -k[3]],\" + \\\n", " \" [k[2], k[3]],\" + \\\n", " \" [-k[0], -k[2], -k[3]]]\"\n", "# q_vector = (3, 5, 7, 13)\n", "q_vector = (3, 5, 7, 11)\n", "\n", "template = cs.CableTemplate(knot_formula, q_vector=q_vector, verbose=True)\n", "cable = template.cable\n", "# cable.plot_all_summands()\n", "cable.is_function_big_for_all_metabolizers(invariant=cs.SIGMA)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Cables with 8 direct summands " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "formula_1 = \"[[k[0], k[5], k[3]], \" + \\\n", " \"[-k[1], -k[3]], \" + \\\n", " \"[k[2], k[3]], \" + \\\n", " \"[-k[0], -k[2], -k[3]]]\"\n", "formula_2 = \"[[k[4], k[1], k[7]], \" + \\\n", " \"[-k[5], -k[7]], \" + \\\n", " \"[k[6], k[7]], \" + \\\n", " \"[-k[4], -k[6], -k[7]]]\"\n", "\n", "\n", "\n", "cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", "cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", "cable_template = cable_template_1 + cable_template_2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Relatively small cables " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T(2, 5; 2, 17; 2, 41) # -T(2, 13; 2, 41) # T(2, 19; 2, 41) # -T(2, 5; 2, 19; 2, 41) # T(2, 7; 2, 13; 2, 43) # -T(2, 17; 2, 43) # T(2, 23; 2, 43) # -T(2, 7; 2, 23; 2, 43)\n", "T(2, 5; 2, 17; 2, 41) # -T(2, 13; 2, 41) # T(2, 19; 2, 41) # -T(2, 5; 2, 19; 2, 41) # T(2, 7; 2, 13; 2, 43) # -T(2, 17; 2, 43) # T(2, 23; 2, 43) # -T(2, 7; 2, 23; 2, 43)\n" ] } ], "source": [ "q_vector = (5, 13, 19, 41,\\\n", " 7, 17, 23, 43)\n", "cable_template.fill_q_vector(q_vector=q_vector)\n", "cable = cable_template.cable\n", "print(cable.knot_description)\n", "\n", "q_vector_small = (3, 7, 13, 19,\\\n", " 5, 11, 17, 23)\n", "cable_template.fill_q_vector(q_vector=q_vector)\n", "cable = cable_template.cable\n", "print(cable.knot_description)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": true }, "outputs": [], "source": [ "# cable.is_signature_big_for_all_metabolizers()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Slice candidate" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T(2, 5; 2, 71; 2, 347) # -T(2, 67; 2, 347) # T(2, 61; 2, 347) # -T(2, 5; 2, 61; 2, 347) # T(2, 11; 2, 67; 2, 367) # -T(2, 71; 2, 367) # T(2, 79; 2, 367) # -T(2, 11; 2, 79; 2, 367)\n" ] } ], "source": [ "\n", "cable_template.fill_q_vector()\n", "# print(cable_template.q_vector)\n", "# print(cable_template.knot_formula)\n", "\n", "slice_canidate = cable_template.cable\n", "print(slice_canidate.knot_description)\n", "sf = slice_canidate(4,4,4,4,0,0,0,0)\n", "sf = slice_canidate(4,1,1,4,0,0,0,0)\n", "\n", "\n", "# cable.is_signature_big_for_all_metabolizers()\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "\n", "\n", "# knot_formula = \"[[k[0], k[1], k[4]], [-k[1], -k[3]],\\\n", "# [k[2], k[3]], [-k[0], -k[2], -k[4]]]\"\n", "\n", "# knot_formula = \"[[k[3]], [-k[3]],\\\n", "# [k[3]], [-k[3]] ]\"\n", "\n", "# knot_formula = \"[[k[3], k[2], k[0]], [-k[2], -k[0]],\\\n", "# [k[1], k[0]], [-k[3], -k[1], -k[0]]]\"\n", "\n", "# knot_formula = \"[[k[0], k[1], k[2]], [k[3], k[4]],\\\n", "# [-k[0], -k[3], -k[4]], [-k[1], -k[2]]]\"\n", "\n", "# knot_formula = \"[[k[0], k[1], k[2]], [k[3]],\\\n", "# [-k[0], -k[1], -k[3]], [-k[2]]]\"" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T(2, 5; 2, 71; 2, 347) # -T(2, 67; 2, 347) # T(2, 61; 2, 347) # -T(2, 5; 2, 61; 2, 347) # T(2, 11; 2, 67; 2, 367) # -T(2, 71; 2, 367) # T(2, 79; 2, 367) # -T(2, 11; 2, 79; 2, 367)\n" ] }, { "data": { "text/plain": [ "127349" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "formula_1 = \"[[k[0], k[5], k[3]], \" + \\\n", " \"[-k[1], -k[3]], \" + \\\n", " \"[k[2], k[3]], \" + \\\n", " \"[-k[0], -k[2], -k[3]]]\"\n", "formula_2 = \"[[k[4], k[1], k[7]], \" + \\\n", " \"[-k[5], -k[7]], \" + \\\n", " \"[k[6], k[7]], \" + \\\n", " \"[-k[4], -k[6], -k[7]]]\"\n", "\n", "\n", "\n", "cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", "cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", "cable_template = cable_template_1 + cable_template_2\n", "\n", "cable_template.fill_q_vector()\n", "# print(cable_template.q_vector)\n", "# print(cable_template.knot_formula)\n", "\n", "slice_canidate = cable_template.cable\n", "print(slice_canidate.knot_description)\n", "sf = slice_canidate(4,4,4,4,0,0,0,0)\n", "sf = slice_canidate(4,1,1,4,0,0,0,0)\n", "\n", "\n", "slice_canidate.q_order\n", "# slice_canidate.is_signature_big_for_all_metabolizers()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T(2, 11; 2, 53; 2, 347) # -T(2, 53; 2, 347) # T(2, 61; 2, 347) # -T(2, 7; 2, 61; 2, 347) # T(2, 7; 2, 71; 2, 367) # -T(2, 71; 2, 367) # T(2, 79; 2, 367) # -T(2, 11; 2, 79; 2, 367)\n" ] }, { "data": { "text/plain": [ "127349" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "-4" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "formula_1 = \"[[k[0], k[5], k[3]], \" + \\\n", " \"[-k[5], -k[3]], \" + \\\n", " \"[k[2], k[3]], \" + \\\n", " \"[-k[4], -k[2], -k[3]]]\"\n", "formula_2 = \"[[k[4], k[1], k[7]], \" + \\\n", " \"[-k[1], -k[7]], \" + \\\n", " \"[k[6], k[7]], \" + \\\n", " \"[-k[0], -k[6], -k[7]]]\"\n", "\n", "\n", "\n", "\n", "cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", "cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", "cable_template = cable_template_1 + cable_template_2\n", "cable_template.fill_q_vector()\n", "\n", "slice_canidate = cable_template.cable\n", "print(slice_canidate.knot_description)\n", "\n", "slice_canidate.q_order\n", "# slice_canidate.is_signature_big_for_all_metabolizers()\n", "sigma = slice_canidate.get_sigma_as_function_of_theta()\n", "# sigma((0, 6, 6, 0, 0,0,0,0))\n", "# 13450/83\n", "sigma((9, 9, 9, 9, 0,0,0,0))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T(2, 11; 2, 71; 2, 313) # -T(2, 61; 2, 313) # T(2, 313) # -T(2, 7; 2, 67; 2, 313) # T(2, 7; 2, 61; 2, 347) # -T(2, 347) # T(2, 67; 2, 347) # -T(2, 11; 2, 71; 2, 347)\n" ] } ], "source": [ "formula_1 = \"[[k[0], k[5], k[3]], \" + \\\n", " \"[-k[1], -k[3]], \" + \\\n", " \"[ k[3]], \" + \\\n", " \"[-k[4], -k[6], -k[3]]]\"\n", "\n", "formula_2 = \"[[k[4], k[1], k[7]], \" + \\\n", " \"[ -k[7]], \" + \\\n", " \"[k[6], k[7]], \" + \\\n", " \"[-k[0], -k[5], -k[7]]]\"\n", "\n", "\n", "\n", "\n", "cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", "cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", "cable_template = cable_template_1 + cable_template_2\n", "\n", "cable_template.fill_q_vector()\n", "# print(cable_template.q_vector)\n", "# print(cable_template.knot_formula)\n", "\n", "slice_canidate = cable_template.cable\n", "print(slice_canidate.knot_description)\n", "sf = slice_canidate(4,4,4,4,0,0,0,0)\n", "sf = slice_canidate(4,1,1,4,0,0,0,0)\n", "# slice_canidate.is_signature_big_for_all_metabolizers()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T(2, 43; 2, 191) # -T(2, 37; 2, 191) # T(2, 191) # -T(2, 5; 2, 41; 2, 191) # T(2, 5; 2, 37; 2, 211) # -T(2, 211) # T(2, 41; 2, 211) # -T(2, 43; 2, 211)\n" ] }, { "data": { "text/plain": [ "40301" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "formula_1 = \" [ [k[5], k[3]], \" + \\\n", " \" [ -k[1], -k[3]], \" + \\\n", " \" [ k[3]], \" + \\\n", " \"[-k[4], -k[6], -k[3]]]\"\n", "\n", "formula_2 = \"[[k[4], k[1], k[7]], \" + \\\n", " \"[ -k[7]], \" + \\\n", " \"[k[6], k[7]], \" + \\\n", " \"[-k[5], -k[7]]]\"\n", "\n", "\n", "\n", "\n", "cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", "cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", "cable_template = cable_template_1 + cable_template_2\n", "\n", "cable_template.fill_q_vector()\n", "# print(cable_template.q_vector)\n", "# print(cable_template.knot_formula)\n", "\n", "slice_canidate = cable_template.cable\n", "print(slice_canidate.knot_description)\n", "sf = slice_canidate(4,4,4,4,0,0,0,0)\n", "sf = slice_canidate(4,1,1,4,0,0,0,0)\n", "slice_canidate.q_order\n", "# slice_canidate.is_signature_big_for_all_metabolizers()\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "sf = slice_canidate()\n", "sf = sf[2]" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sf.plot()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T(2, 17; 2, 83) # -T(2, 11; 2, 83) # T(2, 83) # -T(2, 13; 2, 83) # T(2, 11; 2, 103) # -T(2, 103) # T(2, 13; 2, 103) # -T(2, 17; 2, 103)\n" ] }, { "data": { "text/plain": [ "8549" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "formula_1 = \"[ [k[5], k[3]], \" + \\\n", " \"[ -k[1], -k[3]], \" + \\\n", " \"[ k[3]], \" + \\\n", " \"[ -k[6], -k[3]]]\"\n", "\n", "formula_2 = \"[[ k[1], k[7]], \" + \\\n", " \"[ -k[7]], \" + \\\n", " \"[ k[6], k[7]], \" + \\\n", " \"[ -k[5], -k[7]]]\"\n", "\n", "\n", "\n", "\n", "cable_template_1 = cs.CableTemplate(knot_formula=formula_1)\n", "cable_template_2 = cs.CableTemplate(knot_formula=formula_2)\n", "cable_template = cable_template_1 + cable_template_2\n", "\n", "cable_template.fill_q_vector()\n", "# print(cable_template.q_vector)\n", "# print(cable_template.knot_formula)\n", "\n", "slice_canidate = cable_template.cable\n", "print(slice_canidate.knot_description)\n", "sf = slice_canidate(4,4,4,4,0,0,0,0)\n", "sf = slice_canidate(4,1,1,4,0,0,0,0)\n", "slice_canidate.q_order" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "# slice_canidate.is_sigma_big_for_all_metabolizers()\n", "# slice_canidate.is_signature_big_for_all_metabolizers()\n", "# slice_canidate.is_function_big_for_all_metabolizers()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "slice_canidate.is_function_big_for_all_metabolizers(invariant=cs.SIGMA)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "slice_canidate.is_function_big_for_all_metabolizers(invariant=cs.SIGNATURE)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/plain": [ "-4" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sigma = slice_canidate.get_sigma_as_function_of_theta()\n", "sigma((0, 6, 6, 0, 0,0,0,0))\n", "# 13450/83\n", "sigma((9, 0, 0, 9, 0,0,0,0))" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0: 0, 49/2822: -1, 1/34: 2, 61/1826: 1, 117/2822: -1, 1/22: -2, 105/1826: 1, 215/2822: -1, 3/34: 2, 283/2822: -1, 227/1826: 1, 381/2822: -1, 3/22: -2, 5/34: 2, 271/1826: 1, 449/2822: -1, 547/2822: -1, 7/34: 2, 393/1826: 1, 615/2822: -1, 5/22: -2, 437/1826: 1, 713/2822: -1, 9/34: 2, 781/2822: -1, 559/1826: 1, 879/2822: -1, 7/22: -2, 11/34: 2, 603/1826: 1, 947/2822: -1, 1045/2822: -1, 13/34: 2, 1113/2822: -1, 725/1826: 1, 9/22: -2, 769/1826: 1, 1211/2822: -1, 15/34: 2, 1279/2822: -1, 1543/2822: 1, 19/34: -2, 1611/2822: 1, 1057/1826: -1, 13/22: 2, 1101/1826: -1, 1709/2822: 1, 21/34: -2, 1777/2822: 1, 1875/2822: 1, 1223/1826: -1, 23/34: -2, 15/22: 2, 1943/2822: 1, 1267/1826: -1, 2041/2822: 1, 25/34: -2, 2109/2822: 1, 1389/1826: -1, 17/22: 2, 2207/2822: 1, 1433/1826: -1, 27/34: -2, 2275/2822: 1, 2373/2822: 1, 1555/1826: -1, 29/34: -2, 19/22: 2, 2441/2822: 1, 1599/1826: -1, 2539/2822: 1, 31/34: -2, 2607/2822: 1, 1721/1826: -1, 21/22: 2, 2705/2822: 1, 1765/1826: -1, 33/34: -2, 2773/2822: 1, 1: 0." ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "_, _, sf = slice_canidate((1, 1, 0, 0, 0,0,0,0))\n", "sf" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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gIYIcAJIjyAEgOYIcAJIjyAEgOYIcAJIjyAEguf8HnIINaoEpLxEAAAAASUVORK5CYII=\n", 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