{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 1: Solution of Equation & Curve Fitting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.1, page no. 21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots of above equation are:  [-3.   2.   0.5]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "x = numpy.poly([0])\n",
    "p = 2*(x**3)+x**2-13*x+6\n",
    "print \"The roots of above equation are: \", numpy.roots([2,1,-13,6])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.2, page no. 21"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots of the equation are:  [ 2.00000000+2.64575131j  2.00000000-2.64575131j -2.66666667+0.j        ]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "x = numpy.poly([0])\n",
    "print \"The roots of the equation are: \", numpy.roots ([3, -4, 1, 88])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Example 1.3, page no. 22"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots of above equation are: [ 6.  3. -2.]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "x = numpy.poly([0])\n",
    "p = x^3-7*(x^2)+36\n",
    "print \"The roots of above equation are:\", numpy.roots([1, -7, 0, 36])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.4, page no. 23"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots of above equation are: [ 5. -4.  2. -1.]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "x = numpy.poly ([0]) \n",
    "p = x**4-2*(x**3)-21*(x**2)+22*x+40\n",
    "print \"The roots of above equation are:\", numpy.roots([1,-2,-21,22,40])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.5, page no. 23"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots of above equation are: [ 4.   2.   1.   0.5]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "x = numpy.poly ([0]) \n",
    "p = 2*(x**4)-15*(x**3)+35*(x**2)-30*x+8\n",
    "print \"The roots of above equation are:\", numpy.roots([2,-15,35,-30,8])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.6, page no. 24"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots of above equation are: [ 2.87938524  0.65270364 -0.53208889]\n",
      "let x1 = 0.6527036 x2 = -0.5320889 x3 = 2.8793852\n",
      "So the equation whose roots are cube of the roots of above equation is (x−x1ˆ3)∗(x−x2ˆ3)∗(x−x3ˆ3)\n",
      "(x - 23.8725770741465)*(x - 0.278066086195109)*(x + 0.150644263115026)\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "import sympy\n",
    "\n",
    "x = numpy.poly ([0]) \n",
    "p = x**3-3*(x**2)+1\n",
    "ans = numpy.roots([1,-3, 0, 1])\n",
    "print \"The roots of above equation are:\", ans\n",
    "x = sympy.Symbol('x')\n",
    "print \"let x1 = 0.6527036 x2 = -0.5320889 x3 = 2.8793852\"\n",
    "print \"So the equation whose roots are cube of the roots of above equation is (x−x1ˆ3)∗(x−x2ˆ3)∗(x−x3ˆ3)\"\n",
    "p1 = (x-x1**3)*(x-x2**3)*(x-x3**3)\n",
    "print p1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.7, page no. 25"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots of above equation are:\n",
      "[ 4.48928857  2.28916855 -0.77845712]\n",
      "let x1 = -0.7784571 x2 = 2.2891685 x3 = 4.4892886\n",
      "Now, since we want equation whose sum of roots is 0. sum of roots of above equation is 6, so we will decrease\n",
      "Value of each root by 2 i.e. x4 = x1-2\n",
      "x4 =  -2.7784571\n",
      "x5 =  0.2891685\n",
      "x6 =  2.4892886\n",
      "Hence, the required equation is ( x−x4 ) ∗ ( x−x5 ) ∗ ( x−x6 ) = 0 −−>\n",
      "(x - 2.4892886)*(x - 0.2891685)*(x + 2.7784571)\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "import sympy\n",
    "\n",
    "x = numpy.poly ([0]) \n",
    "x1 = numpy.poly ([0]) \n",
    "x2 = numpy.poly ([0]) \n",
    "x3 = numpy.poly ([0]) \n",
    "x4 = numpy.poly ([0]) \n",
    "x5 = numpy.poly ([0] ) \n",
    "x6 = numpy.poly ([0]) \n",
    "p = x**3-6*(x**2)+5*x+8\n",
    "print \"The roots of above equation are:\"\n",
    "print numpy.roots ([1, -6, 5, 8])\n",
