{ "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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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\n5ddycq4cstqxQz5fzCGxsbGx8PPzQ1xcHOLi4oBz5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"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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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", "