{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Sphere $\\mathbb{S}^2$ (SymPy version)\n", "\n", "This notebook demonstrates a few differential geometry capabilities of [SageMath](http://www.sagemath.org/) on the example of the 2-dimensional sphere, using [SymPy](http://www.sympy.org) as symbolic engine, instead of SageMath's default one (Pynac+Maxima). The relevent tools have been implemented through the \n", "[SageManifolds](http://sagemanifolds.obspm.fr) project.\n", "\n", "Click [here](https://raw.githubusercontent.com/sagemanifolds/SageManifolds/master/Worksheets/v1.3/SM_sphere_S2_sympy.ipynb) to download the notebook file (ipynb format). To run it, you must start SageMath with the Jupyter interface, via the command `sage -n jupyter`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*NB:* a version of SageMath at least equal to 8.3 is required to run this worksheet:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 8.6.rc0, Release Date: 2019-01-03'" ] }, "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 rendering:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex\n", "from sympy import init_printing\n", "init_printing()" ] }, { "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": [ "We ask for all symbolic computations to be performed with [SymPy](http://www.sympy.org), instead of SageMath's default symbolic engine (Pynac+Maxima, implemented via SageMath's Symbolic Ring):" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "S2.set_calculus_method('sympy')" ] }, { "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": 10, "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": 11, "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": 12, "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": 13, "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": 14, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(U,(x, y)\\right)$ " ], "text/plain": [ "Chart (U, (x, y))" ] }, "execution_count": 14, "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": 15, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}x$ " ], "text/plain": [ "x" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN[1]" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 16, "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": 17, "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": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(V,({x'}, {y'})\\right)$ " ], "text/plain": [ "Chart (V, (xp, yp))" ] }, "execution_count": 18, "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": 19, "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": 19, "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": 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": [ "xp = x/(x^2 + y^2)\n", "yp = y/(x^2 + y^2)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_to_S = stereoN.transition_map(stereoS, \n", " (x/(x^2+y^2), y/(x^2+y^2)), \n", " intersection_name='W',\n", " restrictions1= x^2+y^2!=0, \n", " restrictions2= xp^2+xp^2!=0)\n", "stereoN_to_S.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the above declaration, 'W' is the name given to the chart-overlap subset: $W := U\\cap V$, the condition $x^2+y^2 \\not=0$ defines $W$ as a subset of $U$, and the condition $x'^2+y'^2\\not=0$ defines $W$ as a subset of $V$.\n", "\n", "The inverse coordinate transformation is computed by means of the method `inverse()`:" ] }, { "cell_type": "code", "execution_count": 21, "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": 21, "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": 22, "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": 22, "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": 23, "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": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(W,(x, y)\\right)$ " ], "text/plain": [ "Chart (W, (x, y))" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoN_W = stereoN.restrict(W)\n", "stereoN_W" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(W,({x'}, {y'})\\right)$ " ], "text/plain": [ "Chart (W, (xp, yp))" ] }, "execution_count": 25, "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": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 17 graphics primitives" ] }, "execution_count": 26, "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": 27, "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": 28, "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": 29, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A,(x, y)\\right)$ " ], "text/plain": [ "Chart (A, (x, y))" ] }, "execution_count": 29, "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": 30, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A,({\\theta}, {\\phi})\\right)$ " ], "text/plain": [ "Chart (A, (theta, phi))" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher. = A.chart(r'theta:(0,pi):\\theta phi:(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": 31, "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(phi)*sin(theta)/(cos(theta) - 1)\n", "y = -sin(phi)*sin(theta)/(cos(theta) - 1)" ] }, "execution_count": 31, "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": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Check of the inverse coordinate transformation:\n", " theta == -2*atan(1/tan(theta) - 1/sin(theta))\n", " phi == atan2(sin(phi)*sin(theta)/(cos(theta) - 1), sin(theta)*cos(phi)/(cos(theta) - 1)) + pi\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": 33, "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": [ "theta = 2*arctan(1/sqrt(x^2 + y^2))\n", "phi = pi + arctan2(-y, -x)" ] }, "execution_count": 33, "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": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\begin{array}{lcl} {x'} & = & -\\frac{{\\left(\\cos\\left({\\theta}\\right) - 1\\right)} \\cos\\left({\\phi}\\right)}{\\sin\\left({\\theta}\\right)} \\\\ {y'} & = & -\\frac{{\\left(\\cos\\left({\\theta}\\right) - 1\\right)} \\sin\\left({\\phi}\\right)}{\\sin\\left({\\theta}\\right)} \\end{array}\\right.$ " ], "text/plain": [ "xp = -(cos(theta) - 1)*cos(phi)/sin(theta)\n", "yp = -(cos(theta) - 1)*sin(phi)/sin(theta)" ] }, "execution_count": 34, "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": 35, "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": [ "theta = 2*arctan(sqrt(xp^2 + yp^2))\n", "phi = pi + arctan2(-yp/(xp^2 + yp^2), -xp/(xp^2 + yp^2))" ] }, "execution_count": 35, "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": 36, "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, (theta, phi))]" ] }, "execution_count": 36, "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": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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PdPs20RtvuE9cuhTE4msSnblt27al8+fP05kzZ/77iYqKotjYWDpz5gx5OqL5JC4O19m4sdIzcSxWrECo8pIlKNzWuTOKCU6dypUjB8DBWzE5GJs3Ew0YgFC148eJqlTB4z/+CAdWVBTRe+8pOkWHolkzounTEd1SSNevoKAgioiI0HssICCAwsLCCjzuMBw6BAduSIjSM3Ecjh0jGjmSaNgwxPIToRdvw4ZEH36IoIdVq5ynMZALwjV9KQgC0aefosxshw5Ehw9rBT4RtJgPPiB6/32i3buVm6ejERODhJ3z55WeiW0QO2VxwMOH+C40bEi0eLH2cZUKzdi3bsXOuHFjmMY4ysA4psnNZWzgQMaIGJs+nTGNxvBxeXmMde7MWGgoYzdu2HeOjkpWFmPe3owtXmyX06WlpTEiYmlpabY/WXIyPhMrV9r+XM5ATg5jLVowVqoUY/fuGT/u8mXGatZkLCyMsRMn7Dc/zn9wTd8UOTmIOV69Gj9TphiPv/f0RNmFYsWIevXiKelERL6+aCriisXXxKgkHrkD3n0XO59ffyUqV874cTVq4LiqVdGj152qsToIXOgbQ63GVnXLFnyQX3218NeEhqL07I0bREOHcscukVnOXKfi0CGiUqVQe8bdWbkSmegLFxK98ELhx4eGwgzaoAHMpbxgm13hQt8QGRlE3bujrsiWLbDlSyUiAnXH165Fkoq7ExNDdPcu0b17Ss9EXkR7vrvVVcrPyZOoJjt4MBy4UgkKItq+HZ+PLl3QpYtjF7jQz096OsohHz6MD2XHjuaP0a8f0tAnTiTas0f+OToToqPTlbT93FxEqbi7EzcpCbvhiAiir74yfwH094dS1akTFKsNG2wzT44eXOjr8uQJUsfPn4ewbtXK8rFmzsRYr7yCOH53pXRpFJ5zJbv+uXOorunOQj8vD5/trCyijRvhv7GEIkXQNrRPH/SNXrVK3nlyCsDj9EUePUI5hfv3YWN8/nnrxvP0RJOJqCg4dg8dgmbjjsTEuJamf+gQGtlHRio9E+V4/32EX+7ZY335EW9vCHt/f6LXXsOCKsb4c2SHa/pEEPQtW0Lw799vvcAXKVYMjt2rV/EhdlfHbrNmSMpxlYimuDgs5kWKKD0TZVizBoUG//c/63bDunh6Ei1fTjRqFHwECxbIMy6nAFzo376NolAZGUQHDqD/p5zUq0f03XcI51y4UN6xnYWYGBSoO3ZM6ZnIgzsnZZ09SzRkCDLTx46Vd2wPD0QBTZqEom0zZ8o7PoeI3N28Iwp8b2/UAq9Y0TbneeUVRDm8+y66C7VubZvzOCp16iDtPi7OJte+ZMkSWrJkiX2KsiUk4Med2iOKJCfDVFmzJnrk2iJySaUimj2bKCAAeTF5eajZw5ENFWNuanMQqyPm5kLDN5VQIgd5eSg8deYM6u7baoFxVDp1whZ+2zabnSI9PZ1CQkIoLS3NdmWW163DIv7gAeL03QWNBqGVJ0/i8xsebvtzzpwJwb98OfJeOLLgnuYdtZqoZ0+ix49RKdPWAp8IBcfWrkWXpd69EfXgTohJWs5eZTEuDnWX3EngE0H47tmDRc8eAp8I9axGjkSf6e3b7XNON8D9hL4gEA0aBG3l999R991ehIWhrnh8PJxV7rTJiokhSk0lunxZ6ZlYhzva89evJ/rsM6LPPydq29Z+51WpYOPv0gW5LydP2u/cLoz7Cf2JE/EhXr0abe7sTYMGRN9+S/TTT/qVCF2dRo3gqHPmeP2MDEQhuZPQv3AB2bavvILez/bGywvRQnXqEHXtSnTrlv3n4GK4l9BftAihZgsXwiGlFP374ws0YQJCRN2BoCA4sZ05Xv/4cdi23aXIWmoqvieVK0NRUarkREAAyjIHBsIvlpyszDxcBPeJ3tm4kWjcOKJ33iEaM0bp2RDNmQOnrrhtdYf+us2aEe3aJe1YtZooMRG5E7o/SUn6f+fkaF8jRu80aqTfqDw0lKhkSaISJfBb/BH/L1UKrR0LE2pxcYhCql3bvOt2RgSBKDYWAvb4cQheJSlZEv63pk3hj9uzx/IsYDfHPaJ34uJgi+zRA1tFY+WR7c3jx0jyKVECEUR+fkrPyLasWYNdzqNHuGYiRE9dvw4zgu7P9esFnb7FihUU2joJUunZ2RSydCmljRxJweLjgoCexvkXi+xs/bFDQ1FDRvypUwe/w8K0x3TrhkVG6sLlzHz8MdGMGZbXn7IVR46gJHOXLkS//OI432UnwvWF/tWr0DDr1CHaudPxtINTp2AuePllVOd05aqNt27BVPDGG9DkL1yAY1fU1kuV0he84eFaAR8WhnwKE0gO2WSM6OlT7ULwzz+Yh7jgXL6MEFsi1A6KiEBbxGXLsEucPVue++Go/PYbzDqzZ6PcgqOxeTMi4N5+m+iLL5SejdPh2kL/0SNsB3184EAsVkzpGRlm1SqigQOJvvwSaeiuxM2bKFH955+oaZSUBNNL48YQpLqataj9W4hscfq5uUTXrunvPA4fRmy+hwdRdDR2jm3aQKFwpR1afDzem44doUk7qhKyZAnR6NEoXz5+vNKzcSpcV+hnZqIuSEICvrD2ii22lPHjIfT37iVq3lzp2VhOWhpqo+/Zg2u5fVsrKNu0weKbk4P3RGZsmpz17beon/TFF5i7uIAVKQLB37YtTA4NGjiuoCyM9HT4Q7y8YEYJDFR6RqaZNIlo7lw0OerdW+nZOA9K9Wm0OUOHMubn5zx9OHNyGGvVirGSJRlLSFB6NuahVjO2cSNjffowVqQIesdGRDA2dixjmzczlpqqPXbBAhyjVss+DZv2yB08mLH69bX/CwJj587herp3Zyw4GNddsyZ6KV+/Lv8cbIlGw1jPnoyFhDB29arSs5GGRsNYv36MBQUxdu2a0rNxGlxT6K9ejS/gt98qPRPzePiQsfLlGWvUCE3FHZm8PMb27mVsyBAICiLGGjZk7H//M71oHT+OY+PiZJ+STYV+jRqMvfWW8edzchjbvp2xgQMZCwzENTZuzNjChYwlJso/H7mZNo0xlYqx339XeibmkZbGWJUqjD3/vE0UCVfE9YT+tWv40r36KrQxZ+P4cWjCb7zhmPO/cIGxd95hrGxZCLbKlRmbMoWxS5ekvT4nhzF/fywOMmMzof/4Ma511Sppx2dkMLZ2LWM9ejDm7c2YhwdjHTow9uOPjrmYb90KgT9tmtIzsYyTJxnz8cHOklMoriX01Wqs+FWrQgNwVn74AULmq6+UngkQBMZ272asY0fMq0QJxkaPZuzwYcsWplatGOvVS/Zp2kzob9mC675xw/zXPn7M2DffMNayJcYoVQrmn8eP5Z2jpVy9ip1az54wlzgrixbh/v72m9IzcXhcS+iPHYsV/+RJpWdiPWPGQEs8eFC5OeTkMPbTT7BlEzHWoAG03Zwc68b94AMIP5l3MjYT+u+/z1jp0tbP9/JlxkaMYMzXF/6mt95S1hadns5Y7dowXTmzksQY3psXX2QsNJSxO3eUno1D4zpCf/NmCKaFC5WeiTzk5DDWvDmE47179j13aipjn3/OWLlyuKedOzO2Z498QnrbNowrk7Pzyy+/ZLVq1WLVq1e3jdBv0QJOarl49IixTz7Bjkmlwq7n0CH5xpeCIDDWuzecoPHx9j23rUhOZqxCBcaaNbNeMXFhXEPo37mDFb5nT8e0g1vKgwcQvE2a2MdJlZLC2MSJEATe3ohYOX9e/vM8eQKh/+OPsg5rE00/Jwea+bx58o0pkpkJ00+NGrgfTZvCOW4PZs3COTdtss/57EVcHGOentidcQzi/EI/N5exmBhEvSQnKz0b+Tl6FI7dYcNsd46cHNhEw8IYCwjAF+aff2x3PsZgVhgxQtYhbSL0jx6FcDx8WL4x86PRwG/QqBHO1b27bbXv7duxw/joI9udQ0k++wz3cccOpWfikDi/0P/gA6zsStq+bc2KFfgQf/ONvOMKAhxf1atDCAwZYnthLzJsGGL5ZcQmQv+LL7DoZmfLN6YxBAFRP+Hh+EyPGgVTkJxcv85Y0aKMdeni3I5bU2g0CDooUcJ+n2cnwrmF/u7dEFazZik9E9vz1lswuchl+z1xQhtR0r49Y2fPyjOuVL7/Hu9dSopsQ9pE6Pfrh52kPcnKgk8lJARJX3PmyBPq+ewZY3XrIrpNxvvukDx8yFiZMoy1aYOcEs5/OK/Qf/gQTs727V1XY9ElO5uxF15AFMn9+5aPc+8eEoiIYGL54w9l/CBXr2IO27fLNqTsQl8QkI8wcaI845lLUhJCY728GKtYEbsAS98rQWDs5ZdhvrtwQdZpOix790KxmDFD6Zk4FM4r9Pv3Z6x4cTg73YXERAihpk3NNzcIAuL/Q0Kw7f36a/hDlEIQMI8pU2QbUnahf+eOY8R+X76MIAUi/LYkw3fuXLx+/Xr55+fITJ6MMO7Ll5WeicPgnEJ/zx58gL//XumZ2J/Dh/EhfvNN6a9JTIRzkAha/pMntpufOfTsie23TMgu9NeswT2T265uKZs2oTZTsWLQ+qWyezeygidPtt3cHJXMTGSNt2njWpF9VuB8Ql+thuOxRQv3fROXL4cwWr688GPXroWQKFnS8cLz5syBuUGmHYfsQn/0aMaqVZNnLLlISoKfgQi/C1uQbt7E+9+xo/vatrdvx/36+WelZ+IQOJ/QnzYNNs6LF5WeibKMGAGN31goYX7hkJRk3/lJ4e+/MT+ZKqHKLvSff56xQYPkGUtu1q1DiG2JEqhwaoiMDGRRV6rkmuHM5vDSS1B8HGWXqyDOJfSvXUP4HE+8gE2/WTPY+PPbeH/7zTIzgL3JysLCtWiRLMPJKvSfPkXY5LJl1o9lKxITtbb+2Fj9iBxBwGP+/vaPzHJE7t9H0uHIkUrPRHGcR+gLAioVhodDg+EgBrlMGYQUZmdj+z5pkjbBxxlK+jZtiqgSGZBV6O/di/toi4xkOREE1EcKCYEpStwBL1iA+a9Zo+z8HImFCxHNc+SI0jNRFOcR+uvW4UO8davSM3Es4uIQvz9kCGrkeHigbLGz+DveeQfZ1DIgq9CfPh1JTM4SDnz9OpLdAgMxd09P3FuOltxcmOwaNFA2ck1hnKNdYloaUa1aRE2aEG3cqPRsHI+pU4mmTSPy9yfatImoQwelZySdTZvQ6u7uXaLy5a0aStZ2iV264Pcff1g3jj159oyoXz+iHTuIKlVCg3cfH6Vn5VgcP44ewPPnE40bp/RsFMFD6QlI4qOP0L9z4UKlZ+J4bN6Mvq2hoWjoXbSo0jMyj2bN8DsuTtl56CII6IPbtKnSMzEPT0+iR4/wGbh9m+ill/C94WiJjiZ66y3IlHv3lJ6NIji+0D95Ep3vP/3Uak3QpRAEaPcvvkjUrh3R1atEzz8PrfnhQ6VnJ51SpYiqVEHDdEchPp4oNZUoJkbpmUiHMQizS5fQtH3zZqJ9+7A7vnZN6dk5FjNnoum7m2r6jm3Tz8tjLCqKsXr1eH1sXbKyGOvbFz6OadO0dud791Caonlz57pfr73GWGSkxS+XvZ7+smXwjTx9at049mTJEnweVq7UPhYfj7LNISGM7dun2NQcEjHxbts2pWdidxxb6C9bhjfG3g0mHJmMDNQb8vU1nGz199/IYxgzxv5zs5Svv4bj0UohK5sj9/XX0eTdWRDf87ffLvhcaipj7drh8yJjnSOnRxDwPapSxbkUJBlwXEdudjZR1apEL7xAtGaN0rNxDJ4+JerWDSav338natXK8HFLl2Kr/8MPRIMG2XOGlnHhAlHdujBLtG5d8PnsbKIbN2C2evSo4E9WFhERpeflUciff1Ja27YU7OVF5OFBFBZGVLIkfkqU0P5dsSJ+q1QFz1e9OpzhX35p4wuXgfv3iSIjiWrWJNq9m8jbu+AxajXs+zt2EK1bR9Srl/3n6YicO0dUvz7Rd98RvfGG0rOxG44r9L/6imj0aKKLFxG54+6kpBB16kR05QrR9u2mnYyMEQ0dSvTzz0QHDxJFRdlvnpYgCETFihFNmED0yitYBC5cIDp/Hr+vXSPSaLTH+/joC/LAQCIiSs/NpZAtWyitRw8K9vYmyssjSk4mSkrC4pCSon/e4sWJIiKI6tTB74gIotKliarEpanXAAAgAElEQVRVI1q9mujVV+14EywgO5uoZUsI/pMncT+MkZtLNHAg0a+/Eq1cSdS/v/3m6cj060d04gR8YoYWTBfEMYW+Wg0tv1UrolWrlJ6N8iQlQfNMSCDatQsO28JQqyEQEhPxoTYlEJSCMa3jccYMoidPIKiJIJDr1tUK45o1icqWxXUEBRnU0AsN2czNJXr8GDuGmze1i8vFi1hMdReWoUPhJG/RAudzRIYPhwD/+29EpRSGRoPr+vFHomXL8Le7c+ECUb16RN98QzRsmNKzsQ9K2paMsngxHGlXrig9E+W5f5+xWrXgoDU3OzQhAeUYWrZ0HLtlSgpKPPfvj94ARCjFEB4Ou/OuXeiVYAFW2fTVasbOnUNHKX9/xp57DnPz9ETW8JQpjB0/7jhJb998Y1mlWY0GDXmIkKHKQUZ4hQr26Y7mADie0M/KQj2ZgQOVnony3L0LR9Nzz1m+AB44ACff2LHyzs0csrIY+/VXxnr1goBXqRCVNWkShHxGBmN//glBZEWDD1kcuS+8gMgoQUCjl6+/RrGusDDMr3p1xj75BM8phZiF/dZblr1eEBh7911cz+efyzs3Z+TiRXwmly5VeiZ2wfGE/qJF0K6U/FI5AikpjNWpg45Jt25ZN9bixQXD+WyNRgNBPngwWv4RQdDPn2+4b6lY4MyKPsBWC321GgX9vvii4HO5uVigBg1C4S7xer74wuKdiUXkr7dkKYKA3Yu79qXIz6uvQrlSq5Weic1xLKGfmYkPtKOWs7UXajVjrVoxFhqKWGtrEQTcU19fxk6etH48U6jVjH33HVoxEmGn8vHH0joXWVnK2Gqhf/gw5nzsmOnjMjMZ++UXxl58ETuXIkXQ6F2O98oU2dkQ9oYqq1qCIDA2dCh2gjt3Wj+eMxMfD5PykiVKz8TmOJbQHzwY2t7160rPRDk0Gti7ixRB/LVcZGVBM61QwTadoJKTGZs5E3Z6lYqxHj0Y27/fPBv46NFo2m0hVgv9efMY8/Mzz//x+DFjs2Zp/RPdujH211+2sf2/9RbMOsZ6KFhCbi78GEFBjJ0+Ld+4zshLL+E+3Lyp9ExsiuMI/ZQUrLQeHmgFaK1Jw1l5/30IzV9+kX/su3fRdKN1a/mqDCYmIhHM3x87iREjLO9HKmZJKuHIZYyxPn2QzWwJajXMJBERuIbISPQ1kEv4r1iBca0wfxnl6VPMt0wZ9AV2Nx4+hH8pIAD3eOhQpWdkUxxH6M+fj23mO++g4bmnJ7b67tTQ+Kuv8KGbN89259i3D/d2wgTrxsnIQAnfwECYoaZOtd62ffeuVY3IrRL6ggBt3doGPYLA2I4d6MlKhMip48etG/PoUZiRhg2zbhxTJCYigqp2bffpLpWQgCxmPz98jidNgrZfujRMeC6KYwj9jAyEJA4Zgv+fPYODrGxZaL39+rn+1nPzZuxyxo61fVig2GDDkp6hGg1jP/4Ip5e3NxYPmYTErFmz2ANvb/aFtzcrUaIE69mzJ7tsxqJvldC/eVP+fg3bt8MZT8TYgAFY1MzlwQPGypVjrEkT2zsZL19Gt7WWLV3boXnjBmPDh+PzGxqKaCyxneT161CKDDnzXQTHEPqilp/fpKNWI2SuUiWtvVROe6ajcPo0tI3eve3TvFoQEBLr52feYnrgAJytRAhrlNn30rFjR3azUSOW0aABO3PmDOvatSurUKECe/bsmaTXWyX0V63CdcndSzg3FyaZkiVh/po8GUqNFHJyGGvRAprn/fvyzssYBw/Cn/Taa46TkyAXly7hc+/pifdjzhzG0tMLHjd4MJRQF134lBf6Gg0iPAYMMH5Mbi7CDWvWxBezTRu0s3OFD2V6OtrcNWxo3y1lZiYEeHg4nJGmePYMTlYixho1gmCwFYsWwZShVrNHjx4xImL79++X9FKrhP5bb6Eipa1IT2fsww8h+KtWlXYP334bypAt77chfvoJ7/WKFfY9r604fRpKikqFHeqiRaZbrl66hOt35P7SVqC80N+9GzdYSqSKRsPY+vVod0aETMnff3de4S8IWOwCA5XJS7h9G/6Ttm2NO3YPHoSQ8vNDBqet2weeOPFfZdVr164xImLnjWQiq9VqlpaW9t9PQkKC5UK/fn1oeLbmyhV8blUq+K+MLfQ//oj7oFQI4RtvwDkv9tx1Rg4fhnWAiLHKlVG1V6r23rw5Ah5cEOWFft++cB6ZI7gFAXWwmzbFG9qgAaJd7GEakZPvv7fcti4Xe/diu/vee/qPZ2Uha1Olwn22V0mM3FzGAgKYMGcO6969O3vhhReMHjp16lRGRAV+zBb66enwpyxfbuXkJZKXh0zYIkWwez16VP/5kyexIxg8WDmF5tkzfC8jIkxrxY6GIOAzLTrSa9XCzsXcaLWff8brXTCQRFmh/+ABtq+W1gAR3+C2bfEG1awJDclR6syY4tIlaFJvvKH0TOBT0d3Onj+PL4uPD+ye9l5MW7dmpytVYhUrVmQJCQlGD5NN0xd3m5cuWTlxM7l4EbkTHh5wJmo08ClUqIDHs7LsO5/8nD+PxceWUUNyISqCzZppFcFff7V8Z6pWo/SGtVFuDoiyQn/2bHyo5Ij+OHyYse7d8YaHh8MB7KiOmMxMxurWhWCV6tSzJYLAWGwsFqF58xCvXLeuVXVwrGF7VBRL8vBgN2/cMOt1Ftv0P/0UURy2Nl0ZIjcX51epYIpo0QK5FJZE+tiC5cvxnVqzRumZGEajgXBv2FBr8t22TZ4d0jvvIJpJ6cVXZpQT+hoN7GyvvSbvuGfOINZWpULI5/z5jiFYdRkxAouduVUzbcnTp4hYIGKsZ09F7pkgCGzUqFEstlgxzMOQn0MQMNcbN7DQb97M2LffMrZ0KUubPx9Cf/58FM9avZqxPXtQPTMx0fgWv0MHZKUqybZtMPfYu0ZSYQgCY6+8gkzVa9eUno2W3FyYbWrVsl1wx5UrGHvVKvnGdACUE/o7d9q2FWJ8PJK7PD3hrJw5E63jlObXX3Hdy5YpPRMtaWkom6BSwWHbvr0i/pGRI0eykJAQdnDrVsaIWOr06Sx57VqWPWcOzGCNGsHpjUr8+j+enizNwwNCX8zszn+MSoXw327dkIS1ahXs50FB+HwoyerVmGOpUihQ9/vvys5Hl7Q0RNhFRsqXyW0pajW+O5Ur43517Yqqo7aidWvLs7QdFOWEfu/ecBLZ2lF16xZjI0dCiwoJQdic3LHYUklJwZe6d2/HiTi6eRPakihodu+GwLQ2M9UCihKxXkRsMRHL0hHWuT4+sHG//jocoLoa/IMH/wkiPfOOIMBBq7sjWLYMzunOnRkrX15/QWjSBLvCM2fsb+Y5cwaL7YABUEzEBXjOHPvOwxTHjuFzYctscVNkZMD3V64c7k3fvoydOmX7865di8+HM0cx5UMZof/PP9DAFy2y3znv34eNzt8fPxMm2C/hReStt6BV3rtn3/MaIz4eX6KqVfWjFObOxQfdFvV/8vPPP8h+bNwYX2axMmfNmoipvnZN8q7DbJt+aqo2QqlVK5jciLAzHDoU5gJbLwDJydh9NGyojZLRaKCcECGZy1EUhDFj4O+xp78hLY2xzz6Dn8PTEwujPQVwdjbOrWQ/CplRRujPmAHNJiXF/udOSkId8ZAQRKfYq7jbsWMQLgsW2P5cUjh7FlmJtWsXrG8v2nH9/aFNy01aGhJ/2rWD9ujjgzLFK1Ygd4AxdNciMuszYpEj97XXYLZgDA67vXuxyxGzwMuVg7JgC60yLw/+hLAww5/BefMwh7ffdgzBn5qKomy9etn+XMnJqOcUGopyCcOGKVd9d9IkxooWdZl6PPYX+hoNGoO8/rrdT61HaipK4tqjuFtuLjS5hg2Vt4kyhgJgoaGYjzFT17NnjNWrB61brgJcd+5ghxUUhAWwdWs4YQ2Nf+0aBN4ff0ge3iKhX6UKNNj8CALMQqNHQ9MjQi37jRvl83e8/z4WvT17jB+zdKm28qMj5KGsW4f5bNlim/EfPGBs4kT4bnx9seCZCNu1C9ev45p//FHZeciE/YX+9u24gY5SQ8cexd0WLsTY+ZNwlODgQdjvmzQpXIu+cQOLQ6dO1gmckyfRI8DTExrT5MmFf5EFATuRDz+UfBqzhf6DB9LS7XNzGdu0Ca0UiWAOW7LEuqSlX37BWHPnFn7sjz9icejfX3mlQRAY69gRipucEV5372Lx9fXVVrx88EC+8a2lfXuEg7oA9hf6L7+MGHBH2K7qolajMJbcxd3u34dmO3Kk9WNZy/HjsMm2amW40JQhdu2CwJk82fzzXb0KU4CYO7FwIcItpfLii2alwpst9DduxNzMsVEfOQLFwMMDhdCWLzd/QTx/Hu/Dyy9L/x6sX49ExoEDlf/uXL+OwIhJk+QZa+hQbcXLqVO1FS8dCXGRdqSwVQuxr9BXqyEAp02z62nNwlD8759/Wv5Fe+klaKxK+C90uXED82jc2HwNdc4c3Itff5V2fHIyHF9eXoiSWbnSMg3188/hV5CYYW220H/3XTiLLeHGDWjeRFBipLYbfPIEJqW6dc3XlMVIEjN2PzZj+nS8v5bmmly8CKesh4fpipeOwrNn2IUoFb0kI/YV+mJs/pkzdj2tReTP9GvSxPzibvv24bU//WSzaUri8WPGqleHWcKSVomCgMUrIMB0lq5Gg4isokWxuM+aZZ3z69Ah3D+JTUjMFvrNmkHbtoajR7Vmn06dsBgYIy8PSWChoZY7Jf/3P5zr668te71cqNWoStqunXmvO3UKHcp0K146i4NUzJh2cuwr9N96C7ZApben5mCopoeU4m6CgKSOqChlrzczE3MvXty6remzZ9BOq1UzvGu5cQNfCCI0qJDDHqtWI7JHYm0ms4R+VhbGliOaShBgKgoPx8K4dKnh93zKFAi7HTusO9eYMdCQ5Wz4YgkbNuD9PnCg8GMPHcKCJ4bkLl+OcEhnYtky3PfCSpE7OPYT+oKAld1QpIQzIAjQ3MXibjVqIKzQmOlhzx4cp2RmZV4etCo/P9iireX6dWjxXbtq49cFAW0eAwIg9Pbutf48upihjZsl9M3cRUgiPR0lNoigAev2m920CY/Pnm39efLy4Cvx90cosFJoNFCCjPldBAHfg9attRUvV61S3hltKYmJWLSdPIrHfkL/1Cm88bt32+2UNuPIEf3ibkuX6hdlEgSE9zVqpKyWP3UqPqQW9pw1yPbtGPOjjxDu2bGjVru3hU3WkN09IwM24X37EEK4eDFjM2awtClTIPSnTIGNeMUKLLrHjiEhTve9mDvXLH+BWezciTkHBWF+ly7h7z595Ps8ZGYimqRMGet7E1vDb7/h/d+3T/uYIGAX0qQJnnv+eewKlChoJzdNmiCj3omxn9CfOhUJUc5Q9lgqZ89CC1Wp8OWbNw9mkF27zI4xl529ezEvWzjNZ83C9ZUsCbORNeaKwhDrmo8Zg0JwVapoM3f//cnz8mKPPT3ZTbH2TvHi+Kzlr70THIydw7BhaJoSHW27RTk1FQluRKjUWKuW/IviP/8gh6BjR+UEqiBAqLdoAQ3+l1+0TY6aNcN3wJnMuYUxaxZ2tU5cedN+Qr9hQ3wJXJHLl5Fs5uWF7Mry5ZW15T98iEWoTRvbJPSsXYuYew8P+XduggCTy4cfQqvy9IQAKVoU2asTJkCD//tvhISmpv53nwuYd7KzETJ7+jSSiWbPRglpUSgR4T7FxiLCyJKOW6bIy0PGMxGEoi0iuMTgCCXr9IjavljPqG1baP6uJOxFLl7ENW7bpvRMLMY+Qv/uXceuyS0Xt29r27P5+zP2wQeWRctYg0aDKJISJQqWV7AWQYAzkggFr2rVQlSQHNVLr15FI5Hq1TF+WBji4b/+Gk1FRo8udAjJNn0xw3LaNGR/Rkbif19fnHPTJnl6MYh18qdNQ8ROtWq2aYs5eTIWR1tVrDWGWo33Jzwc9y801LYVLx0BQcBuc8QIpWdiMfYR+l9+CS1Y6Vh1WyMIsONHRqJeS0AAhP+4cfYrsibG1G/fLu+4Gg2ir0RnpCBAgIWEwL9hiXlBEGAK69AB4wYFoRzGzp36zr5Bg2BCKATJQn/lSpxPNwno7l3Y+cVdQMmSENaWVmT9tzw0+/RT/H/9OorIlS4tf3Oa3FyYUipUsE9iU0YGop7Eipf9+sGvQoT309WZMAE7RCf1UdhH6HfogC2fqyO23RMTdR4/hsNTLO42YgRKGduKkyexuE6cKO+4eXkwX6lUBfvIbtuGx6dOlT6eRgNbfb16uF8NGyKqw1i89jffQJMtJJtXstB/803sUoxx8SIyqH19Efk0cqR+JE5hXLkC/0GPHvqC4eFD+BLCwvBeycmdO9C0+/WTd1xd0tKw4IsVL197TdtiUhCQ+Neqle3O7yjs34/PrSOUVbEA2wv9tDSkWNuzjLJS9OnDWJ06BW2Zhr4s8fHynjsvD36EevXkdZbn5MBZ7elpvIPQ9On4EmzeXPh4f/6p1aY7d5bW7ejCBRxvqjAZM0Po163L2JAhhc81KQnafokSKDvw/vuF2/3T02HHr1HDsNkrORkO5JAQ+U0hotNb7gCC5GTGPv4YfhUfH0RqGUpCExvByP3ZdjRyc+Gcd4TMaAuwvdAXq/LZo3yxkiQmQss2tbiJ22KxuFvfvvIVd/vyS9xnOQWJRsPYq69i0d6wwfRxvXrBPGPsC3/tmjbMtUkT8+ap0UDgFBKJJEnop6bi3n/3nfTzp6djx+bnhwXgm28Mb+0FAeF8pu4DJorEvcBAeUs2CwJ21JUqyZPlmpjI2HvvYZ5+foWbKdVqRHONH2/9uR2d115DEygnxPZC//XXoVm5OjNnSm/ynr+4m7Ut3/75B+aEYcMsH8MQEydCQK5fX/ix6ekwmdSsqa8NazSw9/r7Ixt77VrLojo6d0ZoogkkCX0x2sWSMtoJCfAviDWZ8isyYijrpk2Fj/XsGXZmZcpoewjIwZUr0Mat0ULv3IHj3NcXC9jkydJzAd591yWbiRdALMDmKA2RzMD2Qr9GDTgAXRmNBhEMgwaZ9zq5iru9+io0LDmdeOLO4YsvpL/m8mUsPj174p7cuqXNxnzrLfMqbOZn+nSYRDQajHP0KMxN8+fD7DJ0KEuLjYXQj41FXP/06Ygu+f13zEWjgZkiLMy6cMI9e+A0DQzE4i0I+klrUnnwAAt/rVry9SxgDP4Vb2+tvV0q167B7OXtDcE9bZr587p61THqTdma+/dxnaZ2wA6KbYX+kycu1XzAKDt2WGdayV/crWlT6cXdxEQwOe/xb78hBn/cOPNfK0atDBgAIV2hgnWx/IIAYTR+vLaTlW7CVUAABGd0NEtr1AhCPzoaW++SJfUbpAcGYk5VqmBO1tTDT0tDSWBxpxYSgtoy5kZ0XLmCRahFC/m046wsFNdr2VLaZ+jCBeQqeHigh/Pnn1uXSNamDYrQuTrPPSd/0IQdsK3Qt2Yr7Uz06iVPjwBBgBMuJkZacTeNBudt3ly+RJjLlyFI+/SxPAyzXTvMPyrK8jDd+HjkBFSpgrHEJK127VDz6MSJAjsHg+YdjQbmij/+QK9VLy8IfyI4Z198EeYrS23gP/2kbfl49qxlY8TFYS5y9lwQv3umSnCcPAkfhJhYtXixPL4A0Y8nd2iqo9G3r1NW3bSt0J82DQ44J41nlcT9+xBIX34p35iCwNhff6Fbj6nibqJdUa6knMxMRP/UqGGZKSY7G6YmIiQiBQVBk5VKTg5MNlFRGCMkBOaGrVuhWUdGwoFmhEJt+mfOaOvEXLiAshnR0docgTFjTJdGzo8gILLJzw9aX1gYMoUt4euvMQ85m9G3aoUQ0fzfv0OH4CMRK15++628FS+zs7HLctbiilIR6zc5WQE52wr9Ll0Kdb45PTNn2rbJ+9GjiPcWi7t99RW27xoNwkM7dJDvXCNHQuO0RGPNzIQg8fGBppeWhsWjVq3CwxyzsuA7eO45XGeHDrCV5jd3vP02hJQRChX6X30FTT+/WefKFewqiheH1t6nj7R78Pnn2uYyjx/DnOLnZ1mCktizIDjYvIXHFGI8+YYNBSte1q6NEE9bCaxJk7Bou7JD98AB5+kPooPthL4gQPP5+GObncIhaNjQ+kYcUshf3G3AAHzg5Oo1/OuvGG/pUvNf+/QphEl+gRcfDw26Vy/jIY5r12IxE/MXTAlbsXNUYqLBpwsV+rGx0OyNkZGB6xeLug0Zgp2cIcQ2ku+/r30sMxOKjo+PZY3DU1MZq1wZc5RL827bFve3USNtxcuNG22/+z5/Xvmig7YmIwOfW6Ub2piJ7YS+WN/EiQsTFYpYU2j1avud88oVbdigtzciVKzdZTx8iGzOvn3N9w1kZMBpFxRkuJnG5s2Y64wZ+o9fvartONW9u7SEnoQEkxEThQr9SpWkOadzcpBvERYG/8aCBfpC8tYtRLd07FjQ35KdjZ2Cl5e0ZLX8HDuG9/WTT8x/rS55eTAVVa2qNRFu326/ImiCgPvtxDVqJNGwIWODBys9C7OwndAXswMtrV3iDCxZokxNoTVrcG/79IE5JjjYuuJur70GIWbue5WXB0eov7/pHYdY13/bNm1LRT8/aNSFZNkWoHx5RPJcuQLhP3cuEogGDWJpvXtD6PfpgxDRTz5Bt6ODB7GoEMH0JJWUFMZGjcLrWraE2SUjAw72ypWNh8jm5sJBamnzmg8+wPtqSXG2nBxEctWooXV8R0fDFGhv39q4cUhEdGWf3siRpkt6OCC2E/qF2F9dAqVqCkVHa235//xjXXE3sY/vt9+aNwdBQAKPlLZ9Gg2qjwYHQ3gS4bVSG4MLAsw+n32GkELdMMygIJZSogQ76efHdvv5Qei/8AIcmGXK6B8rhpL+8ot5juq9e5FYFhiIaA0/v8Jt/pmZiMKypE1lRga05PbtpWvmYsVLMeGve3ftgvP33/o1oeyF+NlSsruXrfnhByg0clSatRO2E/qNG8OG6qooVVNI7ECW33RgSXG37Gxk0DZrZr42tmAB5iHVnnnkCO6Xp6e0jFXGsKDNmKGtSR8QgL89PWErfvBATygaNO+o1RDQnTtDaIsasJ8f+jvs2CFNsKanYyERd1hS7tfjxzhf1arm7wa3bZNWjjx/xcuXXiroWBQE5C3Yu+NTbi7MhlOm2Pe89uTyZbxPTtQR0DZCX2xo7cpF1sRYZDlT6KUwYgS+4MaiLlJTUQ5ASnG3OXNwzLlz5s3h6FGYtaTWWNm3Dzb/atWwGynMd3DxIuykPj44PjYWQjA7G7HlRAZDI03a9Js0QTgpY7DJz54NQShGsnz3nelCdfv2YdcQEwPh+vLL0grb3biBsGVL/CV9+qAUs6EdkblF/BYvxnFy91gojAEDXLsMi1gXavp0pWciGdsI/SNHnLr0qCRiY6H52ZP0dGirUiKiMjIYW7hQqwHmL+6WlgYtzNyEoJQURIM0biwtwmT7dtRwadcO89+4UVuTPz+Jiagf5OGBeX/+eUENOTcXGv9nnxV4uVGhn5WFBWTxYv3HBQHOZzEktlo17ELyC+c7dyBc27bF+TdswK6le3dpIYkbNmD8r74q/Fhdbt/GeT7/XPvY48f6FS/ffFNaue6UFOxu8jvUbc369bh2W5YUV5oOHWC+dBJsI/QXLcIHUo7uQ45ITg6+dObUWZGDZcsgEO/elf4atRqvq1wZX74uXZCcM2MG3qOEBOljCQLqtYeESKua+vvvhoXjhx9iIRJ76woCQiUDA7EQLVhgekFp0waCOh9Ghf7Bg7h2UzXsz57VJsO1b6+tn5+VhaSwihX1Hd3iYta+vbTP+ejRcM6aG9M9YgT8Atevw2EdEADhPX68+cW+Bg9GWQxbtNA0Rno6PmcLFtjvnPbmo4+QjOYk2Ebojx6NaAFX5dAhZRxUkZGWaxS5uch2FYu7eXmhMJo5JgdRY5USAXP0KITTiy8WFOB5eVh8QkNxL0VhO2yYtKJx48drqz/26IGwubJlWVpQEIR+aCjaLjZvjvo43btDQBemlQsCFqpy5eB0/v57VIn19TW8YOzdC0H+yiuF2/izsmDmiIoyT+jGxWGh9/LSXrOlUVriDtzeYdQdOsCn4qqIkYpyN763EbYR+l274sdVmTcPAs2e6ddiyKFUJ6gxNBoIKZUK4zVujESiwoR/ejqEYbduhR97/TrMIc2aGa/lkpKC8by8EGVTWHvHGzewOxG7bREhkqdjR5g4Pv6YpU2fDqE/dSoimvr3x4IgRvCEhODat2wxvZNISdHmQhBB+Btj/XrcSymFt+LiMJ6Ukh26FS+LFMHnzVr/kSBAGRswwLpxzOWTT6yvbOrIiO+rpbWX7IxthH7t2pIaWTstL71k/yqCc+bAqWltQSy1Gl/AUaMgaMUEqXr1oMEb00InTIDgKcysk5EBwVKtmum4/59+gsD38IC2bkggCAIcqF27aqN3YmNhrjIgjA2adwQB5pFBg9CvVnTelikDh7ex0sF//425eXggTNNU9M38+Rjz55+NHyMyfDh2EcYcqhcuYLESK17OnYsIkcIa9EhlyhTssOTsrlYY27fj/pgbuuosJCYWXtzOgZBf6AsChNO8ebIP7TBUrAhN0p40awZTibUYamm3f79+cbfvv9cXCvHxiPww5HzNz9ChWBwuXjR+zNKlONfgwdpEM11nJWOwfbdti+fq1sWcdKNYIiIKNI0xKPTF+u665QDOnME8ixSBAJw/X1/zv3cPArdlS9yb0FCULzC2iAkCFqPAwMITqpKTsQt6/XX9x0+cQLkKseLll1/qL/DGWnGay/HjOMfevdaNYw7Jya5dY18Q8Jk3p/eEgsgv9B8+xBu8caPsQzsE4qouZzXEwnj4ECaEFSusH6tlS/wY4sgRbSRLxYra4m6vvopiaIU5LMXaOKYSvUSB//bbWgE2eTI02127cL733sP/1atDezIk6EaM0M+EzAD1gqMAACAASURBVMlhaTduQOgnJGhf88MPOJ8hjT4xEeN4eGCsY8dwjY0b43rFblFnz8JRFxFhfGeQno7dTcOGhUc1LVyIc169CiezWPGyalWEjhp6/e7dRkNVzUKjQZasJb0SrKF6ddfe/deqhc+0EyC/0BedRXL2/nQkfvsN1ydGd9iD776D0Jfass4Yol+gsFpBusXdihfH78K0mMePYTbq18+4Nrp5M4SdrsBnDCalTp1gc69eHdEes2cbN0GkpqJsLxHi78PCGCNiaUQQ+kQYo3p1hJeWKgXt3ti8zp2DJu/piWxnH5+CTvpLl1CqokUL44vfqVMYY9Ys0/cqMxNzLlkS11CnDt4TUz4ijQYZ7nLY4998E5m79rSxv/YanNiuSpcuCBhwAuQX+uJ23d71aOzF5MlImLHnF6ZnTyQFWcuECRDiUkNpr1zRpvWL7fOMva9Dh0JoG6mAyU6dwhbYWDbr+vVYEIoUMRwVJQgoI9CrF4Sy6GRt2RKJMStWsLSff4bQX7EC9u+xY2FqFBuwVKuGYw1Fv+TkaDXuqCjDXbUOHsT8Bgww/v6/+y6ifQyVRxYEOJHFipeiU1dqNvScOTi/tW0xRRv7+fPWjWMOS5bAKe2qpZZHjXKaRunyC/3ZsxHD7qq0aQMhbC9yciC4pNjTTSEIMFmY09jizh0I4unT8aEWi7vlDxsUoxeMJR+lp8N00bChYUf0L7/AUSnWtenfX1+obt+uLYFQvz5s8LduQYP/4IP/Ditg009JwS5l2TIsGIMGYXxfX4R96grPuDgIpU6dcL9btTIcgieG5xkzYT19Cpu8bvRaXh6c5OI1vPAChH+ZMuYlxyUm4nqsbY2pVuMa8/tRbMmJE7h2S1uKOjr/+x8CDZwgQkl+oT98OL7crkheHmKlC9u+y4lYduDgQXnGMaeq5ccfwzkpCr9//oG9PTAQwlMs7ta6NaJ/jEX+DByI+2YoekPU8GNjYd4Qy1vMm4fzde+O/1u0gPNR90vVq5eef6KA0Bc1Wt3uXY8fI4QwMBC7l59/Rs38MmWwm8rOht08OBj/G1qkhg3D9RtrPC76Nvbv16942b49OqKJTJmC+2JO8bcmTeSpodOqlX1r8eTkYLGdP99+57QnYg6LpTkUdkR+od++Pb6MrsjNm3hjC4splxOx25O1oZpTp8L8IjVULzcXDj9D9dB1SwF4eZnW8kXBa0g7/ftvbXKT7oIxcSI02qAgaPO//lpQgxIEaOve3oiEad2apdWpA6EfGak1iQUFGTZJJSbivEQweZUurW+aOnIEgr1Xr4KLWUaGNvnLkGaXmYl75+uL8Xv0MFyS5PZtXOfy5YbvnSFmzYJGaa2ZZNIk5EnYk8hImAFdEbEQohOUnpFf6FetCtuxK7J3b0HN0dYMGgQno7U0aKAtOCYFsfmJKYd8Whqci2K8/cCB+tpvZibKP7RpU1A43r8PYduyZUEfw6JFOLe3d8HzP3iABUz0NRChUujLL7O0YcMg9AcMQBZokSLacXr2hIkn/zzEJu41ahR0lG/ZguuaOrXgtf/5J16nG1H17Bk02bJltXP74Qfj948xOADNcXBevChPVu2mTRjHnDIc1tK3rzKlyO1BSgru59q1Ss+kUOQV+nl5+ILlL2zlKnz3Hd5Ye9YUqlEDDUGsQezwVViZXl1iYwuvjigKoB9+QBjic89pi7udOoXEIi8vJBfpkpcHk1DZsgW3w3PnYsw330TkTcOG0KyfPoX93tcX9ughQyD4fHzYgT59WK1atVj16tW15h2xMNukSaj70qABxo2O1jaSF9/PKVOg6deoUTBp6tNPcU2G4tr799fuEGbNwiLm6YmF+tIlOI779zd9D8Xm9lJqGTGGRatqVes7Uv3zD87766/WjWMO770HJcBVKVrUet+bHZBX6Ivt7H7/XdZhHYYpUyCo7MWTJ8ZNI+YgJmRJtTdKLSg3diwSjcS48vzF3Xx8DBZGY0uWGE4Q+v57PP7hhxBuZ87AxNKhA8b09YXg13XAxsQgTJTls+mL222xhaPYGDwyEo+/8grmJyZ4XbsGc0fDhvoO3Lw87EYqVy5oYjt+HAuCr6+24qWu8J47F4+bykwWC5ItXGj8mPwMHy5PpEiFChDE9uKrr7Ao2rN8iT15/nm8Nw6OvEJfjNF3su7wkomNlSd0Uiq7duF+5teUzWXsWPM0LNGMdeKE8WOyspCpaqjmTG4uNFzRxNGqFZKLBAHmmZCQAtm07MgR7AqGDtU3wQwfjjHCwws6guPjYVcvUoSx555jad7eEPrBwdpdx+rV+sJao4H2TgRnrm6lynPn4MDt00d/DleuQDCLzUASExGaGRAAIebvb7h0cFISXldYdnqnTjCBSWXFClybsV7AUunXDw5yeyH6d6TuapyNbt2cIlbfg+QkIwO/AwNlHdZhuH2bqFIl+53v8mUiHx+iatWsG+foUaLGjaUfv3UrUdmyRM8/b/yYP/8kSkkhGjSo4HMeHjhn//5EGzYQpacTtW9P1LQp0dChRCoV0ezZ2uOfPiV69VWiyEiir77C80REixYRLVtGVL8+0d27RAkJeHz/fqJWrYhq1SI6cYIoO5uoZ0+imTPx/IQJREWKEPn6Yg7lyhFNnYrzaDREe/cShYbi+Y4diZKS8Lq6dYm+/x5z/uYb7fyqVyd67z2i//2PaPBgovBwzGvsWKK//ybKzCQ6cqTgfShenKhrV6JffzV9v3v0wDWlppo+TqRxYyynx49LO94YdeoQXb1q3RjmIH53bt2y3zntSUCAVgY6MrIuIVu2YCU3lqDj7JQta98a+hMmwC5sDWIXM3PMB1FRcMqaYvhw2JYNRa/kLxkgCNDyoqK01THXrtVGxYwfD21ZN6FJDHt8912Ym9q1Q4hl7954PDIS4Z2iSXH1an3zTni4toH6uHEwwZQtC4eulxfmFh+PuTRqpL8bGDYMUT/37+P/q1exyyPCriJ/kpqp0hZiD9UHD4zfyytXMLbYX6AwNBrsSGbOlHa8MX78Eec1lIhmC7KycL7vvrPP+ezNG2+ghIeDI6/QF7NxnaSutFko8YHt1UvbAN1Sjh3DvMUm2YWRlQVn/JIlxo/RaBDXbixKa9AgOEXzLwhTpkC4t26NOVWvDgeop6d+J6z4eBynm6R1+jTm5eGBvry6WayVKjHWpQtL++wzCP2ZMzG+bt3/O3fgmCbSL1x34gQWBF1b7JMn8FX07ImIJw8POGzbttXPWxD56SeMa6i5TVISXm8qLFMQYCr79FPjx+SnXTvD/hJzOHAA8zZVHE9uypZ13Z65b7/tFFm5tjHv+PvLOqxDcOcOftvTvHPrlvXnE7fvtWtLO/70aaLcXNPmoCtXiBITiTp3LvicRkP0++9EvXtrzTRERHl5RN99R/TaazCvHD0K88wHH+B5X18itZpIEGBCKV8eJhSViuj+fZhvSpUi8vYmiovDazZvJmrRAvfpjz9gwiEi+vBD/H7zTZhlHj0ievwY96JePaLfftOalyIjtWakXbvw2I0bONfmzUR//YXnb90iWrECppw1a/SvuVs3Ii8vmMXyU7w4UVQUxjGGSoX7bchEZIxatYiuXZN+vCGUMLdUqsTNOwojv9D39SXy9JR1WIfg8WP8LlXKfueUw4dw6xZRWBhRUJC0448exXtYr57pY1QqokaNCj535AhRcjLs1Lrs34+FYsgQ/N+oEdHSpRCW9erBDl+pEmzwR44QLV+OL5For2eM6PBhCN6VK2GPfvFFjDV4MOZz/Tr+Hz6cqHRpPL58OXwiHTrAZn/0KNHHH2Ox2bwZxw8dCh/BsGGw8UdHE2VlwTfVrx/RqFG4JxUqwDexdq3+tRUtStSyJdGWLYbvV9OmOK8pGjcmOnYM1ymFSpXw+ZB6vCHKloXPyJ5CuEQJoidP7Hc+e2IjoZ+SkkLjxo2j0aNHU6dOnWjFihWkVqtpzJgxNHr0aIqNjaVLly5JH1DWfcOsWage6Irs3ImtsLXdi6QiV7LHkCHmJf+8+SZKKhR2TO3ahp+bPRsmkPxZrG+/jZo0uiaf2bMRkpmSArv2669rQz1Fu/mHH8KsI7YrvHkT9mwibUz0v/kCaT/8APNOw4awwTMGW3qpUjhe7IEgCDCdFSuGMNZduxBuR4SonzVrMP/33oPZRbfU8dKlMEflL3o2axb8AIZKUYghs6ZCN8V4fanF1MRqr9b6z6pVs28yZWwsIq5ckS++QESXjGRnZ7NXXnmF3f/Xv3T79m2mUqlYjx492M2bN9nOnTuZl5cXGzVqlOQx5df0AwJkHdJhEFdwe13fvXv4Xb68deOYayKSsrs4cwZmEUMcPQotPv9ub9cuoi5d9E0+GzfCNFK0KCJk+vXD4z16EM2ahWv/7DOit99GJFF6OkxKJUtCe/7iC0SwLF2KcV9/Ha8/fRrz2LCB6PPPEZ0zZAjRvHnYKahUeE12NlFEBHYBHh6IEipfnuiVVzD/AQMQoaRrmunWDSasffv0r69JE0QHXb5c8J5ERWnvmzHMNbXIZZopXx7mM3sRGOgUJhCLCAiA+c+a3Vc+vv76axo8eDCVLVuWiIh8fX2JMUbh4eFUqVIl0mg0VK1aNXr11Vcljymv0M/MdE17PpH9hf6zZ/gdHGzdOOaaiKQsEjdvElWtavi5kydhHtElNRXCsFkz7WNJSRDY3btrH1u9GiaYX37BPGrUgIBdsoRo3DiYWf75B/b7zZvx5WraFDb28HC8VqRYMaK+fYnmz4f9/ttvYb4ZPZpo8WII+owMzGPdOphWJk+GCUkUpHXrwqTzxx/acZ97DoIyv7lGFOwnTxa8J+HhWFRMCWilhL69hbCT2L0tIiAAn8msLNmGDA0NpQ4dOvz3/4kTJ4iIqFOnTkRE1LlzZ7p06RLFxMRIHpNr+lLJyICG6Otrv/MRWb+IPnkCZ6IUGMMiER5u/JjMTDhGDS0M2dnYoVSvrv/46dP4rbsYiE7L5s3xWxAgXF98Efe5eHHMZfRoookToaGvWgXN3NOT6MIFXBtjEOBDhuB4InwGly6FvdrLC5p6djZ2Czk52DmIjlovL1yPSoWdiLc30bZtGEelwvzyO1ijowsK96AgojJl4ATOj7c3FgtTArpYMYwhXkNhBAVh7ikp0o43hr2FsKsLfSJZr2/gwIF6/+/bt488PT3phRdesHhMLvSlIl6brnnC1ucjsv5+ZmRIXziysiAcTS0Sd+/id8WKBZ+7cwdCOP+icfMm7lvlytrHzpyBoBPHuXoVAqxFC/x/9CgcwgMGEH36KZyyAQFw1larhh1CZCQigtasgRP16VO81scHz9euDafr9u1wWo4cid2Djw/R+vUwI7VqpRXyQUFYGA4f1s4zKgpzFQTtY9Wq4ZryEx5uXLCHh2vvnSFUKjjczRHicmjpXOjLh/hdFXfpNmDv3r0UGRlJQVIDMwzAhb5U7H1tcgj93Fz8SB1DyjnT0/G7aNGCzyUm4ne5cvqP37kDLbhIEe1jt28TVamiXUTF6AMxaujoUSI/P63vYPduZO3evo0In4wMmGS2bkWkzrFj2rGfPYMZqG5dojFj8FhODtHZs9hN5OQgo5gImvzRo1o7bP36RPHx2rEqV8ZC+OCB9rHwcGQHazT611munP5xuoSEaO+dMcwViHII0IAAmwopg+dzdaFvo+tLSUmhs2fPUqtWrfQe//bbb80ahwt9qSgl9K0x75i7cEg53tQxxspwpKai7IEuDx9iIRBJSIDprEQJ/H/jBvwGXl6I3798Gc5Sf39o3dHRCMeMi4OgDQzULiC5uTAB/fQTQjCXLoVgCwzEzqJMGa1TtUYNaNdiCYSKFfU1cnGOjx5pHwsNhcDPzNS/JlOatxRhZ64Alkvo21vTz8lB3oarIbPQT0pKokaNGtGnn35KREQ7duwgQRCokU6odFJSEsWJeSsS8TJ3Iowxeipuo/OTmoov3oED5g7r+Fy7Bm3QXtd27hzMEAcPWj6GmFtw86a0eYv25KtX9bVyXUQH5tmzBaM+/nUy0Zkz+rbtGzcgJHXncP8+zBniYxcuQLP/+2/tHDw98XxSEu59cjL+P3OGqEIFyqlUiSg6mrwOHiTm40MZ/wrMdCKtFr5mDRzERBDw3t4wY02fjlo6ubl4rnRpnE+txrn8/PBZFseJjsZriSC0iLBAeejoTaIDz9BCbeo53WOOHdPOl8h0JIhajYikJUuMH2MKxrCLIcL1WhN1wphh06fu44xphb2/v/mmUmvnZ6vjxWsUXzN3LnxQBggKCiKVxOvev38/HT9+nLp06UJZWVm0bt06Klu2LD3793OekZFBb7/9Ns2ZM0f6XIlIxZh5dyM9PZ1CQkLMOgmHw+FwiNLS0ihYYkTe06dPafz48eTj40PPnj2jyZMnU3p6On3wwQdUsWJFysnJoYkTJ1I9U4mUBjBb6JvU9Hv2JBIEGnD7Nq366SezJqLLgIEDLX79s4wM6tylC23/4w8KtNAcY/D8y5bBDrxunWWvN/f8/fsjRn3vXskZzgWuPTMTce1TpxK1aVP4AA8fEr30EmLbjZVhOHMG1SV//hkRKbocPYpIm19+0c9c/vJLaLArV2of++ADaNGilrJpE9HixTSwbFn6adUqvObIEUTs5OUhE3bMGJR3mDuX6NQp0jRsSB7bt5NKEIj5+FB6bi5VYIwSiCjY0xPjR0QgVHTZMuweSpaETX70aJRoWLcOGbz37xMFBtI3lSrRCE9PbXbv8eNE7doRHTqEsYjgBB46FH4D3c/Y8OF0evNmavjwYcH79vrrMCOJWcCGaNWKNt68Sb1NOXx1adgQeQPTpxMRFLLy5ctTQkKCZMFCn3yCfIlz54iIKDo6mo5bUb2z0NevXIn38ckTg59ra85v0fXLeH46dw4+or17jeaxmKPp2wqzzTsqlcr4DS1WjCgjg64HBFCwGIVhAVa9Pj2dzhFRYEyMxW+8wfP//TcSjCTMS5brb9AA/0RGSo/Vz3/tommiQgVJ86bkZPyuUsX48aJ5onZtInGOIuKXuHZtlEkQ2b8fyUy6Y9atiygZ8bH0dKIFC+hpkSK4d5cuYSGIjtY6dBMTsZhkZUHgZmQgsmf5cqK7d0n8KgWpVBSs0WCxO3gQAt/XF+eLiIAZsnlz3NebNxHZ82/yS1WNhoKrVdPeczGapnp17WMZGTB/lS6tb6LIziYPT0/Dn7ucHDhzTb2XajWRsdcbIisL37l8xwcHB0sfIy8Pr//3eE9zzm+AQl8vCHgv8vt4pL5eAmZdv5znFz8LpUpZn19jQ+R15P7rFBo1apRVw1j7emsxeH4zHF6yXL8cTiFPTwgnqWNIOaf4ZRUXCF1EzV+sey8SHg7/gq6TsnJl2PrFUMh/t6jviDuSZs0gkESfRpMmyLCtWRMLQoUK0NpTUuB41clIZCVKICv4m28QkkmEqJxBg4hat8bCJe5k9u4l0klsaR4QoF936No1fIHDwrSP3boFh29+jS0hgYrVr2/gpv17vwxFPOmSkUF1DNUzMobonLaGfAEKNv/uFhIQ4ZDffak4ST8RLvSlnl80l+jGa5vzenPPL1ckgDnRGUWKIFbdWNghEbJRVSrD8ejlymGhyf+c2ATmyhXtY5GREFpi2YLy5YnKl6euYvJb3bpIAFu4EDH3ixfj3rdrh/F374bmP38+kq3Cw0n4N79AlZICM8KzZ0QffYTnjxzBTi0zEz+1a6Ma57FjMEsSET18SMUTE/UWATp+HHPVFfBXrhjOSL51i+p07Wr4vhWW6SwIRA8fUrShyqWGYEyeiDIu9OU7v72z9i3EJkJfSYoUKUJTp06lIsaiTyxFfCNlTLGWdL78YYEmMHjtJUuaFuK6qFSmE4yIEFFkLLvUywsavG6cOxG0bC8v/Vj66Gg8JtawUakg3Ddtgob/11+IjNm2DQvDypWwXe/dC/t6Xh4EZXAwSh8vXQrzCRGpcnOxU8jKwiKUnY0onc8+Q+LZsWPwEcyejfPeuEGUloZzq1TodkWEcxw4oL8IMIbX59fIk5Jgpza0GGRmwl9iSug/eIB5Si2ZkZyM69dJpLPos69EKLKNzmez775UnEToy1tl8+OP0VzaFRGrGj58aJ/zxcfjfPv3WzdO585oBiKVHj3Qs9UULVsy1rev4ef69zfcPSgqCg1JdGnXjrH27bX/iz2Wa9bE77p1UbXwtdfwfF4ejg8KQjXMiAg0PPn2W8Y8PFhacDCqbBIx9sILqNy5bBnGiopCtc59+zDWxYv4v1EjVPUMDkY1Tt1r37+/YAOaS5cMd7nauhWPG+qVe/asficxQxw8iGPOnTN+jC5icxxTfYyl0Ly5tiKpPRg6lLHoaPudz558/TUa5hjqJudAyKvp+/ubpZk6FTbOtiuAWF1TbN5iKYVp7vmR0uQiKsp4f9bGjVFrR63Wf7xzZ5RDEOPiiVBV888/kR+wfj3RiBF4/N49NGI5e5ZowQJo+Zs2QWtfvx67jXv3iNq21db+FwREoRDBSRsWBudr/fr4+8QJohkzYONXq4kGDsS17t+P623dGtr4X38hqufBA6Iff4TtXrdm0JYt+Jznd3QfOaKNDMrPsWPYteR3fOsi3nOpmr65xxvjzh34R+yFOyRwKhydUxguZ96xGXaoq1HgfCVLWl9FURTiUiNza9eG89LU+9i4MYSFodDE1q0RqbJ/v/7jPXsiaka3JHHfvhDgkZEIFS1eHOGYz57B3KJSoZBanz6owXPkCJKRkpOJXn4ZSUkVKxK9+y5MRaI/4LnnsJi0aYO5li0LH8GiRQjNHDgQzuA1a/CasDBtFdDx4xHtU7EiFpt+/fQTsDZsQIE3Pz/969uxA41UDH3hjx5F1JApB9+5c5i3VCfgrVswbRmJgpFEbi4WT3t2g3MHoe/oyLpvWLECW87cXFmHdQhu3TKvebUcNG6MxiLWsH495v34sbTjz5wp3Kx05w6O2bix4HOCgKbkI0cWfLx2bZiFsrLQjCQ8HON4eenf13790Izn3j38n5EBc42vL44XG4LfuMHY2LH/PZ5GpDXvEDHWtCkamOTlocl5yZJonOLlBXOdyHvv4bHz5/F/SgrOR4SGKW+8wdi1a9p7s2GD/rWJzdlXrTJ8v2rXRrN1UzRvbtxkZogRIxirX1/68Ya4fh3z3r3bunHMITqascGD7Xc+ezJxImNVqig9i0KRX9Mnck1t/7nnDEem2BJzTTOGqFULv8+elXZ8nTp4H02196tQASUNxOqUuqhU0OpFh6zu44MGwQQTHk701ltwhu7dC21bt9XgV1/hsb594Yz194eZRzQNJSZi11C5MhqphIaiguaOHXh++3b8HjECoZyenkTnz+P3kycwNYkRO+vXY3cxe7Y2+So5Geag995D8tgff+B6+/TBbkS3BwARrsnLC6WZ83PrFnYVOjXRC5CXh1LNTZoYPyY/585p31tLkctEZO457Xk+e+KWmv7vv0Nz+Le1l5IMHz6cERH74osv5Bs0PByrub14/33GKlaUdGhOTg6bOHEii4iIYP7+/qxMmTJs4MCB7P7du3B8zpol/bwtWzLWu7fpY957D5qzRlPwudOn8TnYtAn/p6ZCOy9WDI/XqMHY5cva47/4gjGVCs5MkWPHGPP3Z6xLF7Q8rF6dsVq10CIxIICxokXxXuzYgTE3b2ZpaWnQ9NPSGKtTBxrlmjWMtWiBY1q2ZOyTT/D3jz8y9scfjBUpAuezeB0aDZzFFSow9uwZHsvKYuzTT/E6IsZefFHrQBUEnKtPH8P3acECOIrT043fy1OnCnf06pKdjXkvWMAYY2zWrFksKiqKBQYGshIlSrCePXuyy7r31xjLlv2/vfMOj6Jq2/izqfRA6KGDIISAItUAonSUKoooSBWpKggIiEoVKaLoCyIqikoRkSIIn6AgRRIJXULovYcA6XV3nu+P22FLdrNtypb5XddegWR35uzszn3OeSocj7m5jp3XXdLSCt4RScCcOXOYiPitt96S7Rw2GTQIu0sPR1rR/+svfKhnz0p6WGfZuHEjP/bYYxwRESGt6D/zDEwPSrFsGW5K0x6tNkhOTub27dvz2rVr+fTp0xwbG8vNmzfnxo0bM7dt61wEz/TpzGFhBYvBvn34rE2F2pRmzXC9pk7FsUJDmUeNwmQRHAxziUheHnN0NITWtEfsjh3ooRsejolL/F7dvIm+rmFhRiF+5hlO6dcPot+rF3OZMsa/tWwJc44g4DFkCMw5QUGIVsrONp5z/ny8Zvt28/czYABz2bLMX3zB/MgjeE7nzsxLluDfO3ZYvw5PP20/GkqcyLKyCn6eiBi5ExvLzMydOnXi7777juPj4/nYsWP83HPPcdWqVTldnLRsMWUKrrlS/Psvxr1/vyyHj4uL4+rVq3PDhg3VEf0XXzSPRvNQpBX9Q4ekCSNzg+vXr3OlSpU4Pj6eq1WrJq3oDxmibLiZGMYnNgV3kri4OCYiTh49mrlCBcdDycSV559/2n6OXg/BGDIk/99u3IDQEcHePn48hJoZ9vnq1Zk7djQfz5UrEPc2bcxFeMgQHCc8HGGRpmRnM3ftiublPXpwSuPGEP2nnoKNnAi7DlOSkpj79sXfihY135Vu3oxJdsoU89fs3o3nL1tmfO+rVyNklAg7ku3b819f0Wa+YoXt68jM3KKF/Z2VKf/7H3YPptfJhMTERCYi3mMv3PfZZ+1PSFLy66+4HuJ3QULS0tK4du3a/Mcff3CbNm3UEf3OnbEL9HCkFf07d6w7uhTCYDDwM888w4v+2/ZKLvqzZmEFqRSZmViNfvGFSy//448/WKfTccbq1fhcLl1y7IWCgDj4N98s+HmzZkHwkpPx/4sX4WAU497DwyHulogx7cuXm//+77+xI+jRA4ImisSECcg3EFfX/61wmRnOzP8cg2bmnTNn8Pz/+z88LzmZed48TBAlim7MlgAAIABJREFUS8I0UrYsdiN5eXBmFi4MM41ebzx+Whpz7drYtluasvbvxzlq1sTPZs0wcYjiP2kSzpWZafsa3roF05a9icGUfv1wLhucO3eOiYhPiI5pawgCnOXTpjl+XndZtAiLABni2AcMGMBjx45lZlZP9OvXZx4zRvnzOom0oi8IEIGFCyU9rKPMmTOHO3TowMJ/XyrJRf/HH3Fzp6VJd0x7PPEE88CBTr8sKyuLGzduzP369YPJJDAQySOOMmoUVvLWbPYiN27guFOnwvwRGIhJcc4ciOyqVbheYkKUKUOGQGRPnjT//datEP7oaJh0evbEGAQBi4k6dXDMRo1ghtLpEAnEFqIvCJh0evdmfvVV5mLFYFYaPhw+Amas4AMDseINCcFPU4EWBONrz5wxH6cgYDcRGYlJ4/ffjbuLhg3xXSlXzv7EKZrw7t4t+Hkiej2OO3Gi1T8LgsDdunXjVq1aFXycc+fMJ0UleOstJN5JzJo1azgqKoqz/jOPqSL6KmufM0gr+syKzXYrV67kokWLPnzs3r2by5cvzzdMtuuSi76zWZNSMHKk1RvF8v3v3bv34d9yc3O5R48e3KhRIwggM8wmzz7r+HlFm70tWzUzTCdVq+J5FSvCIZuRYfy7wQDxrls3v18iPR3flVq18mc5b9kCIQwOhjCbYjBgB9C7NyYHItYHBPDl4GDeV6gQRD8qytymX7cuHLGWAQbZ2fB3iHZ/yzEuWGDb8fjdd9ZNYHv2YHcjnnvu3IJ9I82aOWdiiYkp0JcyatQorlatGl+7dq3g46xcieOY+lDkpnt37Ngk5OrVq1yuXDk+duzYw9+pIvqilcNaGLOHIb3oP/ccHjKTmprK586de/iYM2cO63Q6DgwMfPggIg4ICOBqDkbA2OXmTfOoFCVYsQLnvH/f7NeW7z/zvxVqbm4u9+zZkxs2bMhJprH5n3wCkXR0lyLG1VuLSomNxWdMBDOQTsf82WfWj/Pvv1hNf/BB/r9duoTSB02bGk1EBgNW98WK4fyBgbCxW4t+ee897Ab+9z/mCRM45ZVXIPqvvcY8cybMIEWKWM8b2bsXNvngYObGjWF2MLX/i7u6qVPzv/bmTUwqtsoXZGbi75Ur4xjVq2M3YmmDt4xycoRJk2CWMjVB/ceYMWO4cuXKfNFaKYj8T8auSUmiorCDlJCNGzcyEeW770Ut0Fu5TrIglhCx9CF5INKL/pgxuFkVJikpiU+cOGH2iIiI4EmTJjkWvuYIgoCt9XvvSXM8RxBr8FhGk1hBFPz69etzYmKi+R9Fp6Iz/pbPP4dP4dYtvPedO2EDJ0L45I8/QlD79UPNJVvRItOnY+VuuWpnhpO6ZEnUxrl3D34CItjGc3Px2tBQTA4LFjCLOxdmREqYLDDMzDvMEHYiOKaZ8R7+/pu5WzdjPZ7jxyHSjRpBnJOSUMtHp4MJytL+rNdjd1Chgu06TAsXYrI6dw7Hf+klHC8iApOveJ1GjMDvnElmrFs3X3KTIAg8evRojoiI4LOORs41bQrTlVJkZOCaiM5wiUhNTc133zdp0oT79+9fsE9DataswXdKXLx4MNKL/sKFWF15QNEhyc07zBCM9u2lPWZBGAxwuFlGlFiQl5fH3bt358qVK/OxY8f41q1bDx85otmifn3m/v0dP/eDB7C7v/wyIkxEW/ovv5jb+s+fx0p50iTrx9HrEboYEWE9cuPoUfOV8fTp5n+/fBlCFxyMiJt+/TCGYsWM2blsRfRFR/jkyfAzNGhgNPesXGn+Hi5fhg+gRg08Z+RI6/6MDz6AgO/aZf293riB3YdlRvLp04jjFv0eU6di/O+/b/041jh9GmMzzSZm5pEjR3JYWBjv3r3b7HPPtOVATk52K0DAJcQJ+Phx2U+linlnzhwECXgB0ov+hg3KVqMsAFlEf/ZsRKYU5OCUmgEDINgFcOnSJab/yhBYPv4SHakffggRf/DA/jn1euaff4YpQYxM2brV9mQ+cyaEJD7e+t9v3MBuoFEj66aaHTuwGwgKQjikrWPMmoVdhmgzr1IF5qDRoznlnXcg+m+9BYFt1QoiS4T33bcv3oO1z+72bZS9IEIyl7X3KZraZs+2Pj5m5j59sBu0dY0vXcKEII5r3DjHnbgTJ0JYLMTc1uf+3XffWT/OTz/h3FeuOHZeKZg/HxO2AuYWVUR/2DAEXXgB0ou+GONtWo7Wl/jjD7y/hATlzvnLLzjn+fPuHefWLYjq55/bfk5uLrJVxfLGrVrBvGLPpJWdDRtx8+a2HZfHj2MV3LGjeSJSaipMgo88wtyrF8774ovG2jvWmDULk8SoUThew4acUqkSRL9GDYRY9u0LB2358jZj2tlggJmqdGlMcEOH4vxr15o/b+tWXLvXXrM98Ynlt1etsj1uZoh80aIwLxUpgn+b5jJYIzsbO4T/whLd4uWXMfkqSe/eCCbwVdq3t52V7WFIL/oPHuCLv2aN5If2CJKTsb23tYqSg7Q0hBRKsWvp3Ru7BkvhsiyC1q2bceIePx5ibS/SIzYWwmjLzMMMv0DhwrhJ0tMxjuefx/FPncJzfvoJAlekCMwpFk5sZoaJxyJRLp95h9k4YVpG7og+iqZNjZNMYiJ+37cvzi1GaW3YANNSjx627e9XrmAV3rOnfdPm5MkQ+rt38Zg6FbvH0FDm0aOtr8BFm7F4jVwlNxeZzErG5zNjl1fQ98LbqVUL+SRegPSizwzH3EcfyXJoj6BePTjhlKRLF9jF3WXHDvOQv/R0OBcrVsRk9tJL+e2ud+5Yt1NbY948+9VI9+yBPfvJJ+GrsGKn5uRkiERoKARyzBjsIkVBrV4dcd8mWBX9Gzdw/HXrxCdhwn7iCfy+ceP8eQTp6Yi1r1UL1yYwENfF1g4mN9dYRsLaBGXKuXN4T5ZRQQ8ewGxUujQmziFDzMuZtGkjzUr5zz/NndtKcP2614QzuoRej0WBkj4SN5BH9Bs1Yn79dVkO7REMGqT89vjLLyE+7sZVGwwQsx49IDJlykBkBg0yL4JmyWefYVI4cMD+8bt0wcRvmXhlSlycsQDb0KG2n3f7Nlb7om+hbl0kWBGhYJgJVkU/JwcO5KefxnsuVAjvo2NH66UTRE6dwu6KCCYkW7Zo01o+9mrKCALOW62a7UintDTmjz9GdFBAAEwx4m7Flq/DGd54A34QJQMt1q/3mEKMsiCWGlcy0c0N5BH9Xr28ovCQyyxdCgE2TUSSmxs3IFaWpQucJTERSVpEWJ2MGoXIFXvk5WGia9TIfohhcjIiZapWtX2jnzuH3UPJkhjHnDkFHzc3FzfVoEFYDYuO3LJlYaJ57jlOeeEFiH7PnhD5Rx+FGBPh2j31FByKV68WPP4TJ7ATCArC66zF6ouI1Td/+KHgYzLDT0CUv4aQNbKysHIUk9+KFjUvP+EKej0ipEaPdu84zjJxIiYaX0WszSRVaLjMyCP6b78Np5yvIvY8LaggmRx07IjQSVe4cQORIkWK4BEW5nwS3YEDEEFHyjRfuwY7bsOGmGhMSUuDX6F2bZiOJk3CqrZZM8eK9Y0di9X7+vUI73ztNeZu3TilVSuI/tNPY4X81luYoMeOhYAXVAOHGX+fORMr/MhI5oMHYaa0ZZoQK2wWFM0jkpiI1buzBbkOHMA5ypfHz06dEP7oCmLpc3u7Nalp0ULZ6rRKI2ZnO1olVWXkEX0xuaWgGuLejKMFyaRG3CY7E+tsWgStZEmYSpKSsGMgQjcoZ5gyBbscR8rjxsdDrCIjjZEpgoAOUcWKmZt/YmIwERAhaaig4nDNm6MGvgVWzTvMxsxXW2KZl4eIpcqVseuYNMl4A5uO1zRi6+OPccyxY+2bSgwGlFooW9b5CpPdu2NyzM6GM1fMNXjqKfhnnDHTdOuGnZqSpp3bt5UPfFCa8eMd7nvhCcgj+idO4ItpK4HFFxg1Cs5EJW+g3FysFh1JZT91ylgErWxZrFhNxTA3F9Uhnamzz2y79r0tTp/Giv+RRxByKq6crWUG5+XBd1GunNF5euCA+TXOzIQwL16c7+U2RV+vh2jPnWv5AkREVauGMfXubV7nX0TcmdSpA0ft++8bSzQ48vmLzm0HsqrNOHgQr/vxR+PvxNpDYtRR06b4v71xXL2K3ZQzRfek4JtvcF7L3Z4v0aoVvqtegjyiL95kvhzBs327YhmGZojhfbYcgUeOYGWq00FsFy2y7XsQq2A664ASwxO7dnUs2ebiRaxWixWzXc/GlPR0iLpYsrhuXZhdTpww2k+t1DixKfrMCBHt3h3+hvXrcY1CQ2H26dfPfjTL2bO47hUq4PyOfrf37sU57GRU50Ovh7krKsr6NRYEfAfFrmANGiDU1dbnMW0arr/Su+9u3SCKvkpuLoIDPvlE7ZE4jDyiz4waLV7QUMBlsrPhiJw1S9nzXr4MQf/mG/Pfx8QYHbQ1ayKyxVZCkoggoI5MzZr27d2WbNuGFdyYMY6tdo8eNTpV58xxbLLQ63Ge/v3hyCSCcAUFQXS3bsXKPDWVWRDMRT83F6aUAweYv/0WduWgIIxZLCexYEHBCWCmnDpl3BH07evYaxISMDm2bet8S8KlSwuspmnG3r2w9RNhN/Ldd+bny8vDAkDpiLr0dAjiggXKnldJDh/GdZepG5gcyCf6kyc7163JG3nxRWRVKk2XLsyPP46t/p9/mhdBW7nSuQJep0/D3u9MDRiRL7/Eee3d1OnpWInWqgVnsk6H1Z81U4otMjJgw65VC05ocdcgPgoV4pSSJSH6xYub/02nQx4CEXYMFy44fl69HvWkChWCoL7xhmMRODdvYpKIinK+CNft23iPr73m3Ovi4mCuI8K5v/gCvgkx5NPFDmwuI2Yoq9w+VVaWLIG50dlFk4rIJ/riB65kfQ+lEWuSO7palIpdu4yrOiKEF65f73o9oPfewxfXlZAzMbnq+++t/10QYO8sWtRYl2fPHuwuihRBCKW9HYnpsUqXhjNaELDr2bmTfx80iD8sX55nlSkD0Z85E47qLVsQDZSejuQnnQ6rfkc5cgRlHHQ6OGwzMoyln0uUsH297t3DTqJSJfvhodbo1w/5E6alsZ3h33+xGwkIwMKrYkV1SiAMHixL0xSPYsAAdRZ+biCf6N+6BTH4+WfZTqE6Ykeq/zo3yY5ej1jvxx4zxm4XVATNUTIz4Wht0sShJuxmCAKSq3S6fMlSzGxsNC5mxIqkpWHVHBiIypZr19p/H3bKTBdo02fGqtuR1fP16+hWptNBtCx7zaak4Pf16uW3kd+5gzDV0qVd8/esW4f3KEW0y5kzxl1giRIILVWq9K9ejwACXy69wIxcEC9okWiKfKLPjAiP8eNlPYXqPP007KlykpuLCo+PPoobuEMHZMhKmdoeF4fV/ttvO/9agwEJP0RwHIuIlTMnT7b92oQEOIRFZ+SKFbYnnuXLIcQ2hMuu6A8fDqEuaCyvvQYHb9myMI/YssWfOgWfTq9exh3W9ev4jCpUsF1ttCAuXoQ4v/iiNGZRgwFRR61bI+IrNBTHnzrV8cqeriJ2XvMiW7fT3L+fP7rKC5BX9F980bc998ywawcEuLaNt4eYlSkWQeve3Tyxpm1brCqlKvP8ySeOZ4xaIgjIvCSCyJ87hzILnTo55rTds8fYjSsiAsJkWcZhyBC8XxvYFf3vv8fxTevjZGQg/l1svF6xorHHrz3Exu2zZ8OkUr06Mk9dsWHn5CBap0YN6VbjYgnlmBj8/+ZNLMKKFoVp7e235SuNMHQoroVSnavU4PffvdJnIa/of/wxKio6G7ngTaSk4CaSsmphejqchxUrYkLp29d6X15xNfXLL9KcVxCw6g4PR0atK69fsABjLl4czkRnawWdPIkok7AwvLfHH0fW7b59WEUXUPTNruiLzcC//x6PV14xRgU1b45dhqP+BZEPPsDrQ0NhdnPVhzV+PHZacXGuvd4SvR67Gmv9d+/ehR9HrOw5cqRjpTgcJTkZk8qMGdId0xOZPh33ipcFq8gr+qIoKR01oDTDhiGb05moGWs8eIAQUFuVFq3RoYMxY1MKkpKwQrPV7MQeggCTlxhB4oqZgxnvZ+NG7BZLljRG4tSrB1/AV19hd3DmDFbuliGb2dmYuI4cgQls1iw4lMXmJeKEMmuWc9E8puTlYVcj1jGyNjE7grgDkTLW++uvccyC+lpYVvYcPBjX012WLMF1VjrAQWm6dJG80bsSyCv6GRnKt2VTg0OHcINt3uza6xMTmd9917ymuqMrr/h4XOOZM107tzXEZiedOzu/S1u4ENfis89gTw4NhTPXnW2+Xm80PXXpghW/GG8vPgIDOSUkBKIvVsc0fYSHI5GpRg2My12bdkICsmEDArDie+QROIodbTwvsmMHPr+hQ6VbMSYm4v0OGODY8x3dWTqCIMAE58s5Osx4n+HhXrmbkVf0mRFOOHCg7KdRncaNnS9gdv06QgHF7kkTJjhfm4XZWHfembh3e7giRn/+CdGYOBH/z8yE2UKnQ+kGd2yfkydDlMSxZGVBeHfvRoTYF19wyvz5EP3582Gq2bYNpQzExu7MmICKFHF9V6bXw4QVGorJR1xJnzyJ3IE+fRy/XseOuT65FsSgQUgKc7ZlqdhIR0xC69HDeXNTbKxXlRl2mbNn8T4L6hvhocgv+mPG4EvkZXYvp/nqKwieIzZdW0XQXCU9Hde4Y0dpr7NodrBsVG6NS5dgJujQIf+qft8+JFWFhDC/845rjsqnnkKHrQKwa9NnRoarqybHP/7AKlangxPUMiFHTIKaN8/+sS5fhsP6iSec3x0UxJ49GMOyZa4fIzcXIaNiHkjHjvnDVm0xaBAc2kr2kFYDsaikvaY5Hoj8oi96uJWuUaM0qalY6X3wge3nJCSggqStImjusGULrrNlb1d3mTMHx502zfaEkpEBH0CNGrYdt+npmDyKFEHi0eLFjq9uc3KQEbtwYYFPc0j0s7Iw+RTUJ9iS+HhjdE90dMF28ilTMPnv2GH7OefOIZy5Rg3sQqQiJwcVTVu0kEZ09XpEAImVPVu3xv1s63vw4AECNz780P1zezrduyNxzwuRX/TFGjVS2pw9leHDsXqzNB0cOYIKjmIRtM8+k6cBS8+eMIFIvfoQK2NOmJD/hhcEZJAWLuxYmeYbN+Cg1ung/F6wwP7K/59/7Dsl2UHRZzY2TS8IQUBNmx49MNaaNZE4ZW8npdfDXBMejh2dJSdP4jOqU8e1CKmC+PBDLCicLZdtD7GyZ7Nm+ByaNEHGveXE8vnnMAlKOZF5IhkZ+L7Pn6/2SFxCftFnVq9GjdKIzVVWrMD/9+93vgiaO1y9CnPR889Lb04Tk8FGjTK/2Rctwu+dbeUXH49okeBgLArGjbO9G/zkE6z07WQLOyz6EyZgpW2N1FR0wRIFrl49bOWd+dzu38fn/fjj5pP70aPY5TRogPo6UnLggP2m9O4iCNjBtGmDaxMVhRwHvd5YqtuXm6WIiPkZUkQ6qYAyoq9WjRo16NkTq33xxqhXDxl77oZzOorYaGXJEumP/dVXWPX26QNzza5dWFm6k3V98yZMImK/3Kgo7CxMV8m9e8O0YAeHRX/DBpxLXGlnZSHyqm9frOCIUL5g61bXzSTHj8OU9corEMvff8eE3KSJe/4bazx4ADt68+bK5cTs24cdDRFChgcP9g8zLjOCGx59VO1RuIwyoq90jRo1EATY1aOijDHq7hRBc4cxY2C3tlJz3m1++QViFhmJCJF27aSZ0HJycP1MhbdWLeRAlCzpUAlnh0X/8mVjieR27bCLMJ1wCura5Qxr1uC4XbvCzt+li/S1b8TOXmFh0o3bGQ4ehH2bCJ/bkiVe0zbQJfR6NPl55x21R+IyOmZmUoJnniEqXJho2zZFTqcYBgPR+vVEc+YQHT9O1LIlIsNv3SI6c4YoOFj5MWVnEz35JFFmJtHhw0TFikl7/Lg4otatifR6og0biHr0kPb46elEf/xBtHMn0e+/E124gN+XKUMUFYVH7dpE5csTlSuHR1gYpaanU1i9epRy6hSVCAkhunuXKDERj2vXiE6eJIqPJzp3Dp9bcDBRx45EbdviZ1SUtO8jM5OoSROiU6eI+vUj+v57osBAac+xdCnRqFH4Dj7/vLTHdpSvvyYaPpyoc2ei7dvxeUyYgN9J/d1Tm5gY3ON//42f3ohi08unn2L1KWV4mppYK4K2ezdWXqJt37LRiZKcOYPY//79pbXvCwKSfgoVgt07MBARPnKZr0TT4IoVCAbo0we7DCsJWClEWOlbJmYRYXX2zDPI5v3yS9QEatxYnjEzw2fx2GPYFTVoAFu+1GXGjx0zJvOpRU4O/CNiu8CzZ+GoDwpCCO+sWTA/+QqTJiHyzotrCikn+ufPS1snRi3sFUETeeEFPMfZUsVSIrZDlLJt5eef45his5bJk2G6aN7ctXr89hg50rr9VBAQ7nr+PK97+20eVqUKD6xUCaL/yy+IqT9+HJEk1uzcS5dCmKSOosrLQy/ekBD4c44fhw2/enVMMlI127hxA2LbqJG65pSlS+HnsSyOd/kyJiOxsue77/pGn9y6dTGpeTHKiT4z0t8dTQ33NJxNVT9xwnaNeSURm3ivWuX+sXbvxsp+3Djz38fEwJkn9gqV0o/RsKHDN5nDNn1m425s9243B2jC6dOY/HQ6ZCWbivGRI7g+Awa4v/NKTUVkUOXK6gZHZGdjDC+/bPs5N28iWkqs7DlunHyVPeXmzBl8ZzZtUnskbqGs6L/7LqI0lIpkkQLLImjOFKXq0werMTnDNO0hCCiDERyMaBtXuXrVaCKx9vllZDC/+SZuimbNpKmjnpJivR+wzac7Ifp6PVagUiQSpaaiFHShQpj8bL33H3/E9XEmMcyS3FxkyIaFYWGhJosXYwF06pT95yYlYQESFoZd0MiR6jie3WHBAjir5cixURBlRV9MsnE0pVtNEhMRSuhKETSRhASsjNXOUMzNhc/BVaHIykJxsapV7W/R9+5FaQEimLjOn3dtzMzokEXkmKiwk6LPDPHs2tX18eXlwT9QrhwE/9137QvCW29h8eDKPSAIKHPg7gQuBUlJ8FM4u3NPToYPqEwZXIdBg+QxC8pBq1Yw53o5yoq+wYCuQp7cTUssgla4MMoqTJzoXobhxIkQBFfL90pFSgoci5UrO9fwRRCwuylUyPF6NQYD6vZUqgSBGjfONTPEtGnYGTpoLnJa9MV66M6ao/R6xPpHRmJS6t/fcSdtbi5yOMqVcz4j9733pDPVuctrr2ER4eq9kZ6O4I6ICOzmXnrJs2P8ExOxq1EzOEMilBV9ZuYRIyA8nub9vnABzTvEImjTpjnfAMQaaWmoT//ss+oXnbt+HfkD1as7PgktWWJsPOIsGRmo116iBMR/4EDnSva2b+/UStxp0d+xw6mdBGdkwIn/yCPGBK5Dhxwe30Pu3ME90KyZY6Y/QTAKviek/otF66QomS5W9rQXGKE2Yoc8qTOpVUB50T940PWWfHJgWgStXDlEXkhVBE1k0ya85/XrpT2uK1y5AtGqVMm+2O3diy34m2+6d86UFDjBq1QxVm3csqXg7FG9HjstJyKPnBb9lBTHVm8XL8IeXbo0nv/ii3brANklLg5mQ3uN2gUBOyUi2JTVJjcXSWzNmkm7cLMWAu0pZmBBQJRUt25qj0QSlBd9Zth83bGlSoFpEbTKleFck9NB060bhNaVblRSc/MmTBPlytneUl+/jr+3aSNdan9uLkwTos2/dGns/Pbty29iOXoUz9m71+HDOy36zDB5DR6c//d37sBR+eSTGEfRoojxl9JM9913OPaXX1r/u8GAIn5yldVwhfnzMfEdOSLP8fV6VIpt2BDvu1Wrgit7KkFcHMby22/qjUFC1BF9OZuJ28O0CFqtWmgrp0Qs/eXLxpA1T+DuXaxeSpXC7suU7GyEHlau7HwjDkc5fhyJLuLqv1o1OMvXr4dZbckS7DKciGt3SfRHjkTstcEAIVuwAKvMwECc/7nnMFHJlVQ4ejRMX2LzcpG8POxAAwIwOXgC4nd47Fj5zyUIqIckFr5r3BjtM9UoazJ0KIIYPM0k7SLqiL4jteelRBCQrCP2bo2MxI2sdOjovHkQEzlq4rjCgweovV68uNHcJggwOYSGStekuyAMBqzmR47EJEyE3Vd4OJz+P/2E7FYHdhtOiX5iIiJg+vfHOUuVMtaP6dAB9mp3Wyo6Qk4OVrMVKxq7pqWkYCccFIT37yn06KH8blW8d00re65erZwAi03eZ81S5nwKoFztHUuGDyfaupXo8mWioCB5zsFM9NtvRLNno15M48ZEU6eiVkxAgDznLIi8PKJGjVCDKCZGnbo8lqSnE/XvT7R5M9GsWUSlSxONHEn03XdEgwYpP54rV4h27SJ64w0inQ7jI8K1qluXqH59osqVjTV3ypUjKluWKCQEtXdatqSU/fupRNGiRA8emNffSUxEPaSTJ/FvIqKQEKLcXKKXX8Z3skULotBQZd/z7dv4blavTvTll0R9+qB205o1RF26KDsWW6xfT/TCC0Tr1uGnGvz9N9GHH6IeU+3aRJMn47sbEiLfOZcsIXrrLaKrV4kiIuQ7j5KoNt0cPoyZ+9dfpT+22PHHk+yCInFxWMGJfWQ9AYMB0UriKnvYMHXHc+MGxrJuHVbbu3fD3DNyJNom1qmDCCtHa+8EByM08PHHkTswbRqOfeoUdhAVKiAnQ03++Qffi5AQmJs8qVb75cvy9WlwhUOHmHv1wmdbtSp8L1KVtzBFEFA3qVcv6Y+tIuqJPjNqiz/7rHTHy81l/vZb13p7KsnHH2N827apPRIjN27gxg4MxBbaWtcnGcnNzeV33nmHo6Ki+JX/iqmN6d2bbxSUsp+dDYfzkSPMcXGcsmsXRH/XLoT9nTkDE5Y9oXr+eZgP1EIQkMCn0+HpKOcMAAAgAElEQVR78b//qTcWS3JzYQKsVs3zCqedOIF+BQEBmLgXLJDW9xIT47XNzwtCXdH/+mt80Z3NdLUkKwsrwWrV8CH16KGMPdpVDAZMdmXKeEZjmexsRKlUqoRVda1asKn//LNiQ0hOTub27dvz2rVr+d7AgZwVEcHNmzfnxk5UwnTJkcuMSbhwYeUakJhy5w6+r0TwcYm5Ip4Sq/7OO9iBxMaqPRLbnDsHZ2twML63M2dKM0ENHIg+xj7W5F1d0U9LgxPx/fddf/2CBZjlAwJQ+MmZ5B81uXsXJoenn1Y/KmD4cAiNGHt+7x7CWYmQKSl1pyd7NGvG3K8fx8XFMRHxFQezXV0WfXFFZxnFJDc//4yJv0wZYxGv7GysrCtVUj8R6P/+z3MSwhzhyhU02ylUCAmBU6a4Xtnz/n0cZ84cacfoAagr+syI07bWTLwg7t9nnjEDs3pQEKownj0r3xjlYvduTFbTp6s3hq++wo29fLn57wUBURKlSjGXLy+P78UaGRn4TL/4gv/44w/W6XQ2RTw7O5tTUlIePq5du+aa6GdnI1pp0SIJ3oADJCVhMiWCackyLPbGDSxkWrdWZ/chjqFMGXT78raV7q1b8JkVK4Yd3Nixzu+oFy3C91DtiVcG1Bd9MQln40b7z71zB/XbixfHTTpmjPSNKZRmxgwI/19/KX/u2FhjxUNb3LyJ8EEiFNe6f1/eMe3Zw0zE2XFx3LhxY+7Xr5/Np06bNo3pP+et6cNp0WdmbtkSVVHlZtMmTKKlSiFs2Ja/4e+/ITpvvCH/mCzR67EDjYjw7hr49+7BaV+yJL7nI0Y4VtlTENALwUebvKsv+szYznfsaPvv166hOqFURdA8Cb0eNVwqVlS2zvjNmzhndLT95DRBQIJQiRLIov38c7dXoCtXruSiRYs+fOwVM2/nzGGhRAnu1b07N2rUqEABl2ylz4zvVKVKLr4bB4iPNzYSf+45xz7rL74wdg1Tkvffx0JEyl4DapKSgnIeZcsiUGHgwIIre+7di+v+55+KDVFJPEP0xQ5Pls7X8+cRPhgcLG0RNE/j5k1kvz7+uDKJLzk5WNmaJgQ5ws2bcJjpdIiQ2rTJ5RC+1NRUPnfu3MNH5n8hd4Znn+WjZctyw4YNOclJX4LLNn1mY30kqXeOt2/DORsQwFyzJkJFHb1mggDTZWioa4XdXGHFClwHH7Rlc0YGzDZiZc8+fayXIencGSt9bzNrOYhniL5ej9hkMXzz5Enmfv1wo8hVBM3T+PdfrKQ7dZLfjjtyJCZSVyMyjh1DBUwihDpKJEi52dmcGhzMi8uW5UQXzApuif6dO3g/q1c7/1prZGaiwmixYjDlfPKJa810nOll4C47dsCkNGyYZ8Tjy0V2NvOyZYjMsazsKTr1PSkTWmI8Q/SZcbMRGUslKFEEzdPYuRNiPHiwfDfdN9/g+rrbxlEQmLduxYqICHZ/sTG8C+Tl5fGoZ55hJuLzS5fyrVu3Hj5yHKyN5JboM6P6qLs29Hv3EHNfoQI+y7Fj3d+d2utaJgVHj8JX9uyz3tXZzh3y8ph/+AELTrGyZ5MmaOvqo6t8Zk8S/YwM2NsKF1auCJonIrbUkyOi58ABOLRef126Y+blwd5fvz7G3aQJVklOCselS5d4CBEbiLi4hWP2Lwed3G6L/oABKOzlChcuILCgSBGYY4YNQ/y4VOzZg/vj7belO6bIlSsw9TVuLF9hOU9Gr0f4rNgnQQ3nuYJ4jugzI+aeKH/FQX/jww9xHb79Vrpj3roFR+WTT8rTs1cQENfdrp2xauannzpXtGzwYJQ6dhG3RX/ZMgiro8InFot74QWYIsuUgd9Jrsqkn30mrQmKGdFYkZEwdfhgeKJTtGuHZi4+bkr2LNE3GLBi7NBB7ZGoiyAgYSowUJoUcLGSY4UKykQIHT2K6pVBQcbyxKtXo0VeQTz6KPOoUS6f1m3RP3EComqv/+y//yJ0WMwAr10b5cLlqP9iiiCg3HLhwvCruEt2Nnwy4eHe06dWLv4LFeYNG9Qeiex4lugzY5tFhDhlfyYvD3byokXdD50Ta7bv3y/N2BzFWiOSfv1Qcygry/y5d+/iOStXunw6t0XfYIAzffbs/H+7eBFhfw0aYJzh4ZiY9+5V1v6bmYk+CDVquJcpnZ3N3LMnTFH+fq8xw5f4+OO+7cD+D88TfYMBN1a7dmqPRH3S0xElU6iQ6yv+b78tuDuTUly4ADEVHb+FCuG9ffQRfA0bN+L3jiTP2MBt0WdG9FSXLpiw1qyBbb5mTWOt/ZdfRu8BNX1Oly8jX6JDB9dKeGRmIiwxNNRnukG5xa5d8lX89UA8T/SZ0T3JyVZ5PktWFlb8ISHG+iyOIvZhHTrUc1YwggDzyMKFiBQpVgyfdWgoJoK5c7ETuHrV6TG7LPoZGai7s2IFOoYFBBjLMkdGwkG7YYNnOTl37sQ4J01y7nWpqVjVFinis8lHTiEIKHfRuLHn3CMyo14TlYIQBKInniAKD0dDDX8nNxfNIjZsIFq5kqhvX/uvSUxEY45KlYj27FG+MYij5OURHTxI9MorRBkZRNnZxsYpJUoQRUXhUa8eUcWK5s1TwsOJAgMfHio1NZXCwsIoJSWFSpQoYTxHRgauh9hQ5e5dogsXiOLj8bh4ERJPhEYZN28SzZtH9OqrOKensnAh0YQJRGvXovGKPZKT0ZQlIQENjFq1kn+Mns7OnUTt2xNt2ULUtavao1EEzxR9IqJNm4h69SLavZuoTRu1R6M+ej3RkCEQ/eXLiQYPtv3cvDyiDh2ITp8mOnwYwu/J5OYShYURzZmDLkXXrhGdOGEU5fh4dLzKzjZ/nU5HVKYMUdGiRESUKggUdvUqpVStSiUCAogMBqKkJKKsrPznjIgwTiimEwszUcmS6GA1bJgCb94NmDFZbt5M9M8/RA0a2H5uUhJRx47oTLZ9O1GTJsqN01NhJmrdGt+/AwfwffIDPFf0mbFSLV4cwu8nH0iBCALRqFFEy5YRLV5MNHq09eeNHYs2b3/95R2ruQMH0KbwwAGiZs2sP4eZKC3NvPWh+PhP1FNzcihs4UJKGT+eSoSGoiVm6dLGlorizzJlCm6x98QTRA0bEq1YIf17lZqMDKLoaPw8eJCoVKn8z7l1C6vZpCSiP/8seHLwJ3bsIOrUiWjbNs9pS6kEatqW7LJtG+yqa9eqPRLPQRCYx43DdZk2LX/kyA8/4G+LF6syPJdYuFCSJiaSOHKZEe1Up457x1CSCxdQ6qFLl/yO3VOn0BSnUiUtLNOUnByEh0dH+40tX8SzRZ8Z/SkrVkRXeg1g2l6vZ09jkbbDh+EMlbOMgxz07o3et24imeiLBQCdSSxTm+3b4didOtX4u82bUVohMlLx9pcez9y5yIORIt/By/B80b96FfHdPp4a7RKmN/U//6AoV9Om+WPgPRlBcLsx+eLFi7levXpcp04daUT/8mWI/ubN7h1HaebOxbh/+QUtA4nMFwUa4NIl7CzlKGnhBXi+6DOjh2lAgHLlZb2JhARkhAYFMYeFYZL0Ji5ehDht2eL2oSRb6QsCyu86Gw6pNoKAfruBgbimM2b4dOEwlxAEZIhXruy3k2GAuh4FB3nzTURXjBiBiAwNI/XqIVLHYICj86efjOGH3sD+/fgZHa3uOEzR6TCe2Fi1R+IcFy8SnT2Lzz8iApFQAd5xiyvGpk0IV/38cwSJ+CHe8Y0IDiZaupTo0CFErmgYWb2a6IsviD79lGjSJKJ33iHq1w/RHN7A/v2YuMLD1R6JOdHRRHFxCOfzBsQwTL2e6LffiDIzkWcgCGqPzHNIT8cCsmtXop491R6Neqi91XCKYcNQG8VXWiW6y9GjsE0OGGB03K5di2zL2rWVr7XjCg0aIGNYAiQz7zCjNASRsbmGp5KRgZr9Oh2idx48wO+3bsXv5CjR7a2MH4/7xY1SH76Ad4n+vXsoX/vyy2qPRH3u3kWVx8aN81d3PH2auUUL+EEmTvRcx25yMoRJohLSkop+Tg4ioT791P1jyUVMDEJLCxVC2KtluOasWZL5S7yeY8fg65g7V+2RqI53iT6zsYfnH3+oPRL1yMtDQboyZWz3dNXr8QUPCUF0z8GDyo7REX7/HZ+lRPHjkoo+M2qyvPCCNMeSkqws5nfewaTevDli8a1hMCB6p0QJ5jNnlB2jJ2EwYBEUGem/zZlM8A6bvikDBqAsw6hR+dPy/YUpU5Cl/PPPRFWrWn9OYCBs/IcPExUqhIzX99/3LBt1TAyyY+vUUXsk1mnZEmP0JMf4oUPIVF+0iOjDD4n+/puobl3rzw0IIPr+ezh1e/aEo98f+eYblKlYurTgTGx/Qe1ZxyUSElAffsYMtUeiPGvWYHXsjNkhNxfXKigInamOHpVvfM7Qrh2aUkuE5Cv9zZvdLvcsGdnZzO+9BxPFE0+g4YujnD6NfI5evfwvhPPOHeaSJZGwqMHM3mjeEZkyBeV4//1X7ZEox7FjcET17+9axu3hw8xRUTALDBumrkM8Lw9llSW0sUou+mJjl1WrpDmeKwgCGgvVrIlJe8YM18pV/Por3ou1BjG+iiAwv/QSGt54U3a1zHiv6GdmMjdsiE729trw+QJJSeiW1KgRIjZcJSeHedEi1GopVgzOPneO5ypHj0KE9u2T7JCSiz4zHKWjR0t3PGeIjUVtGCL0Hjh50r3jTZsGx/m2bZIMz+P55htcuzVr1B6JR+G9os8MB1aRIr6/ddPr0SWpdGnpTA337yMNPTgY2Ynff6/s1n/xYpxbwr6ysoj+oEFoo6ckFy9ihUoEc5xUQQsGAxrylCzJfP68NMf0VOLjsSseNkztkXgc3i36zMzffed2b1WPZ9IkmGTk6HR0/jwKnhHBVvzXX9KfwxqvvIKICgmRRfS//hrXXomU/QcPEGIbEoIig99+61o7RHvnqF0bZj5P6gQmJRkZiNSpX1+dXayH4/2iLwiwcRcrxnz2rNqjkZ61ayHICxfKe559+5ibNcO5OnRg3rFD3kqd1apJXvBKFtE/eRLXRM7WgnfuwPRSujR2rtOny2uyPHkS90ufPt5VjdVRhg7FKt9dc5iP4v2iz4xVWJ062IZ7aiKSK/z7L0Tg5ZeVuTkNBkwyjRpB6Bo2RH1+qWObr1/H8devl/Swsoi+wQBzyMyZ0h1T5PRp5tdfR3JVkSLwHdy4If15rCH2oZ4/X5nzKYVYFnv5crVH4rH4hugzwzEYGoom1r7A/fuI2HjsMeW3qIKAxttduuAGiohgnjfPmOLvLj//jONKHD0ki+gzw4naubM0xxIE5j17mLt1wzUoXx4RNUlJ0hzfGaZMgenKVxIdz57FDqZfP9/cwUiE74g+M5yDRMwbNqg9EvfQ65k7dUKomdrNL06cgKM8OBg31Lhx6NTkDmPHYkKTCMnr6VsyezbKVrvj6M7JYf7pJ+YmTfAdjYzEajQ7W7pxOosnfc/cJTsbO9Tatf22ZLKj+JboCwISUEqWRCMMb0Vcge3YofZIjNy8yfzuuwj1JGJ+8klMsomJzh+raVP4YSRGtpX+rl14z87mhBgMzLt3w4QjXrd27RAy6Skr0Xv3MAE//rh3Oz3feAMOcE9JPPRgfEv0mWEWqVYNouRmz1VVWLfOs22t6emwmz73HJKFAgNhBlq50rFokIwMvG7pUsmHJpvop6fjfS5bZv+5ggDhmTgRobBE+D5OmeJcFq2SHD8On4K3mkU2bPC+vtAq4nuiz4yklqAg5smT1R6Jc5w4gdaQL73kHTdfYiLzF18wt2yJm050Om/ebHsC2L0bzz1+XPLhyCb6zKhmOnCg9b8JAnJGZs9mrlcP769MGeZRo5j//ts7Sh/89JPz5T08gUuXsLN//nnvuGc8AN8UfWY4HsV+od7A/fvMtWqhvrw3ZhhfusQ8Zw5io4kw6bZqhVDEPXuMEUAffoiqj1LHn7PMov/GG8yPPGL8/9WryBF59VXmSpXwnosWxWp52zbv3GVOnIgdza5dao/EMdLT4SOpVk26IAM/QMfsSSUEJUQQ0EFq40ainTtRMdFTMRiIunVDJcBDh4hq1lR7RO5x5gyu+c6dRH/9RfTgAVGRIkStWxNduUJUsiSqQwYGSnra1NRUCgsLo5SUFCpRooSkx6avviIaPhzdqGJjic6fR1vFRo2I2rYlatcO769oUWnPqyR6PVGXLkTHjqE6q60Krp6AXk/0/PNEu3YR7dmDyqMaDuG7ok9ElJND1KkT0YkTKJH76KNqj8g6771H9NFHRP/3f0QdO6o9GmkxGCAiu3YR/fkn0Y4d+H2RIkT166P3semjYkWIqQtIIvpZWUSnTxPFxxsfJ09isiIiqlyZqHt3iHybNkSlS7t2Hk/l3j20XSxdmmjfPqLChdUeUX6YiUaPxkS8ZQsmKg2H8W3RJ8Iqs1Ur3MyxsUTly6s9InM2bCDq3Zto7lzUv/dlEhIg9AsX4sY1FdWsLDynVCmIf/36RNWrE5Url/9hQ4jsir7BQHT/PtHdu0SJicaft24RnTqFsZw/b+wrW62acSyPPUY0YQJR//5E8+fLc308hWPH0CP4xReJVqxweRKWjblz0VPim2+Ihg5VezReh++LPhFWaU8+SVSpEpqPeMoWPCGBqHlzos6d0RDF024uqfn6a6IRI4iSk4mKFzf+XhCILl0ynwTi44muX8ekbUmxYhD/smWJQkMf/jpVr6ewmBhKiY6mEkFBxmM/eACBT0rK3yg8OBgLgbp1jQIfFUUUGUlkOXG89BLGtH+/RBfEg1m9GubR//2PaMwYtUdjZNUqTLwffEA0Y4bao/FK/EP0ibB6ad0aW/JNm4hEUVCL5GSiZs0gWrGxEDJfZ/BgfA5Hjzr+mtxciHViovnqXHzk5T18ampuLoWtXUspL71EJUw7JJUqZZwkLH+GhTk+2X72GXZjKSlmk43PMm4c0eLFMM21bq32aDCOzp0xGX37re8vkmTCf0SfiGj7dqLnnsOW8Msv1fvSCALswvv3Ex08SPTII+qMQ2nq1IHPYvFiWQ4vqyOXCJ9Vs2aYpFu0kP74nkZeHj6vhAQ4ditXVm8sJ07ATNuiBdFvv2GHpuES3tcj1x06dYKJ4auv4DhVixkziLZtwxbaXwT/7l2ic+c8O4rKHo8/Dn+CP5h3iCCsa9diV9O7NwIj1OD6daJnn0VU27p1muC7iX+JPhFMDNOnE02dSrRypfLn//VXopkziWbP9q+og5gY/IyOVncc7hAcjJW++F78gXLlEGxw/DgiZpQ2DKSkQPADAoi2bs3vZ9FwGv8TfSI4gYYMwWPnTuXOe/o04ryffx7RB/5ETAwc6Z4c++0I0dF4L35kFaUmTWAOXb4cu2SlyM3FDuPaNYQzR0Qod24fxj9FX6fDl7htWwjwgQPynzMlhahnT6IqVTwzDE5u9u+HYHr7+27Zkuj2baLLl9UeibIMGoSV/htvwKchN3o9zrlvHwIvIiPlP6ef4J+iT4St+rp1RA0aELVvT7R3r3znEgSiAQMgFps2mYcr+gM5Ocg09mZ7vsiTT+Knv9j1TfnkE4QY9+6N3Aa5yM0l6tsX9+eqVYi405AM/xV9Iojv9u2w03bubMwWlZrZs5E5uGoVUe3a8pzDkzlyBMIvkz1/yZIlFBkZSU2bNpXl+GaEhxPVq+dfdn2RkBAIsU5H9MILEGepycoi6tUL98v69TiPhrSoU/LHw8jMRHekkBDmX3+V9thbtqAYlxzt9ryFjz9Gz1KZi5DJWnDNlKFD0dHMX4mNxb0yYoS0x01LY27bFt8VT+ol4WP490pfpHBhFGbr1g1b17VrpTnumTNIJOnZE9FC/sr+/dhN+UqoXXQ04sZTU9UeiTq0aEG0ZInRuSsFKSkIqT54ELvvDh2kOa5GPjTRFwkJIfrpJ9gSX3mF6Pvv3TteairEPiICxwrw00vNDFOIL9jzRaKj4adRIgDAU3ntNVQdHTWKKC7OvWMlJSGoIiEBRfk8IfvXh/FTJbJBUBAEeuhQRA4sXeracQSBaOBAohs34Lj159jiixeJ7tzx7vh8S+rUgW3fH+36pnz2GdETTyAC7s4d145x+zbR008jLHP3buwINWRFE31LAgKIli0jeustrGIWLnT+GB99BLFfudJzyzkrhSiMYtSLLxAQYIzX92dCQ+FsNRiI+vQxq4PkENeuET31FAri7dmDSqYasqOJvjV0OqJPP0UC1YQJRLNmOZ6Ms20b0fvvI+u3e3dZh+kV7N+PaJfwcLVHIi3R0YhXNxjUHom6REQQ/fILJsAJExx/3YULMOPk5iJcul49+caoYYYm+rbQ6YjmzEG45QcfEE2enL8sryXnzsEf0LUrhF8Dou9L9nyR6GiitDSUgfZ3WrYk+vxzPH74wf7zExKwwg8JQfJVrVryj1HjIZro22PqVCSlzJ+PmOG0NOvPS0uD47ZCBaIff/Rfx60pKSkQRV+y54s0bQofkD8maVljxAiUNRk+HBU5bbF1K0x94eFY4VepotwYNYhIE33HGDcOhdL+/BNf2PPnzf/OjEJu167Blh8Wps44PY3YWFwbX1zpFymCqpv+btcX0ekQxtmgARy7d++a/52Z6MMPERb99NOYLCtUUGWo/o4m+o7SvTsal+fmYpVnmr07bx4cWj/8gA5MGiAmhqhMGd/NQm7ZUhN9UwoVwn2QnY0uY3o9fp+eDkfve+/BVLpxo39HtKmMJvrOEBmJmOQWLVAW+eOPUf3v3Xdhw+/ZU+0Reha+UmTNFtHRCEm9fVvtkXgOVaqg9efevegydvEirtPvv6NE8/TpmulTZbSr7ywlS6Jzz8SJePTogUzC6dPVHplnodcjeclF087w4cNJp9PRokWLJB6YhIi+Cm21b06bNvCDffIJUcOGqKfzzz+oqaOhOprou0JgINHcuXBc6fWoOHj9utqj8iz+/ZcoI8MlJ+6mTZvowIEDFOHp9dMrV0Z/AE30zWGGGVSnw6o+NhYN5zU8Ak303WH5cpgwkpPRaGLfPrVH5Dns349aO02aOPWyGzdu0JgxY2jVqlUUbKdWT05ODqWmppo9FEdL0jInKwuNgiZOJHr7baJLl+DX0fAYNNF3lyefRJGo+vVRP2TpUv/qqmSLmBiixo3h3HMQQRDo1VdfpYkTJ1J9B1aGH330EYWFhT18VFEj/C86GiGK2dnKn9vTuHoVzcs3bCBaswY+r9Kl1R6VhgWa6EtB2bKI5hk5EqUbBgxAark/40JS1rx58ygoKIjefPNNh54/ZcoUSklJefi4du2aKyN1j+homDIKik33B377Dbu6e/cw4fftq/aINGygib5UBAcjI/HHH9EAIioKEQv+yLVreBQg+qtWraJixYo9fOzZs4c+++wzWrFiBekcjPYJDQ2lEiVKmD0U57HHELPvr0layckoTtitG4qlHTqE/AUNj0XHrNkiJOf6dVTq3LGDaNgwFG3zpxaJa9dipXfrls0EnLS0NLpjUplx3bp1NHXqVAowCeczGAwUEBBAVapUocsO9KRNTU2lsLAwSklJUXYCaNsWCXkbNyp3Tk9g+3aUWE5NJVq0COLvq+G5PoQm+nLBTPTVV0Tjx8OR9e23EAd/4K23kG5vmblcAPfu3aNbFn1XO3XqRK+++ioNHjyYHnWgWqlqov/ee/is79zxD9FLS0Nxta++QrOT5cu1cgpehGbekQudDnVITpwgqlGDqF07ojfeQBijryMmZTlB6dKlKSoqyuwRHBxMFSpUcEjwVaVlS5QduHBB7ZHIz19/odTCqlXonLV9uyb4XoYm+nJTowbRzp1oOLF8Oeydvmz/zcggOnbMN+vt2KJFC/z05dDNjAwsWtq2JapeHYuZ4cP9Y2fjY2iirwQBAURvvgkxLFsWdcQnTPDNML+4ONSYl6Cy5uXLl2ns2LESDEpmSpVCiQ5fFf39+7FYWb4ci5ddu7CY0fBKNNFXkjp1kMA1bx7R4sVEjRr5Xp/VmBgU0/K3DMzoaN/bwWVlYXHSujVRuXJYtLz5plY7x8vRPj2lCQxEtuKRI0TFisE0MGAAQhx9gf37kbDmb8LQsiV6ByQnqz0S9xEE2Ozr1sXiZP58FFCrU0ftkWlIgJ/dmR5EZCRqkixbBmdYnTqIArHVpMUbEAS8J3+y54tERyNiy9t3bnv3EjVvTtS/P5KtTpzAaj8wUO2RaUiEJvpqEhRE9PrrCG0cPx7x/LVrIxROrEXuTZw6hZWuL3bKskft2ig54K12/bNnUQWzTRs4Z/fuRW18X+2F4Mdoou8JFC+OXrxnzyLuefhw2Pu3b1d7ZM6xfz9WhM2bqz0S5dHpvLP42r17yKuoXx8mx1WrUAa5dWu1R6YhE5roexJVqqCMw8GD6CHauTMe8fFqj8wxYmJQlqBYMbVHog4tW0IwvWGXlpODgmi1ahGtWIFFx5kzRK+84n/+GD9D+3Q9kSZNiHbvRlr/xYsQ0tdf9/wOTS4kZfkU0dFoDXjihNojsQ0zOlvVq0c0eTJRv34wL06a5FRFVA3vRRN9T0WnQ/vF+Hh0IBLtqx98QJSYqPbo8pOYCPHwZ9Fv0gSF92Jj1R5JfphhLoyORv/a+vUxOS1ZgtwRDb9BE31PJyQENtfz52HrX7iQqFo1/PvMGbVHZ0S0ZasQubNkyRKKjIykpk2bKn5uMwoXJnriCc+K18/JgfmmYUOYCvV6ZIhv2YLVvobfoYm+t1CqFGyw165htb95M+Koe/RAwpfadfNiYoztAxVm9OjRlJCQQAcPHlT83PnwFGfu/ftEH32EzNnBg1E64a+/kDHtL4X/NKyiib63ER5ONGUK0eXLqNx5/jzRU08hyevnn9VzIvq7PV8kOhqfzc2b6pz/4kVkzVapQjRjBtFzzxElJGBl//TTWq0cDU30vZbQUKzg4uOJtm1DxMxLL8Hu//nncCgqRfvMsbEAAATISURBVE4Ommf4Y1KWJeLEp7Rd/59/iF58EZ//6tXI+7hyhejrrzUzjoYZmuh7OzodUZcusNMeOQLhffttrPTefReNTOTm8GG0DNRW+kQRETClKGHXNxgQ4dWqFUpfHD8Ox+zVq0QzZxKVLy//GDS8Dk30fYlGjYhWrsQWf+hQ1E2pWpWoa1es/uSq5b9/P1oGPvaYPMf3NuS26584ARNfrVpEzz+PiX/jRmREjxiBz0JDwwaa6PsiVasanb6LFqFJe79+WPn17w9zUF6edOeLiUF/1OBg6Y7pzURHY9eVlSXdMa9cIZo7F1E4DRuiZlOnTjDr7NuH8F6tPo6GA2ii78uEhRGNHo2V+MWLWB0eOQLnXkQE/hYT417kDzOOr9nzjbRsiUn10CH3jpOURLR0KUoiVK8Ok039+ojcun0bwu+PJS803EITfX+hRg2iqVNR/vfoUTiBN2+GQNWsib8lJDh/3AsX0CpQs+cbiYqCY90VE09GBkxxXbsSVayIblXFi6M8x507RGvWEHXrhvwNDQ0X0Bqj+zOCgGqKq1cTrVuHCpmPPYYooA4d4COwZzL4/nuiQYMQF16qlCLDtoVqjdGt0b49UdGiRL/+av+5SUmIod+0CY/MTEyir7yCiJxy5eQfr4bfoIm+BsjJIfr9d1RZ3LoVwlOqFGK727VDQk/duvnjvIcPh3nHA4rCeZTof/ABTDOJifmvWVoaJttdu/A4dgy/r18fQv/yy1o7Qg3Z0ERfIz+5ucjc3LkTj3/+gY06IgLiL04CVavClBEdjR4AKuNRor99O8oenDmD6xQbC4HfudPYR7hyZVzLdu2InnkG/9fQkJkgtQeg4YGEhCD2u1UromnTYGf++2/jJLBqFRy4NWvCQdymDez6WuEuoNcbzWK9euEaZWcTlSkDcR84EJPmI49oGbIaiqOt9DWc5949lH5eu5ZowwasWomwE4iKMn9ERsK2rQCKr/QFAYlQ8fF4nDyJn6dOwVwWEABhHzECIt+ggVarXkN1NNHXcA9mouvXEakiil98PKJ6xK9WzZqwV5tOBo8+ilISEiKb6DMjRNL0/Z08iYdY7qJECbwv8X02bQpHuFajXsPD0ERfQx4yM7HiNRXK+HhMEEQwf9SpgzLR5cqZP8qWNf+/g8LptOgLAhLXEhNhnkpMNP/33bsonHbqFKKTiFA+OTLSXOCjomCP10w1Gl6AJvoaypKcbDSDxMcT3bhhFNvERKKUlPyvKV7cfBIIDzczkyQkJFBCQgJlMtPA1FRKGTCASliLY09PNxf1pCSjaUokKMg46ZQtiyzmunWN4l6jhpb5quHVaKKv4Vnk5JivtE0nBPFx/77VLOJUvZ7CDh+mlMaNqUSQRYwCM3wLljsJU4EvV46oZEltxa7h02iir+EzeFTIpoaGh6KFEmhoaGj4EZroa2hoaPgRmuhraGho+BGa6GtoaGj4EZroa2hoaPgRmuhraGho+BFayKaGz8DMlJaWRsWLFyedFmuvoWEVTfQ1NDQ0/AjNvKOhoaHhR2iir6GhoeFHaKKvoaGh4Udooq+hoaHhR2iir6GhoeFHaKKvoaGh4Udooq+hoaHhR2iir6GhoeFHaKKvoaGh4Udooq+hoaHhR/w/m0MBkzI5rlIAAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 30 graphics primitives" ] }, "execution_count": 37, "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": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 40 graphics primitives" ] }, "execution_count": 38, "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": 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.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": 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), 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": 41, "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": 42, "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": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N.parent()" ] }, { "cell_type": "code", "execution_count": 43, "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": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S.parent()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We have of course

