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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Sections\n",
"\n",
"- [SymPy: Symbolic Mathematics](#sympy)\n",
" - [Elementary Operations](#elementary)\n",
" - [Algebra](#algebra)\n",
" - [Calculus](#calculus)\n",
" - [Showcases](#showcases)\n",
" - [Illustrating Taylor Series](#taylor)\n",
" - [Trapezoid Rule](#trapezoid)\n",
"- [IPython's Display System](#display system)\n",
"- [Defining Custom Display Logic for Your Own Objects](#custom display)\n",
"- [Adding IPython display support to existing objects](#ipython display support)\n",
"- [More complex display with _ipython_display_](#ipython complex display support)\n",
"- [Interactive Widgets](#interactive widgets)\n",
" - [Factoring Polynomials](#factoring)\n",
" - [Lorentz Equation Solving](#lorentz equation)\n",
"<br>\n",
"<br>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"<br>\n",
"<a name='sympy'></a>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# SymPy: Symbolic Mathematics\n",
"[[back to top]](#sections)\n",
"\n",
"This notebook uses the SymPy package to perform symbolic manipulations, and combined with numpy and matplotlib, also displays numerical visualizations of symbolically constructed expressions.\n",
"\n",
"We first load sympy printing extensions, as well as all of sympy:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.display import display\n",
"\n",
"from sympy.interactive import printing\n",
"printing.init_printing(use_latex='mathjax')\n",
"\n",
"from __future__ import division\n",
"import sympy as sym\n",
"from sympy import *\n",
"x, y, z = symbols(\"x y z\")\n",
"k, m, n = symbols(\"k m n\", integer=True)\n",
"f, g, h = map(Function, 'fgh')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"<br>\n",
"<a name='elementary'></a>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Elementary Operations\n",
"[[back to top]](#sections)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Rational(3,2)*pi + exp(I*x) / (x**2 + y)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$$\\frac{3 \\pi}{2} + \\frac{e^{i x}}{x^{2} + y}$$"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 13,
"text": [
" \u2148\u22c5x \n",
"3\u22c5\u03c0 \u212f \n",
"\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\n",
" 2 2 \n",
" x + y"
]
}
],
"prompt_number": 13
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"exp(pi * sqrt(163)).evalf(50)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$$262537412640768743.99999999999925007259719818568888$$"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 14,
"text": [
"262537412640768743.99999999999925007259719818568888"
]
}
],
"prompt_number": 14
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"<br>\n",
"<a name='algebra'></a>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Algebra\n",
"[[back to top]](#sections)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"((x+y)**2 * (x+1))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$$\\left(x + 1\\right) \\left(x + y\\right)^{2}$$"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 15,
"text": [
" 2\n",
"(x + 1)\u22c5(x + y) "
]
}
],
"prompt_number": 15
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"expand(((x+y)**2 * (x+1)))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$$x^{3} + 2 x^{2} y + x^{2} + x y^{2} + 2 x y + y^{2}$$"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 16,
"text": [
" 3 2 2 2 2\n",
"x + 2\u22c5x \u22c5y + x + x\u22c5y + 2\u22c5x\u22c5y + y "
]
}
],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"solve(((x+y)**2 * (x+1)), x)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$$\\begin{bmatrix}-1, & - y\\end{bmatrix}$$"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 8,
"text": [
"[-1, -y]"
]
}
],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"a = 1/x + (x*sin(x) - 1)/x\n",
"a"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$$\\frac{1}{x} \\left(x \\sin{\\left (x \\right )} - 1\\right) + \\frac{1}{x}$$"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 4,
"text": [
"x\u22c5sin(x) - 1 1\n",
"\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\n",
" x x"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"simplify(a)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$$\\sin{\\left (x \\right )}$$"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 5,
"text": [
"sin(x)"
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"<br>\n",
"<name a='calculus'></a>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Calculus\n",
"[[back to top]](#sections)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"diff(cos(x**2)**2 / (1+x), x)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$$- \\frac{4 x \\cos{\\left (x^{2} \\right )}}{x + 1} \\sin{\\left (x^{2} \\right )} - \\frac{\\cos^{2}{\\left (x^{2} \\right )}}{\\left(x + 1\\right)^{2}}$$"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 9,
"text": [
" \u239b 2\u239e \u239b 2\u239e 2\u239b 2\u239e\n",
" 4\u22c5x\u22c5sin\u239dx \u23a0\u22c5cos\u239dx \u23a0 cos \u239dx \u23a0\n",
"- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
" x + 1 2\n",
" (x + 1) "
]
}
],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"integrate(x**2 * cos(x), (x, 0, pi/2))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$$-2 + \\frac{\\pi^{2}}{4}$$"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 10,
"text": [
" 2\n",
" \u03c0 \n",
"-2 + \u2500\u2500\n",
" 4 "
]
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"eqn = Eq(Derivative(f(x),x,x) + 9*f(x), 1)\n",
"display(eqn)\n",
"dsolve(eqn, f(x))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$$9 f{\\left (x \\right )} + \\frac{d^{2}}{d x^{2}} f{\\left (x \\right )} = 1$$"
],
"metadata": {},
"output_type": "display_data",
"text": [
" 2 \n",
" d \n",
"9\u22c5f(x) + \u2500\u2500\u2500(f(x)) = 1\n",
" 2 \n",
" dx "
]
},
{
"latex": [
"$$f{\\left (x \\right )} = C_{1} \\sin{\\left (3 x \\right )} + C_{2} \\cos{\\left (3 x \\right )} + \\frac{1}{9}$$"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 6,
"text": [
"f(x) = C\u2081\u22c5sin(3\u22c5x) + C\u2082\u22c5cos(3\u22c5x) + 1/9"
]
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"<br>\n",
"<a name='taylor'></a>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Illustrating Taylor Series\n",
"[[back to top]](#sections)\n",
"\n",
"We will define a function to compute the Taylor series expansions of a symbolically defined expression at various orders and visualize all the approximations together with the original function"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 17
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def plot_taylor_approximations(func, x0=None, orders=(2, 4), xrange=(0,1), yrange=None, npts=200):\n",
" \"\"\"Plot the Taylor series approximations to a function at various orders.\n",
"\n",
" Parameters\n",
" ----------\n",
" func : a sympy function\n",
" x0 : float\n",
" Origin of the Taylor series expansion. If not given, x0=xrange[0].\n",
" orders : list\n",
" List of integers with the orders of Taylor series to show. Default is (2, 4).\n",
" xrange : 2-tuple or array.\n",
" Either an (xmin, xmax) tuple indicating the x range for the plot (default is (0, 1)),\n",
" or the actual array of values to use.\n",
" yrange : 2-tuple\n",
" (ymin, ymax) tuple indicating the y range for the plot. If not given,\n",
" the full range of values will be automatically used. \n",
" npts : int\n",
" Number of points to sample the x range with. Default is 200.\n",
" \"\"\"\n",
" if not callable(func):\n",
" raise ValueError('func must be callable')\n",
" if isinstance(xrange, (list, tuple)):\n",
" x = np.linspace(float(xrange[0]), float(xrange[1]), npts)\n",
" else:\n",
" x = xrange\n",
" if x0 is None: x0 = x[0]\n",
" xs = sym.Symbol('x')\n",
" # Make a numpy-callable form of the original function for plotting\n",
" fx = func(xs)\n",
" f = sym.lambdify(xs, fx, modules=['numpy'])\n",
" # We could use latex(fx) instead of str(), but matploblib gets confused\n",
" # with some of the (valid) latex constructs sympy emits. So we play it safe.\n",
" plt.plot(x, f(x), label=str(fx), lw=2)\n",
" # Build the Taylor approximations, plotting as we go\n",
" apps = {}\n",
" for order in orders:\n",
" app = fx.series(xs, x0, n=order).removeO()\n",
" apps[order] = app\n",
" # Must be careful here: if the approximation is a constant, we can't\n",
" # blindly use lambdify as it won't do the right thing. In that case, \n",
" # evaluate the number as a float and fill the y array with that value.\n",
" if isinstance(app, sym.numbers.Number):\n",
" y = np.zeros_like(x)\n",
" y.fill(app.evalf())\n",
" else:\n",
" fa = sym.lambdify(xs, app, modules=['numpy'])\n",
" y = fa(x)\n",
" tex = sym.latex(app).replace('$', '')\n",
" plt.plot(x, y, label=r'$n=%s:\\, %s$' % (order, tex) )\n",
" \n",
" # Plot refinements\n",
" if yrange is not None:\n",
" plt.ylim(*yrange)\n",
" plt.grid()\n",
" plt.legend(loc='best').get_frame().set_alpha(0.8)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 18
