{ "cells": [ { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The pycodestyle_magic extension is already loaded. To reload it, use:\n", " %reload_ext pycodestyle_magic\n" ] } ], "source": [ "%matplotlib inline\n", "%load_ext pycodestyle_magic\n", "\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\n", "\n", "\n", "# magic functions that do not work in current ipython --version\n", "# \n", "# auto check each cell, E703 - \"statement ends with a semicolon\"\n", "# %flake8_on --ignore E703\n" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "import importlib\n", "\n", "def import_sage(module_name):\n", " \n", " importlib.invalidate_caches() \n", " sage_name = module_name + \".sage\"\n", " python_name = module_name + \".sage.py\"\n", "\n", " if os.path.isfile(sage_name):\n", " os.system('sage --preparse {}'.format(sage_name));\n", " os.system('mv {} {}.py'.format(python_name, module_name))\n", " if module_name in sys.modules:\n", " return importlib.reload(sys.modules[module_name]) \n", " return importlib.import_module(module_name, package=None)\n", "\n", "cs = import_sage('cable_signature')\n", "# sig = import_sage('signature')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Other cables" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T(2, 3; 2, 5; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 5; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "T(2, 7; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[0, 0, 1, 1] -12\n", "T(2, 3; 2, 5; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 5; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = 0\n", "T(2, 7; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[0, 1, 1, 0] -4\n", "T(2, 3; 2, 5; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 5; 2, 11), theta = 2\n", "pp = 85/11, satellite_part = -4\n", "T(2, 7; 2, 11), theta = 2\n", "pp = -85/11, satellite_part = -4\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "[0, 2, 2, 0] -8\n", "T(2, 3; 2, 5; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 5; 2, 11), theta = 2\n", "pp = 85/11, satellite_part = -4\n", "T(2, 7; 2, 11), theta = 2\n", "pp = -85/11, satellite_part = -4\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[0, 2, 2, 0] -8\n", "T(2, 3; 2, 5; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 5; 2, 11), theta = 2\n", "pp = 85/11, satellite_part = -4\n", "T(2, 7; 2, 11), theta = 4\n", "pp = -65/11, satellite_part = -12\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[0, 2, 4, 1] -13\n", "T(2, 3; 2, 5; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 5; 2, 11), theta = 3\n", "pp = 73/11, satellite_part = -4\n", "T(2, 7; 2, 11), theta = 3\n", "pp = -73/11, satellite_part = -8\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[0, 3, 3, 0] -12\n", "T(2, 3; 2, 5; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 5; 2, 11), theta = 4\n", "pp = 65/11, satellite_part = -8\n", "T(2, 7; 2, 11), theta = 4\n", "pp = -65/11, satellite_part = -12\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[0, 4, 4, 0] -20\n", "T(2, 3; 2, 5; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 5; 2, 11), theta = 5\n", "pp = 61/11, satellite_part = -8\n", "T(2, 7; 2, 11), theta = 2\n", "pp = -85/11, satellite_part = -4\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[0, 5, 2, 1] -13\n", "T(2, 3; 2, 5; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 5; 2, 11), theta = 5\n", "pp = 61/11, satellite_part = -8\n", "T(2, 7; 2, 11), theta = 5\n", "pp = -61/11, satellite_part = -12\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[0, 5, 5, 0] -20\n", "T(2, 3; 2, 5; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 5; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "T(2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[1, 0, 0, 1] -12\n", "T(2, 3; 2, 5; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 5; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = 0\n", "T(2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[1, 1, 0, 0] -4\n", "T(2, 3; 2, 5; 2, 11), theta = 2\n", "pp = -85/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 2\n", "pp = 85/11, satellite_part = -4\n", "T(2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "[2, 2, 0, 0] -12\n", "T(2, 3; 2, 5; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 5; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = 0\n", "T(2, 7; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[1, 1, 1, 1] -16\n", "T(2, 3; 2, 5; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 5; 2, 11), theta = 2\n", "pp = 85/11, satellite_part = -4\n", "T(2, 7; 2, 11), theta = 2\n", "pp = -85/11, satellite_part = -4\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[1, 2, 2, 1] -20\n", "T(2, 3; 2, 5; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 5; 2, 11), theta = 2\n", "pp = 85/11, satellite_part = -4\n", "T(2, 7; 2, 11), theta = 5\n", "pp = -61/11, satellite_part = -12\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[1, 2, 5, 0] -27\n", "T(2, 3; 