{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Sphere $\\mathbb{S}^2$\n", "\n", "This worksheet demonstrates a few capabilities of\n", "[SageManifolds](http://sagemanifolds.obspm.fr) (version 0.9.1)\n", "on the example of the 2-dimensional sphere.\n", "\n", "Click [here](https://raw.githubusercontent.com/sagemanifolds/SageManifolds/master/Worksheets/v0.9.1/SM_sphere_S2.ipynb) to download the worksheet file (ipynb format). To run it, you must start SageMath with the Jupyter notebook, via the command `sage -n jupyter`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we set up the notebook to display mathematical objects using LaTeX formatting:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also define a viewer for 3D plots (use `'jmol'` for interactive 3D graphics):" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "viewer3D = 'tachyon' # must be 'jmol', 'tachyon' or None (default)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# $\\mathbb{S}^2$ as a 2-dimensional differentiable manifold\n", "\n", "We start by declaring $\\mathbb{S}^2$ as a differentiable manifold of dimension 2 over $\\mathbb{R}$:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "S2 = Manifold(2, 'S^2', latex_name=r'\\mathbb{S}^2', start_index=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(S2)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "2-dimensional differentiable manifold S^2" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The manifold is a `Parent` object:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "isinstance(S2, Parent)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Category of smooth manifolds over Real Field with 53 bits of precision" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2.category()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Coordinate charts on $\\mathbb{S}^2$\n", "\n", "The sphere cannot be covered by a single chart. At least two charts are necessary, for instance the charts associated with the stereographic projections from the North pole and the South pole respectively. Let us introduce the open subsets covered by these two charts: \n", "$$ U := \\mathbb{S}^2\\setminus\\{N\\}, $$  \n", "$$ V := \\mathbb{S}^2\\setminus\\{S\\}, $$\n", "where $N$ is a point of $\\mathbb{S}^2$, which we shall call the North pole, and $S$ is the point of $U$ of stereographic coordinates $(0,0)$, which we call the South pole:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Open subset U of the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "U = S2.open_subset('U') ; print(U)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Open subset V of the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "V = S2.open_subset('V') ; print(V)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "S2.declare_union(U, V)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "stereoN. = U.chart()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (U, (x, y))" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y is stereoN[2]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "stereoS. = V.chart(r\"xp:x' yp:y'\")" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (V, (xp, yp))" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoS" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Chart (U, (x, y)), Chart (V, (xp, yp))]" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2.atlas()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "xp = x/(x^2 + y^2)\n", "yp = y/(x^2 + y^2)" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_to_S = stereoN.transition_map(stereoS, (x/(x^2+y^2), y/(x^2+y^2)), intersection_name='W',\n", " restrictions1= x^2+y^2!=0, restrictions2= xp^2+xp^2!=0)\n", "stereoN_to_S.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the above declaration, 'W' is the name given to the chart-overlap subset: $W := U\\cap V$, the condition $x^2+y^2 \\not=0$  defines $W$ as a subset of $U$, and the condition $x'^2+y'^2\\not=0$ defines $W$ as a subset of $V$.\n", "\n", "The inverse coordinate transformation is computed by means of the method `inverse()`:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "x = xp/(xp^2 + yp^2)\n", "y = yp/(xp^2 + yp^2)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoS_to_N = stereoN_to_S.inverse()\n", "stereoS_to_N.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Chart (U, (x, y)),\n", " Chart (V, (xp, yp)),\n", " Chart (W, (x, y)),\n", " Chart (W, (xp, yp))]" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2.atlas()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [], "source": [ "W = U.intersection(V)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (W, (x, y))" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_W = stereoN.restrict(W)\n", "stereoN_W" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (W, (xp, yp))" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoS_W = stereoS.restrict(W)\n", "stereoS_W" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 17 graphics primitives" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoS_W.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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KTGTCmpLCr4z/XrqU99HAgfx5RATv43LlLvxesqQSWAkKDmOMsTsICTLnzvGN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\nOnVqttdxOByIjY1FuXLlUK5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spUTIXWlp3K358suBp56yOxrJqFAhvqBMn85Pvv7u4EG+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64Ypoz9ERYGB+FevSzf9tWrMFnUrGlZQev8eVF46NgRPj3MqCxPZLxp5auvUBZDH0KQgLZklEol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\n5ddycq4cstqxQz5fzCGxsbGx8PPzQ1xcHOLi4oBz5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"text/plain": [ "Graphics object consisting of 72 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graphSN1 = stereoS_W.plot(stereoN, ranges={xp:[-6,-0.02], yp:[-6,-0.02]})\n", "graphSN2 = stereoS_W.plot(stereoN, ranges={xp:[-6,-0.02], yp:[0.02,6]})\n", "graphSN3 = stereoS_W.plot(stereoN, ranges={xp:[0.02,6], yp:[-6,-0.02]})\n", "graphSN4 = stereoS_W.plot(stereoN, ranges={xp:[0.02,6], yp:[0.02,6]})\n", "show(graphSN1+graphSN2+graphSN3+graphSN4,\n", " xmin=-1.5, xmax=1.5, ymin=-1.5, ymax=1.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Spherical coordinates

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Open subset A of the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "A = W.open_subset('A', coord_def={stereoN_W: (y!=0, x<0), stereoS_W: (yp!=0, xp<0)})\n", "print(A)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (A, (x, y))" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_A = stereoN_W.restrict(A)\n", "stereoN_A" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (A, (th, ph))" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher. = A.chart(r'th:(0,pi):\\theta ph:(0,2*pi):\\phi') ; spher" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "x = -cos(ph)*sin(th)/(cos(th) - 1)\n", "y = -sin(ph)*sin(th)/(cos(th) - 1)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher_to_stereoN = spher.transition_map(stereoN_A, (sin(th)*cos(ph)/(1-cos(th)),\n", " sin(th)*sin(ph)/(1-cos(th))) )\n", "spher_to_stereoN.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We also provide the inverse transition map:

" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [], "source": [ "spher_to_stereoN.set_inverse(2*atan(1/sqrt(x^2+y^2)), atan2(-y,-x)+pi,\n", " check=True)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "th = 2*arctan(1/sqrt(x^2 + y^2))\n", "ph = pi + arctan2(-y, -x)" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher_to_stereoN.inverse().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The transition map $(A,(\\theta,\\phi))\\rightarrow (A,(x',y'))$ is obtained by combining the transition maps $(A,(\\theta,\\phi))\\rightarrow (A,(x,y))$ and $(A,(x,y))\\rightarrow (A,(x',y'))$:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "xp = -(cos(ph)*cos(th) - cos(ph))/sin(th)\n", "yp = -(cos(th)*sin(ph) - sin(ph))/sin(th)" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_to_S_A = stereoN_to_S.restrict(A)\n", "spher_to_stereoS = stereoN_to_S_A * spher_to_stereoN\n", "spher_to_stereoS.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, the transition map $(A,(x',y'))\\rightarrow (A,(\\theta,\\phi))$ is obtained by combining the transition maps $(A,(x',y'))\\rightarrow (A,(x,y))$ and $(A,(x,y))\\rightarrow (A,(\\theta,\\phi))$:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "th = 2*arctan(sqrt(xp^2 + yp^2))\n", "ph = pi - arctan2(yp/(xp^2 + yp^2), -xp/(xp^2 + yp^2))" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoS_to_N_A = stereoN_to_S.inverse().restrict(A)\n", "stereoS_to_spher = spher_to_stereoN.inverse() * stereoS_to_N_A \n", "stereoS_to_spher.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Chart (U, (x, y)),\n", " Chart (V, (xp, yp)),\n", " Chart (W, (x, y)),\n", " Chart (W, (xp, yp)),\n", " Chart (A, (x, y)),\n", " Chart (A, (xp, yp)),\n", " Chart (A, (th, ph))]" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2.atlas()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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cFhE/jqJ/f05m//NP150gnS4d/4YsWdjxVAzQ+rBYePOWiq/Uc/s2p4SL+NHL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\nu4EKFej6d96koqJ0W3cvISG02cj+SJ5MUBDHNezcqduSe7l8GRgzhteY/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"text/plain": [ "Graphics object consisting of 30 graphics primitives" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(stereoN, nb_values=15, ranges={th: (pi/8,pi)})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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FteIhKcl0pSVPTzSmmz4dDfnu3kUDu/nz4V1ZsoRoyBCIiT594MHYtAmvdfTM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\n", "text/plain": [ "Graphics object consisting of 40 graphics primitives" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_A.plot(spher, ranges={x: (0.01,8), y: (0.01,8)}, nb_values=20, plot_points=200)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point N on the 2-dimensional differentiable manifold S^2\n", "Point S on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "N = V.point((0,0), chart=stereoS, name='N') ; print(N)\n", "S = U.point((0,0), chart=stereoN, name='S') ; print(S)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point N on the 2-dimensional differentiable manifold S^2\n", "Point S on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "N = V((0,0), chart=stereoS, name='N') ; print(N)\n", "S = U((0,0), chart=stereoN, name='S') ; print(S)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point N on the 2-dimensional differentiable manifold S^2\n", "Point S on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "N = V((0,0), name='N') ; print(N)\n", "S = U((0,0), name='S') ; print(S)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Open subset V of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N.parent()" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Open subset U of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S.parent()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We have of course

" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N in V" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N in S2" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "False" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N in U" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "False" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N in A" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Let us introduce some point at the equator:

" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [], "source": [ "E = S2((0,1), chart=stereoN, name='E')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E in A" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(1/2*pi, 1/2*pi)" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E.coord(spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

which is not possible for the point $N$:

" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Error: the point does not belong to the domain of Chart (A, (th, ph))\n" ] } ], "source": [ "try:\n", " N.coord(spher)\n", "except ValueError as exc:\n", " print('Error: ' + str(exc))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (R^3, (X, Y, Z))" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R3 = Manifold(3, 'R^3', r'\\mathbb{R}^3', start_index=1)\n", "cart. = R3.chart() ; cart" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [], "source": [ "Phi = S2.diff_map(R3, {(stereoN, cart): [2*x/(1+x^2+y^2), 2*y/(1+x^2+y^2),\n", " (x^2+y^2-1)/(1+x^2+y^2)],\n", " (stereoS, cart): [2*xp/(1+xp^2+yp^2), 2*yp/(1+xp^2+yp^2),\n", " (1-xp^2-yp^2)/(1+xp^2+yp^2)]},\n", " name='Phi', latex_name=r'\\Phi')" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Phi: S^2 --> R^3\n", "on U: (x, y) |--> (X, Y, Z) = (2*x/(x^2 + y^2 + 1), 2*y/(x^2 + y^2 + 1), (x^2 + y^2 - 1)/(x^2 + y^2 + 1))\n", "on V: (xp, yp) |--> (X, Y, Z) = (2*xp/(xp^2 + yp^2 + 1), 2*yp/(xp^2 + yp^2 + 1), -(xp^2 + yp^2 - 1)/(xp^2 + yp^2 + 1))" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.display()" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Set of Morphisms from 2-dimensional differentiable manifold S^2 to 3-dimensional differentiable manifold R^3 in Category of smooth manifolds over Real Field with 53 bits of precision" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.parent()" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Set of Morphisms from 2-dimensional differentiable manifold S^2 to 3-dimensional differentiable manifold R^3 in Category of smooth manifolds over Real Field with 53 bits of precision\n" ] } ], "source": [ "print(Phi.parent())" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.parent() is Hom(S2, R3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point Phi(N) on the 3-dimensional differentiable manifold R^3\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "(0, 0, 1)" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N1 = Phi(N) ; print(N1) ; N1 ; N1.coord()" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point Phi(S) on the 3-dimensional differentiable manifold R^3\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "(0, 0, -1)" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S1 = Phi(S) ; print(S1) ; S1 ; S1.coord()" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point Phi(E) on the 3-dimensional differentiable manifold R^3\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "(0, 1, 0)" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E1 = Phi(E) ; print(E1) ; E1 ; E1.coord()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(2*x/(x^2 + y^2 + 1), 2*y/(x^2 + y^2 + 1), (x^2 + y^2 - 1)/(x^2 + y^2 + 1))" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.expr(stereoN_A, cart)" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(cos(ph)*sin(th), sin(ph)*sin(th), cos(th))" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.expr(spher, cart)" ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Phi: S^2 --> R^3\n", "on A: (th, ph) |--> (X, Y, Z) = (cos(ph)*sin(th), sin(ph)*sin(th), cos(th))" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.display(spher, cart)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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EDULY5ly73UEhHoD7oS8cEwhELzeWh6xatSrPXfUI8lDE8kLc83DQi09DQ8Oj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\nMJ67oRW55pprJk6caJTd0MT8Xws5SIh99rNEAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_spher = spher.plot(chart=cart, mapping=Phi, nb_values=11, color='blue')\n", "show(graph_spher, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false }, "outputs": [], "source": [ "graph_spher = spher.plot(chart=cart, mapping=Phi, nb_values=11, color='blue', label_axes=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ACgoKWltbT2CDx8yAF/cQRuJPEgdcdyk8CBkwGn4KNoyHP8O/BYXmdSHe0hK2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\n7AHtflkRykeMJBCokfLZMBP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GqAYpy6EBGmMsstWsiFtbOOZFo5Yh604ZrIF1Yfd5i5Q9\nplBV8BTM7i1Lqj7aZlvhHHCc2XAvhHyDv/re9/Jg1jF9jylJknsaku57MuLedxzHuXPo0Ne/9z0L\nWoIT7bXB3dd6pUuIndFsTL0bX134jkhhFI0eHb5qsVHKSt1IXFtV629fetWDqE7tw1KqurpDL7zQ\nKOWeYOQzypunTVsLk2+8sb8XXZaWFsffXQn1ejtWKY9EOy1+ic049JpNf5RAQNn2GvhISqVUQ/f0\nzUmQD3v74Hjx92a//yOkgRNZxsC4ZZQqKipKdBd6IenEPckD0ElFi+P8Nwj4Xnr60SfQ718NfVnO\nXg9xynaPg3+FhghDsjk/f5sug6XXFknZR/9DCTT13yejlJoVYY8rpdZJWQ4tsCuiPH0PNkm5rp9S\nG5Cy10Cxlv5dUu6GRqgLN9Vra397rOK+ti/ZR2E8LWUGTAG91GCJlKv7nO+oaYgRMR47duyjDz98\nAzwKT/cYAGpq+hXRSVWS3wxNxi/JuN37yJN6juz3K6Ucx/nX++57GOyhQw/1ZrWVwuHepHY8vBbx\nDH8MDXpTt34qdZwCv71g23tD13LdA1JWQQtU9FkHPw2rrRifXXV1+VLuiNvVBdGyOTtt+wnIhnek\n/O/uifb9wgv9HYo070KZ9rDrhbh9x+/fErG3aih0/wocCStCF2KPZTWfwt2akpPklykj7gOVX0CP\nUlA7x49f+cYbX4EnHn44zhv7lJyu1NNSNtj2VHgX8qTc+sILz6el/QFUU1O/++q6/U2CDNFo2wtB\n2XaTDpZK+dmOHLrwZG8cOXKkrW/2+0dS+qFFlxGO1VpvRn0h1EGzHj77vHLqKK4buWN4HBZIOR/K\ndGUeKANd/72zXx5/v78elOPkr1zZIyPrdSgS4mkhIvfLXc0JKBg5oEl+mUpGcU/++U7C8b7wwqsR\nKqDn5s/DM9/7no6AlZWV9Tgn0Gej++fB9l8FJ1RvpP9JIEod3dqiv2+qlHKblAHIj7q7qVJKqXLY\nO2FC/Hb0sufiXoe02trNsXz3QWb34VPMCfmRpNwJHdCqXSV9E9z4QU6NT8p1sFFPX0LfSCBQq98b\nCCjX7bTtT6BayqI+9HnV2LHfGTp0xNChPY5PFqJcCKVUT8+MUl4h+tLVVCX5He7KiPsAZTzs6OF7\nEUIHx8LTkx3HCbfFiiBecnp3cmAThCqCfQrvw4ewQsqN/UwF2d3bCv4QTbbdKuUWaIY2LYi1tT0T\nZsKpq3u+t0+0OmjdF8Km2N2o723Y66USQ5AoGe6uq2z7Y9gPbbAN6qEeDkhZEApa6HxHnWMaCKjq\n6qMlgnUpY9teChvAD1WwIVoBHKWU0huuKtVtIHHd2dCjNEWIsrKy0C+kKTJ/xnG0e/3psB1WQ/S9\nUnHqkfxmu0pOcU/yBKOEszLakxYq/fFBxCPnOM6/P/zwt4YO/c++PY1LIKO7w323be8J/nnIthfC\nB+CTcn9QgOITJ8Snd0ktgEao0WOJbfcwn6dD1M1Rwzsc59XPUiGnTVsfI667pjdlj5o4FJUo1Qii\nocvf74RGaIWt0AS7YTt8BI1QC/WwBfZLuVenJPWBOlC2HRljCLhuwHEKLGsRrBXioOP8zrJ+a1md\nnZ3hp+3rngnT5jgVQZs9J6IDr8CB09XzPiAM0CQV9wExMCaKalDvvdftUNgzFn07Dsf5A/zHI4+M\nGzcuVrMl0CBlyF37elg7LXqJZncKpVwGc2ACPAYWrLDtWVLut+39tl0sZb1tK6XqbdsLH8J2KQuh\nBAphI+yCRtihPSHxpwLTpsUvsrg1bsJMj/IDbT1c4dOmNUD8eO8SKSNrtkRlo5Tlx2nP2vaG42kh\nEGjorcbk45b1/fT0r8AvdJmK7v70ej5bv7rFskJaP9eyNneX8nG93bcUxoj7sWPEPRaHLWtHpLkU\nPBKwrI0Rr+4WImTXl5eXjxs3bty4cW5oo2fb/jQi3XBeqByjUpU6pzs+gcBm225x3cfhdzAD5sMe\nKTukXBK+m51td0jZr2w/Te/lEmOb9tMiXtoctqlplDIJkfS5w/N789r3hXxQe/ce89u3QKztNcaN\nGxe9iIXjvAITodayVgmxI6TvjhNuyIevjHsUlFLrhehXCSPDqSRJxX1ADIwJYUvEc1sXZnxtsKwe\n+Yuzokmza9s/GzbsDnh42LC9b74ZeZWGsKztY9iIJ5wSKY+h6kAPPu2LaMa4SqS4K6Uq4EN4Fpp6\nE+5+pa8cl9EdpH+5jJHY9vaI0LfruuPGjYu6nWwP6ixrgxB7YQ6Mh6lgwf8JkQEZ8DP4/yIWxJ5u\naTMDIpqqjLgPMBwnyorNcNPJcUrCLPd5PZYguu4UnYUdVLTDhw93M+RDBKWhMS1t1/FJ8+9OhN59\n3H3j5lhErYIbVdw/te3/hF6DELH2xIjKDtvu10gQi8Jo67b6RU1YCCH699srjtMIr8GU7p8o0ulU\nK8S+08zzbsT9uBgot+8UUw3/r/vT9VEwSUazPlgVUimlLKsJ9lvWUWWMbaJqs4pwMRAAACAASURB\nVC7cHf8LmGfb6oUXDh63Wk05EXqnpk3rU4X02trI3SoixX3XtGnjYYmU26SMMy+p6y2Q24NN4Tn4\nx4G/z+t+YxGA2XAf9Pha+0VLmDfvMywrsmLBCRnSBhADxWmcvN/KQLmDpw7HqQS9C9pfrr226aWX\nlN+fAY3aK+o4XY7ze5gJyu/Pg739368jZOWNu+ceFQjUHHNie4g+bHbRR/piuWsaup/ZTd1qa9fp\nfNDgUJcPTdFEvJfFStHoRyXOuHzQ520IYzEGRqSljT7u/jylN9vrzv6II7P6WfNgoDNQTM/k/UqM\nZyac1rq60rA0Ne/o0b7Ro1+G/4afwHPa7e44WyzrDfgvrV8Rqwr7SHl5+d8OG/ZV+MM99xxnt3fb\ndsMJeuzf748dHcvL/0mMrSoa4ZCUqqvr6N/TpvXbBp827ZhX4fakqOiYR0TXdX/9yCPfGjZMafdO\n/2PX4UzV66S6m+o10X5ax5sjNHDo6Ogw4n68GHHvRmdnzwd+3bq2aE/U233baic+i6T8V3jonnvG\njRt3+PDhY25naW/54/2gtra4758rWnqlVy+MikE1VKelKb0Kqf/elepjygL6/9t78/C4yvPu//t4\nQ5JXwDZgbFkuYZFkDJYh8wxJm7RNQ/Mmb9uALckRoS1v8/7epu9VnVGXq0UuslsD768Bz/ht+msb\nCCHGQnPG2E5YzGbAAcMceZFsSxoZvMwied8tW5JtSc/vj2MNo1nPOXNmzjLP58qVy4zOcs+cme+5\nz/3cS1LOrVuXfvxTUmKXTKN57pey+Cb82uGQmxS1A2NSUcem0Mj4gQuFEXm/fPmy0SYoxbzibpXb\nY3444XBcee652FfOJ7hUMm9l4bNHORmzpifHarRJ/K6sncdYlM6PHkWOv3d0dDBRDCu4zewGuoA9\nmu5G+sadlWfdDA0NybIeu2QanXCyH1A7/SrKizFPinG31SSFWkmX+u2IhZxOU18Pru9RehJ+OfHj\nMhhjjL0H/Cx7cR8eTvT4tCVd6Ct56yj9l7lzVewgiocpfX3atAPK7jGtlO4AOlO3sknFGUFQWJiq\niOHh/QoSZqKZTolLpl+2zpfnHarnWkuLd+yOp+Kc94T09vbCyIm0kCiZWtz5mqrMcEK/gf0A+8u/\njN+uvr4DeNPhkLJ7QP58tD94Iol5NekIh/UV952CkNiFOB2iyCg9ofDpIdr2IBwORUtnlXFQ1wcU\nJjdUSCvu8oVI9TgVOxdF28PTcEvL0Fj5Do7Ny7qYcCHaHI5TBRCZsZAomVrcLfQElEPC4bjCpYFI\nJPGx/YjDER598eUsJPW9uXPPAOl6dTHGGPvHf/zHzI68KEb0flTfpVhzP6G0GwgD7ytoXn+M0tDY\n6aydwGnF3dUztpNUy/7UA0OURMnGpDB6vRfUX4XYmEyUyw5HtJFcktt/S0v6LhE2wEJuOzO5uFvr\no8wRnyB+Vv0elys+O7ul5YuYaMwnWeTSRYArlCoR5eHhYVloUg4pDYd1SyAZ5T3gnIKYybAgRBMc\nRTn1JY33Koonk87dFsUBSoPA7rRnfCvtTCvtJBis/Jmpfaw98sQo5Wfe5HCkmjcSBs7K7nkwmBiZ\nSdIR015Yy9009cWwUNZR7tib6BW2tOwdKzehOD8rFHpR08+sa+lSOYtZVWZb4oKezLmYBjU6kqE/\noigeHxuIuF7EJIojyTT6siAcSRvHP0tpL5B0X5mApuyaDHi90Xmq0Zuo8r0TPyJVt5/0I7CPRd2I\nhCDM5mT+vp2wlrhPgIkpKSlZsmSJ0VYYSihEEl47vXz5Isai/9lLyHSHA7W10VeGJGkCgHAY8+er\nOFckctNrrxV5vQCuqbGxpqYGQGdnZ1NTE4CmpqZx48YBuEGS1BxGKWeBzwm5O+YTiNJKyD3ALaKI\n6uroi4FAAACqqw+43dcIqYzZ8ZrLVeJ0lrjdaU53o99/I3CAkBsIKRUEjN34kNM5Hog9nT44nZeB\nl194IdjbC2DZsmULFy5UvvdgwiszQ6EgIQuSfWhxvEzIQw5Hmg1ura8/vWDBzGSHut3hgCTFfhU5\nRmL03SUDFlq+yAktLXHpw2+PvWQ9MWHQWF5XH5nZEDOaI+kxFSK7mcPDwy/pHYmOEhft6Xj+eXkO\nX9I49ZiokSB8uU04rDYHv5/S4NjHgn25cNsZ+4cnnvgq8PeCENevWCHbkl2+iwoycH6ucABsff31\nr2VCZMbepaoWSnJnJg/LMKs9B+lOR0JeY+wopd3LlgVThxReAkYU6/tVUTwb02xARblQCv6fJ554\nAPheRUWWx0nKGzGSeozSC7Ksp7iRxC0JXKOUuVxMblyuAVFklB4Heihdl7q5rmb6+vr++q//+q+e\neCKb5gHJ0x+93gzVwqFQ+rEnsfQ7HP0OR2KPUuVdIiyH5ULEZr8SBe65tyf8VKLB0zP19QfSusbd\ngvAClDaH+XTu3Fg3Nk2IWTn/F/jlCy889dRToigmbc2YDYeALkojwCUgnNbaJKd2ubJcAj1C6XlZ\n2fV7X6IoPvXUU/WjvnBiZYMKUnwgaYYsdgrCZpVnPA4cSFjtvxYz38NmWM7RNLu4MwveMHUkfmHz\nueeuF8sEg/uB4bE1q4kcFYRPFch02OfrG3sb0CU/PdoFQZYtffV9F3BO1tZIJP2Wiec9ICdHUppx\n33QIwnHgMtAOXMhu3bijoyMay4q++GEOxH2A0uTN4r3eXysI2sTxHhBJ1utCrwZqZsNyjqYFLoPl\nbph68auE3IOo57U/wWNKxb8rmEcxHBuJZoxlF3OPEhcEiEqY5ia0MtcEYScQlt1GBYwJy4jil8W3\nzz+fTd+bT4DrwStRvAgMAL2ajibf9hJj60qKVFOS+oondtd5l9LPgMOajN+VrB/kXpuKu+WwwGUo\nWM89blnsU4AtXcoY63I4LqspBfxZen0Ph8MJ0ZsT2f8+w+GkyfLaJT4cbgOOxAyWagVY2umpMl96\n7pFIopprq86/nnAZiyCckbsHK1NJ+WkmzluP5dNsql7TxOLkkt1RtlG6Q3HsLimHgLi5j63JBrhb\nnd27dxttgmosIO4FS/wTtMNxeNkyNjSkYQzbz4FQCqW4kOC2M5byuV455wUhvZ2iKDY1NTU1NY1E\nG+2mYOvzz1+ltD9RNyORJNMkEmhqapLPl+pNaYi/p+w3EA6fl3tPpv4A5dubKIopi78YY4xtz5G4\njzrvEqVvAUezX1ypr/987Ad4tL6+13Z9CBobG402QTXWEHdrZSDpQ0JvJtnh6gA+0uRseoFfJtvx\nTNLH/+yLj0RRyZJgR0dHU1OTKIrJJT4c7qa0MbWH/hmgqIFiJge/R43MDblcmZ9sBEGO1cSm8USf\nWtLLusxRzT2EM+21DdgmD3LJbiRIlBMOx6UYNd/icHBxNwPWEHfLLWVkz0Dcz6O+ngWD7wMZ6jPT\n4/W+BLwZq2Jeb/LC9OwdOlFU3qFX1nfZkZdfOUjpMaA/4xEikTCQfl1UaQWp4rd8SnmSTDh8jdJ3\ngccBJ/AXS5c+p/gslwUhF4WvbwBtwOfZfIsSeM/h+GLsAbfbLuzOwzK5ogDFPe7ndwnwAl/o8Zvx\nAi+NZscfTfXsf+4c+/TTrE4TDqtVkDcE4UfA702b9jXgfwD777hDyV7b07T3ikQuUPrvS5cqNGBQ\nwRDUtwFVkzQ6Ojr+ThCefOKJJ4ALwCXZl1fgkn8EXNF0i02VD/M+0DnqrQ+mbkymja1jv5zK8+Wt\nghXF3dTtB6J0d3cbbUK+uau+PvY/xwHzgMlp68IVsiwS2Vpd3UzI7wjCTQCSFt9fvIiHHsrmLIHf\n+71+5Vv7fIdqahxAObCzouKziori6dP/7uDBXzNGSGL/hTF8LRIJlZb2OZ1T/f74v1VXT3O5Tsrt\nBxRwg98Pn+8SIVNSlOkfbmhYBMxRUMQPYOXKlfI//lX+hH/+8+t/iES+mD9/nsdzDYhQupBSuFwo\nLY3bvZLSSQrtHsuXP+lw2FdWNh6YD9xJ6bdCoWg7ihu83ktlZVM0HT8p9wMXgLcJ+Q5jACbrd2Qz\n0NzcXFdXZ7QV6jH67qKIQkyYiQm4tzsce/R+lGah0GbgVaA3lReZZecAQci4UNlJ6YdAjzzxNeF0\nn376qRyoyRyhHhnpiQvOJEuMUYoofprC8reUJcPICwnREFNKwuE+Ss8C/cB54CgQAVhdnfxRfAho\nCG5cEYQWYBuwFwjGuOqJ7NMv5s7k2FdLS/SZ5j2LCItCrBhwZ1YJyzDG+vv7jTYhf3SPTSbb4XBo\nyJDJSB/A3n57z7e/vQXYAGwdK1sacwRH8afSQUFoBfYBl+QqpEwBipGRESUS3xnTuPGyyxW7gtrZ\n2anaesZWJxh/2uVKn5wzMjIirxxoLNcKh/cB7O23GaUXgUvASaAbOATsAg4A5+V4jiCcoLRfEJjX\n+w5wmlI/EAK6gRBwjdJuQFJw7XaPzYnMFnmwan297JRsspe4r1+/3mgTtGCZa2DRm6dGxtZwZ7WI\nmoIBSllsprnXOyQIvwZ8wHMA83qzLFI9S6ncO2EvpRdH52acAE7IxUcq5U9uOZneHQ5EC1bH5sZo\nE3fGGHO5Yp8GdqZNq1eY1qmcHcD1SxAOD8uyLopMEAYpZYKwD2CCcED2vuMccMWPLNmMz44nGJRr\nymQv5JfQYZCvebCouBOmLIBoOFYNe2niI0J+NxhEWRkACAIAeDx6nuDEia5bb630elFTk/jHay7X\nrz2eG4FxwDlgElBK6Rngd12uJL1tIxEAkKRBv7/I7WYu1wBQAuz1eCYDJcAkoB8oDYcBJEaW1dLV\n1bVhwwYAy5Ytq6ysjP3TG4TMBhwuF9asiX3d5/NVa27J6/PB6cS8eT8j5FHg5mQ/Fjm2XlFRof0s\nyehwOqdLUqmGn6fiVs+HCLkjJhCfJacJmcmYRCml9ANJ+n1Kdf7SGkRbWxuAqqoqow1RDRd3M/Ix\nIb8zel3eJ+QPWlp07pEdDgfLytJ3995LyH2MweUCEJakgCTdBDBgPHAGmAlMAwaACcANgHygOwVh\nUJK+kKRFgnBako5K0qLcfLsYY6tWrQLQ29v74osvyi/+L0L+EjgHfFPfk/p8v6qpeQiYnXDYHMm6\nzBuE3A/MU/leBlyuYkqT3rOTEA5fLCubptPHtYuQBxgDECRkwOGosIu4r1ixYvXq1UZboQmDnxwU\nU1Axd//odXkfSOyqmj2KZkanebpXkMl3THMNjhqWLVvW1NT00+ef/2Q0YHIoIXji8/myPEvv2Dy/\nzs5OOUyke6vLWIYEQUuHH5WfuarxexmIDt5radmV0BbJulgxCVLGMuLOLBv50sAHo60fdwNZtX5N\nRsDlOqvgmK3Znfc32VTPK+bEiROMsb+YNu1/Ll0qimLLCy8cXro0rmHZ+fPnsznFjtGV4UPAxuef\nV5QGowdt6lcmmPpZGZ/pepmujFbehYCd1nEc02Nd2Rln9JMDJwkHAQBbFywYAebqkdsey1m3exyl\nGTf7qtcLUdR8lhs176mGkd/8ZtDpfOHChf/asCEQCOzv7f3J9On/CnzidGI02vDuu+9qPv4nTmc5\nAL8fgOeJJ37yN39zrqcnmsCeUyYiRQlCWsar3N7J2Bn9gidnW1vlf1xxOIr1OqjRPPLII0aboBEr\niXuhlDKFQt0AvN6HHI7bHY5zeh/+AWB6Yr1PApcAOJ2azzKV0pM5DrmONDTMqK4uGn0vK1euXLly\n5V+5XMX/8A8NkvSYHtN350rSx01N8pG//vDDfsbWTp+Onp7sj5yRC4C84KGKqdpOpv5ESbkEIBQC\ncJckXdTliEbT1tZWXGzV+5Q1KlRlGhsbjTYhL5SV3Qi0L1++mLEwIeX6Lg+Gw5eAGxRseBbIpoKx\nTZK+msXuSrjU25u4GFhZWelyua5u2+aXpKVO58KHH965c6e2Bc+nnU4JWBKXmbNmDXy+k6Wlieur\n+nJW016Jo7Ezsg140OMpVf+UkMhXYsqqLwMIha5nfHGMwEqee3Fx8cDAgNFW5J5Q6NzoXXeu7gev\nrb05FFKyYWlNzeksfvCPCMKw5p0zcZQQ+P14/vmkf509e/bzfv8blP5AkgCcOnVq5cqVTKUW/8jp\nfFOS/u7tt1euXBmXc4nq6tmMXc+SzBmTgSSJp5koVxBwi+PRUGiW2n3SIKd1hUIjwKcLFuh4YEPY\ntGmT0SZkgdFBf3UUQinTwfr66KCyi3pfoKvKDxgO/3s2vaVEUc8CyCgul/IinTbgMHDp0qVomevI\nyEjGOqOmpqbfnjv3TzI1m2SMMVHUZWRVUjQupGtaHd2hXysCeWL4/vr6d4ANQMTivX+tmyrD+IKq\nCbk5Jlg2taVFxyO3E3JG+dalpbslSfvJKFW7uJeRHYQc7uqCggUDmcWMAeiaM4cQsnLlymXLlq1a\ntWrVqlU+ny/p9nJsfcDvr+7t3exyYd68DCeorr6VsS5CjuXAhb+iYR9RhHrPHcCDXu8xnQopigAA\nQUn6/fr6pcGgVcPVAACrxwmsFHMvED5au/b7LS0AThBySzCo45HLgBu9XoUbn+npyWpNrLT0aja7\nJ9BFyFcjkcyCO5YFjN1AyJmGhpvXrKmsrKysrOzq6urq6pIzXpqamgghPp8vEAhgtCgpJDeiHFvm\nmoZKxgB0EHKvrlF4LcfyeJTf+cZQUzO5tlZ5aWsazgE3A/NkZSkri7S2zszyiMaxadMmSxdOWsxz\nf+SRR5qbm422Ioe8Q+k54IQkASgGdFyP2ud0FgFKaxeBm1XKaCK6xdx7etDQUMmYWmWXmeNyjY9Z\nPKisrKyurpZ1vL6+ftmyZYFAoKmpSX4lTMgsYL56mb6XsWOEXNPPhZ+mfpdzWTxpjdOpoPQrweAV\nSudQKrfNOIvR/hkWxPLpeUbHhVRj71LV/wR+Er0ousYrd6gvV1ma3ddDl5i70jlKqfG98AJzuc6n\nMKa2tvbVV1+V/33M5co8+yk9YxtSaicc1tKVM5u4udeb6iNSRzAYAt4aPdTxmAUky2Hd8iUZ633u\n9l5T3QCw7ds3y524dS3gvqz+N/a6IISzEFYl06vTEYlc02Na0PUVVJcr6QSlaLnpoMulV5fEYNY3\nJBYOq12qPSUIfdktil4A0k/WVsgHQGw/d+uWqlpd3C0WlrE3mwhZWl+P22+fCFQ6HNoWx5Kyk5DL\n6vf67273uiyyIbNaz2loQHX1BG0R5LFcn+W0Zs1xoCfZXCfG2KdO5yW3e3IWFbmxlDGG6uqDmWZI\npUOS1H56fmCK4phbUjqhT/PR/WMnMe0HoHilxzzYoVOh0XcXzpd8NHo5turdUua8shFCiWQTmUk5\n2jQTbQD77DOmU2/02H7uXyS0FWtqamKffaZi5rUaLmt98thBaVjlp6dD0/9Q6Ioe37rj9fWxM6Q6\nHI5eCyZEWt1tZxb13K2eopScUCg6M5PJ1ef6oskLfj4LZ3YIQIqkw1SEqqvhdC6OROB0IhvPN4au\nrq7ov+9k7IjbfSVm2fOzDRvefuihmaKooWIoIyV+Pxoa0NCgdscHKS1V9dwWidyT/brl/PkaClwT\nEdeuLY1piFQhCEdHe85YCMuvplouW0bGBp97Iv7a2oe2b5f/PQic1C8m0+tyFWWx+xtaG49cBkJq\nojpH5s0rmzsXfr+2rJhU3HXXXbH/eTtjYUnaM3rn6A8ERijNhbJfZ80aUPr3Ot2oUuJ26xLE64MO\nfWaWOBy3xRgzrra2H9bLmSkvLzfahKwx+tFBCzZcUw2FPgbY8LD8Xy/qupp6ktJs8ig0R2YGKFUa\nC4pEjufsq5h0zF4QOAD8DfCHc+fm6LxxvOdyJc5lTcV+oEvNB3JYj5VnxpgEDGd9qF8kztiTJ6xy\n8oslPXf7saG2ttThwLjrl2MasHn5cr0OTiRJX19YIUVO52EFmddfOJ3nS0tvyVkfrvjOMACAMlGc\nAtwK3PHwwzk6bxx/sGZNo99/TpkLPxOoUPOBXM2mljiGOwShP+tDTQK2jO0qc0ySdMwOyAPyaD2r\nY0lxt26H5VSUSNLcmG//OU01LMkJhycDeOghzQe4T/PPcu7cjH0lLxByl98/I5cdFpM2G2itqSkC\nAsCeDRtyd+pEbmQMTqeipQh5OK0y7tYp6DHT7c6+aUQR8N9i2kMC2CZJh/SdE8lRgCXFvaqqymZr\nqpOB8TFZaAsBvWr3z9bWZtlZe4Xfry3sfjTt7IgAIXA6p+d+hG9iv9+PCbkXmMHYktraqxcvRnLZ\n3DEJfj+qq3cT0p/qvD7fDVAzTDwS0TDWIxVngGyGtPQKwkTgg7VrY1+skmtWrYO1m0GOYklxh10+\n/eskZAFPAiYl3VI9ZyTplqzdunWa0p/nNDRcQfKEmYtOZ0UkorERikrY2PvHTkIqgBLGAPz41Vdv\nXbJkpiQFc73gmcASxkr8/jNOZ+Kt5aLff0TNoa5ll94exwVKz2XhZW9bu/a/B4O7xr44Ayi21IKq\nPWIDVhV3O3FMkr45tvvjcWBEp4PfBi3T2uJYqdXt6kNCU/KenkOETNM7JUYRPT1dhDxI6cxRuSeE\nVH3veyWMMaAv7/oO4Ga/v9Tl2kVI7C2w0+O5W43vrO9vuNLv1/xB/AshtwIADox9/XhWFhlAVVWV\n0SboABd34/lCkhDjK4W93s1AH7A96yfZKy7XFD0ehyu1psfdSmn3qGjudjr3EoJ58+7IfSgmCT09\nx0tLKylN+rjwW4wVUXrpK185rbgZpG5UVz/AGIBuQrB7N4CboO5+PF6nwtooFwCEwxp2vAf4VksL\nysriqjRmQJ/aV44qrCrudXV1tmkPWTL2Pz/0eCYApQ6Hlo7eY9nn8eiTpUDpVU36fnl0NlAPIUuc\nzvuMkHVCCHy+S6Wlt6ZQdpmJfv8Ns2ZN+5u/GcrL/Ot4qqvLGcOhQ9vle6HiT9tPiIrovDLOAdAU\nmaEOR9Id51N6QKd8njxgj1QZWFfc7cQHY+v3/lyS/qu+/gFBOJd1XV8ZdIjJAEBpqbY1gDk+31lJ\nQkPDPMaUd0jXlw+mT79cUzNFQYh/ot8/yeU6v2rV0TwvsUaprv46Y7OBAcVXzam32w7gfsb61Gvx\nTwmZl7qHjO6TW3KHbWokLSzutrkG8ZVw8i+kthbA1mz8blGcqn3nBNT/2nc2NPy6tHQYKgZf6M6J\nhgbHxYuTlU/5WLNmZiRSJEk5nY+ajkhkGCj2++Hz7VawDHBK19XUKMegLjLzG0G4F1+OH/gfY1Mh\nP5ckdd0UDOXRRx812gR9sLC4r1692mgT9CHuF9w3Gp1cytilLJz30x5PlkmQsVxStbXPd5iQB9es\n+WPGrulng1reJ6TI7d7+wgvqFm/nzbuJsRNG6bskXQ9dVVcvYeyo03klrRmzcpOFMkfl9oG1a78R\nMzVs31hXYMRSnntRUTbdOsyE0SWy2rH07NpYXht7FWIbebcAv9HaUa9Tv6nH11Ey68PlimsGuSc3\nDRczI4oDAIv2c0+GPDU75REoDSoZk60r+5P1bDhNadIGA3t06jqQBK9XRRvRYHDr2Iv+F0Aopt/A\n/2cdnWlrazPaBN2wsOdeVVW1YsUKo63QgbjO3RNj/l3LWK825z0cLoWKoXpKCGZKeDjhdILShWNX\nTedTel6/EhuFfE7I5ZqaIsYQ7eeejKampnRH8fuLKD1WWqq2t2U2XElWqX+z37/A74fPFx7rxV/K\nZazjouJAnFhbe3dMG0gALwSD80dXVk95vcvGRmnMzMaNG402QTcsLO6wR+c2uTVuDCfG/ucg8Kr6\nFGyprGyq3r/8NKn3F5xO+Hy3+P2J7RVnOJ1D+c2UOE/I3ZHI5NF7TGzL3zg2ZOo9cKvff1sk0l9T\nE8xXiOZGIGU4qLp6BIDLNTjawGBh7qyiVHmy1o2trXPHXuLnamtfH40Xvb58+Uzr5EHaw1+Usba4\n24O4cGRcXsoTjMXlSirhBmhs4J6GO5Lm5/l8HYRMTybrMkzHSdkZaWgIE8KA2CB70sZhMomdCZIw\nb14JY9Mk6SQhI+o7s6ujp2cGEsq+Yljg98PtLvL7D9XUrNI0XUsp8+dn7Ask8xNCvj22BA/A30qS\nHHZ/kpA/so7bDjsF3K0u7vbw3OO0b3rCBmWUqm33MQVZdQhJzvPPjwlQ+HyHCUF19b1ps9fJmjVZ\nzdtTTCshV9zu8ZTeONYeltq8pD3FknIzY7Ndrn63W8PkDRX4/Qqft+5gbDal9TU1LxFyNusO7Ek5\npmCbDkH4KpC0lmJva+tWQbgDmGUdt729vd1oE3TF6KB/tlh+GtbISNyC6olkF2WjyivVl5sre0Ve\nZAuHtwkCC4cV7pV0MrWeiOJp4Iz6s4yMjKRbUE3GOeBKzpaI29RMQ/wk+n5F8XNK39T7Qz4GZFhC\nb2nZknrwwFJgpdXkxfJiMhZre+6wgfNOyNfr638VE0Y4lWyrfuCEGgdtKPMmWvhckvqcTpSWfsPt\nVl4YWUJprtIKe3oGnM5LNTU3RyI35aX8dQZjkyKRgZqak7r3orlwYT5UPG99PZoEWV19l9//Xcbg\n8yES6XY6d+vxac9M+wzxmSBsXb78O8FgqlrWmXINnaWwTemMjOXF3QbtIW/xeK729sr/DjQ0zJ87\nN3Gbx0Ihv8ejtK7E5Tqpo30AgN0NDbvmzbsJOK1+337gSA7WVM83NIRKS4udzimMpclkZ7qL/rx5\nxYzNpvTi2IZf2TJ9+ngo7vTr8yUpK6uuRmlpud+/RBA+IOR1QgaziNhM8HpTVa4dcLn61679FmPR\nqqVE7gX+NCbz3RLYpnzpOkY/OmSLbZ6kfi5fi2CwM8VF+SXwsbJn9iuUslBIH7PC4Q+AU5R+GYjQ\nFJG4oPc3rQu4qCw8knTMXhS1YZlYjlF6CbgAXHa5NB8kyvt33KH8s+1T9k3YDHRQ2k3pCSU1CnF4\nvf1Jr1oo9BHA6uvT7PoEkLu5iRyFWP4C2EbcdzgcHzkcrKUl1c+m+/nnWF+wNQAAIABJREFUvcp+\nMJ/p8bsKUPppsqhrQNPBjwDss8+yt4ox9jKlKwCmWE/TFDGx7MT9OpReVGNPKs6qOYjqm2U4HKb0\nTeCyGpW/mHCWQ4LwbopY/Nb6+r8F1owOUH3NauJuGyWJYrELkBTblKq+DByQ9T0Fl597bgNw7Lnn\n0h/nbBa1qccE4WNASv3LPE2p8qXUKK1z515ctkybSWOgtEVl1WjOxV2G0qHsyllPKVdDDW74KMOC\nEKL0TeCKgoNcBcY8Aspj3BN2/LnD8TTw9thS6jariXtjY6PRJuiMxS5AUmwj7hfq6zekTj+I4gO2\np/llhkIXgWPPP6/27L8C9ikJdITD/Rqq3kUx0Q1UxTYgpIeDHIsoirqJO2NMFE8Cl7W9zUhkQPmO\nuuTqeL1DgrCN0p8ALBTaH/1GxbgFu+SIHGOMsf8LtMY5DcHgPwFvpmiP8YnVxN1OjQdkLHYBktLQ\n0GC0CbqhMPDSkto3l1wuFTIaDg8IwraMSW9jGdbU0uR4Fo7tOUpP5SYBUU9xZ4wxtgu4AuxR+WYP\nAkMKP1X1j01KkZ30UOi4ILBQ6Igg/AL4HPgvYC3wG+AXwNNASBB+IwgrgbfSdj06YDVxtx92uAAD\nAwNGm6AbXcArCpx3xtirwH8k/f0IwudKflde785sOoup19lPNfndJyk9oSb7Wy26i7tMN3ABCAK9\nyiw/nZeYjFoOUnocCArCp+qVupuLu9FYPhXSZswGHmPssiS1EPJO2kTj5aHQzcCbCRnN+z2eu0Kh\nlLtFIgedzgGnE07nA4xp7ix2WP2OD7lcZ9V0EDvqdEYIuSpJs12uHI3STtN2JkvuYWwaY2WUTpSk\nK4R0EoKenlQb9/7VXymteY9E8tmI+A6/vw845vE8lOYblYK4VmImx261qTJG3130wTaLIWP65ba0\nrAfWp/Wvm4GXxl7E88liLEcEwU9pqiRLDXQCGuIDinI8IpEu4CQQ1MnaPC2opqUbuAgMpHh2CcpB\nJwVkuW6hDq93O9Ch6Yyn6usHtbaqNgTbCEgs3HM3F2Na8dXW1jFWx9gZSfp/nc5/JySxfPEHjBUB\nvyAEQMDpfJkQBrzp8bxPyOdO55DLBVEccbnmuN3U76/Ur5ynkrFz8+er3esYkL7qp4OQSGlphSjO\nEsUynawNBAKp/sTyNdP1HsamMjaBUgAXCDk31vsekqSZSgpTI5GpmuZWqyMc/hUhbYQEamu/xthk\nTce4Ebiqs1m5xTaTf8Zg9N1FH+wTdk9bG8JCIYnSV4CfAVuA14EtAPN6XwLWA3