" ] }, { "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 V" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N in S2" ] }, { "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 U" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{False}$ " ], "text/plain": [ "False" ] }, "execution_count": 47, "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": 48, "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": 49, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 49, "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": 50, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$\\left ( \\frac{\\pi}{2}, \\quad \\frac{\\pi}{2}\\right )$$" ], "text/plain": [ "(pi/2, pi/2)" ] }, "execution_count": 50, "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": 51, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Error: the point does not belong to the domain of Chart (A, (theta, phi))\n" ] } ], "source": [ "try:\n", " N.coord(spher)\n", "except ValueError as exc:\n", " print('Error: ' + str(exc))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 52, "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": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R3 = Manifold(3, 'R^3', r'\\mathbb{R}^3', start_index=1)\n", "R3.set_calculus_method('sympy')\n", "cart. = R3.chart() ; cart" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 53, "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": 54, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\Phi:& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R}^3 \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(\\frac{2 x}{x^{2} + y^{2} + 1}, \\frac{2 y}{x^{2} + y^{2} + 1}, \\frac{x^{2} + y^{2} - 1}{x^{2} + y^{2} + 1}\\right) \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(\\frac{2 xp}{xp^{2} + yp^{2} + 1}, \\frac{2 yp}{xp^{2} + yp^{2} + 1}, - \\frac{xp^{2} + yp^{2} - 1}{xp^{2} + yp^{2} + 1}\\right) \\end{array}$ " ], "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": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.display()" ] }, { "cell_type": "code", "execution_count": 55, "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": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.parent()" ] }, { "cell_type": "code", "execution_count": 56, "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": 57, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 57, "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": 58, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point Phi(N) on the 3-dimensional differentiable manifold R^3\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGEAAAAWCAYAAADQIfLaAAAABHNCSVQICAgIfAhkiAAAAndJREFUaIHt2DloVEEcx/GPZj2IJN6KF4rxQCvxQBAR0lpYCYJHr9hZekAatfNArGw8QATRRlIIoiIqgoWiVoKgYCIaFUVTiHgUsw8mm7frvuzGTLFfWB7///znP7+3//dm5g0tkmU2dkb2SlzHSZzARcwdA10xKWqCdjzL8bfhNKbUk6QDZzGhbE/FW+yOYg7iBSaNVGmDpKgJNuAx/lRpXyE8LP/kDNZG9lF8QCnyzcBP7CssszmkpmkVenEej1QvAvRgT61kS3GrwvcSN3Jin+N2nSKbTYqaMs6rXYRZwnTVljnGVwTsx6XI7sBy9Ock68e6kahskBQ1FeEj+tCdOSqLsBX3I3tx+fo9J9kgOjGxiQLrIUVNRXmAbZkRF2EB5uBV5OssXwdzEmW+ac1UVwcpairKU9EbGxdhibDYxfwqX3/nJMp2T6WcttEkRU1F+SRMqRhahLn4WhE8UCNRtt/91hxddZOipqJ8FrbZGFqEkuFP13thpZ+ek2gKvvj/N5yipqKU8CMz4iIMGH5jg3iCRTmJlglz2/8mRU1FmS6a+uMi9GFmTodebMS4yNcl/AlXK2JXYnJTZNYmRU1FmI03eQ3j8A7zK/zzhFc8/so7JXwYxVvBbmGauNYspTVIUVPGlfKY7TVijuFQtcYL2JHjXyM8fSdxTriphRUxq4Up7XXdchsjJU1zcFM4u/pT/g3gDnblxN/D+mrJNhn+Ohelp8H+o0HPWAuI6MLd2FH5xfxQ2Gt3NTDIWJ5iViMlTQdw5F9By3DZ0EWvXrqxfQT9RpOUNG0R1q662Iy9BQco4XjBPqNNSpracFh0etqiRYsWifEX1YWD0eAy72YAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left ( 0, \\quad 0, \\quad 1\\right )$$" ], "text/plain": [ "(0, 0, 1)" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N1 = Phi(N) ; print(N1) ; N1 ; N1.coord()" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point Phi(S) on the 3-dimensional differentiable manifold R^3\n" ] }, { "data": { "image/png": "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\n", "text/latex": [ "$$\\left ( 0, \\quad 0, \\quad -1\\right )$$" ], "text/plain": [ "(0, 0, -1)" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S1 = Phi(S) ; print(S1) ; S1 ; S1.coord()" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Point Phi(E) on the 3-dimensional differentiable manifold R^3\n" ] }, { "data": { "image/png": "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\n", "text/latex": [ "$$\\left ( 0, \\quad 1, \\quad 0\\right )$$" ], "text/plain": [ "(0, 1, 0)" ] }, "execution_count": 60, "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": 61, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$\\left ( \\frac{2 x}{x^{2} + y^{2} + 1}, \\quad \\frac{2 y}{x^{2} + y^{2} + 1}, \\quad \\frac{x^{2} + y^{2} - 1}{x^{2} + y^{2} + 1}\\right )$$" ], "text/plain": [ "(2*x/(x**2 + y**2 + 1),\n", " 2*y/(x**2 + y**2 + 1),\n", " (x**2 + y**2 - 1)/(x**2 + y**2 + 1))" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.expr(stereoN_A, cart)" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$\\left ( \\sin{\\left (\\theta \\right )} \\cos{\\left (\\phi \\right )}, \\quad \\sin{\\left (\\phi \\right )} \\sin{\\left (\\theta \\right )}, \\quad \\cos{\\left (\\theta \\right )}\\right )$$" ], "text/plain": [ "(sin(theta)*cos(phi), sin(phi)*sin(theta), cos(theta))" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi.expr(spher, cart)" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\Phi:& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R}^3 \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & \\left(X, Y, Z\\right) = \\left(\\sin{\\left (\\theta \\right )} \\cos{\\left (\\phi \\right )}, \\sin{\\left (\\phi \\right )} \\sin{\\left (\\theta \\right )}, \\cos{\\left (\\theta \\right )}\\right) \\end{array}$ " ], "text/plain": [ "Phi: S^2 --> R^3\n", "on A: (theta, phi) |--> (X, Y, Z) = (sin(theta)*cos(phi), sin(phi)*sin(theta), cos(theta))" ] }, "execution_count": 63, "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": 64, "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": 65, "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": 66, "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": 67, "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": 68, "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": 68, "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": 69, "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": 70, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}2$ " ], "text/plain": [ "2" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dim(T_N)" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 71, "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": 72, "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": 72, "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": 73, "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": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_E = S2.tangent_space(E)\n", "print(T_E) ; T_E" ] }, { "cell_type": "code", "execution_count": 74, "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/dtheta,d/dphi) 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.bases()" ] }, { "cell_type": "code", "execution_count": 75, "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": 75, "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": 76, "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": 77, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v in T_E" ] }, { "cell_type": "code", "execution_count": 78, "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": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.parent()" ] }, { "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/dx + 2 d/dy" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display()" ] }, { "cell_type": "code", "execution_count": 80, "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": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.display(T_E.bases()[1])" ] }, { "cell_type": "code", "execution_count": 81, "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/dtheta + 3 d/dphi" ] }, "execution_count": 81, "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": 82, "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": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E = Phi.differential(E)\n", "print(dPhi_E) ; dPhi_E" ] }, { "cell_type": "code", "execution_count": 83, "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": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E.domain()" ] }, { "cell_type": "code", "execution_count": 84, "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": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E.codomain()" ] }, { "cell_type": "code", "execution_count": 85, "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": 85, "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": 86, "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": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E(v)" ] }, { "cell_type": "code", "execution_count": 87, "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": 88, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dPhi_E(v) in R3.tangent_space(Phi(E))" ] }, { "cell_type": "code", "execution_count": 89, "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": 89, "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": 90, "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": 90, "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": 91, "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": 91, "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": 92, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\text{SR}$ " ], "text/plain": [ "Symbolic Ring" ] }, "execution_count": 92, "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": 93, "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": 94, "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: (theta, phi) |--> 2" ] }, "execution_count": 94, "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": 95, "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": 96, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$\\left ( 0, \\quad 0, \\quad 0\\right )$$" ], "text/plain": [ "(0, 0, 0)" ] }, "execution_count": 96, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(N), f(E), f(S)" ] }, { "cell_type": "code", "execution_count": 97, "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: (theta, phi) |--> 0" ] }, "execution_count": 97, "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": 98, "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": 99, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$\\left ( 1, \\quad 1, \\quad 1\\right )$$" ], "text/plain": [ "(1, 1, 1)" ] }, "execution_count": 99, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(N), f(E), f(S)" ] }, { "cell_type": "code", "execution_count": 100, "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: (theta, phi) |--> 1" ] }, "execution_count": 100, "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": 101, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & - 2 \\operatorname{atan}{\\left (x^{2} + y^{2} \\right )} + \\pi \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & 2 \\operatorname{atan}{\\left (xp^{2} + yp^{2} \\right )} \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & - 2 \\operatorname{atan}{\\left (\\frac{\\sin^{2}{\\left (\\theta \\right )}}{\\left(\\cos{\\left (\\theta \\right )} - 1\\right)^{2}} \\right )} + \\pi \\end{array}$ " ], "text/plain": [ "S^2 --> R\n", "on U: (x, y) |--> -2*atan(x**2 + y**2) + pi\n", "on V: (xp, yp) |--> 2*atan(xp**2 + yp**2)\n", "on A: (theta, phi) |--> -2*atan(sin(theta)**2/(cos(theta) - 1)**2) + pi" ] }, "execution_count": 101, "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": 102, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} f:& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & - 2 \\operatorname{atan}{\\left (x^{2} + y^{2} \\right )} + \\pi \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & 2 \\operatorname{atan}{\\left (xp^{2} + yp^{2} \\right )} \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & - 2 \\operatorname{atan}{\\left (\\frac{\\sin^{2}{\\left (\\theta \\right )}}{\\left(\\cos{\\left (\\theta \\right )} - 1\\right)^{2}} \\right )} + \\pi \\end{array}$ " ], "text/plain": [ "f: S^2 --> R\n", "on U: (x, y) |--> -2*atan(x**2 + y**2) + pi\n", "on V: (xp, yp) |--> 2*atan(xp**2 + yp**2)\n", "on A: (theta, phi) |--> -2*atan(sin(theta)**2/(cos(theta) - 1)**2) + pi" ] }, "execution_count": 102, "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": 103, "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": 103, "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": 104, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left\\{\\left(U,(x, y)\\right) : - 2 \\operatorname{atan}{\\left (x^{2} + y^{2} \\right )} + \\pi, \\left(V,({x'}, {y'})\\right) : 2 \\operatorname{atan}{\\left (xp^{2} + yp^{2} \\right )}, \\left(A,(x, y)\\right) : - 2 \\operatorname{atan}{\\left (x^{2} + y^{2} \\right )} + \\pi, \\left(A,({\\theta}, {\\phi})\\right) : - 2 \\operatorname{atan}{\\left (\\frac{\\sin^{2}{\\left (\\theta \\right )}}{\\left(\\cos{\\left (\\theta \\right )} - 1\\right)^{2}} \\right )} + \\pi\\right\\}$ " ], "text/plain": [ "{Chart (U, (x, y)): -2*atan(x**2 + y**2) + pi,\n", " Chart (V, (xp, yp)): 2*atan(xp**2 + yp**2),\n", " Chart (A, (x, y)): -2*atan(x**2 + y**2) + pi,\n", " Chart (A, (theta, phi)): -2*atan(sin(theta)**2/(cos(theta) - 1)**2) + pi}" ] }, "execution_count": 104, "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": 105, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} f:& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & 2 \\operatorname{atan}{\\left (xp^{2} + yp^{2} \\right )} \\end{array}$ " ], "text/plain": [ "f: S^2 --> R\n", "on V: (xp, yp) |--> 2*atan(xp**2 + yp**2)" ] }, "execution_count": 105, "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": 106, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAwAAAASCAYAAABvqT8MAAAABHNCSVQICAgIfAhkiAAAAN1JREFUKJHN0r0uRFEUxfGfyRgFxkemUYgC0VNotd6BB/AAGv1E6z2Uk2m9AgmVTiIjQyNhGuKjuOcm281W6OxmZa99/mef5Cz+WFONfgunuMMXejjGOIMXcI+D4J3gBjMZ0Mcj2sFbxjuOMuAWg8S/xkXdtIrOYxOjBBhhpwmsFX1NgAm66ESgG4YZAIsR+Cj6mQDTRdsReEoO1jVb9CUCY9VHLf0CPDeBCS6xmgAbuKqbVhgMsetnXNbLJefZW1fK6sPgnak+rlMbMQYP2FNFZBtzqmjs4y3b8E/qGxZ9JaWPkmySAAAAAElFTkSuQmCC\n", "text/latex": [ "$$0$$" ], "text/plain": [ "0" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(N)" ] }, { "cell_type": "code", "execution_count": 107, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$\\frac{\\pi}{2}$$" ], "text/plain": [ "pi/2" ] }, "execution_count": 107, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f(E)" ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA4AAAAOCAYAAAAfSC3RAAAABHNCSVQICAgIfAhkiAAAALVJREFUKJHN0DFqAmEQBeBPs2gpJI1dKhHxEJaCTRqrtF7BxkPkBFpbWrlgK1ilS2UlmktICLJJM8XGLK5Y+WD4Zx7/zHsz3IhKAVeLKEKG4zn5hCVO+LkQvbxighQrvOMVG+wxwRu+8YWPGEB87OfUF6hGnhZ5TuKd57hm7JKhESv8Q7WAG2EdeTsGlOIBB3SifsHuGsVhNG+jruMZj2WNY3+P8RmDBmVWp2idWZ+hW9Z4x/gFSJwistd5r64AAAAASUVORK5CYII=\n", "text/latex": [ "$$\\pi$$" ], "text/plain": [ "pi" ] }, "execution_count": 108, "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": 109, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} f:& U & \\longrightarrow & \\mathbb{R} \\\\ & \\left(x, y\\right) & \\longmapsto & - 2 \\operatorname{atan}{\\left (x^{2} + y^{2} \\right )} + \\pi \\\\ \\mbox{on}\\ W : & \\left({x'}, {y'}\\right) & \\longmapsto & 2 \\operatorname{atan}{\\left (xp^{2} + yp^{2} \\right )} \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & - 2 \\operatorname{atan}{\\left (\\frac{\\sin^{2}{\\left (\\theta \\right )}}{\\left(\\cos{\\left (\\theta \\right )} - 1\\right)^{2}} \\right )} + \\pi \\end{array}$ " ], "text/plain": [ "f: U --> R\n", " (x, y) |--> -2*atan(x**2 + y**2) + pi\n", "on W: (xp, yp) |--> 2*atan(xp**2 + yp**2)\n", "on A: (theta, phi) |--> -2*atan(sin(theta)**2/(cos(theta) - 1)**2) + pi" ] }, "execution_count": 109, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU = f.restrict(U)\n", "fU.display()" ] }, { "cell_type": "code", "execution_count": 110, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} f:& V & \\longrightarrow & \\mathbb{R} \\\\ & \\left({x'}, {y'}\\right) & \\longmapsto & 2 \\operatorname{atan}{\\left (xp^{2} + yp^{2} \\right )} \\\\ \\mbox{on}\\ W : & \\left(x, y\\right) & \\longmapsto & - 2 \\operatorname{atan}{\\left (x^{2} + y^{2} \\right )} + \\pi \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & - 2 \\operatorname{atan}{\\left (\\frac{\\sin^{2}{\\left (\\theta \\right )}}{\\left(\\cos{\\left (\\theta \\right )} - 1\\right)^{2}} \\right )} + \\pi \\end{array}$ " ], "text/plain": [ "f: V --> R\n", " (xp, yp) |--> 2*atan(xp**2 + yp**2)\n", "on W: (x, y) |--> -2*atan(x**2 + y**2) + pi\n", "on A: (theta, phi) |--> -2*atan(sin(theta)**2/(cos(theta) - 1)**2) + pi" ] }, "execution_count": 110, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fV = f.restrict(V)\n", "fV.display()" ] }, { "cell_type": "code", "execution_count": 111, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$$\\left ( \\frac{\\pi}{2}, \\quad \\pi\\right )$$" ], "text/plain": [ "(pi/2, pi)" ] }, "execution_count": 111, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU(E), fU(S)" ] }, { "cell_type": "code", "execution_count": 112, "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": 112, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU.parent()" ] }, { "cell_type": "code", "execution_count": 113, "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": 113, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fV.parent()" ] }, { "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 = 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": 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": [ "CU.has_coerce_map_from(CS)" ] }, { "cell_type": "code", "execution_count": 116, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 116, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fU == CU(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The arithmetic of scalar fields:

" ] }, { "cell_type": "code", "execution_count": 117, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} & \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & 4 \\operatorname{atan}^{2}{\\left (x^{2} + y^{2} \\right )} - 4 \\pi \\operatorname{atan}{\\left (x^{2} + y^{2} \\right )} + 4 \\operatorname{atan}{\\left (x^{2} + y^{2} \\right )} - 2 \\pi + \\pi^{2} \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & 4 \\left(\\operatorname{atan}{\\left (xp^{2} + yp^{2} \\right )} - 1\\right) \\operatorname{atan}{\\left (xp^{2} + yp^{2} \\right )} \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & 4 \\operatorname{atan}^{2}{\\left (\\frac{\\sin^{2}{\\left (\\theta \\right )}}{\\left(\\cos{\\left (\\theta \\right )} - 1\\right)^{2}} \\right )} - 4 \\pi \\operatorname{atan}{\\left (\\frac{\\sin^{2}{\\left (\\theta \\right )}}{\\left(\\cos{\\left (\\theta \\right )} - 1\\right)^{2}} \\right )} + 4 \\operatorname{atan}{\\left (\\frac{\\sin^{2}{\\left (\\theta \\right )}}{\\left(\\cos{\\left (\\theta \\right )} - 1\\right)^{2}} \\right )} - 2 \\pi + \\pi^{2} \\end{array}$ " ], "text/plain": [ "S^2 --> R\n", "on U: (x, y) |--> 4*atan(x**2 + y**2)**2 - 4*pi*atan(x**2 + y**2) + 4*atan(x**2 + y**2) - 2*pi + pi**2\n", "on V: (xp, yp) |--> 4*(atan(xp**2 + yp**2) - 1)*atan(xp**2 + yp**2)\n", "on A: (theta, phi) |--> 4*atan(sin(theta)**2/(cos(theta) - 1)**2)**2 - 4*pi*atan(sin(theta)**2/(cos(theta) - 1)**2) + 4*atan(sin(theta)**2/(cos(theta) - 1)**2) - 2*pi + pi**2" ] }, "execution_count": 117, "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": 118, "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": 118, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS = S2.vector_field_module()\n", "XS" ] }, { "cell_type": "code", "execution_count": 119, "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": 120, "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": 120, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS.base_ring()" ] }, { "cell_type": "code", "execution_count": 121, "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": 121, "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": 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": [ "isinstance(XS, FiniteRankFreeModule)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

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

because $U$ is parallelizable:

" ] }, { "cell_type": "code", "execution_count": 125, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 125, "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": 126, "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": 127, "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": 127, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XU.default_basis()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Similarly

" ] }, { "cell_type": "code", "execution_count": 128, "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": 128, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XV = V.vector_field_module()\n", "XV.default_basis()" ] }, { "cell_type": "code", "execution_count": 129, "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": 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 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": 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": [ "eU is S2.default_frame()" ] }, { "cell_type": "code", "execution_count": 132, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 132, "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": 133, "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": 133, "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": 134, "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": 134, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v.parent()" ] }, { "cell_type": "code", "execution_count": 135, "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": 135, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stereoSW = stereoS.restrict(W)\n", "eSW = stereoSW.frame()\n", "eSW" ] }, { "cell_type": "code", "execution_count": 136, "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": 136, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW = v.restrict(W)\n", "vW.display()" ] }, { "cell_type": "code", "execution_count": 137, "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": 137, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW.parent()" ] }, { "cell_type": "code", "execution_count": 138, "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": 139, "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": 139, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vW.display(eSW)" ] }, { "cell_type": "code", "execution_count": 140, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = \\left( - xp^{2} + 4 xp yp + yp^{2} \\right) \\frac{\\partial}{\\partial {x'} } + \\left( - 2 xp^{2} - 2 xp yp + 2 yp^{2} \\right) \\frac{\\partial}{\\partial {y'} }$ " ], "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": 140, "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": 141, "metadata": {}, "outputs": [], "source": [ "v.add_comp_by_continuation(eV, W, chart=stereoS)" ] }, { "cell_type": "code", "execution_count": 142, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = \\left( - xp^{2} + 4 xp yp + yp^{2} \\right) \\frac{\\partial}{\\partial {x'} } + \\left( - 2 xp^{2} - 2 xp yp + 2 yp^{2} \\right) \\frac{\\partial}{\\partial {y'} }$ " ], "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": 142, "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": 143, "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": 143, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(v)\n", "v.display(eU)" ] }, { "cell_type": "code", "execution_count": 144, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = \\left( - xp^{2} + 4 xp yp + yp^{2} \\right) \\frac{\\partial}{\\partial {x'} } + \\left( - 2 xp^{2} - 2 xp yp + 2 yp^{2} \\right) \\frac{\\partial}{\\partial {y'} }$ " ], "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": 144, "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": 145, "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": 146, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}v = 0$ " ], "text/plain": [ "v = 0" ] }, "execution_count": 146, "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": 147, "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": 147, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vN.parent()" ] }, { "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.parent() is S2.tangent_space(N)" ] }, { "cell_type": "code", "execution_count": 149, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 149, "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": 150, "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": 151, "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": 151, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vS.display()" ] }, { "cell_type": "code", "execution_count": 152, "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": 152, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vS.parent()" ] }, { "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.parent() is S2.tangent_space(S)" ] }, { "cell_type": "code", "execution_count": 154, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 154, "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": 155, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 27 graphics primitives" ] }, "execution_count": 155, "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": 156, "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": 156, "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": 157, "metadata": {}, "outputs": [ { "data": { "image/png": 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av2hHRvKFu29fos8+I1q7lujSJT5m8WL3xKhsWRZddyhWzHE7xYsTtWxJ9PrrRN99R/TPPxwWd8b77zu3zV4Ir3//nPs0aybCpCVBJUgWTpwgGjaMf1iWH5QRLF3K4Z8NG4yz4cIFot69+QJjFGYzh1Cfe47o6lXl7Zw+fZqKFy9O//zzz53nPPGQ5sw5TwBo40aTciO85PhxrggybpzzvN7Vq0SlS/NFsmhR9mrUIjubaMQIrrQwYgTR/Pk8PSMjw/Exhw+rH6JbtIi9o9yRDUdbeDjv36sXe1OrV+f0pnKLuKPNNoR39ChRjRp59xFh0gbDJsYKgtosW7YMXbp0QVhY2J3nsrOzERISgtDQUKSnp+d4LTdJSUmIi4uDyWRCwYKuJ8YazdGjPCG1e3f9R9blJjubJ2PbW5Y+LIzrGL72mnVovSekpwMHD/ISNnv3Wv9evuze8cWL89D0XbvcH2lbrx6wZAlQpQq/t8WLecTuoUM592vWjNfOevhh/10HzZcQQRIChuTkZJw6dSrHc/369UONGjUwcuRI1HYxPtnfBMnXaNwY2LEj53NlywKLFgFNmqjbFxFXyrAVqL17WTDUWpAwNpYF/+mn+bEIk/aIIAkBTYsWLVCvXj1MmjTJ5b4iSN6Ru4RQ+/bAd98BRYvqZ4O33pQ9BgwAJk+2VvsXYdKOgJgYKwiC8XTuzH/DwoBPPgFWrNBXjACeZF2vHk+0/ewzYM0a9qQmTlTe5jffAKVKAdeu8eOwMJ6A/O+/wIIFOSt7/PEHL2nSvDkvayK3+54hHpIg3EY8JO/Zt4+rk5Qta7QlORk8GJg+3bs2Jk0Chg7N+7xWHtPOncD+/UDPnq6LOQcK4iEJgqAader4nhgBHLbzhjJlgL597b+mhceUmMhi1q8fC1KwuA0iSIIgBDREnEvyhEKFeDDD999zyO/MGdfLn6gpTOPGWes6LlkCfPmlZ/b7KxKyE4TbSMguMDl5kguquqJ2bR6I0b49r8nl7vpsjlAayktM5OXnzWbrc5GRwNatwH33eWeTryMekiAIAc3hw/afj44GHn+cvY9Tpzj/9dFHLBbeihHgnsfUogUvpmjrFowbl1OMACAjA+jWDTCZvLfLlxEPSRBuIx5SYHLyJI+8M5nYU7J4QS1aWIdy64Ezj+mhh9hjKlUKqFUrryBZ6NoV+PHHwB1SLoIkCLcRQQpcrlwBUlKA8uWNv5hnZ7OovP9+Xu+teHHg0iXnx0+fDgwcqJ19RiKCJAi3EUES9MSZMDkjkPNJkkMSBEEwgLAw4JlneK7R/PlcC9AdAjmfJIIkCIJgIGFhQIMGHFJ0l2PHgP79A29+kgiSIAiCwdgbWeeKQJyfJIIkBD3Tp09HrVq10LBhQ6NNEYKQxEQO2Snh1VeB3bvVtcdIZFCDINxGBjUIRtCnD/DDD8qPL1WK81CuKkn4A+IhCYIgGMSJE8q9IwvnzvGcqkBABCkASUsDSpTgCsFPPeXZkFK92bYN2L7daCsEwRgSEz3PHdnDl3/jnqBCgQz9MJt5qGOhQvpPbjtzBvjlF6B0aR4V4ykhIbyiph7rw/z9NxeEBID//Y+3li2BQYO4VIoaZVHUYMUKoFMn/j+QJ/sJgiNatgTeeUdZHogIOH+er4nDh6tvmxH4fA7JZAJ+/x1YuRL47TeexTx8OC8AphdZWUD+/EBmpnft3HUXcPSo+/MNlJKRwfZmZ+d9rWxZ4MUXgRdeAO6+W1s7XNGhA4s8wHXFDh0CypUzzh7JIQmCsfhcyI4IOHCABadFC6BYMZ4E9t131pIav/+ur03Z2SxK3nLlivei5g6RkVzm3h5nzvAdWdmyvM7KX38ZN5dh3z7r/7ducbl/PT4fd/n7b6BkSb6ROHnSaGsEIfDxCUG6dQv49VcOKVWqBNxzDzBiBLBpk30hqFJFX/vy5QNGjfK+na5d9VvSuWVL569nZnIF4qZNgXvvBWbOBG7e1Mc2ADhyhCss27JtG/DWW/rZ4IwFC3gJggsX+EZCT49cEIIVwwTp1ClgxgyuulukCP+dMcO9O9G6dTU3Lw/jxgHduys/PiQEGD1aPXtc8fDD7u+7dy8wYADnx4YN40Sr1qxcaf/5Tz8Ffv5Z+/6d8cor7D3aemslShhnj5GYzZzry71EgiBoge6CNHs251AqVGCP6NdfeVSYJ8THa2KaU0JCgK+/BqpWVXZ81668AJhe1K8PFCjg2TEmEzB5MlC9OjBxojZ2Wfj1V8ev9e0LnD6tbf/2OHKE/373Xd7XAmGOhxKWLOGBJ488ArRqxeF0QdAK3QXprbeA5GTv2jDCQwJYSBcv5hCeJ+jtHQE85LtZM+XHL1qkni25SUnhcKwjrl/XP580fz6vSaMnO3YAlSvzABRPt6goHu0ZGcmRBa2wHf21bh3fDL76amAW9hSMR3dB8ibsBfBdv5EjserVYy/CExo35iWJ9caTsJ0tkZFcEl8r1q7lkYDO0CufdOsWhyt79QJSU7Xvz5bFi4Hjx9kGT7f0dA6nZWYCX32lnY3XruV8nJ0NTJoEVKsGzJmjzhwaQbCguyBNnsz5gyJFlB2fksKLWD38MDB0KPDtt8CuXfwj1YsBAzwT1m3bOFy3cKH9odhaoUSQihRhwXj8cfXtseAsXGeL1vmkQ4f4ZmHmTO36cEa7duq0o6X3nVuQLFy6BDz3HNCkCbBzp3b9C0EGGcTZs0TNmxNxqtT7LTSUqEYNoqefJho/nuiXX4jOnCEym7Wx32QiqlrVcztr1CBasIAoK0sbu2zJyiKKi3PftipViA4f1tYms5modGn3bSpcmOjUKfXtmDePKCYmd38mAnD7b87XpkxR3wazmahZM+/O+w8/VN8uWx5+2LUNISFEzz9PdPGitra4YscOoq+/Jrp1y1g7BOUYJkhERJmZRO+8wye0uz/AWrWISpZ0f/8iRYhatCB65RWi2bOJdu4kSk1Vx/49e4jy5XP+Q501y/5FRy9h6tDBvc/pgQeILl/W1hYi/sw8vejefz9RRoY6/aemEvXv76gvfQWJiGjdOuVi1KYNUXa2NnZZqFvXfXvi4ogmTeLftd4cP04UHc12tG+v/eciaIOhgmRh9Wqiu+5y76TfsoWPuXSJaO1aos8/J+rbl6hePaLISPfasHhTgwYRXb/une1ffeW4n27deB+zmS88joRp927vbHDG55+795n076+dDbZ8+KGyi+/w4d73ffIkUZ06zvrRX5CUekmlS/NvQCubPvmEz98CBTy37Z57iNav996ONWv4N7pypetIxwsv5LRh4kTv+yfic2bwYKIlS9RpT3COTwgSkfshvORkx21kZBDt20c0fz7RiBF8B+nKm/rsM+/sNpuJunfP225ICNuSe197wtSsmXc2OMOVRxIaarVXqwucLU2aKBMkgGjVKu/6tvc9GS1IRJ57SWFhRH/8oZ09W7cq/45st9q1OWyulLvvtrbVsKFjYTp+nCg8PO9n9Ndfyvu28NJL1jbfeUe7FIDA+IwgEbkO4VWurKxdR95UXByH8LzFXj7J4h3Zw1aYwsKIJkzw3gZHZGdz2NLeRW3mTKLFizlP07y59mGOK1esAqhk69vXu/7Hj/dNQfLUS9LyfCHiqEG1auqI0gMPKLejT5+87dkTptzekWUrU4bPOW9YuDBnmwMHSjhQS3xKkCw4CuE98YR6fWRkqHti2eaT7HlHjtDjjqtLl5yfY8GCRL//bn1drfyMK+bPV35hq1SJaPNm7/o3m4l+/pmofn3fEiQi970kPfJGRJzb3LXLe0F66SXlNmRnEy1dShQf71iYjh3L6x3ZbmrkkyZNytlmjx76/WaCDZ8UJCL7Ibz33jPaKucsXco5ik8+MdqSnEybZv0My5YlSkgwxo5+/VxfwCIj2YPt25fDqWvXqh9KdCxMxgmSO16Slnkjexw8qEyEIiKIHn+caPlydexwJkzFirm2R4180vffc1TB0ma7dkQ3b3rfrpATnxUkopwhvJAQ9kIEz0lN5bu67t1Z6I3ijTdyXihKluQ7/hEj2Hvat0/fO8+8wmScIBE595K0zhvZY8sWz4SoTBmiceOILlzQxh5nwuRsUyuftGJFzlG1TZt6PyhKyIlPC5KFEyfYNRf8m7Q0vmvWwuvxBosw1atnrCA585K0zhvZ45df3Lvgt2xJ9NNP+g33tgiTvdyoM7H0Np9ERLRxI1FsrLXdunWJzp/3vl2B8YnlJ1xRoQIvSyH4N/nyAR07Ao8+ymsM+QohIVyZYuNGfmxUrcSQEGDs2LzPt2nDy7HojaMqDQAQF8eVUg4dAtasATp31m8l4tBQLuGVlOT+Mf/9x0V7vS111Lw5nyeW83fvXl7C5cQJ79oVGL8QJEHQg5AQ/rtpEy+5cN991tfq1NHHhocfzlkUt3Rp4Pvv+SKsN/aKIMfHc9X7s2e5pl316vrbBQDjx3u+aObKlcBnn3nf9333AX/8Ya2peewYi9L+/d63Hez4/BLmgqAXuZcwJwL+/JPF4MEH9bNj2zYWpvBw4Lff+GJnBAkJ/L7T03n5lIEDuXadRbiN4sQJLu6qZBXnsDBg82Z+H95y5gzQujV7iQDXgfz1V66PaI/kZOCZZ4Dt27mwbosW3tsQaIggCcJtcguSkVy4wEJYvLihZuDGDb6Ix8Yaa4ct/fsDs2YpP75YMeDgQf7rLVeuAG3bcoFnAIiJAZYty7tic3o6L0K6bh0/btyYbzyEnIggCcJtfEmQBPv89x9QsaIy78iW6tWtno23JCfzIoYbNvDjyEhgwQLgySf5cVYWr++1dGnO4w4cMGZZGl9GckiCIPgNx497L0aWdtQiNpZDdZ078+OMDKBbN/biiIAXX8wrRgAwd656NgQK4iEJwm3EQ/J9iHhAw44dyo69cIFHDw4bBgwerK5tWVkcTrQVmoce4pyVPUqWBE6f1m90oj8ggiQItxFBErzFbAbeeAP4/HP39v/1V85BCYyE7ARBEFQiNJRXOu7Uyb3958zR1h5/QwRJEARBRZYs4Xls7rB8ufMJyMGGCJIgCIJKrF4N9OrF+Sp3yMgAFi3S1iZ/QgRJCHqmT5+OWrVqoWHDhkabIvgxW7YATzwBZGZ6dpyE7azIoAZBuI0MahCUcuwY0KABTyRWwr59QO3a6trkj4iHJAiC4CXz5ysXIwD47jv1bPFnRJAEQRC85IkneFUCpfzwg+ehvkBEBEkQBMFLatfmsN3OnbyEiKfpyIsXeUBEsCM5JEG4jeSQBDW5eBFYtYqXvVi92vX6TQ8+yNXlgxkRJEG4jQiSoBWZmTwKb+VKrs7gaO2kmzeB/Pn1tc2XkJCdIAh32LiR1wqaPNloSwKLiAhebXbiRODff3lNp+nTeTXgsDDrPvnyGWun0YiHZADHj/MPv1UroGxZo60RLAS7h5SWBlSuDJw7x48XL+aF+QRtSU0Ffv6ZF2IsXdpoa4xFPCSdyM5md71dO6BKFeD55/nuSBB8hVmzrGIE8Dl69Khx9gQL+fPzeknBLkaAeEiac+UK8O23wFdfsZtuS0wMkJJijF1CXrT0kNatA44c4WWrq1c3fhnw3OT2jizcey/nPqKijLFLCC78eiWOlBRgxAjgjz+AKVOAhx822iIrO3ZwjPjHH3n5YnsUKaKPLStX8rorJUooOz42ltd1iYxU1y4AOHWKbWvWTP22fYUjR3IuaV2pEi9n3a4dC5QvXOxze0cW9uwBhg8Hpk3T3yYhCCE/Ze9eourVibiMIVHz5kZbRJSaSvTtt0QNGljtcrbVrau9TVOmuGeLq61fP/VtO3+eKDSU22/RgujmTfX78ASTyUQAyGQyqdru3387/lzz5yfq0IHoyy+JTp1StVu3uXWLqFQp59//4sXG2OaI7Gz+vQmBhd/lkIj4bq5xY+DwYevz//zjfoVdtTl2jBflKlMGeO45YNcu947Tw0O6dEmddi5fVqcdW/75hxc0A3iQR6NGwMGDytubMGECGjZsiNjYWBQvXhydO3fGYduTxE2KF+eRZmpRqxavk2MPS0L75ZeB8uWB+HjgzTfZ61djqW53cOQd2eJL+aSEBKBGDaBoUcersQp+itGK6AnJyUQ9ezq+izt5Ul97Fi1iLy3C7EzQAAAgAElEQVQkRJnX8cQT2tuYlUVUo4b3HtKvv6pv27Zt9j2G779X1t5jjz1Gc+bMoX///Zf++ecfat++PZUrV45SUlJcHpuSQvT00+whASYCiK5dU2aHPWrW9PwzL1SI6OmniWbMILp4UT1bbHHHO7Js997L+xvJqlVEsbFWm7p2NdYeQV38RpByh+jsbStWuG7HbOZQ0erVRH/+yY+VkJTk/UW+cWOihQuJ0tKU2eAu588T3X23cjsbNVL+OTnDniBZtuee8z6Ed+nSJQJAmzZtcrrf/v1EtWrRbSGyCtL58971b0v37t6dKyEhRJs3q2ePhalTPbNj0CD1bXDElStEa9bwTRUR0ddfE4WF5bTnrru0OTctZGURrV1LdOGCdn0IVnxekMxmopkziaKiXP9YPvgg57FpaUR79hDNnUv02mtEjz7KJ7DtMQsWKLMrLY0oIsJ7UQKIunXz/nNyxbp1yj05LbwjIueCBBDVrk104IDy9o8cOUIAaN++fXZfT0tLoxkzUil/fvPtPrUTpAkTvD9Pxo9Xzx4iz7wj202PfJLZzDlWgOiRR4hef92xPQ6+XlV47z3uo3x5IpVTi4IdfFqQXIXocm/NmhF9/DEfU7s2UXi462N++EG5fUeP8mAKby80eoTuiIjGjvXcNq28IyLXggQoD+GZzWbq0KEDNW3a1O7rKSlEdevuydWfdoK0cqV358gDDxBlZKhnD5Hn3pFli40lOnJEXVvsUbu2e/ZMmaKdDbZC+OGH2vUjMD4rSO6E6JRsxYsTtWrFJ9rKlepcbDdvtt7NebL17893m3rdeWVl8d2mJzZq5R0RuSdIls3TEN7AgQOpfPnydObMmTyvWUN0uTftBOm//5SdrzEx3t00OUKpd2TZ9MgnrVzpnlffpYt2NiQmWkeCFikiXpLW+JwgeRKic7aFhxPVqUPUqxfRxImcM9IyDpyVxcnnIkXct9GIobSe5JO09I6IPBMkwP0Q3uDBg6lMmTJ0/PjxPK/NmcNel/0+tBMks9mzc8Pyfg8eVM8GW5R6R7Zbhw7a2EZEdOgQUaVK7tlRpAgPA9eKPn2sfYmXpC0+JUipqUT33efdj+Tdd4n++YcoPd2Y93DlCtFLL7l3Z7d2rTE2uptP0tI7IvJckADnITyz2UyDBg2iUqVKUWJiYo7XUlKI+vZ11b52gkRE9PDD7r/PF17Qdl6WGiMvtTpHNm0iKlzYMzv27FHfDgviJemHT81DevNNYPdu79ooUwaoW1ebqgLuULQo8OWXwN9/8/omzihcWB+bcvPII8CYMc73adTIN2vtpaYCffrYt3/QoEGYN28eFixYgNjYWFy4cAEXLlzA7t1paNTI+GWi69Z1vU9MDK8eOnOmtssQqHXuxcSo046F+fO56PD1654dt2GDunbYUrUq0KsX/3/tmlSt0BKfqmW3eDEXGfSGwYOBqVPVscdbiPgHNmIEcP583tdPnPBu2WNvyM4GWrcG1q+3//qvvwJt22prw/btwP33Kzu2RIm8n2mI3QJxXREZOR8ZGRFutJoEIA6ACUBBnD+vvNySPebM4YnTjqhdG1iyhCd9ao3JxN+9o7JWziDikk+NGvHNjVosWgT06KHs2A4dgBUr1LMlN0eO8PdiNvOE9hMngCAsCK89RrtouTl6lHM+HTo4i/U73po1M/od5CUpiWjEiLzDxI12/R3lk7TOHVlQErIDiKKjOc/oirQ0T3OR2obsnJUQ0jpE5w94MqI29xYXZ52vpBWSS9IenxMkW27dIvrtN6IhQ9xPcMbF6XMxVcKhQ0Rt2rCd7doZbQ1jL5+kde7IgqeCFB1NNHy4+4NTzGaihg19R5Bu3co7sVOrUXT+yOHDPFlcqSjt3Kmtfa5ySYcOsagWKED06qva2hKo+LQg2WI284ijzz7jocvO5hjpXULIUy5f1nZUkKfYzk/Syzsicl+QPBUiW27eJPriC3dHFmorSEQ559ZoOYrOn9m5k4v5ejrSduJE7W2z5yVZhMgiVgBfn3z1xtiX8RtByo3JRPS///H8lBIlrCdCaKiU+fCUrCz2Qps00XbWe25cCZI3QpQb94RJe0FaupSoalX+vIM9ROeKK1eIPv3U/ehI27ba22TrJcXFcZUVWyGy3USQPMenBjUoxWzmytF//MEjmVq0MNoiwR0cDWqIjgYGDeJ1eO6+W90+U1OBb74BPvoIuHgx96vaDmoQlGE2A6tX8/piv/7Kl3t7REfzYI0Id8aveEHnzsDy5a73M5t9byFGXycgBEnwT3bvBurXtz7WUohyY1+YRJB8nRMnePXl2bOBq1fzvr5yJS98qAWHDwMffAAsXGhdNsUZIkie41PzkITgIj6e52oVLswidOIE8Mkn2osRwHN8hg0Djh8HvvhCnz4F76lYEfj4Y+C//3heWaNGOV/fu1f9Pg8f5nlItWrxNA53xEhQhnhIgqEQ+cZdZGoqMGVKEkaNYg+pdOmCOHUKCAsz2jLBFX/+yTc0UVHA77+rNymeiNudNEmZCImH5DkiSIJwm6SkJMTFxeH//s+EJk0KomRJoy0SjOT0aV7FVykiSJ4jITtByEWrVhAxElCmDFczEfRDBEkQBMEOoaHAL79w6S9BH0SQhKBn+vTpqFWrFho2bGi0KYKPERHBgyh++YVr2AnaIjkkQbiNJYdkMplQUCpnCrk4cwbo3h3YssW9/SWH5DniIQmCTuzcCXz+OZCUZLQlghLKlgU2bpQQnpaIhyQIt9HSQzp7FqhWjYeXP/AAsGmT9hUFvOXoUV7bKyqK158yao0xX2TlSl6X69o1x/uIh+Q54iEJgg58/DGLEQBs3Qq8846x9jjj6FGgXz9e/+fzz4Hx47l0j2ClfXsuV9akidGWBBYiSIKgMWfPcpkiWyZO5LtsX8JWiObO5UUcLVy+bJhZPouE8NRHBElwSmoq3yXPnOm4qKXgnI8/tr8ya58+nCg3GmdCJDjHdhReoUJGW+P/iCAZxK1bXI/Llzl4kGuFvf46MGAA3w0KnmHPO7Jw7RqP2srM1NcmCyJE6tG+PZCQAJQqxY8LF5b8kRJEkAzg8mWgXj12+WfONNoa+3z/PdCgAbB/v/W5P/4wzh5/xZF3ZGHLFv3zSSJE2lC2LJcbWroUOHbMaGv8ExEknTGbOVSTmMiP33wTSE421iZbUlOB558H+va1JuEtJCQYY5O/4sw7skWvfNKVKyJEWhMWBnTpwh6S4DkiSDozcSKwapX18bVrwLRpxtljiyVE9+239l/XorR/IOPKO7JFj3zSyy+LEAm+jQiSjvzxh/3wzKefGu8l2QvR5ebYMSAlRT+b/Bl3vSMLeuSTAmHNp+xsXp/o558lLBaIiCDpxOXLQI8e9u9OjfSSnIXockME/PuvPnb5O554Rxa0zid99hkweLB27avNjRvA5s3A1KlA//7svcfGcsixY0fgvvucT0wV/I9wow0IBix5o7NnHe/z6ad8sYiN1c+ugweBrl2de0W5SUgA7r9fO5sCAU+9I1smTgQeeohHbalNvnx8cW/enG9CfKWEUXY2D7RISOCwsOXv6dPOj0tKAtLS9LFR0IeA8pDGjePRa7/95t7+ei1FnDtvZA+9vSR3QnT20CKPlJLCn8+hQ/ydKN18BSXekS1a55OeegrYvZs9DCMhYmG0eD3dugEffsjhOFdiBAA1a1qHWWuJ5Nx0hAKEv/4i4lOcqEABomPHHO+7fTtRvXpExYsT7dihrV2bNxOFhVltc7YVKUKUlKStPcnJRK1bu2ePva1pU/Vtevxx5fZYtpAQom7diMxm5XYMHGgiAPT55ybFbVy6RJQvn/fvByA6eFD5e3GHtDSiwYPds2X2bPX7T0z07vN5/XX1bcrNsmVEcXFE/fpp35dAFBAeEhEPn7aQkgL06gVkZeXcLzubvagmTbgO1aVLHKPWCmd5I3vo4SU1aAD8/rvy4xMS1K/Y4I03YYEIWLxYWRhq+vTpKFNmCGbM4Mfe1G07d06d9wNwQVMtsYTwliwBjFhto3Jl4N57lR+vRVgzN3PnAiYTMGcO/xW0JSBySL/9lnfS5tat7P5bftQnTwK9ewN//mndp3Fj4IUXtLHJnbyRPbTOJd244d3xSUnAqVNAhQqqmAMA+O47dUIvzZsDcXGeH1eq1KDbtdpYzVq2VG5D3bp8U6H0Ruf6dWDNGi5J8+STyu3whKeeYmHo1o1DeXoRGgr8+CNQv77no0xjY4GmTbWxyxGpqcrOL8EDjHbRvCU7myg+3r5LHxZGtGUL0fz5RAULWp8PDSUaPZooI0M7uyZMUB6KGD9eO7v27ydq1YqodGnl9i1bpr5dN24QVarkXQhnwwbP+kxLI3rlFds2OGT377/KQ3b+jLMQnhYhOwuLFnn+XT/5pHb22PL009Y+T5zQp89gxu8Fad485yduTEzOxxUqEP35p7Y2eZI3srfpkUsiIjp+nGjaNKJ27Yiioty37733tLFn1y6iyEhln1mLFp6/94YNc7fDgpSYGJyCZGHJkpw3cADRBx9o2+fLL3v2fX/7rbb2WOjd29rn4cP69BnM+HUOKSMDGD3a+T43b1r/792bc0cPPqidTWfPAq1bezcyR68RdxUrAoMGcdmaq1e5YvHAgUD58s6P06qEUP36PFdGCZ7kW376iUNUO3cq6yvQsYzCK1fO+lx0tLZ9fv45j5B1l7ZttbPFlnz5rP+rlRsUHOPXgvTNN8CJE+7t+8orPNRZ6xjwRx+pMzfi55+9b8MT8ufnJPH06fyZ/vsvD19u3pzrc9ly9ap2dgwa5HnupEUL3lyRng4MHQo88YQkqF1RuTJXROjZk2/khg3Ttr+oKB6U4k7utH59oEQJbe2xIIKkL34rSCkpwAcfuL//99/rs/bMs8/yjwvg8vOhoZ5vcXFcBNMoQkKAe+7hhcc2buSinIsXczWHpk2Bt97Stu/Zs4FKldw/xh3v6MQJoFkzYMoU5bYFG1FRwLx5/NvJfVOiBVWrulf9Xo/RdRZsl20XQdKeECIio41Qwvvvez4stkULYO1afX5cgnf8/TcPz8/IcL5fixbAhg3O9/npJxZ4115REoA4JCaaULWqAeOgBQAcNv7yS8evb9/OZYTUwmzmYd1797LoZGTw3/R0fs5SM69mTfaYbPfJzOQQ/dy5fDMpeIdfCtLlyxxSUFKQ9OOPZclhf2HaNGDIEOf7bNjgOFyXns7ftftekQiSL5CWBjzwAOd7c3PXXcCFC+pe/H/5BejQwbs2EhPZwxO8wy81ffx45dWx33lH37kWgnJc5ZOc5Y4kROe/OMsntW2rvidStKh3x5cvr+68vGDG7wTp1CncmVGvhMxMFjTB93GVT3IUss3M5MmtMorOf3GUT9Iif/TAA8Cjjyo//vXXeSKz4D1+J0hDh7rOK7jCk+GlgrHExfHdsm1yGXDuHYWG8kAMwb95+mlgwICcz7VurU1fEyYoO65YMS4QK6iDXwnSzp3A8uXu758vH1CnDi+xMHo0jxhKSNB2zRlBfezNT3I2oCUsjHNLDz2krV2C9kyebF0OvFIloFAhbfpp2JDnX3nKK6/wlAlBHfxqUMP8+Vw0NTclSnD5+urV+a/l/3LlZERdoEAEPPccj2bq1o1roLnDxo0sXu7VlpNBDb6IycQFYHv0AGJitOvn8GGe7uDupPaYGF4mo0gR7WwKNvxKkIh4gt6xY0DnzkB8PAuPFDwMDoi4EkbJkp7faLgnTCJIwc6AAe7NhQKAV1/lChOCeviVIAmBy5UrHFYtUoSrnZcsqU0/zoXJNwRpwwYezNGqFVdKCA+Imvz+wdmzQJUqrqutREQAx48DZcroY1ew4Fc5JCFw+eYb4KuveARkpUp893n+vPr9tGgBbNrk2zmmF1/k8PSzz3L4+bvv8q7tJWhD6dKcF3JFz54iRq549913UatWLWRmZrp9jAiS4BPY1sdLSwMmTdJPmKpUybloVYEC6vfnCbafxbFjIkx68+abrgdPyOR618ydOxdZWVmI8GBMvAiS4LPoJUxHjpTGhg3W+oFaJs6VIsKkH4ULAyNHOn69UycuIyQ45tChQzhz5gwGDhzo0XEiSEHM1q0cevjmG+/ndmmJXsI0aZL67aqN1sJ07hyvojx2bHDP5XrlFcerGL/5pr62+CNr1qxB/vz58eyzz3p0nAhSEDN0KLBgAecsqlQBvv5ahMlf0EqYJk3iARXvvcflcEaNCk5hyp/f/ly35s2B++/X3x5/Y82aNejZsycKeThxTAQpiLHNVZw5A7z0kn8KkxrrT/krtsL000/et2d7Tty8yet7Basw9euXd7FKZ6E8gcnKysLGjRsxaNAgj48VQRJy4I/CpLTsiysuX76McePGoWTJkujRo8ed57OzszFq1CgUK1YMw4cPx4ULF7QxwAOOHeNCtJalEtQkWIUpIiLn2l9FigBt2hhnj7+wfft2xMfHo27duh4fK4Ik2MWfhMlRrN9b7rrrLvTs2RMTJkzA8uXLceb2Co9hYWF47733MGrUKHz66acoodfypS4oWFDbEYLBKEz9+/Ny99HRfPMTEmK0Rfpz/fp1DBs2DIMHD0abNm3w7bffIi0tDUOGDMHgwYPRs2dPHDhw4M7+e/bsweDBg5V1RkLQUqkSEdc/cL2VLUv01VdE6ena2PLaa+7bYtkiIogmTyYym9WxwWQyEQAymUx3nps7dy6lpKRQjx49aPjw4Xee37hxI23dulWdjnNRpIjnn0XVqkR79njf93PPud9nTAzRm28SXb7sfb+Cb5Kenk7du3ens2fPEhHRyZMnKSQkhDp27EjHjx+n1atXU3h4OA0aNEiV/sRD0hGz2WgLlGPrMc2fb7Q1fJf+1188GkrLu9akpCTExMTglVdewcyZM5GSkgIA2LlzJxo2bKhdxx7QvTuvsKt3FXtbj+ntt70fWOHPv49A5auvvkK/fv1Q6nYYIioqCkSEChUqoGLFisjOzkbVqlVzhLS9QQRJJ/bt4yKwFSrwSqj+mog/c4YL3Bq5yGGXLsCePVyhWUvIpqrW/fffj+rVq2P27NkAOHEbZnDl3nz5OJy6YIH9xez04uZNrrAxdaryNtau5cmo99zDVfllnpVvULhwYbS2WfNj165dAIA2t5Npbdu2xYEDB/Dggw+q0p8Ikk789BMvvX7qFC/LXbmy/wpTdLQxFY4jIng5gv/9T7tlCGxJSEjAPffcc+fxkCFDMHnyZNy4cQMFCxpbfLVqVWDbNi4G6it5DW9yeQsX8irQBw4AvXuLMPkKvXv3zvF4w4YNCAsLQ9OmTTXpTwRJJ3L/sM6d809hKleOy+3ovWSzXiE6W/766y80adLkzuNu3brh1q1bePXVV9G8eXN9jLCDUSE6R0RHA99+y8uCKCX37yMxUYTJF1m/fj3q16+PWI1cchEkg/EnYerYkUNljRvr269eIbqkpCQAwK1btwAAycnJiIqKuvN6ZGQkXnrpJaxatSqH56QXvhKis6VGDWDHDp6zo8WNggiT73D9+nXs3bsXLXIt1Txr1izV+hBB8hF8WZjCw3ndl2XL9A3V6RWiu3nzJvr3748qVaoAACpXroz4+HhMnToV06ZNy7HvSy+9hMcff1w7YxzgiyG63r15FefatbXvS4RJfy5fvoxGjRrhvffeAwCsWrUKZrMZjRo1yrHPli1b1OtUlbF6gktGj/ZsGG+pUkRTpxLduqWdTe4M+y5XjmjbNu1ssNC5c85+K1Qg2rFD+36JiDp16kQA8my2w7z1JDIy52fRvTtRUpI+fbsz7Ds6mujbb9Ubbk9E1KePZ7+PatWIfviBKDNTPRuEnCxZsoQA0JgxYyg1NZU6depEpUqVorlz5xIRUUpKCnXv3p1OnTqlWp9BKUhmM9FnnxG98ALRjRv69OmpIFm20qWJdu/WxiZXgtSxI9HVq9r0bUtmJlHRotZ+27Ylun5d+36JiPbv329XjABQ/vz56YZeJ8htNm60fg6hoURff63uhd8VrgSpRg2iffvU79dTQbJsNWsSnTypvj0Wjh8n6tWLaOFC7frwVZKSkuj555+nl19+mXr37k0HDhygbdu20SOPPEL9+vWjnj170t69e1Xt0+O1KIkIycnJajlohrByJfD66/x/+fLuLcjlLenpyo47exb44gsO46mNo3kfYWHABx8AAwdyeOh2akUzDh2y1lCrWZNHXOnRb3p6OtauXevw9dTUVOzevRv169fX1hAbli61/v/OOzyAQc+fm7OKHE8/zaHbAgXU/26UVgI5eJCr1WtRY46I85d793LYuF079fvQm9jYWIS4GfONjY21mx9at26d2mbdweMlzJOSkhAXF6eVPYIgCIJGmEwmw6csOMNjQVLLQ2rYsCF27typehsmE/D++0BkJC+rkHt48sqVwDPPWB7txunTVRAXp/wLcvd9fPghMHGiZ21XqwZ8/73rxcCUfpa57ytatcrEN99EKBq4oNX3qWUb6enpSEtLQ4sWLXD8+PE8r7dq1Qr/93//p6kNWrWh9PjWrYHt262PK1fOxrx5YahVS1s7XnwRWLTIs7YbNQLmzHG9lLgjG1atAhYvBh57DHjqKY4MWCDiJe4TEizPdMOZM7MUX8x94ZwAPPOQDEHVAKAH1KxZU5M2ZsywxpfDwzlPdPw4v2Y2E9WrZxuDbp+jbplaNtjD0xxS375EKSnq2pCbnH0Opxs3lH8WWn2ferRx4MABqlixYo78UYMGDejChQu62aB2G0qPb9nS9pxYQWfP6vP78DSHNHIkUUaGdzbcfbe1verViebNI8rK4teWL7e+VrduFgHw6lrhC+eEP2DYsG8la2W404btei5ZWcCsWexp9O8PzJwJ/PMPv1avXjaAlZrY4A3R0XzXN3eu+0tpK7Xh3Xf579ixtwB86tVwYq2+Tz3aqFmzJo4cOYI5c+YAABYvXoydO3fi7rvv1s0GtdtQevzChcDjjwOjR6cB6Oh19XC1fx9FinCU46OPeFqANzbYXisOH+aSWJZh5baL840apTAB7IYNerfh8xitiGrzwQfu3WH9+ONNr+96PMEdD6lmTaJ//9XFnBzYq3IdjJw5c4YA0JkzZ4w2xXD0Pifc8ZCaNCE6fVq9PsPDXfd5771EN27I70MvgnZi7KpV+fDKK18gX758RpsCAOjblycZGlAAAPny5cOYMWN85rMwCsv7D/bPAfC9c2LkSGDjRqBsWX37vXQJ+OmnaIwePdZnPotAxuNh34HCnDlhCA8fhtRUXhWyYkVj7IiOBmbM4GWojSJfvnwYO3ascQb4CCJIVnzlnChSBPjhB+OGXJ89C/TrF4Hq1cegenUehm9wkfeAJmg9JCBvjknLeS/2SgHVrMlekZFiJAi+gL2Bu02acM7XF+b/2OaYVnqfehYcENSCZMEiTG+/rV0fiYk5HxsZohMEX+PEiZyPjQrRueLwYaBTJ+D8eaMtCUxEkGzQ8uR/9FHr/5984tkoOkEIdCzL64SF8dwgT0bR6U3RokD+/EZbEZgEbQ7JlrAwYNw4YPhw7foYMoRDEMWKcbkiQRCsTJ3KpYmqVwfuustoaxwTH8+CKcVqtCHoPaTSpYF27T7BqFEhmDJlkqZ91a/ve2KUmZmJkSNHok6dOoiJiUGpUqXQp08fnDt3zmjTBAOYMGECGjZsiNjYWBQvXhydO3fG4cOHdem7aVPfFiPgazRr9gaqVzfajsAlqAWpTRvgww9/xenT81HKm/WX/RhLAdHRo0dj9+7dWLp0KRITE9GxY0ejTRMMYNOmTRg0aBC2bduGNWvWICsrC61bt8bNmzeNNs0w8ufPRrFiQxEfPwPh4ZlGmxPQBGXIzhKi69nzLB54YABWr16N9u3bG22WIcTFxWHNmjU5nps6dSoaNWqE06dPo1y5cgZZJhjBqlWrcjyeM2cOihcvjr///hsPPfSQQVYZR+3a2UhObodZs97AuHF7jTYn4Ak6D6l0aWDDBmDECDP69u2NN954w5DlqH0Zk8mEkJAQFNJymVbBLzCZTACAInouFewjDBgAxMe/iC5daqFly5ZGmxMUBJWH1KYNV8++6y5gwoSPER4ejlf0WAzJj0hLS8Obb76JZ555xqfL1AvaQ0R47bXX0LRpU9TWY51yH6FAAeDrr4HQ0EX48MPtXlfYFtwn4Dwke4tphIaaERHxLjZvjkXFigWwadMmTJ48GXPnzvXtUuwaMH/+fBQoUODO9scff9x5LTMzE927d4fZbMaMGTMMtFJfpk+fjlq1aqFhw4ZGm+JTDB48GAkJCVi4cKHRpmiCvWtFfDywaxfQrNkZDB06FPPmzUNUVJT+xgUpHq+H5Os8+yzw3XfWx6VLA7Nnp6JyZeuosSVLluDtt99GaKhVj7OzsxEaGoqyZcvi5MmT+hmsM8nJybh48eKdx6VLl0Z0dDQyMzPRrVs3HD9+HOvXr0fRokUNtNIYLItP+voiZnowZMgQLFu2DJs3b0ZFo+pqaUxoaE5RGjAAmDSJy3ktW7YMXbp0QZhNnaDs7GyEhIQgNDQU6enpOV4T1CHgQnaxsdb/69cHfvsNuOuu/ACq3Hl+wIAB6NChQ47jHnvsMfTu3Rv9+vXTyVJjiI2NRazthwTcEaMjR45gw4YNQSlGAkNEGDJkCH766Sds3LgxYMUIAMLDgcxMFqbvvwd69rS+9uijj2Lfvn059u/Xrx9q1KiBkSNHihhpRMAJ0iefANevA3ffzf+H2glKFi1aNM9FNyIiAiVKlED1IJtkkJWVhaeeegq7d+/G8uW/ICsrGxcuXADAiezIyEiv2t+8GRg0iFfl/OQTeLXmkqA9gwYNwoIFC7B8+XLExsbeORfi4uIQHR1tsHXq8uOPnCv64AMgd7Q2NjY2T94sJiYGRYsWDap8mt4EnCBFRfECW4J7/Pfff1ixYj+AD1C/fhdWivMAACAASURBVA0AmwA8BgDYsGEDWrRoobjtzEwOoZ44Afz7L4dPX31VBaMFzfjyyy8BIM/3PmfOHDwbYFWAu3ThTfAdAi6HJLjP0aM8H2vePCA72/r8qVOAGtOPvv0WeP556+PwcODPP4HGjb1vWwskhyQIxhJwo+wE1xw9yp5LjRo8AMRWjACufu4tmZksdrnbffpp4No179sXBCHwEEEKIlwJkZr88EPeJQUA9r769bM/5FbwD06d4jWKqlQB9uwx2hohkBBBCgL0FCLAvndky4oVPLxW8D9WrADuvZdHrx47BkyerE0/ixcDn33G55IQPATcoAbBiqMckdY48o5sGTGCl+Pw1XySkJOMDGDUKODzz3M+/88/6vc1dy570QBw+TKvjSQEBzKoIUB5/33elAjRsWNApUrK+s3M5DVtXAkSwEtx7N4N+EqZNBnUYJ9Tpzj3t3173tciIoCUFMDL2QF32L+fh2DfusWP8+cHTp709WUpBLWQkF0AQqRcjLzFHe/IguSTfJ8VK4B69eyLEcA3IGotl3TzJtC1q1WMACA1Ffj0U3XaF3wfESQfwWzmENvSpcCYMcBTTwFvv61MVEJCACNqxrrKHdlD8km+SUYG8PrrQKdOwI0bzvfdq9KqDIMGAQcP5n1+2jQO3QmBj+SQDCApCdi3j3/ICQn8d98+vkPMTevWQPPmnvfx2WfAPfcAgwcDaWne2+wOnnhHtkg+ybdwFqKzR0KC933OnZuzBqUtFi/p44+970fwbSSHpDE3bwKrVlmFJyHBs4t2YiJQtary/hMSOAySmOj+MUpySJ7kjuzhC/kkySGxx9q3r2uvyJbWrYHVq5X3mTtvZA+1c0mJiUBcHJcYE3yHoPWQDh4Ejh/nNZK0qpNoNgMNGgCHDik7vmpV78QIsJbTf/llYP5879pyhlLvyMKpU5yr2LePLxRGYAkLJScDRuiR2cx11WbO5PPywQeVtVOoEB/vSek5R6Po3MEbD8le3sgeanpJixcD3bvzefbnnxxJcERyMvD778D993PpK0FjKAi5fp0oKooIIJo9W7t+0tKIChTgfpRsQ4eqZ4vZTDRrlvV9O9uOHfO8/UaNlL9P261wYaLMTPXet7ukpxNVqWIiANSjh0l/A4goIUGdzxAgGjTI/X6PHSO6+27v+rt4Udl77tvX/T7y5ye6dElZPxZSU4nKlLG2GR/Pv1N7/PUXUcWKvF+5cvwbErQlKAc1HDtmzav8/bd2/eTLB3z4ofLj27dXz5aQEK4rt307UK2aeu1aUOvu8fp19hT0ZNq06ShWbCWOHuXHRoxOBJQPtbdHaqr7+77wAmCzRJYilHhJzvJG9lBjxN306cB//1kfJyQAb72Vc5+sLGDsWKBZM6vXHxsro0H1IChDdrZzJtLTte1ryBBg40bgp588Oy4mBnjoIfXtsYTwXnoJWLBAvXYXLQK2bvXsQmjL2rUc13/+efXmtLjD9evA2rWDkJwMAEkAgGee0a9/W2JiAJMJqFuX8yXeMGSI+/u2aQNs2OBdf3v3Ai1bur///v3AwIGe9zNtGjB8uLJc0o0bwPjxeZ///HP+DFq14jB+z57Atm3W15s04cnl9payEVTGaBfNCA4ftrrsvXtr39/160QVKngWAunUSVubzGaimTPth/CUhOz8kW3biMqXt33vHLJLTDQmZGfh7Fmiu+5SHj5Tcu6cOkX05ZdEXbooCzP36eN+XykpRDVrKn9/I0Z4/v6IiN56y3GbJUsSTZuW872HhRG9954xIeRgJSgF6eRJ60nXrZs+fe7YQRQR4f6P7ptv9LFr716iKlVy9p2YqE/fRmE2E33xhb3vwzcEiYho9WqikBBlF+zdu73rOz2daO1aoldfJape3b0+69Z1v/2OHZWLEaAsl3TuHB/nbh+VKhFt3epZH4L3BKUgnT+vnydiy+TJ7v8g/vtPP7uSkogaN+Z+8+VznOQNBK5d4+/c/ufuO4JERPT2255frLU4n48eJZoyheixx/j8sNdvRIR7nsT48d6JkWUbPdqz9/Dyy+63/eyz/JsQ9Ccoo6K2OYqMDP36HTLEvRUq69bVd4hpbCzHzHfsAM6f58EYgcj27Vypevlyoy1xj7FjPc8jjhmjvh2VK/O5u2oVcPUqz1V68UWgTBnrPoUKuTd9wt3Jtq6wHZjgiqNHeSi9O+TLx8PfY2OV2SV4R1ANajCbeRCD7ZyH69c5wZqRwa+lp/P/cXE8h0jNRGZICK+iumeP86S1mqPrPKFhQ2P61RoiXiZhxAj/Ws4gPBxYuJDnZ7lTOqdTJxZcLYmJATp04I2Il6bfsQNo2pTPb1fMmsUDX1JTWejCFVyBihYFhg51f//Ro91fdDI9nQc1bNnChWMFnTHaRdOSL7/kZGX+/Jyg9DQs8N572tjlKp/011/a9BuMOA/R+XbIzoK7+SRvc0eByO7dykKCb71ltOXBSUCH7D7/nENQqanK5pacO6e+TQB7Io7mUxQpIjXd1MLfQnSOaN0671yZ3OjhHfkjo0YpO27CBGDzZnVtEVwT0ILUpo13x1sWCdMCR/kkLUsZBROzZ/PExlOnjLZEHVzlk7TIHfk7GzYor7FHBPTu7bqkkaAuAS1Ib7/NMW8ltGihradiySeVL5/zeaPyR4FEejrX7vOnfJErLPkkexNCxTvKCxHnDL3h9GnOLwv6EdCCdPfdvKaLEt58U11b7FGoELBkSc5k8GOPad9voBMZyUn2QKNUKa4YkHvwgHhHefnyS65IopQSJYABA0To9Sbgl59ISuLRPFeuuH9MvXq8FII7o4bUYORIXqSudWvg55/16TPQyczk6uYffMDlYNwjCUAcEhNNqFrVd5efeOcda43ETp2AZcuMtccXuftu4NIl5/tERHA1/Ro1eOmUGjWs/xtVcT7YCXhBAvhi/+qr7u+/cCGXpxf8H8+EyT8EKSuLPfgjR4AZM2RZBHs8+CAP3QZ4oNA991hFx/K3QgVlw84F7QgKQUpL45Pw9GnX+1aqBBw+LCdqoOGeMPmHIAmuIeJK/hUr8rwlwT8I6ByShago4P333dt3+HARo0AkIgJ49lleLHHOHHWXehB8j5AQntguYuRfBIWHBPA8pLp1nY+aKV6cKyh4stKm4J/Y95jEQxIEIwkKDwnguT321kKxZdgwEaNgwdZj6tVrHSIirPFcJWvtCILgPUHjIQEcV27a1JrstCU2lnNMhQrpb5dgPJmZwObNSWjZMg4mkwkFC4qHJAh6EzQeEsBx5Y8+sv/aSy+JGAUzERGBW1xWEPyFoBIkgMvJtGuX87nISA7XCYIgCMYRdIIEcOFEWzp35lnwgiAIgnEEpSDFx3M1BgsjRxpniyAIgsAEpSABwO+/A08+CUyfDtx3n9HWGMOWLVyGRqtlNgRBEDwhqEbZCVYuXuQafzdvchWLXbuAAgWMtspYkpKSEBcno+yMJiMDOHOGJy/rVU9S8A2C1kMKdj75hMUI4FJJL7/Mw+IFwSjOnOHlxsuVA6pU8WyZciEwEEEKQi5e5KKctsybx+szqUlmJrBvH5CSom67QuBABKxbBzzxBNedGzeOz08AWLvWWNsE/ZGqbUHIJ5/YXwlz8GCeixMfr04/zz3HQhcZyQsetm/PQ+6rVFGn/UCDSN8Q1Y0byr3isDDAm6imyQR89x3fGB0+bH8fNZeAOHcO+OILDk+/8IJ67QrqIjmkIOPiRb4TdbQ0c7VqnE+KjfW+rxo17F9sqlWzitNDD7Fg+QJG5pDmzwf69gUKFwY2bQJq1dKur5s3eZpDUpJ37Tz1FLB4sWcimpDAA4nmzQNSU53v264dsHKldzYCPICpVy/g8mV+vG8fULu29+0K6iMhOx8kIwN44w1e02X3bnXbduQdWUhM5KoVatym1KjhuI8vvgBateJqzE88Acya5d1ov8zMTIwcORJ16tRBTEwMSpUqhT59+uCcgkabNgXeflu5LUqYPp0LAF+5AtSvzysJa8WBA96LEQD89BPb7IqMDGDRIp6UXrcu8M03rsUIYHH2hqwszkm1aWMVIwDYutW7dgUNIcGnuHaNqEULIpYEojZt1Gv7wgWi6Ghr2862mTO97+/dd93ry3a7916it98m2rKFKCvL/b5u3LhBLVu2pB9//JEOHTpEW7dupcaNG1P9+vXdbmPGDBMBIMBEAFFKioI3rZAnn8z7WQwcSHTrljb91anj+XeTe+va1XkfR48S9etHVKyYsvaHDFH+/s6eJWre3H67gwcrb1fQlqAVJLOZKD3daCuIbt60/n/sGFGNGjl/PPnzq2fn66+7fzGIiiLau9e7/v7v/7y74IWHE338sfL+d+zYQQDo1KlTTvdLSSHq25duC5FVkM6fV963p7z0kmOBPnJE/f6uXSMqW9a772ffPsftnzpFFBrqXfsDBhBduuT5e1u9muiuuxy326yZ+22ZzUQmk+c2CMoIypBdaipPhi1cGFi/3jg73nmHE8MvvshhhPvv5+UQbElNBXbu9L4veyPrnJGWBnTtCiQnK++zbl3lxwIccpk0SfnxJpMJISEhKOSgam56ejp27EhBgwbZ+O475f1oyZ49fK6qHcIrXBj4v//jorJK6NrVeR7m4kXAbFbWtoVvvuFcl7ujPx2F6HKTkMDSlBvLb23WLOCVV4DmzXn587g4Li9m7xhBZYxWRCM4f956t1SzpmehITW5//6c3oCjO7oPPvC+L0+8I9vtmWf4LlEJ2dlEMTHK75BDQog+/VRZ37du3aL69etTz549He7TqdNPBKTY9Ol7HpLtpkUIb9Ik9b0jC6NHux8idrb16eO6L2chOnvbX38R/fwz0bhxHHqsXt25RxcXx+ezoC1BKUhmM1HTptaTbeFCY+xYuZIvuq5+PI884l0/nuSO7G3e5JNsRdeTrWpVooQEx+3OmzePYmJi7mybN2++81pGRgZ16tSJ7r33XjLZibdYQ3S5N98WJED9EJ7ZTNS5s2ffjavckS3XrxMNG0YUFub5OdCmDR974oTzPn7/3XmIzputdGmitm2J1q716mMW3CQoBYmITzDLSWeEl5SZ6f5FKCqKKC1NeV9KvSPLFhFBtH27sr4HDPC8v169iJKTnbeblJRER44cubOlpqYSEYtR586dKT4+nq5cuZLnuP37iWrVctS37wsSQBQbS7R4sXp9X7tGVKGC+/274x3l5t9/+cbKk/NgyxbnbWZlsRfmzk2dqy1fPqL77uNBGJMmEa1fT2Tn9BE0JmgFyUgvKSmJ77o8+cFs3KisL5NJnbBJgQLK+p8+3f0+oqKIZs1SHiK0iNE999xDl+xkw+fM4UEijm3wD0GybGqG8LZv5xsPV3164h3lxmwmWrKEqFw5997fwYOO2zp6lMNsSs/nEiWI3nyTf/f79/MNomA8QStIRMZ4Sf/9R1S3ruc/oDFjlPV38qQ6d5AhIcp+tH/84V77NWo4D9G5IjMzkzp27EhlypShf/75h86fP39nu3Yt3UGIzr8FCeAQnpKRaPZwJ5+kxDvKzc2bPCUgXz7nfV286LiNQoW8O5+rVfP+fQjqE9SVGoi4UsCff/LjhQuB7t216+/kSZ50efas58c+9BDP4FfC//7HdcGUfNPXrnHRy759ecKsp5hMrpeG79UL+PJL76qNnzx5EhUrVrTzSk2UL78Tp07FuNFKEoA4ACYABXH+PFCihHKbPOHll4GvvlJ27OjRwPvve28DEU9SXrbM/utdu3JlBrU4cQJ47TXH/WVkOB4FWKCAtTiwEkJCeARpjDunhaAfRiui0ejpJb39tvI7ushIottpEr/DUX4iKopo9mzlITpXpKcTlSnjyefsfx5SRATRunXq2eEsn6SGd2SP1avzht9chYj37SPq0oUHvyj9TSnNiwraEZTzkGx55BH2WgDg4EH78z0syzP06cOlXZTSqZPycigZGbygnj9ibz5SjRrAjh1cgFWrgqJhYTyfKhAJD+cioYcP8zmsFoULAz/+mNczcTXvyBtat+a5QZ98YvWSGzZ0fkzt2sDSpVyG6tw5YPZs9u48qcG4d69ymwWNMFoRfQFHXtKhQzziy3Z+whdfeNdXcjLRV18pK93y9tvev1cjGD065/twZxSdWhw8SNSpU+B4SOHhRC+8QHT8uLb25M4naeUd5ebCBR5BeP26suPT09ljfO21vFVPcm9SQsj3EEGivCPuPvssrxBZNqWDC+z1uXkzUffuzifF2m5NmqjTt97s38/hufz5vRtF5w1//03UsaP/CpJeQmTBbOYh0ADPBfJXjh0jmjKF5zTlHkTRu7fR1gm5CepBDbasWwe0bOl6vzFjgLFj1e37wgVg5kzg66+dD3gIC+M1bPxxqfEbNzgMZHQSefdu4L33gBUr7L3qe4MawsOBZ58F3nqLlw3Rm6QkDoMFwlLiN29yqbCVK4FLl3gxQC2X+RA8J+hzSADH4efONa7/EiV4pNTJkzwizlFOIDsb+PlnXU1TjUKFjBcjgOvCLV8O/P030LGj0dY4xpIjSkzkmxUjxAjgWouBIEYAn38dOrDwL10qYuSLBLUgHT4M9O7NJ+a8eUZbwxehJ55gb+3AAWDIkLyrci5fboxtgYZFmHbt8g1hsgys8RUhEgQjCEpBunEjpxB5W5VYC2rWBKZM4RDep5+yh5E/Py8zLqhH/fpWYWrb1vp8/vzqLqHtip49eaTZ6dMiRELwEpQ5pCFDgGnTlB2rRQ5J8A0sS5gPHWrCY48VzCFQgiBoT7jRBhhB9epGWyD4Mu+/nzdUKgiC9gRlyG7QIGD6dCAy0mhLBEEQBAtBKUghIcDAgbxKa+XKRlsjGM306dNRq1YtNHRVHkAQBE0JSkGycN99PPy3a1ejLRGMZNCgQThw4AB2qrFWvCAIiglqQQJ4JNWPP0oITwh8iHiEqSD4KkEvSEDOEF6lSkZbIwQjJhMwahQP/f7/9s47Pqoqi+O/yRBIjBRTNpREiigapTcbICrFRBDEAkqRVVF21xU/KysCioUiWEAwsHxQVpayKBZ0DXwoUkVXcd0EQUGykBgCiRjChBLIZObsH8dhSqa8NvMm5Hw/n/eBTN67977JzP29c+6554SL9u05eWqzZrwR/GJNPCvUXupk2HcwbDbg0Uf9Z/0GJOz7YsYV9m2z2dAowmF27dsDe/fyxtjDh4G0NOP7iI0FqqvdPyclcbb18eP173v69FNg40bgqqv4HtRSrx4wYADQsqW+cQBsCR44wCm2wvE+CuFDBMkPRFww7qmnuOyDJ0YVQxOij0CCRBTe9Dnnz/Pk6RKLHj2AXbu0TezB6NqVc/n5YrHwpuA//hEYOBCIUek3OXCAy4noJS2N02dZreqvPX2aM5zk5ADr1vGG8rg4XiOWFEG1B3HZ+SGYCy8/35wxCZHnk0+A+Hie2PxN5Eaxc6e35fLNN+F56HnwQf+vE/EknpUFXHkl1yUqK1PebqCqrmqpqlInRvn5wJtvsmWVlAQMGcJZLlwJis+dY7EUag8iSEHo0oUnoj593K8lJZk3HiEyOJ3AzJnA0KE8qVVV8UQXLtatq/na9OnApk3G9tO3b+hzDh0C/vpXtlbGjgWUBB62aQNMnKh/fE8+Gfz3588Dmzez56JdOxbPCRPYVejryXBxzTX6xyVEDnHZKYAImDEDKCoCFiy4eKPxSkuBt9/map39+5s9msjjctndeqsNW7Z4ryHNmgVMmhSeftu142SqvqSkALm5QPPmxvTjdALJyUB5ubrrundnd97997O16A8iFnCtyX8TE3ntzHfp7uhRFuycHBaj06eVtxkXB5w6ZbzrUwgfIkjCBUaPBpYv5/9nZgLz5vFTqNEQAcePa7/eauUJzOh1nfXrK5CZ6a6H5Mn8+ZwD0Wjy84O/x3368ERs1KQ6dCiwdq22a7t0YYsp0BpTeTnQuTNQWKi+7RkzuOaTi1OneF3q6FFtYwWAbt2UWXhC9CAuO+ECP/7o/v+6dcC117JVoOapNBRnzwIdOwKpqdqP5GRjM2y4XHRZWca1qRR/7jpPtm83dj1JidsuEN9/z0IRiMsuA95/X/2aUmJizSz2a9fqEyMA6NBB3/VC5BFBEi5w4oT3z3Y7MHs2u5RWrWLLRi8FBTyxGdGOEWVDjh/nCLMpU4y5P7Xk5IQ+x8j1JK2CZLFwAEGokhw9egBz5qhr++abgQYNvF+75x79rsrmzaOztIwQBHMqpwvRSJMmRDwt+z969SLKzdXXh8NB1L598H6UHCNG6L/f7duJmjf3bNdGAH7717u/+fP19+fLqVNE9esru9+UFKLiYv19OhxEycnq3uv4eKK1a5X34XQS3XWXuj7S04kWLSI6d87djt1ONGUKkcWi/XOSkEB0/fVE48YRZWcT7dxJZLPpfx+F8CCCVIvYuZNo4kSiggLj266uVvYFj4khGj+eqKxMe18ffKBPjPr04fFqxeEgmjGD78W77cgK0iefqL9vu11/v/fco7zP1FSi3bvV93HiBFHLlur/tv6EacMGFmQ9nxnfo3VrFs3nn+fP48GD/LkQzEUEqZZQUkJ0ySXuL1N5ubHtl5Wp+0InJvLEoUUY9FhJqalEx45pv89ffiHq3z9Q+5EVpHHj1N//c8/p7zc7W1lfbdvqe/j5+mui2Njgn6GtW4nuvDO0MBUXE/Xurfx9atSIaMgQojZtlF/ja0198YVYU5GmzgrStGn8pLhvn3ljWL+eKDOTaNYsooqK4Of+5S/eX55hw9g1opeiIqK77ybq3FmbQHTuzF9ctWixkiwWos2btd9rXp6vi848QXI6idLStL0HGzfq6/uHH5T1lZ6u/8Fn7tzA7c+Y4T5v9+7AwuRyE9vtRFOnKnPhZWW527bZiHbtIlq4kOixx4huuIHFR+l73ro10eLF+t4HQRl1UpCKiryf0v79b3PG0a2bexxJSYGFqaSE/fi+X5QFC/SPYfp0bULke3TqRHTmjPJ+tVhJ06bpu9ehQ0P1ETlBysvT/l6npBCdPKm9b6eTqGnTwO0nJrr//957+u4z0HpSYqJ/68OfMPmuFypx4U2eHHxcDgdRfj7Rhx/y52rIEBaeQO1dcom49CJBnRQkp5PoppvcH7aEBKJNmyI/jkWLaq5j+BMmX+vIddSvr82/78mePUTt2hkjSlOnqutbjZXUt6++dSMioiVLokeQZs7U915v26av/+HD/bc7fTrRkSNEt91G1LMn0fHj+u/V33qSp3Xkj927WSTatiVat67m70O58Fav1jZWm40tfk9rqnlzokmTtLUnqKNOChIRf/BuucV7cv/gg8iPY/9+opEjAwtTfr5/68h1GLWe9I9/6JsgY2KIvvlGXZ9KrSS960ae5Oayi9JsQfJ8IFJztGjBQSVVVfr6X7y45sPNqlXG3Js/PNeTAllHagnmwvvxR/3tC5GnzgoSEVFlJdHgwd6T6ttvmzOWQMIUFxd6kjJiPemtt7RNkBkZRK+9pl0UQ1lJeteNAuFfmCIjSOfP+4vw8z4aNCDq0oVo7Fheh9myxRhrxcX//uceQ2Ii0Y4dxrUdiE8+4bUdo/+evi68uDhjohGFyFOnBYmIP7hjxnhPBnPmmDeeQMIU6tC7nvTyy8r7slo5IGTrVv1CGMpK0rtuFApvYYqMIDkcRFdd5W313HEHu4VWreJAm0hMqO++yxFlP/0U/r7CTXExu3UBoscfN3s0glbqvCAR8QTx1FPeE9AzzxgTxaaV/fuJrrlGuUjoXU/yvX9/R7NmLBBHjhh2m0QU2EoyYt1IKbm5RIMGRc5lZ7Oxi9NIq0fgACAzv7eCPiR1EDhZ5Ouvc4oWF7NnA489Bjgc5oypSRNOj6OUqirgvvuAkye19eebNsiTPn04R1lhIVfLbdFCWx+BGDqUK6Z6kprK6Yq0FGvTQseOwIoV/P9Bg8LfX6NGnEU7OTn8fdUlUlPDW0xRCC8iSL9hsXA+s4UL3R/oJUuAESO4DksoKir4WdooXn0VqKxUd83hw8Ajj2gbh29fl17Kpa2//x7Ytg24917jCrH5EhPDpeFdWCzAypVA06bh6S8UK1Zw2Ye77+af69UDbrzRnLEIQp3CbBMtGlm1iqhePbe7pl8/zjsWiHnzOIKoe3fvlCdaCbTvKJzrSR9/zHstrr2WAxwivUPd4eAF75gYotdfj2zfLmw2dtnZPG6+sJDo8GFzxmMkmzZxwI64s4RoRuohBWD9emDYMLflcP31nJk5MdH7vHfeYavExZo1nKlYD08/zS5ErVitwJYtQO/e6q4jMtfdQcQVWuPjzenfVaDPZrOhkW+luFpMbi7XKQKArl05c/hll+lrc/Jk4KOP+Dvy8MNcNVYQ9CKCFIRdu7hGjs3GP193HbBhgzst/kcfsSvLM8V9Vhbw2Wfa+zx1iv3gat11vsTHA2fOiD9dDWYLEhGvAx48yJVXW7Y0pt2VK4GRI90/t2zJD07du2trz+GoWTDw6qv5s5+ZyeUkLtaqykJ4EUEKQV4eMGAAl/cGgFat+AmzoIC/gFVV3udbrVzqvFkzbf0VFwOXX25MHZeqqvCt+1yMmC1IS5YA48bx/7t0Af7zH2Pa3biRP8OexMbyOuWf/6ztoeXSS/mBxx8NGwL9+7M4ZWaatxYo1D5EkBSQnw/06+eOektMZAsmkBXz6qvsdtNKTg5PIlr+MidP8jjHjGFXiqAcswWpUyd+AHKRl2dM1VN/guRiyBBg6VL1LrwXXgBefFHZuV27sjBlZbFV5lkC3W7n6NZTp9hy0yKOSUkcqXnJJeqvFaILESSFHD3KT3379oU+NyMD2LtX3GW1DaWCFI61ti++AHr18n5Nr/vXRTBBAtjqf/99dS68oiIWELWzR0oKMHAgrz0NHgyMHQssW6auDX9MmADMnau/HcFcJOxbIc2bcziwEhfYDz8A334b/jEJkcXh4LUYEmfGlQAADaxJREFUqxW44gpjw/xnz675Wk4OsHOncX0EoqAAuOkmLlGu9J7S09lroJbjx4Hly9kyW7gQSEhQ34Y/5LH64kAESSGlpRzAYLcrO//dd8M6HCHClJbyBLxyJU9+hw4B5eXGtL13b2BLaNKkyEy2djtbGXffrfy+HnpIX59nz7IIXn21vnasVuBPf9LXhhAdiCApwGZjN0N+vvJr/vlPDmEWaj9bt/L6ztat3q9XVxvT/pw5gX/35ZfGuO2UsnYtB1Ts3h363CFDOOOEFm69FXjiCY7W+/xzduVpZeRIoG1b7dcL0YMIUgjOnuVUMrm56q4rLwc+/TQ8YxKMJTs7GxkZGejus4jicAAvvQTcfjtQUhKevgsLOUVSMJ59NrIprJS68OLjgeHD1bffvTsLX1wc/+xyh2tZl7NagalT1V8nRClm7citLdx/v/aMCXfcYfboBTV4ZmooKeEidcH+vqWl+vt84glln6Vly7T3sWGD9s/w008Hb/urr9S1d801gRPKTpmifnxjxmh/X4ToQyykINjtvPlVKxs2cHSeEH6IgCNHgNWrgexsfRbFjh3sovv8c+PG549ffwXeflvZuc8/ryynotGEchf27Am0a6esrbQ0jvgLlFD2hRfUZxe5/XYJaLiYEEEKQmwsMGuW9jQrTqc7g7RgDJWVvD/n/ffZnfbAA7zPpWFDjvwaMYIXuEePVt+2S8QGDw6fi86TBQuUZ+QoLAT+9rfwjseX9HTgrbeCn2OxKA9uqFcv+IbvevV47VXNetKoUcAtt/D6nghT7Uf2ISmguhr4+msOw123znvzYiiuugrYv1/2JKmBiAVh/34+Dhxw/1tYqGziGTRI3RpeaSlw//0V2L69MQAbgNCr9aWlwO9+p7wPT06f5owcaiL1kpM5uq9hQ3V9hdqH5Et6OueqGzsWaNAg9PmhsotYLO6/WVoaZzoJFlm3cSMHEamdmXr3Zivrllvk+1ZrMdtnWBspKiJavJjorruIEhJC+7k3bTJ7xLWHgweJ2rbVvuYBcLHCo0eV97llC1HTpkTBKsYavYb0xhva7k1LBV2la0hpaUSLFmnLWD9woP824+KI3nuP6Mor3a8lJ4cuJhlqPWn0aKIVK7wr77qO3r35byqZzWsfIkg6OXeOv/BPPhl4Ir3tNrNHaRwrV3I13ZwcorNnjW9/4UJ9YgQQvfii8v7mzfMsFx8ZQTp/nid/Lfd26aXq+1UqSG++qe1+iIhWr67ZntVK9Omn/PvSUqJOnbzvY8uWwO3Z7Sws/sZptfKDCxFXFBZhungQQTKYAweI5s4luv56bRNkNHPoUM2n38xMouxs42oGFRcTXXaZdjFKSQleu8qTs2c9xShygvT3v+sT3KeeUtdfIEFKTyeaNMn9c1qa9npelZVEjRt7t798ufc5J08S9erl/n2DBlyHKxDFxfz39B23v8i66mp+WGrXToSpNiOCFEYqKogKCswehXEcPhx8oszIIJo4kWjrVqKqKu39rFmjfbKeP195P04nh+ZHWpC8+1R/9Oqlrr8dO2oKkadrbtAg9+8WLtR2T0TeIeyBrK2zZ4nuvNN9XkwMC3QgNmwgsljc53taR/4QYardiCAJinE6iRo1UjZpNm5MdO+9PNmUlKjva+xY9RN1q1bsDlODw8ECeN11kROkWbNCt22xEDVrxvfUrh1Rhw5E3boR9e9PtH27uv6qqogGD2aXmb81om+/NcZKOn2avQEffhh6PCNHet/vG28EPt9zPUnpviMRptqJCJKgiptv1vZU37Ur0bhxbD0poaKC6Ior1PXh6yJSg8NBtGxZ5IIajh/n4JhffuFy8ZWVPIb27bnt+HjtbWvBKCtJKQ5HzU3BU6b4Fwm7nWjyZA5kKCtT148IU+1CBElQxR/+oM/dBCjPOrB5s7e7JtjRoQNPcnpwZWp44IHwC1IgunXjtmNijG87GEZZSWpwOoleeMH7PR0/Xv/f0R8iTLUD2Rh7kfHTT1yYb9ky/roZTceO+ts4fDj0OV98wfeh9B5mzvQu/KaHzZvd/4900k5X6W+n07jkrUro2pX3bgGc8WLp0vD3abEA06YB8+e7X1u0CHjwwZqVmPVitfIm6n37OGO7Z3aJHTs42atssI0CzFZEwVjuusv95DdsGEc26cXpJDpyhEO9x4/XZx0NHRr8CbiqimjqVO/oN6s1eJu9etV8uh03bhwBoLlz5yq+T5eF5HLZDRvmu8YUfgupb193+2fOGN9+MMywklysWOH9dx44MLz3LxZTdCKCdJGRmur95WrThicapVRW8vlLl/Leqr59iRIT9bvpkpOJ1q8P3vfBg0Q9enhfd/PNHCXWsGHgtnft8m7n448/po4dO1Lz5s1VCVJJibcg5eW5f+crTNddF54Jy3OD6YkTxrcfikivJXnyr3/xVgJX/zfeGP73QIQpuqizgvTVV7yWUV5u3hiKingPz+rVRD/8wIu3eigp8T9h169PtGCB/y9WdTVnnRg+nMO2Q1kjWo5evdjCCsaKFd5ZL6xWounTeXxEHLDgr+3Bg73bOXLkCLVo0YL27t1LLVu2VCVIr7ziFqRhw/yf43AQff89R5SFA08L99ix8PQRDDOtJCKOIPSM5OzQQVuUplpCCVNubvjHINRRQfr1V6LYWP6wNW7M6VjMECbf8gZxcRyN9vvfcwaBrVvVRRVt3BhcGPy58BYsCC0oTZtyuPHEiSwct9+uXIwmTw4ttIcOEdWr576mbVuir7/2PsfpJBoxwrtti4Vo7173OQ6Hg/r27Uvz5s0jIgopSOfOnSObzXbhuPrqExcEydM6iiT33ee+v8JCc8bgaSW5Mi1Eku++894Q+/jjkes7kDA1axa5MdRl6qQg2WxELVp4f+DMEKYxY5RN6mlpRFlZRM8+G9yaevXV0G35uvA8N6HGxhJ17Mjhta+9xjn4/K2TvPRS6H6UuOhclJURNWnC1z38cOBMC+XlRJdf7u7Dd0/KzJkzqV+/fuT8zRQMJUjTpk37TYBcxz8JAD30kE3ZwMPAO++4RTkc0WZKyMtjKyU2Vp2710gOHOA9WADRyy9Hvn9fYerWLfJjqIvUSUEi4qfPRx7xfjKPtDBVVxN99hl/4e65h/NxKQ1z9mdN3Xuvsms9XXhOJ6/d7NmjPLvC2rX6XXS+/PKLMotg1y5OLZSUdJri46+khIQESkhIoG3btlFqaioVFxdfOFethXTwYBEBoPJy8wSJiGj//sgHNPhSXEz088/mjuH8ebaAzVzDqa4m2reP98UJ4afOl584fJhDht991zvMtnFjYMIEPpo0idx4zpwB9u4F9uzhMhd79vBhsxnf17BhwDvv8L2qoaAAaN3a/+8mTwZefJFr24SL8+eByspT+PXX0guvrVmzBlOmTEGMR+y3w+FATEwM0tPTUVBQELLdiooKNG7cGDabDY0ahS4/IQiCsdR5QXIRbcLkCRHw889ugXL9e/Ag/04PbdpwsbuuXdWNp0kToKLC/VpyMrB8OdexMYOysjIcO3bM67UBAwZg1KhRGDt2LNopKGsqgiQI5iKC5EM0C5MvLmsqLw/YsgV47z1t7VitXGV13jzl19x6K28iBIBevbjSZ4sW2voPF61atcKECRMwYcIEReeLIAmCuUimBh9atwaWLOGMB4884nY92WzsimrViqtSnjxp5iiZhASgZ09g3DggK0t7Ow4H8OabwJw5yq+ZNQvo1w+YMYPFMNrESBCE2ocIUgDCJUyff85lnB98ELDbjRvvnj3621BT9rlnTy41PXlyeNeL9FBQUKDYOhIEwXxEkEJgpDDZ7cCjjwLFxcCqVcBzzxk3zrw8bdelpLClk50NTJxo3HgEQRDUImtIKtGzxrR0KScM9SQnB8jM1D+upk2B0tLQ51ksQI8e7OLLygI6dTIuKWltR9aQBMFcRJA0olaY7HbOMOyb6TopCfjvf4H0dO1jKS1lQQpEkyYc/ZaZyf+mpGjv62JGBEkQzEUESSdKhcmfdeTixhuBbduA2FhtYzh0CLjiCu/X2rdnCygzE7jhhuhd54kmRJAEwVxEkAwimDA98QTv0SksDHz9M88Ar7yirW8i4I03gO++4xDszEzg8su1tVWXEUESBHMRQTKYQMKkBKPWkwRtiCAJgrnIcrbB+EblWa3Krx09GigqCt/YBEEQohkRpDDhEqYZM5RfU1YGDB9u7P4kQRCE2oIIUhix24HFi9Vd8+WXxu5PEgRBqC2IIIWR5ctrhnkrYfZsYN0648cjCIIQzYgghQm7HZg+Xfv1o0bJelKkyM7ORkZGBrp37272UAShTiNRdmEi2L4jpbRsycER9esbMyYhOBJlJwjmIhZSmFi6VH8bhYXa9yYJgiDUNkSQwsS11xrTTufOxrQjCIIQ7YjLLkwQAT/+CJw+re36M2fYZdemjbHjEgIjLjtBMBfJcBYmLBYgI8PsUQiCINQexGUnCIIgRAUiSIIgCEJUIIIkCIIgRAUiSIIgCEJUIIIkCIIgRAUiSIIgCEJUIPuQBOE3iAinTp1Cw4YNYbFYzB6OINQ5RJAEQRCEqEBcdoIgCEJUIIIkCIIgRAUiSIIgCEJUIIIkCIIgRAUiSIIgCEJUIIIkCIIgRAUiSIIgCEJUIIIkCIIgRAUiSIIgCEJUIIIkCIIgRAX/By9INgFKAg2TAAAAAElFTkSuQmCC\n", "text/plain": [ "Graphics object consisting of 82 graphics primitives" ] }, "execution_count": 157, "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": 158, "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; this will be corrected in Sage 8.3. " ] }, { "cell_type": "code", "execution_count": 159, "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": 160, "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": 160, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ex = stereoN.frame()[1]\n", "ex" ] }, { "cell_type": "code", "execution_count": 161, "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": 162, "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": 162, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ey = stereoN.frame()[2]\n", "ey" ] }, { "cell_type": "code", "execution_count": 163, "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": 164, "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), viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The same scene rendered with Tachyon:" ] }, { "cell_type": "code", "execution_count": 165, "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": 166, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field v(f) on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} v\\left(f\\right):& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & \\frac{4 \\left(- x + 2 y\\right)}{x^{4} + 2 x^{2} y^{2} + y^{4} + 1} \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & \\frac{4 \\left(- xp^{3} + 2 xp^{2} yp - xp yp^{2} + 2 yp^{3}\\right)}{xp^{4} + 2 xp^{2} yp^{2} + yp^{4} + 1} \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2 \\left(2 \\sin{\\left (\\phi \\right )} - \\cos{\\left (\\phi \\right )}\\right) \\left(\\cos{\\left (\\theta \\right )} - 1\\right)^{3} \\sin{\\left (\\theta \\right )}}{- \\sin^{4}{\\left (\\theta \\right )} + 4 \\sin^{2}{\\left (\\theta \\right )} + 2 \\cos^{3}{\\left (\\theta \\right )} + 2 \\cos{\\left (\\theta \\right )} - 4} \\end{array}$ " ], "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: (theta, phi) |--> 2*(2*sin(phi) - cos(phi))*(cos(theta) - 1)**3*sin(theta)/(-sin(theta)**4 + 4*sin(theta)**2 + 2*cos(theta)**3 + 2*cos(theta) - 4)" ] }, "execution_count": 166, "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": 167, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAwAAAASCAYAAABvqT8MAAAABHNCSVQICAgIfAhkiAAAAN1JREFUKJHN0r0uRFEUxfGfyRgFxkemUYgC0VNotd6BB/AAGv1E6z2Uk2m9AgmVTiIjQyNhGuKjuOcm281W6OxmZa99/mef5Cz+WFONfgunuMMXejjGOIMXcI+D4J3gBjMZ0Mcj2sFbxjuOMuAWg8S/xkXdtIrOYxOjBBhhpwmsFX1NgAm66ESgG4YZAIsR+Cj6mQDTRdsReEoO1jVb9CUCY9VHLf0CPDeBCS6xmgAbuKqbVhgMsetnXNbLJefZW1fK6sPgnak+rlMbMQYP2FNFZBtzqmjs4y3b8E/qGxZ9JaWPkmySAAAAAElFTkSuQmCC\n", "text/latex": [ "$$0$$" ], "text/plain": [ "0" ] }, "execution_count": 167, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf(N)" ] }, { "cell_type": "code", "execution_count": 168, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAwAAAASCAYAAABvqT8MAAAABHNCSVQICAgIfAhkiAAAAKJJREFUKJHF0DEOQVEQheEv4kUiotbR6ixCpRKVDYhaokFDZxtUKrECSptQ24BGNBReIc+9vELiNJPMzD9nZvixxpi8JgofmutYoJQXmKGcTcaAHvahQgiooINNXmCKZcT5DWjhglMMKGbgEQax5qzDECvc8gA1NEU+E1qpnQK7l1qSxr7nbWtsPw1r4I55aKWQkkyMqooDzqnDFUd0v4F/0gODNxSArSaJWwAAAABJRU5ErkJggg==\n", "text/latex": [ "$$4$$" ], "text/plain": [ "4" ] }, "execution_count": 168, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf(E)" ] }, { "cell_type": "code", "execution_count": 169, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAwAAAASCAYAAABvqT8MAAAABHNCSVQICAgIfAhkiAAAAN1JREFUKJHN0r0uRFEUxfGfyRgFxkemUYgC0VNotd6BB/AAGv1E6z2Uk2m9AgmVTiIjQyNhGuKjuOcm281W6OxmZa99/mef5Cz+WFONfgunuMMXejjGOIMXcI+D4J3gBjMZ0Mcj2sFbxjuOMuAWg8S/xkXdtIrOYxOjBBhhpwmsFX1NgAm66ESgG4YZAIsR+Cj6mQDTRdsReEoO1jVb9CUCY9VHLf0CPDeBCS6xmgAbuKqbVhgMsetnXNbLJefZW1fK6sPgnak+rlMbMQYP2FNFZBtzqmjs4y3b8E/qGxZ9JaWPkmySAAAAAElFTkSuQmCC\n", "text/latex": [ "$$0$$" ], "text/plain": [ "0" ] }, "execution_count": 169, "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": 170, "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": 171, "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": 171, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.display()" ] }, { "cell_type": "code", "execution_count": 172, "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": 173, "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": 173, "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": 174, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field df(v) on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\mathrm{d}f\\left(v\\right):& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & \\frac{4 \\left(- x + 2 y\\right)}{x^{4} + 2 x^{2} y^{2} + y^{4} + 1} \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & \\frac{4 \\left(- xp^{3} + 2 xp^{2} yp - xp yp^{2} + 2 yp^{3}\\right)}{xp^{4} + 2 xp^{2} yp^{2} + yp^{4} + 1} \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2 \\left(2 \\sin{\\left (\\phi \\right )} - \\cos{\\left (\\phi \\right )}\\right) \\left(\\cos{\\left (\\theta \\right )} - 1\\right)^{3} \\sin{\\left (\\theta \\right )}}{- \\sin^{4}{\\left (\\theta \\right )} + 4 \\sin^{2}{\\left (\\theta \\right )} + 2 \\cos^{3}{\\left (\\theta \\right )} + 2 \\cos{\\left (\\theta \\right )} - 4} \\end{array}$ " ], "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: (theta, phi) |--> 2*(2*sin(phi) - cos(phi))*(cos(theta) - 1)**3*sin(theta)/(-sin(theta)**4 + 4*sin(theta)**2 + 2*cos(theta)**3 + 2*cos(theta) - 4)" ] }, "execution_count": 174, "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": 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": [ "df(v) == v(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 176, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 176, "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": 177, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Real number line R\n" ] } ], "source": [ "R. = RealLine() ; print(R)" ] }, { "cell_type": "code", "execution_count": 178, "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": 178, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R.category()" ] }, { "cell_type": "code", "execution_count": 179, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAASCAYAAACNdSR1AAAABHNCSVQICAgIfAhkiAAAAF5JREFUKJFjYKAC4GJgYLhEjEJTBgaG0wwMDP/RJViQ2JoMDAw9DAwMrxkYGP6S4owF2ExmIsWEUcVUV8wBpblwaRRjYGDYycDAcIUBEnv/GSBRv5+BgSGaFBfQGAAA/84M5lOscPUAAAAASUVORK5CYII=\n", "text/latex": [ "$$1$$" ], "text/plain": [ "1" ] }, "execution_count": 179, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dim(R)" ] }, { "cell_type": "code", "execution_count": 180, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left(\\Bold{R},(t)\\right)\\right]$ " ], "text/plain": [ "[Chart (R, (t,))]" ] }, "execution_count": 180, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R.atlas()" ] }, { "cell_type": "code", "execution_count": 181, "metadata": {}, "outputs": [], "source": [ "R.set_calculus_method('sympy')" ] }, { "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": 182, "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": 183, "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": 183, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.parent()" ] }, { "cell_type": "code", "execution_count": 184, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} c:& \\Bold{R} & \\longrightarrow & \\mathbb{S}^2 \\\\ & t & \\longmapsto & \\left(x, y\\right) = \\left(e^{\\frac{t}{10}} \\cos{\\left (t \\right )}, e^{\\frac{t}{10}} \\sin{\\left (t \\right )}\\right) \\\\ & t & \\longmapsto & \\left({x'}, {y'}\\right) = \\left(e^{- \\frac{t}{10}} \\cos{\\left (t \\right )}, e^{- \\frac{t}{10}} \\sin{\\left (t \\right )}\\right) \\\\ & t & \\longmapsto & \\left({\\theta}, {\\phi}\\right) = \\left(2 \\operatorname{atan}{\\left (e^{- \\frac{t}{10}} \\right )}, t\\right) \\end{array}$ " ], "text/plain": [ "c: R --> S^2\n", " t |--> (x, y) = (exp(t/10)*cos(t), exp(t/10)*sin(t))\n", " t |--> (xp, yp) = (exp(-t/10)*cos(t), exp(-t/10)*sin(t))\n", " t |--> (theta, phi) = (2*atan(exp(-t/10)), t)" ] }, "execution_count": 184, "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": 185, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 185, "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": 186, "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": 187, "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": 187, "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": 188, "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": 189, "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": 189, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent()" ] }, { "cell_type": "code", "execution_count": 190, "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": 190, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent().category()" ] }, { "cell_type": "code", "execution_count": 191, "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": 191, "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": 192, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{c'} = \\left(- \\sin{\\left (t \\right )} + \\frac{\\cos{\\left (t \\right )}}{10}\\right) e^{\\frac{t}{10}} \\frac{\\partial}{\\partial x } + \\left(\\frac{\\sin{\\left (t \\right )}}{10} + \\cos{\\left (t \\right )}\\right) e^{\\frac{t}{10}} \\frac{\\partial}{\\partial y }$ " ], "text/plain": [ "c' = (-sin(t) + cos(t)/10)*exp(t/10) d/dx + (sin(t)/10 + cos(t))*exp(t/10) d/dy" ] }, "execution_count": 192, "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": 193, "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": 194, "metadata": { "scrolled": false }, "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", "

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": 195, "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": 195, "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": 196, "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", "

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

" ] }, { "cell_type": "code", "execution_count": 197, "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": 198, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAD0AAAAWCAYAAABzCZQcAAAABHNCSVQICAgIfAhkiAAAApdJREFUWIXt10lolEkUB/BfTI8L7ksUdVxIooE5uaEiEsjVg6cBQdSzIl5yVEcC4sxNHQZPMx5cUEH0oIjMICKiHrw4qCdBXHDXuKA5DOJyqG6pVCpJd7qdiOQPHx/vX//v1Xtdr15VM4QvaMDayG7BSezBbhzEtEGIK8ZSIaazuIH9mBmN1+N3jC7H2Vjsww9FezweYF2k2YqbGFFN1FWgBX9jQtEeg4t4hrmRbr6wQP3iDyyK7F1FZ4WIm4T32DSQiGuAU2hOuIX4hGMJ34H1fTlrxLmEu4XTGe0NnC83yhrjHe5jasK/wouEm4LrQrmDYYlgMw5F9ljMw6PMxI+wuPJ4a4I7Qk9J92sdRiXcCzxEW4lIk16FS5E9p/h+l5m4C+MwvLJ4a4LlQmx3Im620H+uZvSXsbpkxEnPFMrldsSNK767Mo5K3ITM2NdGF54k3EZ8xLaM/l9RVcZJzxUaVowPxffHjKNSdy9kxv5vNGILfsOVzHinsE3RPelpeJOIn/cxUWk/va08xppiBI7gT2zvRfNSKH10T7qg54o+FY6BiRlHo/Ha4Cf9F/5Bex+aAv4rGXHSz/VMrgvXMCvjqFnYK4OJDuFI3RFxGzK6iaKtGyf9EJMzH5zBMuE4KKFJ+CGOJ9oWjCw34iqxToh/Z8KvzGgbcC/npA6PMSPhpwtlHN9q9gqXk/i4ahO2wolyo64CrUJlHk6eYzia0f8q39XBAazJ8AuEFd8jNIwT+DHR/FQM5G4l0Q8QncIPnHvSlSfcy5f05myFniVbKTqq/L7WaMKFmEhvZFeE87epikkG659Xb2jHL/2JmoVzr64/YQZt+HkA330ttAr9pyysFK51laAg3Ii+FdQLl5X6/oRDGMJ3hM/YvHO2AhCuFgAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left ( 0, \\quad 2\\right )$$" ], "text/plain": [ "(0, 2)" ] }, "execution_count": 198, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.tensor_type()" ] }, { "cell_type": "code", "execution_count": 199, "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": 200, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{4}{x^{4} + 2 x^{2} y^{2} + 2 x^{2} + y^{4} + 2 y^{2} + 1} \\right) \\mathrm{d} x\\otimes \\mathrm{d} x + \\left( \\frac{4}{x^{4} + 2 x^{2} y^{2} + 2 x^{2} + y^{4} + 2 y^{2} + 1} \\right) \\mathrm{d} y\\otimes \\mathrm{d} y$ " ], "text/plain": [ "g = 4/(x**4 + 2*x**2*y**2 + 2*x**2 + y**4 + 2*y**2 + 1) dx*dx + 4/(x**4 + 2*x**2*y**2 + 2*x**2 + y**4 + 2*y**2 + 1) dy*dy" ] }, "execution_count": 200, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

We may factorize the metric components:

" ] }, { "cell_type": "code", "execution_count": 201, "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": 201, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[1,1].factor() ; g[2,2].factor()" ] }, { "cell_type": "code", "execution_count": 202, "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": 202, "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": 203, "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": 203, "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": 204, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{4}{xp^{4} + 2 xp^{2} yp^{2} + 2 xp^{2} + yp^{4} + 2 yp^{2} + 1} \\right) \\mathrm{d} {x'}\\otimes \\mathrm{d} {x'} + \\left( \\frac{4}{xp^{4} + 2 xp^{2} yp^{2} + 2 xp^{2} + yp^{4} + 2 yp^{2} + 1} \\right) \\mathrm{d} {y'}\\otimes \\mathrm{d} {y'}$ " ], "text/plain": [ "g = 4/(xp**4 + 2*xp**2*yp**2 + 2*xp**2 + yp**4 + 2*yp**2 + 1) dxp*dxp + 4/(xp**4 + 2*xp**2*yp**2 + 2*xp**2 + yp**4 + 2*yp**2 + 1) dyp*dyp" ] }, "execution_count": 204, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(stereoS.frame())" ] }, { "cell_type": "code", "execution_count": 205, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\sin^{2}{\\left (\\theta \\right )} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$ " ], "text/plain": [ "g = dtheta*dtheta + sin(theta)**2 dphi*dphi" ] }, "execution_count": 205, "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": 206, "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": 207, "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": 207, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(v,v).parent()" ] }, { "cell_type": "code", "execution_count": 208, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} g\\left(v,v\\right):& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & \\frac{20}{x^{4} + 2 x^{2} y^{2} + 2 x^{2} + y^{4} + 2 y^{2} + 1} \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & \\frac{20 \\left(xp^{4} + 2 xp^{2} yp^{2} + yp^{4}\\right)}{xp^{4} + 2 xp^{2} yp^{2} + 2 xp^{2} + yp^{4} + 2 yp^{2} + 1} \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & 5 \\left(\\cos{\\left (\\theta \\right )} - 1\\right)^{2} \\end{array}$ " ], "text/plain": [ "g(v,v): S^2 --> R\n", "on U: (x, y) |--> 20/(x**4 + 2*x**2*y**2 + 2*x**2 + y**4 + 2*y**2 + 1)\n", "on V: (xp, yp) |--> 20*(xp**4 + 2*xp**2*yp**2 + yp**4)/(xp**4 + 2*xp**2*yp**2 + 2*xp**2 + yp**4 + 2*yp**2 + 1)\n", "on A: (theta, phi) |--> 5*(cos(theta) - 1)**2" ] }, "execution_count": 208, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(v,v).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 209, "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": 209, "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": 210, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\nabla_{g} g = 0$ " ], "text/plain": [ "nabla_g(g) = 0" ] }, "execution_count": 210, "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": 211, "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": 211, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.christoffel_symbols_display(chart=stereoN)" ] }, { "cell_type": "code", "execution_count": 212, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, {\\theta}} \\, {\\phi} \\, {\\phi} }^{ \\, {\\theta} \\phantom{\\, {\\phi}} \\phantom{\\, {\\phi}} } & = & - \\frac{\\sin{\\left (2 \\theta \\right )}}{2} \\\\ \\Gamma_{ \\phantom{\\, {\\phi}} \\, {\\theta} \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} } & = & \\frac{1}{\\tan{\\left (\\theta \\right )}} \\end{array}$ " ], "text/plain": [ "Gam^theta_phi,phi = -sin(2*theta)/2 \n", "Gam^phi_theta,phi = 1/tan(theta) " ] }, "execution_count": 212, "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": 213, "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": 214, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\nabla_{g} v = \\left( \\frac{2 \\left(- x + 2 y\\right)}{x^{2} + y^{2} + 1} \\right) \\frac{\\partial}{\\partial x }\\otimes \\mathrm{d} x + \\left( - \\frac{4 x + 2 y}{x^{2} + y^{2} + 1} \\right) \\frac{\\partial}{\\partial x }\\otimes \\mathrm{d} y + \\left( \\frac{2 \\left(2 x + y\\right)}{x^{2} + y^{2} + 1} \\right) \\frac{\\partial}{\\partial y }\\otimes \\mathrm{d} x + \\left( \\frac{2 \\left(- x + 2 y\\right)}{x^{2} + y^{2} + 1} \\right) \\frac{\\partial}{\\partial y }\\otimes \\mathrm{d} y$ " ], "text/plain": [ "nabla_g(v) = 2*(-x + 2*y)/(x**2 + y**2 + 1) d/dx*dx - (4*x + 2*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": 214, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab(v).display(stereoN.frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

Curvature

\n", "

The Riemann tensor associated with the metric $g$:

" ] }, { "cell_type": "code", "execution_count": 215, "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": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Riem}\\left(g\\right) = \\left( \\frac{4}{x^{4} + 2 x^{2} y^{2} + 2 x^{2} + y^{4} + 2 y^{2} + 1} \\right) \\frac{\\partial}{\\partial x }\\otimes \\mathrm{d} y\\otimes \\mathrm{d} x\\otimes \\mathrm{d} y + \\left( - \\frac{4}{x^{4} + 2 x^{2} y^{2} + 2 x^{2} + y^{4} + 2 y^{2} + 1} \\right) \\frac{\\partial}{\\partial x }\\otimes \\mathrm{d} y\\otimes \\mathrm{d} y\\otimes \\mathrm{d} x + \\left( - \\frac{4}{x^{4} + 2 x^{2} y^{2} + 2 x^{2} + y^{4} + 2 y^{2} + 1} \\right) \\frac{\\partial}{\\partial y }\\otimes \\mathrm{d} x\\otimes \\mathrm{d} x\\otimes \\mathrm{d} y + \\left( \\frac{4}{x^{4} + 2 x^{2} y^{2} + 2 x^{2} + y^{4} + 2 y^{2} + 1} \\right) \\frac{\\partial}{\\partial y }\\otimes \\mathrm{d} x\\otimes \\mathrm{d} y\\otimes \\mathrm{d} x$ " ], "text/plain": [ "Riem(g) = 4/(x**4 + 2*x**2*y**2 + 2*x**2 + y**4 + 2*y**2 + 1) d/dx*dy*dx*dy - 4/(x**4 + 2*x**2*y**2 + 2*x**2 + y**4 + 2*y**2 + 1) d/dx*dy*dy*dx - 4/(x**4 + 2*x**2*y**2 + 2*x**2 + y**4 + 2*y**2 + 1) d/dy*dx*dx*dy + 4/(x**4 + 2*x**2*y**2 + 2*x**2 + y**4 + 2*y**2 + 1) d/dy*dx*dy*dx" ] }, "execution_count": 215, "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": 216, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, x} \\, y \\, x \\, y }^{ \\, x \\phantom{\\, y} \\phantom{\\, x} \\phantom{\\, y} } & = & \\frac{4}{x^{4} + 2 x^{2} y^{2} + 2 x^{2} + y^{4} + 2 y^{2} + 1} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, x} \\, y \\, y \\, x }^{ \\, x \\phantom{\\, y} \\phantom{\\, y} \\phantom{\\, x} } & = & - \\frac{4}{x^{4} + 2 x^{2} y^{2} + 2 x^{2} + y^{4} + 2 y^{2} + 1} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, y} \\, x \\, x \\, y }^{ \\, y \\phantom{\\, x} \\phantom{\\, x} \\phantom{\\, y} } & = & - \\frac{4}{x^{4} + 2 x^{2} y^{2} + 2 x^{2} + y^{4} + 2 y^{2} + 1} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, y} \\, x \\, y \\, x }^{ \\, y \\phantom{\\, x} \\phantom{\\, y} \\phantom{\\, x} } & = & \\frac{4}{x^{4} + 2 x^{2} y^{2} + 2 x^{2} + y^{4} + 2 y^{2} + 1} \\end{array}$ " ], "text/plain": [ "Riem(g)^x_yxy = 4/(x**4 + 2*x**2*y**2 + 2*x**2 + y**4 + 2*y**2 + 1) \n", "Riem(g)^x_yyx = -4/(x**4 + 2*x**2*y**2 + 2*x**2 + y**4 + 2*y**2 + 1) \n", "Riem(g)^y_xxy = -4/(x**4 + 2*x**2*y**2 + 2*x**2 + y**4 + 2*y**2 + 1) \n", "Riem(g)^y_xyx = 4/(x**4 + 2*x**2*y**2 + 2*x**2 + y**4 + 2*y**2 + 1) " ] }, "execution_count": 216, "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": 217, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\theta}} \\, {\\phi} \\, {\\theta} \\, {\\phi} }^{ \\, {\\theta} \\phantom{\\, {\\phi}} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} } & = & \\frac{\\sin{\\left (2 \\theta \\right )}}{2 \\tan{\\left (\\theta \\right )}} - \\cos{\\left (2 \\theta \\right )} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\theta}} \\, {\\phi} \\, {\\phi} \\, {\\theta} }^{ \\, {\\theta} \\phantom{\\, {\\phi}} \\phantom{\\, {\\phi}} \\phantom{\\, {\\theta}} } & = & - \\frac{\\sin{\\left (2 \\theta \\right )}}{2 \\tan{\\left (\\theta \\right )}} + \\cos{\\left (2 \\theta \\right )} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\phi}} \\, {\\theta} \\, {\\theta} \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, {\\theta}} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} } & = & -1 \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\phi}} \\, {\\theta} \\, {\\phi} \\, {\\theta} }^{ \\, {\\phi} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} \\phantom{\\, {\\theta}} } & = & 1 \\end{array}$ " ], "text/plain": [ "Riem(g)^theta_phi,theta,phi = sin(2*theta)/(2*tan(theta)) - cos(2*theta) \n", "Riem(g)^theta_phi,phi,theta = -sin(2*theta)/(2*tan(theta)) + cos(2*theta) \n", "Riem(g)^phi_theta,theta,phi = -1 \n", "Riem(g)^phi_theta,phi,theta = 1 " ] }, "execution_count": 217, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem.display_comp(spher.frame(), chart=spher)" ] }, { "cell_type": "code", "execution_count": 218, "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": 219, "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 $\\mathbb{R}^3$:

" ] }, { "cell_type": "code", "execution_count": 220, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Riem}\\left(h\\right) = 0$ " ], "text/plain": [ "Riem(h) = 0" ] }, "execution_count": 220, "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": 221, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Ric}\\left(g\\right) = \\left( \\frac{4}{x^{4} + 2 x^{2} y^{2} + 2 x^{2} + y^{4} + 2 y^{2} + 1} \\right) \\mathrm{d} x\\otimes \\mathrm{d} x + \\left( \\frac{4}{x^{4} + 2 x^{2} y^{2} + 2 x^{2} + y^{4} + 2 y^{2} + 1} \\right) \\mathrm{d} y\\otimes \\mathrm{d} y$ " ], "text/plain": [ "Ric(g) = 4/(x**4 + 2*x**2*y**2 + 2*x**2 + y**4 + 2*y**2 + 1) dx*dx + 4/(x**4 + 2*x**2*y**2 + 2*x**2 + y**4 + 2*y**2 + 1) dy*dy" ] }, "execution_count": 221, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric = g.ricci()\n", "Ric.display()" ] }, { "cell_type": "code", "execution_count": 222, "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: (theta, phi) |--> 2" ] }, "execution_count": 222, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R = g.ricci_scalar()\n", "R.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

\n", "

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

\n", "

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

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 223, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 223, "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": 224, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 224, "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": 225, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2-form eps_g on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\epsilon_{g} = \\left( \\frac{4}{x^{4} + 2 x^{2} y^{2} + 2 x^{2} + y^{4} + 2 y^{2} + 1} \\right) \\mathrm{d} x\\wedge \\mathrm{d} y$ " ], "text/plain": [ "eps_g = 4/(x**4 + 2*x**2*y**2 + 2*x**2 + y**4 + 2*y**2 + 1) dx/\\dy" ] }, "execution_count": 225, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps = g.volume_form()\n", "print(eps)\n", "eps.display()" ] }, { "cell_type": "code", "execution_count": 226, "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(theta) dtheta/\\dphi" ] }, "execution_count": 226, "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": 227, "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": 228, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}\\epsilon_{g} = 0$ " ], "text/plain": [ "deps_g = 0" ] }, "execution_count": 228, "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": 229, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A,(x, y)\\right)$ " ], "text/plain": [ "Chart (A, (x, y))" ] }, "execution_count": 229, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_chart()" ] }, { "cell_type": "code", "execution_count": 230, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A, \\left(\\frac{\\partial}{\\partial x },\\frac{\\partial}{\\partial y }\\right)\\right)$ " ], "text/plain": [ "Coordinate frame (A, (d/dx,d/dy))" ] }, "execution_count": 230, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_frame()" ] }, { "cell_type": "code", "execution_count": 231, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A,({\\theta}, {\\phi})\\right)$ " ], "text/plain": [ "Chart (A, (theta, phi))" ] }, "execution_count": 231, "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": 232, "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/dtheta,d/dphi))" ] }, "execution_count": 232, "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": 233, "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/dtheta*dtheta + 1/sin(theta) d/dphi*dphi" ] }, "execution_count": 233, "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": 234, "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(theta)]" ] }, "execution_count": 234, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a[:]" ] }, { "cell_type": "code", "execution_count": 235, "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": 235, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e = spher.frame().new_frame(a, 'e')\n", "print(e) ; e" ] }, { "cell_type": "code", "execution_count": 236, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}e_{1} = \\frac{\\partial}{\\partial {\\theta} }$ " ], "text/plain": [ "e_1 = d/dtheta" ] }, "execution_count": 236, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[1].display()" ] }, { "cell_type": "code", "execution_count": 237, "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(theta) d/dphi" ] }, "execution_count": 237, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[2].display()" ] }, { "cell_type": "code", "execution_count": 238, "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/dtheta,d/dphi)),\n", " Vector frame (A, (e_1,e_2))]" ] }, "execution_count": 238, "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": 239, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAASCAYAAACNdSR1AAAABHNCSVQICAgIfAhkiAAAAF5JREFUKJFjYKAC4GJgYLhEjEJTBgaG0wwMDP/RJViQ2JoMDAw9DAwMrxkYGP6S4owF2ExmIsWEUcVUV8wBpblwaRRjYGDYycDAcIUBEnv/GSBRv5+BgSGaFBfQGAAA/84M5lOscPUAAAAASUVORK5CYII=\n", "text/latex": [ "$$1$$" ], "text/plain": [ "1" ] }, "execution_count": 239, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[1],e[1]).expr()" ] }, { "cell_type": "code", "execution_count": 240, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAwAAAASCAYAAABvqT8MAAAABHNCSVQICAgIfAhkiAAAAN1JREFUKJHN0r0uRFEUxfGfyRgFxkemUYgC0VNotd6BB/AAGv1E6z2Uk2m9AgmVTiIjQyNhGuKjuOcm281W6OxmZa99/mef5Cz+WFONfgunuMMXejjGOIMXcI+D4J3gBjMZ0Mcj2sFbxjuOMuAWg8S/xkXdtIrOYxOjBBhhpwmsFX1NgAm66ESgG4YZAIsR+Cj6mQDTRdsReEoO1jVb9CUCY9VHLf0CPDeBCS6xmgAbuKqbVhgMsetnXNbLJefZW1fK6sPgnak+rlMbMQYP2FNFZBtzqmjs4y3b8E/qGxZ9JaWPkmySAAAAAElFTkSuQmCC\n", "text/latex": [ "$$0$$" ], "text/plain": [ "0" ] }, "execution_count": 240, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[1],e[2]).expr()" ] }, { "cell_type": "code", "execution_count": 241, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAASCAYAAACNdSR1AAAABHNCSVQICAgIfAhkiAAAAF5JREFUKJFjYKAC4GJgYLhEjEJTBgaG0wwMDP/RJViQ2JoMDAw9DAwMrxkYGP6S4owF2ExmIsWEUcVUV8wBpblwaRRjYGDYycDAcIUBEnv/GSBRv5+BgSGaFBfQGAAA/84M5lOscPUAAAAASUVORK5CYII=\n", "text/latex": [ "$$1$$" ], "text/plain": [ "1" ] }, "execution_count": 241, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[2],e[2]).expr()" ] }, { "cell_type": "code", "execution_count": 242, "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": 242, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[e,:]" ] }, { "cell_type": "code", "execution_count": 243, "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": 243, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(e)" ] }, { "cell_type": "code", "execution_count": 244, "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": 244, "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": 245, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left[\\left[0, 0\\right], \\left[0, 0\\right]\\right], \\left[\\left[0, - \\frac{1}{\\tan{\\left (\\theta \\right )}}\\right], \\left[\\frac{1}{\\tan{\\left (\\theta \\right )}}, 0\\right]\\right]\\right]$ " ], "text/plain": [ "[[[0, 0], [0, 0]], [[0, -1/tan(theta)], [1/tan(theta), 0]]]" ] }, "execution_count": 245, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e.structure_coeff()[:]" ] }, { "cell_type": "code", "execution_count": 246, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}- \\frac{1}{\\tan{\\left (\\theta \\right )}} e_{2}$ " ], "text/plain": [ "-1/tan(theta) e_2" ] }, "execution_count": 246, "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": 247, "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": 247, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.frame().structure_coeff()[:]" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.6.rc0", "language": "", "name": "sagemath" }, "language": "python", "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 1 }