2, 5; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 5; 2, 11), theta = 3\n", "pp = 73/11, satellite_part = -4\n", "T(2, 7; 2, 11), theta = 3\n", "pp = -73/11, satellite_part = -8\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[1, 3, 3, 1] -24\n", "T(2, 3; 2, 5; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 5; 2, 11), theta = 4\n", "pp = 65/11, satellite_part = -8\n", "T(2, 7; 2, 11), theta = 2\n", "pp = -85/11, satellite_part = -4\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[1, 4, 2, 0] -27\n", "T(2, 3; 2, 5; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 5; 2, 11), theta = 4\n", "pp = 65/11, satellite_part = -8\n", "T(2, 7; 2, 11), theta = 4\n", "pp = -65/11, satellite_part = -12\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[1, 4, 4, 1] -32\n", "T(2, 3; 2, 5; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 5; 2, 11), theta = 5\n", "pp = 61/11, satellite_part = -8\n", "T(2, 7; 2, 11), theta = 5\n", "pp = -61/11, satellite_part = -12\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[1, 5, 5, 1] -32\n", "T(2, 3; 2, 5; 2, 11), theta = 2\n", "pp = -85/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = 0\n", "T(2, 7; 2, 11), theta = 3\n", "pp = -73/11, satellite_part = -8\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[2, 1, 3, 1] -20\n", "T(2, 3; 2, 5; 2, 11), theta = 2\n", "pp = -85/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 2\n", "pp = 85/11, satellite_part = -4\n", "T(2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[2, 2, 0, 0] -12\n", "T(2, 3; 2, 5; 2, 11), theta = 2\n", "pp = -85/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 2\n", "pp = 85/11, satellite_part = -4\n", "T(2, 7; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[2, 2, 1, 1] -24\n", "T(2, 3; 2, 5; 2, 11), theta = 2\n", "pp = -85/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 3\n", "pp = 73/11, satellite_part = -4\n", "T(2, 7; 2, 11), theta = 4\n", "pp = -65/11, satellite_part = -12\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[2, 3, 4, 0] -31\n", "T(2, 3; 2, 5; 2, 11), theta = 2\n", "pp = -85/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 4\n", "pp = 65/11, satellite_part = -8\n", "T(2, 7; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[2, 4, 1, 0] -31\n", "T(2, 3; 2, 5; 2, 11), theta = 2\n", "pp = -85/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 5\n", "pp = 61/11, satellite_part = -8\n", "T(2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[2, 5, 0, 1] -17\n", "T(2, 3; 2, 5; 2, 11), theta = 3\n", "pp = -73/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "T(2, 7; 2, 11), theta = 5\n", "pp = -61/11, satellite_part = -12\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[3, 0, 5, 1] -31\n", "T(2, 3; 2, 5; 2, 11), theta = 3\n", "pp = -73/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = 0\n", "T(2, 7; 2, 11), theta = 2\n", "pp = -85/11, satellite_part = -4\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[3, 1, 2, 1] -16\n", "T(2, 3; 2, 5; 2, 11), theta = 3\n", "pp = -73/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = 0\n", "T(2, 7; 2, 11), theta = 5\n", "pp = -61/11, satellite_part = -12\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[3, 1, 5, 0] -23\n", "T(2, 3; 2, 5; 2, 11), theta = 3\n", "pp = -73/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 3\n", "pp = 73/11, satellite_part = -4\n", "T(2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[3, 3, 0, 0] -12\n", "T(2, 3; 2, 5; 2, 11), theta = 3\n", "pp = -73/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 3\n", "pp = 73/11, satellite_part = -4\n", "T(2, 7; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[3, 3, 1, 1] -24\n", "T(2, 3; 2, 5; 2, 11), theta = 3\n", "pp = -73/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 5\n", "pp = 61/11, satellite_part = -8\n", "T(2, 7; 2, 11), theta = 4\n", "pp = -65/11, satellite_part = -12\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[3, 5, 4, 0] -35\n", "T(2, 3; 2, 5; 2, 11), theta = 4\n", "pp = -65/11, satellite_part = -12\n", "-T(2, 5; 2, 11), theta = 2\n", "pp = 85/11, satellite_part = -4\n", "T(2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[4, 2, 0, 1] -13\n", "T(2, 3; 2, 5; 2, 11), theta = 4\n", "pp = -65/11, satellite_part = -12\n", "-T(2, 5; 2, 11), theta = 3\n", "pp = 73/11, satellite_part = -4\n", "T(2, 7; 2, 11), theta = 2\n", "pp = -85/11, satellite_part = -4\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[4, 3, 2, 0] -27\n", "T(2, 3; 2, 5; 2, 11), theta = 4\n", "pp = -65/11, satellite_part = -12\n", "-T(2, 5; 2, 11), theta = 3\n", "pp = 73/11, satellite_part = -4\n", "T(2, 7; 2, 11), theta = 4\n", "pp = -65/11, satellite_part = -12\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[4, 3, 4, 1] -32\n", "T(2, 3; 2, 5; 2, 11), theta = 4\n", "pp = -65/11, satellite_part = -12\n", "-T(2, 5; 2, 11), theta = 4\n", "pp = 65/11, satellite_part = -8\n", "T(2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[4, 4, 0, 