spZaFQjrrKJEF9\n2D1IaVLX9SClEWB/LmPrSens7MyP5x7L8R//+MwddwwAvQCLRD6idFDhJcv1h+P1vgF0AidjTnSK\nUg0LMyfSf41NRltbm30EJAabiLtt0pg+Ao5kfJ5N+mPzepvlgEw+9VHt4l4kEpcpuB04BHyRy4FH\nacIyOqdCqmSE0gjQB1xQ+PZzOXdpmxyBSShs7qNUyxKu1cTdaBNygk3CMosXLzbaBH34ZkvLnIxN\nX5MuZtbU/MDr3ebx/DyPkzEOeTzqmqvMmzcIABjx+T4gJEyIk9LfcrnuTNscJkvShGXS/CkPEL9/\nHmNh4CJwubQ0SEgbIW+PDuKIx+VK2lk3G9Y5na8RspuQix7PNwRhIWNICLVN8fs1zEbfu3atTjbm\nA5v1C/sSo+8uumGT22/q9gNK2AaIwJvAdkrfzI8Lr/IsHwMHgJxmN8ZhhgXVNPTEdO5lotgLRIAL\nQI8cpxJFeeF6n74/1VDoXaBdQS7ssCAcU3/q3ZYSFluupjLbeO72IUUDVYUsBqrXrftuKPQ1v382\n8DYhL+remVYre53OICF3AzcBsxnLUXajKli+FlRTcaqhYUb0P6qrUV19O2PzGJvG2FzG7hYE+P0H\n5s8/R8hc4AtCPiTkdPpUyEhE/v89TidEEZEIRPGKy9XrdO4gJEDILkL2E3KorOzbjN2vIBd2nNs9\nMf0WyZiReRMTUVFRYbQJOYEY/v3Wi8HBQXuMyPqCkLu0XpTzhMwYu+8ep/OoJAGYRunXRVF5E3YV\nuFxIkcD+LiHTgVnAMDAEVLhcWLPmOCG3muNbxxhbtWrVypUrDbOgoaHP7Z6a6dM4RcgsUQSlkKRB\nt7tfksYBl4FBIASMAFOBWcB4gAETgHHAEHAGuJvSScBESi9J0hS5/7vKAoWdTuccSbpd5fXaT8g9\n5rjESrCNdMRj8JODrtijr9uRLC7KaYAlXfcPhX4NvAFsAN7Q1PkrDSdjAgt9LtdHQBfQDewBrlGa\nuFSoohpTD/70T/80zV+NDctcVtZTIfmQqXCYCcKlaHRLvqZ6Nyc4IQga8q/C1hEWm4Rzk2GZa6AE\ne1wn7aVGgpC5yMXr3QK8Cfwym94DsYjixlE175CLdDL1GOij9GR+f/yiKCbt6p7q9fzwIaXXFHwO\nPcYKZSh0Sb0BB60j7s3NzUabkCvyM7s4T7z00kv/9m//ZrQV2bIgi7rtPmBq+i1qar4jP5hHIi3z\n599SWzsZ6AdGgKvABGAiMACMB4aAAWA2MJ/SPZI0HjgOzAL+KBzudbsPejyzgCLgKnAvcAL4uuLH\n8Ck+31BpKXp6cpchA8Dn81VXV8v/jv4jjurq6pUrV1ZWVubOjDTcI0kTFHxoN+udJKMOSboKqC1l\nuqO+PifGcNRgn5g77BI7G6S0SFM64+uEUHmtUgOieD0a6/OBUpSWIhI5WFPzFUp7JGkepWFJugEI\nSdIsSu+Q5SY2zi6v4ykO6HcRcjelE3Kzpurz+ZBa0Lu6umLVfOXKlcbE3Ht6BkpLizNeLJ8PKd5I\n3jhKyBw1X6qjlF5obS23iLDYQzSSY/Sjg57YI+bO6us1ZkMKgj6RFm2oLHW5pHdzdpn0iY9ROjs7\nR0ZGDKlQldmvrHDpsAl+oWrXSE6mHThjKuwRyE2FrVIh6+rq7NDdjVJEB9uroUuSNNSb6MVJj0fV\n9kf1NkB22Imy1M/KykpCyMsvv5y7xpDp+S0gc1QqElmgpOeMyZiGbDN684Zty5cAALYSdxhdc6gb\nKoVSplLTLUEvZofDI2q60d4ZiVxR0wE4DenjMGn4yU9+UlZW5lNVZKsHZ53OiUoi6TU1hsdkAIyo\n3H5Pa2tO7OCoxG7ibge0ej1Bj0eby68PpaXnVD03zJt3DujXozu5BlmX8fl8kydPlnfPmws/7PON\nSJKiGi5jl1K1cpPRBiinvLzcaBNyiN3Eva6uzmgTdCCkqTXHBMDAsAyAmxmDy6V8+1sZy8ZglvWS\nXXV1dbQ6UV5lzcPi6kW3u0TBZkFCUpWG5ZmzKre3kKbYpidVUix0IQoIbb2wb6d0SFM8R09UivUw\nMnR4T4oswQrD62nw+XxxeZDykXMaqBknSSUKIunmibZPU7m9rdKrrQwXdzOi7aqEPJ4Jhj/IU3o9\nLVIZU1O3LkiK7K3r5V9XVlYmjcbkMFDj800EMkfSc9ADUjM3qNo6FLKKpqxYscJoE3KLVS6ECmxw\nzW7TVMd0HDAy5i7jdgdVTWhas6ZfktLMF40iy3r23noslZWVaVbgKysrv/jii5dfflnHM3bW1JQo\niCad8Hhy0gVIE+cAKJ8AJUnzeAWTObChuD/66KNGm5AtlzXtdScMjrnLLFB5g4kAZ9MKmaocR1X4\nfL5ly5al2eCuu+76sz/7M8aYLl78sYaGrygz6xbTxGQATDLagBxhz9F6MdiqQlXGBiVnRymdQ6na\nhEi1lYQ5JBJR5XgOEJK5VjM3xBWspoExluUN5gAhd4pixphMNm1Bc4GqFo/vEvJwS4v589xtoBIZ\nsaHnboNrNkcQNIRcS6Dm8TmXHFU5O7sPQEND3Iv5cTs2bNigcEtZ2RljmiP+s6Eg2g6YStkBDAKJ\nk9lTMQxrVDDZu3xJxobiDuuH3fd6PNLy5Wr3YkDimDRDmMOYqhyY2ZFIf8Kyai7iMHEwxpqamlTt\nQgjRJu4iIdMVLDUHTTNcJco4qOgCvyCXlujIxo0bjTYh59hT3K3OfZJUpX5NVVukPkeEVQ2FmDfv\nJDD48MM5Myc5gUBg1apV+TnXt6Cg34DLZZ4MyCiqHoRNd2tKgQ1W5jJiT3G3wVLJYfU13KaabTZf\nZU7k+WnTzr73Xu7sScqWLVsmT1bbzjYeuUlT+m32O52KOvdKkhn6DcTRq3jLQ5TeEwzm0BT9sHf5\nkow9xX1wcNBoE7IjFLpR/U4D+tuRBX5/r+IYkc/nu//Chdk5tScZc+bMmTNnTpYHIYTIEaQ0GTXT\nJSlj7W4bIWaYK5vIg4qXf4ZaW1FWlktb9MEO7QUVYE9xLyoqsnbYvaysX/1OBGZZUJWZy9iBTBFk\nWRDloqEJong2vxHn+++/f+JEDfOfk1NZWZm8tLWnZzoyLaW6XFXmC8jI7JQkRQuqXq9V1KQQVlNh\nV3G3AXPUx9wnwiwLqlHuFISkK6uMsc7OTox2dLmOLH8KCpr0QnkepELku1RclOZgaWmJkgiV+QIy\nMrOhaEH1lMdzp8nyfAoc24q75fu9UYpQSNUeZgxFud2J3QVWrlxJCFm4cGHi5jdSeimPlZnpK5g0\nI0dp5LsXenrOI8NSasQ0PcKSMl3ZZhpWiYziBz/4gdEm5AMbFjHJWL5IIRR6d8GCh9VcnROE3GLK\nqxkgpIIxKGsh0EfI1Egkp+NVozDGAoFATmeohgi5ldIiUwbTFRIhpDTT92pYEMZD4xyCPLNixQob\nJFwowbaeu7WVHUBZ2RSVe2jrJZkHKhjDypU+ny+69piGo5R258t5DwQCOW3j3kNIGaVFfn86F0qP\njva5Y6vTebuCBdVX1661hLIDiDZ5tj22FXcAr776qtEmZMUMh0NFIzBRNG0PEMYYLlxQOFLjbr//\nRuBcXiSvq6srR5EZAOjpmQLICTDyLS1xufW802nODJko3/J6xysQ9/vyYApHJXYWd6uP3KuUpF3K\np3bU1Ji2foTIMWXFczxuFcVJ+eqAprz9gFoCpaU3jn3L8u0tKvH7CZmhZraJIXxWVpZxPeBNQhZZ\nJL29oLCzuFt+TRUocTjg9RpthRaS1Oi73VsUZjpWV092ucK5T4sMBAKaR/RloKGhglKsWZP4F/mM\nr7744j2UmjZDJsotCraZBVgivV2mQFZTYW9xt8HIvQpJUt7FNwwVDZ5ySqruWiHlh1izZjJwKsfB\nmYqKipwkFPh8F93u9PGWr/7oR3j77esZNaYlHL6mYCu1o5oMpEDKl2TsLO6wfgcxAG2KIzM3AFeM\n7ueevvf6jxnbrFivZ4riTbl/O7kIy5yoqZmUNk497HJ9JRzGjBlyPqja5mX5JHNagiCUW2c6R4GU\nL8nYXNxtQD8QUlb//RVKrxkn7rITmjHKMYNSpfkh1dVfABdyGZzJRRLkrwiZCqTPfbwmSbH97uXm\nZSb04gc9nozFdB3WyZOBLUK1yrG5uNvAc/86YxFl5SElgtBvhLiPjIwASFqUlMjvut2gVOHiajlj\n0ykN5Uzfu7q6dI65+3zfBTLMv3Y6k0r/woULm5qa5A/TJByTpPRhmfOCcLemkZCcfMBszcDAgNEm\n6MA2gLW0KNnyTH4vaEdHx/DwsIYdz6mxsy9nb6qpqamzs1PHA/YAzOXKsBGl6f8+PDzc0dGhm01Z\n8A7AgsE0G7xtKQFpbm422oS8YnPPvaioyPIdIoFvMNanzCXPW0v3zs5On8+3cOHCceO0fIVmMKY8\nM3KKy5U4p0kX9K1nOeF0TgGSZshE6VHQ+nHcuHHyY5DhXvx8ZEiD+W1Lue0FFZOB7cMysMsSSkjZ\nsuo15LwxZFTWdQhoKGz4vmbNKbc7R/quGz09xZI0I23uTYCQeWqSc7TdOHUkfcPM04Iw2VJ5uoUw\nfSkW+4u7Pa5oL6CkWvUictvfQxRFfWQdgNt9QHEPy1mMXXK7z6V1ijUQCAT0ct4DpaXT0obaQy5X\nhfJ64wQMWW5Nrw5B5RV25qAQpi/FYtvGYXYjFOpYsODeTBfrmsvV6fEszsE17ezsVLhkqoqfEvK/\nFVrb0HDE7b5d17fm8/mWLVuW/bDWTYR8C5iW1raThMzO2viRkZG8ufOfOp1fYyxNmcXnhNzN1cPE\n2N9zhw0GMwEoK7ukYKuJgqB7mFb2GXOh7AD+VBRDCoPva9ZcBI7qmjlTWVmZfY+Kj53Ob2RSdvh8\n2Ss7gHHjxuUtEO9MXx3t9d7d0pIfS3TBDiKgkoIQd8t3iAQAOFta3s8obfPn61guKIpijhz2KFOr\nq6cqjiOVMzYFek7z0KWCabYkZZiP6vPp2B1M9txFUcy1yg+krY7euXw5amtzaoC+FEib31gKQtxt\nkO0OALW1Shp9ZDvveZSRkZGampqcKrvMzWoyZ6aJ4nFdGwJnWcfU4XTeDqTX7iM1NbrP4qipqRk3\nbpyYy24Th1pbU8n3NkoXWSpPBoXU6TdKQYi7bVhUX59xPNPFrM8iu4R5TdVQ3jOyunoC9OyBnnzq\nqUIikZmSNDVTQEbfdYJYakan3+XCi08zov1BSm/IYnHYEB555BGjTcg3BSHu9nki83g+XLAg/SZH\nAOWOcBwdHR0wKANvWJLwyitKtpzJ2Fn9CnG1Z/74fAfmz78tre+8P1+DOMaNG6d7g5o0t4sDa9da\nKyYDu8RmVVEQ4g4bLaf8XqYmTfcpa0QTR0dHhyiK9957ryajdGD8unW9jz+ucOObBOFs7hsCp+eY\n230jMky1nixJeWvqKzeo0U3iQ6EJqf7k9d5vte7tVp/bo41CEXd7ZLsDgCCcSSvfH0jSbpWp7rKs\n1yiYcJ9D7rxzrigqjbe43Tcpb0CWFo2pwD7fFEmamXbfICHzclxQlogs8cPDw1ke56MFC25PoeA7\nly+3UPd2GavP7dFGoYi7fSgrS99HrEZOKVGGvCJnsKxHqa4GpUrLVv3+i5KEbCLmADJN607F7pqa\nqemDzpHIgnAY+RoGG8f48eMxenG1MTXF60Ner4kamymmAFdTUTjibo8mBDK3ZxrPlDEbcnh42Fyy\nHsXthmKTpolimxH2B53OO4H0CTBH5883StmjyBdXm8RPQ/KuMjuXL3fwwiWLUCjibp81VWC2JG1d\nvjzNBukvqiiK48ePN52sR6H0guKG7+OBv80u+K46LONyjZOk9CVLHxIyxzQKKF9oVYGa04JwKtnr\nWwm5zWoZkDKFM1ovlkIRd9hoTRXyU3Nq5z1V+zA5Gca8si7jdk9X3PD9PsYmAL/Rqu8VFRWqwjIB\np/O0xzM/vXBHIr+naU07p4wfP76pqUmhxEtr134t4T1uIORbwWCZ0aO+NFCYq6koKHG3z5oq4Ghp\nQWoF2QbE1RYangyjDre7TfGa8P9hbApwSJO+q1pn+4SQWZkWUQH01dToWI+qI6tWrZJj8fI9PhVb\nKP1mgnu+iZBl9fWWW0eVKczVVBSUuNuK2tqPUye8f5fSWHF3u93GJ8OopIoxpjgZZgljdwjCaU36\nrjQsE4ncC8zKtPFZp3OqKZU9lnvvvVe+2Sf969TW1iljPYMdlN6B3HYb5eQE4+aEcLLioMPxaorL\nd66+/nOAMbZv3778GqUzpzINLRqDIFwCWDisfA95rF3GzQYozTg+iTG21IK/pqeeemrMf7e0dMW9\ni5aWTgu+Lw6z/SQmG3OHJN2G5JH3GR6P3ITAMnGYFMx0uVQkO7rdI5RemD8/+/zIWN4ipIjSjJGW\nNwnZYJpFVOXIefH79u2T/3Pr8uUVY3s97l2+vNJqJUux2GmlTS2FJe426SA2yjcZe3f58rhuM16v\nd2ho6AE13bjMS3X1kN+fuRfmKFP9/umi2F9TE1Ic0km/oLqPkEXIkPWISARO5/csqOxRFi1a5PV6\ntz7xxCKHI7avwJuE3BcMWjTULmOnHGi1FJa424+HGds6Gnx/6qmnANTW1k6YMAHAQY/HBvo+we3+\nA1H8RHk8vbq6RBSnKa5vStNyawchiyjNOBhvz/z55lxBVUVtbe3VX/yirbd3aGhIfsVP6fcsu4ga\npdDmpsZSWOJuyyv9LcY+IuRzr/ef//mfY1//SjAYsMciWHX1bzO2U42+3ySK/TU1FzLd2xhjqbqk\nvU9Ixl6+ss9+v5V99ljuAP6wt3fChAler/cFQkpaW22wiLpp0yajTTCMwhL3uro6o03QH6/X+7vB\nYDAhPoOysknGWJQTHmSsjRCl8fTq6hJRHO/xaIu/7yfkfiBDq16f77gtfHaZ9wi5ezS2Xkvpnzgc\n2/78z6NevHUpzPIlmcISdwDNzc1Gm6Ab8m+vtrYWZWUzHY53E5Ijb3I4+vLVdTYPVDG2t6ZGub5P\nEcXBmhq1sakdhMzImPXo88HtvtUuPvuA13sbRvsNhEKtCxbMkqT6l16aMGFCdK2VYzkKTtzt0UJI\nlnU5ti7zgCRdAcSxsYubJOmkJOGnP823fTnjPsYibndQcX+ConD4hJq1h05CvioIGVX7sFkrlbRx\n2uOJzl5/c8GC2O4xixYtAuBN28vItBRsbapMwYm71dm9e/fQ0FCsrEf5I8ZqgsH9cZWrDsfRN97I\nk3F5odTvPy5JRxTqe2npLYwd93iU9AfeR8hCSjPkxvh8Rwj5Lbv47ADg9c4a/ecOQmiy7jG1tbUA\nvF6vtVTelmtsKjA60Z6jlGvXru3atSvjZjscjg1jL2t8WYo9CIfPqClx6gF6Ez6H2BKeTwEmihmO\nIopXVdVVWQG/w8GCQcaYD2D19Rm3v3r1as5t4uhBIXruVgy7P/XUUxMmTFiyZEnGLR+UpJnArhj/\nvSIY3G303CL9KS2dRmmn4vc1l7HbKe1OsX2YkIcoTT816YzT2e92T7RRNAbABa/3FgBlZe9TejsU\n9RiYOHEiYuqeTEt7e7vRJhhMIYq7tZCz1+PSHNPzTcYGYgd6lJXdoLtZJmCC272Qsb3K71t+/3Qg\nbj5f+4sv7iFkXsYaVJfrZkpL7KXsAN5bvnyBIOwRhFmtrQ+piTXJsXgzY6dGgdooRHF/9NFHjTZB\nEXv37oVKWY/y24xtjVGxhS0t7fZz3gEA9zEWUPzW5jAGSi+Obn+yt/fjH/3oflEcl1a1DxICpzND\nLN6KeL0VACg9u3ZtNtn68hfVbBR6wB0gzE5LQ8pobm42ecL7tWvXMPr8mw0fE/I78vX94ouuu++u\ntPG1drlGgHHK9LeXkFnADYw9SMh/UrokrbJ3E1Ju088tTOk4INLa+jU9egxcu3Yt+2+sjgwODhYV\nFRlthZFwz910PPXUUxMnTtTld/I7weCvZS/1rrsmffvbJ803REI33O53PB6FVaxzGWsHwoSMB9Ir\n+7v2VXaEQodaW7e3tn6tpUWXHgPyN1aOIpqBAld2FKa4FxUVmXOxpaWlBVrjMMkpK7vD4XiPEAB3\nvvvu+bSTta3Of2PsQVFUWLQ1HTgIjAf+T+rtDxPysF2VHYDHcyPw6NhOYdkjf3vlR08DsWLShO4U\norjDfIst8o9hedrJqNpYKEnfDgbfIgRAP6C8w6Ilqa6eSum+tO8x6HL5CSkXhN9nbGTatPGS1J9U\n310uWyWzJyCtXQtgUm7G5k2cOPHatWvmjMUXDgUq7uZZbNErvJ6OsrLvBoMiIfczVpbD05gDt3tR\nOJw89dPne4OQqx6PUxTl1dFvC8LfdXSUUHqCkNhbwlVbLp/GsJaQWxyOxbm8e02cOPG+++7bu3ev\nIRJfyJ1+oxTigqpJuHr1KoBJk/LU3evgww/fVl7+ydq10wBVSW+WJBLZP3/+PdG3KYrbamsppUWi\niNLS6FZNTU3ytApEIqipOSdJR4Aw8F37fj6HKO1rbR0BqvL7Hvfu3Xvffffl7XR8NRUF67nD6BEt\ne/funTRpUt6UHcBX3n33/bVrTwK35e2UBlJaeg9jnxCy3+X6iJD9tbXfFIQivz9W2eO2h99/o9c7\nHvgqsI8QG7TCjycU2kbIqdbWc0DV2HFLeSCfyt7e3s6VHYUs7qtXrzbkvPJTaj6/61H+hLEyoA9g\ngpD/s+efYeCax3MLcA9jmcMsLteR2tpyxmYxtkgQzns8+whBiinS1sJHyA5CAJTW158Dfre+Xt9F\nVFXs2bMn16cIBAK5PoUlKFxxz3/YXU6GMUTWo/wOY0eBg2vXGmhDHgg7nd2EfFMQ7mWswuvNrNGi\neMjj+bKBu9s9g7FFjMHjOWxdiQ+F3iaki5Dq+vqvMgaga+3a7zBm7AiO+++/H6O/BU5uMbq5jWGs\nX78+b+dqb29vb2/P2+kycPbsFqBHQYsoS+L1HgBYOBz72glKmSAkbnu9cVg4nPSv1wmHTwIBoNNS\nLcPeB3bHNAJbC3xivh/7ihUrjDbBzpjueueNgYGBPJzl1VdfNZGsx/Au8BogtwO0B78G9gPM641T\n9ih9Cer81FNPbamoCClRPUE4DpwC0t0GzEBLyxYgMPbK/hrYaj5ljzI4OKjvbyQ/P23zY95LbnXa\n29tN7ZjU1+8DmoG3gV8Bmx0Oow3SzrNAJ3Ago355vYNj9f33587tUCXWXu8QpcdNKfEn6uu3A90J\nN2wf0GOFi2tOH8jSFLS47969O0dHHhwczNGR9aS+fg/AWlrkf28G3rSCCsQy4vU2ABfVSO1FSq+7\n9l7vH86dq+28PcBJ+dHHDLS0rAcuJV67lhYzO+xJaW5uzvK3k89wq8mx2LXXl1x8D7L/duaTq/X1\ne4FLo5HZq/X1rwOiJcI1Xm8rMKApDv4roJ3SLZTGDuvQQBA4Dew0TkCPCcK2FBM2PnA4LOGwJyWb\nH1FbW5u+xliXghb3/v5+HY/W3Nys49HyRzB4xuE4HCsEwWC3w7EJOFxfz7xe4yxLgdf7GbBLq6Se\nEYQPgDeBFuAhrZ77l4RCzOs9AezNr8SfEoTtqSNRnzgclvPZE7HqD8o0WP4bkCW6rL2sWLHC6hHD\n7cAJh+P8WB9woL5+C7CHUhYKGWVYLEFBeAe4otkeQfh4rOT9MaX9lkHuAAASA0lEQVRPT5v2uR5p\nMAOUngX2AYyxQ7mLyHu98r2tNZV2B4OblU3LswpqF674amqUQhf3xsbGbHYfHBw09aqpSnYD25KF\nbjscjteBj4zLBewRhI9kR1WbrHu9u5OpYTQsc5jSDcAn2b9Br/dzIAj0AIeBg0AQ6AaCwG7gc8AP\nSEAbsB14GWgHmNd7RRC2Uvo5pczrZYIgUXpREJjXe0IQGGMn5VuF1xug1C+/i1RBs2Bwa3QRxV4o\n9OK5ssfCxV27uNvysfGIwxFOEasdqK9/E9gE7M9XrshVr5eFQqcp/VxrkGEXcC61ZMfF3M8LQjel\n7wDncup6M9YbNUkQmNfLQqHr/xCE6P/OU8oEYR/QDewGQsBA2hj6vwOHLRtkV0Jzc3PGeDpfTY2l\n0MVd27fB3os2bwN7UovpLkoPU7oZeD9rP/ea1xsQBBYKDQtCK6XrgK3Ah8CHwGejTq5fW95hKLRD\nwY6pFlQvCcKbwBnz5Tum4lx9fa+tlT2WNE4V99xjKXRxV0tbW5u9lT3KDmAobeh2SBDeAnzAwUQR\nHA2e/IpSFgp1UfoKIAKvAe8A7wDbgN8A24FtwHG5fNTr1Wfx1uv9FDiv7MaTMVvmdWCLXBhlYn5p\niewmXRkYGEj6zJ275GYrwsVdKW1tbYXmF5x3ON7KKBxe73uACLwEvApsAT4BtgGfAR8BTBCOU/oh\nwEKhgzkO2e+mNGlgPQ1KUyFDoXeAfSZsP9DSstn6WTHZEPvkzWMycRT0N0NGSdi9QLz1pGxX6Bga\nlVETCh2hdJ8mjVOX5x4KbQF+ldOIvBq2OBzBggnFpGFgYEB22Lm4x1G4XSGjpG8PKQ9jXLx4cb7M\nMR1fY2zfggVSxuHa8+fnxZwvOeJyfUrIpdraOX7/vXkYPTF//ncY+2PGwpL0DiG/UTasNUf8KyHf\nobQsN0PyrEVRUVFVVdX27du3b99utC3mgos7HnnkkaSvy0O06+rq8muOGVnEWAXwrnnmr4riLkIm\nS9LXGJvi9+f55Pf5/X/I2Df8/gNO59tyQ+A89AQOhY4KArzenxLyn4T8fX29sZ17zUY4HP6P//gP\no60wF1zcUVxcHPeKvGpayN56ItMk6eGWllZj9T0c3kJIgBBI0gOMzci7rMdxp9//HcYABD2eL/Rw\n5Ltdrk2Uyjr+S0L+i5A3CdlIyD5KBzyeOZSC0v8dDP4vo3uym422tjbuhCXB6LiQKYiG3devX88X\n3NOzA2jLf6g3FPo58IHeX9cse8vEcZjSt5Wl1gx5vczr/YjStyhtAX4JeIH++vp9DgcLBq/YqL40\nD/AfbComGH1zMQWnTp0aGBjo7u7m9/+MPMiYnxAfIdX5mrDc4XRelaQnBCHzqDxDWeD3LwAgil84\nnWFJmisI5ZQelaROSdovSVMAAkwFlnq94wEA30x48rgXADCJe+WKWbFihVHzMs0PF3cA+PGPf7x7\n9+6vf/3rRhtiDZyMfVUQPiNkPDAB6Ad6AafDcTOlUwXhZwsW/M/oEDWnU/NC63GXa1CSbgLuNTr8\noo6amrtqau4CIIqoqZkDzHG7v220UbaEK3t6CMuX/2VyZM+9qqrKaEMsTigEjwceTy+lJ1tb5zsc\nB1pb5zocxcCB1tYrwAgwETgGALgNmE5pSJK+LQg3UDokSfuAKkE44vG4PZ7nvF7U1OTU2KamplWr\nVuX0FJwc0dbWxn+t6eHiPobm5mYemTEGUQSlX64T5iUCw8XdonCfXQlc3OPhHkHhwMXdigwODhYV\nFRlthQXgqZDxVFVVtbW1GW0Fh8NJQnNzM1d2hXBxT0JVVdWKFSuMtoLD4YxhxYoVPGqqHC7uyVm9\nevXAwIDRVnA4nOu0t7fzOLsquLinpLi4WG4sw+FwjKW5uZlXjKuFi3s66urqeHyGwzGWwcFBHo3R\nABf3DMjxGR6i4XAMga+gaoaLe2aKi4u7u7sHBweNNoTDKSz4Cmo2cHFXRFVVVVFREQ/B24mhoSFe\n5GFmmpub+QpqNnBxV0FdXR33323DhAm8sZJ54T579nBxV0dRURHXd3swNDRktAmc5PCsR13g4q4a\nru/2IBAIGG0CJwkrVqzgWY+6wMVdC0VFRTxF0uosWrTIaBM48fCOYDrCxV0jq1ev5vrO4egIX0HV\nFy7u2lm9enVbWxsP0XA42dPe3s5XUPWFi3tWVFVVBQIBniLJ4WQDj7PnAi7u2VJVVVVeXs71ncPR\nBo/G5Agu7jpQVVX16KOPcn3ncNTCozG5g4u7PhQVFdXV1bW3txttCIdjGXg0JqdwcdeTxYsX8xQa\nC1FRUWG0CYULz3rMNVzcdYanSFoIXsdkFFzZ8wAXd/1ZvXo1j79zOKng3QXyAxf3nFBXV8f1ncNJ\nhM9Uyhtc3HOFvL7KS5w4nCjNzc08NyZvcHHPIYsXL964cSNPoTEtfEE1n/CsxzzDxT23yN9mHqLh\nFDg8GpN/uLjnnMWLF/NB2ybE6/Vyzz0/8MkbhkD4pLG8wQOOpmLfvn2BQKC2ttZoQ2xOe3s799kN\ngXvu+YOn0JgK3s89D/BojIFwcc8rPD5jHrxeb3l5udFW2Bn+qGosPCxjAPxB1SR4vV4elskRXNkN\nh3vuBrB48WIenzEDvP1AjuDKbga4524Yzc3Njz76aFFRkdGGFCjXrl0DMHHiRKMNsRu8b4xJ4OLO\nKVx4WEZ3uM9uHnhYxmB4iwID4WEZfeHKbiq4uBvM4sWLi4qKeApN/mlpafmnf/ono62wD1zZzQYP\ny5gF/tvIPy0tLcuXLzfaCsszODjY3d3NE8DMBvfczQJPgc8z165dW7p0qdFW2IGNGzdyZTchXNxN\nBJ/ilE9ee+211157zWgrrE17ezvvG2NaeFjGdPD4TH7Yu3cvgPvuu89oQywML8czM9xzNx28BU1+\nqKio2Lhxo9FWWJXBwUHeN8bkcM/dpMj5kbzEKafs3buXe+7a4M+X5oeLu3lpb28PBAL8J5Q7rl69\nOmnSJKOtsBjt7e3l5eXc7TA/PCxjXuQpHzxEkyPkmDtHLRs3buTKbgm4uJsdniKZO7q7u402wUq0\nt7c3NzfzvjFWgYu7BVixYgXXd90JBAK8n7sqNm7cyIOEFoKLuwUoKiriKfC5gAfclcN7PVoOvqBq\nJXiKgo5cvXq1u7ubZ8sogX/xrAgXd4vR1tZWUVHBV7Syh6fKKIHnxlgXHpaxGFVVVYFAgHcJzp6N\nGzdevXrVaCtMzeDgIFd268LF3XpUVVUVFRVxfc+S8vJy3s89PYFAgCu7deHiblU2btzIU+CzoaKi\ngqdCpkKeIVNVVWW0IRztcHG3KnV1dbzEKUt4KmQquM9uA7i4Wxte4qSZf/mXfzHaBJMyODjIc2Ns\nABd3y8NT4LVRUVFRUVFhtBWmo62tjfvs9oCLux1YvXo1j8+oJRAI8FTIWNra2nic3U5wcbcJPD6j\nlkcffZSnQkZpbm6Ws7CMNoSjG1zc7YMcn+EpkgopLy/nnruMPOHaaCs4OsMrVO1GW1tbd3c3XxDL\nyJUrVwDccMMNRhtiMIODg7wjmC3hnrvdqKqqKi8v5yH4jHBfFUBbWxtjjCu7LeHibkPkNbG2tjaj\nDTE1gUCgwN12+SGvuLjYaEM4OYGLuz2pq6srLy/nS6xpqKio2LNnj9FWGIb83eA+u43h4m5biouL\neYokJylyc3ae9Whv+IKq/eHNuJNy5cqVwgzLDAwM8FBMIcA9d/vDW9AkZfXq1XLCTEHR1ta2adMm\no63g5AMu7gWBrO98iTWWAuwa1tzcvGnTJv4YVyBwcS8U6urquru7BwYGjDbELHR3dxdUWEZeQeVz\nUAsHHnMvLHiJU5T29vaKiooC0ffm5uZHHnmEh9oLCu65FxZVVVWPPPIID8ED6O7uLpBJTPLjGlf2\nQoOLe8FRXFzMu4zJLF682GgTco58I+fPagUIF/cCZfXq1Xx91fbZMvIl5j57YcJj7gWNXMxitBXG\n0N7eXl5ebuMmtzyfvcDhnntBU+AlrDZW9kK+rBwZLu6FTsGWOHV3d9u1931bWxvPjeFwcedc1/cC\nTIG3pecu36q5snO4uHOA0RInvsRqD3hHMA64uHOiyIpQOCEa+7Uf4FmPnFi4uHO+RC5xKpD4jM0q\nmOQaVKOt4JgILu6cMRQXFxcXF/P4jLXgK6icRLi4c5JQCFOcbJMtw7sLcJLCxZ2ThOLi4sbGRtvr\nuw2yZeRrxFdQOYlwceckR57SZ3t9tzRtbW3l5eXcZ+ckhbcf4GSgubm5vLzcfr5hW1ubpd/UihUr\nGhsbubJzUsE9d04G7Drlw9LT5nh/dk5GuLhzMlNXV7dp0yaeQmMSBgYGGGOWfuzg5AEu7hxFyKUx\ndipxsmgRkxyKeeyxx4w2hGN2uLhzlFJVVfX973/fNv57d3e30SaoprGxkVcqcRTCxZ2jgpKSknvu\nuWf9+vVGG1KINDY2NjY2LlmyxGhDONaAiztHHSUlJY899lhjY6PRhmSLtcIy69evf/rpp0tKSow2\nhGMZuLhztPD0009bXd8tJO6NjY08yM5RCxd3jkaefvrp9evX796922hDNGKVVEjZZzfaCo714OLO\n0Y68uGdRfbeE597f3899do42uLhztFNSUiKv71lxidX82TLr16/nQXaOZri4c7JlyZIl3d3dVtR3\nM7N+/Xrus3OyYYLRBnDswNNPP93f3797926eqKcLXNk52cM9d44+lJSUlJeXWz2Fxgzwz5CjC1zc\nObpRUlJioRRJc/ZDlSuVuNvOyR4u7hydkVMkjbbCkqxfv76xsZEvonJ0gYs7R3/sUcKaZ+S+MVzZ\nOXrBxZ2TE2T/vb+/32hDrEFjYyPvLsDRFy7unFzx2GOPbdq0iet7RmRlN9oKjt3g4s7JIY899hhP\ngU+PvIJqtBUcG8LFnZNblixZUl5ezvU9KTwaw8kdXNw5OYfre1J4NIaTU7i4c/LBkiVLeApNLFzZ\nObmGizsnf1ioxCmn8C6+nDzAxZ2TV7i+874xnPzAxZ2Tb+QU+F27dhltiAHw1gKcvMHFnWMAjz32\n2ObNm422It80NjZaYkIIxx7wlr8cY5DjM9///vcfeOABo23JB3wFlZNnuOfOMQxZ7AohPsOVnZN/\nuLhzjOSBBx7Yv3+/0VbkFvkBxWgrOAUHD8twDOaxxx575ZVX9u/fb0vflvvsHKPgnjvHeH74wx/a\nMkWSKzvHQLi4c8yCzfS9sbHxySefNNoKTuHCxZ1jImyj77LPPnnyZKMN4RQuXNw55kLW91deecVo\nQ7TDozEcM8DFnWM6ZGW0qAvPlZ1jEri4c8zID3/4w3vuucdy/vuTTz7JlZ1jEri4c0zKD3/4Q1iq\nxOnJJ5985plnjLaCw7kOF3eOecmp/84Y0/FoXNk5ZoOLO8fUTJky5fvf/77J/fdXXnmFKzvHbHBx\n55idKVOmPPDAA6bNGX/llVfkCBKHYyq4uHOswTPPPGNCfX/yySe5snPMCRd3jmUwm77zODvHzHBx\n51gJWd8vXbpktCFc2Tlmh4s7x2I888wz3d3dxtrAlZ1jfri4c6zHgw8++Morr2SZIql54h1Xdo4l\n4OLOsSRyCnw2IXht7j9Xdo5V4OLOsSoPPvjgM888o9l/1+C5c2XnWAgu7hxro9l/V+u5c2XnWAsu\n7hxrI/vvOU2R7Ovr27lzJ1d2jrXg4s6xAznV92efffbBBx/M0cE5nBzBxZ1jE2R97+vrU7j9Pffc\no2QzHo3hWBQu7hz78Mwzz2zevFnHA3Jl51gXLu4cW/H444+vW7du586dGbfcv39/mr/29fVxZedY\nGi7uHLvx+OOPb968ed26dek3SxOW6evr27x5M1d2jqXh4s6xIbIup9H3NKH5nTt3Pvvss48//nhO\nLONw8gUXd449kdU5VQrN1KlTk77OfXaObZhgtAEcTq6Q9X3dunVJ3fDEmHtfX9+zzz7LlZ1jD7jn\nzrE5jz/+eFL/PS7mzpWdYzO4uHPsT9ISpzjPnSs7x2ZwcecUBM8888y6deuSrqP29fWtW7eOKzvH\nZnBx5xQKjz/+eKyCM8YA7NixY/PmzTw3hmM/uLhzCohnn3123bp10RTJHTt27N+/nys7x5YQ2X/h\ncAqKurq6S5cuVVRUPPvss0bbwuHkBO65cwqRpUuXFhcXc2Xn2Jj/H9XTxZykvcM7AAAAAElFTkSu\nQmCC\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_stereoN = stereoN.plot(chart=cart, mapping=Phi, nb_values=25)\n", "show(graph_stereoN, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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V9enT54Ybbji+rmFRUVE8KDvEbk5m586dx73NvLy8tLS0zMzM496y5kV4BJIh\nGZ6GZHgU+sEiw8gWwplFnA3PNucJKBLi0JGGMQAWgxLi4FyiUsqyhkAxKCGmB3fOhW/hXcgR4ktn\nWlIIVeZ/5rGUt6EAvLAEPgIvlMA8GAzZsAN2wJcw1ZkI9fs/gp2Gofz+WTANpsB2UH7/eBjhdk+X\nshTWCzETpsIyIWbBouTkyfANTIFCUIZRbhhZsN2Z5xQiE5Tfrwzja/jamRe1rDWGMSrsRzQdXm/F\nzp1+ZVmZ4AMfWOA3jIWwGMYHd/4MvoYAFDnNKqWUein46W6ogar77x8I70O7a+lyPn7LUkqNgq9h\nlRDKMObDHJgE/4F/wHswXojNwSlrTTTy8vLy8vJOUONxMpuqlIrlhPvXX399Ipp1yj7s3r37RDR+\nCrL+3XfnBGX9PugHz8BXMAYeBhu88Ghz3J1x/8odqAx8EVIry9oIa+AfsCIk637/CiHmwb9glBBK\nqWmGsV6IDVAKc+Aj+BpGw3BQlrV+vPUxzApTwGFhYvpWWPrNu7DDMJRSk2EsZMJu2AzD27a1g9kv\nK4Tww3SY4XY7xoyC+eCDkWAlJ49w9jSMciE+g9FQCgthgRDjgzbUWpYVlpYzxtluWfsNYxR4wQcB\nWADFQiyD9+BNIf4MHsiEITABDoTdkEpYDcqyBtd1trJhO+TB3FvFHT+lyy8OfppVdzcLssGG4fAR\n2PCxTqSJQlpaWlpa2gk9hRZ3pZRasGDBiWt89+7dmZmZmZmZJ66LPhVYZxgD4F54CJ6GbBgBXwZl\nbo7bvQDevEV06Ix4SNSq2vfd7iwogvVhcvyPoNasFWJHMBdwp2VlwGuwBHbAXiH2Oy68YWwEZVlZ\nrRkBH8ECGAXfg7KsfCE+gh+EUIZRKMREmAI+qICx8DlsAmWa86UMCWVtIDASRsMOUKaplJoj5Rj4\nDmbAfBgCyrYnwvfOCCPIOOf/fr8yjH/AcNgOu2AXjAY/bIMdUAEjoTw4NNlmGFPhjzfCXyGVQS3J\ngVIhlFL3QhZ8D8uhJnxwo5SyrAnOjQ2JfpBvhfgcNsDU5kzsayilai1rdINuYAI8ClNhIWx07NGE\n0WRj+hMqa0dFLJ+ApunidKzmR/MgvA5Pw/3wMOTUy622rDnwRUpKqy4opdTcublSvgerwmTd4VUY\nA5X1tluWMoyR8DksDSraRCgDVeE3xhoI/tyKfFCWVSpEnpRPwCxYK+VS2Cvl6zAOlJQqENhhms86\n0ZIgnzm+v5R+UFL+CyyYAyoQULadCzkwH8YED5kEy6VUtr0CimGs81HIYMvKDZPjMWHoWJsJAAAg\nAElEQVTJ70qpiUJMCft0mRBWS9ROv3hZ8CvuPJ8vYIZjrWEopbYZhjIMv/Nn8BTLDaPaMKqcO1BX\n4icKoZTaKkQANsNOIT6BT+rKt1eIqfChEAFYCWsjtXNq0gTeeoj4UXaVwJ57PTIzM9PS0rQXf4Q8\n5nY/DO/D3+AlUH7/EiHK3G4VCIT2+RRsIf7QilfasRTWwUC3+7OGDqNh5MK/w+Ine4SY6bj2Qiil\nBsD7MBos8MKQM+BuxEMi5xVjhxDh/cHy5ORwA5RtL5Yy9Nc3UmZBwDSVaVbAWhgGFaZp2/bBPQKB\nsfAtrINiGAVj3e4xMB2mw1Ipq0tLnR3nmuY3oKTMh22wFkbA5DCtr7asirq6OTT8wv3+obBUCK8Q\nA1pRBIvgPx0pbHhzhFgOi+BtOBTqsawdzv35z3+cDRnBj76bZ/U8n/1CbHRWWtVlOoyBV8APs2A1\nbCfSSU8Z+vTp06dPn6Y8Y/zEZFRsxT0mOLGa7du3x9qQ+CUZnoPJ8DbkgBMlV8nJ4fv0hX/CCigA\nZVnVpqmUslNSPgqTkiohdgYVPA3GC1EK+ZAHVbA7KI6bLesV8MIcmAUTIRsWC3Ew/hPkQGnpcFAh\npVYqV8piKbdLWSZlOSyHLJgWjL0opWpt+yv4h/NnIKBMswxmwVfgDfns8+blQj4sg7lOIF6p4fBD\nqNsIBFQgMBT2S7kRymA7rIJvYDsUwQpYBYvAgmVQBhthORTCBNgrhFLKWmudfT//7khRpM7vfZgG\ni4RQQsyBmcFBwMrLLy+H1XVHCXTD898Hd/gMSiE3rOOcAbsNY7lhvA9joAS8sPHU0/eFCxc2saw7\nHOPS1uNLjL/1WI1iHn/88VtvvTUmp45zkuE9+Bo+hB1CKKWmwIq66vCZ270EiuGZqymZcyg343W3\ne5wQSqnlUA0rhNgoxATD+CusFmK8EB/AzKDehVhsGOtgxpnQm3t+hlJKmaYFy+F7WAHz4QcYAmtg\nBZTDCqiAz2GhI+WBgCP6X9VVf6XUUBgFRbAVlGnONM2/wFQYB1NhFCwNXVogsEXKtTAVJtW93nmm\nOb7ulq22PdaJ8AQCyjSVaSrbHuW49mFDjUmwMnix8gJ4hDfPZ3ndpqZCmRBLYH2wv1lgGC/Ch7Bd\niDVCvASjYVewHWuu9cyVB8cQb8M8IZRhFEOxo/JKjQzOHufBesNw+rMdp4a+O9mNCxcujJUBWtwP\nEcNRzLJly2bPnt2nT5+srKxY2RBvvAzvwnD4Z9DjXi/E6qAuLH711e/hQxgNX8Lb7eHxOs/P21JO