    "print \"let x1 = -0.7784571 x2 = 2.2891685 x3 = 4.4892886\"\n",
    "x1 = -0.7784571\n",
    "x2 = 2.2891685\n",
    "x3 = 4.4892886\n",
    "print \"Now, since we want equation whose sum of roots is 0. sum of roots of above equation is 6, so we will decrease\"\n",
    "print \"Value of each root by 2 i.e. x4 = x1-2\"\n",
    "x = sympy.Symbol('x')\n",
    "x4 = x1-2\n",
    "print \"x4 = \", x4\n",
    "x5=x2-2\n",
    "print \"x5 = \", x5\n",
    "x6=x3-2\n",
    "print \"x6 = \", x6\n",
    "print \"Hence, the required equation is ( x−x4 ) ∗ ( x−x5 ) ∗ ( x−x6 ) = 0 −−>\"\n",
    "p1 =( x-x4 )*(x-x5)*(x-x6)\n",
    "print p1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.8, page no. 28"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots of above equation are: [ 3.          2.          1.          0.5         0.33333333]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "x = numpy.poly ([0]) \n",
    "p = 6*(x**5)-41*(x**4)+97*(x**3)-97*(x**2)+41*x-6\n",
    "print \"The roots of above equation are:\",numpy.roots([6,-41,97,-97,41,-6])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.9, page no. 28"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots of above equation are: [ 2.00000000+0.j        -1.00000000+0.j         0.83333333+0.5527708j\n",
      "  0.83333333-0.5527708j  1.00000000+0.j         0.50000000+0.j       ]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "x = numpy.poly([0]) \n",
    "p = 6*(x**6)-25*(x**5)+31*(x**4)-31*(x**2)+25*x-6\n",
    "print \"The roots of above equation are:\", numpy.roots([6,-25,31,0,-31,25,-6])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.10, page no. 29"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots of above equation are: [ 2.+3.46410162j  2.-3.46410162j -1.+0.j        ]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "x = numpy.poly ([0]) \n",
    "p = x**3-3*(x**2)+12*x+16\n",
    "print \"The roots of above equation are:\", numpy.roots([1,-3,12,16])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.11, page no. 30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots of above equation are: [ 0.28571429+0.24743583j  0.28571429-0.24743583j -0.25000000+0.j        ]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "x = numpy.poly ([0]) \n",
    "p = 28*(x**3)-9*(x**2)+1\n",
    "print \"The roots of above equation are:\",numpy.roots([28,-9,0,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.12, page no. 31"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots of above equation are: [-5. +0.00000000e+00j  2. +2.90013456e-08j  2. -2.90013456e-08j]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "x = numpy.poly ([0]) \n",
    "p = x**3+x**2-16*x+20\n",
    "print \"The roots of above equation are:\",numpy.roots ([1,1,-16,20])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.13, page no. 31"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots of above equation are: [ 1.08727971+1.17131211j  1.08727971-1.17131211j -1.17455941+0.j        ]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "x = numpy.poly ([0]) \n",
    "p = x**3-3*(x**2)+3\n",
    "print \"The roots of above equation are:\",numpy.roots ([1,-1,0,3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.14, page no. 33"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots of above equation are: [ 6.  4.  3. -1.]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "x = numpy.poly([0]) \n",
    "p = x**4-12*(x**3)+41*(x**2)-18*x-72\n",
    "print \"The roots of above equation are:\",numpy.roots ([1,-12,41,-18,-72])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.15, page no. 34"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots of above equation are: [-2.30277564  2.61803399  1.30277564  0.38196601]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "x = numpy.poly ([0]) \n",
    "p = x**4-2*(x**3)-5*(x**2)+10*x-3\n",
    "print \"The roots of above equation are:\", numpy.roots ([1,-2,-5,10,-3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.16, page no. 35"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots of above equation are: [ 3.73205081+0.j         -2.00000000+1.73205081j -2.00000000-1.73205081j\n",
      "  0.26794919+0.j        ]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "x = numpy.poly ([0]) \n",
    "p = x**4-8*(x**2)-24*x+7\n",
    "print \"The roots of above equation are:\",numpy.roots ([1,0,-8,-24,7])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.17, page no. 35"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The roots of above equation are: [ 6.05932014 -1.65491082  1.59559067]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "\n",
    "x = numpy.poly ([0]) \n",
    "p = x**4-6*(x**3)-3*(x**2)+22*x-6\n",
    "print \"The roots of above equation are:\",numpy.roots ([1,-6,-3,22.-6])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.18, page no. 37"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "From the graph, it is clear that the point of intersection is nearly x = 1.43\n"
     ]
    },
    {
     "data": {
      "image/png": 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+Nv1vnFPxHA4lH+Jw8mFGzR+lRUekVFMbvpRKGe3yGRb8toA3Fr7B92u/p1fT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\nWrV6jlWrKFRGoGyg6KiGLyK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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa769850290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy\n",
    "import math\n",
    "\n",
    "x = numpy.linspace(1 ,3 ,30)\n",
    "y1 = 3-x\n",
    "y2 = math.e**(x-1)\n",
    "plt.xlabel('X axis')\n",
    "plt.ylabel('Y axis')\n",
    "plt.title('My Graph')\n",
    "plt.plot(x, y1, \"o-\" )\n",
    "plt.plot(x, y2, \"+-\" )\n",
    "plt.legend([\"3-x\" ,\"e**(x-1)\"])\n",
    "print \"From the graph, it is clear that the point of intersection is nearly x = 1.43\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.19, page no. 40"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "From the graph, it is clear that the point of intersection is nearly x=2.3\n"
     ]
    },
    {
     "data": {
      "image/png": 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Bdwe/Y8raKWRkZXBepfNoUqMJ9avWp36V+t5/C9yKMtmpAFJyQnWSOS0NBg+GtWth0KCl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\nUimmIhIcCgpBdOCAUkxFJLQ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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa7698ce210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy\n",
    "import math\n",
    "\n",
    "x = numpy.linspace(1 ,3 ,30)\n",
    "y1 = x\n",
    "y2 = numpy.sin(x)+math.pi/2\n",
    "plt.xlabel('X axis')\n",
    "plt.ylabel('Y axis')\n",
    "plt.title('My Graph')\n",
    "plt.plot(x, y1, \"o-\")\n",
    "plt.plot(x, y2, \"+-\")\n",
    "plt.legend([\"x\", \"sin(x)+pi/2\"])\n",
    "print \"From the graph, it is clear that the point of intersection is nearly x=2.3\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1.20, page no. 41"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "From the graph, it is clear that the point of intersection is nearly x=2.3 \n"
     ]
    },
    {
     "data": {
      "image/png": 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vVn3zTdUlS1SXLlVdtkz13HP9lx84cLquXKm6apXq6tWqH3+sOniw/7IXXjhd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\nMcYEZIHCGGNMQP8fXmj88edlNkgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fa7696dc7d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy\n",
    "import math\n",
    "\n",
    "x = numpy.linspace(0, 3, 30)\n",
    "y1 = -1/numpy.cos(x)\n",
    "y2 = numpy.cosh(x)\n",
    "plt.xlabel('X axis')\n",
    "plt.ylabel('Y axis')\n",
    "plt.title('My Graph')\n",
    "plt.plot(x, y1, \"o-\" )\n",
    "plt.plot(x, y2, \"+-\" )\n",
    "plt.legend ([\"-sec(x)\", \"cosh(x)\"])\n",
    "print \"From the graph, it is clear that the point of intersection is nearly x=2.3 \""
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}