{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\def\\CC{\\bf C}\n", "\\def\\QQ{\\bf Q}\n", "\\def\\RR{\\bf R}\n", "\\def\\ZZ{\\bf Z}\n", "\\def\\NN{\\bf N}\n", "$$\n", "# Rauzy induction of polygon partitions and toral $\\mathbb{Z}^2$-rotations\n", "\n", "This file contains the Sage code contained in the preprints:\n", "\n", "> - [arXiv:1906.01104v1](https://arxiv.org/abs/1906.01104v1), June 2019, 36 p.\n", "> - [arXiv:1906.01104v2](https://arxiv.org/abs/1906.01104v2), May 2020, 40 p.\n", "> - [arXiv:1906.01104v3](https://arxiv.org/abs/1906.01104v3), January 2021, 40 p.\n", "\n", "The Jupyter notebook `arXiv_1906_01104.ipynb` is created from `arXiv_1906_01104.rst` with the command `sage -rst2ipynb arXiv_1906_01104.rst arXiv_1906_01104.ipynb`. The file `arXiv_1906_01104.rst` is in the `slabbe/demos` directory of the optional SageMath package [slabbe](https://pypi.org/project/slabbe/).\n", "\n", "Running all examples below with `sage -t arXiv_1906_01104.rst` takes 10 seconds with sage-9.1 and slabbe-0.6.1 (or with sage-9.2 and slabbe-0.6.2)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%display latex # not tested" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we construct the golden mean as a element of a quadratic number field because it is more efficient for arithmetic operations and comparisons:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "z = polygen(QQ, 'z')\n", "K = NumberField(z**2-z-1, 'phi', embedding=RR(1.6))\n", "phi = K.gen()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We import the polygon partition $\\mathcal{P}_0$ of $\\mathbb{R}^2/\\Gamma_0$ : which is predefined in `slabbe` :" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|partition|\\phantom{\\verb!x!}\\verb|of|\\phantom{\\verb!x!}\\verb|24|\\phantom{\\verb!x!}\\verb|atoms|\\phantom{\\verb!x!}\\verb|with|\\phantom{\\verb!x!}\\verb|11|\\phantom{\\verb!x!}\\verb|letters|\n", "\\end{math}" ], "text/plain": [ "Polyhedron partition of 24 atoms with 11 letters" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from slabbe.arXiv_1903_06137 import jeandel_rao_wang_shift_partition\n", "P0 = jeandel_rao_wang_shift_partition()\n", "P0" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 145 graphics primitives" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P0.plot() # optional long" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We import polyhedron exchange transformations from the package:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "from slabbe import PolyhedronExchangeTransformation as PET" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We define the lattice $\\Gamma_0$ and the maps $R_0^{e_1}$, $R_0^{e_2}$ which can be seen as a polygon exchange transformations on a rectangular fundamental domain of $\\mathbb{R}^2/\\Gamma_0$ :" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "Gamma0 = matrix.column([(phi,0), (1,phi+3)])\n", "fundamental_domain = polytopes.parallelotope([(phi,0), (0,phi+3)])\n", "R0e1 = PET.toral_translation(Gamma0, vector((1,0)), fundamental_domain)\n", "R0e2 = PET.toral_translation(Gamma0, vector((0,1)), fundamental_domain)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following allows to compute the induced partition $\\mathcal{P}_1$ of $\\mathbb{R}^2/\\Gamma_1$, the substitution $\\beta_0$ and the $\\mathbb{Z}^2$-action $R_1$ on $\\mathbb{R}^2/\\Gamma_1$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "y_le_1 = [1, 0, -1] # syntax for the inequality y <= 1\n", "P1,beta0 = R0e2.induced_partition(y_le_1, P0, substitution_type='column')\n", "R1e1,_ = R0e1.induced_transformation(y_le_1)\n", "R1e2,_ = R0e2.induced_transformation(y_le_1)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|Exchange|\\phantom{\\verb!x!}\\verb|Transformation|\\phantom{\\verb!x!}\\verb|of|\\\\\n", "\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|partition|\\phantom{\\verb!x!}\\verb|of|\\phantom{\\verb!x!}\\verb|2|\\phantom{\\verb!x!}\\verb|atoms|\\phantom{\\verb!x!}\\verb|with|\\phantom{\\verb!x!}\\verb|2|\\phantom{\\verb!x!}\\verb|letters|\\\\\n", "\\verb|with|\\phantom{\\verb!x!}\\verb|translations|\\phantom{\\verb!x!}\\verb|{0:|\\phantom{\\verb!x!}\\verb|(-phi|\\phantom{\\verb!x!}\\verb|+|\\phantom{\\verb!x!}\\verb|1,|\\phantom{\\verb!x!}\\verb|0),|\\phantom{\\verb!x!}\\verb|1:|\\phantom{\\verb!x!}\\verb|(1,|\\phantom{\\verb!x!}\\verb|0)}|\n", "\\end{array}\n", "\\end{math}" ], "text/plain": [ "Polyhedron Exchange Transformation of\n", "Polyhedron partition of 2 atoms with 2 letters\n", "with translations {0: (-phi + 1, 0), 1: (1, 0)}" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R1e1" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R1e1.plot() # optional long" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|Exchange|\\phantom{\\verb!x!}\\verb|Transformation|\\phantom{\\verb!x!}\\verb|of|\\\\\n", "\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|partition|\\phantom{\\verb!x!}\\verb|of|\\phantom{\\verb!x!}\\verb|4|\\phantom{\\verb!x!}\\verb|atoms|\\phantom{\\verb!x!}\\verb|with|\\phantom{\\verb!x!}\\verb|4|\\phantom{\\verb!x!}\\verb|letters|\\\\\n", "\\verb|with|\\phantom{\\verb!x!}\\verb|translations|\\phantom{\\verb!x!}\\verb|{0:|\\phantom{\\verb!x!}\\verb|(-1,|\\phantom{\\verb!x!}\\verb|-phi|\\phantom{\\verb!x!}\\verb|+|\\phantom{\\verb!x!}\\verb|1),|\\phantom{\\verb!x!}\\verb|1:|\\phantom{\\verb!x!}\\verb|(phi|\\phantom{\\verb!x!}\\verb|-|\\phantom{\\verb!x!}\\verb|1,|\\phantom{\\verb!x!}\\verb|-phi|\\phantom{\\verb!x!}\\verb|+|\\phantom{\\verb!x!}\\verb|1),|\\phantom{\\verb!x!}\\verb|2:|\\phantom{\\verb!x!}\\verb|(-1,|\\phantom{\\verb!x!}\\verb|-phi|\\phantom{\\verb!x!}\\verb|+|\\phantom{\\verb!x!}\\verb|2),|\\phantom{\\verb!x!}\\verb|3:|\\phantom{\\verb!x!}\\verb|(phi|\\phantom{\\verb!x!}\\verb|-|\\phantom{\\verb!x!}\\verb|1,|\\phantom{\\verb!x!}\\verb|-phi|\\phantom{\\verb!x!}\\verb|+|\\phantom{\\verb!x!}\\verb|2)}|\n", "\\end{array}\n", "\\end{math}" ], "text/plain": [ "Polyhedron Exchange Transformation of\n", "Polyhedron partition of 4 atoms with 4 letters\n", "with translations {0: (-1, -phi + 1), 1: (phi - 1, -phi + 1), 2: (-1, -phi + 2), 3: (phi - 1, -phi + 2)}" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R1e2" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 32 graphics primitives" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R1e2.plot() # optional long" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|partition|\\phantom{\\verb!x!}\\verb|of|\\phantom{\\verb!x!}\\verb|30|\\phantom{\\verb!x!}\\verb|atoms|\\phantom{\\verb!x!}\\verb|with|\\phantom{\\verb!x!}\\verb|28|\\phantom{\\verb!x!}\\verb|letters|\n", "\\end{math}" ], "text/plain": [ "Polyhedron partition of 30 atoms with 28 letters" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P1" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 186 graphics primitives" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P1.plot() # optional long" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llllllll}\n", "0\\mapsto \\left(\\begin{array}{r}\n", "7 \\\\\n", "3 \\\\\n", "9 \\\\\n", "0\n", "\\end{array}\\right)\n", ",&\n", "1\\mapsto \\left(\\begin{array}{r}\n", "5 \\\\\n", "7 \\\\\n", "9 \\\\\n", "0\n", "\\end{array}\\right)\n", ",&\n", "2\\mapsto \\left(\\begin{array}{r}\n", "4 \\\\\n", "10 \\\\\n", "9 \\\\\n", "0\n", "\\end{array}\\right)\n", ",&\n", "3\\mapsto \\left(\\begin{array}{r}\n", "7 \\\\\n", "3 \\\\\n", "3 \\\\\n", "1\n", "\\end{array}\\right)\n", ",&\n", "4\\mapsto \\left(\\begin{array}{r}\n", "6 \\\\\n", "7 \\\\\n", "3 \\\\\n", "1\n", "\\end{array}\\right)\n", ",&\n", "5\\mapsto \\left(\\begin{array}{r}\n", "7 \\\\\n", "8 \\\\\n", "3 \\\\\n", "1\n", "\\end{array}\\right)\n", ",&\n", "6\\mapsto \\left(\\begin{array}{r}\n", "5 \\\\\n", "2 \\\\\n", "7 \\\\\n", "1\n", "\\end{array}\\right)\n", ",&\n", "7\\mapsto \\left(\\begin{array}{r}\n", "5 \\\\\n", "5 \\\\\n", "7 \\\\\n", "1\n", "\\end{array}\\right)\n", ",\\\\\n", "8\\mapsto \\left(\\begin{array}{r}\n", "6 \\\\\n", "5 \\\\\n", "7 \\\\\n", "1\n", "\\end{array}\\right)\n", ",&\n", "9\\mapsto \\left(\\begin{array}{r}\n", "5 \\\\\n", "7 \\\\\n", "8 \\\\\n", "1\n", "\\end{array}\\right)\n", ",&\n", "10\\mapsto \\left(\\begin{array}{r}\n", "4 \\\\\n", "10 \\\\\n", "8 \\\\\n", "1\n", "\\end{array}\\right)\n", ",&\n", "11\\mapsto \\left(\\begin{array}{r}\n", "5 \\\\\n", "4 \\\\\n", "10 \\\\\n", "1\n", "\\end{array}\\right)\n", ",&\n", "12\\mapsto \\left(\\begin{array}{r}\n", "6 \\\\\n", "4 \\\\\n", "10 \\\\\n", "1\n", "\\end{array}\\right)\n", ",&\n", "13\\mapsto \\left(\\begin{array}{r}\n", "7 \\\\\n", "3 \\\\\n", "3 \\\\\n", "9 \\\\\n", "0\n", "\\end{array}\\right)\n", ",&\n", "14\\mapsto \\left(\\begin{array}{r}\n", "6 \\\\\n", "7 \\\\\n", "3 \\\\\n", "9 \\\\\n", "0\n", "\\end{array}\\right)\n", ",&\n", "15\\mapsto \\left(\\begin{array}{r}\n", "7 \\\\\n", "8 \\\\\n", "3 \\\\\n", "9 \\\\\n", "0\n", "\\end{array}\\right)\n", ",\\\\\n", "16\\mapsto \\left(\\begin{array}{r}\n", "5 \\\\\n", "2 \\\\\n", "7 \\\\\n", "9 \\\\\n", "0\n", "\\end{array}\\right)\n", ",&\n", "17\\mapsto \\left(\\begin{array}{r}\n", "6 \\\\\n", "2 \\\\\n", "7 \\\\\n", "9 \\\\\n", "0\n", "\\end{array}\\right)\n", ",&\n", "18\\mapsto \\left(\\begin{array}{r}\n", "5 \\\\\n", "5 \\\\\n", "7 \\\\\n", "9 \\\\\n", "0\n", "\\end{array}\\right)\n", ",&\n", "19\\mapsto \\left(\\begin{array}{r}\n", "6 \\\\\n", "5 \\\\\n", "7 \\\\\n", "9 \\\\\n", "0\n", "\\end{array}\\right)\n", ",&\n", "20\\mapsto \\left(\\begin{array}{r}\n", "5 \\\\\n", "7 \\\\\n", "8 \\\\\n", "9 \\\\\n", "0\n", "\\end{array}\\right)\n", ",&\n", "21\\mapsto \\left(\\begin{array}{r}\n", "4 \\\\\n", "10 \\\\\n", "8 \\\\\n", "9 \\\\\n", "0\n", "\\end{array}\\right)\n", ",&\n", "22\\mapsto \\left(\\begin{array}{r}\n", "6 \\\\\n", "4 \\\\\n", "10 \\\\\n", "9 \\\\\n", "0\n", "\\end{array}\\right)\n", ",&\n", "23\\mapsto \\left(\\begin{array}{r}\n", "6 \\\\\n", "7 \\\\\n", "3 \\\\\n", "3 \\\\\n", "1\n", "\\end{array}\\right)\n", ",\\\\\n", "24\\mapsto \\left(\\begin{array}{r}\n", "6 \\\\\n", "7 \\\\\n", "8 \\\\\n", "3 \\\\\n", "1\n", "\\end{array}\\right)\n", ",&\n", "25\\mapsto \\left(\\begin{array}{r}\n", "6 \\\\\n", "5 \\\\\n", "2 \\\\\n", "7 \\\\\n", "1\n", "\\end{array}\\right)\n", ",&\n", "26\\mapsto \\left(\\begin{array}{r}\n", "6 \\\\\n", "4 \\\\\n", "10 \\\\\n", "8 \\\\\n", "1\n", "\\end{array}\\right)\n", ",&\n", "27\\mapsto \\left(\\begin{array}{r}\n", "6 \\\\\n", "5 \\\\\n", "4 \\\\\n", "10 \\\\\n", "1\n", "\\end{array}\\right)\n", ".\n", "\\end{array}\n", "\\end{math}" ], "text/plain": [ "Substitution 2d: {0: [[0, 9, 3, 7]], 1: [[0, 9, 7, 5]], 2: [[0, 9, 10, 4]], 3: [[1, 3, 3, 7]], 4: [[1, 3, 7, 6]], 5: [[1, 3, 8, 7]], 6: [[1, 7, 2, 5]], 7: [[1, 7, 5, 5]], 8: [[1, 7, 5, 6]], 9: [[1, 8, 7, 5]], 10: [[1, 8, 10, 4]], 11: [[1, 10, 4, 5]], 12: [[1, 10, 4, 6]], 13: [[0, 9, 3, 3, 7]], 14: [[0, 9, 3, 7, 6]], 15: [[0, 9, 3, 8, 7]], 16: [[0, 9, 7, 2, 5]], 17: [[0, 9, 7, 2, 6]], 18: [[0, 9, 7, 5, 5]], 19: [[0, 9, 7, 5, 6]], 20: [[0, 9, 8, 7, 5]], 21: [[0, 9, 8, 10, 4]], 22: [[0, 9, 10, 4, 6]], 23: [[1, 3, 3, 7, 6]], 24: [[1, 3, 8, 7, 6]], 25: [[1, 7, 2, 5, 6]], 26: [[1, 8, 10, 4, 6]], 27: [[1, 10, 4, 5, 6]]}" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We keep $\\mathcal{P}_2$, $\\Gamma_2$ equal to $\\mathcal{P}_1$, $\\Gamma_1$ and we change the base of the action to get the $\\mathbb{Z}^2$-action $R_2$ on $\\mathbb{R}^2/\\Gamma_2$." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "Gamma2 = Gamma1 = matrix.column([(phi,0), (0,1)])\n", "P2 = P1\n", "R2e1 = R1e1\n", "R2e2 = (R1e1 * R1e2).merge_atoms_with_same_translation()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following confirms that the $R_2^{\\boldsymbol{e}_2}$ is now a vertical rotation on the torus $\\mathbb{R^2}/\\Gamma_2$." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|Exchange|\\phantom{\\verb!x!}\\verb|Transformation|\\phantom{\\verb!x!}\\verb|of|\\\\\n", "\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|partition|\\phantom{\\verb!x!}\\verb|of|\\phantom{\\verb!x!}\\verb|2|\\phantom{\\verb!x!}\\verb|atoms|\\phantom{\\verb!x!}\\verb|with|\\phantom{\\verb!x!}\\verb|2|\\phantom{\\verb!x!}\\verb|letters|\\\\\n", "\\verb|with|\\phantom{\\verb!x!}\\verb|translations|\\phantom{\\verb!x!}\\verb|{0:|\\phantom{\\verb!x!}\\verb|(0,|\\phantom{\\verb!x!}\\verb|-phi|\\phantom{\\verb!x!}\\verb|+|\\phantom{\\verb!x!}\\verb|1),|\\phantom{\\verb!x!}\\verb|1:|\\phantom{\\verb!x!}\\verb|(0,|\\phantom{\\verb!x!}\\verb|-phi|\\phantom{\\verb!x!}\\verb|+|\\phantom{\\verb!x!}\\verb|2)}|\n", "\\end{array}\n", "\\end{math}" ], "text/plain": [ "Polyhedron Exchange Transformation of\n", "Polyhedron partition of 2 atoms with 2 letters\n", "with translations {0: (0, -phi + 1), 1: (0, -phi + 2)}" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R2e2" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 16 graphics primitives" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R2e2.plot() # optional long" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following allows to compute the induced partition $\\mathcal{P}_3$ of $\\mathbb{R}^2/\\Gamma_3$, the substitution $\\beta_2$ and the $\\mathbb{Z}^2$-action $R_3$ on $\\mathbb{R}^2/\\Gamma_3$." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|Exchange|\\phantom{\\verb!x!}\\verb|Transformation|\\phantom{\\verb!x!}\\verb|of|\\\\\n", "\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|partition|\\phantom{\\verb!x!}\\verb|of|\\phantom{\\verb!x!}\\verb|2|\\phantom{\\verb!x!}\\verb|atoms|\\phantom{\\verb!x!}\\verb|with|\\phantom{\\verb!x!}\\verb|2|\\phantom{\\verb!x!}\\verb|letters|\\\\\n", "\\verb|with|\\phantom{\\verb!x!}\\verb|translations|\\phantom{\\verb!x!}\\verb|{0:|\\phantom{\\verb!x!}\\verb|(-phi|\\phantom{\\verb!x!}\\verb|+|\\phantom{\\verb!x!}\\verb|1,|\\phantom{\\verb!x!}\\verb|0),|\\phantom{\\verb!x!}\\verb|1:|\\phantom{\\verb!x!}\\verb|(-phi|\\phantom{\\verb!x!}\\verb|+|\\phantom{\\verb!x!}\\verb|2,|\\phantom{\\verb!x!}\\verb|0)}|\n", "\\end{array}\n", "\\end{math}" ], "text/plain": [ "Polyhedron Exchange Transformation of\n", "Polyhedron partition of 2 atoms with 2 letters\n", "with translations {0: (-phi + 1, 0), 1: (-phi + 2, 0)}" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x_le_1 = [1, -1, 0] # syntax for x <= 1\n", "P3,beta2 = R2e1.induced_partition(x_le_1, P2, substitution_type='row')\n", "R3e1,_ = R2e1.induced_transformation(x_le_1)\n", "R3e2,_ = R2e2.induced_transformation(x_le_1)\n", "R3e1" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|partition|\\phantom{\\verb!x!}\\verb|of|\\phantom{\\verb!x!}\\verb|21|\\phantom{\\verb!x!}\\verb|atoms|\\phantom{\\verb!x!}\\verb|with|\\phantom{\\verb!x!}\\verb|20|\\phantom{\\verb!x!}\\verb|letters|\n", "\\end{math}" ], "text/plain": [ "Polyhedron partition of 21 atoms with 20 letters" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P3" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 129 graphics primitives" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P3.plot() # optional long" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llllllll}\n", "0\\mapsto \\left(2\\right)\n", ",&\n", "1\\mapsto \\left(9\\right)\n", ",&\n", "2\\mapsto \\left(10\\right)\n", ",&\n", "3\\mapsto \\left(20\\right)\n", ",&\n", "4\\mapsto \\left(21\\right)\n", ",&\n", "5\\mapsto \\left(22\\right)\n", ",&\n", "6\\mapsto \\left(26\\right)\n", ",&\n", "7\\mapsto \\left(1,\\,0\\right)\n", ",\\\\\n", "8\\mapsto \\left(6,\\,5\\right)\n", ",&\n", "9\\mapsto \\left(7,\\,4\\right)\n", ",&\n", "10\\mapsto \\left(8,\\,4\\right)\n", ",&\n", "11\\mapsto \\left(11,\\,3\\right)\n", ",&\n", "12\\mapsto \\left(12,\\,3\\right)\n", ",&\n", "13\\mapsto \\left(16,\\,15\\right)\n", ",&\n", "14\\mapsto \\left(17,\\,15\\right)\n", ",&\n", "15\\mapsto \\left(18,\\,14\\right)\n", ",\\\\\n", "16\\mapsto \\left(19,\\,14\\right)\n", ",&\n", "17\\mapsto \\left(22,\\,13\\right)\n", ",&\n", "18\\mapsto \\left(25,\\,24\\right)\n", ",&\n", "19\\mapsto \\left(27,\\,23\\right)\n", ".\n", "\\end{array}\n", "\\end{math}" ], "text/plain": [ "Substitution 2d: {0: [[2]], 1: [[9]], 2: [[10]], 3: [[20]], 4: [[21]], 5: [[22]], 6: [[26]], 7: [[1], [0]], 8: [[6], [5]], 9: [[7], [4]], 10: [[8], [4]], 11: [[11], [3]], 12: [[12], [3]], 13: [[16], [15]], 14: [[17], [15]], 15: [[18], [14]], 16: [[19], [14]], 17: [[22], [13]], 18: [[25], [24]], 19: [[27], [23]]}" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following allows to compute the induced partition $\\mathcal{P}_4$ of $\\mathbb{R}^2/\\Gamma_4$, the substitution $\\beta_3$ and the $\\mathbb{Z}^2$-action $R_4$ on $\\mathbb{R}^2/\\Gamma_4$" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{l}\n", "\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|Exchange|\\phantom{\\verb!x!}\\verb|Transformation|\\phantom{\\verb!x!}\\verb|of|\\\\\n", "\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|partition|\\phantom{\\verb!x!}\\verb|of|\\phantom{\\verb!x!}\\verb|2|\\phantom{\\verb!x!}\\verb|atoms|\\phantom{\\verb!x!}\\verb|with|\\phantom{\\verb!x!}\\verb|2|\\phantom{\\verb!x!}\\verb|letters|\\\\\n", "\\verb|with|\\phantom{\\verb!x!}\\verb|translations|\\phantom{\\verb!x!}\\verb|{0:|\\phantom{\\verb!x!}\\verb|(0,|\\phantom{\\verb!x!}\\verb|-phi|\\phantom{\\verb!x!}\\verb|+|\\phantom{\\verb!x!}\\verb|1),|\\phantom{\\verb!x!}\\verb|1:|\\phantom{\\verb!x!}\\verb|(0,|\\phantom{\\verb!x!}\\verb|-phi|\\phantom{\\verb!x!}\\verb|+|\\phantom{\\verb!x!}\\verb|2)}|\n", "\\end{array}\n", "\\end{math}" ], "text/plain": [ "Polyhedron Exchange Transformation of\n", "Polyhedron partition of 2 atoms with 2 letters\n", "with translations {0: (0, -phi + 1), 1: (0, -phi + 2)}" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x_le_phi_inv = [phi^-1, -1, 0] # syntax for x <= phi^-1\n", "P4,beta3 = R3e1.induced_partition(x_le_phi_inv, P3, substitution_type='row')\n", "R4e1,_ = R3e1.induced_transformation(x_le_phi_inv)\n", "R4e2,_ = R3e2.induced_transformation(x_le_phi_inv)\n", "R4e2" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|partition|\\phantom{\\verb!x!}\\verb|of|\\phantom{\\verb!x!}\\verb|21|\\phantom{\\verb!x!}\\verb|atoms|\\phantom{\\verb!x!}\\verb|with|\\phantom{\\verb!x!}\\verb|20|\\phantom{\\verb!x!}\\verb|letters|\n", "\\end{math}" ], "text/plain": [ "Polyhedron partition of 21 atoms with 20 letters" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P4" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 129 graphics primitives" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P4.plot() # optional long" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llllllll}\n", "0\\mapsto \\left(8\\right)\n", ",&\n", "1\\mapsto \\left(9\\right)\n", ",&\n", "2\\mapsto \\left(10\\right)\n", ",&\n", "3\\mapsto \\left(15\\right)\n", ",&\n", "4\\mapsto \\left(16\\right)\n", ",&\n", "5\\mapsto \\left(18\\right)\n", ",&\n", "6\\mapsto \\left(19\\right)\n", ",&\n", "7\\mapsto \\left(7,\\,0\\right)\n", ",\\\\\n", "8\\mapsto \\left(7,\\,2\\right)\n", ",&\n", "9\\mapsto \\left(8,\\,1\\right)\n", ",&\n", "10\\mapsto \\left(11,\\,2\\right)\n", ",&\n", "11\\mapsto \\left(12,\\,2\\right)\n", ",&\n", "12\\mapsto \\left(13,\\,3\\right)\n", ",&\n", "13\\mapsto \\left(14,\\,3\\right)\n", ",&\n", "14\\mapsto \\left(15,\\,5\\right)\n", ",&\n", "15\\mapsto \\left(15,\\,6\\right)\n", ",\\\\\n", "16\\mapsto \\left(16,\\,5\\right)\n", ",&\n", "17\\mapsto \\left(16,\\,6\\right)\n", ",&\n", "18\\mapsto \\left(17,\\,4\\right)\n", ",&\n", "19\\mapsto \\left(19,\\,6\\right)\n", ".