{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Sphere $\\mathbb{S}^2$\n", "\n", "This notebook demonstrates some differential geometry capabilities of SageMath on the example of the 2-dimensional sphere. The corresponding tools have been developed within\n", "the [SageManifolds](http://sagemanifolds.obspm.fr) project (version 1.3, as included in SageMath 8.3).\n", "\n", "Click [here](https://raw.githubusercontent.com/sagemanifolds/SageManifolds/master/Worksheets/v1.3/SM_sphere_S2.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 7.5 is required to run this notebook:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 8.3, Release Date: 2018-08-03'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we set up the notebook to display math formulas using LaTeX formatting:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We also define a viewer for 3D plots (use `'threejs'` or `'jmol'` for interactive 3D graphics):" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "viewer3D = 'threejs' # must be 'threejs', jmol', 'tachyon' or None (default)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $\\mathbb{S}^2$ as a 2-dimensional differentiable manifold\n", "\n", "We start by declaring $\\mathbb{S}^2$ as a differentiable manifold of dimension 2 over $\\mathbb{R}$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "S2 = Manifold(2, 'S^2', latex_name=r'\\mathbb{S}^2', start_index=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

\n", "

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\n", "

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

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

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

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

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

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

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

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

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

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

Spherical coordinates

\n", "

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

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

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

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

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

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

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

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

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

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

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

" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 30 graphics primitives" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.plot(stereoN, number_values=15, ranges={th: (pi/8,pi)})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

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

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

\n", "

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

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

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

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

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

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

We have of course

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

Let us introduce some point at the equator:

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

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

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

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

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

which is not possible for the point $N$:

" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Error: the point does not belong to the domain of Chart (A, (th, ph))\n" ] } ], "source": [ "try:\n", " N.coord(spher)\n", "except ValueError as exc:\n", " print('Error: ' + str(exc))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

\n", "

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

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

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

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

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

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

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

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

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

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

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

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

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

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

We may also add the two poles to the graphic:

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

Tangent spaces

\n", "

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

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

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

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

Its dimension equals the manifold's dimension:

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

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

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

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

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

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

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

Differential of a smooth mapping

\n", "

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

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

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

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

Algebra of scalar fields

\n", "

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

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

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

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

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

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

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

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

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

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

A specific element is the zero one:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The arithmetic of scalar fields:

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

Module of vector fields

\n", "

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

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

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

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

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

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

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

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

because $U$ is parallelizable:

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

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

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

Similarly

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

" ] }, { "cell_type": "code", "execution_count": 157, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_v = v.plot(chart=cart, mapping=Phi, chart_domain=spher, \n", " number_values=11, scale=0.2)\n", "show(graph_spher + graph_v, viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 158, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial x }$ " ], "text/plain": [ "Vector field d/dx on the Open subset U of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 158, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ex = stereoN.frame()[1]\n", "ex" ] }, { "cell_type": "code", "execution_count": 159, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_ex = ex.plot(chart=cart, mapping=Phi, chart_domain=spher,\n", " number_values=11, scale=0.4, width=1, \n", " label_axes=False)\n", "show(graph_spher + graph_ex, viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 160, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial y }$ " ], "text/plain": [ "Vector field d/dy on the Open subset U of the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 160, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ey = stereoN.frame()[2]\n", "ey" ] }, { "cell_type": "code", "execution_count": 161, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_ey = ey.plot(chart=cart, mapping=Phi, chart_domain=spher,\n", " number_values=11, scale=0.4, width=1, color='red', \n", " label_axes=False)\n", "show(graph_spher + graph_ey, viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may superpose the two graphs, to get a 3D view of the vector frame associated with the stereographic coordinates from the North pole:" ] }, { "cell_type": "code", "execution_count": 162, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_frame = graph_spher + graph_ex + graph_ey + \\\n", " N.plot(cart, mapping=Phi, label_offset=0.05, size=5) + \\\n", " S.plot(cart, mapping=Phi, label_offset=0.05, size=5)\n", "show(graph_frame + sphere(color='lightgrey', opacity=0.4), \n", " viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The same scene rendered with Tachyon:" ] }, { "cell_type": "code", "execution_count": 163, "metadata": {}, "outputs": [ { "data": { "image/png": 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\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": 164, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field v(f) on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} v\\left(f\\right):& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & -\\frac{4 \\, {\\left(x - 2 \\, y\\right)}}{x^{4} + 2 \\, x^{2} y^{2} + y^{4} + 1} \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & -\\frac{4 \\, {\\left({x'}^{3} - 2 \\, {x'}^{2} {y'} + {x'} {y'}^{2} - 2 \\, {y'}^{3}\\right)}}{{x'}^{4} + 2 \\, {x'}^{2} {y'}^{2} + {y'}^{4} + 1} \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2 \\, {\\left({\\left(\\cos\\left({\\phi}\\right) - 2 \\, \\sin\\left({\\phi}\\right)\\right)} \\cos\\left({\\theta}\\right) - \\cos\\left({\\phi}\\right) + 2 \\, \\sin\\left({\\phi}\\right)\\right)} \\sin\\left({\\theta}\\right)}{\\cos\\left({\\theta}\\right)^{2} + 1} \\end{array}$ " ], "text/plain": [ "v(f): S^2 --> R\n", "on U: (x, y) |--> -4*(x - 2*y)/(x^4 + 2*x^2*y^2 + y^4 + 1)\n", "on V: (xp, yp) |--> -4*(xp^3 - 2*xp^2*yp + xp*yp^2 - 2*yp^3)/(xp^4 + 2*xp^2*yp^2 + yp^4 + 1)\n", "on A: (th, ph) |--> 2*((cos(ph) - 2*sin(ph))*cos(th) - cos(ph) + 2*sin(ph))*sin(th)/(cos(th)^2 + 1)" ] }, "execution_count": 164, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf = v(f)\n", "print(vf)\n", "vf.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 165, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$ " ], "text/plain": [ "0" ] }, "execution_count": 165, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf(N)" ] }, { "cell_type": "code", "execution_count": 166, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}4$ " ], "text/plain": [ "4" ] }, "execution_count": 166, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vf(E)" ] }, { "cell_type": "code", "execution_count": 167, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$ " ], "text/plain": [ "0" ] }, "execution_count": 167, "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": 168, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1-form df on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "df = f.differential() ; print(df)" ] }, { "cell_type": "code", "execution_count": 169, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}f = \\left( -\\frac{4 \\, x}{x^{4} + 2 \\, x^{2} y^{2} + y^{4} + 1} \\right) \\mathrm{d} x + \\left( -\\frac{4 \\, y}{x^{4} + 2 \\, x^{2} y^{2} + y^{4} + 1} \\right) \\mathrm{d} y$ " ], "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": 169, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.display()" ] }, { "cell_type": "code", "execution_count": 170, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module Omega^1(S^2) of 1-forms on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(df.parent())" ] }, { "cell_type": "code", "execution_count": 171, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\Omega^{1}\\left(\\mathbb{S}^2\\right)$ " ], "text/plain": [ "Module Omega^1(S^2) of 1-forms on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 171, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.parent()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The 1-form acting on a vector field:

" ] }, { "cell_type": "code", "execution_count": 172, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field df(v) on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\mathrm{d}f\\left(v\\right):& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & -\\frac{4 \\, {\\left(x - 2 \\, y\\right)}}{x^{4} + 2 \\, x^{2} y^{2} + y^{4} + 1} \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & -\\frac{4 \\, {\\left({x'}^{3} - 2 \\, {x'}^{2} {y'} + {x'} {y'}^{2} - 2 \\, {y'}^{3}\\right)}}{{x'}^{4} + 2 \\, {x'}^{2} {y'}^{2} + {y'}^{4} + 1} \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & -\\frac{2 \\, {\\left({\\left({\\left(\\cos\\left({\\phi}\\right) - 2 \\, \\sin\\left({\\phi}\\right)\\right)} \\cos\\left({\\theta}\\right) - 3 \\, \\cos\\left({\\phi}\\right) + 6 \\, \\sin\\left({\\phi}\\right)\\right)} \\sin\\left({\\theta}\\right)^{3} - 4 \\, {\\left({\\left(\\cos\\left({\\phi}\\right) - 2 \\, \\sin\\left({\\phi}\\right)\\right)} \\cos\\left({\\theta}\\right) - \\cos\\left({\\phi}\\right) + 2 \\, \\sin\\left({\\phi}\\right)\\right)} \\sin\\left({\\theta}\\right)\\right)}}{\\sin\\left({\\theta}\\right)^{4} + 2 \\, {\\left(\\cos\\left({\\theta}\\right) - 2\\right)} \\sin\\left({\\theta}\\right)^{2} - 4 \\, \\cos\\left({\\theta}\\right) + 4} \\end{array}$ " ], "text/plain": [ "df(v): S^2 --> R\n", "on U: (x, y) |--> -4*(x - 2*y)/(x^4 + 2*x^2*y^2 + y^4 + 1)\n", "on V: (xp, yp) |--> -4*(xp^3 - 2*xp^2*yp + xp*yp^2 - 2*yp^3)/(xp^4 + 2*xp^2*yp^2 + yp^4 + 1)\n", "on A: (th, ph) |--> -2*(((cos(ph) - 2*sin(ph))*cos(th) - 3*cos(ph) + 6*sin(ph))*sin(th)^3 - 4*((cos(ph) - 2*sin(ph))*cos(th) - cos(ph) + 2*sin(ph))*sin(th))/(sin(th)^4 + 2*(cos(th) - 2)*sin(th)^2 - 4*cos(th) + 4)" ] }, "execution_count": 172, "metadata": {}, "output_type": "execute_result" } ], "source": [ "print(df(v)) ; df(v).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 173, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 173, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df(v) == v(f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 174, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 174, "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": 175, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Real number line R\n" ] } ], "source": [ "R. = RealLine() ; print(R)" ] }, { "cell_type": "code", "execution_count": 176, "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": 176, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R.category()" ] }, { "cell_type": "code", "execution_count": 177, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}1$ " ], "text/plain": [ "1" ] }, "execution_count": 177, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dim(R)" ] }, { "cell_type": "code", "execution_count": 178, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left(\\Bold{R},(t)\\right)\\right]$ " ], "text/plain": [ "[Chart (R, (t,))]" ] }, "execution_count": 178, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R.atlas()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 179, "metadata": {}, "outputs": [], "source": [ "c = S2.curve({spher: [2*atan(exp(-t/10)), t]}, (t, -oo, +oo), name='c')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 180, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Hom}\\left(\\Bold{R},\\mathbb{S}^2\\right)$ " ], "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": 180, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.parent()" ] }, { "cell_type": "code", "execution_count": 181, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} c:& \\Bold{R} & \\longrightarrow & \\mathbb{S}^2 \\\\ & t & \\longmapsto & \\left(x, y\\right) = \\left(\\cos\\left(t\\right) e^{\\left(\\frac{1}{10} \\, t\\right)}, e^{\\left(\\frac{1}{10} \\, t\\right)} \\sin\\left(t\\right)\\right) \\\\ & t & \\longmapsto & \\left({x'}, {y'}\\right) = \\left(\\cos\\left(t\\right) e^{\\left(-\\frac{1}{10} \\, t\\right)}, e^{\\left(-\\frac{1}{10} \\, t\\right)} \\sin\\left(t\\right)\\right) \\\\ & t & \\longmapsto & \\left({\\theta}, {\\phi}\\right) = \\left(2 \\, \\arctan\\left(e^{\\left(-\\frac{1}{10} \\, t\\right)}\\right), t\\right) \\end{array}$ " ], "text/plain": [ "c: R --> S^2\n", " t |--> (x, y) = (cos(t)*e^(1/10*t), e^(1/10*t)*sin(t))\n", " t |--> (xp, yp) = (cos(t)*e^(-1/10*t), e^(-1/10*t)*sin(t))\n", " t |--> (th, ph) = (2*arctan(e^(-1/10*t)), t)" ] }, "execution_count": 181, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 182, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 182, "metadata": {}, "output_type": "execute_result" } ], "source": [ "c.plot(chart=stereoN, aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

\n", "

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

" ] }, { "cell_type": "code", "execution_count": 183, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_c = c.plot(mapping=Phi, max_range=40, plot_points=200, \n", " thickness=2, label_axes=False)\n", "show(graph_spher + graph_c, viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 184, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{c'}$ " ], "text/plain": [ "Vector field c' along the Real number line R with values on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 184, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc = c.tangent_vector_field()\n", "vc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

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

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

" ] }, { "cell_type": "code", "execution_count": 186, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathfrak{X}\\left(\\Bold{R},c\\right)$ " ], "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": 186, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent()" ] }, { "cell_type": "code", "execution_count": 187, "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": 187, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent().category()" ] }, { "cell_type": "code", "execution_count": 188, "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": 188, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.parent().base_ring()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

A coordinate view of $c'$:

" ] }, { "cell_type": "code", "execution_count": 189, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}{c'} = \\left( \\frac{1}{10} \\, \\cos\\left(t\\right) e^{\\left(\\frac{1}{10} \\, t\\right)} - e^{\\left(\\frac{1}{10} \\, t\\right)} \\sin\\left(t\\right) \\right) \\frac{\\partial}{\\partial x } + \\left( \\cos\\left(t\\right) e^{\\left(\\frac{1}{10} \\, t\\right)} + \\frac{1}{10} \\, e^{\\left(\\frac{1}{10} \\, t\\right)} \\sin\\left(t\\right) \\right) \\frac{\\partial}{\\partial y }$ " ], "text/plain": [ "c' = (1/10*cos(t)*e^(1/10*t) - e^(1/10*t)*sin(t)) d/dx + (cos(t)*e^(1/10*t) + 1/10*e^(1/10*t)*sin(t)) d/dy" ] }, "execution_count": 189, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vc.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 190, "metadata": {}, "outputs": [ { "data": { "image/png": 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\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": 191, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph_vc = vc.plot(chart=cart, mapping=Phi, ranges={t: (-20, 20)}, \n", " number_values=30, scale=0.5, color='red', \n", " label_axes=False)\n", "show(graph_spher + graph_c + graph_vc , viewer=viewer3D, online=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Riemannian metric on $\\mathbb{S}^2$\n", "\n", "The standard metric on $\\mathbb{S}^2$ is that induced by the Euclidean metric of $\\mathbb{R}^3$. Let us start by defining the latter:" ] }, { "cell_type": "code", "execution_count": 192, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}h = \\mathrm{d} X\\otimes \\mathrm{d} X+\\mathrm{d} Y\\otimes \\mathrm{d} Y+\\mathrm{d} Z\\otimes \\mathrm{d} Z$ " ], "text/plain": [ "h = dX*dX + dY*dY + dZ*dZ" ] }, "execution_count": 192, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h = R3.metric('h')\n", "h[1,1], h[2,2], h[3, 3] = 1, 1, 1\n", "h.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The metric $g$ on $\\mathbb{S}^2$ is the pullback of $h$ associated with the embedding $\\Phi$:" ] }, { "cell_type": "code", "execution_count": 193, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Riemannian metric g on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "g = S2.metric('g')\n", "g.set( Phi.pullback(h) )\n", "print(g)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we could have defined $g$ intrinsically, i.e. by providing its components in the two frames stereoN and stereoS, as we did for the metric $h$ on $\\mathbb{R}^3$. Instead, we have chosen to get it as the pullback of $h$, as an example of pullback associated with some differential map.\n", "\n", "The metric is a symmetric tensor field of type (0,2):" ] }, { "cell_type": "code", "execution_count": 194, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module T^(0,2)(S^2) of type-(0,2) tensors fields on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(g.parent())" ] }, { "cell_type": "code", "execution_count": 195, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(0, 2\\right)$ " ], "text/plain": [ "(0, 2)" ] }, "execution_count": 195, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.tensor_type()" ] }, { "cell_type": "code", "execution_count": 196, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "symmetry: (0, 1); no antisymmetry\n" ] } ], "source": [ "g.symmetries()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expression of the metric in terms of the default frame on $\\mathbb{S}^2$ (stereoN):" ] }, { "cell_type": "code", "execution_count": 197, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\mathrm{d} x\\otimes \\mathrm{d} x + \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\mathrm{d} y\\otimes \\mathrm{d} y$ " ], "text/plain": [ "g = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dx*dx + 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dy*dy" ] }, "execution_count": 197, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We may factorize the metric components:" ] }, { "cell_type": "code", "execution_count": 198, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{4}{{\\left(x^{2} + y^{2} + 1\\right)}^{2}}$ " ], "text/plain": [ "4/(x^2 + y^2 + 1)^2" ] }, "execution_count": 198, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[1,1].factor() ; g[2,2].factor()" ] }, { "cell_type": "code", "execution_count": 199, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\frac{4}{{\\left(x^{2} + y^{2} + 1\\right)}^{2}} \\mathrm{d} x\\otimes \\mathrm{d} x + \\frac{4}{{\\left(x^{2} + y^{2} + 1\\right)}^{2}} \\mathrm{d} y\\otimes \\mathrm{d} y$ " ], "text/plain": [ "g = 4/(x^2 + y^2 + 1)^2 dx*dx + 4/(x^2 + y^2 + 1)^2 dy*dy" ] }, "execution_count": 199, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A matrix view of the components of $g$ in the manifold's default frame:" ] }, { "cell_type": "code", "execution_count": 200, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rr}\n", "\\frac{4}{{\\left(x^{2} + y^{2} + 1\\right)}^{2}} & 0 \\\\\n", "0 & \\frac{4}{{\\left(x^{2} + y^{2} + 1\\right)}^{2}}\n", "\\end{array}\\right)$ " ], "text/plain": [ "[4/(x^2 + y^2 + 1)^2 0]\n", "[ 0 4/(x^2 + y^2 + 1)^2]" ] }, "execution_count": 200, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display in terms of the vector frame $(V, (\\partial_{x'}, \\partial_{y'}))$:" ] }, { "cell_type": "code", "execution_count": 201, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\left( \\frac{4}{{x'}^{4} + {y'}^{4} + 2 \\, {\\left({x'}^{2} + 1\\right)} {y'}^{2} + 2 \\, {x'}^{2} + 1} \\right) \\mathrm{d} {x'}\\otimes \\mathrm{d} {x'} + \\left( \\frac{4}{{x'}^{4} + {y'}^{4} + 2 \\, {\\left({x'}^{2} + 1\\right)} {y'}^{2} + 2 \\, {x'}^{2} + 1} \\right) \\mathrm{d} {y'}\\otimes \\mathrm{d} {y'}$ " ], "text/plain": [ "g = 4/(xp^4 + yp^4 + 2*(xp^2 + 1)*yp^2 + 2*xp^2 + 1) dxp*dxp + 4/(xp^4 + yp^4 + 2*(xp^2 + 1)*yp^2 + 2*xp^2 + 1) dyp*dyp" ] }, "execution_count": 201, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(stereoS.frame())" ] }, { "cell_type": "code", "execution_count": 202, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}g = \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$ " ], "text/plain": [ "g = dth*dth + sin(th)^2 dph*dph" ] }, "execution_count": 202, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(spher.frame(), chart=spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The metric acts on vector field pairs, resulting in a scalar field:" ] }, { "cell_type": "code", "execution_count": 203, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Scalar field g(v,v) on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(g(v,v))" ] }, { "cell_type": "code", "execution_count": 204, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}C^{\\infty}\\left(\\mathbb{S}^2\\right)$ " ], "text/plain": [ "Algebra of differentiable scalar fields on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 204, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(v,v).parent()" ] }, { "cell_type": "code", "execution_count": 205, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} g\\left(v,v\\right):& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & \\frac{20}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & \\frac{20 \\, {\\left({x'}^{4} + 2 \\, {x'}^{2} {y'}^{2} + {y'}^{4}\\right)}}{{x'}^{4} + {y'}^{4} + 2 \\, {\\left({x'}^{2} + 1\\right)} {y'}^{2} + 2 \\, {x'}^{2} + 1} \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & 5 \\, \\cos\\left({\\theta}\\right)^{2} - 10 \\, \\cos\\left({\\theta}\\right) + 5 \\end{array}$ " ], "text/plain": [ "g(v,v): S^2 --> R\n", "on U: (x, y) |--> 20/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1)\n", "on V: (xp, yp) |--> 20*(xp^4 + 2*xp^2*yp^2 + yp^4)/(xp^4 + yp^4 + 2*(xp^2 + 1)*yp^2 + 2*xp^2 + 1)\n", "on A: (th, ph) |--> 5*cos(th)^2 - 10*cos(th) + 5" ] }, "execution_count": 205, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(v,v).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **Levi-Civita connection** associated with the metric $g$:" ] }, { "cell_type": "code", "execution_count": 206, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Levi-Civita connection nabla_g associated with the Riemannian metric g on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\nabla_{g}$ " ], "text/plain": [ "Levi-Civita connection nabla_g associated with the Riemannian metric g on the 2-dimensional differentiable manifold S^2" ] }, "execution_count": 206, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab = g.connection()\n", "print(nab)\n", "nab" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a test, we verify that $\\nabla_g$ acting on $g$ results in zero:" ] }, { "cell_type": "code", "execution_count": 207, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\nabla_{g} g = 0$ " ], "text/plain": [ "nabla_g(g) = 0" ] }, "execution_count": 207, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab(g).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The nonzero Christoffel symbols of $g$ (skipping those that can be deduced by symmetry on the last two indices) w.r.t. two charts:" ] }, { "cell_type": "code", "execution_count": 208, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, x} \\, x \\, x }^{ \\, x \\phantom{\\, x} \\phantom{\\, x} } & = & -\\frac{2 \\, x}{x^{2} + y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, x} \\, x \\, y }^{ \\, x \\phantom{\\, x} \\phantom{\\, y} } & = & -\\frac{2 \\, y}{x^{2} + y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, x} \\, y \\, y }^{ \\, x \\phantom{\\, y} \\phantom{\\, y} } & = & \\frac{2 \\, x}{x^{2} + y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, y} \\, x \\, x }^{ \\, y \\phantom{\\, x} \\phantom{\\, x} } & = & \\frac{2 \\, y}{x^{2} + y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, y} \\, x \\, y }^{ \\, y \\phantom{\\, x} \\phantom{\\, y} } & = & -\\frac{2 \\, x}{x^{2} + y^{2} + 1} \\\\ \\Gamma_{ \\phantom{\\, y} \\, y \\, y }^{ \\, y \\phantom{\\, y} \\phantom{\\, y} } & = & -\\frac{2 \\, y}{x^{2} + y^{2} + 1} \\end{array}$ " ], "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": 208, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.christoffel_symbols_display(chart=stereoN)" ] }, { "cell_type": "code", "execution_count": 209, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\Gamma_{ \\phantom{\\, {\\theta}} \\, {\\phi} \\, {\\phi} }^{ \\, {\\theta} \\phantom{\\, {\\phi}} \\phantom{\\, {\\phi}} } & = & -\\cos\\left({\\theta}\\right) \\sin\\left({\\theta}\\right) \\\\ \\Gamma_{ \\phantom{\\, {\\phi}} \\, {\\theta} \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} } & = & \\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)} \\end{array}$ " ], "text/plain": [ "Gam^th_ph,ph = -cos(th)*sin(th) \n", "Gam^ph_th,ph = cos(th)/sin(th) " ] }, "execution_count": 209, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.christoffel_symbols_display(chart=spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\nabla_g$ acting on the vector field $v$:" ] }, { "cell_type": "code", "execution_count": 210, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field nabla_g(v) of type (1,1) on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(nab(v))" ] }, { "cell_type": "code", "execution_count": 211, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\nabla_{g} v = \\left( -\\frac{2 \\, {\\left(x - 2 \\, y\\right)}}{x^{2} + y^{2} + 1} \\right) \\frac{\\partial}{\\partial x }\\otimes \\mathrm{d} x + \\left( -\\frac{2 \\, {\\left(2 \\, x + y\\right)}}{x^{2} + y^{2} + 1} \\right) \\frac{\\partial}{\\partial x }\\otimes \\mathrm{d} y + \\left( \\frac{2 \\, {\\left(2 \\, x + y\\right)}}{x^{2} + y^{2} + 1} \\right) \\frac{\\partial}{\\partial y }\\otimes \\mathrm{d} x + \\left( -\\frac{2 \\, {\\left(x - 2 \\, y\\right)}}{x^{2} + y^{2} + 1} \\right) \\frac{\\partial}{\\partial y }\\otimes \\mathrm{d} y$ " ], "text/plain": [ "nabla_g(v) = -2*(x - 2*y)/(x^2 + y^2 + 1) d/dx*dx - 2*(2*x + y)/(x^2 + y^2 + 1) d/dx*dy + 2*(2*x + y)/(x^2 + y^2 + 1) d/dy*dx - 2*(x - 2*y)/(x^2 + y^2 + 1) d/dy*dy" ] }, "execution_count": 211, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nab(v).display(stereoN.frame())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Curvature\n", "\n", "The Riemann tensor associated with the metric $g$:" ] }, { "cell_type": "code", "execution_count": 212, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Tensor field Riem(g) of type (1,3) on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Riem}\\left(g\\right) = \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\frac{\\partial}{\\partial x }\\otimes \\mathrm{d} y\\otimes \\mathrm{d} x\\otimes \\mathrm{d} y + \\left( -\\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\frac{\\partial}{\\partial x }\\otimes \\mathrm{d} y\\otimes \\mathrm{d} y\\otimes \\mathrm{d} x + \\left( -\\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\frac{\\partial}{\\partial y }\\otimes \\mathrm{d} x\\otimes \\mathrm{d} x\\otimes \\mathrm{d} y + \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\frac{\\partial}{\\partial y }\\otimes \\mathrm{d} x\\otimes \\mathrm{d} y\\otimes \\mathrm{d} x$ " ], "text/plain": [ "Riem(g) = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) d/dx*dy*dx*dy - 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) d/dx*dy*dy*dx - 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) d/dy*dx*dx*dy + 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) d/dy*dx*dy*dx" ] }, "execution_count": 212, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem = g.riemann()\n", "print(Riem)\n", "Riem.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The components of the Riemann tensor in the default frame on $\\mathbb{S}^2$:" ] }, { "cell_type": "code", "execution_count": 213, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, x} \\, y \\, x \\, y }^{ \\, x \\phantom{\\, y} \\phantom{\\, x} \\phantom{\\, y} } & = & \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, x} \\, y \\, y \\, x }^{ \\, x \\phantom{\\, y} \\phantom{\\, y} \\phantom{\\, x} } & = & -\\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, y} \\, x \\, x \\, y }^{ \\, y \\phantom{\\, x} \\phantom{\\, x} \\phantom{\\, y} } & = & -\\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, y} \\, x \\, y \\, x }^{ \\, y \\phantom{\\, x} \\phantom{\\, y} \\phantom{\\, x} } & = & \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\end{array}$ " ], "text/plain": [ "Riem(g)^x_yxy = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) \n", "Riem(g)^x_yyx = -4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) \n", "Riem(g)^y_xxy = -4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) \n", "Riem(g)^y_xyx = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) " ] }, "execution_count": 213, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem.display_comp()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

The components in the frame associated with spherical coordinates:

" ] }, { "cell_type": "code", "execution_count": 214, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{lcl} \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\theta}} \\, {\\phi} \\, {\\theta} \\, {\\phi} }^{ \\, {\\theta} \\phantom{\\, {\\phi}} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} } & = & \\sin\\left({\\theta}\\right)^{2} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\theta}} \\, {\\phi} \\, {\\phi} \\, {\\theta} }^{ \\, {\\theta} \\phantom{\\, {\\phi}} \\phantom{\\, {\\phi}} \\phantom{\\, {\\theta}} } & = & -\\sin\\left({\\theta}\\right)^{2} \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\phi}} \\, {\\theta} \\, {\\theta} \\, {\\phi} }^{ \\, {\\phi} \\phantom{\\, {\\theta}} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} } & = & -1 \\\\ \\mathrm{Riem}\\left(g\\right)_{ \\phantom{\\, {\\phi}} \\, {\\theta} \\, {\\phi} \\, {\\theta} }^{ \\, {\\phi} \\phantom{\\, {\\theta}} \\phantom{\\, {\\phi}} \\phantom{\\, {\\theta}} } & = & 1 \\end{array}$ " ], "text/plain": [ "Riem(g)^th_ph,th,ph = sin(th)^2 \n", "Riem(g)^th_ph,ph,th = -sin(th)^2 \n", "Riem(g)^ph_th,th,ph = -1 \n", "Riem(g)^ph_th,ph,th = 1 " ] }, "execution_count": 214, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Riem.display_comp(spher.frame(), chart=spher)" ] }, { "cell_type": "code", "execution_count": 215, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Module T^(1,3)(S^2) of type-(1,3) tensors fields on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(Riem.parent())" ] }, { "cell_type": "code", "execution_count": 216, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "no symmetry; antisymmetry: (2, 3)\n" ] } ], "source": [ "Riem.symmetries()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Riemann tensor associated with the Euclidean metric $h$ on $\\mathbb{R}^3$ is identically zero:" ] }, { "cell_type": "code", "execution_count": 217, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Riem}\\left(h\\right) = 0$ " ], "text/plain": [ "Riem(h) = 0" ] }, "execution_count": 217, "metadata": {}, "output_type": "execute_result" } ], "source": [ "h.riemann().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Ricci tensor and the Ricci scalar:" ] }, { "cell_type": "code", "execution_count": 218, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{Ric}\\left(g\\right) = \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\mathrm{d} x\\otimes \\mathrm{d} x + \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\mathrm{d} y\\otimes \\mathrm{d} y$ " ], "text/plain": [ "Ric(g) = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dx*dx + 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dy*dy" ] }, "execution_count": 218, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric = g.ricci()\n", "Ric.display()" ] }, { "cell_type": "code", "execution_count": 219, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\begin{array}{llcl} \\mathrm{r}\\left(g\\right):& \\mathbb{S}^2 & \\longrightarrow & \\mathbb{R} \\\\ \\mbox{on}\\ U : & \\left(x, y\\right) & \\longmapsto & 2 \\\\ \\mbox{on}\\ V : & \\left({x'}, {y'}\\right) & \\longmapsto & 2 \\\\ \\mbox{on}\\ A : & \\left({\\theta}, {\\phi}\\right) & \\longmapsto & 2 \\end{array}$ " ], "text/plain": [ "r(g): S^2 --> R\n", "on U: (x, y) |--> 2\n", "on V: (xp, yp) |--> 2\n", "on A: (th, ph) |--> 2" ] }, "execution_count": 219, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R = g.ricci_scalar()\n", "R.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hence we recover the fact that $(\\mathbb{S}^2,g)$ is a Riemannian manifold of constant positive curvature.\n", "\n", "In dimension 2, the Riemann curvature tensor is entirely determined by the Ricci scalar $R$ according to\n", "$$ R^i_{\\ \\, jlk} = \\frac{R}{2} \\left( \\delta^i_{\\ \\, k} g_{jl} - \\delta^i_{\\ \\, l} g_{jk} \\right)$$\n", "Let us check this formula here, under the form $R^i_{\\ \\, jlk} = -R g_{j[k} \\delta^i_{\\ \\, l]}$:" ] }, { "cell_type": "code", "execution_count": 220, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 220, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta = S2.tangent_identity_field()\n", "Riem == - R*(g*delta).antisymmetrize(2,3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly the relation $\\mathrm{Ric} = (R/2)\\; g$ must hold:" ] }, { "cell_type": "code", "execution_count": 221, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{True}$ " ], "text/plain": [ "True" ] }, "execution_count": 221, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ric == (R/2)*g" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **Levi-Civita tensor** associated with $g$:" ] }, { "cell_type": "code", "execution_count": 222, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2-form eps_g on the 2-dimensional differentiable manifold S^2\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\epsilon_{g} = \\left( \\frac{4}{x^{4} + y^{4} + 2 \\, {\\left(x^{2} + 1\\right)} y^{2} + 2 \\, x^{2} + 1} \\right) \\mathrm{d} x\\wedge \\mathrm{d} y$ " ], "text/plain": [ "eps_g = 4/(x^4 + y^4 + 2*(x^2 + 1)*y^2 + 2*x^2 + 1) dx/\\dy" ] }, "execution_count": 222, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps = g.volume_form()\n", "print(eps)\n", "eps.display()" ] }, { "cell_type": "code", "execution_count": 223, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\epsilon_{g} = \\sin\\left({\\theta}\\right) \\mathrm{d} {\\theta}\\wedge \\mathrm{d} {\\phi}$ " ], "text/plain": [ "eps_g = sin(th) dth/\\dph" ] }, "execution_count": 223, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps.display(spher.frame(), chart=spher)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The exterior derivative of the 2-form $\\epsilon_g$:" ] }, { "cell_type": "code", "execution_count": 224, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3-form deps_g on the 2-dimensional differentiable manifold S^2\n" ] } ], "source": [ "print(eps.exterior_derivative())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course, since $\\mathbb{S}^2$ has dimension 2, all 3-forms vanish identically:" ] }, { "cell_type": "code", "execution_count": 225, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\mathrm{d}\\epsilon_{g} = 0$ " ], "text/plain": [ "deps_g = 0" ] }, "execution_count": 225, "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": 226, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A,(x, y)\\right)$ " ], "text/plain": [ "Chart (A, (x, y))" ] }, "execution_count": 226, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_chart()" ] }, { "cell_type": "code", "execution_count": 227, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A, \\left(\\frac{\\partial}{\\partial x },\\frac{\\partial}{\\partial y }\\right)\\right)$ " ], "text/plain": [ "Coordinate frame (A, (d/dx,d/dy))" ] }, "execution_count": 227, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_frame()" ] }, { "cell_type": "code", "execution_count": 228, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A,({\\theta}, {\\phi})\\right)$ " ], "text/plain": [ "Chart (A, (th, ph))" ] }, "execution_count": 228, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.set_default_chart(spher)\n", "A.set_default_frame(spher.frame())\n", "A.default_chart()" ] }, { "cell_type": "code", "execution_count": 229, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A, \\left(\\frac{\\partial}{\\partial {\\theta} },\\frac{\\partial}{\\partial {\\phi} }\\right)\\right)$ " ], "text/plain": [ "Coordinate frame (A, (d/dth,d/dph))" ] }, "execution_count": 229, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.default_frame()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 230, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\frac{\\partial}{\\partial {\\theta} }\\otimes \\mathrm{d} {\\theta} + \\frac{1}{\\sin\\left({\\theta}\\right)} \\frac{\\partial}{\\partial {\\phi} }\\otimes \\mathrm{d} {\\phi}$ " ], "text/plain": [ "d/dth*dth + 1/sin(th) d/dph*dph" ] }, "execution_count": 230, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = A.automorphism_field()\n", "a[1,1], a[2,2] = 1, 1/sin(th)\n", "a.display()" ] }, { "cell_type": "code", "execution_count": 231, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rr}\n", "1 & 0 \\\\\n", "0 & \\frac{1}{\\sin\\left({\\theta}\\right)}\n", "\\end{array}\\right)$ " ], "text/plain": [ "[ 1 0]\n", "[ 0 1/sin(th)]" ] }, "execution_count": 231, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a[:]" ] }, { "cell_type": "code", "execution_count": 232, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Vector frame (A, (e_1,e_2))\n" ] }, { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(A, \\left(e_{1},e_{2}\\right)\\right)$ " ], "text/plain": [ "Vector frame (A, (e_1,e_2))" ] }, "execution_count": 232, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e = spher.frame().new_frame(a, 'e')\n", "print(e) ; e" ] }, { "cell_type": "code", "execution_count": 233, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}e_{1} = \\frac{\\partial}{\\partial {\\theta} }$ " ], "text/plain": [ "e_1 = d/dth" ] }, "execution_count": 233, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[1].display()" ] }, { "cell_type": "code", "execution_count": 234, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}e_{2} = \\frac{1}{\\sin\\left({\\theta}\\right)} \\frac{\\partial}{\\partial {\\phi} }$ " ], "text/plain": [ "e_2 = 1/sin(th) d/dph" ] }, "execution_count": 234, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[2].display()" ] }, { "cell_type": "code", "execution_count": 235, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left(A, \\left(\\frac{\\partial}{\\partial x },\\frac{\\partial}{\\partial y }\\right)\\right), \\left(A, \\left(\\frac{\\partial}{\\partial {x'} },\\frac{\\partial}{\\partial {y'} }\\right)\\right), \\left(A, \\left(\\frac{\\partial}{\\partial {\\theta} },\\frac{\\partial}{\\partial {\\phi} }\\right)\\right), \\left(A, \\left(\\frac{\\partial}{\\partial X },\\frac{\\partial}{\\partial Y },\\frac{\\partial}{\\partial Z }\\right)\\right), \\left(A, \\left(e_{1},e_{2}\\right)\\right)\\right]$ " ], "text/plain": [ "[Coordinate frame (A, (d/dx,d/dy)),\n", " Coordinate frame (A, (d/dxp,d/dyp)),\n", " Coordinate frame (A, (d/dth,d/dph)),\n", " Vector frame (A, (d/dX,d/dY,d/dZ)) with values on the 3-dimensional differentiable manifold R^3,\n", " Vector frame (A, (e_1,e_2))]" ] }, "execution_count": 235, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.frames()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 236, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}1$ " ], "text/plain": [ "1" ] }, "execution_count": 236, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[1],e[1]).expr()" ] }, { "cell_type": "code", "execution_count": 237, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}0$ " ], "text/plain": [ "0" ] }, "execution_count": 237, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[1],e[2]).expr()" ] }, { "cell_type": "code", "execution_count": 238, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}1$ " ], "text/plain": [ "1" ] }, "execution_count": 238, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g(e[2],e[2]).expr()" ] }, { "cell_type": "code", "execution_count": 239, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rr}\n", "1 & 0 \\\\\n", "0 & 1\n", "\\end{array}\\right)$ " ], "text/plain": [ "[1 0]\n", "[0 1]" ] }, "execution_count": 239, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g[e,:]" ] }, { "cell_type": "code", "execution_count": 240, "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": 240, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(e)" ] }, { "cell_type": "code", "execution_count": 241, "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": 241, "metadata": {}, "output_type": "execute_result" } ], "source": [ "eps.display(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

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

" ] }, { "cell_type": "code", "execution_count": 242, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left[\\left[0, 0\\right], \\left[0, 0\\right]\\right], \\left[\\left[0, -\\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)}\\right], \\left[\\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)}, 0\\right]\\right]\\right]$ " ], "text/plain": [ "[[[0, 0], [0, 0]], [[0, -cos(th)/sin(th)], [cos(th)/sin(th), 0]]]" ] }, "execution_count": 242, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e.structure_coeff()[:]" ] }, { "cell_type": "code", "execution_count": 243, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}-\\frac{\\cos\\left({\\theta}\\right)}{\\sin\\left({\\theta}\\right)} e_{2}$ " ], "text/plain": [ "-cos(th)/sin(th) e_2" ] }, "execution_count": 243, "metadata": {}, "output_type": "execute_result" } ], "source": [ "e[2].lie_derivative(e[1]).display(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "

while we have of course

" ] }, { "cell_type": "code", "execution_count": 244, "metadata": {}, "outputs": [ { "data": { "text/html": [ " $\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left[\\left[\\left[0, 0\\right], \\left[0, 0\\right]\\right], \\left[\\left[0, 0\\right], \\left[0, 0\\right]\\right]\\right]$ " ], "text/plain": [ "[[[0, 0], [0, 0]], [[0, 0], [0, 0]]]" ] }, "execution_count": 244, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spher.frame().structure_coeff()[:]" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.3", "language": "", "name": "sagemath" }, "language": "python", "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.15" } }, "nbformat": 4, "nbformat_minor": 1 }