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With this function defined, we can now use it for any sympy function or expression"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot_taylor_approximations(sin, 0, [2, 4, 6], (0, 2*pi), (-2,2))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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sPfqok1H0+7UfHY4tIbblSerGXuLpts/x+JPFdGu9DRvkbOqOHTJiO8H16/Di\ni9IZ8vWVlZQff9x6271paYyIi+PItWu8Wbs2Q6pVo5QOs94zz55lZFwc85o1030OQXn0Cmsoj95O\nctMoWxz4ipi7z9Dgj2SGdXux+AZ5gPvug1dfhUcflbUenKBECfjhB/i//5ObmD/xBHz/vfW2zcuV\n4/c77mBWkyb8duEC9aOj+ezUKa64qaRCWlYWLxw6xPsnTrAxNFT3IK9QuIJiF+gvXbtE9zkPUnfv\nSPY/4MPtK9IY/cwLdO/h3H6pZvZZb2h/6y2oXBneeMPpPr28pCP0wQeyxM4LL8j9UQrinsBAVrVo\nwbKQELalpFA3Opo34+I4ZkP6p6PX/vdLlwiNiSE9J4cdrVpxe9myDvXjLGb+7ID5PW6z67cFLQJ9\nN+AgcAR408rz4UAysMtye0eDczpEZnYmvef2IyD2QY49VJ/QeRlMevsZ2t9jJAdLR7y9YeZMWLZM\nVjDTgFGj4Kuv5P2RI+G99wrfwa6lvz8Lbr+drXfeSbYQtN25k25//82cs2dJ0Wjh1R/JyfTYs4dX\njhzh8wYNmNm0KQG+WmyfrDASixcvZsSIERw/flyzPnfs2MGiRYvYsGGDZn2aAR/gKBAMlAB2A03z\ntQkHltnQl0vrROTk5IgBvz4lWrz0hKiyaIno3mOhOHLEpac0Lxs3ClG9uhDnz2vW5axZQvj4yBo5\nb79t+8Zb17KyxM9nz4qH9uwR5TdvFr327BFfnT4t9qal2bXD06lr18TU06dF65gYUWfbNvH16dMi\nPTvbwXfjWlStG22IiorSvM+5c+eKEydOiO+++07zvovCmVo3zg5j2iAD/XHL8S9Ab+BAvna6D5nf\nWTeR2G2JnL3vRcJ+FHz1ZX9s3DO4+BEeDgMGyBnVBQs02SVr0CBZbufxx6WdAzBxYtFdl/bx4Ymg\nIJ4ICiLp+nVWXLxIRFISU06dIiU7m+Zly9KwTBkalClDoK8vpby9KeHlxcXr1zmdkcHJjAz+Sk3l\n4vXrdK9YkXHBwXStWFHzDb0VxqNx48bs3buX8+fP06lTJ036HDBgALNmzTLcnrZF4ax1UxM4lef4\ntOWxvAjgbuBvYBXQzMlz2s0Pf85lye9rOHvvi4T9CF9/1VfzIG9mn9Wq9vffh4MHYc4czc7z8MPw\nyy9yEe4HH8C77xZu4+QnsEQJBlarxvQmTYhr147dYWGMrl2bsnv2kJiZyY7UVDZcvsyyCxc4dPUq\nFXx9ebAmBIVWAAAgAElEQVRiRRbdfjvn2rdnTrNmdK9UyXBB3syfHTCux71582aaN2/Otm3bCm1n\nj/6pU6fy6KOPMmXKFGfluRVnR/S2/DfdCdwGXAW6A0uBRtYaDhkyhODgYAACAwMJDQ0lPDwcuPmf\nwd7jjCBfPls4hTOBfWj84T6+mT+a4GDH+yvoePfu3Zr2p/txdDQMG0b48OHQpQuRhw5p0v/DD4cz\nbx48/ngk778PXl7hjB8PmzY51l+X8HB8q1SB06f1vV4aH+cGH39/f3Vsw/Hhw4c5dOgQf/zxB0FB\nQQQHB1OlShWio6Pp0KGDQ/0nJCRw6tQpNmzYQEBAAE2aNKFp06asXbuWdu3akZqa6tb3m26pBhsZ\nGcmMGTMAbsRLV9MOWJPneBTWJ2Tz8g9Q0crjmntae04fEY3faCmqLFosunZbLo4f1/wUns+oUUI8\n9pjm3c6ff9OzHzNG8+5NTXHz6FNTU8W7774rvv/+e/HJJ5/YNfeSy5kzZ4QQQjz//PMiPT1dZGVl\nOa3LFX06g5716GOAhsjJ2JLAY/x74jWImx59G8v9S06et0gSki7x8JSBJLUbzZ3T4duve1KnjqvP\n6oG8845cRLVmTdFt7eCRR2DuXJnoM24cfPaZpt0rTMTQoUP5z3/+w3PPPcf06dM5efKk3X2UK1eO\nxMREqlatSkZGBleuXHFalxZ9Tp061WkdWuBsoM8CXgF+B/YDvyInYl+w3AAeBmKRGTmfAwWskdSO\nqxmZ3DfuCdLaDKfFnOt88UlflxcnM7PPWqh2Pz9Z1vill0DjQmSPPipXz4Lc3vbHHx3rx8zXHsyv\n3xmP/tixY8THx1PHMgpbu3btjfv2MHHiRCIjIylbtiwRERGUL1/e5tcWpN+ZPnO5cOGC3a9xBVok\nD6+23PLyXZ77Uy03t5CdLWj/1vNcbf0UzRZnMnnMQJo0cdfZPZQHHoC2bWHCBJg0SdOuBw+GlBQY\nOhSeew78/eUXgMLcHDt2jGnTphX4fLt27ejduzcREREEBgYye/ZskpKS8Pf3Z8iQIbe0DQkJYebM\nmbRs2bLA/iZPnqyVdJf2qRcetUpECOj8xhhS7wyn/tprTHj9P4SGuufcuZNoZsQm7Z99Jjcrefpp\naGR1Lt1hXn0VkpNlFs6TT0K5cnJPFFsx87UH8+nfuXMn0dHRxMfHExYWRnZ2NitXrmR67s8zoF69\nekyyYVCQmJjI3r17+eWXXwDo0KED7du3p2HDhjfaTJgwgUYaf+bykjvh6W6WLVuGj48PW7ZsISQk\nhDVr1jB69GiauGBk6jGBXgjo++aPnGtei9rR6Yx+6nnatdNblQdRrZosXjNyJPz2m+bdjx4tg/0n\nn0D//nJKoGNHzU/jMXhpYPcIB79gzp07R5MmTVi3bh0TJ05ECMFIB/c0KF++PCEhITeOa9euzdq1\na28J9H369Cnw9d4OFMDz8vIiOzubyZMnc62AEhuDBw+mno052Ln9ARw4cIBZs2bdeC4qKupGtgzI\nL7IePXpw8uRJmjVrRoMGDXjvvfd46623CAgIoHbt2na/H1vwmED/0sQNHK93har7vRne4yU6d3Zv\nGZ/IyEjTjcxysVn7a6/Bt9/KcsadO2uqwcsLJk+WNs7338NDD8nThIUV/VozX3twTL+jQVoLunXr\nxqhRoxg0aBAAGzZsIDTfT2dbrZvbb7+dLVu23Hjc29ubHDtKVtvTNj//93//B3BLmqSzfTdt2vSW\nXzLjxo1jzJgx/2qXG9ATExPx9/cnMDCQnj172n0+W/GIQD952kF2lf0Dv8QAXmj1X3r2LHa12txD\nqVIyGr/+Ouzc6dT2g9bw8pLzvikpcmFVjx6wbRs0aKDpaRQasHHjRt566y0A5s2bx6BBg1ixYsWN\nYGWrddO+fXvefvvtG8dxcXGMHTv2ljZLliyha9eulLVSdC45OZn169dz+PBhRo0axZEjR4iNjSU2\nNpaHHnqI4OBgpk2bRtWqVWnRogWtWrVy6P0uXLiQcuXKcfjwYYYOHepQH3k5ePAgGRkZ7Ny5k3vv\nvReAVatW0cMez9IOTB8R5y+/wIqzP5HpXZlH/J/liSe0DT62YuYRpV3a+/eHgAD46SeXaPHxgVmz\n5Pzv+fPyb2Ji4a8x87UH8+m/evUqgYGBBFi2YAsMDCQ5OZnq1avb3VepUqUYO3Ys7733Hu+88w4v\nv/wy9evXv6XN+PHjiYuLs/r6gIAAwsLCyLSU1l6xYgW1atVi+PDhfPzxx8ycOZNOnToxaNCgAlez\nFuXRR0REUKNGDbp166ZJkAeZXbRixQqEEKSnp7N06VKqVq2qSd/WMPWIfmt0Jl9vHc+5hnfS52Af\nXv+4jN6SPB8vL5gyBXr1kvVwXFDat0QJWLhQltz56y/o2RM2bpSTtAr98fPzY02edRWffvqpU/11\n69aNbt26Ffj8rl27bO7r9ddfB2D//v3UrVuXY8eO8fDDD+Pr68ulS44t31m2bBnt2rUjKSkJPz8/\nu76Yy5SxHpO0+sKwFdOO6A8dEoye8wbH7riLe7bcx6TJ+m4YYeZcaLu1h4VBhw7w5Zcu0QMyqK9c\nCfXrQ0yMrJNT0PayZr72YH79Rqt1I4RgyZIljB49mpycHHwsFqNXATWOitJ//fp17rzzTnr06MHX\nX39tl5bceQC9MWWgT0iA5z58m4OdOtJ6YVO+mVZbiwKLCnsYNw4+/VSmyriIoCCZfVOlCvz+Ozz7\nrH1F0BTFA5HvQ7F8+XKGDh3KmTNnaNy4MYmJiaSnpzu04AmgRYsWNyZmfTSel3IXRgqPIv8/mDWS\nk6HXi1PY91hdwqb7sWjeA65wDxS2MGQI1Kkjg74L2b4dOnWSC3NHjbpZ5thTUXvG2k5aWhrfffcd\nmzZt4oMPPuDIkSN88MEHBAYGEh4ezosvvsj06dMJCAggJCSEu+66y+5zXLlyhe+++47AwEBuv/12\n2rZt64J3UjTO7BlrqkB//To8+NR8dj3qS4uZV/n1h4FUruwmdYp/c+wYtG4Nhw7h6n+I1atlymV2\ntnSMXnnFpafTFRXoFdYoFpuDCwFDXonmYO8sQhaf4IfPjBXkzeyzOqy9Xj1Zr8ANS8W7d5cbjoMs\nl7Bo0c3nzHztwfz6jebR24vZ9duCaQL9uxNP8XfYbupHH2fSK6+7vEiZwkZGj5YR+Nw5l59qyBC5\nK5UQslTC1q0uP6VC4RGYwrqZOeca35z9Ap90b4Y3fYP+/U3z/VQ8+O9/oWJFuSuVixFCFtL89luo\nVAmioz1vQZWybhTW8GjrZvNmwfT975Pu50/fUi+rIG9ERo6UkdeFGTi5eHlJj757d7h4Ua6evXjR\n5adVKEyNoaPm4cMwZu67nGrWmLv39WTEG8ZNrzGzz+q09nr1ZOT95htN9BSFry/8+ivccQccOQKd\nOkWSkeGWU7sEM392wPwet9n124JhA/358/D82I/Z3/VO7ljegC//V0flyhuZt96Czz/XfHOSgvD3\nhxUroEYNiI2FZ55ROfYKRUEYMtBfuwaPvzSHvY81JGR2NrN/vEvr+lmaY7Z6JXnRRHvz5nJzkjw1\nyV1NrVpy9Wy5cuHMnQtWigS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ArxFm9vkMqz0sDM6dgxMnCm1mWP02Yov+MmVg5Eg4dkyu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\nUCgUCoVCoVAoFAqFQuH5/D+mBoVLNxFhcQAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7ff8fab06510>"
]
}
],
"prompt_number": 19
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot_taylor_approximations(cos, 0, [2, 4, 6], (0, 2*pi), (-2,2))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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zJlSrZrQiwQgk0OuE23Nxu3VT6ZZTpuR7WGQkvPUWaKk+7HmgJafiM+m7I/9J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\nAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x7ff8f7debf90>"
]
}
],
"prompt_number": 20
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# For an expression made from elementary functions, we must first make it into\n",
"# a callable function, the simplest way is to use the Python lambda construct.\n",
"plot_taylor_approximations(lambda x: 1/cos(x), 0, [2,4,6], (0, 2*pi), (-5,5))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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O/emnn9K3b1/T+/fp04fPPvssIFp0RQK4G3T2MEH0W40Z/SEh/nl5Q69evejZ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\nrkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7ff8f7ecd4d0>"
]
}
],
"prompt_number": 21
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"<br>\n",
"<a name='trapezoid'></a>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Trapezoid Rule\n",
"[[back to top]](#sections)\n",
"\n",
"A simple illustration of the trapezoid rule for definite integration:\n",
"\n",
"$$\n",
"\\int_{a}^{b} f(x)\\, dx \\approx \\frac{1}{2} \\sum_{k=1}^{N} \\left( x_{k} - x_{k-1} \\right) \\left( f(x_{k}) + f(x_{k-1}) \\right).\n",
"$$\n",
"<br>\n",
"First, we define a simple function and sample it between 0 and 10 at 200 points"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 22
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def f(x):\n",
" return (x-3)*(x-5)*(x-7)+85\n",
"\n",
"x = np.linspace(0, 10, 200)\n",
"y = f(x)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 23
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Choose a region to integrate over and take only a few points in that region"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"a, b = 1, 9\n",
"xint = x[np.logical_and(x>=a, x<=b)][::30]\n",
"yint = y[np.logical_and(x>=a, x<=b)][::30]"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 16
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plot both the function and the area below it in the trapezoid approximation"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.plot(x, y, lw=2)\n",
"plt.axis([0, 10, 0, 140])\n",
"plt.fill_between(xint, 0, yint, facecolor='gray', alpha=0.4)\n",
"plt.text(0.5 * (a + b), 30,r\"$\\int_a^b f(x)dx$\", horizontalalignment='center', fontsize=20);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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Jcr+KWbOgqAjuvx/uvFNt27t3L6WlpVJn18D48eNxc3OTqQqFuA6S3Btx6BB8\n/rl6EvWdd9S2xMREfv31V8LCwrQNzkEdOnSIwYMHm8e1FkJchST3BhiN8Moran3GDDVOe35+PlFR\nUQwcOFDq7Br5+eef0el0fPvttyxatIjExEStQxLCZklyb8C2bRAdDf7+apiBysrK6v7svr6+Wofn\nENauXcvYsWN59NFHSU1NBeDgwYNMmTKFcePG8Zvf/Ibly5drHKUQtkuS+xUqKtSojwBz54Kvr6qz\nFxcXS529hRw6dIj33nuPZcuWUVRUxBtvvEFWVhZGo7G66+nFixfJy8vTOFIhbJck9yt8+qkaP6ZH\nDzWFXlJSktTZW9gHH3zATTfdRGhoKEajkcDAQOLi4oiIiKj+zIEDBxg9erSGUQph2yS511JYCK+/\nrtYXL4aSkny+/vprqbO3oBMnThAXF8edd96Jm5sbmzZt4q9//Suenp7VUxampaWRmJjIo48+qnG0\nQtguSe61LFumJr0eORLuv1/V2YOCgqTO3oK+/vprgHqt8uHDh+Pk5MS2bdtYs2YNK1aswN3dXYsQ\nhbALWvQpMxqNRg0ue3WXLpl7xcCuXeDkFM3p06cZMmSI1qE5lPHjx+Pl5cW6deu0DkW0EhUVFezb\nt4+ZM2dqHUqTmLoAX3fOlpa7ydKlKrGPHQshIWc4duyYjBvTwtLS0jh//nyd2roQwjKS3IHsbDW8\nAMBrrxURFRXFoEGDcHV11TYwB/PLL78AyKQnQliBJHdg0SIoLoYJE4ycO7eJwMBAqbNr4NChQwD0\n69dP40iEsH9NTe7OwFFgq+m9P7ADSAC2AzafIdPS1MxKAA88cITi4mJ69OihbVAO6siRI+j1erp3\n7651KELYvaYm9xnAScB8h3Q2KrmHArtM723aokVQVgYTJhSSn79X6uwaSU1NJTc3l549e+Ls7Kx1\nOELYvaYk987AvcA/qbmDex+w2rS+GpjUhPM3u/R0WLkSdDoj4eGbGDhwoNTZNXL06FEA+vTpo3Ek\nQrQOTUnu7wGvAFW1tgUC2ab1bNN7m/XWW1BeDjfdlEpYmB4/Pz+tQ3JYR44cAaBXr14aRyJE62Dp\nY5cTgPOoentkI58xUlOuqWP+/PnV65GRkURGNnaK5nP2LHzyiVq/885f6NmzZ4vHIGrExMQAtpHc\nKysrLS4NNeVYIWqLjo4mOjra4uMtTe6jUSWYewF3wBv4N6q13hHIAjqhfgHUUzu5a2XpUlVrDw8/\nzbhxXbQUI7dQAAAPeUlEQVQOx6FdunSJjIwMdDqd5r9kd+/eTVFREb/97W8tOn7VqlWMHDlS7t2I\nJruy4btgwYIbOt7SssxrQBegO/AIsBuYCmwBppk+Mw3YZOH5m1VWFnz8sfqj4tlnc6TOrrHjx48D\n4Ofn1yJdUNPT03nxxRf54IMPePPNNzE/MX348GGOHj1qcWIHeOyxx/j0009JSUm57mPee+89xo8f\nz/Dhwzl8+LDF1xaiNmv1czeXXxYDd6K6Qt5uem9zli41UlqqY/jwDIYNk8SuNXNyb4mSTHl5Oc8/\n/zxjx44lJyeHzZs3U1RURGFhIR988AHPP/98k87v4uLC7NmzmTdvHpWVldd1zMyZM5k2bRp6vV5a\n/MJqrDHU4R7TCyAXuMMK52w2OTmwYoUR0DFjxmWtwxHU1Nt79+7d7Nfav38/mZmZDBkyhB49elSP\nZfPhhx9yzz334Obm1uRrdOzYkR49erBt2zYmTpx4XcccPXqU/v37o9frm3x9IcABn1D96CMoKXFi\n0KAM+vYt0Toch1dZWUlcXBzQMi33w4cP4+fnR3BwMAMGDGDEiBGUlJSwadMm7r33Xqtd5+GHH2b1\n6tXX/qDJsWPHZJA6YVUOldyLiuCDD9T6vfee0DYYAUBKSgqlpaXodDpCQ0Ob/XqxsbH079+/zrYf\nf/yRoKAgvL29rXad0NBQ8vLyOHXq1DU/m5GRwcWLFyW5C6tyqBkoVq5UZZlBg0ro0ycLaK91SA7v\n5MmTADg7OzfrsA/z588nNzeXX3/9lZCQEF544QWCg4OZNWsWBw4cuOpMW3FxcURFReHk5ERmZiZz\n585l48aNFBQUcP78eZ555hk6d+5c5xgnJyfCw8PZv39/vQezfvnlFzZu3EhQUBAFBQXVT+WGh4c3\n+bpCmDlMci8vh3feUetPPpmDTouR7EU95uTevXv3Zp3tav78+Zw9e5ZJkyYxffr0Ol3MEhISuP/+\n+xs8LiMjgy1btjBr1qzq8zz22GMsWLCAqqoqnnrqKfr27cuUKVPqHdutWzdOnz5dZ9umTZtYsWIF\nn3/+Oe3btycrK4vf/e539O/fv87kI025rhDgQGWZ9eshNRVCQ+H22wu0DkeYmJN73759m/1a5hLJ\nleWfzMzM6in8rvTFF1/wwgsvVL8vKSnBx8eHQYMG0bFjR6ZMmdJo18m2bduSmZlZ/T4hIYHFixfz\n0ksv0b69+quxY8eOeHh4MHToUKtdVwhwkORuNMKSJWr91VdBHiC0DZWVlSQmJgItM8xvQkICXl5e\nBAUF1dleWFiIl5dXg8dMnToVDw+P6vcxMTGMGDECgMDAQGbMmNFord7Hx4eCgpqGxPLly/H09GTs\n2LHV286cOUN+fn69entTrisEOEhy374djh+HoCCQOZVtR0pKCmVlZeh0uhZJ7qdOnWrwpq1Op6Ox\nqR9r/yJISUnhwoULDBs27LquZzQaq89bUFDA/v37GTlyZJ3hCQ4fPoyTk1O92aeacl0hwEGS+7vv\nquWf/gRW6MYsrCQhIQFQD/60xGiQp0+fbjC5t23blvz8/Gsef+jQIVxdXevcfD179myjn8/Pz68u\n96Snp1NVVVXvxu2hQ4fo168fHh4ejZ7rRq8rBDhAco+NVS33Nm3g6ae1jkbUZk7uvXr1avYhIPLz\n88nOzm4wuQcFBTWY3EtLS3n//ferS0cHDhygd+/e1Q86VVVV8fnnnzd6zcuXLxMcHAyAp6cnoGrs\ntc9/5MiR6pLM2rVrrXJdIcABesssW6aW06aBv7+2sYi6kpKSABgwYECzX8t8M7Whp2AjIiJITk6u\nt/2nn37i888/p1+/fri4uJCenl7nxuuqVauYMGFCo9dMTk5m5MiRAHTt2pXevXtXt7grKip46623\nKC8vp3PnzuTm5uJv+gFt6nWFgFae3C9cgH//W63PmKFtLKI+c8u0JZJ7fHw8bdu2bbDlftNNN/GO\nuZ9sLUOHDmXChAnExcVx6tQpPvvsMxYvXsyiRYvQ6/VERkY2GntFRQXHjx+v7vGi0+lYvHgx7777\nLtnZ2VRVVfHEE08wdOhQtm3bRlxcXPVnm3JdIcxadXL/+9/BYIDx40Em+LEtBQUFXLhwAZ1Ox8CB\nA5v9evHx8QwfPhwnp/qVyMGDB5OTk8OFCxequygC+Pr6Mm/evDqfvd7hqmNjYwkMDKzzl0LXrl1Z\nZv5T0qRz5871WuFNua4QZq225m4wqHFkAGbO1DYWUZ+5JOPt7U1ISEizXOOzzz5j+vTpgOpPX7sL\nYm16vZ6HHnqINWvWWO3a//nPf3hUumYJDbXa5L5mDWRnQ1gY3H671tGIK505cwagXhdAa/rmm2/Q\n6/WcPn0aV1fXRpM7wLRp09i3bx+XLzd9pNCUlBQyMzPlISOhqVaZ3I1G+PBDtT5jBjLUgA0yJ/fB\ngwc32zWmTp1KQEAAK1euZOnSpVed/s7d3Z25c+eycOHCRvu8Xw+DwcCSJUtYuHAhOvnBExpqlTX3\nAwfgyBFo1w4mT9Y6GtEQczfI5my5T5gw4YZ6lQwYMIAHHniAdevW8cgjj1h0zVWrVjF9+nS6detm\n0fFCWEurTO5/+5taPvEE1HqCW9iQxMREPDw8WmRMmRsxatQoRo0aZfHxf/zjH60YjRCWa3VlmfPn\nYcMGVYp59lmtoxENOXfuHAUFBQwcOPCqpRIhhOVaXXL/5z+hrAwmTIBm6oQhmsg889KVIyEKIayn\nVSX3igpYsUKtm3rACRsUGxsLUD3KoRDC+lpVct+6FTIyoHdvuPNOraMRjYmJicHT01OeshSiGbWq\n5G5+aOm556CBBxGFDSgtLSU2NpaRI0c2+LSoEMI6Ws2/roQE2LVLjf742GNaRyMac+jQIcrKyrjt\nttu0DkWIVs3S5N4F+B6IBU4A5vnA/IEdQAKwHfBtaoDX65//VMtHHgHfFruquJa3336byZMnU1FR\nAcC3336Lt7f3VZ8WFUI0naXJvRyYCQwARgHTgX7AbFRyDwV2md43O4MBVq1S6zJmu205ePAgpaWl\nVFVVkZWVxe7du5k8eXL12ORCiOZh6UNMWaYXQCEQBwQD9wHmv7dXA9G0QILfvBkuXlTjyEgHDNsS\nHh6Ov78/ly9f5i9/+Qtdu3blMambCdHsrFFzDwEGAweAQCDbtD3b9L7ZffyxWj79tIwjY2umT59O\nbGwskyZNQq/X8+GHH+Li0nCboqKighUrVvDll1+ydu1aZs6cSUZGRgtHLETr0NThB7yAr4AZQMEV\n+4ymVz21x6aOjIwkMjLS4gBOn4bdu9UwA1OmWHwa0Ux8fX35m3k8iGt488036d27N7///e/Jy8vj\nH//4B507d27mCIWwTdHR0URHR1t8fFOSuysqsf8b2GTalg10RJVsOgHnGzrQmhMPmG+kPvyw3Ei1\nZ6dPn2bHjh3MmjULUGPPmOcWFcIRXdnwXbBgwQ0db2lZRgd8CpwEak8tswWYZlqfRk3SbxZlZXIj\ntbU4cOAAERER6PV6QN2IHTZsGAUFV/5BKIS4HpYm95uBR4ExwFHTaxywGLgT1RXydtP7ZrNli5on\ndeBAaMJAfsIG+Pj40K5dOwCKi4v5/vvvCQ8P55tvvtE4MiHsk6VlmR9p/BfDHRae84atXKmWTz4p\nN1Lt3d13382xY8f47rvvKCsr4+677+ann36yuSGBhbAXdjue+9mz8N134OoqN1JbA71ez9y5c7UO\nQ4hWw26HH/j3v6GqCu67DwICtI5GCCFsi10md6Ox5kbq449rG4sQQtgiu0zu+/ergcI6dYK779Y6\nGiGEsD12mdzNN1KnToVGHnYUQgiHZnfJvagI1q1T61KSEUKIhtldcv/qKygsVP3apZecEEI0zO6S\n++rVaimtdiGEaJxdJfeMDPj+e3BzU2PJCCGEaJhdJfc1a1Q3yN/+Fnx8tI5GCCFsl10l9y++UEt5\nIlUIIa7ObpL7iRPw66/g5wf33KN1NEIIYdvsJrmbW+0PPqhq7kIIIRpnF8m9qqomuT/6qLaxCCGE\nPbCL5P7jj5CeDl27ws03ax2NEELYPrtI7p9/rpZTpoCTXUQshBDasvlUaTDAhg1qXXrJCCHE9bH5\n5B4VBXl5EBEBAwZoHY0QQtgHm0/u0rddCCFunE0n97w82LpVzY86ebLW0QghhP2w6eT+1VdQVgZj\nxkBwsNbRCCGE/bDp5C5924UQwjLNkdzHAfHAaWCWpSfJzoY9e0Cvh/vvt1psQgjhEKyd3J2Bv6ES\nfH9gMtDPkhNt3KieTL3rLvD1tWKENuTQoUNah2Az5LuoId9FDfkuLGft5D4CSARSgHJgLTDRkhOZ\n+7Y/9JB1ArNFhw8f1joEmyHfRQ35LmrId2E5ayf3YCC91vsM07YbUrskc999VotNCCEchouVz2e0\nxklql2SaY1IOnU5Hbm4uR44csf7Jb8C5c+c0j8FWyHdRQ76LGtb4LqqqqnBxsXaqs306K59vFDAf\nVXMHmANUAW/V+kwi0NPK1xVCiNYuCeil1cVdTAGEAHrgGBbeUBVCCGFb7gFOoVroczSORQghhBBC\nCGEJqzzg1Ap0Ab4HYoETwAvahmMTnIGjwFatA9GYL/AlEAecRN3HclRzUP9GYoD/AI40weZKIBv1\n327mD+wAEoDtqJ8Vm+CMKtWEAK44dj2+IxBhWvdClbEc9bsw+z/gC2CL1oFobDXwB9O6C9AM/cXs\nQghwhpqEvg6Yplk0Le9WYDB1k/sS4FXT+ixgcUsH1ZibgG9rvZ9tegnYBIzVOggNdQZ2AmNw7Ja7\nDyqhCdVKPQX4oX7JbQXu0DSilhdC3eQeDwSa1jua3jeqJQcOs8oDTq1QCOo39AGN49DSe8ArqG6z\njqw7cAFYBRwBPgHaaBqRdnKBd4A0IBPIQzUAHFkgqlSDaRl4lc+2aHK3ygNOrYwXqr46AyjUOBat\nTADOo+rt1n7uwt64AEOA5aZlEY77121P4EVU4ycI9W9FpuypYeQaObUlk/tZ1I1Esy6o1rujcgW+\nAj5HlWUc1WjgPiAZWAPcDvxL04i0k2F6/WJ6/yUqyTuiYcA+IAeoADaiflYcWTaqHAPQCdUosgny\ngFMNHSqBvad1IDbmNhy75g7wAxBqWp9P3ae7HUk4qieZB+rfy2pguqYRtbwQ6t9QNfcynI0N3VAF\necDJ7BZUffkYqhxxlJohGxzZbUhvmXBUy/1XVGvVUXvLgOoZYu4KuRr1166jWIO611CGulf5OOom\n805ssCukEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEMIB/X+HJuq2U7ADmgAAAABJRU5E\nrkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7f917f1d5b10>"
]
}
],
"prompt_number": 17
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Compute the integral both at high accuracy and with the trapezoid approximation"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import print_function\n",
"from scipy.integrate import quad, trapz\n",
"integral, error = quad(f, 1, 9)\n",
"print(\"The integral is:\", integral, \"+/-\", error)\n",
"print(\"The trapezoid approximation with\", len(xint), \"points is:\", trapz(yint, xint))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The integral is: 680.0 +/- 7.54951656745e-12\n",
"The trapezoid approximation with 6 points is: 621.286411141\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"<br>\n",
"<a name='display system'></a>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# IPython's Display System\n",
"[[back to top]](#sections)\n",
"\n",
"In Python, objects can declare their textual representation using the `__repr`__ method. IPython expands on this idea and allows objects to declare other, richer representations including:\n",
"\n",
"- HTML\n",
"- JSON\n",
"- PNG\n",
"- JPEG\n",
"- SVG\n",
"- LaTeX\n",
"\n",
"A single object can declare some or all of these representations; all are handled by IPython's display system. This Notebook shows how you can use this display system to incorporate a broad range of content into your Notebooks."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"By default, image data is embedded in the Notebook document so that the images can be viewed offline. However it is also possible to tell the Image class to only store a link to the image. Let's see how this works using a webcam at Berkeley."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.display import Image\n",
"img_url = 'http://www.lawrencehallofscience.org/static/scienceview/scienceview.berkeley.edu/html/view/view_assets/images/newview.jpg'\n",
"\n",
"# by default Image data are embedded\n",
"Embed = Image(img_url)\n",
"\n",
"# if kwarg `url` is given, the embedding is assumed to be false\n",
"SoftLinked = Image(url=img_url)\n",
"\n",
"# In each case, embed can be specified explicitly with the `embed` kwarg\n",
"# ForceEmbed = Image(url=img_url, embed=True)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 13
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Embed"
],
"language": "python",
"metadata": {},
"outputs": [
{
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oJ2n2596IH6ZxQAIJMj1fxQAqCntzQAAScDtH/enkHBwfaoAABOTH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W5bWtJ5BUJScFPDveqPy2t6Xrrt7qTqEFl1txq/SLgNMkIQCU5bWA2Ik4ASU42mq/FTeml6P3Nz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\nUwPj4pqiZ2/NQH//2Q==\n",
"metadata": {},
"output_type": "pyout",
"prompt_number": 14,
"text": [
"<IPython.core.display.Image at 0x7f1a79cde350>"
]
}
],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"SoftLinked"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<img src=\"http://www.lawrencehallofscience.org/static/scienceview/scienceview.berkeley.edu/html/view/view_assets/images/newview.jpg\"/>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 15,
"text": [
"<IPython.core.display.Image at 0x7f1a79cde9d0>"
]
}
],
"prompt_number": 15
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"<br>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"IPython makes it easy to work with sounds interactively. The Audio display class allows you to create an audio control that is embedded in the Notebook. The interface is analogous to the interface of the Image display class. All audio formats supported by the browser can be used. Note that no single format is presently supported in all browsers."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.display import Audio"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"max_time = 3\n",
"f1 = 220.0\n",
"f2 = 224.0\n",
"rate = 8000.0\n",
"L = 3\n",
"times = np.linspace(0,L,rate*L)\n",
"signal = np.sin(2*np.pi*f1*times) + np.sin(2*np.pi*f2*times)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 17
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Audio(data=signal, rate=rate)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
" <audio controls=\"controls\" >\n",
" <source 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\" type=\"audio/wav\" />\n",
" Your browser does not support the audio element.\n",
" </audio>\n",
" "
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 18,
"text": [
"<IPython.lib.display.Audio at 0x7f1a79bf9410>"
]
}
],
"prompt_number": 18
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.display import YouTubeVideo"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 19
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"YouTubeVideo('1j_HxD4iLn8')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
" <iframe\n",
" width=\"400\"\n",
" height=300\"\n",
" src=\"https://www.youtube.com/embed/1j_HxD4iLn8\"\n",
" frameborder=\"0\"\n",
" allowfullscreen\n",
" ></iframe>\n",
" "
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 20,
"text": [
"<IPython.lib.display.YouTubeVideo at 0x7f1a79bf9310>"
]
}
],
"prompt_number": 20
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"<br>\n",
"Python objects can declare HTML representations that will be displayed in the Notebook. If you have some HTML you want to display, simply use the HTML class."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.display import HTML"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 21
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"s = \"\"\"<table>\n",
"<tr>\n",
"<th>Header 1</th>\n",
"<th>Header 2</th>\n",
"</tr>\n",
"<tr>\n",
"<td>row 1, cell 1</td>\n",
"<td>row 1, cell 2</td>\n",
"</tr>\n",
"<tr>\n",
"<td>row 2, cell 1</td>\n",
"<td>row 2, cell 2</td>\n",
"</tr>\n",
"</table>\"\"\""
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 22
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"h = HTML(s); h"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<table>\n",
"<tr>\n",
"<th>Header 1</th>\n",
"<th>Header 2</th>\n",
"</tr>\n",
"<tr>\n",
"<td>row 1, cell 1</td>\n",
"<td>row 1, cell 2</td>\n",
"</tr>\n",
"<tr>\n",
"<td>row 2, cell 1</td>\n",
"<td>row 2, cell 2</td>\n",
"</tr>\n",
"</table>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 23,
"text": [
"<IPython.core.display.HTML at 0x7f1a780d4e90>"
]
}
],
"prompt_number": 23
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"You can import whole webpages:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.display import IFrame\n",
"IFrame('https://en.wikipedia.org/wiki/Axiom_(computer_algebra_system)', width='100%', height=350)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
" <iframe\n",
" width=\"100%\"\n",
" height=350\"\n",
" src=\"https://en.wikipedia.org/wiki/Axiom_(computer_algebra_system)\"\n",
" frameborder=\"0\"\n",
" allowfullscreen\n",
" ></iframe>\n",
" "
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 25,
"text": [
"<IPython.lib.display.IFrame at 0x7f1a79bf9290>"
]
}
],
"prompt_number": 25
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"<br>\n",
"And we also support the display of mathematical expressions typeset in LaTeX, which is rendered in the browser thanks to the MathJax library."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%%latex\n",
"\\begin{align}\n",
"\\nabla \\times \\vec{\\mathbf{B}} -\\, \\frac1c\\, \\frac{\\partial\\vec{\\mathbf{E}}}{\\partial t} & = \\frac{4\\pi}{c}\\vec{\\mathbf{j}} \\\\\n",
"\\nabla \\cdot \\vec{\\mathbf{E}} & = 4 \\pi \\rho \\\\\n",
"\\nabla \\times \\vec{\\mathbf{E}}\\, +\\, \\frac1c\\, \\frac{\\partial\\vec{\\mathbf{B}}}{\\partial t} & = \\vec{\\mathbf{0}} \\\\\n",
"\\nabla \\cdot \\vec{\\mathbf{B}} & = 0\n",
"\\end{align}"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"\\begin{align}\n",
"\\nabla \\times \\vec{\\mathbf{B}} -\\, \\frac1c\\, \\frac{\\partial\\vec{\\mathbf{E}}}{\\partial t} & = \\frac{4\\pi}{c}\\vec{\\mathbf{j}} \\\\\n",
"\\nabla \\cdot \\vec{\\mathbf{E}} & = 4 \\pi \\rho \\\\\n",
"\\nabla \\times \\vec{\\mathbf{E}}\\, +\\, \\frac1c\\, \\frac{\\partial\\vec{\\mathbf{B}}}{\\partial t} & = \\vec{\\mathbf{0}} \\\\\n",
"\\nabla \\cdot \\vec{\\mathbf{B}} & = 0\n",
"\\end{align}"
],
"metadata": {},
"output_type": "display_data",
"text": [
"<IPython.core.display.Latex at 0x7f1a79bf93d0>"
]
}
],
"prompt_number": 26
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"<br>\n",
"<a name='custom display'></a>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Defining Custom Display Logic for Your Own Objects\n",
"[[back to top]](#sections)\n",
"\n",
"This Notebook shows how you can add custom display logic to your own classes, so that they can be displayed using these rich representations. There are two ways of accomplishing this:\n",
"\n",
"- Implementing special display methods such as _repr_html_.\n",
"- Registering a display function for a particular type.\n",
"- In this Notebook we show how both approaches work.\n",
"\n",
"Parts of this notebook need the inline matplotlib backend:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 29
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Implementing special display methods\n",
"The main idea of the first approach is that you have to implement special display methods, one for each representation you want to use. The names of the special methods are self explanatory:\n",
"\n",
"- `_repr_html`_\n",
"- `_repr_json`_\n",
"- `_repr_jpeg`_\n",
"- `_repr_png`_\n",
"- `_repr_svg`_\n",
"- `_repr_latex`_\n",
"\n",
"As an illustration, we build a class that holds data generated by sampling a Gaussian distribution with given mean and variance. Each frontend can then decide which representation it will display be default. Further, we show how to display a particular representation.\n",
"\n",
"The next cell defines the Gaussian class:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.core.pylabtools import print_figure\n",
"from IPython.display import Image, SVG, Math\n",
"\n",
"class Gaussian(object):\n",
" \"\"\"A simple object holding data sampled from a Gaussian distribution.\n",
" \"\"\"\n",
" def __init__(self, mean=0, std=1, size=1000):\n",
" self.data = np.random.normal(mean, std, size)\n",
" self.mean = mean\n",
" self.std = std\n",
" self.size = size\n",
" # For caching plots that may be expensive to compute\n",
" self._png_data = None\n",
" self._svg_data = None\n",
" \n",
" def _figure_data(self, format):\n",
" fig, ax = plt.subplots()\n",
" ax.plot(self.data, 'o')\n",
" ax.set_title(self._repr_latex_())\n",
" data = print_figure(fig, format)\n",
" # We MUST close the figure, otherwise IPython's display machinery\n",
" # will pick it up and send it as output, resulting in a double display\n",
" plt.close(fig)\n",
" return data\n",
" \n",
" # Here we define the special repr methods that provide the IPython display protocol\n",
" # Note that for the two figures, we cache the figure data once computed.\n",
" \n",
" def _repr_png_(self):\n",
" if self._png_data is None:\n",
" self._png_data = self._figure_data('png')\n",
" return self._png_data\n",
"\n",
"\n",
" def _repr_svg_(self):\n",
" if self._svg_data is None:\n",
" self._svg_data = self._figure_data('svg').decode('utf-8')#.encode('utf-8')\n",
" return self._svg_data\n",
" \n",
" def _repr_latex_(self):\n",
" return r'$\\mathcal{N}(\\mu=%.2g, \\sigma=%.2g),\\ N=%d$' % (self.mean,\n",
" self.std, self.size)\n",
" \n",
" # We expose as properties some of the above reprs, so that the user can see them\n",
" # directly (since otherwise the client dictates which one it shows by default)\n",
" @property\n",
" def png(self):\n",
" return Image(self._repr_png_(), embed=True)\n",
" \n",
" @property\n",
" def svg(self):\n",
" return SVG(self._repr_svg_())\n",
" \n",
" @property\n",
" def latex(self):\n",
" return Math(self._repr_latex_())\n",
" \n",
" # An example of using a property to display rich information, in this case\n",
" # the histogram of the distribution. We've hardcoded the format to be png\n",
" # in this case, but in production code it would be trivial to make it an option\n",
" @property\n",
" def hist(self):\n",
" fig, ax = plt.subplots()\n",
" ax.hist(self.data, bins=100)\n",
" ax.set_title(self._repr_latex_())\n",
" data = print_figure(fig, 'png')\n",
" plt.close(fig)\n",
" return Image(data, embed=True)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 111
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = Gaussian(); x"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stderr",
"text": [
"/usr/local/lib/python2.7/dist-packages/IPython/core/formatters.py:239: FormatterWarning: Exception in image/svg+xml formatter: 'ascii' codec can't encode character u'\\u2212' in position 134498: ordinal not in range(128)\n",
" FormatterWarning,\n"
]
},
{
"latex": [
"$\\mathcal{N}(\\mu=0, \\sigma=1),\\ N=1000$"
],
"metadata": {},
"output_type": "pyout",
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f3Ey5DeMt0Qdho1+ZzkV9fQclrpWNG2sADAH4QDmTNbEdQC0oFwq1mXZ31+LZ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\nWWb0C3jpHyYZeae1dU86MdfulEuuRSLLJKphOQGGKNe4l8Y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"prompt_number": 112,
"text": [
"<__main__.Gaussian at 0x7f1a5cc91fd0>"
]
}
],
"prompt_number": 112
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x.png"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"png": 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TKZeyXE+6vtvQ8EJ0ck+zPd8trJNgBQKBdQJ9QxeAZ84EteenpZ0RPvGB/Mor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\nIiIiIiIiIiIiIiIiIiIiYpP/A7jtdd/lE1DMAAAAAElFTkSuQmCC\n",
"prompt_number": 31,
"text": [
"<IPython.core.display.Image at 0x7f1a5f250f10>"
]
}
],
"prompt_number": 31
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.display import display"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 33
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"display(x)\n",
"display(x.png)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$\\mathcal{N}(\\mu=0, \\sigma=1),\\ N=1000$"
],
"metadata": {},
"output_type": "display_data",
"png": 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TKZeyXE+6vtvQ8EJ0ck+zPd8trJNgBQKBdQJ9QxeAZ84EteenpZ0RPvGB/Mor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\nIiIiIiIiIiIiIiIiIiIiYpP/A7jtdd/lE1DMAAAAAElFTkSuQmCC\n",
"text": [
"<__main__.Gaussian at 0x7f1a5f250e10>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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TKZeyXE+6vtvQ8EJ0ck+zPd8trJNgBQKBdQJ9QxeAZ84EteenpZ0RPvGB/Mor\nOf2WqJ//2QJSUbFZ0CN3s6Xl/6yucXT7l5NzneT65TWTTyJh01YPAXlLppNGMJ8vXkOnTW32COJp\n8dw9s5Wq0p9n2hYXFVXbXlf0WjD5rVdUbCbLlj1KgsE7iep9Ys2lq0+Bx6/dSKz15f69WtuA6R04\nUwNe/cbF86i3kn359f2HUhhO79MN5PJTiis9/QYyd+5qo7uh1eW4Pto3OfVEYzVUjxM1cxX9Fw5/\ny7bMO3e2k0DgJs27cq5np2cXXSuZRIdcr3pKrqSk2kgziV5MM2dyLyade7fOywdJpG5SAVcd0MTL\n8UHDnjNNJm/pzefY3cCi92dnE9cqpbOsEq7VaBx0vPCUcpnt68qk95+fv8rhuvy96DsLIVSM7mZD\nGWgSCzV5iPguZI5Y57Lovh2YRNdycq4n2dnXk7S0Wul7cbKy582d/cbN5+rLL08G4jMnJ4lKPH7e\n+sWSKtRliq2g9cxyKTu5lfJ2tpLo6jkQuCmptiZrnbQTQI53YBOTTi9q5852Eg7rJrOHLIO8abGG\ns3Ogd5d9SQwOYauCsrJax6TaiUelesvxycrqtFNhx6pBMTNn3igkWtYZD8W/9UkyvPjmmo2A1vO8\nrOhNg2VR0VJDsNLS6P3NZbDbeXBDvDrAM6PsH5G0tPss79U+elPsiGL0Jx1IMjNvVJJiW9tEPDtE\n/XPqI1Kt7V9sF97vrSKe8tsL64nvyPvqXa0j3s/s/dXdwk1Us37HRzNviQsRszpnPIGf/Bg6diYH\nKTTGOrsLMl5Ox+eHQqJIPwfjTOPRq9Bx25S7rwR1MaP+9V1dlXj66d0SZyiX1Z5/a2h4GT093JAK\nAKdPXw5qQDQZD9dGjYcVoHx9JRjnnJV1AI8+uhhvvnlYsBXYP/Phw2KOVPu62rhxMbZuXSe5mQUC\na7Fxoxt/cmpf6Ot7JWqQbRJ+awNwmeH+1Pj8i1+8gzvv7IkaGuvBjawUQ0M5wicxEcZ+jI8XIxL5\nKQih/Hwo9CG++MVci82CQcdd9/aGsG/fU8L1yzEyYi2H6gbp1i7BnBEGB7tx5EiekNOWc+6ZmSdj\nSTLocQU4ceIeyG1EzAfsLRGPDm5iV8yxAWI/Vd0vaf1kZ/8FgsFlAIK4+GKrHUkHeRxoin5bA+Bh\nADwXcDj8EB5/vNpYznhzTlvjOmh7KC3dELPjVVbWa2MUCgtXAThP+1yinScZgmpukMKBnnfKjIz/\nxDe+cWml2pxKAAAgAElEQVRsMFywYHXMKHfxxdkAgK4ueWDknjYyWEP0YvDgL/rZ2HcsUMWNSqV4\nnebmNoRCn6CoqBrFxTxICkDMMPzOO8c0JWdVb2887O7uxYcffgzgPxEIZEcnpA1CAm93z/zhhx8J\nn+wnXWpw3YHt22swOhpCIDCEjRvLtYZY6wChGhPF31lgWgWA54UycOPzqVPioKqbRNRJsRzh8D+h\nuPgC7Nu3I/YdUI6hIWDWrAaLwVQ0Al98cTa2bKmJHbNkSZPlGd0YZp3an3VwUSePckQiwJEjLZg/\n/7LoIHU1mpvbsG+feBxtI4HALzE6+pXod1aHAK+Cb8eO9WgdHOrqrjUOjCw2QJwo33sPOHhQvUM5\nLr30Ffzyly22TgBieZqb2/D2279Hfz+LUREzPfF6KCr6LZ59dr1xgbh/fy2Ki1+WhAHdB5ANg7a1\nSrBk9sABHD/O27RpoKbt1Hny5/2HxeXQPjI42GO47tSFsi15LOYbbeKxMjPv1tIBmZnM/7aRAJtJ\nOHyvhe/SUT/uEmLQ7ZKetmgngcANLrJTmULwdXlbWRnsKQwnGsmtRsfMmTcR1fgJLCXp6bfFLdTF\njpfLqNvust/vJzK3XEuA6wlwreF8Uyi86BO/lGRn17gSaHPDm7qjI2gZGD0ltgmT+BlvV6pdRldP\n/F2b6DlK94i5bzlfnZ5+q+u8AvL7o9cIhVZInLkX/l6v+UL7vFN7ZsZLzvGLbcHZ+OoubmQTmTt3\ntWNbIYRRN2KCI/pPlMcw23mui45X8v1nzryB5ObeGuPzly171NgmkUTqJhUgokeKODjTSrLrWGKQ\nRS0JBO41dlD7wUduUHZ8pLVjWbVJsrKWkpyc242N3/ryr9M0/ntJWto9hue3C3iiin5eU8lRjtPq\nHVRYWONYbybtD5FjLiqihkrTRJmTc73Q8MWB+l5iHtztxK1M4mTmwcjc3uQE9Pa8Pb03Vxm1ti99\nW2xUyuxGz4UuMEwJb5Yte5RQw7a7QVgHN4O4F/6e6+HI7Yy1HdO9eD2ZDNNsYVBDAoE7tMZbazn1\ndZqerlt4WessvvaiKtDWkrS0m0h29jJy/vmqgZ+QjIzVJBy+U3sPOnYmBymhbiorgaEhIBQCFi36\nw9jW7Te/+RjAxdGjxK1LDzIy7sDY2KXgW/T1GB2V6ZyenluwalUL5s+XfYedtmZ2fOTs2TkK763q\noLwWDWf2kuT6DyBy7MAYgHtw4YU/wDnn9ODAAf2W+U/+5CfCNdQwcvch362tHRgZGYQYlEOf61mM\njkbQ2tphU29qIhF637ff7rSEoBcUbMbGjYvx4osqhbELeXlzo9RKB4Dd0Xo4DuAVcI65A0APgPsB\n/CXYNp1x10eOHBHyGKgUkUpHybIZDzxQYbPN5u/NXudfl/Sc1YleuoDbfFpAt/LcDmPl3EXQ9z06\n+kUAPwTw17Ff0tOX4te/HsLAwAWgQenm59Fx1qxcZ84E8ItfdNmeD3izf9Fj5cAgeuxuDA2ZKTDe\n9pqEX1gdVYK2XUq1jo7qNYGs5dTVaQvGxx+CG/mUBx6oQEfHsxrJB1nTaGTkdwgEbkQwmI/h4QGM\njv5L9ChaD4QAX/1qA/79398BIc9K1xkb+2v09t5hvUGSkZKBnhku9DzlKPggxriwORgb64Y8wJ6E\nDNXoxwc+JwOHt2hS8Vpt4I3OrG3R26tmVRmGrvF/4Qu7sWvXFrS2dliCWWg5xCAqdWDrQFdXGlas\neA4LF+q5ToDX+cmTfwLKi68GjQClE4uoQ6Ovt7ZoAI1snN6+XRV3o4Pd3r0NFt5WjhgV66Ep+j/T\nRQmDdmZqr8jMfB9f+lK+ZJPghm+zQNvs2XnRQJ5XNKJc52ieUR60TME6Io/PI3/5AuWtt96LTZoM\n3OazAVxTh5cXaEB+/scYHz+OEyfEa7ZEz2kBnQz5b+Pjl+Do0TRQjt9siDVx1kB+1AjcAcA+wAvw\nZv+yO5ZHiFrvxScBNeEJYK0D/cQqay2pCYnYGHMZVJ4fGENJiXXBVFVVjssuexn79lnLzDWNKkEX\n3lsxOgqYon6HhjJw+rQ+6Gp8XDOTnIWw2SYy1yuRa9Rt03VbKC+Uh3VrZsdti7/JVEQjkWklvXum\nzLnF515mr6njPimJ1RfY7HNt1TFpJ4DK7RMCbCIzZ9YQu0QL7igC8TvnZNE8AKVGCJxx8xz0H41f\niN/Vz/oszu9Bbj9uyiW6TOqC5VTbjpm7dq5zs+uuyZ1YpOlM9KGdrcIUXMTLquPE3SezaWxsiQbj\nbSayrhG7vjf3TDnBEf0XCKwR9PadxiVOtwJV2t+ACq28OXCWUTcM1hUjnUHT07+P8XEnb42rYb/V\nBYAOvPXWe5g9O99RC8S0alO3uhUVF+Hv/565Go4q9z0KgLqMZWcPYtu2h9Dc3IaeHtGL5j1QdUvZ\nq6a4+IQLhUJx5fFe9O8dAP4PgH+RjjdRB3KdlwPQa7F0d/eir28UVk+YEHQaH0NDV0PnnTQ4eFR7\nfa5NUwy2Mygo+A+EQkya1t4Vzeop1aGEqnMZjL/4iw+112J5SqnXjTdXP/2znIRppQkgqlqYLvxa\nA523ExCMut+ylTyjs3Ty2erKV5aFDgTGkZd3Lt5+uxNvvfWxpvRqHlr3q1uApvTr6/sB+vqAzs4O\nvPGGVd3TaUdkkmLg2kV3xcoTDL6L2bOzNJ48+lSg3/3uTgwPl4F7NO0AcCNoOwa4J41IYX6E994b\ntOzGAODNNw9jdJSXBxjD6Ojd6O9n1K2dpLJMtwLV4FTUCxB31pGIVd78hhu+Y33oOJHSgV7P9ZWj\nsLAFfX12FcZ4P4BXuLrlpJXa3/9ytFK968LrtrpZWdUYHd0Qve8xAL3gL5BvxcfH1wHQiXM1KZ8p\nTGJdDLyuRJGzCgBzAXxFcwad5JYsaZLsFW5Fm3p6jkepGHWC+pb2+GAwB0ND1gkgLW2DzVPlQ3Qp\nDIUextq1n8fevQ146633FGladgztzDptotFRWbqW0QN2rrhuk4I7Ix8m+q67u1doRyK1wttwYeFH\nuPLKCzW0Fvu7Apy+ESeHUeF38XsqCz06Cuzb14F33nkJo6O68uny0LoT25LfwQ4A+y30GGBvM7Kb\nBIqLXxbyOtBjhoeB/PzVKC11TrxOKco8yJTvIQCPgOsYzQFdNJopTLF8fMEll3l4+HvRv9T+xCWV\nx8chuIcC9F3+DwB94EJ8nPqLRC5BZmYPdu36vqV+zgZIWzpTNCp3FROpgBZSVFRNLrzwDpKeLkc7\nWj0hEs9Co6eWVLe9FkLdJWWPIOB+Q35L9655Tnox1BXRtD10cvVk5V1DKJUkvwOrt1GjTfl1Ifnm\n7bS+buX34yRN69bzw5QFyW2WK7GtMp2SgoKVpKzsfo1LnVt9Ji9ugeLfjMbgXiwZGUtIIFArXLue\npKWpNJaZWrJG/rrXi5HldpMjE6y/vvxv3rw1pKyslmRnX08CAerBIr4PuQ5XKvUgup+KXj3uxguZ\npuP9PSPjduW61jrUPw+jjkztlLtuAmcpdWO3dfvd7z7Ej37EvAvYLPdvCAROY3j48xgfvwViZOja\ntYuxcOH82LX27/9YuyL0EmEm0xxs1a6uitYD+L+QPVjE7ZlKKVjV8AKBlyQjsmwgo+jq2ozlyy/A\n3r2ip8es2DXl1ZxO8bAy6pF0GQj5LYLBYxgeZgqYO5CefiNCoXxkZY1g+XJdlK1p5UhXU3l52dr6\nHhzslhREr7pqNt588zB+/vNu68Ggq192fF7eUSxYwCWURUVGJ1VIBu71AYjb7csuG8Xbb3di1aoW\nR+llJoVLaQS6a9u3D1i9+mE8+6zYTvR1k5VVLHgHyUbXRYs+ZwmoGxzsQWHhRvT3b1euuR6ifHZm\n5kkcOVKGnh6xL/wO5513Hj6U2KqA5d5MOvfZZ+/H22934rvfvR6RSCYIOYMZM25GaenFjjtfvjtk\nEc5WqP3NTaSq9foiOqKGdZ71iu5a5BU4fyfZsfOomK7aN14A9eo6X1sGsT2y9sspJe5EMjbGnAZ2\nA/gEQA2ys9Pw1a9+PlaHeuMzoyjVzGYUQ0N/6Zh4ZqrC1WxuNnC5M6ya/bev067K7MtgvypKT7/B\noXxUnIsZrubOvcvBz9ytL7O6UmS+yrdZ7m+uQ6uxi/nK2/sDy4E03v3N9fVkUl209082rz5NO4Nl\nyx7VGNXW2iSXUY3YdDUnJ77mvt3ASpKVdYONEZS/T7qDlZOfpKffKbzPWhIM3mxROnSn8GrfnuyC\nxtzES9ByN7pqs24C/pzeHU/IY38/efxYTvjqXbeqZvEJ7tojfd/iit7dbtb+edoJYG9kBs6yFb2b\nWZ3PyOosZ+8qybi5vj6Vy+xAevp2nDxZBua2uW9fALfd1ozbb29FX1+mpTyya5h5VZSXFxZWULry\nlSMc/jsMDZ0bM1wB1M+8uFhc7anXkMOgu7u5dAJd7SwGD3VnvOFqlJRkK8YqXR12gK5mPgUg++d3\ndaWhufnnuOiiTGVFfXlsRxEKAXV1qy3vzawTQ8sh7mysvstiAhcKc95XPSdvMhqqu0a6kmc2CFrH\no6Pn4rvfbbWs6vU7O5ZeEDhx4nrI7qAUY2PfBCDquludAVpbO/DEE+3Kc7dhfPzHUhmGh2HJjWBy\nGw6HC1BQYKepLrs4UoO4KKvQgZ6eQTz++K8g+nnr4yU6kJ7+JMbHH4GTL7rX3La6d3foUHF0p2nf\nR+S++3K0XDtAV9wi6PkzZqQjM5O9I/pdWto7iET+P6iuxNnZ34XseLDScj3qXvvvWLBgvSS3oLoa\nL1okxpmI/D3HROSRTclAf8cdP5ICglSjjZywgQ1KXFtCB7ORTtQCuQJcFIweMzzcIVBE+vI8/bRq\nHJQTChBChIFen9CaGjd/IH3X1bUVubm3RD+pzygPKABw8OC6mCdAUdEIgH0AykC9N4YAnEFeXj7y\n83OExMqA9bV2R68dBjVGMci0U38/UFq6GY8/frVRf0RNbCEeZ9WJUT1+AGA1MjKOIS+vAMPDelrN\nTLfR7FV79qj3kaEz+I2O/g10dXzyZCXy8m5DenpejM6RKQTr9np4+ErQ9y4a/dowPHwBamr+HDk5\nX4jGHnCqcfnyxaiqKseCBesRiai0hzthK1Pg0pw556Gu7ppYMpCenuPIyQng5ElZf6mqqlyTAYvV\nSRCEyAGJXV1bsX17tRIvUY7xcSAr6yXLMz766GKNIdP5uUSo766ysj460IvxNvo+AtC+u3fvaQwM\nMEPsNeCLI1FTiS18voG0tLkg5DkQstZyfWAzIhEx0O2PQZMEiYFclMKNRKyZwbZtq4zFyjQ0vIDm\n5vdw5kwEubm34ZxzstDb6z5TWCJIyUAvDvKAPKtbV+RHIVd2B+wEm6zug0wt7x4MDJyEtaO2QRzk\n1fK4VaXkgRlMZIsLHwWDncjJKdSs3DswNDQDfDUoPuP3APyTdHQk8kzMVe8f//E/QVX7doN6fBQA\neAaDg5SvDIdrUVJSg/5+YGBgEOPjEK79CejKswmyl4C75NRu1f7ceficj7GxlejvVwNaOEKhMdCd\nq/43O5h2j4FABNbn3QHgYpw4cRfYu/vTP92N8vIChMPp6OlR0wuKCeG/IHzH2+vJk/U4eZJ5U9Bn\niEQuwauv/goLF3bgwIGTsAZtifXEFwCdnQdig5iT8JjO/RGgu8i6umtsVDZZEOCz0EGf4a0cJSV/\nhzlzdksZu9TJNR5FWRVyEFQzgH+Qfmd9ROy7lZX1aGtTI9obAHSC9jHRa269MMEdB3A3ZNfWSvDF\n5g4AvwPw30A9d8RALnNfAmCx+QBAdvbDePRR6nXGJuisrGJjYNlUh4XnBDbHEuNaA3puVj5TT5GM\njCptdhYTb5mTcx2hnLbJm8SeX2Mcm0kkjSUbMPHenIvTcae6oA2ztjwVihJ5Yb09IhhcTeQALVWv\n3C4Ii1+nsLBa4mndilo58+rq/c0eC3ZeOCbhNTtOuLGxhQDLlGfQBeoRkp5+H2lsbCFlZbUkPf1a\nTVnFd6DWTaP2mqHQOkGj3KqfBKzWnme1n+iFx+z6gsqbFxTcKrRXxre75f/113T/PvR2FadEP7QP\n3GHsI+rxPMhK9DZj71/k80WenHnSiNffREKhG4X20iicL/Yf87jipJljard07EwOUuR1o0ocBHDg\nQC+amnbYBPTIK6WxMSASkVcngMrN0dVQZuZ+nD49Dsppqxyd3rLf2XkA8+evRU/PcRQXF8cCQNi2\ni69o6T06OvYiI4NtQQ9DTowMRCIbLEFbXKtbFxyUo/mOrn727z8J4PNCnRRrjnwZw8N/DboaYQFb\nYvANYNW2f0+5Bo9FEGUlsrJOacumbsHZe2looLLTwAwUFg4BoDuNwUGCsTFAlBimkP3Kzflur8Xb\nb3fiiSf2W7R3AHtOeNeuLfjhD/cqtows6FZi4+PPYe/eBmzZshLLl38fx4+vAyDmdS0HXR2uA92Z\niTB7U/zud8tAaTc5v0Ba2n7U1FyCtja9rIRMn+glmFtbO6IBUjKHDVRI7+nttztx+nQReFDSe6C7\nEzEgkXHWB5GfD2RmPix5hNnLL+upUFOuWurh9M9RTyJa7j17mvHYY50x2wn3YFHrmkLdIXDpAnEM\nqQfAvNZEeyCLuWAS2NbYkECgKurHnxWrU1pXYt5aPYU7ONiN998fAdf0ksF1fqw5MIA/054zWbgW\nwG9BW8wfa343rpyystZqwtW9+bmKMz6VN2Wr6wc1qyfmJSH6kbNVp9kX3d4jSOdrT/9deOEdUoox\nc9g0vbYuDJquwFYSvopUdz3sHyuDbpUhlruFAEtJWtpSkpV1DSks3KCpezerOh4LwHY78+aticqz\nflM6Tva8Ma98nLBzZ7thp0RiOy87WQbrymmpbXm45K7pHYveG7qVo/iPpVDkq3Km7shku01+5KbU\njtbnEsvL6mApKSm5zab+xN0J6x/rpGPC4fuk/MxedxF24B4tct8LBr8p3cdrfATdwYkqleL5mw3f\n6XfV8+c/SHbuFJVERZntdcQkc1JQcHfUC81+RT9v3hrLufRz8lb06c6H2CIDwHbQwf6LoHoAGgfb\nYuhWOXRVNozSUlGJjnoMuDVQAXQGnzUrjKGhZQDaQVcrR8BDvCtBI+F+BMqRrQLNQLQSubnfj3on\nmDi23cKu42XlmNkAXoI+QrIDx44Voa9vAwYG5qCv7zJ0d3+CwsKN4CsCjtLSXXj00ctRWdmAxYub\nUFnZgG3b6OqHJmMpB63HFwAUWc6n3jSAOfKR1cE7AF4BIa8gEmnDjBkRLFiwAYsXN6GwUBcyT706\nwuGHY89Fr/NCNBbgauzbdz727avBu++ei5MnF2Bk5K+Es1XPG3f+8DpQSQGz//bgIDM6V4DLVbTg\n44/fAUDbybZtlbE6LikZBfAbY3normQraP2J77gDdPX1OkKhMRQUrIje99sAfgBqP4FyfDuojWVz\n9HpbADQhK6sXW7ZQLw5rRiOK8fHj2u9PnDgWqxe6og6CGwi/DbpKvwQHDwaxYMF6NDS8rKm/cgCL\nkZZWG/07DBYtytDT8xxmzToHjzxyNQghePLJ11FZWY/W1o6EMiS1tnbg/fd1thNgePiv8PTTfDfO\n4yPYTqgJQAMuu2xU68Hz5puHQaPIGcTzmUKq+N3HMO2qL7ggF1VV5di8+ToEAi9Fj98N6tjwewSD\nT4DuolnZ1gKoxuDgQHQnVAFuwGXoQDB4Bw4dOoHf/lYUcGRQPyeGRKmbK0EtUx9EP78M4GYovbmw\nsAf9/V+ADlx/RN7uHzvWK6j5cej0LZqb26IBOSyQow1c+Q+gL7MN3KWMb3+zslZFv9NXBTOS6BU0\nGWXTAb3r4AbIHj8AsBQLFryCM2dG0dNTg+LisGOgypYtNVi9+mH09OSANlKrdg5wAtwozP5XJX/F\nOqDo6XkOV1zRgF27mqJGLOvWPxgcAzAAHjYeBDVMAXI6O1VmFrB63jDKQzaun3POGM49t1obzNTU\ntAPbt7fj+PE0UArLilBoDIOD4kDHKIhRHDzYhQUL1scySYn1fNddf4xXXqnF+DiXnWbURHW1KOEr\nSub+M1gqu5MngUDgJsgdU9W0Ye3SrCvT2tqBI0fU7Fk0Td7MmTNw4oT8PbAJhJwBIDokBMHfh0x9\n7tvH0nHq1DvX48tfXo3zzmvA3r3dGBiwHiHLOlBwRVArTBO3aCzv7DwAQjLgPYMXrcdw+D4AIYvs\nB68TceBW3XtfALAXaWm1IOQ50HrTuQBzl1GeeW2HkHntVuzZ0xulOtn7fQ3ADzA+3hT9zL5/AcAy\npKUdR2bm5zA8/A/o7OwA70sTh0QH+gtAp0KGbgD/RT3ohz9cjzvvbEEkYr0AaxCDg+ejv59Gm/X3\nU549GFwjRHOa9S243jcbnNhKXhxU7FJ+ASbunkblsUnjEuV3s6/9BRcUo7NTt1L5MWbNkv2jnVBV\nVY5nnwUaGl7Avn16fZLs7JuRm9uDnp7dAH4JOgn9LdiEEAp9iIyMUZzS0O2sQ1111Wy8/vpLSq7Y\ndRgYGEZPzwugkZo1kD00Asr/Js8beQLJzb0FCxZ8GYOD3Th8+DB+9KMLIAqEbd26DqwDbN26P+oD\nXw+raFQb0tK60NtbiJER3UBHBaT27fsUN974NC6++Fk0N/N4gJde+gvcfXdHbKExPBxBb28GNmz4\nEKdPDwrPwer6KdCBXnjC0QXWSsVRZGTcjNzcAoyMjODUqRLhOlZdGVkMjwqUATNw6tQAzj33Iljz\nGVyLvDxqz6Kr3Q7QVSNbsb8MdQChGkBW3f709O9hZGQuCCEoKZmpleU1uQuXlYk6NPR9hEIfobc3\nxyISJvfXNlAbieheLC8wVOlogPP9LJeuGLch2gZonYjPyspxDTIzL8bICG3DhFBNrPPOC6C319ll\ntKlpvSXuorJS1DMS+7wquUyvc8451ejr+yvheP3iZSrhdsi+issBPK0cQxobG8nixdeTQOArBPhZ\njIeySpTqsznpvG04PyhyZkuJzDmKfGg10XFkZWW1ghaMfG85AvZBzTFOUsnx89H2nKaVK87NvTXG\nketTFxJNOjvKYzOO2MS3Ul0b5qHA+EZ2DVav5ndIoz71kZi07vW8e1FRtUE3poXQrF1yth7KPzcK\n5VG5U1rmzMy7pShpWQ9ok3L+Q0q5dJnF7LJisXZkLwcs68iYoin1PDjn3sU+oG8n1I4lZviSdY8K\nCm4lGRl3SO0jHL7XmNKQpbyUUwCy/r1Jw+fr6vgaQr2OxDr8BgmFbjFGtOv7gU47idtDsrKW2p7n\nNi2nCtn206g8h9XrSK5L0U7ws+jnRpKR8RWCJHL0ia7oD0EmLz8HuqqX0NTUBADRBBu7MTS0R9Iy\n4Too6gq4HJFIuSVCkIFuz8RzOkGz8SyGGkFKt3my9wDb+tHk3i3RIJMa5ORkoLc3F5GIqBKZA+vW\nuwfB4Dej3i78mr29IQwPjyE9vVfwZ+fw4kes+oWvWLEIP/iB+BwdyMj4O5w48RO8+y7ALfdWhMMF\nyMxUdTuAI0ceRlPTDoOsLTA8PAjuoRAA9Rp6CTJtxSgjdl26i/jiF3Nx/HgIBw/KO5uenqcEb5J7\nYs8iruoikSFkZop8N9ul7QewACoNFYlsQHr696J1ztoGiwLlVMbIiKyVwjluRj+x83mQF1th00A1\nFRUKBSD6b78WjSKVPW3U1aKsI6PasqweXOLutqqqHKWlP0FnJ6uf7wGYpylnOS677AWcd97uqH7S\nccXLpwPHjxdCVRk9c2YjTp/+VL0YAK4Iak1ibo3JsPZX5gUWBl8vdoAmyLkSQ0NbMTQk6wxVVZWj\nqWkHDh7U++hbM4XJvv5PPvm6VvJ4aCgjbmVT+0BLQPUqa25uE3SlRG0mlnltDJdf/mXs2/dLz2Ux\nIdGB/hegfMZFoFxBNahBVguxImW3LLb18WbYoZ1DPGc+KG1xBHQyrEFmJvClLxXh8cfvAWC/9Sso\n2Iznn69Ec3MbPvzw25AlZq3bwNLSTVi+fE5MJsB6zR2gwVGM/7Wmt7NrWCbXNSbtq09rp9Mwp5gz\n5zwEg32CFCxFT88t0XSBeqPyyEgmgI9AB7ynQOuZDTqcf0xP/wDp6TdjxoxsXHppIR5/nFIkS5Y0\naTpXB44fZwuWCHRRj0NDtcjIUDlgZhdp0pS1HHPmPI1jx9YhEjk3WhfMkGkOaKEDEBPBYhDrkEoA\nU6yGyuMCu3DxxcdxySUqx63ek3bkoqLf4vnn5QAjzkGLAVr8uWiAktlNkafAXA8a1GPlm0Ohddiy\nZaUhUxYrryqPAPT3L8WpU9tBjcm8vxQWbkBdXTUA0U5glvGgxmbRtZhNTO87lqGn56nYpLF9ezs4\njSrfb3CwJ3aObuCWg5H0wWnxwBxoWY7S0l3Ytq1Wuja3N6jjCh0jRkZ0LtTxI9GBfhTARtAemgE6\noundKhTIPs86v1QO0wr4gQcq8MYbIvffBjWX68iI7G/M/q+srDeuQPTqhPQ8O4176zWp+mBRUQ3C\n4XxtejuxTCpMfuF79zagru4aNDe3aSIXe6FLcBEM3one3lk4ePC05k5tguaHzqj84+izlIPaKj7S\nXON8jI8/i/Fxa05PziGzDtkNIA9jY38QPWIxdJHB4+PPYdas2xGJrIsmf2gD3zDqJ7PLLvsCduy4\nJmrP+AhAYfQX8yKCe+uIE53YJsV3sBJ0xcn58nC4B83NDwpRmexYfdT2/PlNRo2eVataNBHVdJK2\ns+vIxkqWuhJSOWfPPu4QyWwaDtowPLzR8tynTqlaTOZ4mYUL50eNzerwcBhAifDZPCSxBR9t82L6\nSXl3ajdgy5G2soaRqkfvRXmTwU3sQFVVOd5+uxPbt1Png7GxXpx//iqEQiFpjAC22d5rqkHLa1l9\nhlnG9FoLp2XHlclKgCo/RnnGwsJqFxnjOedojdalHF9RkfU68V3Tyil6ud68eWsETnCFUlYxKpZp\nmDSoTrAAACAASURBVFcK/vK6cqj1Vh+ttxqBT2TXXkmskb3Oao3WCFmVw1ytvcbixY1k2bJHhXwE\n9qkcxfcj+2iby8hjOaz8elqaGo1J22lGxk2koGClJTpV5mvdRara5yFw7gPitSor60l29vWWugEe\ni9li9GVl5TW1D+d8AtxOYBcvo0aRq7Yve59zQkRbk3P6SVa2kpLbSCBwA8nIoPEjWVlMw19vr/Kq\nvKl7F6ZoX9O15Xa4mWAKcfRxw7qaoCse5uZlmg1VNDWtx8KF1GvinXeORhP0yjRAfz+drd9+uxNv\nvnk45tqlA72nmuCYIBQ6iAsv1CeWZjD5QcvJj2XY6Xebysg9IJiODVuFsx0N08mmK69gMCOqdQ7o\nXcgOCLsiq4Ab5xPzAcyE1fNFz+2zZ6Pp2MTIYZ23ksaXFrTu+voyBfdHtfzcFqCmBPzc50pw8KDo\n2sZcTSmYPYXvcmROPiNjHDNnjilJu6lGytgYcPy4vHMB5BVdd/cxHDxo5tZN1JyYh8BNHxDvzaiy\n9varYfLSEZGXdxSFhctASBDnnHMGn36aiePH1VR7zCZihciJUzuBPl7mgw9WRT/NB/ArUIb3NOiO\nSWwHxwD0Q+dmWld3KwBg48bF2Lp1HUZH9ZGyYp9qbe2IRjefB0Y30ra+DDq68MCB+2N90El507Ti\nd4oWNl27sHCVUqbk+dKnbKAXK2VwsBsDAye0Ak0ih6g717SFGhw8H6OjK6HfbtNEHJSHZhRFN2iH\n5q6CrOM/+eTryMs7ipKSGhw+XIihob+MGYV06cZYGU1+0HV1txqFikRaytpA9HlReWKLNtBQBtap\nGa0huvB1YGhI9AfnnYolwuDSqXzLnZV1AIsW0eQudNJLA+Vnxe0586vXp9Rjz2YNqtG5nXUYDY6y\n4qK1/Dr5ZMCUjpEaxi66KFOwp9QrZ1JOfmwMOHFCfAfOInBiWw0GaW7g/n46kJaUyPlp7ag5L+63\n+ueW3TgBIBTiAUjWHLxAUdFmPPjgBXj11V/hd7+rwunTxaCyxUxOQwSdBPbv/zhmb6J2Ajs3ZjUF\np+ouS8sbDN6JOXO60N+vz+vL/Nm3bv0/0YWduUzNzW04fjwTqkQJUAq7xB9OgWB2g7nTJGG6Nq0j\na5nOFihbFVWSQC/Q5LTNMYdhm8LVdVt+fv+SkmolaYazW5sI2UXUGt7uRuBJn8qwlgD/jQDXkfT0\nO0lu7q2Ci5i6pdZteZ23woTokmHISUDk1IHsGW8RPutTRFZUbCaFhaprq+gSS7fNWVlLybJlj2rd\n26wyGfTfggXrHbfPpjq3thk7uoUmknEvRWCqE7nduk2P6IYK8Er/OFGJ1t9FysUsvmbqM2VltZrf\nGoXr8T7DBA+dQJOo2KVF3BSlHnXvrZ3QhDH6+vdeP/x3PS29meTnryIVFZuN7Zm6qIpU7FlG3cgz\nnDhj6QWazOdSdHVtRUPD6tjK6Te/EakDFgGqgkW16u8/MFCNvr6npDPswu1VHD7Mri+vpFgScDdG\nGn3CiwWgr+kZjI/TJManTi2Npp4rgLwi0nlafIShIaunSCi0DnV1dwGgq5Pt29VkGLIg2MKFbYKR\nkZX5Q+UzDxhbvvxrQsIK1chbjoKC7+P0aZ7eMBIB3nprM7Ztu0bTDoYt5Qfuw3vvfaqNimSQaRRZ\nBpa/L7n8GRm/jwqvQfp9/nyqw0/rQO/pYW7ncn2aJYMpdNHfptUjAFf0j5iWccaMUeX5OVjbtq46\nqWNBYeEyAERJes13Io8+uhhPPGHdmW3ZshJ/8ic/MaSr1AeR6aAyA0NDZyBLEMtlKiqqNlypHOnp\n3zG6Py9aNBuvv75OCR5ci0WLrgBg72V0wQWzhO+PgTIMz2BgAGhro5Licv4IXkcNDS9rA9YSRUoG\nernROLthmc9l6MCBA5mCh4u69bYOeGlp79E50nD/SEQn++O+I3Z1HdEeq+ZQdZczU1SerIYYMQoA\n4+M/xshIFcrKinHgwI+iGj90kA0G9+Fzn1uFOXMujmZ9ysG+fVYPDKYRwvMB2E9qNGpWbPii8h+g\ncvtvvnlYcjFj92f+xL29YezbZ010ocs+lJc3B5yeygClqApw4sTfSCqbgJVS0+m0d3ZS7ykZtPwF\nBdVarxfW+X/606UYH78EYtv64IONGt0XZ5uMXSYqEXZUACFqJi4r/dPUtAPf+c4+Kd4jGLxDWz7W\ntvWTUDmuvJL6pctumfzZmM1Mt6CR/ccBU85d9fnZ4H7o0LGoVwqrr3rwGAkpaW4M4XABxsaORRVI\neT1nZKzB0qWX46239DknqEcbj5IFxjA6ejf27t0t1I/Ip+8A0I533x3Eu+92gubVYGqyVtmRsrLV\nKC7msi95eTTX7ZYtNZY8GGcLlG3O/dptlqpWx6Df5ugoDmv+Uqa4V1ZWSzIybiDc+0KnQa6LJjUr\nSoqwRvyxZ7rDQgexLa5Jv5vn82TbPz1dkJ+/KnaOXTSfE2XE342braq4xV5JdDr8QC1pbGxxpCW8\n0BbWbbI5n6uuDem32fp3a0d70LZo9vSw5hy2Kmk6RW7qctja1ZVTPe7c2U6CQZ3aaTsJBr9JdM/p\n1G7iVaw05RlesGB9LL/y/PkPavoE60M67X/2vb3eu+h1k5t7W6yeTf3Hrl5ZJHBa2q3R71k/0Hl4\n6a8je87xsYFRpZWV9QQ4y6ibQ4eOCYa2o9D5TFO1OmtmI52BMzPzA4yMiGfTwItA4EZkZxchEIhg\n7VouilVZWY+xsTDoCuIFAN+HnDcVGB9/SGMM3IXlyy/Hq69aZ14RdCVnXTVnZo5K2zNANQqz7/g2\n/NSpPlDPGbZL0QgEAQgEeIQmoVuV2P8inCgjfcwAe341k5e4xa4H9YGWVz3ASuzduxszZujbqP2K\nUR8zYV35irsye19oAAaawhyEpFuRAohmhyrRXIuuZh955GrBW2sENEqbr6IDgXVYtOhyAOoqnZY1\nEgH27rXSFnZ1pXvn7Dd2n+HhfO3zZ2Z+F1//ur5dOLUb2SvNXQo8/TXvAWDdcbE+0dDwMnp62M7P\nZNQPQNbTZ3VA6Um7iFfTbyYPusHBbsGI/a3ot+3geR9UYT/9uzNpBzGqtKqqHGlp39aeGw9SMtC/\n++7dAF5AWtrNIGQMJhEflfuWhZ74YBIKnVQGepofcnT0X2JRiS++uBkLF3YIVu6rwS3+34IV+o5P\nr3UoKrjGXTUBaLhWmWsMBldpRMTapEEe4DaHwcHzceLEl6PfsoF3MVS1x0BgLTZudHbjkr2VCB55\nxJoLVi47wOq5qOi32LZtvQ2fXAFal1bvjqGh15VBj0IcDHQJY5gYVlPTjpgbLI02zpPEptLTfxnl\nVlUenCY6X7HiOSxc2IYHHqiI1omeVjMFIek6f2VlfVQUzJy45sknEfPWev/9YRAiLyZGR5/Bq6+u\nxptv1guyHzJ09h+5riisaS3tJugzwtU4ZXnmzLglkQ+D6ulWV1fhehKwg6luTdTU+++LHUjXBpmX\nnZme9Iqmph14913RbZkiHH4IQFAoK1PHZEGLOmE//QKKe87JcCPvPFVBZEpjpe02y82W1brtcWsh\ntxc4c/amsQZW2G1z9bST/pm4Z4ouWOsOAlxHZs68mxQVVce2nXZbaLcBH17SvanH6SkBOYjGiVay\nimHp0g+aaJdGIteVKQhFT6uJqSGdAmGo94YuwUQ7ychYI7UPKmKme8/twrN6o59YXeooDrt6pm1E\nTEhi3ybcCpQlE3I/lwMdc3JuJ3bvuKDgVpKVdY3nQEsT5OQsVg86a1lFUT734oxu6C8kkbpJBZSH\nMXW81Qbu2zyQscYtu/7xf2a3t1qiKh+aGoY5s806SwdR88vOm7fGwgPr3c/aSSBwh1A+d5GRyYrE\nZZ27sLCaFBbq1QLVZ6ysrE8oitP8jk08rDzRsuxd9hMCEdqG2GlrSUaGrNoYDj9kW25Z+bOWUNe8\nlQS4VvPOGg3l0bl0Og++Yv1zXp9ms0pPv4HMnbvaOFlxu899xKQSarUbOE9CTnledTCdY1avJSQY\nvI6ogyawlGRn15CyslrFvdLeVdsNzKqz7dH+Ua3UyxoCLCHWnL/25XGzwMLZPdAz6Vfe8YLB27VG\nKLerTadBjQ1k2dnXCzO/u4ZhTexrv/qyllmeza2DYzvJyKjV3MNZdsGbL688+TnXs7sVXLzSrgzW\ncqqf9YburKy1Sl2q59H3lJFxk6YevPvl69O9PUZmzqwh1kFdX+a0NNVvW5XU5uUuLFxpGUCtstzu\nJwia6PxWonvuefPWKPEO4uTqlKzcXXtxitMwTzBrCHArEVfW4fC9CRmFWZ3oJh3aHu2cPfRpA2fO\nvJHk5t5GgsFvEOA6MmNGDSkq0hvXxTLY9R2c3QM9raycnOtjK8iSkqXGbbSbgUTfiB5TGhHRvEDn\nhrFzp5pR3kvwlv4e4jPl5t5sc2371bHdROglyCjRvJ925XNa9Tmv6HWDIS8fq0s5KEvtmOqAq+rX\n0H+FhSuNz2L1OqonNJBKl3dWHIydtNAblfNkLy1xpyEPQva7XbXeZUpCvB/TlxIDDe3voc8hbNbw\nKSurJcGgTsdfzjucnb1MKJdzXgovixmxTLqdtpwf2invhDngKRF9HBU42wZ6le8Lh+91jGhzWzlO\nbmrytlCleOiqYebMm7WuXQx80DRFTS6NdSp9gga67dMNeDTxt1ge+gyBwE0Jrah5YmuxHFZhK0K8\ndxhv78X+vep2QDJHT0hmpt6mwsrX2NhCQqElBLjX8J5ovRYWriSVlfUK7ysO9DUen+cxm2hQGk0r\n0lw67ls+135ylmkF/Tszue1ZbRWiK6DqFsg+6+/hJkJYdiu+X3Mta3Q0T9DiLiLdKz3Jxwn7hYM6\nnlgXBvp6sUaA8wnAK81FSHIH+pR43fzDPyyTLPS9vSFBs905gtAOTm5qXGtclaHlmi2nTxOcPr3V\n4trF7s+DGFStcHoNmiSbfmMNxKHH9Pe/HD2mA2+80YLS0p9g9uwcjI6KXgXcgyU3d5nj89t5RliD\njMzCVl5cHd3CjSgUoE8RNzBwAkePVkWfKxvp6cOKlxUvX1PTDmzZsgfj4/8VPLGH6tFC6/Xyy5uw\na1cTFixYjX37rDlYL7rI6jorQhQAU3VrrNGgu2JeS62tHVi9+nn09BSDRkpWIzMzDV/6UhFuvJHp\nDG0FoMnzCOD996l7qCzL7c1tjwpmiZ4p74GmG2yCnH5RrBdV34YiENC7/LL2IrtEslzLqiBgG+T8\nvsD4+A5Ql1R3EelO3kgiaHtk+X7N1xcTlrBo6jNnCE5KHrp610uamAZQJbk7O9MwMsJdJZ3kyScC\nKRno1YQjy5eLmvHeko2ocArlpoOYriGrSa051AHJrBXuJhuQNeOQqEkfDF4PWML7nQcdJ9dKN8JW\nDHYdJh5NbsBdIgoRhBB88skRHDwYkJKqMzVSnbhbXd21WLWqBePjfwA58bsaKc2enQ5EW7asjA68\nPHNUMDiAm26q0J6nEwBjqpWtrR14883DKCkh6OmpRnGxNVdBQ8ML0axevLOPjGwGIUelSNKf/vS4\nIL/A621g4GMsWLAeeXnnobh4FN3dazA8vBxe3Pa4iyVrE03Rz2LyHtlFMTv7JHJzraH6y5eLkxP/\nng2wskvky6AR1Kqb4UlY+89h8GhSuQ7UpCKANzdP2h5ZHl379qFGU8vjRgdoXVpdL4uLs9Hfrypi\n1kuDPOBtIXs2QbN9chLicm9QcZNPUxYKYlsytv10T1tYt+/m7bPeI8gkWnYb0Rmb7ODGAO3FI6ax\nsYUUFS0l+fmrYkakRIy0pmjhrKy1FhuM1YZiFhZTKSpKI5hoAfOz6+w64fB9WluRqa7dcrJ6UbfN\nJCPjTuk+nG6ztzGEw/cJ0aTVrtz2rGUVaRpzH9K1C/bedJThzp3tJBAQtd7FnAAt0XvdTICbNO+t\nUTjPavB08oxybo+iB1Y8AoP1yrPJrpf68cj9+KICSaRuUgFN5dk3ZLcueubBZI10vr2MgrvkBQxi\nA3djlJIbjPjSza5YJokEEdztUw6xFxuQW48Y04Bup7LnVL7GxhZiSlLuXD/mRNQq6DtwPzHo72tq\nh3TQNtkwTJys2nasdhhz6Dt1hXR2G7Vrn6YJXhy0c3KuE5LRWKUszHIQ5ome33sp4Zz/Zs09mL1A\n7T+qVIr753bCzp3tJC1N9MAS7WE3WJ7J9M6d7BNWG53398f6FpI40Kc08QjfzqtbxF/j0ks3IDd3\nVjStWxBPPvk6mpvbbKkCk/RASYnMf+mEgsLhwxgaWoHjx4OwS3Kgoy5YNKU1P6SVI5RpEZFX1ato\nErJaUH2k0HF6PP2duPXdjMHBo7FPdqHfaoITOe+syOuqUAXl9OV7883DAOZq7y1qessJyZlQlD6S\nVWcz2LhxcZSjl5NlZGTQRDG6aGBAJ5ZnthWZ5Bw4JytDpR0vvjhbUCQ032fXri149llgxYrnhATT\nqqIppTLeeus9bco8E50B0Ahv8T2Hw7VYsID1u1GkpdG/2Tlu7SwM/PjVAHpA32ctePQqo95OgeeL\nFaO+KwSKTswty2GidJ0oxqqqclx8cQsOHhS178sBbMKXvnS+Jr+Fnod3sk/w3L0M7oTb2DPIdOyf\nau81VRGbrbzRDXS1GgqtMAbweLW6q6tbOXUXD6bJzb055vKlEyXz6v7JjpHdupxWieZIXELi12i3\n1rObsnhfoej9kfmxZt9pUzq6NcaVZGNjC8nJuZ6kpf0RoVt++/el18jX1wETsXIf+axPZcfbkfk+\nDFZxNPudgNO75s9rFlnTwas3Fj++kcgrdtXjTXWF5SvrxsYWjbusc9926+FFd0z2NCk/TqWOvuUY\nJKgrSzh8LykpqXYMSLSOZ1ODurkTwLug7hz6PGMUDi9Ep6Rov70V/XOtA7H7yEx9ggD30grxQO/3\nLQ6uK7XPr0biJuIS6ey7Tv/JvC4dJNLS9HSVel8nWs38rsUctd6SUXhfSKjv2l5tUp3QvdhBnN67\n6oNuLWd8MSD8OrqAr0229eo1vsKqhCrWsXgtZ9dfL3Wb6ILPfD0rD+/mGurvbikwa5+eGgP9FwD8\nAYCfweVA71RJ/EHdG7+YYSqeyEz34ffeB1MnmBoyDapxbriJBDk5T3BywJns/+3uvk7xDVbNEHpM\nevq1SXwu+X2ZDGw0aO+2qGYN/z0QWGsb2cie00tksNsBTLyuHEwk/2NRrTp7ify8+gm6qKg64bJa\nj7fanzIzbxRkkZmx1Xll7aZukx0HkqzMXwxu++pErugT4eh/G89Jdrwx9+fWF+uDD07GVCQZenqe\nwxVXNGDXribPZbG6FdrlNuVw41/uhjMErFxqQ8MLAD7SXlPkJ734EKvQJ2YHiopqMH/+Fyxuas3N\nbQInb+Yc1WemWY52C8+3waCGyXO6BgL/geFhs83E23NRsOQvVsVI7l8/Y8YoDh6U3eBGR5/RygaL\ncGsHUduAk0uget3KynohwxdDBw4eTMO77+rtJbIdolhbxuJifYJtBrvYARWyD/on6OmpQXFxOOpu\n+t+l5x4cTENa2qdRmwBQV3ePYx2YkOw4kGRl/tJnwAOYrWXv3u5YbtuqqnJtn55K+BkcVvRuZj02\nO9qJKnHhr+StsJknwsyZNxPgOtcrXVP5nUKsnUBXE/cTN3yq19WkeJ6XlZp+B1BP8vNXOdAYbjw0\n+PF2qoHxPpcchZ0cbaD46zj+cHj7+tKvFPVcv7udUjLK77bfJ3qe1/bs5v6JaGyZXVnVMYX28czM\nG0lu7q1k/vwHSVlZbYyhQApX9LsB6Kb8TQD+xe1NVqzYjP7+P4p++ga6ul4DYE771tDwAg4cuD+a\nIo97loyO2gc6eEVra0fUE4EF6FRCzW0aDv9PzJ4teyOY9Lv57G5NH+Y2SIKuJuYDeAly5vpvYtGi\nMulYtyseFV71xPU7gHIsWsTT1Vk1xa3a8E47mkOHiqMeC3KgF8u7G88uSY7CNu9Gmpt1eYbjb1tO\nHituA9HE4/Lyjsa8ZOT6YpBXilddNVtYIbr3/jCXvxKrVrXE8ucyvX8xhysQRF7eebE8Aj09t4B5\nCr3xRgsefbQzlhBIB6dAQLd1o+bIdRvoJ97HqX/o05zqmAex7sXgTTrmjIwQjIxsRWfnHgB7UFj4\nr7j2Wn3OjsmE44rey0pCnFWtfuo60advJRhEoZtx6wmwhgQCNxj1b8zXIiQRbl8fdOGuztj58ayi\nnK7ptMKR/Yfj8xDxpq/Pha7sJHplH3b9boQQurNTNXYCgTWOHL0JTqno4s8VwI+T68usNCly/W68\nP/Tl1wdumTWr3AXMeWkD5rrhHnolJUtJScnSlOjpm8qql01vJ4WFNYIfvrM4HZK4ok8GfgbgKza/\nxz3o6RubasS5L+4XKLuD2Tdqp4YilzUxbx29MJpznSW63babJJxoIjfa8G4md9OE4mZQU8trpQHN\nZTGpU8brYWU3YMVvnJOPk+tL9BRhlB93Fa6o2OwpAMqdZ5YdNdQYVztwS6HZB19688KJd2EUj9st\nL7dp7OHPiyQO9IkYY28F0AzgXACtAPYBuM7tyWxLbLeFtVIGbaD5VDl6emChRJqadmD79naMjmYh\nEIhg48bF2u0iv77uPt6E1uSyesturz67NeiCwolG8BrgIt6fb7WfEs7lW2YnmigcLkBfH3vm+PSL\n7LbMTz4pirE5vx9eF6pQl/5dWHPisjJbReDcgBvWKsGoi6ysA1i0aDH27NEH46j1Y6IG2HFife3d\n242BAVFnhf594sSzMcG9N96oRiTCAqYozdPVlYlVq1rw/PMyNeLsqKB+p3Nk8N4O3BpCed2IbYH9\n3QRVJweosNzXC02kg11wGg2ktL77hQvnR+s1LXqV5AsKThY0qy+dVrx1hWH93Xm212/B10oaHVY/\nfHWF6G5VYe/Tr9fQtl8NqIkYrHVmh8SSjehcD/UJMHSQV8TufMW9rKS8UmMm983CwpqEfbHdwpRs\nw22glZcyWRPk6BwaVikrX/uVvbiLk3ds7HrVhvuxY7xTkNZ22ULS02+IptHUyY+L77kxel81KxUh\nwCaLUX+i8jAQ4pxohbssm7X3kcQVfSogdTQxY5LXJB1yOjd91KhJf4bd1+SHLwpEuU2skIhPv5tt\nuVePGu8Dg3icOjB6o4D0QT76iSoeiklPU5if02sn9uLfbjdBib+b2pHVK4N27rlz75LyIthFYarl\noJr8onhfY+za1qAlvVebXapAXhaTTpX1nRcU3Cr4zpvrVK07lhd31qwqQlP08fPZok1PzbFALHdR\n4xORh4HBy9jGxp65c+9SJoezbqDXv+R4MsToQ5O5qp1JdCg/f5WtO5S+UZsbaKKrgdQl+3CbbzZ+\nVzzx/qLhTzfp6Y3s3q6vd199TBKDiydq2mlyTeYO1Pos+pWdOPizMplWi3IGK9OgvonoJwF+HROX\nz1yR5efhQWe6d+52waKrW5qIxFp/LMhLXhkTwgd4d31rIlf08fTvqRow5RqLFzdpXZS8BjpUVZWj\nuPhl9PTI/GxPz1MxftYkOhQIDBk4T71IFw32MbtXWa+lD4IQoQqJeXl2J7Brh0KfoKhIr4suwira\nJNoVzNyqnU3FicdnnGhfn3NiCdN9xLwGIje6aNEcixicKNrl5ELqpvxONhDr7/btmxCCw4cHEIm8\nDDkvAs9b8OGH9JuCgs2oq7sGAPDEE+0C187LUVa2GqWlqjulmCyHPRtLKKK3dWzfXq0Vudu7twHz\n518W4/z5NWnQ2Z49Tdrn9Z5AiGJ8vEh77OhoKHZd5qpK7RSnMTAAuOW9Ewk6dEI8QVym3BrJQEoG\nelMDiKeiR0aC2u8PHToBgKoZbt0qJ6kIBNZi48byqKKiijYMDf2l9E1X11a8+upqzJpFQwgIsU6s\n8ovkRrCBAaCtTc4ixfyNZcOPOZmGV9AMRv8sGVIzMx/Gn//5NcZONjDQBzmZQhuAd5CRUYXMzAwM\nDVnPGRzsTsh4xTuzfTyEGyOZLnJUHSjcRk279Wl3Mo5af9cb5RctmiM8HyubeK7Z2EwIQSSinyjz\n8uZgy5arhejTo/j97z/FiRPiUfS5aHIcfVTs6GiW8TknIhsZYKpb86JNBGsLPHrYnTOE13gSL/A6\ntrW2dqCrS6/aerbAdovjlYu24+AZ6BazOposoVoyxKrbQ5nXZFtRMWEy5S9FnRbrtXTbY/lcfWJo\ne810t/CqZLlzJ0vGwhKfrJPKlJ5+p+UZgsHbDc8QD11lz+HHs6WOlwrzYi9wKpf+d+s71kesujM2\nO6mCunu+xww0DOtLphy4S420WaI+6vq6ayFWjt4a2yBy+7xsco6HZPvQu4GXsU0vAniWUTd28Brd\nKbvxMWxCOJwf+9TUtF7rTqmPnMwRtMLZyjwMQiogRuVGIjQv6MKFHVKZuWsbu4Y1F2YkArz//l3C\nPbjbVzicb9zxuIWcuk38Xr8VbG5uw9DQhaCruzbIUbxtGB//MWjKNR6dOzwMfPxxjfZ6bDflBL4a\nlHMIFBX9NpZfFfCehlC+toxkuqQ6rdL0v++Sng2A4irKVp9iVLb5WQgh0K1Ys7LWoq7ubss5dqvW\nhQvna/MpWFMFdiAQeAl9fa9E0xTuQHr6jQiF8pGVNYLlyxc7uu86Rafq664bV155DtraajA6GkIg\nMISKirl4883DWLKE6hNdddVshbLrQFZWNUpLGXW52tX4Em/KTDt4Gdv0uTXOLiR1lkx2YIt+Ze5t\n1WR1/TMFl3iPFHTjhmiWPK7RXpOuClnGH3X12EjkuhD/eVdANNe1eTXoNg2heF3ZKOd+pRmPQ4AX\niVp3OwPanrOzb1K8L6w7Sl6HelVQr5A9P2SPH7NrZeJRvfHWrVe9H7d1kExdonig39GcZV43yYT1\npTiHwru5ZmVlvRKe7H4AsE4WunPbSVrarZ4apdsGyHONitd9zCgGxn2u7dK56Z5Bp2n+mCutZIya\ndgAADsBJREFUeLWunRK1uO3AVrdOb9v1ifS8MMHNhOfkhx2PmJ238vB25hz1TWkdcTEyEfUqR8Oy\nfqaTG/DmvTYZbUCF7h3gszTQ61a09m528c/EckPytlIQy5Sers+Vmp1d46lRetH9cJM5Rzye2yas\nbn004MxuV5Kc3ZQd3MpAJNpJ4w1OSxROg3UqBx9vtgd1AaBf4ccr4yFC7Ptckz/5yYH0UiubYy7Z\nqVrZq20Cn5WB3mmlkezOIN9PnzDZzUvXr8bsNTB0E5rXSFcvqzy5LHJAW2Nji5YKkSV/J3ZQdPtu\nkxGPkOwVcjIwkcE8Xu9lH6ymf0/xxkow6APw1Ohf00TjrU161VFKFZDEgX7SjbF2cDKUObm7eYVq\nuNIlTHZjXGlqWo+FCztsNDDs3O3Yc25GXl6/5dqA3sDo1agtJ0ynvtClpZtihsOmJquvel3dPVL9\nJNMdTYVb97RkuPvFK/c8EQY8holyY4znXmK/6O4+hoMH1yESYW7B+j4YDhegoCB+H3W574vSvs8q\nR9KyFRYuw+WXXxpXm5TbmnedKx8Ucc9oVr0SyssVFlZPGA840dAZv9yHyid3BT0VV7Ii3PL5k0W9\nTKQBL5XP5fVeYhsOBPTRq+x9xdu+5L4v/u1OJyieOpDtdO520W7lMOKhgJDEFX0qEHflOyULd5OR\nPdna7MlAPKHy8XSWqfr8ycZkTFipWGSk8rm83kv2/klejggGc3asxKka9/c1v1enid7N7059E5+V\ngZ5Xln1CCl0DnQouUya40/pObNCYys8/HZBKDj1eTORELy/CkpcjgkHP0fPB3k4ZNnn3NU8k8QXP\nmZLo6PsmkjjQTypH7zY13IoVz6FfQ1cPDWUY+VWv2uyphNtQ+UQ0N6by8ycTE8mT2yGVHLoTdHUA\nqJIb3uQqnCDrwTvniPAKq73sqGIv2zAh7znRNIJmOQz++2T0zUkb6N3ombAGDJzRXsOuU8UTXZkq\n6HOwAkVFNZg//wtJMXIm21DtFV4G4HgH60QTRySCiRTE8gJTHfy/9u4+RI67juP4+5rkVIyXy5XW\nvZrIyWlFEWLU1iranGK6lWqlCFUhYhuKUCRRK23zSA5isURULqHBIiqptKHQBDG5cuSUuxyoNKJp\nrdrY5LTaxCTVmNBgSIPx/OM3m32a2Z3n+c3M5wVHdvf2LjPfm/3OzPf31Nd3ltnZnU3vjTOZ1I/h\n5I6zsI3kafy/3U70nb5/8WK2n82kuN4iBVsmLXhdrtPoylr3wcWLPzfX39957cwkpNHQlmVDdZCy\nUZQSU9aN8TY0ZgdbtzS+0pKfsmqRdfsMd/q+3+OWItTou9U424PxyBzcOTdv3p1NK810+kO4j648\nONfbW5u0q/56f/+queXL702t4TLpJJF2b5TGenCQPtRRknUe6uRJ84qB17QYcTcWh516ogi6fYaD\ntR+2x4wi1Oi73fo0lx5mgBPAk1y+DGfOzLBt2yPs2fPilWmAW2+1brvtZoaH97qsvXqAS5eup3ki\nrxnOnXsrhw+nVwJI+rY0ySlYW7WXD0Zd3+d2axqlxGRTnTwrXjEYGlrIwECypaXW+eCTPs5s0+0z\n7PX9ND+bcfk28ALwHLAXWOTyHs+zYac5a5pHbjZe9bmNWA0yreyWufbujPHcfpalO2OrKL2IolzR\nZ9WH3iadYmBDaUnCw6LSzUrgKufxw85XK88daRx40TplQKWyumG4fS0xB5uDxu1DYMo5ndZLDVcC\nKHN3Rve5Qvwl4KjJWslMMSgqYkz0PXH9IuAO4LPAqpbXnW32ZlaG+Wbb68uX38O11w5y6NBRzp6t\nLbc2H7fSwIoV7kuZmdvKyYYl5wZ59NHfcupUhXp3xk00l3Lq//8111R89Qbx2odqdTMTE1u9dj2U\nrLoUenHf9xmuvnpnQy8i79WuWv9Gnd4r8bHtOJJmPT09EFOOjrNGvxrYHeYHveq0fX1LmJgYdWrA\nG5mdXYDf9SBr3OpkN9www+bNj/HSS18Aelm8+DUuXLivaSm+SmU1J0/2t60lW/udfvehW6056Ict\nyy6FXvwsuDE+PkO1uinUWrNSF1dytvE4SoqfmOmkB5PA8y5fn254z0Zgj8fPz23ZsuXK19TUVNst\nip867f79B53eHG5dJr8cy0i8xtvfTjNNuglTaw5T7sm6S6GXTuWDMpe14hRnHG09juLmJ2a2HJ9T\nU1NNuRKLavQAdwG/BF7v8f2uO+i3Tts8v0b01XU6CbPyUNBac5pro2apLEklaXHGMY/HURh+Ymbr\n8UmMiT5q6eZW4H5gBXCxy3s9+e1uVH9fYz03maHQnbrudbrNC9JlKky5J49dCrMepVsU7V2OzYjv\nQ4eOMj4+E+hzkMfjKAw/x16Wx2daJaOoiX4H0Isp7wD8Gmhblbta3dR1B/zWadOq53oNcfeaO95t\n2zrVpSHch82WofdBlCWpJK0ex9oi9uYYOHvWrHMA/uvreTyOwvBz7GV1fBatnSS3NVm3unNc05h6\nv6d710I/I/Js6s+v/u7xiHvagay6ZaZ5fPo59uI8PoPsW7dcgmU1+m4CH4i2JapGfmubQU4IaS70\nnBX19Y7H/v0HE5/HJklZHJ9+jr04js+g+9Ytl5DXRO/nQLQ1UdWkuZZpktvXyOYTa9ryEAtbGw/9\nyPO2dxN039K8ok91rhs/NS/b51FPcy3TMII2LBWtThhFXmKR5/p6kg2fWfeFD7pvaf4dU0v0fnfA\n9h4afnvXZPVhDHqCsf3Emqa8xMLmSbG6JdukLoBsOEkH3Teb/45hBKp5FenWLou6dNCGpbL0p/ZD\nsYgmyQ4I3diQN+LeN/JWugky10ueb0tbZTG0P+hVgro+1ikW0fi5I0rqKtaGSoDNV+iZrhnrxuZg\n5UWQE0yRTqxRKRbR+E22SVwA2XKStnXeJusSPdgbrCLK64k1iYa3vMbCFlkmW52kO4tzmmIvTrlJ\nJB5uDW/DwxsZG6sqKWfI/e+ygbGxdE6WRZvuOs5pilNN9Fl3f5JiSHPufwmmaMk2S7bOR9+RDd2f\npBhsaHhrpYsYQ2VXO6WW6PPSR1nsZ0vDW40uYsR2V3V/SzxsvAoT+9VmAB0ZGaVa3cT4+Axr197C\n8PDGpveZhreVmWyj90XMpMdPiKQrtSt6267CxH5eV8pjY1XGxqrW9I7RRYzYLrVEr+5PElSnct/E\nxFZryiKvvvqK6+u6iBFbpJbo1UdZgsrDlfL4+AwnT76GWTa5flKqVL7OmjV3ZLZdIo1SHTClFnkJ\nIg/lvu3bD3Dq1A8xqz5tBuYBlxkcPK9jXaxh5chYEchHua9+13Gz82X09Y1msTkirqIk+q3A7ZgZ\n1s4AdwEvx7BNIkA+yn15uOsQiTLq6k3AeefxGmAZcI/L+zQFghRW1sP+pbhsGRl7vuHxQuBfEbdF\nJHfycNchEvVs8RDwReACcBNwzuU9uqIXEQkozUnNJoGKy+sbgH0Nz9cB7wTudnmvEr2ISEBplm78\njil/Anja65ujo6NXHo+MjDAyMuLz14qIlMP09DTT09OJ/O4oZ4t3AEedx2uAGzFlnFaeV/Sa8U9E\nxJ0tjbHfwpRrLgOzwL1Bflgz/omIpCOzFaa0eISIiLc4r+hTm6a4VR7mMRERKYLMEr1GFIqIpCOz\nRG/b4hEiIkWVWY0etJCwiIiXNAdMxUEDpkREAipEY6yIiKRDiV5EpOCU6EVECk4rTEWgKRxEJA+U\n6EPSFA4ikhcq3YS0ffuBpiQPMDv7EDt2TGa0RSIi7pToQ9IUDiKSF0r0IWkKBxHJCyX6kDSFg4jk\nhUbGRqApHEQkKZoCQUSk4DQFgoiI+KZELyJScEr0IiIFF0ei/wbwP2Aght8lIiIxi5rolwIrgb/F\nsC2FNz09nfUmWEOxqFMs6hSLZERN9N8FHohjQ8pAB3GdYlGnWNQpFsmIkug/AxwHfh/TtoiISAK6\nzV45CVRcXt8IrAduaXgtjT75IiISUNjk/B7gF8AF5/kS4ARwI/BKy3uPAcMh/x8RkbKaBd6e9UY0\n+ivqdSMiYqW4+tFrjgMRERERkSK6FTgCHAUezHhbkrYUmAL+CPwBWOu8PoBp1H4ROAD0N/zMekxs\njtDcsF0U84DDwD7neVlj0Q88BbwA/An4IOWNxXrMZ+R54AngdZQnFj8CTmP2vSbMvr/f+R1HgbEE\nt9eXeZiG2CFgAfAs8K4sNyhhFeC9zuOFwJ8x+7uN+liDB4GHncfvxsRkASZGxyjelBT3AY8DP3Oe\nlzUWu4DVzuP5wCLKGYsh4C+Y5A7wJPAlyhOLjwLLaU70Qfa91nnmEKbjC8DTmAvqzHwImGh4vs75\nKoufAp/AnI3f7LxWcZ6DOVs33uVMADeltnXJWwL8HPgY9Sv6MsZiESa5tSpjLAYwF0CLMSe8fZiR\n9WWKxRDNiT7ovg9i7gxrPg98v9t/muTZ8S3Ayw3PjzuvlcEQ5sz9DOaPeNp5/TT1P+p1mJjUFC0+\n3wPux8yDVFPGWLwN+CfwY+B3wA+AN1LOWPwb+A7wd+AfwDlM2aKMsagJuu+tr5/AR0ySTPRl7Ymz\nENgDfBU43/K9OTrHpSgx+xRmPMVhvMdqlCUW84H3ATudf/9D+51tWWIxDHwNcyF0HeazsqrlPWWJ\nhZtu+x5akon+BKaBsmYpzWeiIlqASfI/wZRuwJyla6OLB6kPKGuNT23QWRF8GLgdM75iN/BxTEzK\nGIvjztdvnOdPYRL+KcoXiw8AvwLOAP8F9mJKvGWMRU2Qz8Rx5/UlLa9nGpP5mJFdQ0AvxW+M7QEe\nw5QsGm2jXmtbR3tjSy/m9n6WYk4jsYJ6jb6ssZgBrncej2LiUMZYLMP0SHsDZp92AV+hXLEYor0x\nNui+P4PpudWDBY2xAJ/ENL4cwzQuFNlHMPXoZzEli8OYP8AAplHSrfvUBkxsjgDVNDc2RSuo97op\nayyWYa7on8NcxS6ivLF4gHr3yl2Yu+CyxGI3pm3iEqb98m7C7Xute+UxYHviWy0iIiIiIiIiIiIi\nIiIiIiIiIiIiIiIiIiIiYpP/A7jtdd/lE1DMAAAAAElFTkSuQmCC\n",
"text": [
"<IPython.core.display.Image at 0x7f1a5cea0610>"
]
}
],
"prompt_number": 35
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x2 = Gaussian(0.5, 0.2, 2000)\n",
"x2.png"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"png": 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vnSEafcp1r9fjSFVRxFbvgNcQv3t3ba+XU0pKSlxjk+tGGnovu6yDkpKHCYdz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nPftq0Fg4M9EP42DtVsg16ZbnCwBbt2NeOOOzajoECnSegCEQ46oSfc/e53rXZIMNOizIRaCa8Z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\nOSXm+6VmGc4HU08qz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"prompt_number": 37,
"text": [
"<IPython.core.display.Image at 0x7f1a5cdc8450>"
]
}
],
"prompt_number": 37
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"display(x.hist)\n",
"display(x2.hist)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": [
"<IPython.core.display.Image at 0x7f1a79f90c10>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": [
"<IPython.core.display.Image at 0x7f1a5c7ef3d0>"
]
}
],
"prompt_number": 38
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"<br>\n",
"<a name='ipython display support'></a>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Adding IPython display support to existing objects\n",
"[[back to top]](#sections)\n",
"\n",
"When you are directly writing your own classes, you can adapt them for display in IPython by following the above example. But in practice, we often need to work with existing code we can't modify. We now illustrate how to add these kinds of extended display capabilities to existing objects. We will use the NumPy polynomials and change their default representation to be a formatted LaTeX expression.\n",
"\n",
"First, consider how a numpy polynomial object renders by default:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"p = np.polynomial.Polynomial([1,2,3], [-10, 10])\n",
"p"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 26,
"text": [
"Polynomial([ 1., 2., 3.], [-10., 10.], [-1., 1.])"
]
}
],
"prompt_number": 26
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we define a function that pretty-prints a polynomial as a LaTeX string:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def poly2latex(p):\n",
" terms = ['%.2g' % p.coef[0]]\n",
" if len(p) > 1:\n",
" term = 'x'\n",
" c = p.coef[1]\n",
" if c!=1:\n",
" term = ('%.2g ' % c) + term\n",
" terms.append(term)\n",
" if len(p) > 2:\n",
" for i in range(2, len(p)):\n",
" term = 'x^%d' % i\n",
" c = p.coef[i]\n",
" if c!=1:\n",
" term = ('%.2g ' % c) + term\n",
" terms.append(term)\n",
" px = '$P(x)=%s$' % '+'.join(terms)\n",
" dom = r', domain: $[%.2g,\\ %.2g]$' % tuple(p.domain)\n",
" return px+dom"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 27
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"poly2latex(p)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 28,
"text": [
"'$P(x)=1+2 x+3 x^2$, domain: $[-10,\\\\ 10]$'"
]
}
],
"prompt_number": 28
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.display import Latex\n",
"Latex(poly2latex(p))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$P(x)=1+2 x+3 x^2$, domain: $[-10,\\ 10]$"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 116,
"text": [
"<IPython.core.display.Latex at 0x7f1a5cb98f10>"
]
}
],
"prompt_number": 116
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"But we can configure IPython to do this automatically for us as follows. We hook into the IPython display system and instruct it to use poly2latex for the latex mimetype, when encountering objects of the Polynomial type defined in the numpy.polynomial.polynomial module:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ip = get_ipython()\n",
"latex_formatter = ip.display_formatter.formatters['text/latex']\n",
"latex_formatter.for_type_by_name('numpy.polynomial.polynomial',\n",
" 'Polynomial', poly2latex)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 117,
"text": [
"<function __main__.poly2latex>"
]
}
],
"prompt_number": 117
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Once our special printer has been loaded, all polynomials will be represented by their mathematical form instead:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"p"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$P(x)=1+2 x+3 x^2$, domain: $[-10,\\ 10]$"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 118,
"text": [
"Polynomial([ 1., 2., 3.], [-10., 10.], [-1., 1.])"
]
}
],
"prompt_number": 118
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"np.polynomial.Polynomial([-20, 71, -15, 1])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$P(x)=-20+71 x+-15 x^2+x^3$, domain: $[-1,\\ 1]$"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 119,
"text": [
"Polynomial([-20., 71., -15., 1.], [-1., 1.], [-1., 1.])"
]
}
],
"prompt_number": 119
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"<br>\n",
"<a name='ipython complex display support'></a>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# More complex display with _ipython_display_\n",
"[[back to top]](#sections)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Rich reprs can only display one object or mime-type at a time. Sometimes this is not enough, because you need to get javascript on the page, or you want LaTeX and a PNG. This can be done with multiple calls to display easily enough, but then users need to know more than they should.\n",
"\n",
"In **IPython 2.0**, there exists a special _ipython_display_ method, that allows your objects to take control of displaying. If this method is defined, IPython will call it, and make no effort to display the object itself. It's a way for you to say \"Back off, IPython, I got this.\""
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import json\n",
"import uuid\n",
"from IPython.display import display_javascript, display_html, display\n",
"\n",
"class FlotPlot(object):\n",
" def __init__(self, x, y):\n",
" self.x = x\n",
" self.y = y\n",
" self.uuid = str(uuid.uuid4())\n",
" \n",
" def _ipython_display_(self):\n",
" json_data = json.dumps(zip(self.x, self.y))\n",
" display_html('<div id=\"{}\" style=\"height: 300px; width:80%;\"></div>'.format(self.uuid),\n",
" raw=True\n",
" )\n",
" display_javascript(\"\"\"\n",
" require([\"//cdnjs.cloudflare.com/ajax/libs/flot/0.8.2/jquery.flot.min.js\"], function() {\n",
" var line = JSON.parse(\"%s\");\n",
" console.log(line);\n",
" $.plot(\"#%s\", [line]);\n",
" });\n",
" \"\"\" % (json_data, self.uuid), raw=True)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 12
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"x = np.linspace(0,10)\n",
"y = np.sin(x)\n",
"FlotPlot(x, np.sin(x))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<div id=\"b55666ca-1642-49d5-8177-e8d05c3e20e1\" style=\"height: 300px; width:80%;\"></div>"
],
"metadata": {},
"output_type": "display_data"
},
{
"javascript": [
"\n",
" require([\"//cdnjs.cloudflare.com/ajax/libs/flot/0.8.2/jquery.flot.min.js\"], function() {\n",
" var line = JSON.parse(\"[[0.0, 0.0], [0.20408163265306123, 0.20266793654820095], [0.40816326530612246, 0.39692414892492234], [0.61224489795918369, 0.57470604121617919], [0.81632653061224492, 0.7286347834693504], [1.0204081632653061, 0.85232156971961837], [1.2244897959183674, 0.94063278511248671], [1.4285714285714286, 0.98990307637212394], [1.6326530612244898, 0.99808748213471832], [1.8367346938775511, 0.96484630898376322], [2.0408163265306123, 0.89155923041100371], [2.2448979591836737, 0.78126802352626379], [2.4489795918367347, 0.63855032022660208], [2.6530612244897958, 0.46932961277720098], [2.8571428571428572, 0.28062939951435684], [3.0612244897959187, 0.080281674842813497], [3.2653061224489797, -0.12339813736217871], [3.4693877551020407, -0.32195631507261868], [3.6734693877551021, -0.50715170948451438], [3.8775510204081636, -0.67129779355193209], [4.0816326530612246, -0.80758169096833632], [4.2857142857142856, -0.91034694431078278], [4.4897959183673475, -0.97532828606704558], [4.6938775510204085, -0.99982866838408957], [4.8979591836734695, -0.98283120392563061], [5.1020408163265305, -0.92504137173820289], [5.3061224489795915, -0.82885773637304272], [5.5102040816326534, -0.69827239556539955], [5.7142857142857144, -0.53870528838615628], [5.9183673469387754, -0.35677924089893809], [6.1224489795918373, -0.16004508604325057], [6.3265306122448983, 0.043331733368683463], [6.5306122448979593, 0.24491007101197931], [6.7346938775510203, 0.43632342647181932], [6.9387755102040813, 0.6096271964908323], [7.1428571428571432, 0.75762841539272019], [7.3469387755102042, 0.87418429881973347], [7.5510204081632653, 0.95445719973875187], [7.7551020408163271, 0.99511539477766364], [7.9591836734693882, 0.99447136726361685], [8.1632653061224492, 0.95255184753146038], [8.3673469387755102, 0.87109670348232071], [8.5714285714285712, 0.75348672743963763], [8.7755102040816322, 0.60460331650615429], [8.979591836734695, 0.43062587038273731], [9.183673469387756, 0.23877531564403087], [9.387755102040817, 0.037014401485062368], [9.591836734693878, -0.16628279384875641], [9.795918367346939, -0.36267842882654883], [10.0, -0.54402111088936977]]\");\n",
" console.log(line);\n",
" $.plot(\"#b55666ca-1642-49d5-8177-e8d05c3e20e1\", [line]);\n",
" });\n",
" "
],
"metadata": {},
"output_type": "display_data"
}
],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"<br>\n",
"<a name='interactive widgets'></a>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Interactive Widgets\n",
"[[back to top]](#sections)\n",
"\n",
"IPython includes an architecture for interactive widgets that tie together Python code running in the kernel and JavaScript/HTML/CSS running in the browser. These widgets enable users to explore their code and data interactively."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 61
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.html.widgets import interactive\n",
"from IPython.display import Audio, display\n",
"import numpy as np"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 62
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def beat_freq(f1=220.0, f2=224.0):\n",
" max_time = 3\n",
" rate = 8000\n",
" times = np.linspace(0,max_time,rate*max_time)\n",
" signal = np.sin(2*np.pi*f1*times) + np.sin(2*np.pi*f2*times)\n",
" print(f1, f2, abs(f1-f2))\n",
" display(Audio(data=signal, rate=rate))\n",
" return signal"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 63
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"v = interactive(beat_freq, f1=(200.0,300.0), f2=(200.0,300.0))\n",
"display(v)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(253.7, 252.6, 1.0999999999999943)\n"
]
},
{
"html": [
"\n",
" <audio controls=\"controls\" >\n",
" <source 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\" type=\"audio/wav\" />\n",
" Your browser does not support the audio element.\n",
" </audio>\n",
" "
],
"metadata": {},
"output_type": "display_data",
"text": [
"<IPython.lib.display.Audio at 0x7f1a5c7ef950>"
]
}
],
"prompt_number": 64
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"v.kwargs"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 65,
"text": [
"{u'f1': 220.0, u'f2': 224.0}"
]
}
],
"prompt_number": 65
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"f1, f2 = v.children\n",
"f1.value = 255\n",
"f2.value = 260\n",
"plt.plot(v.result[0:6000])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(255.0, 260.0, 5.0)\n"
]
},
{
"html": [
"\n",
" <audio controls=\"controls\" >\n",
" <source 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\" type=\"audio/wav\" />\n",
" Your browser does not support the audio element.\n",
" </audio>\n",
" "
],
"metadata": {},
"output_type": "display_data",
"text": [
"<IPython.lib.display.Audio at 0x7f1a5cf8ce50>"
]
},
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 66,
"text": [
"[<matplotlib.lines.Line2D at 0x7f1a5c5eecd0>]"
]
},
{
"metadata": {},
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v9UvbZ1987WvADTeYcxIGEr8qQhh0VDZRERoUN5BjTKRPfjLZJ4fT/t1++Aqq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\nAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x7f1a5cf8c3d0>"
]
}
],
"prompt_number": 66
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"<br>\n",
"<a name='variable inspector'></a>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"<br>\n",
"<a name='factoring'></a>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Factoring Polynomials\n",
"[[back to top]](#sections)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.html.widgets import interact\n",
"from IPython.display import display"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 103
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from sympy import Symbol, Eq, factor, init_printing\n",
"init_printing(use_latex='mathjax')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 104
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = Symbol('x')"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 105
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def factorit(n):\n",
" display(Eq(x**n-1, factor(x**n-1)))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 106
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"factorit(12)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$$x^{12} - 1 = \\left(x - 1\\right) \\left(x + 1\\right) \\left(x^{2} + 1\\right) \\left(x^{2} - x + 1\\right) \\left(x^{2} + x + 1\\right) \\left(x^{4} - x^{2} + 1\\right)$$"
],
"metadata": {},
"output_type": "display_data",
"text": [
" 12 \u239b 2 \u239e \u239b 2 \u239e \u239b 2 \u239e \u239b 4 2 \u239e\n",
"x - 1 = (x - 1)\u22c5(x + 1)\u22c5\u239dx + 1\u23a0\u22c5\u239dx - x + 1\u23a0\u22c5\u239dx + x + 1\u23a0\u22c5\u239dx - x + 1\u23a0"
]
}
],
"prompt_number": 107
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"interact(factorit, n=(2,40));"
],
"language": "python",
"metadata": {},
"outputs": [
{
"latex": [
"$$x^{10} - 1 = \\left(x - 1\\right) \\left(x + 1\\right) \\left(x^{4} - x^{3} + x^{2} - x + 1\\right) \\left(x^{4} + x^{3} + x^{2} + x + 1\\right)$$"
],
"metadata": {},
"output_type": "display_data",
"text": [
" 10 \u239b 4 3 2 \u239e \u239b 4 3 2 \u239e\n",
"x - 1 = (x - 1)\u22c5(x + 1)\u22c5\u239dx - x + x - x + 1\u23a0\u22c5\u239dx + x + x + x + 1\u23a0"
]
}
],
"prompt_number": 108
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<br>\n",
"<br>\n",
"<a name='lorentz equation'></a>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"# Lorentz Equation Solving\n",
"[[back to top]](#sections)\n",
"\n",
"The Lorentz differential equations are defined as:\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\dot{x} & = \\sigma(y-x) \\\\\n",
"\\dot{y} & = \\rho x - y - xz \\\\\n",
"\\dot{z} & = -\\beta z + xy\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"This is one of the classic systems in non-linear differential equations. It exhibits a range of different behaviors as the parameters ($\\sigma$, $\\beta$, $\\rho$) are varied."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 29
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.html.widgets import interact, interactive\n",
"from IPython.display import clear_output, display, HTML"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 30
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"from scipy import integrate\n",
"\n",
"from matplotlib import pyplot as plt\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"from matplotlib.colors import cnames\n",
"from matplotlib import animation"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 31
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Computing the trajectories and plotting the result\n",
"\n",
"We define a function that can integrate the differential equations numerically and then plot the solutions. This function has arguments that control the parameters of the differential equation ($\\sigma$, $\\beta$, $\\rho$), the numerical integration (`N`, `max_time`) and the visualization (`angle`)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def solve_lorenz(N=10, angle=0.0, max_time=4.0, sigma=10.0, beta=8./3, rho=28.0):\n",
"\n",
" fig = plt.figure()\n",
" ax = fig.add_axes([0, 0, 1, 1], projection='3d')\n",
" ax.axis('off')\n",
"\n",
" # prepare the axes limits\n",
" ax.set_xlim((-25, 25))\n",
" ax.set_ylim((-35, 35))\n",
" ax.set_zlim((5, 55))\n",
" \n",
" def lorenz_deriv((x, y, z), t0, sigma=sigma, beta=beta, rho=rho):\n",
" \"\"\"Compute the time-derivative of a Lorentz system.\"\"\"\n",
" return [sigma * (y - x), x * (rho - z) - y, x * y - beta * z]\n",
"\n",
" # Choose random starting points, uniformly distributed from -15 to 15\n",
" np.random.seed(1)\n",
" x0 = -15 + 30 * np.random.random((N, 3))\n",
"\n",
" # Solve for the trajectories\n",
" t = np.linspace(0, max_time, int(250*max_time))\n",
" x_t = np.asarray([integrate.odeint(lorenz_deriv, x0i, t)\n",
" for x0i in x0])\n",
" \n",
" # choose a different color for each trajectory\n",
" colors = plt.cm.jet(np.linspace(0, 1, N))\n",
"\n",
" for i in range(N):\n",
" x, y, z = x_t[i,:,:].T\n",
" lines = ax.plot(x, y, z, '-', c=colors[i])\n",
" plt.setp(lines, linewidth=2)\n",
"\n",
" ax.view_init(30, angle)\n",
" plt.show()\n",
"\n",
" return t, x_t"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 32
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"t, x_t = solve_lorenz(angle=0, N=10)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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CbIWG0yAiCb58BJ7vWTrHPZkPPS6I3LweTrDar3QCWLJTt3Hx7Mf4V95STOyO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\ngg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7ff8f77d0890>"
]
}
],
"prompt_number": 33
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Using IPython's interactive function, we can explore how the trajectories behave as we change the various parameters."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"w = interactive(solve_lorenz, angle=(0.,360.), N=(0,50), sigma=(0.0,50.0), rho=(0.0,50.0))\n",
"display(w)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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C8mIiwxnKOl9/Agt/19oNPCAghqpV/8DMzICIiMna51UsBhJ5wD4+JJ1kmvI+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rtME3jvQAzNPwSlWsXlX3/lZ29vjn399XMXvxQFkiRxYPJkkCTqDS+OTca4IYe8bSgKfb9aiQYi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\nrkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7ff9223e9910>"
]
}
],
"prompt_number": 34
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"w.kwargs"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 93,
"text": [
"{u'N': 10,\n",
" u'angle': 110.4,\n",
" u'beta': 2.6666666666666665,\n",
" u'max_time': 4.0,\n",
" u'rho': 28.0,\n",
" u'sigma': 10.0}"
]
}
],
"prompt_number": 93
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"t, x_t = w.result"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 100
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Creating histograms of the average positions (across different trajectories) show that on average the trajectories swirl about the attractors."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"xyz_avg = x_t.mean(axis=1)\n",
"plt.hist(xyz_avg[:,0])\n",
"plt.title('Average $x(t)$')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 101,
"text": [
"<matplotlib.text.Text at 0x7f1a5c6f59d0>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": [
"<matplotlib.figure.Figure at 0x7f1a5cbf5150>"
]
}
],
"prompt_number": 101
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.hist(xyz_avg[:,1])\n",
"plt.title('Average $y(t)$')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 102,
"text": [
"<matplotlib.text.Text at 0x7f1a5c8c8a90>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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FpM/k49TC+yvAha0a9/J/rTxN7Qc2DXiqh32PxSXAJ0g3QAE8V2AtnXwaWFJ0ER3cRfrG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\niuz/AZoHAow2WaV5AAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x7f1a5cb45550>"
]
}
],
"prompt_number": 102
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.display import Image"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A NumPy array in its simplest form is a Python object build around a C array. That is, it has a pointer to a contiguous data buffer of values. A Python list, on the other hand, has a pointer to a contiguous buffer of pointers, each of which points to a Python object which in turn has references to its data (in this case, integers). This is a schematic of what the two might look like:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Image('http://jakevdp.github.io/images/array_vs_list.png')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"png": 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kam1MjKkJvzo6qla+F469DetrhMmNDb5rXpCP5Wmon0TDqpTQxfouQJEeXsma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\nYdw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L/uabb2yOJavRJhaqJAJEgAgQASJABIiAEwmoVKr//e9/TpygE6LnzJlz5513Wgvw\nunjxonUt1RABIkAEiAARIAJEgAgQATkBOtcop0FlIkAEiAARIAJEgAgQAdsEyGq0zYVqiQARIAJE\ngAgQASJABOQEyGqU06AyESACRIAIEAEiQASIgG0CZDXa5kK1RIAIEAEiQASIABEgAnIC/x8z/3YL\n3VenhgAAAABJRU5ErkJggg==\n",
"prompt_number": 2,
"text": [
"<IPython.core.display.Image at 0x7f78ac524150>"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It's easy to see that if you're doing some operation which steps through data in sequence, the numpy layout will be much more efficient than the Python layout, both in the cost of storage and the cost of access."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}