{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Sphere $\\mathbb{S}^2$ (SymPy version)\n", "\n", "This worksheet demonstrates a few capabilities of\n", "[SageManifolds](http://sagemanifolds.obspm.fr) (version 1.2, as included in SageMath 8.2)\n", "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).\n", "\n", "Click [here](https://raw.githubusercontent.com/sagemanifolds/SageManifolds/master/Worksheets/v1.2/SM_sphere_S2_sympy.ipynb) to download the worksheet file (ipynb format). To run it, you must start SageMath with the Jupyter notebook, via the command `sage -n jupyter`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*NB:* a version of SageMath at least equal to 8.2 is required to run this worksheet:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 8.2, Release Date: 2018-05-05'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we set up the notebook to display mathematical objects using LaTeX 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": [ "" ], "text/plain": [ "2-dimensional differentiable manifold S^2" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The manifold is a `Parent` object:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "True" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "isinstance(S2, Parent)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "Category of smooth manifolds over Real Field with 53 bits of precision" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S2.category()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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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\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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": [ "" ], "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": "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\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": "iVBORw0KGgoAAAANSUhEUgAAARwAAAArCAYAAACq/DdBAAAABHNCSVQICAgIfAhkiAAABtVJREFUeJztnVmMFFUUhr8ZUDYZiIqMyxjEKCMokYC4DLLEEcHEFQURjQYNGlyCDyKimPZBMW6JiRviRjAaFNQYt4gaNCSKivigMSZgXJFBEhVhAEXGh3MrXdN019bVdbuqzpdMart1z5m/qm7frU6BoihKQjTYdkBRMkgjcAPQx2zfn3G7AAOAgcCPcWU4GFgLHB1XhoqSUc4HWsz6KmB0xu0CNAFrgFFeiRoDZnYY8C6wEPipKrcUJfsMBWaa9U0UC4Gs2gXYDlwBLAOGV5NRI/A+MDcGpxQlD/QC+pv1d4AjMm7XzWTga6Bv1AwWAR+i/T155FTgFqAArAbGW/UmfbQBCzJitz/STAvSpfIs8EQUI0OATqqsIimp5CBgsWt7OnIvHGnHndTRBNwZ8pxLLdn141rgbqALKRP8OBzYCZwc1tAK86fkj5HAPuBYs92E3HDTrXmULuYAB5i/9oDnFCzZDUrQAgfgEeCDMJkPBf4DxobzKXa0Wm+HBkR7pyk9ArnhRgE9kD695yjeH0cBHyfsoy3agKuBR4FpwHXAq8gzAzAD6UTdBvwBnBgw34LPcT/do9oNSpgC5ziTPnAt5wHgu/A+xYpW6+uH5cBDZv0S4FDgJYo1nqvMdtZpAq4x6xcA68z6MqC5yrwLPsdt6x6mwAHR5in3jkodwQ3AZmApcFcUz2JiJPAVUlpuQi72X0hJ/rJFv/LGbKAVuA256QaY/RuRG3An8qu7DnjSgn9J0htpav4D3Af8aZZhGQzMo/szOA6Z6+bwN3CPazsO3W+mWBMrx2fAixWOdQHHAD8EtHUrMpVmELDXK+FYk/mEgBnXCq9qPfhXbZXqORcpcEAetiFm/TJgpSvd98AJyblVF6wHTjHrA7wSBqQQII1N3cPWcEabcyY6OypN/JsC7AY+jehYXHQhpXeX2V4APAxsQGo7rcDzSN/OfGAJ8qvQmbSjGWU8MuLwNtJcmGK2QeZ4bDTrw4B+wLdJO2iBqUif4hCKNXCQpk0SpEn3DUif0mRnR88KCU9D/ok9CTgVlNnAb0i1HqRKu9ysnw68ZtaTuvBZZyjwJsWJZA7OL/nrSP/a5UgT96PkXLNKMzJydx5wB9JE6SS50Vwbus9Cmnsgzce1SKvCj33AN8AYv4QdFB/meqBStd4h7qqtEo7VSNNWqY6Z/km6kQbdlwK/eyUYiDRhCkl4E4DxyKhAs/m7EKnRuKu2/yLzDkB+cZTaMgL4FelbawM+p6i/UjvSqPsipDxpgvJNKueFry1JeeSBV7V+GnartnlmG/AMcCXyEExFCn2ltqRR9w6zbEGaV/txDlIiXZSUR4qiZJaLkfKkHcqPUvUzSx3pURSlWnabZV8oX+D0KUmoKIoSFWekuw8ED8ClKIoSBaeM6YLynca7zLK3RyZdHsfySJKxglT7/VH97eKlv1OOdEL5AmeHWXpF7PK7wHkMIu0wDAkkXasmaZCHS/VX/ZO064VTjuyolOAkpBSfU4WRPAaRBpiEaLcqYbulqP52yav+5bgJuSbHQ/k+nJ/NsppX7fMYRBpkzsE27F9o1d8uedW/HIPN8hevRFuQlyKjkucg0mB/lrbqb5e86+9mBa4vvVQapVqPzGSMyh7kre025OWyzVXkVS92wwSR7hWj3Sio/nbJu/5uhgNf+iVahAT3qeY9jbQEkQ5iM0wQ6UlIZDbbqP52yav+bvoiUR0W+iUcYzI/I0TmpaQliHQYm36C96R7SFSbqP52yaP+pZxN94B5nk2qzcBZHpl5RdubATyIxK/ZSnwvggYJIl0Lu0HZC9yegJ0gQbxV/9qh+gejHXm7fUOQxIup8HYntQskXfA5Xosg0n423YQt4WtB1oJ4+9l0o/qnR/8GJPbxve6dlSL+gQRlno80r74oORZHtL1KQaTdM5xLg0ivNst2pF0JEi81aNSzKDbrjbgiHar+0VD9gzEOGZZfEuak5VSO4O4QZ7S9QoA0cQeRDmLToR5+Yd1kIYh3EJsOqn969H8DeKF0p9/LmwuR2YutJfttBpJOUxDpWqBBvO2i+vszCqmF7Tc61cPnxO3I1zdvpHuM4zOReTqHIB1WY5Ev7K1EhtOjMhFY45OmA2nLHohc+E3AKzW2OQvprBuDfLWgGfl+jw1qpT2o/kFQ/b31b0S0eBp4K4pDDchnQq6PcnJIbASRDmszy6j+dsmC/vOA96gy9M3BwCfIcKBN0hhEOkuo/napd/0nIEPggyol8GtSOexCeuMfQ6pf26v1LCKNyMhaC1K1nYvHa+9K7Kj+dqln/VuAx5E+362WfVEURVEURVEURVEURVEURVHSwP8P0gBvIH8nWgAAAABJRU5ErkJggg==\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": [ "" ], "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", "