{ "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 0.9.1)\n", "on the example of the 2-dimensional sphere.\n", "\n", "Click [here](https://raw.githubusercontent.com/sagemanifolds/SageManifolds/master/Worksheets/v0.9.1/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": [ "First we set up the notebook to display mathematical objects using LaTeX formatting:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also define a viewer for 3D plots (use `'jmol'` for interactive 3D graphics):" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "viewer3D = 'tachyon' # must be '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": 3, "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": 4, "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": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "2-dimensional differentiable manifold S^2" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The manifold is a `Parent` object:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 6, "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": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Category of smooth manifolds over Real Field with 53 bits of precision" ] }, "execution_count": 7, "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": 8, "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": 9, "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": 10, "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": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "stereoN. = U.chart()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (U, (x, y))" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 13, "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": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "stereoS. = V.chart(r\"xp:x' yp:y'\")" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (V, (xp, yp))" ] }, "execution_count": 15, "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": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Chart (U, (x, y)), Chart (V, (xp, yp))]" ] }, "execution_count": 16, "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": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "xp = x/(x^2 + y^2)\n", "yp = y/(x^2 + y^2)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_to_S = stereoN.transition_map(stereoS, (x/(x^2+y^2), y/(x^2+y^2)), intersection_name='W',\n", " restrictions1= x^2+y^2!=0, 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": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "x = xp/(xp^2 + yp^2)\n", "y = yp/(xp^2 + yp^2)" ] }, "execution_count": 18, "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": 19, "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": 19, "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": 20, "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": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (W, (x, y))" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_W = stereoN.restrict(W)\n", "stereoN_W" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (W, (xp, yp))" ] }, "execution_count": 22, "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": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 17 graphics primitives" ] }, "execution_count": 23, "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": 24, "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": 25, "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), 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": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (A, (x, y))" ] }, "execution_count": 26, "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": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (A, (th, ph))" ] }, "execution_count": 27, "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": 28, "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": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher_to_stereoN = spher.transition_map(stereoN_A, (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:

" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [], "source": [ "spher_to_stereoN.set_inverse(2*atan(1/sqrt(x^2+y^2)), atan2(-y,-x)+pi,\n", " check=True)" ] }, { "cell_type": "code", "execution_count": 30, "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": 30, "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": 31, "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": 31, "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": 32, "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": 32, "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": 33, "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": 33, "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": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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cFhE/jqJ/f05m//NP150gnS4d/4YsWdjxVAzQ+rBYePOWiq/Uc/s2p4SL+NHL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\nu4EKFej6d96koqJ0W3cvISG02cj+SJ5MUBDHNezcqduSe7l8GRgzhteY/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"text/plain": [ "Graphics object consisting of 30 graphics primitives" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(stereoN, nb_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": 35, "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": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_A.plot(spher, ranges={x: (0.01,8), y: (0.01,8)}, nb_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": 36, "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 (facade) Parent being the manifold subsets, an equivalent writing of the above declarations is

" ] }, { "cell_type": "code", "execution_count": 37, "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": 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((0,0), name='N') ; print(N)\n", "S = U((0,0), name='S') ; print(S)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Open subset V of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N.parent()" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Open subset U of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S.parent()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We have of course

" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N in V" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N in S2" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "False" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N in U" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "False" ] }, "execution_count": 44, "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": 45, "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": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 46, "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": 47, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(1/2*pi, 1/2*pi)" ] }, "execution_count": 47, "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": 48, "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": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (R^3, (X, Y, Z))" ] }, "execution_count": 49, "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": 50, "metadata": { "collapsed": false }, "outputs": [], "source": [ "Phi = S2.diff_map(R3, {(stereoN, cart): [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): [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": 51, "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": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.display()" ] }, { "cell_type": "code", "execution_count": 52, "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": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.parent()" ] }, { "cell_type": "code", "execution_count": 53, "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": 54, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 54, "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": 55, "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": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N1 = Phi(N) ; print(N1) ; N1 ; N1.coord()" ] }, { "cell_type": "code", "execution_count": 56, "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": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S1 = Phi(S) ; print(S1) ; S1 ; S1.coord()" ] }, { "cell_type": "code", "execution_count": 57, "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": 57, "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": 58, "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": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.expr(stereoN_A, cart)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(cos(ph)*sin(th), sin(ph)*sin(th), cos(th))" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.expr(spher, cart)" ] }, { "cell_type": "code", "execution_count": 60, "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": 60, "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": 61, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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3msRMmDDh4MGD6ebYFQlKdcLGga/wYA/Y80dojqyNdf31i2A+7M/5HMt4+Hyn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RlS3CUusHz58l27du3atcttQ0qKVHZJKZHiLnGH++6777777qsefZe5MZISI8Vd4ia9vb3VoO+y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\nxARoAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_spher = spher.plot(chart=cart, mapping=Phi, nb_values=11, color='blue')\n", "show(graph_spher, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

For future use, let us store a version without any label on the axes:

" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false }, "outputs": [], "source": [ "graph_spher = spher.plot(chart=cart, mapping=Phi, nb_values=11, color='blue', label_axes=False)" ] }, { "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": 63, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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FAOyGVVApxPuQDx/DW9AspVLqEyFme87wvufvv8CG8HX/BuuF2CpEBZTCh7AH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\nliMERO0aeooAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_stereoN = stereoN.plot(chart=cart, mapping=Phi, nb_values=25)\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": 64, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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DiGlCfO0bhGYJMRqUYdQKMUGINFAej7KsZUJM9n8uy5oBfc9j4zRrl2F8AAth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\nI8R0oBAIAouA2cBMYBbAUu4XImpr7/L5ihRlKlHQ41lApG1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GqE6IolRS8nEY+7OY6Cu9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\nw8/wW/gM9oLfALAL2sEv8B/YB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/PpSmlM5J7amC3WRjNo0CATmcZl48aNW7ZsMcqe6hhx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\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_stereoS = stereoS.plot(chart=cart, mapping=Phi, nb_values=25, color='green')\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": 65, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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eYiorK8eNG9e9e/cXX3yx6c/e/LCsYb163Q7rAOgAt0EXTXvCHn5cs2bafffV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//9b+Q/nY8bGLnX4naAwv0yLoO8MFZ6FryyYMjJ6OuuS/zkL4We/BeR/xFKaBS+UuiVAxW+VOgG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\nJnds0eVy2e12lB2GfQKVGmHF2/UjnwAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pointN = N.plot(chart=cart, mapping=Phi, color='red', label_offset=0.05)\n", "pointS = S.plot(chart=cart, mapping=Phi, color='green', 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": 66, "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": [ "" ], "text/plain": [ "Tangent space at Point N on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 66, "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": 67, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Category of finite dimensional vector spaces over Symbolic Ring" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_N.category()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Its dimension equals the manifold's dimension:

" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "2" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dim(T_N)" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 69, "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": 70, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Basis (d/dxp,d/dyp) on the Tangent space at Point N on the 2-dimensional differentiable manifold S^2]" ] }, "execution_count": 70, "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": 71, "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": [ "" ], "text/plain": [ "Tangent space at Point E on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_E = S2.tangent_space(E)\n", "print(T_E) ; T_E" ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_E.bases()" ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Basis (d/dx,d/dy) 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.default_basis()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 74, "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": 75, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v in T_E" ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Tangent space at Point E on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.parent()" ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = -3 d/dx + 2 d/dy" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display()" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = -3 d/dxp - 2 d/dyp" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display(T_E.bases()[1])" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = -2 d/dth + 3 d/dph" ] }, "execution_count": 79, "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": 80, "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": [ "" ], "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": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E = Phi.differential(E)\n", "print(dPhi_E) ; dPhi_E" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Tangent space at Point E on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E.domain()" ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Tangent space at Point Phi(E) on the 3-dimensional differentiable manifold R^3" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E.codomain()" ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 83, "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": 84, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Tangent vector dPhi_E(v) at Point Phi(E) on the 3-dimensional differentiable manifold R^3" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E(v)" ] }, { "cell_type": "code", "execution_count": 85, "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": 86, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E(v) in R3.tangent_space(Phi(E))" ] }, { "cell_type": "code", "execution_count": 87, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "dPhi_E(v) = -3 d/dX + 2 d/dZ" ] }, "execution_count": 87, "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": 88, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 88, "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": 89, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Category of commutative algebras over Symbolic Ring" ] }, "execution_count": 89, "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": 90, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Symbolic Ring" ] }, "execution_count": 90, "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": 91, "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": 92, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 92, "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": 93, "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": 94, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(0, 0, 0)" ] }, "execution_count": 94, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(N), f(E), f(S)" ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 95, "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": 96, "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": 97, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(1, 1, 1)" ] }, "execution_count": 97, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(N), f(E), f(S)" ] }, { "cell_type": "code", "execution_count": 98, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 98, "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": 99, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 99, "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": 100, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 100, "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": 101, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 101, "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": 102, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "{Chart (A, (th, ph)): pi + 2*arctan((cos(th) + 1)/(cos(th) - 1)),\n", " Chart (A, (x, y)): pi - 2*arctan(x^2 + y^2),\n", " Chart (U, (x, y)): pi - 2*arctan(x^2 + y^2),\n", " Chart (V, (xp, yp)): 2*arctan(xp^2 + yp^2)}" ] }, "execution_count": 102, "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": 103, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "f: S^2 --> R\n", "on V: (xp, yp) |--> 2*arctan(xp^2 + yp^2)" ] }, "execution_count": 103, "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": 104, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(N)" ] }, { "cell_type": "code", "execution_count": 105, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/2*pi" ] }, "execution_count": 105, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(E)" ] }, { "cell_type": "code", "execution_count": 106, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "pi" ] }, "execution_count": 106, "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": 107, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 107, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU = f.restrict(U)\n", "fU.display()" ] }, { "cell_type": "code", "execution_count": 108, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 108, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fV = f.restrict(V)\n", "fV.display()" ] }, { "cell_type": "code", "execution_count": 109, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(1/2*pi, pi)" ] }, "execution_count": 109, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU(E), fU(S)" ] }, { "cell_type": "code", "execution_count": 110, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the Open subset U of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 110, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU.parent()" ] }, { "cell_type": "code", "execution_count": 111, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the Open subset V of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 111, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fV.parent()" ] }, { "cell_type": "code", "execution_count": 112, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 112, "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": 113, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 113, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CU.has_coerce_map_from(CS)" ] }, { "cell_type": "code", "execution_count": 114, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 114, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU == CU(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The arithmetic of scalar fields:

" ] }, { "cell_type": "code", "execution_count": 115, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 115, "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": 116, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Module X(S^2) of vector fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 116, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS = S2.vector_field_module()\n", "XS" ] }, { "cell_type": "code", "execution_count": 117, "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": 118, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 118, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS.base_ring()" ] }, { "cell_type": "code", "execution_count": 119, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Category of modules over Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 119, "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": 120, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "False" ] }, "execution_count": 120, "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": 121, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "False" ] }, "execution_count": 121, "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": 122, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 122, "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": 123, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 123, "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": 124, "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": 125, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate frame (U, (d/dx,d/dy))" ] }, "execution_count": 125, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XU.default_basis()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Similarly

" ] }, { "cell_type": "code", "execution_count": 126, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate frame (V, (d/dxp,d/dyp))" ] }, "execution_count": 126, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XV = V.vector_field_module()\n", "XV.default_basis()" ] }, { "cell_type": "code", "execution_count": 127, "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": 128, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 128, "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": 129, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 129, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eU is S2.default_frame()" ] }, { "cell_type": "code", "execution_count": 130, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 130, "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": 131, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 131, "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": 132, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Module X(S^2) of vector fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 132, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.parent()" ] }, { "cell_type": "code", "execution_count": 133, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate frame (W, (d/dxp,d/dyp))" ] }, "execution_count": 133, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoSW = stereoS.restrict(W)\n", "eSW = stereoSW.frame()\n", "eSW" ] }, { "cell_type": "code", "execution_count": 134, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 134, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW = v.restrict(W)\n", "vW.display()" ] }, { "cell_type": "code", "execution_count": 135, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Free module X(W) of vector fields on the Open subset W of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 135, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW.parent()" ] }, { "cell_type": "code", "execution_count": 136, "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": 137, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 137, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW.display(eSW)" ] }, { "cell_type": "code", "execution_count": 138, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 138, "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": 139, "metadata": { "collapsed": false }, "outputs": [], "source": [ "v.add_comp_by_continuation(eV, W, chart=stereoS)" ] }, { "cell_type": "code", "execution_count": 140, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 140, "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": 141, "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": [ "" ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 141, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(v)\n", "v.display(eU)" ] }, { "cell_type": "code", "execution_count": 142, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 142, "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": 143, "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": 144, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = 0" ] }, "execution_count": 144, "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": 145, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Tangent space at Point N on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 145, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vN.parent()" ] }, { "cell_type": "code", "execution_count": 146, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 146, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vN.parent() is S2.tangent_space(N)" ] }, { "cell_type": "code", "execution_count": 147, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 147, "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": 148, "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": 149, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 149, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vS.display()" ] }, { "cell_type": "code", "execution_count": 150, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Tangent space at Point S on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 150, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vS.parent()" ] }, { "cell_type": "code", "execution_count": 151, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 151, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vS.parent() is S2.tangent_space(S)" ] }, { "cell_type": "code", "execution_count": 152, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 152, "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": 153, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 27 graphics primitives" ] }, "execution_count": 153, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.plot(chart=stereoN, chart_domain=stereoN, max_range=4, nb_values=5, \n", " 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": 154, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 154, "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": 155, "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": 155, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.plot(chart=stereoS, chart_domain=stereoS, max_range=4, scale=0.02, 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": 156, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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HloMLTjTW9yRW/EWLFsVR1mWCKbuUMp5hGaC0tDSORx87duzYsWOPHz8+ffp0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CKxxK/vdXXr4a8QhczOKoaxb+FChNhlGCxcqEu0+sEA3y6DwSEvLUL8xjCaDeNZ285oabAvkfgY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\n3GGj5+fnVqtF2WGwfwCnvoooqQ8rLgAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_v = v.plot(chart=cart, mapping=Phi, chart_domain=spher, nb_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": 157, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Vector field d/dx on the Open subset U of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 157, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ex = stereoN.frame()[1]\n", "ex" ] }, { "cell_type": "code", "execution_count": 158, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YDUAthAC3+5Hs7L4PBEoe5syZM2fOnHPPPTfRhnzCunXrkmvnuETfOiSFZ6Y9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E3auXNrw+FjSg0HDGOVafaHoR5xb4ZD0Oy8XynHW1ZLcq+m/btt74HL4A3YAUg5zY2cAfC6xQBN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\ndeIhui1Z6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zXVhoaGs/yFCYfHwtNwFAY7YYgJlPoWvO7+dhvkw8dQDw1K3aTU1bbdIISl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\n4Ol04lEZbiLu+Cvz+bz+ICfZgzRG0xt18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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_ex = ex.plot(chart=cart, mapping=Phi, chart_domain=spher,\n", " nb_values=11, scale=0.4, width=1)\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": 159, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Vector field d/dy on the Open subset U of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 159, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ey = stereoN.frame()[2]\n", "ey" ] }, { "cell_type": "code", "execution_count": 160, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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jKmpnlscwDkHhWYn3enswFl6koqrLLYT4+PgTJ2qXrdvYRM70JZPwi3ukXe5M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U3F7QBYZitide09zcsEiW9VKhK5yrEjLw9No0ULhFggZVvT/BmqQBUQsBtqwRbY14xNG6lxm2yy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\nLTweUlLwenG7v6rnbt0MzvUk71TePw8yOpVfHyQezp5m67/Yl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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_ey = ey.plot(chart=cart, mapping=Phi, chart_domain=spher,\n", " nb_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 frame associated with the stereographic coordinates from the North pole:

" ] }, { "cell_type": "code", "execution_count": 161, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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6bVrWNrsctqkdwyG4f+tb39qyZcuXvvSliooKQRDYD0NEly8Uwj33/PLECduM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JadNOwdqB3AI03fzJF4OyWROHr9/uBNuaz2qnVAxKajNwFOYUhf03gFjposmTefdd1pGrZpPi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I+X/0BK1TSAo4DZC+hXOQile5aMRsrLJ0EQctas0V/nBOD1ylHN3r18/esfNzaqC37NSnZf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\nz/T390+ceL7dXlxWVmu3W886i7POo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2H1ar57W4K1A13H90EWEAj2bNzmGgym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K0aX0izdt5LYXiwqfOqzcWAMqFX4VomBNHGKlYO3BIMEggQAaDRYLw8P09rJxI9fIXFGz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\nO+RyeXl5Q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XsUIIPwrl1HH3zw4Ntv+43G0mnThn3LGfwLsW3btnPPPbek5DRTtTP4AiPj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\n3bt365QlEZkFCu4ikhm7d+82pcp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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(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", " sphere(opacity=0.5),\n", " 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": 162, "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": [ "" ], "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": 162, "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": 163, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "execution_count": 163, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf(N)" ] }, { "cell_type": "code", "execution_count": 164, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "4" ] }, "execution_count": 164, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf(E)" ] }, { "cell_type": "code", "execution_count": 165, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "execution_count": 165, "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": 166, "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": 167, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 167, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.display()" ] }, { "cell_type": "code", "execution_count": 168, "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": 169, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Module /\\^1(S^2) of 1-forms on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 169, "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": 170, "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": [ "" ], "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))/(sin(th)^4 + 2*(cos(th) - 2)*sin(th)^2 - 4*cos(th) + 4)" ] }, "execution_count": 170, "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": 171, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 171, "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": 172, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 172, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.lie_der(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": 173, "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": 174, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Category of smooth manifolds over Real Field with 53 bits of precision" ] }, "execution_count": 174, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R.category()" ] }, { "cell_type": "code", "execution_count": 175, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1" ] }, "execution_count": 175, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dim(R)" ] }, { "cell_type": "code", "execution_count": 176, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Chart (R, (t,))]" ] }, "execution_count": 176, "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": 177, "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": 178, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 178, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.parent()" ] }, { "cell_type": "code", "execution_count": 179, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 179, "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": 180, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Hb7zBPuykn6FDZQdoxQrVkSjF7XRn0TTpUT1wIFC0qFT3Nm2qOiqyE7fTc+nL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\nz3RUYmXz52vc6F2YT+IAV+OhoVrR2YmXF7e3Dh3iC7G2bdl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Ur286IslGGoAilhEfDwwY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\nAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 180, "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": 181, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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LgkPX95gNulxSCKfLJYUoMHMmhShwuaQQZUJIWNWt2wYohGzIgUzIggOQCy7I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\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_c = c.plot(mapping=Phi, max_range=40, plot_points=200, thickness=2)\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": 182, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Vector field c' along the Real number line R with values on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 182, "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": 183, "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": 184, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 184, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent()" ] }, { "cell_type": "code", "execution_count": 185, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Category of modules over Algebra of differentiable scalar fields on the Real number line R" ] }, "execution_count": 185, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent().category()" ] }, { "cell_type": "code", "execution_count": 186, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the Real number line R" ] }, "execution_count": 186, "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": 187, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 187, "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": 188, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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kZFkFv2cPULCgXnP9u++AHj0MbRplLsjoBhClKTERKFBAVuO6ol49z7SHyF9o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"text/plain": [ "Graphics object consisting of 31 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(vc.plot(chart=stereoN, nb_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": 189, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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FCxZMnDhxw4YNLbZHXwKPwhLYAjujVXUOfAe/wBpYAptnz+7HHE3b6GILRxwC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\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_vc = vc.plot(chart=cart, mapping=Phi, ranges={t: (-20, 20)}, nb_values=30, \n", " scale=0.5, color='red', 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": 190, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "h = dX*dX + dY*dY + dZ*dZ" ] }, "execution_count": 190, "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": 191, "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": 192, "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": 193, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(0, 2)" ] }, "execution_count": 193, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.tensor_type()" ] }, { "cell_type": "code", "execution_count": 194, "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": 195, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 195, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We may factorize the metric components:

" ] }, { "cell_type": "code", "execution_count": 196, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "4/(x^2 + y^2 + 1)^2" ] }, "execution_count": 196, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[1,1].factor() ; g[2,2].factor()" ] }, { "cell_type": "code", "execution_count": 197, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = 4/(x^2 + y^2 + 1)^2 dx*dx + 4/(x^2 + y^2 + 1)^2 dy*dy" ] }, "execution_count": 197, "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": 198, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[4/(x^2 + y^2 + 1)^2 0]\n", "[ 0 4/(x^2 + y^2 + 1)^2]" ] }, "execution_count": 198, "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": 199, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 199, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(stereoS.frame())" ] }, { "cell_type": "code", "execution_count": 200, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = dth*dth + sin(th)^2 dph*dph" ] }, "execution_count": 200, "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": 201, "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": 202, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 202, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(v,v).parent()" ] }, { "cell_type": "code", "execution_count": 203, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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)^4 - 4*cos(th)^3 + 6*cos(th)^2 - 4*cos(th) + 1)/(sin(th)^2 + 2*cos(th) - 2)" ] }, "execution_count": 203, "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": 204, "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": [ "" ], "text/plain": [ "Levi-Civita connection nabla_g associated with the Riemannian metric g on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 204, "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": 205, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "nabla_g(g) = 0" ] }, "execution_count": 205, "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": 206, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 206, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.christoffel_symbols_display(chart=stereoN)" ] }, { "cell_type": "code", "execution_count": 207, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Gam^th_ph,ph = -cos(th)*sin(th) \n", "Gam^ph_th,ph = cos(th)/sin(th) " ] }, "execution_count": 207, "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": 208, "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": 209, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 209, "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": 210, "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": [ "" ], "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": 210, "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": 211, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 211, "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": 212, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 212, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem.display_comp(spher.frame(), chart=spher)" ] }, { "cell_type": "code", "execution_count": 213, "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": 214, "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": 215, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Riem(h) = 0" ] }, "execution_count": 215, "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": 216, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 216, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric = g.ricci()\n", "Ric.display()" ] }, { "cell_type": "code", "execution_count": 217, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 217, "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": 218, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 218, "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": 219, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 219, "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": 220, "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": [ "" ], "text/plain": [ "eps_g = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dx/\\dy" ] }, "execution_count": 220, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps = g.volume_form()\n", "print(eps)\n", "eps.display()" ] }, { "cell_type": "code", "execution_count": 221, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "eps_g = sin(th) dth/\\dph" ] }, "execution_count": 221, "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": 222, "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": 223, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "deps_g = 0" ] }, "execution_count": 223, "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": 224, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (A, (x, y))" ] }, "execution_count": 224, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_chart()" ] }, { "cell_type": "code", "execution_count": 225, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate frame (A, (d/dx,d/dy))" ] }, "execution_count": 225, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_frame()" ] }, { "cell_type": "code", "execution_count": 226, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (A, (th, ph))" ] }, "execution_count": 226, "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": 227, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate frame (A, (d/dth,d/dph))" ] }, "execution_count": 227, "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": 228, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "d/dth*dth + 1/sin(th) d/dph*dph" ] }, "execution_count": 228, "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": 229, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[ 1 0]\n", "[ 0 1/sin(th)]" ] }, "execution_count": 229, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a[:]" ] }, { "cell_type": "code", "execution_count": 230, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector frame (A, (e_1,e_2))\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "Vector frame (A, (e_1,e_2))" ] }, "execution_count": 230, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e = spher.frame().new_frame(a, 'e')\n", "print(e) ; e" ] }, { "cell_type": "code", "execution_count": 231, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "e_1 = d/dth" ] }, "execution_count": 231, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[1].display()" ] }, { "cell_type": "code", "execution_count": 232, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "e_2 = 1/sin(th) d/dph" ] }, "execution_count": 232, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[2].display()" ] }, { "cell_type": "code", "execution_count": 233, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "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": 233, "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": 234, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1" ] }, "execution_count": 234, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[1],e[1]).expr()" ] }, { "cell_type": "code", "execution_count": 235, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "execution_count": 235, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[1],e[2]).expr()" ] }, { "cell_type": "code", "execution_count": 236, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1" ] }, "execution_count": 236, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[2],e[2]).expr()" ] }, { "cell_type": "code", "execution_count": 237, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[1 0]\n", "[0 1]" ] }, "execution_count": 237, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[e,:]" ] }, { "cell_type": "code", "execution_count": 238, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = e^1*e^1 + e^2*e^2" ] }, "execution_count": 238, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(e)" ] }, { "cell_type": "code", "execution_count": 239, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "eps_g = e^1/\\e^2" ] }, "execution_count": 239, "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": 240, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[[[0, 0], [0, 0]], [[0, -cos(th)/sin(th)], [cos(th)/sin(th), 0]]]" ] }, "execution_count": 240, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e.structure_coef()[:]" ] }, { "cell_type": "code", "execution_count": 241, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-cos(th)/sin(th) e_2" ] }, "execution_count": 241, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[2].lie_der(e[1]).display(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

while we have of course

" ] }, { "cell_type": "code", "execution_count": 242, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[[[0, 0], [0, 0]], [[0, 0], [0, 0]]]" ] }, "execution_count": 242, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.frame().structure_coef()[:]" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 7.4", "language": "", "name": "sage-7.4" }, "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": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }