{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "skip"
}
},
"source": [
"%pylab inline\n",
"%config InlineBackend.figure_formats = ['svg']"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# A Brief Overview of Python"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Python …\n",
"\n",
"- general-purpose programming language\n",
"- extremely portable\n",
"- interpreted (i.e. no compilation stage)\n",
"- supports multiple paradigms: object-oriented, structured, …\n",
"- dynamic and strong typing\n",
"- free software\n",
"- huge selection of free extensions (including many scientific packages)\n",
"- can be used for high-level scripting of numerical codes (e.g. C/Fortran)\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Hello World"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Hello World!\n"
]
}
],
"source": [
"print(\"Hello World!\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## How to get it\n",
"\n",
"- distribution packages<br/>\n",
" Debian/Ubuntu: `python3`, `python3-numpy`, `python3-matplotlib`, `ipython`, …\n",
"- official Python package manager `pip` also works without root access\n",
"- third-party package: [Anaconda](https://www.continuum.io/downloads) (Linux, OS X, Windows)\n",
"- compile it yourself\n",
"- …"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Syntax by Examples"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Is a greater than b? No\n"
]
}
],
"source": [
"a = 5\n",
"b = 16\n",
"if a > b:\n",
" # White space is significant.\n",
" # Indentation is used to signify code blocks.\n",
" c = \"Yes\"\n",
"else:\n",
" c = \"No\"\n",
"\n",
"print(\"Is a greater than b?\", c)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0 is even.\n",
"1 is odd.\n",
"2 is even.\n",
"3 is odd.\n",
"4 is even.\n",
"5 is odd.\n",
"6 is even.\n",
"7 is odd.\n",
"8 is even.\n",
"9 is odd.\n"
]
}
],
"source": [
"def iseven(x):\n",
" \"\"\"Returns True when x is even.\"\"\"\n",
" return x % 2 == 0\n",
"\n",
"for a in range(10):\n",
" if iseven(a):\n",
" print(a, \" is even.\")\n",
" else:\n",
" print(a, \" is odd.\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"# Mathematical Types and Operations"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# integers\n",
"i = 15\n",
"j = 7\n",
"k = 0xff # same as 255\n",
"# floating-point numbers\n",
"a = 1.0 / sqrt(2.0)\n",
"b = 1e20\n",
"# complex numbers\n",
"c = a + 1j * a"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
"2.142857142857143"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# division of integers always results in floats (was different in Python 2)\n",
"i / j"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
"2"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# explicit integer division\n",
"i // j"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/plain": [
"0.99999999999999978j"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# ** is the power operator\n",
"c**2"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Some Data Structures"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Lists can store objects of different types. Index starts at 0.\n",
"things = [42, \"a string\", [\"another\", \"list\"]]"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"'list'"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"things[2][1]"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"# Sets are like lists but without ordering.\n",
"birds = {'seagull', 'crane', 'crow'}\n",
"machines = {'car', 'computer', 'crane'}"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"{'crane', 'crow', 'seagull'}"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"birds"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"{'crane'}"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"birds.intersection(machines)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": true,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"# Dictionaries store key-value pairs\n",
"sirius_a = dict(magnitude=1.42, parallax=379.21)\n",
"sirius_a['mass'] = 2.02 * 1.9891e+33"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mass is 4.01798e+33.\n",
"Parallax is 3.79210e+02.\n",
"Magnitude is 1.42000e+00.\n"
]
}
],
"source": [
"for k, v in sirius_a.items():\n",
" # Loops can directly iterate of key-value pairs\n",
" print(\"%s is %0.5e.\" % (k.capitalize(), v))\n",
" # printf-style string formatting is supported."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Numerics with Python"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1000 loops, best of 3: 998 µs per loop\n"
]
}
],
"source": [
"def simpledot(x, y):\n",
" \"\"\"Computes the dot product of x and y.\"\"\"\n",
" d = 0.0\n",
" for i in range(len(x)):\n",
" d += x[i] * y[i]\n",
" return d\n",
"\n",
"a = list(range(5000,10000))\n",
"b = list(range(-50,4950))\n",
"%timeit simpledot(a, b)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Straightforward usage of lists is extremely inefficient due to type-checking and storage overhead.\n",
"Remember lists support a mixture of types."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Numpy\n",
"\n",
"A Python package featuring a multidimensional array object (`ndarray`). Operations on these objects are implemented using C."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The slowest run took 5.20 times longer than the fastest. This could mean that an intermediate result is being cached.\n",
"100000 loops, best of 3: 5.71 µs per loop\n"
]
}
],
"source": [
"import numpy as np\n",
"a = np.array(range(5000,10000)) # or simply np.arange(5000,10000)\n",
"b = np.array(range(5000,10000))\n",
"np.dot(a,b)\n",
"%timeit np.dot(a,b)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1, 2, 3],\n",
" [ 0, 5, 20],\n",
" [21, 22, 23]])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"A = np.array([[1,2,3],[0,5,20],[21,22,23]])\n",
"A"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 2, 5, 22])"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# selecting array slices\n",
"A[:,1]"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[ 1 4 9]\n",
" [ 0 25 400]\n",
" [441 484 529]]\n",
"[[ 3 5 7]\n",
" [ 1 11 41]\n",
" [43 45 47]]\n"
]
}
],
"source": [
"# array operations always act element-wise\n",
"print(A * A)\n",
"print(2 * A + 1)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/plain": [
"matrix([[ 1.00000000e+00, 4.44089210e-16, 0.00000000e+00],\n",
" [ 0.00000000e+00, 1.00000000e+00, -1.33226763e-15],\n",
" [ -1.11022302e-16, 1.11022302e-16, 1.00000000e+00]])"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# linear algebra operations\n",
"Ai = np.linalg.inv(A)\n",
"# Converting to the matrix type redefines the product\n",
"# to the matrix product.\n",
"np.matrix(Ai) * np.matrix(A)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Plotting\n",
"\n",
"`matplotlib` offers a wide range of plotting functions. Labels can be rendered using $\\mathrm{\\LaTeX}$.\n",
"It can display the plots in a window, in a brower-based Notebook, or save it in a variety of formats (PDF, PNG, …)."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f2cd07468d0>]"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
},
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"source": [
"### Plots of 2D Data"
]
},
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"source": [
"### 3D Surface Plots\n",
"`matplotlib` has rudimentary support for 3D plots. More advanced functions are availabe in packages like `mayavi` and `yt`."
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" <image height=\"217\" id=\"image9d1aaf641c\" transform=\"scale(1 -1)translate(0 -217)\" width=\"267\" x=\"26\" xlink:href=\"data:image/png;base64,\n",
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"text/plain": [
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"kx, ky = meshgrid(rfftfreq(500), rfftfreq(500))\n",
"k = sqrt(kx**2 + ky**2)\n",
"D = k**(-5./3.) * exp(2j * pi * rand(*kx.shape))\n",
"D[0,:] = 0\n",
"D[:,0] = 0\n",
"E=irfft2(D)\n",
"pcolormesh(E, rasterized=True)\n",
"colorbar()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Animations\n",
"\n",
"Plots with changing parameters can be automatically rendered to a video file"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
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"\">\n",
" Your browser does not support the video tag.\n",
"</video>"
],
"text/plain": [
"<matplotlib.animation.FuncAnimation at 0x7f2d05301c18>"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# example from http://matplotlib.org/examples/animation/simple_anim.html\n",
"from matplotlib import rc, animation\n",
"rc('animation', html='html5')\n",
"fig, ax = plt.subplots()\n",
"x = np.arange(0, 2*np.pi, 0.01)\n",
"line, = ax.plot(x, np.sin(x))\n",
"def animate(i):\n",
" line.set_ydata(np.sin(x + i/10.0)) # update the data\n",
" return line,\n",
"ani = animation.FuncAnimation(fig, animate, np.arange(1, 200), interval=25)\n",
"close(fig)\n",
"ani"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## IPython/Jupyter\n",
"\n",
"- IPython is a convenient interactive shell for Python\n",
"- renamed to Jupyter in 2014 as support for new languages (Ruby, R, Julia, …) was added\n",
"- browser-based notebook interface to store description, code, and results in one file\n",
"- notebooks can be exported to HTML, PDF, markdown, LaTeX, slides and shared with collaborators\n",
"- compute kernel can run on different machine (even multiple kernels in batch queue)\n",
"- Jupyterhub offers web-based remote access to notebooks and kernels (e.g. for homework assignments)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"### Example Notebook"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"this presentation"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Computer Algebra\n",
"\n",
"Symbolic manipulations can carried out using the `sympy` package."
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"text/latex": [
"$$- 2 a x \\sin{\\left (a x^{2} \\right )}$$"
],
"text/plain": [
" ⎛ 2⎞\n",
"-2⋅a⋅x⋅sin⎝a⋅x ⎠"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sympy import *\n",
"init_printing()\n",
"a, x = var('a, x')\n",
"f = cos(a*x**2)\n",
"f.diff(x)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"image/png": 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ZPeC+/3/6nvoXqdT/VP7dC7TrR/M5YPnkfOl3vjvhyqk/nyoyGzLF7n6zLtDX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\ngccO/P858P8B5L90QzxVb5MAAAAASUVORK5CYII=\n",
"text/latex": [
"$$3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198$$"
],
"text/plain": [
"3.1415926535897932384626433832795028841971693993751058209749445923078164062862\n",
"089986280348253421170679821480865132823066470938446095505822317253594081284811\n",
"174502841027019385211055596446229489549303819644288109756659334461284756482337\n",
"867831652712019091456485669234603486104543266482133936072602491412737245870066\n",
"063155881748815209209628292540917153643678925903600113305305488204665213841469\n",
"519415116094330572703657595919530921861173819326117931051185480744623799627495\n",
"673518857527248912279381830119491298336733624406566430860213949463952247371907\n",
"021798609437027705392171762931767523846748184676694051320005681271452635608277\n",
"857713427577896091736371787214684409012249534301465495853710507922796892589235\n",
"420199561121290219608640344181598136297747713099605187072113499999983729780499\n",
"510597317328160963185950244594553469083026425223082533446850352619311881710100\n",
"031378387528865875332083814206171776691473035982534904287554687311595628638823\n",
"53787593751957781857780532171226806613001927876611195909216420198"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"N(pi,1000)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAKcAAAArBAMAAADvSoV8AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nrkJggg==\n",
"text/latex": [
"$$\\frac{1125899906842623}{1125899906842624}$$"
],
"text/plain": [
"1125899906842623\n",
"────────────────\n",
"1125899906842624"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n = var('n')\n",
"summation(1/2**n,(n,1,50))"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAKsAAAAOBAMAAACiF/F3AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nj4XbpgAAAABJRU5ErkJggg==\n",
"text/latex": [
"$$0.999999999068677$$"
],
"text/plain": [
"0.999999999068677"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"N(summation(1/2**n,(n,1,30)))"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAPBAMAAAArJJMAAAAAHlBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAACGjDitAAAACXRSTlMAVO8Qq5l2zWYZcMvdAAAACXBIWXMAAA7EAAAOxAGV\nKw4bAAAAHUlEQVQIHWNgAANGZQYGk5DJQDYbqQSr03QPsBkAJYgIYEZbtZEAAAAASUVORK5CYII=\n",
"text/latex": [
"$$1$$"
],
"text/plain": [
"1"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"summation(1/2**n,(n,1,inf))"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAFoAAAAtBAMAAADcoWFIAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRU5ErkJggg==\n",
"text/latex": [
"$$\\frac{\\sqrt{\\pi}}{2} \\operatorname{erf}{\\left (x \\right )}$$"
],
"text/plain": [
"√π⋅erf(x)\n",
"─────────\n",
" 2 "
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"integrate(exp(-x**2))"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAADcAAAAVBAMAAAAQkWtIAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVO8Qq5l2zWbdiTIi\nu0T8UsK3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABI0lEQVQoFWNgwAJ4/oPBByxSDAwsD7AKQwSP\no8sxR3VtgIkFwhgMjMpgJrsA8xyoGPMEmKRJyGcws4mBYTlUjFUAJsnABpG8wsAgbwARtITLwSS/\nMDC8h+pYgS7J/BUomQAWBVmZD/QoUASqk+cXA8P+BWBJtgYGrtViJ3IOICSB6oCS74ACnAwMGxnW\nsG0AqYQ4CGIsmzpQIA0keoEF7Dqoa4EOkhc4nP+AgQFoJQO3A1A/EEAl7zIw9Bsw2F9g4FgAFGRt\n4EfWCQyEcKDgHwZOkKi9Af8DIAXWaV/AwCnArM3AwPOVoQskmMnAtABIsTp992DgdGBgXpayAcj1\nN5gMJBluMLAsANGoYP/CAFQBZB67OtghyEIINiMo0HCCGiQZAITaS1WkUPlxAAAAAElFTkSuQmCC\n",
"text/latex": [
"$$1.0 \\sqrt{\\pi}$$"
],
"text/plain": [
"1.0⋅√π"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"integrate(exp(-x**2),(x,-inf,inf))"
]
}
],
"metadata": {
"celltoolbar": "Slideshow",
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.3"
}
},
"nbformat": 4,
"nbformat_minor": 0
}