\n", "\\end{array}\n", "\\end{math}" ], "text/plain": [ "Substitution 2d: {0: [[8]], 1: [[9]], 2: [[10]], 3: [[15]], 4: [[16]], 5: [[18]], 6: [[19]], 7: [[7], [0]], 8: [[7], [2]], 9: [[8], [1]], 10: [[11], [2]], 11: [[12], [2]], 12: [[13], [3]], 13: [[14], [3]], 14: [[15], [5]], 15: [[15], [6]], 16: [[16], [5]], 17: [[16], [6]], 18: [[17], [4]], 19: [[19], [6]]}" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following allows to compute the induced partition $\\mathcal{P}_5$ of $\\mathbb{R}^2/\\Gamma_5$, the substitution $\\beta_4$ and the $\\mathbb{Z}^2$-action $R_5$ on $\\mathbb{R}^2/\\Gamma_5$." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|partition|\\phantom{\\verb!x!}\\verb|of|\\phantom{\\verb!x!}\\verb|22|\\phantom{\\verb!x!}\\verb|atoms|\\phantom{\\verb!x!}\\verb|with|\\phantom{\\verb!x!}\\verb|22|\\phantom{\\verb!x!}\\verb|letters|\n", "\\end{math}" ], "text/plain": [ "Polyhedron partition of 22 atoms with 22 letters" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y_le_phi_inv = [phi^-1, 0, -1] # syntax for y <= phi^-1\n", "P5,beta4 = R4e2.induced_partition(y_le_phi_inv, P4, substitution_type='column')\n", "R5e1,_ = R4e1.induced_transformation(y_le_phi_inv)\n", "R5e2,_ = R4e2.induced_transformation(y_le_phi_inv)\n", "P5" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 137 graphics primitives" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P5.plot() # optional long" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llllllll}\n", "0\\mapsto \\left(3\\right)\n", ",&\n", "1\\mapsto \\left(4\\right)\n", ",&\n", "2\\mapsto \\left(5\\right)\n", ",&\n", "3\\mapsto \\left(6\\right)\n", ",&\n", "4\\mapsto \\left(12\\right)\n", ",&\n", "5\\mapsto \\left(13\\right)\n", ",&\n", "6\\mapsto \\left(14\\right)\n", ",&\n", "7\\mapsto \\left(15\\right)\n", ",\\\\\n", "8\\mapsto \\left(18\\right)\n", ",&\n", "9\\mapsto \\left(\\begin{array}{r}\n", "0 \\\\\n", "4\n", "\\end{array}\\right)\n", ",&\n", "10\\mapsto \\left(\\begin{array}{r}\n", "0 \\\\\n", "5\n", "\\end{array}\\right)\n", ",&\n", "11\\mapsto \\left(\\begin{array}{r}\n", "1 \\\\\n", "5\n", "\\end{array}\\right)\n", ",&\n", "12\\mapsto \\left(\\begin{array}{r}\n", "2 \\\\\n", "5\n", "\\end{array}\\right)\n", ",&\n", "13\\mapsto \\left(\\begin{array}{r}\n", "0 \\\\\n", "6\n", "\\end{array}\\right)\n", ",&\n", "14\\mapsto \\left(\\begin{array}{r}\n", "8 \\\\\n", "13\n", "\\end{array}\\right)\n", ",&\n", "15\\mapsto \\left(\\begin{array}{r}\n", "10 \\\\\n", "14\n", "\\end{array}\\right)\n", ",\\\\\n", "16\\mapsto \\left(\\begin{array}{r}\n", "10 \\\\\n", "15\n", "\\end{array}\\right)\n", ",&\n", "17\\mapsto \\left(\\begin{array}{r}\n", "11 \\\\\n", "16\n", "\\end{array}\\right)\n", ",&\n", "18\\mapsto \\left(\\begin{array}{r}\n", "9 \\\\\n", "17\n", "\\end{array}\\right)\n", ",&\n", "19\\mapsto \\left(\\begin{array}{r}\n", "11 \\\\\n", "17\n", "\\end{array}\\right)\n", ",&\n", "20\\mapsto \\left(\\begin{array}{r}\n", "7 \\\\\n", "18\n", "\\end{array}\\right)\n", ",&\n", "21\\mapsto \\left(\\begin{array}{r}\n", "9 \\\\\n", "19\n", "\\end{array}\\right)\n", ".\n", "\\end{array}\n", "\\end{math}" ], "text/plain": [ "Substitution 2d: {0: [[3]], 1: [[4]], 2: [[5]], 3: [[6]], 4: [[12]], 5: [[13]], 6: [[14]], 7: [[15]], 8: [[18]], 9: [[4, 0]], 10: [[5, 0]], 11: [[5, 1]], 12: [[5, 2]], 13: [[6, 0]], 14: [[13, 8]], 15: [[14, 10]], 16: [[15, 10]], 17: [[16, 11]], 18: [[17, 9]], 19: [[17, 11]], 20: [[18, 7]], 21: [[19, 9]]}" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We rescale the partition $\\mathcal{P}_5$ :" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "P5_scaled = (-phi*P5).translate((1,1))\n", "R5e1_scaled = (-phi*R5e1).translate_domain((1,1))\n", "R5e2_scaled = (-phi*R5e2).translate_domain((1,1))" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 137 graphics primitives" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P5_scaled.plot() # optional long" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following allows to compute the induced partition $\\mathcal{P}_6$ of $\\mathbb{R}^2/\\Gamma_6$, the substitution $\\beta_5$ and the $\\mathbb{Z}^2$-action $R_6$ on $\\mathbb{R}^2/\\Gamma_6$." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|partition|\\phantom{\\verb!x!}\\verb|of|\\phantom{\\verb!x!}\\verb|18|\\phantom{\\verb!x!}\\verb|atoms|\\phantom{\\verb!x!}\\verb|with|\\phantom{\\verb!x!}\\verb|18|\\phantom{\\verb!x!}\\verb|letters|\n", "\\end{math}" ], "text/plain": [ "Polyhedron partition of 18 atoms with 18 letters" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P6,beta5 = R5e1_scaled.induced_partition(x_le_phi_inv, P5_scaled, substitution_type='row')\n", "R6e1,_ = R5e1_scaled.induced_transformation(x_le_phi_inv)\n", "R6e2,_ = R5e2_scaled.induced_transformation(x_le_phi_inv)\n", "P6" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 111 graphics primitives" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P6.plot() # optional long" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llllllll}\n", "0\\mapsto \\left(8\\right)\n", ",&\n", "1\\mapsto \\left(14\\right)\n", ",&\n", "2\\mapsto \\left(17\\right)\n", ",&\n", "3\\mapsto \\left(20\\right)\n", ",&\n", "4\\mapsto \\left(4,\\,1\\right)\n", ",&\n", "5\\mapsto \\left(5,\\,1\\right)\n", ",&\n", "6\\mapsto \\left(6,\\,3\\right)\n", ",&\n", "7\\mapsto \\left(7,\\,2\\right)\n", ",\\\\\n", "8\\mapsto \\left(8,\\,0\\right)\n", ",&\n", "9\\mapsto \\left(14,\\,9\\right)\n", ",&\n", "10\\mapsto \\left(15,\\,13\\right)\n", ",&\n", "11\\mapsto \\left(16,\\,10\\right)\n", ",&\n", "12\\mapsto \\left(16,\\,11\\right)\n", ",&\n", "13\\mapsto \\left(17,\\,13\\right)\n", ",&\n", "14\\mapsto \\left(18,\\,12\\right)\n", ",&\n", "15\\mapsto \\left(19,\\,10\\right)\n", ",\\\\\n", "16\\mapsto \\left(19,\\,11\\right)\n", ",&\n", "17\\mapsto \\left(21,\\,12\\right)\n", ".\n", "\\end{array}\n", "\\end{math}" ], "text/plain": [ "Substitution 2d: {0: [[8]], 1: [[14]], 2: [[17]], 3: [[20]], 4: [[4], [1]], 5: [[5], [1]], 6: [[6], [3]], 7: [[7], [2]], 8: [[8], [0]], 9: [[14], [9]], 10: [[15], [13]], 11: [[16], [10]], 12: [[16], [11]], 13: [[17], [13]], 14: [[18], [12]], 15: [[19], [10]], 16: [[19], [11]], 17: [[21], [12]]}" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta5" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following allows to compute the induced partition $\\mathcal{P}_7$ of $\\mathbb{R}^2/\\Gamma_7$, the substitution $\\beta_6$ and the $\\mathbb{Z}^2$-action $R_7$ on $\\mathbb{R}^2/\\Gamma_7$." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|partition|\\phantom{\\verb!x!}\\verb|of|\\phantom{\\verb!x!}\\verb|21|\\phantom{\\verb!x!}\\verb|atoms|\\phantom{\\verb!x!}\\verb|with|\\phantom{\\verb!x!}\\verb|21|\\phantom{\\verb!x!}\\verb|letters|\n", "\\end{math}" ], "text/plain": [ "Polyhedron partition of 21 atoms with 21 letters" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P7,beta6 = R6e2.induced_partition(y_le_phi_inv, P6, substitution_type='column')\n", "R7e1,_ = R6e1.induced_transformation(y_le_phi_inv)\n", "R7e2,_ = R6e2.induced_transformation(y_le_phi_inv)\n", "P7" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 133 graphics primitives" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P7.plot() # optional long" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llllllll}\n", "0\\mapsto \\left(1\\right)\n", ",&\n", "1\\mapsto \\left(2\\right)\n", ",&\n", "2\\mapsto \\left(3\\right)\n", ",&\n", "3\\mapsto \\left(12\\right)\n", ",&\n", "4\\mapsto \\left(13\\right)\n", ",&\n", "5\\mapsto \\left(14\\right)\n", ",&\n", "6\\mapsto \\left(15\\right)\n", ",&\n", "7\\mapsto \\left(16\\right)\n", ",\\\\\n", "8\\mapsto \\left(17\\right)\n", ",&\n", "9\\mapsto \\left(\\begin{array}{r}\n", "0 \\\\\n", "1\n", "\\end{array}\\right)\n", ",&\n", "10\\mapsto \\left(\\begin{array}{r}\n", "0 \\\\\n", "2\n", "\\end{array}\\right)\n", ",&\n", "11\\mapsto \\left(\\begin{array}{r}\n", "0 \\\\\n", "3\n", "\\end{array}\\right)\n", ",&\n", "12\\mapsto \\left(\\begin{array}{r}\n", "8 \\\\\n", "9\n", "\\end{array}\\right)\n", ",&\n", "13\\mapsto \\left(\\begin{array}{r}\n", "4 \\\\\n", "10\n", "\\end{array}\\right)\n", ",&\n", "14\\mapsto \\left(\\begin{array}{r}\n", "4 \\\\\n", "11\n", "\\end{array}\\right)\n", ",&\n", "15\\mapsto \\left(\\begin{array}{r}\n", "6 \\\\\n", "12\n", "\\end{array}\\right)\n", ",\\\\\n", "16\\mapsto \\left(\\begin{array}{r}\n", "5 \\\\\n", "13\n", "\\end{array}\\right)\n", ",&\n", "17\\mapsto \\left(\\begin{array}{r}\n", "8 \\\\\n", "13\n", "\\end{array}\\right)\n", ",&\n", "18\\mapsto \\left(\\begin{array}{r}\n", "7 \\\\\n", "14\n", "\\end{array}\\right)\n", ",&\n", "19\\mapsto \\left(\\begin{array}{r}\n", "5 \\\\\n", "15\n", "\\end{array}\\right)\n", ",&\n", "20\\mapsto \\left(\\begin{array}{r}\n", "7 \\\\\n", "17\n", "\\end{array}\\right)\n", ".\n", "\\end{array}\n", "\\end{math}" ], "text/plain": [ "Substitution 2d: {0: [[1]], 1: [[2]], 2: [[3]], 3: [[12]], 4: [[13]], 5: [[14]], 6: [[15]], 7: [[16]], 8: [[17]], 9: [[1, 0]], 10: [[2, 0]], 11: [[3, 0]], 12: [[9, 8]], 13: [[10, 4]], 14: [[11, 4]], 15: [[12, 6]], 16: [[13, 5]], 17: [[13, 8]], 18: [[14, 7]], 19: [[15, 5]], 20: [[17, 7]]}" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta6" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We rescale the partition $\\mathcal{P}_7$ :" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [], "source": [ "P7_scaled = (-phi*P7).translate((1,1))\n", "R7e1_scaled = (-phi*R7e1).translate_domain((1,1))\n", "R7e2_scaled = (-phi*R7e2).translate_domain((1,1))" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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WxnzmzgV++IEei7x0UyoWNmCA9XYFix5ELGD+fKbpzZlDN8/27Qw6lykTHi6Jdeuo+ahRI29/9dy57Avdo4ctpnmCQDQ1irFjOZC88oo9tmnsITUV6NCBmXYLFuS97ebNnIRlVwrHafQgYgE9ewJvvpm+9KxShc2F4uK8P4j4fMDjj3OFlVcwGNDaBn8C1dQoPviAlVzdWvFYY4y2bZk88OGHrIGVG+++y1WrWzMbdUzEApKTs7oo8uULjxTfHj3Ybe2NN9hRLTeUtqFGDa1tUChNTVxczpoaxaFDwO+/A3Xq6ISEcOLHH+mtuPlmoGPHvLdXmY1unYDqlYgFxMYyBnLttXRn/fADMzCcbHJkBocOMSOrdGl+vrzo3z+ytA15kVFTE4hYTK3eAjnX4UZSEjP/FPv20S1cvHjumWxeoFEjal8CWcn/9htw8CAD8G6dSOhBxAI++IClvF9+mVk4ZcpwxpFTZVavoDJJFi8ObPuZMyNL25AXgWpqFEuXAldcwZVcpLF1K/Dgg+mP1aDbrl3OdaW8QFwcXdsdOwIVKuS9/Ztvpr/Prbh6EPFqU6pixYD33+ctXJg1i6nKMTHAPffkvX0kahtyI1BNjWLVKs7GO3Sw3jY3UqeOs90lreD0aU4kL7sMGDcusPd89BFX/rfeaqlpIeHSBRLRTancQWoqZ06FCtGXGwha25CO0tRccknemhrFgAF0eaiilRrv07QpEytmzw7MNaUyG597znrbQsHVKxGNO3jySSYLTJiQdyYJoLUN/ihNzezZgdU8Sk4Gtm0Dbrst7+C7xht8/DHrgdWqFbjoeOhQDjZuaIGbG65eiWic5/vvqaatVIl9nwMhPp4DSbjVCTNCRk1NbtVZMzJ4MGNPOi06PPD5OBHLn5/FNgPh7Fngp5+A6tXdn9moVyKaXGnShG6Vjz4K/D1jxlDb4KaeB04QrKZGMXUqqz8/8YR1tmnso1Mn4K+/2BI60DYI/foxJuSFZBy9EtHkyODBTC/s2DHwLmpa25BOz56Ba2oUO3awf7Yq3qnxNvv20Q1ctmxwbqmZMxlDi4mxzjaziPCfuSYnTp/mbOiyy+ieCpRI1jZk5NAhZueVKhXcuVDFKocOtcQsjc00bMgVRTD9ULZs4eSjWTPLzDIVPYhosqVxY8Y15swJbkURydqGjChNTSClTRQ+H+MnZcsGpiHQuJuJEykwbdECuOOOwN+nVixemYjpQUSThdWrWbr+gQeCEwoqbUOkN54KVlOjmDaNPbZfesk62zT2kJLCxJIiRZiVFyg+H/Dll6xqcM011tlnJjqwrsmEkUwShdI2RHKZEyOaGsV77zEI3727NbZp7OPxxzmQzJzJYpuBojIbvVS1WQ8imky8/DILJw4ZwnhIoGhtA3nqqeA0NYqTJ9k/u1at4C46GvexeTNX5bffzu9DMIwezQlcly7W2GYF2p2l+Y/ffqMf99pr0wO8gaK1DdTULFzI6qyBamoU77zD+/79zbdLYy/NmzOOGExaN8BWub/95r3MRg+ZqrGamBhmkqxcGfx7p03T2galqVm9Ovj3zpvHlV9eTao07qZ3b+DoUTahCzamoSZggwaZbpalGBpEhBAvCyH2CSFShBDbhBD357F9VyHEbiHEP0KIg0KIUUIIl+swI4sJE+hOadmSLqlg2LGDPxwv5LRbhRFNjWLdOroQW7a0wjKNXZw4AQwbxuzEd98N/v1LlgAlSgA1a5pvm5UEPYgIIVoCeB/AYADVAGwE8LEQItsq/0KIJwEMBdAfQCUAzwFoCcDFxY0ji+RkzpyKFmW/i2BRri83l6u2EqOaGoVKRPDaDFSTmZgYdiBcsCB4d9Tq1WxW5sXMRiMrkW4ApkgpJ0spd0kpuwI4CCCnxMR7AHwlpZwjpfxDSvkpgLkA7jRkscZ0nniCmSQTJgQf1NXaBrqxjGhqAGZzffUV4yhu7J+tCYzFiykSrFePMY1g6d+frlAvxsSC+soLIQoCqA7gU7+XPgVwbw5v2wSguhDirov7KA+gAYAcqzGdP38eZ8+e/e927tzZYMzUBMFXX7EuVtWqTO0NlkjXNqxeDWzcCNx/v7HmWyNHcvaq03q9S1oa8MwznIAFIy5VpKSwCdett3ozszHYFN+SAPIBOO73/HEApbJ7g5RynhDiCgCbhBDi4jHHSylzLOwQFxeH/l4ckj1IixacPQdTYDEjI0ZErrYho6Ym0G6F/owfz4uP11snRzLPPUdX1JgxrHcVLEOG8LsUbEakWzCaneXfc0xk8xxfEKIOgN4AXgZwB4BmAGKEEO/ktPNevXohMTHxv9vq1QcNmqnJjbfeYrG/bt2M9f04eZJlHe69NzK1DUpTM2BAcJoaxb59wIEDdIF4KaVTk87PP1NQeMMNxrUdkyczs7F1a3Nts4tgVyInAVxA1lXHlci6OlEMBDBTSjn54uOfhBBFAUwUQgyWUvr83xAVFYWoqKj/HhctGqSVmjw5dgwYPpyZJMOGGduH0jYMGGCeXV4hFE2NQr1Pd3/0Lo0a8d7oSvTnn5nZ2Ly5eTbZTVDzHyllKoBtAOr5vVQPwNc5vK0IAP+B4gK4ehHBHF9jHiqTZNEi47NgpW0wEkj0OkpTE2xpmIysXMkqv8GmVGvcwciRbHvQti2bthlBaUO8nNlopOzJSAAzhRBbAWwG8AKAawF8CABCiAQAh6WUan62EkA3IcQPAL4FcAO4OlkhpbwQov0aAyxYwBIljzzCIotG2LCBrpyOHU01zRNk1NRUrWpsHwsWMLVad3/0JmfPciV56aV0RxnB5wPWrKEosWJFc+2zk6AHESnlfCFECQB9AJQGsANAAynl/oubXIvMK49BYLxkEICrAfwJDiwu7xwcnqSlMRAYFcVViFGUKyvStA2hamoUcXFM6Xz7bdNM09hIs2ZMz543j4kVRpg5k5mNXp+IGfr4UspxAMbl8Fodv8dpoNBQp1u5gPbtWa7daCYJENnaBqWpmTXLeDJBUhJLxVevHlyRRo07+Pxz3mrWBJo2Nb6f4cPpSn79dfNscwKdExJB/PwzBXEVK4ZWJTRStQ2bN4emqVH07894yjs55idq3IrPRzdmvnzGg+kAMxt37mS/Ga9nNupBJIKIjeW9kQKLGYlUbUOzZpw5hnr+ZsygO0xl9mi8Q/fuwKlTDIhfeaXx/fTpw/twkMPpQSRCGDGCuoT27YGbbjK+n0jVNmTU1ITScW7rVuDPP1kqReMtDhygG7hMmdDT2ufNA6Kjgbp1zbHNSSLoMhC5ZMwkmTgxtH0pbcPQHOsNhB9maGoUqn+21oZ4j5gYurOWLQttP5s2AX/9xe6H4YDubBgBNG0K/PsvGyYZzSRRKG3DrbeaY5sXiI0NXVMDpPfPvv56ihQ13iEhAfjpJ6BxY6BGjdD2pTLyBg8O3S43oFciYc7nnwNffAHcfTd/AKGgtA3PPGOObV5g0SK6oOrXN66pUXz4IQfzzp3NsU1jD6mpwIsvAoUK0Q0VCmlpXIncdFNoMRU3oVciYYzPx5TU/PlDDwYDkadtUNVZo6JY6jtU3n+f/4tXXgl9Xxr7aNMG+OcfigoLhdhKT2U2vvaaOba5Ab0SCWO6dmXDpLffDl3PEYnaBqWpefdd45oaxbFjwN69XM2E6lLU2MfWrZxA3HILRbqhMm4cMxs7dAh9X25BDyJhyv797LJ39dXpnfNCIdK0DWZpahRe7Z8d6TRtytW30VYJGdm3j7/LunXDK7MxjD6KJiOxsXRnLV1qzv4iTdugPqcZbkCAs9nixSku03iDAQOAQ4fYcK1cudD3pyYS4ZaZ5+pBJD4+HpUrV0bbtiGmQ0QYM2Ywk6RJk9AzSYDI0zao6qzt2oWmqVGsWcM061BU7hp7OX0aGDiQA/8HH5izzxUrgKuuMl600624ehDp1KkTdu7ciYSELU6b4hlSUjhzKlwYmDvXnH2qQHq4zaCy4+xZ4M03qamZNMmcffbrR5dIJPZd8SqNGjGxYt48c1xPixczs7Fdu9D35TZ0iC/MUJkkU6eGnkkC0CX2xRdA+fKRoW0wU1MDcFD/7jvqaox0P9TYz6pVLDBapw4rM5jBkCGcSIRjTNHVKxFNcGzdyhjIrbeap+VQ2gYzgstux0xNjWLYMA7Eb7xhzv401uLzAU89BRQoYF48MSkJ+OEH4I47Qs/ycyN6JRJGNGnCpfeqVebtU2kbwl0gp6qzmqWpUUyaxBWhV/tnRxodOwKJiRz8zVo5DhjAzMbeYdpBSa9EwoT+/YHDh4GXXzYnkwSILG1D166sztq7t3k9Unbt4v/kscfCK6UzXNm7F5gyhb8fM3t8qMzGUHqPuBn91Q4DTp6k/qB4cWD0aPP2Gynahoyamn79zNtvOPTPjiRiY7liMHMl//33wIkT4Z0arweRMMDsTBLF4sVAiRLhr20wW1MDcH+ffMKByYw0YY21jBsH7N5Nt6OZxUWVCyucJxJ6EPE4y5ez496DD5qXSQJEjrbBbE2NYs4cZma98IJ5+9RYQ3Iy+8QULcpqvWbh8zFZ47rrzHMxu5Ew93SHNz4f0LYtM0lC7XHgj9I2hEPntZywQlOjGDaMq8I33zR3vxrzadECOH+eEwozY38TJkRG1WY9iHiY55/nauG99yiOM4tI0TaYralRnD7N2lt33+39/tnhzqZNwMcfs7Boy5bm7nvUKA5Kr75q7n7dhnZneZTdu4Hp09ngqHt3c/cdCdoGKzQ1ir59GaAN51VcOODzAc2bA/nysSSJmajMxlq1wj+zUQ8iHiU2lvdmf/mByNA2WKGpUcyZw5WhmTEqjfn06sXMqe7d2TfdTFSpoHDPbAT0IOJJxo7lLMfsTBIgMrQNVmhqFF99RXdW8+bm7ldjLkeOACNGsLugFZlTCxcy5f6++8zft9sI08tE+JKUBPTowfIJM2aYv/9w1zZYpalRqNpIkVCs0ss0asQOg4sXmz9ZWruWscpWrczdr1sJc29d+KEySRISzPe1RoK2wSpNDcD9btzIRlalSpm7b415zJ8PbNvG1XatWubvXwlWBw40f99uRK9EPMSGDdRvVK/O3ulmE+7aBqs0NYoxYziQhFP/7HAjNZVtbqOigEWLrNn/N9+wnW7x4ubv3424eiUSHx+P+Ph4JCdfcNoUx/H5uArJl8+aYDAQ3toGKzU1irFjuf+OHa3ZvyZ02rcHzp1jmZsiRczf/9Ch/K6ZWXvL7bh6JaKbUqXz5pvsLtizpzWuEqVtqFkzPLUNL7xAP3VcnLmaGsWBA+yh/dBD4ZuQ4HV27KCo9MYbmVRhBRMnMrPxqaes2b8b0V93D6AySUqVsi7gbZa2Yfx44LbbeKG+9FLW3fr4Y3NsNMrevRQUWqGpUfTqxXszA+pxcawa0LWrefuMZGJjeT6tWsnv3s2sv0ceCW0iERfHEjzFijF7rEkT7tut6EHEA8TEcIlshQ9XYZa24ZpruKTfupW3hx5ig6effzbHTiM0bMh7KzQ1iuXL+YO/4w5z9rdlC2e1t91mzv4ineHDgT/+YDykYkVrjmFWZuP69UCnToytrF3LOFv9+nTDuRFXx0Q0XH7/8APQoIF1OedK2/Dcc6HvS4kgFYMHc3Wigo12ozQ1bdqYr6lRLF/OH7hZLpKkJBa+nDQpMsRqVnPmDMV/0dGsZ2UFPh+wejVFi5UqhbavTz7J/HjaNE5Qtm1jbx+3oVciLiY1FejQgZkkCxdadxylbTD7gnXhAlNpz51zppy81ZoaxcCBdJP06WPO/jp14urp4YfN2V+k07QpCyHOmmVdvGruXGY2duhg/r4TE3nv1mwvvRJxMe3a8QL84YfWZJIA1mgbfvqJg0ZKCi/gS5cClSubs+9gePxx6zQ1iuRkNh6qWtWc/tnz5nF/W3QuiSmsXQusWwfcey/dwlZhVWajlCxTX6uWdSvpUNGDiEv58UdeUG6+2dqU0dGjzdc23HQTsH073QiLF3MwXL/e3oFkwwa6BazS1CgGDjSvf/bBg6z4+umn5lYVjlR8PqrG8+cHVq607jhnzjDz6667zP+/de7Ma8GmTebu10z0IOJSGjWyNpNEER9vvrahYEHghhv49513clY9erR1/mh/7NDUKKZP5yrRjFpZ27axIGD16unPXbjAAXHsWK6q8uUL/TiRQpcujPUNHGitK0hlNvbta+5+u3RhMsiGDUxYcSt6EHEhQ4ey73eHDkCFCtYdR2kbHn3UWm2DlLwA2oXS1Lz5prXlR378kSW/zaqRVLcuXYEZeeYZrkbfeEMPIMGwbx8TOq65Jr2irlXMns103MceM2d/UnIAWbqUrrjrrzdnv1ahA+su48wZBmijoxkLyQnVeTDjLdgLptI2mKk9eestxlj++IMXxN69+UOwq82u0tRcdRUzw3Lj8GGKwkqU4GqialWuBgJFnb+hQw2bm4lixej3zngrWpT2udUf7lZiY3kxXro0723HjeOFulAhrgI3bgz8OJs3A6dOmVu1uVMnJgHMmcPvxLFjvP3zj3nHMBO9EnEZTZowk2TOnLxXB7fcAnz2WfrjYGeqSttQtWqwVubM8ePA008DR49yILztNsYm7OqtERtLd1Ze1Vn/+osp0w8+SDHklVcCv/0WeCdHn4/nvly58O6f7UWmTKEuqVkzulNzY/58ijnHjeP3YcIErih27gSuvTbvY6lVTl4TlmAYP573depkfn7aNJZtcRt6EHERH3/MAHStWtSF5EX+/MbdNWZrGxRTppi7v2CYO5eZTYFoaoYNA8qW5Q9Tcd11gR9r8mSmYFtVPkOxbp21+w83UlLoCipShN+HvBg5kvqo55/n4/ffZ5HT8ePzXqGnpTFeccMN5ja1ktK8fdmBdme5BJ+PLp/8+XmBD4S9e/nlvf56+uV//z3w45mtbXCaYDU1K1Zwlvr441yFVKtGcV+gjBrFlV+3bsZt1phPq1Z0+4wfn3cNuNRUui/r18/8fP36wNdf532ssWM5kIR7D/W80IOIS+jcmS6Wvn0DyySpWZP6hzVrePE7doy58KdO5f1epW2oVs0cbYMbUJqaUaMC09T8/jsvNBUr8hy++CLwyis8p3lx4gTwyy+R0T/bS3z7LSdgVaqwYnNenDzJ7Lerrsr8/FVX8feUFx98wMxGq1ejbkf/BFzAvn0MopctG3gmScZMkCpVKO6rUIHK7Lxmx0rboGr9eB2lqbnpJuCllwJ7j8/HlYgqmFitGv3o48fnfQFS/6MBA4zbrDGfZs0YBws2rVuIzI+lzPqcPwcOcCJSv76u2hzhH98dxMTwixtKn4uiRTmY7N2b97bTppmnbXADSlPz0UeBv6d06azix0qVeHHIiwULgMsvd2cdo0ilTx9m5r3ySmABcQAoWZIuSf9Vx4kTWVcn/qgJmJkBda/i6kEkPj4elStXRtu2NZw2xTImT2YmSIsWoVWAPX8e2LWLF8fc+PFHZlA1amT8WG5CaWqefz44Tc1992Utr71nT96ZVl98wVpGkdI/2wucOMEVZYkSTO8OlIIFmdK7dm3m59eupWs4N5YvB664Iu/sr4hASummW7asX58oAcj16xNz2sST/POPlIUKSVmkiJTnzwf33u7dpVy3Tsrff5fym2+kjImRslgxKf/4I/f3NWggJZD3dm5j1izaPWtW+nN//SVlgQJSRkdLeeFCcPv77jsp8+eXcvBgKffulXL2bP4fMu4/O2rVoh2nTgX7CZwlu/MXLtSsyc/2+efBv3fePH6HpkyRcudOKbt2lbJo0dx/H8uX83jduhm32Qm2baPd27bluImh67aOiThIy5ZMSZw5M/hugocOAa1bMzh4xRXA3Xez3HpuM+lw0zYoTY2R6qw1alCI1qsXYxvXX8/0ztxEkampFJdVruzeiqqRxtKlDKjXrcveNcHSsiWTUQYMoLbp1ltZ0j2334fKbDS7zIlX0YOIQ3z7LdNMb7vNWCvNefOCf49d2gY7WLOGmpr77jNenTUmJrj3vvsus3l69DB2PI25pKVRfFewILBkifH9vPxy4L+J5GSmBavunRo9iDhG06acPQcTDA6VkSPDQ9vg83EVlj+/td0K/ZkwgTqUdu3sO6YmZzp0AM6eZVq3XRf0QYPCK7PRDFwdWA9X3nmHS+dXX7WvOueJEwwkh4O2IVhNjRn89htLtYfaP1tjDrt2MZ29fHl7e9BPmwYULmxtewGvoX8ONnPiBMsplCwJvPeefcdV2gavt1s9cSJ4TY0ZqGZDSleicRaVXWjnSlRVbbayuZUX0YOIzcTG0q++cKG9M1qlbahVy75jWsGIEaFraozw0UdMn3aiT7wmM6NHA7/+yliinf8P5cIys+p1OOD6QSQ5mQFUrzNlCrUg333Hirb+FTqt4tAhLr29rm2YNYv3hw+HrqkJhl9/ZUHHf/5hoT6vYiQRw21s2kQxYbduLJE+dap9xx40iAVSy5a1tsePlRw8yPuzZ03esdHcYItumTh6lDnbAHUiTz7pTZ1I6dLMz1a3P/+057iff575uA89ZM9xzSZ//syfI1hNjVEWLsx83CeesOe4ZlOgQPpn+N//nLbGGB06ZP5fvPiifccuWDD9uAUL2ndcMxkzJv0z5M8v5Y4d2W4WfjqR7t1ZVE8xZ4553cPsIimJQfSM1KtnT5qofx2pL75gFzYv8f33TOXMSNWq5vQ0zwtVHlyxYIH3lP6ffEItjcLn48rKriZhZjF5cubHU6bY45pduJBp8YrUVCbE3HWX9cc2kzfeSP87LY2Nr8xqMyCkdFXx+kzGtG1LIR5wFkA0gEQAOjlbo9FoQuGhh4DPP8/ydB5lJ7PH1YPI6dNUEp89y0GkVq1EvPii9waRtm05AwQYTJ861Z40299+y6yqrVaNqzuv4S/GVPERq/m//6PAUHHvvd4Uaj79dHqjIyHUxMxb9O7NGmmKLl3YDsEOMv5+ixQBJk6057hmsm5d+mquQAGmSGcT2zE0iBjygQF4GcA+ACkAtgG4P4/tLwMQD+DoxffsAtAgm22zcP68lO+/793aWaNGpccjxo+399h79vDYlSvnWi/H1bz1Fj/DTTfZX/vpm294zDvuyNGH7AlKlZJSCO/Wzjp4kLGcK66Qcvhwxkrt5LLLWONu4UJ7j2s2a9bwO7BpU46b2BMTEUK0BPD+xYHkKwAdAXwshKgspcxSSFsIURDAWgAnALQAcAhAWQB/B3K8ggU5g/YiZ8/SF1msGMt02C3y69WL9wsWeDM19dgxtrEtWZKakKeftvf4SoeyfLl9olCzUdqGmjVZaseLxMRwJbB8Ofvm2Mm6dcCZM2xa1qKFvcc2m5IleV+4sLn7NZLi2w3AFCnlZCnlLillVwAHAeTUDuhZAMUBNJFSfiWl3C+l3CSl/D9jJnuH5s0ZiJs2zRmV+OrV3tY2NGqUrqnJq0mQ2fh8vIBUqODdAQRI1zZ4VWE9axbdijEx9g8gQHr76IED7T+2VwhqELm4qqgO4FO/lz4FkFMF/kYANgOIF0IcF0LsEEK8JYTIl9Nxzp8/j7Nnz/53O3fO7MRm6/niC1bMvesuZ5o/zZ3rbW3D4sXAli32amoyEh/PLJYuXew/tln4fOyNUbZs3k2W3EhqKtCxI1CoEDB/vjPH//pr4Oab02fxmqwEuxIpCSAfgON+zx8HUCqH95QH3Vj5ADQAMAhAdwA5JmnGxcUhOjr6v1uDBmWDNNNZfD7O/PLlA1audMaGoUMZxLcjFdZszKrOGgqjR3P16OVBZOpUXggDbRnsNp58kmLjDz5gQNtuRozQVZsDwahi3T+lS2TzXMZjnADwgpRym5RyHoDByNn9hV69eiExMfG/2+rVBw2a6Qzdu7NHwVtvAVdeaf/xz5wBfvqJXdcKFbL/+KHy7LPU1wwfDlxySe7bbtjAUjJlytDl5V8O5fhxDkhlyvBC9OijebcQPnSImW116ni72OKIEZzIeDEj7/vvgUWL2LLYX69jF+PHs2rzM884c3yvEOxP5CSAC8i66rgSWVcniqMA9kgpL2R4bheAUhfdY1mIiorCpZde+t+taFHvpPUeOACMGcNYxIABztjQvz9TOr3YNOfnn+kHr1CBoq68OHcOuP12YOzYrK9JycZVv//OoOwPP7DZ0MMPZxax+qNWb14utnjyJPDLL0xLDrbhmRto0oSTAjtbJWREVW2uV8/bEwk7CCrcK6VMFUJsA1APwNIML9UDsDyHt30FoI0Q4n9SyovZ1rgRwFEpZWoO7/EssbF0Zy1dmve2VjFrFjPCGjRwzgajKEV4oG7Axx7LuYrB3r3s9rhjR3pywbhxXB3OnZvzDHfpUvrAa9QIznY3oTLLnJrIhMLgwbyAv/gidWJOoDIbdbHFvDEyxo4E8LwQ4lkhRCUhxCgA1wL4EACEEAlCiIynfjyAEgBGCyFuFEI0BPAWqBsJKxISmFLZuLF9Qih/vv2Ws9CmTZ05fiiMHMlVQ9u2dGOEyvnzvM/o0suXjzPzTZuyf8/q1cDffxvrNukm5s8HLrvMmaSEUDh9GujXjxWn4x28QqxaBZQqxXa5mtwJehCRUs4H0BVAHwDbATwACgeVnvRaAKUzbH8QQH0ANQD8CGAMgNEAhoZgt+tQAcxChZytmKpmoIMHO2eDEc6e5eyvWLGsdZKMcvPNdF/16sUmVqmpTDg4dixrPTNF//50o/Tvb44NTvDFF4yLtWzptCXB07gxEytmz3bOjTR/PjMbn33WmeN7DUP/JinlOCnldVLKKClldSnlhgyv1ZFStvfbfrOU8m4pZSEpZQUp5RC/GIlpxMXRDVGsGN0WTZqwo19Gzp9n1k3JkkDRonShHDoU2nHbtGEmydixzgWzvaxtaNbMfE1NgQJMFd6zhx0QixTh+XnsMa5I/ElJAbZuBapU8Xb/bBULM9qALK9kBSm5WihThsK1OnUYywqV1au5QnzgAWcLrcbFeTez0QnCLmS0fj0rVH7zDXPk09KA+vUzB1K7dqXfe948fmmTkihmumBwWPv+e16sKld2VpehtA2BBKTdxOef82aFpqZ6dWD7ds7Mjx5lVdtTp7L3tQ8ZwoHYy/2zU1OBzZtD0zbklqwAMGtu5Ei+vmUL3T716tENaBSfjym9+fMzCcIpzp6lS7p6dWfSij2J0XopFt2yZf1647WzTpxgvZj16/n4zBn2V5g3L32bw4dZm+eTT4LevZRSyrJlWZvo99+Nvd8sKlRgr4ALFwJ/z/r1UsbEpPc8Wbo08+vt2mXu4wBIWbOmeTZfuCBliRJS5ssn5fHjOW83a1betZ+ys9+fPXv4v16zJutrpUtLWbhwQGa7liFDeB4mT878fCDnLzv8z6nPx1pcQ4emP5eSImV0tJQffmjUaik7duSx4uKM78MMunWjHStXOmuHFWzbxs+WSx09Q9ftsFuJ+JOYyPvixXm/bRv7K9Svn75NmTIMoH39dfD7HzSImSQvveRcJglgXNuQ16wToLbi6NH02+rVIZv7H6FqapKSuNLYvp2P9+3j3wcuVnFbuJAuLJXmW68eXZwZ//8A3TFHj3ozoy0j48czccAqbcO+fYwpZTx/UVFA7drGfj8Av7cTJzJ+pXrZO8XMmdQm6T7qgePqplShIiVbadaqlZ5lcewYf2SXX55526uu4mvBcPo0A7CXX05VrZMY1TbkliKriIqiy8JszNDUbN0KPPhg+uNu3Xjfrh0wfToHhm7dKDosXZqZX++8k3U/4dA/W2kbGja0LiitfiP+ZVSuuipzqfZgiInhb3XFitBsC5WtW4E//7S/0KfXCetBpHNn+jdzSufMiJTBF/lr1IgxiLlznRckLVlinbZh3TquEi67jDPOwYPNUeKr6qyhaGrq1EnvlZEdr7zCW274fKyyXLYsULGicVucRmkbhtqQ9+j/WzHy+wGACRMoimzZErjtNnNsM0o4iEydIGzdWV26cGbz5ZeZM5VKlWLw8a+/Mm9/4kRwRepWrQK++ooX1UceMcdmo6xeTbeOFTOoxx5juuUXX7CMxpYt7IqmNBhGSUhgaZZGjZzT1ChmzuTn6djRWTtCxQ5tg1qR+q/ag/39AMxm7NqVGZIJCaaYZxifj9eK8uW9l9noNGE3iEjJFciSJbzw+ccpqldn6ufatenPHT1KVfO9OdUh9sPnoxitQIGs6Y9OoLQN/fqZv++WLekeufVWpn1+/DFTZkMpR5GaSjWyU9VZ/Rk+nCm/PXs6bYlxlLbB6jpP11/PgSTj7yc1lVmRgf5+FE88wbTqCROcL80ybhxjpV4uuOkUYefO6tQJmDOHQdRixdJnTNHRzGmPjmYabvfuQIkSDLj36EFtwMMPB3aMjh0ZsB82jC4eJ0lOtlfbULo0A6B5FTHMjdatecGbPNn5ApEnTwI7dwL33ef8hSwU4uI4kVBi01BISgJ+/TX9sUpWKF4cuPZarh6GDKHrr2JF/l2kCLVSgfLVV5yIVKvG1F6nUVWbO3d22hIPYjSty6JbtgST4uufjqpu06alb/PPP1J27ixl8eJM6YyJkfLAgTx3LaVkiqgQUpYrF9j2VvP22/x8GVOWjRJIiuzJk1JGRUk5Y4axY2zZIv9r2RsMRlNU8+Kll7jfzz4zd792kpjI7+Sdd+a8TTDn78svs/8NtWvH130+Kfv2ZapvVJSUDzwg5U8/BWdzqVJMtT58OLj3WcHhw/x8des6bYm1WJXiG3YrkdyCrIpChZhNZSSjKjbWHZkkiilTuMIyWuIit1ln8eJ0kTVvzhXIH38wi6lkSeO1uZo25Yx51Spj7zebefO4Oq1b12lLjKOqNmeXdWaEvJIVlOvUqPv0rbfoIejRg+n1TqMC6l4rFeQWXD2IxMfHIz4+HsnJllRICZrx41lCpVUr5zNJgHRtQygq79xSZMePZ/A7IYGK79Klue38+XQVBsuAAdSzOK2pUWzaxASLDh2ctiQ0lLZBVUB2M8eOMQZ1xRV0B7uBxYvp2nY6wcOzGF3CWHTLllAU62Zx7hyX7kWLSvnvv46ZkYlGjbg83bPHaUvy5tQpqukvvzw4Rb3CCndW7drcZ25Kebfz3Xf8DE8+mft2VrkDg+XOO2WmChJOs3o17XnlFactsR7tznKYFi2YBjpjhnkFAkPBa9qG2Fj3aGoA2rJpE3DTTc50nzQLL2kbFizgyveRR1hk0Q2EQ9Vmp3HBz9n9bNrE1NY77nBPee0ZM7yjbVixgiUx3KCpUYwcyYKbyn3nRVTV5vLlmTXlZtLSmBUZFcW2t24gJYW6p1tvdT7L0su4YE7tbnw+xhz+97/Au+3ZwXvveUPb4POx1IhbNDWKceOY0utU/24z8JK2oX17JnGMGcP4jRsYOpTfT6X01xhDr0TyoHdvqnG7d3dHJgmQrm24+273axuUpmbQIPfM9vbtY52nunXd4Vozile0DT//TO1WxYruGvAmTWKmZuvWTlvibTz8E7KeI0eAd9+lz9yOekSB0qcP793ux927lynI5coBr7/utDXpqGKLXogj5MSRI0zNfuABd8TociM2lvduWsnv2sVz6PWqzW5ADyK50KgR/eaLF7trxuoVbYNbqrP6s2IF6zxVreq0JcZRA6HR7oV2MWIEV37t2zOJwS3YWawy3HHRpdFdzJ/P3iOPPspS8m5hwwZqG554wmlLcmfcONbYcoumRrF4MUvFWF1jymqWLKG24Z57nLYkZ86e5cX60kvZL8QtqMzGa67xRmaj29GDSDZkzCRZvNhpazKjXFlunoEmJzPrqWhRZpG5iSFDmNJplrrbCT7+mK1o3VBzKjeaNmXgPyHBXS63WbOYmeV1kalbcNG/1j20a8eOf/Hx7uqz7BVtQ0ZNjZsC/0lJwA8/MFXbTf/XYPGCtuHzz1lF++67gcaNnbYmM8OH0z3tdBfFcEGvRPzYsYOCuBtvBF5+2WlrMuMFbYMbNTWKAQMYo1ECPS/iBW2Dz0d3a/787gqmA+xG+vPP3shs9Ap6EPFDZZK4pUBgRtyubXCrpkYxYwZdbEaLR7qBIUN4nt94w2lLcqZrV16s336bxTrdhHJjGm3HrMmKHkQy8O67rFT77LPuC7gpbcPDD7srUywjvXq5T1Oj+P572uY210qwTJnibm3D/v10A199NdC3r9PWZMUrmY1ewqWXI/s5c4Zujuhod2WSKFRKZ1ycs3bkxJEjTOd0m6ZGoVxYbj1/gZBR2+DWiURsLFdKS5c6bUlWNm3iCqlFC6ctCS9c+lW0n2bNmEkya5Y7f6BK2+CmdNmMuFVTA/Ci9vnnwHXXub/GVG4obYNbRZIzZrB1QNOmQI0aTluTFeXKcnNmoxdx2c/dGdauBb78kj2iY2KctiYrixa5W9vgVk2NYsIEThDcXh4kN3w+4JNP6CZyk2hPkZLCPjGFC7PEidtISwM2bmTCTKlSTlsTXrg6xdeOplQ+HwVx+fOzL7sbcbO2ITXVvZoaxahR/P+++qrTlhhn1iymTb/wgtOWZE+bNsA//wBTpzJm4zZGj3Z/ZqNXcfVKpFOnTti5cycSErZYdoxXX3VvJglAbcP27e7VNrRvT03Ne++5075jx1jD6/773SV4CxY3axu2bmUM5NZb3btaHjuWmY1aYGg+rh5ErGb/fqbNujWTBHC3tkFpaipWdK+r6O23eT9woLN2hILSNtSs6U5tQ5MmHODcmBYP8Hf+xx/AQw+5L14XDkT0KW3YkO4sN/W58MfN2obYWLrZPvrIaUtyZuFCoHhx4L77nLbEOMqN6UaFev/+wOHDQKdOrNbsRlRCgpcz89xMxA4iU6ZwdtesGXDnnU5bkz1u1jYMH+5eTY1i7VoWAWzTxmlLQmPuXBYxrFfPaUsyc/IkM52KFwfef99pa3JmxQqmnnu5arObichBJCWFzXEKFwZmz3bampxxqzbkzBm6idyqqVH06+f+GlN5sWkTqzY//rjTlmSlUSNmPc2b51430dKljNm1b++0JeGLh0ONxmndmpkk06e7M5MEoJvtiy/cqW3IWJ3VrReP1FTgm2+AypU5U/YqbtU2LF8ObN4MPPig+1ZIGRk82L2ZjeGCSy8B1rFlC2MgVaqwWq9bcau2Ye1aYN06amoaNXLampxR/bPd1FExWJS2oWJFd2kbfD6gbVugQAF3xxOTkugSrlbNPX3dw5GIW4m4PZNE4UZtg8/Hyrxu1tQoJk7kKvOpp5y2xDijRlHb8NprTluSmeefZ6zpvfcYq3ErAwcys1Fl6GmsIaJWIn36sPZQ587ucxFlxK3ahi5d6J93q6ZGsXs3M4YefdS97rZAGDeOs/2OHZ22JJ3du+kGvv56Ftp0M27ObAwnPPwTC46TJ6n8LlGCMzw340Ztw759wPjx7tbUKFRCgltrTAWC0jbUreuugVC1Slixwlk78mL7duD48XR7Ndbhoq+ntcTG0jUwf767fpTZ4UZtQ2wsXQNu9oEDdLmtXs1S9JUqOW2NcdyobRg7livk1q2pTnczaiLhxorS4YbLL6fmsHQpM3Ueesj9fQTWrHGftsELmhrF3Lnh0T/bbdqGpCSgRw8GqGfMcNqa3FFVm8uVc68AMpwI+0EkLY054gULurPHgT9u65/tFU2NYtgw99aYChSlbXBT9mCLFiwAOWWKu+J02TFpElO8O3Vy2pLIwOVfh9Dp0IEz+xEj3J1JAvCL/+23wC23uEfb0KqV+zU1ijNnWM+rZk3325obStvQp4/TlpANG7hCrl6dvdPdzqhRQL587stqC1fCeiWyezeX3uXLe6MEtNI29OzptCXk22+Zyut2TY2ib1/Gbfr1c9oS47hN2+DzcRWSL5/70+IBlgnavZt9bdy+YgoXwnoQ8UomicJt2oZmzbyhqVHMng0UKwY88ojTlhhHaRtUYNhp3nwT+PNPTmzcJHjMCVXt2m0K/3DG1YNIfHw8KleujLZtg++1+cEHzCR56im6h9yO27QNXtHUKDZvBk6dApo3d9qS0Jg+nX1Z3PA5jhyhG7hUKXdlieXGwoXA5Ze7s8NmuOKCy1XOGG1KlTGTZOpUi4wzGTf1zz5xwjuaGoXS1gwe7KwdobB9O8+9W8rJxMTQnbVokdOWBMbnnwOJiUxB1thHWHoNmzdnkHr2bG/4RX0+4OOP3aNtaNTIO5oagBl4GzawxlSZMk5bYxw3aRvmzgV++AFo0MBdeqXcUCJYN4l0IwEPXCKCY9064NNPqWdo0cJpawLDTdqGpUsZUPeCpkYxdiwHkldecdoS47hJ25Cayu9iVBTdQ14gNZUuTa9XbfYiHpinB47PxxTEfPmAlSudtiZw3KJt8JqmRvHBB6wx9fLLTltiHKVtcMNnaNeOOpUPP2R8xgsMH+79qs1eJaxWIj17MpPkjTe8kUkCpGsb7rrLeW2Dqs4aF+d+TY3iwAHg99/Z18ILrrecGDmSkx+nU9F//JFNpm6+2V2FH/NiwgSunJ5+2mlLIg8P/+wyc+gQW3SWKuWt4GqfPu7QNuzaxSZTXtHUKFQcwUv/c39OnAD27HGHtqFRIwodvZLWDTAL89Ah92Q2Rhphc8pjY7mcXbLEaUuCY84cd2gbVEaQVzQ1iuXLgSuucH9Nr9xwi7Zh6FBWD37+eaBCBWdtCQY3FquMJMJiEJk9m+mRDRsC99zjtDWB4xZtw+jRwK+/suijFzQ1ihUrmM7tdReGG7QNZ85wVRwdzViIl1i9Gihd2h2ZjZGI5weR1FTghRcYT1iwwGlrgsMN2oakJAYjL7mEQjcvMXAgXS9u72+SG0rb0KqVs3Y0bsx2zHPmeMslNHcua7s9/7zTlkQuns/OeuopIDmZgTWvZJIA7tE2NGvmLU2NIjkZ2LYNuP127yQBZIcaAJ10ZX38Mb+LtWpRF+Ilhg7loOeWMjGRiIfmHFnZvp2ugJtv5mrES4wZ47y2Yd06YO1ab2lqFIMHMyFB+cO9iBu0DT4f8OSTnEAsX+6MDUY5cwb46Sd+f53ObIxkDA0iQoiXhRD7hBApQohtQoj7A3xfKyGEFEIsM3Jcfxo39l4miSI+3lltg88HPP649zQ1iqlT2ePEC6XJc8IN2obOnYG//uKKyGsivf79OZHwsjszHAh6EBFCtATwPoDBAKoB2AjgYyFErmX6hBDlALx3cfuQiYujRuCFF7yVSQK4Q9vQsyf7zr/+unc0NYoffwSOHWNtJy+Tm7ZhwwZmHJYpw4mSf1tiIbK/vftu4Mfft49B9LJl0+NzXmLmTGY2es0FF24YuYR1AzBFSjlZSrlLStkVwEEAL+X0BiFEPgCzAfQF8LsRQzNy+jQzSS67DBg3LtS92Y/T2oaMmho3FHwMFnX+vJzSqbQNjzyS/UTi3DnGe8aOzf79R49mvk2dykEkmEy/hg05k/cfoLzAt98ys7FZM6ct0QQVShVCFARQHYB/ibhPAdyby1v7APhTSjklUNdXbjRpwniC1zJJFMuWOattUNVZvaapAXjRW7uW5em9tgLNSF5Vmx97jLec8F89Ll/OlW358oEdf+JECkxbtADuuCOw97gJtXLy4iQo3Ag2H6ckgHwAjvs9fxxAtk4RIcR9AJ4DUDXQg5w/fx7nz5//7/G5c2f/+3v1amDjRuD++3P/kbmVFSs4y3SqpMSsWcD//Z/3NDWK9esZkH4px3WvN1DaBjN0OcePAx99xC6egZCSArz6KrMZZ88O/fh2k5bGpJAKFbxdtTlcMDqPl36PRTbPQQhRDMAsAB2klCcD3XlcXByio6P/uzVoUBZA5kwSLy7BAWe1DampHLy8qKlRrF7tjhpToWC2tmHGDMYGAnXttGzJgWTCBBbb9Brx8RxIXn3VaUs0QPCDyEkAF5B11XElsq5OAKACgOsArBRCpAkh0gC0BdDo4uNsHRK9evVCYmLif7fVqw8CYJG6M2eAAQO8l0kCOK9tUJqa0aO9panJyJEjwL33evPip4iLM1fbMHUqJ1eBpLnu3cvV8G23uacNc7CMGcPMxk6dnLZEAwTpzpJSpgohtgGoByBjsfB6ALLLMv8FQBW/5wYBKAbgVTAgn4WoqChERUX997hoUd6vXElfuFe1AYMGOadt8LKmxp8BA5y2wDiqanONGuZoGzZuZGvl+fMD2370aA5gH30U+rGd4NAhZjbWq+fNeGg4YkSjPBLATCHEVgCbAbwA4FoAHwKAECIBwGEpZS8pZQqAHRnfLIQ4AwBSykzP58TJk5ldV14TRGVk2jSuAJzQNnixOmtGZs3ifcGCQJ06jpoSEmZrG6ZMAapX5+o2N1RJmzNngNdeA665xpzj240qVunlqs3hRtBjuZRyPoCuYMbVdgAPAGggpdx/cZNrAZQ2w7j9+/llV32+y5QBqlY1Y8/2o7QNDRvaf+zBg4GDB72pqQFY1+uTT/h3air94UbIS3sBMGOpUSMWIixWDLj7bup6zCJQbUNSEleP27fz8b59/DujLWfPcnWZV2wlKgr47LP0x++9Z8Bwl7BkCVCyJFdyGpcgpXTTLRMtW0rJeVuiBCD/979E/008Q8OG/Cy//mrvcU+dkjJ/fikvu0zKCxfsPbYZbNyovgPpt2eeMbav1aul7N1bysWLuZ+lSzO//uuvUhYvLmXPnlJ+/72Uv/0m5apVUh4/HvLHkFJK+c03PG7btnlv++WXWT83IGW7dunbTJggZeHCUp45k/N+JkzIuo9+/UL9JM6wciXtf+01py3xJtu28fxt25bjJoau264uuVe4cObHQjhjR6j4fM5pG7yuqbn88qzPlShhbF95aS969+YKYfjw9OcC1V0EQjCumDp1eMnPjRdeyDu+VbJkYM95gQEDeA1wuoGbJjOuvqx88AFFeQqjAeG83BhJSawhdM01HLgqVQLGjzdsdhamTnVG2+B1TQ1AHcVll6U/LlgwuNIegeLzMdh8441UkV95JVCzpnmp5Glp1LhUqGBvPEI1G1MUKWJeVtPffwNduwLlyvF3c++9wJYt5uzbH5XZeNtt3q7aHI64ehC55BK2Dp05k4+N9lzIq4TEa6/R5z5rFn3ir70GdOliXhB/xAj7tQ3hoKlRZLxoTJ1qzTFOnOBkYuhQtln99FOgaVNqL9avD33/TmkbnnuO92oSMXGieft+/nmusGfOZDXd+vWBhx8GDh827xiKuDh+p72amRnWGPWDWXTLlvXrGRNZvz70mEh2vvBbbpFywIDMz91xh5Rvvx3y4eSff/KY998f+r6CoWNHHnfQIHuPaza//srPUbUq72fNMme//t+Dw4f5XOvWmbeLjZWyVavQj1e+vJQFCtgbl9q5U0ohpKxQgefNzPOXnCxlvnyMGWXk9tsZdzKb0qUZ/9EYx6qYiKtXInZRqxYFWIcP0w/95ZfAnj3m9D1XNX7s1Db89htnnGXLpvvhvYqaebZsae1xSpbkqq1y5czPV6oUenaW0jbUrm1vXEpVObai1H9aGnDhQlatS+HCwKZN5h7r559ZZNKJzEZN3uhBBFTAVq5MX3XBgnRnjBtnTs/r+fPp07dT2xATw8FwxQr7jmkVq1ax2GDZstYep2BBpo3u3p35+T176PMPBTWQ21kscORIDlxPP21N7/FixVh7beBAVhG4cIHu4G+/5QXfTJSyf6h/2VeNK3B1dpZdjBkDfPMNL7rlyjEQ//LLLJD38MPG97tuHcVdL75olqV5M2EC8MsvbDjlVU2NYsEC1ph67TVz9peUBPz6a/pjpb0oXpyZcz17csXzwAOsiPvJJ5zFr1sX2nHt1jacPcsVXLFiFCNaxcyZwLPPAldfzZjfHXcAbdoA339v3jF8PmDNGk4ivKhxigiM+sEsumWLlTGR5GT6qv19u889J+Ujj4R2rPvv5/H+/DO0/QTKuXNSFiokZZEiUp4/b88xraRqVfr0z50zx6cfiPZiyhQpb7iB5/H226Vctiy0z+CEtuHhh3nMRYvSnzM7JpKRpCQpjxzh3088IWWDBubte+rU8IjtuYGI1InYwb//8ubvq86Xj7Mgo6SmAl9/zVpVduXlP/EEq7POnOntAoUAZ9P/938s6WFWschAtBfPPsubWditbfjiC6rT77oruAZVoVC0KG9//cVVQ0adTai8+y5/iz17mrdPjblExCCSlxujdm1+SQsXpjtr/XogIYF+ZaOMGEE/cY8eIZsfEJs3U+dw++3erc6aEVVj6p13nLbEOErbUKWKPdoGn48TiXz5rAmm+7NmDf9HN93E31fPnvz7mWfM2f/Jk0y5r1XL+5OicCYiBpGtW+njVii9Rrt2LEw3bx59yE8+yda75cpRVRxKLGP8eNYsMusHlRfNmnE15dUCi/7MnEmdkL9YzksobYNZJd/zont3tox9+22KJa0mMZG/m0OHOCFr3py/mwIFzNl/nz6879/fnP1prMHVg0h8fDzi4+ORnHwhpP3k5cYoVYoVds3it99Y8LBhQ3tSOt96i8Udu3XzbnXWjGzdCvz5JzOLvMyUKVzdWp2eDDANecwYJoMMHGj98QCueqysSD1vHgthPvSQdcfQhI6rU3w7deqEnTt3IiHBoloKFqG0DXakJB47Rh/0FVdYUw7ECZxIiTWbHTvs1TbExnLVs3Rp3tt6gQ0bGGNxom2CJjhcPYh4FaVtuPVW648VG8vYy4IF3iyw6I/PR7Fn+fLeXlXZOZFISGCrgUaNWO8rHFCxsEGDnLVDkzdhcNlxF/PnU9tgZoZPTixaRNdP/frebtSUkXHjmC3XpYvTlhhHVW22Q9uQmsrYXaFCgXc3dDtpacBXXzGz0Y7YjiY0XB0T8SKqf7bV5UbS0hi0L1gQWLzY2mPZyZgxLD/SubPTlhhnxgzg/HmgY0frj9WmDSctkyaZ027XDYwcydV19+5OW6IJBD2ImMjZs3QrmKltyIn27Zm6PGYMs5jCgSNHgL17GUjN7+Fvpl3ahu+/5wSicuW8uxt6iXHjODmyYzWvCR3tzjIRu7QNP//MJlM33OBtt48/avXmZT+40jbcc4/12oYmTShkDJe0boAarv37WW4oHGJ8kYD+N5mIXdoGtf9wungAnFWXKMELsFdREwirtQ2DBjGN/MUXgeuvt/ZYdqISEuLinLVDEzh6EDGJLVuobWja1NrjqOqs7dpRHRwufPwxO+U9+aTTloTG/PnWaxtOn+YgdfnlOTda8yorVzKz8bbbnLZEEyh6EDEJO7QNZ88Cb77JEhqTJll3HCdQNaa8rE62S9vQqBETK2bPDi+Xz6JFLBXTvr3TlmiCwcPhS/fg87FcuNXahqZNmf46f763A8/+pKQA331HXU3Gfupeww5tw6pVTH+tXTu95W24MGQIJxJerpcWiYTRPMY57NA2fP45K7TWrGm9y8xuhg7lQPzGG05bYhylbbjpJuu0DT4fi2sWKAAsW2bNMZwiKYlFUe+4w/rMRo25hNF81jlGj7ZW2+Dzsf5Svnzh0a3QH6VxaN3aaUuMo7QNqrinFXTsyKKHcXHeXrFlx4AB3q/aHKnolUiIHDnCMti1a1vnYnrtNXurs9rJrl08hw0aeNu/r7QNVuk19u5lQcdy5RgXCzdmzGBPksaNnbZEEywe/tm6A1Xme/Bga/a/fz8zcMqUsa+xkZ2EQ/9sO7QNsbGcqYfjSvT774ETJ/QA4lX0IBIiS5ZQ22BV4TtVnTXcfOAAP9cnn7BHd8WKTltjHKu1DePHA7t3A61ahWfqq5pIaG2IN9GDSAhYrW2YMQP46SfO0GrUsOYYTjJrFjOzXnjBaUtCY+VK4KqrrLnAJyfTnVm0KL8P4YbPx4SR669nl1GN93B1YN2splRW0b+/ddqGlBTgpZfY1GjePPP37waGD6f7x8s+fqVteOUVa/bfogWLOU6bFp4tYidMYGajlwtuRjquXom4uSlVSgpV6lZpG1R11g8+CJ/qrBk5fRrYuRO4+25vXxyt1DZs2sTVbrVq3s5cy41Ro5iQYtUgrLEeVw8ibsZKbcPWrexQd8stwHPPmb9/N9C3LwPFXk4WsFLb4POxZ/n//hd+NdIUx44x6+z++8NLPBtp6EHEIFZqG1R11o8+Mn/fbmHOHJZvqVfPaUuMY2XV5t69mbHUvTsz88IRFVC3qye8xhr0IGIAK7UN/fsDhw8zHlKunLn7dgubNtGd9fjjTlsSGgkJ1mgbjhxhT5Irr/R26nNeLF4MFC8O3Hef05ZoQkEPIgawqn/2yZOsu1S8OGMh4Uo49M+2UtvQqBHV7wsXeluAmRtr1rCgqNerNmv0IBI0VmobVHXWefPC9+KRlsaVyI03suS3V7FK2zB/PrBtG/DII8ADD5i7bzehMhsHDHDaEk2ohOmlyjpmzWLKpdnahuXLgc2bgTp1vB0nyIvRozmQdO3qtCXGsUrbkJbGRIqoKIpYw5WUFODbb5k4Em41wCIRnRMRJFZoG3w+oG1bVmddutS8/bqRsWP5OTt2dNoS43z4IbUNnTqZu9927YBz5+jKDOdKtsOGeb9qsyYdvRIJgtOn2d/cbG3DCy/QPzxoUHjPzPbvB/74A6hb19vuuvffZ0rqq6+at88dO4C5c+kiDXfhncpsbNPGaUs0ZuDhn7L9qICwmdqGvXuBqVOB664DXn/dvP26kXCokWSVtiE2lvcrV5q3TzeyezezDx991NsTCU06+t8YBHPnmq9taNiQWoNwv3gAjPtceSVQtarTlhjHCm3Du+9yhfbss2xqFc6ozEYr20hr7EUPIgGyaRP7Z5upbRg7lrPa1q1ZPiWcWbqU/v527Zy2JDTM1jacOUNhYXQ0MHGiOft0Kz4fy7hcfTVQqZLT1mjMQg8iAWK2tiEpCejRg2K1hARz9ulmBg9mSmefPk5bYhylbTDTl9+sGYP0CQnh796ZM4eZWR06OG2Jxkx0dlYApKUBGzeaq214/HGmCickhH/doORkivOqVQMuucRpa4xjdtXmtWuBL78E7rmHGqFwR2U26qys8CLM5z7mMGoUFcRmaRs2bKBgsXp14IknzNmnmxk4kHGft9922hLjZNQ2FC8e+v58PjaZyp8/PLsV+nPmDDPQ7rorPKtSRzJ6EAmAcePM0zb4fOwRkS9fZFw8APbCKFIEaNrUaUuMY7a24dVXmTL+9ttAyZLm7NPN9Onj/arNmuxx9SASHx+PypUro21b59r6ma1tePNN4M8/w7s6a0a2bweOH/e+u8ZMbcP+/ZyYXH01S+JHArNnM7PxkUectkRjNq4eRNzQlMrM/tlHjgAjRjDN1ctaiWBQKbFerkZrtrahYUOuapYtC31fXmDzZq66mjd32hKNFbh6EHEDK1aYp22IjeXFY8mS8M/EAfhZP/+cJe29XNbeTG3DlCmsetC0KXDnnaHvzwuoWJjWhoQnEXApM46Z2oa5c5mh9NhjkdM/YfJkIDXV/BpTdmKmtiElBejSBShcmOmukUBaGhNJKlb0dtVmTc6EeXJpaJilbUhNZW58VBSwaJE5tnmBkSOZQPDaa05bYhwztQ2tWwP//ANMnx45GUpjxni/arMmd/QgkgNJSeZpG1R11vj48K7OmpETJxhLqF3b2zqYYcPM0TZs2cIYSJUq3lftB4Oq2vzii05borEK7c7KAbO0DT/+yCZTN94IvPyyObZ5gd69ee/l7oVnzjB+YYa2oUkTDkarVplhmTc4cADYtw946KHIiAFGKvpfmwPTp5ujbWjUiC6xSLp4AGztevnlQK1aTltiHLO0DX36MDOvUydzm1i5HZWZpwPq4Y0eRLJh+3a6Y0LVNgwdSk3Ac8+Z30rXzXz+OZCYyBiAlzFD23DyJC+iJUqwD0kksWwZcMUVwB13OG2Jxkr0IJINZmgbzpzhDDQ6GpgwwRSzPIMS0JlZLt1uzNI2xMayZM78+ZHl0lmxIjyqNmvyJoK+1oFhlrahSRNWZ501K7IuHqmpvABXrmxOjSmnMEPbsHw58M03jAnUrWuOXV5h4EC6cSNFkR/JRNDlLTAmTeKFMJQg+Jo1wPr11IPExJhnmxcYPpwDsZe7NJqhbUhLA9q2ZRvlpUvNtc/tJCcD27YBt9/u7arNmsAwNIgIIV4WQuwTQqQIIbYJIe7PZdsOQoiNQoi/Lt4+E0LcZdxka1Hahm7djL3f52MsIFKqs/ozcSL1ME8/7bQlxjFD29ChA3uPxMUxrhJJDBrEhASl9NeEN0EPIkKIlgDeBzAYQDUAGwF8LITIKe+kDoC5AB4EcA+AAwA+FUJcbcBeSzlxAtizhxlFRrUNnTuzA2Lfvt525xhh717g4EEGor3swgtV27B7NzBjBlC+vPHJiJdRVZsjoc2BxthKpBuAKVLKyVLKXVLKrgAOAngpu42llE9KKcdJKbdLKX8B0OHicV3nJQ5V27BvH/Dhh8A113i7d4ZRwqF/ttI2PPig8YEwNpb3kbgS/fFH4Nix9HOgCX+C+pkIIQoCqA7gU7+XPgVwb4C7KQKgAIDTwRzbDkLVNsTEcBm/fLm5dnmF1auB0qXZuMmrqMy8wYONvf+DD7gia9PG2+fBKOr8RUqVak3wZU9KAsgH4Ljf88cBBBqCHArgMIDPctrg/PnzOH/+/H+Pz507G5yVBli7ltqGl7JdT+XN5MnAzp1MCY3EvPi5c1kXqkcPpy0JDaVtMFJhNymJn/+SSyhWjTR8Pv6Orr0WuP56p63R2IVRz7X0eyyyeS4LQojXAbQG0ExKmZLTdnFxcYiOjv7v1qBBWYNmBo5SJRtxZanqrEWKRE51Vn+GDqX7R81Evcjy5aFpG5o3Z2bftGnerhdmlKlT+fmNTsQ03iTYQeQkgAvIuuq4EllXJ5kQQvQA8BaA+lLKH3PbtlevXkhMTPzvtnr1wSDNDI7UVObzG9U2tGzJgWT8eKZ0RhpnzgA//cTZu5er04aibVi3Dvj0U56DFi1MN80TjBgRWmajxpsENV+SUqYKIbYBqAcgY/Z7PQA5RgKEED0BvA3gESnl1ryOExUVhaioqP8eFy0ajJXBE4q24dtvGUCtUoW6gEikf3/GgrwsLEtOZtVmI9oGn4+ZSPnyAStXWmOf2zl5EvjlF+CBByJzIhXJGFl0jwQwUwixFcBmAC8AuBbAhwAghEgAcFhK2evi49cBDATQBsAfQgi1ikmSUiaFaL8pTJhgXNvQtGnkVWf1Z+ZMoFgxoEEDpy0xTijahp49gT//5HsjtfGSykb0cqkbjTGCHkSklPOFECUA9AFQGsAOAA2klPsvbnItAF+Gt7wMoCAA/3ZM/QH0C/b4ZrN3L3DoEIstBpvS+c47wNGjFKVFUnXWjHz7LXDqlPdrJBnVNhw6xMKKpUp5O7U5VObPBy67jCsRTWRhKPwnpRwHYFwOr9Xxe3ydkWPYhVFtw4kTTGMsUYK+4EglHPpnK21Dy5bBvzc2lu6sJUvMt8srfPEF42K68VRk4mFdsTkY1Tao6qwLFnhbnR0KaWkMKFeoAJQp47Q1xlETiWC1DbNns21Aw4bAPfeYbpZnCIeqzRrjROjljyhtw/PPB/e+xYuB775jZdaHHrLGNi8QH8+B5NVXnbbEOD4f8NlnwWsbUlOBjh2ZjbZggXX2uR1VtblSJaBkSaet0ThBBGazpxMXF7y2IS0NeOYZZqBEsgsDYKHCAgXYsc+rGNU2PPUUNSUffshYSqQyYgRX5N27O22JxikidiVy5gywY0fw2obnngP+/hsYNizyqrNm5NAh4PffgTp1vO3OM6Jt2L6dJXJuvpmrkUhm/HhmNj7zjNOWGGPDBrqmy5ShRmjZssyvL1nCgqIlS/L17dudsNLdePjnHxpGtA27djGdtXz50MqEhwOqWKXRGlNu4MQJahvuuy84bUPjxrygRHJaNwD89hurNter592JxLlz1AaNHZvz6/fdF1qX03AnYt1ZRrQNkVyd1Z8lSzg7q1HDaUuM06cP74MJCMfFsdJvx45MKIhkjCYkuInHHuMtJ5R27I8/bDHHk3h0/hAaStvQtGng73n/fc68nnoqMquzZmTVKhYb9HLjKSB4bcPp0xx4LrsMGJdtgntksWoV9TG33uq0JRonichBJFhXTFIS8MYbXLlMnWqdXV5hwAC6c1TRSi+itA2tWgX+niZNmFgxe7Z33TdmMX8+MxuffdZpSzROE3HurLQ09j+vUIHNowKhaVNm8MyZE5nVWTOi+mffdpu3EwuC1TasXg1s3Ajcf7+3y7uYhcpsVBMyTeQScfOpYLUNX3xBHUGNGiz1HenExVFb4eX+2cFqG3w+4MknOYHwz96JRM6epcq/evXITm/WEFfPq+Pj4xEfH4/k5Aum7TMYbYPPx1IY+fLpTBzFlClA4cLGSoS4hWC1DZ060fU1aJCxVgHhhspsVIkJmsjG1SuRTp06YefOnUhI2GLK/pS2oXbtwHzaPXqwxPUbbwBXXmmKCZ5mxw4WnGzY0GlLQiMYbcO+fazyXLasdt0oZs5kufyYGKctCZ2kJGo/lP5j3z7+feAAH58+zcc7d/Lx7t18fOyY7aa6FlcPImajlOmBFAs8dAgYPZp1tbyshTAT5cLycs58sNqGBg0469Zp3WTLFpa9Dyaz0c1s3QpUq8YbQNFptWrpq6wVK/hYTZxateLjDz90xl434mp3ltksXRq4tqFhQ7qzFi+23i4voPpnly3rbX3Em2/yPhBtw4QJFCM+/jhQtaqlZnkGtRrzctXmjNSpw0lCTrRvz5smZyJmJRKMtiEhgYHDmJjIrs6akRkzgPPnvV/m46OPAtM2JCezKkGRIsCsWbaY5np8PlZtLl8+8MxGTfgTMYNIoNoGVYyvUCHmwmvIu+8ywaBnT6ctMU4w2oaWLYGUFK5GdLtXMm4c8O+/QJcuTluicRMR4c5S2oYqVfLWNjz5JLefNEmnLypOnmTdsFq1vH1BDVTbsHkzV663384KBRoyejTTnDt3dtoSjZuIiJXI4MFciudV8v3774FFi6gfCLbHSDijgoz9+ztrRygEo21o1oyDjU7rTufIEeDXX5nZGOmCW01mImIQmTYtMG1DkyZ0eX30kS1meYZ581gvyssNuPr1C0zb8NZbTN/s2lX7/TOiJmA6U1HjT9gPIoFqGwYNYupnx47BdbgLdzZsAP76ixlKXmbWrLy1DceOAcOHA1dcwRiQJp0lS4ASJYCaNZ22ROM2wn4QCUTbcPo0XTWXX86yKJp03nmH94MGOWtHKASqbWjUiEr2BQt0gcWMfPwxG7E9+aTTlmjcSFj/VALVNjRurKuzZkdaGvDVV+zg52XFfiDahkWLONjUq0ftgCad/v3p5vVyTExjHWF9yQxE27BqFbBpE3tK5NacJhIZOdL7/bMD0TakpbEESsGCdNto0klJ4eB6662Mi2k0/oT1IJKXtsHnYwpn/vzA8uX22JRXT+eMdOzIbd5/3x7b/Bk3jhdWL/eMUNqGV17JeZtnn6UQ9b33GDfRpDN0qPerNmusJWwHEaVtuPvunLUNL74IJCZSiGjXLCuvns6KZcvYgbFMGVvMysK+fcD+/cDDD3vbxae0DTkJ5H7+mUH3G27QIrrsmDSJwtvWrZ22RONWwjbjWwWEc/Lj/vYbMHkycO219s6y8urpDACHD1PQtWaNcxVzw6F/ttI21K2b80DYqBHvtSYkK7t28Rw2a+a0JRo34+E5Zu7MmwdER/MCkh0xMdQNrFxpr1154fOxvlfPns72cl+5kjWmbrvNORtCJS9tw8iRbA3Qrh1w00322eUVwqFqs8Z6XD2IxMfHo3LlymjbNoCyuxnYsIFNhJ54IvvXx49nddaWLd13kRw2jO6X3Hz4VrNoEUu/BNJvw83kpm04e5YXyUsvpcvGCnKLf/37L/vUVKkCFC3Kbdq25czfDfh8wCefMBmhYkWnrdG4GVcPIkabUuWmbUhOBl57jT/chAQTjDSRbdvow58+nRcdpxgyhMd/+23nbAiVvLQNzZqx2Ob06daV8cgt/pWczDI777zD+yVLgD170t1rTjNrVnhUbdZYT9jFRFJTqW246abstQ2PP84fx5Qp7ismuHEjcOIE4zQKlWL7/vvAH39Yb4Pq9HbHHd4uQJmbtuHzz3mrWdPa5kq5xb+io6lhysgHHwB33cWuehm/A04wfDjjSK+/7qwdGvcTdoOI0jZ065b1ta++AlavZmcyN6pvn36a2VAZeeQRPm+Xa0n1z1arOS+Sm7bB56MbM18+93UrTEzkwOe0HuP0aWat3Xuv+yZaGvcRdoPI+PH84vtX4fX5gObNna/OmpTEjCGF6ulcvDhnnyVKZN6+QAEGuO0K/CYk0NXXuLE9x7OCIUNy1ja89hpw6hTQt6+7VPgpKey62KZN3u0KrEZNIAYMcNYOjTdwdUwkWPbtoysgO21D797A8eNcoTilvQDy7unsJN9/T3dakyZOWxIaU6awarO/tuHAAcYnypTJuzmZnfz7L3t3+3wURzpNXpmNGk1GwmolkpO24dgxqtevuILZT06SV09nf+yIgyhUSqyX+2fnpm2IieGFOrcqAXbz77/MIty3D/jiC+dXIZs20Z2l++loAiWsBpGVK4GrrsqathsTwzjJokXeVl9bic/Hi9j11zsf1A2FnLQNCQnATz/RTVcjuIxxy1ADyN69wJdfZnVlOoFyZem+IZpACZtLak7ahgULmDr7yCMssqjJng8/5EUt2NanedUC69ePVYCLFmWp/YcfZjkXK8hJ25CSwhI3hQvTVWMXKtNt+3Y+VvGvAwdY9LFFC7o3Z8/mJOfYMd5SU+2zMSNpacwQvPFGd8WLNO4mbAYRpW3ImFWUlgY89xwQFcVBRpMz779vTOSYVy2wG2/kaz/9RFfJddcB9euzv4fZzJyZvbbhySeBf/5hCm2hQuYfNydyi38dOsTssEOHgKpVgdKl029ff22fjRkZNSrnzEaNJifCwp2Vk7ahXTu+NmaMrs6aG8eO0aXy4IPBC+/yqgXWpk3mxyNHMvD944/mB27ffTertmHrVgr5brmFEwo7ySv+FUxszA5U1eYOHZy2ROMlwmIlkp22YccOYO5cujV0ddbcUQH1gQOtPU5qKjBxIjN/br/d3H0rbYN/1eamTblC/egjc48XbuzfzySOhx7ScUNNcITFSmTGjKzaBlU+wm0FFt3I4sXUqdx3nzX7X7WKKazJyXTXrF0LlCxp7jGy0zYMGEB30csvA+XKmXu8cCMcqjZrnMHzc46tW+lfzziAjBjBIGb79ro6a16sWcNihFYq+B98kO7Gr78GHn2UGUknTph7jLlzM2sbTp7kyqp4ccZCNLmzYgWD6VWrOm2Jxmt4fhBRRQLVDCpjddaJE52zyyuoGlNWqpOLFmXTp7vvZjwkf37em8WmTcBff7EumqJxYyZWzJun3TN5sXQpEyTat3faEo0X8bQ7KzttQ5MmTFVduNC66qzhQkoK021vucXeek1SMovKLPy1DStWcNVTpw5Qr555xwlXBg/Omtmo0QSKpy+zStvQqRMfr11L0dbdd3u79pNdDBvGgfiNN4zvI7daYCVK8ALVqBFjIadOMQPo0KHMq4ZQ8Nc2+Hzsy1GgAGfYmtxJSmK5m2rVdAajxhiuHkTi4+MRHx+P5OQL2b6utA2vvsqLR6tWfKyD6YGh+mf7p+EGw9atjHkolMagXTsO8r/8wsSHkyc5qNSowYu+WV0b/bUNHTuyGu6wYc5Xw/UCAwdyZejl3jEaZ3H1INKpUyd06tQJGzacRe3a0Zle89c2dOnCNM9+/czP/AlHdu9mL/emTUOLGeSlhViyxPi+AyE+Pl3bsHcvYy3XXaf7YATK9OmMWVnZV0UT3ng25JhR27B/P90kV1/NEt+avAmHlM79+3mrW5cDYUwMBzS9Eg2M7duZJeeWbooab+LqlUhuZNQ2VKlCd5b2gQeGz8f2sVdf7e0UaDUQDhnCScSePSz/fuutztrlFdREzMsTCY3zeHIQUdqGzp2BadOoTm/SxD3VWd3OnDnMzPJ6eQulbbjxRiZTFC3Kar2avPH52CK4XDktxNSEhicHkX79mJLYqxf1B4ULU2ymCYxhw+j+CSUry2mUtqFTJ1bDPX+eA4hO6w6MSZNYhkZlNmo0RvFcTCQlBfjuO2b3dOrE6qzx8fZWZ/UyZ86wxlTNmt4+Z0rb8NBDdM1Vr04lvCYwRo1in/nXXnPaEo3X8dwgorQNLVqwd8Wtt2btIaLJmT59GHz2cgKC0jZUrUpNSL58dG1pAuPECWbn3X+/XrlpQsdzg4jSNkyYQJfMqlVOW+QtZs9mSZhHHnHaEuMobUO5crwgdu/OpliawOjdm/dWV23WRAaeGkT276e2oVw54OhRXZ01WL76ilqa5s2dtiQ0pk9nHGzlSgbWdXZRcCxcyC6TtWo5bYkmHPDUIKIKKu7dy/Te0aOdtcdrqNpIQ4Y4a0co/PEHVx+FClGpvmSJLrAYDD//TEV/69ZOW6IJFzz18/v2W9ZE8vl0ddZgUTWmKlYESpVy2hrjLFzI+7/+YkdFq3qghCuqTbR2ZWnMwlNhtX//5f2DD+rqrMEyZgwHkq5dnbYkNHbsYFZWwYLpF0RN4Pz6K1C5MlfyGo0ZeGoQAZiJs2yZ01Z4j7FjuYp78UWnLQmNCxdrcY4aBRQp4qwtXkRKXVdMYy6ecAj9/Xf638OGMbtIEzgHDrBEe7j0z65YEXjpJaet8Cb58wNPP+20FZpwwvWXlGuvZWE9gDPP7t2dtcdL+HzAnXeyqi0APPWUo+YYplmzzLZ/9JFztniRdu3Sz1/RouExkdAEx/HjLBMFpGvtzMI17iwhhEhMTAQAnD9/HufPn0eHDoVx8GABAGcBAMnJZ7Fhg4NGeox33wW2bUt/3KVLegdIr3DqVNbCmvHxHFg0efP775nriSUmsuf87bc7Z5PGfvr2BTZv5t8LFrDW3HPPZd4mOjr6UgB/S5lbc4esiCC3twwhxKUAEp22Q6PRaCKYaCnl2WDe4KZBRCQmJvqA9JXIsmX50KVLEQB/AyiLyy/fj2XLLjN8jLZtayAhYUtIdjq9j3PnzqJBg7JYvfogihbNPTi0aVO6OhlgleP33gvdBoVd+6hdO/PjOXNYxh4I7nyEaocX9uF/PlJSgEcfzdw47KOP8m6F64bPYsY+wun7Ecr7ly5lJ1gAKFhQ4tNPBapVy7xNdHR0NAysRCCldNMtC7NnS1mp0mkJQB48eDC7TQKmUqVKIb3fDftITEyUAGRiYmJA23/0kZRNm0rZr595Nti9j6NHpaxYUcqyZaXcuDHza8Gej1Ds8MI+sjsfhw5JeffdUtaoIeWvv9pjh1v2EU7fj1Dfv2RJkgRekd9883dOmxi6brsmJpITbdoADzxwDmXLhr6vTibUvXbLPgKlQQPerLDBrn2UKsWGU1bipfMRLFdfne4Pt9MOt+zDDNzwWUJ9f926FwCMQaVK5ipNXePOuki2xhw6dAhly5bFwYMHcc0119htk6s4e/YsoqOjkZiYiEt1rrM+H37o85EZfT7SCeBcCCP79USyX1RUVKb7SCYqKgp9+/bV5+Ii+nxkRp+PzOjzkY5V58ITKxE9m9BoNBrLMbQScdsgki0Z0n+jZZDpZxqNRqOxDq8MIgJAMRhJP9NoNBqNZXhiENFoNBqNO/FEYF2j0Wg07kQPIi5ECPGyEGKfECJFCLFNCHF/Ltt2EEJsFEL8dfH2mRDiLjvttZpgzoff+1oJIaQQYpnFJtpKsOdDCHGZECJeCHH04nt2CSGyUQ95EwPno6sQYrcQ4h8hxEEhxCghRCG77LUKIcQDQoiVQogjF7/3TQJ4T+2L5yxFCPG7ECLoZhF6EHEZQoiWAN4HMBhANQAbAXwshMipdGIdAHMBPAjgHgAHAHwqhLjacmNtwMD5UO8rB+C9i9uHDcGeDyFEQQBrAVwHoAWAmwB0AHDYBnMtx8D5eBLAUAD9AVQC8ByAlgDi7LDXYooC+D8AnQPZWAhxPYDV4DmrBmAIgDFCiOZBHdWo1F3frLkB+BbAeL/ndgGIC/D9+cCyx22d/ixOnY+L52ATeIGYDmCZ05/DqfMB4EUAvwEo4LTtLjkfYwF87vfcCAAbnf4sJp8XCaBJHtsMA7DL77kPAWwO5lh6JeIiLs4aqwP41O+lTwHcG+BuigAoAOC0iaY5Qgjnow+AP6WUU6yyzQkMno9GADYDiBdCHBdC7BBCvCWEyGehqbZg8HxsAlBduXyFEOUBNAAQiV1q7kHWc7cGwJ1CiAKB7sT1tbMijJLgLPq43/PHAZQKcB9DQVfFZyba5RRBnw8hxH3gCqSqpZY5g5HvR3kADwGYDV4sKwKIB3/7A6wx0zaCPh9SynlCiCsAbLooHcgPrmSGWmqpOymF7M9dfvDcHg1kJ3oQcSf+edcim+eyIIR4HUBrAHWklClWGOYQAZ0PIUQxALMAdJBSnrTDMIcI5vvxPwAnALwgpbwAYJsQogyAnvD+IKII+HwIIeoA6A3gZdAVdgOA0UKIo1JKcysTeoPszl12z+eIHkTcxUkAF5B1FnUlss4YMiGE6AHgLQAPSyl/tMY82wn2fFQAA8grOckEcDF5RAiRBuAmKeVvllhqD0a+H0cB/HtxAFHsAlBKCFFQSplqvpm2YeR8DAQwU0o5+eLjn4QQRQFMFEIMllKa2DjW9RxD9ucuDcCpQHeiYyIu4uIPehuAen4v1QPwdU7vE0L0BPAOgEellFuts9BeDJyPXwBUAV1Z6rYCwJcX/z5oiaE2YfD78RWAG4QQGX/rNwI46vEBxOj5KALAf6C4AM7ADdWO8jCbkfXc1QewVUr5b8B7cTqLQN+yZEy0BJAK4FkwBXEUgCQA5S6+noAMmScAXgdwHkBzcFahbpc4/VmcOB/ZvH86wis7K9jvR1mwNegH4ODREJyl93b6szh0PvqB2YutAFx/8SL6K4D5Tn8WE87FJUifPEkAr138+9qLr8cBSMiw/fUAzgEYefHcPXvxXDYP6rhOf3B9y/bL8DKAPy4ODtsAPJDhtXUApmd4/MfFL4z/rZ/Tn8OJ85HNe8NqEDFyPsAsnG8ApIDpvm8ByOf053DifIAu/L4XB45/QF1VPIDLnP4cJpyHOjlcC6ZffH06gHV+76kN4PuL524fgBeDPa6unaXRaDQaw+iYiEaj0WgMowcRjUaj0RhGDyIajUajMYweRDQajUZjGD2IaDQajcYwehDRaDQajWH0IKLRaDQaw+hBRKPRaDSG0YOIRqPRaAyjBxGNRqPRGEYPIhqNRqMxjB5ENBqNRmOY/wenUW0SYolh6gAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 133 graphics primitives" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P7_scaled.plot() # optional long" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following allows to compute the induced partition $\\mathcal{P}_8$ of $\\mathbb{R}^2/\\Gamma_8$, the substitution $\\beta_7$ and the $\\mathbb{Z}^2$-action $R_8$ on $\\mathbb{R}^2/\\Gamma_8$." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|partition|\\phantom{\\verb!x!}\\verb|of|\\phantom{\\verb!x!}\\verb|19|\\phantom{\\verb!x!}\\verb|atoms|\\phantom{\\verb!x!}\\verb|with|\\phantom{\\verb!x!}\\verb|19|\\phantom{\\verb!x!}\\verb|letters|\n", "\\end{math}" ], "text/plain": [ "Polyhedron partition of 19 atoms with 19 letters" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P8,beta7 = R7e1_scaled.induced_partition(x_le_phi_inv, P7_scaled, substitution_type='row')\n", "R8e1,_ = R7e1_scaled.induced_transformation(x_le_phi_inv)\n", "R8e2,_ = R7e2_scaled.induced_transformation(x_le_phi_inv)\n", "P8" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 119 graphics primitives" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P8.plot() # optional long" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llllllll}\n", "0\\mapsto \\left(5\\right)\n", ",&\n", "1\\mapsto \\left(8\\right)\n", ",&\n", "2\\mapsto \\left(14\\right)\n", ",&\n", "3\\mapsto \\left(15\\right)\n", ",&\n", "4\\mapsto \\left(18\\right)\n", ",&\n", "5\\mapsto \\left(20\\right)\n", ",&\n", "6\\mapsto \\left(3,\\,1\\right)\n", ",&\n", "7\\mapsto \\left(4,\\,2\\right)\n", ",\\\\\n", "8\\mapsto \\left(5,\\,1\\right)\n", ",&\n", "9\\mapsto \\left(6,\\,0\\right)\n", ",&\n", "10\\mapsto \\left(7,\\,1\\right)\n", ",&\n", "11\\mapsto \\left(8,\\,1\\right)\n", ",&\n", "12\\mapsto \\left(12,\\,11\\right)\n", ",&\n", "13\\mapsto \\left(13,\\,11\\right)\n", ",&\n", "14\\mapsto \\left(14,\\,9\\right)\n", ",&\n", "15\\mapsto \\left(15,\\,10\\right)\n", ",\\\\\n", "16\\mapsto \\left(16,\\,11\\right)\n", ",&\n", "17\\mapsto \\left(17,\\,11\\right)\n", ",&\n", "18\\mapsto \\left(19,\\,9\\right)\n", ".\n", "\\end{array}\n", "\\end{math}" ], "text/plain": [ "Substitution 2d: {0: [[5]], 1: [[8]], 2: [[14]], 3: [[15]], 4: [[18]], 5: [[20]], 6: [[3], [1]], 7: [[4], [2]], 8: [[5], [1]], 9: [[6], [0]], 10: [[7], [1]], 11: [[8], [1]], 12: [[12], [11]], 13: [[13], [11]], 14: [[14], [9]], 15: [[15], [10]], 16: [[16], [11]], 17: [[17], [11]], 18: [[19], [9]]}" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta7" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following allows to compute the induced partition $\\mathcal{P}_9$ of $\\mathbb{R}^2/\\Gamma_9$, the substitution $\\beta_8$ and the $\\mathbb{Z}^2$-action $R_9$ on $\\mathbb{R}^2/\\Gamma_9$." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|partition|\\phantom{\\verb!x!}\\verb|of|\\phantom{\\verb!x!}\\verb|21|\\phantom{\\verb!x!}\\verb|atoms|\\phantom{\\verb!x!}\\verb|with|\\phantom{\\verb!x!}\\verb|21|\\phantom{\\verb!x!}\\verb|letters|\n", "\\end{math}" ], "text/plain": [ "Polyhedron partition of 21 atoms with 21 letters" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P9,beta8 = R8e2.induced_partition(y_le_phi_inv, P8, substitution_type='column')\n", "R9e1,_ = R8e1.induced_transformation(y_le_phi_inv)\n", "R9e2,_ = R8e2.induced_transformation(y_le_phi_inv)\n", "P9" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 135 graphics primitives" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P9.plot() # optional long" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llllllll}\n", "0\\mapsto \\left(2\\right)\n", ",&\n", "1\\mapsto \\left(3\\right)\n", ",&\n", "2\\mapsto \\left(4\\right)\n", ",&\n", "3\\mapsto \\left(12\\right)\n", ",&\n", "4\\mapsto \\left(13\\right)\n", ",&\n", "5\\mapsto \\left(14\\right)\n", ",&\n", "6\\mapsto \\left(16\\right)\n", ",&\n", "7\\mapsto \\left(17\\right)\n", ",\\\\\n", "8\\mapsto \\left(\\begin{array}{r}\n", "0 \\\\\n", "2\n", "\\end{array}\\right)\n", ",&\n", "9\\mapsto \\left(\\begin{array}{r}\n", "1 \\\\\n", "3\n", "\\end{array}\\right)\n", ",&\n", "10\\mapsto \\left(\\begin{array}{r}\n", "1 \\\\\n", "4\n", "\\end{array}\\right)\n", ",&\n", "11\\mapsto \\left(\\begin{array}{r}\n", "1 \\\\\n", "5\n", "\\end{array}\\right)\n", ",&\n", "12\\mapsto \\left(\\begin{array}{r}\n", "7 \\\\\n", "12\n", "\\end{array}\\right)\n", ",&\n", "13\\mapsto \\left(\\begin{array}{r}\n", "6 \\\\\n", "13\n", "\\end{array}\\right)\n", ",&\n", "14\\mapsto \\left(\\begin{array}{r}\n", "6 \\\\\n", "14\n", "\\end{array}\\right)\n", ",&\n", "15\\mapsto \\left(\\begin{array}{r}\n", "8 \\\\\n", "14\n", "\\end{array}\\right)\n", ",\\\\\n", "16\\mapsto \\left(\\begin{array}{r}\n", "11 \\\\\n", "15\n", "\\end{array}\\right)\n", ",&\n", "17\\mapsto \\left(\\begin{array}{r}\n", "9 \\\\\n", "16\n", "\\end{array}\\right)\n", ",&\n", "18\\mapsto \\left(\\begin{array}{r}\n", "10 \\\\\n", "16\n", "\\end{array}\\right)\n", ",&\n", "19\\mapsto \\left(\\begin{array}{r}\n", "7 \\\\\n", "17\n", "\\end{array}\\right)\n", ",&\n", "20\\mapsto \\left(\\begin{array}{r}\n", "10 \\\\\n", "18\n", "\\end{array}\\right)\n", ".\n", "\\end{array}\n", "\\end{math}" ], "text/plain": [ "Substitution 2d: {0: [[2]], 1: [[3]], 2: [[4]], 3: [[12]], 4: [[13]], 5: [[14]], 6: [[16]], 7: [[17]], 8: [[2, 0]], 9: [[3, 1]], 10: [[4, 1]], 11: [[5, 1]], 12: [[12, 7]], 13: [[13, 6]], 14: [[14, 6]], 15: [[14, 8]], 16: [[15, 11]], 17: [[16, 9]], 18: [[16, 10]], 19: [[17, 7]], 20: [[18, 10]]}" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta8" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We rescale the partition $\\mathcal{P}_9$ :" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "P9_scaled = (-phi*P9).translate((1,1))\n", "R9e1_scaled = (-phi*R9e1).translate_domain((1,1))\n", "R9e2_scaled = (-phi*R9e2).translate_domain((1,1))" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 135 graphics primitives" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P9_scaled.plot() # optional long" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following allows to compute the induced partition $\\mathcal{P}_{10}$ of $\\mathbb{R}^2/\\Gamma_{10}$, the substitution $\\beta_9$ and the $\\mathbb{Z}^2$-action $R_{10}$ on $\\mathbb{R}^2/\\Gamma_{10}$." ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\verb|Polyhedron|\\phantom{\\verb!x!}\\verb|partition|\\phantom{\\verb!x!}\\verb|of|\\phantom{\\verb!x!}\\verb|19|\\phantom{\\verb!x!}\\verb|atoms|\\phantom{\\verb!x!}\\verb|with|\\phantom{\\verb!x!}\\verb|19|\\phantom{\\verb!x!}\\verb|letters|\n", "\\end{math}" ], "text/plain": [ "Polyhedron partition of 19 atoms with 19 letters" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P10,beta9 = R9e1_scaled.induced_partition(x_le_phi_inv, P9_scaled, substitution_type='row')\n", "R10e1,_ = R9e1_scaled.induced_transformation(x_le_phi_inv)\n", "R10e2,_ = R9e2_scaled.induced_transformation(x_le_phi_inv)\n", "P10" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 119 graphics primitives" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P10.plot() # optional long" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llllllll}\n", "0\\mapsto \\left(3\\right)\n", ",&\n", "1\\mapsto \\left(7\\right)\n", ",&\n", "2\\mapsto \\left(12\\right)\n", ",&\n", "3\\mapsto \\left(17\\right)\n", ",&\n", "4\\mapsto \\left(18\\right)\n", ",&\n", "5\\mapsto \\left(19\\right)\n", ",&\n", "6\\mapsto \\left(3,\\,0\\right)\n", ",&\n", "7\\mapsto \\left(4,\\,0\\right)\n", ",\\\\\n", "8\\mapsto \\left(4,\\,1\\right)\n", ",&\n", "9\\mapsto \\left(5,\\,2\\right)\n", ",&\n", "10\\mapsto \\left(6,\\,0\\right)\n", ",&\n", "11\\mapsto \\left(7,\\,0\\right)\n", ",&\n", "12\\mapsto \\left(13,\\,9\\right)\n", ",&\n", "13\\mapsto \\left(14,\\,10\\right)\n", ",&\n", "14\\mapsto \\left(15,\\,10\\right)\n", ",&\n", "15\\mapsto \\left(16,\\,11\\right)\n", ",\\\\\n", "16\\mapsto \\left(17,\\,8\\right)\n", ",&\n", "17\\mapsto \\left(18,\\,9\\right)\n", ",&\n", "18\\mapsto \\left(20,\\,10\\right)\n", ".\n", "\\end{array}\n", "\\end{math}" ], "text/plain": [ "Substitution 2d: {0: [[3]], 1: [[7]], 2: [[12]], 3: [[17]], 4: [[18]], 5: [[19]], 6: [[3], [0]], 7: [[4], [0]], 8: [[4], [1]], 9: [[5], [2]], 10: [[6], [0]], 11: [[7], [0]], 12: [[13], [9]], 13: [[14], [10]], 14: [[15], [10]], 15: [[16], [11]], 16: [[17], [8]], 17: [[18], [9]], 18: [[20], [10]]}" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta9" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We show that $\\mathcal{P}_8$ and $\\mathcal{P}_{10}$ are equivalent:" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\n", "\\end{math}" ], "text/plain": [ "True" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P8.is_equal_up_to_relabeling(P10)" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llllllll}\n", "0\\mapsto \\left(1\\right)\n", ",&\n", "1\\mapsto \\left(0\\right)\n", ",&\n", "2\\mapsto \\left(4\\right)\n", ",&\n", "3\\mapsto \\left(3\\right)\n", ",&\n", "4\\mapsto \\left(5\\right)\n", ",&\n", "5\\mapsto \\left(2\\right)\n", ",&\n", "6\\mapsto \\left(10\\right)\n", ",&\n", "7\\mapsto \\left(9\\right)\n", ",\\\\\n", "8\\mapsto \\left(11\\right)\n", ",&\n", "9\\mapsto \\left(8\\right)\n", ",&\n", "10\\mapsto \\left(7\\right)\n", ",&\n", "11\\mapsto \\left(6\\right)\n", ",&\n", "12\\mapsto \\left(15\\right)\n", ",&\n", "13\\mapsto \\left(18\\right)\n", ",&\n", "14\\mapsto \\left(17\\right)\n", ",&\n", "15\\mapsto \\left(16\\right)\n", ",\\\\\n", "16\\mapsto \\left(13\\right)\n", ",&\n", "17\\mapsto \\left(14\\right)\n", ",&\n", "18\\mapsto \\left(12\\right)\n", ".\n", "\\end{array}\n", "\\end{math}" ], "text/plain": [ "Substitution 2d: {0: [[1]], 1: [[0]], 2: [[4]], 3: [[3]], 4: [[5]], 5: [[2]], 6: [[10]], 7: [[9]], 8: [[11]], 9: [[8]], 10: [[7]], 11: [[6]], 12: [[15]], 13: [[18]], 14: [[17]], 15: [[16]], 16: [[13]], 17: [[14]], 18: [[12]]}" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from slabbe import Substitution2d\n", "tau = Substitution2d.from_permutation(P8.keys_permutation(P10))\n", "tau" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llllllll}\n", "0\\mapsto \\left(17\\right)\n", ",&\n", "1\\mapsto \\left(12\\right)\n", ",&\n", "2\\mapsto \\left(\\begin{array}{r}\n", "10 \\\\\n", "16\n", "\\end{array}\\right)\n", ",&\n", "3\\mapsto \\left(\\begin{array}{r}\n", "9 \\\\\n", "16\n", "\\end{array}\\right)\n", ",&\n", "4\\mapsto \\left(\\begin{array}{r}\n", "7 \\\\\n", "17\n", "\\end{array}\\right)\n", ",&\n", "5\\mapsto \\left(\\begin{array}{r}\n", "7 \\\\\n", "12\n", "\\end{array}\\right)\n", ",&\n", "6\\mapsto \\left(16,\\,2\\right)\n", ",&\n", "7\\mapsto \\left(14,\\,4\\right)\n", ",\\\\\n", "8\\mapsto \\left(17,\\,2\\right)\n", ",&\n", "9\\mapsto \\left(13,\\,3\\right)\n", ",&\n", "10\\mapsto \\left(13,\\,2\\right)\n", ",&\n", "11\\mapsto \\left(12,\\,2\\right)\n", ",&\n", "12\\mapsto \\left(\\begin{array}{rr}\n", "11 & 1 \\\\\n", "15 & 5\n", "\\end{array}\\right)\n", ",&\n", "13\\mapsto \\left(\\begin{array}{rr}\n", "10 & 1 \\\\\n", "18 & 4\n", "\\end{array}\\right)\n", ",&\n", "14\\mapsto \\left(\\begin{array}{rr}\n", "10 & 1 \\\\\n", "16 & 3\n", "\\end{array}\\right)\n", ",&\n", "15\\mapsto \\left(\\begin{array}{rr}\n", "9 & 0 \\\\\n", "16 & 2\n", "\\end{array}\\right)\n", ",\\\\\n", "16\\mapsto \\left(\\begin{array}{rr}\n", "6 & 1 \\\\\n", "14 & 4\n", "\\end{array}\\right)\n", ",&\n", "17\\mapsto \\left(\\begin{array}{rr}\n", "8 & 1 \\\\\n", "14 & 4\n", "\\end{array}\\right)\n", ",&\n", "18\\mapsto \\left(\\begin{array}{rr}\n", "6 & 1 \\\\\n", "13 & 3\n", "\\end{array}\\right)\n", ".\n", "\\end{array}\n", "\\end{math}" ], "text/plain": [ "Substitution 2d: {0: [[17]], 1: [[12]], 2: [[16, 10]], 3: [[16, 9]], 4: [[17, 7]], 5: [[12, 7]], 6: [[16], [2]], 7: [[14], [4]], 8: [[17], [2]], 9: [[13], [3]], 10: [[13], [2]], 11: [[12], [2]], 12: [[15, 11], [5, 1]], 13: [[18, 10], [4, 1]], 14: [[16, 10], [3, 1]], 15: [[16, 9], [2, 0]], 16: [[14, 6], [4, 1]], 17: [[14, 8], [4, 1]], 18: [[13, 6], [3, 1]]}" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta8*beta9*tau # the self-similarity for P8" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may check that the self-similarity for $\\mathcal{P}_8$ satisfies $\\zeta^{-1}\\beta_8\\beta_9\\tau\\zeta=\\beta_{\\mathcal{U}}$." ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}\n", "\\end{math}" ], "text/plain": [ "True" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "zeta = Substitution2d.from_permutation({0:0, 1:1, 2:9, 3:7, 4:8, 5:11, 6:10, \n", "7:6, 8:2, 9:4, 10:5, 11:3, 12:18, 13:14, 14:16, 15:13, 16:12, 17:17, 18:15})\n", "betaU = Substitution2d({0: [[17]], 1: [[16]], 2: [[15], [11]], 3: [[13], [9]], 4: [[17], [8]], 5: [[16], [8]], 6: [[15], [8]], 7: [[14], [8]], 8: [[14, 6]], 9: [[17, 3]], 10: [[16, 3]], 11: [[14, 2]], 12: [[15, 7], [11, 1]], 13: [[14, 6], [11, 1]], 14: [[13, 7], [9, 1]], 15: [[12, 6], [9, 1]], 16: [[18, 5], [10, 1]], 17: [[13, 4], [9, 1]], 18: [[14, 2], [8, 0]]})\n", "zeta.inverse()*beta8*beta9*tau*zeta == betaU" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llllllll}\n", "0\\mapsto \\left(17\\right)\n", ",&\n", "1\\mapsto \\left(16\\right)\n", ",&\n", "2\\mapsto \\left(15,\\,11\\right)\n", ",&\n", "3\\mapsto \\left(13,\\,9\\right)\n", ",&\n", "4\\mapsto \\left(17,\\,8\\right)\n", ",&\n", "5\\mapsto \\left(16,\\,8\\right)\n", ",&\n", "6\\mapsto \\left(15,\\,8\\right)\n", ",&\n", "7\\mapsto \\left(14,\\,8\\right)\n", ",\\\\\n", "8\\mapsto \\left(\\begin{array}{r}\n", "6 \\\\\n", "14\n", "\\end{array}\\right)\n", ",&\n", "9\\mapsto \\left(\\begin{array}{r}\n", "3 \\\\\n", "17\n", "\\end{array}\\right)\n", ",&\n", "10\\mapsto \\left(\\begin{array}{r}\n", "3 \\\\\n", "16\n", "\\end{array}\\right)\n", ",&\n", "11\\mapsto \\left(\\begin{array}{r}\n", "2 \\\\\n", "14\n", "\\end{array}\\right)\n", ",&\n", "12\\mapsto \\left(\\begin{array}{rr}\n", "7 & 1 \\\\\n", "15 & 11\n", "\\end{array}\\right)\n", ",&\n", "13\\mapsto \\left(\\begin{array}{rr}\n", "6 & 1 \\\\\n", "14 & 11\n", "\\end{array}\\right)\n", ",&\n", "14\\mapsto \\left(\\begin{array}{rr}\n", "7 & 1 \\\\\n", "13 & 9\n", "\\end{array}\\right)\n", ",&\n", "15\\mapsto \\left(\\begin{array}{rr}\n", "6 & 1 \\\\\n", "12 & 9\n", "\\end{array}\\right)\n", ",\\\\\n", "16\\mapsto \\left(\\begin{array}{rr}\n", "5 & 1 \\\\\n", "18 & 10\n", "\\end{array}\\right)\n", ",&\n", "17\\mapsto \\left(\\begin{array}{rr}\n", "4 & 1 \\\\\n", "13 & 9\n", "\\end{array}\\right)\n", ",&\n", "18\\mapsto \\left(\\begin{array}{rr}\n", "2 & 0 \\\\\n", "14 & 8\n", "\\end{array}\\right)\n", ".\n", "\\end{array}\n", "\\end{math}" ], "text/plain": [ "Substitution 2d: {0: [[17]], 1: [[16]], 2: [[15], [11]], 3: [[13], [9]], 4: [[17], [8]], 5: [[16], [8]], 6: [[15], [8]], 7: [[14], [8]], 8: [[14, 6]], 9: [[17, 3]], 10: [[16, 3]], 11: [[14, 2]], 12: [[15, 7], [11, 1]], 13: [[14, 6], [11, 1]], 14: [[13, 7], [9, 1]], 15: [[12, 6], [9, 1]], 16: [[18, 5], [10, 1]], 17: [[13, 4], [9, 1]], 18: [[14, 2], [8, 0]]}" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "betaU" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Observe that the $19 \\times 19$ incidence matrix of $\\beta_8\\beta_9\\tau$ is not hyperbolic but, as shown by its characteristic polynomial, it is hyperbolic on a 8-dimensional subspace:" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "\\begin{math}\n", "\\newcommand{\\Bold}[1]{\\mathbf{#1}}x^{3} \\cdot (x - 1)^{4} \\cdot (x + 1)^{4} \\cdot (x^{2} - 3x + 1) \\cdot (x^{2} + x - 1)^{3}\n", "\\end{math}" ], "text/plain": [ "x^3 * (x - 1)^4 * (x + 1)^4 * (x^2 - 3*x + 1) * (x^2 + x - 1)^3" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(beta8*beta9*tau).incidence_matrix().charpoly().factor()" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.3.beta5", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.0" } }, "nbformat": 4, "nbformat_minor": 4 }