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+ {
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+ "metadata" : {
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+ "name" : " notebook1"
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+ },
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+ "nbformat" : 3 ,
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+ "nbformat_minor" : 0 ,
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+ "worksheets" : [
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+ {
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+ "cells" : [
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+ {
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+ "cell_type" : " heading" ,
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+ "level" : 1 ,
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+ "metadata" : {},
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+ "source" : [
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+ " A simple SymPy example"
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+ ]
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+ },
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+ {
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+ "cell_type" : " markdown" ,
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+ "metadata" : {},
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+ "source" : [
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+ " First we import SymPy and initialize printing:"
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+ ]
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+ },
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+ {
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+ "cell_type" : " code" ,
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+ "collapsed" : false ,
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+ "input" : [
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+ " from sympy import init_printing\n " ,
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+ " from sympy import *\n " ,
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+ " init_printing()"
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+ ],
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+ "language" : " python" ,
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+ "metadata" : {},
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+ "outputs" : [],
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+ "prompt_number" : 2
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+ },
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+ {
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+ "cell_type" : " markdown" ,
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+ "metadata" : {},
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+ "source" : [
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+ " Create a few symbols:"
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+ ]
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+ },
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+ {
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+ "cell_type" : " code" ,
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+ "collapsed" : false ,
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+ "input" : [
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+ " x,y,z = symbols('x y z')"
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+ ],
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+ "language" : " python" ,
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+ "metadata" : {},
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+ "outputs" : [],
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+ "prompt_number" : 4
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+ },
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+ {
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+ "cell_type" : " markdown" ,
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+ "metadata" : {},
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+ "source" : [
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+ " Here is a basic expression:"
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+ ]
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+ },
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+ {
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+ "cell_type" : " code" ,
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+ "collapsed" : false ,
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+ "input" : [
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+ " e = x**2 + 2.0*y + sin(z); e"
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+ ],
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+ "language" : " python" ,
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+ "metadata" : {},
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+ "outputs" : [
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+ {
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+ "latex" : [
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+ " $$x^{2} + 2.0 y + \\ sin{\\ left (z \\ right )}$$"
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+ ],
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+ "metadata" : {},
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+ "output_type" : " pyout" ,
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+ "png": "iVBORw0KGgoAAAANSUhEUgAAAKMAAAAZBAMAAACvE4OgAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAACz0lEQVRIDa1UTWjUQBT+ZpvdzW7TGlrxItjYSg/C6vbiDwjmoCgUpHioPYhdqig9\nFJYiPYmW4klB14NgFGnw4EHpj7UgUtTFXhSEBgVBxIOFggWVrrUqiMY3mZkkLNIK7oN575vvvfky\n8yYJIGzgkSlRrULKrivVSkvq6LbxtcaSjV3aSo0lgWyl5pK69V+SRlEsPxNTGYhhDrV3M2Ue2etc\nEDmuMmM+IjolrCuHXNoLoQDNSAXdzbjsfFVKTY1vCgFXFIxenG4cFSSzRewAPnN0FugXjPDr45MQ\nJwoKtitgXL9zT+CsJeIHYG+Z4H1gwhRU4G/FcAQbbYU3KdDo+0sCK8lRU0guA72uKqMYk9RehHxP\niDIu0NS2v90KGShJYi7T7tgvkrQ2vIT2XtRISWNra6lzGc8/PW3ji4PL7Vmge095YIX0iB71NCaZ\n5N3XyM0VCuNIyFNIyY3AMG/KDUvjn90DGmwq9wpIl5AyU5WsTYy0aJf6JFGB5An3Der5jExKHjNR\n4JKPge/EXqDBoOXpkxkmkJHFfAFRVhDIveWA0S57N2Me6yw+DSX1n1uCq3sIfCF2IcjNkjeWyKli\nginHubboOB4vSNAjyaiXE26ygrkyTfod55Lj3CTE+n2P73ImJpnk6wJJKjYJSwt3OQbNJu4icM5s\nKGGbzMuD70N6JSbJD44x7pLDyJrbkfiLpOEhYVMJSVEj83x5YFLyNrAzJsmvJ+uhLrieXvcJDshy\nHtQuD54c2IWWEnSXfUTDZJJfAjcpOW5imp9aHvw4ZZ4NDV4FGjw0tzadKgbFwinJUd//AT0P1tdW\nBtuRU39oKdk9ONQ163fM+nvu/s4D/FX30otdQIZGlSnJKpq6KUxKVqV1WxGHFIhishjhEO1Gi3r4\nkZCMg+hH1henV8EjmFoly1PTMs/Uadaox+FceY2STpmvt9co/Pe0Jvt1GvgDK/Osw/4jQ4wAAAAA\nSUVORK5CYII=\n",
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+ "prompt_number" : 6 ,
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+ "text" : [
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+ " 2 \n " ,
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+ " x + 2.0\u22c5 y + sin(z)"
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+ ]
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+ }
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+ ],
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+ "prompt_number" : 6
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+ },
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+ {
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+ "cell_type" : " code" ,
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+ "collapsed" : false ,
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+ "input" : [
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+ " diff(e, x)"
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+ ],
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+ "language" : " python" ,
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+ "metadata" : {},
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+ "outputs" : [
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+ {
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+ "latex" : [
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+ " $$2 x$$"
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+ ],
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+ "metadata" : {},
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+ "output_type" : " pyout" ,
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+ "png" : " iVBORw0KGgoAAAANSUhEUgAAABQAAAAOBAMAAADd6iHDAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\n AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpm7MhCriUTv3c12\n VGZoascqAAAAgElEQVQIHWNgVDJ2YICAMAb2H1BmKgPDTChzFgNDvgOEvT8AzgQKrA9gPZPYUwNk\n cXxnCGd4dWA1kMllwFDKUB9wEchUZmAIYNgMZDDwJIDIPyDiEgOjAAPLFwZWBhYFBh6BqzwfGI4y\n SJUXZXH8Zf7A+IBh////v1hzjh5/xwAAW80hUDE8HYkAAAAASUVORK5CYII=\n " ,
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+ "prompt_number" : 7 ,
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+ "text" : [
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+ " 2\u22c5 x"
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+ ]
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+ }
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+ ],
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+ "prompt_number" : 7
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+ },
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+ {
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+ "cell_type" : " code" ,
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+ "collapsed" : false ,
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+ "input" : [
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+ " integrate(e, z)"
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+ ],
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+ "language" : " python" ,
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+ "metadata" : {},
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+ "outputs" : [
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+ {
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+ "latex" : [
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+ " $$x^{2} z + 2.0 y z - \\ cos{\\ left (z \\ right )}$$"
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+ ],
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+ "metadata" : {},
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+ "output_type" : " pyout" ,
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+ "png": "iVBORw0KGgoAAAANSUhEUgAAALsAAAAZBAMAAACbakK8AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nYII=\n",
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+ "prompt_number" : 8 ,
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+ "text" : [
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+ " 2 \n " ,
131
+ " x \u22c5 z + 2.0\u22c5 y\u22c5 z - cos(z)"
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+ ]
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+ }
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+ ],
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+ "prompt_number" : 8
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+ },
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+ {
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+ "cell_type" : " code" ,
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+ "collapsed" : false ,
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+ "input" : [],
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+ "language" : " python" ,
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+ "metadata" : {},
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+ "outputs" : []
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+ }
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+ ],
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+ "metadata" : {}
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+ }
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+ ]
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+ }
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