\ngBWwAebCavgBdoYy8yxrFnwM1eG5en5/Ebx7JV3vO9TUEtNc1kCM5sLq3r3Dt2Q22CcdskMet22X\nQgWMciq6KJUL86VckZOjlPoM5oAXekNyWDvfSZkH42AdLIUNUirbHgeFYfEfhxENzv4VVAUHDQ61\nljUzuNtwx4Uvsc6/g0IYD5NhNpQEVdu51ZvrZpHmwtvwLfwAO2CLEJt3+rk3uJvffygxxu/fLEQJ\nLIN8Z6NleUEZxgonBTPRUySbPghTj8rKyhievSGnrriHyMrKCj0W5eXlsTYnRvj9yTAZ8uBvsDAo\nMQNA+f37DWOW4+T6/UWGMQ4y4Pzf0b+gf6iBFSkp2fBPJ0+j3jye37/L8Z2VUkp9CWsMQ/n9Y4RY\nC19cwPW/PfQc5plmruMUh7HWCYLX1oZvHAEVdcV0rJRToBx2OhOttq2Uertbt++cyUzTVEqtz8mZ\nCeugTEplmqPgE3gZBkuplMqrK9l7pPTDbJgPW6U86KorpZQa3tAXtu0xDTbmCDELXg6Lpy8XYhYU\nwsxI3vR6x/gw9z8Dyg1jPIyGZVAB/3Qz5cyDx34a6YyFQsyGLYbxNDwAJYaxAmZCQIjEk3gnAhNb\nWXeIBzULJ8biHlejmPvvv//UjNWMN4xkGAb/hMyQsvj9A+BbyKsr1v1hghCzgL+ilFo4YMAkKIVN\nMB76NUiV2StEdYON5aY5CsbBh83xNGeNaYbCKbMahFaUUhETty1nz0BAmaYftsBu+ADm1/Wy89u1\ny5HyO9hgmntMcy2EDwsmQCFMgmmQC0saeOjrTXMu1Di9iJTboSpYmX2jlOFBIWXbw+t1S7Y9CkbC\nxGDse00wZqKq/FNaR/GmLWsz7AvOVSwO9+X9/gIhtsKuoMufHiXeUmEYoyEbFsBgyDOM5TAftoBa\nsybiIScjsQ3C1EOLe33iSt/Hjh2bkZERD15A0+H33wsjwPHcnWjMIsOY4oSe64qyUmoojIA7buLO\nt8UyITbAdliUkuJ8utgwxobEyO8vDzZYj81STuxI3jumDVNhFnwP08GCLKgO98cDAaXUGMiTUgUC\nP6SkTAcfbIZJEAhlr5umOnBgT2lpjW2PC+pduZTLYOB11ymlsmAJTIGldWM7DqPc7kL4HgogUFff\nP4+onrY9AZRpbpJyCVRBabCc2QzYBtuhAjaDknKRswir7iBDKTW9yPr6ArZEuj/K71dCfF93Sjmc\nV89hC5SBDYOjhFwsUJa10TBWC5ENU6EvfOKkSJ7k+u6MtuNH1h3iSspUPIh7vAWqQiR8OH59Ts7X\nQiTDAEiGQvBBFrzkFF6PmCK9YMEQyIM//ZwKKI0kPQNBWdaChontQVZJuR5m+uu457lSfg1LYTEU\nQAEsc6QWxsFiCMAiWAA/OA67aQ6G7Q0UUyn1ndt9wDSVlEVu94IBAz5s2XIdrANl23NgdEObA4EV\noLKzlW0HoAyWhEYPtj0virx+E2n7Xtse1mD7ftMskDIn0v5/+IfIhu2R9P1DGA8bGi53UkopZa22\nut3Od7AQPofp8B1Mhk3h35rff2hmeM2aSZAGb0Gm88WdtCnwffr0qa6ujrUV9amsrIw3KYu9uMfb\nWCacrKysxx57rGfPnvn5+bG25fizXohkeMztvhf6QSZ8B8+53V+73bMiKdE6y3oBPoBlzug+SvR2\nk2Fk1l1PVIdAoBzu+F2ET8dFCsgopcbCvkgingaqf/96G7eOGDHd7R4BK6Sc5XQwUtaEDt+/f4WU\n2WG2feV2r4DC4MhDKZXXu/cBKYvhW5gGixsEapyrsCNd4C7How/HtieDUioTaiNdRcdeLHNWfoUx\nFKaEtghREulcPMlHZ/MWfAK7YA3sM4yFQnwKH0CFYUwxjH87NXYcDGMxKMvywRBYCftOKn2vrq6O\nZ38r3tx2pcX9CMnPz8/KyopDf+FHswSmCeER4jmwwHIqZJWUqJKSb+tJiWU5hWWeg0EwD7KbR39s\nsrO3wErDGACTGsqibW+Ac/8e+fAIU5RKKaWmRdk+IyUlJ0yUlVJvSvk9TITR8G0wElKYnV3vwClO\nOrxtFzpLgepO3oZ4DRbDViiFknrXYtv171KQ7OBErsM3YYI+K9K5/Mp/di8WBpMdFwkxH9bU9dbz\nnbIKdbXY+N74zW30Cy1VNYwK2BZ2YKYQD8Ew+A8ME0IptdBpxDAWwUgYAdUng74PHTo0TqZMGyEO\ndSz24h5XC3Ybx/EdEkDil8IUWG0YH8EX0DdMp7YZxjRQljVciFTYbBjbLEspVSLEFngNPqZ+BmSI\nbNgLy4JLgYa43R/DmpC62fZmuPrP2FsjuOcLYbGUWxr6toHAlCgyWmiaeWFLjaZDRbA4uwoEJkKl\naSqllixZ0vDYH6TMdiQ+OrmhT6XcCBthX3AG9QuI6LkrpeZJuTR83Wz4Fdl2dqSj3vjU/Hsrvoc8\nZ9ojCqVQWVf0+TsvQJ3FsU71nrBoWH8hngZlWWOFeANWgAHpMA/ega9gVXzre58+fU6KcbMW98jE\nW6yqcU4KP6IRsuAx6A9rYHBYiZKS4cO/drunwSSorBu6zQvOi74Fb7TBmNxADubNW+xkH9YjO3sU\nDIch8DkkPRxZ2b1Bb/eVSPmFpREDI0op03SqNm6DCvC73eGqut00HaGcMWNGvePypVwHyjQLnMLC\nkZgL2xt464NgIqyEqTDfuV4nWyacQGBqsM03pQzU7a6+hJxgs5tNU9n2RilXQx68fwGTYXXE+dUQ\nzqLfILe/LfpF7GaEWB/cuM6yXgrfwe9/CXKEcF4h+whkUn9dVTyQn59/cv3E4lDE4uJLjcNO77Dk\n5+cPHTp06NChe/bsibUtR4FTk/1xWAMT4FXINYxcISwYCQOcqdRwhNgcFhCYCv0bCEF2cvK2SNkg\nId6FQpgGw2HaLbKeGgZMMxRxTm7Q+HcwUcrcAQOqg+H1XNgMWyHgLOm0bX8U9V8q5QSoU1DItrdI\nWRZ2lgpnqrOu8Qt6914SUe8CgVwpN0n5vXOIbe+XcidshWpYB15YAQtgMTiLoVQgUCLlbNgr5Top\nl8LqYJWCUtgTFsMxZ5jyDxTWzdSMyM7QN7LePyJs8Wo4BUKkO/n1fv+3DXZweohJTub7mjUV8ZQ/\ns2fPnvT09KFDh8bakKMgDpVdxYm4x+FcxJGTnp6enp4eayuOiFRw/mXDFHgSHq478xkeAPG53evr\nxgG+g7904t260rNZiC2NKvvm/v2z4dnraf8kTvnGaTAX8mAGOOkok0KTjbbtCeqmMs2JMBv8sBk2\nQiVUgbLt7+Bz+HtYTcdoTHe7Pw+GiSY7uYmR5mwdL14FArtLS6elpCxotNnvpYyY2ujYv1PKkTAf\niqFCSmWapU6oXUrH058K9Sddg/Ak9/ycJcESwVHx+9eCEuJbIXpfwZTWUa2dIsSWYJppvRacmsC+\noKxvPdydbAIcWY+1FT+G+FSw2H+jSqnc3NxYm3CsOBIf1+6GYbwEj0ImjIZHYUDd2chyw8gTQilV\nYxiLYDWsGTAgfIeF0LoHLzdnfFB6qutGCRqSJWUppN4ELxFQDeYtAwEbqqSslrJKykoplWl6YTFs\ndqTQtg8VAnP8/UCgn5TJUDB8uFLKb5r50YI2Qb6HkVAG1Y3uuds0lZROPujySLnwISZIuU5KpdQi\nZ9ltgznSz2Cco+xRmBv9pvEc//uiLICqJ55oxAal1EcwCW79FVfdQ3njnYFhLG2YlmoYTibrwVxP\ny1oXO30fOnRoenr6SRFbj0iTlRQ+KuJF3ONzXPMjiFNH3rKmCqGU+gZKIBm+aqBfb8F0IbYIEbkO\neHb2i5fDn1FKDYJ8IZY4CZEHDjRy2uUwvTUd/kb/wvo5iw6+Bq70ipyc8OBMeFJmQMqBDRQzmhes\nlFqbk1Mm5WqYBwWH6wMccqAYVkJ13SqY4dQrTrm1QVmuL53C8dGpNc1o+m6X2ryAqgiUQrRwk1Jq\np2WNgs1C7ASjM3mH0+WRQkxw6qyFUcrB106tc/oGy1rf5Pru/F4KCgqa+LzHF+25N0bCiLsKji7T\n09PjJRzv938erDPlh5dgimFUBWuXh/aZ6NQQj5I78U0LeICSXSVKqffhs2jxjTByYXJLzknF/bq7\ndHdpwx02mGZVJP3KMc1vgt76DEduoqvh+ChLmRZIuQmUlFnduq0zzYa9SH1sewbsknLliBGFvXvn\nQ4WzsrQB9UMcwcMPTa4GAkWH60tmR0/B5EnkZ3LQLZeXRNvH758Yts5gUfTUnRBFhuEsdt1c9yt2\nqr3PgW3ORsMoayp9PxmnrKKhPffGOBnnVA9LPHgl4w2jV/DnOgVedObQ6lJpGK+Bv5GhvWWlnw33\nH4zSbnW7B8Dq6HF2pdReKee1QHokvaM+Y7nRg/XvgVJqh2lOgH6wJ7ouT5JydZiSlo0YUQhbnCWp\nSqlgKuQ208yDbdFtXgqLwnWttFTZtpJyM6wN6xj+49S4j4KzIMBsNKPRYaGU5dE7APmx5EnU+kBx\nw3Ysq34G5wb/AOc1hNHZaVlDgjvUCKHCKog5s6mhKmb7hKhqPMhzzDhBmBN6iqYkPt12pcW9Caip\nqYlhrCYU4igTYha80UACpsBEeL9xMTKMa+/i3XeMwqBoLhsx4iO3e3wUeSqRUkl59v/C81Gb/RKW\nw57SCB69UkoFAh9IuVjKwBGEUxxd+6F371zYGibrDofy3G17kfPG1AYUN+rXr4FK2AxznXr0jfZq\nM02zX+h9fo3SeCwFk4AKzILw5anFQkQU8et/Tf6Zh3lvar23b68JufCG4bzvMJQVeuij443zQxg2\nbNiJaDxWDBkyZNeuXbG2IgLxIu6JFJaJSEFBwbBhw5r4sU6GNx0vbP/+JZAKa+vWUi+EDUIopb6k\nsXrfmefwP5ex0lkfFMZH8Bnk1xM701wJSimeRQ6OLM01paXzQJWURD5fIOCF0TAMVh9O3NeZ5iQo\nckoNR5JdO0y1d5pmdgMnd0Gj2T7hDAUvbG90Xauz9nU2bJByb+PGO/XOonBnnzt5ioAK5EqZD8uk\n3C7rZ5GGML4zOjzITiG2Npw4DfJFA+n3OUXELCsfVgoxOSwhclHjnf3R42j6yR5bj4j23A9PAuTM\nHJaQF98ET3ly8DUUO0tLvc5ClTB3LKduPZOhjf6YP21FdTTfNhAYDmPd7jwntaZ/f+elbjyDXRnV\nF86KtnAmECjl4GKobbb9cXRxL0lOXut2b4N9MKvRMEjDFaoFsF5KpdQKKVfApiOba1VKTYEFoGy7\nXMqdsANy4AcnMzIQUEoVB4Mth0I3prkpeueR2+ht97xj/qs5+VAcPXsyBI8eTHrZHcXvjjhkmSnE\nOnDKGywVIjzgs/Y46XsCy7pDfLrtKq7EPT4nJU4QvXr1uvXWW1966aUT1P6bQjzmdm92gh6WNSPs\nRZqToRiW1I2rRvzlOywRouZwQYZ1pmnDR+CDQindf3G7X3c3sr+3YVdh2wcXfIaxrG6dFqXUFilX\nQwVsh40pKaH9v4HcKBodsfzAJJjkvDz6cMGTcBY3vEvBBPYq2OHcZNse76TwH+7qlNMHNNg4R8rJ\nkAurYGZzHroApdQLML/R4YXltyZ9YSillGXtDQ7Iwvkq+le8WQg/5MF34QM4wzjG4Ew8zDmdymhx\njyXDhg178cUXU+rmmx87zss3Qn8+F7bocSxEUKgob8NQSqlAYBuo8YdJjFFKKdteC1NgMrzWnJcf\nS1k2YkS0NleGnW6xlOVRhgUrpMyWcouUy6AIqmCD2x1xz7zevaPNKNpRVi35HXE/XM5PiBIpo5X/\ndSiEA1Iq01wWrFq8HjZBcfCVfgtgBFQ60RXbDkiZA8sgB1ZDgfN+KCgGNXhwqFnZT8p/SBUI+A9n\nbceHD5lXVW9+uNH+2yEPZtVNEPqh0WBdI8RpQvAJIDMzM9YmRCWOxP1UCMtEZMSIEY8//nh6enpN\nTc1xafD/oHj48IN/WNZToAzjCyG+gqVROpKI4r4BdsM1dx3RQzItKD1/vomJv5bTIQdmwEQYBSPd\n7jFSfifl6gEDRjgvNa2tLU5OrpYyGwpSUgLBVamOlK+DjTAG1jm9USDQeEL99tLS7yDigqYDDQ6c\nF4z87DfNFdBI1sohAoGCRsVxR9jLpFQgcFAinS2mucoZgjjOu5TjmxNwXud0HnnghSd/xjmpvPuI\nXLbQbrjai+ewK2xl22sateHWW+tPmYYK7mcbRuORN4eZzsvQQ4K+Zs0PRxmccWT9eD3J8U88u6Rx\nJO67du2K26mJE015efmiRYsWLVrUt2/fvXv3HktTyVAeNpo2YBh85mSmNyh+G+KTBr/hEkcBAwHT\nc/jJxl1SbnBC7U+ErUStrS0dMaJIync70PtnTIYFkA3LoRCKYQUsg/VQCsWwGuY74mLbjiyOgeLo\ns4j1GT68fjBEKVVX3POkXEndAmclJasOt3hVKTXJeYdqNAKBep/6omsiD0I3xs+yv+sulZQzneW4\nYdjl9uBlgx8Y9oD0SP4KveA+eB45UI5uQxEopezVkV34mpl1HO1qZ4o1+C7cxq9RKaUsaw7MdOo/\nhy7uCPR97969w4YNO0W89XDi2SWNI3FXcTzv3JQMHjw4OTk5JSVl1apVR3vsgJSUDPehYPdCw+jr\nxH8PFzz1hPtrth1wIgxKnXX3ETwhtr3FUfZe8DKB2oBSyv2AO+U/KXSDhzFzTHuHbW+yd6jAcFgF\nN/+RG28jc9yAxV8OUPPmRWt4cfA9G4VH5j9OjxTCDon7NinXR5nbnAVrQy9KbUhJSVGjBmxroPv1\nik0GVIAn4ckINRiWSzn9CKJDcqDERClVANOBPyP7Sx6Fh+EWxF+EMdoQA8XtDYZZ30NV9Nf1NaRU\niIHwHawLRe0NY2Wjhw8bNqxv376LFi06wlMkEtpzP1Li+U41MY4Xf1Q/mOGmWaeqYknJOCfh+gjC\npsWGcXC3QKAyTAEfjfKrnrdhnlIqoAKDe8gN0Pt6uA9ehN8jn5YpgyMHf1bDHBjZK0UpZY41eRru\nhmux50WIRSilVkq51tHNkpIjCo7Pm+dtYPDwTz5Rtl3OYdLAlW2vcuLdDRI0ZzYqvhFiQYHAfFBK\nSY/kcewdh7H8IymHSLnUySCKPkyR/5H8HeVk5Ufph3gGHql/me86FdaOxHNXSinVB8bAbA5VNQhE\neYr69u177GPNk5d4dtuVFvc4Z+/evc7v50h2ToZA2C9wpRBHke3g978HKhDYWVfIECilSMVeZ5tz\nTB6DJ+Ap5MdSvi8feVWuBSXl716TvMh+tT9y47ZdCUqpeb17r4iksAEVkB9InoPnsAOHzj4ybPp0\nSSN58WHsMc1poGprQ1tmtWu37ciOVUqVSrkWVoaNfpZKubqRXqGkZEe9oEqZPfi3ci4MHGlG7LEi\ncrAEfCBQK2WNlCvuvDPibjyPXWFXmmbEjspeYHf7H5RS4iFhfHLoqx8NTopk2ZEtPR0kxERQfn+N\nYRQEk9/rDZ4cb/0Iry5RiefZVBVv4h63GaMxx5F4K7oPHq7s3wrxPMw84pG4w0DHUwt6jgEVkO9I\n+ZCUHmnOjKxTm4LpfTxPymcRvPVH4H0p1YEDjtpOcruXuRtLkVRKlagS+YnkaczvTRtmhe0fYS1+\nJLwwze1WtbWLpKx0XqN6VBw4EHC7nbd5KNv2N3p4KFHd3mDzMPwde6vd92GZf5QnrVfSSz3wwObg\nnEf4Zv6IE5zZIGXEUDjdDm70Kz9/QXjE4JDT7fevPuLslyFhnn4ubBZis2HMgflz5jT+HJ5SxLkz\nGl/iruK+M4wte/fuNQzjt7/97dKlS8O318l99Ps98Co0Ule2IcWm2Qs8QSdUDpDmXLPDNdjZUUMK\nhVLudkLtf6V+ARnbrj9vqZSKmCfeKJ4H5fcgPdIJNSz4eEDjq34cNpnmDNgM62HPgAH17tWRkw35\n0Ei0fck75s9+D72QGXWudItpHknVhDrYdsPAvVJqDUyDzDAb7HKb3lSrQEGk4ExI3B3uvJjBbXhz\n7CEvfs8RTMAopZTfvzTMzZ8Od8BvIf2RR07N2HpEtLgfHXF+v2LOxIkTJ0+eXCdW4/e/HPzxzxNi\nGPxgGCOOJkN5TbAu+ftSprah9cPYW2yl1PiZdiPivgFqXjDN0ab7dfeA6Qcrv38VfCVFw/03mWbj\nmXwRKClx0k5KVAlPw5O8cg3mvMayd3KlXALbYHbwXHXexHQ0bDPNItgi5c4GMioHSZ6AJyNfziho\nPCO+Ie9FWX9wEGdlQOidTfNN+Yk8OI9ddzKAG/jylYOm5hvG97DZMKyVljEjKOh+f7QlrPWYAP8A\npdTevXvvFkK2bXvX0V9XYhPnkYa4+6q0uB85lmXd37Pn40K81bOnUmoiLBdCKbUgTNoOS/mAAWXg\npKz0eEH+G8qCS5Y6dI7aSLWUq2DI5P48h1L7lVLfRQojhDMh+jRgVEpK5te9kBJV8pYh77oDnqhv\n21Ipc6E6eBZfsMLXgLqvHDlSbPtQxS7bXg3lUC6l12PyNKsW2I0kCL54xCH+cHyNzqY6bJcyB+YP\nNHkSc675bQO15U/M9ZhKqQLTnAp7gyJurbbEf4Rf+Z0/t8Dew8Xf+8Ev4P6ePUNBmHHOc6VjMkqp\nY3Aamoy4E/c4n4CON0Ybxj1t296alCTBe8cdSillWUOOOOC+P/hCUdlP8leUUqtNcwAopQK23apL\n5Ea2meZ6yHkghRd58FYWQOPvY3JY9aOcvoi91MGc+pdJHppcsCRnlpQLobJBXbOFP0pklVI/jBix\ntOGxo+3FzSmH+VDSoC5COM/8qCtd22ibdbDtf18Cz7I8x94kZfg6I/mxHPiYHCPl1Cg28CiOxG+A\nfdH1vW/fvrcnJV0Nz9TdZ7Nh1C84fKoS/25oPH5POux+5IyAuUJ8Cs/07Nm3b99/PvLI5/AN1B7B\nuHuTlKtOJ6AC/B17Q1BWDhx4DwaDCgTqBXAPYttboWDcCB7jnL8cxfL9xlPFo1HvtUeHkFJVlHx+\nAZtgD5RGjHGXlCyAkZ98crQnnQ41dRs0x5pO4pBSaiVUOG+hsu2InUf2j7rSUtM8qlqM9habF/nl\nNZQ7nY1SSqnnesqsRivOK6W4D+ER694wKqInOFqW9ekjj3zt1J6rm0M5XDvvSqmTQaa0uJ/EvALv\nwMiwn1/ftm27wq2g9u1r/NgyqISOKZjz64dK1s+b94Xb/SmkXBjh8egLecBTyM+PZs7QNA9T/zYK\nUyKK+/DhJbANdsH/Z+/L46Ooz//fsV4opN9qvRetpdqv0Naq1XlS25/Ht6X1bNVsQEHkEC+O/QyH\nQLWBar2QBLwARUBB2Z0FkUMEUS4hB/cVkHt3J+EKIYQr3Hl+f0x2M7s7uzuzWSSz5P3y5Yvsznzm\ns3O8P888x/vZS/TgMw7Hv4yTcDYTlVik2lKiCEFEGkYBDpK41nGJmZn7Av8C+gOriPQsbzVVJgSr\nAWc8A/QBezzlwELgU+Ab4J0rTA0iDZMueQLbdDfP6tWrIzJhJgGH3e5Xowz86QkbAJwFaPg01RCv\nUMN/32kI8LvdrwGfhj9jOwH2+R4HtIjr6tWrjXd2uRY1Rasco6bVQfwb+DCcWJcAM4DprVvnPEH4\nk7U7Z6GJIkxDjNF76gOBDURrgeNADREryrpgoqSYLIzfM5jHAIbN/AxxWIiIxfsWrC0AACAASURB\nVAAu3Z+KYhA2CASY6DhQCawHtoUKr6yjNEYsOg4u+hP+eB2mBqUdXm5Hv82OXWobDtdk10N/QDGg\nut3dOnWKzlv3AOzzZUfz+LZtKRd8txcavsOdG8ndvngaiBCEOSZJzFwWqjVldrvd//73v3Nzc0+e\nPKnf7MMbsOGHBFR7bxP88W6MB8YD7wKrHY5vgcMAf+3BANBrVvgrEDCZoh6Nr4gWASzEduAwUAGc\n0jHX1vB6JbigHFUiRvhCiKVAfNmvEPzA9qCYpVKl0MdhPzOBuRoIsBCbga3Ad8Ae8z70IDYQmcn1\nDGGvELOBdcCEcxEILp83PQHt9eIbbV2MG6R9+4O3W1zR7KEYibOaSvBUl6tj9Le62+wsRMM327lh\nknsDTzBqCHgBGBldUC5JzPwa8Fn4o9ivXz/NkD9x4gS7XNHp54a4+RJc1QE7gfmy7HE4xgGTgU1E\naAsab9EyDQTWWif3vUJUEM0ElgHlmqkeharCwoj4npY0qZTXUbyW574cWB1fWjkQUINZQ3nT8/Bs\n5IQNDFgjFKCWW5moHDgMbNdafAQCiaO7fn8CFR2/X1NV+x7YDGilT690JPTGW1fWpuSjd/hLkseT\nDQwhirhb6m4JZmZeDuyMOvS3kqTtFf3bN7pcyQVR0gO2MEAb4uU5dOiQLRbGM4jXop6r3UGuj6Ui\nMnLk27/JwH0OB1dWxhva7y8AngZuvgRXtak9yl5V/QSYDswA8s7F2HuskftUIF4FfwiBACvKJGAr\nUKVVlgrBgUDC3Or/Rm1AY4lG1k4yJBy2RksiMuzaqihrgv4fx72OaCHM7aa9JQaU5/EcIFKBKuAA\nsAvYrMmmC7GaaL+WP+r3M/MXRMXA4ffe4337NBLfQlQtxDGiJUApsFnToNfLCzOzJkzWB18DmwC4\nYqSc+v2LifoDNwGdHnusd1TI3QdUAA++WudhfyN4L70qSdVR288zF7dPSzSSe/JoJPd4cLuXtGgR\n8VmoK/TEKHIJHA/sY9/3F4GF+Mbjyc3Nzc3NNWhh4fEs1Dm4HbdCTKv9t+r1VgDXPIL2d2AV0ZwW\nLb4C1mqmtAk93sWxMtw1aV+PZwawDQgAFUBF1PxnJUqQX5OXd9TIrkcfiO+FotRZ8UtjaL4PBJYL\nEeBAtOoWM2cDASXS2xMLhuI5EdileWyE0Oh+E1AKVAD7gb3ABiAAbNdaYxMdImKP52ii1QUuXPEE\nSgFxA4bHKFDIzc196rHHuv71ryfd7uHAbElit1vvXdkPTLsCP3sUri9crMnJBQ2Ff0X9rjeA/ebE\nahpxRtBAyd0WC+OZgh/g6mr9J2U6az0iwXnRvkWQsbApIrzea9asyc3NXbxo0fdCLNM8CTqaDng8\nTbqiYFetGO9aYPFFwIu1AdhdhYXMvIFovxDfAoXAt8BsYBXRt8AEYIMQC4V4n2iRECVCaNHUw0LM\nB74FioH1QRl3FTCOUuqwQ4iD8V1JNTWsKIYGvlggHL3DEmm26BIHNfQHxhPd8yrhBeR9HVnxVBO3\njXUEPgMOJBtN1TAP2B5DNSwh0AtfatKSUZ2zPB5Pbm6uYcdBdrs/Bj4EdrtcX0nSYWDCpdA6ss6R\npKNB29zvdofa3vrd7hGSxG53tAbn2QBbRFO5kdxth+gSwZOSxCEDyuebpHvecCsu6wj35ag08hWM\nBToBjxD1ESLCkP9EltGxdpc5QDVwSSeDpEk9TglRRnSIaBfRLGAL0WCgH9AN6A8M1+pXhdAUUTYR\ncUFB/OZKephKLhTC0Knd+cXOEFCqgqZ3IPAp0RgiZv4kO3sWMK0p0Bt1yY7Rw5rGvGTLpurg8dTH\nlw0XAsAJ3QIT80UtBj4DKoEhDuRcjveAIkkqcLn8bverkjQdeEOS2gMjJemIdhO63cvOPn5vJPd6\nwS6n78dGILAr6lkKs1h9PjfAzNKTkpYaWAJU6cro1xDNACIMLk/QVxP65F9EWkSxUlUPAyOuth5E\nDaKIaKVV1YEomBRBM9Su0dwymtKk9skeRVkKLCPyAyN+HS9h32qSj9WcekMkV8qrwc/+QVfXVupq\nL2f6y2oWbvch4J+Ed4CNmuXu87HPt0xTAA5HnJ5T6Qq7OI0b7oWxyxn8MTEfmArM1Eex3G4O93tO\nAvBXSE9KzHzU5doLbCDyar4IIY7H5dl+/fo99NBDQ4YM6dgjWxNvWQt8ew0wAKfYrJUdge8TeczN\nYLbpQaqiuEbPbvQRiULBzJOJ/MBGIP+LmMOWWaWtQCC5Qq0IJF0DpSGze2b3n+BvDoexE8YkfL5K\n4DvgQETINNrJ7nbvO8s873YxPRsuuTd6ZqKhPfYDAT58WPskMkfN55sI3HIFnMAkoAzYkp1t6RDV\n1dVr1qxx/E8mLsJjl11WBbT+Z7xap4RIiTG7Q4hIxfPY2BN3y3uG0dyHaAuwClimBS0NHSnWF6TV\n1kuQDDE12YIvZvZ4PK0fbn1pJgrqMYiGXZK0FWh9h1GGezjOqoKmw4cPN5J7fdFI7hGYShTyb37l\ndI50OF4B2gEdgLeBCYAbGAp8DhS7XF9rscpk8dCTdO6NkIDrL8JlrS+rDo/fWsLWFD35JquQNESn\n3NRBUY4Ck68MbiCEL+q1wGTL1giYSvc0gT1ECQLIRtCHTNEDj/3ZKNBiEV7gB8DlDWNzg5+5bdvZ\nU9B0OGhXNXw0XHK3y/L4oyGiJVDZ++8vAnjRIv2HzdrgI+CEy7W3fg9284dRAGwGLvwz6P/R888/\nr69xtYBAII40riVMA5Zaobzq4HH1zTpKiSqAv77gQK+6+LCPyA9UE1WpKjPvTc61oiiGZVbJYOZM\n80OdPHlSo3V9yPTDq/HaeLHw4sQawnGwwuWaCrDLtRZ4+R86x4uWQBmOJIrUbAobGZ0N+pI08nsI\nJ1yunURHdQU4K1q0qAl3uaAl/u95aQzqKtGTxrNP005g9NVQj9Ue0WrSRS2s5BHGxyIheoeLDSTE\nYSLWkftCYE1TXNEFyiGFmZVqRZ8hsxUo0WqLksL2FPlkmNnXrp2Zl4CTJ0/mBhHx1ZKLwcxP3YJv\nrkr+Ad8dTHJfFV2DFuVk32TE+GkJG5FSgyb3xphqCOuBHeFPVHS4D0+Bfb6PgW31DnCNATY0RV5R\nZNJ3dF5NfKwkYtPlPwnxATA+UQvWCCwGykeNYuZKYPkFuPzpcLnHj+vkHk8pyg9AaVLkvl2I5Dw5\nsZAwYUa7EMavU36/Ru7MvLwplj+Y5PvEFN0cKoHtupsq2tU2SZIsqeLYFzYipQZ9PWz0BnS6Ef3a\ne0BX6qLuVNEdzCe3AP8F5tfPP7DS6dwLPHB/vHtjwIABZgz51fXP+9ZhnxBLrDPIMq1ayun83XMO\nei/yzNDw4CdErCjfARutp/fMIbLcQTAu1sR+99IW1/hesrqF/5jfcn9wZmZe5XKt17H5cZdrL/By\nt+Anbnd0WPVs6MBnI7OdGzi52+tUnj6sdjj077z7VHU7UPn886FP0BHZ7uy5qO2N+Wk9HjO1Sn3x\nYcfsq7BweILudKdOndKIZuDAgbG2MVOLbx4lsmw192YlsBdYDVAuKdXG7xBilTj0utghy6FPdgDb\nrRxofkrXMNYEgqJg/p1Jb1nPbYIkogjvA0ci6Nvt3gfwEZ/2VyB6hmeBTqS9zM0GTe42yjo6fajQ\n0jn0OHlS30/O0ctBb9AGp3Nz0CU9HCi2mAEZwlcvyeNaYkkzCzeGx+Np3br1R0YNjyJnXm8s0eQK\nzCAQ2A0w0ZTXX9+5QBl/U8yZHCSSb0MNh3vzhagwfazUrmGsrRZByz20iJrf/ak76+bTdQAlEV13\nG+7idq84P1gIFhSM1H+b9p6ZRnJvRCpxyuWKfGaGDDmoa/rsKnApD0n6xMepRAuT88zU1GwBPpEc\nE861fGMMHDhQ46CQCuNyoh2pftq3Zmeb8ZksBI4GrenMpzLRH2xU38TMPiLOzmZmGhN5xvxEJcCe\nRFZ5WepCqXUQgoUIRTj0CT9mcNlzYb+06GJYWmXfBubE2l6SeLK77t96+HyN5N6g0NAvho3CF6cJ\nK4CtOo8Bh/vfpeHSgG9ckemGp06NTeoxW+d0HgDG5cv1IWWNj6qrq9/IzNx0Gp72dUBxnKUrEPDp\nnCrKMgV96+YQ0RlVL0cT4EBY06UgjhNVAYdiHzHlZjszdyK6A9CvlJZwSbgYPdrDvOf9ZSB+C+w1\nQXWj6K7oW9O9VNVGSe7c8MndXktlyrFQltdHJbOHKjCd7zt/68QPUVJizPw90WiLiSUlXu8eYMX/\nOtRDauv/q9eNoShKu3btfnvBBbefDlNOUWJJa+3RZNN1REyf0Sj3qLCNhKjNpxTiSBRlo4/xyD5g\nF7AxmuIVxcD7XA8cPHiwZ8+eT7Ru3a4ew/7miXDtoB2e3JtgpklLbW57IuzTbjmfLyKsesLlig60\npg1s5yJu6OR+llvuO4WIeFpOBn2d7s3un3dGSTCIGoHjHs/HwEHDxhQxsJyoCuj2jpOZ0SsFN0Y/\noH3Llrm5uYqiKKlLiGTmiBeCysLCeQ7HHmB/+OcaU0cf+oDD8YPDweHvQxpUVvFSjN8eCGwFKoAT\nOidMaepCqYqi5ObmulwuZt4kRH0qe7u9Ecnjv38Q5Uhc0zTT3EHLJEm7BNGeLvMqEbaD7QxNG1wJ\n2y2YKcRiRLZV0sx23wkfnsPUi1HmcBwsLDTc9z1gtMNRaZrftwF974BaqTLzZZ1TcGMUBAOSGm2l\nkN/XEWlihGWFhfsUZQNwAJEtlmhsLcFFH3d/dnZ5bA6Sv5XlYgPe5+BwO4ACgAOBg0IklxcfgbVr\n10aEK1hT7U8KYpr45+BIcvfs8qyJ61xi5rlEMV3tUdgjSex2L4+6P2elL7nbztC0wZWw3YKZQkRk\n/qlOpxYZk4ZLr12FPVH9mCIwAvjcZGRViN2Af8IQZmZV/c3jKbgx1oVnm4QoLBkR2ihsBFhRtgMH\nATXqN9IndZ9ERCO3EO3Wtpfl/THWRTaKr4ZBiHJgB7C13pID2rIX7Vu3rEkZhJ/9H31uEOC9/Z/Y\nHWdMjydg8bcEgEXRL45nQUKkXWADcj+bLfeIl9wKh4OZXV5X+1vwA1ChS3U3xMq8vI+AKfEbQzMz\n8zagw1/q1B8vfxqFvpjEZxKGtmeI4oUQJSUlSQ6tqhuASqDaiI+c48J+r95y3w6EvDHH8/Kqouz9\nEOTv5Vh58Rr8QuwA9gFbk/LMaG8zcUKmScdpPbs9XGHgfsFzmJ0Z1scjhNlEi5I4nNtdGq1Pp5nz\naYfly5ef6SlYRhpehrTBCkkKM4t8vqMOBzNf1wYbjYKohpiXnT06obNViP3AbzrW3QwXP5qCGyN+\nHdDrr7/erl27gQMH1liRi2HmH4gKgT2AYY2+4w2HciCMlEM1VgYN8AoL41SWUjdSVsbk9+JQIasQ\nO4H9wB5zlq+2vCmKEj/B0WqfkBD87OcYEs2vOBCthzwZKEv2/WOZJjsT7plJy4TIl1566UxPwTLs\ncRnslYGUKqyOeEhcrhn3EZ7DuKY4ZCXnLCBE/JrVRcA4BzwH6urdH+9Lnqp6SY8xc3TTqGisXbt2\n4MCBiqIkpnhFWQXs1pmKM4Hvww8hT5HRz/ig0Xl7+pFjfYM7jfdSZdnAxUG0HzgaW04n9NZiJm99\nhXUVBA2iIOZeTZ/FUtSlzWwUohDYUT/PkqpFIHSI7gSZBmgk99MF24UyUoKIjjylwCWP4PHbkETy\nuF+I8cAaI7LYRHQEuLxH2Jj3DaZlXF9vmPnCGY3fBw4cGK1ksFZRmLkQOAxEZN9Xy3LEIRz/Mcj+\nHNy5czxfswZVNUyeYWZ5ucHnW+IUrwpRBVSFt+HW1jBLwYbvks3D8fhjrspikXj2d7VtF5cSFZvI\nn0kMtzvCM/NBjAwuW6PRLXO6cDaSu9sdZv64XMUX4+LOKEr2mV9I5AbUKH73Ae/+L8SKiM/3jds6\nLomjhHBcUZLoFlJTU6NRvGbbLiYaAbwMxHLj7iPaEEznd/Q2zutfYzrf39CPFJ05MytqmTGAohwE\nvgKeyMx8hOg1Iax6n0qStdyv6RBvbr+9G+uAVckObgy3O0wT2EhWzO5oJPfThbMwYSai73CVJI2/\nCq/cWF+byAN8CHyrs1IPAZdFVWZWcUCvdZ4E1t11V9KZ2l2zs2/LzMwCBgArdeKXhggAW/PymBm9\now6nqmXAazFMcgOo6iGjOSO8mt+kplhfIR5q2fKezMxi4ACwV1uVTeeDrk6Wf2O9MK0UgoVYCizX\ngsCpw0mXS5/bszPtSpk+++yzMz2FZGAPcj8LE2Yi4mnfXAHXjdYUQmLhSyIv8J3TWamqx4iKmqHF\nmwYplfUk90VE8XuZGkOW1wBVwA/AW5076634WFgjy36g88tRjmNZNlOTaYCovZS9ivxd7QqxjSiW\nAycEzQkT6WJSlCqgGqiOo9yiw0rTsmURiM6hnAAsAUqANUDxUIF/Y6NF2cuE6HE+1ukGXJheMVU7\nOtzZLuTOzPVp42k/+HzF+sej2nfzg0ilhkkgMA6YCCwEfvdn0BADErz/4XodzguUwVzjpIKCtUQB\nYAdQ6XDslWV9emKEo8YQWwFv0/DZ6qKaSSRcbgTUcGKlccTMp2Q5TmPSmpoaLXKQoFxLUViIamA3\nsBU4TrTTaBH6LlnLfc7lwRn6/YuADVrCaHAoP/vxIl6/GsdTyr+jgLmhOKrP9316kXuj5X56YdPF\nMzlscbnKdfkwcGF1qoNUuwoLvwVmAFOBckMSqV8SxbcOR0LLfR5QBhwAtgOniGKlnDNzSUnJwCAi\nvlJ3q49LKNXZuZvCs9eTy6afLssRFvrlbbEMOBnjtGhzs+ZYVxQWghWlHDgA7Ad8wGGiDQAHAkn4\n3D8DWIgSYD3g12xzo3gpjaRLno6UaqgnJt8lPfibOvtjQSO5NwDY5hrY9Pwmhwqd19K1wNXtRhw9\nDXp7h4Cet0N5hNYTzQC8wB6dSmJ9G1vn5Rlm9XiBImAjUKnRscXgsMbysizLQeZ1DnQyM8vyOu1F\nIYp8X3/99WTmr0EfnIiiew0aradGXEFRuF07FmIvsBOoBCYDW4BtgAqUAusAP7AJ2AyowAagOPjv\nNQALsR749PIEF84T8OAlzDjXlJSYSWx2udAF71wFTQd4dhqR+/Lly+0YTeVGcm+YWK5rN3x1Tkod\nMkFsAUouAgbUjrzO653ndH4BTAO8wNQ/0/R6H3QBsE+I40LMChLQVuAYUXVegh5PCZGXl6dR6i33\n3kKP1TLUeo3golAYW2PADEJLlAqMcoWxYSppPQpLEebF5kCgNh4bWoADAQPT3uMZ1jzxhUMP3Po3\nHE7pfXXDb0H31c55chqlutvXZ2Abcj+rfO4LHI4TQct92unJGt4P/O5BOF6PShM8dWo10UJgEVAE\nLAbmAFOAL4DjQnh03o9yIRbKMivKVw7HQqdzM5EbWEY0EfAC64CdgF8rmUl5LwtmZlZmKxe0vOAW\nukWj1/c1R4TFjEMzqAQ+Aw4TMXOmnFlSUqK9QJwmWtcwJbYLKA6WCDE8N/HZ9gQ81+RgfUoTIuUL\ngZ7I+zlWABPTy3I/01NIEna6BmeP8R5qPL+lj2vF6XhOPJ5yAH1g2J5Cw2Jgd/DJX0fEQmwhWgQs\nBZYAq4AfgLXA0qBDQHMf1/4nxETgeOre+g2Bnmj9UuupU6f2ILrd4eiSnd0eGBN1umbNmlXfI8ny\nQYAVpaSkhO6j7A5JtjC0hFVJZcvkA98uNlVajJfxSRPEiQ9bxdsAeuCHBe6FwGzgu3Thd/vSjp0u\ngH3PslUUA8vz8pi5SKvfSfUb7jrgg+uAATjFMRv9vJtZ18bTACFfRwxLeV6EV+E0AP2xek3hTqez\nAnCPGnXXXXc9ctddBMweFdadY9y4elVjsapWACNatuzYuvW9mZkP/qM1HvkxnpoSJOUTN72Lp9Lz\n83YGUjPJw+1u8iik9yR2u9cAu9OlK5N9fQbnwD744YcfzvQUfiScA9zaq9dqp/M84PwLgbZtUzv+\ndcCsX8BxseMcxLwBjgHIyoo5ROirjAzD768i+nl9ppgIWaOyNnUtPHp/zsWlpZcyt3366fnz50+e\nP/+SzMxBXbv+6Ve/6tat2/79+wGsX7++PgdyXXtt55Ytdzmddzmdw2X5k90HLr8YpShN0e+Iif0A\nZNnqXr7iYpNbtvlZm4rrsA04EucqW0LbtjcuxeIfFqNt2yMAp2bQM4wVK1Y0adLkTM8iSZx7pidg\nAS+99NKZnsKPhFLgdqBm0qSlV+DvT1h+wuNjdUZGzcWY/icUOr1xNgvU7ygbiotvqd8ICXAerm/X\n62JZbtarl/7jGfv3L23e3L11a+mWLUOHDj1w4MCMGTPeeOON5A7yVFbW9szMd7zeVq1a1X40aNDs\nizLo0mu3Dzu99FWZ1F4rLsP1pjemy+iLXxTfbHo9SIhLDwEZAHCH2z3v8cevSNW4jUgKdrLcmzRp\ncuTIkTM9ix8DBwF4PJXAWMIviFI5tKq2AFrnABlwXOqIs2FmdvbONm2SPs4fs7NPJb1zItz2ZMaX\nnYqrnc6rw5ldw+2lpS5Anj170KBBW7ZsOf/885988skPPvjA0iG8Xu99rVpdUFz83f79dcwOALi5\nmrefI8d7rUkFmgLIybG615C3LdwtIkd89H84AUBRrB7IEFft0+5dgOgkAL8/JcOeQUyePPlMTyF5\n2IncAbz22mtnego/BrYBqx5/fNTdeHQzcMcdKRz52NChR4CKy+Hp72l+afM4W3Z4IHt6WVnSB7rM\n6bw46Z1jY3NRUXlOTvEWupI504jZNVynqr8CljVvPm3atGnTpj300ENlZWWDBg3SfJHxDzFo0KBB\ngwZ9O3p0x/Xr+8XaKD//9ariihguqZTgV0nt9dD1Fsi9zdVtqq5AewkYNiypo0XiM5/vklKIIrFp\n2LAMoDrV7sQfH48++uiZnkI9cGZd/lZh35xTC/D5PgaGXA/0QOH5Kb5APsB9eV16e3x0ubIeRw8E\n9qb67gp4vYeByQ5zw6qq1ig1VNQaKnONlcKofatVtMYpRg2BPiaW5eQUYBIiCW0vMV98M95aaiPl\n0WN3wFAuLRn4fHQN4MIsSTruchVE9fGwF6qrq+2bB8nMdvK5ny0oLr4ZeOViXF2FG46neOzLgbnX\nQPxNJNyydFfphGb4OOkjXXvtsaT3jYGf5OTsOFp4qGKLqa2bN99LdE5GxjlEGDQIQKtWrVq1arVu\n3bp169YNGjQIwMCBAzMyMrxerxZ01T4EoGZltQR+UlQU/wjF64qRX4TSUmRlIdHGVpGER794W/HQ\nTtamUdSrKEPNeH0JblQU1MMLV4tf/MKxHU32YHvJ4vOE2P3OO/Ud8Ixi8uTJ7dq1O9OzqAfO9Opi\nDcuXL0//hEi3m10uPI5xDnBlZQoH3kk0+zKgf12v1PhocgMKtyRZ3nlKVUtTeHcFtRgxAN7FXvP7\nlQFLMzMNvxo4cGCPHj2ys7OjNWFMJgiqrCr7FeZgr4+UmvDl1s8eXkzmhNMH1PsmxOtUZQXZwCX3\n4q2mYJ8v3+YJkXb3E9iM3NnOaacmkQfMGOyCSGWBiYY9wH0PwDwFNLkB3iILTKrHrsLCxP2PzOFo\nsO5Udss00mLqd2HhaiCOSG/btm0nTJig/2QNYnbNjgb66n6jqiZu4mESgUAS5N7v9qTI/S3Cy6hI\n0cy/crmyLseM4GhL7GY+6mF3O9JmAVWke0x1bvPmlUDFK+/gJHZdkMqRv8nKagrMbAnxz8Q+GQ03\nXuooVZNM6D5eVpaCbBmvF1lZF6iqlk1fdqxMbmcxMTQr63eKUjV06J4YyS2//vWvH3/88dCfgYyM\n3xKhebxQcxj0vqfmza9iPpmVVRo70msels+eqvZqmkxiVdGLRajGWsQtazCNB4YNu74c5wX/PEeS\n0iBnxqawH7mnN06WleW4XJccgmMFtjznSuHIdwPlAM7F0KyhJndZVRQo3ZUkuTcnOi/xVvGwKytr\n19ChKCoKUW1RWVFOU8vZgcjJ+R9Z5uJixOBcDubPFGRkZAKWvOf8DkcUNJ1bVNQ8P/+NeibSFBf/\nxOouRUWXz03S70/XUIkDh1OU8H4OcDHgqfQAuE2InfbMmfn888/t7XCHnV+a0hA+3yKAmb8Fns/E\ntOzUaZj4/fuAv98PGmPNreEwmZpihJKk766amiqiY+FqjvIkWdmejFNby37xAXuM1FrqBOKT7dxU\n63aPhiwfS1ZdZzGR1WyZ7Ho8y3723/tXVKakXzZzT2ARIH1c622P1f+2gcPuPhm2o1sGQLqWMk2/\n/vo73W4ADPQ4gIcmTkzZ0MXFx4BZv0VepzxL+zlvoE3J5oGcAnZZL8OB17vv2mvPyc8/P9xLUHSg\nKOdq66MB69atA/AL5j3A3hgJIZVZWQe1twTryMnMMVYjyM8/X5ZjvS7Exx1EF1rc5ZdXJ3GcWlyH\n61Y4sB7AddclP0oQNwA7mtSWqiJYkVf/YX9kpIHYiS3JPQ3OuyGaAmjbtrwmcBxIrTDLjrZt294P\nHMMf8Udre57EhaVJemYOAdVW9t2cn78zIwNO589KS5uFM3spSmHZT1GLG2+8UfvHTcyXElVGOUzG\ntGp1bnFxM1VN8gDAtT2vNf4iJwf5+fsyMvZZdWdnZR2ytL3X++um1o4QgZEve3yZKE9FWdZPgLt7\nuBYXL9b+vMvnW6qLatgFN91005meQn1hS3K3dU1wLMwlai7LALqP7ru1KfZKUqpGriwtbQacfyHE\nI2ZDqSFc8res3smmPzcDfmma1Fbk5Dh6976K2VCJLOfjnKIOSb5AnHeezvlfVLQD2Bs8xOH9+78e\nOvSW9eszZdlCEDUKyuNK6YmYy9jPmH+WlVVmxYRf0KbNpZZmQNR5Vb3UgNr8ss3bd6JZfYYI4tC5\nyLyTpExJfCL88NN7bd9tkYpxf1zY3uFuU3JPS1QtXvyrO+4AMHHTRD6JwEco7gAAIABJREFUdYsX\np2rkS1T1J8DGZhj6/8yGUkN4+aX8pI97AthjQsDgRGnpxubNb83ObhJbGKBsX/JCCBHKML9hLge2\nZ2QAmDN06PkHDpwry8hP/mcCyMnKyfkorssoP9/RV3ZmZKz6ypv1VFbWU1m9RvTKejpL+y/j9xlZ\nT2VltKr9f0arjGsBdyYy7szIejVLnpE4Qaj4uuvQJMbbg2k0/yMdBRCo1yJB/6Eh96Gb6/HFGxa/\nM+Wdti+3xQU4dH49p/ZjY8WKFWd6CqnAmXb6JwNb1wQbokJR5gLMvKhyEQQGt3B8m8JLI0Q5AJHM\ngIUlhdnAYdN533qUE/0A7Dfat4Zri4YWOZ1+4GDcxnuOV6LaRVmBodjAUmAP8AyQk6KOInFOr7JX\nwXNAd8gzZOcNcF2S+EL4AJ5WN210BroC7cDMATboOrsyMzV3y5dXJd9YVeouoQ3adZcGBoPwmvC9\na5jrrXNt1nUvPRjGluTOaVfKVDFkiHb3e+Z7aChNAWYAVUlRajR2A584UHCgILnd773FMdxE3k4N\n12SPz/YWeum/BIHswdn5F2M7cLPL4XjFge6AAJ4HegEuoB/wIuZ+IA+9HsyscrxfalIJxyoOAGOB\ntvfck6oB5cW1pVIqqyqr8vcyekKpVpTKyNXlMCUQpTkYe2kXHoGWoA4kvHUyMi/ekZpTdN/dyTRW\nlfpIaAc8UbvjVKDA5WJm3AlmRku8da7NeMbutakabHbSQ0iDRCU9pgSz9NASzDxd61KWknagilIN\nyxmQetADjn/Ftua8i73oCkdvh+NfDnqL1GNqoa9Q3acy89ZlhXsArggj7lqbXVWZqARQtivyFBkC\neBb0FuUtywsZ9Rry5uQp1fUq668xOo1rASbqD9CFF9ZncD3oM0I30CdEHyU+2yrRPiLjUthAwGSl\nK56GWCh2ET0yODXvH2K6qLaSEOnyuNAWaF8325Nu97Rgjz3fEZ+UK+EuvP5TmymINVruZxLpRO4n\n9vomnotFPyyS35I1cs9vghHAV+/Gc1aYhC87e0UmvCuTVBFg5hs6OZ4AKnQ0VMM13mIvvUV4ATSM\n1BMx7e5dwN7CSHWaFYCfiKM+Z2bnaKdyRFFOKHKRTJ8SvUHoVd9bNJLcFWUPEDKNJWBOKjxg6Av0\nSWacBVFqB+ssJrmrAL1L6JiaZ3ni5WbJHY8CHSIPqgDFLtcESWJm3xEffgP8BXn2dP/aHXY96WlF\n7pPcl/8eQyYNwe3AH4A7gFvgaAXcB+dA50k+WZ/BtwKfXYUIc9gS1AqVfo1Cr1c9pDrfczr6OvAs\nZLfsXeWNP2yVqv4QUTekKJuBaq+plSZvep5SruAlyAvk+ixOenKvlGUVqNZxzXPZ2X4gaRkceo1C\n8jJygRzfvxQTirIJ4Pffr50kkSWll0nX1G4svhM0pL4m/Mj2FN/t7me/9G8J7SG9GiUK5nYvBJj5\nVY3cj/nwB7jXuRdK0gmXq54Ta4RV2JXcOZ343e1eketiZuf7TtcC1/Kv3I81xcL/J33wNyIX4T6I\nT4X/VJKlg/uADk/WKyDJzLlX4t4mwKOQJ8uFmyzoRK4DAg4HM7MsbwQMrfU4qOEaeoe8y7zOT53o\nA6VKqc8qxYqyM6rr9MCBA7mmhmX5oBW9MGZWWaVRkSQoL4+pUJYQh154YSnAgcA8gIVZWfYfiOa0\nr5tGgAPoCvpvvSh+Q+zwLL1K6ABpsLHW46TgmqSVy7o+dLlmuZj5beCIfcg9PXwy3EjuDQS5PwUz\n4zkUbCtg5lclabEkfQiou1XvAi/uB/4O6mv5iV3vdJY0q9cl9s73Ono6XvgdJiaVRLHO6dwF7HA4\nKp3OJHZXWfUur7XZa7gmb14ejSf6mOQJFjhUs9wDRIejmJ118gOlRNXAbhM/k94neZnxBGh8fQ3n\nA0KUAhwwSIkxhqLwgsiYhGenh95NfiZ33I+3votcXag34QlQfrxh1aDAbzbgXuRGS0gjJGbe4XKt\nt4/2b9oQi43JPT0i2sy8XpJ6XAFJltATNVxzuLDwhCSxzg5iZu98L8mE+0AvkKfYY3LkFcCai5K/\nxGKOQNfa9LuF1h0X2woLi4l8wH5zfphoZE/LVisMrGn6iNALyiGzgdYdrVsfjTH/Om0ZZlbVg0YL\nQAh4NsFJUA6mQNJ9H1BBZNJ4j6MMLOYKepcMUyfjI+8FWjey7ujic4HHQHkJVovxur5Lt18B6UlJ\nelKSXpOYeY/LZaOA6pEjR870FFIDG5N72mCNJA3KBO4Jai253T6AmctcrkVR9g71I9wH3GXiwtXU\n7APeGp+MoyDAARoRxgtbrJB7paoudDj6A2peXgVwKKmcTnWnCle8g6qsYgBi6nYFsR44EnvyYeTO\nzMwHgbKo7VvktmgxtEX8A6UGihLS8V8FLE502qOnGgHKJ88ms9aAhuGdSWtXIsYIPBSWDBMHc3Uz\nufr62mwZH/uYmd1uG7ll0gY2Jve0cY2NBmZ8mIe/QhoiMfNRSeKTJ5l5RV7eFKNHt2BzgeNJBx4A\n/ow8d+yMmkDgWFJxQnqVxKJIs/Hh2007ghWl3OE4Ulh4TFUrVTVg0ZcdguyR6T0TOYWs0mhSyowp\n3gfsjtGJiYNNU6M/3wsEdKcOMsxHSunj+nlmonrP7iBaGeM6biL64f3EF8Wz0yNmWeit+t1Gz+IL\n8fc/Ah0gZpracZxuhq4xLs3n7l7oxu/BzIOBozYh9xUrVpzpKaQMNiZ3ThfPzGcAMzvfcOJhMPMG\n3evtN3FdwNSfcB/wJwROGLx6O3o6nnnLGtEEagJoCaXAgCgH9KYtjsSB2d1EXFNzRBc43QKosRsh\nxUF0uDIO5EIZPSNv5hXAZuB7I/rWUFNTY0juzHyE6ADguQjx3x6iAblez9TXMfxCuw0dNYrCc806\ngvCU2YnRW4TuGOu1sB6E0kldn7rcK93vSxIzuxe6pS4SM39gn1TI9KAUDbY56YZIj9DHp8FbH/0w\nZN4Q1jsoT578Mu6DUcM1JBMeAO7FlCVT6r44darHXTjgs1CVSkMIz8c71s64M1kH/GC4AVGZiVUh\nGuhu+eaksaQFCbYSVQKaCazpuRtCUZRY5D7Tp3yTib1xW/QZj7lPSegpioM1RqLzIWwMT6QZ1NTC\nKaKXiEzUOqE9aDiN+JWFUqZPdOaIe4ObtVRIn893xCc9Kb0NLLRPNDVtHO7cSO4NAeO1cj72SWMk\n/AN33B6WLDHR4XAnMnzUcnXI7CG4H9SX8CcwMxcUrG2KvJmmyqA8Ozw0PPFjr1wZYxqBQJxe2D6i\ngHVyL/yh0PHfZJYEldX77kGpaVI2JHe8AC2pcTtRedwQqyHqUw8cfwXVsDJI8dNetmBcM7On1EOv\nx5ybZ6MH3Wqbp79xPapM/+rZIevkweDkfb6pLhcz//YKjLaP2Z5msPd5Tw+3uwdg5hN8wlXgYmZk\ng3WFS1vz8iabezyqjlY5nnTg78BfMPdu2gd4FydOU0FXKHtMWZqP/SEqRU9REhLf0ry8JEqEkhYL\nGwfsB/hlmT6snZih/ICGaMtdZTW6gXglUBNLKsAIeC75x+qA6XP1NPDsfWQhaZKZmekNEl9HLgme\nzR56iyDg2VUbeh3ZiUz2Z38f8EsS65mdmX0+zXJ/y1bMnk4Od7ZpJ6YQbr311s8///xMz6K+YOB4\nYeGXy7/U+grvmoR7bz839O0ve/W6wOGYZ0IY/acX/LR0XCnPZPoNfXSo+KZHgeMJdlH2KIGPAjk/\nN9XhaNJSxtA60WB/RgaIEncvKiu7CDhgsclR2f5kNH63ZWS0AS4iwqv5Rc8UZfTPAJARuwGF0+nU\n/1mK0mtfvJbfilQe/hlzRlZW1bXXmmyr1MKRrH6512u+8eydRCNHKwBmZmTA64W5ZiNF/YuKNxQH\nUKfrq/iVtkPbohl4KLe5ola7/7y7yaRMb0ugaITIyMng6brz9otfTBs2bOF/h53XIWVtCX4ErF+/\n/kxPIaU406tLfZEGxvskYKrTmTczDy5wTc0O4IU3s/GY7tIUFEwCjhaYdqDX1OQ7cOvfgafh6Onw\nLjK238VkQe9bcyC8B3Ag8DqwwHQJ5XRZDgB+i57rUE2/SWwi2qp1SY0Y50XECSToA6rygkTiAYqy\nDagw4fBRDiqFx6zV4moosOIC6npt+O9SlNmmS1tDwVUaSnDBUxGZK7liuafKBDl8Awz7n1ot4ghk\nAw4JriJ7JMloSKdoKtvdLcPpcT1OnPgM+Nib5xjo8Hu9mhPD+ZYT/6y7OsuJJpr3XNfUHASuao/C\nzYUO2YH2kEca8JFV78GsvLxsYIhFB/QKr7cMmG7R7U6fmj1KuSzPAKpiJ1xmv5tNnYxHC5G7hcwc\noiNGq0gE5IJkEoS2W6lNfezDmHP+EmBPvNx2zwYPHgeeBo0wHoT60PpEv3ER8Ph1QBu4Sw202rOB\nm38Zb2VtgEgzt4ydTr0h0iOm+r0kvXAlHP91cCCgiUap5aoz3+l8pa5q/wvTr1mVeXl7gM8m57Em\n+zWI0AmO7nX06i3yWshFCQRKiQo13qkO7ImdyxELG53OAxbJ3Wz1qSzviJtewsyFSwvV46omt2kw\nQB8ZL1h/CogOxD0ujU4mprrL9CXea2aJ9XhmAOuJookeT4E+ojjJkX72L2wW7z1gLDD5XOBhY2af\n6nJlAz72SeNskyeTfmgk94aCz4FOAyQ+eXK7jgcdzzmcrzuZuUpVxwOFJq3mgoJdgL5uRR4na5Za\n7bD9HfJEE6ZlIDA/ypbc96q1DA1mXpqXZ0mWS9llgtkVpVjTd0y02IQCqnAa3O2Z/xuzxCkBZPmA\nUS2rBvrEMrkXaKFgc4hTcxuJQOCAENOBpUSs2ezdQCOJmf3sx5Mxxxl8FfbFOMrXwH8vBf5q8O1s\nlytPkrKBLoB7m9u10DZumbRhkhBsT+6cFm53Zma3u//PwT4fDxkS+ixvYh46g/oTM/u8Xi/wtQnn\ndbHDsbkp8mZF5kE68514Gngc8ucJBikEdsRYSK5pDz5gLUOjWlV3AVvj9tLTA88kuC17A4c197cJ\n6LNl9KqNyhol85HM1o+0NjkrY6jqiWBvCj3Qw/KTtatFCzNubmZmReEZlt+fenQkPAEIUOu6o/jZ\nH8t+f+IWRGe4rhRiOuAnQhvUSgswM/NOt3uUJE2UpFDCezbg3uLWb9PAkQ4O3nA0kntDgY99eBrz\nAQ4v1PYu8Dpkh3eut0JVpxEpwPZEwrk7gBlXonBr5GZqueoQDkdPB7pAeCIN8H2FhetleRWwLb6C\n4wCR0Fg2mBJRmWlnfbwKflXtB3xOlMQcNMjLZaVcoXeIJlCcIiYLUNU9wL7wdwilyvL09pl4C9Hw\n+f9afmzFOIEXag12ZmaP52tgNVH1FM9P7zce7ZFfR1ruBzye74AyIjxSJ+b+viRNk6StUdJgr2mW\n+2LbWO5p5nDn9CD3Xr16nekppAa/ehxeGDckw+9RuLKwSlXnOZ0Tgfmx7fdDqroVePgRgyvr6OZw\njnGq5Wre7LxQw2UNASt0eeieZMSHVdOeBLnY+Ne5AZ+RmWwVNIros9qfkAJyZ2bmY0RHtHR4ZjYf\nMwhiDVG1yd8VCPS/zdoZEF8LCHgqjUKsHs+Xd1H/y/E+8B6QD7wFrBdCFeLibGwF9gtx2ONhv7/S\n4ykE1BfFJX9DkzvBzGMkKQ/YFkM0pjPgVu1E7umHdCD39KgY9rHvb+9IY4BZMWq18QDksTIzL5Zl\nLzA4BhcEvN5jwC2PR34rj5cdL9V58z+akHe/BHQE2qGE6JgVbS+f07nbtI8lhErTbneDPEhV3aCl\nCaaiaTheBJ6r1QJLFbnXgugosBUYP85aV6bvTZvt5cDzA80urgEO4FmgdyLlSCNZAhpCFZr4sMfz\nH6AQGN0Ew4DXmuA1YHoiRYEnAR/73IcMwq2N+HHQSO4NCNIn0kpgWgzjnZlpKNV23Tt5chKw2Ugn\n/TuinQANC3tc1QoV3eEt8DLznsLCYqINwGaiwk2F6AR0AfUhdbdZMvp6Qt5eYJ/FtkpMdMycZyay\nfF9RktAAiAUMCKZ4j6PWnVunmNyZmXkzcBgoMf+GUVKyw/TKN/4G0/pf/yL0gEk9d8/2SLvez/43\nbwILwX7/NGB/HyFmCk2cwAxelST3Zrc03h7ZMunnk+H0IHdOl2CIa5lrb9AgmgiMB9gdafjUtST2\neD4H3o9ikBKHY00mxNwwl7o8Qc6bkrdOlhcDGxyOnV5vlY6ane858RTQEd55ZrtqVFpXaZ8dVPKK\nD33McxnRduCwaavWEPqAakTWI+5Gl+e7JD1yfIy5EtVApTmVG5O1/qXAYyZUgJgZT1nTs0SnyI3F\nl2LE1dgLFADlfQX9hzy7zerCz3e5prpcrikuu6RCpgeBRKCR3BsKfOyTxkqHw992F0jSROBjII8o\npNKH9rXqTuz3fw7M0Zm0uwsKthPl3YTeHWiR0/mFwzEJmABMAeYRlcnynsLCA0akrJareALoAupL\nanli1kZ7U0wdfgzVjHDKfz+V+aS6lmi9lhpYbz9MSBUyWs+r6mCV47b6NpiNhVCq+3ot3BqH4mV5\nu7mT+WmMbH09xFcCzyJakT8+PL5IzfeeD9AYoADo34Gs9t1e63K9ah8lyHRFmpB7enhmIBuY6hoW\nCTGFaDnRXCLe7W/SBszMfn8R0URgFDASmARMB0qAAbdjw5uCFy3SmNHhcsjm+jF5F3rRBWiLvOkJ\nXOqKqsy42vLNk7DgiFV1JVABxOkelxzQC/LiyJNQUlJCfyX0Oi1PQdiwssyyXK5V0soy796t37LU\n5KuJEIMowVTR1bIAfd2+XepeCr8C1gBjr8Y+4HcPWx7Q73Ixszvgdh+xgc99xYoV6UEgEUgTck8P\nl5k0WtotSbvjmzwez8fAFODzpsi9DieEYOY9QiwJ2u9lwE0dwy5rhIsmIfKW5eFpUC7VcEw9RWZ+\n8wbTvZmCWB1L8535mCwvA8qBGdek+J6sqamR58vKAQP2DKVC0kepcejrEa0uycw8c6YP2Bd+Hkzm\nEe1HPAe6sllBdyRXGathXL5YcC8VAUeCRa1XtEMVwHvM+tlD+DD4i6SRNrDf04M9opEm5J4ekD6V\n2O1m0w3J4EIowFVENA5YJ8RB4EpdH2dPmSdha2PjwTsCHUG5MfcVk4XfumfmcNQuC4lUra2dLHNS\nPTriQ1mqKEeM7eJQmz25UFaOpqC3tR70QezTrigsy4eAEqDAhFKNtksc1w0eBwREgeXi4RAWEi0E\n1ukO4Wc/uuJr02JkevxHa7O3wy29awNy//zzz8/0FE4L0ofc02D5lcZbI3cOZ5AJgBuYDVyaXXdZ\nkxFOCULMEOgEdIw5wpRzLT/5em33GcBuYGO4Y70+tqch4q8WdaqQS60lLyZErGz9OqgqK8ouYC/w\nfaLowg6g+xsGZwb3A89BFCdJ64eE8Gs9Wj0eZg5daz/76R3CUyjQJe+bR0+AmV1z7JHkngYRO0M0\nknsDQq2X1mIrYfqQxLe1z7aPaAYwGhgb5FCror4Gs3oC6AzxlQF9tHrSoEI9PkqAucB+Ij/gM9oX\nIpX3JJ4H9Y15BiJ6qNLYVK4rcoFcxVUJNysFDhIx0QZgH7AbWAls0gS/mGuFfQKBv2cbnavuQA7E\nvGSYfS1REbAkSj/Ss9PjZ7+WlIWeGNsMJ62TeyeAmRPm1zcQNFruDR12D4n42Kfpo26xHksUswUN\nImZeBHS/CeMfpmnAdMANbLL+Th2NAAfwDNAp0ucb4EC3my3kKe6W5R3ADuBobL5IISMoqhL/xSWC\n3FVW69MhLwKUb2IoRYn0UwUCWwAW4hRROXAAqACWaSysKKFTHeAADafE5yoQYObviTgQYI+HPR4W\nYjdRSbgHRg88BP3r4Ky42pCx8G+N3FO6Tp8+2J06YsEeZ98k7K7rJn0msSbqbR1innjgDdoNPBjq\n8rHP/94TNAmYBbyXiuQTeoPQFWHd1Jjb3IsE8UBFKSFaB2wBdgH7iQ7G3l7ZpchFySihG094HDHz\nU089FWebiCImeb6sVKfG+W6G3IvMFWdtB0pbUzmwF9gBBICvrsL9j2L6/xEzsxAsRKUQc4AvgZnA\nUmAtEAB8wA6gDCgFqohOEn2P2rokwwOJzwTahF2d0dfE1IaMA03vF/1tQC9p8MYfCzY4++Zh6+vk\nYx9kMPOaZIl44NN0GLiye22Uta7m0O9nv38KMB2YV786zwAHxGyBrhCza605pUqZoM9vUVVW1SVE\nXwFLgG1aWogs6637+EroqeJWdEMo20dRlFC2e9ixjD43rMW3CpVVxa9Ahsqqyqo8V0Zn0AdEI0ie\nK9NwUsqVv/QiFeCZCX7vcsChk8m85Anc9yh4jlIK7AeWAipwQqv+VZRVidp0xIFnlQfdIKaG2elv\nX2G9oMHnywakwZK70gZ5kOnqk+E0I/fu3buf6SnUC9IoiZkPJl394ffvB24MlrDiWYOLOxmYASjA\nIrLcWzkEMVOgV93L+00d8TXwDVAMrAU2a6/8ihIrQrgxtrmqsirPT43lTr1NcbSh/ICFxkz6vYYS\nngP6gcaSckyRv5dpaFBHrNyAwQ/LcgXw+2ygO9AVeME403FZJv4RrErFM0C/0/LM0isU6szl2VO3\nPIy8LBnhh6kulzRKsoXebyO52wN2951pmdGH61HatxdAH6A7PH4PGSVXaDgoxEaiWcA0YCywlGg2\n0XoiFmIuESvKEk0kUlE4END+Oxxua+d2pHZ/xlxgA7BZM89Ne2bHvycfBT54gKgD4X6gJyAAATwL\n9AUNJ3qPlIPJ2++KosQp5Ikw1WNpy5jMnJEXyDSW8lbn5S2JLPtS9ib4CbvCFzmVVWWvgudA71Id\nyytK17+CmZVNCgSU4ynO19RAAym0DjGzXpjosSycskju+ZKUjcRqZQ0EdieNOLDHBTAJ2/vcP5GY\nmV0uqwkztfD7NwPPz3x+F+/CszCl8eTxsBAcCJwQgoVgRSklYkUJEC0H5gJzgeLgf0uA5UAhMAPY\nCKwBFlyM3zyB/30Ebf4Ur/mnskyhV4k+IhpDmlb7SmDGucb3XohVax0ai2UaTfgzqAOZIdyampqB\nSwcm3LKkpKSmpqakpCQWuccJBqqsUj6hF+TlcvwAbLxpRIdS9V/uUNABSkDZDNz8ACiPMADK4dPD\n7IMJ3cIld7rU/Tl2vLBquT8DPPtPyRbkbmtHbkLY4AJYgq2vlvuw213lZuZYqpAJ4Pf7gdYftWat\nBOl5g672pwM0itAN3/w08l5SOWbnUmaOVbkTx2ZX9irySpk+NLbrleC7RbxeH+Ho06dPdna28bHK\nlOhWeSqrEDAfFZAXxnQxrTEnOfDcb4DnEVKyTDnwNKL7Xul77z38IsVqJRgLQyTpBoItoqlp7JPh\n9CN3WxvvPvZJH1quY9KjpBmW8lJmRlcwM2R4dvwo/P4hoTdC6fb0DsWrz2Rm5q3AaiPWMOlzV1nF\nANCnpLKq6FjSal5/nz59lBgkqzfe5e9lGk6xKl1jzdDQ1a7BTFXqq58I9AaNIzFLmFTutQR6izx7\nDW4PeqfuHI4ZLkwqVobQFrjEqFdMA0QjudsJtiZ3DqmNJ+uWKWgGZl5btTZUiY6OiNMEOYUQcwX6\nAS6gp7nDybJhEZMlAi05UkL5hJagLrV8lLguVH8sXZs943SaQ4pcIGtLiPlha/ctU2LuJcsJ8wuV\nbQr6IXQ26E2KUyqcBCIU/8O+Gkx6n943FhXisnG6or4ph61f9BPCHtfg7IFWK2/Ieonh8Yz/dTDh\nQWew0wdk3GItdcA/gW647RE42gA9IU81xbDbooRwqQMpy8ySu16oXTmiYIDpdUWHCLNd74KXC2S8\nCEPFMTOQ58Q8CaVxxQYCHKCPCAMQ7fdHRyjbU+B5j1/bJaYKsaAuPG5VNfOBC4B/NRLLmUfjNWhY\nkD6UBs5ybUw21b2kKZiZXo983fazP5TolnKI74QoFMz88Du0pAnEHIF+pjhoO9GG8F+q+EwxV6wo\nKI0kS1Z2rPz3lh1bomdtANNqN9QQYk1jK9GhOKHUMgUyLumOL67BoRiuGET1UDQPP/vNFI7Wic35\n/ehj7XA3XwfXUnuoyqQ3Gsm9YcE10/U/z2BTUuReTvTtFeBwn6keqRdcrFAiEi1mBwua0NMgUheN\n6IyR+BWqems9AuhRO5S8TKaxpii+pKQk2uFOn5KmEKnxfrQKvEnE8nssj222BziAfkA//HAvrflH\nvOBBdOMks7MyF5PA0zrtOUPt4ljw+Rx/hmu5Dcg9XfXCQjgHaYeXX375TE8heQz7+7Cqn8N/UTL7\nXiYE7iIAxeuLDTfg9zhDzqjP9PTIGp6F88Dvs/7DzQ8SZBkAv8N0C2X0yfDu9sYZ5AIiZGWF/ixF\nKWqMt2RmABkZMedPt5L2j/zb8os6FhXtL+q1pFf8n9CqVav169eH/vTu8mb0zSjqUJRzQY727aZN\nm3a6d2YNz4o9RmxcbPRhaemNAJo3j/4mo3PGdS9dx28yv8mXzi3+7ZSiOGPzGM54ytqlzHo7K6N7\nRlG3eMPW4dy6f/5uM+SFssmjBIqLy1ph2K3DLM2tEacFZ3p1ST3sHiSBwLu/jNkjOw6G3oiXfwdm\nRud4lxW94VHr64KPYwDOaRqeNC0ncIUfi/DMRAVUY2WzhM1niLGpTmNI2R07t1LnlqERJC8zNtIh\nw9B7Ex/ybIPR9sSozoULNL7u8+UXmnow9QnpCbZ81lpAQu/E+/1jFpTil89yW7P0G3HakIaXwe4l\nZ65i1y2tkUTCDGR88ygxc4vcFvG3FIsEjUxeQUXLs4yFaW0jhQ3wLCAQqw/n+vCwKj2bVGsROW7N\nUWwtX42141fcaEmNcTxChoiuEN4ly/4ocyrAAfSFFrTQsAJg04mPNDDx6RLfCVMVbTrovW2XPWWB\nJehq2ILc7c4SZmCDy3C2wTXXdVWnmM1U4wD/wvTPhJgizMROxTy75Cy8AAAgAElEQVSRnCKrKW9v\nlHGqlCvoA8OJrSXar6M86lC7ryUyjS44igD6Gk87u322mVpKTY2Zo1SC400pSqDmEFHEmaE3KDpr\ncNt71iR241SKcbKBFhpeN8+WbaBXm4kPx532oBS7v9+bgT2uhFXYPVRyVTdMM/diroeWfyYmiq93\nf21me88uj9UyQpgz4vJi9EFFdxjm1fm0vp3MzNy6X2tLU2JmGmHW2Fcqwlw0oyaPcjzsMLOjvNRy\nWDX6l0bIK6IH6PPImW8emYz+fix+DwWZrUL/JtH1Liv+HJtouNudIswgDQOqaYCd5+Py1pLl3RgI\nBHAxWl7e0szmba5oE3gjkDXabLQw44UM/oQTbwf0KmN9mLRugu8xtaCM/hneXWFR1l8oysniYuzf\nD2D28dkm51OH80xveT5KUar9sxSlvd/u3eWWLmb2y/9DfmhHk6CWpP8zkJV1CdV+4vV5M/pliM6i\n6Imw8Ga1LP/cYxwMT4CmkKdExjwzns8IvBtIZjRgmFIXEX11gZU9jyd3wB8bjz322JmewunHmV5d\nGmEAaYzU/k/WLfd+YGbxnfCUW4uXog/qxN9jbfOksSBtLGxqEnP+8nQZcqRCSzVQ0rkzx+8rHQOW\nykdVVtEL6AalQhk8ePDgwYNN7hgrs7OmpsbQgxQRni0NismgAzAghrpvs+SfRzjr9hUzhFhcrw5c\neh+9+aqLz+62h17YWYL0tNyPHj16pqdQL1Ar+q6F9d1OAgDdSG0ua2NpP36b0RQq1FgbqFB5HF+L\na82PeUO1sfEOIP/BfM7nNgPaZMgZvb7tBcDr9f5Els8fMwaIkUEYG95D3uYwyCyMheZoLj8k4wLk\nXJpz9dVXX3311Wb3jJF5mJGRoSVorlu3Tv85/bbOcj/Zq9dFAHJyMrpl4Bqor6vRJ3N/VtYN8xWz\nk4mCaCO0K5g1LKt4R/HQO4YmPZSyRRlWUGu5y4p8oKnZHS9buviNf7iSPu6PhpUrV57pKfwoONOr\ny+mC3X1qV5qoAIoAeqH4A8FWfNB6BDgQK/gWP7cyJqYp8dViB84diL5AsLtIFcDM8iJr3m360NqP\nVVl9YeYLzIwe6PJSFzN5lvp9428Qa7RNwCcOoG9YvmPEnpMd9X0Y6b8k5gixMAVdc8XcoAZcLm0F\nYrXlC4PPt9kmfJLeemEhpKflngbYdYnlXe7fDOmFoQCEUyRxxGtxrecVT0bfSAM148kMHm3K1R6J\nh3Kmby2GavBCwMwlJSWD7hnEg5nuoozuGd4y70oAWVmX7YX3QLy6pwjI7c3W1wDwHvC+OfvND/7+\nAQB+l9etX9eqVSvzu+eMyDEe1u8tRWmvgl64F84xzr+N+FvWqKys/NoXl9Jeva4F+j0C5TWlqL1x\nDdG0rm3WtiXDr8yD7iacwtA/JW+za1B2KOKe2lvoZ+dg67nAddcl3GtT27af9rMeKGrE6cOZXl1O\nF+wuD6m13LOE7cDGVR5O1nIPASLMI1wnM2IdG9YrpVH3WHQqIY0g9Ea730NTI5AnmTXeLalotRAt\nIjImC1cVUo6FXxdK8FcqFblQRn/QmFo1G+2/ui07YeaKmdljs+VF8opm8DiA7tAaq0YPuw546IH6\nPolaSAA5KXiiPXs8IZ97i7sQMMcSM9OXTGyKtL0edi9SQE9M81tLdd8dfLoMu6daO7qobZQcv17J\nDG75W10HvlixR2ZWqpSfdsLaZphzLi65AegBDIC8QlYOKfK7Mu4EBgC9ARfCODRuirceeYV50S6R\nmpoax70Ok/VcKqvoAfrYlKp7KCPwyo7Ypus5pexWxPcCHUCv1R30nZusBasNDvdoUA10WwrkP/3s\nD5H7DX8xRe5lLteCpvYgE7s7bM3DHtfjLIRrpusyi+JQe4B/vkVcb8tdA42gVAmNdboLPHCgoT9a\nflfGs5CLZXmJzMw9e9A+4MrWJmQLx5K8SoYT1IHU44mzZQyLmDThsITNTuljog9JS3U3mZlDo0hl\nFf/GmJuwn8hwSRNzhBgpVjVDwgqsBMfqELY72td7adcJAv/pbmwwQe5+l4vLffU87o+Ds8ThzulN\n7na/im3vtSZCUIVa/ZAkZM0NgQ6IL/xtdpyumKtL8lNZpVFEA0l+18D9UkPU426YXFc0qlWPq/gD\n4tBurPRKRakVFTCUfpRnyPJSmcaF7WtS3h1dgGdx18PQN+WIXt42/Jmevgv1kfANdb+qO7Sz3uSu\ne/P7PzLV+nylfXwydqcF87DNJUkCdn//mvKANM/KM1MBiPmCdbXyKQGNofr3eOv4l2CW91NIqJC+\nvinwYmJ+l7+KZGRyEwZEsryyU9EkfKOhKEqIcCMStGkCGe5lJg0f3YGXITrSbqNGqaEjfgf4gf/M\nFcyMThBfWctyEcVCLDHYxbOpXp4ZP/tFUd2wys8T30tFkrTuHsshojOFRnJPB9g9plrBvgVWyL0c\nGPWZ4BTptosZul48/SzoAmqIiJqKb0Sv2zDW3M85SrT1QqAN0AtxMiP1muMhVHFVi9daQNRRfBxN\nMf0kVVZpGCl7FZoQTws+fq87ZZOCnkAv7GF1e1SfKT3Wrl3rB67QLcMBDphvpIdO8BwyJvEAB8R3\nyWdDRuidLbko8ZS+so/Zflah8ao0aFS7XOYVxFYCz9wJDtdrTRoR1EmjSSw1SxkRLmZ0hVgkbngE\nE02zwJqmtcyIlxBLIAWuuDx7QMGLMfet3UYJ03pEv8RuKL2iVgTkmTJeBLoCPTEP2Bv3x54guikH\nncd2jhw/n5StCd5sYomg1Q0yNHknvr7HiPhUrDNxycw45RsIzga9sBBsc1WSg909M8y81PSTsx64\nuS2Ymd5NQUDVU2FgGCZspxnhVtYXRgU4cNUj+Je5n5N9BfYFLV/0Ao02sKbNvKDIRTL6gPJj+ty1\nCcsLZO2nyXMTZGHK0403kGfItc3NmV9sisNxu6RyIDDylwh5P3Jzc/Vf0tuxW1e/aWqJTbpPE4db\nBn72J2znW+VyJdnP/Uzg7PHJcCO5N3wsh1n532NEI34FZqZhVM9sSH2iXgTECmHogl+7dm3kIG9S\nqNBRQ4ADjzTBdBMBOtyJHUQHgswiL5DRHxFpLXJhIiL+vnYDpVIxtLhLSkq6dOtCIykUJpUXyEqZ\n5aap6A69cm9hjI4cIaj30lXdIi+Q/gTSYIM4h1KqmHx5ErOTd8uIeXX7Tn5XPJ+V4EYyb3w0BDRa\n7ukDu2e7M/Px6e5SyVy0yuMpD6W6R3GHJcSX9lUOKnqXyKlTp6K3odfJMCMTLXHv/xiEGSMgfy9X\nsarvW6SyipdAn9aN2U5pF2+Ed+UIYx/PQdkVdtyWf25JAyLfCeKHTOUZkSsKuoLcdbvMBI7E5bsD\nRD1iMGZubm7oZIpvwgiaPiTD8Kkhkrbc/ewX03TR1IcpvoRvxytw1OTN2TDQSO7pgzQgd7ZiHFWE\nyD1ZIW8N9F4Cx45yUKGxVLCqwJjZB1Mc19Cv7kWViV+k7FGY+Uh4WBIv1aZ7VnFV/N1hRKBygRxi\nZ5VVx20Ow/55SiDe2hNqMSjPlNEDYeuoohxM9NNKLoI+HSUap06dWrt27ah5o0IZ6+hvrcrJat+l\nEKhr2FV79ldwFcVzuYwwEW5tODirfDKc9uTO6cHvZT6TG4Zq/cV8kTsnN/7GcZDQa7927drO4zuj\nlwHpKD6F3oy3O42g7D8mNt5rs/VluTqix8ULwAAgbgcJuSimx4aGE31ClEfoAX0P1bBDxK7LlafJ\n6AqVVfkLGf2A3sD/Z+/M46Oqzv//pqWVoNKWVu1if7Vfa2uiFQHrfdwVURFckEUIISwBws6cIAgY\nXKq41oXgjruCc24VtHXHXUEShQRRiPvccUVU3CEg9fz+uJPJrFmAMJnkvF/8EWbuzJyZe+/nPvdZ\ni/ErV38zmBWwtN5CzTVwQKOn1p04+UTyaTB8mgynoT/dloTIhIrfv/Qj+F1al2DVi8FV1ifTgsmm\nfbNttI49uqJxZ5EHZqtnjNEf621ojO4TNuF6xqq99tprsVFTWSix+RXuG66fa18/crtU7NpQGvvz\nEYH+CIxE+rec/8L5Ex6YwCQoRcrSBx7rbRXJGPxbk3Ti7n7qRj898obXi9wqKEqWlVAIhVCauP6X\nRV7fnY9fcuUmUeWKIhJmcz8Ps/6OKm+sd8Vd71JIbE5qI9Hv620w3vVSrcriPmvIkQS/TSvuV/V2\ntmGMewZpBRG4JtH6xb117NFyCE9vOCdB78nD8yPn5zYXl2pPp5vdoXWKx1W5itb7NP6Kst9Q0k2B\ncD9w5VqRa6XkpRJ3k2u+eP8LeH3AiSvMiug2cqUwG/rCcDgS9yXXfcmNvrx+y913sjORkmkl6Xrd\nyI3yvnm/ZHmJu9VN9t0nj8f71nVroNcpid+IsTAcuVyMMWFgdmN3StiEfe9Np+GdTKp4dT0kNCRo\nJOQhhSKFopdqz3g3XaN+OwJOJbg0GNoUSt5+SaND/S2E1mHnNZ7WL+6tg/8FAo0x3hnK/bWF/kxh\no9m4DZ8VG1KL0qC4yA0iVzRBU+QGcU7mxdjq/A9duVJisy2jBvjWCRO+j//67gbX/cKlJ/SO1Cu9\nv/n9knkldIch6Z0qL5S430euAe+b9/kLqYcoVZQQSLS7fRhLyqqot+CSvyHzU/8CP34VXg+Nrxzm\nrDp/l/uuG/07ZYQjmUaa7epGJcOEPCL/DsXEdA175FiHSQTfCBpjnELH3yZQFrEwrr4rkEXp7W2T\nNrF7WoPbvXGeGblMdK3Vpr/Qr33fBHMvSkIiXSNtRrlAmNq0GnqGkJ/D+64r1wgTUigjxXxqPvX/\nDonElgWVPBaxzUseLGFmXBqM+5IrSuSmxDQYt9xN8OQsW75MBsd33SpCbo084n4VJ+6u51JCSWUJ\noxJ3xHqlvoAX3nLThj3D4eLDUS8pRjYcGk0Ohsderhqj7/U0/pVSkWnC4dAlPpKRlGBTEwgklzWQ\nR2BuIPhJMJDbtMZHGad1iECTaBPi3koIBOY21OhDLVFHnVa3zfiHxm/D50QbuGutG+8NkH+KMUbu\nlGgySWPIOZAn4c3q1MHVt83bsVVFH8ZkzsQma8qVwjmkbJcmN0i0KkeKExd2/vnny5m1XpopiWNd\nY4uJGASzIu0bk9serAMTTt88wHVX7M6ptQlI7qeu76VJRt2v5LYUTyVfD7TW9ai8vy/q/nuByJUi\n54sOpw2lJN+OXJGfeiBqYG5gV4cns81sbx3u2SaRZXto22gl+zUUWtnQGaU/0F0L6rZJN9O5Qc67\n47xGegB8wibsfuxG/27klGT3Tdf9zP3dmPr6DsYly5eU1JNoKHcKM0hW2JJlJXJj6qqu888//7Fl\nj8lNUlKe2kfv676USWzKSkIuzQO1yfjp+sJ/BgcVJH568ggU9YxK55EPm7BelUKXU4ZAjDEyR/Sb\nmkEwGrlCGvTSaE/rjYlvdf4fyUmV2BOYHxjya/6XVentpu3lQRor7tnFS1C5Jm0IS7+qOZFT+tAv\nD5ku6j7FQK5ddW1TP+XEa09c/cXqJr0k+aaeAO7XaZMd1TzFsREHhfutW3xwWn1PHN9aUuKneyZk\ns/jIHcIMksv3ZZKUPFeSXNFaNKaoU5dOJn03HobAeEoq416ono9ZqhuZE+t+mebLuu6oo9O8eUzj\ndUYk3jckblzvWJLoldgzHv1hLLEpTA2SslKp5/E4N6VQcM5mTOcs88kY65axtHRCofP/WrfLgsuD\nwVVBDoE86IV+R2tPM51gZ+RikX+KelwxHvWEkmuEETAUBqM/1PrD1Klyq1dHNL2piXQppcT93k1Z\nDOUuc2V43OO/Gc3K3THphjTFdx34GL4XKXkylbifL3K9UEqsayjqeXc/c2NTJOUy6bR/p7r/JjXb\ncitdFMxCrpeS50vkFmEyTIEpyJ2iXlFH9mIDVJ8gcpMwOYUzfb1Sy3evz8nuFwQ05kYnOmspJQPK\nBuSNzetU3KnTuE6e8erpbpaSlLWvf++f4hMpoubHUCMTcy2Zpa3spFZz3V4Gsx8IGGOCy4LOZMdP\nZoiF6XFWcMrUDrlc/P4zFMBQ5FJZWrk0eo/fZGVP34jGJJmcMkzUvEQpecu8NeAo1qWRDL9BmPu2\nq55RKIq68zWccSRMhvEwE7lb3E3u++b9qBuK0rrxRglWOcWUVJSUXFsiSmJb/iY3F+MsmAVTEtU5\n6n5ZTOSnDpuwzBe1VDGU2LGuHoxJ4173cT9yE29N0qDfSeWWWabJg8Gop+t6kA2YM0B/0YQKJrku\nld8mFEo2550bnEBlwBjTd4z1yWQBbUXcs723ex2BwILdcWY7HJ5GCmfwVUzXqqtevEotrS+DZe9x\ne59YdiJjYAwUox5QnvHUQ01JemmokwklkUwYNU8lK3uUK/6aot+W3CqcRUK3sirYkOpKQDFyu3AW\nKJgA05B/SkLSizGGg+FYjDHnn39+XMvfMbgfuxTBeJiGKlfJ5rxaHFnJRyLR1SZ44eVaUU+oVXDJ\nP+r7ZdRy5da4jaxRiv36YRNWzysGktJXoxYpdVETdp/ckuLyMzYXY0IJD/rN0TrnEqzOpvR204oc\ns03Cinu2EQq9DOmU3RiTU8xde8Xbqun7nidE5DzjqWeVqlBMgjE00oRvjHtXlSs/UbqebX49mJdr\nk/TDJsxE1CsRJU1uc/g9vJuk77FeoJLlJXKzUJo4+EkuEHeZa4whj6Ixce3UmQETQcHZde+cYLar\nxyMrCYMJR55KoY/h8M37kXKcSOQlZSILIq9qZM2R/EvUI4qhJPTaTNwsmgubJtwaS2wPyFh0ZxKq\nT+sa3RxH8N0sE3drubdmWtOl+yvH6fcHnKtS3xqrF9XoI+J2a8HdBQlpglu3bq3/zGcknvH0Bk0J\nTCc5tSPuE59olJ3IETTYiHj4xfIh7F6U5AlJ5bv/NkZefZK921ImlBJ117ifu9Ewb3hzmN2I/FF7\n1aEorvrUt5Hj3vBqMcZUxrSrTOlS/xjG+7mh14jrJd06xOePh01YPVrfbxg2YfUfxWj0lw3rdcIV\ntJ4dLZdIysxLY0zCjI7A4wHfbOcInlydZcpurLhbsojLf5k6rdsY4xmv+6Ck3JWYjRtl0CX1YZdb\nhKkppl7otboxDQujTUuYSD39hGWePLpb6p5iyekoL3QkIbLnfhK3TZ0LfipMhKLEq1TeYXl0QUbX\nelcKYRai4pPE/c4BJhw2YXeD+8sz+UBkPZjab52cAblGZNasuCuEXBn5r3JVcrq9iS9TikU9oBhD\n2IR1ta6/HZuPfk2n7Au0devWFB+a5lrbZ7bjJTRrK8EYE1gQoK9VjKyhDe2qVhNTNcYshQevCji3\npTbemYbx4jwq+gv96LpHo8kwDaI/0unaCvpp7HKL+P1n9IeNit2p++uuFsnmsI/cIL6GPt0xRWZk\nbAKMfzk5rAefwUwIm7DcIOpJJdfVzbjw3yr6EqZDKfTFfT1yAVBa8X9wPIzE9Vxm4XcmiKj55jDd\nkGFCd9SCusVcviefwMq1LhOR+cI4kj0bryU1hgybsJwnfq1/yt8ntsdA5PveKExCr4/8vLpa63WN\nMNsHpD2jzzvvvASJ19+nfsODTojLdAw8HHDucR5+IeiUZlkc1adtmu2mTYl763G7G/Pbv2CMCdwT\nCDyWIt24Sw/M83Hn7ZV3XhmbVd0YGjPLiWkwmQZbyqRM45OSmFmdj6rYxgDuOvftVPFS9YJSLyvO\nwt3kRgQ9IKUwb29qTFjmCqORoDADimBUnG+HibjrXc6Fccgl4n7iym2izlJf1XxFf5iJ3+XY3eAy\nEfVSTLpRTG/hGqU+i/cF+e1i3C9dJqAeVMaYp9N0uySP+n3rDK6tpL1Okrtahk049gKZ9k0a0S1u\n9erVG8yGeqZwLNgz3myfztw5AXpmq1a0Jpdsk8jWHbYNtCZxdyY7x41xTJralm9Ebtqn7vGrr77a\nGKPX6Sb1iWzMhFJjjP5Iy5Uid4ncmGIyXOSt0vhh5C4Jm7B6RCW71F+9RG2MyZxhGExNnHbtfuD6\nKYBrYAXcdG+c9jEC9YpiMu7Xrnoq8pT7ictsmBzx/heNKeJgOAcmQB/8TB45J77bTG0u0BPwSfwl\nR82Ly+H50oSf3pXn30p0H4U3h2WYhH8My7n1ivuh0AO9Jr2LvKG4q391aQydRnQacMeAlE8N3YeX\nTqmz0J3bnNXLgrv+I/uCqFGsuFuyDI4i+ErQb9eX8NTGQOCW/TAxRUmRl6RPm0kmmhbSwDIGxiWW\nMB1drsOb6yRv2YfLElzhsciVkjIT3xhz61CpOEbUEypqR4dNOKFZfDQ2sAGqd+Wj2bUi/pnrbqj7\nUIqRWyLXHvdzl+FwNnKJsCccCjOQ60TmxNQ3xcwqYThTz5R3RT6HfwyMuxtI8J4/LfJOpaueUHJJ\nzFsNk9ibEo5PdRMzrD6PTWSbCxvuIlDPjJFYPOOplalnc5tQaM+YOzznRufUCxz6po3eW1oyVtyz\nGI4h9L+QU+hEG7FG+QCufObKhAf1x5ppjd3jnvHUC40Yu3FxCoN9xQcryGPCQxNMrQs77cuvEfcb\nl6m4HyReAC55QPU6MTG4mlCtShFhE2Ycp1wp79Ra1u43rruhbhpU9HrABBiBelIZYxgHU+CPqCsj\nz8bmq9APpiG3CtPZNZ9X4UtYvdxlNO73LpNgMoyO87YPgDvPiXmHvEhuSUIajAyLJGJG/nuBRCfb\nyQX12vXpupLVolfrlBnrKd4qqWzq1Vdf9f8og+jtXeDpAOPh5PoC4C2f1hRpaypZvNu2gVZ2gzZg\nqMNRhDaH6BbTkyAY/OGHHx6G//RPcarLHRKtZmyQxvcfT4fcI/U0uY2N/hHAH5pq/DuAYnwdn79H\nYnBVrhW5WpiC3C6UEJV79xP34T15G9ZerhiK3COMRa6rm+bqhly1PJJ8QnFE3GVa7TXgaRVtO0xM\nN5iXY7IeYxuxyXWinldyifz3n8qIFMann7rLXPKIvYOp+6anoR5UyS7vlG30615V2FClWONuy+RW\nURUpPigYDD507rnH9oxkYQXXBpkOx+Ncnd02e1sb0BGLFffshsPhCIJLg06hc+6559Y9EQot3gv9\ncQoHbnKT7nR4xtOfNJChkZCUkuLjhqA3aaaT3MAkNqZqjHG/dikhbMIJ7vtXe8hjYGoTddRSFc1V\nd993o5cE9133OxM2Sq2Dov1rg5NXCCXItaIeV36DybAJE4hMtc47PI8joRi5Q0yMe13NU759vQY+\nrvWzR9teGmNiW7o/3x7iBzBRFHl/jkv8qd11LvkpMkqNMeoBVc8vqT+vb0eox1Vjpvd5xvPT1VNy\nw+67n9iTm5ffbPw7m378tU/W64O13NsKrSmmGsWZ7DgTnZz9+MJ8Efv4V47zwK0pTni9VKv7Gm28\np2mXGEv9gb7YlEr3SzfqYXc/dsM/pjJsi0nwG4RN+Ajh6fZ4L0bk1ZfOyN+F+BcYtURJmYRNeMEe\nfFfb9YX82lT3gTAJ9agigMwX9ZhSS1Te4XkyUZgV8TzIP0U9r5gCI9j9QFZDVUdyz0AtVepFxRgI\noJ5Xcq5EOzpUtefqPpHUSZksxo/Z1vYHdsNubGomM9Df67AJy6UpfjH9QdqKgZSNZWKJa4ycHmbW\ntzdfBsby4lcvMhAGcXDSyMBspM3mQZq2Ju6tkn/d/C+nxOl8QGJxf3B9sGea81MKG9s1sDEtqPad\ntW+6p8ImnPruYTopU3eitTyxtxcUoJ5TfY9heUyyilwt7pcuM2AqFON+76rHlF+jpBarS/7Md3DB\nvjAB9bxSjyh3g+u3NIi2b2QA/A5jjPu+y1kQgEJqE0bDz0a7tNe2l4kqLxNQL6rZZ8iHcPCfY5Y0\nWyhO9EFxGuolxUzk9piwan6K715PoS+FqP8qz3jqQaXf1t6Pnl6qjTHqJuUZT6/R9YxeqlverfXt\n9ArH6XUUDME51yGfLn0o6+H88MMPDb6tpcXS5sS9NRnvseceZ5BzBBxI7Czj341JO8I41k1fPw0m\nUF67tr6W8Slnbat/K/W4krPFfTd1Io37rctU1H8VtdW2YRPuPIa1sPyfSq4TpkSaxsT6haKOafmX\nmK3hr+CLUmWM4UwYClPxLW65JjK7I8/Jk8ki94rMEybCDBjKqRfIs7B4bw44DfKQs4ViqJ22IVcK\nQzCu+x/o/GfoEXMRmor8S9TiuHItJpFcYUDS7A5jjFwqcrmETViuEblaGINcL57xOBG/ha96TKnH\nlDFGxosxRoaJ9jRHQz6cCqch54jMSK3gMl9iry7JvAQUwwAYzEG965YXjbVaso42J+6tI8CSbFIF\n3wgyAHrAgTGpbNc5eq/Uu1h/rJMrZVJv+aFOKdCx1NM7LGWcMFaRfSe4ekwl27OcGddlwf3MZSIP\n7so1v8IYw7BaM38cjICpMAomwiSYANM58Sg+gdVAAZTAROQa8bvbh01YLhZ+DwPxMywZBWNhBnf8\ngTU/55SLxRjDSbVe+OeV+43LYH69P8aYSdA5l7AJu+tcuULUE0rurg3M1jbUZCZqReTSkvi9Yq5Y\n+lvNaJgEhegNqe5y6k1wjPVQ+XjG43jogbfZiz4SbYCcmkDgpANhPBSx55kpBnEE05gILZy27JMx\nVtyzjhUrVtRzszx5jEMfAtdFTs7g+iCTWD8+9SRVtVylyzFPoMEcu+SZ0XVPpUrzIClSp+5VFBM7\ntsJd57qfuXKlRPXdrzLdfTirwCilnlMMR72iXM/1ExzlAgmbsPqv8l0cjGDtUvfNjjCF3Qrwk3+Y\ngpSJXC3qcdXp/zoNuHYA43A/c+VCuft6dUIv5u9P6RhhLGqJYjRhE44GFXL2Y+yJMgBy+hL9yoyL\n6/7ofuQyFPVi3SVNLYrPzX9K0R8mQ4DYxJV0s2dTNk3z8YxXjz2u7lQcgVqg6nfIGGOe6gAjYCw3\n5LA5/fy8YDCYXSqf7Sf7dtLmxD17+eGHH1asWNHgZmP2hd+9eIAAACAASURBVDNwVOQUZQp3ph+r\n3chhpzJMfCevZzwKoQBGQjFMhCm19vJImADjIQ/GIreJXCf6c82gFKmQyZ6KaA2R3CGU4H7rxqaU\nSJnElqdSzGV7ct/u7F5rAjMS91uXYpgAM2AKcqMwHEbxuzE8uxserFjlMg75lzAOuV5cz2VvOAn1\ntGIUXU7m4Y682pE9B8KMSAmrnzcpE0SVKfLo0pkBcNwFop5UjIAz4SzUCypswuQTNmEpE/dzN2zC\nsaOowyYsV4uqUEyIeN6TM8f1BzplI9/6zfZ6dL/uHQYjY+vbbOXDQfrAJEb8lspGjFjasmVLg9tY\nWgJtUdyz0e0el+ZYP6EQveAMAncFjDGMY9ThmIRCxBjqmd8WrZxUZYpujL9n/Jfmy7Qbz0utIAyF\nUTAZzgYVMWmTewgntEVkLDJfoqWtjELKIl5j8pFrhcmsOk5Ww28GwljcL1x/dKpaotx3XcYjlwvD\n4SwYzqyAbIAVu3Lxg4qBMBa5WhhJpz914hjIp1cur8Fjv6fXPOFs5DphOoyGYSCRSHWf9vTJgVFE\nMyYZR9TDjiL2HoU+hE1YPaRkodCPhH70KbzwqUKspt4mEOruBlKePOP52fTeVo/0Y0NyBkGANUuD\nS0ns4V4PLd8X38bNdmPFveXTBFmvZbnjHPt36Iszwwk8HthzGKbeWfUJaTa+lZqQ4Dj+kvFSVG8J\nZXHqY0m/leiyD5uwXCWMAQU9oRD1aFzJvqkdLuqnD0ZF0/3YZWRdwSRjKc5lJVx0l1JLFArG437t\nhk1YPagowu89qZYqprBXMc/vzjro2hcKYTj0g99Cb3ocRTUp+lASiDSCv+gyJZ246Sg5TokxRj2u\n/GuPMYYzUY8q91vXGEPt0FG5TihGVUTy1rWX6ElPGPDkGS/ltKzkZsJRVJmSCxvylc2q2yPqRsUh\niTvIme0wBcZBMY/B+noPkqyj9RW1NJW2KO7ZUtewatWqbX7t5kBg7J+hP5wBk7j2T7yX/tRVDyiO\nRL+qvR88mSH8PfVRocqU75xJR0qvsZ+BnvAgfYkNqKonFUNgPGpZZCRp3YdqxWiYih8CVU8ouVH8\ndJewCVPA+AN4Ay6LufCo+xRjSK7DDJuwEVm7GyP+AhNgHPyReeMHvAH/SxrvF1lnACax9+GRLgjk\noe5SjCNswuphxVjkLonW2dIXhtcGUU+v+4IJ3Rz1W1p/EPczpgxLqH+resRdJjak7EnRFLoRmFcX\nKXWucH49mqn7QxHq7ymCqI1new7U5iO7bLjmoC2Ke8vf61u2bNl+z2ZNILAIOp4IQzjoFF7MqW9f\n61c0A0kQnWTkCqmnbWG6JiTJTcb1e4kFO7GTKBgExcg9Ejbhuka45wujcde7xm8ENl/ccMQVY4z5\nXMTvxKvuVckjrWP5QmQNTNoXd4N74uHyDKlng0TpOgBmcHFtUNRd5rprXLVEMTDS45chMBlZIOph\nFe0k4yfh6De1MUYuEfWc8n39dbGKCREPD0OgGPqRUKmUziHD3xtoHWxSKbsxJrg86Ix0jDHBV4NM\ngQBX7UKX3kw4iI07wmZvab74bLHhmo+2KO4tfK9vgx8mHVsDgSv2gNNgEkceztrH0qY60Au5StIl\nbMQi19frnEk5svkhlZAQqd/SxI+LinVDR6v55RahEFWp3M/daMSVsbjr3Vjd91kGuUdAoD5l9/lQ\n5HMwrvsP+K5eZb8XjOu6611m1bU20y9rmSP6I00+Ml/8aGr0W8h1IjcJw5FbxO9nGXvN02/q2CaR\nxhi5qO6/nvE846n7FSPhJPz/xm7s1Xj1N480xqDSDr/lABgMARjNgaczZ08Yz+uNCKI2nh149Fq2\nk7Yo7qalBlvuvffeHf6eT8Plv4OCSHgweQNvi0ev2mzu5SpaOl8P9SRQejWenJdqjNzwSHMY42eG\nPK3kaolmu6sXFEOIDnWKaqV+N2LgS5kwCn/skVwl6jGVXAcklwpTmXZgow7pb0Uq4NhOnerZZm2M\n6un1mqlEKwM4DFkg9EbOFYbBUBgK04leb6L+d2NMbKJk7OPGj3kmWejqORXtJMOpyLkiZ9WN0vZq\nUgt3ZPt6u34yAqbglDkoJv6FPYdy0MnNogAZt+Jb/t35TqCNintLC7Y068nwMJy9B4yCQijGOTfu\nHpyj4wy9DWZDg2nRnvFiZxUlQB66ojZvcgwUwhiYDMOQOyLGbCSmOoSwCetK7Ru/coXIAlGvKIpg\nOkyGkTAO9aSSc8Xvx8JAmJyiCa16QkU6Fij1ciNM0Q9hDRwFT6TJI9pY6+eJotdpZkUGNullWoYJ\nY/D971G/U7RpTLRwSX+gY/PcE+6NkkuQ1DKV3N9RZgmHJLaXSHzhIyrdWF1jTMiEmACnwUicO52K\nV4In/wOKt8vVXj9btmzJoC/eirtps+Lecvb9zrFxHocRJ+7LBDxgRJwJn9Ca0RijnknRkDaZdE5h\nGS3kQR7q5vhWvUlVrNGcQmOMzK7rBBnVSrVIqYeU3CYUw3Q4C4ahnlGJeZOnEXczEQ4vS6/v98KH\ntc+enJd3W0xH3ygr0r+cyfg/DnmEt4YZiXpGMRQmQz7+OuUCYQJyvTACJiI3CMUwDPojl4gORaxy\nKZOEklS5UFK2WfaMJyNFhgkHp16YZ7x6xig6lznOfCe4LsiJOLc6xph3AgFG8+Lc5lL2KKtWrcqI\nxLc06y0jtFFxbwls3rx58+bNO+3j7u3AHkPp0xNvViC4LkghgUcCzjhHv5YiQOoZj3MaODY848ld\ndbKoqzUnRKxLz3gyJVU3+fhcePWYig3h1nlj3tMMi6TH+NchuUz0B1rdpuRikQsltqsihxP1WtSh\n9WtJAv2VUsvg9ZghqP4coq0iG+AzEaO10Xp1Q4Y/w2EiHIZephmMflv7K1ePKP2ZNjGtY9R/6xws\ncrl4xtMh7RlPLhMGwcn4EdfIBudJypoy9YiKentS+tzVvSphJlTcakcReC4QfCXIQfgTrisdpxIe\nu6XZlT2WnSzxLTyutnNou+Ke2d2/882ZN8ePfx6YzHMdIxLszHUYxVazNeX2jdR3huIZjwEkd35P\nLmtSD6jYrBhjDENQDymZIJEEkkmRprj0J5IiOQL9paYfcrnIPEmYfC2XSuwA6wSiMv2hUsthbZJq\nxw2Z0/ozeBPWp0mLjPsizysmQlc4FgphIoyG0TARCmAw6nGlFqnYWq24CtuByK2i39UMgNMwxqgH\nFWen+CJyrcR2Moi83Im54ymUdPmpfhqPc5MTKAuQB92Z8Ttegqv24dLRrSqlPYGWGVHb+bRdcc/U\njVsGHZEbA4E9BjPzYM7cC6fQ2Wg2cgaMwrk87anONNQD9U4IOp10E+BkviT3GVdlSoaJulcxBiYh\n18Sb4bXGu3ok4ppnMDJH1FOKkcj1EpHFkDbG0D/SLjEtWj8Ar8B7MdZ6LAni/iEYpcLwUZrt4774\nGJiEukXJdDH+desiMbXhU/WwYjTqKcUw9LuaorrAhv5Y6+/jsx6Hw+mpbPYXlKpK/eNLoXib0mbO\nBO4LcDbOHU5wbfC4fOePuZTsRyU8CEP25s5fZfKsr6qqau6PaDlO18zSdsV95x8BzZEM01S+WBKk\nmEd3Y+gAxx+uHTKhwJIAo9HvpTEAZ5CumobT0Z72jCd3pB7fLJdLbHcUvVrj4PczqHuT4USHh8j5\nQl/0Oi3XC+NRLyj1rPIvHn7mOGeiFiuZKeSjnqq3/j4cfsm31pUyOvVXixX3t2LteqU+gi9Sla1G\nnncVhVAEo5GzxB/fIfOEgfgpm7FqzijUw4r+6Ne1elYlNOOM1j3JTNGvx3hpbhe5Lb2zJY/o8NVY\nQibEOPza1G82hE7rjNue1+G2Tkz+PY86zh5DWsQp36znghV3nxaxpzPCzjwCqqqqdoLB0kjm9XeY\njLk/6N+tB5cGjTHOFQ6jU4/lM8bob7U/iC6WBGOTElI2/vWMJ3NFZklsiotMEL0ixtt+GLpKU4zc\nJHKV+JOYGIRfo8QwGA6ToACGwiDoQ7puB8aY50RWwTsx1vdXvj89iYi4h8OpRTwcXg8biBsSEllw\nPvSHnlAEAeiHekQxFJkn+hPNGZAfEffY0DTj4VR0lY7+MgmZi3KWqDuUWqbqkXVVpjgCda3SryR+\nI86E6YRMyBjz5szA7BxeBz93qMf+/Ad+079lne+zZ8/O9BJaMy1rZ+9Mdo7P/d577205sh7lpnsD\ni8EY83/7Qjec4ohbJrguyBj0u2lCrDNRz9VWYPZKceQwJnW6nlwYGY4Rt3ERer02ta1s6IrMrs0j\nLESHtX5PMw7GoD+ORCwZAX0hH4Yl1nP6VCv1rG+tp3Kq6CRn+nnnnfdgXl6owdRJpTx4EbYqFfk6\nveBMKEIuFwbCROgHI/GMJ5fX1i4NIS7bfWqk1w2noKu1MSZlt156QvrcczVf6S21EdqYNCf1uGJC\nRNaNMQ/DaurmtFwCD8ABves2aFHU1NTs2HPERlN92q64NzdVVVUt1jD53IR+PYzp/8cj8K+fMymH\nTvvFGZhyjaj/pGpldbuolxRHIbPSOGrySMjdjmZ8y12Jrht6QSHREs2ou0a/ppmIX8rPacgVwggY\ng8wV+sN4GEJCG8VPlVoE78L36cOhjym1JP7ZHnvvvSaN4yUFIp/BazBnb+gHRZAPo+BM/CZo+n3N\nZDgDY4xcJ/5AcE5HzpOEDHQGpPgB9Zva782bzpNOl/g3Ob62YKog4ocxweB9UEVc9vr7gcBtP2eP\nUwk8s1PTY5pKC7SBsp02Le4rV65spneuqalppnfeUfy4NbTwt9zQkcva44KGCTnUbAj5zwaeCTAJ\nxqUoZPeMR++48RTJMBO/S0FCQSZj8SXPGKNf03KZeMaLTVGnW51HXiaJekQxGrlK1FNK3a0YCMPg\nTBgII2tb74bDj0IVfN2ILBdjzLfR6iSte+29d2NeEiX8kp73Rz6EF2DG76EQBkIRfuN4JqEWKzlP\n/D6Xxv+tZkEf1D2Rbx3NH+W4mFDEck0XoqWneqmOjUkY38OeNPaWXtAfzuaEMqf6ueDjsBrW9IiL\njS+AG3djj94E12XHkI2FCxdu57ljHe5R2rS4N8dxsP1H586kS1/+057cP2OCwf/Af+GeGB9F4MkA\nJST3LJRpIjeL3JI6iOqj12n6p7g26HWaCchFEttTxW+HwnG1TvYTUPNVpJv8YXjGw+/TWwQDYTiM\nhIH8+gRmd2B6+rBnOu6F10QeEzkvfZv7ehg0WW7vzAZ4blfm78Ive0b8M3KeMAF/5gYno55QemPE\nhaKrtVqsOJvYPBkOw9fxBCk3xnB0bbnApZL8rDGGYpiGM9+Z8TseguDveeEMJ8Hr8h+Y/Tt+0RPn\nmixLfNyek8jmQUZp0+K+cePGHfhuWTqwsUt/Fu/KzN515/8S0DFzG/QXmpK6uXGx3aw4m3Ql7+pu\npRYpvSHFpFZ1r1L/TSyy53g4NibDpF/Ev2H8dlf5UARDYDicwsGH8wS80XRZN8YYrT8SWQIL4fi8\nvCa/3P8K96vf9ODe3/ApvA/9/sZ1CxXHQ3+YAoNhApxYW5P1nWYiUS+Kjz8FJa0HphsESNmjTd2l\nGAvTGHIwS+DR3fnX35LeJBh8DO7KgVMJfpIdNnsyWXpCtRzatLibHRR7mT17dlZ7DPcqZG1M/M0Y\nc++FgdvbsxjuBON5xhimwBTkeuHYuGNGPa/kHknOSqR3TG7MzcJZMcJ9am0y+zIlN4n6j5KzIqnr\neoNmKvJP8fMy5Ubh5Eis0pfCQ//EI7AWvmucEyYOrZ+Jj532FZkNa7fhrYyRUuEEGMy83/EphCE8\nSw0eIJyOX68kZ4lcJ3JP5P5GpkT+8API6gbl1XjJ80/0u5piOD51Z0cCMJ0DzmQFrIHxh6SIkV4O\n9+XgB2YDT7RoP3tjaGrgykZTo7R1cd/OUqaampoWGzVtPE6Zw1hu6cxz8dq3YknwYXgMXFij1G3X\nKblZmErCICEfzq3To5TCpF5WcrvoN5IS+PrDYKITU9UtinzUSqWWKnrCICiEQRz9N1yohvk5nLVX\nE49bratSpcRE3TIhkbthXRPvAxiEb63vUcSsPXiuPe+D254zDoYpMJoLhsjqGcp43sMiJadLz73o\nvB9/jDG08w6q+3u3fuw2JpKPFLX6o6hnFCNhBu6evAknHZ069eVeuL8DeQfCQJwrsswbUw+NtOKt\nssdixX3bxb013TYGPwnuewIX/oJV8Sa8MSa4JTjkUHyVf1bklL1hLExBPZ4ohXq9lrtEr9T8AxVM\nLZT0hrPjpoL4cu8ZT2YIBXBCbR8Vfxj3GP5xBPPhDXgyByZBzyYctC/Va+Mn+Nw3K/UAPAzpip5i\n8YxHf+gHp6Df0ZwGYzijB4va81x7rv8LTGF2LmF4C96Cd+BdeAc+gLfhAwhDNXgQgtfgDVgB1fAG\nvATPwUvwuUj5scI0mMnM7qyCLn+GIwl6ic6WTcHgw3D/cc5vnBRdM1sBCxcubNCfbqOpsbTCg6BJ\nbNvR0CqDNsFPggyn519YC48ml+2cDTMZdjBPwn0wel86jYJC9LpEHfSMp+YrCpFbUqhqtFUWE2AW\n6hkVHc1hjAk/oI/oykkOnfNgBBST/zdegU0iY2cJp8KYSDOWBlnSCI98uoDqKpHFDUm8XqEZBEPh\ndNRKRd/aCEFPZJjIaOFwKMLPbvSJ7XT/m3z2PB0G8/pbMZ/iRe54SjthlBp7EMWH0m0Y+x3EfTkc\n/Ge+/iZkknKQjDEmGHwc5p/o0JPAI1nviqmfeowqa7nH0tbFvalUVla2SmX3CTwdYCK/Pgq3PV+n\nGr3m3O78pYBRB/EQPA5/7QOToQT9VpwO+nl7+gstt4ncIYEzI6K2YoketifG8zYoZbS+sAN37o4L\n/4XH4Vl4Cl6GBzpAXw44had6y6N95YQDYBLqWcWpyI2Ssg1LlLDWI+CNxrnRG8iW8bzH4T+1UYcE\n/LZfcqnI9UI/OBXykanC34l28qIr0e4LaoGiP4yG8XA2nvHUbSrl/Q0HIP8UhsNMOJVoFbGPMyMx\nK2ZNIFDanpwjYAjOla3HFVMPmzZtSnnP3XzJzdmIFffGUllZ2UbsAsZDP+5pT0VMzkwszg0Op/DX\nwdzWkXtyOKonjIWp6I+10fojpc7K4RmR6+E+eAAehJfgBXgBlsIyKIcPRIznVR4t4/8UUc8PX9Gn\nFAlHwElQhMwRtVh5xuN09NvaMx6noV5QCWknUa4WOTONEKejsamQWj8BNfH3AQxCuSrqROIftX/4\nTY9rPLVA0QcKYTQMJSEQbYxRt6dQdvWw4iyYAX3QS3VoUyj2WWeG4/wrRr5DoYscR34Bp8MkAo+3\ncps9mdg7b+uTScCKe6Pc7q3YWk8JE2EM8y4NvOc4X6Ua1sPJOFc5zKDzSEZ2YwnM+QtM57o/8O/d\neRaWRr0iMWp73Vz1y14wFUajN2iZJ57xOCk+J7IHcoUYfwTH6citIlcLBaiVinwYnMKh/KrvRWk6\nTctz1/opWCNitFZlSt2h6IlMEATyiKQ2Horft12VqehgDblUGIlcGHczoZfq2DxIvVyrhxSTYCrq\n4dTepNDWkHN1nbJ/Ewze2IGuf4MxBJa1OVmPsmnTJt9gt+KegBX3Bo6JNnvEBJ4OUMDR+2OCwfJU\n0hm1oPUG3XkCh/ZGbhKZJ74zPV0fYH/uc/SF6knFIJgI05HbhT6RMaTqMWWMoTf6fa3DmiHIv4QT\nkXMEgdpBqY9uW05kLdtWxPQgPALzj5Oue1N6pZJhkTojdbuKjkOS6XHFRwyBEXjG8zZ5xhi/W68q\nU+omRV84EYphJoyGHmlPyWgjB2PM18HgNb/k2INA4dzQJlwx9fPiiy+OGzcu06toWVhxT1vK1Nas\n9WSC7wSd6xznKufsM52Xklw05OGMiJMVtVwxDSZF3MpMg7GJ+dr6Va3+nWiZykwxxnAK5KNX6miI\nVb+tGYT+XuuPtG/gqzK1z5+Z3UeeaE/K7MYmsQ3izhFwCDJMzusjFSLjoEtn9t4bDoFTYSQMQ6/V\nDITDoCsMhJNhAIyC0UhxpHaJ4/CMpx5VnIUsqOuuk/JDN20IddmLxy4NmFDIfBm6/Shn7L6Qj3Oj\nlfUIbdYIqwcr7ilYuXKljcxEca5xGEPnv3F5DrfG66lT6ATKUjsE5HJBYAycDdPjJF7OSbS1ZaZw\nPNHJqLHuafpgjNEvafLovhc3tacSVsGSpZqDSVma33iaJO7qAUV3Ij0s8+Bg1ELV+TDOOVKGwLz2\nfPetZ4xRdym/iUJk/d3rylDlcqEAvVTLVNFvaybCOXXNdnoPEPNhKHIFDYWWOM4bgYCGRXA3/Btu\nzWHG/6NvN37TG8YSWNp2XTEJ2LM1JVbcjYlxuy9YsMAeKClx5joMosseDInXd/JICPrFPXsw3g+e\n3y6Y6VAMZ8HZcAYUQQkUoTdoekABnIn+VFMAx8AoGAAj4BjowpDOTOzEkxD4f9T4+e/HQB4yUTgZ\nvbrhtPRY1LVKabXBbFBTG3VtkAuELpESWd+9bvzuLhOQs4XToDf9D8TtwEMwqhPL1tS2lFmuExp+\ndRwAp0IRnEP/Q5h7qtwAV8EtEITVjrPacX4IBEwoVBMIPH1e4K9/pdd+cAYMwrnMCb4bZDCBFVbW\n67AnbDqsuBtjTHFx8caNG+1RUj/ONQ5FdD6MPrvixRQ6NaDvMa4Gz3hMhUKkRPzpdMYY/Y6mAPWQ\niu3iq9/X0WKlx4+U1+E1eOZd7fdflBnij4pmGHKFcDqcilqkYvvepERmCUfVynQu7F5XMBW7SGOM\nzBGOg75wANE+MKpM6dc0BXAG+lVtjFHPK7VMGWNkmjCQEXlc/Rvu7chtu3B+H3H24pwj5UmlPKVm\n7sLBB7JbPhQjN8oHy7TR2oRCq5YEf7lfnMvLKXScQocuMDguASbweIDpBDdma6+Y5iBTwzKzAivu\nxhizatWqF198MdOryA6C64MMpPPJjPkdSx1nFPRpj3RCT0ttTg44XXrkxyeKbNRMh3z8oh76of6r\njDHq3yraLMwY8839+ob2vAajD4ARMBoG1OaM+76Ro/GM5z/OIBgCvWAknAj9kHNFrhX6INcIveEY\n6AmjoR/0ghNgH+hYK/SHw0AYAr2hD5wEhxJrrasyxUlwPPpTrau1nC2Mhl5E65Lk5rphsLPmq5yB\n9D6SS04X6cTxv+Bvp4GCWXA6HAOD8DZ5kbnV0X9d4DDoAt2gBxTjlNW51Mkn8Io12OOwyl4/7Ywx\nWGDTpk3V1dXdunXL9EKyAPWoKltU9vd3Obybs+mFCq8zuR+xpBNdV7AZpLtTqNQ9c+euq6j4Hr6D\njtAbvoE94SCR18vLbxVe+huf/xJWw648c74+bg+hvLzv/XM/e6/8yl7q35fM3WdfVu7KPYfAJrx7\nvT/xJ+Cwiw4r/285G9EP6PIPyufeNJfNyN9FX6z3OXIf8uBD2AX+CO/CVvgThOHXsA72hm/h57AF\nvoP/QSX8ofZb/Qp2hw7wHgBbAegIGyEHjoEvkV8LW9Blep+p+5irDdCudzt+hhwgyy9Z7r9NmPA+\n0/dRh6hrBl0DtBvajr3hPSRP9Ew9d/7ca6ZcI5dKxdIKPNgL80ziCdjuzHb8FjMv8ni7wnbsibnK\nnqdxVFZW2rO1ATJ9dWlZ2Jh743FudAJPBXxfSvDToHOtQxGMJFgVDP0YMsbEFlIeN9zhCJYsiXGO\nf+hJQDgTFMyEcRx/LLftweV70ON4ojVBPoxH3as843E0eqmWYmEySiuOhUGolxWnQV8YB/3geOgH\nA6A3+D7uYXAsnASHw2lwGhwGJ8Ne0B1OqHO8cHC8Kd0LYwzHQT5ylaCQCcKhGGPUg0qur13GccgY\nUbcrpiEzxEQb48yCyUih+BmQcd9oCIHFKSxx5ybHmRcx2P0i1ZY5Gy+zWJu9MVhxT8R63htPyISc\nGx0mEwwHo49QCKfDgdAP8mEEnAJ5cBLkw8lwFJwCR8AZcBhSKJGAailMRb2oPOPJWOFU1H21Y5uW\na46FAjiYqFDKFJFrhBJUuZIZQk+8rZ5nPI6Fo6EHnIC6R9ETjoARUAAnIRcIJ0MhdKHT7ztxNOph\nxQnQlTgnSR4cD4ORS0W/qmWieFs84+fM5MMJyGUxI0wXK4bDEXAY6kHFBPzQAofWtSKIErg5wDCC\nnwRjfVAhE2ICgYqI3DMWAgSes36YFLSRQvHtx4p7Cqy+N4mQCQWWBhhXZ2MGngkwIrXJGVgSYCDG\nmIRqHZkoHIucLzJfOAcmIZcKXeFopFg4Bn+mq7fJ41iYgJwv0f5ZnvE4EiainlFyi3AUTECuE3rD\n6ahHlEwSKRX1kGICDIJT0Ws0PWAPOAZ1s/Ln2Pm1Rd4PnjFGCoU8vE2e/FPU04qeMCXSqN0Ywz/w\n/ucZY/R7miOhO8YY9V/F2NpcoINSDMYLzA8woO5ncWZHLPTAggDjCH4dNH4/tVIbNU2LvbduPFbc\nU2Pv+7YB51aHsQQerTU/C6AoxQEWMiGOwJf4BORC4Tjohf5KMxtmw3DoETGlY50b/jgLuVuYBEVw\nHExGr9fqecVJ6LXaGCMXCT1gPIxGPaI4Ee9HT7+syYcz4RCKRhd16t4pkgbziqYL9IXJUAgHQh56\nqdZLtbfJ8+XbxzOe0iqawK5XagbUpngehp875AdLow2/AmUBjiOwPNES5xRQMJnAooBzi0OpPR/r\nw56VTcIeTGnZsUP42g6BFwPOjU7w86AxJhgKMi5xOnNoS8iZ5YRMiDMIhlKYqHqp5jBwUA8p/Z1m\nFkyBoXB4XPpK7Es4KjJ0VD2j9MuaUyOzTOVs4XAifwyEcdCbSAf5Tz06wt/gWPRrWpRwKr7vxTOe\nBES/r40x3ibPt+g5KOLV8addyxiJpN9MheHQncCNSdqdBwfCgdA18URzrnbIh97QH6bCdHsmNoCt\nGG8q9pCqD3sPuM04tzpMw7nRCb4XDDwVcK53nH/WYyt3SQAAEetJREFUxgmPJPDviA4G7ggwAue8\nupy/0KaQlIpzgRN4NMCRyE2iFiu5WuQu8W3wSDbh3+Gg2qqiQvGtbHWr8oynFitOQn+tZZ7IrUIx\n9CY628/fWAqFfZCjxBjjbfb8kKn+VjMRvUZzGFIiDEQ9HbmExDX5Cmm9TqNgOPQmZZp/4OaAM9Zh\nGCETCq4IOsUOBxLaFAr9L+QUOhRCAI6EU3Husi0EGsaeiduAFfcGsHeC20NgWYCzoITAswGKQOEo\nJ3mGXKAs4CiHQ+FInPGJYhcyIc6GIXAI9IYxcA6MRMbFVPnn4ZvYvhdFCkWK657VKzTHRMKbUQ+P\n9Bd2Q0qE/okzSzk6aVZJF/RKzbBaO70Qp9QJLg0md4PhKBiMc40TeDnOkA/cHyCfiLUegGkpvDSW\nlNgI6rZh89wbZtOmTUBOTk6mF5KteHiD7xxcsaqCb2AV/BbWEXoptE+HffwNZLhUrKpwDnVoR8X7\nFc7BjhqhBu8/OOF9ZJhUVFXwJ/gDtIc34c+wO/IXKf93uXkuciSHa8J/6vCndge0k+7iP1L+Rrns\nL0D5ynLArIls+ccD//jhPz40d5jDLjqsfGm5dJfyJ8v5NfwC1kEOrIefw+6wP4EhATlIBu8at6p2\nB7Qza4xX4/256M/8En5CcE5w8C/jtpF/ScW6CnLgc/gl/BRzsT3pGsvChQsLCgoyvYrsJNNXl+xg\n5cqV1nzYfoJfBOkNvWAcnAyHwslwGsGX4zzvkfr7PDiUwJ1x5q0zPMaBY0IhEwo8EXDudjibiJ9k\nOPRGikWVKd8Dk+Cd9x8kj6hbJgpH4Yx2oj6WkAk5FzhMhSL8EELdF1kajNaXOpc7zvwUrpXgZ0EU\nDIXRMA6mk2DLWxrE3jdvD9ZybwLWiNiByAKpWFnBj7AJcgj0C5QvLy+fWZ6wmVfjDS4eXLGywhFH\nukrZjWVRuzuBdse2Yz/oDJtw9nX4gfJp5TJKKsorgvODQMXKirk3zwWc7o6er+fOmXu/e/9HP/8o\n8vpO8A3Bu4P8irl3za1YV8EW+Bw+g2/xX1WxtoL/wZGwgdDC0D7s41vu0TWoRxU/oezhMj6D38H3\n8Cv4AnObPcuajD3dthMr7k2jpqamQ4cOmV5Fq6Ld9HZsgR/ge/glTp7Dd5Sflajy+G6ZlRXB+cH8\n4nyATrAJIDAhUL6qvOLFCn4B7eFX0B72hHbwE/gMDLwNEFpW5wsC1FQl/WXurXMr3qrg9/Aj7AE/\n4vza4Wsqnq/AvxLcqff5yT7J6wHaHdoueGtw7pK5Fesr+AR2g63QAXYndEloH1K/ytIgs2fPnjNn\nTqZXkd1YcW8yVt+bA5kvtKPizQrWQ0foBF9AB4KXBvkS+ZP4QplgKUfxajxg7vy5ZfPLAsUBVayi\nIq6/1nP/PbfitQraw/vQnuCsIN+T3zefLfAP2APnCEdyZW6PudE3VPNU2c1ljuOU3554mVEPqfL7\nyisqK+gAe8C+sAW2wG/gJzj7O+VFKa5MlsZTVVXVtWvXTK8i67Hivi1YfW9W1HJVXl1e8VYFP4XN\nEIafwefQHVaDR2hNCEhnF8swkUNk7pS5sQ/qNTp/Zj7/D34O/4PvYRl8DafBJngDZ39Hz9flK8vZ\nhbmL51a8WcHuBK8Mzl0wt6K6gp/A7rAFvodd4V3IgV1gL2hP8Lzg4I6J4V/LtmFt9h2FFfdtxB6C\nOwEPr3xjef6F+bSHj2E3WAk/gRz4Y8T7gYEa+Emt8v4CtsLP4RtYDQYM5EBn+BnkELw8KH8QYO2r\na6dNmLZ22Vq5Tipeq6AdbIWvYAv8HH4KP8BP4WfwPc7+Dj+FjlS8XsEf4EeCFwf5jsF7Wk3fkdjT\nagdixX3bsQdiRtAhnX9jPga+h62wAT4nUBgou6+MTbArbIIOYGA3+BF+CrvAVviAwNAAMHd8xKjf\ne7+9B5w1oPyd8ooPKwAMzkFOxRsV/ATawU8B+BH+h3OQIweIOllZN3rzYSOoOxYr7ttFZWVlXl6e\nddFkEP2VLn+ovPyNcnah4tUK3zwnB7bAbrAR2oOBH+B/sDu0gx/hO3gD3oNetdb9ZpwjnIq3KthK\n6ObQ3Ofmzj12bsMfb9lBWD/7DseK+/ZSWVlZXV1tLY5s5LzzzrvwwgszvQqLvQluFn6S6QVkPd26\ndcvNzV24cGGmF2KxZCULFy60yt4cWHHfAXTr1q1///5W3y2WplJVVWXvepsJK+47hg4dOhQUFFRV\nVWV6IRZL1jB79mzrZ28+rLjvSLp27Tp79uxMr8LSWPLy8jK9hLaL9bM3N1bcdzBz5syx+p4trF27\nNtNLaKNYZd8JWHHf8cyZM8f63y2WdFRVVVll3wlYcW8WCgoKrL5bLMksXLjQ+tl3Dlbcmws/vlpT\nU5PphVgsLQVbg7ozseLejHTt2nXRokU2h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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_stereoS = stereoS.plot(chart=cart, mapping=Phi, nb_values=25, color='green')\n", "show(graph_stereoN + graph_stereoS, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We may also add the two poles to the graphic:

" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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zfn+A6TAHJsE0OKBphbADjuv6GOsOuFzS4bCWU43y3BOLWQ89VKTrUsr77Azv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quvjmn5OwJjjP9jPxNQZcpf7ZebRD2smIhaW/t2cQq+FbpeHpX5fot4IdNqpdbth3qxob8kRTRx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\nRU5ErkJggg==\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pointN = N.plot(chart=cart, mapping=Phi, color='red', label_offset=0.05)\n", "pointS = S.plot(chart=cart, mapping=Phi, color='green', label_offset=0.05)\n", "show(graph_stereoN + graph_stereoS + pointN + pointS, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Tangent spaces

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tangent space at Point N on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "Tangent space at Point N on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_N = S2.tangent_space(N)\n", "print(T_N) ; T_N" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Category of finite dimensional vector spaces over Symbolic Ring" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_N.category()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Its dimension equals the manifold's dimension:

" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "2" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dim(T_N)" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dim(T_N) == dim(S2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Basis (d/dxp,d/dyp) on the Tangent space at Point N on the 2-dimensional differentiable manifold S^2]" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_N.bases()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

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

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

" ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tangent vector v at Point E on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "v = T_E((-3, 2), name='v')\n", "print(v)" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v in T_E" ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Tangent space at Point E on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.parent()" ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = -3 d/dx + 2 d/dy" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display()" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = -3 d/dxp - 2 d/dyp" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display(T_E.bases()[1])" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = -2 d/dth + 3 d/dph" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display(T_E.bases()[2])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Differential of a smooth mapping

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Generic morphism:\n", " From: Tangent space at Point E on the 2-dimensional differentiable manifold S^2\n", " To: Tangent space at Point Phi(E) on the 3-dimensional differentiable manifold R^3\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "Generic morphism:\n", " From: Tangent space at Point E on the 2-dimensional differentiable manifold S^2\n", " To: Tangent space at Point Phi(E) on the 3-dimensional differentiable manifold R^3" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E = Phi.differential(E)\n", "print(dPhi_E) ; dPhi_E" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Tangent space at Point E on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E.domain()" ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Tangent space at Point Phi(E) on the 3-dimensional differentiable manifold R^3" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E.codomain()" ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Set of Morphisms from Tangent space at Point E on the 2-dimensional differentiable manifold S^2 to Tangent space at Point Phi(E) on the 3-dimensional differentiable manifold R^3 in Category of finite dimensional vector spaces over Symbolic Ring" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E.parent()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Tangent vector dPhi_E(v) at Point Phi(E) on the 3-dimensional differentiable manifold R^3" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E(v)" ] }, { "cell_type": "code", "execution_count": 85, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tangent vector dPhi_E(v) at Point Phi(E) on the 3-dimensional differentiable manifold R^3\n" ] } ], "source": [ "print(dPhi_E(v))" ] }, { "cell_type": "code", "execution_count": 86, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E(v) in R3.tangent_space(Phi(E))" ] }, { "cell_type": "code", "execution_count": 87, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "dPhi_E(v) = -3 d/dX + 2 d/dZ" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E(v).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Algebra of scalar fields

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 88, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CS = S2.scalar_field_algebra() ; CS" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 89, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Category of commutative algebras over Symbolic Ring" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CS.category()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 90, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Symbolic Ring" ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CS.base_ring()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 91, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(CS.an_element())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 92, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "S^2 --> R\n", "on U: (x, y) |--> 2\n", "on V: (xp, yp) |--> 2\n", "on A: (th, ph) |--> 2" ] }, "execution_count": 92, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CS.an_element().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

A specific element is the zero one:

" ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field zero on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "f = CS.zero()\n", "print(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 94, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(0, 0, 0)" ] }, "execution_count": 94, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(N), f(E), f(S)" ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "zero: S^2 --> R\n", "on U: (x, y) |--> 0\n", "on V: (xp, yp) |--> 0\n", "on A: (th, ph) |--> 0" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 96, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field 1 on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "f = CS.one()\n", "print(f)" ] }, { "cell_type": "code", "execution_count": 97, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(1, 1, 1)" ] }, "execution_count": 97, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(N), f(E), f(S)" ] }, { "cell_type": "code", "execution_count": 98, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1: S^2 --> R\n", "on U: (x, y) |--> 1\n", "on V: (xp, yp) |--> 1\n", "on A: (th, ph) |--> 1" ] }, "execution_count": 98, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 99, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "S^2 --> R\n", "on U: (x, y) |--> pi - 2*arctan(x^2 + y^2)\n", "on V: (xp, yp) |--> 2*arctan(xp^2 + yp^2)\n", "on A: (th, ph) |--> 2*arctan((cos(th)^2 - 2*cos(th) + 1)/sin(th)^2)" ] }, "execution_count": 99, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f = CS({stereoN: pi - 2*atan(x^2+y^2), stereoS: 2*atan(xp^2+yp^2)})\n", "f.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 100, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "f: S^2 --> R\n", "on U: (x, y) |--> pi - 2*arctan(x^2 + y^2)\n", "on V: (xp, yp) |--> 2*arctan(xp^2 + yp^2)\n", "on A: (th, ph) |--> 2*arctan((cos(th)^2 - 2*cos(th) + 1)/sin(th)^2)" ] }, "execution_count": 100, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f = S2.scalar_field({stereoN: pi - 2*atan(x^2+y^2), stereoS: 2*atan(xp^2+yp^2)}, name='f')\n", "f.display()" ] }, { "cell_type": "code", "execution_count": 101, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 101, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.parent()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 102, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "{Chart (A, (th, ph)): 2*arctan((cos(th)^2 - 2*cos(th) + 1)/sin(th)^2),\n", " Chart (A, (xp, yp)): 2*arctan(xp^2 + yp^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": 102, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f._express" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 103, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "f: S^2 --> R\n", "on V: (xp, yp) |--> 2*arctan(xp^2 + yp^2)" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.display(stereoS)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 104, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(N)" ] }, { "cell_type": "code", "execution_count": 105, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1/2*pi" ] }, "execution_count": 105, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(E)" ] }, { "cell_type": "code", "execution_count": 106, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "pi" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(S)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 107, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "f: U --> R\n", " (x, y) |--> pi - 2*arctan(x^2 + y^2)\n", "on W: (xp, yp) |--> 2*arctan(xp^2 + yp^2)\n", "on A: (th, ph) |--> 2*arctan((cos(th)^2 - 2*cos(th) + 1)/sin(th)^2)" ] }, "execution_count": 107, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU = f.restrict(U)\n", "fU.display()" ] }, { "cell_type": "code", "execution_count": 108, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "f: V --> R\n", " (xp, yp) |--> 2*arctan(xp^2 + yp^2)\n", "on W: (x, y) |--> pi - 2*arctan(x^2 + y^2)\n", "on A: (th, ph) |--> 2*arctan((cos(th)^2 - 2*cos(th) + 1)/sin(th)^2)" ] }, "execution_count": 108, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fV = f.restrict(V)\n", "fV.display()" ] }, { "cell_type": "code", "execution_count": 109, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(1/2*pi, pi)" ] }, "execution_count": 109, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU(E), fU(S)" ] }, { "cell_type": "code", "execution_count": 110, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the Open subset U of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 110, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU.parent()" ] }, { "cell_type": "code", "execution_count": 111, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the Open subset V of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 111, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fV.parent()" ] }, { "cell_type": "code", "execution_count": 112, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 112, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CU = U.scalar_field_algebra()\n", "fU.parent() is CU" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 113, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 113, "metadata": {}, "output_type": "execute_result" } ], "source": [ "CU.has_coerce_map_from(CS)" ] }, { "cell_type": "code", "execution_count": 114, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 114, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU == CU(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The arithmetic of scalar fields:

" ] }, { "cell_type": "code", "execution_count": 115, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "S^2 --> R\n", "on U: (x, y) |--> -2*pi + pi^2 - 4*(pi - 1)*arctan(x^2 + y^2) + 4*arctan(x^2 + y^2)^2\n", "on V: (xp, yp) |--> 4*arctan(xp^2 + yp^2)^2 - 4*arctan(xp^2 + yp^2)\n", "on A: (th, ph) |--> 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": 115, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = f*f - 2*f\n", "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Module of vector fields

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 116, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Module X(S^2) of vector fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 116, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS = S2.vector_field_module()\n", "XS" ] }, { "cell_type": "code", "execution_count": 117, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module X(S^2) of vector fields on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(XS)" ] }, { "cell_type": "code", "execution_count": 118, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 118, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS.base_ring()" ] }, { "cell_type": "code", "execution_count": 119, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Category of modules over Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 119, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS.category()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 120, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "False" ] }, "execution_count": 120, "metadata": {}, "output_type": "execute_result" } ], "source": [ "isinstance(XS, FiniteRankFreeModule)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 121, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "False" ] }, "execution_count": 121, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2.is_manifestly_parallelizable()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 122, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 122, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XU = U.vector_field_module()\n", "isinstance(XU, FiniteRankFreeModule)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

because $U$ is parallelizable:

" ] }, { "cell_type": "code", "execution_count": 123, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 123, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U.is_manifestly_parallelizable()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 124, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Bases defined on the Free module X(U) of vector fields on the Open subset U of the 2-dimensional differentiable manifold S^2:\n", " - (U, (d/dx,d/dy)) (default basis)\n" ] } ], "source": [ "XU.print_bases()" ] }, { "cell_type": "code", "execution_count": 125, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate frame (U, (d/dx,d/dy))" ] }, "execution_count": 125, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XU.default_basis()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Similarly

" ] }, { "cell_type": "code", "execution_count": 126, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate frame (V, (d/dxp,d/dyp))" ] }, "execution_count": 126, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XV = V.vector_field_module()\n", "XV.default_basis()" ] }, { "cell_type": "code", "execution_count": 127, "metadata": { "collapsed": false }, "outputs": [], "source": [ "eU = XU.default_basis()\n", "eV = XV.default_basis()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 128, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 128, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eU is U.default_frame()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 129, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 129, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eU is S2.default_frame()" ] }, { "cell_type": "code", "execution_count": 130, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 130, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eV is V.default_frame()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 131, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 131, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v = S2.vector_field(name='v')\n", "v[eU,:] = [1, -2]\n", "v.display(eU)" ] }, { "cell_type": "code", "execution_count": 132, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Module X(S^2) of vector fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 132, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.parent()" ] }, { "cell_type": "code", "execution_count": 133, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate frame (W, (d/dxp,d/dyp))" ] }, "execution_count": 133, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoSW = stereoS.restrict(W)\n", "eSW = stereoSW.frame()\n", "eSW" ] }, { "cell_type": "code", "execution_count": 134, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 134, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW = v.restrict(W)\n", "vW.display()" ] }, { "cell_type": "code", "execution_count": 135, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Free module X(W) of vector fields on the Open subset W of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 135, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW.parent()" ] }, { "cell_type": "code", "execution_count": 136, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Free module X(W) of vector fields on the Open subset W of the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(vW.parent())" ] }, { "cell_type": "code", "execution_count": 137, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = -(x^2 - 4*x*y - y^2)/(x^4 + 2*x^2*y^2 + y^4) d/dxp - 2*(x^2 + x*y - y^2)/(x^4 + 2*x^2*y^2 + y^4) d/dyp" ] }, "execution_count": 137, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW.display(eSW)" ] }, { "cell_type": "code", "execution_count": 138, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = (-xp^2 + 4*xp*yp + yp^2) d/dxp + (-2*xp^2 - 2*xp*yp + 2*yp^2) d/dyp" ] }, "execution_count": 138, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW.display(eSW, stereoSW)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 139, "metadata": { "collapsed": false }, "outputs": [], "source": [ "v.add_comp_by_continuation(eV, W, chart=stereoS)" ] }, { "cell_type": "code", "execution_count": 140, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = (-xp^2 + 4*xp*yp + yp^2) d/dxp + (-2*xp^2 - 2*xp*yp + 2*yp^2) d/dyp" ] }, "execution_count": 140, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display(eV)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 141, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field v on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 141, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(v)\n", "v.display(eU)" ] }, { "cell_type": "code", "execution_count": 142, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = (-xp^2 + 4*xp*yp + yp^2) d/dxp + (-2*xp^2 - 2*xp*yp + 2*yp^2) d/dyp" ] }, "execution_count": 142, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display(eV)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 143, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field v on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "vN = v.at(N)\n", "print(v)" ] }, { "cell_type": "code", "execution_count": 144, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = 0" ] }, "execution_count": 144, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vN.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 145, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Tangent space at Point N on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 145, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vN.parent()" ] }, { "cell_type": "code", "execution_count": 146, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 146, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vN.parent() is S2.tangent_space(N)" ] }, { "cell_type": "code", "execution_count": 147, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 147, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vN == S2.tangent_space(N).zero()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 148, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field v on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "vS = v.at(S)\n", "print(v)" ] }, { "cell_type": "code", "execution_count": 149, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 149, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vS.display()" ] }, { "cell_type": "code", "execution_count": 150, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Tangent space at Point S on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 150, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vS.parent()" ] }, { "cell_type": "code", "execution_count": 151, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 151, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vS.parent() is S2.tangent_space(S)" ] }, { "cell_type": "code", "execution_count": 152, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 152, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vS != S2.tangent_space(S).zero()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 153, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "Graphics object consisting of 27 graphics primitives" ] }, "execution_count": 153, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.plot(chart=stereoN, chart_domain=stereoN, max_range=4, nb_values=5, \n", " scale=0.5, aspect_ratio=1) + \\\n", " S.plot(stereoN, size=30, label_offset=0.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 154, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "v = d/dx - 2 d/dy" ] }, "execution_count": 154, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display(stereoN.frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 155, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YAYAuXSR5tYrY2DgULhyGxo1jsXOntZM6ABg3DnjtNdePnz4dGD3ae/EQkTkY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"text/plain": [ "Graphics object consisting of 82 graphics primitives" ] }, "execution_count": 155, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.plot(chart=stereoS, chart_domain=stereoS, max_range=4, scale=0.02, aspect_ratio=1) + \\\n", " N.plot(chart=stereoS, size=30, label_offset=0.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 156, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bmnaoi56ZIhNruBZGTa+qqrrrrrvC1XtDwjxyDy8DBw60fgqWby7c5kQWQhy1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ZTBZzxPS9R/KW3zYrF/Amz7MLRCDlwRCDQK8ZwQIe88VXZrLBbT9T26niEM37Zd9U+Vcsu6Rtnd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\nfcsttxQUFPT2RLKUI0eOALm5ub09kYGGX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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_v = v.plot(chart=cart, mapping=Phi, chart_domain=spher, nb_values=11, scale=0.2)\n", "show(graph_spher + graph_v, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 157, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Vector field d/dx on the Open subset U of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 157, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ex = stereoN.frame()[1]\n", "ex" ] }, { "cell_type": "code", "execution_count": 158, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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m6e+4m0h0QlOmZ9693gWI99MlsbxUU6dOdblcQ4cOnTp16sKFC+NtzpngxAkJ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LW2fST7JBL5TnjP1J+Oc0iIcqVmFhYSi/WJx1NB/Tor+5FQt/RpaZ8+sD+c69C7U1JT5JRPhl4v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\nQNgE2Bko+xAoDR44hkAUvgpfh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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_ex = ex.plot(chart=cart, mapping=Phi, chart_domain=spher,\n", " nb_values=11, scale=0.4, width=1)\n", "show(graph_spher + graph_ex, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 159, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Vector field d/dy on the Open subset U of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 159, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ey = stereoN.frame()[2]\n", "ey" ] }, { "cell_type": "code", "execution_count": 160, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YDv5HoLib+C1shVOqGmTqTSOiaes17UJeoMOxFRph/PDcuQs1F+32M5DqdO6q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\nVfXNwsKduu6125cVFh5wu3eYEToHD8qpUz8PP+/Dqjub7GzuzybrPu7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gwoQkgE8/Xety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\ngyoA9jFjvP2HJcwpKKiEU3AcesMeqBzCmUlsG8LhmbyfXLbDn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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_ey = ey.plot(chart=cart, mapping=Phi, chart_domain=spher,\n", " nb_values=11, scale=0.4, width=1, color='red', \n", " label_axes=False)\n", "show(graph_spher + graph_ey, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We may superpose the two graphs, to get a 3D view of the frame associated with the stereographic coordinates from the North pole:

" ] }, { "cell_type": "code", "execution_count": 161, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Lo0VFqcXFmX6/v6zMDeDdd/+1svL3n7beVOC/ABtgTkk5UFys3HbbXTfe6MnM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\nfP/7//tv//bjN9MXPNQcmMSDqopY7ON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ZqCoikYGnBsdB0/r8G2T7uJ/E6zXWrHl9yxYR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9b2XldXAVSfOGEzmxscDqOqRgOBaCzms9sdZWV5JpOxoeEEZEDaf/DDxP79+5999tnE2zRl//jg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\n7dp1YPXqk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DjMzp2cfz4mU/J0o1quJiDSwJMsUzQ04HJRWZk82he+cM2//3sdZL7zDpP/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\n9UWiUR8QDYffeutoe6fPbgpdMGteVAnHw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BHgJKiuNl+Ew3zta88d2W28xFXCiyUN+2F8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GIIh7T088mj502Gy0tyNJTJ/OkSMi4UHdJRiVz8e+fRQWYjSmeEyxLWLMdTomTUKWyczk8OHB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TJLqsAll8yMxeyhUN3fKzk1GmXfPkIhnn02etNNm1JZOyjCxpkyUwOjHG5JfpS/t8kNlKYG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\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7dg0MiAF2AdDrVSqVIicnCT9bupScHHJyFL/73dCMNRW9i9RdikChwOHg/vvdoVAgJ4cf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\nkkY04y4iaSx0uWpyR5IuFE9DOc0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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph_spher + graph_ex + graph_ey + \n", " N.plot(cart, mapping=Phi, label_offset=0.05, size=5) + \n", " S.plot(cart, mapping=Phi, label_offset=0.05, size=5) + \n", " sphere(opacity=0.5),\n", " viewer='tachyon', figsize=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Vector fields acting on scalar fields

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 162, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field v(f) on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "v(f): S^2 --> R\n", "on U: (x, y) |--> -4*(x - 2*y)/(x^4 + 2*x^2*y^2 + y^4 + 1)\n", "on V: (xp, yp) |--> -4*(xp^3 - 2*xp^2*yp + xp*yp^2 - 2*yp^3)/(xp^4 + 2*xp^2*yp^2 + yp^4 + 1)\n", "on A: (th, ph) |--> -2*((cos(ph) - 2*sin(ph))*cos(th)^2 - 2*(cos(ph) - 2*sin(ph))*cos(th) + cos(ph) - 2*sin(ph))*sqrt(cos(th) + 1)/((cos(th)^2 + 1)*sqrt(-cos(th) + 1))" ] }, "execution_count": 162, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf = v(f)\n", "print(vf)\n", "vf.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 163, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "execution_count": 163, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf(N)" ] }, { "cell_type": "code", "execution_count": 164, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "4" ] }, "execution_count": 164, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf(E)" ] }, { "cell_type": "code", "execution_count": 165, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "execution_count": 165, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf(S)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

1-forms

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 166, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1-form df on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "df = f.differential() ; print(df)" ] }, { "cell_type": "code", "execution_count": 167, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "df = -4*x/(x^4 + 2*x^2*y^2 + y^4 + 1) dx - 4*y/(x^4 + 2*x^2*y^2 + y^4 + 1) dy" ] }, "execution_count": 167, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.display()" ] }, { "cell_type": "code", "execution_count": 168, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module /\\^1(S^2) of 1-forms on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(df.parent())" ] }, { "cell_type": "code", "execution_count": 169, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Module /\\^1(S^2) of 1-forms on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 169, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.parent()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The 1-form acting on a vector field:

" ] }, { "cell_type": "code", "execution_count": 170, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field df(v) on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "df(v): S^2 --> R\n", "on U: (x, y) |--> -4*(x - 2*y)/(x^4 + 2*x^2*y^2 + y^4 + 1)\n", "on V: (xp, yp) |--> -4*(xp^3 - 2*xp^2*yp + xp*yp^2 - 2*yp^3)/(xp^4 + 2*xp^2*yp^2 + yp^4 + 1)\n", "on A: (th, ph) |--> -2*((cos(ph) - 2*sin(ph))*cos(th)^2 - 2*(cos(ph) - 2*sin(ph))*cos(th) + cos(ph) - 2*sin(ph))*sqrt(cos(th) + 1)/((cos(th)^2 + 1)*sqrt(-cos(th) + 1))" ] }, "execution_count": 170, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(df(v)) ; df(v).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 171, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 171, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df(v) == v(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 172, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 172, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.lie_der(v) == v(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

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

" ] }, { "cell_type": "code", "execution_count": 173, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Real number line R\n" ] } ], "source": [ "R. = RealLine() ; print(R)" ] }, { "cell_type": "code", "execution_count": 174, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Category of smooth manifolds over Real Field with 53 bits of precision" ] }, "execution_count": 174, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R.category()" ] }, { "cell_type": "code", "execution_count": 175, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1" ] }, "execution_count": 175, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dim(R)" ] }, { "cell_type": "code", "execution_count": 176, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Chart (R, (t,))]" ] }, "execution_count": 176, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R.atlas()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 177, "metadata": { "collapsed": false }, "outputs": [], "source": [ "c = S2.curve({spher: [2*atan(exp(-t/10)), t]}, (t, -oo, +oo), name='c')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 178, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Set of Morphisms from Real number line R to 2-dimensional differentiable manifold S^2 in Category of smooth manifolds over Real Field with 53 bits of precision" ] }, "execution_count": 178, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.parent()" ] }, { "cell_type": "code", "execution_count": 179, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "c: R --> S^2\n", " t |--> (x, y) = (cos(t)*e^(1/10*t), e^(1/10*t)*sin(t))\n", " t |--> (xp, yp) = (cos(t)*e^(-1/10*t), e^(-1/10*t)*sin(t))\n", " t |--> (th, ph) = (2*arctan(e^(-1/10*t)), t)" ] }, "execution_count": 179, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 180, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Hb7zBPuykn6FDZQdoxQrVkSjF7XRn0TTpUT1wIFC0qFT3Nm2qOiqyE7fTc+nL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\nz3RUYmXz52vc6F2YT+IAV+OhoVrR2YmXF7e3Dh3iC7G2bdl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Ur286IslGGoAilhEfDwwY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\nAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 180, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.plot(chart=stereoN, aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 181, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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jmeLCBaGqW1U1HpZDIvykKNmadgQWKUqSsUO7XUCkpq20WIx1GY0EPAz5xmqP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m/Y9A3Ghmoflsgk9UpbE0kvcU+BGzS7XRlGyHhIxcCB42ASmPAqvBdWRQbBW1E4ekIoWAErhKiF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\n", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_c = c.plot(mapping=Phi, max_range=40, plot_points=200, thickness=2)\n", "show(graph_spher + graph_c, viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 182, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Vector field c' along the Real number line R with values on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 182, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc = c.tangent_vector_field()\n", "vc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 183, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field c' along the Real number line R with values on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(vc)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 184, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Module X(R,c) of vector fields along the Real number line R mapped into the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 184, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent()" ] }, { "cell_type": "code", "execution_count": 185, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Category of modules over Algebra of differentiable scalar fields on the Real number line R" ] }, "execution_count": 185, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent().category()" ] }, { "cell_type": "code", "execution_count": 186, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the Real number line R" ] }, "execution_count": 186, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent().base_ring()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

A coordinate view of $c'$:

" ] }, { "cell_type": "code", "execution_count": 187, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "c' = (1/10*cos(t)*e^(1/10*t) - e^(1/10*t)*sin(t)) d/dx + (cos(t)*e^(1/10*t) + 1/10*e^(1/10*t)*sin(t)) d/dy" ] }, "execution_count": 187, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 188, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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BrABXooRrTYeICPbeX38dKF/etmaKhAL11EUyOHXqFBwOB0qUKGF3U0JDvnzAk08CO3dy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"text/plain": [ "Graphics object consisting of 31 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(vc.plot(chart=stereoN, nb_values=30, scale=0.5, color='red') +\n", " c.plot(chart=stereoN), aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 189, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Nr7cqyrKEBADazmQdhAZz4K3xrziWLQuAdPi/s5s1JHBXaM+p6Cjttpr2qqpT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\n3Bz57rtms8l57sdSq9UYElqEcLfA4OAgK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"text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_vc = vc.plot(chart=cart, mapping=Phi, ranges={t: (-20, 20)}, nb_values=30, \n", " scale=0.5, color='red', label_axes=False)\n", "show(graph_spher + graph_c + graph_vc , viewer=viewer3D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 190, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "h = dX*dX + dY*dY + dZ*dZ" ] }, "execution_count": 190, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h = R3.metric('h')\n", "h[1,1], h[2,2], h[3, 3] = 1, 1, 1\n", "h.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 191, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Riemannian metric g on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "g = S2.metric('g')\n", "g.set( Phi.pullback(h) )\n", "print(g)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 192, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module T^(0,2)(S^2) of type-(0,2) tensors fields on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(g.parent())" ] }, { "cell_type": "code", "execution_count": 193, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "(0, 2)" ] }, "execution_count": 193, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.tensor_type()" ] }, { "cell_type": "code", "execution_count": 194, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "symmetry: (0, 1); no antisymmetry\n" ] } ], "source": [ "g.symmetries()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 195, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dx*dx + 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dy*dy" ] }, "execution_count": 195, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We may factorize the metric components:

" ] }, { "cell_type": "code", "execution_count": 196, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "4/(x^2 + y^2 + 1)^2" ] }, "execution_count": 196, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[1,1].factor() ; g[2,2].factor()" ] }, { "cell_type": "code", "execution_count": 197, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = 4/(x^2 + y^2 + 1)^2 dx*dx + 4/(x^2 + y^2 + 1)^2 dy*dy" ] }, "execution_count": 197, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 198, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[4/(x^2 + y^2 + 1)^2 0]\n", "[ 0 4/(x^2 + y^2 + 1)^2]" ] }, "execution_count": 198, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 199, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = 4/(xp^4 + yp^4 + 2*(xp^2 + 1)*yp^2 + 2*xp^2 + 1) dxp*dxp + 4/(xp^4 + yp^4 + 2*(xp^2 + 1)*yp^2 + 2*xp^2 + 1) dyp*dyp" ] }, "execution_count": 199, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(stereoS.frame())" ] }, { "cell_type": "code", "execution_count": 200, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = dth*dth + sin(th)^2 dph*dph" ] }, "execution_count": 200, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(spher.frame(), chart=spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 201, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field g(v,v) on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(g(v,v))" ] }, { "cell_type": "code", "execution_count": 202, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 202, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(v,v).parent()" ] }, { "cell_type": "code", "execution_count": 203, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g(v,v): S^2 --> R\n", "on U: (x, y) |--> 20/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1)\n", "on V: (xp, yp) |--> 20*(xp^4 + 2*xp^2*yp^2 + yp^4)/(xp^4 + yp^4 + 2*(xp^2 + 1)*yp^2 + 2*xp^2 + 1)\n", "on A: (th, ph) |--> 5*cos(th)^2 - 10*cos(th) + 5" ] }, "execution_count": 203, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(v,v).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 204, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Levi-Civita connection nabla_g associated with the Riemannian metric g on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "Levi-Civita connection nabla_g associated with the Riemannian metric g on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 204, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab = g.connection()\n", "print(nab)\n", "nab" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 205, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "nabla_g(g) = 0" ] }, "execution_count": 205, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab(g).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 206, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Gam^x_xx = -2*x/(x^2 + y^2 + 1) \n", "Gam^x_xy = -2*y/(x^2 + y^2 + 1) \n", "Gam^x_yy = 2*x/(x^2 + y^2 + 1) \n", "Gam^y_xx = 2*y/(x^2 + y^2 + 1) \n", "Gam^y_xy = -2*x/(x^2 + y^2 + 1) \n", "Gam^y_yy = -2*y/(x^2 + y^2 + 1) " ] }, "execution_count": 206, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.christoffel_symbols_display(chart=stereoN)" ] }, { "cell_type": "code", "execution_count": 207, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Gam^th_ph,ph = -cos(th)*sin(th) \n", "Gam^ph_th,ph = cos(th)/sin(th) " ] }, "execution_count": 207, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.christoffel_symbols_display(chart=spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 208, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field nabla_g(v) of type (1,1) on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(nab(v))" ] }, { "cell_type": "code", "execution_count": 209, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "nabla_g(v) = -2*(x - 2*y)/(x^2 + y^2 + 1) d/dx*dx - 2*(2*x + y)/(x^2 + y^2 + 1) d/dx*dy + 2*(2*x + y)/(x^2 + y^2 + 1) d/dy*dx - 2*(x - 2*y)/(x^2 + y^2 + 1) d/dy*dy" ] }, "execution_count": 209, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab(v).display(stereoN.frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Curvature

\n", "

The Riemann tensor associated with the metric $g$:

" ] }, { "cell_type": "code", "execution_count": 210, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field Riem(g) of type (1,3) on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "Riem(g) = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) d/dx*dy*dx*dy - 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) d/dx*dy*dy*dx - 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) d/dy*dx*dx*dy + 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) d/dy*dx*dy*dx" ] }, "execution_count": 210, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem = g.riemann()\n", "print(Riem)\n", "Riem.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 211, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Riem(g)^x_yxy = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) \n", "Riem(g)^x_yyx = -4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) \n", "Riem(g)^y_xxy = -4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) \n", "Riem(g)^y_xyx = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) " ] }, "execution_count": 211, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem.display_comp()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The components in the frame associated with spherical coordinates:

" ] }, { "cell_type": "code", "execution_count": 212, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Riem(g)^th_ph,th,ph = sin(th)^2 \n", "Riem(g)^th_ph,ph,th = -sin(th)^2 \n", "Riem(g)^ph_th,th,ph = (cos(th)^2 - 1)/sin(th)^2 \n", "Riem(g)^ph_th,ph,th = 1 " ] }, "execution_count": 212, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem.display_comp(spher.frame(), chart=spher)" ] }, { "cell_type": "code", "execution_count": 213, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module T^(1,3)(S^2) of type-(1,3) tensors fields on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(Riem.parent())" ] }, { "cell_type": "code", "execution_count": 214, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "no symmetry; antisymmetry: (2, 3)\n" ] } ], "source": [ "Riem.symmetries()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 215, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Riem(h) = 0" ] }, "execution_count": 215, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h.riemann().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Ricci tensor and the Ricci scalar:

" ] }, { "cell_type": "code", "execution_count": 216, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Ric(g) = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dx*dx + 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dy*dy" ] }, "execution_count": 216, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric = g.ricci()\n", "Ric.display()" ] }, { "cell_type": "code", "execution_count": 217, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "r(g): S^2 --> R\n", "on U: (x, y) |--> 2\n", "on V: (xp, yp) |--> 2\n", "on A: (th, ph) |--> 2" ] }, "execution_count": 217, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R = g.ricci_scalar()\n", "R.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

\n", "

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

\n", "

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

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 218, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 218, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta = S2.tangent_identity_field()\n", "Riem == - R*(g*delta).antisymmetrize(2,3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 219, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 219, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric == (R/2)*g" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The Levi-Civita tensor associated with $g$:

" ] }, { "cell_type": "code", "execution_count": 220, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2-form eps_g on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "eps_g = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dx/\\dy" ] }, "execution_count": 220, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps = g.volume_form()\n", "print(eps)\n", "eps.display()" ] }, { "cell_type": "code", "execution_count": 221, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "eps_g = sin(th) dth/\\dph" ] }, "execution_count": 221, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps.display(spher.frame(), chart=spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 222, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3-form deps_g on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(eps.exterior_derivative())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 223, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "deps_g = 0" ] }, "execution_count": 223, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps.exterior_derivative().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Non-holonomic frames

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 224, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (A, (x, y))" ] }, "execution_count": 224, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_chart()" ] }, { "cell_type": "code", "execution_count": 225, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate frame (A, (d/dx,d/dy))" ] }, "execution_count": 225, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_frame()" ] }, { "cell_type": "code", "execution_count": 226, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Chart (A, (th, ph))" ] }, "execution_count": 226, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.set_default_chart(spher)\n", "A.set_default_frame(spher.frame())\n", "A.default_chart()" ] }, { "cell_type": "code", "execution_count": 227, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Coordinate frame (A, (d/dth,d/dph))" ] }, "execution_count": 227, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_frame()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 228, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "d/dth*dth + 1/sin(th) d/dph*dph" ] }, "execution_count": 228, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = A.automorphism_field()\n", "a[1,1], a[2,2] = 1, 1/sin(th)\n", "a.display()" ] }, { "cell_type": "code", "execution_count": 229, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[ 1 0]\n", "[ 0 1/sin(th)]" ] }, "execution_count": 229, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a[:]" ] }, { "cell_type": "code", "execution_count": 230, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector frame (A, (e_1,e_2))\n" ] }, { "data": { "text/html": [ "" ], "text/plain": [ "Vector frame (A, (e_1,e_2))" ] }, "execution_count": 230, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e = spher.frame().new_frame(a, 'e')\n", "print(e) ; e" ] }, { "cell_type": "code", "execution_count": 231, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "e_1 = d/dth" ] }, "execution_count": 231, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[1].display()" ] }, { "cell_type": "code", "execution_count": 232, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "e_2 = 1/sin(th) d/dph" ] }, "execution_count": 232, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[2].display()" ] }, { "cell_type": "code", "execution_count": 233, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[Coordinate frame (A, (d/dx,d/dy)),\n", " Coordinate frame (A, (d/dxp,d/dyp)),\n", " Coordinate frame (A, (d/dth,d/dph)),\n", " Vector frame (A, (d/dX,d/dY,d/dZ)) with values on the 3-dimensional differentiable manifold R^3,\n", " Vector frame (A, (e_1,e_2))]" ] }, "execution_count": 233, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.frames()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 234, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1" ] }, "execution_count": 234, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[1],e[1]).expr()" ] }, { "cell_type": "code", "execution_count": 235, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "0" ] }, "execution_count": 235, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[1],e[2]).expr()" ] }, { "cell_type": "code", "execution_count": 236, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "1" ] }, "execution_count": 236, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[2],e[2]).expr()" ] }, { "cell_type": "code", "execution_count": 237, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[1 0]\n", "[0 1]" ] }, "execution_count": 237, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[e,:]" ] }, { "cell_type": "code", "execution_count": 238, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "g = e^1*e^1 + e^2*e^2" ] }, "execution_count": 238, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(e)" ] }, { "cell_type": "code", "execution_count": 239, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "eps_g = e^1/\\e^2" ] }, "execution_count": 239, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps.display(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 240, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[[[0, 0], [0, 0]], [[0, -cos(th)/sin(th)], [cos(th)/sin(th), 0]]]" ] }, "execution_count": 240, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e.structure_coef()[:]" ] }, { "cell_type": "code", "execution_count": 241, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "-cos(th)/sin(th) e_2" ] }, "execution_count": 241, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[2].lie_der(e[1]).display(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

while we have of course

" ] }, { "cell_type": "code", "execution_count": 242, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "[[[0, 0], [0, 0]], [[0, 0], [0, 0]]]" ] }, "execution_count": 242, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.frame().structure_coef()[:]" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 7.4.beta5", "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": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }