{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Sphere $\\mathbb{S}^2$\n", "\n", "This worksheet demonstrates a few capabilities of\n", "[SageManifolds](http://sagemanifolds.obspm.fr) (version 1.0, as included in SageMath 7.5)\n", "on the example of the 2-dimensional sphere.\n", "\n", "Click [here](https://raw.githubusercontent.com/sagemanifolds/SageManifolds/master/Worksheets/v1.0/SM_sphere_S2.ipynb) to download the worksheet file (ipynb format). To run it, you must start SageMath with the Jupyter notebook, via the command `sage -n jupyter`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*NB:* a version of SageMath at least equal to 7.5 is required to run this worksheet:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "'SageMath version 7.5.1, Release Date: 2017-01-15'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we set up the notebook to display mathematical objects using LaTeX formatting:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also define a viewer for 3D plots (use `'threejs'` or `'jmol'` for interactive 3D graphics):" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "viewer3D = 'threejs' # must be 'threejs', jmol', 'tachyon' or None (default)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $\\mathbb{S}^2$ as a 2-dimensional differentiable manifold\n", "\n", "We start by declaring $\\mathbb{S}^2$ as a differentiable manifold of dimension 2 over $\\mathbb{R}$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "S2 = Manifold(2, 'S^2', latex_name=r'\\mathbb{S}^2', start_index=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The first argument, 2, is the dimension of the manifold, while the second argument is the symbol used to label the manifold.

\n", "

The argument start_index sets the index range to be used on the manifold for labelling components w.r.t. a basis or a frame: start_index=1 corresponds to $\\{1,2\\}$; the default value is start_index=0 and yields to $\\{0,1\\}$.

" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(S2)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathbb{S}^2$ " ], "text/plain": [ "2-dimensional differentiable manifold S^2" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The manifold is a `Parent` object:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "isinstance(S2, Parent)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

in the category of smooth manifolds over $\\mathbb{R}$:

" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathbf{Smooth}_{\\Bold{R}}$ " ], "text/plain": [ "Category of smooth manifolds over Real Field with 53 bits of precision" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2.category()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Coordinate charts on $\\mathbb{S}^2$\n", "\n", "The sphere cannot be covered by a single chart. At least two charts are necessary, for instance the charts associated with the stereographic projections from the North pole and the South pole respectively. Let us introduce the open subsets covered by these two charts: \n", "$$ U := \\mathbb{S}^2\\setminus\\{N\\}, $$ \n", "$$ V := \\mathbb{S}^2\\setminus\\{S\\}, $$\n", "where $N$ is a point of $\\mathbb{S}^2$, which we shall call the North pole, and $S$ is the point of $U$ of stereographic coordinates $(0,0)$, which we call the South pole:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Open subset U of the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "U = S2.open_subset('U') ; print(U)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Open subset V of the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "V = S2.open_subset('V') ; print(V)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We declare that $\\mathbb{S}^2 = U \\cup V$:

" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "S2.declare_union(U, V)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Then we declare the stereographic chart on $U$, denoting by $(x,y)$ the coordinates resulting from the stereographic projection from the North pole:

" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "stereoN. = U.chart()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expression `.` in the left-hand side means that the Python variables `x` and `y` are set to the two coordinates of the chart. This allows one to refer subsequently to the coordinates by their names. In the present case, the function `chart()` has no argument, which implies that the coordinate symbols will be `x` and `y` (i.e. exactly the characters appearing in the `<...>` operator) and that each coordinate range is $(-\\infty,+\\infty)$. As we will see below, for other cases, an argument must be passed to `chart()` to specify each coordinate symbol and range, as well as some specific LaTeX symbol." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,(x, y)\\right)$ " ], "text/plain": [ "Chart (U, (x, y))" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The coordinates can be accessed individually, either by means of their indices in the chart ( following the convention `start_index=1` set in the manifold's definition) or by their names as Python variables:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}x$ " ], "text/plain": [ "x" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN[1]" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y is stereoN[2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Similarly, we introduce on $V$ the coordinates $(x',y')$ corresponding to the stereographic projection from the South pole:

" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [], "source": [ "stereoS. = V.chart(\"xp:x' yp:y'\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, the string argument passed to `chart` stipulates that the text-only names of the coordinates are xp and yp (same as the Python variables names defined within the `<...>` operator in the left-hand side), while their LaTeX names are $x'$ and $y'$." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(V,({x'}, {y'})\\right)$ " ], "text/plain": [ "Chart (V, (xp, yp))" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoS" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

At this stage, the user's atlas on the manifold has two charts:

" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left(U,(x, y)\\right), \\left(V,({x'}, {y'})\\right)\\right]$ " ], "text/plain": [ "[Chart (U, (x, y)), Chart (V, (xp, yp))]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2.atlas()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We have to specify the transition map between the charts 'stereoN' = $(U,(x,y))$ and 'stereoS' = $(V,(x',y'))$; it is given by the standard inversion formulas:

" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {x'} & = & \\frac{x}{x^{2} + y^{2}} \\\\ {y'} & = & \\frac{y}{x^{2} + y^{2}} \\end{array}\\right.$ " ], "text/plain": [ "xp = x/(x^2 + y^2)\n", "yp = y/(x^2 + y^2)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_to_S = stereoN.transition_map(stereoS, \n", " (x/(x^2+y^2), y/(x^2+y^2)), \n", " intersection_name='W',\n", " restrictions1= x^2+y^2!=0, \n", " restrictions2= xp^2+xp^2!=0)\n", "stereoN_to_S.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the above declaration, 'W' is the name given to the chart-overlap subset: $W := U\\cap V$, the condition $x^2+y^2 \\not=0$ defines $W$ as a subset of $U$, and the condition $x'^2+y'^2\\not=0$ defines $W$ as a subset of $V$.\n", "\n", "The inverse coordinate transformation is computed by means of the method `inverse()`:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} x & = & \\frac{{x'}}{{x'}^{2} + {y'}^{2}} \\\\ y & = & \\frac{{y'}}{{x'}^{2} + {y'}^{2}} \\end{array}\\right.$ " ], "text/plain": [ "x = xp/(xp^2 + yp^2)\n", "y = yp/(xp^2 + yp^2)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoS_to_N = stereoN_to_S.inverse()\n", "stereoS_to_N.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

In the present case, the situation is of course perfectly symmetric regarding the coordinates $(x,y)$ and $(x',y')$.

\n", "

At this stage, the user's atlas has four charts:

" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left(U,(x, y)\\right), \\left(V,({x'}, {y'})\\right), \\left(W,(x, y)\\right), \\left(W,({x'}, {y'})\\right)\\right]$ " ], "text/plain": [ "[Chart (U, (x, y)),\n", " Chart (V, (xp, yp)),\n", " Chart (W, (x, y)),\n", " Chart (W, (xp, yp))]" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2.atlas()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us store $W = U\\cap V$ into a Python variable for future use:

" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [], "source": [ "W = U.intersection(V)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Similarly we store the charts $(W,(x,y))$ (the restriction of $(U,(x,y))$ to $W$) and $(W,(x',y'))$ (the restriction of $(V,(x',y'))$ to $W$) into Python variables:

" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(W,(x, y)\\right)$ " ], "text/plain": [ "Chart (W, (x, y))" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_W = stereoN.restrict(W)\n", "stereoN_W" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(W,({x'}, {y'})\\right)$ " ], "text/plain": [ "Chart (W, (xp, yp))" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoS_W = stereoS.restrict(W)\n", "stereoS_W" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We may plot the chart $(W, (x',y'))$ in terms of itself, as a grid:

" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 17 graphics primitives" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoS_W.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

More interestingly, let us plot the stereographic chart $(x',y')$ in terms of the stereographic chart $(x,y)$ on the domain $W$ where both systems overlap (we split the plot in four parts to avoid the singularity at $(x',y')=(0,0)$):

" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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KTGTCmpLCr4z/XrqU99HAgfx5RATv43LlLvxesqQSWAkKDmOMsTsICTLnzvGN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\nOnVqttdxOByIjY1FuXLlUK5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spUTIXWlp3K358suBp56yOxrJqFAhvqBMn85Pvv7u4EG+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64Ypoz9ERYGB+FevSzf9tWrMFnUrGlZQev8eVF46NgRPj3MqCxPZLxp5auvUBZDH0KQgLZklEol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\nazEIERERkddiECIiIiKv9X9afwyr+xcduAAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 72 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graphSN1 = stereoS_W.plot(stereoN, ranges={xp:[-6,-0.02], yp:[-6,-0.02]})\n", "graphSN2 = stereoS_W.plot(stereoN, ranges={xp:[-6,-0.02], yp:[0.02,6]})\n", "graphSN3 = stereoS_W.plot(stereoN, ranges={xp:[0.02,6], yp:[-6,-0.02]})\n", "graphSN4 = stereoS_W.plot(stereoN, ranges={xp:[0.02,6], yp:[0.02,6]})\n", "show(graphSN1+graphSN2+graphSN3+graphSN4,\n", " xmin=-1.5, xmax=1.5, ymin=-1.5, ymax=1.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Spherical coordinates

\n", "

The standard spherical (or polar) coordinates $(\\theta,\\phi)$ are defined on the open domain $A\\subset W \\subset \\mathbb{S}^2$ that is the complement of the \"origin meridian\"; since the latter is the half-circle defined by $y=0$ and $x\\geq 0$, we declare:

" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Open subset A of the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "A = W.open_subset('A', coord_def={stereoN_W: (y!=0, x<0), \n", " stereoS_W: (yp!=0, xp<0)})\n", "print(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The restriction of the stereographic chart from the North pole to $A$ is

" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A,(x, y)\\right)$ " ], "text/plain": [ "Chart (A, (x, y))" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_A = stereoN_W.restrict(A)\n", "stereoN_A" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We then declare the chart $(A,(\\theta,\\phi))$ by specifying the intervals $(0,\\pi)$ and $(0,2\\pi)$ spanned by respectively $\\theta$ and $\\phi$:

" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A,({\\theta}, {\\phi})\\right)$ " ], "text/plain": [ "Chart (A, (th, ph))" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher. = A.chart(r'th:(0,pi):\\theta ph:(0,2*pi):\\phi') ; spher" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The specification of the spherical coordinates is completed by providing the transition map with the stereographic chart $(A,(x,y))$:

" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} x & = & -\\frac{\\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right) - 1} \\\\ y & = & -\\frac{\\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right) - 1} \\end{array}\\right.$ " ], "text/plain": [ "x = -cos(ph)*sin(th)/(cos(th) - 1)\n", "y = -sin(ph)*sin(th)/(cos(th) - 1)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher_to_stereoN = spher.transition_map(stereoN_A, \n", " (sin(th)*cos(ph)/(1-cos(th)),\n", " sin(th)*sin(ph)/(1-cos(th))))\n", "spher_to_stereoN.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also provide the inverse transition map, asking to check that the provided formulas are indeed correct (argument `verbose=True`):" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "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))\n", " ph == pi + arctan2(sin(ph)*sin(th)/(cos(th) - 1), cos(ph)*sin(th)/(cos(th) - 1))\n", " x == x\n", " y == y\n" ] } ], "source": [ "spher_to_stereoN.set_inverse(2*atan(1/sqrt(x^2+y^2)), atan2(-y,-x)+pi,\n", " verbose=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The check is passed, modulo some lack of trigonometric simplifications in the first two lines." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\theta} & = & 2 \\, \\arctan\\left(\\frac{1}{\\sqrt{x^{2} + y^{2}}}\\right) \\\\ {\\phi} & = & \\pi + \\arctan\\left(-y, -x\\right) \\end{array}\\right.$ " ], "text/plain": [ "th = 2*arctan(1/sqrt(x^2 + y^2))\n", "ph = pi + arctan2(-y, -x)" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher_to_stereoN.inverse().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The transition map $(A,(\\theta,\\phi))\\rightarrow (A,(x',y'))$ is obtained by combining the transition maps $(A,(\\theta,\\phi))\\rightarrow (A,(x,y))$ and $(A,(x,y))\\rightarrow (A,(x',y'))$:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {x'} & = & -\\frac{\\cos\\left({\\phi}\\right) \\cos\\left({\\theta}\\right) - \\cos\\left({\\phi}\\right)}{\\sin\\left({\\theta}\\right)} \\\\ {y'} & = & -\\frac{\\cos\\left({\\theta}\\right) \\sin\\left({\\phi}\\right) - \\sin\\left({\\phi}\\right)}{\\sin\\left({\\theta}\\right)} \\end{array}\\right.$ " ], "text/plain": [ "xp = -(cos(ph)*cos(th) - cos(ph))/sin(th)\n", "yp = -(cos(th)*sin(ph) - sin(ph))/sin(th)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_to_S_A = stereoN_to_S.restrict(A)\n", "spher_to_stereoS = stereoN_to_S_A * spher_to_stereoN\n", "spher_to_stereoS.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, the transition map $(A,(x',y'))\\rightarrow (A,(\\theta,\\phi))$ is obtained by combining the transition maps $(A,(x',y'))\\rightarrow (A,(x,y))$ and $(A,(x,y))\\rightarrow (A,(\\theta,\\phi))$:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {\\theta} & = & 2 \\, \\arctan\\left(\\sqrt{{x'}^{2} + {y'}^{2}}\\right) \\\\ {\\phi} & = & \\pi - \\arctan\\left(\\frac{{y'}}{{x'}^{2} + {y'}^{2}}, -\\frac{{x'}}{{x'}^{2} + {y'}^{2}}\\right) \\end{array}\\right.$ " ], "text/plain": [ "th = 2*arctan(sqrt(xp^2 + yp^2))\n", "ph = pi - arctan2(yp/(xp^2 + yp^2), -xp/(xp^2 + yp^2))" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoS_to_N_A = stereoN_to_S.inverse().restrict(A)\n", "stereoS_to_spher = spher_to_stereoN.inverse() * stereoS_to_N_A \n", "stereoS_to_spher.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The user atlas of $\\mathbb{S}^2$ is now

" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left(U,(x, y)\\right), \\left(V,({x'}, {y'})\\right), \\left(W,(x, y)\\right), \\left(W,({x'}, {y'})\\right), \\left(A,(x, y)\\right), \\left(A,({x'}, {y'})\\right), \\left(A,({\\theta}, {\\phi})\\right)\\right]$ " ], "text/plain": [ "[Chart (U, (x, y)),\n", " Chart (V, (xp, yp)),\n", " Chart (W, (x, y)),\n", " Chart (W, (xp, yp)),\n", " Chart (A, (x, y)),\n", " Chart (A, (xp, yp)),\n", " Chart (A, (th, ph))]" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2.atlas()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us draw the grid of spherical coordinates $(\\theta,\\phi)$ in terms of stereographic coordinates from the North pole $(x,y)$:

" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Z3ZYJQooQ8SMYw6VLrBapVImNCRcuBNatY+8eIWEKF+aKWsSPeVCKeVjeXuKeWurXpxdo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\nfdvzc+4cJ617Yr7PkwgKApY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XrwMDB7L8vHt3Nh7csoUjGpo0cV0TuZAQwGqNGx3hqRw8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\nSDCTn9hYRJGuX0dV0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Js0UapaNckVtZKVK3kMueNJ9gD0iJ/ISB7gOrv2+iLj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\nCc6lSnH4qF3dug88wJLf3buBChXo+nfepKKidFt3LyEhtNnI/kieTFAQx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"text/plain": [ "Graphics object consisting of 30 graphics primitives" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(stereoN, number_values=15, ranges={th: (pi/8,pi)})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Conversly, we may represent the grid of the stereographic coordinates $(x,y)$ restricted to $A$ in terms of the spherical coordinates $(\\theta,\\phi)$. We limit ourselves to one quarter (cf. the argument ranges):

" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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FteIhKcl0pSVPTzSmmz4dDfnu3kUDu/nz4V1ZsoRoyBCIiT594MHYtAmvdfTM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\n", "text/plain": [ "Graphics object consisting of 40 graphics primitives" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_A.plot(spher, ranges={x: (0.01,8), y: (0.01,8)}, number_values=20, plot_points=200)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Points on $\\mathbb{S}^2$

\n", "

We declare the North pole (resp. the South pole) as the point of coordinates $(0,0)$ in the chart $(V,(x',y'))$ (resp. in the chart $(U,(x,y))$):

" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point N on the 2-dimensional differentiable manifold S^2\n", "Point S on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "N = V.point((0,0), chart=stereoS, name='N') ; print(N)\n", "S = U.point((0,0), chart=stereoN, name='S') ; print(S)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Since points are Sage Element's, the corresponding Parent being the manifold subsets, an equivalent writing of the above declarations is

" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point N on the 2-dimensional differentiable manifold S^2\n", "Point S on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "N = V((0,0), chart=stereoS, name='N') ; print(N)\n", "S = U((0,0), chart=stereoN, name='S') ; print(S)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Moreover, since stereoS in the default chart on $V$ and stereoN is the default one on $U$, their mentions can be omitted, so that the above can be shortened to

" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point N on the 2-dimensional differentiable manifold S^2\n", "Point S on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "N = V((0,0), name='N') ; print(N)\n", "S = U((0,0), name='S') ; print(S)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}V$ " ], "text/plain": [ "Open subset V of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N.parent()" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}U$ " ], "text/plain": [ "Open subset U of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S.parent()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We have of course

" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N in V" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N in S2" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{False}$ " ], "text/plain": [ "False" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N in U" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{False}$ " ], "text/plain": [ "False" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N in A" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us introduce some point at the equator:

" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [], "source": [ "E = S2((0,1), chart=stereoN, name='E')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The point $E$ is in the open subset $A$:

" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E in A" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We may then ask for its spherical coordinates $(\\theta,\\phi)$:

" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\frac{1}{2} \\, \\pi, \\frac{1}{2} \\, \\pi\\right)$ " ], "text/plain": [ "(1/2*pi, 1/2*pi)" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E.coord(spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

which is not possible for the point $N$:

" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Error: the point does not belong to the domain of Chart (A, (th, ph))\n" ] } ], "source": [ "try:\n", " N.coord(spher)\n", "except ValueError as exc:\n", " print('Error: ' + str(exc))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Mappings between manifolds: the embedding of $\\mathbb{S}^2$ into $\\mathbb{R}^3$

\n", "

Let us first declare $\\mathbb{R}^3$ as a 3-dimensional manifold covered by a single chart (the so-called Cartesian coordinates):

" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\mathbb{R}^3,(X, Y, Z)\\right)$ " ], "text/plain": [ "Chart (R^3, (X, Y, Z))" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R3 = Manifold(3, 'R^3', r'\\mathbb{R}^3', start_index=1)\n", "cart. = R3.chart() ; cart" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The embedding of the sphere is defined as a differential mapping $\\Phi: \\mathbb{S}^2 \\rightarrow \\mathbb{R}^3$:

" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [], "source": [ "Phi = S2.diff_map(R3, {(stereoN, cart): \n", " [2*x/(1+x^2+y^2), 2*y/(1+x^2+y^2),\n", " (x^2+y^2-1)/(1+x^2+y^2)],\n", " (stereoS, cart): \n", " [2*xp/(1+xp^2+yp^2), 2*yp/(1+xp^2+yp^2),\n", " (1-xp^2-yp^2)/(1+xp^2+yp^2)]},\n", " name='Phi', latex_name=r'\\Phi')" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\Phi:& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R}^3 \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(\\frac{2 \\, x}{x^{2} + y^{2} + 1}, \\frac{2 \\, y}{x^{2} + y^{2} + 1}, \\frac{x^{2} + y^{2} - 1}{x^{2} + y^{2} + 1}\\right) \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(\\frac{2 \\, {x'}}{{x'}^{2} + {y'}^{2} + 1}, \\frac{2 \\, {y'}}{{x'}^{2} + {y'}^{2} + 1}, -\\frac{{x'}^{2} + {y'}^{2} - 1}{{x'}^{2} + {y'}^{2} + 1}\\right) \\end{array}$ " ], "text/plain": [ "Phi: S^2 --> R^3\n", "on U: (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))\n", "on V: (xp, yp) |--> (X, Y, Z) = (2*xp/(xp^2 + yp^2 + 1), 2*yp/(xp^2 + yp^2 + 1), -(xp^2 + yp^2 - 1)/(xp^2 + yp^2 + 1))" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.display()" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Hom}\\left(\\mathbb{S}^2,\\mathbb{R}^3\\right)$ " ], "text/plain": [ "Set of Morphisms from 2-dimensional differentiable manifold S^2 to 3-dimensional differentiable manifold R^3 in Category of smooth manifolds over Real Field with 53 bits of precision" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.parent()" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Set of Morphisms from 2-dimensional differentiable manifold S^2 to 3-dimensional differentiable manifold R^3 in Category of smooth manifolds over Real Field with 53 bits of precision\n" ] } ], "source": [ "print(Phi.parent())" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.parent() is Hom(S2, R3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

$\\Phi$ maps points of $\\mathbb{S}^2$ to points of $\\mathbb{R}^3$:

" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point Phi(N) on the 3-dimensional differentiable manifold R^3\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0, 0, 1\\right)$ " ], "text/plain": [ "(0, 0, 1)" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N1 = Phi(N) ; print(N1) ; N1 ; N1.coord()" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point Phi(S) on the 3-dimensional differentiable manifold R^3\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0, 0, -1\\right)$ " ], "text/plain": [ "(0, 0, -1)" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S1 = Phi(S) ; print(S1) ; S1 ; S1.coord()" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point Phi(E) on the 3-dimensional differentiable manifold R^3\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0, 1, 0\\right)$ " ], "text/plain": [ "(0, 1, 0)" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E1 = Phi(E) ; print(E1) ; E1 ; E1.coord()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

$\\Phi$ has been defined in terms of the stereographic charts $(U,(x,y))$ and $(V,(x',y'))$, but we may ask its expression in terms of spherical coordinates. The latter is then computed by means of the transition map $(A,(x,y))\\rightarrow (A,(\\theta,\\phi))$:

" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\frac{2 \\, x}{x^{2} + y^{2} + 1}, \\frac{2 \\, y}{x^{2} + y^{2} + 1}, \\frac{x^{2} + y^{2} - 1}{x^{2} + y^{2} + 1}\\right)$ " ], "text/plain": [ "(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": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.expr(stereoN_A, cart)" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), \\cos\\left({\\theta}\\right)\\right)$ " ], "text/plain": [ "(cos(ph)*sin(th), sin(ph)*sin(th), cos(th))" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.expr(spher, cart)" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\Phi:& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R}^3 \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(\\cos\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), \\cos\\left({\\theta}\\right)\\right) \\end{array}$ " ], "text/plain": [ "Phi: S^2 --> R^3\n", "on A: (th, ph) |--> (X, Y, Z) = (cos(ph)*sin(th), sin(ph)*sin(th), cos(th))" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.display(spher, cart)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us use $\\Phi$ to draw the grid of spherical coordinates $(\\theta,\\phi)$ in terms of the Cartesian coordinates $(X,Y,Z)$ of $\\mathbb{R}^3$:

" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_spher = spher.plot(chart=cart, mapping=Phi, number_values=11, \n", " color='blue', label_axes=False)\n", "show(graph_spher, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We may also use the embedding $\\Phi$ to display the stereographic coordinate grid in terms of the Cartesian coordinates in $\\mathbb{R}^3$. First for the stereographic coordinates from the North pole:

" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_stereoN = stereoN.plot(chart=cart, mapping=Phi, number_values=25, \n", " label_axes=False)\n", "show(graph_stereoN, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

and then have a view with the stereographic coordinates from the South pole superposed (in green):

" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_stereoS = stereoS.plot(chart=cart, mapping=Phi, number_values=25, \n", " color='green', label_axes=False)\n", "show(graph_stereoN + graph_stereoS, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We may also add the two poles to the graphic:

" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pointN = N.plot(chart=cart, mapping=Phi, color='red', \n", " label_offset=0.05)\n", "pointS = S.plot(chart=cart, mapping=Phi, color='green', \n", " label_offset=0.05)\n", "show(graph_stereoN + graph_stereoS + pointN + pointS, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Tangent spaces

\n", "

The tangent space to the manifold $\\mathbb{S}^2$ at the point $N$ is

" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tangent space at Point N on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}T_{N}\\,\\mathbb{S}^2$ " ], "text/plain": [ "Tangent space at Point N on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_N = S2.tangent_space(N)\n", "print(T_N) ; T_N" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

$T_N \\mathbb{S}^2$ is a vector space over $\\mathbb{R}$ (represented here by Sage's symbolic ring SR):

" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Category of finite dimensional vector spaces over Symbolic Ring\n" ] } ], "source": [ "print(T_N.category())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Its dimension equals the manifold's dimension:

" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}2$ " ], "text/plain": [ "2" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dim(T_N)" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dim(T_N) == dim(S2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

$T_N \\mathbb{S}^2$ is endowed with a basis inherited from the coordinate frame defined around $N$, namely the frame associated with the chart $(V,(x',y'))$:

" ] }, { "cell_type": "code", "execution_count": 71, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left(\\frac{\\partial}{\\partial {x'} },\\frac{\\partial}{\\partial {y'} }\\right)\\right]$ " ], "text/plain": [ "[Basis (d/dxp,d/dyp) on the Tangent space at Point N on the 2-dimensional differentiable manifold S^2]" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_N.bases()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

$(V,(x',y'))$ is the only chart defined so far around the point $N$. If various charts have been defined around a point, then the tangent space at this point is automatically endowed with the bases inherited from the coordinate frames associated to all these charts. For instance, for the equator point $E$:

" ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tangent space at Point E on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}T_{E}\\,\\mathbb{S}^2$ " ], "text/plain": [ "Tangent space at Point E on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_E = S2.tangent_space(E)\n", "print(T_E) ; T_E" ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left(\\frac{\\partial}{\\partial x },\\frac{\\partial}{\\partial y }\\right), \\left(\\frac{\\partial}{\\partial {x'} },\\frac{\\partial}{\\partial {y'} }\\right), \\left(\\frac{\\partial}{\\partial {\\theta} },\\frac{\\partial}{\\partial {\\phi} }\\right)\\right]$ " ], "text/plain": [ "[Basis (d/dx,d/dy) on the Tangent space at Point E on the 2-dimensional differentiable manifold S^2,\n", " Basis (d/dxp,d/dyp) on the Tangent space at Point E on the 2-dimensional differentiable manifold S^2,\n", " Basis (d/dth,d/dph) on the Tangent space at Point E on the 2-dimensional differentiable manifold S^2]" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_E.bases()" ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\frac{\\partial}{\\partial x },\\frac{\\partial}{\\partial y }\\right)$ " ], "text/plain": [ "Basis (d/dx,d/dy) on the Tangent space at Point E on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_E.default_basis()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

An element of $T_E\\mathbb{S}^2$:

" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tangent vector v at Point E on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "v = T_E((-3, 2), name='v')\n", "print(v)" ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v in T_E" ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}T_{E}\\,\\mathbb{S}^2$ " ], "text/plain": [ "Tangent space at Point E on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.parent()" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = -3 \\frac{\\partial}{\\partial x } + 2 \\frac{\\partial}{\\partial y }$ " ], "text/plain": [ "v = -3 d/dx + 2 d/dy" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display()" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = -3 \\frac{\\partial}{\\partial {x'} } -2 \\frac{\\partial}{\\partial {y'} }$ " ], "text/plain": [ "v = -3 d/dxp - 2 d/dyp" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display(T_E.bases()[1])" ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = -2 \\frac{\\partial}{\\partial {\\theta} } + 3 \\frac{\\partial}{\\partial {\\phi} }$ " ], "text/plain": [ "v = -2 d/dth + 3 d/dph" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display(T_E.bases()[2])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Differential of a smooth mapping

\n", "

The differential of the mapping $\\Phi$ at the point $E$ is

" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Generic morphism:\n", " From: Tangent space at Point E on the 2-dimensional differentiable manifold S^2\n", " To: Tangent space at Point Phi(E) on the 3-dimensional differentiable manifold R^3\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}\\Phi_{E}$ " ], "text/plain": [ "Generic morphism:\n", " From: Tangent space at Point E on the 2-dimensional differentiable manifold S^2\n", " To: Tangent space at Point Phi(E) on the 3-dimensional differentiable manifold R^3" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E = Phi.differential(E)\n", "print(dPhi_E) ; dPhi_E" ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}T_{E}\\,\\mathbb{S}^2$ " ], "text/plain": [ "Tangent space at Point E on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E.domain()" ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}T_{\\Phi\\left(E\\right)}\\,\\mathbb{R}^3$ " ], "text/plain": [ "Tangent space at Point Phi(E) on the 3-dimensional differentiable manifold R^3" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E.codomain()" ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Hom}\\left(T_{E}\\,\\mathbb{S}^2,T_{\\Phi\\left(E\\right)}\\,\\mathbb{R}^3\\right)$ " ], "text/plain": [ "Set of Morphisms from Tangent space at Point E on the 2-dimensional differentiable manifold S^2 to Tangent space at Point Phi(E) on the 3-dimensional differentiable manifold R^3 in Category of finite dimensional vector spaces over Symbolic Ring" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E.parent()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The image by $\\mathrm{d}\\Phi_E$ of the vector $v\\in T_E\\mathbb{S}^2$ introduced above is

" ] }, { "cell_type": "code", "execution_count": 85, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}\\Phi_{E}\\left(v\\right)$ " ], "text/plain": [ "Tangent vector dPhi_E(v) at Point Phi(E) on the 3-dimensional differentiable manifold R^3" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E(v)" ] }, { "cell_type": "code", "execution_count": 86, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tangent vector dPhi_E(v) at Point Phi(E) on the 3-dimensional differentiable manifold R^3\n" ] } ], "source": [ "print(dPhi_E(v))" ] }, { "cell_type": "code", "execution_count": 87, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E(v) in R3.tangent_space(Phi(E))" ] }, { "cell_type": "code", "execution_count": 88, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}\\Phi_{E}\\left(v\\right) = -3 \\frac{\\partial}{\\partial X } + 2 \\frac{\\partial}{\\partial Z }$ " ], "text/plain": [ "dPhi_E(v) = -3 d/dX + 2 d/dZ" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E(v).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Algebra of scalar fields

\n", "

The set $C^\\infty(\\mathbb{S}^2)$ of all smooth functions $\\mathbb{S}^2\\rightarrow \\mathbb{R}$ has naturally the structure of a commutative algebra over $\\mathbb{R}$. $C^\\infty(\\mathbb{S}^2)$ is obtained via the method scalar_field_algebra() applied to the manifold $\\mathbb{S}^2$:

" ] }, { "cell_type": "code", "execution_count": 89, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}C^{\\infty}\\left(\\mathbb{S}^2\\right)$ " ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CS = S2.scalar_field_algebra() ; CS" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Since the algebra internal product is the pointwise multiplication, it is clearly commutative, so that $C^\\infty(\\mathbb{S}^2)$ belongs to Sage's category of commutative algebras:

" ] }, { "cell_type": "code", "execution_count": 90, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathbf{CommutativeAlgebras}_{\\text{SR}}$ " ], "text/plain": [ "Category of commutative algebras over Symbolic Ring" ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CS.category()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The base ring of the algebra $C^\\infty(\\mathbb{S}^2)$ is the field $\\mathbb{R}$, which is represented here by Sage's Symbolic Ring (SR):

" ] }, { "cell_type": "code", "execution_count": 91, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\text{SR}$ " ], "text/plain": [ "Symbolic Ring" ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CS.base_ring()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Elements of $C^\\infty(\\mathbb{S}^2)$ are of course (smooth) scalar fields:

" ] }, { "cell_type": "code", "execution_count": 92, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(CS.an_element())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

This example element is the constant scalar field that takes the value 2:

" ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & 2 \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & 2 \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & 2 \\end{array}$ " ], "text/plain": [ "S^2 --> R\n", "on U: (x, y) |--> 2\n", "on V: (xp, yp) |--> 2\n", "on A: (th, ph) |--> 2" ] }, "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CS.an_element().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

A specific element is the zero one:

" ] }, { "cell_type": "code", "execution_count": 94, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field zero on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "f = CS.zero()\n", "print(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Scalar fields map points of $\\mathbb{S}^2$ to real numbers:

" ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0, 0, 0\\right)$ " ], "text/plain": [ "(0, 0, 0)" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(N), f(E), f(S)" ] }, { "cell_type": "code", "execution_count": 96, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} 0:& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & 0 \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & 0 \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & 0 \\end{array}$ " ], "text/plain": [ "zero: S^2 --> R\n", "on U: (x, y) |--> 0\n", "on V: (xp, yp) |--> 0\n", "on A: (th, ph) |--> 0" ] }, "execution_count": 96, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Another specific element is the algebra unit element, i.e. the constant scalar field 1:

" ] }, { "cell_type": "code", "execution_count": 97, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field 1 on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "f = CS.one()\n", "print(f)" ] }, { "cell_type": "code", "execution_count": 98, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(1, 1, 1\\right)$ " ], "text/plain": [ "(1, 1, 1)" ] }, "execution_count": 98, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(N), f(E), f(S)" ] }, { "cell_type": "code", "execution_count": 99, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} 1:& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & 1 \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & 1 \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & 1 \\end{array}$ " ], "text/plain": [ "1: S^2 --> R\n", "on U: (x, y) |--> 1\n", "on V: (xp, yp) |--> 1\n", "on A: (th, ph) |--> 1" ] }, "execution_count": 99, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us define a scalar field by its coordinate expression in the two stereographic charts:

" ] }, { "cell_type": "code", "execution_count": 100, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & \\pi - 2 \\, \\arctan\\left(x^{2} + y^{2}\\right) \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & 2 \\, \\arctan\\left({x'}^{2} + {y'}^{2}\\right) \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & \\pi + 2 \\, \\arctan\\left(\\frac{\\cos\\left({\\theta}\\right) + 1}{\\cos\\left({\\theta}\\right) - 1}\\right) \\end{array}$ " ], "text/plain": [ "S^2 --> R\n", "on U: (x, y) |--> pi - 2*arctan(x^2 + y^2)\n", "on V: (xp, yp) |--> 2*arctan(xp^2 + yp^2)\n", "on A: (th, ph) |--> pi + 2*arctan((cos(th) + 1)/(cos(th) - 1))" ] }, "execution_count": 100, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f = CS({stereoN: pi - 2*atan(x^2+y^2), stereoS: 2*atan(xp^2+yp^2)})\n", "f.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Instead of using CS() (i.e. the Parent __call__ function), we may invoke the scalar_field method on the manifold to create $f$; this allows to pass the name of the scalar field:

" ] }, { "cell_type": "code", "execution_count": 101, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} f:& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & \\pi - 2 \\, \\arctan\\left(x^{2} + y^{2}\\right) \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & 2 \\, \\arctan\\left({x'}^{2} + {y'}^{2}\\right) \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & \\pi + 2 \\, \\arctan\\left(\\frac{\\cos\\left({\\theta}\\right) + 1}{\\cos\\left({\\theta}\\right) - 1}\\right) \\end{array}$ " ], "text/plain": [ "f: S^2 --> R\n", "on U: (x, y) |--> pi - 2*arctan(x^2 + y^2)\n", "on V: (xp, yp) |--> 2*arctan(xp^2 + yp^2)\n", "on A: (th, ph) |--> pi + 2*arctan((cos(th) + 1)/(cos(th) - 1))" ] }, "execution_count": 101, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f = S2.scalar_field({stereoN: pi - 2*atan(x^2+y^2), stereoS: 2*atan(xp^2+yp^2)}, name='f')\n", "f.display()" ] }, { "cell_type": "code", "execution_count": 102, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}C^{\\infty}\\left(\\mathbb{S}^2\\right)$ " ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 102, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.parent()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Internally, the various coordinate expressions of the scalar field are stored in the dictionary _express, whose keys are the charts:

" ] }, { "cell_type": "code", "execution_count": 103, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\left(A,(x, y)\\right) : \\pi - 2 \\, \\arctan\\left(x^{2} + y^{2}\\right), \\left(A,({\\theta}, {\\phi})\\right) : \\pi + 2 \\, \\arctan\\left(\\frac{\\cos\\left({\\theta}\\right) + 1}{\\cos\\left({\\theta}\\right) - 1}\\right), \\left(U,(x, y)\\right) : \\pi - 2 \\, \\arctan\\left(x^{2} + y^{2}\\right), \\left(V,({x'}, {y'})\\right) : 2 \\, \\arctan\\left({x'}^{2} + {y'}^{2}\\right)\\right\\}$ " ], "text/plain": [ "{Chart (A, (x, y)): pi - 2*arctan(x^2 + y^2),\n", " Chart (A, (th, ph)): pi + 2*arctan((cos(th) + 1)/(cos(th) - 1)),\n", " Chart (V, (xp, yp)): 2*arctan(xp^2 + yp^2),\n", " Chart (U, (x, y)): pi - 2*arctan(x^2 + y^2)}" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f._express" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The expression in a specific chart is recovered by passing the chart as the argument of the method display():

" ] }, { "cell_type": "code", "execution_count": 104, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} f:& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & 2 \\, \\arctan\\left({x'}^{2} + {y'}^{2}\\right) \\end{array}$ " ], "text/plain": [ "f: S^2 --> R\n", "on V: (xp, yp) |--> 2*arctan(xp^2 + yp^2)" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.display(stereoS)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Scalar fields map the manifold's points to real numbers:

" ] }, { "cell_type": "code", "execution_count": 105, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$ " ], "text/plain": [ "0" ] }, "execution_count": 105, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(N)" ] }, { "cell_type": "code", "execution_count": 106, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{1}{2} \\, \\pi$ " ], "text/plain": [ "1/2*pi" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(E)" ] }, { "cell_type": "code", "execution_count": 107, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\pi$ " ], "text/plain": [ "pi" ] }, "execution_count": 107, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(S)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We may define the restrictions of $f$ to the open subsets $U$ and $V$:

" ] }, { "cell_type": "code", "execution_count": 108, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} f:& U & \\longrightarrow & \\mathbb{R} \\\\ & \\left(x, y\\right) & \\longmapsto & \\pi - 2 \\, \\arctan\\left(x^{2} + y^{2}\\right) \\\\ \\mbox{on}\\ W : & \\left({x'}, {y'}\\right) & \\longmapsto & 2 \\, \\arctan\\left({x'}^{2} + {y'}^{2}\\right) \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & \\pi + 2 \\, \\arctan\\left(\\frac{\\cos\\left({\\theta}\\right) + 1}{\\cos\\left({\\theta}\\right) - 1}\\right) \\end{array}$ " ], "text/plain": [ "f: U --> R\n", " (x, y) |--> pi - 2*arctan(x^2 + y^2)\n", "on W: (xp, yp) |--> 2*arctan(xp^2 + yp^2)\n", "on A: (th, ph) |--> pi + 2*arctan((cos(th) + 1)/(cos(th) - 1))" ] }, "execution_count": 108, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU = f.restrict(U)\n", "fU.display()" ] }, { "cell_type": "code", "execution_count": 109, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} f:& V & \\longrightarrow & \\mathbb{R} \\\\ & \\left({x'}, {y'}\\right) & \\longmapsto & 2 \\, \\arctan\\left({x'}^{2} + {y'}^{2}\\right) \\\\ \\mbox{on}\\ W : & \\left(x, y\\right) & \\longmapsto & \\pi - 2 \\, \\arctan\\left(x^{2} + y^{2}\\right) \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & \\pi + 2 \\, \\arctan\\left(\\frac{\\cos\\left({\\theta}\\right) + 1}{\\cos\\left({\\theta}\\right) - 1}\\right) \\end{array}$ " ], "text/plain": [ "f: V --> R\n", " (xp, yp) |--> 2*arctan(xp^2 + yp^2)\n", "on W: (x, y) |--> pi - 2*arctan(x^2 + y^2)\n", "on A: (th, ph) |--> pi + 2*arctan((cos(th) + 1)/(cos(th) - 1))" ] }, "execution_count": 109, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fV = f.restrict(V)\n", "fV.display()" ] }, { "cell_type": "code", "execution_count": 110, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\frac{1}{2} \\, \\pi, \\pi\\right)$ " ], "text/plain": [ "(1/2*pi, pi)" ] }, "execution_count": 110, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU(E), fU(S)" ] }, { "cell_type": "code", "execution_count": 111, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}C^{\\infty}\\left(U\\right)$ " ], "text/plain": [ "Algebra of differentiable scalar fields on the Open subset U of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 111, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU.parent()" ] }, { "cell_type": "code", "execution_count": 112, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}C^{\\infty}\\left(V\\right)$ " ], "text/plain": [ "Algebra of differentiable scalar fields on the Open subset V of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 112, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fV.parent()" ] }, { "cell_type": "code", "execution_count": 113, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 113, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CU = U.scalar_field_algebra()\n", "fU.parent() is CU" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

A scalar field on $\\mathbb{S}^2$ can be coerced to a scalar field on $U$, the coercion being simply the restriction:

" ] }, { "cell_type": "code", "execution_count": 114, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 114, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CU.has_coerce_map_from(CS)" ] }, { "cell_type": "code", "execution_count": 115, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 115, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU == CU(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The arithmetic of scalar fields:

" ] }, { "cell_type": "code", "execution_count": 116, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & -2 \\, \\pi + \\pi^{2} - 4 \\, {\\left(\\pi - 1\\right)} \\arctan\\left(x^{2} + y^{2}\\right) + 4 \\, \\arctan\\left(x^{2} + y^{2}\\right)^{2} \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & 4 \\, \\arctan\\left({x'}^{2} + {y'}^{2}\\right)^{2} - 4 \\, \\arctan\\left({x'}^{2} + {y'}^{2}\\right) \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & -2 \\, \\pi + \\pi^{2} + 4 \\, {\\left(\\pi - 1\\right)} \\arctan\\left(\\frac{\\cos\\left({\\theta}\\right) + 1}{\\cos\\left({\\theta}\\right) - 1}\\right) + 4 \\, \\arctan\\left(\\frac{\\cos\\left({\\theta}\\right) + 1}{\\cos\\left({\\theta}\\right) - 1}\\right)^{2} \\end{array}$ " ], "text/plain": [ "S^2 --> R\n", "on U: (x, y) |--> -2*pi + pi^2 - 4*(pi - 1)*arctan(x^2 + y^2) + 4*arctan(x^2 + y^2)^2\n", "on V: (xp, yp) |--> 4*arctan(xp^2 + yp^2)^2 - 4*arctan(xp^2 + yp^2)\n", "on A: (th, ph) |--> -2*pi + pi^2 + 4*(pi - 1)*arctan((cos(th) + 1)/(cos(th) - 1)) + 4*arctan((cos(th) + 1)/(cos(th) - 1))^2" ] }, "execution_count": 116, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = f*f - 2*f\n", "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Module of vector fields

\n", "

The set $\\mathcal{X}(\\mathbb{S}^2)$ of all smooth vector fields on $\\mathbb{S}^2$ is a module over the algebra (ring) $C^\\infty(\\mathbb{S}^2)$. It is obtained by the method vector_field_module():

" ] }, { "cell_type": "code", "execution_count": 117, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathcal{X}\\left(\\mathbb{S}^2\\right)$ " ], "text/plain": [ "Module X(S^2) of vector fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 117, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS = S2.vector_field_module()\n", "XS" ] }, { "cell_type": "code", "execution_count": 118, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module X(S^2) of vector fields on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(XS)" ] }, { "cell_type": "code", "execution_count": 119, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}C^{\\infty}\\left(\\mathbb{S}^2\\right)$ " ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 119, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS.base_ring()" ] }, { "cell_type": "code", "execution_count": 120, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathbf{Modules}_{C^{\\infty}\\left(\\mathbb{S}^2\\right)}$ " ], "text/plain": [ "Category of modules over Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 120, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS.category()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

$\\mathcal{X}(\\mathbb{S}^2)$ is not a free module:

" ] }, { "cell_type": "code", "execution_count": 121, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{False}$ " ], "text/plain": [ "False" ] }, "execution_count": 121, "metadata": {}, "output_type": "execute_result" } ], "source": [ "isinstance(XS, FiniteRankFreeModule)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

because $\\mathbb{S}^2$ is not a parallelizable manifold:

" ] }, { "cell_type": "code", "execution_count": 122, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{False}$ " ], "text/plain": [ "False" ] }, "execution_count": 122, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2.is_manifestly_parallelizable()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

On the contrary, the set $\\mathcal{X}(U)$ of smooth vector fields on $U$ is a free module:

" ] }, { "cell_type": "code", "execution_count": 123, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 123, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XU = U.vector_field_module()\n", "isinstance(XU, FiniteRankFreeModule)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

because $U$ is parallelizable:

" ] }, { "cell_type": "code", "execution_count": 124, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 124, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U.is_manifestly_parallelizable()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Due to the introduction of the stereographic coordinates $(x,y)$ on $U$, a basis has already been defined on the free module $\\mathcal{X}(U)$, namely the coordinate basis $(\\partial/\\partial x, \\partial/\\partial y)$:

" ] }, { "cell_type": "code", "execution_count": 125, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Bases defined on the Free module X(U) of vector fields on the Open subset U of the 2-dimensional differentiable manifold S^2:\n", " - (U, (d/dx,d/dy)) (default basis)\n" ] } ], "source": [ "XU.print_bases()" ] }, { "cell_type": "code", "execution_count": 126, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U, \\left(\\frac{\\partial}{\\partial x },\\frac{\\partial}{\\partial y }\\right)\\right)$ " ], "text/plain": [ "Coordinate frame (U, (d/dx,d/dy))" ] }, "execution_count": 126, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XU.default_basis()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Similarly

" ] }, { "cell_type": "code", "execution_count": 127, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(V, \\left(\\frac{\\partial}{\\partial {x'} },\\frac{\\partial}{\\partial {y'} }\\right)\\right)$ " ], "text/plain": [ "Coordinate frame (V, (d/dxp,d/dyp))" ] }, "execution_count": 127, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XV = V.vector_field_module()\n", "XV.default_basis()" ] }, { "cell_type": "code", "execution_count": 128, "metadata": { "collapsed": false }, "outputs": [], "source": [ "eU = XU.default_basis()\n", "eV = XV.default_basis()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

From the point of view of the open set $U$, eU is also the default vector frame:

" ] }, { "cell_type": "code", "execution_count": 129, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 129, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eU is U.default_frame()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

It is also the default vector frame on $\\mathbb{S}^2$ (although not defined on the whole $\\mathbb{S}^2$), for it is the first vector frame defined on an open subset of $\\mathbb{S}^2$:

" ] }, { "cell_type": "code", "execution_count": 130, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 130, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eU is S2.default_frame()" ] }, { "cell_type": "code", "execution_count": 131, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 131, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eV is V.default_frame()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us introduce a vector field on $\\mathbb{S}^2$:

" ] }, { "cell_type": "code", "execution_count": 132, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = \\frac{\\partial}{\\partial x } -2 \\frac{\\partial}{\\partial y }$ " ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 132, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v = S2.vector_field(name='v')\n", "v[eU,:] = [1, -2]\n", "v.display(eU)" ] }, { "cell_type": "code", "execution_count": 133, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathcal{X}\\left(\\mathbb{S}^2\\right)$ " ], "text/plain": [ "Module X(S^2) of vector fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 133, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.parent()" ] }, { "cell_type": "code", "execution_count": 134, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(W, \\left(\\frac{\\partial}{\\partial {x'} },\\frac{\\partial}{\\partial {y'} }\\right)\\right)$ " ], "text/plain": [ "Coordinate frame (W, (d/dxp,d/dyp))" ] }, "execution_count": 134, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoSW = stereoS.restrict(W)\n", "eSW = stereoSW.frame()\n", "eSW" ] }, { "cell_type": "code", "execution_count": 135, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = \\frac{\\partial}{\\partial x } -2 \\frac{\\partial}{\\partial y }$ " ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 135, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW = v.restrict(W)\n", "vW.display()" ] }, { "cell_type": "code", "execution_count": 136, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathcal{X}\\left(W\\right)$ " ], "text/plain": [ "Free module X(W) of vector fields on the Open subset W of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 136, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW.parent()" ] }, { "cell_type": "code", "execution_count": 137, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Free module X(W) of vector fields on the Open subset W of the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(vW.parent())" ] }, { "cell_type": "code", "execution_count": 138, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = \\left( -\\frac{x^{2} - 4 \\, x y - y^{2}}{x^{4} + 2 \\, x^{2} y^{2} + y^{4}} \\right) \\frac{\\partial}{\\partial {x'} } + \\left( -\\frac{2 \\, {\\left(x^{2} + x y - y^{2}\\right)}}{x^{4} + 2 \\, x^{2} y^{2} + y^{4}} \\right) \\frac{\\partial}{\\partial {y'} }$ " ], "text/plain": [ "v = -(x^2 - 4*x*y - y^2)/(x^4 + 2*x^2*y^2 + y^4) d/dxp - 2*(x^2 + x*y - y^2)/(x^4 + 2*x^2*y^2 + y^4) d/dyp" ] }, "execution_count": 138, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW.display(eSW)" ] }, { "cell_type": "code", "execution_count": 139, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = \\left( -{x'}^{2} + 4 \\, {x'} {y'} + {y'}^{2} \\right) \\frac{\\partial}{\\partial {x'} } + \\left( -2 \\, {x'}^{2} - 2 \\, {x'} {y'} + 2 \\, {y'}^{2} \\right) \\frac{\\partial}{\\partial {y'} }$ " ], "text/plain": [ "v = (-xp^2 + 4*xp*yp + yp^2) d/dxp + (-2*xp^2 - 2*xp*yp + 2*yp^2) d/dyp" ] }, "execution_count": 139, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW.display(eSW, stereoSW)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We extend the definition of $v$ to $V$ thanks to the above expression:

" ] }, { "cell_type": "code", "execution_count": 140, "metadata": { "collapsed": false }, "outputs": [], "source": [ "v.add_comp_by_continuation(eV, W, chart=stereoS)" ] }, { "cell_type": "code", "execution_count": 141, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = \\left( -{x'}^{2} + 4 \\, {x'} {y'} + {y'}^{2} \\right) \\frac{\\partial}{\\partial {x'} } + \\left( -2 \\, {x'}^{2} - 2 \\, {x'} {y'} + 2 \\, {y'}^{2} \\right) \\frac{\\partial}{\\partial {y'} }$ " ], "text/plain": [ "v = (-xp^2 + 4*xp*yp + yp^2) d/dxp + (-2*xp^2 - 2*xp*yp + 2*yp^2) d/dyp" ] }, "execution_count": 141, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display(eV)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

At this stage, the vector field $v$ is defined on the whole manifold $\\mathbb{S}^2$; it has expressions in each of the two frames eU and eV which cover $\\mathbb{S}^2$:

" ] }, { "cell_type": "code", "execution_count": 142, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field v on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = \\frac{\\partial}{\\partial x } -2 \\frac{\\partial}{\\partial y }$ " ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 142, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(v)\n", "v.display(eU)" ] }, { "cell_type": "code", "execution_count": 143, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = \\left( -{x'}^{2} + 4 \\, {x'} {y'} + {y'}^{2} \\right) \\frac{\\partial}{\\partial {x'} } + \\left( -2 \\, {x'}^{2} - 2 \\, {x'} {y'} + 2 \\, {y'}^{2} \\right) \\frac{\\partial}{\\partial {y'} }$ " ], "text/plain": [ "v = (-xp^2 + 4*xp*yp + yp^2) d/dxp + (-2*xp^2 - 2*xp*yp + 2*yp^2) d/dyp" ] }, "execution_count": 143, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display(eV)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

According to the hairy ball theorem, $v$ has to vanish somewhere. This occurs at the North pole:

" ] }, { "cell_type": "code", "execution_count": 144, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field v on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "vN = v.at(N)\n", "print(v)" ] }, { "cell_type": "code", "execution_count": 145, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = 0$ " ], "text/plain": [ "v = 0" ] }, "execution_count": 145, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vN.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

$v|_N$ is the zero vector of the tangent vector space $T_N\\mathbb{S}^2$:

" ] }, { "cell_type": "code", "execution_count": 146, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}T_{N}\\,\\mathbb{S}^2$ " ], "text/plain": [ "Tangent space at Point N on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 146, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vN.parent()" ] }, { "cell_type": "code", "execution_count": 147, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 147, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vN.parent() is S2.tangent_space(N)" ] }, { "cell_type": "code", "execution_count": 148, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 148, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vN == S2.tangent_space(N).zero()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

On the contrary, $v$ is non-zero at the South pole:

" ] }, { "cell_type": "code", "execution_count": 149, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field v on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "vS = v.at(S)\n", "print(v)" ] }, { "cell_type": "code", "execution_count": 150, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = \\frac{\\partial}{\\partial x } -2 \\frac{\\partial}{\\partial y }$ " ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 150, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vS.display()" ] }, { "cell_type": "code", "execution_count": 151, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}T_{S}\\,\\mathbb{S}^2$ " ], "text/plain": [ "Tangent space at Point S on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 151, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vS.parent()" ] }, { "cell_type": "code", "execution_count": 152, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 152, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vS.parent() is S2.tangent_space(S)" ] }, { "cell_type": "code", "execution_count": 153, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 153, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vS != S2.tangent_space(S).zero()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us plot the vector field $v$ is terms of the stereographic chart $(U,(x,y))$, with the South pole $S$ superposed:

" ] }, { "cell_type": "code", "execution_count": 154, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 27 graphics primitives" ] }, "execution_count": 154, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.plot(chart=stereoN, chart_domain=stereoN, max_range=4, \n", " number_values=5, scale=0.5, aspect_ratio=1) + \\\n", " S.plot(stereoN, size=30, label_offset=0.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The vector field appears homogeneous because its components w.r.t. the frame $\\left(\\frac{\\partial}{\\partial x}, \\frac{\\partial}{\\partial y}\\right)$ are constant:

" ] }, { "cell_type": "code", "execution_count": 155, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = \\frac{\\partial}{\\partial x } -2 \\frac{\\partial}{\\partial y }$ " ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 155, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display(stereoN.frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

On the contrary, once drawn in terms of the stereographic chart $(V, (x',y'))$, $v$ does no longer appears homogeneous:

" ] }, { "cell_type": "code", "execution_count": 156, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YAYAuXSR5tYrY2DgULhyGxo1jsXOntZM6ABg3DnjtNdePnz4dGD3ae/EQkTkY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"text/plain": [ "Graphics object consisting of 82 graphics primitives" ] }, "execution_count": 156, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.plot(chart=stereoS, chart_domain=stereoS, max_range=4, scale=0.02, \n", " aspect_ratio=1) + \\\n", " N.plot(chart=stereoS, size=30, label_offset=0.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Finally, a 3D view of the vector field $v$ is obtained via the embedding $\\Phi$:

" ] }, { "cell_type": "code", "execution_count": 157, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_v = v.plot(chart=cart, mapping=Phi, chart_domain=spher, \n", " number_values=11, scale=0.2)\n", "show(graph_spher + graph_v, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Similarly, let us draw the first vector field of the stereographic frame from the North pole, namely $\\frac{\\partial}{\\partial x}$:

" ] }, { "cell_type": "code", "execution_count": 158, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial x }$ " ], "text/plain": [ "Vector field d/dx on the Open subset U of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 158, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ex = stereoN.frame()[1]\n", "ex" ] }, { "cell_type": "code", "execution_count": 159, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_ex = ex.plot(chart=cart, mapping=Phi, chart_domain=spher,\n", " number_values=11, scale=0.4, width=1, \n", " label_axes=False)\n", "show(graph_spher + graph_ex, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

For the second vector field of the stereographic frame from the North pole, namely $\\frac{\\partial}{\\partial y}$, we get

" ] }, { "cell_type": "code", "execution_count": 160, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial y }$ " ], "text/plain": [ "Vector field d/dy on the Open subset U of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 160, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ey = stereoN.frame()[2]\n", "ey" ] }, { "cell_type": "code", "execution_count": 161, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_ey = ey.plot(chart=cart, mapping=Phi, chart_domain=spher,\n", " number_values=11, scale=0.4, width=1, color='red', \n", " label_axes=False)\n", "show(graph_spher + graph_ey, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may superpose the two graphs, to get a 3D view of the vector frame associated with the stereographic coordinates from the North pole:" ] }, { "cell_type": "code", "execution_count": 162, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_frame = graph_spher + graph_ex + graph_ey + \\\n", " N.plot(cart, mapping=Phi, label_offset=0.05, size=5) + \\\n", " S.plot(cart, mapping=Phi, label_offset=0.05, size=5)\n", "show(graph_frame + sphere(color='lightgrey', opacity=0.4), viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The same scene rendered with Tachyon:" ] }, { "cell_type": "code", "execution_count": 163, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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4ZFkvLc0oiv6Xf3n50qVzQqHcjBmSpgGApiH/a374Bh/joqNH+wcGBvbsaW9t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tiOA+zAiCEATSle0tjk6fQqFiPaGggO5ugJEj0XWam/F6icXSPYhOxEZxoz0eU2IhIC6L+Hfn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HfhzxrFiPuZQ1EtcxbxpS+JIZMcDWpoqLjpJlnJEAqF9HrbqlXNEAoEpP37e4HRZLbj2Jgv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\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PnahtmZdIgSIH0pmNz8daLYVh7VrAB6qR5caN6k7a2/H7aW+nsfE1n2+m398P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RCh\nSGOEEjJgR/J7hXFCGEvFZLMkEdQj8V4vgUA8WXYE1l4NvCb2FlpznSKLllIysv8OAGZz2sxdFb1E\nqyjicLBsGc88Q2PjoI2m2/0hlIEqy4b+frb0EwnFHCqTIIrs3PnEwYMH4J/1zlNPqWj25BqmTJkw\ndeqEqMFysB+DSLaJbCMWw5BPrxcxYJ/IpIlAy6SvJO6SJLIEdvCn+M2yemWbt7mg/U3Ab68oaH/z\nw6qlyq7/mDiwv9x7oMJ3KO3NSQzvh0EAESS4q+kPr171XDiprapGo35IZu2+Pi3QHlGUrGjU19kp\n7t07XBYA0Afe+vqvfVGGjxUVuFzZX8ipRw8tXHLfffetX78+Q98zyEBDJuI+hrB8+fIZM2bcdttt\nX/RAzgCcVgbDgtCq/T+65lrQnXTcPQAGh8NeWSmLYthgyHM6sx98sE7jcwEPr69+t9XjASKCpGDw\n4gwLWWZzXiikRCLRcDiYZ/Jmm8NWAwgSgpjlyNm1f2Bno7u9xwb5IIK/hhVX8pfkSzjeoEcwf+wq\nuviFL799883Mm6fdjdHdhqEwGunt5Yc/BPjtb5P3+nz8/vdtb721ORr1KErE642Gw1pRom6NQPs8\nue1dhSOfwmkPVhT3luQOxLc4HFWFeeeUlczRhhx3m+nt7ejofD8CFZOu6U0Jnsgy4TB9fcMtiOen\ntSVJdPuJb+nrw+lkwQJ27KC5GaeTSZNidPzxx1cdO/ZqMBj65jcf8/nKtMOdTpqbY06Iceza9c6e\nPUEoLy8X6+omm0xYLITDWCwk1lsNBHjppf/T0WFMELWnZe19cR+ayy8/Lz8/Z2gDFTCI5JoximSZ\nCCGOtO4AkoRFwKESAi/J+bJ9fZ6DB9cDshxQFDkY9B8+vN/n6wdm0tOBFbgsH6VgwtIf/Pv7//3g\n+JYt47xHgD15M89v3yKCCC/esNVvK43/QSlKpKC08MIvO4qHLnH84oEPD/QZI5EBWTY0N0eOHfMP\nM2QvBCDc3Hxn+XDCsgyGIm7kNcbp+/bt2xsbGzMP8TGODHEfQ3jyySebmpoyq2wjQ1uc5bRj7Yya\nuIfgfSAdcZ8AByDPYIhMmSKbTAOSlCVJ9oaGqwBBQBB4rOFgrmcv4BckL4IKA+YZkiBEMcsyoEaj\nqhrsyDaFciwIgiAgCoJ4wN1+4Gj0gDsb7ONpvINvHnfEBVAA06ELCiA8fPHUdVz0mOUWiyUbsFpF\nYNGiiyMR36RJ58yejdFIYSFGI0Yjfj82GwYDqQskBgOCwN13I8ssXsyVVw7Z6/Oxfz/r1n2wa9du\nWQ4LgkGWs32+Y5FID+D1Znd0lA4zuuRLrCjqqSjutZgG005Li2odWeX5zulWq6DRyp4Bb+uxN4AJ\nk68truCAe/BwRYk5VMoykMrdy1KXJYxGDIZYeSZZHvStF4TBULrZjM+HxUIkEmuzefNdoVArMGHC\nXVVVQ4q5WCxDSPnatT/u67sUiquqzFddVU5CKaj4ZCES9P5q7f8Jhb6S4viSeH8G9IJI5OU56upm\nWa3xBcD0jyGDiMEgmq1DZgip0GZEWaBNtvohBJEIHR2N7e1bQyFfKOQPBr2trS2h0BAynZc31WIR\nSkvLbr75y7Knc8cWlzdBJ1RYdEFu7kxA9h+TbLEPgKqqM+eX1w31o29u5lcN24JyJBLxQf5HH/UO\nDKT1xpfBqxlfnoo8pq7ub2vXXjEGSX+GvmdqpmZAhriPKWzbtm3Dhg2Zv/nhsHPnTq2+7GlC2TkZ\n1q7hkF7RKOmvOxcK4WPIMRqFqqqoydQnCIalS2+LB7OPHuXpx47aGBhHsyCIfoQoqKaciGjro0DR\nBcBebyQcDsmyf3y232pUTJIkCgZg51H1g22d3wt/OT5iG9jADxN1sm5LN+JgotfgUHTguJV/O+41\nT58+ccaMCYoSLShwXHxxtaJECgocNpsAmEyoKnY7//Zvf/F6TVOmTK6vLzcaYwaRqorJRHc3qsrG\njZu3bNkBgu7jO4gAACAASURBVCRZZdkXDof8fm9zc4UsJwbGj/9eTC/rqCgevCBJshoMVrPJOWnS\n14vHWdq79ueX5EqOgv37MRqx2/F4YiKZuM+MKKIoh0AGAYIgQCVY057ObOaGG3DrEwCHA48HLStg\n3z7y8igri3lf1tbS2MjAAC7XX5qbHzUYpOnTV375y6WqiiRRXU1jI2Vl1NbS0oIo8swzPP30zw4e\nvBDyiooiN944hC2JkA+7jzT9+eXfw5XpfBrjYu7Bu+GwitfdeHk4iqKoo8w1NRhEzZk+LYMXhNh2\nIzhAAi+8u/0pr7etv78rHA7293cnUPZcCI4bN8FgsBoMBbm5ioSSn7AOoCHO2pNGeOvdE+3ZQ+x3\nVjc07zzUEw4PqKoFHHv3dnV3p52EBjSN0KkH2gXhN/HXa9b84+ksUv8soC2HAsuXLzfFM8HHBjIC\n9wzIEPexhsyffVqcblH2OGpr123detEJsnYSgu4MpR2Fuo9kE2QZDMKkSUpeXjgcDt1zzzeqqmKN\n1q2jqakXokVCU5EYNqIiWQJGuwJhTGHMYUwBrRCnooZCUZ8vYBB8uZaIzSQbJOlQX/bfvTGlSw+o\nMwxTT4Kie72n4g1mPcw3TvAOAOTnO4CLLppWUOAAuro8RqN/+/ZtOTmOO+5YXFGRRpvj9Xh+1fBo\nKMHYZs8eh88nnfhbAFA77bAzK8bhZMGqGhwRMfuBH3/T4+GFF5oPHz48ceKlgQCRmIk5FguShMUS\nWzGIRmNOOKLYqihemDLCuTRJzIIFQzaKYprFBy0k//3vP63ZQX7/+3+oqxsM1SdZ2r/n4pu3/9jn\nuxjyb7hhVnGKSOfVV3/a0tIjy8Ot3QsQgkH5UN1U+8LZWZHcmT6EgII/BBAMppPMp4PRKNpsaei7\nKCIIKAoodLe1vPb2TwGv1yPLsZsrSUZZjtjt430+e9KxBbmmaDhiMQnBsOrMEoNhtcCZXT3liv2H\nD0yZOAnItmXtO3zg0gsuvu0ep6LEFhw0/OiBfa2dnbIcglww7t3b293tT/dp6QF/ff11p65oT2Tt\nSRhTJH7NmjWNjY3V1dWng23A54bMEzwDMsR9rCFTPzUJccp+OmSgpqK5mcrKh+D6EastpsWeBOOO\nxL/xqfqLgyAYjeZx4+TCwojJxI9+dGMwSHs7H33U+fHH7TAgCNjIK+ewRVKNxmxVMgf04jUyUj85\nYawyEgiRiOrzRRUlYpP6I6J06aFHbvrk/57oxfYNo5bZzYR7+McT7W0Eqi1JqiwLwPe/f/20aeP2\n7j0GlJVm5Rc4Nm/aeKCxMYQ5EMUU9bQcy23pHUXi54iYXtZRVBz0kQVEIpFZs855//09kiSFw8aq\nqtsgNG5cjtGYXIxJVenoQFWx2XA48PlipZ0kKZlbJ+H++2N6d1EkNRyppZwCN9ywVFUB9Sc/eWzq\n1ORmwJZNfNJIT5f3v5/4aTDyNbDddttszfFGg9fLvn0vvf9+E1yZ5vgYgomej9+9tthhlSJZE1WD\nFQggevVdGhsOBAiHRyLxoijm5CRvVBSCQdraQps3H4K+QOC/Ug+cNm1eVpZj1672SGTE2zcKzJ49\nd86cOZs2bWxvbxs3buK4cRMPHTpiNtu6unrD4XLdzjSsv4hVVqqv/9rKlcdJkzgunn6aJUuGJe46\nQjU1s12uK07xXGcKVqxYAYwFBp/RyWSgIUPcxxaWL1++aNGieZowYsxjxYoVgiCcblH2JAiCNrxv\nQNZxmg7BAOxM+FX7M4+AM0HPEIB2MBYUKBMnhq6+uq60NCcalXNyHGvWbIE8yBMEAwhGQqUcVK1V\nAcFkJmAXjsX7DWMKYA2QpTN4fD45Gg0sPvDjK4/+4YSudDi1jApX8poujz4KYQiBeXjflZNKXwXo\nhYMVRfn9/d2TcugNTTnYf87JdjUEdnu0pKQNAqqqgFUUcyQpLzfXLIoCkJtbXVdXtXQpJhOPPhpT\nvHR0oCgYjeh+6/T2EgqRnY0oxkQ+w2HuXO68E6MxJnPXyLqixCi7Fln/4Q//uG/fG8C6dY/FDzzY\nGPtHQpbnL5/4TZ/vfDB861tz7faYLqW1tcvl+t2xY3OHKWOqoR806Y9alm+6ak7OhHyTIlmi2TGl\niIKYXF9Kh98fC6tHIhiNKEpsYpMYa9+374jdXvDRRwe6uoKBQA5kw174pX7PnbNnz/n7v78tP98J\neDzep59+7cUXPxjpxn3KEMAEE8Gydu2SW2451e5aWqioOC5rH4Jly65vaBh3qic+7aFF37XXmgj+\nrESGuGegIWMHObawaNGiDRs2ZIi79kW/ePHiMyfD6a9wDkwadftsMMdzAXWDSCNshQXESkJaQQRP\nV5cTlFdeef+yy6ovuWTKa6/tDYf7JckmSQZVRRDUCObDzBBDJqNRGMDQLcywi71RRXKI3VYhaCKc\nQ38YUw/5RmPU6LR4PKZ1k+8b7/lwxsC20V9h2vrzQCeFYAItejxdvxwN2gV2gRmO6r+mzQscDexA\nc0c38GGHDT4d1g74fIYDB8rM5kBFhcdmk0RRFkWfKJpAAKG3t+nll3dOm3ZTeTk338zKlQwMxKoy\nxd3r4wqNcBibjdxcvN5BjU0Sduxg2TK+/W3mzh12SNOmLdCI+5YtTJrARy4O7tb3CagiKIgifn9P\nn08EA4SzDUhGgGCQ55//jSxfNoyBJ0mej06r9N0rCrVplmoaDJiLKIXgRYxqlQUSYNP1VakGtu3t\n0Y6O1n379vf0OMEAE8AAInwCvywrqzKb7VlZTpPJFInwP//zwtKlixwOezgsfy6sXcthrYKq+Ey7\nubnkU0kkbWg4eqKHrFr1/KpVAMuWXV9fP+40KbH0qSNes6mxsXHnzp1nzrf6CSNTMzUDMhH3MYiM\nSE5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1RQVz57JgQWxvVdWWQGAEx1h/wntohhl6JSYDaMWUfCBfMCvk8RlMdvv5NbmHDnkq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\nkNVq9fHjx/fv36c+CAAv9h98L/s0urHHAQAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph_frame + sphere(opacity=0.5), viewer='tachyon', figsize=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Vector fields acting on scalar fields

\n", "

$v$ and $f$ are both fields defined on the whole sphere (respectively a vector field and a scalar field). By the very definition of a vector field, $v$ acts on $f$:

" ] }, { "cell_type": "code", "execution_count": 164, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field v(f) on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} v\\left(f\\right):& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & -\\frac{4 \\, {\\left(x - 2 \\, y\\right)}}{x^{4} + 2 \\, x^{2} y^{2} + y^{4} + 1} \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & -\\frac{4 \\, {\\left({x'}^{3} - 2 \\, {x'}^{2} {y'} + {x'} {y'}^{2} - 2 \\, {y'}^{3}\\right)}}{{x'}^{4} + 2 \\, {x'}^{2} {y'}^{2} + {y'}^{4} + 1} \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & -\\frac{2 \\, {\\left({\\left(\\cos\\left({\\phi}\\right) - 2 \\, \\sin\\left({\\phi}\\right)\\right)} \\cos\\left({\\theta}\\right)^{2} - 2 \\, {\\left(\\cos\\left({\\phi}\\right) - 2 \\, \\sin\\left({\\phi}\\right)\\right)} \\cos\\left({\\theta}\\right) + \\cos\\left({\\phi}\\right) - 2 \\, \\sin\\left({\\phi}\\right)\\right)} \\sqrt{\\cos\\left({\\theta}\\right) + 1}}{{\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)} \\sqrt{-\\cos\\left({\\theta}\\right) + 1}} \\end{array}$ " ], "text/plain": [ "v(f): S^2 --> R\n", "on U: (x, y) |--> -4*(x - 2*y)/(x^4 + 2*x^2*y^2 + y^4 + 1)\n", "on V: (xp, yp) |--> -4*(xp^3 - 2*xp^2*yp + xp*yp^2 - 2*yp^3)/(xp^4 + 2*xp^2*yp^2 + yp^4 + 1)\n", "on A: (th, ph) |--> -2*((cos(ph) - 2*sin(ph))*cos(th)^2 - 2*(cos(ph) - 2*sin(ph))*cos(th) + cos(ph) - 2*sin(ph))*sqrt(cos(th) + 1)/((cos(th)^2 + 1)*sqrt(-cos(th) + 1))" ] }, "execution_count": 164, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf = v(f)\n", "print(vf)\n", "vf.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Values of $v(f)$ at the North pole, at the equator point $E$ and at the South pole:

" ] }, { "cell_type": "code", "execution_count": 165, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$ " ], "text/plain": [ "0" ] }, "execution_count": 165, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf(N)" ] }, { "cell_type": "code", "execution_count": 166, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}4$ " ], "text/plain": [ "4" ] }, "execution_count": 166, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf(E)" ] }, { "cell_type": "code", "execution_count": 167, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$ " ], "text/plain": [ "0" ] }, "execution_count": 167, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf(S)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

1-forms

\n", "

A 1-form on $\\mathbb{S}^2$ is a field of linear forms on the tangent spaces. For instance it can the differential of a scalar field:

" ] }, { "cell_type": "code", "execution_count": 168, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1-form df on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "df = f.differential() ; print(df)" ] }, { "cell_type": "code", "execution_count": 169, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}f = \\left( -\\frac{4 \\, x}{x^{4} + 2 \\, x^{2} y^{2} + y^{4} + 1} \\right) \\mathrm{d} x + \\left( -\\frac{4 \\, y}{x^{4} + 2 \\, x^{2} y^{2} + y^{4} + 1} \\right) \\mathrm{d} y$ " ], "text/plain": [ "df = -4*x/(x^4 + 2*x^2*y^2 + y^4 + 1) dx - 4*y/(x^4 + 2*x^2*y^2 + y^4 + 1) dy" ] }, "execution_count": 169, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.display()" ] }, { "cell_type": "code", "execution_count": 170, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module /\\^1(S^2) of 1-forms on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(df.parent())" ] }, { "cell_type": "code", "execution_count": 171, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\Lambda^{1}\\left(\\mathbb{S}^2\\right)$ " ], "text/plain": [ "Module /\\^1(S^2) of 1-forms on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 171, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.parent()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The 1-form acting on a vector field:

" ] }, { "cell_type": "code", "execution_count": 172, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field df(v) on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\mathrm{d}f\\left(v\\right):& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & -\\frac{4 \\, {\\left(x - 2 \\, y\\right)}}{x^{4} + 2 \\, x^{2} y^{2} + y^{4} + 1} \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & -\\frac{4 \\, {\\left({x'}^{3} - 2 \\, {x'}^{2} {y'} + {x'} {y'}^{2} - 2 \\, {y'}^{3}\\right)}}{{x'}^{4} + 2 \\, {x'}^{2} {y'}^{2} + {y'}^{4} + 1} \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & -\\frac{2 \\, {\\left({\\left({\\left(\\cos\\left({\\phi}\\right) - 2 \\, \\sin\\left({\\phi}\\right)\\right)} \\cos\\left({\\theta}\\right) - 3 \\, \\cos\\left({\\phi}\\right) + 6 \\, \\sin\\left({\\phi}\\right)\\right)} \\sin\\left({\\theta}\\right)^{3} - 4 \\, {\\left({\\left(\\cos\\left({\\phi}\\right) - 2 \\, \\sin\\left({\\phi}\\right)\\right)} \\cos\\left({\\theta}\\right) - \\cos\\left({\\phi}\\right) + 2 \\, \\sin\\left({\\phi}\\right)\\right)} \\sin\\left({\\theta}\\right)\\right)}}{\\cos\\left({\\theta}\\right)^{4} - 2 \\, \\cos\\left({\\theta}\\right)^{3} + 2 \\, \\cos\\left({\\theta}\\right)^{2} - 2 \\, \\cos\\left({\\theta}\\right) + 1} \\end{array}$ " ], "text/plain": [ "df(v): S^2 --> R\n", "on U: (x, y) |--> -4*(x - 2*y)/(x^4 + 2*x^2*y^2 + y^4 + 1)\n", "on V: (xp, yp) |--> -4*(xp^3 - 2*xp^2*yp + xp*yp^2 - 2*yp^3)/(xp^4 + 2*xp^2*yp^2 + yp^4 + 1)\n", "on A: (th, ph) |--> -2*(((cos(ph) - 2*sin(ph))*cos(th) - 3*cos(ph) + 6*sin(ph))*sin(th)^3 - 4*((cos(ph) - 2*sin(ph))*cos(th) - cos(ph) + 2*sin(ph))*sin(th))/(cos(th)^4 - 2*cos(th)^3 + 2*cos(th)^2 - 2*cos(th) + 1)" ] }, "execution_count": 172, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(df(v)) ; df(v).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us check the identity $\\mathrm{d}f(v) = v(f)$:

" ] }, { "cell_type": "code", "execution_count": 173, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 173, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df(v) == v(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Similarly, we have $\\mathcal{L}_v f = v(f)$:

" ] }, { "cell_type": "code", "execution_count": 174, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 174, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.lie_derivative(v) == v(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Curves in $\\mathbb{S}^2$

\n", "

In order to define curves in $\\mathbb{S}^2$, we first introduce the field of real numbers $\\mathbb{R}$ as a 1-dimensional smooth manifold with a canonical coordinate chart:

" ] }, { "cell_type": "code", "execution_count": 175, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Real number line R\n" ] } ], "source": [ "R. = RealLine() ; print(R)" ] }, { "cell_type": "code", "execution_count": 176, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathbf{Smooth}_{\\Bold{R}}$ " ], "text/plain": [ "Category of smooth manifolds over Real Field with 53 bits of precision" ] }, "execution_count": 176, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R.category()" ] }, { "cell_type": "code", "execution_count": 177, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}1$ " ], "text/plain": [ "1" ] }, "execution_count": 177, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dim(R)" ] }, { "cell_type": "code", "execution_count": 178, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left(\\Bold{R},(t)\\right)\\right]$ " ], "text/plain": [ "[Chart (R, (t,))]" ] }, "execution_count": 178, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R.atlas()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us define a loxodrome of the sphere in terms of its parametric equation with respect to the chart spher = $(A,(\\theta,\\phi))$

" ] }, { "cell_type": "code", "execution_count": 179, "metadata": { "collapsed": false }, "outputs": [], "source": [ "c = S2.curve({spher: [2*atan(exp(-t/10)), t]}, (t, -oo, +oo), name='c')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Curves in $\\mathbb{S}^2$ are considered as morphisms from the manifold $\\mathbb{R}$ to the manifold $\\mathbb{S}^2$:

" ] }, { "cell_type": "code", "execution_count": 180, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Hom}\\left(\\Bold{R},\\mathbb{S}^2\\right)$ " ], "text/plain": [ "Set of Morphisms from Real number line R to 2-dimensional differentiable manifold S^2 in Category of smooth manifolds over Real Field with 53 bits of precision" ] }, "execution_count": 180, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.parent()" ] }, { "cell_type": "code", "execution_count": 181, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} c:& \\Bold{R} & \\longrightarrow & \\mathbb{S}^2 \\\\ & t & \\longmapsto & \\left(x, y\\right) = \\left(\\cos\\left(t\\right) e^{\\left(\\frac{1}{10} \\, t\\right)}, e^{\\left(\\frac{1}{10} \\, t\\right)} \\sin\\left(t\\right)\\right) \\\\ & t & \\longmapsto & \\left({x'}, {y'}\\right) = \\left(\\cos\\left(t\\right) e^{\\left(-\\frac{1}{10} \\, t\\right)}, e^{\\left(-\\frac{1}{10} \\, t\\right)} \\sin\\left(t\\right)\\right) \\\\ & t & \\longmapsto & \\left({\\theta}, {\\phi}\\right) = \\left(2 \\, \\arctan\\left(e^{\\left(-\\frac{1}{10} \\, t\\right)}\\right), t\\right) \\end{array}$ " ], "text/plain": [ "c: R --> S^2\n", " t |--> (x, y) = (cos(t)*e^(1/10*t), e^(1/10*t)*sin(t))\n", " t |--> (xp, yp) = (cos(t)*e^(-1/10*t), e^(-1/10*t)*sin(t))\n", " t |--> (th, ph) = (2*arctan(e^(-1/10*t)), t)" ] }, "execution_count": 181, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The curve $c$ can be plotted in terms of stereographic coordinates $(x,y)$:

" ] }, { "cell_type": "code", "execution_count": 182, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Hb7zBPuykn6FDZQdoxQrVkSjF7XRn0TTpUT1wIFC0qFT3Nm2qOiqyE7fTc+nL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\nAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 182, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.plot(chart=stereoN, aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We recover the well-known fact that the graph of a loxodrome in terms of stereographic coordinates is a logarithmic spiral.

\n", "

Thanks to the embedding $\\Phi$, we may also plot $c$ in terms of the Cartesian coordinates of $\\mathbb{R}^3$:

" ] }, { "cell_type": "code", "execution_count": 183, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_c = c.plot(mapping=Phi, max_range=40, plot_points=200, \n", " thickness=2, label_axes=False)\n", "show(graph_spher + graph_c, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The tangent vector field (or velocity vector) to the curve $c$ is

" ] }, { "cell_type": "code", "execution_count": 184, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{c'}$ " ], "text/plain": [ "Vector field c' along the Real number line R with values on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 184, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc = c.tangent_vector_field()\n", "vc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

$c'$ is a vector field along $\\mathbb{R}$ taking its values in tangent spaces to $\\mathbb{S}^2$:

" ] }, { "cell_type": "code", "execution_count": 185, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field c' along the Real number line R with values on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(vc)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The set of vector fields along $\\mathbb{R}$ taking their values on $\\mathbb{S}^2$ via the differential mapping $c: \\mathbb{R} \\rightarrow \\mathbb{S}^2$ is denoted by $\\mathcal{X}(\\mathbb{R},c)$; it is a module over the algebra $C^\\infty(\\mathbb{R})$:

" ] }, { "cell_type": "code", "execution_count": 186, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathcal{X}\\left(\\Bold{R},c\\right)$ " ], "text/plain": [ "Module X(R,c) of vector fields along the Real number line R mapped into the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 186, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent()" ] }, { "cell_type": "code", "execution_count": 187, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathbf{Modules}_{C^{\\infty}\\left(\\Bold{R}\\right)}$ " ], "text/plain": [ "Category of modules over Algebra of differentiable scalar fields on the Real number line R" ] }, "execution_count": 187, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent().category()" ] }, { "cell_type": "code", "execution_count": 188, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}C^{\\infty}\\left(\\Bold{R}\\right)$ " ], "text/plain": [ "Algebra of differentiable scalar fields on the Real number line R" ] }, "execution_count": 188, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent().base_ring()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

A coordinate view of $c'$:

" ] }, { "cell_type": "code", "execution_count": 189, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{c'} = \\left( \\frac{1}{10} \\, \\cos\\left(t\\right) e^{\\left(\\frac{1}{10} \\, t\\right)} - e^{\\left(\\frac{1}{10} \\, t\\right)} \\sin\\left(t\\right) \\right) \\frac{\\partial}{\\partial x } + \\left( \\cos\\left(t\\right) e^{\\left(\\frac{1}{10} \\, t\\right)} + \\frac{1}{10} \\, e^{\\left(\\frac{1}{10} \\, t\\right)} \\sin\\left(t\\right) \\right) \\frac{\\partial}{\\partial y }$ " ], "text/plain": [ "c' = (1/10*cos(t)*e^(1/10*t) - e^(1/10*t)*sin(t)) d/dx + (cos(t)*e^(1/10*t) + 1/10*e^(1/10*t)*sin(t)) d/dy" ] }, "execution_count": 189, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us plot the vector field $c'$ in terms of the stereographic chart $(U,(x,y))$:

" ] }, { "cell_type": "code", "execution_count": 190, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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XQPfutjZNchZldwNEMpWSApQsydW4nmjc2DftEQkX5vz6ddcB+fNbxwcMYHKa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"text/plain": [ "Graphics object consisting of 31 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(vc.plot(chart=stereoN, number_values=30, scale=0.5, color='red') +\n", " c.plot(chart=stereoN), aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

A 3D view of $c'$ is obtained via the embedding $\\Phi$:

" ] }, { "cell_type": "code", "execution_count": 191, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_vc = vc.plot(chart=cart, mapping=Phi, ranges={t: (-20, 20)}, \n", " number_values=30, scale=0.5, color='red', \n", " label_axes=False)\n", "show(graph_spher + graph_c + graph_vc , viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Riemannian metric on $\\mathbb{S}^2$

\n", "

The standard metric on $\\mathbb{S}^2$ is that induced by the Euclidean metric of $\\mathbb{R}^3$. Let us start by defining the latter:

" ] }, { "cell_type": "code", "execution_count": 192, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}h = \\mathrm{d} X\\otimes \\mathrm{d} X+\\mathrm{d} Y\\otimes \\mathrm{d} Y+\\mathrm{d} Z\\otimes \\mathrm{d} Z$ " ], "text/plain": [ "h = dX*dX + dY*dY + dZ*dZ" ] }, "execution_count": 192, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h = R3.metric('h')\n", "h[1,1], h[2,2], h[3, 3] = 1, 1, 1\n", "h.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The metric $g$ on $\\mathbb{S}^2$ is the pullback of $h$ associated with the embedding $\\Phi$:

" ] }, { "cell_type": "code", "execution_count": 193, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Riemannian metric g on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "g = S2.metric('g')\n", "g.set( Phi.pullback(h) )\n", "print(g)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Note that we could have defined $g$ intrinsically, i.e. by providing its components in the two frames stereoN and stereoS, as we did for the metric $h$ on $\\mathbb{R}^3$. Instead, we have chosen to get it as the pullback of $h$, as an example of pullback associated with some differential map.

\n", "

The metric is a symmetric tensor field of type (0,2):

" ] }, { "cell_type": "code", "execution_count": 194, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module T^(0,2)(S^2) of type-(0,2) tensors fields on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(g.parent())" ] }, { "cell_type": "code", "execution_count": 195, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0, 2\\right)$ " ], "text/plain": [ "(0, 2)" ] }, "execution_count": 195, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.tensor_type()" ] }, { "cell_type": "code", "execution_count": 196, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "symmetry: (0, 1); no antisymmetry\n" ] } ], "source": [ "g.symmetries()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The expression of the metric in terms of the default frame on $\\mathbb{S}^2$ (stereoN):

" ] }, { "cell_type": "code", "execution_count": 197, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\mathrm{d} x\\otimes \\mathrm{d} x + \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\mathrm{d} y\\otimes \\mathrm{d} y$ " ], "text/plain": [ "g = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dx*dx + 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dy*dy" ] }, "execution_count": 197, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We may factorize the metric components:

" ] }, { "cell_type": "code", "execution_count": 198, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{4}{{\\left(x^{2} + y^{2} + 1\\right)}^{2}}$ " ], "text/plain": [ "4/(x^2 + y^2 + 1)^2" ] }, "execution_count": 198, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[1,1].factor() ; g[2,2].factor()" ] }, { "cell_type": "code", "execution_count": 199, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\frac{4}{{\\left(x^{2} + y^{2} + 1\\right)}^{2}} \\mathrm{d} x\\otimes \\mathrm{d} x + \\frac{4}{{\\left(x^{2} + y^{2} + 1\\right)}^{2}} \\mathrm{d} y\\otimes \\mathrm{d} y$ " ], "text/plain": [ "g = 4/(x^2 + y^2 + 1)^2 dx*dx + 4/(x^2 + y^2 + 1)^2 dy*dy" ] }, "execution_count": 199, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

A matrix view of the components of $g$ in the manifold's default frame:

" ] }, { "cell_type": "code", "execution_count": 200, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rr}\n", "\\frac{4}{{\\left(x^{2} + y^{2} + 1\\right)}^{2}} & 0 \\\\\n", "0 & \\frac{4}{{\\left(x^{2} + y^{2} + 1\\right)}^{2}}\n", "\\end{array}\\right)$ " ], "text/plain": [ "[4/(x^2 + y^2 + 1)^2 0]\n", "[ 0 4/(x^2 + y^2 + 1)^2]" ] }, "execution_count": 200, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Display in terms of the vector frame $(V, (\\partial_{x'}, \\partial_{y'}))$:

" ] }, { "cell_type": "code", "execution_count": 201, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{4}{{x'}^{4} + {y'}^{4} + 2 \\, {\\left({x'}^{2} + 1\\right)} {y'}^{2} + 2 \\, {x'}^{2} + 1} \\right) \\mathrm{d} {x'}\\otimes \\mathrm{d} {x'} + \\left( \\frac{4}{{x'}^{4} + {y'}^{4} + 2 \\, {\\left({x'}^{2} + 1\\right)} {y'}^{2} + 2 \\, {x'}^{2} + 1} \\right) \\mathrm{d} {y'}\\otimes \\mathrm{d} {y'}$ " ], "text/plain": [ "g = 4/(xp^4 + yp^4 + 2*(xp^2 + 1)*yp^2 + 2*xp^2 + 1) dxp*dxp + 4/(xp^4 + yp^4 + 2*(xp^2 + 1)*yp^2 + 2*xp^2 + 1) dyp*dyp" ] }, "execution_count": 201, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(stereoS.frame())" ] }, { "cell_type": "code", "execution_count": 202, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$ " ], "text/plain": [ "g = dth*dth + sin(th)^2 dph*dph" ] }, "execution_count": 202, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(spher.frame(), chart=spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The metric acts on vector field pairs, resulting in a scalar field:

" ] }, { "cell_type": "code", "execution_count": 203, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field g(v,v) on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(g(v,v))" ] }, { "cell_type": "code", "execution_count": 204, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}C^{\\infty}\\left(\\mathbb{S}^2\\right)$ " ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 204, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(v,v).parent()" ] }, { "cell_type": "code", "execution_count": 205, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} g\\left(v,v\\right):& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & \\frac{20}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & \\frac{20 \\, {\\left({x'}^{4} + 2 \\, {x'}^{2} {y'}^{2} + {y'}^{4}\\right)}}{{x'}^{4} + {y'}^{4} + 2 \\, {\\left({x'}^{2} + 1\\right)} {y'}^{2} + 2 \\, {x'}^{2} + 1} \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & 5 \\, \\cos\\left({\\theta}\\right)^{2} - 10 \\, \\cos\\left({\\theta}\\right) + 5 \\end{array}$ " ], "text/plain": [ "g(v,v): S^2 --> R\n", "on U: (x, y) |--> 20/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1)\n", "on V: (xp, yp) |--> 20*(xp^4 + 2*xp^2*yp^2 + yp^4)/(xp^4 + yp^4 + 2*(xp^2 + 1)*yp^2 + 2*xp^2 + 1)\n", "on A: (th, ph) |--> 5*cos(th)^2 - 10*cos(th) + 5" ] }, "execution_count": 205, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(v,v).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Levi-Civitation connection associated with the metric $g$:

" ] }, { "cell_type": "code", "execution_count": 206, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Levi-Civita connection nabla_g associated with the Riemannian metric g on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\nabla_{g}$ " ], "text/plain": [ "Levi-Civita connection nabla_g associated with the Riemannian metric g on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 206, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab = g.connection()\n", "print(nab)\n", "nab" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

As a test, we verify that $\\nabla_g$ acting on $g$ results in zero:

" ] }, { "cell_type": "code", "execution_count": 207, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\nabla_{g} g = 0$ " ], "text/plain": [ "nabla_g(g) = 0" ] }, "execution_count": 207, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab(g).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The nonzero Christoffel symbols of $g$ (skipping those that can be deduced by symmetry on the last two indices) w.r.t. two charts:

" ] }, { "cell_type": "code", "execution_count": 208, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, x} \\, x \\, x }^{ \\, x \\phantom{\\, x} \\phantom{\\, x} } & = & -\\frac{2 \\, x}{x^{2} + y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, x} \\, x \\, y }^{ \\, x \\phantom{\\, x} \\phantom{\\, y} } & = & -\\frac{2 \\, y}{x^{2} + y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, x} \\, y \\, y }^{ \\, x \\phantom{\\, y} \\phantom{\\, y} } & = & \\frac{2 \\, x}{x^{2} + y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, y} \\, x \\, x }^{ \\, y \\phantom{\\, x} \\phantom{\\, x} } & = & \\frac{2 \\, y}{x^{2} + y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, y} \\, x \\, y }^{ \\, y \\phantom{\\, x} \\phantom{\\, y} } & = & -\\frac{2 \\, x}{x^{2} + y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, y} \\, y \\, y }^{ \\, y \\phantom{\\, y} \\phantom{\\, y} } & = & -\\frac{2 \\, y}{x^{2} + y^{2} + 1} \\end{array}$ " ], "text/plain": [ "Gam^x_xx = -2*x/(x^2 + y^2 + 1) \n", "Gam^x_xy = -2*y/(x^2 + y^2 + 1) \n", "Gam^x_yy = 2*x/(x^2 + y^2 + 1) \n", "Gam^y_xx = 2*y/(x^2 + y^2 + 1) \n", "Gam^y_xy = -2*x/(x^2 + y^2 + 1) \n", "Gam^y_yy = -2*y/(x^2 + y^2 + 1) " ] }, "execution_count": 208, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.christoffel_symbols_display(chart=stereoN)" ] }, { "cell_type": "code", "execution_count": 209, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, {\\theta}} \\, {\\phi} \\, {\\phi} }^{ \\, {\\theta} \\phantom{\\, {\\phi}} \\phantom{\\, {\\phi}} } & = & -\\cos\\left({\\theta}\\right) \\sin\\left({\\theta}\\right) \\\\ \\Gamma_{ \\phantom{\\, {\\phi}} \\, {\\theta} \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} } & = & \\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)} \\end{array}$ " ], "text/plain": [ "Gam^th_ph,ph = -cos(th)*sin(th) \n", "Gam^ph_th,ph = cos(th)/sin(th) " ] }, "execution_count": 209, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.christoffel_symbols_display(chart=spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

$\\nabla_g$ acting on the vector field $v$:

" ] }, { "cell_type": "code", "execution_count": 210, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field nabla_g(v) of type (1,1) on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(nab(v))" ] }, { "cell_type": "code", "execution_count": 211, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\nabla_{g} v = \\left( -\\frac{2 \\, {\\left(x - 2 \\, y\\right)}}{x^{2} + y^{2} + 1} \\right) \\frac{\\partial}{\\partial x }\\otimes \\mathrm{d} x + \\left( -\\frac{2 \\, {\\left(2 \\, x + y\\right)}}{x^{2} + y^{2} + 1} \\right) \\frac{\\partial}{\\partial x }\\otimes \\mathrm{d} y + \\left( \\frac{2 \\, {\\left(2 \\, x + y\\right)}}{x^{2} + y^{2} + 1} \\right) \\frac{\\partial}{\\partial y }\\otimes \\mathrm{d} x + \\left( -\\frac{2 \\, {\\left(x - 2 \\, y\\right)}}{x^{2} + y^{2} + 1} \\right) \\frac{\\partial}{\\partial y }\\otimes \\mathrm{d} y$ " ], "text/plain": [ "nabla_g(v) = -2*(x - 2*y)/(x^2 + y^2 + 1) d/dx*dx - 2*(2*x + y)/(x^2 + y^2 + 1) d/dx*dy + 2*(2*x + y)/(x^2 + y^2 + 1) d/dy*dx - 2*(x - 2*y)/(x^2 + y^2 + 1) d/dy*dy" ] }, "execution_count": 211, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab(v).display(stereoN.frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Curvature

\n", "

The Riemann tensor associated with the metric $g$:

" ] }, { "cell_type": "code", "execution_count": 212, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field Riem(g) of type (1,3) on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Riem}\\left(g\\right) = \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\frac{\\partial}{\\partial x }\\otimes \\mathrm{d} y\\otimes \\mathrm{d} x\\otimes \\mathrm{d} y + \\left( -\\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\frac{\\partial}{\\partial x }\\otimes \\mathrm{d} y\\otimes \\mathrm{d} y\\otimes \\mathrm{d} x + \\left( -\\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\frac{\\partial}{\\partial y }\\otimes \\mathrm{d} x\\otimes \\mathrm{d} x\\otimes \\mathrm{d} y + \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\frac{\\partial}{\\partial y }\\otimes \\mathrm{d} x\\otimes \\mathrm{d} y\\otimes \\mathrm{d} x$ " ], "text/plain": [ "Riem(g) = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) d/dx*dy*dx*dy - 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) d/dx*dy*dy*dx - 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) d/dy*dx*dx*dy + 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) d/dy*dx*dy*dx" ] }, "execution_count": 212, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem = g.riemann()\n", "print(Riem)\n", "Riem.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The components of the Riemann tensor in the default frame on $\\mathbb{S}^2$:

" ] }, { "cell_type": "code", "execution_count": 213, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, x} \\, y \\, x \\, y }^{ \\, x \\phantom{\\, y} \\phantom{\\, x} \\phantom{\\, y} } & = & \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, x} \\, y \\, y \\, x }^{ \\, x \\phantom{\\, y} \\phantom{\\, y} \\phantom{\\, x} } & = & -\\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, y} \\, x \\, x \\, y }^{ \\, y \\phantom{\\, x} \\phantom{\\, x} \\phantom{\\, y} } & = & -\\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, y} \\, x \\, y \\, x }^{ \\, y \\phantom{\\, x} \\phantom{\\, y} \\phantom{\\, x} } & = & \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\end{array}$ " ], "text/plain": [ "Riem(g)^x_yxy = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) \n", "Riem(g)^x_yyx = -4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) \n", "Riem(g)^y_xxy = -4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) \n", "Riem(g)^y_xyx = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) " ] }, "execution_count": 213, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem.display_comp()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The components in the frame associated with spherical coordinates:

" ] }, { "cell_type": "code", "execution_count": 214, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\theta}} \\, {\\phi} \\, {\\theta} \\, {\\phi} }^{ \\, {\\theta} \\phantom{\\, {\\phi}} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} } & = & \\sin\\left({\\theta}\\right)^{2} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\theta}} \\, {\\phi} \\, {\\phi} \\, {\\theta} }^{ \\, {\\theta} \\phantom{\\, {\\phi}} \\phantom{\\, {\\phi}} \\phantom{\\, {\\theta}} } & = & -\\sin\\left({\\theta}\\right)^{2} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\phi}} \\, {\\theta} \\, {\\theta} \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, {\\theta}} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} } & = & \\frac{\\cos\\left({\\theta}\\right)^{2} - 1}{\\sin\\left({\\theta}\\right)^{2}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\phi}} \\, {\\theta} \\, {\\phi} \\, {\\theta} }^{ \\, {\\phi} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} \\phantom{\\, {\\theta}} } & = & 1 \\end{array}$ " ], "text/plain": [ "Riem(g)^th_ph,th,ph = sin(th)^2 \n", "Riem(g)^th_ph,ph,th = -sin(th)^2 \n", "Riem(g)^ph_th,th,ph = (cos(th)^2 - 1)/sin(th)^2 \n", "Riem(g)^ph_th,ph,th = 1 " ] }, "execution_count": 214, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem.display_comp(spher.frame(), chart=spher)" ] }, { "cell_type": "code", "execution_count": 215, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module T^(1,3)(S^2) of type-(1,3) tensors fields on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(Riem.parent())" ] }, { "cell_type": "code", "execution_count": 216, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "no symmetry; antisymmetry: (2, 3)\n" ] } ], "source": [ "Riem.symmetries()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Riemann tensor associated with the Euclidean metric $h$ on $\\mathbb{R}^3$:

" ] }, { "cell_type": "code", "execution_count": 217, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Riem}\\left(h\\right) = 0$ " ], "text/plain": [ "Riem(h) = 0" ] }, "execution_count": 217, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h.riemann().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Ricci tensor and the Ricci scalar:

" ] }, { "cell_type": "code", "execution_count": 218, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Ric}\\left(g\\right) = \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\mathrm{d} x\\otimes \\mathrm{d} x + \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\mathrm{d} y\\otimes \\mathrm{d} y$ " ], "text/plain": [ "Ric(g) = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dx*dx + 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dy*dy" ] }, "execution_count": 218, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric = g.ricci()\n", "Ric.display()" ] }, { "cell_type": "code", "execution_count": 219, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\mathrm{r}\\left(g\\right):& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & 2 \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & 2 \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & 2 \\end{array}$ " ], "text/plain": [ "r(g): S^2 --> R\n", "on U: (x, y) |--> 2\n", "on V: (xp, yp) |--> 2\n", "on A: (th, ph) |--> 2" ] }, "execution_count": 219, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R = g.ricci_scalar()\n", "R.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Hence we recover the fact that $(\\mathbb{S}^2,g)$ is a Riemannian manifold of constant positive curvature.

\n", "

In dimension 2, the Riemann curvature tensor is entirely determined by the Ricci scalar $R$ according to

\n", "

$R^i_{\\ \\, jlk} = \\frac{R}{2} \\left( \\delta^i_{\\ \\, k} g_{jl} - \\delta^i_{\\ \\, l} g_{jk} \\right)$

\n", "

Let us check this formula here, under the form $R^i_{\\ \\, jlk} = -R g_{j[k} \\delta^i_{\\ \\, l]}$:

" ] }, { "cell_type": "code", "execution_count": 220, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 220, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta = S2.tangent_identity_field()\n", "Riem == - R*(g*delta).antisymmetrize(2,3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Similarly the relation $\\mathrm{Ric} = (R/2)\\; g$ must hold:

" ] }, { "cell_type": "code", "execution_count": 221, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 221, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric == (R/2)*g" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Levi-Civita tensor associated with $g$:

" ] }, { "cell_type": "code", "execution_count": 222, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2-form eps_g on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\epsilon_{g} = \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\mathrm{d} x\\wedge \\mathrm{d} y$ " ], "text/plain": [ "eps_g = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dx/\\dy" ] }, "execution_count": 222, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps = g.volume_form()\n", "print(eps)\n", "eps.display()" ] }, { "cell_type": "code", "execution_count": 223, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\epsilon_{g} = \\sin\\left({\\theta}\\right) \\mathrm{d} {\\theta}\\wedge \\mathrm{d} {\\phi}$ " ], "text/plain": [ "eps_g = sin(th) dth/\\dph" ] }, "execution_count": 223, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps.display(spher.frame(), chart=spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The exterior derivative of the 2-form $\\epsilon_g$:

" ] }, { "cell_type": "code", "execution_count": 224, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3-form deps_g on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(eps.exterior_derivative())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Of course, since $\\mathbb{S}^2$ has dimension 2, all 3-forms vanish identically:

" ] }, { "cell_type": "code", "execution_count": 225, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}\\epsilon_{g} = 0$ " ], "text/plain": [ "deps_g = 0" ] }, "execution_count": 225, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps.exterior_derivative().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Non-holonomic frames

\n", "

Up to know, all the vector frames introduced on $\\mathbb{S}^2$ have been coordinate frames. Let us introduce a non-coordinate frame on the open subset $A$. To ease the notations, we change first the default chart and default frame on $A$ to the spherical coordinate ones:

" ] }, { "cell_type": "code", "execution_count": 226, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A,(x, y)\\right)$ " ], "text/plain": [ "Chart (A, (x, y))" ] }, "execution_count": 226, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_chart()" ] }, { "cell_type": "code", "execution_count": 227, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A, \\left(\\frac{\\partial}{\\partial x },\\frac{\\partial}{\\partial y }\\right)\\right)$ " ], "text/plain": [ "Coordinate frame (A, (d/dx,d/dy))" ] }, "execution_count": 227, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_frame()" ] }, { "cell_type": "code", "execution_count": 228, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A,({\\theta}, {\\phi})\\right)$ " ], "text/plain": [ "Chart (A, (th, ph))" ] }, "execution_count": 228, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.set_default_chart(spher)\n", "A.set_default_frame(spher.frame())\n", "A.default_chart()" ] }, { "cell_type": "code", "execution_count": 229, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A, \\left(\\frac{\\partial}{\\partial {\\theta} },\\frac{\\partial}{\\partial {\\phi} }\\right)\\right)$ " ], "text/plain": [ "Coordinate frame (A, (d/dth,d/dph))" ] }, "execution_count": 229, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_frame()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We define the new frame $e$ by relating it the coordinate frame $\\left(\\frac{\\partial}{\\partial\\theta}, \\frac{\\partial}{\\partial\\phi}\\right)$ via a field of tangent-space automorphisms:

" ] }, { "cell_type": "code", "execution_count": 230, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial {\\theta} }\\otimes \\mathrm{d} {\\theta} + \\frac{1}{\\sin\\left({\\theta}\\right)} \\frac{\\partial}{\\partial {\\phi} }\\otimes \\mathrm{d} {\\phi}$ " ], "text/plain": [ "d/dth*dth + 1/sin(th) d/dph*dph" ] }, "execution_count": 230, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = A.automorphism_field()\n", "a[1,1], a[2,2] = 1, 1/sin(th)\n", "a.display()" ] }, { "cell_type": "code", "execution_count": 231, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rr}\n", "1 & 0 \\\\\n", "0 & \\frac{1}{\\sin\\left({\\theta}\\right)}\n", "\\end{array}\\right)$ " ], "text/plain": [ "[ 1 0]\n", "[ 0 1/sin(th)]" ] }, "execution_count": 231, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a[:]" ] }, { "cell_type": "code", "execution_count": 232, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector frame (A, (e_1,e_2))\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A, \\left(e_1,e_2\\right)\\right)$ " ], "text/plain": [ "Vector frame (A, (e_1,e_2))" ] }, "execution_count": 232, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e = spher.frame().new_frame(a, 'e')\n", "print(e) ; e" ] }, { "cell_type": "code", "execution_count": 233, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}e_1 = \\frac{\\partial}{\\partial {\\theta} }$ " ], "text/plain": [ "e_1 = d/dth" ] }, "execution_count": 233, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[1].display()" ] }, { "cell_type": "code", "execution_count": 234, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}e_2 = \\frac{1}{\\sin\\left({\\theta}\\right)} \\frac{\\partial}{\\partial {\\phi} }$ " ], "text/plain": [ "e_2 = 1/sin(th) d/dph" ] }, "execution_count": 234, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[2].display()" ] }, { "cell_type": "code", "execution_count": 235, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left(A, \\left(\\frac{\\partial}{\\partial x },\\frac{\\partial}{\\partial y }\\right)\\right), \\left(A, \\left(\\frac{\\partial}{\\partial {x'} },\\frac{\\partial}{\\partial {y'} }\\right)\\right), \\left(A, \\left(\\frac{\\partial}{\\partial {\\theta} },\\frac{\\partial}{\\partial {\\phi} }\\right)\\right), \\left(A, \\left(\\frac{\\partial}{\\partial X },\\frac{\\partial}{\\partial Y },\\frac{\\partial}{\\partial Z }\\right)\\right), \\left(A, \\left(e_1,e_2\\right)\\right)\\right]$ " ], "text/plain": [ "[Coordinate frame (A, (d/dx,d/dy)),\n", " Coordinate frame (A, (d/dxp,d/dyp)),\n", " Coordinate frame (A, (d/dth,d/dph)),\n", " Vector frame (A, (d/dX,d/dY,d/dZ)) with values on the 3-dimensional differentiable manifold R^3,\n", " Vector frame (A, (e_1,e_2))]" ] }, "execution_count": 235, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.frames()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The new frame is an orthonormal frame for the metric $g$:

" ] }, { "cell_type": "code", "execution_count": 236, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}1$ " ], "text/plain": [ "1" ] }, "execution_count": 236, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[1],e[1]).expr()" ] }, { "cell_type": "code", "execution_count": 237, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$ " ], "text/plain": [ "0" ] }, "execution_count": 237, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[1],e[2]).expr()" ] }, { "cell_type": "code", "execution_count": 238, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}1$ " ], "text/plain": [ "1" ] }, "execution_count": 238, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[2],e[2]).expr()" ] }, { "cell_type": "code", "execution_count": 239, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rr}\n", "1 & 0 \\\\\n", "0 & 1\n", "\\end{array}\\right)$ " ], "text/plain": [ "[1 0]\n", "[0 1]" ] }, "execution_count": 239, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[e,:]" ] }, { "cell_type": "code", "execution_count": 240, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = e^1\\otimes e^1+e^2\\otimes e^2$ " ], "text/plain": [ "g = e^1*e^1 + e^2*e^2" ] }, "execution_count": 240, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(e)" ] }, { "cell_type": "code", "execution_count": 241, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\epsilon_{g} = e^1\\wedge e^2$ " ], "text/plain": [ "eps_g = e^1/\\e^2" ] }, "execution_count": 241, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps.display(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

It is non-holonomic: its structure coefficients are not identically zero:

" ] }, { "cell_type": "code", "execution_count": 242, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left[\\left[0, 0\\right], \\left[0, 0\\right]\\right], \\left[\\left[0, -\\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)}\\right], \\left[\\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)}, 0\\right]\\right]\\right]$ " ], "text/plain": [ "[[[0, 0], [0, 0]], [[0, -cos(th)/sin(th)], [cos(th)/sin(th), 0]]]" ] }, "execution_count": 242, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e.structure_coeff()[:]" ] }, { "cell_type": "code", "execution_count": 243, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)} e_2$ " ], "text/plain": [ "-cos(th)/sin(th) e_2" ] }, "execution_count": 243, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[2].lie_derivative(e[1]).display(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

while we have of course

" ] }, { "cell_type": "code", "execution_count": 244, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left[\\left[0, 0\\right], \\left[0, 0\\right]\\right], \\left[\\left[0, 0\\right], \\left[0, 0\\right]\\right]\\right]$ " ], "text/plain": [ "[[[0, 0], [0, 0]], [[0, 0], [0, 0]]]" ] }, "execution_count": 244, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.frame().structure_coeff()[:]" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 7.5.1", "language": "", "name": "sagemath" }, "language": "python", "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 0 }