{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Manifold graphics in SageMath" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook illustrates some plotting capabilities of manifold objects in SageMath.\n", "\n", "More examples can be found on the [SageManifolds page](https://sagemanifolds.obspm.fr/examples.html)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The 2-sphere example" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us consider the sphere $\\mathbb{S}^2$. In SageMath, we declare it as a 2-dimensional \n", "differentiable manifold:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "S2 = Manifold(2, 'S^2', latex_name=r'\\mathbb{S}^2', start_index=1)\n", "print(S2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We then introduce the standard spherical coordinates $(\\theta,\\phi)$ as a chart on $\\mathbb{S}^2$, denoting the chart as spher and the coordinates th and ph.\n", "We shall be lazy here and consider that the spherical chart covers the whole manifold $\\mathbb{S}^2$; this amounts to authorize coordinate singularities:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left(\\mathbb{S}^2,({\\theta}, {\\phi})\\right)\$$" ], "text/latex": [ "$\\displaystyle \\left(\\mathbb{S}^2,({\\theta}, {\\phi})\\right)$" ], "text/plain": [ "Chart (S^2, (th, ph))" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher. = S2.chart(r'th:[0,pi]:\\theta ph:[0,2*pi]:periodic:\\phi')\n", "spher" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle {\\theta} :\\ \\left[ 0 , \\pi \\right] ;\\quad {\\phi} :\\ \\left[ 0 , 2 \\, \\pi \\right] \\mbox{(periodic)}\$$" ], "text/latex": [ "$\\displaystyle {\\theta} :\\ \\left[ 0 , \\pi \\right] ;\\quad {\\phi} :\\ \\left[ 0 , 2 \\, \\pi \\right] \\mbox{(periodic)}$" ], "text/plain": [ "th: [0, pi]; ph: [0, 2*pi] (periodic)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.coord_range()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For 3D plots, we shall require the Euclidian space $\\mathbb{E}^3$:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\mathbb{E}^{3}\$$" ], "text/latex": [ "$\\displaystyle \\mathbb{E}^{3}$" ], "text/plain": [ "Euclidean space E^3" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E3. = EuclideanSpace()\n", "E3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us call cartesian the chart of Cartesian coordinates $(X,Y,Z)$:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left(\\mathbb{E}^{3},(X, Y, Z)\\right)\$$" ], "text/latex": [ "$\\displaystyle \\left(\\mathbb{E}^{3},(X, Y, Z)\\right)$" ], "text/plain": [ "Chart (E^3, (X, Y, Z))" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cartesian = E3.cartesian_coordinates()\n", "cartesian" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The canonical embedding of $\\mathbb{S}^2$ into $\\mathbb{E}^3$:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\begin{array}{llcl} \\Phi:& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{E}^{3} \\\\ & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(\\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), \\cos\\left({\\theta}\\right)\\right) \\end{array}\$$" ], "text/latex": [ "$\\displaystyle \\begin{array}{llcl} \\Phi:& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{E}^{3} \\\\ & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(\\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), \\cos\\left({\\theta}\\right)\\right) \\end{array}$" ], "text/plain": [ "Phi: S^2 → E^3\n", " (th, ph) ↦ (X, Y, Z) = (cos(ph)*sin(th), sin(ph)*sin(th), cos(th))" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi = S2.diff_map(E3, (sin(th)*cos(ph), \n", " sin(th)*sin(ph),\n", " cos(th)), \n", " name='Phi', latex_name=r'\\Phi')\n", "Phi.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot of a chart" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Each chart is endowed with a plot() method.\n", "For instance, we may use it to plot the chart of spherical coordinates plotted in terms \n", "of itself:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 18 graphics primitives" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "More intersting is to the plot the chart of spherical coordinates in terms of $\\mathbb{E}^3$'s Cartesian coordinates, via the embedding $\\Phi:\\; \\mathbb{S}^2\\to\\mathbb{E}^3$:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=cartesian, mapping=Phi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a better image, let us increase the number of coordinate values:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=cartesian, mapping=Phi, number_values=11)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One can customize the color of coordinate lines:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=cartesian, mapping=Phi, number_values=11, \n", " color={th: 'red', ph: 'green'})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One can fix the value of some coordinates, thereby obtaining a partial plot:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=cartesian, mapping=Phi, number_values=11, \n", " color={th: 'red', ph: 'green'},\n", " fixed_coords={th: pi/4})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "or limit the range of some coordinates:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=cartesian, mapping=Phi, number_values=11, \n", " color={th: 'red', ph: 'green'},\n", " ranges={ph:(0, pi)})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One can also restrict the coordinates of the ambiant chart; here is a example of plot of the chart spher in terms of the coordinates $(X,Y)$ of $\\mathbb{E}^3$:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 22 graphics primitives" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=cartesian, mapping=Phi, number_values=11, \n", " color={th: 'red', ph: 'green'},\n", " ambient_coords=(X, Y))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Same thing with only the coordinates $(X,Z)$:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 22 graphics primitives" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=cartesian, mapping=Phi, number_values=11, \n", " color={th: 'red', ph: 'green'},\n", " ambient_coords=(X, Z))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us introduce the chart of **stereographic coordinates from the North pole**:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left(\\mathbb{S}^2,(x, y)\\right)\$$" ], "text/latex": [ "$\\displaystyle \\left(\\mathbb{S}^2,(x, y)\\right)$" ], "text/plain": [ "Chart (S^2, (x, y))" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN. = S2.chart()\n", "stereoN" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left\\{\\begin{array}{lcl} x & = & -\\frac{\\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right) - 1} \\\\ y & = & -\\frac{\\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right) - 1} \\end{array}\\right.\$$" ], "text/latex": [ "$\\displaystyle \\left\\{\\begin{array}{lcl} x & = & -\\frac{\\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right) - 1} \\\\ y & = & -\\frac{\\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right) - 1} \\end{array}\\right.$" ], "text/plain": [ "x = -cos(ph)*sin(th)/(cos(th) - 1)\n", "y = -sin(ph)*sin(th)/(cos(th) - 1)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher_to_stereoN = spher.transition_map(stereoN, \n", " (sin(th)*cos(ph)/(1-cos(th)),\n", " sin(th)*sin(ph)/(1-cos(th))))\n", "spher_to_stereoN.display()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Check of the inverse coordinate transformation:\n", " th == 2*arctan(sqrt(-cos(th) + 1)/sqrt(cos(th) + 1)) **failed**\n", " ph == pi + arctan2(sin(ph)*sin(th)/(cos(th) - 1), cos(ph)*sin(th)/(cos(th) - 1)) **failed**\n", " x == x *passed*\n", " y == y *passed*\n", "NB: a failed report can reflect a mere lack of simplification.\n" ] } ], "source": [ "spher_to_stereoN.set_inverse(2*atan(1/sqrt(x^2+y^2)), atan2(-y,-x)+pi)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot of spherical coordinate in terms of the stereographic ones:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 30 graphics primitives" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(chart=stereoN, number_values=15, ranges={th: (pi/8,pi)},\n", " color={th: 'red', ph: 'green'})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot of stereographic coordinates in terms of spherical ones:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 30 graphics primitives" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN.plot(chart=spher, number_values=15, plot_points=200,\n", " color={x: 'blue', y: 'orange'})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expression of the embedding $\\Phi$ in terms of the stereographic coordinates is computed by Sage:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\begin{array}{llcl} \\Phi:& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{E}^{3} \\\\ & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(\\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), \\cos\\left({\\theta}\\right)\\right) \\\\ & \\left(x, y\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(\\frac{2 \\, x}{x^{2} + y^{2} + 1}, \\frac{2 \\, y}{x^{2} + y^{2} + 1}, \\frac{x^{2} + y^{2} - 1}{x^{2} + y^{2} + 1}\\right) \\end{array}\$$" ], "text/latex": [ "$\\displaystyle \\begin{array}{llcl} \\Phi:& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{E}^{3} \\\\ & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(\\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), \\cos\\left({\\theta}\\right)\\right) \\\\ & \\left(x, y\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(\\frac{2 \\, x}{x^{2} + y^{2} + 1}, \\frac{2 \\, y}{x^{2} + y^{2} + 1}, \\frac{x^{2} + y^{2} - 1}{x^{2} + y^{2} + 1}\\right) \\end{array}$" ], "text/plain": [ "Phi: S^2 → E^3\n", " (th, ph) ↦ (X, Y, Z) = (cos(ph)*sin(th), sin(ph)*sin(th), cos(th))\n", " (x, y) ↦ (X, Y, Z) = (2*x/(x^2 + y^2 + 1), 2*y/(x^2 + y^2 + 1), (x^2 + y^2 - 1)/(x^2 + y^2 + 1))" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This means that we can use $\\Phi$ for a 3D view of the stereographic chart:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "