{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Premiers calculs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Je vais calculer $sin(\\pi)$ avec Sagemath !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 1,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin(pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.14159265358979"
      ]
     },
     "execution_count": 3,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi.n()?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "pi?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "sin?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cos(x)\n"
     ]
    }
   ],
   "source": [
    "print sin(x).diff()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'Function_sin' object has no attribute 'diff'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-7-fb976cde9c21>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0msin\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdiff\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m: 'Function_sin' object has no attribute 'diff'"
     ]
    }
   ],
   "source": [
    "sin.diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Graphics object consisting of 1 graphics primitive"
      ]
     },
     "execution_count": 18,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sin(x).plot((x,0,2*pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "f(x)=sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<html><script type=\"math/tex; mode=display\">\\newcommand{\\Bold}[1]{\\mathbf{#1}}x \\ {\\mapsto}\\ \\sin\\left(x\\right)</script></html>"
      ],
      "text/plain": [
       "x |--> sin(x)"
      ]
     },
     "execution_count": 11,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "f: x |--> sin(x)\n",
      "f(0)= 0\n"
     ]
    }
   ],
   "source": [
    "print 'f:',f\n",
    "print 'f(0)=',f(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  }
 ],
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