0] -20\n", "T(2, 3; 2, 5; 2, 11), theta = 4\n", "pp = -65/11, satellite_part = -12\n", "-T(2, 5; 2, 11), theta = 4\n", "pp = 65/11, satellite_part = -8\n", "T(2, 7; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[4, 4, 1, 1] -32\n", "T(2, 3; 2, 5; 2, 11), theta = 4\n", "pp = -65/11, satellite_part = -12\n", "-T(2, 5; 2, 11), theta = 5\n", "pp = 61/11, satellite_part = -8\n", "T(2, 7; 2, 11), theta = 3\n", "pp = -73/11, satellite_part = -8\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[4, 5, 3, 0] -35\n", "T(2, 3; 2, 5; 2, 11), theta = 5\n", "pp = -61/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "T(2, 7; 2, 11), theta = 3\n", "pp = -73/11, satellite_part = -8\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[5, 0, 3, 1] -27\n", "T(2, 3; 2, 5; 2, 11), theta = 5\n", "pp = -61/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = 0\n", "T(2, 7; 2, 11), theta = 3\n", "pp = -73/11, satellite_part = -8\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[5, 1, 3, 0] -19\n", "T(2, 3; 2, 5; 2, 11), theta = 5\n", "pp = -61/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 2\n", "pp = 85/11, satellite_part = -4\n", "T(2, 7; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[5, 2, 1, 0] -23\n", "T(2, 3; 2, 5; 2, 11), theta = 5\n", "pp = -61/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 4\n", "pp = 65/11, satellite_part = -8\n", "T(2, 7; 2, 11), theta = 5\n", "pp = -61/11, satellite_part = -12\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[5, 4, 5, 1] -32\n", "T(2, 3; 2, 5; 2, 11), theta = 5\n", "pp = -61/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 5\n", "pp = 61/11, satellite_part = -8\n", "T(2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "-T(2, 3; 2, 7; 2, 11), theta = 0\n", "pp = 0, satellite_part = 0\n", "**********\n", "[5, 5, 0, 0] -16\n", "T(2, 3; 2, 5; 2, 11), theta = 5\n", "pp = -61/11, satellite_part = -8\n", "-T(2, 5; 2, 11), theta = 5\n", "pp = 61/11, satellite_part = -8\n", "T(2, 7; 2, 11), theta = 1\n", "pp = -101/11, satellite_part = -4\n", "-T(2, 3; 2, 7; 2, 11), theta = 1\n", "pp = 101/11, satellite_part = -8\n", "**********\n", "[5, 5, 1, 1] -28\n", "\n", "OK\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 33, "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": 3, "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": 6, "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" ] } ], "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": 5, "metadata": { "scrolled": true }, "outputs": [], "source": [ "# cable.is_signature_big_for_all_metabolizers()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Slice candidate" ] }, { "cell_type": "code", "execution_count": 8, "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": 9, "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": 11, "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": 11, "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": 12, "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": 12, "metadata": {}, "output_type": "execute_result" }, { "name": "stdout", "output_type": "stream", "text": [ "not verbose\n", "not verbose\n", "not verbose\n", "not verbose\n", "not verbose\n", "not verbose\n", "not verbose\n", "not verbose\n" ] }, { "data": { "text/plain": [ "-28" ] }, "execution_count": 12, "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": 13, "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": 14, "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": 14, "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": 15, "metadata": {}, "outputs": [], "source": [ "sf = slice_canidate()\n", "sf = sf[2]" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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bGLyEXGZwY+aq2U08nhH3+5fA84B/7u6Jf72qrpjZ0GMacc8nlRH3vB+4LMkXge8Bf1xV8/pKd9Q9/yHw90nexuDG8Vvm+C91JPkQg5hv6u57XAf8GEBVfYDBfZDXAcvA08Bvjf2cc/zrJUmagJP1rSFJ0ogMgSQ1zhBIUuMMgSQ1zhBIUuMMgSQ1zhBIUuP+Dx1J0gxS2y6OAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sf.plot()" ] }, { "cell_type": "code", "execution_count": 17, "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": 17, "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": 18, "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": null, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "not verbose\n", "not verbose\n", "not verbose\n", "not verbose\n", "not verbose\n", "not verbose\n", "not verbose\n", "not verbose\n", "**********\n", "[0, 0, 1, 1, 0, 0, 0, 0] 0\n", "not verbose\n", "not verbose\n", "not verbose\n", "not verbose\n", 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"outputs": [], "source": [ "cs = import_sage('cable_signature')\n", "sg = import_sage('signature')\n", "\n", "slice_canidate.plot_sum_for_theta_vector([0,4,0,4,0,0,0,0], save_to_dir=True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "sf.plot()\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.0", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 4 }