{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Sphere $\\mathbb{S}^2$\n", "\n", "This worksheet demonstrates some differential geometry capabilities of SageMath on the example of the 2-dimensional sphere. The corresponding tools have been developed within\n", "the [SageManifolds](http://sagemanifolds.obspm.fr) project (version 1.2, as included in SageMath 8.2).\n", "\n", "Click [here](https://raw.githubusercontent.com/sagemanifolds/SageManifolds/master/Worksheets/v1.2/SM_sphere_S2.ipynb) to download the worksheet file (ipynb format). To run it, you must start SageMath with the Jupyter notebook, via the command `sage -n jupyter`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*NB:* a version of SageMath at least equal to 7.5 is required to run this worksheet:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 8.2, Release Date: 2018-05-05'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we set up the notebook to display mathematical objects using LaTeX formatting:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also define a viewer for 3D plots (use `'threejs'` or `'jmol'` for interactive 3D graphics):" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "viewer3D = 'threejs' # must be 'threejs', jmol', 'tachyon' or None (default)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $\\mathbb{S}^2$ as a 2-dimensional differentiable manifold\n", "\n", "We start by declaring $\\mathbb{S}^2$ as a differentiable manifold of dimension 2 over $\\mathbb{R}$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "S2 = Manifold(2, 'S^2', latex_name=r'\\mathbb{S}^2', start_index=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

\n", "

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\n", "

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

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

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

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

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

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

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

" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "Graphics object consisting of 18 graphics primitives" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoS_W.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

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

Spherical coordinates

\n", "

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

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

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

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

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

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

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

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

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

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

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

" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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1x47Af//ptkwQ0oWIH8EYLl1itUiNGmxMuHAhsH49e/cIyVOyJFfUIn7Mg1LMw/L0EveM0rgxvUATJwLr1jGfr39/jqQRBDdAxI+QMWJigCFDmNezYAFze8LDgVde8b4KrvTi40PvjyQ9m4dTp4CICBE/aSFTJi54jh8H+vZlMnTZssD48cz3EwQTI+JHcAybDZg6lZ1ihw0DPviAycw9ewJZs+q2zn0ICmLehFTQmAO7F65ePb12uBO5c3MBdOwYw93duzM8tmSJJEULpkXEj5B+1q8HatUC3nqLnosjR4DRo4F8+XRb5n4EB7O0eu9e3ZYIAL1wlSoB+fPrtsT9KF4cmDKFPYKKFQNatABeeAHYv1+3ZYLwECJ+hLQTGQm88w7ncGXLxhvF7NkcRCo4RvXq7K4reT/mwNOGmeqgRg1gzRp6fi5dYt7fF1+Id1MwFSJ+hLSxZg1d2XPnMslRbhLGkDUrK2Yk70c/kZHMV5PzOuP4+DAEtn8/myR+8w0r6A4e1G2ZIAAQ8SM8itu3gQ8/BF58kcmMBw8yyVGSmY0jKEgmaZuB7dv5GYj4MY4sWYAvv+SxTUigF+ibbyQhWtCOiB8hZTZtYqPCqVOBn37iaIqSJXVb5XkEBwOXL7NFgKCPsDCgQAEm8QvG8tRT7Pn1ySfsGG3PFRQETYj4ER7mzh22sW/QgH1o9u8HunXjvB/BeOwzpCT0pRd7KFe8ms4hWzZ6fSwWhhhr1GChhNWq2zLBC5G7mZCU7dt5URo/Hhg1Cti4kQMNBedRoABQoYIkPevEagW2bZOQlyuoW5fVjd26sT/Qc8+xV5AguBARPwK5d48dWoOCAD8/Xpw+/piNzATnY8/7EfQQHs78NhE/riFHDuC77xhav3yZ4fVx49g/TBBcgIgfgVOsa9Xixejrr+mBqFhRt1XeRXAwk8llPIAewsKAzJmB2rV1W+JdPPMMw+rvvssGqY0aAadP67ZK8AJE/Hgz8fHAV1/RDZ05MxMSBwzgz4JrCQ5mpdH27bot8U4sFibl5sih2xLvI1cuen3WrqXwqVoV+PVXqX4UnIqIH28lPJwt/L/+muGu7dt50RH0UK4cc39MGvoaPnw4fHx88NFHH+k2xTlYLImJ54IeGjYEDhwAOnTguJzGjYFz53RbJXgoIn68jYQE4Ntv2W/j7l0meQ4ZIvO4dOPjw3wTEyY979y5E7/99huqeqo4vnSJHofgYN2WCH5+9PqsWAEcPgwEBnJkhniBBIMR8eNNHD3KGPvAgcBHH3EGT61auq0S7AQFUYyaqAHc7du30bFjR0ycOBH5PHV2m11wivgxD40b0zsdEsKROi1bUqQKgkGI+PEWZsxgCfuNG8CWLcCIEZwpJZiH4GBWHIWH67bkf3Tr1g3NmjXDCy+8oNsU52GxsHlnsWK6LRHuJ29e4I8/gEWLmI9YvTqwebNuqwQPQcSPp2O1spdGhw5Aq1bAvn2S22BWatXiOACT5P3MnDkTe/bswfDhw3Wb4lxkTp25admSuUCVKjEvaMIECYMJGUbEjydz8ybQtClL2MeMAf78E8iZU7dVQkrkyMGKIxPk/Zw7dw69evXCtGnTkN2TPYR37jD8K+LH3AQEAKtWcc5g165Aly7sTSYIDuKjlEhoj+TQIeCVVyiAZs0CPDls4Un06QPMn699ztfChQsREhKCTPc1ubRarfDx8YGvry/u3buX5LmoqCj4+/ujSZMmyPxAq4T27dujffv2LrM9XWzZAtSvz15XNWrotkZIC1OmsBqsZk1g3jyO4BGEdCLixxNZuBDo1AkoVYo/ly6t2yIhrcybB7RuDZw/Dzz2mDYzoqOj8d9//yX53dtvv40KFSqgX79+CAwMTPKcXfxERkbCz8/PlaZmjJEjWe1465b0t3Intm8HXnuNP8+fz15lgpAOJOzlSVy8yOqIkBDg5ZcZPhHh417Ywy+aQ1958uRBYGBgkkeuXLlQoECBh4SPWxMWltjkU3Af6tZlEnTJksCzz9Kzffu2bqsEN0LEj6cQFQW89FKi12f2bCB3bt1WCemlaFF67EyQ9+PxKMXjLCXu7knRosDq1WwOunYtx2PEx+u2SnATZLnjCRw/zvyeCxeAOnWAxYuBEyeAsmV1WyY4QnCwaSq+7mfDhg26TTCWEyeAa9ck2dmdGTwYiIgAevfmiIxTp4A5c5ggLQipIJ4fd2fFCg5jtNkYB1+1CihSBHj1VSA6Wrd1giMEBQF79wKxsbot8WzsArNePb12CI4xYwarWO2PdeuAI0fYMmLvXt3WCSZHxI+7ohQbFTZtyq7N27cDFSoA/v4MfZ07B7z1lvTDcEeCg9nleedO3ZZ4NhYLULkym+kJ7oV9EnynTkCPHvxd/frMAwoI4Hdoxgy9NgqmRsSPOxIby6aFn33GKeyLFlH02KlQgT195s/nHC/BvahcmTOOJO/HuUi+j3ty/TqLOipU4BwwH5/E5x5/nF2gW7fmNbJvXzZ6FYQHEPHjbvz3Hy/Yixcztj10KHBfv5X/8eqrwKBBnOO1fLnr7RQcJ1MmhmJMmPfjMdy6xV5Yku/jXlitQPv2LPBYsICNQR8kRw5g6lTg++8ZDmvalGN9BOE+RPy4Exs2MJ4dGQls3crVTWp8+SW/+B06MLlTcB+Cg/kZ22y6LfFMtm7lvyJ+3IuBA1nZNXs2y9xTwseHw5tXrmQorHZtU83ME/Qj4sddGD+evSyqVWMuSNWqj36Pry8wbRpQsCDdxNIHw30ICuJq9ehR3ZZ4JhYLc0PKlNFtiZBW5sxhnuPIkZzxlRYaNaL4yZ2b3tTFi51ro+A2iPgxO0qxA223bkD37qzuKlAg7e/Pm5cJ0GfOAG+/LQnQ7kLduhSvkvfjHCwWDvi9P19EMC/h4bx+hYZyBEx6sPfNatyYXaElEVqAiB9zoxSTmr/4AvjmG+CHHxzrRFu5MmPgc+dy1SSYnzx56N2TvB/jSUhgdaQkO7sHN28yh/HJJ4FJkxwTrLlyMVT2+utAx47A778bb6fgVkiTQ7NiswG9egE//UTR06tXxrb32musDOvfH6henasgwdwEBwNr1ui2wvM4cACIiZF8H3fAaqVYuXGDPcxy5XJ8W5kyAZMnAzlzAu+9x6pZe5m84HWI+DEjVivQuTOnF//2G/D++8Zsd8gQNv9q355xcJn7ZW6CgoCff2YX4oIFdVvjOVgsQJYsLB4QzM2XXzJpeflyY65Xvr78TuXKxXEYMTH0rgteh4S9zEZ8PBt3TZ3KXj1GCR+AK5+//wby56cbOSbGuG0LxmMPy0jej7FYLEDNmkD27LotEVJjwQK28vjmG84tNAofH4b/v/iCnvBBgyQX0gsR8WMm7t0D2rZlbs6sWYxPG02+fEyAPnWKHVLlS29eSpQAihUT8WM0YWES8jI7R44Ab7zBdh59+xq/fR8fepVGjqTA+vhjuRZ6GRL2MguxsUCrVsD69RQnTZs6b1+BgQyptW1L1/8nnzhvX4Lj+PiYdsip23L+PHD2rCQ7m5nISLbmKFmS1ylnVuR9+ilzgLp35zV4/HiGxgSPRz5lMxAdDTRrBmzaBCxd6lzhY6dNG6BfPz4kqda8BAWxr1NcnG5LPAN7c8Onn9Zrh5A8Nhs9PpcvM+yVO7fz99mtG0XWxImch5iQ4Px9CtoRz49ubt0CmjQBDh9mNYMrV6TDhjEBul07JkCXKuW6fQtpIziY4dA9e2T6uBFYLDzPixbVbYmQHEOHAv/8w0fZsq7b71tvcSzG668Dd+4wNzJrVtftX3A54vnRybVr7FR67BhbtrvaFZ8pExt++fvTzRwb69r9C4+menVelCXvxxgk38e8LFnCJOQhQ+gJdzXt2gHz5rEL9GuvAXfvut4GwWWI+NHFpUtAgwbAhQuJM7t0kD8/c4yOH2dlmST9mYssWYA6dSTvxwhiY+nplHwf83HsGPv5vPIK+5HpomVLirB164DmzaUi1oMR8aODc+eA555jyGvTJqBKFb32VK3K5l/Tp7OhomAugoPp+RFhmjF27WI+h3h+zEV0NFtvFCvG9h66E45ffJG9hXbsYDPYyEi99ghOQcSPqzl5Eqhfn/18Nm8GypfXbRFp146VD59+ylWPYB6CgpgAevq0bkvcG4uFCbSBgbotEewoxXyb8+eZ4Oznp9siUr8+C0EOHeJw1OvXdVskGIyIH1fy77/As88C2bJR+Jgtwfibb4Dnn2cJ/H//6bZGsGOvTJLQV8YIC2PSeKZMui0R7Hz7LTB/PvDXX0CFCrqtSUqdOkxJOHuWKQqXL+u2SDAQET+u4sABCp/8+YGNG4HixXVb9DCZMwMzZ3KoZkgIqx4E/eTPD1Ss6BZJz6GhoWjZsiVmmG1ytlI8fpLvYx5WrAAGDgQGD2aujxmpVo2pCTduMFXh0iXdFgkG4aOUJBI4nf/+44qzaFFg9WqgQAHdFqXOvn0MtbRqxRi8M5uMCWnj/fc5ifzAAd2WJEtUVBT8/f0RGRkJP7OELu7n6FF6FlauNHZUguAYJ0+yyOOZZ4BFi/Tn+TyKU6e4eC1UiIvXPHl0WyRkEJOfcR7AzZvs45MjB4fzmV34ACyvnjQJmDYNGDtWtzUCQDEaHi7Jl45isVDE162r2xLh9m0mOAcEMNxlduEDcKjq8uUUbW3aMGdTcGvc4KxzY+7dY/joyhV+cQoX1m1R2unQAejThzNvNmzQbY0QHMzQzbZtui1xTywWVlX6++u2xLtRijMFT59mgnPevLotSjtVqtDmdeuALl2k+tLNEfHjLGw2VjFs28amWWap6koPI0Ywzt22LZP+BH2ULQsULOgWeT+mRJobmoPRo4HZs4GpU4HKlXVbk34aNuQojClT2IxRcFtE/DiL/v05mf3vv903yTJzZv4NOXOy46kkQOvDx4c3b6n4Sj83bnBKuIgfvaxeDXz2Ga+NrVrptsZxOnZkZeyXX7I/muCWiPhxBj//DIwcCYwZ495fcoDehvnz2e/igw/E1auToCB6EmXwYvqwhwpF/Ojj9GkgNJQNBL/+Wrc1Geezz3g97NyZVWuC2yHix2gWLQJ69gQ++ogPT+Cppzjx+M8/KewEPQQHs93+wYO6LXEvLBbm25UurdsS7yQ2lp7jvHnZRd4T+iz5+ADjxgFNmzIBes8e3RYJ6UTEj5Fs3w60b88v+nff6bbGWF5/nWKud2/2vRBcT82anPUloa/0Yc/3kZYNrkcpekeOHWOycP78ui0yjsyZORi6YkUOYj1zRrdFQjqQPj9GceIEO/GWL8+26Nmz67bIeOLj2SPl8GHOSXr8cd0WeR9PP83O4NOnu37fd++y1D6ZS0ZUdDT8y5VD5LFj8EuuB4qvL298mTO7wND7iI+nx+Grr4BPPnHtvgXOCuzdmyIhNFS3Nc4hIoLfy6xZKbQ9SeB5MCJ+jODqVa4sM2Xiye8OvXwcJSKCzcmKFKEHyBNFnpn5+GNg7lxjxo9YrZxZFBGRtkd0dIqbigLgDyASQKotDvPnZ6O4gAD+e//PD/4uf/6Mh0h27+b5arEkjgkRXMP69czx6d0bGDVKtzXO5fhxnl8VKzKxW66LpkfET0aJjWX54+nTTKw027wuZ7BrFzuzdugA/P67hBNcyfz5TKI/dy5tI1KU4kyi8PCkj9OngWvXHvbiZMvG/Bi7CHnw4e+fbFO6qNhY+Ldrh8jZs+GXM+fDdiQkJAqtq1cTBdX9Pz/YOM7Xlwn35ctzGGlgIMujAwPTvsAYN44en6go/m2Cazh7lmHaatWYEOxqj58Otm3jbMQWLTgmyB2aN3oxIn4ygtXKG9Hq1Wx5XquWbotcx59/Am++CYwfD3Ttqtsa7+HyZY5JmTWL/Zfu58YNCptDh5IKnRs3+HyOHEClShQPZcokL3Jy53ZIzGZ4vIVSFCgPiqJLlzgQODycIyrsAqlIkYcFUaVKD08FDw2lUJQ8Kddx5w6nol+7xoVSwYK6LXIdCxcy57N3b8/L+/QwvECOOwmlmAD8zz+s8PIm4QMAb7zBC1vPnux8+swzui3yDooUYdXS6tVspLljR6LIsQ9dzJyZc6wCA5mjZRcJTzxh3kobHx96lfz92dAxOeLjGV64X9gtW8YRLDYHVHnCAAAgAElEQVQbX1OiBP9W+zm5ZQs9lIJrUIol4IcOMdToTcIH4NiOsWOBHj2YE+kpFb8eiHh+HGX0aODTT4EJE9jq3BuJjwcaNWIlx+7dwGOP6bbIc4mKondx3Trgjz+AW7f4+9KlgapVEwVOYCDFQ9asLjZP42DTO3cSvUN2z9e+fcCFC3y+XDmWIzdsyNw8ycdwHj/9xBv/X3+xQtRb6duX94g5c9y/15uHIuLHEWbOZEn7gAHAsGG6rdHLlSv0ej32GG/OkldhDHfvAlu3AmvX8rFzJ8OsJUrwWG/bRtFZpoxuSwGYcKq7Usz36dULaNmSXohr13h+BgdTtDdsyHPXG/JRXMHmzTym3bsD33+v2xq92GzsBL1gAb+/7trl34MR8ZNeNm5kKKFtW+a9SLIvb8z16zMU9ttvuq1xT6xWes/sYicsjAKoYEHeUBo25A37ySfp3ahaldU0DRrothyACcUPQOGzdCnbUNhsPG7r1vH4btzI6rU8eTi/zi6GAgMlUdURzp9ngnOlSsCqVexH5e3cuwc0bsympGFhDEULpkHET3o4f57VC9Wrc0q7i0MLpmbKFOCdd7w7DJheEhJ4M/77b+aNRUYy4fi55xLFTpUqD9+MrVaWgfftCwwcqMf2BzCl+KldmzfjqVMffi4hgTlrdjEUFsabVeHCXNh07AjUqSOLm7Rw7x7w7LPMOdu1i4nzArl5k14fHx/m5+XKpdsi4f8R8ZNWEhJYxnjmDPMJPLmXj6N068YxGBs2yByllFCKF8Hp01mxdeUKc1JCQ7lKrF07bavml19m8vLSpc63OQ2YTvzExDB5+uef0ybG795laGzJEoa1L11iPlWHDnxUrOh8m90RpYD33wemTWNyubcVfqSFw4f5vQ4NZWsQwRwoIW18/rlSmTIptXmzbkvMy717Sj3zjFJFiih14YJua8zFv/8qNWiQUk8+qRSgVNGiSvXurdSuXUrZbOnf3ldfKZU3r1JWq/G2OkBkZKQCoCIjI3WbQtav53E+cCD9701IUGrtWqXefVcpf39up3p1pUaNUurcOcNNdWsmTODxmTJFtyXmZvJkHqdp03RbIvw/4vlJC2vXJk4jNkmYwbRcvszYf8mS9AB5c2jw4kV6EaZPZz6Pnx/QujU9CQ0aZKzsfO1a4IUXmMdSubJhJjuK6Tw/33wDjBjBsENGcnju3WOIe/p0trWwh3g6dmQVjzePMrBYeB536cLkciFllGJO5MKFvBaUK6fbIq9HxM+juHKFeT6BgcDKlebtk2Imtm1j3srbbzMHyJuIjATmzWMez/r1DGE1b07B06yZcWXW0dGcWfXLLxwcqRnTiZ/mzRmqXrHCuG1GRbF6Z/p0zu/LlAlo0oSf7SuveFcJ/cWLXOSULUshLgnOjyY6mmHBnDlZyelN54sJkbKG1LDZqNaVYkxbhE/aqFePuRa//socIG/gv//Y1bV4ceC99/i7SZMonufNo5fAyItdnjwU5RaLcdv0FGw23lyMnuXl58eu5itX8uY/ejQ/39BQejqHDuUID08nLo4ezEyZ2MdGhE/ayJOHeX5HjsiQXRMg4ic1Ro5kJ91p09hZV0g7773HTq/du9MT5Kns3s2eT08+yaqiXr04TmHtWla/5c3rvH0HBYn4SY6jRznSw5m9VQoXZnfzbdvYYLFVK/b8evxxJv6fOOG8feumVy+e9/Pm8TgIaad6dWDMGC4O58/XbY13ozflyMSEhTHBuX9/3Za4L/fuKRUUpFSxYkpduqTbGuOwWpVaskSpBg2YxFi6tFLjxil1+7Zr7Zg+nfu/csW1+00GUyU8T5qklK+vUlFRrt1vRAQT0QMClPLxUSokhNcRT2LSJJ5zEyfqtsR9sdmUatWKyfSnTum2xmsRz09y3LjB1XzdusCQIbqtcV+yZgXmzmXYsHVrusvdmbt3GcoKDGROyZ07/PuOHaOHy9U9POztBLZude1+zY7FwiaQefK4dr8BAcDgwQyB/vorwxvBwfyc5s1jfyZ3ZscO4MMPmeBsD+0K6cfHh9eRfPl4n7EP6xVcioifB1EKePddJqfNmCGt7zNK0aK88O/YwZwYd+T6deZzlCzJ5OLy5dnTZOtWhjt05YLZR12YaGJ5aGgoWrZsiRkzZugzIixMb5+pHDnY++bQIVaIZctG8V+uHGdfxcTos81RrlzhtPKaNYEff9RtjfuTNy8rQXfvlgpiXeh2PZmOsWPp1l20SLclnsWvv/K4/v67bkvSzqlTSnXrplSOHEplz67UBx8odfSobquS0ratUsHBuq0wT9jr6lVz9lPZtUup9u0ZSs+XT6kBA2irOxAXp1T9+tK/yxmMGsXzddky3ZZ4HeL5uZ89e5iF37MnhyEKxtG5M1fDXbvSC2Rmbt3ieVChAjB7NvDZZ8DZsywrN1t/jqAgjhS4d0+3JebAnlxvtg7jNWuyRP7kSbaAGDuWQ2lHjWI41cx8/DGP69y5QLFiuq3xLPr0AZo2ZVXxhQu6rfEqRPzYiY4G2rVjPsfIkbqt8UzGjQOeeoru8ytXdFvzMPHxtLFMGfYn+vxz4PRp5nEEBOi2LnmCgyl89uzRbYk5CAtjqPWJJ3RbkjwlSwLffQecOgW8/jrQvz9HZ8yaxZC72Zg6ld+JsWNlMrkz8PXlMc6alf2iEhJ0W+Q1iPgBeNH54APekGfNYoxeMJ5s2RITP9u0MU+in1IcLBoYCHz0ERASAhw/DgwaZP5BhNWqsWmaifJ+tGKx0Otj9oGkAQHM/zl0iMnZoaHsS2Sm1gW7dzO5+Z13ZFixMylYkPmlW7ZwioDgEkT8AJxIPn06KzTKlNFtjWdTrBjd51u30p2um927ObD21Ve5Kt+7l40ZixbVbVnayJKF08dF/FBM79xpfHNDZ1K+PIX3unW0PziYC4OTJ/XadfUqPbRVq7InjdnFpLvz7LPAl19S/Kxbp9sar0DEz+HDLFN+912WHQrOJziYbvRx4+jy1cG5c4yz16rFC/2yZezcW7WqHnsygr3ZoRnDJq5k3z62H3DH8Mzzz1O4TZ3KhUHFilwc3LzpelsSEpgCcPcuPbUyhsE1DBjA86BjRyAiQrc1Ho93i587d/glL1WKN2PBdXzwQaI7fdcu1+03Opq5POXKUexMmADs388ZTe66ug0O5sXy1CndluglLIyh1aee0m2JY/j6UpAfO8Y8s19/ZefwH35wbY+sfv2AzZs5uuLxx123X28nUyZOE7BagU6dOKZFcBreLX4+/pju5dmzmTchuA4fH7rTq1Wje93ZKx2bjY3FypZlwmmfPszr6dLF/Xs51avHf7099GWxALVrM3nUncmZkwL9xAmGwD7+GKhcGVi82Pn7nj6d4xfGjGEoRnAtRYtSAK1aJf2UnIz3ih+LhaXLo0bxwiK4nuzZ6Va/dw9o29Z5CdBnzgAvvMBS+xdf5OynYcM4qNITyJ8fqFTJXMmyrkYp/c0NjaZIEXp/9u+nB+iVV1gh5qxQ2L597NzcqRNTAQQ9vPQSj/+gQQzPC07BO8VPfDzDLrVr819BH8WLMwE6LAzo29fYbSvF5OUqVejhW7MG+Osvdkb2NIKCvNvzc+4cJ627Y77PowgMBJYvB/78E1iyhIu1pUuN3cf166xyrFiRgstdQ8CewtChHM/y0Ue6LfFYvFP8jB3LEtMJE/SNJhASqV+feQ0//EBxYgTnz7N5WOfOzOs6eBBo1MiYbZuR4GCe07du6bZED3bh506VXunBx4cemUOHGCpu3pw5c5GRGd+21cpij+hoThrPkSPj2xQyhr8/r4fz51PwCobjfeLn3Dngiy/oVnTXxEhP5MMPgbfeoljJSMM+pbhCDgxkuGDpUub6eEqIKyWCgvi32zscexsWC5PYzdqM0igee4yViRMn0mNapQqwenXGtjlwILB2LXMfS5Y0xk4h47RtmxgCi43VbY3H4X3ip1cv3gilmZS58PFhDlZgIN3v166lfxuXL/O9b74JtGgBhIfT++MNlC3LZmneGvqyNzf0Bnx8mJtz8CA/95de4tiY27fTv63Zs4ERI9jVvmFD420VHMdeFHL5styvnIB3iZ8lS4AFC5hF7+meAHcke3a6ee0tCNLT6n32bAoni4Xb+OsvJgJ7Cz4+if1+vI3bt+nl8xbxY6dkSXp9fv6Z3s4qVYANG9L+/oMHOWcsNJTVj4L5KFOGnrnRoxnyFAzDe8RPbCzdh40bA61b67ZGSInHH2d/kY0b2W/kUVy7RqHUrh3QoAEvECEhTjfTlAQHA9u3e998oB07mLfiicnOj8LXlyHjAwf43Xn+eXq3HxUmuXmT35MyZRgWlgRn89K3L1C6NItzpPePYXiP+Pn6a7oPpVW7+XnuucReI9Onp/w6e+XL6tV83Zw5np/zkRpBQUBMDG+E3oTFAuTNC1SooNsSfTz5JL0+338P/PYbUL06RWFyWK3sInzjBj3hZp9f5+1ky8aUgC1b9HXE90C8Q/wcOkS34cCBvEgI5qdHD3a7fe899h+5H5uNSestWrBdwaFDrFbxdlFbqxYb/Hlb3o/FwiovX++4nKWIry9Lo/ftA/LlYxXllCkPv+6LL4AVKzhMs3Rp19sppJ+GDdnj6dNPHcuHFB7C868WSjEZsHRp4/vICM7Dx4etCCpV4tBR+xc+Koru+q+/Zi+Mf/5xnyGkziZ7dqBmTe/K+7HZOAvL2/J9UqN8eWDTJi4e3nkH6NkzsYHo/Pls8DlsGFMABPdh9Gh67dKSDiA8Es8XP1Onck7NL7/QfSi4Dzly8GIdE8OkzMOHOcphwwa2+h84ULw9D+JtzQ6PHGFvIxE/ScmWjeGvX37h48UXGTZ5803mPH72mW4LhfRSuDDw7bfA5Mn8LIUM4aOUB4+Cvn6deQCNG3NeiuCerF/P8RRZsgBPPAEsXOjd+R2psWABZ6WdPevSoZRRUVHw9/dHZGQk/FxZSfnbb0z4vXULyJ3bdft1JzZvBlq1YpJziRKsjJNj5Z7YbEzsj44G9u7lNVFwCM/2/Hz2Gd29332n2xLBUZRi4qZSnAHWt68In9Swe0C8xftjsQBVq8rNPDWCg9kVWimOAPnnH90WCY7i68t0gH//ZXK74DCeK34sFpZwDh9Od6HgfsTGAh06UMT278+k5u7duXIVkqdwYSb1e0vej8XinSXu6eHrrxM7OLdpw+9U377MHxHcj2rV2M7gyy85tFlwCM8Me8XHM/EzRw5eHGV+l/tx5gwTm48dY95W69YUQ888wxDHrl3e1cQwPbz5Jivgdu1y2S61hL2uXgUKFWKbg/btXbNPd2PxYk6D//pr4PPP6f358Ufgk084627GDPkeuSPR0SwGqV6dn7HkPqYbz/T8yOBS92bDBpawR0ayksfelDJnTiZAR0XxZicr1+QJCmK5syPjDtwJu3dLkp2T5+hRDkN99VVgwAD+zseH5fArV1Ic167NMTCCe5EnD0XskiXAokW6rXFLPE/82AeX9ugB1Kih2xohvYwfz+TmatWAnTuZz3E/TzwBzJoFrFnDai/hYYKDKQx37nT5rkNDQ9GyZUvMmDHD+TuzWDjos0QJ5+/L3YiKougpVoye0wd7IDVqRPGTOzcrKBcv1mOn4DghIUCzZrzXefpCxwl4nvjp1Qvw9weGDNFtiZAelGLfnm7dmNezYgVQoEDyr23UiIMYR4xgHoOQlEqV+B3QkPQ8c+ZMLF68GO1dEYayDzMVl39SbDbgrbeACxdYGZlSGLJUKR7Dxo1ZIegKwSoYh48PMG4cq5q//FK3NW6HZ4mfjRtZ6jtmjAwudSeUolt+0CAKoB9+ADJnTv09ffow9PX22xzQKCTi68uOx55c8RUXR8+WhLweZvhwXgenTWPDw9TIlYsLiNdf58iL3393jY2CMZQqxWvnuHFsbyGkGc9KeG7QgIlgu3bJatBdsNmA3r2Zp/X998xHSCuxsbz53b7NG2G+fM6z0934+mu2eLhxw5ixD3fvMsE4IoKPqKgkT0fFxsL/nXcQOXky/HLmTHzCx4cJtQEBTE4uWNCY3iTbtlHgbd8O1KmT8e15CsuXMxQyaBDw1Vdpf5/NRo/rL7/wu9ijh/NsFIzl9m2KoFatmOcqpAnPET/r13P+yeLFnPkkmB+rlZOKf/+dF90uXdK/jdOnOdOqTh0m/0mCO1m3juHBgweBwMDUX3vjBgsEDh0Czp9PFDipiJ0HiQLgDyASwCN9rvnyUQjZBZH951KlOKi2UqVH9+0ZM4bVS5GR0ujNzokTTGB+5hkmwaZX9CrFEvjRo+k9ki7Q7sPIkfw+HD8OlCyp2xq3wDPEj1KcBH7nDhviidfH/CQksCR75kzgjz9YleIoq1cDL7/Mi/WwYYaZ6Nbcvs1J5+PHA50783cxMRwREh6e9HHxIp/PnJkJsnZBcr8wefB3/v5JvmdRUVHwf+wxRF64kLTU3WplZ+HkBNX9P0dE0A775ahUKYq2ypX5b2AgQzjZs/P51q35/o0bXXAw3YDbt+kJu3eP18C8eR3bjlL0GH31FW+mQ4bI9dQdiInhd+bVV9n1XHgkniF+1q5lhdCSJXT5CuYmLo75OosXs0dLmzYZ3+aoUVy1zp1L96+3Y7NRMOTKBRQvDhw4QC+ZUryZlS6dKCrsj3LlOBXeAQzp8xMby1ld9wuzQ4dYwQnQk1G2LKs4ly3jOfTLL3JzVgpo144hr+3b6TnLKCNHcoBm794Mn3r7MXYHvvuOC8BjxyiEhFRxf/GjFFC/PhsbbtsmX1Kzc+cOxcm6dRQqzZsbs12lOPx06VLeACpXNma77sSpU1wIrF3L43v1Kr8Pzz3Hpp92kVOxIkWRgTi1yWFkZGJYLjycE8v37eNzJUowvNewIR/Fihm7b3fALlTmzWPVllH8/DPzgLp0oQfRiNwxwXnExnJR06yZJK6nAfcXP6tXAy+9xJVgkya6rRFS4/ZtoGVLipNFi+itM5KYGLr+79xhArSjrn934fJlihy72Dlzhjeo2rUpBHx9GQa8fNnpI15c2uH5779ZnTRtGosb1q5NrPirUCFRDD3/vOcnwa9axeues0K+kycD773H4z158qOrMAW9/PADu3cfPcoxN0KKuLf4UYoN3Ww2dgIWr495iYwEmjblTWrZMiZlOoOTJ3nzf/pphtU8LQH6xg1gzhyGCzdt4u8CA3mzb9SIXh5/f/7+3Dl6RubPZ0M0J+JS8dOtGwXPv/8m/i4igkUPdiF48iRv1I0bs4S7ZUvDvV3asSf7165Nj6ezzvWZMyl+QkIoPB0MjQou4M4dip6XXmIupZAyyp1ZsUIpgP8K5uXWLaVq1lQqXz6lduxw/v5WrFDKx0epzz93/r5cQUyMUjNnKtWihVJZsijl66tU48ZK/fGHUpcvp/7e4sWV+uQTp5sYGRmpAKjIyEin70tVr67U22+n/pozZ5QaO1app5/mNSJnTqU6dFBq6VKl4uKcb6OziYlRqlo1pUqXVurGDefvb+FCpbJm5TkYH+/8/QmO8+OPvEYcO6bbElPjvuLHZlOqbl1e3Gw23dYIKXHvnlLPP69U3rxK7dvnuv0OH86b3vz5rtunkcTHU8R16qRU7tz8W+rW5Q39UYLnftq1UyooyHl2/j8uEz9RUbywT5qU9vecPKnU0KFKVazI41iwoFIffqjUli1KWa3Os9VZ2GwUcjlzKrV/v+v2u2yZUpkzK/X++3LNNTN37ihVrBivHUKKuK/4WbaMF7JVq3RbIqSEzabU669zxbhpk+v33bo1hcOhQ67dd0Y4cUKpXr2UKlSI53f58koNGcLfO8KPP/L437ljrJ0P4DLxs3o1j8vhw+l/r81GAd63r1KPP87tlCyp1ODB6ROUuhkzhrbPnOn6fU+Zwn1//bXr9y2knZ9+4iLh3391W2Ja3FP82GxK1a6tVHCwrEDMzIAB+i7SSikVHa1U5cpKlS3L0JuZsViUatWK4bqCBZXq00ep3bszfn7v2sXPICzMGDtTwGXi56uvGD7NqMfGalVq40alOndWKlcupbJlU+q99xwTVa5k7VqlMmVS6tNP9dkwZAjPqT/+0GeDkDp37zLk3aGDbktMi3uKnyVL+OVbs0a3JUJK/PorP6NRo/Tacfw4Q27Nm5svxJGQoNS8eQxLAUqVK8fjFhtr3D7i4hgecfLn4DLx89JLSjVrZuw2b9xgmLRoUX4OzZoptX69+RZWZ85QGL/wgt68G5uNQjFzZvG8m5lffuFiyp083y7E/cTPtWtKFSig1FNPme/iJJB//qHLtXt3c3xGS5fyIvDFF7otITExSv38s1JPPsmb7bPPKrV4sfPE2fPPK/Xqq87Z9v/jEvGTkKCUnx/zd5zBvXv0ZlSpws/lqaeU+vtvcyRIx8bSniee4DVQN3FxSjVpolSePK7N5RPSzrlz/L7kyydJ6sngfl2rpk4Frl8H9uwBXnmFPWME87BzJ7vNtmzJnhNmaD/QtCkHfX71FfsL6eLaNWDwYJaf9+jBxoPbt3NEQ4sWzmsiFxwMWCyJoyPclcOHOWMsONg528+alSNX9u8HVq7kENaOHVk6PGYMm8jpQCnOwDt8mG0LChTQY8f9ZMnCafBly/L7JRPFzcOFCxwQXa4cx53cvAns3avbKvOhW32lC5uNq59nn+UKrXx5rtBeeMGcbmpv4+RJJurWq0fvhpmwWpUKCeFK9cgR1+77zh2lRo5Uyt+f+SW9eil16pTr9m8vDjh+3Gm7cInnZ8IE5rvcvu28fTzI/v1KvfkmWww89hivO64On44bx8/vr79cu9+0cOkSvVGVKrmm5F5ImZMnmcOWNSu9PV98kfj5tGmj2zrT4V7iZ+FCXgQ2bOD/ExKUmj2b/S4A5k4sWyYiSAfXrjFnpUwZpSIidFuTPFFRLHcuX14pV/SjsdmY7P3EE7xpd+um59jcvOn0BFWXiJ9OnZSqVct520+NEydYPQgoVaOGUuvWuWa/mzYxt+ajj1yzP0c4coQ32+eeY6Kt4FoOH+Z3I1MmLj5HjOC1zs6kSTxvXdkWwQ1wH/FjtVLkPP/8w8/ZbMwzqVcvMVY/d675Elw9ldhYVt4VLOhU74IhHD3KOPgrrzj3/LBYEhvstWjhem/Tg1SuzFWhk3CJ+HnySaV69nTe9tNCWFjidcbZn+u5c7yZNWhgjryj1Ni8mRVzoaFy3XUVe/fSo+PjQ6/kjz8m73GPi2MzzNdec72NJsZ9xM+8ebzgpNYvxmZjKejzz/O1FSvSVSzJXs7DamWJdo4cSm3bptuatPHPPzw/vvrK+G2fOqVU27bcfvXqPB/NQOfOFEBp5JtvvlG1atVSuXPnVgEBAeqVV15R/6bSM8Tp4ufyZR7TWbOcs/308KBH78MPjffo3b2rVJ067Ed05Yqx23YWc+fyRty3r25LPJutW1m9ClDU/Pbboz1ukyfz9Xv3usZGN8A9xI/NRldzo0Zpf4/FwpJV+wny66/iknUGAwawsmvhQt2WpI+vvuKF+p9/jNnerVscI5E1K7urTpnCsKxZmDqV34WbN9P08saNG6spU6ao8PBwtW/fPtWsWTNVokQJdTuFfBuni58FC2j/2bPO2b4j3J/L5een1LffGneNee89elJ27jRme67ihx/4OU2dqtsSz8JmY15ro0aOLezj4+k5bdfOqWa6E+4hfrZt4we+bFn63/uga/D7782XjOuurFrF4/rNN7otST9WK0Nffn4MhWWEFSt4buXMSVHlyoTctHL8uOPfIaVURESEAqA2btyY7PNOFz+ffEIviBm5elWpHj2Ym1OlilJ79mRsexMm8LOaMsUQ81zOm28ysV93qNcTsNnYqsPeC6x6dcdTOsaMYeK+u3gSnYx7iJ+332Yb+oyspA8fVuqNN+imDgjgDdvsXX/NzKVLzEd46SX3jfFHRjL5uWLFpAmCaSUqiuEkQKkXX1Tqv/+Mt9EobDZ+Xg4Oez1+/LgCoA4ePJjs804XP0FB5l+17tvHvMTMmZX68kvH8nTCwniD6tbNePtcRXS0UhUqKFW1qrENO70Jq5WpHjVq8PpSrx6b+2akmOf6dXoTR4wwzk43xvzi5+ZN5pMY1djs1CmlPviA4Ql/f6UGDTJH0zB3IiGB7tciRdxrJlJyHDnC8veQkPSJuHXrmPORKxc7qbpDheGrryZfMPAIbDabatGihXrmmWdSfI1Txc/du/y+/vij8ds2mnv3eE3JlImFFymIxWS5cIHfqWee4Xbcmf37lcqeXamuXXVb4l7Exys1bRpbBwBKNWzIvEGjri+vv87wl7suWA3E/OJn3DiupC5eNHa7588r1bs3QxW5cin18cfG78NTGTqU4S5PGS9ib6GQFoEdE8MQh70z88mTzrfPKEaN4vmeTo/Ehx9+qEqWLKnOnTuX4mvs4qdJkyaqRYsWSR7Tp0/PmN1hYTzeu3ZlbDuuZOdO3sCyZqWX+VG5GffusTqwWDF6VT0Be/hu9mzdlpife/eUmjgxset7s2bMWzWazZu5/dWrjd+2m2Fu8WOzKRUY6NwSvYgIJu36+dEl2LWrUqdPO29/7s7mzUxwdjB8YloGD6agW7o05deEhbGPUfbsTOx0t9WTAyKie/fuqnjx4urUI5oyOtXz46Bo086dO0r168fvS926qefA2L3RW7e6zj5nY7Ox8tHPz70WCa4kNlapsWM5hNTHh5Wzu3c7b382G0V5q1bO24ebYG7xY79Yr1zp/H3dvMmVf4EC9DS99ZZSqZT2eiXXrvFLWr++57UPsFpZPurv/3Cvonv3OEXbx4ex94wmSOvCHj4aO/aRL7XZbKpbt26qWLFi6tixY498vVPFT0gIe924KxYLG4Bmz86CiwdDGPYmdBMn6rHPmdy6xWrb2rXdP5RnJFFRzL0pVIgh0k6dmJfqCn78kfc4T/EwOoi5xc8bbyhVqpRrV9i3b2A7ff0AACAASURBVDMrvmhR3uzatpXOmErxgt2ihVL587P5midy6xZvUpUrJyZAX77MHIwsWXixMlP5uiOkMXG4a9euyt/fX23YsEFdunTpf4/YFBJYnSZ+7InaAwYYu11XExvLLs0Aj7+9InDbNgpSJzag1M7Onfz+9Omj2xL93LjBZPh8+XhM3n+f3cNdbUP27EoNG+ba/ZoM84of+wekq4z6zh0msj7xRGI3V3dp4ucMvv+ex2HxYt2WOJfDh5XKnZtu4R076OkqUsQ58XcdfPppmkrGAST7mJJC+bXTxM+JEzzvUgtHuhNz5jDHsFo1nl+PPUZvoqf3ILNfP4zqq+VuXLnCEGiePLyv9eypt2fVW2/x3uZuoXsDMa/4MYtrLi6ODbsqVOCXt1Ej7xuial+59e6t2xLXMH8+P+vMmdll9/x53RYZh5OaBTpN/Pz5J+29ft3Y7erkwAGGgjJnpgfgwgXdFjkfm02pli0923OcHOfOUejkyMFFVb9+5qiQ3bqV36vly3Vbog0fpZRy5RT5NKEUEBgIVKoEzJmj2xpitQLz5wPDhgH79wNBQcDAgUCTJoCPj27rnEdUFPDUU0C+fEBYGJA1q26LnEtCAtCvHzBmDP+/aBHQsqVem4wkIgIoXBiYMQMIDU35dTYbcPEiX5/S4+ZNflcBRCUkwH/3bkTWrAm/zJm5jUyZgAIFgEKF+AgISPpvkSK0JbXvT9euwMaNwOHDBh4EE9C5MzBpEuDrC3z3HdCzp2dfRwDg+nWgenXgiSeA9esB+3niiZw6BXz7LfDHH0Du3ECvXkCPHkD+/LotI0rxsyhdGliwQLc1WjDn2RcWxovdjz/qtiSRTJmANm2A1q2BZcsogpo1A2rUoAgKCeGFzNP44APe6Fau9Hzhc+MG0K4dL8w//MC/+c03gV27gCef1G2dMRQqBJQpw+9YaCgvgpcuAeHhSR+HDgGxsUnf6+eXKGQKFQIqVuT3AgDi4oDdu4HKlRPPk/h43vAOHgSuXuV5FBOTdJt583KhU7ky/7X/HBDA58PCgOBg5x4TVzN1KjBxIjBuHHDmDPDRR8DevcCECUD27Lqtcx4FClB0N2gADBnCh6dx5AgwfDgwfTr/3qFDKeDz5NFtWVJ8fIAuXSi6L1wAHntMt0WuR7frKVncoRGTfYhqw4aJs1b+/NOzqqAWL+bfNm2abkucjz0UUaAAGxgqxQrAMmU4ssCMIyscITaWXbkLF2bVXr58/IwBlpPXrs2O6qNHs6Psrl0Mkd25k+pm0xz2un2brSR27GAIbtgwpdq3ZzfgLFkSbbFPMweY7Owp36tdu9hS4+23E0Pn06YxD6R2be8ICX3xBUN+4eG6LTGOPXuUat2aRTLFi7Oi0uxjlG7dShzJ44WYT/xcu+Z+Lbjvn7JbqpRnDFG9fZsjRRo39vz8ppUrmYRaterDPZ7Cwxmrb9vWPY9DfDzPz6FD2d05W7ZEgRESwt8vWsQ+LBlYbBiS8xMXx4Tz2bN5g6xbN9HWPHnY+G3MGI6RMPPCKCUiIphsXqvWw2Jy924+V7gwhbgnc/cuqyrr13fP79T9PDhAOy0T1s3Eu+/yvHP3KlYHMJ/4cefha540RPWzz3ijfLDnjaexcCFLjZs1S9m7M28eL24jR7rWNkeJjqY3wT641S4emjfnOWlP6F671rBdOiXh+YsvmCC7dSs9RI0aJYq3ggXpMVq82D36x8TH05MVEJBysvmVK5zllD+/+01zTy9r1rjv8Fabjd7h+73+06a5p3dyxw6vrcIzl/ix2Thosm1b3ZZkjCNHONnYXYeohofTLT1kiG5LnMvMmfyM2rR59A10wAB26l21yjW2pZe4OIap2renKxtgT5+hQyke7r8wW61K5c1r6OfrFPHzwgtsMXE/d+7wxjNwILu/AxQLXbootXGjeT1CffrwXNuwIfXX3bzJ0nc/P6W2bHGNbbro2JFhZneZrWiz8Tv29NM872rUcHzCulmw2fh3NG+u2xKXYy7xs3Gj4StSrbjjEFWbje7ocuXcy32bXqZMoZjp1CltK7aEBKWaNGGOjFla9VutvEF27cqbCMAGjd98w3MvNZo0YUjTIAwXPwkJDDcOH5766w4coJeyRAn+/Y8/rlTfvgyNmSWk8vfftC2tg1mjouglypnTc+bnJcfly7wuvvuubktSx2qlyLFPWH/6afadMsv5lVF+/ZXXQp19hzRgLvHToYNSZct6zkll58IFrvzcYYjqlCn8gnvyRffnn/k3dumSvlXbjRtMxK9aVW8CdGwsh0aWK8e/o3jx9N/whw6ld8GgVavh4mffPv5tj/KU2LFaOXfufiFYpw7zh3SGI/buZY+X119P33UtNlapl19mmG/JEufZp5tffuFnZUYvV3y8Un/9xbCWvcfbunWed3+KiuJCY/Bg3Za4FPOIn6tX6SEZNUq3Jc7j6lW66806RPXaNeZSdOyo2xLnMWoUL2S9ezt2ETt4kAK2fXvXXwQjIpgHU7AgV2qtWrHhpiMCZt06HoeDBw0xzXDxM348Q6+O5MzFxTGJ256T8cQT9LpERxtjW1q5do37rlGDYia93L3LpPTMmT13MrrVysT2wEDzDK69e5eJy6VL8/xp3tyzBs4mR5cuShUr5p55Sw5iHvEzejTFz9Wrui1xPrduMYGzYMHEIapmGJb53nt0Q5uhA6nR2Gws6QQ4kT4jwmX2bG5n9Gjj7EuNo0d5ccqend7D7t0zPg/o9m3moEyYYIiJhoufjh1Z+p1Rdu/mtjJlYp7TZ5+5pqNyQoJSL75IL9SZM45vJz6eHnFfX3aa90T27uXfp7ugICaGItk+Yb1NG9rmDezZw2vaggW6LXEZ5hA/9kTn9u11W+Ja7ENUixXjl61dO31DVLds4ck/frye/TubAQP49xk1K65fP16wnRkePHRIqVdf5blRuDBDVUbmjNWsyeHBBmC4+ClVioNAjeLsWaU++YRe1yxZmGfizLEl9vPDiPzFhAQuTAClfv8949szI717U9hnRCg6SmSkUt9+y+IUV09YNxO1az9cYODBmEP8HDrEL7Ynx7ZT4+5drsB1DVGNi2Mjv9q1PbPfw9ixxntqEhLYLLBAAeNDl1euMFE+Uya63n///ZFNBh2iZ0/mMBmAoeLn4kV+XrNmZXxbDxIZyfMgIIA328GDjQ+HzZpl/Plms9H7lymT5wx5vZ+oKLYHadnSdfu8fp1hZPuE9c6dzVPMoINRo+hd9pSGro/AHOJn+HBeiJxxgXcndA1RHTWKq9Tdu527Hx3Mn0/PSZ8+xm/7+nV6KKpXN6afU2wsPVN58jBE8913zq24mzmT55kBYU5Dxc/cubTLmZ6ZW7cSe1kVKaLUxInGCP8DB3gtc0ZOWEICxUHOnJ7ZB8j+uS9c6Nz9XL7MAoHcuZmM3quXd3TWfhTHjnlV6Msc4qdePSb2CSQhQak5c5SqVi2xX4uzSivPnmUCb69exm9bNxYLVzJt2zqvF8e+fbyAduzo+OdjtbJJWokSzAHr1cs1LRHOneP5NX9+hjdlqPjp04fdxV3BmTPMqQHo/Vy50vFt3V8N6KzmpjExTBAuVOjR7QzcDZtNqaZN2a7AGd6Hs2eV6tGD14Q8eSh+3bGZrjOpWJE5qF6AfvFz6RJX5u7Y6dPZJNdUa84cY2/k77zDC6mRzenMwLFjDEnVr+98j+KMGfx8vv8+/e89cIAl2fZxE8eOGW9fapQowdYLGcRQ8VOvnuvz/7ZvV+qZZ/g5NG2afk+AK/tARURw5lz58ubvG5ZeTp7kAsDI5OcTJ5gzlSULP5+vvqJQFR6mXz8W4nhi+sMD6Bc/kyYx5BIRodsS8/JgO/UKFRgey2hZ4okTzCEYM8YYO83ClStcgVeowNCUK/jkEx5L+1DURxEfzxBXlixsTLhxo3PtS4nQUIrrDGKY+ImN5TEZNy7DNqUbm42jTIoVY9XjH3+k3Zs3cCCvYytWONdGO8eP8yYVFORYGb2Z6dKFf1tGc7EOHaJH1teXC7wRI5hbJKSMxcJ7zObNui1xOvrFT4sWXHEJaePBIaoTJjieF/LWW8x38KSLZ0wMPSmFC7u2h1J8PHO0ChZ8dMXKkSO00deXKy2dnbTHjWOLiQx6xwwTP5s389zesydj28kIN26w4sdefPCohqT22W/ffusa++xs28aQ62uvedZK/b//KIAf1d07JXbv5jGxNwAdO9azrnHOJCGBQvHTT3Vb4nT0ip+YGMZfPbmxobO4f4hqsWIMuaQnTn78OD0VP/zgPBtdjT0hNFcupXbtcv3+7U3tnnoq+YttQgKTmLNnZ3dmMzRO273bkJWeYeJnxAh+fmZotrZwIW8E+fMrNX168l6gQ4eYONu6tZ7Ov4sWUUR7Ws5e16487uk5n8LCGHoE6PmdONE9ht6ajXff5fXJw9ErfhYt4olqhgZ/7sr9Q1QLFmTzxLQMUX3jDaWKFvWsFVHv3jwOy5bps8E+zqBTp6Q3w5MnmX/k48P+Nc5KiE0v8fEUGyNGZGgzhomfli0Z3jULV6+y/xbAjtr3h+dv3eJNonJl13ePvp/x4z2vR9e5c/RIDh2a+utsNvbaev55HoNKldx3wrpZWLyYx/LIEd2WOBUfpZSCLt59FwgLA/79V5sJHsPp08DIkcDkyUCOHECPHkCvXkDBgg+/9tgxoGJF4Icf+DpPYNEi4NVXgR9/BHr21GvL9OlAx46JtixbBrRvDxQoAPzxB/Dss3rte5BGjYA8eYCFCx9+LjoaOHwYuHgRiIh4+BEVBQCIslrhv38/IqtVg1+mTICPD5AvH1CoEB8BAYk/lygBVKgAZM+edF9K8fmuXYEhQ1zwh6eDOXNoV86cPE7Vq/N827QJ2LkTKFtWr33duwMTJwLbt9M2T6BHD+Dvv3lt8/dP+pxSwNKlwLBhwLZtwFNPAQMH8jPx9dVjr6cQG8v7xpdfAn376rbGaegTP1YrULQo8PbbwIgRWkzwSC5eBL77DpgwgTegDz4APv6Yx9pOp07A+vXAiRMP34DckbNnecFv0ACYN49/t2769KH4efddYNIkoHlzYNo0wM9Pt2UPM3gwMH48sGYNEB6e9PHff4mv8/VNFDH2f/39AR8fRMXFwX/yZDR5/HFk9vVF+yefRPsCBZIKpRs3eNOyb6tMGSAwEKhcmf/6+QFNmgDLlwMvv6znWKTG+fNASAiPS9OmwIIFwJIl/Fk3d+8CTz/NG9euXRSz7s7Fi0Dp0hQ1gwbxd1YrMH8+Rc/+/UBwMJ9/+WVzfO89hVdfBa5epXPCU9HmcwoLM+80X08gpSGq//7LHIGfftJtoTHExbHipUQJc5Wv3rrFfBGA+RjO6jPkKDabUuHhnGVUrx7ttD9KlGC5d9++Sv35J/OCrl5N9W9IU9grPp6tLSwW5mP06sUk8SJFku6/VSs+b8Y+NrGxiSGW4GBzhVeOHmX+UUZ6TpmNXr1YeXf1Ks9FewPYF15QasMGz/k7zcbkyQzRe+Kcx/9Hn/jp148t5j2pSsGMPDhEtVQp3mx0VhgZSf/+zPMJC9NtSSKnTrHRXc6cPO61apmje3lMDLs6d+iQKDiyZuVNHOCxTEu+WDJkOOfn6lUmqxYsyDErvr6JFY3vvssmn2aY+n30KBvkVanC8+7FF13XTiEt/P03j9vkybotMYbTp1n5lTdvYvWdGQoFPJ0rVyh+PHWWnNIpfipWVOrtt7Xt3uu4fZuC0766btuW3YndmZUr+QV1dYlxaqxdy+aKpUsrdfAgvSbZs7OtgI5Vany8UsuXK/X660xsBliN1q+fUqtWJSZeBwayEZyDGJLwXLky5ysppdTNm6y26tmTzfwACqMPP6S3WIcnLSqK160KFViFtGZN4md94IDr7UmJd96h8D50SLcljhMTw0rUxx7jZ58li1KbNum2yrsIDnbtrDUXo0f8eNkMEdMQGsq+F+PGJQ5Rbd7cPVdSly4xrNS4sXlCSjNn0hvw0ktJvQF//slj7cpQ4969SnXvTu8qQAExZAgbWyZHly68sTtIhsXPzZspd3q32fj3fPopz1+A4y/693fdIEqrlR248+Rh6NjOqVMcQ+PnZ54Q/u3brHoKDDRPVWFaiYxkfx/7hPU33mAbhhw5lPr8c93WeRcjR/K4u9s5lEb0iJ/Ro71qeqwpCA/nzWXCBP7/wSGqDRvSa+EOMfSEhMRcEbPM5pkyhaGaTp2SzwPp1YthR2euXm02lvnbO4EXK8bRFbt3P/pznTqV73EwhJNh8bN8Off/qPEeViu7YXfuzFEFvr7ssbNtm2P7TSvDhtG+RYsefi4qSqnnnqO3Ze1a59qRVsLDeeN6/33dlqSN69eVGjyY4a2sWSnG78/5+vRTCk9PG+dhZv79N+Vz3gPQI36efZYeB8F1hIZytfxg068Hh6g+/TTniZlZBA0bRiG3Zo1uS8jPP/PYdemSshcqLo43yEKFjJ8gffcuczwqV6YdtWsrNWtW+pJxT5zge5cscciEDIufQYO42k/PeRcTo9QvvyhVtmxiAvL8+cbnES5bxvNt8ODUbWncmMUFDh5Dw5k4kcdl5kzdlqTMpUsUNrlyUax99JFS588//LqICL5m0CDX2+jNlC/PMKoH4nrxc/UqV2u//ebyXXstly7R6/Djjym/5sEhqtWrKzV7tvkS0g8fZvy/f3/dlpBRo3i8Pvro0TfuK1cYtqlTx5gE6Hv3+Jnak5dbtKBXxBHharNxJMiAAQ6ZkmHx06iRUq+84th7rVbmB9kHk5Ypk3JH5vRy/Di9Ec2bPzq8eveuUq++yvNz7tyM7zuj2GzsAh8QYK6kbKU4Yb1798QJ6/37P9qL260bz3UzJL57C337emxhkuvFj929/qh5OYJxDBvGVdXNm49+bUpDVM1wwbHZ6D0pU0Z/9ZTNxunQAFsKpPVGu3MnvQPvvOP4zdlmY75cmTJcSLz9tjHdWENCeHwdIEPix95l2ohJ3tu2MUkToMjMyNiO6GjmzZQtm/YquLg4TqT39WWul24uXWI+kj2RXDf3T1jPn595aGltUXHgAD9XMwhLb2HLFh5zM1XTGoTrxc9rrylVt67Ld+u1WK1Mbn7rrfS/9/4hqk88kbEhqkZgF86rVumzwU7//rRl2LD0v3fKFL73l1/S/96dOxk2BphYbWSV0ejRFMkOCN0MiZ89e4yfJL1+PavaAF5zjh9P3/vtXpPcudNfNZWQwPJ8Hx+lJk1K33udwU8/6b+B3T9hvXBhekwdmbD+9NNsLyC4hoQEen769tVtieG4VvzcucMVniM3DMExVqzghS8jFV379rE03j5EdcwY1yerX7/OL2FoqGv3mxw//MBjOnq049vo3p2r37RWCEVEJE4ar1yZCcJGY7Fw+zt3pvutGRI/P/3EY2G0N89qVeqvvxhqzJJFqT590n7ejhjBYzFvnuP77tqVN/t//nFsG0aRkMBeU1WquN6De/+E9ccf52edkXmCf/zBbaVUtSgYzzvvMALgYbhW/KxezRPXTD0xPJ2QEDbcMyL/4cgRepDSO0TVCDp3pvted7h07lyKwE8/zdh24uI46LRw4eQTPO9n3jwKvwIFlPr1V+d1Fb57lyG5H35I91szJH7at2eXaWcRG8sBmdmzM1T4KMG5ahVFS0bzyhIS+P3LmVOpHTsytq2MsmsX/6aMCPb0sGVL0gnrkyYZM2E9NpY5WP36ZXxbQtqYN4+f49mzui0xFNeKnyFDeOKapS+Lp3PhAoWK0f1lTp/mqjZbNraeHziQiezOwu6RGDfOeftIC2FhvIGGhhpzDl++zCZu9eolH068fp3dmAEmA7ui1XxwML186SRD4qdkSXplnM3RozzWPj5KffJJ8p6mU6eYi/Lyy8YkecbGMlQTEKDfW9GzJz3vzrqJ2Wxc4DZokOih/Ptv48V6z548nkaIKeHRXLzIz3POHN2WGIprB5s2bw7ExwMrV7psl17N0KHA8OEcEPjgVGQjuHSJQ1R/+YX/tw9RLVbMuH0kJAA1awJZsnBidaZMxm07PRw9CgQFAVWq8PzNls2Y7e7YAdSvD7z5JvDbb4m/X7oUeP994M4dYNw4Tol3xeDGfv04SfvcuaT7u3YN+Pdf4PLlhye7x8cjKj4e/suXI7JJE/hlyQLkyJF0AGpAAM+LSpWSDne9cAEoXpwDaV97zfl/n9XKc3bQIA7NnDoVqFOHz8XGclBmVBSHg+bLZ8w+r13juQMAFgsnZusgKgqoUAGoV4/DQY1CKQ54HTaM39GaNTls9JVXnDNh/fBhDsOdORNo18747QsPU7Ik0LYtMGqUbkuMw2Uyy2ZjqET6NLiGhAQOqHRFj4arV9l91d+fDco++IDeISP47juu1B3IQzGMy5c5Y6pSJecMT/39d66sfv2V4bAePfj/Jk0eHRIzmgULuO9vv00cPFq4cNLBo5kzM/erenUmn7ZooSJffpmen5dfZsl9w4bMMSlcOHFOV3KDU7t311P9eegQ82B8fZl8a7XSy5Yzp1L79/8fe9cdHkX1Re8moZeEDqEFJIg06R1EpHcE6ShNkN6rCgICgnQQERCQjiBVFClCREqoUiW0BEINJSSQutl5vz8O77cls7szszO7GdzzfX6R3Zk3b2dn552599xz1T/ezZuIVtSs6ZrmxVX8/DPO9+7dro+VkgI/Ke4RVrs2tGju8AirUwcNZr1wDzp2xDl/g+A+8nPrlksmal7IxN69ON+hoe475osXjM2YAZLr68vYJ59YtwKQi3v3UG0zeLBqU5SNuDiYBhYowFhEhHbHGTgQpKJiRfxdssR9RpN370JI2qOH2TPIYGCsZEmIVSdNwqJ5+TLIn8i8HKa9TCY48547BwHyuHGMtWhhbrFChHLy/v1xHC1TqJYwGs397nhlmJaGgKGhqKb78EPPpf4FAWaMRYsqJ2HcHZ73XGvYENV17jRGXbcOxw4Lc98x/8uYO1dxJWhahfvID+82HBXltkP+p9GmDZ7MPeHU/OoVY/PnIzpgMKBk+Px5+eN89hlEvu4SVYvh00/xoz93TtvjhIZCQ+XjA5dirXH/Pqr2Klc2k52KFaGFCQyU3RZBseanYkU8UQ4caF5MDQZEjlau1CbSZosvv8Rx8+Vj7M4dbY+1c6frlYKu4vp1PJzIFbYnJsLugpPWVq20bytiDwkJ0GaNGuWZ4//XwP1+zp719ExUg/vIz9ChUP17oT3u3cPNTYmPjJpITEQqp1gx+U1UIyJQnjxzprZzdITNmzFvrb1aNm4EweJpolq1tBFzvnqFFNsHH4BgpE+PaqTNm617JvXsCVIiA4rIT1wcolzffWd+7d49nG/LObZtC7GlFk+dd+4gUlmtGqIhefLAJVtLjBmDz+0p4sAYvuP8+aVFf2wfZjp2hP2FpzFiBB6OPG14+l9AfDyu2aVLPT0T1eA+8lO9OnLqXmiPKVNQ1aG01YDaMBrhdvvOO9KbqPbrh0Xp5Uv3zdMSN2/Cdr9LF+2iZ5Yu0d264QZz4oRZN6UWHj5ERV6OHFi83n8fBMOe4/fy5YhAyTChU0R+QkLw2e0tpPfvY9GtUgXbFSqEiIlakcD4eES+ihZFqu3JE5wbPz+kVbRCcjLuh0FB0lzXtcCtW3hAmjfP/jYxManT2Go4iasF3nhzwwZPz+S/gcqVGfv4Y0/PQjW4h/wkJuKG7qi3lBfqICUFZmJpsZuzyQSfnIoVcdOqUUO8iWp4OBagWbM8Mk2WmIgfeokS2hFIQYDgl4ixadOszwFvSLlihWvHuHIFTsPp00M7NXy4NCH6lSs4vozGsYrIz8yZmJeUkvILF7D4pksHUjpypGspKkHAeBkzWqc0jUa0CzEYELXUCuHhKBBo395zTYT79EGjXVvjx6dPkQrkHdY/+8y6w3paQv36iluyeCETgwYhNf2GwD3kJzQUN1NPhnn/K9BDLxZBgCC7Vi3xJqp9+yL94G4XaY7hw3HT1yq/bTKZq5zmzxffpn9/zEHJb+bePSzs3JF71ix5EQaTCVGiKVMk76KI/LRsCbGsHNy/z9j48eaFedQoZdGTxYtx/sUiPFK+HzXAzeM8lUrgDxnffot/P3wIzRfvsD5ihPurDeVi1Spc5+7wwPqvY+1aXK/u0OG5Ae4hP4sW4Ublyb5Q/xWMGQPdiB6MJAUBVSIffIAf1dtv40ZseUN2N3btwly0ilKmpMB+wFlkITERZdEFC2JRkoKXL/HEnikTyOP33yvXDjVvjt5hEiGb/AgCBKuTJimb38uX5vRuzpz4vqRqgkJCcI0NH+54fjwy9/XXyuYoBYMHQ+iupCBADfTrh/P36aeYR/bscLbWS2FKVBRStGmhh9qbjuvX8XvYt8/TM1EF7iE/3bpBUOiF9nj7bURO9IaTJ1E9QoSb2YIF7hcyRkVBQNmmjTapCKPR3PFbiqbk/n2IUuvUcUxiBAGlx/nzYwGbMMH1dN3XXyO9JNHlWDb54XqNP/5wYZIM/kC8iWhwsPMbc2QkUj316zsnS4IAV3oiaKa0QEIC0sClS7vfsfjGDcY6dcLny5QJ6VdPaZBcQZ06uHd4oS34A4uMiHBahnvIz1tvodrLC23BFxQ1DMw8gZs3IaysUAGLWYEC8JdwV/qrZ0+kex4/Vn9sQUBLEF9feTbxx45B5zJwoPj7Dx4gfUSEthtqeREdPowxJRr+ySY/PF2hlnj5wgWIlYkQxRATaycm4iGscGF53/Hs2dqmwC5cwHXhrsrGy5dRfOLjA8JcsyaueyVd1tMCZs+GdisuztMzefPRtCnMV98AaE9+njzxKvLdhdmz8QSn15tAz55I2cXFgcj17In0RO7ciERo+VTKK4+WL9dm/G++UV42v2wZ9l21yvyaIKBEPkcOnLNdu9SbK2P4Dnx9rfUoSUmMXboEvdaqVfhMI0cy1qcPi+nRA+SnLcVUYQAAIABJREFURw9EHseORWXWTz/B9TcszDqK1KcPGu6qCUFAqi9LFlRwHTpk/V7fvoiMKXELHzMGZE2r/kajR+O3q6Ww+MwZWBtwl+0lSxB5ioyELGH6dO2OrSXCwvCZdu709EzefHz1FaI/nhLpqwjtyQ93GvZ0U7//AmrXZqx1a0/PQhkePADRmTvX+nXLJqrZszM2caL6DsBJSUg71KypjVaKG3wq1bcwZtZknDqFaEmHDuZoj6VHj1owGhkrVQpRuI4dcX78/KzbVAQEwAW6WjUWU6UKIyLWzN+ftQoIYBvz5kXazHL7jBkxXvfuSD116KDN+b51CxVARIg4JyWZCeTq1crGNJlwrjNkYOzoUTVnC7x8iYhU8+bqLyyWHdZLlABxtU2xDRgAEq1XB99SpdzTyue/jt9/x3V0/bqnZ+IytCc/kybhyf0NYIppGlFReDL98UdPz0QZvv4aT772ojsPHqCyJ0sW9F8aMQKaGDUwcyaiHFoYt/35J9JWPXu69htITIQ3TL58WMD8/VEhpyYiI6G1atnSTFwMBhCJQYMQBfrrL2xns3jaTXslJKAk/eBBjP3pp2bfHiLcGz76CGX9z56p91lMJhwvXTpEmPz88BlcQWIizkXOnNr43XD3519+cX0ssQ7rGzfa13BduqTvzt1jx0LkL1Gj5oVCPHtmv0pSZ9Ce/DRpgqcZL7TF6tX6LflMSUGaomdP59tyDxK1mqiGh4N0aWGTf/Uq5tmokTpP1GvW4DvOnBlePGrg+XOk+urXx9gZMsCEcvp0EFIiSdVmsjQ/PBq8bh2ExDVrQn+SLh2Eq5s2qZe63bkTY6dPz9jx466PFx0NIhEUpE1FVOvWMHNUqr8RBGj+qlfHOa5SBc1qpUTYatWSbz2QVnDsGD7v3397eiZvPkqWdP1BIg1AW/LD/UKmTtX0MF4wtACoWdPTs1CG337DjUtq6wvGzE1U8+RB1Objj+U/jQsCohyFCqnvJB0Xh0WyTBnXK68EAWTEYEBli6+v6wUEly8jTZA+PchBo0Yg0JZzvXcP38u2bU6Hk0V+Jk5EBMsyEvboESwx+KKdLRsI6d278j8bR1ISfhP58qGiKkMGeJW4ijt3cN01a6Z+2i4iAuR25Eh5+9l2WK9TB5VvcqKNP/2EfW/ckHfstICUFKRSx4719EzefPToAVKtc2hLftQqZ/XCMeLjccP85htPz0QZ2rZFakJJWiguDumNggXlN1H94w/10gy26NsXESVXIzQmEyq9uGbIZEIvLCIsVnIgCEjDNW+O/QsWxDXz4IH9fYoUkbQQyyI/9etDeGsPN2+i23pAANJVXbsqb4ybPj1IdUICIotEjls6SAXXPmjhR/XNNyC4UkhIcjIigrwpbKNGjB05ouy48fF4WNUrgejd+41yIE6z+O47/C6l9IVLw9CW/PAnCT16R+gJe/bgPF+96umZyMf9+7jRWza3VILERKRvihfHuWjRwnGaQxAQZahRQ3092saNmIOr+quUFCzYBoN1FZogoAVDhgyo4JGCCxewMBKBaK5dK81XpksXnCcnkEx+kpNB1KWQhpcvYV7Iu4h36ya9pcXKlamr9wQBpEot48Jx47AIyIlYSkF8PJy5HfVRSkhAZRs/N23aQAzvKoYNQ1TL3Z5DaoAblF675umZvNk4cybtdxGQAG3Jz8CBXibuDnz6KUSwehSVT52KxVAtvxejEVoS3kT1/ffFm6jyVJvaUckbN9CvqmtX176P5GQY0Pn6iosLExIYq1oVFUKOtCfcBNDHByaAO3bIm9eSJdDiOHnKk0x+lNw4jUaQmHz5QPjGj3ecSgwNRcSnX7/U7wkCzPyIYAbp6ndUsyb0ampb/i9ejO8sLMz69VevELniHdY7dZLsxSQJV6/i3GzerN6Y7kJcHKKts2d7eiZvNpKTUbmpRgTVg9CW/FStivygF9rBZIJRmRaCXa3Bm7BqUaJqMiGdZdlEdc8eLHaCgGuzVi11CWNiImOVKoGIumIYZzQiLZQunWO9zd27Zrdio9H6PUFA5Cl7drhWL1qkTHR97hzO319/OdxMMvlxpdVNbKy5fUdgIFJPtnj0COm8GjUcH2PePHyuUaNcuwYiIpCea9dO3WspIQGfo1s3/Jtr3HLnRrSpZ0/tIhx16+KhQY9o0waWH15oi5o1zdemTqEt+cmRAz9YL7TD6dO4iSvN83sSv/6KuYeGancMQUCUhzdRffddRA6IUAqsJqZOxcLkSkNUQUDEwtcXZM0ZxPpUPXiAtB8RFklXohJGIyJZ3H1YEJB6OnwYAtslSxibPJnFjB4N8jN6NOzvv/8exO2vv0BIODHo1AnfhSu4cwd9x4igreKEKzkZC3f+/NJsEHhzU1tvKbngDUq3bHFtHFt89x2iP599pl51oxRwXyrbqJMesHIlImJeqYW26NFDvwU2r6Ed+XnxAj+gTZs0O4QXDJoIvTaNbd0apnfuSNfZNlHNlAlCUbVM3W7cMKdkXMH06andnJ3BskP5zp1m12c12pw8foyKtaJFcbOzNS5Mn56xwEAWU7gwyE/hwji2r6/1drlywSMna1ZESVxNcwoCjAuzZIEo+8QJxoYMARGUU+48YYI6aZ527dCORa307YMH0N8YDDiXI0eq52vlDImJ+L5Gj3bP8dQEd3v2Ftloi0mT8JChY2hHfs6fl1++7IV8dO0qSZCa5hAbi4VTq35J9rB7N67LmjXxNygIUQpXmqgKAiIRRYu65k+zdi3m9NVX8o//ySdmwtGunWuuz1evwn+nbFkzefH1hTPzN98gYhcWhoX+NXFNlfYymTCHy5cRGZk61dyDjDevrVaNsVmzpIuYxXD7Nr5L7j4tVzgvCPhc6dMjiqYUd++CiA0ZonwMxnAuBg0yO5o3awYCdPmya+PKxYAB+G3oTUcoCF57FXdg9Wr83nRc8aUd+dm+HSdHj6Z7eoJem8Zu3YrrQ8teRmKoWpWxevVwk7xwAWkYV5uobtmCzyIlTWUPR45gAe/dW/6CExNjJhYBAcrM92JjYRlQoYJ5nE8+YWz9enMaxIHGRJLmZ/Nmc5pzxQq0t8iYEa/Vq4dInJIqo+PHzcRv4ED50bykJBg7BgS4Zts/dy5IndQKPEtcv47v3s8PURfeyy4pCaTa3fqKfftwPi9edO9x1UCTJkj7eqEdjhzRb4Xxa2hHfubNQxWP3p4c9AQ9N43t0YOxcuXce0xeaWSbDgoLQ+m4kiaqMTEgTm3bKp/X48cYo359+Qv3w4c4j9mz42ksTx4s5LYCaHu4dw++Lv7++PwdOqAizDKN+uIFCKKDVJwk8jN0KKwILBEbi4gX1/AUKAB9kVSdUlQURPNVq0JM7eeHkn65JPbFC1TDVayoPIVsNEJTVqWK9DYLly7BToB3WJ87N7Xh5rffIjKldk87R0hMRIpz2jT3HVMtTJ4MAulde7TD3bv4ve7d6+mZKIZ25GfIEDRD9EI76LVprNGI/kiff+7e4376KSpo7BGDiAjrlMPEic6jKLzfmNLUjcnEWNOmIC2OzAbFEBkJq/nAQLOZ4uHDZo2II0RHY+7p0+Ozjh2L8eyhXDmUzNuBJPJTpYrj6s+rV80NXP39UbLsKB1pNIIw5sljdoI+dAjfR9268p21z53D+XAldXXiBIjiDz843u70aRBm3mF96VL7n/XJE8xrzhzl81KCjz7Sp5Mvt7HQ231RT0hJQTXqkiWenoliaEd+Wrb0hh61hl6bxvKQqRqmbFIRG4tFcfJk59s+eACxJ2+iOnw4IiRi22XMKG1Me5g9G+dCrGzbEW7dgiajaNHUN/kFCzDmxo2p90tJgUA6Vy58tq++kkYSPvsMnbPtwCn5iYtDVGbZMufHevSIscGDQeKCgpBWFLvGR4zANraVjsePgzxVrSq/WSoXj2/fLm8/S3TpgpYpYhGkv/5CWoYIkabVq6VF+7p0AdF15299/XrMU+zaT8t4+hTzXr/e0zN5s1GihD4tVl5DO/JTpswb0fwsTaNxY30SzJEjkd5Quy+SIyxbhtSCo+iGLXgT1YAAPHn372+tURo6FIus0rLakydBCOS2E4iMxOIaHCze+0oQEGHJlMm6U31YGMTBBgOiOHIiTVyMbUdI7ZT8HD6M/eUY8l27hkanXMRtqR/kOqSFC8X3PXsWBK9SJXl92wQBxwoIUB7N+/dfXGtcfC0IjO3fD10TEaJomzbJ60DOHxj+/FPZnJTg2TOQy++/d98x1UJwsOvicy8co1Ejxj780NOzUAxtyI8g4KnS3WHa/xJMJtyg9VbVIAgQaffv795jVqyIhVQJYmKgQ7FsonrkCNIzSs9/UhIeEKpWlafzefECi2eRIo5Ln+PjsfAHBSFtsmgRyFCJEso6X9+6Ze4ntn8/NH1DhkAw/v77LKZyZZCfypXRGbxrV0TMlizBufr8c6TX5Cz4HNu2IcKZOzf+//x5fJYePRxHQv75B7qVpk3lnePnz5EebdlSeaSle3eMsXUrvmPeYX3XLmWkXxAQeevYUdl8lOL993H+9IYePVBN6IV26NcP91WdQhvyExWlXcNILwC9No29csX9QrlTp3DMX391bRzLJqpEyHk7cT62i2++QXRATsPOpCT4FAUESGuYGhEBbVW+fJjvoEHyhcAxMUif9epl7d2TKRPIW4MGjHXuzGJ69AD56d4dWpH33kNrm3TpzPtkyYJ01q5d8q0FHj/GUyYRSFSFCtLKbPfvR3StTx95RIYbF+7YIW+ejIHgcQdpXsn2xx+up6zmz8f5fPzYtXHkYMECRD1dcSz3BHhbFlcsLLxwjJkzcS/SKbQhP6Gh+NGfO6fJ8F4w/TaNnTkTi6A7b0p9+yJSoiTqIIZbt7Cg5siB76B5c8dNVG0RHg7yMGKEvOP27o2FSKqbd3g4Ij1EMJSUCpMJZfsffWQuRS9TBhG70qVh6GhzLu2mvZKTUdGUJQsiUbzxrL8/CMnRo9JJgdEI3QsRBM1S9Txr1mAf7lItBYKAlHKhQtLTZsnJ0PDwORYogNSbWl4oz54h2vjNN+qMJwW3b+OzbN3qvmOqAe587/WZ0w7cukJva9BraEN++ElRu9mfF2botWlszZruzRMnJ2Oh/fJL9cYcNQrE59kzaU1UbdGqFaJHcp6m+QK+Zo207S9dQsSnWDGIt6W4GMfHQxvFF+9334Ugm+uK5swBGRLx4nGo+eHNMnk7katXGfviCzMRqloVc3NGTseNQ7Rs1ixEtEqXlq5b+vxz7CsnUnf7NkiqM1En77BetKiZaJ46BZLo4yNN5C0VnTq5P9VQrpz+ejQmJeFaXbDA0zN5c6HzIIc25GfmTCw4XmiHypVhQqcnxMcjYrJ0qfuOefCguj/QhAQsvJbW/7yJaqVKqZuo2uL33+U/SV+9Cg1dz57Studi3woVkIIWBGhwMmcWFxybTCBxhQtDDN2+vfgT84kTdqv0HJKflStBAmzJnsmEsuQGDTBu2bIw1xPDzz9jG64jvHYNBLJECWnCZKMR0aKCBeX55cyciXSfmMEj77BeoIC5w7qtKWCrViAralVpbdqE8+CKK7ZcDB8OEq031KrFWOfOnp7Fmwudy1u0IT/9++PG64U28ASJUAN//+3+J4WhQ7Goq7X48PJfsaaPvIlq7drmyMmWLeaIhiBA9Fq7tvT5xMfjybtUKWl6ndOn8eBRrZp15DUuDr/J4sWt00UXL2JbXlHlqJklf5oWaUnikPz06oVz4QgnTzJWp445jWhZxcbTZp07W5+327exKBcpIo0MREaCFLZoIf38JyYi9WXpsPziBXqw8Q7rvXrZP2+8ea9atg4vXuCY7vRX4YRLiXO4JzFypD5Jm14gCPhd6rSwSRvy07gxbqReaIOTJ3EzOn3a0zORh7lzkUaQ6j7sKgQBqQg1LRfq1kV6y9lxjxxBKSgR0pNr1kA8K7eb/Pjx0HlIaTNw6xZjefOi15sYCQkPx+LfuDEW9RkzIAotXVp6X6u6deECbQOH5Oftt9EryhkEAU+RBQuCwK1eDaL21luMlS8vTv4iI1HRVrq0tDQ7JyOrVzvflmPpUkSujh1Dus7fH9/JwIEQlTtCSgrImQODSNlo2BDXlrvAdT+utG/xBDZu1LUmRRcoW1a3ljbakJ/gYPliTi+kg/+o5TrYehodO+Lp3l24cEHdijheqSanA3hoKDQgvAP6W29JF8BevoynfCnl9E+fQqtTooTjJ/QDB5CiKVoUC/q4cfLaOXz2GSo8hg5F5VlwMGP+/iyGCOSHCGnBUqUQwRk8WH7D0efPYSdABCIUEABiZw///gsN1nvvSfss3bqBBEpt/hoejpJ5X1886Y4aJc8jaepUpBzV6vi+eDFIq1rjOYMggFS725HdVfAqT51qUnSBVq3wO9chfEhtCALRnTtExYqpPrQXrxEeTpQzJ1H27J6eiTycPElUo4b7jrdrF1G2bETvvafOeMuXE+XOTdS2rfR9qlXDPBYuJEpOJrp9m+itt4jmziV69cr+fowRDRhAVLw40dixjo9hMhF16EAUHU20bx9Rnjz2t82XjyggAL/RL78k+uYbogwZHI9/8SLR+PFEJUoQLVtG9OIF0Z49RP7+RK1bE33+OT4fEdH8+URjxhA1bUrk40P08894fdAgovLliaZPxzlwhBw5iH76iahNG6L79/F5HM2xVCmi3btxfQ0a5HhsIpx7k4lo3DjH2925g/FKlSIyGrHPvn1Ec+YQFSjg/DgcffoQJSURrV8vfR9HaN0a8/n9d3XGcwaDgah6daLQUPccTy3wNSg83LPzeJNRrJh+z6/qdCoyUp8hUj2hb18InvWEhw/dXzJbpYp6pnBGI6IFlkJnOahTB/+FhVl37542TTwsz6u7Dh50PvZXXyGK46wEnrd9qFABT2xZskBPI4aUFLR4qFkT88iZE6Zm3GLBpnUAT3s1a9aMtWrVim3krTXGj4c55IYNEF1nyWLW9TiqjNu+HdsNHgzNllgbD1v8+KP0Rr/LlmHbY8dSv2fZ6DZXLuh7eANVpemrNm1Q1aYWKlRAywt3Yfp0+Cu505XdVQgCY1mz6laTogvMnw8pg95aLDEt0l5Hj+Kmcvmy6kN78RoffICKHD1h505cF2LtGLTA/fvq9vfh7QVCQ+Xve/ky9t2yxfyabRPVCRPM6aqkJOhERLQ1qXD4MIjPlCnO52/Z8PPVK+ho3nortVbmwAG8xw36duywLm8vWTJVnt+u5qdePWtrg1evoLcpVw7j16+P6jRLXL2KRatDB9xU795Fei0wECkuexAEpLSyZmXs+nXH58NkQhXWe++ZX7PssF6gQOoO69OmKU9frVuHz+vIlVsOJk8GkXWXfo5XTUox10xLKFdOt5oUXYDf1x8+9PRMZEN98sN7AMl1kvVCOt56S3kEwlOYMAELirueELZsUfdHOWKE8n5kQ4ci+iHij8MePjQ3Uc2UibFhw1BebTA4X2hevkQ0on59xx45586BEDRsaP27vHULWpmmTbF/VBQIBxEq0uwZN/bqlaqaU5T8JCejOmzu3NRjCAKiw++8g886ZAjm9uIFyFWZMtbE4+FDvFaokONGm7GxIEo1azr/rnbvxmdduhSRGSJEmOx1WL9/H7ofJZVWavfJCgnBfC17t2mJmBh8T6tWued4aqF1a91qUnQBrquUY/KaRqA++ZkyBTd6L7RBSgrEjnIEpGkBDRow1rat+443ciQWMjXA+5H16yd/3/h4CHadNS99+pSxSZPwNE+E4zkS+TLG2JgxIBeOtrtzB6StShXxB5I//kCko1Mn/G5z5YKg3hFJXbEC+1gQHVHyw03QHLnsGo3m0HmJEogU+fuLR27u3QPZK1/esdifR+lWrLC/Dd8ue3ZsW6KEtA7r7dohmqCExNevz1izZvL3E8OrVyBTP/ygznhSUKaMst+AJzFsGAi2F9ogNlZ6qjmNQX3yM2CAc08PL5Tjzh1cbL/95umZSEdKCqpl3GnLX7u2enofV/qRcY3MjRvStp83D0/YOXJgcevRA2kgW1y8iPenT7c/VmIiUjtBQdYd0S0hCFiQibCtve0swVPbHTpg3/LlWUyBAiA/BQvC7LFNG0Sa/Pyk+cOEhYGkETkmipcvgxy1beuYgHzyCc6h7bEFAYSvbl1zpIcIPcCkgJtUKnnSnT9f3T5ZFSogCucu9O6tv3v7ggW61aToBhkzonGyzqB+tVdcHFHWrKoP68VrcGW9nqrpIiOJXr4kqlDBPcczGonOnkWFihrYtYsoc2aiBg3k77txI1H9+qiUcgbGiH78kahdO6J794jmzSM6fJioTBlUc50/b9525EiMOXq0/fHGjCG6epVoxw5UedlCEIiGDUPVUKlSRNevEz17Jj7Wy5dE339PVKcOUd26eO3gQSI/P/y7Rw+81qULUdWqRAkJRH//TZSSgsqoZs1wLpKTxccPCyN6+JDo3XeJZs82V4/ZokwZVILt3Em0ZIn9z/7tt/g7ebL5s+7ahWuiSRNUX+3aRXTrFlHZsqhik4LGjYkKFSLatEna9pZo3Rqf/48/5O8rBndXYJUvT3TtGs6lXlCsGK7Fx489PZM3F1myYN3XG1SnU+3bw0TNC23Aq4DUapboDvz5p31XZC1w9qz9Sh4lqF1bWcouJgYpyoULpW3PHbAtoxCJiYwtX27ug9W8OVKeRIxt22Z/LG7mZ0+fIghIYRgMSJ28fAnDsuBg6+qz2Fj0RQsIQKSpeXNcgx98YGW0lyrtJQiI5PTrBw0Nj7QEBuIp0VL/dO0a0k9t2yJKOGYMtv32W/ufb9gwRFEcmT9yE8fFi80Ca7EO60uW4LNJFSMPHAhBupJoQpky0tuUOMPq1fj+3OX3s2uXuqJtd+DiRd1qUnSDIkVg/qkzqE9+mjb1ujtricmTGcuf39OzkIdVq3CTlmOm5wqWLkW6RQ2CmJSEiiwlDRJ5P6rwcGnb9+gBkiMm1DUaUblWujTGzJIl9SLO8eoVbkhNmthfoCdNSu10fPMmSE6LFpjDzz+jOWrGjNBQWVbqzZiBVOZroXUq8hMRgfF37jTvc/ky0lE+PhA1h4SAIL7zDkwRLYnT559j/7VrxeefmIj9atcWP1/JySCJvr4Yp0kT+01NX7xAFde0aeLv2+KPP5SLjdVsSGzbMFZrcCLx99/uOZ4aePlSt5oU3eCdd9D/TWdQn/zUq8dY9+6qD+vFa3z8MSpZ9IQvv4RTr7vwySfq+SBxl9iTJ+Xv2707xLlSEB0NkjFzpuPteHSIR4KqV0fVkiXJGTsWY9nzxeH9ycQ0WFzTUrYs/n74oXjfLC4qfk0AUpEf7kIupve5eBGeRwYDSFDWrKlL2AXB7Idkb7E9fBjHWLnS/FpCAkhPkSJ4r0wZaVGd3r2h/5FSzZeUhEiVM3sBMXANmJRWHM5gMkH/9PXXro8lBZxIrFvnnuOphdy5pRNbL+SjShXGPv3U07OQDW00P5kzqz6sF68REaEvvQ8RdEpBQe473unT6ul9Tp4kSp9evl7JaCTauxc6DynYu5coMdGsnbGHH36A6/P169DqpEuHY1SoADfl8HC4LE+YACdpW4SFEfXvj+OIOUe/+y40OpcvEw0fTrRtG1GRIqm3q1oVep+QEOiK/voLrx87hrn9/TdRcLC423S5ckRHjkA/c/06UcmS0NFYwmCADqd6deiInj9PPU79+kTduhF98QXRkydwbi5WjGjIEKLatYkuXcJ8MmQgWrXK8Xnt0QOOzufOOd6OCNdDs2bQDMkFdzg/fVr+vrbw8YGDuBpjSUHWrPg+9eboq2cXYj0ga1Zdan60IT9Zsqg+rBevER6uT/LjrjkLAtHNm0SlS6szXmgoiIWzFhC2OH8e7SaaN5e2/e7dRFWqEBUsaH+b589BcPr1I/L1RQuJo0dBQPLlI+rUiahiRcx18ODU+5tMRN27g2gsXQqCYYnISKJ69bCoNmwI8fW1a6nHCQszt8UYPhwi5Fat8F7z5kRvvw1xdGwshMf37qUeY/9+/Ne9O9GNGxAhx8Zab5MuHYTFcXH221aMGkUUFQVyPX48SMm//0JcXbYsWnB07ky0YgU+vz3UqYO2GlIJTfPmIErR0dK25wgOxnFOnpS3nz2UKoXr3V3QI5HQ45z1BJ0Knr3kR09ISUGvo6JFPT0TeXAn+XnwABU1akWaQkOVRZFCQxEhqFTJ+bbJyYjiOIsSrV+PBbxnT+vX69UDkdizBwTi1Ssc9/vvEU3iWLaM6MwZotWrU1dkRkeDgBiNIFTbtyPi07YtUUwMtjl3Dot+qVJEixaBROXIAfLFIyZnzmAeRET58xNNmoTvont3c0+vW7eIunYlatEClVsHDxJduULUvn3qarDChVH5tXkzPiPH06eI+NSvj38zhmjVqlWIJFmif3+iu3eJDhywf279/DCf3bvtb2OJmjXxV27UxWBAtEatKi2+sDOmznhSjuesN1taQ5EiIPZeaAMv+XkNL/nRDnFxiGwEBHh6JtKRlARC4i7yo6YVwPPneKpW0oxVTsQoJASl5M7Iz7ZtiPaIla0TgXhkyUJ04gQW58GDkSKbOxc3/88/J/r0U/PCzSEISC09fowy7GLF0BB2xw681rUrxqpcGWnXtWuJHj0imjYN5yg42JxiCw4mypQJi/GGDdh//nykud55h2jKFDQszZOHaN06c+pm506kzkaMSP25unUjev99oqFDQWJGjcIDwIIF+DxHjqCc+exZ8fNStSoI0bZtjs9vmzZo4hoR4Xg7ItgM5MypLIJTowauDzUIS7FiRPHxiH65A3qMomTP7riJsBeuQafkR33Bc4YMujQ80gV4vyolZnueQlgY5nz4sHuOx9urxMW5PtaxYxjLUTm1PZQogZYNUjBxIqqqHJVOP3mCKil7rsVGI0Tl/fubX7t+3SwazpQJZd9idgOs+5D6AAAgAElEQVSzZkF8LGb0t2oVzoGfH0z6LHtJ8etx2zZrwfPUqRDiWoqH4+IgxDYYIEAWc31euhTjbd+e+j3eisLXF2N/8QXOCUf9+ii2sIcxYxjLm9dxG5DoaBzjp5/sb2OJpk2VtU7YuhXHsZy/Uvzzj3MXbTXxww+4Dp05YaclzJ2LykQvtMHgwdILO9IQ1I38mEx40vdGfrQBZ9d6Or/8KdFdgufwcERG1BDdK40iPXuGiJHUdBlPrdlqcCyxdy8iBVxbY4tDh5AS7dfP/FpwMHQ7//yDlKkgIAoycSIEwkSY56RJiKY0amQ95u3bMAkMCMD+xYsjPcQRGIjv9dgx6/2OH0d0ycfi9pI5M1GuXPgMGTNCw2Orl/nsM0RfBg0yp9quXyfq1Yvoww+hAcqRA5GZadOIcuc279u/PyJH9lIybdogOuIo3RQQgJSe1GiO0ggOv57UiKCoOZbU4wkCInB6QZYsiPy4KzX4X4NOIz/qkp/4ePzV0+KsJ/ALTE/VdFzsalvNoxXUrCwLD8cCK9ex/J9/8LdKFefbCoK06rT9+zGevZTXrl0gJxUrpn7v77/xYHLqFEjC4sVIGw0fjnRWvnxEX31lvc/z50ixZciAVFC7dqiICgvD+4xBG5Q+PSrQChfG60FB0Na8eoX9OA4cQAXahAkgSxER0BNZanwMBswtNhZz69wZZOSPP+D6vHs3tD6WTtccLVtirvYEyzVqgDhZ6obsbSdVj1O5MoiumKDbEYoXx181CEv27Ei/uYv88O/5/n33HE8NZMmC69VS/+aFeuDkUmdQl/zoMTKhJ+jx/L56BbJmGTHQEmqKq5WOFR6OhVzKvteuYbF3Rn5CQ4lq1RJ/jzEQg9atxaNHK1dCzFupEkhERARaX/z4I4hF8eLW9v+MIdry7BnRvn1Y8H76CZGetm2J/vwTJKFePUSQEhKgxyFCxZnJBPHxu+9CIH3oEIhM48aI2Lz7LuZ74gR0SJZ49AgVb2vWIIK0dCmiOSNGQJBdqhQ+jy2yZiX64AP7gmVfX2nEpnp1ogsXzA9yjsB1TnKJR44cqEJTi7C4U4fDHwT09KTP75d6mrOe4KbIT3R0NA0fPpwGDx5MTZs2pVWrVlFiYiINGTKEBg8eTN26daOrV69KHs9LfvQEPZ5fdwvg79xRN/KjZKzwcES60qd3vu2FC/jrqCrs6VNUSNkjSP/+iydxsbL6yEgIobt2Nb+WKxeEx61aIWpw5QoEwT16YKzNm0EiVq0yL/BcAB0eDpKRkgLidOgQyBInZu+8A6IRHo4y9WvXkE7z80P5ua8vtqtdm2j6dIixT51CyqpJE4ifTSacu759kQrLmBH7GAwQZv/6q3iPsBYtEOVKSBA/TzVq4FiO0h+VKuH4YiX+tuDXhhLioSZhCQrCde8O6JFI6JGw6Qmc/GiYVkxOTqaBAwfS2LFjacmSJfTDDz9Q3759qVOnTjRy5Ehq3bo1/fzzz7R06VLJY3rJj56gx7Siu8lPdDQWdzWg1FBSDmmKiEAkIEcO+9vwcmp75Cc0FMRA7P09e0A8mjWzfj0mBmRmzBjMgVdklS4N0vH++9DJWGLzZmj6iBBlatwYzS6zZTNHVE6exGsBAYgCVa0K7c+TJyAtlhg+HOepUSOi995D1GfzZqTWunVDSb7tDbVNG0TKQkJSf9aaNUHK7BkVVq+OdJ6jUm05KalMmVDO72nykyOHWSOlNfRIfvQ4Zz0ha1bN04rLli2jXr16UWBgIBERZcyYkRhjFBQURMWKFSOTyUTBwcHUpUsXyWNqQ370pEnRE/RILt1NftR0GL93z6xxkAM56TIp216/Dj2LPUIVGgrSkj176vdCQrDo+/tbv75vH25WXbvifA0ZguhSr14g2YcPI5LExcy//IJo0cyZ+DtlCkTYvr4Yn4uELdNzCxbAlHHdOozbpw/K0QUBpe21auHzx8YiHffPPyBMvr4gPxERqfU95cujTJ47SluiXDkQEnuC5Xfewd8bN8TfJwJxzppVupeNUhJTuLB6uhl3Ck7TpweZ1hOR8JIfbeGG85sjRw5q3Ljx//995swZIiJq2rQpERE1a9aMrl69SrVr15Y8plfw7ASbNm3y9BTMiIvDEz5PA+gBGpEf0e8lORlP/mocLzkZhn/Zssnf9+5d6UaUUsgPjyT52Pm5cn2NGEJDxX2KfvsN+1i2rkifHtVfDRvCUPHOHTgf16mDaFC7dkTjxsFcsFUrEKeQEHzH3EDw9m3oh3btQlRpzBikqr7/Ho7L7duDwLRrh++J+wpdu2atV6pXD4Ttt9+s520w2Nfu+PnhGPby/gULomLMEbExGBD9kUpoihZVVvmkZksAJ+RH9XuY3qp70iD5SVPriqtww/ntYdP25/Dhw+Tr60t16tRRPKY37eUEaeoi5VENRyXRaQ0a9XoT/V7UvP5cGSs2VroRZWSkc6LkLP0WEWFO11giJgYERkxPdOIEUd261q89eQLNTNeuiLxcugSn54gIohcvQBr27MH1t24dFvD33wf5EgTzOL/+CnJTqRLRjBkgkRs2YPw7d0Cyjh419/fq1AkaI8sx0qWzjihZolIl60oySziKxPj6guw5IzZyHIGzZ4dBpVyoSSC85McxvORHW3jg/P75559UuXJlyqbk4fQ1vORHT9Cje7Y755wWyA9jiIBKJXyxseLpKks8eGDfKsCRgzZ3KrYlRvHxSP3YkqJjxzD/hg3xbx8fkJhs2UBysmWD5ubdd9HeIioKhMLy6StfPvgLpU8P7c7MmXBD7t0bpfplyiDlY7lPo0YQdduKjCtXNgvCLcGr08Qqspy1XyhUCOfLEeQ4AislAmqTH3eWGuutkSX/DeuwHFsXcPP5jY6OpgsXLlB93trmNVaKVYE6gDbkJ1MmtzDbN4k9S/osLhIJd50vq+PomPxsUjJWUhIiGFL3i4ujTdevO97m1Sv7XkPR0SAsefOmfo9HL4oWtf5OOCmy7fp+8SJ8jSx1TvfugZQMGmRuolqgANGXX4L49OuHvmT8+OnTg1j17o15T5oEonPpEgTW3bqhQsyyySgnYbbRnOLFoYuxqezaxBt5ikVn8uQR7wDPIYV0ZMlCm6SmslwhP/HxtGnDBvn7io2VkGAdOdMSIp/ZI/cWqZAZmfjPrSuuHuPPP/E/GhHiJ0+eULVq1WjKlClERLRv3z4SBIGqVatmtc3x48dljauu+QpPcfj40KZNm2Qpr5XAHcdwFyR9FhXIjzvOl9Vx4uKsdSVaQgPy00XuWHLmwBiOc+kSOfxWHH3vjooMeJf07NmtvxPu7mxrmBgZmVpUffky/nKCUq8eSFOhQhAYL10KbQ7vLRUZibmuWIHeZmFh6AXGS9yrVMGc7941R6sCAhBtsSUc+fPjHD1/jv9/jU0hIThfYukmy7JbsfRwlizOO7FnyUKboqIcfye2x5OL19/npg0bqEu3bvL3twQnxvHx8g05OSyr6uyVLPPXM2fGtZWS8v/XN23YQF06dHA+lrN/O9lm0/r11KV1a+f72b6fIQOii7wqztEx1q6lLk2aSB/b0b/tvZeUhOpGuedH5r83rVpFXXgBgkbH2vTLL/it8PuKyggJCaHTp09T8+bNKSEhgbZs2UKBgYH06nWkKS4ujoYOHUqzZs2SNa4k8sMYo5dS8tqPHiFX/9dflPLsGcWKVWSoiDflGJKPc+sWbjgK5+ORzxIVhUiByscV/Sw8cnD1qutPIRcvUgoRxcodi5OAW7ecf+aUFCKTiVISEhx/LzExGFdsm1u38Pf69dRGktxp+vRp6/PFxcKXL1ubG96+jeiB5XH+/ht/b9wwR1p4BdaIEbiJr1pFsa+3iyUyC/N5yXm6dKnnXby4NTlhDGLq8eOtXyPC9WOxbQpjOE7VqqkJDt/Hx0ec/Fi+bw+M4bt3tI3lWESKdXgpv/9OsWpp+OzoH1KI1DsGx7Fj0HFZHkOKr5WLSCGiWKUEb9w4/CflGGrZZTg6RoECmh7j/8fRuLVQCr3+3c+ZA1d4CciWLRsZJF6TTZo0oT59+lBUVBT179+fZs6cSbGxsTRx4kQKCQmh5ORkmjBhAhWR+ZBtYMy5M1FsbCz525bKeuGFF1544YUXXshETEwMZXemddQYksiP5MjPd98hx3/okBpz88IW332H6pd16zw9E+kYMgQpC9s2Blrg1i1oTb7/Hr43nhjr1Ss4DU+eTNSggfPtGzWCi3H79va36dyZqH59bGeLx4+JOnYk+vZbuCNb4vBh9Ozau9c6HXLlCtHAgdYOzkRECxfCh2ft2tTbrlgBF2giVEv17o3IR+bMRBkzUmxMDBVOSaFIHx/KXrQotDqCgOOePWtuQrp9Ozx/bt82m1EKAjRD06ej9xjH7t1wnQ4PhxM1x5kzcJk+ehRl85b44Qdca0+fip/Lbt3gb/TLL+LvE6E8/9gxtNdwhtmzcUwegZOKzZvxWaOikJJxBXysx4/dY4PxwQdoM/Ldd9ofSw0whuvn229h2eCFurh3D4UM27albo5sB3IiP1pBUtrLYDBIY2kFCiCUX6uW+3o5/Zdw4ABKlOvV8/RMpKNAAegb3DFnXhFVsqTrxytYEH+Dg+WNxXUQRYtK2y9bNpwjR9vmzg2iILbNs2f4W6xY6vf5XEqWRMUVR7FiIDR581rvc/48iFLNmuZUVeXKcGKOj4eYeOZMtKnIkAGkpUEDePVky0YUHU3Zg4Mpe1gYyuU3bcJ+5cphcR49GsQlKMi6Ou32bZTDly1rXfn29ClMC4sWtU4rcSfZIkVSV8qZTCBc9u5XyclmjZE9GI14X8o9z2TCZ5f7FCsI0EHlzu26dQUfK08e99hgJCbCVdrDT+6SwYsQ8uTRz5z1BJ4ezpdPV+dX3WqvNOin8EZBb/4aRO6ds5rXn9Kx/PxQ8SR1Pynnx9/fvkg3Z0487Yt1FrfXeyowEPvwDu0cVatioeBaIT6/atUQQSpdGtGkefMQ6ciZE74/7dqZ5xceDkK0cSM6zN+9SzRqFKJMQUFopmobEeNePlWqWL9+7RoiU7YLeng4yBknqJaIjBR/nePFC+c3aDmFBUqLEPh+apAVNceSczy9wGvBoi10en695EdP8JIf58ciUpf8SOnuLbav1DnkyuW8SqJoUXN5ui0MBpAKMeO+woVBEmxJjq8vIjq2LslVq4Jo7dmDf584YW4WGh1NNHgwHKCHDkW0JioK5GTLFvMYyckwLyxcGNvExxNNnQpzw0aNEDVYs4aoZ0/zvPbsQWVYnjzW8zl1CnOyxfXriBzxCjJLhIeLGz5yREQ4N5V8+tRxrzVLxMUpq7BSk0B4ooWMnhY6nS7OuoFOz6+X/OgJWbLgydzSIyWtw53kJ1Mm/FXjeLx0XMlYuXKZq76cwR5xsYSz/lHFi4v3q0qXDoaEp06lfq9ePURxLK+ldOkQxVm+HKaGtWqBLKxbB53Hzp0oL79/Hxql2rXRBb5TJzNx8fWFB9CFC4gMtWsHAvTwITyC+vZFJ/cDB9Brq21b+P906mQ9vydPEIGydaEmAmmzjRJx3Lxpn/zExeF7kdJORGpvtidPrPVIUuElP+6DThdn3UCn59dLfvQEV6IRnsJrMze3wNcX6Rw1rj9fX6RHuKZGDooVsx+pEdtWCvl58ABGdmKoVAmd38VqF2rUEBfutmqFhZu/xxgiMKdPQzgbEQFx8qVLRN27o8N6UhKanbZpA6L088/4+++/5hLXKlVgNZAjB8jSjRsQbDdrhojL/PnQEN2+DTH5kSMY9/Bha5K2ezf+tmhhPe/4eGiTxDrYR0eLO1dz8PPsiNikpFh7EDmDHKJkiejo1M1mlcKdZIQ7mOtpodPp4qwbcGdnnZ1fdcmPK0/LaRz9+/cng8FACxYs8Nwk9EguVY78GI1GGjduHJUrV46yZMlCgYGB9PHHH9MD3rIga1b1bNYdpZscQU6n76AgpIQcufOWK4e/Yq0eiEBwnjwRn2uTJtDn2LaOqF4d81y5EiSmQgWi1q0hBuZVY02amMWMhQvDyfniRfj3TJsGgWNsLAgSJyM1apjbZJQrh2q/PXsQMfr9d3OKKEMGEKmUFBznzh2M0bgxIkQ//og2G7bO1QcPIrVma0JHBOLG5yAG7k9Upoz4+0TQDJlM0ggNY8rJD29WqwZevUq18MycOZOqVq1K2bJlo7x581Lbtm0pzDb9qQQJCfjcelro0ujiPHPmTDIYDDR8+HBPT8U16JRceiM/ErBz504KDQ2lwMBAz05Ej+dXZfITHx9P586doy+//JLOnTtH27dvp+vXr1Pr1q2xQb58SLGoATkRHEtISWVxlCiBxdzRcd59F2RBrJM5EUiDwQDSYIsPPsBDyY4d1q+bTND9rFuHlFO+fNj/779hXvfoEaqzLHHmDKI0RYqgXL1jR5Q7M2YmHNWrI0q1fDnIy6xZOI/R0dbl4IKAFFj27NAMXbmCv48fo6z/xAmMZRvN2rmT6O238Z8tQkJQPWVZ2WaJ0FDs50jPw1uN2Lb+EMPTp7i2lZIfJfuJ4dGjVCQxJCSEBg0aRCdPnqQDBw5QSkoKNW7cmOJc/S3qcaFLg3M+ffo0LV++nMrbWjXoEXFxiACLmZmmZTA18eQJY0SMbd+u6rCexL1791jBggXZ5cuXWdGiRdn8+fM9N5nQUJzfCxc8Nwe5WLKEsfTpNT3EqVOnGBGxO3fuMNayJWMtWqgz8LBhjJUqJX+/TZvwPUVHO982KgrbbtrkeLsaNRjr0sX++zVrMvbhh+Lvde3KWHAwY4LAWEICY999x1jRojhuunSMdeyYep/vv8f7y5fj38eOYduBAxkzGvF6yZLYhojFFC/OiIjFFCr0/9dY1aqM/fILY8nJjDVsyFju3IxFRGC8sWMZMxgYO3DA+riCwFilSoxlzIgxKlfG/cRkYiw2lrGsWRmbPFn8c5Ypw9jHH9s/R5UrO36fMcamTGEsRw4czxn47/HcOefbWiIlBefyu+/k7WcPJUsyNmKEw02ioqIYEbGQkBDXjnX7Nj7z/v2ujeNO/Pwz5vzihadnwhhj7OXLlyw4OJgdOHCAvffee2zYsGGenpJrmDULvxmdQZvIj540KQ4gCAL16NGDxowZQ2UchcrdBT2mFXPkQGRDikmmQsTExJDBYKCAgADl0Rox8LGc+4Bag5sB/vuv823z5MFx7EV1OGrXRmTD3lxat4bfjpguqH9/aGEGDMCxhgyBl8/Fi0RTpsDw79Kl1PsMHAhjxQULIHCuXh2aHT8/ok8/RSqtenX48zRrhv3at0cUols3aHg+/BBPhJs34/7Qrh3RxIkwB5w3z9xBnmPPHqTV1q+HKDprVoxRvjzRsGG4t4gZ1d26hehRmzbi5+fFCwioeZ8jewgNRdrPWWsLInMqUUqUyBL378NLSI3IjyDgGnUyVszrnlY5lYizLcEtDfTk+J/GIj+DBg2iFi1aUEPba1+v0JsA/jXUJT8ZMyL8rqfF2QFmzZpFfn5+NHToUE9PBdBj2ovrGtQiJDZITEyk8ePHU9euXWHEyfU2cgmLGIoVQ2m2Zf8rKShb1nGayhbVqzvftkULpJPOnhV/v317XBe26a0XL0CafH2RimreHIv2pk3Q5IwcCSPH3r2tu6cbDESLFqEkfcQI6CY2boSHEYcggHB07040YwZemzoVRMiW+OXKBUJz8SKMEmfOhPDZEs+eoXt806YgPA0bQhD9998wsFy9GhV9+/en6vRO69aBKDVuLH5+fvsNqT5bAbUlGMP3YE8zZIvQUDgdyzV2u30bf9UgPw8f4lw4GIsxRiNHjqQ6depQ2bJlXTse/x1r3C9KVcTF4bpNA8a7mzdvpnPnztHMmTM9PRX14CU/hBumHr1oiGjDhg2UNWvW//8XEhJCCxcupDVr1njchvv/0GNkjd+UFZIf2+/l6NGj/3/PaDRS586dSRAEWrp0KV4MCsL5UaPDMC+ZvnlT3n7p06PiSCr5qVED0Q5H32udOoii8SooWwQHQyuzfDn+HRWFCEvRoiAmjRtjce/eHdtyZMiAdhYXLhCNHWs9pq+v+b+EBESXLJueXrwIUmQbTalVC1EWLjRlDJVj3bubFyDbm6XJBKKVkIBWGpa/udq1Qe4MBpyrPn2g6/nuO2yfkgLhdteu9j13du+Gxom7gIvh+nUQMLFKMjGEhkrf1hKc/DjzG5ICCRVsgwcPposXL9KmTZvUOV7mzKk9mdIy0sjiHBkZScOGDaP169dTRne0IXEX0sj5lQ3VE2l58zI2bZrqw2qN2NhYduPGjf//N2PGDGYwGJivr+///yMi5uPjw4oWLeqZSb56hdz1xo2eOb4SmEyMZcjA2MKFina3/V7i4+MZY4wlJyeztm3bsvLly7OnT5+adzh/Hufo5EnX556cDO2JEp3X8OGMFSsmbdtr1zDn3bsdb9etG2OlS0MXIwauNerWjbFMmaCPGTOGsYcPsU+1aoyVLYvPZYvFi7Hv4sXm15Yvx2srVjB2+jRjVarg3/XqMbZ+PWOzZ0O7Eh/PYmJioPmJiWHs0iVst3UrY0uXMla+PP7dtCljt27h3Pj5Mcb1J4LA2NChjPn4MLZ3b+q5PXsGvVC3bvj35cvQMfn4MJYvH3Q8RIydPSt+XuLjGcueHXoeR5gzB9/3q1eOt+Nj+vlBGyUXAwYo05KJYe1afHY7cx48eDArVKgQu337tjrHGzQI2io9YdIkxgoV8vQs2I4dOxgRpVpT+DqTkpLi6SkqQ48ejNWt6+lZyIb65KdYMcbGj1d9WHfj6dOn7NKlS1b/BQYGsnHjxrFr1655ZlKCwFjmzMoWY0/i7bex4KkETnzKlCnDoqKirN988QKLwebN6hysVi3GOneWvx8nIo8fS9u+ZEnG+vRxvM3vv2PM48dTv3frFvbnIuZJkxizJIWMgRz4+DD2zTfi448cif2XLgV5TJ+esf79ze+bTBAw162L7QwGxrJkYezjj1nMsGEgP4MHM9apE45DxJivL0Tof/5pHsdoZOz99/GgdPcuY6NGmY8rht69GfP3B4mzxI0beI8IRGTqVHGR+U8/YZsbN8TH56hXD3OVgr//ViZ2ZgyC7k8+kb+fGKZMwXm0gSAIbNCgQSwwMJBdv35dnWMxxljz5tLPUVrBwIGMlSvn6Vmw2NjYVGtKlSpVWPfu3dmlS5c8PT3laNcODzY6g/rkp2xZxoYMUX3YtACPV3sxhif/oUM9Owe5aNqUsTZtVBnKaDSy1q1bs0KFCrF//vmHPXz48P//JSUlYaMcORibMUOV47ERI6RHcCxx5445+iEFo0djEXNUZWQyMRYUxFjPnubXrlxhrHt3kIy8eVHxZTAg+mLvOOnSIZJjCx6BIULUqGZNxvg5tUVEBGM5cyIKULMmiwkKAvkpXhwkonBhRHzskb/HjxkrWJCxXLlwvEWLxLfjlTq86swWO3bg/XbtELXJlo2xCRNQRcdRqxaqzRzhyRMQthUrHG/HMWMGiJ9YFM0R4uLwXSmJGImhZ0/GqldP9fKAAQOYv78/O3LkiNVvhEdOFeOdd/R3f2/WjLHWrT09C1G8EdVejRsz1r69p2chG+pqfoh0q/nRDeR4yKQVqFiBde/ePdq9ezfdu3ePKlSoQAUKFPj/f8e5W3HZsmZDO1dRvTrOt9R2FRxFimAevE+WM7RujWOIuTFz+PigymrLFgiBO3TAMY4cQeVUeDiEzEFBaCYqJvqePh2+QR07wqfGEgYDqrCKFoVex9cXHjJi8PMjev4cAufjx80GjOfPQ2Ddrx+cknPnFt//wQOIl589QyuNwYNTbxMWhsqujh3FK7ySkojGj0ej1O3b8fk/+4xo8WJ8hhEjYIp4/Diq1xxhzx4IuFu2dLwdx+7d0FHJ9TY5dw76JiVaITH884+oaeP3339PMTExVL9+favfyBbLPmxywZikyrI0BzU9lbxIDaX97TwN1elUgwYIe3uhDQYNQnRNT5g9G5oLe1oVtTF6NGNFiqgzVni4ND2OGCZORGTDaHS+LY/qOEuH7NljTim99RYiFbbRmT178P6WLeJj3L6NKFGNGohEWGLgQESGFi6ETiJrVkQ5bCMGW7bgGK9TUVaaH8YYO3QI71++bL3fs2eIpvn5IRUxbRq2s42EPHyI81G6tH1/lmnTMI7tMZ4+RdovIADnKmtW6KocQUp0yHJuBgNja9ZI294Sc+ZAjyXlmnCGV6/w+exFxdTGw4f4rnbudM/x1IAgICK4YIGnZ/LmokIF3Dd0BvXJT6tW+ssJ6wlz5iDc7i4ioQZ46uLZM/ccb+tWHO/BA9fHEgQQhYkT5e/LTfCkGstNn44b9fPnqedw4ABj9etjvFy5sJ0jPVG7dozlz490jhhOnYJ+rHFjMwH68UeM/8MP+PeLFzB69PPDOZgyhbHISLw3bJhVOjAV+Xn5EgszH+vaNZCebNlARr7+mrHERLw3eDAI17Fj+Pfjx0iZFSiA9KEY/v0XQvpx4+yfgxMnQFKyZkWq6eOPsZ8tLl7E5962zf5YllixAp/N3rl1hA4d1BOHhoS41/T0+HH9maw+eIA579rl6Zm8uQgORmGFzqA++enUCdEfL7TBL7/gx6zkxuspnD6NOZ85457j3b2L4+3Yoc54HTvCHVguTCYs4KNGSdv+4UMQDa5/EQTctKtXt3Y7fvgQxGXCBPtj3b+PCqkWLewT5UOHQKTfe4+xgwchcP7009Tb3byJCqWMGUEm6tZlLDCQsQ8+YOzRI8YEwZr8CAK+g+LFEaWsWBHzDwjAnB89sh4/OZmxOnVA1k6dQiVUgQLQM4khPh5Ro1KlHFdmdegAJ+voaBQJBAZi/h07MvbPP+btBg3CsaXqd1q2VEZgjEbo0T7/XP6+Ypg1C9+fu6qENmzA9xgb657jqYFjxzDnixc9PZM3F4GBjH31ladnIVqRmjYAACAASURBVBvqk5/evUUFeF6ohLNn8WM+dcrTM5GOZ8+ktXBQC4KAxVOtqsP16zF/HvWQg/79kYKTukC1b49FfeNGc4l4nTqM7dtnTWImTkTkw1EF09692P/bb+1vc+wYKqn8/Bh7911zNEYML14wtno1CBVvYUHEWPr0LCZ/fpCfvHkxFn/P1xfVctu2pU6dWeLhQ0S0/PxAWOx9LkEAQcuY0fGC9uefOP7q1ebXEhMRiSpWDO+1bAnSlz279Mje8+c473PmSNveEocPq/vb/fBDRAPdhSlT8B3pCfy3+/Klp2fy5sLf3/E9Jo1CfcFz9uxwlfVCG3Dhnp5EzzlzQoTLu25rDW6GJ9Vk0BmaN4f4V6p42RK9e0P4u3+/822NRjgGX7sGw778+SEePnoUXcwtjf8mTsT7gwfbd7Nu3pxo3DiYF+7cKb5N1apm08MbN4jWrLE/nr8/jAh5w9Ndu9AaY+5cvE4EA8JFiyAIXrAA4t5Fi2BSmCmT+LjJyUTLluG+YTIRvfee/eak8+fDBHHJEnO3e1skJaGVR+3aRB9/bH49QwYIsa9fJ/rpJ5hXNmwIcXeFCtJcwdeuxRy7d3e+rS127SIqUABmi2rg5En1hNNScOYMzDv1hPBwiO71KMjVAwQBvx+vySFjbN48CPr0pEnRG/z97Xu1pFV06sRY7druO94330DroVZK4P33lXlZCAIEgY5K/Xmz0SJF8JSaNy+iE87mvnu3c08jk4mxjz5CpETMH2jIEERb9u9HRIUI6SxHviPTpyNaYjG/VJofxlAO70wgGxKCiJOfH0TKy5aZjRVtsXkz3nMW0eNCaGepjqdPkTbKnRvj1q7N2G+/2b93CQJKvT/6yPG49vYtVszaN8kVREa6t4m0IDCWJw9jX3zhnuOphd690WDXC21w/77yghAPQ33yw303bPP6XqiHd99V7ybqLsybhwVYri+KUvAUg6W2wxUsWABNjBK9w9KlSP/cu2f9+suXCBfnzw8BbZcuWLC5UFqKk3f79tCR2BMGMwZyVbcuxMZHj5pf5+Z/luaCv//OWIkSmE/v3uJVUs2bQyhtAVHyIwjQA4wdm3qMkydBCHn3d0s9WL9+ONeWLt0bN+Icduvm2AspNBTER0rKc/JkXJP376NCrkYNzKdSJWjrbI/DBcYHDzof2xbc9fq33+TvKwZeRHD/vjrjOQPv5r5nj3uOpxbefx8aLy+0ATf71KFJo/rkh7cXOHFC9aG9eI22bRlr0sTTs5AHXiniLtFzQgKe6qdPV2c8fvP/+Wf5+8bEYC68vUJ0NNyIc+bEQt27N2O2LrzNm6OUPSHB8djPnsFQsHZtx+XTL19CH5I5M6I8Z85Au9K7d+pIR1ISyF7+/PjMLVqgtD0+HoQgR45UrSJEyQ9jiJLwiF90NGMrV+LfRCBZGzakJhmJiTBYDAzEQ9TKlRAq9+jh+DNGR6M8vnp1++aMHA8fIno1YoT5NUEAseFVdaVLY378mF27Ys6OyJc9fP01rgFn36dU9OyJKJS7sHEjzomto3paR1CQ44pAL1zDunW61VSpT354ewE99Z/SG0aMQDsEPSEhAeXM333nvmN++KG64vtKlWDloAT9+iG9MnIkIjAZM6LE217E5upVnK/Jk52PfewYoiJiERZLxMfD7dbXF5VXVas6XowTExlbtQrbEWHxrlcP/z9vnpV1ASc/zZo1Y61atWIbN2wAwRgwAMerXx/RHIMB1aA7djhO692/j75dBQvieJ995tz9ul07pITDwx2fB8ZAZHLntm+/cOwYzhX3U/rmG3wfSoTOggARu1r+ZykpmLs72wgNG4bqPT3BaMS1t2yZp2fy5mLqVKRDdQj1yQ9jeDJU64nbi9RYtAgLiZInUE+iShV4rbgLPK1j2xNKKb7/HukguVVfkZF4Un9dGcXGjJGWFp44EdtL6c00d661R489xMfDvJAIpeBS03jXr8Ps8J13rCu9AgIYK1mSxVSujMhPpUogC9myWW9Xpw6ME6WmaR48MDdSrVvXuYZw9GgQKykGfAcOYNyffnK+7dmzINFE+O7nzHFctSYGV9JlYjh61H6PN61QowYIo57Ao7V//OHpmby56NULDZN1CG3IT6VK4n4hXqgDLnS11ZCkdQwahCan7gLv16SWAy5PX0n1tLh5E7+DdOnwQFCxIp7YpXQNZwzmg8WKwXnY2eIvCDi/Pj6M/fqr/e24aeEXX+CzBAVZNx11hp49UYJ/6RKsC2bNYmzUKBbTowfIz8cfIwL17bcQ4166hPTa3LnSxhcERI1z5oTwe9gw50Rl0SLH/cEskZAAU7b33pNelBEejnNWsaK5k/zs2dKJoyvpMjGMHo05uOvhJzERJHzhQvccTy1wl3FnDW29UI769XXb0UEb8tO+vXSreC/k48YN/Kh//93TM5GHtWsxb1sHYy0hp1O3FHz6KSInjrQnvNmojw8W8G++AXHii+isWdKPxzu5S1l4UlIgIs6cWTzKwM//kiX4961bIAFEiMhJiWgFB4Nk2cCu5ocxRG6kND68fNmcaurUCeRVEKBLypBBXC+2Zg0iPqNHOx+fMVS3ZciAtKJU9O2L7/HVq9SEdsoUx9fzkycgDmr6oJQsiTm5C1yAbylA1wMWL8b35Ez/5YVyFC3q3vSritCG/IwahdC3F9pAEPBkrDdXzbAw94eh58yBvkZqtMUZzpyxX9ppmSIpXBiRCNsUCdf+iJEEexg2DAvo2bPOt42PR0l+hgzWEaCzZ3Eeeva0jniYTNBE5MkDi4rx4+2nCaOi8Nk2bEj1lkPyM348xNP2Ii2cUPj44L5hW76dkADdUeHC1oLb777DfPr1kxYF2b4d28vRnd28CcJqG7m6e5exoUPNneTHjxdvNzJnDr47tRzZ//3X/aXFCxfiMzgywEyL6N5dtykZXSA52bqFjc6gDflZsgSM21226/9FNG2Kp2Q9gZO2SZPcd8zr19VtdcEY2kw0b27+999/4/vgFUwrV9p/2rx7F5GZoUOlHy8xEankEiWkpVoSE1ERmC4dUlNRUfAQqlLFvsA5JgYLeJYsWOh694YTsSVh2bkTn1FEUOyQ/PA0reV+KSlIS3z4ISI3uXNDRG3vvEVGIvpSvz5uujNnYszhw6Wlr8LDoU9q3156uksQ8BsrXDh1A1iOR4+Q5suaFeRx+HBzOtpkQpSmSxdpx5OCWbNw/cjVHbmCzp316dofHCzvd+aFPNy6hd/g/v2enokiaEN+uK3+3buaDO8FQxVQrlz6M5Ps1ElZnyxXULq0ugvQ6tXmTuQ8bVSmjHVZtCN8+y2emKREcjhu3ECEoV07aQ8VyckoDScC8cmdW9rv8flzpOkCA7FvcDDI6vHjSC0FBopecw7Jz9OnGGvVKuiLRo40j//223hylLKYh4SgeqdUKew7aZK06//VKxC/oCCUw0vFtm3Sm2I+e4bfZEAAyGO/fvBPIgI5VgtVqoDYugtGIx5Y1OpH5i7wa04kSumFSjh4UNeaKm3Iz9Wr8rpZeyEfXAuitwuPN0dU0idLKdRMPZhMWBQzZMDnqFIFUSU54tPkZDT8rFpVXnR0926QpmHDpG0vCNDbEOHJ3V5ZtxiMRjzR9ewJPxzepyt/fkQ61q2DBuT2bcZevTKTnxcvEEW6cQNVSStXIhqSKRP2J4JYd8gQeIHJIe8REeZKtcGDpX+Oli0R0ZJDNmNjQdBat5a+D2P47DNnml2j8+eXpy9yBN7XT0pFm1o4cgTHDA113zHVwG+/Yd43b3p6Jm8uVqxA1FanmiptyE9cHC68NWs0Gd4LZm4Wum6dp2ciD8+fYxG0dBXWGlx0qsSjhSMlBSmkcuVw3kuWxN9z55SNx51R5Z4HrnOZN8/5tpxoDhiAiESBAo4rwezBaDRHXd55x9yGw+K/GCKQH5vXmcGA6FGRIiATFy7Ir1ISBNxos2WDwLJlS5Cp8+ed7/fZZ5i33OKA4cORXoqIkLcfB2+omTs3zsFHH7nuNt6vH3yPpEQX1cKIEbhu9GarMWkSzr3eIuN6wsSJSAnrFNqQH8bwdCfFoM0L5QgOlv4EnJbQoIGyPlmuoEsXEBa5N8PkZKRrgoOxmDVpwthff2EBeustxz27nKFvXyzocqN3Y8diQV2/3v4258+DIPTogc98755Zl9SrF9ICcsAdunlH8hcvsJgfOMDY+vUsZtEikJ9Fi+AG/eefqN7iWpkVKxC1kiP0ZgwmkLwCrHdvHDc+HhqooCDHn2PKFOy3cqW8Y4aEYK6zZ8vbj8NkQhq0cWPor5Yvt+4kr8T9PjYWuiJ33lMFAcaGemulwxh+py1aeHoWbza6dEE1rU6hHfmpUYOxTz7RbHgvGKoZ9Ni0z5U+WUrBw/dSPW3i4yHc51GOdu0YO33aeps1a/CenHSKJWJiQKAqV5ZXSWMyIR1lMDD244+p33/6FMSgUiVrLY1lBCUgABVMUo87Zw7IlJ3ebA41P4yZU+FSxZFcgJ0hg3jEKiICT/YNG6aOhAgCnkqJ5JutRkUhQvXee8oLNngDVkuSYzTCaoCbRDZogGtRKhlftkyZwaYruHxZ3X5k7gJvwTJ1qqdn8mZD52u8duRH56xQF+A+Fmr1C3IXuPPq1q3uO6YgQFzrzJCLNxvNlw+LTdeu9pv2GY2ICLlSdXfmDL7D4cPl7WcyIaVDhOvAck4NG4IY2EvZPHqEfX188GT/44/OSVC7diAEduCU/PAFyZk9Q0wMiBYvvf/yS/sk+dAhfAbLth6CYDZGlJvmNJlQxZc7t3ID0eRkEBx71wTXjFWsiDnWrIkCEUckSBCwvdLWKkoxfbq6/cjchWvXdF2FpBvky6c/uxULaEd+JkzQdT5QFzh1Sr9NZMuVQ0rGnZg7F0RDzI/l+XOkSXiz0T59pKWjeEWQKyLUhQulVxVZQhBQOUWEm5DJhNYZvr7SIlxXrpg7q+fPj8VOrHGlIKDMfOJEu0M5JT+MgVjYa8gbEQF/sOzZ8R317i0tysHbemzZAgLXq5cyLRVjIEuuRjp4JZ8zLZgggPTUrIljVqyIa0lMW8NNBpXotVxB9erSzCnTGnhbGzmVfV7IA9f1SmkRk0ahHflZvlzXSnBdICkJaYH58z09E/n4/HMQDXeKN58+xfmaOdP82uPH6PospdmoGCy9YJR2NhYEkJAcOfDUKnffr7/GjahaNeliaEtcuwZdR8aMIH7Nm0NPxD/PzZsYd+9eu0NIIj9ffw1yw9NJT5/CLoBXpAUEINUltf8XY/j8XbogSvTuu0inKikCOHwYn33MGPn7cty5A5G01Go8xjD/Q4eQBiOCLcP69da/i169kH51p2/agweYz9q17jumWhgwwL0d7/+LuHIF18dff3l6JoqhHfnhzQO9pYbaomZNmJDpDfxp9sgR9x63Tx9EMcLCYICWKROEpGPHSms2KoZbt0AcXFk4o6Ox8AUFKWvEOn8+zqe/v/Lf3JMnqCarXRtjpU8PU0HuWu0gEiOJ/Pz6K8bp0wdEzccHUaqmTUFYlJLHI0dAXHx9laU6Ll3CeWvY0K6mSRLatIFeSK6om+PYMRBPIqQjly/HdZouHbyX3IkffsD5lCuMTwuoVAmaOC+0A/8tu1ODpjIMjDFGWuDWLaISJYgOHCBq2FCTQ3hBRCNGEO3aRXT7tqdnIg+CQFSoEFGHDkSLFrnvuEeOEDVoQGQwEPn7Ew0bRjRkCFHOnK6NO3060eTJROfPE5Urp2yMu3eJatQgCgzEPLNmlbbf8+dEVaoQZchAZDQSPX2Kc9qjBz6nEoSHE+3ZQ3ToENG+fUTJyRjrrbeIypQhCg4mypePKG9eoty5KdZoJP+2bSlm507K7utL9OQJUVQU0ePHRNeuEV25gs9HRJQtG1GLFkQffEDUujXGUIKUFKI5c3Dey5bFb6BGDaJffyXy9ZU2xv372CdnTqKjR4myZ1c2l127iNq2Jdq6Fde0Kzh/nmjGDKJffiHKnBmvhYcT5cnj2rhy0KwZUUICrkM9IT4ev+vFi4k++8zTs3lzsWQJ0ahRuEZ8fDw9G2XQjFYlJanbUdsLcWzaBAYupmNJ6xgzBqkOd1j1X7nCWLduuCYzZoSQU0mExR4SE+E8XLu2a54o588jEtW8ubSUYEoKSqpz5UILh+hos7Nz69bqfMYyZeAqvGoVNEaNG6NKjZsf2vP5yZED9gItWyK1uG4dxure3fU5XbsGTYrBgOsoMRFRHx8fh9okK8TEoEN94cLKBc6MIWJVuDAiWGr6yuzfj89nMEBcOmuWeyok79zBeVyxQvtjqY2jR3HtOfOA8sI1jByJYg8dQzvywxhuCDrt+Kob3L+v39w8706vpWjuzBnrZqOLF2PhTJdOXnd1KTh8GMdxtYP3H38gjdOli/M0zLhxWKhsu7jv2IH0Xq5cIC1K9SLR0Vh8V60Sfz8hgbHISBZz8SLIz8WL0IvYm/fQoehRphQJCUgBZcyIm++xY9bvz5qF7+CXXxyPExuLalR/f5R0u4J+/TAftVP8PEV78aJ1J/mvvnLcSd5VfPklNHBK05CexOTJ+E7dqSX8L6JtWzwE6Rjakh89Nt/UI6pWZaxDB0/PQhk++ICxWrXUH/foUcfNRvv3R0mz2jf4sWNBXE6edG2crVsxTrt29svQf/7ZcUn3kyco1SeCGNiWIEnBvn3YPyzM4WaSND+MmT1w5OqrBAFRzqAgaFFGjBBvNioIcFPOmhXRPjE8fw7Nkb8/zBtdAY+8qh0luXkTn9Oym7xtJ/lx49SP+CYnw1dpwAB1x3UXKlRQt4+fF+IoWVKfBrsW0Jb86LX5pt7w9de42csxyksr4Au4PS8dORAEpArq1cOYZcsytnGj+FPgnTt4kras/FIDyckw/5LbRFMMv/6K6rSmTVOnBi9eRGVR587Of18nTphLqlu0kNen6csvJbUJkEx+IiMxjx07pB1fEBAJq17dnMpzVhH38iW+++BgOEJb4vFjEMFcuZSbU3LwZrNSvgO56NkT9gNiBO/RIxAf3kl+6FD1hKfbt+M8u9qKwxOIiMDcN2/29EzebOi1tZINtCU/em2+qTdcvIjzLLd/UVpAUhJC+0OGKB/DZIJHTtWq8pqNDhiAcnul1Tn2EB4OLVP79q4vigcOgOTUr29eyJ8/h+amfHl0LJcCQQDRLFEC56huXZwzZ+eoQQNJzT0lkx/GkH4cPdrxNklJcNDmvdSqVJHuzs0Y7jn+/jAG5J8xMhIl0PnyuU62ExNRVfTWW+pfPzduIOqzYIHj7Z49QwosRw4Q+X79UHnoCpo0AdHUI7jpqy3h9UJdvCHrurbk5w1hiGkegoBIg15D1ePHY6ESe8p1BNtmo/XqIUoglXBERoJYjBghf87O8Msvys32bHH0KM5PqVJI5TRrBtJ2+7b8sVJS8HRfqxbmFxwMc8Pw8NTbGo0QhkvQRskiP5062U91XroEg9QCBcyRKjltICyxdy/0Sl99hUay+fKBeDlJ4UnCsGGwAnA1emQLQcBnLlRIeiFAbCy+o7x5QZp69FDWSf72bcf6rrSOhg0Za9TI07N48/GGZHS0JT+M6bf5pt4wbBg6PuvxguQmeqtXS9s+KQktGWybjSrB7NnSHHmVYNAgLJBqGIGFhYH8ZMiABUoN6/7jx6EJypwZ57FWLfQz46Tq7Fm8fvSo06FkkZ+FC3FeEhNxvV65AhEzJ7E5c6L9hpIF3BbTpmFMPz9Eu5R6OVli3TqMuWiR62PZgqedpKYFLREXh3NbqBCukQ4d5FU9TZig7CEkLSA6Gt/xkiWensmbj6ZNUY2qc2hPfvTafFNvOHTItSabnkajRtDKOEJ8PELbhQvbbzYqF8nJ0IdUr+5aiboYkpKQNsqRQ52FnC+6BgNjM2aoR3RfvmRswwbc0Hx9cYxixfB9+PqiGspJtZhk8pOcbBY9N2qEaAwRtCudOzO2e7d6rvBJSRC2EyEdcvGi62MePIixevVS/0EjNhbEpVUr18bmneSLFzdHz5y1wElOxneh1wfVjRvxWe/e9fRM3mwIAu5nU6Z4eiYuQ3vyo9fmm3pDcjJ0JpMmeXomysB7ZF24kPq92FhEaHiz0S5d1BFIc3BvkGXL1BuT48ULkKuiRVECrhSXLyMF1aEDWoPwiJfaDqvR0dACDR2KKAD37MmUCd3nP/4YaaSlS/Gd/fUXY5cusZiTJ0F+Tp7Ed/jnn+i3tXgxY198gVRXmTK4F/AxCxeGcHf/fvWjDZcuQZOTLh0iNKVK4T9X9DkXLsDbqEkT15yg7WHkSETh7DWklQujEa0ypHSS37pVvcIDT6BzZ/RH80JbhIXhOtm3z9MzcRnakx89N9/UG7p2RamnHpGcjNYAls1OebNRLujs21c7kV3v3iCPaqRFbHH3LlKSlSopM6mLjoZQuVw5s8D5999xvvz9IQzWIt1ZuDDSTwcOoH0Gb0tRoIA5QuTI5JBHXAIDkXIaMADtM0JCYAbZrp36czYaERVLnx7tQnhk8No1VGa1basswhcZie+wQgVtjAbPn8c51aKNhVgn+V9/NV8zgoDXatdW/9juQFISSKmOO4zrBmvX4hrS0mfKTdCe/PDmm84qF7xwHTydIKcxZ1rCokWI7Bw7Zt1sdMgQ7cPZT55AxKdVp/kLF/B5mjaVFzUwmZCOCghIbaL3/LnZzblVK9ciS7a4e9exWaDJhIKGf/9l7MQJFnPwICMi1qxmTdaqTh22cd48RL3skbKJExHJU5O0/fsv0pc+Prh+bKPNu3bhM339tbxxefSuSBF1zzGHyYR5lymjTUSJQ6yT/Nat6GKv12pRxhA59Lo6uwcDBzL29tuenoUq0J78MKbf5pt6w4sXeNJevNjTM1GGGzeQ2vH1hYfJuHHaRGLs4ccfcRM9cECb8Q8cwPfTpo10T6YvvoDGx9HCtHMnKn2yZkXllhrtQjiRltgeQ5bgmTEswmo1Pn72jLHhw3FuS5Z0bFw4aRLO52+/SR+7WjWQTzV0W2JYutS9HbIFAekv3kk+Y0ZEFrUkXlpi8GAQUz0We+gNlSsz9sknnp6FKnAP+Rk+HAJKL7RHo0b6K/e8eRMprXTpoC0xGFx3SFYCkwkLQoEC2vVK27sXkdAmTZzrXHjlz4wZzse1JACFC0Mc7YqAe+hQeNhIhGzyw20wXGnLkpgIB+SAAOnEz2RCr7GAAOcp1MeP4aWkhiGiPVy5gmu+Xz9txneGOXPMKUreSV5PZqmCgOtdr0JtPSE+HhV1ath3pAG4h/xwC/ioKLcc7j8NPRl9Xb4MnZKPD1Igs2cj/VS4sOcs6h88YCxPHqSn1K7+4jh40GxcaE8/cvUqFvQOHeQ90d64Ye5lVrkyokJKPkflyrJSgP9r77zDmyrfN363ZYNsEEH2UCxDNrbKFkRlCCJbVBBRljhQEVmCCggCoqIC4mA5AEEUkKFAy15S9t57tKV05/39cX/za4G2JOk55z1Jns915aK0yTlPkjPu95luix+lmIj7yivu2+ZsgFiuHI+dV15xz0N47RrbJFSpkv54k9OnmSBdrFjmZ3+lR0wMQ13BwXrKyx0ONo989FG2eujQgQuPEiVYMu8NJe/bt5vrrRVSWL+en7UZbUE0YI34OXqUH9qSJZbszq85ccL+g063bmWya+pho6lX7F99xYtwerOZzMY5z2rcOPP2sX49kzTr179zDMb16wzfBAd7Pnts7VomsALc1rRprofDbtxg6NGN6jePxE/PnvSsuMrVqxxHUrx4Sp6Tp8Jkzx6Kyw4d7hSXx45RWJUsqdTBg55t3xV69aLXxyxxdTcWL+bnuGpVyu/27mVFX1AQFwGffGJ8B2sjGTqU55FR7RGE9JkwgcerjwyNtUb8OBw8kYYOtWR3fk+TJqyusRtr1zLc4xw2OmNG2het+HjG8Dt2tN5GJ++8QxevmVWKW7awoV/16ilJ6u6EZVwhPJxjNgICOKNr2LC759msXs3vyI2+OB6JnxkzaFdGXkqHg3OmBgxgPlj27BQNRuTfOLtwp66w2rGDvXbKlzeu5DwtnH1pZswwbx8Z4XCw+rBBg7Q9i0eO0KOWLRurLYcPZ6jSTiQmUgjrChn6Gx062PO+4iHWiB+luEpr1syy3fk18+fzwqrLc5Ia52DK1MNG5869a9M89fXXvDHqWhUnJDBRv3Rpc8s6d+/mPooUYQn48OF830uXGrufw4eZF5E7N7+HevVYXZdWuOjDD1lC70a4zCPxs38/bVm+/M6/HT3KHJ7gYD6ncGEOWTU6AX7IEIbOVqzgcZkzJ0XBmTPG7ic1Bw/S69Sli74k3UWL+Ln+80/Gzzt9mrlkOXPS5sGDrS1CyAjne/DWxq7eRqlSd5/J50VYJ35Gj6Z70qw8CiGF+HjeTAcO1GdDcjJb9Neu7d6wUSfx8RQFHTqYamaGHD9OD0y7dubepC5dUqpx45TeOaNGmbevmBhWcrVqRc9WUBAXJWPHMhyZlMTZYS1auLVZj8SPw8Fk4mHD+H2vW8e+Ts5S7Fy5KBCWLjWvEikpie81Rw7us2tXY6rl0iMujiXmFSqY0y/IFZKT6W1s3Nj111y4wBl8VrafuBstW/K6IpjP2bM8P375RbclhmGd+Pn7b354ZpWLCrcyeDBv3GZeyNMiKYku/SpVPBs2mppvv+U2Nm0y3k5XWbjQs94w7vLffyndj3v2tKbi5vJl5vW0aJEy38vZUPLJJ+mJunzZpU25JX4cDpbQ//03k54LFUrxSOXPz3ywOXNcn1ifGa5eTSn5Ll7c3H06HCwTzpZNb9KoM+TmSWm9s/FowYIpjUeNaFfgLseO0UP67bfW79sfcV4Hje4orxHrxM/16zxYXR1eKWSOQ4d4sH7/vTX7i49Xavp0rmgBVku5MBAzQxIT2VG3Rg29SXajRpn7WUZGsrKocmWWkWbLxrCUmcm2bLY8SAAAIABJREFUtxMfz5vhq6+mDAJ1lkDfdx/bJwwcyCTwWbPYJ2frVuYqXbigIg8fpvg5fJhhkSNH2K5g8WIeFx9/zG03aMAbZ+oO0EFB/PuWLXcPhxrJxo08XgsWZIm309Nklpfvgw/4nmfPNmf7rnD9OivYMttd2zlypmhRhg27drU2zP7++/RCeVoQILjHu+9yceBDWCd+lOLFvU8fS3fp1zRrxkndZmLGsNHUbNxI0Tx5snHbdBeHgyvcLFmML6lNTmbTw7x5OTdHKXq6ypdnnsXkydaGir/+mjezK1eYbzVvHgsV2rZlZ9fU875cGW/hfBQsSG9gx44UkwsWUNw5k6t37rTuPcbF8WIeGMihy0eO8PfOxo4TJhi/z2++uTO5Wgf9+jF3x6gVvPP8d06Sb9/efK9WQgIF3GuvmbsfIYVGjRj+9yGsFT8vvCDD56zEzGGFtw8b7drVvOTkPn24yjMzCfVuJCTQm3XPPWkPX/UUp1fp9jYQN24o1bcv/9aoEd38VtCjx93P0bg4JsJu3862AIsXq8h58yh+5s2jt2fFCn5O585lnK8TE0NR+cUXhr6NdNm2jSIsa1YmVN/uUXz7bXqiUpd/Z5alS7nNV1/V24V4yxaeqxMnGr/t+HiGoMqX5zH75JMZd9rODM4qPSPPQyF9kpIYlh47VrclhmKt+Jk2jRcBK2L5Am86997L5ESjuHKFAwStGDbq5OpVutefe87c/dyNqCgKgxIljFk5L1nC1fLIkek/Z+VKVlnkyUOvjNk3zwoVPOqW61HCs5M6dZTq1s3917lDfDwTq4OC+B2mV8afmEiPaeHCxszI27KF4bTWra0N6d1OUhIbV1avbm4IOTGRYb2HHqJAadyYQtLI47Z5c/bHEqxh1y5+l//+q9sSQ7FW/OzZww/R6DJeIX3ee4+hisx2az1/PmXYaM6c7LtiZbXHTz/x2Fm2zLp9psXZs6xCq1Ilc120DxxgqKtNm7uHtSIjKTIBzplav97z/WbEhQvcx9y5br80U+LHzPE3DgeTNStWpIdp+PC7V45dvqxUmTIUC5kpGDh6lKK9Xj393ZI//5xC28y+ValJTqaHpmZNHlP16986Sd5Tjhzh9iR31DqmTOFC18ecFtaKH4eDblFPWtoLnuHsru3pxeLkSXqOcuSg8HnnHfPmXmWEw8GqnPLlra9gu529e1mVlFZ3ZleIjGT+24MPutc9959/Um4m7dsbX2XjrOjwwOORKfHz88/cr9ET07dsUaphQ267eXO3mjaqHTso8p9/3rMbtrNLdPny+sf6nDnDc1fHddfhYHJ8SAi/h4cfZjje0zy2d981ZjEnuE7Tpjx/fAxrxY9SSg0axOoR6fdjHZ64iQ8dYsl11qxMVh050txmf66wfz8roT74QK8dSqV0Z65Rg316XCU5mUnh99zD9+MuyckcXXL//fxu3njDuO/l7bcZ0vOATImf06d5Y/ztN4/2fQcnTjAHDWCTxL/+8mw7Tm/j55+797oDB1gAUK6cdblaGdGxI/t+6Tx/HQ6l1qzhjRSg8P/hB/dCcPHx9KQZGcYXMubaNWtz8izEevGzZg0P/s2bLd+13+JOguDu3bcOGx0/Xl8ztrT44APe9D0RDkbz33+8GAcHu+61GD2a38Xvv2du3zEx7MScOzfDZ2+/nfk8pJAQj/OqMiV+lGIo8c03PXutk717GR7Mnp3H7jffZD6/5fXXefF3Nd9h927u+8EHKep045xT9+OPui1JYcMGjnBxTpL/+mvX+lo5PYS6ur77I86eUD7U38eJ9eInMZHJsjLnyzqcpaEZzcDZsoXlzAATbKdO1R9eSoubNxlKqFfPvK6/7rB/P70lFSvePQdq6VLmXQwfbtz+z51jQ8t8+XiT7taNIRt3iYujV23SJI/MyLT46dzZsyRWp0fhqadSehJ99JFxgj0hgdV2RYve/QawdSsbNlavric0fDtXr1JUNm6st8osPXbupNh2TpKfNCnjcFajRhzWK1hHx44Mtfsg1osfpXiBrlpVy679lk8+ocfk9mGNtw8bnTnT/hOSN27kjX7wYN2WkKNHmSBbunT6eTiHDlGgtGplTsg3Kkqpzz6jcAVYsbR4sesCMSyMr/OwR1Omxc/nn1N8xca69vwbN+jNcOZAVanC5otmHLsXLjCMVbdu+vaFhdEDV7eu/vCwUhQ7zzzD3DQzB7Qawb59t06S//jjO3Ph1q3j9/zrr3ps9Efi43lMZ1SN6sXoET9O9+XRo1p275dER7N8t3dvXhiXLeOEXoBC1JVho3Zi/Hja/uefui0hp04pVakSu6DeHl6MimLpb6VKmasQc4XERH6XzplqhQqxv8y6dRmLrvHjWZLtoTct0+Jn+3bam1FX8IQEft/duqWMw3j8cc/Hp7jD1q0Mp/Xseee+VqygPQ0auJfAbiZTp/LzWbBAtyWuc/RoyiT5/PnZmsA5Sb5JE6WqVZNcUStZsYLHkCeeZC9Aj/iJiuIBrrNrrz8ydixXV1Wr8qCuU4e5J954QUlO5mDDwoX1Nj9MzfnzrGbJnTtlhepwsDIrTx5r59o5HBRhgwendN8uXZrVMtu23fmdt23LsIKHZFr8JCbyc7u9A3JiIgVR3770CgCslBs9OqUzs1XMmsX9T5vG/zsc9LYFBbEBpl0qkLZv5/XVWxODb58k36mT9wk5X6BvX14z7BgyNQA94kcphlqaNNG2e7/C2XiscmVeRIoVo6r39oP64kV6Who3to/XKiaGcXKA84fGjNF/4U5OZsJu797MtwMoGjt0UOqrr1idVLgw7fWQTIsfpXg9aN2auSATJzKP5557aO/99zOpe8cOvcdtv34MH69erVT37rTtrbf0zp5LTVQUw9c1algzHNdMLlxgn7KgIOYF9e2rf5K8v+BwcNHkrQLaBfSJny+/5EFth/i4r+IcNupsOf/EE7yAZMniOyHHf/5hZZqd4tIOBz0YAQEpN0e7EB/PG/f77yv1yCM8B53zt5o25Vyr5cvpTXNDZHgkfpKTWQq+ZAnzPCpXTvnMcuSgPWPGMMfLLt7JhAR6TLNkoY06h5TejsPBSs08eawdimsmztlvXbqkTJLv2dP8rvL+jjMMbfQsQxsRoJRS0MHp00DJksDs2UCXLlpM8FliY4Hp04Hx44FTp4B27YAhQ4BatYCbN4Fy5YCnn+ZzfIGRI4FRo4DVq4GGDXVbQ44cAapXB+LjgfLlgd9/Bx54QLdVdxIVBQwfDkyaBNSoAezfz+MHAAoUAKpUAYKDgVKlgKJF73zkzv2/zUQhX758iIyMRN68eSmnoqKAixeBS5f4r/Pno0eBiAhg717gxg3uK29e4P77+bsffgA6dABy5ND0oWTA+vXAM88A167xc9myBciWTbdVZOZMoGdPYM4coHNn3dZkHqV4Pt+8yc85Jgb46itgwgQeR507A++9x+9BMJYRI3hNuHQJyJpVtzXmoFV61azJEIFgDFFRzOspWjTjYaMTJ3LFb3XOhFkkJTFfpXhx9xoOmsWNG8yrqlCB1VOVK7Nqwq45C717s1eRUvSwHD6s1KJFzKvp1InvpVChtKe1BwUplSWLigwKoufnf/9XgYF3PjcggHk7NWtygOq4cUxgPnmSXourV/m8WbO0fhxp4nAwiThLFnaN/vNP5tW8+qpuy0hEBHNkevXSbYlx/P03j4c//rj19zdv8rtw5rK1a8c8NsE4atTgue/D6BU/I0fypmD30mq7c+UKe8c4h42+/HLGow9u3mTez4svWmai6Zw5wxtr8+Z6+/84HOxdkjt3ivCMjGTZMcCSXk9GYphJcDCPmbuRmMi+Qrt28cY0ezZzhr76SkVOnKgAqJbBwapV1apqzksvKTV/PsMWERHMz3IlLys4OON+VDo4eZLHFcAcCOfx9e23/N306Xrtu36d1YTBwfZJus4sDgebbtatm374NT5eqRkzuMgAWABh1tw7f+LECY9n/HkTesXPjh38kFes0GqG13L+PKt58uThqm/gQNc7cU6axFW7L8XOV61KyQnQlRQ7blza/UgcDs5Xy5uXDd10D2h1cu2aId4WQxKelaIIc3qhdJP6OytePO22Cs7S7E2bLDdPKUUB0LQpS8OtrCY0m+XLeVy6MprEWdARHMzXNGqk1MqV3l/QoYvPP6eH0+y2HJrRK34cDjZl69dPqxlex+3DRt991/2Osjdvshtujx6mmKiNH37gBVBHAvSKFQz3vPde+s85eZK9aQB6OHSPDvnzT9qSSRFsmPj57juGx3R7x86eTRnB8Pzz6RdmxMUxcbxECS5GrMThYM+jbNmY+O8rOBzs4F6/vnsCJjmZoeVatfi91avHRp8igtzj8cfZJNXH0St+lKLwKVVKDlBXuH3Y6KhRmauWmzKFN2tfqQxx4pyf5ekke084epRhxyeeuHt4x+Fgr5jcudkZes0aS0xMk6FDGS7M5PlnmPg5eND1Fb8ZOBz0IhQowBldixbd/TVnzjCM/Nhj1oZchwzxzfCEU5AvX+7Z6x0OHj+hodxO9epsrGuXdhh25vp13l/cHebrhegXPz7eRdIQUg8bLVaM3XijozO/3dhYrli7d8/8tuyEw8HwSZYsnl9A3eHGDXafLVfOPTF65Ai7AgP8DnT0MGncWKk2bTK9GcPEj8PBnkM6Zv9FRFC8Akz2dCd5fv16Hm9WebGnTaOd48dbsz+rcDjYSiA0NPMLYoeDHrFmzfhZPfCAUt9/b4+ZgHZl7lx+VidO6LbEdPSLHx+fH5Ipbh82+sUXrs8+cpUvvmCYYetWY7erm8REpZ58kmHBnTvN24/DwaGcuXJxyru7JCfzRlakCMOY779vXSgsMZF2jxuX6U0ZJn6UYqNDKxugnj/PEGRgIAWsp1V5X35pTbXakiW0tV8/3/OYO0cfrVxp7HY3buRcPYDe1mnTvL8JpBl07swu9X6AfvGjFMvda9XSbYV9SD1stGJFDhs1a7WSmEi3cO3avucWjo7mcVW8uHkrmQkT+D39/HPmthMZyVyh7NkZbvn6a/O7Bm/dStvDwjK9KUPFz9ixDAma/f5jYhgizZOHYa6JEzN3Q3Q4lHrpJX6HZi0mNm2iYG3b1vfO18hInqsGeCLTJfUk+eLFOZ7kxg3z9udNJCRw+PLw4botsQR7iJ/Zs3kRdrVSyRdJa9jovHnWXOA2bODFYOpU8/dlNefOcaUXHGx8Eu3KlVyBv/OOcds8cYL9mZyTyv/6y7zV/ZQpTJY1YAVsqPhxTvDevj3z20qL5GQmxt9/P/MbXn89ZYBmZomNZdimZEmW9xvJ4cP0ED7yCAsWfI2BAynsrAi57NvHYo+gIIZZP/rI56ub7oqzr5Kf9Eyyh/i5epUHoR8kWd1BcrJSCxemTOGuU4dJlla38+/dm+HHc+es3a8V7NvHlX39+sYJoGPH2PiveXNzBOrmzSlCuH59ls4bvZ+OHdlLxQAMFT+xseYkXcbGsjePc8Zd+/bmtHo4eZKNRhs1Ms57dfw4Q3IVK9qjkafRbNvGhYTVOUxHjyrVpw8XAfnyKfXBB0pdvmytDXahXz+Kdl8LpaaDPcSPUozHPvyw33zwd/SmaNhQ77DRK1e4quzcWc/+zWbzZgqgmjUzf/OIieGxWrascR6DtHA42N22YUMeI+XKURAY5aYvWZLDQg3AUPGjFAWfUcfipUusjCxalB7ONm2UCg83Ztvp8c8/XNANGpT5bR08yO+qbFmKbl8jKYmLvqpV9SUjnz7N7ypnToZc33rLNxeC6REXRw+YEcerl2Af8fPHH7zAb96s2xJzcQ4btWNX0u+/9+2mk7t28QYYHOz5hc3hYFgqVy5uzyo2b6anJjCQIu799zN3cT55kt/1woWGmGe4+HnjDaVKl87cNg4e5PiJnDmZTN6nDyfYW8XkyfyMf/rJ821ERLDC88EHeYP2Rb74wrDcs0xz8SJbCNxzD3O3+vb1i8onNWcOvwNfapR5F+wjfpKSWNHUs6duS8zh5k3mWKSeR2O3CiuHg16GihWNryqzC/v2MdGxYkXPSss/+4zf37x5xtvmCseOMUcld2666rt2ZV8Ud8MrzpJWgxrzGS5+fv2V9rl7w795k8nnrVqlzBIbOdL4/BtXcDjYwiBnTs/yl7ZtY2i1WjX3m5h6C+fOMdzuyngVK7l6ld7CggXZwuCll3yvH1pqGjZk2w0/wj7iRykebLly+VbimavDRu3C3r3MtxgxQrcl5nHkCJOgS5d2b7jr6tUMZRgUKsoUV68q9ckn7F0C8Cbfrx/DOa6ETvv3V6p8ecPMMVz8nD3L9/XLL3d/bmIi+zn16MEVuzN37ptv9CcG37zJIZGlS7sXbg0PZw5KnTrmhlZ106ULwy12fY/R0Up9+im9b4GBDMXu3q3bKmPZt4/nzJw5ui2xFHuJn9OneXP54gvdlmQed4eN2okhQ+jy9eWVzsmTSlWqRC/Qvn13f/6JE7xIN2tmfgm2Ozgc9BC8+SbfizM3aOjQjF3YNWtybINBGC5+lGKOS3o5CA4He7cMGMDWAM62ECNGWBvacoXjx+nBcfXYWb2anr3HHmP5t6/irC4yuy+SEcTG8r5UqhRtbtuWfdh8gUGDeG3zs75H9hI/SjEZsVo17018PneOngFPho3ahZgYekYef9x7vwdXOHeO5eRFimTcCPHmTYqFMmXsXQmSlMThrj170mvgbOjWsyeT6505QtHRXGR8/bVhuzZF/HTtyvlMTo4dY75cly5ciQOcTzdoEEPIdj5WV62i52Dw4Iyf9+efzE96/HHf7j8TG0ux2rChvb+327l9knyLFmzN4K3cvMkF+ltv6bbEcuwnfpxzXTZu1G2Je5w4wbBDZoaN2omlS31zbtDtXL5MYVOgQNpdZR0Oekhy5vSuESyxsRzqOGBASkUhwJ+fecbwBFNTxM/HH1OkvfACvUAABUSdOuyttHq1dzX6czbEnD8/7b//+CO9xK1a+W7OnZMRI/hevTXBNimJ18YqVfidNmigt1rXU5yDoH3Zy58O9hM/SUmMj7/4om5LXOPgQSbDZclizLBRO9GuHVfYvpSDlRbXrnGlHRTEhObUF7ApU3hxmD1bn31GcO4cY/o9eyqVP3+KGCpThtPL332XVUk7d3p0482U+Llxg9VsM2eyyqt5c86cc9pYtixF3KJF+qe9ZwaHgzPDbh+FkpjI9w0wb8nXZ08dPMhk/SFDdFuSeZKTeVw6+7TVravU7797jwgKDbV2lIyNCFBKKdiNMWP4OHsWyJ9ftzVpExEBfPQRMH8+ULQo8NZbwCuvAHny6LbMOE6fBipXBtq3B2bN0m2NuSQlAe++C0yYAPToAUybBmzaBDRtCgwYAEycqNtC42jZEoiNBXr25HHsfJw8yb8HBQEVKgAPPggUK8bjO61HwYJAYCAAICoqCvny5UNkZCTy5s3L7SQlAZcvA5cuARcv8uH8+dIl4MwZYO9e4NgxPj8gAChfHggOBqpU4aNnT+CDD/jd+AIxMUBICP/dsgVwOIBOnYA1a3iM9e/Pz8FXSUriOXXqFI+5XLl0W2QMSgErVvC+tW4dUK0aMGQI8OyzPJ/syJ49PMfmzweee063NdajW32lydmz9KTYsePz5s3MSzJz2KidcPb++eEH3ZZYw08/MXRZvTo9eU2a2CvBObMkJzMf6MMP7/zb9eusMvrmG3panniCIUHnGAinJyaNRyRAz08Gz1EAE+lLluTMtaeeYq7BrFnM2YmJudOmZs0YBvIljhxhmDU0lF6tQoUYwvMHhg1j6PLff3VbYh7//kvvJcCiiu++s6c3r39/ViHHx+u2RAv29PwA9DYcPAj89589VkJr1wKjRwN//w1UqgS89x7QtSuQNatuy8ynRw/gt9+AbduABx7QbY35hIcDjRtzlbp4MfDUU7otMo6ICKBqVWD1ar5HV1EKiIpK8eBcvAhcvcrfA4iKjUW+AQMQOWUK8ubMydcEBgKFC6d4iooUoWfUnfN5+HDgiy/oKbLDdcAoPviA15N77wU2bgTKlNFtkfmsXg00awaMHMn37+ts2UJP0O+/A6VLA++8A7z4IpAjh27LgJs3geLFgVdfBT7+WLc1etCtvtJl+XL9XT8dDg6WfPRR2lKtmnXDRu1EdDT7yVSv7tteLqX4nb/wAj0UNWrQ42FgVZR2vv6auU0ZVBIlJCSowYMHqypVqqhcuXKp++67T3Xv3l2dOXMm3deYkvCsVMp1YP9+Y7eri6Qk5roAPJ8ApX77TbdV5nP+PPMHmzTxv+vnrl3szh4QwOrEiRP1V/J99x2PPXf6nPkY9hU/ycl0CffooWffCxbQNQ+w3HbxYu9JYjODXbsoCF57Tbcl5jJ1Kr/zH3+kO/jVV/n/Pn18Q/g9/zyP6wy4fv26atasmZo/f77av3+/2rBhg6pXr56qlcHrTBM/16/zpjFzprHb1cG1awz1BQYqNW4crzPPPsu2GHv26LbOPJKTGQYqWpQpDf7K/v1cWGXJwr46Y8boKyapV4/fiR9jX/GjlFIffcT8C6uqpxITmfPhLA1u3Jjlz/4selLz5Zf8XH79Vbcl5rB2LS9MAwfe+vtvvqEH6KGH7DeSxF0qVGA+j5ts3rxZAVAn0plzZJr4UYoDL3v1Mn67VrJsGSvY8ufnz06io3m9qVjRuyvZMuLjj3ndWL5ctyX24NgxLqqck+SHDs38sGV32LnTfzyOGWBv8XPuHG9Gkyebu5+4ON7gypfnQfHkk/YYsmc3HA6l2rfnCetr06VPneLKtFGjtJMTd+3iJPegICZtemOS4PnzHs8l+/vvv1VAQEC64sZU8fPKK0pVrmz8dq0gKord3QG2U0hrntyhQxRFTz9NL4kvERbGc+a993RbYj/OnGGLg1y52NH7zTet8Yy9+irDb3ZMwrYQe4sfpegWfughc7wvMTEUVvffT9f6s896NoDQn7h2jb1h6tXznZMnNpb9OUqWzLgxZXw8hU9QEIVQ6l4t3sCCBbwJuznQNTY2VtWqVUt17do13eeYKn6cjdjsOv8pPVavZs+y3LmVmjYt42vY0qW8Bg0fbpV15nPlCs+p0FDfqpg0Guck+bx5U1ILjh83Z1/R0WzCO3SoOdv3IuwvfpzzX4xsIR4ZyaGQRYvyRta9u/d2GtXBpk30yNlhwGdmcTjYpDJ7dtdn9WzdylBF1qwMzXrLhf2tt3gzuo2ffvpJ5c6d+/8fa9eu/f+/JSQkqDZt2qgaNWpkKGyc4qdly5aqVatWtzzmZHZg4uHDvAYsXZq57VjFjRvs9g7Qk3j0qGuvGz2ar/n9d3PtswKHQ6nWrVnSn06oVLiNa9fYgqJQIV5fX3zR+M7L335LkW2WuPIi7C9+kpMZjurWLfPbunyZK/f8+RlvfeUVv852zxTjx/NC/eefui3JHF99xffx3XfuvS42liMWAgPpNXJlOKpuHnmEHYZvIyoqSh06dOj/Hzf/Nwk9ISFBtW3bVlWrVk1dvstMM1M9Pw4HFyrvv2/8to1m3Tper3LmZHdwd8JYyckcPXLPPd5f3TZ5su8IOau5fZJ8p07GeZlr12Zah+AF4kcppcaO5crcU7f3uXNc9ebOzYvS669zgrzgOcnJSrVsyaqFDEqgbc369fTe9Ovn+TbCw9nILEcOVvDYdTJybCwF/5QpLj3dKXyCg4PVxYsX7/p8U8WPUhQFjRubs20jiIpi/kZAgFIhIZ6v2CMjlXrwQT68daL7li08r15/Xbcl3s3tk+TbtGGTXU/Ztk0EaSq8Q/xcuMCTacIE91534oRSfftSOOXNy7iqCxdywUUuXlSqeHEO9fO2BOAzZ7iyeuyxzOcuxcTwQh8YqFS5ckr98ov9KgTXr+eFb9u2uz41MTFRtW7dWt1///1q586d6ty5c///iE/nezZd/Iwfz8RQu4UYExPpPSxalAJ4/PjM97HZv5/Xq7ZtvS8B+upVer5q1bLvQsDbSEhgq4eKFVMmyacKTbtM796sOLTbOaQJ7xA/SrE/wn33KfU/l3yGpB42WqgQ46i+Wkaqm3Xr6FHo1s1+N/z0iItTqn59XgjOnzduuxER9IYBTPLcuNG4bWeWcePo+XThwnfs2DGF/42ruP2xZs2aNF9juvgJC+PnapdWAw6HUn/8wSo0gP2TTp0ybvu//87tjh5t3DbNJi6OC6GCBZmnJRhLWpPkly937bp7+jSdAN50PJmM94ifw4eZnDxpUvrP+e8/xkcDA7mqnzCB8VPBXObN48noLVOae/emYNu0yZztr1jB3jSAUp072yO5sE0bU6c3my5+4uLcCtuZys6dSjVtmpLQ7II3zSOGD2cYzRvy6pKT2cU4e3Z6GQXzcE6Sr1OHx2CdOhTLGXkJ+/Vj8rm3hlJNwHvEj1LMfi9W7E7vz6ZNrCwAWFr65Ze+0Y3Xm3AmQNt9FMTXX9POGTPM3U9SklLTp/N4zZ6dydG6urk6HEoVKaLUBx+YtgvTxY9SzKVJI2HbMs6c4TUoIIDjXszu+p6czN4/+fOzF5Cdeestfi6+2gDVjjgc9Pw0aMBrWtWqaY9fOnWKCwfx+tyCd4mfI0cYypo4kV/8P/+wcZhzeu6sWb7Te8bbcDi4uggMZDjAjmzYwNwxK0d0REezwjBnTiaHT5mS9vRyMzl4kOfIX3+ZtgtLxE86pfqmc/Uqv8NcufgdTp1q3XXm+nVe26pUsa8Xe8oUHl9mN6MV0mftWuYCpTVJ/tVXGYqMitJqot3wLvGjFHN5ChRgzoZz2Oj8+f43LM+OJCUxSTNXLtd75ljF2bPMGQsN1ZOcffo089YCA5mHNmxYxg0VjeS777gqNzHvzRLx42GTRo85ckSp/v2ZK5U9u1KDB+vx3u3Zw/lfHTrYL69uwQIeW2++qdsSQSlWg7VtmxIFGT2aC76PP9Ztme3wPvHz44/8YktWEZI1AAAgAElEQVSVUmrJEvtdDPydmBgK06JF7dNDKT6eIZPixdn2QCdHj3K2lvOG2ru3+T1dXn6ZngMTsUT8ZGI8h1ts3Mhu76mFqpGJ8Z7w22987+PG6bUjNWFhrHB77jnvq0rzdf77j/mGAI9jb21HYiLeJ36Sk5Vq1Yo5DDdu6LZGSIuLFzlAs1IlNpbUjXOI4IYNui1J4coVdocuVowXqFatlPr3X3PE/EMPUWSZiCXiRymWUXswmPWuJCUptXAhPYMAy4q/+sr6EGVGDBnCG9mKFbotUerAAQrDxx6T/Eq7cuwY00TattVtiS0JhLcRGAh8/jlw/Trw5Ze6rRHSokgR4K+/gKtXgTZtgNhYfbbMmAF89RXwxRdA/fr67LidggWB994Djh8HvvsOOHoUaNgQqFcP+PlnIDHRmP1cuwbs3QuEhhqzPd2EhADh4cZtLyaGx8eDDwLPPAMEBAALFwL79gF9+gC5chm3r8wyahTQvDnQqRNw7Jg+Oy5cAJ54AihaFFi0CMiRQ58tQvqMGcPrzE8/6bbElnif+AGA0qWBl14Cxo0DbtzQbY2QFhUqAH/8AWzfDjz/POBwWG/Dpk3Aa68Br7wC9Opl/f5dIXt24IUXgN27KRjz5gU6dgTuu4+2h4Vl7rPbsIH/+pL42bGDosVTkpKAZcuA7t2Be+8F+vUDatQANm4E1q0D2rYFgoKMs9kogoKAOXOA/Pkp1G7etN6GmBjg6ae5oPnrL95cBftx9CgwaxbwzjtA7ty6rbEl3il+AGDIECAykit6wZ7UqwfMnQssWAC89Za1+z5/HmjfHqhVC5g82dp9e0JAAFfTK1cC//0H9OxJ8fjoo0C5cjzeIyLc3254OFfo5coZb7MOQkOB5GRg61b3XqcUhWC/fkDx4kDLlsCWLbw5HD5Mb1u9eubYbCQFCtDbcugQ8PLLfF9WkZREr9P+/cCff3IRKtiT0aOBQoXovRTSRnfcLVNICZ93MHUq8yiGDbMmQT0+XqlHH2V119mz5u/PLJKTmQfUuzcrHJ3VjZ984vqk7EaNOBfLZCzL+UlK4uiHMWNce/6ePcyVKVOGn1+JEiyZ377du4sl5s/n+5k40Zr9JSYq1b07G80uW2bNPgXPOHSI39Nnn+m2xNZ4t/hxNm9y9UIo6OOTT3ixfust8286ffuyvDMszNz9WEl8PLu4duzIChuAyaZjxrA6Ka2xFQkJbDtgQYWQZeJHKaWaN09/MnVsrFJr1ig1dKhS1avzc8qfnxVva9b4VkuMt9/mTW71anP3Ex/PMvugII5XEOxNjx6uj4LyY7xb/CjFG5207fYOnM3QXnvNvNLYmTO5j2nTzNm+HYiKUuqHH1ghds89fL958/L/kyYptXs3BeaWLfybBSLQUvEzciQ9vsnJFH2bNrFyrlmzFGFYqBC7QS9a5LsDNhMT+Z4LF3bdE+gusbFKPfUUF5mLFpmzD8E4DhxgRaAdxsDYnAClrAwam8CZM0D58sDQoXwI9mbGDOYq9OgBTJ9ubGLpli3AY48xkfWbb5hH4+skJjL/ZdUqYPVqJkgnJDDPp0QJ5g/t3s1qJhM/j6ioKOTLlw+RkZHImzevafuBw8FjqHdvoHFjYNs2ICoKyJOH1XJNmgBNmwJVq7Iy1Ne5cgWoXZv5HevWATlzGrftmBhWa4aHswKuRQvjti2YQ/fuwJo1zGOTKrwM8X7xAwADBgA//siy4Xz5dFsj3I05c1gB9uyz/N6yZs38Ni9c4E2gRAng339ZReWPxMZSAK1aRQF49Sp/ny8fUKUKH8HBKT8XKWLIbg0XP0pxYbNnDxO9nY+9e1OqnB58EOjalWKndm1jjiNvZOdOVsF16MAKHyNEbmQk8NRTwK5dwNKlQIMGmd+mYC779/Pc/vxzVooKGeIb4ufsWXp/3nsPGDZMtzWCKyxcyJLuJ58E5s/PnFhJTASaNQMOHKAnoEQJ4+z0VpQCSpYE2rXjin337hQBsW8fvUMAPUROIVSlCit4ihblo3BhIFs2l3bnkfiJiwMuXQIuXuTj8OFbxU5kJJ+XKxcv6k7R9vDDwKBBQJ069AIJXFB07cobX79+mdvWlSusPDx8mC0BvKEKTgC6dAHWr2cloL8u/tzAN8QPALz+Olc9x4+zD4Zgf/76izfnBg0ohjxtKDdgABvVrVnD0nABOHmSQmbRIoYuUpOUxBtbao9KRAQvmrf3FCpQgN4hpyByPvLlu8XDEBUXh3xDhiDyo4+QN7W73eGg98kpcFKLnejoW/eVLRu9OanFWHAwUKbMnSGsvn3p3dq/P/Ofla/wxhsUP6tXM/zrCRcucCFx/jzw998UmoL92buX58uXX0p5u4v4jvg5d469TN55BxgxQrc1gqusXg20bs1+PH/8Adxzj3uv//57Ngn84gtx9aZm7lyuBC9coFhxhbg4Pt8pTjJ6REXd8tIopZAvJgaRuXMjb+qwS0AAG+EVLXqriErr5/vuA7Jkcc3W2bOBbt0opgoXdvFD8XGSkoDHH+eNcNs24P773Xv96dMMIUZHU1hWrmyOnYLxdOrEPlaHDrnsrfV3fEf8AFz5zJhB70+BArqtEVwlPJxN5ypXpjfI1e9u2zY2vevShd+7PyQ4u0r//gxZHDpkye4sS3h2cuwYFztLlrDjsEAuXmT+0333AWvXuh7+OHqUwkcpCp/y5c21UzCOiAigWjXg669ZTCK4hG+VQ7zzDt3skvfjXYSE0AN06BCrdS5duvtrLl5ki/9q1ejqFeFzK2FhvjPSIi3KlAGKFeP7FFIoWpQd1XftYmjQlbXt/v0MPWfNSsEkwsd7UAoYPJjnwwsv6LbGq/At8XPvvRz+9+WX7re/F/RSqxbwzz8MX9aty4t3eiQmAs89B8THA7/9JiWdt3PjBj8/XxY/AQF8f0YOOfUVatemF2DGDFb8ZcTKlfwc8+en8ClVyhobBWNYsIDe8kmT/Lfa0UN8S/wAdPdXrcqkr+Rk3dYI7lC1KoeRFihAb9DPP6f9vMGDueL/5RdWNAm3smkTPaAhIbotMZeQEGDzZoph4VZ69GDVV//+aQtEpYCJE1kJWKcOewQVK2a9nYLnREez2KNNG+ZNCm7he+InSxZg2jROE582Tbc1gruULs1yzTZtWAo/ZMitIvann7jKmThReo+kR3g4V/IaElY7deqE1q1bY+7cuebvLCSESdo7d5q/L29k4kSgfn0O+D17NuX3sbHss/Xmmxw4vHSp5Eh6I8OGAdevA1Om6LbEK/GthOfUvPIKMG8e49n33afbGsFdlAI+/RR49132HJk9m0mZoaEURd99J3k+6fHEEywN//NPy3ZpecIzwLBnvnzAJ5+w1YVwJxcuMKRcqhTDyufPM1du3z5g5kxWCQnex44dDG+OHUsBK7iN74qfq1fZM6RZMzYAE7yT5ct5gS5UiJ19ixc3vo2/L5GczNLywYOB99+3bLdaxA/AfjbFijEEKqTNpk30kj7xBMuhc+Zk/6caNXRbJnhCcjLwyCP04G3fLrk+HuJ7YS8nBQvSczB3Lpt1Cd5Jixa8YJ8/z8drr4nwyYi9e9mDx9fzfZyEhDDM56NrOEOoW5ejZBYv5nVx61YRPt7MN99wjuG0aSJ8MoHvih+AQ94aNmTJZ1ycbmsET5k+nauc0FCgVy9g9Og7OxELJCyMw2Lr1tVtiTWEhDCf5dQp3ZbYk/h49n6ZM4cdgI8e5UPwTs6f5xinXr18u5rTAnxb/AQEcOzB8eOMjQrex5w5wIQJTN78919g+HDggw84xPHGDd3W2Y/wcK7qc+fWbYk1OD1cUvJ+J2fPAo0acXjwzJn0+NSuzZEy58/rtk7whDffpLfnk090W+L1+Lb4AVjx8vbbwMcfW9btVjCInTu5wunenSWdgYEUPwsXAitWMO59+LBuK+1FWJj/hLwAjsaoWFGaHd7Ohg0UOidPsn/Piy+y2/Ovv9Jr2qFDynBbwTtYuZKLwU8/ZQ6kkCl8X/wATPwsXtz1jqeCfq5cYVVK5cps2Ja6sqttW2DjRoYyq1dnU0sJg3E176yI8yeceT8CBc2wYUwEL1OG3p7UU9mLF6cA2rSJXgTBO4iLY75jw4ZsUyBkGv8QP7lyAVOnMvF5/nzd1gh3IymJFV43brCDaVoJzsHBLPd8/nmK2ubNucr1Z5wCwJ88PwDF3q5dEgb97z8KnY8/BoYOZZg4rTYfoaHA5Mm8Jn7/vfV2Cu4zbhzTN776Slp8GIR/iB8AePJJNvsaNAiIjNRtjZARQ4YAa9aww3Pp0uk/L08eXgyWLwcOHGBC58yZ/uvdCwtjPxd3p3l7OyEhLP/dskW3JXpISgLGjGGYKymJXp0RIzKuBOrTB3jpJfZD27bNMlMFDzh0CPjoI6ZvaGhc6qv4j/gB2Bn4xg2uigR7Mn8+MH48H40bu/aa5s2B3bspbnv25JTv1B1t/YXwcP/z+gC8IeTP7595P3v3Mvdt2DA2u9u6FahZ8+6vCwgAvviCg4Gfeca1YcKC9ShFz3bx4pb27fIH/Ev83H+/DD61M//9x9Voly7ud+zNn59dn5csYeOvKlXYFdpfvECxsVzB+1u+D8BE+Pr1/SvvJzmZC4SaNTnjKTyc3oHs2V3fRo4cHAwcH89BwUlJ5tkreMb8+UzXmDqV6RuCYfiX+AFk8KlduXqVK9CKFYFvv/U8rv3000BEBLvZdutGb9DFi8baake2beOAT38UPwDf94YN/pH4fugQOza/8w69Ajt23JrU7A4lS7I79vr17Aou2Ifr15mm0b490zYEQ/E/8SODT+1HcjLQuTNP9oULM7/CKVSIJaG//spRGMHBXOH6MmFh7O1TtapuS/QQEsLjZ98+3ZaYh8PBIZbVq3Nm19q17IGV2Y7nDRpwO599JqOA7MTQoUzTmDRJtyU+if+JH4Au8t69mVh77pxua4ShQ9nDYv58oGxZ47bbvj2wZw8v7s8+y3Car3qBwsN5XGfJotsSPdSty/CXr4a+jhwBmjYFBg5kXtuuXcCjjxq3/f792U+rVy/21xL0smUL0zM+/ND/Chgswj/FD8By0OzZpfePbn79ld1Kx47lEFqjKVqU+5g9G1i2DKhQgd99bKzx+9KFUv6b7OwkTx56RHxN/Fy7xkTmhx4Cjh0DVq0CPv/c+A7eAQHsp/Xggww/X7li7PYF10lIYBVe9epAv366rfFZ/Ff8FCjAAXELF7JcWrCeiAjghRfY08fMhmsBAfT6HDrEhOphw3iRnzPHN3JEDh0CLl/233wfJ6GhvlPxlZDAXjwVKjA8P3QoK7uaNDFvnzlz8noYHc1zUhKg9fDuu7w2Tp/uv55cC/Bf8QOwU3D//kwqE1evtVy7xs+/fHme5FY07ipUiPHzvXuBWrWArl0ZKlq/3vx9m0lYGD+/+vV1W6KXkBAKQW8u21aKAiQ4GHjjDYZuDx3iPDsrqn1Kl2Z/rdWrpbRaB0uWMPdq3DheowTT8G/xA7BcNDgY6NhROsRaRXIyhcfVq7zQWz2Es2JFdo7+9196fh57jDcZb50TFhbG0v58+XRbohdvH3K6ZQvHF7Rrx0XBzp30TqfVpdlMmjThdXHcOAohwRpOnaInvHVr5nYJpiLiJ3t2JtqePcvZKYL5DB/Orszz5gHlyumzo0EDYPNmTr3esoV5FYMGUZR5E/6e7+OkVCk2g/M28XPiBBcDdevSI7psGR86K/cGDWIF5osvsoGoYC5JSQzN587NfmUywsJ0RPwA9ARMm8aboMy6MZcFC9iK/+OP2ZlZN4GB7Ad04ABHAkyfzjyLzz7zjqnXV6+yvNvf830A3jBCQ71H/ERGAu+9BzzwAMNM335Lb0+LFrot42c5fTqvjc88Q1EmmMeIEexTNXcuULCgbmv8AhE/Trp2ZTLsa6/5dq8QnezdC/ToAXTowDk1diJnTrY+OHyY9jkrbObNs3fi54YN/FfEDwkJoRfPzsI1NpajJSpWZFLz4MHM6+nVCwgK0m1dCrlyMSx97Rqvj9IU1hxWrmR37g8/lPPYQkT8pGbKFCb8dezoW6XQduD6dSY4lynD4aN2deveey9LfnftAipVouvfeZOKjtZt3Z2EhdFmI/sjeTMhIRzXsGOHbkvu5NIlYORIXmP692fX3oMHOXInTx7d1qVN2bL0RixfznC1YCznz9Pz3KwZO3YLliHiJzW5czPB79AhVloIxuBw8AS/dIkrSbte6FNTpQrw55/sBB4aylL8UqUYprDT0NTwcNpnVzFpNTVq0Itnp9DXgQMcp1OqFPtZdehA0TNrlnc0sGvenJ6JMWMYthaMITmZ18WAAKZcBMrt2Erk076dKlW4yp82jTNvhMwzciSFxJw5zKfxJmrUAH76iQ3mevViuKJMGVZl6E4ETUxkwrYkO6eQNStQp47+fj9KcbRKmzacOr9oEXv1nDrFY8jbzoPBg9klvUcPhq+FzPPJJ8z1+uknem8Fa1HCnTgcSj33nFJ58yp15Ihua7ybhQuVApQaM0a3JcZw/bpSn36q1P338321aKHU33/zmLGazZtpw4YN1u/7NiIjIxUA1bJlS9WqVSs1Z84cfca8+65SxYrp+U4SE5WaP1+pOnX43Tz0kFIzZigVG2u9LUYTHa1UcLBSlSrxPBA8Z+1apQIDlfrgA92W+C0BSslshzSJjARq1mRjvPXrgWzZdFvkfezbx2nTjz/OERO+FJpJTGSI9NNPWaFTrRqTpDt2tO5YmTSJ3WAjI9myQSNRUVHIly8fIiMjkTdvXq224I8/gFat6K0rU8aafUZHM5dt0iTg+HH2ynnrLVZu+VI44/BhetYee4zeLF96b1Zx5Qrw8MPMp1q9Wro4a0KO3PTIl4/9f3buZBWQ4B6RkSyRLVmSuQ2+JHwAhle6dmVO0KpVQIkSwPPPs2/Rhx9yEKXZhIfzRqRZ+NgOZ6drK/J+du9m5WLJkhQ7oaEpx0TLlr4nDipUYPj6jz94nAvuoRRD5rGx/BxF+GjDx85Mg6ldmwmKEyYAS5fqtsZ7cDgoBM6f5+rwnnt0W2QeAQFc5f/5J+fxtGjBY6ZCBeCRR4CpU82ZJK8U81ok3+dOChdm7xyz8n6OH2efqqpV6fGbORN4+WXg6FHmb9SoYc5+7ULLlhQ+I0YAixfrtsa7mDSJwvH7770j2d2HkbDX3VCK7cY3bKAXSA7YuzNyJB9LlgBPPaXbGuu5eZM3BeckeaUY+uvSheX+RojBEycY0vn9dx6fmrFV2AsAevakB8aokvfLlxnmnDOHoipXLiYzd+nCaih/C4s7HEyAXrWKSfcPPKDbIvuzZQs9gwMGMFwuaEXEjys4Y7TlyvFkF1dl+ixezJvCqFEcxujvXLnCqsHZs5k7ljNnyk2zRQvPb5pz5jDsdvEiUKSIsTZ7gO3Ez4wZQO/e7C/lqdi8cYPics4cYMUKitgWLfjdtWnjHS0bzCQ6mjl9SgGbNgF2+N7tSmQkPYJFirAK0N/Esg2RsJcrFCrEC+D69RLnzogDB4Du3endkInQpFAh9nhZt47hkmHDGB5r3ZoDK51/czjc225YGJsw2kD42JKQEH6mmze797qEBIYlunRh+XG3brxxTZkCnDvH8HfXriJ8AIrKhQvZ96pHD/ePYX9BKbbJuHqVHeNF+NgC8fy4w+jRvHmtWMGOnEIKUVFMNJVVoGvs3k1v0Jw57P1y//0MjTVpAjRtevdJ3jVq0Bv53XfW2HsXbOf5cTiY+/P66zxnM+LoUVbdrFrFc/vqVfb76toV6NTJuooxb8Xp7R09WhY9aTFtGvDqq/QAP/usbmuE/yHixx2Sk5nDsnEjV97BwbotsgcOB9C+PW8gEv93D4eDx9KCBbz5OhsnVq5MEdSkCdCoEVCgQMproqOB/Pk5hqNXLy1m347txA8APP0057ItW3br78+dA9as4ee9ejU9coGBLHB4/HG2K9A5Ud0bGTGCoe6lS5kQLRBn1d/LL7O5pWAbRPy4S1QUe1xcu0YRVLy4bov0M3o083sWL2Z/FcFzLl5MuTGvWkWvRGAge045xVBCAj/nvXspkmyALcXPRx+x8u7oUYYWnWLH2aG4SpWUz7RhQ7a3EDzD4aD3Z/16JvZ6WwdrM/jvP94rHnmExR9Zs+q2SEiFiB9POHOGIZ5ChYC1a/07xLN0KW/Ew4fL4EMzOH48JSSzahVw4QInfwcEcFxCgwb0UhQurNVM24gfpdhiYedO4IcfmGMRGMibc7lyKWKncWMZKWA0kZFA3brMadmwwb/zok6f5j2iaFHg3399u92HlyLix1MiIoBHH+XJvnSpf6r6Q4fYZK9hQyY++lpDN7uhFL0Wzz5Lz2NcHG84AG/kVarc+ggOtuyiq0X8XLnC83DPHv7rfFy7xr/fey89ad26MSQjuTvms3cvK8BatmSTWF9rbuoKkZG8N0RHUwTeLX9P0IKIn8ywZg1LX7t2ZaMzfzrRo6O5sklOZoKzhAysITmZ+T/vvsthk4cO3Xrjj4jgCAJn5U3p0neKogcfBHLkMNQsU8VPdHSKwEktdM6f59+zZOF7cgo+5/ssX56Lk4ceYlM5wRoWLGAO4NixPEb9iYQE4Ikn2F8qPNw2YWnhTqRhTWZo3JjVNt268SYzYoRui6zB2aL91CkmOIvwsY6ICIqB0FDe9CtX5qNDh5TnxMYC+/ffKojmzgVOnuTfAwOBUqXokr/bo3Bhc7yasbHApUt8XLzIR1o/nz/PEILT7vLlKWxefjlF7FSsmH75cEgIu28L1tGuHau+3nuPFYnNm+u2yBqUAl56iQUMK1eK8LE5In4yS9euvKkMGcIbyksv6bbIfD75hKu7hQu54hasIzycoqdOnfSfkzMnS+FvH7MQGcmwREQEk4CdAmPPHnoxL14EYmLu3F7BgiliKH/+tD2ciYn8t3PntMVSUhLDVE5hEx1953Py5uU+ihThvzVq8N8HHkjxWOXMmf77TouQEPbouXBBcnysZORIdtju1AnYupX5Vr7O+++zfcX8+Ux0FmyNhL2MQCngtdeAb79lg7QnntBtkXksWwY8+SSTbUeN0m2N/9GtG3DwoPvN+1wlJuZOj0zqx/Xrab4sKjER+ZYvR2Tz5siblvgJDKQXySlsUosc589mDGg9fZpDRxcuZPNNwTquXaNIz52boj13bt0WmcdXX/EeMGEC8MYbuq0RXEDEj1EkJXGK+T//sALMF4cbHj7Mi9mjj7LtvyQ4W0+5ciwp/uwz3Zbcgm2qvdKiVCl6IMaN022J/xERwQToNm3oFfHFvMjFi3nt79+f56UvvkcfRO5eRpElC8tqK1emZ+TECd0WGcuNGzzBixQBfvxRhI8Ozp0Djh2TSe7uEhJi3oR3IWOqVGFe5Ny5nGjua2zeTGHdti29PiJ8vAa5gxlJ7txsZpUzJ0s9nSW33o4zke/4cWDRIuZ9CNYTHs5/Q0P12uFthIQw7yQ+Xrcl/slzz7Hq6+232bPKVzh8mF3Ea9QAfvqJ/bcEr0HEj9Hcey/w119MsGzb1jcuuOPGcS7N99+zbFjQQ3g4qwqlq7h7hISwBHn7dt2W+C8ffcTmkh07+oZX/NIlLnALFGDYy91EfEE7In7M4IEH6AHavNn7px0vX86S1fffZwmroI+wMPH6eEL16kCuXCmeM8F6goIY+sqTh9eR2FjdFnnOzZvsah8VxQKQQoV0WyR4gIgfswgJYYLfzz+zIZ03cvQoS5efeIKlq4I+YmPpuZB8H/fJmpXNDiXvRy+FCrHqbt8+oE8fhtO9jeRkoEsXDiBeuhQoW1a3RYKHiPgxk3btmP0/frz3TfSNiWHYrmBBijiJZ+tl61b20hHPj2eEhNDz4403XF/i4YeB6dM5d23qVN3WuIdSwIABbGfyyy9A7dq6LRIygYgfsxk4EBg0iGWQixbptsY1lAJ69qTnZ9EixrUFvYSHM2RQtapuS7yTkBDm4R07ptsSoUsXXhMHDeLQT29h/Hjgyy/Z0+fJJ3VbI2QSET9W8OmnHEbZsSP749idCRPYpXTWLJaqCvoJC+MsNfHAecYjj/BfCX3Zg3Hj2AX5uedSxpfYmS++AN55h81dX35ZtzWCAYj4sYLAQJZCtmnDgX/z5um2KH1WruRJ/u67FGyCfpSi58cLQl6dOnVC69atMXfuXN2m3ErBguzBJUnP9iBLFuZDZs/Oa2JcnG6L0mfcOKBfP3Zulq72PoN0eLaSpCT2y/npJ2DGDODFF3VbdCvHjjGOXacOk/nEy2APDhzgXKvly207JNLWHZ6d9OrFCsz//tNtieBk2zaK+q5dmQtkpyaBSnFY9ahRwLBh/NlO9gmZQjw/VpIlC0NJvXtTBNkpCfrmTXZwzp8fmDNHhI+dCA/nRbd+fd2WeDchIRy3EBmp2xLBSa1awNdfAzNn8l+7oBSbMo4axUHOI0eK8PExZKq71QQGMmEuVy66Um/e5EmmE6UYxz50CNi4kSECwT6EhTHR2a4eFW8hNJTH+qZNtvWg+SU9erCaccAAHue6w7sOB9C3LzBtGvD557xOCz6HiB8dBAQwqTh3brZ9v3mTblVdK4vPPqO3Z/58qSayI2FhQOPGuq3wfipVorAPDxfxYzcmTgR27WKe4bZt+rqYJyWx0vXHH5ma8NJLeuwQTEfCXroICAA+/JBt30eMYJKxjvSr1avpeRo8mJUXgr24cgXYv1+aGxpBQEBKvx/BXmTNyt45QUEUQDrGAiUksAx/9mw+RPj4NCJ+dPPee5x2PH48ewFZOQrjxAkKnqZNKcIE+7FhA//VHQrwFUJDGdpNTtZtiXA7994L/PYbPT8DB1q777g4Vp39/jtt6NzZ2v0LliNhLzswcCBzgF55hSGwb781P+HYmeCcNy9n7kiCsz0JDwfuuw8oU0a3Jb5BSAgQHc3E5+rVdVsj3E69emwk2KsXK0979bOU+K4AABUDSURBVDJ/n85u9uvXc0hpixbm71PQjogfu/Dyy5wM/MILnOP0ww90BZuBUqw427+fngUZzGdfwsJ4w5ZKE2OoXZtVl+HhIn7sSs+ewJYtTDquWpWCyCwiI4GnnmK+0bJlQMOG5u1LsBUS9rIT3box6fi334AOHcyLe0+Zwpj2jBlyA7AziYnsSyMhL+PIlQuoWVPyfuzO5Mksg2/fHjh/3px9XLkCNGsG7NnD5q4ifPwKET92o317ztNatowdoW/eNHb7//wDvPkmHxLXtjc7djAXQZKdjUWSnu1P9uzAr78yN6tDByYjG8mFC0CjRsDx48CaNeZ6lwRbIuLHjjz5JDssr1tHl2x0tDHbPXmSF5JGjdi4S7A34eFAjhxAjRq6LfEtQkI4tNcsj4JgDMWLUwBt2sTFmlGcPg00aEDPz9q1nDQv+B0ifuxK06bAihXA9u3sSXL9eua2FxsLtGvH3kLz5jHvQbA3YWEcNZItm25LfAunJ028P/YnNJRh+qlT2R0/sxw9yoGq8fFcXFaunPltCl6JiB87ExoKrFoFHDwINGkCXLrk2XaUAvr0YWx74UKgcGFj7RSMx4uGmXodJUoApUuL+PEWXnmFSdB9+rATtKfs30+PT9as9PiUL2+cjYLXIeLH7tSuzTyds2eBunVZleAuU6eyemz6dAmheAsnTvA7l3wfcwgJoWdNsD8BAbyGVatG77Uni8CVK7mQyJ+fwqdUKePtFLwKET/eQNWqrPopWBB45BFWhLnKv/8Cgwbx0bWreTYKxuK8MT/yiF47fJWQEIaU4+J0WyK4Qo4crIKNj2dj1qQk116nFEdntGjBEPK6dUCxYubaKngFIn68hVKleOK2bQt06sTO0HfrUnvqFBOcH3sMGDfOGjsFYwgPBx54QEKUZhEaygqibdt0WyK4SsmSHIGxfj3H8dyN2Fjg+eeZLP3WWywiKVDAfDsFr0DEjzeRKxf784wfTzHTqlX6idDOdu05cgA//ywJzt5GWJjk+5hJ1apM/pe8H++iQQN6cj77jNfC9Dh5Enj0UXqL5s4Fxo6VLvbCLYj48TYCAriK+fNPdmeuWxfYt+/W5ygFvPYasHs3E5yLFNFjq+AZUVH87iTfxzyyZGFvF8n78T769aNH5+WX2QvrdtauZa7k5cv8fjt1st5GwfaI+PFWWrRgC/hs2XgRX7Ik5W9ffQV89x3wzTfskip4F5s2ccCteH7MxdnsUCndlgjuEBAATJvGMvV27divB+D3+OWXbBMSHMzKMCnwENJBxI83U6ECvT9Nm7Ib9OjRXPUMHAgMGAB0767bQsETwsOZ3F6pkm5LAACvvPIKAgICMGnSJN2mGEtoKCuHjhzRbYngLjlzAgsWADdu0LMTE8N5hX370uu9YoV4vIUMkUQQb+eeexjX/vBD4IMP2Ba+Xj3g0091WyZ4inOYaaD+tcmiRYuwadMmFC9eXLcpxlO/Pv8NC+NCQvAuSpdm5WuzZlwoXLlCj/cLL+i2TPAC9F9dhcwTGAgMHw68+CIrWK5cYcKf4H0kJwMbN9oi5HXmzBn069cPs2fPRtasWXWbYzz58zM8IknP3kuuXFwAnj3LXmYifAQXEfHjS8ycyXL4pCT2tPj7b90WCe4SEcFZbpqTnR0OB7p37463334bwcHBWm0xFRly6r3MnMlJ7FWqMMz13HO6LRK8CBE/vkZoKBsi1qsHPPEEMGGCJHR6E2FhrESqU0erGWPHjkWWLFkwYMAArXaYTmgox75kdnaeYB2JiUD//hx50aMHsHo18Pjjuq0SvAwRP75IgQLAH38Ab7/Nsvjnn2fDL8H+hIcDNWsyodMiZs+ejTx58vz/499//8XkyZMxa9YsBAQEWGaHFkJCuDjYuFG3JYIrXLpEoTNtGh/ffMM8R0FwkwClxC3g08ydyxXSQw+x50/JkrotEjKibFngmWfYyM0ioqOjceHChf///y+//IL3338fgakSrpOTkxEYGIiSJUvi+PHjd2wjKioK+fLlQ8uWLZHltoaanTt3RufOnU2zP1MoBRQtCrz6KjBqlG5rhIzYvp3nRlwcizwefVS3RYIXI+LHH9ixg2Mx4uKA779nOEywH2fPcuL4L78Azz6rzYwrV67g3Llzt/yuRYsW6N69O1588UU88MADd7zGKX4iIyORN29eq0w1hjZtWDK9apVuS4S0UIrXrVdfZYK6LOIEA5Cwlz9QowYbfj38MNCyJfthREfrtkq4HWfireZk50KFCqFKlSq3PLJmzYpixYqlKXy8ntBQNpZ0dVimYB3nz3Ph9uKL7Oezbp0IH8EQRPz4C0WKAMuWMU4+Zw5nG61Zo9sqITVhYUCZMoAv9tSxMyEhbJK3e7duSwQnSgHz5tHTs3EjGxp+952luXCCbyPix58ICABeeYUX+TJlgCZNWDURE6PbMgGg58cG/X3S4vjx43j99dd1m2EOtWoBWbPKnC+7cOkSy9Y7d2b3+j17mOsjCAYi4scfKVuW5aGTJwMzZjAcJhd+vdy8yYROGWZqPTlzssJO+v3oZ8ECenvWrGH35p9/BgoX1m2V4IOI+PFXAgM5/2vnTobEHnuMZfFxcbot80+2bmXOiU09Pz5PaKiIH51cvQp07Qq0b88FQESENC0UTEXEj79TqRKTCMeOBT7/nMnRmzfrtsr/CAtjm/4qVXRb4p+EhAAnTgBnzui2xP9YupTH/Z9/Aj/+yGquYsV0WyX4OCJ+BCAoiA0Rt28HcufmjWDoUM4JE6whPJyDNoOCdFvinzjDjRs26LXDn4iMBF56CXj6aYbeIyKAbt2YmygIJiPiR0ghOJgX/+HD6QmqU4dhMcFcHA5bJzv7Bffdx1w4yX2zhhUr6O359Vdg+nR6f0qU0G2V4EeI+BFuJWtW4IMPgC1b+P86dYAPP+Q8HcEcDh5kzoMkO+tFhpyaT3Q00KcP0KIF8OCD9Pb07CneHsFyRPwIafPwwxRA77wDjBwJPPIIS04F4wkLYwJ6vXq6LfFvQkIY+pU5eOawZg1QrRrw00/Al1/S+1OqlG6rBD9FxI+QPtmyAaNHMxR28ybLgceNA5KTdVvmW4SHs+mkt42F8DVCQ1lxt3Wrbkt8i5gYVpY2aUKx899/HFUh3h5BIyJ+hLtTpw5XxAMGAO++y7J4yQUyjrAwyfexA1WqAHnySN6PkfzzD73I334LTJpE70+5crqtEgQRP4KL5MgBjB/PsvirV+kFeuklDuMUPOfyZeDAAcn3sQNBQay4k7yfzHPgAAfGNm4MFC0K7NoFDBzI8K4g2AA5EgX3CA3leIzPPweWLAEqVgRGjJARGZ7iLK0Wz489cCY9K6XbEu/k8mWOzKlShYJnzhwumCpV0m2ZINyCiB/BfbJmBfr2BQ4fBvr1Az7+mCJo5kzJB3KXsDAOMi1dWrclAkAReuUKcOiQbku8i7g4eoYrVAB++IG5gvv3cz6XeHsEGyJHpeA5+fKxH9D+/UCDBixZrVULWLlSt2XeQ3g4vQ2S/GkP6tXjdyGhL9dQijO4KlcG3nuPTQoPH2aVaI4cuq0ThHQR8SNknrJlgXnzGMLJlQt4/HF2bd23T7dl9iYhge0EJORlH/LlY8hGkp7vTng4W2B06sRqxYgIYOpUzgoUBJsj4kcwjvr1edP4+Wdg715eEF97Dbh4Ubdl9mTHDoYLJNnZXsiQ04w5cgTo0IGfU0ICsHo1sHgxmxYKgpcg4kcwloAAXhj37QM++YQJjxUq8GeZGH8rYWFAzpwcJivYh5AQivdr13RbYi+uXQPefJMhrg0bgO+/Z0+kxo11WyYIbiPiRzCH7NmBt95i/P+FFzgy44EHKIYcDt3W2YPwcPZQyppVtyVCapyeuI0b9dphFxIS2KOnfHng66+BYcM4kuX55yWZWfBa5MgVzKVwYWDKFI7GqFED6NqVeQL+nlOhlDQ3tCvlygH33ivHqFLAggUcePzmm8Czz3IxM3Qoc/sEwYsR8SNYQ6VKwKJF7PCalAQ8+igvpkeO6LZMD8ePA+fPS76PHQkI4Pfiz+Jn82ZWcLZvz7D1rl3AN98AxYrptkwQDEHEj2AtjRqxwumHH4BNm5gk+fzzvLj6E84bq4gfexISQgGQlKTbEutQCli/HnjmGZb8R0YCy5cDf/3FCjhB8CFE/AjWExgIdO/OFvhjx6bM/2nenJOe/aG7bng4E0cLFtRtiaF06tQJrVu3xty5c3WbkjlCQjjM1x9EeVIS8MsvDEc/9hjPy5kzWY3YvLlu6wTBFAKU8oc7jWBrEhOBX38FPv2UA1SrVmWydKdOnCzvi1SvzmTn6dN1W2IIUVFRyJcvHyIjI5HXF6bTx8cDefPymOzfX7c15nDjBkXOZ58xDNu4MXN7WraURGbB55EjXNBP1qxsg791K3uGlCwJ9OjB5oljxwLXr+u20FiiojgfTZKd7Uv27EDt2r7Z7+fsWXZjLlkSeOMNerm2beO599RTInwEv0COcsE+BARw9bl0KavDWrZkWW3JksCgQcCJE7otNIaNGxnak3wfe+NrSc+7d7PtRJkywBdfcBzN0aPA7NlAzZq6rRMESxHxI9iThx5iSOjECWDgQDZUK18+xUPkzYSHA4UKyaRruxMSApw6xYe3ohTw999AixZAtWrAqlUcRHzqFEN6pUrptlAQtCDiR7A3xYpxQvSpU2y0tnkzc2UaNwb++MM7GyaGhckwU2/A6ZnbsEGvHZ6QkMCKSmchwaVL9PAcPcq8nnz5dFsoCFoR8SN4B7lzA/36sbPsr78CsbFAq1ZswDZ9uveMzkhKYthL8n3sz7330tvoTXk/168zT65sWebN3X8/c3m2bQO6dJFu4oLwP0T8CN5FUBAbr23YwJ4kDz4I9O4NlC5ND9GVK7otzJiICFbZiPjxDrwl7+f4ceD11yl2hg0DnnySeXNLl9JLKl5GQbgFET+CdxIQQAGxcCGwfz/Qrh0wZgxQvDibtP3yC71DdiMsjKvvWrV0WyK4Qmgo+93ExOi25E4iI4FZsxjWKl8e+PHHlMKAb79l3pwgCGki4kfwfipVAr76Cjh5ki7/M2eA555j2OKFF5jwmZys20oSHk7hkzOnbksEVwgJ4bFjlyT7uDgK/g4deHy/9BL7ZH39NfPiPvxQRlAIgguI+BF8hyJF6PrfvJldat98k2KjeXOgRAn+bcsWvR2kncnOgnfw0ENsdqgz9JWczLydXr0obNq140y8MWMo+Nes4d9k2KgguIx0eBZ8G6WY7Dl7NjBvHoeJVqzI5M8uXawtNz9zhjkZv/3GG5gP4XMdnlPTogVDlX/8Yd0+lWK3c+dxe+4cQ1tdurDdQ+XK1tkiCD6IiB/Bf0hO5ip59mwKkOhodvHt2hXo2BG47z5z9//LLwzHnTvnc6EJnxY/o0YBkyezXNzs7seHDgFz5vBx8CBQtCjHvHTpAtStK4nLgmAQEvYS/IegIKBZM+C774ALFyhGSpYE3nmHHpnHH+ffIiPN2X94OFCunM8JH58nJAS4epWhVDM4d449rOrWpSdywgQOGV2xgt7CyZM5ZV2EjyAYhogfwT/JmRN49llgwQKGwr75hp6hnj2ZSPrss0wsjY83bp+S7+Od1K1Lj4+R/X4iIym0mzWj8H7nHeal/fILhfmsWRTjWbIYt09BEP4fCXsJQmpOnwbmz2dobMcOdsJt2jTlUamSZyvwmze5rc8/B/r0Md5uzfh02Atgp+RatYAZMzx7vcPB2VqrV3PExMqV7MLcuDFDWu3aAQUKGGuzIAjpIuJHENJj3z7g5595o9q4kd2ZS5QAmjShEGrShGEzV/j3X6BRI2DXLs5Y8jF8Xvz07UvRsn+/a89XCjh8mK9ZvZq5ZpcvAzlyAI8+yqG9HTvyeBIEwXJE/AiCK9y4Aaxbl7Jy37mTN7iKFVO8Qo0aAYULp/36jz5iD6KrV5l75GP4vPiZPRvo1o1Jz+l9x2fOpIid1avZdycoiGEz5zFSvz4FkCAIWhHxIwiecOUKV/NOMXTwIMNh1aun3OgeewzIk4fPf/ppNqNbvlyv3Sbh8+Ln2DEmqy9Zwu8SuPUYWL06JSHaeQw0aQI0aADcc48+uwVBSBMRP4JgBKdOpdwEV62iFyBLFlbpNGkCfPYZRw+MGqXbUlPwefGjFFshNGgAlCrF73jXrlu9f02aMIcnPc+QIAi2QcSPIBiNUvQErVqVktwaFcVwR4MGvEnWrAlUqcKydx8oYfY58aMUk98jIjhEd/VqVnspxTwdp9hxJ+9LEATbIOJHEMwmMpJVQrGxzBtat47VXwBQsCBFUOpHcDB/70V4rfhRCrh4kRPQIyJSHnv2ULACQKFC9OiUKQNUrQp07+4TglUQ/BkRP4JgNcnJzCFJfbONiGDOSFISn1O8+J2i6KGHgNy59dqeDl4hfq5du1XkOH++fJl/z56dYyOcAtT5uZcqZX5nZ0EQLEXEjyDYhYQEhstuF0VHj9JDERAAlC17pyh64AEgWzatpttK/Ny4Aezde6c35+xZ/j0oiP2abve2lS8vTQUFwU8Q8SMIdicmhj2HbhdFZ87w71my8GZetixnQRUtygn3zp9T/84kkWSJ+ImLY4jq0qVb/3X+fP48vWfHjvH5AQGs0Lrdk1OpEr08giD4LSJ+BMFbuT2Mc+pUihi4eJEekNvJnz9jgZT6UbCgy+Eej8RPYiJFy+0iJr2fo6Pv3EbevLe+l4oVU0RO5cpArlyu2SIIgl8h4kcQfJXY2FsFxN0eiYm3vj4wkAIoo6aM/0v8jXI4kO/iRbTMlg1ZAgLQOUcOdM5IeMTGAtev3/n7nDk5Wy21MEvv58KFpWGgIAgeIeJHEATmFEVF3SmIrlzhXKr0XvM/ouLikO+jjxA5ZAjy5shxy9/SJHv2tEWNTRO6BUHwLUT8CIKQaWyV8CwIgnAXpH5TEARBEAS/QsSPIAiCIAh+hYgfQRAEQRD8ChE/giAIgiD4FSJ+BEEQBEHwK0T8CIIgCILgV4j4EQRBEATBrxDxIwiCIAiCXyHiRxAEQRAEv0I6PAuCkGmUUoiOjsY999yDgP/N+xIEQbArIn4EQRAEQfArJOwlCIIgCIJfIeJHEARBEAS/QsSPIAiCIAh+hYgfQRAEQRD8ChE/giAIgiD4FSJ+BEEQBEHwK0T8CIIgCILgV/wf8TurhA619okAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 30 graphics primitives" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(stereoN, number_values=15, ranges={th: (pi/8,pi)})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

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

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

\n", "

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

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

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

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

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

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

We have of course

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

Let us introduce some point at the equator:

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

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

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

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

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

which is not possible for the point $N$:

" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "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": [ "

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

\n", "

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

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

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

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

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

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

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

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

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

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

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

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

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

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

We may also add the two poles to the graphic:

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

Tangent spaces

\n", "

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

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

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

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

Its dimension equals the manifold's dimension:

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

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

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

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

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

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

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

Differential of a smooth mapping

\n", "

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

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

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

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

Algebra of scalar fields

\n", "

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

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

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

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

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

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

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

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

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

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

A specific element is the zero one:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The arithmetic of scalar fields:

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

Module of vector fields

\n", "

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

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

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

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

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

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

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

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

because $U$ is parallelizable:

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

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

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

Similarly

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

" ] }, { "cell_type": "code", "execution_count": 157, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_v = v.plot(chart=cart, mapping=Phi, chart_domain=spher, \n", " number_values=11, scale=0.2)\n", "show(graph_spher + graph_v, viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The code in the following cell is a workaround for a bug that has been revealed in Sage 8.2; it has been corrected in Sage 8.3.beta2, so that the code below can be removed when Sage 8.3 is released. " ] }, { "cell_type": "code", "execution_count": 158, "metadata": {}, "outputs": [], "source": [ "S2._frames = S2._frames[:-1]\n", "U._frames = U._frames[:-1]\n", "V._frames = V._frames[:-1]\n", "W._frames = W._frames[:-1]\n", "A._frames = A._frames[:-1]\n", "S2._top_frames = S2._top_frames[:-1]\n", "U._top_frames = U._top_frames[:-1]\n", "V._top_frames = V._top_frames[:-1]\n", "W._top_frames = W._top_frames[:-1]\n", "A._top_frames = A._top_frames[:-1]" ] }, { "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": 159, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial x }$ " ], "text/plain": [ "Vector field d/dx on the Open subset U of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 159, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ex = stereoN.frame()[1]\n", "ex" ] }, { "cell_type": "code", "execution_count": 160, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_ex = ex.plot(chart=cart, mapping=Phi, chart_domain=spher,\n", " number_values=11, scale=0.4, width=1, \n", " label_axes=False)\n", "show(graph_spher + graph_ex, viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 161, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial y }$ " ], "text/plain": [ "Vector field d/dy on the Open subset U of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 161, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ey = stereoN.frame()[2]\n", "ey" ] }, { "cell_type": "code", "execution_count": 162, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_ey = ey.plot(chart=cart, mapping=Phi, chart_domain=spher,\n", " number_values=11, scale=0.4, width=1, color='red', \n", " label_axes=False)\n", "show(graph_spher + graph_ey, viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may superpose the two graphs, to get a 3D view of the vector frame associated with the stereographic coordinates from the North pole:" ] }, { "cell_type": "code", "execution_count": 163, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_frame = graph_spher + graph_ex + graph_ey + \\\n", " N.plot(cart, mapping=Phi, label_offset=0.05, size=5) + \\\n", " S.plot(cart, mapping=Phi, label_offset=0.05, size=5)\n", "show(graph_frame + sphere(color='lightgrey', opacity=0.4), \n", " viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The same scene rendered with Tachyon:" ] }, { "cell_type": "code", "execution_count": 164, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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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": 165, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field v(f) on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} v\\left(f\\right):& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & -\\frac{4 \\, {\\left(x - 2 \\, y\\right)}}{x^{4} + 2 \\, x^{2} y^{2} + y^{4} + 1} \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & -\\frac{4 \\, {\\left({x'}^{3} - 2 \\, {x'}^{2} {y'} + {x'} {y'}^{2} - 2 \\, {y'}^{3}\\right)}}{{x'}^{4} + 2 \\, {x'}^{2} {y'}^{2} + {y'}^{4} + 1} \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & -\\frac{2 \\, {\\left({\\left(\\cos\\left({\\phi}\\right) - 2 \\, \\sin\\left({\\phi}\\right)\\right)} \\cos\\left({\\theta}\\right)^{2} - 2 \\, {\\left(\\cos\\left({\\phi}\\right) - 2 \\, \\sin\\left({\\phi}\\right)\\right)} \\cos\\left({\\theta}\\right) + \\cos\\left({\\phi}\\right) - 2 \\, \\sin\\left({\\phi}\\right)\\right)} \\sqrt{\\cos\\left({\\theta}\\right) + 1}}{{\\left(\\cos\\left({\\theta}\\right)^{2} + 1\\right)} \\sqrt{-\\cos\\left({\\theta}\\right) + 1}} \\end{array}$ " ], "text/plain": [ "v(f): S^2 --> R\n", "on U: (x, y) |--> -4*(x - 2*y)/(x^4 + 2*x^2*y^2 + y^4 + 1)\n", "on V: (xp, yp) |--> -4*(xp^3 - 2*xp^2*yp + xp*yp^2 - 2*yp^3)/(xp^4 + 2*xp^2*yp^2 + yp^4 + 1)\n", "on A: (th, ph) |--> -2*((cos(ph) - 2*sin(ph))*cos(th)^2 - 2*(cos(ph) - 2*sin(ph))*cos(th) + cos(ph) - 2*sin(ph))*sqrt(cos(th) + 1)/((cos(th)^2 + 1)*sqrt(-cos(th) + 1))" ] }, "execution_count": 165, "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": 166, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$ " ], "text/plain": [ "0" ] }, "execution_count": 166, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf(N)" ] }, { "cell_type": "code", "execution_count": 167, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}4$ " ], "text/plain": [ "4" ] }, "execution_count": 167, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf(E)" ] }, { "cell_type": "code", "execution_count": 168, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$ " ], "text/plain": [ "0" ] }, "execution_count": 168, "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": 169, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1-form df on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "df = f.differential() ; print(df)" ] }, { "cell_type": "code", "execution_count": 170, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}f = \\left( -\\frac{4 \\, x}{x^{4} + 2 \\, x^{2} y^{2} + y^{4} + 1} \\right) \\mathrm{d} x + \\left( -\\frac{4 \\, y}{x^{4} + 2 \\, x^{2} y^{2} + y^{4} + 1} \\right) \\mathrm{d} y$ " ], "text/plain": [ "df = -4*x/(x^4 + 2*x^2*y^2 + y^4 + 1) dx - 4*y/(x^4 + 2*x^2*y^2 + y^4 + 1) dy" ] }, "execution_count": 170, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.display()" ] }, { "cell_type": "code", "execution_count": 171, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module Omega^1(S^2) of 1-forms on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(df.parent())" ] }, { "cell_type": "code", "execution_count": 172, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\Omega^{1}\\left(\\mathbb{S}^2\\right)$ " ], "text/plain": [ "Module Omega^1(S^2) of 1-forms on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 172, "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": 173, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field df(v) on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\mathrm{d}f\\left(v\\right):& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & -\\frac{4 \\, {\\left(x - 2 \\, y\\right)}}{x^{4} + 2 \\, x^{2} y^{2} + y^{4} + 1} \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & -\\frac{4 \\, {\\left({x'}^{3} - 2 \\, {x'}^{2} {y'} + {x'} {y'}^{2} - 2 \\, {y'}^{3}\\right)}}{{x'}^{4} + 2 \\, {x'}^{2} {y'}^{2} + {y'}^{4} + 1} \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & -\\frac{2 \\, {\\left({\\left({\\left(\\cos\\left({\\phi}\\right) - 2 \\, \\sin\\left({\\phi}\\right)\\right)} \\cos\\left({\\theta}\\right) - 3 \\, \\cos\\left({\\phi}\\right) + 6 \\, \\sin\\left({\\phi}\\right)\\right)} \\sin\\left({\\theta}\\right)^{3} - 4 \\, {\\left({\\left(\\cos\\left({\\phi}\\right) - 2 \\, \\sin\\left({\\phi}\\right)\\right)} \\cos\\left({\\theta}\\right) - \\cos\\left({\\phi}\\right) + 2 \\, \\sin\\left({\\phi}\\right)\\right)} \\sin\\left({\\theta}\\right)\\right)}}{\\sin\\left({\\theta}\\right)^{4} + 2 \\, {\\left(\\cos\\left({\\theta}\\right) - 2\\right)} \\sin\\left({\\theta}\\right)^{2} - 4 \\, \\cos\\left({\\theta}\\right) + 4} \\end{array}$ " ], "text/plain": [ "df(v): S^2 --> R\n", "on U: (x, y) |--> -4*(x - 2*y)/(x^4 + 2*x^2*y^2 + y^4 + 1)\n", "on V: (xp, yp) |--> -4*(xp^3 - 2*xp^2*yp + xp*yp^2 - 2*yp^3)/(xp^4 + 2*xp^2*yp^2 + yp^4 + 1)\n", "on A: (th, ph) |--> -2*(((cos(ph) - 2*sin(ph))*cos(th) - 3*cos(ph) + 6*sin(ph))*sin(th)^3 - 4*((cos(ph) - 2*sin(ph))*cos(th) - cos(ph) + 2*sin(ph))*sin(th))/(sin(th)^4 + 2*(cos(th) - 2)*sin(th)^2 - 4*cos(th) + 4)" ] }, "execution_count": 173, "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": 174, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 174, "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": 175, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 175, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.lie_derivative(v) == v(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 176, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Real number line R\n" ] } ], "source": [ "R. = RealLine() ; print(R)" ] }, { "cell_type": "code", "execution_count": 177, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathbf{Smooth}_{\\Bold{R}}$ " ], "text/plain": [ "Category of smooth manifolds over Real Field with 53 bits of precision" ] }, "execution_count": 177, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R.category()" ] }, { "cell_type": "code", "execution_count": 178, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}1$ " ], "text/plain": [ "1" ] }, "execution_count": 178, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dim(R)" ] }, { "cell_type": "code", "execution_count": 179, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left(\\Bold{R},(t)\\right)\\right]$ " ], "text/plain": [ "[Chart (R, (t,))]" ] }, "execution_count": 179, "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": 180, "metadata": {}, "outputs": [], "source": [ "c = S2.curve({spher: [2*atan(exp(-t/10)), t]}, (t, -oo, +oo), name='c')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 181, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Hom}\\left(\\Bold{R},\\mathbb{S}^2\\right)$ " ], "text/plain": [ "Set of Morphisms from Real number line R to 2-dimensional differentiable manifold S^2 in Category of smooth manifolds over Real Field with 53 bits of precision" ] }, "execution_count": 181, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.parent()" ] }, { "cell_type": "code", "execution_count": 182, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} c:& \\Bold{R} & \\longrightarrow & \\mathbb{S}^2 \\\\ & t & \\longmapsto & \\left(x, y\\right) = \\left(\\cos\\left(t\\right) e^{\\left(\\frac{1}{10} \\, t\\right)}, e^{\\left(\\frac{1}{10} \\, t\\right)} \\sin\\left(t\\right)\\right) \\\\ & t & \\longmapsto & \\left({x'}, {y'}\\right) = \\left(\\cos\\left(t\\right) e^{\\left(-\\frac{1}{10} \\, t\\right)}, e^{\\left(-\\frac{1}{10} \\, t\\right)} \\sin\\left(t\\right)\\right) \\\\ & t & \\longmapsto & \\left({\\theta}, {\\phi}\\right) = \\left(2 \\, \\arctan\\left(e^{\\left(-\\frac{1}{10} \\, t\\right)}\\right), t\\right) \\end{array}$ " ], "text/plain": [ "c: R --> S^2\n", " t |--> (x, y) = (cos(t)*e^(1/10*t), e^(1/10*t)*sin(t))\n", " t |--> (xp, yp) = (cos(t)*e^(-1/10*t), e^(-1/10*t)*sin(t))\n", " t |--> (th, ph) = (2*arctan(e^(-1/10*t)), t)" ] }, "execution_count": 182, "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": 183, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 183, "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": 184, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_c = c.plot(mapping=Phi, max_range=40, plot_points=200, \n", " thickness=2, label_axes=False)\n", "show(graph_spher + graph_c, viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 185, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{c'}$ " ], "text/plain": [ "Vector field c' along the Real number line R with values on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 185, "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": 186, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector field c' along the Real number line R with values on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(vc)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 187, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathfrak{X}\\left(\\Bold{R},c\\right)$ " ], "text/plain": [ "Module X(R,c) of vector fields along the Real number line R mapped into the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 187, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent()" ] }, { "cell_type": "code", "execution_count": 188, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathbf{Modules}_{C^{\\infty}\\left(\\Bold{R}\\right)}$ " ], "text/plain": [ "Category of modules over Algebra of differentiable scalar fields on the Real number line R" ] }, "execution_count": 188, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent().category()" ] }, { "cell_type": "code", "execution_count": 189, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}C^{\\infty}\\left(\\Bold{R}\\right)$ " ], "text/plain": [ "Algebra of differentiable scalar fields on the Real number line R" ] }, "execution_count": 189, "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": 190, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{c'} = \\left( \\frac{1}{10} \\, \\cos\\left(t\\right) e^{\\left(\\frac{1}{10} \\, t\\right)} - e^{\\left(\\frac{1}{10} \\, t\\right)} \\sin\\left(t\\right) \\right) \\frac{\\partial}{\\partial x } + \\left( \\cos\\left(t\\right) e^{\\left(\\frac{1}{10} \\, t\\right)} + \\frac{1}{10} \\, e^{\\left(\\frac{1}{10} \\, t\\right)} \\sin\\left(t\\right) \\right) \\frac{\\partial}{\\partial y }$ " ], "text/plain": [ "c' = (1/10*cos(t)*e^(1/10*t) - e^(1/10*t)*sin(t)) d/dx + (cos(t)*e^(1/10*t) + 1/10*e^(1/10*t)*sin(t)) d/dy" ] }, "execution_count": 190, "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": 191, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 31 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(vc.plot(chart=stereoN, number_values=30, scale=0.5, color='red') +\n", " c.plot(chart=stereoN), aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 192, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_vc = vc.plot(chart=cart, mapping=Phi, ranges={t: (-20, 20)}, \n", " number_values=30, scale=0.5, color='red', \n", " label_axes=False)\n", "show(graph_spher + graph_c + graph_vc , viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Riemannian metric on $\\mathbb{S}^2$\n", "\n", "The standard metric on $\\mathbb{S}^2$ is that induced by the Euclidean metric of $\\mathbb{R}^3$. Let us start by defining the latter:" ] }, { "cell_type": "code", "execution_count": 193, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}h = \\mathrm{d} X\\otimes \\mathrm{d} X+\\mathrm{d} Y\\otimes \\mathrm{d} Y+\\mathrm{d} Z\\otimes \\mathrm{d} Z$ " ], "text/plain": [ "h = dX*dX + dY*dY + dZ*dZ" ] }, "execution_count": 193, "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": 194, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Riemannian metric g on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "g = S2.metric('g')\n", "g.set( Phi.pullback(h) )\n", "print(g)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we could have defined $g$ intrinsically, i.e. by providing its components in the two frames stereoN and stereoS, as we did for the metric $h$ on $\\mathbb{R}^3$. Instead, we have chosen to get it as the pullback of $h$, as an example of pullback associated with some differential map.\n", "\n", "The metric is a symmetric tensor field of type (0,2):" ] }, { "cell_type": "code", "execution_count": 195, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module T^(0,2)(S^2) of type-(0,2) tensors fields on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(g.parent())" ] }, { "cell_type": "code", "execution_count": 196, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0, 2\\right)$ " ], "text/plain": [ "(0, 2)" ] }, "execution_count": 196, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.tensor_type()" ] }, { "cell_type": "code", "execution_count": 197, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "symmetry: (0, 1); no antisymmetry\n" ] } ], "source": [ "g.symmetries()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expression of the metric in terms of the default frame on $\\mathbb{S}^2$ (stereoN):" ] }, { "cell_type": "code", "execution_count": 198, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\mathrm{d} x\\otimes \\mathrm{d} x + \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\mathrm{d} y\\otimes \\mathrm{d} y$ " ], "text/plain": [ "g = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dx*dx + 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dy*dy" ] }, "execution_count": 198, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may factorize the metric components:" ] }, { "cell_type": "code", "execution_count": 199, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{4}{{\\left(x^{2} + y^{2} + 1\\right)}^{2}}$ " ], "text/plain": [ "4/(x^2 + y^2 + 1)^2" ] }, "execution_count": 199, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[1,1].factor() ; g[2,2].factor()" ] }, { "cell_type": "code", "execution_count": 200, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\frac{4}{{\\left(x^{2} + y^{2} + 1\\right)}^{2}} \\mathrm{d} x\\otimes \\mathrm{d} x + \\frac{4}{{\\left(x^{2} + y^{2} + 1\\right)}^{2}} \\mathrm{d} y\\otimes \\mathrm{d} y$ " ], "text/plain": [ "g = 4/(x^2 + y^2 + 1)^2 dx*dx + 4/(x^2 + y^2 + 1)^2 dy*dy" ] }, "execution_count": 200, "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": 201, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rr}\n", "\\frac{4}{{\\left(x^{2} + y^{2} + 1\\right)}^{2}} & 0 \\\\\n", "0 & \\frac{4}{{\\left(x^{2} + y^{2} + 1\\right)}^{2}}\n", "\\end{array}\\right)$ " ], "text/plain": [ "[4/(x^2 + y^2 + 1)^2 0]\n", "[ 0 4/(x^2 + y^2 + 1)^2]" ] }, "execution_count": 201, "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": 202, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{4}{{x'}^{4} + {y'}^{4} + 2 \\, {\\left({x'}^{2} + 1\\right)} {y'}^{2} + 2 \\, {x'}^{2} + 1} \\right) \\mathrm{d} {x'}\\otimes \\mathrm{d} {x'} + \\left( \\frac{4}{{x'}^{4} + {y'}^{4} + 2 \\, {\\left({x'}^{2} + 1\\right)} {y'}^{2} + 2 \\, {x'}^{2} + 1} \\right) \\mathrm{d} {y'}\\otimes \\mathrm{d} {y'}$ " ], "text/plain": [ "g = 4/(xp^4 + yp^4 + 2*(xp^2 + 1)*yp^2 + 2*xp^2 + 1) dxp*dxp + 4/(xp^4 + yp^4 + 2*(xp^2 + 1)*yp^2 + 2*xp^2 + 1) dyp*dyp" ] }, "execution_count": 202, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(stereoS.frame())" ] }, { "cell_type": "code", "execution_count": 203, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$ " ], "text/plain": [ "g = dth*dth + sin(th)^2 dph*dph" ] }, "execution_count": 203, "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": 204, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field g(v,v) on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(g(v,v))" ] }, { "cell_type": "code", "execution_count": 205, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}C^{\\infty}\\left(\\mathbb{S}^2\\right)$ " ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 205, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(v,v).parent()" ] }, { "cell_type": "code", "execution_count": 206, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} g\\left(v,v\\right):& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & \\frac{20}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & \\frac{20 \\, {\\left({x'}^{4} + 2 \\, {x'}^{2} {y'}^{2} + {y'}^{4}\\right)}}{{x'}^{4} + {y'}^{4} + 2 \\, {\\left({x'}^{2} + 1\\right)} {y'}^{2} + 2 \\, {x'}^{2} + 1} \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & -\\frac{5 \\, {\\left(\\cos\\left({\\theta}\\right)^{4} - 4 \\, \\cos\\left({\\theta}\\right)^{3} + 6 \\, \\cos\\left({\\theta}\\right)^{2} - 4 \\, \\cos\\left({\\theta}\\right) + 1\\right)}}{\\sin\\left({\\theta}\\right)^{2} + 2 \\, \\cos\\left({\\theta}\\right) - 2} \\end{array}$ " ], "text/plain": [ "g(v,v): S^2 --> R\n", "on U: (x, y) |--> 20/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1)\n", "on V: (xp, yp) |--> 20*(xp^4 + 2*xp^2*yp^2 + yp^4)/(xp^4 + yp^4 + 2*(xp^2 + 1)*yp^2 + 2*xp^2 + 1)\n", "on A: (th, ph) |--> -5*(cos(th)^4 - 4*cos(th)^3 + 6*cos(th)^2 - 4*cos(th) + 1)/(sin(th)^2 + 2*cos(th) - 2)" ] }, "execution_count": 206, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(v,v).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **Levi-Civita connection** associated with the metric $g$:" ] }, { "cell_type": "code", "execution_count": 207, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Levi-Civita connection nabla_g associated with the Riemannian metric g on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\nabla_{g}$ " ], "text/plain": [ "Levi-Civita connection nabla_g associated with the Riemannian metric g on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 207, "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": 208, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\nabla_{g} g = 0$ " ], "text/plain": [ "nabla_g(g) = 0" ] }, "execution_count": 208, "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": 209, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, x} \\, x \\, x }^{ \\, x \\phantom{\\, x} \\phantom{\\, x} } & = & -\\frac{2 \\, x}{x^{2} + y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, x} \\, x \\, y }^{ \\, x \\phantom{\\, x} \\phantom{\\, y} } & = & -\\frac{2 \\, y}{x^{2} + y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, x} \\, y \\, y }^{ \\, x \\phantom{\\, y} \\phantom{\\, y} } & = & \\frac{2 \\, x}{x^{2} + y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, y} \\, x \\, x }^{ \\, y \\phantom{\\, x} \\phantom{\\, x} } & = & \\frac{2 \\, y}{x^{2} + y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, y} \\, x \\, y }^{ \\, y \\phantom{\\, x} \\phantom{\\, y} } & = & -\\frac{2 \\, x}{x^{2} + y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, y} \\, y \\, y }^{ \\, y \\phantom{\\, y} \\phantom{\\, y} } & = & -\\frac{2 \\, y}{x^{2} + y^{2} + 1} \\end{array}$ " ], "text/plain": [ "Gam^x_xx = -2*x/(x^2 + y^2 + 1) \n", "Gam^x_xy = -2*y/(x^2 + y^2 + 1) \n", "Gam^x_yy = 2*x/(x^2 + y^2 + 1) \n", "Gam^y_xx = 2*y/(x^2 + y^2 + 1) \n", "Gam^y_xy = -2*x/(x^2 + y^2 + 1) \n", "Gam^y_yy = -2*y/(x^2 + y^2 + 1) " ] }, "execution_count": 209, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.christoffel_symbols_display(chart=stereoN)" ] }, { "cell_type": "code", "execution_count": 210, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, {\\theta}} \\, {\\phi} \\, {\\phi} }^{ \\, {\\theta} \\phantom{\\, {\\phi}} \\phantom{\\, {\\phi}} } & = & -\\cos\\left({\\theta}\\right) \\sin\\left({\\theta}\\right) \\\\ \\Gamma_{ \\phantom{\\, {\\phi}} \\, {\\theta} \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} } & = & \\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)} \\end{array}$ " ], "text/plain": [ "Gam^th_ph,ph = -cos(th)*sin(th) \n", "Gam^ph_th,ph = cos(th)/sin(th) " ] }, "execution_count": 210, "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": 211, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field nabla_g(v) of type (1,1) on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(nab(v))" ] }, { "cell_type": "code", "execution_count": 212, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\nabla_{g} v = \\left( -\\frac{2 \\, {\\left(x - 2 \\, y\\right)}}{x^{2} + y^{2} + 1} \\right) \\frac{\\partial}{\\partial x }\\otimes \\mathrm{d} x + \\left( -\\frac{2 \\, {\\left(2 \\, x + y\\right)}}{x^{2} + y^{2} + 1} \\right) \\frac{\\partial}{\\partial x }\\otimes \\mathrm{d} y + \\left( \\frac{2 \\, {\\left(2 \\, x + y\\right)}}{x^{2} + y^{2} + 1} \\right) \\frac{\\partial}{\\partial y }\\otimes \\mathrm{d} x + \\left( -\\frac{2 \\, {\\left(x - 2 \\, y\\right)}}{x^{2} + y^{2} + 1} \\right) \\frac{\\partial}{\\partial y }\\otimes \\mathrm{d} y$ " ], "text/plain": [ "nabla_g(v) = -2*(x - 2*y)/(x^2 + y^2 + 1) d/dx*dx - 2*(2*x + y)/(x^2 + y^2 + 1) d/dx*dy + 2*(2*x + y)/(x^2 + y^2 + 1) d/dy*dx - 2*(x - 2*y)/(x^2 + y^2 + 1) d/dy*dy" ] }, "execution_count": 212, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab(v).display(stereoN.frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Curvature\n", "\n", "The Riemann tensor associated with the metric $g$:" ] }, { "cell_type": "code", "execution_count": 213, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field Riem(g) of type (1,3) on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Riem}\\left(g\\right) = \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\frac{\\partial}{\\partial x }\\otimes \\mathrm{d} y\\otimes \\mathrm{d} x\\otimes \\mathrm{d} y + \\left( -\\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\frac{\\partial}{\\partial x }\\otimes \\mathrm{d} y\\otimes \\mathrm{d} y\\otimes \\mathrm{d} x + \\left( -\\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\frac{\\partial}{\\partial y }\\otimes \\mathrm{d} x\\otimes \\mathrm{d} x\\otimes \\mathrm{d} y + \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\frac{\\partial}{\\partial y }\\otimes \\mathrm{d} x\\otimes \\mathrm{d} y\\otimes \\mathrm{d} x$ " ], "text/plain": [ "Riem(g) = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) d/dx*dy*dx*dy - 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) d/dx*dy*dy*dx - 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) d/dy*dx*dx*dy + 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) d/dy*dx*dy*dx" ] }, "execution_count": 213, "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": 214, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, x} \\, y \\, x \\, y }^{ \\, x \\phantom{\\, y} \\phantom{\\, x} \\phantom{\\, y} } & = & \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, x} \\, y \\, y \\, x }^{ \\, x \\phantom{\\, y} \\phantom{\\, y} \\phantom{\\, x} } & = & -\\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, y} \\, x \\, x \\, y }^{ \\, y \\phantom{\\, x} \\phantom{\\, x} \\phantom{\\, y} } & = & -\\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, y} \\, x \\, y \\, x }^{ \\, y \\phantom{\\, x} \\phantom{\\, y} \\phantom{\\, x} } & = & \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\end{array}$ " ], "text/plain": [ "Riem(g)^x_yxy = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) \n", "Riem(g)^x_yyx = -4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) \n", "Riem(g)^y_xxy = -4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) \n", "Riem(g)^y_xyx = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) " ] }, "execution_count": 214, "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": 215, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\theta}} \\, {\\phi} \\, {\\theta} \\, {\\phi} }^{ \\, {\\theta} \\phantom{\\, {\\phi}} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} } & = & \\sin\\left({\\theta}\\right)^{2} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\theta}} \\, {\\phi} \\, {\\phi} \\, {\\theta} }^{ \\, {\\theta} \\phantom{\\, {\\phi}} \\phantom{\\, {\\phi}} \\phantom{\\, {\\theta}} } & = & -\\sin\\left({\\theta}\\right)^{2} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\phi}} \\, {\\theta} \\, {\\theta} \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, {\\theta}} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} } & = & \\frac{\\cos\\left({\\theta}\\right)^{2} - 1}{\\sin\\left({\\theta}\\right)^{2}} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\phi}} \\, {\\theta} \\, {\\phi} \\, {\\theta} }^{ \\, {\\phi} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} \\phantom{\\, {\\theta}} } & = & 1 \\end{array}$ " ], "text/plain": [ "Riem(g)^th_ph,th,ph = sin(th)^2 \n", "Riem(g)^th_ph,ph,th = -sin(th)^2 \n", "Riem(g)^ph_th,th,ph = (cos(th)^2 - 1)/sin(th)^2 \n", "Riem(g)^ph_th,ph,th = 1 " ] }, "execution_count": 215, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem.display_comp(spher.frame(), chart=spher)" ] }, { "cell_type": "code", "execution_count": 216, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module T^(1,3)(S^2) of type-(1,3) tensors fields on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(Riem.parent())" ] }, { "cell_type": "code", "execution_count": 217, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "no symmetry; antisymmetry: (2, 3)\n" ] } ], "source": [ "Riem.symmetries()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Riemann tensor associated with the Euclidean metric $h$ on $\\mathbb{R}^3$ is identically zero:" ] }, { "cell_type": "code", "execution_count": 218, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Riem}\\left(h\\right) = 0$ " ], "text/plain": [ "Riem(h) = 0" ] }, "execution_count": 218, "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": 219, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Ric}\\left(g\\right) = \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\mathrm{d} x\\otimes \\mathrm{d} x + \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\mathrm{d} y\\otimes \\mathrm{d} y$ " ], "text/plain": [ "Ric(g) = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dx*dx + 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dy*dy" ] }, "execution_count": 219, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric = g.ricci()\n", "Ric.display()" ] }, { "cell_type": "code", "execution_count": 220, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\mathrm{r}\\left(g\\right):& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & 2 \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & 2 \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & 2 \\end{array}$ " ], "text/plain": [ "r(g): S^2 --> R\n", "on U: (x, y) |--> 2\n", "on V: (xp, yp) |--> 2\n", "on A: (th, ph) |--> 2" ] }, "execution_count": 220, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R = g.ricci_scalar()\n", "R.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hence we recover the fact that $(\\mathbb{S}^2,g)$ is a Riemannian manifold of constant positive curvature.\n", "\n", "In dimension 2, the Riemann curvature tensor is entirely determined by the Ricci scalar $R$ according to\n", "$$ R^i_{\\ \\, jlk} = \\frac{R}{2} \\left( \\delta^i_{\\ \\, k} g_{jl} - \\delta^i_{\\ \\, l} g_{jk} \\right)$$\n", "Let us check this formula here, under the form $R^i_{\\ \\, jlk} = -R g_{j[k} \\delta^i_{\\ \\, l]}$:" ] }, { "cell_type": "code", "execution_count": 221, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 221, "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": 222, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 222, "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": 223, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2-form eps_g on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\epsilon_{g} = \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\mathrm{d} x\\wedge \\mathrm{d} y$ " ], "text/plain": [ "eps_g = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dx/\\dy" ] }, "execution_count": 223, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps = g.volume_form()\n", "print(eps)\n", "eps.display()" ] }, { "cell_type": "code", "execution_count": 224, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\epsilon_{g} = \\sin\\left({\\theta}\\right) \\mathrm{d} {\\theta}\\wedge \\mathrm{d} {\\phi}$ " ], "text/plain": [ "eps_g = sin(th) dth/\\dph" ] }, "execution_count": 224, "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": 225, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3-form deps_g on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(eps.exterior_derivative())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course, since $\\mathbb{S}^2$ has dimension 2, all 3-forms vanish identically:" ] }, { "cell_type": "code", "execution_count": 226, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}\\epsilon_{g} = 0$ " ], "text/plain": [ "deps_g = 0" ] }, "execution_count": 226, "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": 227, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A,(x, y)\\right)$ " ], "text/plain": [ "Chart (A, (x, y))" ] }, "execution_count": 227, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_chart()" ] }, { "cell_type": "code", "execution_count": 228, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A, \\left(\\frac{\\partial}{\\partial x },\\frac{\\partial}{\\partial y }\\right)\\right)$ " ], "text/plain": [ "Coordinate frame (A, (d/dx,d/dy))" ] }, "execution_count": 228, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_frame()" ] }, { "cell_type": "code", "execution_count": 229, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A,({\\theta}, {\\phi})\\right)$ " ], "text/plain": [ "Chart (A, (th, ph))" ] }, "execution_count": 229, "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": 230, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A, \\left(\\frac{\\partial}{\\partial {\\theta} },\\frac{\\partial}{\\partial {\\phi} }\\right)\\right)$ " ], "text/plain": [ "Coordinate frame (A, (d/dth,d/dph))" ] }, "execution_count": 230, "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": 231, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial {\\theta} }\\otimes \\mathrm{d} {\\theta} + \\frac{1}{\\sin\\left({\\theta}\\right)} \\frac{\\partial}{\\partial {\\phi} }\\otimes \\mathrm{d} {\\phi}$ " ], "text/plain": [ "d/dth*dth + 1/sin(th) d/dph*dph" ] }, "execution_count": 231, "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": 232, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rr}\n", "1 & 0 \\\\\n", "0 & \\frac{1}{\\sin\\left({\\theta}\\right)}\n", "\\end{array}\\right)$ " ], "text/plain": [ "[ 1 0]\n", "[ 0 1/sin(th)]" ] }, "execution_count": 232, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a[:]" ] }, { "cell_type": "code", "execution_count": 233, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector frame (A, (e_1,e_2))\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A, \\left(e_{1},e_{2}\\right)\\right)$ " ], "text/plain": [ "Vector frame (A, (e_1,e_2))" ] }, "execution_count": 233, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e = spher.frame().new_frame(a, 'e')\n", "print(e) ; e" ] }, { "cell_type": "code", "execution_count": 234, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}e_{1} = \\frac{\\partial}{\\partial {\\theta} }$ " ], "text/plain": [ "e_1 = d/dth" ] }, "execution_count": 234, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[1].display()" ] }, { "cell_type": "code", "execution_count": 235, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}e_{2} = \\frac{1}{\\sin\\left({\\theta}\\right)} \\frac{\\partial}{\\partial {\\phi} }$ " ], "text/plain": [ "e_2 = 1/sin(th) d/dph" ] }, "execution_count": 235, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[2].display()" ] }, { "cell_type": "code", "execution_count": 236, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left(A, \\left(\\frac{\\partial}{\\partial x },\\frac{\\partial}{\\partial y }\\right)\\right), \\left(A, \\left(\\frac{\\partial}{\\partial {x'} },\\frac{\\partial}{\\partial {y'} }\\right)\\right), \\left(A, \\left(\\frac{\\partial}{\\partial {\\theta} },\\frac{\\partial}{\\partial {\\phi} }\\right)\\right), \\left(A, \\left(e_{1},e_{2}\\right)\\right)\\right]$ " ], "text/plain": [ "[Coordinate frame (A, (d/dx,d/dy)),\n", " Coordinate frame (A, (d/dxp,d/dyp)),\n", " Coordinate frame (A, (d/dth,d/dph)),\n", " Vector frame (A, (e_1,e_2))]" ] }, "execution_count": 236, "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": 237, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}1$ " ], "text/plain": [ "1" ] }, "execution_count": 237, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[1],e[1]).expr()" ] }, { "cell_type": "code", "execution_count": 238, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$ " ], "text/plain": [ "0" ] }, "execution_count": 238, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[1],e[2]).expr()" ] }, { "cell_type": "code", "execution_count": 239, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}1$ " ], "text/plain": [ "1" ] }, "execution_count": 239, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[2],e[2]).expr()" ] }, { "cell_type": "code", "execution_count": 240, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rr}\n", "1 & 0 \\\\\n", "0 & 1\n", "\\end{array}\\right)$ " ], "text/plain": [ "[1 0]\n", "[0 1]" ] }, "execution_count": 240, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[e,:]" ] }, { "cell_type": "code", "execution_count": 241, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = e^{1}\\otimes e^{1}+e^{2}\\otimes e^{2}$ " ], "text/plain": [ "g = e^1*e^1 + e^2*e^2" ] }, "execution_count": 241, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(e)" ] }, { "cell_type": "code", "execution_count": 242, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\epsilon_{g} = e^{1}\\wedge e^{2}$ " ], "text/plain": [ "eps_g = e^1/\\e^2" ] }, "execution_count": 242, "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": 243, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left[\\left[0, 0\\right], \\left[0, 0\\right]\\right], \\left[\\left[0, -\\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)}\\right], \\left[\\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)}, 0\\right]\\right]\\right]$ " ], "text/plain": [ "[[[0, 0], [0, 0]], [[0, -cos(th)/sin(th)], [cos(th)/sin(th), 0]]]" ] }, "execution_count": 243, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e.structure_coeff()[:]" ] }, { "cell_type": "code", "execution_count": 244, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)} e_{2}$ " ], "text/plain": [ "-cos(th)/sin(th) e_2" ] }, "execution_count": 244, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[2].lie_derivative(e[1]).display(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

while we have of course

" ] }, { "cell_type": "code", "execution_count": 245, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left[\\left[0, 0\\right], \\left[0, 0\\right]\\right], \\left[\\left[0, 0\\right], \\left[0, 0\\right]\\right]\\right]$ " ], "text/plain": [ "[[[0, 0], [0, 0]], [[0, 0], [0, 0]]]" ] }, "execution_count": 245, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.frame().structure_coeff()[:]" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.2", "language": "", "name": "sagemath" }, "language": "python", "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.14" } }, "nbformat": 4, "nbformat_minor": 1 }