{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Sphere $\\mathbb{S}^2$\n", "\n", "This worksheet demonstrates some differential geometry capabilities of SageMath on the example of the 2-dimensional sphere. The corresponding tools have been developed within\n", "the [SageManifolds](http://sagemanifolds.obspm.fr) project (version 1.1, as included in SageMath 8.1).\n", "\n", "Click [here](https://raw.githubusercontent.com/sagemanifolds/SageManifolds/master/Worksheets/v1.1/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": [ "*NB:* a version of SageMath at least equal to 7.5 is required to run this worksheet:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 8.1, Release Date: 2017-12-07'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we set up the notebook to display mathematical objects using LaTeX formatting:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also define a viewer for 3D plots (use `'threejs'` or `'jmol'` for interactive 3D graphics):" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "viewer3D = 'threejs' # must be 'threejs', jmol', 'tachyon' or None (default)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $\\mathbb{S}^2$ as a 2-dimensional differentiable manifold\n", "\n", "We start by declaring $\\mathbb{S}^2$ as a differentiable manifold of dimension 2 over $\\mathbb{R}$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "S2 = Manifold(2, 'S^2', latex_name=r'\\mathbb{S}^2', start_index=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
The first argument, 2, is the dimension of the manifold, while the second argument is the symbol used to label the manifold.
\n", "The argument start_index sets the index range to be used on the manifold for labelling components w.r.t. a basis or a frame: start_index=1 corresponds to $\\{1,2\\}$; the default value is start_index=0 and yields to $\\{0,1\\}$.
" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(S2)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "2-dimensional differentiable manifold S^2" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The manifold is a `Parent` object:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "isinstance(S2, Parent)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "in the category of smooth manifolds over $\\mathbb{R}$:
" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Category of smooth manifolds over Real Field with 53 bits of precision" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2.category()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Coordinate charts on $\\mathbb{S}^2$\n", "\n", "The sphere cannot be covered by a single chart. At least two charts are necessary, for instance the charts associated with the stereographic projections from the North pole and the South pole respectively. Let us introduce the open subsets covered by these two charts: \n", "$$ U := \\mathbb{S}^2\\setminus\\{N\\}, $$ \n", "$$ V := \\mathbb{S}^2\\setminus\\{S\\}, $$\n", "where $N$ is a point of $\\mathbb{S}^2$, which we shall call the North pole, and $S$ is the point of $U$ of stereographic coordinates $(0,0)$, which we call the South pole:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Open subset U of the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "U = S2.open_subset('U') ; print(U)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Open subset V of the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "V = S2.open_subset('V') ; print(V)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We declare that $\\mathbb{S}^2 = U \\cup V$:
" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "S2.declare_union(U, V)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we declare the stereographic chart on $U$, denoting by $(x,y)$ the coordinates resulting from the stereographic projection from the North pole:
" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "stereoN.Similarly, we introduce on $V$ the coordinates $(x',y')$ corresponding to the stereographic projection from the South pole:
" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "stereoS.At this stage, the user's atlas on the manifold has two charts:
" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Chart (U, (x, y)), Chart (V, (xp, yp))]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2.atlas()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have to specify the transition map between the charts 'stereoN' = $(U,(x,y))$ and 'stereoS' = $(V,(x',y'))$; it is given by the standard inversion formulas:
" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "xp = x/(x^2 + y^2)\n", "yp = y/(x^2 + y^2)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_to_S = stereoN.transition_map(stereoS, \n", " (x/(x^2+y^2), y/(x^2+y^2)), \n", " intersection_name='W',\n", " restrictions1= x^2+y^2!=0, \n", " restrictions2= xp^2+yp^2!=0)\n", "stereoN_to_S.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the above declaration, 'W' is the name given to the chart-overlap subset: $W := U\\cap V$, the condition $x^2+y^2 \\not=0$ defines $W$ as a subset of $U$, and the condition $x'^2+y'^2\\not=0$ defines $W$ as a subset of $V$.\n", "\n", "The inverse coordinate transformation is computed by means of the method `inverse()`:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "x = xp/(xp^2 + yp^2)\n", "y = yp/(xp^2 + yp^2)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoS_to_N = stereoN_to_S.inverse()\n", "stereoS_to_N.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the present case, the situation is of course perfectly symmetric regarding the coordinates $(x,y)$ and $(x',y')$.
\n", "At this stage, the user's atlas has four charts:
" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Chart (U, (x, y)),\n", " Chart (V, (xp, yp)),\n", " Chart (W, (x, y)),\n", " Chart (W, (xp, yp))]" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2.atlas()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us store $W = U\\cap V$ into a Python variable for future use:
" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "W = U.intersection(V)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly we store the charts $(W,(x,y))$ (the restriction of $(U,(x,y))$ to $W$) and $(W,(x',y'))$ (the restriction of $(V,(x',y'))$ to $W$) into Python variables:
" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (W, (x, y))" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_W = stereoN.restrict(W)\n", "stereoN_W" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (W, (xp, yp))" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoS_W = stereoS.restrict(W)\n", "stereoS_W" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may plot the chart $(W, (x',y'))$ in terms of itself, as a grid:
" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 18 graphics primitives" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoS_W.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "More interestingly, let us plot the stereographic chart $(x',y')$ in terms of the stereographic chart $(x,y)$ on the domain $W$ where both systems overlap (we split the plot in four parts to avoid the singularity at $(x',y')=(0,0)$):
" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "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": [ "The standard spherical (or polar) coordinates $(\\theta,\\phi)$ are defined on the open domain $A\\subset W \\subset \\mathbb{S}^2$ that is the complement of the \"origin meridian\"; since the latter is the half-circle defined by $y=0$ and $x\\geq 0$, we declare:
" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Open subset A of the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "A = W.open_subset('A', coord_def={stereoN_W: (y!=0, x<0), \n", " stereoS_W: (yp!=0, xp<0)})\n", "print(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The restriction of the stereographic chart from the North pole to $A$ is
" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (A, (x, y))" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_A = stereoN_W.restrict(A)\n", "stereoN_A" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We then declare the chart $(A,(\\theta,\\phi))$ by specifying the intervals $(0,\\pi)$ and $(0,2\\pi)$ spanned by respectively $\\theta$ and $\\phi$:
" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (A, (th, ph))" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.The specification of the spherical coordinates is completed by providing the transition map with the stereographic chart $(A,(x,y))$:
" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "x = -cos(ph)*sin(th)/(cos(th) - 1)\n", "y = -sin(ph)*sin(th)/(cos(th) - 1)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher_to_stereoN = spher.transition_map(stereoN_A, \n", " (sin(th)*cos(ph)/(1-cos(th)),\n", " sin(th)*sin(ph)/(1-cos(th))))\n", "spher_to_stereoN.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also provide the inverse transition map, asking to check that the provided formulas are indeed correct (argument `verbose=True`):" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Check of the inverse coordinate transformation:\n", " th == 2*arctan(sqrt(-cos(th) + 1)/sqrt(cos(th) + 1))\n", " ph == pi + arctan2(sin(ph)*sin(th)/(cos(th) - 1), cos(ph)*sin(th)/(cos(th) - 1))\n", " x == x\n", " y == y\n" ] } ], "source": [ "spher_to_stereoN.set_inverse(2*atan(1/sqrt(x^2+y^2)), atan2(-y,-x)+pi,\n", " verbose=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The check is passed, modulo some lack of trigonometric simplifications in the first two lines." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "th = 2*arctan(1/sqrt(x^2 + y^2))\n", "ph = pi + arctan2(-y, -x)" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher_to_stereoN.inverse().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The transition map $(A,(\\theta,\\phi))\\rightarrow (A,(x',y'))$ is obtained by combining the transition maps $(A,(\\theta,\\phi))\\rightarrow (A,(x,y))$ and $(A,(x,y))\\rightarrow (A,(x',y'))$:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "xp = -(cos(ph)*cos(th) - cos(ph))/sin(th)\n", "yp = -(cos(th)*sin(ph) - sin(ph))/sin(th)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_to_S_A = stereoN_to_S.restrict(A)\n", "spher_to_stereoS = stereoN_to_S_A * spher_to_stereoN\n", "spher_to_stereoS.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, the transition map $(A,(x',y'))\\rightarrow (A,(\\theta,\\phi))$ is obtained by combining the transition maps $(A,(x',y'))\\rightarrow (A,(x,y))$ and $(A,(x,y))\\rightarrow (A,(\\theta,\\phi))$:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "th = 2*arctan(sqrt(xp^2 + yp^2))\n", "ph = pi - arctan2(yp/(xp^2 + yp^2), -xp/(xp^2 + yp^2))" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoS_to_N_A = stereoN_to_S.inverse().restrict(A)\n", "stereoS_to_spher = spher_to_stereoN.inverse() * stereoS_to_N_A \n", "stereoS_to_spher.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The user atlas of $\\mathbb{S}^2$ is now
" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Chart (U, (x, y)),\n", " Chart (V, (xp, yp)),\n", " Chart (W, (x, y)),\n", " Chart (W, (xp, yp)),\n", " Chart (A, (x, y)),\n", " Chart (A, (xp, yp)),\n", " Chart (A, (th, ph))]" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2.atlas()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us draw the grid of spherical coordinates $(\\theta,\\phi)$ in terms of stereographic coordinates from the North pole $(x,y)$:
" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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xg80YBZdFxI+jGDiQk9n/+MN1O8qmS8e/IUsWdjyVBGh9WCy8eUvFV+q5dYtT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\n+BQifgRBEARB8Cn+DwC+pYgRiwJbAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics object consisting of 30 graphics primitives" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(stereoN, number_values=15, ranges={th: (pi/8,pi)})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Conversly, we may represent the grid of the stereographic coordinates $(x,y)$ restricted to $A$ in terms of the spherical coordinates $(\\theta,\\phi)$. We limit ourselves to one quarter (cf. the argument ranges):
" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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OyCCqW1ftUbgHKSkcT80YJj8f1zsWD85FtWro+N21a9nn0tOJrl9H5aiTJ4n+/pto4UI8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\n", "text/plain": [ "Graphics object consisting of 40 graphics primitives" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_A.plot(spher, ranges={x: (0.01,8), y: (0.01,8)}, number_values=20, plot_points=200)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We declare the North pole (resp. the South pole) as the point of coordinates $(0,0)$ in the chart $(V,(x',y'))$ (resp. in the chart $(U,(x,y))$):
" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point N on the 2-dimensional differentiable manifold S^2\n", "Point S on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "N = V.point((0,0), chart=stereoS, name='N') ; print(N)\n", "S = U.point((0,0), chart=stereoN, name='S') ; print(S)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since points are Sage Element's, the corresponding Parent being the manifold subsets, an equivalent writing of the above declarations is
" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point N on the 2-dimensional differentiable manifold S^2\n", "Point S on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "N = V((0,0), chart=stereoS, name='N') ; print(N)\n", "S = U((0,0), chart=stereoN, name='S') ; print(S)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Moreover, since stereoS in the default chart on $V$ and stereoN is the default one on $U$, their mentions can be omitted, so that the above can be shortened to
" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point N on the 2-dimensional differentiable manifold S^2\n", "Point S on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "N = V((0,0), name='N') ; print(N)\n", "S = U((0,0), name='S') ; print(S)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Open subset V of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N.parent()" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Open subset U of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S.parent()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have of course
" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N in V" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N in S2" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "False" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N in U" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "False" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N in A" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us introduce some point at the equator:
" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [], "source": [ "E = S2((0,1), chart=stereoN, name='E')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The point $E$ is in the open subset $A$:
" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E in A" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may then ask for its spherical coordinates $(\\theta,\\phi)$:
" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(1/2*pi, 1/2*pi)" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E.coord(spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "which is not possible for the point $N$:
" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "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": [ "Let us first declare $\\mathbb{R}^3$ as a 3-dimensional manifold covered by a single chart (the so-called Cartesian coordinates):
" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (R^3, (X, Y, Z))" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R3 = Manifold(3, 'R^3', r'\\mathbb{R}^3', start_index=1)\n", "cart.The embedding of the sphere is defined as a differential map $\\Phi: \\mathbb{S}^2 \\rightarrow \\mathbb{R}^3$:
" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [], "source": [ "Phi = S2.diff_map(R3, {(stereoN, cart): \n", " [2*x/(1+x^2+y^2), 2*y/(1+x^2+y^2),\n", " (x^2+y^2-1)/(1+x^2+y^2)],\n", " (stereoS, cart): \n", " [2*xp/(1+xp^2+yp^2), 2*yp/(1+xp^2+yp^2),\n", " (1-xp^2-yp^2)/(1+xp^2+yp^2)]},\n", " name='Phi', latex_name=r'\\Phi')" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Phi: S^2 --> R^3\n", "on U: (x, y) |--> (X, Y, Z) = (2*x/(x^2 + y^2 + 1), 2*y/(x^2 + y^2 + 1), (x^2 + y^2 - 1)/(x^2 + y^2 + 1))\n", "on V: (xp, yp) |--> (X, Y, Z) = (2*xp/(xp^2 + yp^2 + 1), 2*yp/(xp^2 + yp^2 + 1), -(xp^2 + yp^2 - 1)/(xp^2 + yp^2 + 1))" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.display()" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Set of Morphisms from 2-dimensional differentiable manifold S^2 to 3-dimensional differentiable manifold R^3 in Category of smooth manifolds over Real Field with 53 bits of precision" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.parent()" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Set of Morphisms from 2-dimensional differentiable manifold S^2 to 3-dimensional differentiable manifold R^3 in Category of smooth manifolds over Real Field with 53 bits of precision\n" ] } ], "source": [ "print(Phi.parent())" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.parent() is Hom(S2, R3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\Phi$ maps points of $\\mathbb{S}^2$ to points of $\\mathbb{R}^3$:
" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point Phi(N) on the 3-dimensional differentiable manifold R^3\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "(0, 0, 1)" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N1 = Phi(N) ; print(N1) ; N1 ; N1.coord()" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point Phi(S) on the 3-dimensional differentiable manifold R^3\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "(0, 0, -1)" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S1 = Phi(S) ; print(S1) ; S1 ; S1.coord()" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point Phi(E) on the 3-dimensional differentiable manifold R^3\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "(0, 1, 0)" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E1 = Phi(E) ; print(E1) ; E1 ; E1.coord()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\Phi$ has been defined in terms of the stereographic charts $(U,(x,y))$ and $(V,(x',y'))$, but we may ask its expression in terms of spherical coordinates. The latter is then computed by means of the transition map $(A,(x,y))\\rightarrow (A,(\\theta,\\phi))$:
" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(2*x/(x^2 + y^2 + 1), 2*y/(x^2 + y^2 + 1), (x^2 + y^2 - 1)/(x^2 + y^2 + 1))" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.expr(stereoN_A, cart)" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(cos(ph)*sin(th), sin(ph)*sin(th), cos(th))" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.expr(spher, cart)" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Phi: S^2 --> R^3\n", "on A: (th, ph) |--> (X, Y, Z) = (cos(ph)*sin(th), sin(ph)*sin(th), cos(th))" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.display(spher, cart)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us use $\\Phi$ to draw the grid of spherical coordinates $(\\theta,\\phi)$ in terms of the Cartesian coordinates $(X,Y,Z)$ of $\\mathbb{R}^3$:
" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_spher = spher.plot(chart=cart, mapping=Phi, number_values=11, \n", " color='blue', label_axes=False)\n", "show(graph_spher, viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may also use the embedding $\\Phi$ to display the stereographic coordinate grid in terms of the Cartesian coordinates in $\\mathbb{R}^3$. First for the stereographic coordinates from the North pole:
" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_stereoN = stereoN.plot(chart=cart, mapping=Phi, number_values=25, \n", " label_axes=False)\n", "show(graph_stereoN, viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and then have a view with the stereographic coordinates from the South pole superposed (in green):
" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_stereoS = stereoS.plot(chart=cart, mapping=Phi, number_values=25, \n", " color='green', label_axes=False)\n", "show(graph_stereoN + graph_stereoS, viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may also add the two poles to the graphic:
" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pointN = N.plot(chart=cart, mapping=Phi, color='red', \n", " label_offset=0.05)\n", "pointS = S.plot(chart=cart, mapping=Phi, color='green', \n", " label_offset=0.05)\n", "show(graph_stereoN + graph_stereoS + pointN + pointS, viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The tangent space to the manifold $\\mathbb{S}^2$ at the point $N$ is
" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "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": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_N = S2.tangent_space(N)\n", "print(T_N) ; T_N" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$T_N \\mathbb{S}^2$ is a vector space over $\\mathbb{R}$ (represented here by Sage's symbolic ring SR):
" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Category of finite dimensional vector spaces over Symbolic Ring\n" ] } ], "source": [ "print(T_N.category())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Its dimension equals the manifold's dimension:
" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "2" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dim(T_N)" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dim(T_N) == dim(S2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$T_N \\mathbb{S}^2$ is endowed with a basis inherited from the coordinate frame defined around $N$, namely the frame associated with the chart $(V,(x',y'))$:
" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "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": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_N.bases()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$(V,(x',y'))$ is the only chart defined so far around the point $N$. If various charts have been defined around a point, then the tangent space at this point is automatically endowed with the bases inherited from the coordinate frames associated to all these charts. For instance, for the equator point $E$:
" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "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": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_E = S2.tangent_space(E)\n", "print(T_E) ; T_E" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "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": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_E.bases()" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "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": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_E.default_basis()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An element of $T_E\\mathbb{S}^2$:
" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tangent vector v at Point E on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "v = T_E((-3, 2), name='v')\n", "print(v)" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v in T_E" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Tangent space at Point E on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.parent()" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = -3 d/dx + 2 d/dy" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display()" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = -3 d/dxp - 2 d/dyp" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display(T_E.bases()[1])" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = -2 d/dth + 3 d/dph" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display(T_E.bases()[2])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The differential of the mapping $\\Phi$ at the point $E$ is
" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "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": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E = Phi.differential(E)\n", "print(dPhi_E) ; dPhi_E" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Tangent space at Point E on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E.domain()" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Tangent space at Point Phi(E) on the 3-dimensional differentiable manifold R^3" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E.codomain()" ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "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": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E.parent()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The image by $\\mathrm{d}\\Phi_E$ of the vector $v\\in T_E\\mathbb{S}^2$ introduced above is
" ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "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": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E(v)" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tangent vector dPhi_E(v) at Point Phi(E) on the 3-dimensional differentiable manifold R^3\n" ] } ], "source": [ "print(dPhi_E(v))" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E(v) in R3.tangent_space(Phi(E))" ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "dPhi_E(v) = 3 d/dX - 2 d/dZ" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E(v).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The set $C^\\infty(\\mathbb{S}^2)$ of all smooth functions $\\mathbb{S}^2\\rightarrow \\mathbb{R}$ has naturally the structure of a commutative algebra over $\\mathbb{R}$. $C^\\infty(\\mathbb{S}^2)$ is obtained via the method scalar_field_algebra() applied to the manifold $\\mathbb{S}^2$:
" ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CS = S2.scalar_field_algebra() ; CS" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the algebra internal product is the pointwise multiplication, it is clearly commutative, so that $C^\\infty(\\mathbb{S}^2)$ belongs to Sage's category of commutative algebras:
" ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Category of commutative algebras over Symbolic Ring" ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CS.category()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The base ring of the algebra $C^\\infty(\\mathbb{S}^2)$ is the field $\\mathbb{R}$, which is represented here by Sage's Symbolic Ring (SR):
" ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Symbolic Ring" ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CS.base_ring()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Elements of $C^\\infty(\\mathbb{S}^2)$ are of course (smooth) scalar fields:
" ] }, { "cell_type": "code", "execution_count": 92, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(CS.an_element())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This example element is the constant scalar field that takes the value 2:
" ] }, { "cell_type": "code", "execution_count": 93, "metadata": {}, "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": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CS.an_element().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A specific element is the zero one:
" ] }, { "cell_type": "code", "execution_count": 94, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field zero on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "f = CS.zero()\n", "print(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Scalar fields map points of $\\mathbb{S}^2$ to real numbers:
" ] }, { "cell_type": "code", "execution_count": 95, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(0, 0, 0)" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(N), f(E), f(S)" ] }, { "cell_type": "code", "execution_count": 96, "metadata": {}, "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": 96, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Another specific element is the algebra unit element, i.e. the constant scalar field 1:
" ] }, { "cell_type": "code", "execution_count": 97, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field 1 on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "f = CS.one()\n", "print(f)" ] }, { "cell_type": "code", "execution_count": 98, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(1, 1, 1)" ] }, "execution_count": 98, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(N), f(E), f(S)" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "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": 99, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us define a scalar field by its coordinate expression in the two stereographic charts:
" ] }, { "cell_type": "code", "execution_count": 100, "metadata": {}, "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) |--> 2*arctan((cos(th)^2 - 2*cos(th) + 1)/sin(th)^2)" ] }, "execution_count": 100, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f = CS({stereoN: pi - 2*atan(x^2+y^2), stereoS: 2*atan(xp^2+yp^2)})\n", "f.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Instead of using CS() (i.e. the Parent __call__ function), we may invoke the scalar_field method on the manifold to create $f$; this allows to pass the name of the scalar field:
" ] }, { "cell_type": "code", "execution_count": 101, "metadata": {}, "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) |--> 2*arctan((cos(th)^2 - 2*cos(th) + 1)/sin(th)^2)" ] }, "execution_count": 101, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f = S2.scalar_field({stereoN: pi - 2*atan(x^2+y^2), stereoS: 2*atan(xp^2+yp^2)}, name='f')\n", "f.display()" ] }, { "cell_type": "code", "execution_count": 102, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 102, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.parent()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Internally, the various coordinate expressions of the scalar field are stored in the dictionary _express, whose keys are the charts:
" ] }, { "cell_type": "code", "execution_count": 103, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "{Chart (A, (xp, yp)): 2*arctan(xp^2 + yp^2),\n", " Chart (A, (th, ph)): 2*arctan((cos(th)^2 - 2*cos(th) + 1)/sin(th)^2),\n", " Chart (V, (xp, yp)): 2*arctan(xp^2 + yp^2),\n", " Chart (U, (x, y)): pi - 2*arctan(x^2 + y^2)}" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f._express" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expression in a specific chart is recovered by passing the chart as the argument of the method display():
" ] }, { "cell_type": "code", "execution_count": 104, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "f: S^2 --> R\n", "on V: (xp, yp) |--> 2*arctan(xp^2 + yp^2)" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.display(stereoS)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Scalar fields map the manifold's points to real numbers:
" ] }, { "cell_type": "code", "execution_count": 105, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "execution_count": 105, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(N)" ] }, { "cell_type": "code", "execution_count": 106, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/2*pi" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(E)" ] }, { "cell_type": "code", "execution_count": 107, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "pi" ] }, "execution_count": 107, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(S)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may define the restrictions of $f$ to the open subsets $U$ and $V$:
" ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "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) |--> 2*arctan((cos(th)^2 - 2*cos(th) + 1)/sin(th)^2)" ] }, "execution_count": 108, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU = f.restrict(U)\n", "fU.display()" ] }, { "cell_type": "code", "execution_count": 109, "metadata": {}, "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) |--> 2*arctan((cos(th)^2 - 2*cos(th) + 1)/sin(th)^2)" ] }, "execution_count": 109, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fV = f.restrict(V)\n", "fV.display()" ] }, { "cell_type": "code", "execution_count": 110, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(1/2*pi, pi)" ] }, "execution_count": 110, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU(E), fU(S)" ] }, { "cell_type": "code", "execution_count": 111, "metadata": {}, "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": 111, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU.parent()" ] }, { "cell_type": "code", "execution_count": 112, "metadata": {}, "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": 112, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fV.parent()" ] }, { "cell_type": "code", "execution_count": 113, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 113, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CU = U.scalar_field_algebra()\n", "fU.parent() is CU" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A scalar field on $\\mathbb{S}^2$ can be coerced to a scalar field on $U$, the coercion being simply the restriction:
" ] }, { "cell_type": "code", "execution_count": 114, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 114, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CU.has_coerce_map_from(CS)" ] }, { "cell_type": "code", "execution_count": 115, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 115, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU == CU(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The arithmetic of scalar fields:
" ] }, { "cell_type": "code", "execution_count": 116, "metadata": {}, "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) |--> 4*arctan((cos(th)^2 - 2*cos(th) + 1)/sin(th)^2)^2 - 4*arctan((cos(th)^2 - 2*cos(th) + 1)/sin(th)^2)" ] }, "execution_count": 116, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = f*f - 2*f\n", "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The set $\\mathfrak{X}(\\mathbb{S}^2)$ of all smooth vector fields on $\\mathbb{S}^2$ is a module over the algebra (ring) $C^\\infty(\\mathbb{S}^2)$. It is obtained by the method vector_field_module():
" ] }, { "cell_type": "code", "execution_count": 117, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Module X(S^2) of vector fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 117, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS = S2.vector_field_module()\n", "XS" ] }, { "cell_type": "code", "execution_count": 118, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module X(S^2) of vector fields on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(XS)" ] }, { "cell_type": "code", "execution_count": 119, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 119, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS.base_ring()" ] }, { "cell_type": "code", "execution_count": 120, "metadata": {}, "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": 120, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS.category()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\mathfrak{X}(\\mathbb{S}^2)$ is not a free module:
" ] }, { "cell_type": "code", "execution_count": 121, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "False" ] }, "execution_count": 121, "metadata": {}, "output_type": "execute_result" } ], "source": [ "isinstance(XS, FiniteRankFreeModule)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "because $\\mathbb{S}^2$ is not a parallelizable manifold:
" ] }, { "cell_type": "code", "execution_count": 122, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "False" ] }, "execution_count": 122, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2.is_manifestly_parallelizable()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On the contrary, the set $\\mathfrak{X}(U)$ of smooth vector fields on $U$ is a free module:
" ] }, { "cell_type": "code", "execution_count": 123, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 123, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XU = U.vector_field_module()\n", "isinstance(XU, FiniteRankFreeModule)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "because $U$ is parallelizable:
" ] }, { "cell_type": "code", "execution_count": 124, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 124, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U.is_manifestly_parallelizable()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Due to the introduction of the stereographic coordinates $(x,y)$ on $U$, a basis has already been defined on the free module $\\mathfrak{X}(U)$, namely the coordinate basis $(\\partial/\\partial x, \\partial/\\partial y)$:
" ] }, { "cell_type": "code", "execution_count": 125, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Bases defined on the Free module X(U) of vector fields on the Open subset U of the 2-dimensional differentiable manifold S^2:\n", " - (U, (d/dx,d/dy)) (default basis)\n" ] } ], "source": [ "XU.print_bases()" ] }, { "cell_type": "code", "execution_count": 126, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate frame (U, (d/dx,d/dy))" ] }, "execution_count": 126, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XU.default_basis()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly
" ] }, { "cell_type": "code", "execution_count": 127, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate frame (V, (d/dxp,d/dyp))" ] }, "execution_count": 127, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XV = V.vector_field_module()\n", "XV.default_basis()" ] }, { "cell_type": "code", "execution_count": 128, "metadata": {}, "outputs": [], "source": [ "eU = XU.default_basis()\n", "eV = XV.default_basis()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the point of view of the open set $U$, eU is also the default vector frame:
" ] }, { "cell_type": "code", "execution_count": 129, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 129, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eU is U.default_frame()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is also the default vector frame on $\\mathbb{S}^2$ (although not defined on the whole $\\mathbb{S}^2$), for it is the first vector frame defined on an open subset of $\\mathbb{S}^2$:
" ] }, { "cell_type": "code", "execution_count": 130, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 130, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eU is S2.default_frame()" ] }, { "cell_type": "code", "execution_count": 131, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 131, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eV is V.default_frame()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us introduce a vector field on $\\mathbb{S}^2$:
" ] }, { "cell_type": "code", "execution_count": 132, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 132, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v = S2.vector_field(name='v')\n", "v[eU,:] = [1, -2]\n", "v.display(eU)" ] }, { "cell_type": "code", "execution_count": 133, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Module X(S^2) of vector fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 133, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.parent()" ] }, { "cell_type": "code", "execution_count": 134, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate frame (W, (d/dxp,d/dyp))" ] }, "execution_count": 134, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoSW = stereoS.restrict(W)\n", "eSW = stereoSW.frame()\n", "eSW" ] }, { "cell_type": "code", "execution_count": 135, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 135, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW = v.restrict(W)\n", "vW.display()" ] }, { "cell_type": "code", "execution_count": 136, "metadata": {}, "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": 136, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW.parent()" ] }, { "cell_type": "code", "execution_count": 137, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Free module X(W) of vector fields on the Open subset W of the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(vW.parent())" ] }, { "cell_type": "code", "execution_count": 138, "metadata": {}, "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": 138, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW.display(eSW)" ] }, { "cell_type": "code", "execution_count": 139, "metadata": {}, "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": 139, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW.display(eSW, stereoSW)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We extend the definition of $v$ to $V$ thanks to the above expression:
" ] }, { "cell_type": "code", "execution_count": 140, "metadata": {}, "outputs": [], "source": [ "v.add_comp_by_continuation(eV, W, chart=stereoS)" ] }, { "cell_type": "code", "execution_count": 141, "metadata": {}, "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": 141, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display(eV)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At this stage, the vector field $v$ is defined on the whole manifold $\\mathbb{S}^2$; it has expressions in each of the two frames eU and eV which cover $\\mathbb{S}^2$:
" ] }, { "cell_type": "code", "execution_count": 142, "metadata": {}, "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": 142, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(v)\n", "v.display(eU)" ] }, { "cell_type": "code", "execution_count": 143, "metadata": {}, "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": 143, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display(eV)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "According to the hairy ball theorem, $v$ has to vanish somewhere. This occurs at the North pole:
" ] }, { "cell_type": "code", "execution_count": 144, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field v on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "vN = v.at(N)\n", "print(v)" ] }, { "cell_type": "code", "execution_count": 145, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = 0" ] }, "execution_count": 145, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vN.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$v|_N$ is the zero vector of the tangent vector space $T_N\\mathbb{S}^2$:
" ] }, { "cell_type": "code", "execution_count": 146, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Tangent space at Point N on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 146, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vN.parent()" ] }, { "cell_type": "code", "execution_count": 147, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 147, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vN.parent() is S2.tangent_space(N)" ] }, { "cell_type": "code", "execution_count": 148, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 148, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vN == S2.tangent_space(N).zero()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On the contrary, $v$ is non-zero at the South pole:
" ] }, { "cell_type": "code", "execution_count": 149, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field v on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "vS = v.at(S)\n", "print(v)" ] }, { "cell_type": "code", "execution_count": 150, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 150, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vS.display()" ] }, { "cell_type": "code", "execution_count": 151, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Tangent space at Point S on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 151, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vS.parent()" ] }, { "cell_type": "code", "execution_count": 152, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 152, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vS.parent() is S2.tangent_space(S)" ] }, { "cell_type": "code", "execution_count": 153, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 153, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vS != S2.tangent_space(S).zero()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us plot the vector field $v$ is terms of the stereographic chart $(U,(x,y))$, with the South pole $S$ superposed:
" ] }, { "cell_type": "code", "execution_count": 154, "metadata": {}, "outputs": [ { "data": { "image/png": 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WA+5YuzZYT6u2HnBHSUlwTM/MmbYnSY7QhZCJEwkgrpszhwDiun37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\nAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics object consisting of 27 graphics primitives" ] }, "execution_count": 154, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.plot(chart=stereoN, chart_domain=stereoN, max_range=4, \n", " number_values=5, scale=0.5, aspect_ratio=1) + \\\n", " S.plot(stereoN, size=30, label_offset=0.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The vector field appears homogeneous because its components w.r.t. the frame $\\left(\\frac{\\partial}{\\partial x}, \\frac{\\partial}{\\partial y}\\right)$ are constant:
" ] }, { "cell_type": "code", "execution_count": 155, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 155, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display(stereoN.frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On the contrary, once drawn in terms of the stereographic chart $(V, (x',y'))$, $v$ does no longer appears homogeneous:
" ] }, { "cell_type": "code", "execution_count": 156, "metadata": {}, "outputs": [ { "data": { "image/png": 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YAYAuXSR5tYrY2DgULhyGxo1jsXOntZM6ABg3DnjtNdePnz4dGD3ae/EQkTkY\nJqkDpB3HSy/JySyzqEaPBqKigP375XLggHy1v2Fnx17VS5vsVa9u/aqenb8md5s2ye4cyclye8YM\n868IvVVqqsy1vHoVqFzZWqtE7Xu/rlwZi06drJ/UXbggP0NXqnXdukmLF6v9zRKR+wyV1NmtXw/0\n7ZvxKtj58x0rG+2UAk6dck7y9u8HfvvNtXljwcFS1Us7hGu1qt6t/DG5+/RTGeYH5HUtXQp07ao1\nJI9r3FgWigDyQceVhtVmYE/qmjaNxY4d8qJeeAHYvl0udh06AKtWaQrSg3bulHNgdol5pUoyf7Zw\nYZ+E5ROHD8vPsEsXoEYN3dEQmYshkzog8+HYgwdd20UAkFVkhw45Ej1W9dLzt+RuwgTpfwgA+fPL\n71eDBnpj8qQhQ4APPpDr330HNG2qNx5PsSd19jl11avLm39AgCwIeeUV+Vv/+GPZEs6sdu6U0QpX\neivmySMLg6z0+wsA1aoBf/wh59lRo2QhlFU+nBB5m2GTOiD9cGyhQjIskSdPzv9NVvUy5i/JnVJA\nv37AF1/I7ZIlpbJVqZLWsDzmvfccDar/+19g6FC98XjKrUldRhV7M8ssmQsLy/xD6MyZ1tvP+Pp1\n+bCVVqlSsijooYckiSeizBk6qbPbtAn46CNpTtyli3eeg1U94Q/JXWIi0KaNtI4AgIgI4PvvrTGE\ntWMH0KyZXB88GJg9W288nrJ6dRw6dpSkrnr1UBw+bP4VzEDmyVylSrJYokMHOY/cOrfOqvPozpwB\nypTJ+LHGjYFZszJvvk5EJknqdPFEVS8yEnj1VUkizCSr5O4//wFWrjT3dm0XL8qbxLFjcrtVK+Db\nb83/JhkXJ9UdQFq57NypNx5PadYsDjt2SFI3f36o6at0CQnyIfXWpsr2ZK5/f8eIxK0rYY06j27P\nHokzMREoUkR6R4aHZ3391lGXw4dlJCQzNpv0XHztNaBYMe++HkAaum/dKrvSdOli/vPDlSvAc89J\ns+rx4+UrWQuTuhxwt6pXs6Ycb0aZJXcTJ8p9ZvbHH5L4xMTI7QMHgDvv1BuTJ1StKhPsy5eXxsNm\nl5AAFCgQByAMVavG4ujRUNNX6T7/3LH1GZBxMmeXdiWskefRde0q5wp3FCzonOylprrW1qpIEZlH\nOXiw90ZDkpOdfxZ16sh5z8zJ3aJF0j0CkHPf6tXy/04WosgjUlOVOnFCqRUrlHr1VaUeeECp6tWV\nKlJEqTe3Xfv9AAAgAElEQVTe0B1d7qWkKLV0qVINGypVoYJSP/6oOyLP+OEH+Tm1aKFUYqLuaDzj\n00+VKlFCfg+tIDlZqZ49YxUA9Z//tFOdOnVSCxYs0B1Wrhw/rlREhFK1ain18cdK3biR9fErVijV\nurVSy5f7Jr6cWLBAqUKFlJJxDN9cChdW6q+/vPN6UlKU6tUr/XPWqaPUsmVyzjeb06fl/8z+WmrW\nlPvIOlipI7+X2W4UZBz2hRKxsbEI5VJIw0pOBi5flukNFy/KLkGuXk9KytlzjholfSe9QSnZqWPS\nJGD3bufHzFq5O3BApgOdPSu3K1WSqSfVqmkNizyESR0RGR6TOmtTyrF/7csvu/59YWHAzz9nv6NO\nblktufvjD2nU/eefcrtkSekPm3avcDInLhAnIiKtbDaZX+dKiSEwUBYubN4sVT5vJ3T2+Dp0AH76\nSRoj16/veGzfPlmNXLeubM1nhjJJ1arSx9K+KOXsWaB5c5mvSebGpI6IiAzh4sXMHytdWipiJ08C\nX34JtGjh+8qYlZK7MmWkrVOjRnI7Nlaqd998ozcuyh0mdUREZAgZdRC45x5J4k6ckOHPzPrY+ZJV\nkrvwcGDDBkfLrYQE2ZFl4UK9cVHOMakjIiJDaN1avhYsKLuhHDok28A98EDudhLyFm8kd1evAikp\n3ok3IyEh0i/xgQfkdnKy7N7x/vu+i4E8h0kdEREZwoABQHQ08M8/ss1dVo2IjcRTyd28eZLQNm8u\nyZ2vBAdLde6xx+S2UpJU27foJPNgUkdERIZRtqxUj8woN8ldfDzw9NNy/fvvgeHDfRc3IAtQPvgA\nGDvWcd+4cRJTaqpvY6GcY1JHRETkQTlJ7mbNcl4oMm+eXHzJZgOmTAGmTnXcN2MG8MgjMixLxsc+\ndURkeOxTR2aWXZ+7MWOkMnfr6t/8+YFdu/QMQ3/yCfD4444qXZcuss1Yvny+j4Vcx6SOiAyPSR1Z\nQVbJXWbuuEMqfjqGpJculb1ib9yQ2y1bSnWRf4LGxeFXIiIiH8hqWDYzhw/7fn6dXffuwOrVjoRy\n82bg3nuB8+f1xEPZY1JHRETkQ2mTu/79sz9ex/w6u9atgU2bpKcdAOzZA9x9N3DqlJ54KGtM6oiI\niDS4ckUqdq4YOhT45RfvxpOZhg2B7dtlZTIAHD0KNG0qX8lYmNQRERFpcOuK16wkJADt2kkiqMMd\nd8h+sdWqye1Tp4BmzYCff9YTD2WMSR0REZGPJScD06a59z2nTgHt23snHldUqiSJXZ06cjsmRvbg\n3bpVX0zkjEkdERGRj125krOq259/ej4Wd5QsKQsmmjWT2/HxQNu2stUY6ceWJkRkeGxpQla0bp0k\nQ9nt2KCUVOmuXAGmTwfq1fNNfFm5dg3o1UtWxwKyI8WcOa4t/CDvYVJHRIbHpI7IeJKSgIEDgQUL\nHPe9/TYwcqS2kPweh1+JiIjIbXnyAJ9/Dgwb5rhv1ChgwoT0e9uSbzCpIyIiohwJCADefVcSObtX\nXgFGjMh+WJk8j0kdERER5ZjNBrz0kgy92v33v0DfvjJES77DpI6IiIhybeRI4LPPZNEEACxcCHTt\nKosqyDeY1BEREZFH9OsHLFsGBAfL7TVrpOXJ5ct64/IXTOqIiIjIYzp1knYthQrJ7e++kybFZ89m\nfPyvvwInT/osPEtjUkdEptG7d2907twZCxcu1B0KEWXhnnuALVuA4sXl9v790rD4r7+cj5s5U7Yg\ni4gAjh3zdZTWwz51RGR47FNHZE5HjwL33SfNkwGgTBlg/XqgZk3g00+lz53dqFHAjBlawrQMVuqI\niIjIK2rUAHbsAG6/XW7//TfQvDnw5pvAo486Hzt/PnDjhu9jtBImdUREROQ15csD27YB9evL7YsX\ngTFjgJQU5+NiYmRhBeUckzoiIiLyquLFgU2bst+3dt48n4RjWUzqiIiIyOtOnwZOnMj6mNWrgXPn\nfBOPFTGpIyIiIq86eVIWTMTEZH1ccjLwxRe+icmKmNQRERGR1yQlSQPi6GjXjp87F2BfjpxhUkdE\nRERec/gwcOSI68cfPAjs2+e9eKyMSR0RERF5Ta1awJNPAgULuv49H3/svXisjM2Hicjw2HyYyPwS\nE4Ht26VtyerVWe8gkScPEBcH5Mvnu/isgEkdERkekzoi6/n9d0eCt2VL+sbD69YBbdpoCc20mNQR\nkeExqSOytitXpI/dnDmSzJUsKVuMBQfrjsxcmNQRkeExqSMiyh4XShARERFZAJM6IiIiIgtgUkdE\nRERkAUG6AyDylAsXgNhYwGZz7fiyZYG8eb0bky/873/A448Dd90lq8jYAoCIyD9xoYQf+esv2Vev\nWjXdkXjeu+9Kc0t3FCsG7NkDVKjgnZh85bbbpDWA/frq1fLVSrhQgogoexx+tbjkZGDJEqBVK6By\nZeD224Ft23RH5Xnr17v/PTExwC+/eD4WXwsJcVz/7TegXj1g8WJ98XjTxYvA3XdLVfLCBd3REBEZ\nC5M6izpzBnj5ZaBSJaBnT+n/AwApKcCuXVpD84p333V/2LF0aaBFC6+E41Nlyzrfjo8HevcGnngC\nuH5dT0zeUr8+8N13si/kCy/ojsZ9v/8uf4+PPw4sXy69uYiIPIVJnYUoJVuw9O4tQ4oTJwKnT6c/\nrnBh38fmbZUqSWfyADd+o8eOBfLn91pIPpPZa549G2jcWKp3RjNlyhQ0bNgQoaGhKFmyJLp164Zj\nmewZpBTw0UdyPW11rkABHwTqYW+9JZXzjz4CunUDihaVjvlvv23MnxMRmQuTOgu4ckXewGvXBpo3\nl6G35OTMjw8P911svtSypSSyrihVCnjsMe/GYwT79hlzOHb79u0YMWIEfvzxR2zYsAFJSUlo06YN\nEhISnI6LjQUefBB45pn0/0aZMj4K1oNunQ544wbw7bfA6NFA9eoyF3LUKLkvMVFPjERkXkzqTO6z\nz4CwMBlqO3jQte+5dAmIjgauXpUqiJW8+KLMH8zOlSvAe+/J/4HV2Ydjhw41znDsmjVr0K9fP0RE\nRODOO+/EvHnzcPLkSezZs+fmMT//LAnpV19pDNTDIiOzfvz334GZM6V6FxoqSd66db6JzZtOnpQP\nnQ0byrmHiLyDLU28SCkgKcm7bTM++ABITXXvex591HE9b16p3BUpIl9duV62rHGHvgIDgS++AOrU\nAf75J/PjrlyR6s/UqcCYMcCQIc4LDqzo/feBU6eAlSt1R5Le5cuXYbPZEB4eDqUk1tGj02/wbXa1\na7t+7I0bkuT17QucP++9mDxJqYxbCj3/PHDggFzv3Vs2bw8yybtPUhKQJ4/uKDwrs58TWYAij0hI\nUGrPHqXmzFFq1CilWrZUqmhRpQIDlRo71nvPu2OHUgULKiV/pr65hIUptWWL916TJ2zapFRAQMbx\n33WXUjab830REUpdvqw76pzp2NH1n13x4rqjTS81NVV16NBBNW/eXF2+rNQDD2QUe6wC8O9XuW/q\nVN2Ru+/GDaXy5nXv761VK91Ru2b2bKWCgpRq0ECplSuVSk2V+3/9Nf3fmzfPiZ6SmqpUp05KFSok\n53Ur+P13pUqVUqpGDaVOn9YdDXmD5ZK6v/9WqmdPeeM+fNjz/35qqlLR0UqtXq3UlClK9e6t1B13\nSPKW2Uk5MtLzcaSVmKjUtGly8nHlTWLgQKW6d5fEs3ZtpSpUcD8xfPll774mT3jppfRxly6t1LVr\nSh06pNSDDzq/2fzyi+6Ic8bVpK5qVaU2bNAdbXpDhgxRlStXVn/88beqWTOz+O1JXTsFdFJAJxUR\n0Ul16tRJLViwQPdLcEudOq79vAIDlXr+eUdyZHTdujnHX6+eJHd9+mT8+tas0R1x1q5eVSo4WGIN\nCJBzvtl9+aXj/3/wYN3RkDdYqvnwt9/KUMW5c3J70CDHqrmcuH5d+pgdOADs3+/4evGia99furQM\nA06YADRqlPM4XHXmjAxzfPpp5scEBwMJCRmX3m/cAC5fltd38aLMvcvoeokS8jzFi3vvtXhCSgrQ\nti2wcaPjvpkznZsU//ILMG8eULEiMGyYOYckOnUCVq3K/PGqVYHx44GHHjLekNfw4cOxcuVKbN++\nHbGxFbKYcxYHIAxALABZbTB1KvDss76J05MGDsz6bxSQ1euLF/vmvOEpx47JopZ9+1w7vmhRObZc\nOe/GlRsvvABMmSLXCxaU7gJ16uiNKTcuXpROAfHxMqT8229y7iML0Z1VekJyslLjx6cv8dev79r3\n56T6lvaSN698+h4wQKm33pJqyLlzXn3JWfr+e/mUnFGspUvri0uHf/6R4QZAqbJlpUpnNZlV6qpW\nVWrePKWSknRHmLFhw4apcuXKqT/++EMpJX+Hzz0nQ3hWHX5VSs4RWZ1POnVS6sIF3VHmTGqqUsuX\nu16NbNrUuL+fSimVkuI8HaBMGaVOndIdVe6MG8dqnZWZPqn7+2+lWrTI+ISRL1/6E0ZCglK7d8sc\niZEjZQgyPNz1YcfSpZVq21apMWOUmj9fqYMHZZ6M0SQnK/Xhh0oVK+Yc/x136I7M9377TU5kZh1e\nzU6XLuZK5pRS6oknnlCFCxdW27ZtU//888/NS0JCgvrzT6Uef/zW5M46Sd2GDRmfW4KCJOEzy3Br\nVlJTlZo1y7VzqtHn1127plTjxo54IyOVio3VHVXOXbjgmKqTJ49Sf/2lOyLyJFMndd9+q1SJElmf\nMGbPVmryZKm+RUS4X33r319OtN9+q9TZs7pfsfsuXlRq+HDHooE+fXRHRJ62cKEkBNWqGT+Zs7PZ\nbCogICDd5dNPP715jHNyZ52k7ty59OebChWU2rlTd2SeldlcuowuRp9fd+6cUlWqOOK9/35z/J1l\nhtU66zLlnLqUFNkC65VX5Ncyt0qVkv5RtWvLJTJS9ki10jL2X38FfvgB6N5d+tqRtVy/7v42aWZx\n4gQwaVIc5s1znlP35psZNyU2gwoVpL0MAHTuDMyda62m4EeOAHfc4fr5uVAhmd9avrx348qNo0dl\nh5ZLl+T24MHSeseM83A5t866TJfU/fkn0LWro+eRO/LkkRONPXGzfy1RwvNxEpHnxMXFISwsDAMH\nxmL+/FAEBckesPXq6Y4sZ5YvB6ZPB3r1Mu8Cnaz07w98/rl731O6NPD3396Jx1O2bgXuu0961wHm\nXawDyOKpV1+V64MHy65EZH6mSuoSE6XK5M72OVWqSFXPitU3In9hT+piY2ORkhKKGzeAkiV1R0WZ\nqVsX2LvX/e9LSXFv/2Yd5s8H+vVz3P7qK6BnT33x5BSrddZksAYHWbt61f39EJOSpJUDEVlDkSK6\nI6DsvP22VCKvXcv+2HPngAsXZKcJoyd0gLTNOn7csc90v37SliWj9jOJidJGyojCw4GRI6Val5Qk\nrVtYrTM/U1XqAGDWLOC//5VhWFcTvAsXrDVfhcjfpK3UhYaG6g6H/JxSwMMPO/oNFi8uc5arVJHb\n164Bjz0mvQbHjnUMcxoNq3XWY4LPRc6GD5dJ/5cvy0bXTz4pzVWz4upG90RERNmx2YAPPwTuvVdu\nnz8PtG8vSdLZs0DLlsCCBTKc/NZb7o8w+Yq9Wgc4qnVkbqar1GVEKfmEsXq1XLZtc0xkBYC1a2Vn\nASIyJ1bqyIguXwaaNJFCAwDUry8J3okTzsdt3Qo0b+77+FzBap21mK5SlxGbDaheHRg9GtiwQYZb\nly4Fhg6VRRKtWumOkIiIrKZwYWDNGkcHhd270yd0ALB5s2/jcgerddZiiUodEVkbK3VkZBMnSgEh\nM/fcA2zZ4rNw3MZqnXVYolJHRETka0oBEyZkndABwM6dQEKCb2LKCVbrrINJHRERkZtSUqTJ8iuv\nZH/sjRuS2BnZ6NGyswcAzJmT8TAyGR+TOiIiIjctWyaNiF1l5Hl1AKt1VsGkjoiIyE2VK7u337LR\nkzqA1TorYFJHRETkpnr1gP37pVeqK2t3fvpJdkUyMlbrzI+rX4nI8Lj6lYzsyhXgiy9kt6Osmt2b\noWcqV8KaGyt1REREuVCwIDB4sFTutm8HoqIkIbrVu+/6PjZ3sVpnbkzqiIiIPMBmA5o1ky3CTp6U\nPV+LFXM8fv26vtjcwbl15sWkjoiIyMNKlQJefBE4cwaYMUPan3z1le6oXMNqnXlxTh0RGR7n1BH5\nFufWmRMrdUREROSE1TpzYqWOiAyPlToi32O1znxYqSMiIqJ0WK0zHyZ1RGQavXv3RufOnbFw4ULd\noRD5hcxWwl68CIwfD9x5J/Dmm/riI2ccfiUiw+PwK5E+48dLexYAGDAAKF8emDlThmUB2S7t6lUg\ngGUi7ZjUEZHhMakj0ufiRZlLd+VK5sekpDCpMwL+CIiIiChDFy9Kn70bN3RHQq4I0h0AERERGUti\nogy5ph1mJeNjUkdEREROxo/nAggz4vArEREROSlQQHcElBNM6oiIiMjJCy9IOxMyFyZ1RERE5CRv\nXmD6dGDZMqBwYd3RkKuY1BEREVGGunYF9u4FGjbUHQm5gkkdERERZapSJWD7dg7HmgGTOiIiIsoS\nh2PNgUkdERERucQ+HFu3ru5IKCNM6oiIiMhllSoBO3cC7drJ7Tp1uEWYUbD5MBEREbklb15gzRog\nNZUJnZHwR0FEREQ5woTOWPjjICLyouho4KmngI0bdUdCRFZnU0op3UEQEWUlLi4OYWFhiI2NRWho\nqO5wXKYU0Lgx8OOPQFCQtIVo1Eh3VERkVazUERF5ydq1ktABQHIy8OCDwMWLemMiIutiUkd+b9Mm\nYMoUICZGdyRkJUoBkyY533fyJDBwoDxGRORpTOrIbyUmAiNHAq1ayebVL76oOyKykrVrgZ9+Sn//\nypXAjBm+j4eIrI9JHfml48eBZs2Ad95x3Ldtm754yFoyqtKl9dxzwA8/+Cwcn7twARg3DmjeHFi9\nWnc0RP6DferI7yxdCjzyCBAb63z/sWNAQgKQP7+euMg6MqvS2dnn1+3dC4SH+y4ub7twQbaSeucd\n4MoVuS8+HujQQW9cRP6CSR35jcREYMwY5+pcWqmpwC+/APXr+zYuT7p+XeZtBbn4l12kiFzIc7Kr\n0tnZ59d9/TVgs3k7Ku/KKJmzi4/XExORP+LwqxddvAgsXw7ExemOJGsnTkjC44p9+6QKYbaJ3hkN\nt2Zk/37fxOMN584BYWFAjRpA1aquXYoXBz79VHfk2fvmG/m6d6/eOFyRXZUurZUrJRkyqwsXZC5q\npUrA5MnpEzqzO3lSho+TknRH4hlKAd99J+dxsiYmdV7yzTdARATQrZtcjOrpp+WE3Lo1kJKS+XE7\ndwL33w/cdZfs9zd7ts9CzLUlSyTu3buzP/bAAe/H4y2HDgE3brj3PSkpwI4d3onHU3buBHr3luuv\nvKI3luy4WqVL69ln5cOfmVy5Yu1kDpDKfb16QMeOwFtv6Y7GM7ZsAe6+G6hbF/jtN93RkDcwqfOw\nhARgxAigfXupnACyR54RLVzoqBJ89x2weHH6Y+zJXJMmwLp1jvuDg30TY2517Qr07Ol6tdTMlbqW\nLWVjbXc99JDnY/GUVauA++5z3N6ypTc6d+6MhQsX6gsqCydOuF6ls1NKPlyZyaOPWjeZs7t2zdHm\naMUKvbF4ir1CpxSwZ4/eWMg7mNR50P79Mh9r1izHfe3bG3N469gx4PHHne97+WVHtS6zZK5SJWDO\nHODhh30Wao4p5f7JeP9+8w0t29ls8km8UiXXv6dlS+Cee7wVUc4lJcn8x06dgKtXHfd/8MEirFix\nAlFRUfqCy0Lp0kCDBu5/3/33ez4Wb3K3ImxGBQs6/pYOHpTKndml/TDuDz9Df8SFEh6QmgrMnAmM\nHev4Q8mXD5g2DRg61HiToBMSgF690n/KPnoUePVVSejSJnKAnNzGjQP69wfy5PFZqLlis8mbpTtz\nAC9flr06y5f3bmzeEhYG/O9/koy7ctKeONH7Mbnr5EkZbt25M/1jhQr5Ph53BAfLDhIXLrj+O1eg\nABAS4t24PO2DD+T8sWGD7ki8KzIS+Osvea1//inzUM0sbVLn6jxqMhdW6nLp77+Btm1lw277m2jt\n2lLaHjbMeAkdAIwenfkw46RJ6StzH38slb1HHzVPQme3Zo2svvv6a6lMliuX/feYeQgWkHlArswB\nMmKVbtUqmf+YUUJnFjYbUKyYLEJx5WK2hA4ASpSQD0svvwwEWPhdpHZtx3Uzz7e1Y1JnfRb+c/S+\nZcuAO+90/rT69NPySf2OO/TFlZWFC+VTdnbMnsylFRICdO4sr/vkSUnapkyR1bAZvSGdOOH7GD1t\n2DCgR4+sjzFSlS7tcCv3RjWHwEBg/Hg5/5UqpTsa74iMdFw3+4c9wHl+N5M6a+Lwaw5cuSLVro8/\ndtxXpozMnWvdWl9c2cloHl1GSpUCfv1VhpCtxmaTE3VkpAyXX7wIrF8vbQvWrZNPsq1a6Y4y92w2\n4JNPpAXI8ePpHzdSlS6r4VYyvpYtZQJ+374ZD8eadY4q4Fyps0JSxzl11sdKnZt27ZLl4GkTum7d\npDRv5IQus3l0GfnnH9l1wR+Eh0tC8fnnslr51Cng9tt1R+UZYWHAl19mvPraKFW66GgZLmZCZ24l\nS2Y+HGvm5sNVq8qcR4DDr2QOTOpclJIiQ3ZNmjj6+xQoIMndkiVA0aJ648vOQw+590kz7UpYMq+M\n5tcZqUq3Y4ejbQSZW9rh2LTnw7Srl80mIECm2ABS8U7bGsmMFUgmddbHpM4FJ04A994LvPCC7NkI\nSNuCfftkvpkRF0Ok9fHHMv/PHUePciNuq7h1fp27zXG9qUsXY/fJI/e1bCnb7dnbgTRurDWcXEs7\nBPvKK8ATTwBNm0olvFo1WR1rFpxTZ32cU5eNRYuAIUMcm7/bbJLcTZxonsUDOZ34b+XGov7EZpPh\n5UaN5E2oeXPdETnkywfMny+LJF5+WareZH4lSzoqW2FhuqNxT3y8VBsPHJDRje3bHY9Nm5b+2O3b\n3esNqRPn1Fmf3yZ1330HPPmktCOZPDl9tS02Fhg+XN5w7CpUkNt33+3bWHNr0iRJ0KKjgerVZZgk\nO9WqAQ8+6PXQyEfy5weeeUZ3FJmLjJT+egcOMLmzCpvNfAndjRsy3OrOB+G6db0Xj6dx+NX6/DKp\nS0yUlVonTsjqwCpVgMceczy+Y4c8nras3qcP8N//AoUL+zzcXAsMBGbM0B0FUfayS+6MPtWBzO3a\nNfnw66qKFY3bviojTOqszy/n1M2e7fxJbNQoafeRlARMmCDDU/aELjRUqnNffGHOhI7IjOzJ3f79\nzvMB69fXFxNZX+HCwPPPu358+/bm+qDBpM76bEqZcQ1PzsXFyTL1W1fc1aolQ1S7djnua9pUEjqz\nzJcgsqo//ohDtWphiI2NRWhoqO5wyMKSk6U91dat2R+7ahXQoYP3Y/KUM2ekpyogi5SWL9cbD3me\n31Xqpk/PuIXCoUOOhC4wUFY5ubs5OhF5R/HiuiMgfxEUBCxYkP3vXL58stLXTLhQwvr8Kqk7dy77\nPTHLlJE5dePGyR83ERH5lzJlZJQmq6HVli0djYnNgsOv1udXSd1rr2XfpiMgAKhRwzfxEBGRMbVp\nA7z4YuaPm2nY1Y5JnfX5TVL355/A++9nf1x0tPSl86+ZhkREdKuJEzPffaV9e9/G4gmBgY7qI5M6\na/KbpG7iRFnd6orFi2W1KxER+a/M5tfVqAFUrqwnptyw2RzVOs6psya/SOr273duIuyK2bO9EwsR\nEZmHfX5dWvXq6YnFE+xJHSt11uQXSV3Pnu4NpwYFcTcFIiISbdrI+4hd2t6JZsOkztr8Yn1nZhsu\n58sn22bdfruU0+1fq1cHChXyaYhERGRgixdLV4SSJYHu3XVHk3N588pXJnXW5BdJ3aRJwIcfSoPh\n++6T5O3222Uv1wC/qFUSEVFuBATIPuFmxzl11uZ3O0oQkfnExcUhLIw7ShDlVs2awOHDQMGCQHy8\n7mjI01inIiIi8hMcfrU2vxh+JSIi8jdJScCGDcA//8hwa2IicOGC47ExY+R++1BsVBRw99364qXc\n4/ArERmeffi1Xbt2CAoKQlRUFKKionSHRWRoY8YAb77p+vHFigHnz3svHvI+VuqIyDQWLVrEOXVE\nLnJ3zlzp0t6Jg3yHc+qIiIgs6Mkn3evw8PTT3ouFfINJHRERkQVFRAADB7p2bLlyMqeOzI1JHRER\nkUVNmuToTZeVp592rIwl82JSR0REZFHlywPDh2d9THg4MGiQb+Ih72JSR0REZGHPPw9ktb5oxAhp\nRkzmx6SOiIjIwooWlfYmGSlQIPtKHukzadIk3HbbbUhJSXHpeCZ1REREFjdqFFCqVPr7Bw2S/nRk\nTHPnzkVgYCACAwNdOp5JHRERkcWFhAATJjjfFxgIPPWUnngoe0ePHsWpU6cwdOhQl7+HSR0REZEf\nGDRIFkXYtWgBVKyoLRzKxvr16xESEoKBrvalAZM6IrKAmJgYvPbaayhTpgz69Olz8/7U1FS88MIL\nKF68OMaMGYNz585pjJJIrzx5gOeec9x+5RV9sVD2NmzYgD59+ri1iw73fiUiw7Pv/RobG5vpCe7E\niRPYsmULhg0bhqNHj6Js2bIAgKSkJMyaNQujR4/2ZchEhrVli1TsIiN1R0KZSUlJQXh4OLZv345I\nN35QrNQRWUxiIjBjBvD++8CVK7qj8Z2tW7eiV69e6Nq1K2bOnHnz/p07d6Jp06YaI8vYunXAyy8D\nx47pjoT8TYsWTOiM7scff0RkZKRbCR3ApI7IchYulMnPQ4cClSsDb74JXL2qOyrvi4+PR/78+TFi\nxAh89NFHuHbtGgBg165daNCggebonMXFAZ07AxMnylZO/fszuSMihz179mB4DnrNMKkjspjoaMf1\nmBjpT1Wpkv8kd//5z39w++2345NPPgEAJCcnw2azaY7K2fnzwI0bcj01Ffj8cyZ3RFZ2+fJljB49\nGk7fKWoAACAASURBVCNGjEC7du0wd+5cJCYm4sknn8SIESPQt29f/PrrrzePHzFiBB588EG3n4dJ\nHZEfsHpyd+DAAdSsWfPm7eHDh2PmzJmIjY1FWFiYxshcx+SOyJqSkpIwdOhQPPfcc3j33XfxwQcf\nYNCgQejduzeefvppdO7cGV9++SXef//9XD8XkzoiP2LV5G7Hjh1o0qTJzdu9evXCtWvXMHr0aNxz\nzz0aI3Mfkzsia5k9ezaGDRuGUv92f86XLx+UUqhcuTIqVqyIlJQUVK9eHVFRUbl+LiZ1RH7IntzV\nr2+NxRTx8fHImzfvzdt58uTBkCFDsG7dOkRERGiMLOfsyV3NmsCmTbqjIaKcKlasmNNird27dwMA\n7r///ptfDx06hMaNG+f6uZjUkV86cwY4flx3FPodOQKYuXXb7t27MXDgQMyaNQvvvfee02NDhgxB\nx44dNUXmOcnJwA8/6I4ic0eOABcu6I6CyLhurcBt2rQJQUFBXlmVz6SO/E50NFCtGlC1KtC2LbBz\np+6I9LDZpPlolSq6I8m5+vXrY968eTh58mS6rXRKlCiBDz74QFNkntO0qaxkNqJPP5Vh4rJlgSef\nBE6f1h0RkfFt3rwZ9erVQ0hIiMf/bSZ1PrBw4ULdIVAau3YB/3a7wPr1QJMmQGTkQr9K7ooXB9au\nBcaN0x0JZeX556VRbOHCuiPJ2JYt8jUxEXj3XfmgdP/9C5ncGRzfk/S5fPky9u/fjxYtWjjdb1+t\nn1tM6nyAf0DGd/DgQjRp4h+Vu+bNgX37gDZtdEfiuosXLwKQLuv+oGhR4JtvgMmTgaAg3dG4LjER\nWLduIapWZeXOyPie5DsxMTFo2LAhxo8fDwD45ptvkJqaioYNGzods9NDbzxM6ojSsFfurJjc2WzA\niy8CGzcCZcrojsY1p0+fRpcuXVDl3zHiO++8Ex9//LHmqLyrWTNJuv+dQ21KaSt3TO7In23duhW7\nd+9Gnjx5cP36dXz55ZcoW7Ysrvy7Qu3q1at48sknMWnSJI88n+GSOl99grDiJxUr/t/p+jnZk7uu\nXR1DtZ7g29fjeK5ixaTy8+qrnq/8eOs13bhxA61atcKKFStg36L69OnTeOyxx/DFF1945TntfPdz\ncn6esWOBzZuBcuU8/Cya/o7SJnfTpnn23+b5zvj4fwe0bdsWgwYNwrlz5zBkyBC8/vrrWLp0KT77\n7DMMGjQITzzxBF544QWU89QfvTKYTp06WeZ59uxR6qGHlGrc2Dqv6f33lapQoZOKifH6UymlvPOa\nli5VCrj10imD++SyZInnntsXP6MmTZxfU/PmSkVHe+/5vPWaFi5cqABkeKlZs6ZXntPO2z+njRud\nf0ZFiyq1Zo33ns9br2fgQPf+lhITPffcvvhbmjtXqfLlO6kzZ7z+VEop77+ma9eUGj1aqerVO6nU\nVK8+lVLKd+/nvn4uI3PpM7tSCvHx8Z7JIrORnJyMuLg40z9PQgLQrp20iyhY0BqvaetW4IknACAZ\n06bF4fnnvfZUN3njNWVceUsGkP55ypUD6taVvTo9wRe/399/f/PZ8NhjcXj9danOeetpvfWasppj\n8ssvvyAmJsapN50nefvnNGXKzWdCeHgctm+XFaRm+xnZtzq75dmQ0d9Sz55yXrx+3TPP7e2f0a5d\nwMMPA0AyJk+Ow6uveu2pbvL2axo/HnjnHQBIxqZNcfD2lsi+ej/35XMVKlTIcNsOpmVT6t9xjSzE\nxcWZZqsdIiIiIm+IjY1FaGio7jAy5VJS58tKnRUkJACRkY6mrjt2ALVq6Y0pt7ZuBTp3luu33Qb8\n+CMQGKg3ppxauRLo2zfzxwMCgEmTgBEj5LrZnDsnE+1btgTy5NEdTc5duHABNWvWREJCQrrHRo8e\n7bGJxTqkpko7kNtuA8qX1x1Nzj3xBLBgQeaPlywJzJkjiz/MZNcuoHVruV6hArBnD+ClorDPOKp0\nwODBwNSpeuMxK6NX6lwafrXZbIbOTI1m7lxHQtejh0y4NzOlZJ9Qu5deAooU0RdPbhUokPlj5coB\nixeb+2cWGirNlc0uNDQUS5YsQVRUFGJjY2/e361bN0yZMgXBwcEao8u9rl11R5B7WSU6990HzJ8P\nlCjhu3g8Je2ijvHjZaGRmZ07B9gXjQcHAxMmyHmCrMeEdQhjS0gAXn/dcXvCBH2xuEsp2WFg0CDn\nbYk2bwa2b5frt98O9OqlJz5va99eKlxmTuispl27djh9+jQ+/PBDAMC2bduwdOlS0yd0VpGamv6+\ngABZZb12rfETujfflHlz9vMbIOe+tWvleqVKQP/+WkLzqGnTHHOJBw82T0sjygGdqzSs6O23HSu9\nevTQHY179u51Xql2//1Kff+9Unff7bhvwQLdUebenDnOrzMwUKmpU5VKSdEdGWUmNjZWAVCxsbG6\nQ6E0mjVz/lsqXVqpLVt0R+WaY8ecY7/3XqW2bZPznv2+jz7SHWXunT2rVIEC8nqCg5U6fVp3RORN\nJupVbnxmrtIBwL9N+29au9bxiRWwZpWuUCHp3+aFfZWJLC/tjOyGDWW+qtGrc3a3nu82bZKLHat0\nZEYcfvWgDz8E/vlHrvfoIYsl7AYPHoyAgAC8Y5+pakLBwTKB2OwGDJBFH82aAYcOJWPFiucQGRmJ\nggULomzZshgwYADOnDmjO0wiw5szByhdegqKFWuIX38NxZ13lkS3bt1w7Ngx3aHlWr58siDMzM6d\nA/77X7keHAw895xcnzJlCgICAvDUU0/pC468gkmdh2RVpVu+fDl++uknlC1b1veBedD+/UDjxtJ/\n76efdEeTcwEBwNdfyzyawoWvYd++fZg4cSL27t2LZcuW4ejRo+jSpYvuMIkMr3p1oE6d7Zg+fQR+\n/PFHbNiwAUlJSWjTpk2Gq5bN5MgR2Se5VSvpYGBGGVXpdu3ahY8++gi1a9fWGxx5h+7xX6vIbC5d\ndHS0Kl++vDp8+LCqVKmSmjlzpr4gs+Hocp/9JTBQ5ttZ0a5du1RAQIA6deqU7lDoX5xTZx7nz59X\nNptNbd++XXcoWfrhB9fPdwEBcn40k4zm0sXHx6vq1aurjRs3qhYtWqjRo0frDpM8jJU6D8isSqeU\nQv/+/TFmzBhEREToCc5LUlKAs2d1R+Edly9fhs1mQ+HChXWHQmQ69r+f8PBw3aF4TGoq8PffuqNw\nT0ZVumHDhqFTp06499579QZHXsOFEh6Q2Vy6119/HXnz5sXw4cP1BeclY8YAVhyhTExMxNixY9Gn\nTx8ULFhQdzhEpqKUwqhRo9CsWTPccccdusPxmBEjgKgo3VG4LqO5dIsWLcK+ffuwe/duvcGRV7FS\nl0uOKt0CAIXwzTeFEBoaim3btuGdd97B3LlzNUfoWeHhwKpVwBtvAAZuqp2pBQsWoFChQihUSH5O\nO9JMlklOTsYDDzwAm82G9957T2OUROY0dOhQHD58GIsWLdIdikeEhQFLlshODGbaQefWKl1qajRG\njRqF+fPnI4+Zt5mhbLm0TRhlbuZMYNQoALiKtm3Pwp4LfPnllxg3bpzTdiIpKSkICAhAhQoVcPz4\ncS3xZmXTJpkUnJnGjWW3BTNva3T16lWcTTNuXLZsWQQHB99M6P766y9s2rQJRcy8ZYYF2fefNvq+\ni/5s+PDhWLlyJbZv344KFSroDidbP/4INGqU+eP16gFffglUqeK7mDzh3DmgcmVJ6oKDgePHgV27\nvkb37t0RGBgI+1t+SkoKbDYbAgMDkZiYaOitr8h1HH7NBee5dCGYOrXKzRPA4MGD0dm+Weq/2rRp\ng/79++Phhx/2aZye8OyzwGuvmXsvUQAICQlBlVvO0vaE7vjx49i8eTMTOiI3DR8+HF9//TW2bt1q\nioQuOyNGyG4TZty4JKO5dK1bt8bBgwedjhs4cCAiIiIwduxYJnQWwqQuF7LqS1ekSJF0yUGePHlQ\nqlQp3HbbbT6M0nUZ1WzDw4HPPgM6dPB9PL6QkpKCHj16YN++fVi1ahWSkpJuVvLCw8M5VEGUjaFD\nh2LhwoVYsWIFQkJCbv79hIWFIV++fJqjc09oqPTe69FDdyQ5k1lfupCQkHRzHENCQlC0aFHLLeLz\nd0zqcignu0cY/dPQratZGzWS4QczD7dmJzo6GqtWrQIA1KlTB4BM9rbZbNi8eTOaN2+uMzwiw5s9\nezZsNhtatGjhdP/cuXPR38BbMly65Hy7bl0531WtqiceT3Bn9wijvx9RznBOXQ455tLJp7r//U9v\nPJ5w4oTMH0lNBXr2BBYsMP9wK1kD59SRp50/D5QuLe2Z2rUDli0z53CrXUZz6bglmP9hpS4HzL7H\na2YqVgSio+UTrIW6ERARpVO8OHDmjFzSTp0xK+7xSgBbmmTp6lXZH7R6dWDGDMcfTFZz6cyudGkm\ndETkH4oXN9/5e8YMoFQpoF8/4OhRuS+zuXTkfzj8moW1a6Usb1eyJPDUU8D06Y75Z/v3m++kQGQ2\nHH4lEuXLy4gKIPtY9+kjidwnn8h9Tz4p04PIP3H4NQuJic63z551/gTUpQsTOiIi8p2070upqcD8\n+Y7befKwSufvOPyaC9995zwsS0REpEtysmzhaB+WJf/DpC4XLlyQ4dgqVYD339cdDRER+TOlgC++\nkHnRffvKCl/yL0zqPODsWWDoUODbb3VHQkRE/i41VZK74cN1R0K+xqTOQwIDgRIldEdBREQkypbV\nHQH5GpM6DyhRAli3DqhdW3ckREREwDPPAG+8oTsK8jWufs2lli2lzF26tO5IiKyvd+/eCAoKQlRU\nFKKionSHQ2Q4RYoAn34KdOqkOxLSgUldDtlsspPE+PEy9EpE3rdo0SL2qSPKRKNGwOLFQIUKuiMh\nXZjU5UDJklKda9VKdyRERORPUlMzvv+ZZ4DJk7lft79jUpeFW5sPAzLcumCBbNNCRETkSwkJzrc5\n3EppcaFEFuxbgdlNnChtS5jQERGRDklJjut16wL79jGhIwcmdVl46CEgPBwoUECGWydN4vw5IiLS\np2tXICgI6NAB+OEHzp8jZzallNIdBBFRVuLi4hAWFobY2FgulCAiygQrdUREREQWwKSOiIiIyAKY\n1BERERFZAJM6IiIiIgtgUkdERERkAUzqiIiIiCyASR0RERGRBTCpIyIiIrKA/7d33+FNVu0fwL8p\nbSlYhkAdgMgUEChDcKDwIoosBUUZRUFxgMorCsgSVERFRRzwQ1wIwssQFEU2qCDDhQoUByAiQ0BQ\naJtCKZ3n98f95k3Spk3S5Ml5nqffz3XlasaT5k5Hcuc+59yHSR0RERGRDTCpI7Kw1FRgxw6A+8IQ\nERGTOiKLOnMGaNNGNvUePlx3NEREpBuTOiKLmjkT2L9fzk+bBixerDceIiLSy6EUB26IrObMGaBO\nHeDkSfd1FSoAP/4INGigLy6jpKeno1KlSnA6nahYsaLucKgIKSkyFaBqVd2REJVOrNQRWdDMmd4J\nHQCcPg306QOcO6cnJiq9lAJefRW46CKgRg1g717dERGVTkzqiDycOgXMng388IPuSIp25gzw8su+\nb9u5ExgxIrLxUOmWkgLceiswciSQkwNkZQFLl+qOiqh0YlJHBEnmxo8HatcG7rsPuO46wOnUHZVv\nvqp0nt58k/PrKDK+/RZo2RJYvtz7+l279MRDVNoxqaNSzTOZmzxZqmCAVBuOHtUamk/FVek8PfAA\nsG+f8fFQ6eQabm3XDjh8uPDtycmRj4mIgGjdAdhdXh5QpozuKMLHtazG4dAbR6hOnZI3penT3Ymc\nFfir0rm45td98w0QF2d8XEZzPeczZwCrr5O4/35g7lwgPh6oXx+I8vPROiZGqseDBkUmPn9SUoB7\n7gFWrCj6mN9+AzIzgXLlIhYWBUgpOfn7uyNr4q/VQG+8AVSqBDz9tO5IwkMpoHNnWdn29de6oymZ\noipzVhBolc5l506gXz/j4omUc+eAevXk/JgxemMJh9mzgdxcIC1N5m5u21b86auvgKFDzdFg2jXc\nWlxCBwD5+cAvv0QmpmBs3Qpcey3w/PPFH5eXByxcCDRrJh8iPvssMvEZSSlg3jzgkkuA5s2lcTnZ\nD5M6A737LpCRAcyYoTuS8DhxQl7cUlOB117THU3wduyQ5MBqyZzLwoWBVek8ffop8MEHxsQTCamp\n8ibsMn9+P/To0QOLFi3SF1SImjQJ/j6tW+uvjj/4INC2re/hVl/MNgR7+DDQs6d8IJ0wwfcHU1cy\n16QJcOedwM8/S9Xb6kldaiqQlATcfbdMK/n5Z07PsCsmdRGQkaE7gvCoVs09lGfFidDr1pl38UMg\nSjpckpkZ3jgi5bvvpCq0fbv7unHjPsDy5cuRlJSkL7AQff890KhRcPd56iljYgnU0qXA228HVy00\n02tETo5UrVNS3Nc984z7fMFkzrMlS/v2wKhRkYs13DZtksqc5+KpwYNlNxqyH86pM1DZsvI1K0te\nDHV/0g5VdLS86P34o3zKO3sWKF9ed1SBu+8+YMEC+ZRqRYMGSWIdSKUkPx/4/Xfg8svNMxcrUEoB\nr78OjB4tw5SeWrTQE1M4xcXJatErrpAqkD/XXgvccIPxcRWnZs3g72OmSt348TK/1NP69cCWLcCf\nfwKTJhXurdeunSR+HTpY87U7O1um/rz0kjsZr1xZkvM+ffTGRsZhUmeg2Fj3+dxcmfBsdc2bS1Kn\nlCRHV16pO6LAJSRI9WfYMOC993RHE7wyZaQfmJ2lpsok/IItMuymQQOZnhHInMeJE/UnFVddJZW3\n99+XyunWrYUT7oJ27TLHh9mVK4uei9qli3w49WT1ZA6QBPXOO+W12qVDB/ecOrIvDr8ayFWpA6Ra\nZweJie7zZhpeCVT58sCsWfLiZqUqY2ngGm61e0Ln0rcv8NBDxR9jhiqdS7NmwCuvABs3yoKjjz4C\n7r1XdpHwJTUVOHYssjEWdPiwzCMrimdC164dsGGDDFdef701Ezql5MNCq1buhC4mRqp1n3/OhK40\nYFJnIDsmdc2bu8+baXglWAMGyMrDpk11R0JKycKb664DDh3SHU1kvfpq8UPKZqjS+VKxInD77VLx\nPnpU/pcmTZKKniveChVk9b8uvubR+VK5svWTOUAWUd12m8yXcyWrDRvKsPPo0fZqrUVFY1JnIM/h\nV7skdVav1Hlq3FiqQ/fdpzuS0isnB+jVS7Y28zecZ0dxccCSJZIAFWSmKl1xoqJkfuCTT0rLkxMn\nZNX19u3Si08XX/PofElLkw/gVk3mAJkf2KyZ/NxdHnxQqnVXXKEvLoo8JnUG8qzUZWfriyOcqlRx\nT5pOTjZH76xQeA7HFmyUmpOjJ6bSZPlyYNky3VHo5ZpfV5BZq3T+JCQAPXpIY2VdPv00uJ6Onith\nreTcOWD4cOkfevy4XFetmjz/N98EzjtPb3wUeUzqDGTH4VfAXa1zOmWxxKZNsjPD4MEyBJOXpze+\nkhgwQD7VVqvmvu7CC/XFU1q0aOH9My+tCs6vs0qVzoz27ZOh4WCsXx9YVc9MXAvVXn/dfV3nzsBP\nP0lSTaUTV78ayE7Dr3l58mKZnCzDFS6ew7EurVoBN98cudjCpXFj4MABaUzarl3RE8ApfOrVA/bs\nseaWbeH26qsy/2vPHuCtt6xZpTODWbNK9sFy61bgmmvCH0+4KSUN7UeNcr+vlC0LTJkC/Pvf3P6r\ntGNSZyA7DL8qJXtVLlwopf5AVKlibExGio/3/uRLxqtaVbZtGjGidCd3cXHW3v3DLIYNk9er1FRZ\nBBHI/rO1a8uOC7p9/LEk9oMG+V7YcPy43LZ2rfu6Zs2k/2azZpGLk8yLSZ2B7DD8evCg7FUZqCpV\nZAUcUbCY3FE41KghDYWtZtky97Dx3r2F5wSuWCEtZDy3CnzsMeCFF9w7/RCxUGsgOyR1tWsH12C4\nSxcunafQuJK7gweBJ57wXkHJPltkR7m5wNix7suvvCJtVgBpT/LQQzJPzpXQXXSRVOtee40JHXlj\nUmcgzzl1Vh1+dThkSCjQflPduxsbD5UensndSy/JdU2aaA2JyBBz53pvU6YUMHCgNHpu1UrmWLr0\n7CntpDp3jnycZH5M6gxkh0odANSpA8yZ4/+4qCi+0FD4Va0qPbeI7CgzU/ZoLejoUVkB7Ur2ypeX\nfVs/+UTaxhD5wqTOQHZJ6gDpVP7oo8Ufc/XV8gZMRESBeeMNSeB8cfUBveIKaeY8eDBXRVPxmNQZ\nyE4tTQBZMt+6ddG3c+iViChwaWnA5MnFHxMbK83RGzaMTExkbUzqDGSHliaeYmOBxYuLnl/HpI6I\nKHAvvyytV4qTnS2rXrnDDQWCSZ2B7DT86lK3ru8WJzVq+G5ETEREhf31l6xeDcR33wHPPmtsPGQP\nTOoMZLfhV5devaTBp6f27TnXg4goUBMnyiKJQD3/vHt/V6KiMKkzkN2GXz1NmQJUr+6+fPXV+mIh\nIrKS7duBd94J7j7R3CqAAsA/EwPZcfjVpWxZYN06aTackOC9GTkRERVtwgT/xyQkyOKIRo3kdPPN\n3I+a/GNSZyA7J3UA0LQpcOSI7iiIiKzl1luBNWvkfK1aQIsW7uStYUM5sT0UlQSTOgPZPakjIqLg\nDR4M3H23zEP2nHtNFComdQaywzZhREQUfp4f+onChUldmOXmSgKXlQWcPu2+/q+/gB9/dN+WkABc\nfjlXjBIREVF4OJRybURCoVAKuOsuYNEi99Yu/rz9tpThiah46enpqFSpEpxOJypWrKg7HCIiU2JL\nkzDJyAAWLgw8oQOAw4eNi4fIjvr164cePXpg0aJFukMhIjIdVurC6KabgM8+C+xYhwPYvZv7+REF\ngpU6IiL/WKkLoxdeCPzYXr2Y0BEREVH4MKkLoyuuAPr0CezYMWOMjYWIiIhKFyZ1Yfbcc0CZMsUf\n07Ej0KZNZOIhIiKi0oFJXZg1aADcf3/xx4wdG5lYiIiIqPRgUmeAp54CypXzfVvLlsCNN0Y2HiIi\nIrI/JnUGqF4deOwx37eNHcuGw0RERBR+bGlikLQ0oG5dIDXVfV29esDevf7n3BGRN7Y0ISLyj5U6\ng1SuDIwb533dqFFM6IiIiMgYrNQZKDNTkrvsbCAmBkhPB+LidEdFZD2s1BER+cdKnYHKlQOWLpX2\nJYsWMaEjIiIi47BSR0Smx0odEZF/rNQRERER2QCTOiIiIiIbYFJHREREZANM6oiIIuD0aelfSURk\nlGjdARAR2V1yMtCqFZCfD0yYAEyaZN6dZQ4fBl58EUhIAKpU8X98dDTQpYs0VycivZjUEZHlKGXe\npMiXTz+VhA4AnnsO2L8fePttoEIFvXH5ctVVwPHjwd3n4oslGYw2yTtKaqq0kTp3Dhg6FChbVndE\nRJHB4VciG3ElDna1Zo30f4yNBbZs0R1N4GrX9r68aBFwxRVSwTObmJjg75Oba47dcrZvB+6/H6hR\nQ5K5kSOB2bN1R0UUOUzqiGzinnukUtKqlQzxffMNkJenO6rCcnNzMWbMGCQmJiI+Ph41atTA3Xff\njb/++qvI+7iS1X79pPqSmwu8+26EAg4DXxWsffukKvb221J5NIvVq4OvbD32mL7KaVYWMH8+cM01\nkii/957s5uPiuf82kd0xqSOyiQ8/lORgxw7g+eeBtm2BCy8E7rpLKkMpKbojFGfPnsXOnTvx9NNP\nY8eOHfjkk0+wd+9e9OzZ0+fxJ08CvXsXvr5OHYMDjYCsLODBB4H+/WUbQTNo2hRYuDDw46tUAf79\nb+PiKcqhQ7K/ds2awIABwLff+j4ukHmBRHZhkhkQROZ06hTw559Aixa6I/GvTh3gl1+8rzt1Cliw\nQE5RUVLN6N4d6NYNSEzUU12pWLEi1q1b53XdjBkzcNVVV+HIkSOoWbPm/67fulWqc0ePFv4+8fFG\nRxo5H3wA/PgjsGSJOf7WevUChg0Dpk/3f+y99wKR3ORj7lzgnXckiQtkusH55xsfE5FZsFJHVIS0\nNBnOadkSGDtWdzT+JSYWf3t+PvDVV8ATT0jicN55wPffRyY2f9LS0uBwOFC5cmUAEuuLLwIdOvhO\n6Oxo3z7g6qvNM6w8ZQrQurX/4157DRg8GDh40PCQMGqUTDP4+uvA54+uXg288YZUq9euBbZtA37/\nXT7wmHF6AlEoWKkz0JkzwObNwLXXApUq6Y4mPA4dkhfEjh2ttfqwOF9/LXOIWrXyfk7Tp8vzBYCX\nXpIqVxEjhKbQvLm8cQUqMxOYMUMqHzplZWVh7Nix6N+/P+Lj43HypAynrV2rNy4dsrIkQWrZMrCE\nykhlywKLF8v/hdNZ9HF5eZKIzpkDDBoEPPusDPsb4c8/g7/PvHlyKkrlylLNq1LF/dXzfKNGUtmO\nsngJJC9PPjj8+itw2WUyzE42pMgwAwYoBSh1xRVK5ebqjiZ0Z84oVbWqPKeBA5XKz9cdUehWr5bn\nAyjVvr1SGzbI80pNVapyZfdtgFw+cEB3xEVbs8Y7Xn+n+Hil9u41Pq4FCxao+Ph4FR8frypUqKC2\nbt36v9tycnLULbfcolq3bq1Onz6ttmxRqkYNX/E6FYD/fpXrpkwxPvZwWbAg8N9LTIxSP/2kO2K3\npUt9x3n++UqNGaNUxYre17dta1wsmZlK3XyzUlFRwf2th3qaOjW0uPPzldq3L3LvA6dOKbVxo1LT\npil1771KtW6tVFyc99/Yb79FJhaKLFbqDJSRIV9//FE+8fbvrzeeUEVHy6pDQD751q0LPP203phC\n5VmZ27xZKpDt28tzK9j9Py0N6NtXWmnExkY2zkD4G371dNddwJtvRmZeWs+ePXH11Vf/73KNGjUA\nyCrY3r17488//8SGDRuQnh6PLl3c/ze+9YNrgGHOHPldJCUlISkpybgnEEEdO0ofOzNVUYqaX/f4\n4zKUP2YM8PrrckpPN7aCHxcHrFgB/PabrLhds8b/fRYuBLKzZRVsSoqcfJ1PTS16SDeU53TsiM05\nnQAAIABJREFUmLz2b9okFb9Vq0r+vQrKzZXq265d0h7H9fXIkeLvp5Q5WtCQAXRnlXa2YYP7k1HD\nhvao1n30kVIOh/t5zZunO6LQLVkiv59AP7UPH647Yt/y85WqVq342MuVU2r2bP1V1pycHHXrrbeq\nxMREderUKaWUUocOSQXBd+z2rtR17KjUpk26oyzauXNS7XHFW6WKUk6n9zEpKUqtWydfIyE/X6nl\ny5WqW7fon6vDoVReXmDfLy9PqbQ0pf74Q6kfflDqs8+UWrxYvubklCzGdeuUSkjwjik1tWTfy1/1\nrbiTw6FUgwZK3XGHUpMmKbVrV8liIPNjUmeg/HwZ0nP9Yy1YoDui8Hj5Ze8y/saNuiMKXW6u/H4C\nTe6WLdMdsW8dOxYdc6NG5hjWy83NVT169FC1atVSu3btUsePH//faf36bK/kwe5JndmTOU/79yt1\nwQUS94wZuqNxy8xU6vnnlSpfvvDPt0oVPTHl5Cg1frz3B2DXyd/vOydHqV9/VeqDD5QaN06p7t2V\nqlkz8A+dFSsqdd11Sg0dqtQ77yj17bcydYZKByZ1BrNjtS4/X6kHH3Q/r8qVldq9W3dU4XHypO83\nh4Ins86vGz7cd7wDBih1+rTu6MTBgwdVVFSU18nhcKioqCi1adMmlZ+v1MqVqkByZ+2kbuVK6yZz\nnv75x7xVnsOHlerb1/vnXL9+5OM4etT7w3zB0//9n/vYcFbfPv1UXpN0V+FJLyZ1BrNrtS4nR6mu\nXd3Pq04dpU6c0B1V6J55JvBPxFdeqVRWlu6Ivc2Z4x2jWYZbS8I7ubN2UpeZqdQDDyjVp481kzkr\n2bhRqWbN5G/kyScj+9i+hlsLnpo3Z/WNjONQSim9s/rsb+NGmQANAA0bSoNYO0xSPX0aaNfOvX/l\n1VcDGzbI3pxWlJYmDXwLLpAoTt++0jjWLPbvl3YF+fnSiuHDD8016b4klAI++igdffpUAuAEIJ1u\nZ8yQ/T2JClJKdiJJSIjM4+XmAhMnApMny2OXlMMB1K8v7YkSE91fL73UPi2kyFhM6iJAKWmiunmz\nXF6wwPorYV2OHpX9K10NYm+/XbriW7Gn0/TpwKOPBn+/Tz8FevQIfzwltW6dJHcDB9pn14X09HRU\nqlQJS5Y48dZbFZGXJz35Lr5Yd2RU2h04IB/ag22+XLFi4eStaVNpCk5UUkzqIsSu1TpAKnXXXSfN\nlgHp+j5lit6YSmLGDOCRR4K/35IlvvcmpfBxJXVOpxMVI7knFZEfl18O7N4d3H2++AK4/npW3yj8\n2KcuQjp0kP5nmzcDe/fao2+dS/Pmktjccot0LX/5ZaBePWDIEO/jTp1y94Iz4w4bDz4om4P76/EE\nyPDmvn2y3RYTOqLSq1at4JO6U6eY0JExWKmLIDtX6wDgrbeAhx6S82XKACtXAl26yOXvv5ek78QJ\n4LbbgI8/1hcnWQ8rdWRWeXnA/PnAl19KM+z9+/3fZ/x4aTJNFG5M6iLIznPrXEaNAqZOlfPx8cDW\nrTLnpH9/2WsUAGJipHs7545QoJjUkRUoJRX8VauA1atlF4mcnMLH9ewJLFsW+fjI/pjURZjdq3X5\n+UCfPsDSpXK5UiXZOqjgX9m6dcBNN0U+PrImJnVkRadPA59/Lgne6tWyZRgg265Nm6Y3NrInJnUR\nVhqqdZmZ8hy3bSv6mLFjgRdeiFhIZHFM6sjqlAJ27pQ5u507m3P/aLI+CzaesDaHQ/oZuUyaJHMy\n7CQvz/9CiI0bIxMLEZEZOBxAy5Yyt5gJHRmFSZ0GrpWwgHslrF0cOybP7bPPij/uhx9kaIKIiIjC\ng0mdBnat1h0/Lo2Id+zwf2xenqwUIyIiovBgUqeJHat1S5cG1uPNhUOwRERE4cOkThM7VutuuUW6\nqweKSR0REVH4MKnTyG7Vulq1gJ9+kqX7N9/sv2P6jh1AWlpkYiMiIrI7JnUa2bFaFxUFdO0KrFgh\nndVHjwaqVvV9bH6+JIBEREQUOiZ1mtmtWuepTh3gpZdknt3cucCVVxY+Zs6cyMdFRERkR0zqNLNj\nta6guDhg4EDgu+9kD9g77nAPzV5zjd7YiIiI7II7SphAadhloqCTJ6UFStOmuiMhK+COEkRE/jGp\nMwm77wlLFAomdURE/nH41STsPLeOiIiIjMekziRKw9w6IiIiMg6TOhPxV63LyACOHo14WESm0a9f\nP/To0QOLFi3SHQoRkelwTp3J+Jpb53QCr74KTJ8OnDkjyV7v3nrjJIokzqkjIvKPlTqTKVitu/12\noHZt4PnngdOnZaXs2rU6IyQiIiIzYlJnMg4HMGKE+/Knn0oy54m1VSIiIiqISZ2JpKQAEyYAAwbo\njoSISos9e4CePYF33pGt+4jIupjUmcTbb3sPsxKRvXTuDFSrJvsim0nXrsDy5cCQIUCtWsDLLwOn\nTumOiohKgkmdCWRnAw8+yGSOyK62bQPWr5dkqV8/cyVN5cu7zx89CoweDdSoAdxzj2zrR0TWEa07\nAAJiYoBu3YDVq3VHQkRG+Pxz9/mzZ4G775bqWJQJPlYPGQI8+qj3dVlZwNy5cmrTBnj4YaBvX6Bc\nOePj+fln4OuvgerV3XtEF+eCC4DWrQM7lsju2NLEJLKzgXHjpHWJP4MGAbNnGx8TkVlYvaVJ+/bA\nli3e102ZAowapSceT3v2AI0b+z+uShXgvvuAoUOBSy81JpZffwWaNAn+fmb5WRLpZoLPiQQAsbHA\nK6/Iatfzz9cdDZF1ZGQAbdsC550HvPWW7mgKS02VylNB48b5vj7SGjYELrrI/3EpKTLfrkUL4MgR\nY2JJSyvZ/f76K7xxEFkVkzqT6dED2LEDuOoq3ZEQmd8vvwBNmwLffCPDmi+8oDuiwtat873lX16e\nDGnqnl/ncADXXx/48WlpkuAZoW1beQ0MhsMBPPCAMfEQWQ2TOhO69FJg82Zg5Ejft3PAnAh4/32Z\n73XwoPu6ChV0RVO04ubKHjki8+t0txIJJqmbPBlITDQuliVLZI5coPr1C2z4mKg0YFJnUrGxwNSp\nvodjPd/EiEqbjAxZmTloEJCZ6X3bxRdrCalIeXnAmjXFH7NqlUy90CmQpC42Fli4UIaNjVS2rGyF\nWKmS/2MdDuntGWl5eVIdnjBBtnUcP54ftskcmNSZnGs41vOTaFaWvniIdNq9W6pzc+f6vt1sKyC/\n/x44edL/cbrn19WrB9SsWfTtDof8zJOSIhNP3bqBLQZTChg8WFYXG51UpaQAixYBd90FXHihDBU/\n/7zs1z15MnD8uLGPTxQIJnUWcOmlwM6dwK23Ag0amHMyOFEkdOggiZ1VBNqmyDW/TlevSn/z6pQC\nnn7auLl0vvTqBQwb5v+4r74COnUC2rULb3KnFJCcLAnbddcBCQlA//7AggWF50FGRQVWWSQyGpM6\ni4iNBT75BPjtN2PnsxCZTUaGNOcGgHPn9MYSrFWrAj/2yBHg22+Ni8UfX0ndlVcCl10m53/7Dbjt\ntsiOFEyZUvT8urZtvUcwwpXc5ebK94mPl5W+48fL9y5u3mODBt5NnIl0YVJHVIps2yYrq+vV83+6\n8EJ5o2raFMjJ0Rdz794y7GU1x48D27cHdmxsrOy/2ratsTEVp2BS17cvsGmTrN698EK5bvNm6VUX\nqfljRc2vcziAWbOAn34CPvggvMnde+/J/c6eDfw+/KBNZsGkjqgUmTlTErs//vB/+vtvWYjwyy/e\nOyJE2q+/6nvsUKSmFn97w4YylPfTT8CZM8CyZdJrT5fatWUBSrlysgBg4UIgLk6uX7HCvZvEggUy\nFBspvubXuVa8likjyWc4k7sbbwSig9xr6bffpKq4bp30zOOiCdKFO0oQlSKzZ0ulJRgVK0qCV7as\nMTH58/33wODB6di5sxIAJ4Cid5To1En2WDWLt96Sal2jRkDz5sDllwN16sgQZsOGspuD2eTm+k5q\nli2TeW6ud4w5cyQJjJTHHgOmTZNEc/t2321M8vKAjz4CJk0q/GHg2muBiROBG27wv6Dm0CHg9tuB\nH38sWawJCfL7Tkx0f23cWN//EJUeTOqISpGcHJkjFWhbnLg4eWO7/HJDw/LL6UxH5cqV0KKFEzt3\nWiep8+WKKyQpiYqShRFWmov12mvAiBFyPjpaKlMdO0bmsZWSOYq1avkf7gxHcpebCzzzjKxwDce7\nZHS0O7n3TPYuush8q7bJupjUEZUy770H3H9/YMfOnQsMHGhsPIFw7f26dq0TXbpYO6kbNEgaJwMy\nFN6mjdZwgqIU8MgjwBtvyOVKlaQVi+6kvyjhSO7Wr5c2Jv/84/v2ypWlrclPP8lq2V275OvffwcW\nY0KCO8ljVY9CxaSOKAzOnJE5SE2ayJuFWeXlyZyo++/3v/jh3nslATQDV1J3/fVObNwoSd2wYTJv\nynOIrFu34Fac6vD668Dw4XL+3XcDT7DNIjdX2iu5fs61a8uqXddiCjMKNbk7dkx69G3eXPi29u1l\nQUlBJ054J3m7dslj5+b6j5dVPSoxRUQhGzVKKaljKNWrl1IHDuiOyFturlILFijVsKE7zuJOTZoo\nlZGhO2o3p9OpACjAqQCl6tZVKjtbqfx8pVasUOrKK5U67zylPvxQd6T+bdjg/jk/8ojuaErm9Gml\nWrZ0P482bcz191KU3FylPvhAqcsvL/w3f+21Sn32mfxN+ZKTo9SECUo5HN73C+Z3mJWlVHKyUvPm\nKfX440p16qTUBRcE9j8JKJWQoNSNNyo1YoRSc+cqtWOHUufOhednQ/bASh1RGHTpIvOLXOLigLFj\ngdGj3asGdcjLk5YQkyYBe/d631a2rO+eY+XLAz/8YK79NF2VOtdCidmzZRjTk1LWqGKcOgVUqybn\ni6ryWMGxY9Ie58gRuXzrrVINK1NGb1yBCKVyV3A4NhxTFFjVo3BhUkcUBldeKas0C7r0UuDVV6Vp\nayRfYItL5tq1kwng+/cDDzxQ+L5mmUfnaf36dHTuLEld3boVsWcPEBOjO6qSq1kTOHpU5mOlpFj3\nzXfXLtltwbUTxvDh8vduFSVN7o4dA556Sha7zJghfQbDLTtbdk/xTPSCnavHFbilD5M6A23fLv/w\nvXsDXbvqjiY83ntPJnf37w/861+6owldRgbw5JPAgQNAlSpyOv/8os9XrCgv5AXVry9JUlFuvBGY\nPj0y1a+ffpK/uaKSuQ4d5E3K10pYM82j89SxYzo2bpSkbvbsioWqdFbTrRuwZo2cP3RIVnRa1fr1\n8nzy8uTym2+6dwCxCn/J3ccfAxdcoCe2gsJR1evTR/YbDrYfH1mAzrFfu+vUSeZBOBxKzZihO5rQ\nOZ3e8zs6dFDqyy91RxWa2bMDn88CKBUVpVTVqkrVry/zuDp3ViopSamyZf3fNzpa5sI4ncY+p27d\nvB+3XTuZx+VrrtCsWeadR+dy9qz671w6qNq1nSo7W3dEoRs71v1z37JFdzShe+cd9/OpU0d3NCVX\n1Jy7UaN0R1a8rCyldu6UuXojRwY2V+/bb3VHTUZgUmegKVO8/4kmTSp6Eq4V5OTIJN2CLw5WTu72\n7FHqkkuCS+xCPcXEKDV/vnHP6Z13ZNHAv/5VdDLnkpOj1MMPS3K6b59xMYUiN1epLl0kqWvTpqu6\n5ZZb1MKFC3WHFZIDB+TvrmVLpdLTdUcTHi++qFSFCkqNHq07ktDl5Sm1eLFSzZsrVbmyUp9/rjui\nkjl+XKl165R6+WWl7rpLqcREef1JTLTP3x154/CrgZSS7XYmT3Zf9+ijMufE1xCeFeTmynY8kyYB\n+/Z539ahg8xBsdqwbG6uzFNJSZGtnVJSAjufllbypqR16shWXBQY10IJp9OJihWL7lNnNVZZ3BGo\n/HzrvraVFvwd2RuTugh45RXg8cfdlwcOlHlLVp7PYMfkLlj5+ZLY7dwpk6kD5XAAL7wAjBljXGx2\nY9ekjogonJivR8DIkZLEuT4dzZsn+wpmZuqNKxTR0bKs/9dfgf/8B2jQwH3bl19KYtexo3XbNQQi\nKkoWUASaYzRuLAtn0tKY0BERUfgxqYuQe++V1VWupe/Ll8uK2PR0vXGFqrjkbuPG0pHcpaQUfVuZ\nMsAdd8jP4pdfgKFDA08CiYiIgsGkLoJuuw1YvRqIj5fLmzYB119f9J6CVlKak7u0tMLXXXSR9LE6\ndAj48EN3GxEiIiKjMKmLsBtuADZsAKpWlcvbt0v/sMOH9cYVLp7J3bx54UnucnNLviAhElq1As47\nT863by9Nfw8flp5wNWrojY2IiEoPJnUatGkjG0O73vD37pUGl3v26I0rnKKjgQEDQk/u5syRDug9\nekiHdTOqXx/4/Xepym3aJI09rbzbARERWRNXv2p06BDQqZN79Wi1atJlvnVrvXEZITcXWLQIePbZ\nwqtlr78eePrpwqtl09KA2rUBp1MujxwJTJ0akXDJZLj6lYjIP1bqNLr0UmDrVqBFC7l88qQkOBs3\n6o3LCCWp3E2b5k7oAGkNs3x5xEImIiKyFFbqTMDpBG65BdiyRS6XLSvzsnr21BuXkfxV7kaMkLl5\nnkkdIPuv7tghCTGVHqzUERH5x6TOJDIzZS7WypVyuUwZ6W1399164zJaccldUa66SuYkutrDkP0x\nqQs/pYA33pCN6vv00R0NEYUDh19Nolw54OOPgTvvlMt5ecA99wCvvaY1LMMVNyxblO++A554wvjY\niOzs2WeBRx4B+vYF+vUz70IkIgockzoTiYmRxOaRR9zXjRgh+8favZ7qmdzddpv/4zm/jig0v/3m\nPr94MXDddcCBA5F7/Guvlde8li2Bd94BjhyJ3GMT2RWTOpOJipIFAhMnuq97/nnZiSA/X1tYEXPm\njPTxC8Q998gKYiIr2b5d+hqefz5w7Ji+OBo29L78/feSYH3yifGPrRTw9dcy/WLnTmDIEOCSS4Dm\nzaUKv3Wr3EZEwWFSZ0IOh7T4mD7dfd2bb8rQrN2HSAqueC1OaqpstWb3nwnZy9ChwNmz0rJnyBB9\ncZQpU/g6pxPo1Qt47DFj/68cDunvWNCuXcALL0hD9gsuAPr3B+bPl84AROQfkzoTe+QR2XLL9eL7\nwQfArbfKG4IdZWYGP4dw926ZE0RkBYcPA9u2uS+vWQMcPKgtnCJNm2b8cKznaIQvqamyiGrAAEnw\nuna1x5aKREZiUmdyd90FLFsGxMXJ5TVrgJtu8r3fqNWlpQHp6cHfb9eu8MdCZIRXX/WeRpGXJ3sE\nm5HRw7G33QYEupBZKWDtWs6jJfKHLU0sYvNm6WXnSnoSE4F162TjeDtZvBhYvdr/wpD8fJlPl5UF\nzJxpz104yM0OLU1OnpT+igUr7Q4HkJwMNGsW2XgmTwbGjw/s2LFjZVg03AYPBt59N7Bjzz9fPsDV\nrFnyx/v5ZxnxqF07sJZI8fHyITo+vuSPSRRJTOosZMcOoHNn9xBEvXrAZ58BderojYvIaHZI6iZO\nBJ55xvdtN98MrFgR0XCCSuoAWS0bSMuhYHz9tayC9ee884DPPweuvrrkj5WbKyMeeXnB3a93b2DJ\nkpI/LlEkcfjVQlq2lFVhtWrJ5f375QXx55/1xkVkVkrJpP+YGKmE6foIm5EB/N//FX37ypXyv21W\nzZoB1auH//tecw1w2WXFHxMTI0PAoSR0LiX5/Z8+HfrjEkUKkzqLuewy4KuvgEaN5PJffwHt2wPf\nfqs3LiKzcTqBO+6QSf+5ufLhJyVFTyyzZvl/7LFjzdePsnp1SUa3bZNqWbg5HNKaqDgVK7o/yIYi\nOlr6WwbLs28okdkxqbOgmjVln9g2beRyaipwww0yFEtEwI8/Aq1ayS4tnnS0v8nJCSyZ+OorYNUq\n4+MJ1IgRMhrw73+7F2oZYcAA6c9ZlFOnZCXu9u2hP9ZjjwEPPRT48W3ayKpbIqtgUmdR1aoBX3wB\ndOwol8+eBbp3Bz76SG9cRDopBcyYAbRtC/zxh+5oxKJFwJ9/BnbsuHHBz/kKp8qV3ed/+cXYZM6l\nZk2gU6fC148fL82IAVlk0qEDsGlT6I/36qtAixaBHTtunFQTiayCSZ2FVaggn+xd22rl5EjPtkBX\nkxHZidMpk9ofecQ8Danz84GXXgr8+J9/jtwHM88hTdcw6+HDsjIUkNX133wTmVgKDsGOGgU89xzw\n5ZfuhRSnT8tCsVDbmsTFycKHChX8H/vww9IEPjMztMckihQmdRbneoEaNEgu5+dLm4Ci3kjy86Ut\nQFZW5GIkMppruHXpUt2ReDtxQvYzDobnnqxG6tdP9lx9/333MGuFCrLXtEtRq3XDrWdP97ZlQ4a4\nX78qVwbWrwe6dZPLWVmy48W8eaE9XoMGgX34PX4cePRR6TTA5I6sgC1NbEIp+XTrOXdn1Ch5cXQN\nH2RmSuuEDRtkZ4pI7PFIFA6uliZdu3ZFdHQ0kpKSkJSUBKWAN94ARo4MrDp37Bhw8cXGx+uiFHD/\n/VJdiomR3mgOh3sXiYQEoGlToGxZOdWuDTz5JFC1auRiLCgnRxZkuWL8+mtZpWq09HSpFDZt6jum\ne+4BFi50X/f665JwheLhh2ULxoKaNJGfQcHXyIsvlgUtDzwAlCsX2mMTGUKRbeTnK/XCC0rJW4mc\n7rtPqdxcpbKzlbr5Zu/bdu/WHTFRYJxOpwKgnE6n1/WzZ3v/Tfs7HTum6Ql4+OMPdzz9+umOxrdZ\ns9wxdu6sOxqRl6fU0KHev88nn5TXvZLKzFSqRYvCfyerVsntO3cq1atX4dsvvlipadOUOns2PM+N\nKFw4/GojDod8inzrLXd17r33gD59gIEDpReWp7lzIx8jUTj99ZfuCIJXtqz7vFmnQQwcqGduXXGi\nomTe35NPuq979lmZQ+m59VowfM2v81zx2ry5DOnv3CnDvi5//cVhWTInJnU2NGSIrLiLiZHLH38s\nW+MUNG+e3pV2ZA9KybDmqlXSMiKSCcDjjwNjxgDly0fuMUNlhaQuJkbP3Dp/HA5g0iTgtdfc173x\nhrRFyckp2fds0ED6CEZFAWXKyHZoBVe8Mrkjq+CcOhtbt072iy3uxW7tWllRRuTPuXPAvn3Anj3A\n3r3ur3v3enfdL1NGjo2ODt9j+9sm7J9/gKlTZZ5VcXPrIj2nzpfTp90b2d9wg2x/ZUa65tYFat48\n4N573R9Mu3UDPvyw5An+Tz/JB5TERP/HJidLclmwDyLn3JFurNTZ2N69/j+9zpkTmVjImvbsAW6/\nHahbV94sExNlOP/JJ4EFC4AffvC9jVKke3slJEgLjAsvjOzjloRnpc4srVd8KVitmzhRWyg+DRwo\nSZXr57l6tXxATUsr2fdr1iywhA5g5Y7Mi0mdTc2fH9jKsGXLZEcKIl+efVbeOA8cCHwLq1GjpFoX\nafPmuZv8Xn89MHp04apNbGzk4yrINS0CMO/wq8vAgUCdOnJ+/XpzzK3z1KOHjDa45sRt3SpNik+c\niMzjM7kjs2FSZ0NbtvjfT9ElKwtYvNjQcMjCgt1EvWZN4OmnjYmlODk5Uqlzef55aedz8KAkd5dc\nIkNiOluFuDgc7uqS2ZO6mBjZ2cHFLHPrPHXoAGzcKLvsADI0et117mHjSGByR2bBpM6GliwJbgHE\n++8bFgpZ3MMPA+3bB378M89EZmupgubNc7+Jd+7snvuVkCDJ3eHD0mjXLFwVQzMPv7qYcSVsQVdc\nIR9mL7lELv/+u+xEEWzj51AxuSPdmNTZ0ODBgc8NAYDvvgN27zYuHrKuMmUkYapUyf+xjRpJAhBp\nBat0OiqFwbJKpQ4w70rYgho1kuFX184Ux44B7drJ61ukMbkjXZjU2VCzZjIEsX+/9HXq0sV7crYv\nnr2fiDxVrw507Oj/uMmTw7viNVBz5/qu0pmZlZI6wBrVOkD2s92yRSp3AJCSoneFMZM7ijS2NCkl\nMjJke7DVq6WfmGtCuUulSiVfNUb29fvvwJ13Atu2FX/cVVfJG71Rq16LammSnS2VGVdS9803wc8D\n1KFePeCPP2Qe2D//6I4mMO+9J1ueAZI8r12rN57ipKfLfrJffimXY2Nli7Hbb9caFluhkOFYqSsl\nzjtPeta9+SZw6BCwa5dUVmrWlCG2O+7QHSGZiVLS7qZFC3dCFxUlG6z78uKLkW9jAnjPpevSxRoJ\nHWCtOXUuVqnWAdIHcM0aWR0LyM+5Tx9JTHVi5Y6MxkodEXlJSZF5mUuXuq+rV0/60uXmysIJz22Z\nIlG18VWps2qVDpBkOTlZhmHPndMdTeCsVK0D5O/1/vu9t0ScMkXa7pgBK3cUbqzUEWk2YYK8ubdq\nJXMbv/lG3/ZtGzbIIhvPhO6++6SycNVVsqLQc9I8INsq6WDVKh3gPafOSh+rrVStA2SO5+zZsn2d\ny+jRkjCZ4efOyh2FnSIirerUUUreYtynqlWVuvNOpRYuVOrUKeNjOHdOqVGjlHI43DGcf75SH31U\n+NicHKVuuEGOGTrU+NiUUsrpdCoAyul0KqWUyspSqnZtd6zffBOZOMKlXTt37NnZuqMJzqxZ7thv\nukl3NIHJz1fquee8/8ceeECp3FzdkXnbuVOpXr0Kvx5cfLFS06Ypdfas7gjJ7Dj8SqRZx47SPLUo\nUVGyorN7dzk1axbe+Wu7dwP9+0u1wOWGG2TIqkYN3/fJzZW5mXXrRmYuXcHh11mzZGgKkCrdmjXG\nxxBON94IfPGFnD99GoiP1xtPMAruCfvVV0DbtlpDCtibbwJDh7qrdL17A//5j//uAJHGYVkqKQ6/\nEmnmr6dgfr68cT7xhAzXlC8vQ1+hUgqYOVOGfV0JXUwMMHWqbAlVVEIHyLBWvXp6FkdkZ8uOES5W\n6EtXkGcSYZW2Ji5W6Vvny0MPydxQV+udDz+UBWRnzuiNqyAOy1JJMakj0qx58+COP3cOePnl0B7z\n77/lzWzoUPdE/caNZaXryJFSHTQrK8+lc7FyUgd4z61bvx74+mut4QQlKQn49FN3pesgETg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"text/plain": [ "Graphics object consisting of 82 graphics primitives" ] }, "execution_count": 156, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.plot(chart=stereoS, chart_domain=stereoS, max_range=4, scale=0.02, \n", " aspect_ratio=1) + \\\n", " N.plot(chart=stereoS, size=30, label_offset=0.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, a 3D view of the vector field $v$ is obtained via the embedding $\\Phi$:
" ] }, { "cell_type": "code", "execution_count": 157, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_v = v.plot(chart=cart, mapping=Phi, chart_domain=spher, \n", " number_values=11, scale=0.2)\n", "show(graph_spher + graph_v, viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, let us draw the first vector field of the stereographic frame from the North pole, namely $\\frac{\\partial}{\\partial x}$:
" ] }, { "cell_type": "code", "execution_count": 158, "metadata": {}, "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": 158, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ex = stereoN.frame()[1]\n", "ex" ] }, { "cell_type": "code", "execution_count": 159, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_ex = ex.plot(chart=cart, mapping=Phi, chart_domain=spher,\n", " number_values=11, scale=0.4, width=1, \n", " label_axes=False)\n", "show(graph_spher + graph_ex, viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the second vector field of the stereographic frame from the North pole, namely $\\frac{\\partial}{\\partial y}$, we get
" ] }, { "cell_type": "code", "execution_count": 160, "metadata": {}, "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": 160, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ey = stereoN.frame()[2]\n", "ey" ] }, { "cell_type": "code", "execution_count": 161, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_ey = ey.plot(chart=cart, mapping=Phi, chart_domain=spher,\n", " number_values=11, scale=0.4, width=1, color='red', \n", " label_axes=False)\n", "show(graph_spher + graph_ey, viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may superpose the two graphs, to get a 3D view of the vector frame associated with the stereographic coordinates from the North pole:" ] }, { "cell_type": "code", "execution_count": 162, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_frame = graph_spher + graph_ex + graph_ey + \\\n", " N.plot(cart, mapping=Phi, label_offset=0.05, size=5) + \\\n", " S.plot(cart, mapping=Phi, label_offset=0.05, size=5)\n", "show(graph_frame + sphere(color='lightgrey', opacity=0.4), \n", " viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The same scene rendered with Tachyon:" ] }, { "cell_type": "code", "execution_count": 163, "metadata": {}, "outputs": [ { "data": { "image/png": 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WrQe3bj345JPvtLX5gBhQDDgAO2AHQkAMyAVEQAWygDggAGHAAQhAFBCBqMul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\nDxBpqY8//nhJNHbuMdnRAVi+u7n5w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EAFGeJ+0pAxcf+c0ZpkuR828Wc7X41dPL6CPcPD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\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CcT9BsXDhwl/+8pcvvfTS5/S1Ogo4hgiYzYOJRKnJ1CciQH6/I5EISJK1oSG/m53eCzIa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fF2BhJIzGj9Gtt+r1GqdT/Om8zfe3frYiOJYTSwrSosMACjRxAHSxOqF5UJJGzdUwpHqwI+Pf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\nQQB4sv8DLz/ZOh6CHa0AAAAASUVORK5CYII=\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph_frame + sphere(opacity=0.5), viewer='tachyon', figsize=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$v$ and $f$ are both fields defined on the whole sphere (respectively a vector field and a scalar field). By the very definition of a vector field, $v$ acts on $f$:
" ] }, { "cell_type": "code", "execution_count": 164, "metadata": {}, "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) - cos(ph) + 2*sin(ph))*sin(th)/(cos(th)^2 + 1)" ] }, "execution_count": 164, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf = v(f)\n", "print(vf)\n", "vf.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Values of $v(f)$ at the North pole, at the equator point $E$ and at the South pole:
" ] }, { "cell_type": "code", "execution_count": 165, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "execution_count": 165, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf(N)" ] }, { "cell_type": "code", "execution_count": 166, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "4" ] }, "execution_count": 166, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf(E)" ] }, { "cell_type": "code", "execution_count": 167, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "execution_count": 167, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf(S)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A 1-form on $\\mathbb{S}^2$ is a field of linear forms on the tangent spaces. For instance it can the differential of a scalar field:
" ] }, { "cell_type": "code", "execution_count": 168, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1-form df on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "df = f.differential() ; print(df)" ] }, { "cell_type": "code", "execution_count": 169, "metadata": {}, "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": 169, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.display()" ] }, { "cell_type": "code", "execution_count": 170, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module Omega^1(S^2) of 1-forms on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(df.parent())" ] }, { "cell_type": "code", "execution_count": 171, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Module Omega^1(S^2) of 1-forms on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 171, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.parent()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The 1-form acting on a vector field:
" ] }, { "cell_type": "code", "execution_count": 172, "metadata": {}, "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))/(cos(th)^4 - 2*cos(th)^3 + 2*cos(th)^2 - 2*cos(th) + 1)" ] }, "execution_count": 172, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(df(v)) ; df(v).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us check the identity $\\mathrm{d}f(v) = v(f)$:
" ] }, { "cell_type": "code", "execution_count": 173, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 173, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df(v) == v(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, we have $\\mathcal{L}_v f = v(f)$:
" ] }, { "cell_type": "code", "execution_count": 174, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 174, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.lie_derivative(v) == v(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to define curves in $\\mathbb{S}^2$, we first introduce the field of real numbers $\\mathbb{R}$ as a 1-dimensional smooth manifold with a canonical coordinate chart:
" ] }, { "cell_type": "code", "execution_count": 175, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Real number line R\n" ] } ], "source": [ "R.Let us define a loxodrome of the sphere in terms of its parametric equation with respect to the chart spher = $(A,(\\theta,\\phi))$
" ] }, { "cell_type": "code", "execution_count": 179, "metadata": {}, "outputs": [], "source": [ "c = S2.curve({spher: [2*atan(exp(-t/10)), t]}, (t, -oo, +oo), name='c')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Curves in $\\mathbb{S}^2$ are considered as morphisms from the manifold $\\mathbb{R}$ to the manifold $\\mathbb{S}^2$:
" ] }, { "cell_type": "code", "execution_count": 180, "metadata": {}, "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": 180, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.parent()" ] }, { "cell_type": "code", "execution_count": 181, "metadata": {}, "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": 181, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The curve $c$ can be plotted in terms of stereographic coordinates $(x,y)$:
" ] }, { "cell_type": "code", "execution_count": 182, "metadata": {}, "outputs": [ { "data": { "image/png": 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Hb7zBPuykn6FDZQdoxQrVkSjF7XRn0TTpUT1wIFC0qFT3Nm2qOiqyE7fTc+nL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\nAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 182, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.plot(chart=stereoN, aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We recover the well-known fact that the graph of a loxodrome in terms of stereographic coordinates is a logarithmic spiral.
