{ "cells": [ { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# Some hack that I need later\n", "\n", "from sage.misc.latex import _Latex_prefs\n", "from sage.misc.latex import png\n", "from sage.misc.temporary_file import tmp_filename\n", "import os\n", "from IPython.display import Image\n", "from IPython.display import display\n", "\n", "def viewLatex(objects):\n", " engine = _Latex_prefs._option[\"engine\"]\n", " if type(objects) != list:\n", " objects = [objects]\n", " L = []\n", " for o in objects:\n", " file_name = tmp_filename() + \".png\"\n", " png(o, file_name, debug = False, engine = engine)\n", " L.append(Image(filename = file_name))\n", " return display(*L)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Permutohedron" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "A 2-dimensional polyhedron in ZZ^3 defined as the convex hull of 6 vertices (use the .plot() method to plot)" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Permu3 = Polyhedron(list(Permutations(3)))\n", "Permu3" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Permu3.plot()" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "A 3-dimensional polyhedron in ZZ^4 defined as the convex hull of 24 vertices (use the .plot() method to plot)" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Permu4 = Polyhedron(list(Permutations(4)))\n", "Permu4" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Permu4.plot()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Finite poset containing 6 elements" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P3 = Permutations(3)\n", "W3 = Poset((P3, lambda x,y: x.permutohedron_lequal(y, side=\"left\")))\n", "W3" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Finite poset containing 6 elements" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "W3_right = Poset((P3, lambda x,y: x.permutohedron_lequal(y, side=\"right\")))\n", "W3_right" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 61 graphics primitives" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P4 = Permutations(4)\n", "W4 = Poset((P4, lambda x,y: x.permutohedron_lequal(y, side=\"right\")))\n", "W4.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Binary Trees" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "BT8 = BinaryTrees(8)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bt = BT8.random_element()\n", "viewLatex(bt)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Finite poset containing 5 elements" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "BT3 = list(BinaryTrees(3))\n", "Tam3 = Poset((BT3, lambda x,y: x.tamari_lequal(y)))\n", "Tam3" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "Finite poset containing 14 elements" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "BT4 = list(BinaryTrees(4))\n", "Tam4 = Poset((BT4, lambda x,y: x.tamari_lequal(y)))\n", "Tam4" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "viewLatex(Tam4)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "def numberOfLeaves(bt):\n", " if bt.node_number() == 0:\n", " return 1\n", " return numberOfLeaves(bt[0]) + numberOfLeaves(bt[1])\n", "\n", "def LodayCoordinatesGen(bt):\n", " if bt.node_number() == 0:\n", " return\n", " yield from LodayCoordinates(bt[0])\n", " yield numberOfLeaves(bt[0])*numberOfLeaves(bt[1])\n", " yield from LodayCoordinates(bt[1])\n", "\n", "def LodayCoordinates(bt):\n", " return tuple(LodayCoordinatesGen(bt))" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "viewLatex(bt)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1, 6, 2, 1, 10, 1, 7, 8)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "LodayCoordinates(bt)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "A 2-dimensional polyhedron in ZZ^3 defined as the convex hull of 5 vertices (use the .plot() method to plot)" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Asso3 = Polyhedron([LodayCoordinates(bt) for bt in BT3])\n", "Asso3" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Asso3.plot()" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Asso4 = Polyhedron([LodayCoordinates(bt) for bt in BT4])\n", "Asso4.plot()" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [], "source": [ "matrix = Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1], [-ZZ(1)/3, -ZZ(1)/3, -ZZ(1)/3]])\n", "proj = lambda x: list(Matrix(x)*matrix)[0]\n", "Permu4Proj = Permu4.projection(proj)\n", "Asso4Proj = Asso4.projection(proj)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Asso4Proj.plot()" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Permu4Proj.plot() + Asso4Proj.plot()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.1.beta7", "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": 2 }