\n", "Thanks to the embedding $\\Phi$, we may also plot $c$ in terms of the Cartesian coordinates of $\\mathbb{R}^3$:
" ] }, { "cell_type": "code", "execution_count": 183, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_c = c.plot(mapping=Phi, max_range=40, plot_points=200, \n", " thickness=2, label_axes=False)\n", "show(graph_spher + graph_c, viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The tangent vector field (or velocity vector) to the curve $c$ is
" ] }, { "cell_type": "code", "execution_count": 184, "metadata": {}, "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": 184, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc = c.tangent_vector_field()\n", "vc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$c'$ is a vector field along $\\mathbb{R}$ taking its values in tangent spaces to $\\mathbb{S}^2$:
" ] }, { "cell_type": "code", "execution_count": 185, "metadata": {}, "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 $\\mathfrak{X}(\\mathbb{R},c)$; it is a module over the algebra $C^\\infty(\\mathbb{R})$:
" ] }, { "cell_type": "code", "execution_count": 186, "metadata": {}, "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": 186, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent()" ] }, { "cell_type": "code", "execution_count": 187, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Category of modules over Algebra of differentiable scalar fields on the Real number line R" ] }, "execution_count": 187, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent().category()" ] }, { "cell_type": "code", "execution_count": 188, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the Real number line R" ] }, "execution_count": 188, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent().base_ring()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A coordinate view of $c'$:
" ] }, { "cell_type": "code", "execution_count": 189, "metadata": {}, "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": 189, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us plot the vector field $c'$ in terms of the stereographic chart $(U,(x,y))$:
" ] }, { "cell_type": "code", "execution_count": 190, "metadata": {}, "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, number_values=30, scale=0.5, color='red') +\n", " c.plot(chart=stereoN), aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A 3D view of $c'$ is obtained via the embedding $\\Phi$:
" ] }, { "cell_type": "code", "execution_count": 191, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_vc = vc.plot(chart=cart, mapping=Phi, ranges={t: (-20, 20)}, \n", " number_values=30, scale=0.5, color='red', \n", " label_axes=False)\n", "show(graph_spher + graph_c + graph_vc , viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Riemannian metric on $\\mathbb{S}^2$\n", "\n", "The standard metric on $\\mathbb{S}^2$ is that induced by the Euclidean metric of $\\mathbb{R}^3$. Let us start by defining the latter:" ] }, { "cell_type": "code", "execution_count": 192, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "h = dX*dX + dY*dY + dZ*dZ" ] }, "execution_count": 192, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h = R3.metric('h')\n", "h[1,1], h[2,2], h[3, 3] = 1, 1, 1\n", "h.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The metric $g$ on $\\mathbb{S}^2$ is the pullback of $h$ associated with the embedding $\\Phi$:" ] }, { "cell_type": "code", "execution_count": 193, "metadata": {}, "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", "\n", "The metric is a symmetric tensor field of type (0,2):" ] }, { "cell_type": "code", "execution_count": 194, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module T^(0,2)(S^2) of type-(0,2) tensors fields on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(g.parent())" ] }, { "cell_type": "code", "execution_count": 195, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(0, 2)" ] }, "execution_count": 195, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.tensor_type()" ] }, { "cell_type": "code", "execution_count": 196, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "symmetry: (0, 1); no antisymmetry\n" ] } ], "source": [ "g.symmetries()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expression of the metric in terms of the default frame on $\\mathbb{S}^2$ (stereoN):" ] }, { "cell_type": "code", "execution_count": 197, "metadata": {}, "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": 197, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may factorize the metric components:" ] }, { "cell_type": "code", "execution_count": 198, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "4/(x^2 + y^2 + 1)^2" ] }, "execution_count": 198, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[1,1].factor() ; g[2,2].factor()" ] }, { "cell_type": "code", "execution_count": 199, "metadata": {}, "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": 199, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A matrix view of the components of $g$ in the manifold's default frame:" ] }, { "cell_type": "code", "execution_count": 200, "metadata": {}, "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": 200, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display in terms of the vector frame $(V, (\\partial_{x'}, \\partial_{y'}))$:" ] }, { "cell_type": "code", "execution_count": 201, "metadata": {}, "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": 201, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(stereoS.frame())" ] }, { "cell_type": "code", "execution_count": 202, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = dth*dth + sin(th)^2 dph*dph" ] }, "execution_count": 202, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(spher.frame(), chart=spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The metric acts on vector field pairs, resulting in a scalar field:" ] }, { "cell_type": "code", "execution_count": 203, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field g(v,v) on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(g(v,v))" ] }, { "cell_type": "code", "execution_count": 204, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 204, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(v,v).parent()" ] }, { "cell_type": "code", "execution_count": 205, "metadata": {}, "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": 205, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(v,v).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **Levi-Civita connection** associated with the metric $g$:" ] }, { "cell_type": "code", "execution_count": 206, "metadata": {}, "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": 206, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab = g.connection()\n", "print(nab)\n", "nab" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a test, we verify that $\\nabla_g$ acting on $g$ results in zero:" ] }, { "cell_type": "code", "execution_count": 207, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "nabla_g(g) = 0" ] }, "execution_count": 207, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab(g).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The nonzero Christoffel symbols of $g$ (skipping those that can be deduced by symmetry on the last two indices) w.r.t. two charts:" ] }, { "cell_type": "code", "execution_count": 208, "metadata": {}, "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": 208, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.christoffel_symbols_display(chart=stereoN)" ] }, { "cell_type": "code", "execution_count": 209, "metadata": {}, "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": 209, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.christoffel_symbols_display(chart=spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\nabla_g$ acting on the vector field $v$:" ] }, { "cell_type": "code", "execution_count": 210, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field nabla_g(v) of type (1,1) on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(nab(v))" ] }, { "cell_type": "code", "execution_count": 211, "metadata": {}, "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": 211, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab(v).display(stereoN.frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Curvature\n", "\n", "The Riemann tensor associated with the metric $g$:" ] }, { "cell_type": "code", "execution_count": 212, "metadata": {}, "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": 212, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem = g.riemann()\n", "print(Riem)\n", "Riem.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The components of the Riemann tensor in the default frame on $\\mathbb{S}^2$:" ] }, { "cell_type": "code", "execution_count": 213, "metadata": {}, "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": 213, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem.display_comp()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The components in the frame associated with spherical coordinates:
" ] }, { "cell_type": "code", "execution_count": 214, "metadata": {}, "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": 214, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem.display_comp(spher.frame(), chart=spher)" ] }, { "cell_type": "code", "execution_count": 215, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module T^(1,3)(S^2) of type-(1,3) tensors fields on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(Riem.parent())" ] }, { "cell_type": "code", "execution_count": 216, "metadata": {}, "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 $\\mathbb{R}^3$ is identically zero:" ] }, { "cell_type": "code", "execution_count": 217, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Riem(h) = 0" ] }, "execution_count": 217, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h.riemann().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Ricci tensor and the Ricci scalar:" ] }, { "cell_type": "code", "execution_count": 218, "metadata": {}, "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": 218, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric = g.ricci()\n", "Ric.display()" ] }, { "cell_type": "code", "execution_count": 219, "metadata": {}, "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": 219, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R = g.ricci_scalar()\n", "R.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hence we recover the fact that $(\\mathbb{S}^2,g)$ is a Riemannian manifold of constant positive curvature.\n", "\n", "In dimension 2, the Riemann curvature tensor is entirely determined by the Ricci scalar $R$ according to\n", "$$ R^i_{\\ \\, jlk} = \\frac{R}{2} \\left( \\delta^i_{\\ \\, k} g_{jl} - \\delta^i_{\\ \\, l} g_{jk} \\right)$$\n", "Let us check this formula here, under the form $R^i_{\\ \\, jlk} = -R g_{j[k} \\delta^i_{\\ \\, l]}$:" ] }, { "cell_type": "code", "execution_count": 220, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 220, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta = S2.tangent_identity_field()\n", "Riem == - R*(g*delta).antisymmetrize(2,3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly the relation $\\mathrm{Ric} = (R/2)\\; g$ must hold:" ] }, { "cell_type": "code", "execution_count": 221, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 221, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric == (R/2)*g" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **Levi-Civita tensor** associated with $g$:" ] }, { "cell_type": "code", "execution_count": 222, "metadata": {}, "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": 222, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps = g.volume_form()\n", "print(eps)\n", "eps.display()" ] }, { "cell_type": "code", "execution_count": 223, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "eps_g = sin(th) dth/\\dph" ] }, "execution_count": 223, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps.display(spher.frame(), chart=spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The exterior derivative of the 2-form $\\epsilon_g$:" ] }, { "cell_type": "code", "execution_count": 224, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3-form deps_g on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(eps.exterior_derivative())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course, since $\\mathbb{S}^2$ has dimension 2, all 3-forms vanish identically:" ] }, { "cell_type": "code", "execution_count": 225, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "deps_g = 0" ] }, "execution_count": 225, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps.exterior_derivative().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Up to know, all the vector frames introduced on $\\mathbb{S}^2$ have been coordinate frames. Let us introduce a non-coordinate frame on the open subset $A$. To ease the notations, we change first the default chart and default frame on $A$ to the spherical coordinate ones:
" ] }, { "cell_type": "code", "execution_count": 226, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (A, (x, y))" ] }, "execution_count": 226, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_chart()" ] }, { "cell_type": "code", "execution_count": 227, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate frame (A, (d/dx,d/dy))" ] }, "execution_count": 227, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_frame()" ] }, { "cell_type": "code", "execution_count": 228, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (A, (th, ph))" ] }, "execution_count": 228, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.set_default_chart(spher)\n", "A.set_default_frame(spher.frame())\n", "A.default_chart()" ] }, { "cell_type": "code", "execution_count": 229, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate frame (A, (d/dth,d/dph))" ] }, "execution_count": 229, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_frame()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We define the new frame $e$ by relating it the coordinate frame $\\left(\\frac{\\partial}{\\partial\\theta}, \\frac{\\partial}{\\partial\\phi}\\right)$ via a field of tangent-space automorphisms:
" ] }, { "cell_type": "code", "execution_count": 230, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "d/dth*dth + 1/sin(th) d/dph*dph" ] }, "execution_count": 230, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = A.automorphism_field()\n", "a[1,1], a[2,2] = 1, 1/sin(th)\n", "a.display()" ] }, { "cell_type": "code", "execution_count": 231, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[ 1 0]\n", "[ 0 1/sin(th)]" ] }, "execution_count": 231, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a[:]" ] }, { "cell_type": "code", "execution_count": 232, "metadata": {}, "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": 232, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e = spher.frame().new_frame(a, 'e')\n", "print(e) ; e" ] }, { "cell_type": "code", "execution_count": 233, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "e_1 = d/dth" ] }, "execution_count": 233, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[1].display()" ] }, { "cell_type": "code", "execution_count": 234, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "e_2 = 1/sin(th) d/dph" ] }, "execution_count": 234, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[2].display()" ] }, { "cell_type": "code", "execution_count": 235, "metadata": {}, "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": 235, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.frames()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The new frame is an orthonormal frame for the metric $g$:
" ] }, { "cell_type": "code", "execution_count": 236, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1" ] }, "execution_count": 236, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[1],e[1]).expr()" ] }, { "cell_type": "code", "execution_count": 237, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "execution_count": 237, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[1],e[2]).expr()" ] }, { "cell_type": "code", "execution_count": 238, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1" ] }, "execution_count": 238, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[2],e[2]).expr()" ] }, { "cell_type": "code", "execution_count": 239, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[1 0]\n", "[0 1]" ] }, "execution_count": 239, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[e,:]" ] }, { "cell_type": "code", "execution_count": 240, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = e^1*e^1 + e^2*e^2" ] }, "execution_count": 240, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(e)" ] }, { "cell_type": "code", "execution_count": 241, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "eps_g = e^1/\\e^2" ] }, "execution_count": 241, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps.display(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is non-holonomic: its structure coefficients are not identically zero:
" ] }, { "cell_type": "code", "execution_count": 242, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[[[0, 0], [0, 0]], [[0, -cos(th)/sin(th)], [cos(th)/sin(th), 0]]]" ] }, "execution_count": 242, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e.structure_coeff()[:]" ] }, { "cell_type": "code", "execution_count": 243, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-cos(th)/sin(th) e_2" ] }, "execution_count": 243, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[2].lie_derivative(e[1]).display(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "while we have of course
" ] }, { "cell_type": "code", "execution_count": 244, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[[[0, 0], [0, 0]], [[0, 0], [0, 0]]]" ] }, "execution_count": 244, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.frame().structure_coeff()[:]" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.2.beta8", "language": "", "name": "sagemath" }, "language": "python", "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.14" } }, "nbformat": 4, "nbformat_minor": 1 }