removing problem statements

1 files changed, 502 insertions, 27 deletions

diff --git a/Engineering_Thermodynamics:_A_Computer_Approach_(SI_Units_Version)/ch11.ipynb b/Engineering_Thermodynamics:_A_Computer_Approach_(SI_Units_Version)/ch11.ipynb
index 3ddc5480..34fb61dc 100644
--- a/Engineering_Thermodynamics:_A_Computer_Approach_(SI_Units_Version)/ch11.ipynb
+++ b/Engineering_Thermodynamics:_A_Computer_Approach_(SI_Units_Version)/ch11.ipynb
@@ -1,6 +1,7 @@
 {
  "metadata": {
-  "name": "ch11"
+  "name": "",
+  "signature": "sha256:bdd5f9e441ccb7e3a87f4d8c5492d0aa1d228caba299fc1b0c667abb12780a1e"
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -10,7 +11,23 @@
     {
      "cell_type": "code",
      "collapsed": false,
-     "input": "'''\nEXAMPLE 11.1\nAdding an Assignment Operator to the Ratio Class\nHere is a class interface for the Ratio class, showing the default constructor, the copy constructor,\nand the assignment operator:\n'''\nclass Ratio:\n    def __init__(self,n=None,d=None):\n        if d==None:\n            self.num = n.num\n            self.den = n.den\n        elif n==None:\n            self.num = 0\n            self.den = 1\n        else:\n            self.num = n\n            self.den = d\n        \n    def equals(self):\n        return self  # retuns calling object.",
+     "input": [
+      "\n",
+      "class Ratio:\n",
+      "    def __init__(self,n=None,d=None):\n",
+      "        if d==None:\n",
+      "            self.num = n.num\n",
+      "            self.den = n.den\n",
+      "        elif n==None:\n",
+      "            self.num = 0\n",
+      "            self.den = 1\n",
+      "        else:\n",
+      "            self.num = n\n",
+      "            self.den = d\n",
+      "        \n",
+      "    def equals(self):\n",
+      "        return self  # retuns calling object."
+     ],
      "language": "python",
      "metadata": {},
      "outputs": [],
@@ -19,7 +36,15 @@
     {
      "cell_type": "code",
      "collapsed": false,
-     "input": "'''\nEXAMPLE 11.2 The Preferred Prototype for an Overloaded Assignment Operator\n'''\nclass Ratio:\n    def __init__(self,n=None,d=None):\n        pass\n        \n    def equals(self):\n        pass\n",
+     "input": [
+      "\n",
+      "class Ratio:\n",
+      "    def __init__(self,n=None,d=None):\n",
+      "        pass\n",
+      "        \n",
+      "    def equals(self):\n",
+      "        pass\n"
+     ],
      "language": "python",
      "metadata": {},
      "outputs": [],
@@ -28,7 +53,30 @@
     {
      "cell_type": "code",
      "collapsed": false,
-     "input": "'''\nEXAMPLE 11.3 Implementation of the Assignment Operator for the Ratio Class\n'''\nclass Ratio:\n    def __init__(self,n=None,d=None):\n        if d==None:\n            self.num = n.num\n            self.den = n.den\n        elif n==None:\n            self.num = 0\n            self.den = 1\n        else:\n            self.num = n\n            self.den = d\n        \n\nz = Ratio(22,7)\ny = z\nx = z\n\nx = Ratio(22,7)\ny = Ratio(x)\nz = x\nw = x",
+     "input": [
+      "\n",
+      "class Ratio:\n",
+      "    def __init__(self,n=None,d=None):\n",
+      "        if d==None:\n",
+      "            self.num = n.num\n",
+      "            self.den = n.den\n",
+      "        elif n==None:\n",
+      "            self.num = 0\n",
+      "            self.den = 1\n",
+      "        else:\n",
+      "            self.num = n\n",
+      "            self.den = d\n",
+      "        \n",
+      "\n",
+      "z = Ratio(22,7)\n",
+      "y = z\n",
+      "x = z\n",
+      "\n",
+      "x = Ratio(22,7)\n",
+      "y = Ratio(x)\n",
+      "z = x\n",
+      "w = x"
+     ],
      "language": "python",
      "metadata": {},
      "outputs": [],
@@ -37,7 +85,16 @@
     {
      "cell_type": "code",
      "collapsed": false,
-     "input": "'''\nEXAMPLE 11.4\nmultiplication operator overload\n'''\n\nclass Ratio:\n    def __init__(self,n=None,d=None):\n        self.num = n\n        self.den = d\n    def __mul__(self,y):\n        pass\n",
+     "input": [
+      "\n",
+      "\n",
+      "class Ratio:\n",
+      "    def __init__(self,n=None,d=None):\n",
+      "        self.num = n\n",
+      "        self.den = d\n",
+      "    def __mul__(self,y):\n",
+      "        pass\n"
+     ],
      "language": "python",
      "metadata": {},
      "outputs": [],
@@ -46,14 +103,68 @@
     {
      "cell_type": "code",
      "collapsed": false,
-     "input": "'''\nEXAMPLE 11.5 The Ratio Class with Assignment and Multiplication Operators\n'''\ndef gcd(m,n):\n    # returns the greatest common divisor of m and n:\n    if (m<n):\n        m,n = n,m\n    while (n>0):\n        r = m % n\n        m = n\n        n = r\n    return m\n\n\nclass Ratio:\n    def __init__(self,n=None,d=None):\n        self.num = n\n        self.den = d\n        self.reduce()\n    def __mul__(self,y):\n        z = Ratio(self.num * y.num, self.den * y.den)\n        return z\n    def print_(self):\n        print self.num , '/', self.den\n        \n    def reduce(self):\n        # enforce invariant(den > 0):\n        if (self.num == 0 or self.den == 0):\n            self.num = 0\n            self.den = 1\n            return\n        if (self.den < 0):\n            self.den *= -1\n            self.num *= -1\n        # enforce invariant(gcd(num,den) == 1):\n        if (self.den == 1):\n            return\n        # it's already reduced\n        sgn = 0\n        if self.num < 0:\n            sgn = -1\n        else:\n            sgn = 1\n        g = gcd(sgn*self.num,self.den)\n        self.num /= g\n        self.den /= g\nx = Ratio(22,7)\ny = Ratio(-3,8)\nz = x\nz.print_()\nx = y*z\nx.print_()\n",
+     "input": [
+      "\n",
+      "def gcd(m,n):\n",
+      "    # returns the greatest common divisor of m and n:\n",
+      "    if (m<n):\n",
+      "        m,n = n,m\n",
+      "    while (n>0):\n",
+      "        r = m % n\n",
+      "        m = n\n",
+      "        n = r\n",
+      "    return m\n",
+      "\n",
+      "\n",
+      "class Ratio:\n",
+      "    def __init__(self,n=None,d=None):\n",
+      "        self.num = n\n",
+      "        self.den = d\n",
+      "        self.reduce()\n",
+      "    def __mul__(self,y):\n",
+      "        z = Ratio(self.num * y.num, self.den * y.den)\n",
+      "        return z\n",
+      "    def print_(self):\n",
+      "        print self.num , '/', self.den\n",
+      "        \n",
+      "    def reduce(self):\n",
+      "        # enforce invariant(den > 0):\n",
+      "        if (self.num == 0 or self.den == 0):\n",
+      "            self.num = 0\n",
+      "            self.den = 1\n",
+      "            return\n",
+      "        if (self.den < 0):\n",
+      "            self.den *= -1\n",
+      "            self.num *= -1\n",
+      "        # enforce invariant(gcd(num,den) == 1):\n",
+      "        if (self.den == 1):\n",
+      "            return\n",
+      "        # it's already reduced\n",
+      "        sgn = 0\n",
+      "        if self.num < 0:\n",
+      "            sgn = -1\n",
+      "        else:\n",
+      "            sgn = 1\n",
+      "        g = gcd(sgn*self.num,self.den)\n",
+      "        self.num /= g\n",
+      "        self.den /= g\n",
+      "x = Ratio(22,7)\n",
+      "y = Ratio(-3,8)\n",
+      "z = x\n",
+      "z.print_()\n",
+      "x = y*z\n",
+      "x.print_()\n"
+     ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "output_type": "stream",
        "stream": "stdout",
-       "text": "22 / 7\n-33 / 28\n"
+       "text": [
+        "22 / 7\n",
+        "-33 / 28\n"
+       ]
       }
      ],
      "prompt_number": 5
@@ -61,7 +172,30 @@
     {
      "cell_type": "code",
      "collapsed": false,
-     "input": "'''\nEXAMPLE 11.6 The Ratio Class with an Overloaded *= Operator\n'''\ndef gcd(m,n):\n    # returns the greatest common divisor of m and n:\n    if (m<n):\n        m,n = n,m\n    while (n>0):\n        r = m % n\n        m = n\n        n = r\n    return m\n\n\nclass Ratio:\n    def __init__(self,n=None,d=None):\n        self.num = n\n        self.den = d\n        self.reduce()\n    def __imul__(self,y):\n        self.num = self.num * y.num\n        self.den = self.den * y.den\n    def print_(self):\n        print self.num , '/', self.den",
+     "input": [
+      "\n",
+      "def gcd(m,n):\n",
+      "    # returns the greatest common divisor of m and n:\n",
+      "    if (m<n):\n",
+      "        m,n = n,m\n",
+      "    while (n>0):\n",
+      "        r = m % n\n",
+      "        m = n\n",
+      "        n = r\n",
+      "    return m\n",
+      "\n",
+      "\n",
+      "class Ratio:\n",
+      "    def __init__(self,n=None,d=None):\n",
+      "        self.num = n\n",
+      "        self.den = d\n",
+      "        self.reduce()\n",
+      "    def __imul__(self,y):\n",
+      "        self.num = self.num * y.num\n",
+      "        self.den = self.den * y.den\n",
+      "    def print_(self):\n",
+      "        print self.num , '/', self.den"
+     ],
      "language": "python",
      "metadata": {},
      "outputs": [],
@@ -70,7 +204,23 @@
     {
      "cell_type": "code",
      "collapsed": false,
-     "input": "'''\nEXAMPLE 11.7 Overloading the Equality Operator == in the Ratio Class\n'''\n\nclass Ratio:\n    def __init__(self,n=None,d=None):\n        self.num = n\n        self.den = d\n        self.reduce()\n    def __imul__(self,y):\n        self.num = self.num * y.num\n        self.den = self.den * y.den\n    def __eq__(self,y):\n        return (x.num * y.den == y.num * x.den)\n    def print_(self):\n        print self.num , '/', self.den\n\n",
+     "input": [
+      "\n",
+      "\n",
+      "class Ratio:\n",
+      "    def __init__(self,n=None,d=None):\n",
+      "        self.num = n\n",
+      "        self.den = d\n",
+      "        self.reduce()\n",
+      "    def __imul__(self,y):\n",
+      "        self.num = self.num * y.num\n",
+      "        self.den = self.den * y.den\n",
+      "    def __eq__(self,y):\n",
+      "        return (x.num * y.den == y.num * x.den)\n",
+      "    def print_(self):\n",
+      "        print self.num , '/', self.den\n",
+      "\n"
+     ],
      "language": "python",
      "metadata": {},
      "outputs": [],
@@ -79,20 +229,44 @@
     {
      "cell_type": "code",
      "collapsed": false,
-     "input": "'''\nEXAMPLE 11.8 \nPython does not use << operator for printing. So here we are just declaring function name as print_.\n'''\n\nclass Ratio:\n    def __init__(self,n=None,d=None):\n        self.num = n\n        self.den = d\n    def __imul__(self,y):\n        self.num = self.num * y.num\n        self.den = self.den * y.den\n    def __eq__(self,y):\n        return (x.num * y.den == y.num * x.den)\n    def print_(self):\n        print self.num , '/', self.den\n\n\nx = Ratio(22,7)\ny = Ratio(-3,8)\nx.print_() ,  y.print_()\n",
+     "input": [
+      "\n",
+      "\n",
+      "class Ratio:\n",
+      "    def __init__(self,n=None,d=None):\n",
+      "        self.num = n\n",
+      "        self.den = d\n",
+      "    def __imul__(self,y):\n",
+      "        self.num = self.num * y.num\n",
+      "        self.den = self.den * y.den\n",
+      "    def __eq__(self,y):\n",
+      "        return (x.num * y.den == y.num * x.den)\n",
+      "    def print_(self):\n",
+      "        print self.num , '/', self.den\n",
+      "\n",
+      "\n",
+      "x = Ratio(22,7)\n",
+      "y = Ratio(-3,8)\n",
+      "x.print_() ,  y.print_()\n"
+     ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "output_type": "stream",
        "stream": "stdout",
-       "text": "22 / 7\n-3 / 8\n"
+       "text": [
+        "22 / 7\n",
+        "-3 / 8\n"
+       ]
       },
       {
        "metadata": {},
        "output_type": "pyout",
        "prompt_number": 8,
-       "text": "(None, None)"
+       "text": [
+        "(None, None)"
+       ]
       }
      ],
      "prompt_number": 8
@@ -100,7 +274,62 @@
     {
      "cell_type": "code",
      "collapsed": false,
-     "input": "'''\nEXAMPLE 11.9 \nPython does not have >> for input. so we will use input function.\n'''\ndef gcd(m,n):\n    # returns the greatest common divisor of m and n:\n    if (m<n):\n        m,n = n,m\n    while (n>0):\n        r = m % n\n        m = n\n        n = r\n    return m\nclass Ratio:\n    def __init__(self,n=0,d=1):\n        self.num = n\n        self.den = d\n        self.reduce()\n    def __mul__(self,y):\n        z = Ratio(self.num * y.num, self.den * y.den)\n        return z\n    def print_(self):\n        print self.num , '/', self.den\n        \n    def input(self):\n        self.num = int(raw_input('Numerator : '))\n        self.den = int(raw_input('Denominator : '))\n        self.reduce()\n    def reduce(self):\n        # enforce invariant(den > 0):\n        if (self.num == 0 or self.den == 0):\n            self.num = 0\n            self.den = 1\n            return\n        if (self.den < 0):\n            self.den *= -1\n            self.num *= -1\n        # enforce invariant(gcd(num,den) == 1):\n        if (self.den == 1):\n            return\n        # it's already reduced\n        sgn = 0\n        if self.num < 0:\n            sgn = -1\n        else:\n            sgn = 1\n        g = gcd(sgn*self.num,self.den)\n        self.num /= g\n        self.den /= g\n\n\nx = Ratio()\ny = Ratio()\nx.input()\ny.input()\nx.print_()\ny.print_()\n",
+     "input": [
+      "\n",
+      "def gcd(m,n):\n",
+      "    # returns the greatest common divisor of m and n:\n",
+      "    if (m<n):\n",
+      "        m,n = n,m\n",
+      "    while (n>0):\n",
+      "        r = m % n\n",
+      "        m = n\n",
+      "        n = r\n",
+      "    return m\n",
+      "class Ratio:\n",
+      "    def __init__(self,n=0,d=1):\n",
+      "        self.num = n\n",
+      "        self.den = d\n",
+      "        self.reduce()\n",
+      "    def __mul__(self,y):\n",
+      "        z = Ratio(self.num * y.num, self.den * y.den)\n",
+      "        return z\n",
+      "    def print_(self):\n",
+      "        print self.num , '/', self.den\n",
+      "        \n",
+      "    def input(self):\n",
+      "        self.num = int(raw_input('Numerator : '))\n",
+      "        self.den = int(raw_input('Denominator : '))\n",
+      "        self.reduce()\n",
+      "    def reduce(self):\n",
+      "        # enforce invariant(den > 0):\n",
+      "        if (self.num == 0 or self.den == 0):\n",
+      "            self.num = 0\n",
+      "            self.den = 1\n",
+      "            return\n",
+      "        if (self.den < 0):\n",
+      "            self.den *= -1\n",
+      "            self.num *= -1\n",
+      "        # enforce invariant(gcd(num,den) == 1):\n",
+      "        if (self.den == 1):\n",
+      "            return\n",
+      "        # it's already reduced\n",
+      "        sgn = 0\n",
+      "        if self.num < 0:\n",
+      "            sgn = -1\n",
+      "        else:\n",
+      "            sgn = 1\n",
+      "        g = gcd(sgn*self.num,self.den)\n",
+      "        self.num /= g\n",
+      "        self.den /= g\n",
+      "\n",
+      "\n",
+      "x = Ratio()\n",
+      "y = Ratio()\n",
+      "x.input()\n",
+      "y.input()\n",
+      "x.print_()\n",
+      "y.print_()\n"
+     ],
      "language": "python",
      "metadata": {},
      "outputs": [
@@ -108,30 +337,41 @@
        "name": "stdout",
        "output_type": "stream",
        "stream": "stdout",
-       "text": "Numerator : -10\n"
+       "text": [
+        "Numerator : -10\n"
+       ]
       },
       {
        "name": "stdout",
        "output_type": "stream",
        "stream": "stdout",
-       "text": "Denominator : -24\n"
+       "text": [
+        "Denominator : -24\n"
+       ]
       },
       {
        "name": "stdout",
        "output_type": "stream",
        "stream": "stdout",
-       "text": "Numerator : 36\n"
+       "text": [
+        "Numerator : 36\n"
+       ]
       },
       {
        "name": "stdout",
        "output_type": "stream",
        "stream": "stdout",
-       "text": "Denominator : -20\n"
+       "text": [
+        "Denominator : -20\n"
+       ]
       },
       {
        "output_type": "stream",
        "stream": "stdout",
-       "text": "5 / 12\n-9 / 5\n"
+       "text": [
+        "5 / 12\n",
+        "-9 / 5\n"
+       ]
       }
      ],
      "prompt_number": 1
@@ -139,14 +379,78 @@
     {
      "cell_type": "code",
      "collapsed": false,
-     "input": "'''\nEXAMPLE 11.10\nAdding a Conversion Operator to the Ratio Class\n'''\ndef gcd(m,n):\n    # returns the greatest common divisor of m and n:\n    if (m<n):\n        m,n = n,m\n    while (n>0):\n        r = m % n\n        m = n\n        n = r\n    return m\nclass Ratio:\n    def __init__(self,n=0,d=1):\n        self.num = n\n        self.den = d\n        self.reduce()\n    def __mul__(self,y):\n        z = Ratio(self.num * y.num, self.den * y.den)\n        return z\n    def print_(self):\n        print self.num , '/', self.den\n        \n    def input(self):\n        self.num = int(raw_input('Numerator : '))\n        self.den = int(raw_input('Denominator : '))\n        self.reduce()\n    def __float__(self):\n        return float(self.num)/self.den\n    def reduce(self):\n        # enforce invariant(den > 0):\n        if (self.num == 0 or self.den == 0):\n            self.num = 0\n            self.den = 1\n            return\n        if (self.den < 0):\n            self.den *= -1\n            self.num *= -1\n        # enforce invariant(gcd(num,den) == 1):\n        if (self.den == 1):\n            return\n        # it's already reduced\n        sgn = 0\n        if self.num < 0:\n            sgn = -1\n        else:\n            sgn = 15.py\n        g = gcd(sgn*self.num,self.den)\n        self.num /= g\n        self.den /= g\n\nx = Ratio(-5,8)\nprint \"x = \" , \nx.print_() \nprint \", float(x) = \" , float(x) \nP = Ratio(22,7)\nPI = float(P)\nprint \"P = \" ,\nP.print_() \nprint \", PI = \" , PI\n",
+     "input": [
+      "\n",
+      "def gcd(m,n):\n",
+      "    # returns the greatest common divisor of m and n:\n",
+      "    if (m<n):\n",
+      "        m,n = n,m\n",
+      "    while (n>0):\n",
+      "        r = m % n\n",
+      "        m = n\n",
+      "        n = r\n",
+      "    return m\n",
+      "class Ratio:\n",
+      "    def __init__(self,n=0,d=1):\n",
+      "        self.num = n\n",
+      "        self.den = d\n",
+      "        self.reduce()\n",
+      "    def __mul__(self,y):\n",
+      "        z = Ratio(self.num * y.num, self.den * y.den)\n",
+      "        return z\n",
+      "    def print_(self):\n",
+      "        print self.num , '/', self.den\n",
+      "        \n",
+      "    def input(self):\n",
+      "        self.num = int(raw_input('Numerator : '))\n",
+      "        self.den = int(raw_input('Denominator : '))\n",
+      "        self.reduce()\n",
+      "    def __float__(self):\n",
+      "        return float(self.num)/self.den\n",
+      "    def reduce(self):\n",
+      "        # enforce invariant(den > 0):\n",
+      "        if (self.num == 0 or self.den == 0):\n",
+      "            self.num = 0\n",
+      "            self.den = 1\n",
+      "            return\n",
+      "        if (self.den < 0):\n",
+      "            self.den *= -1\n",
+      "            self.num *= -1\n",
+      "        # enforce invariant(gcd(num,den) == 1):\n",
+      "        if (self.den == 1):\n",
+      "            return\n",
+      "        # it's already reduced\n",
+      "        sgn = 0\n",
+      "        if self.num < 0:\n",
+      "            sgn = -1\n",
+      "        else:\n",
+      "            sgn = 15.py\n",
+      "        g = gcd(sgn*self.num,self.den)\n",
+      "        self.num /= g\n",
+      "        self.den /= g\n",
+      "\n",
+      "x = Ratio(-5,8)\n",
+      "print \"x = \" , \n",
+      "x.print_() \n",
+      "print \", float(x) = \" , float(x) \n",
+      "P = Ratio(22,7)\n",
+      "PI = float(P)\n",
+      "print \"P = \" ,\n",
+      "P.print_() \n",
+      "print \", PI = \" , PI\n"
+     ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "output_type": "stream",
        "stream": "stdout",
-       "text": "x =  -5 / 8\n, float(x) =  -0.625\nP =  22 / 7\n, PI =  3.14285714286\n"
+       "text": [
+        "x =  -5 / 8\n",
+        ", float(x) =  -0.625\n",
+        "P =  22 / 7\n",
+        ", PI =  3.14285714286\n"
+       ]
       }
      ],
      "prompt_number": 3
@@ -154,14 +458,71 @@
     {
      "cell_type": "code",
      "collapsed": false,
-     "input": "'''\nEXAMPLE 11.11 Adding a Pre-Increment Operator to the Ratio Class\n'''\ndef gcd(m,n):\n    # returns the greatest common divisor of m and n:\n    if (m<n):\n        m,n = n,m\n    while (n>0):\n        r = m % n\n        m = n\n        n = r\n    return m\nclass Ratio:\n    def __init__(self,n=0,d=1):\n        self.num = n\n        self.den = d\n        self.reduce()\n    def __mul__(self,y):\n        z = Ratio(self.num * y.num, self.den * y.den)\n        return z\n    def print_(self):\n        print self.num , '/', self.den\n        \n    def __iadd__(self,n):\n        self.num += self.den\n        return self\n    def reduce(self):\n        # enforce invariant(den > 0):\n        if (self.num == 0 or self.den == 0):\n            self.num = 0\n            self.den = 1\n            return\n        if (self.den < 0):\n            self.den *= -1\n            self.num *= -1\n        # enforce invariant(gcd(num,den) == 1):\n        if (self.den == 1):\n            return\n        # it's already reduced\n        sgn = 0\n        if self.num < 0:\n            sgn = -1\n        else:\n            sgn = 1\n        g = gcd(sgn*self.num,self.den)\n        self.num /= g\n        self.den /= g\n\nx = Ratio(22,7)\nx += 1\ny = x\nprint \"y = \" ,\ny.print_()\nprint \", x = \",\nx.print_()\n",
+     "input": [
+      "\n",
+      "def gcd(m,n):\n",
+      "    # returns the greatest common divisor of m and n:\n",
+      "    if (m<n):\n",
+      "        m,n = n,m\n",
+      "    while (n>0):\n",
+      "        r = m % n\n",
+      "        m = n\n",
+      "        n = r\n",
+      "    return m\n",
+      "class Ratio:\n",
+      "    def __init__(self,n=0,d=1):\n",
+      "        self.num = n\n",
+      "        self.den = d\n",
+      "        self.reduce()\n",
+      "    def __mul__(self,y):\n",
+      "        z = Ratio(self.num * y.num, self.den * y.den)\n",
+      "        return z\n",
+      "    def print_(self):\n",
+      "        print self.num , '/', self.den\n",
+      "        \n",
+      "    def __iadd__(self,n):\n",
+      "        self.num += self.den\n",
+      "        return self\n",
+      "    def reduce(self):\n",
+      "        # enforce invariant(den > 0):\n",
+      "        if (self.num == 0 or self.den == 0):\n",
+      "            self.num = 0\n",
+      "            self.den = 1\n",
+      "            return\n",
+      "        if (self.den < 0):\n",
+      "            self.den *= -1\n",
+      "            self.num *= -1\n",
+      "        # enforce invariant(gcd(num,den) == 1):\n",
+      "        if (self.den == 1):\n",
+      "            return\n",
+      "        # it's already reduced\n",
+      "        sgn = 0\n",
+      "        if self.num < 0:\n",
+      "            sgn = -1\n",
+      "        else:\n",
+      "            sgn = 1\n",
+      "        g = gcd(sgn*self.num,self.den)\n",
+      "        self.num /= g\n",
+      "        self.den /= g\n",
+      "\n",
+      "x = Ratio(22,7)\n",
+      "x += 1\n",
+      "y = x\n",
+      "print \"y = \" ,\n",
+      "y.print_()\n",
+      "print \", x = \",\n",
+      "x.print_()\n"
+     ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "output_type": "stream",
        "stream": "stdout",
-       "text": "y =  29 / 7\n, x =  29 / 7\n"
+       "text": [
+        "y =  29 / 7\n",
+        ", x =  29 / 7\n"
+       ]
       }
      ],
      "prompt_number": 5
@@ -169,14 +530,72 @@
     {
      "cell_type": "code",
      "collapsed": false,
-     "input": "'''\nEXAMPLE 11.12 Adding a Post-Increment Operator to the Ratio Class\n'''\ndef gcd(m,n):\n    # returns the greatest common divisor of m and n:\n    if (m<n):\n        m,n = n,m\n    while (n>0):\n        r = m % n\n        m = n\n        n = r\n    return m\nclass Ratio:\n    def __init__(self,n=0,d=1):\n        self.num = n\n        self.den = d\n        self.reduce()\n    def __mul__(self,y):\n        z = Ratio(self.num * y.num, self.den * y.den)\n        return z\n    def print_(self):\n        print self.num , '/', self.den\n        \n    def __iadd__(self,n):\n        self.num += self.den\n        return self\n    def reduce(self):\n        # enforce invariant(den > 0):\n        if (self.num == 0 or self.den == 0):\n            self.num = 0\n            self.den = 1\n            return\n        if (self.den < 0):\n            self.den *= -1\n            self.num *= -1\n        # enforce invariant(gcd(num,den) == 1):\n        if (self.den == 1):\n            return\n        # it's already reduced\n        sgn = 0\n        if self.num < 0:\n            sgn = -1\n        else:\n            sgn = 1\n        g = gcd(sgn*self.num,self.den)\n        self.num /= g\n        self.den /= g\n\nx = Ratio(22,7)\ny = Ratio(x.num,x.den)\nx += 1\nprint \"y = \" ,\ny.print_()\nprint \", x = \",\nx.print_()\n\n",
+     "input": [
+      "\n",
+      "def gcd(m,n):\n",
+      "    # returns the greatest common divisor of m and n:\n",
+      "    if (m<n):\n",
+      "        m,n = n,m\n",
+      "    while (n>0):\n",
+      "        r = m % n\n",
+      "        m = n\n",
+      "        n = r\n",
+      "    return m\n",
+      "class Ratio:\n",
+      "    def __init__(self,n=0,d=1):\n",
+      "        self.num = n\n",
+      "        self.den = d\n",
+      "        self.reduce()\n",
+      "    def __mul__(self,y):\n",
+      "        z = Ratio(self.num * y.num, self.den * y.den)\n",
+      "        return z\n",
+      "    def print_(self):\n",
+      "        print self.num , '/', self.den\n",
+      "        \n",
+      "    def __iadd__(self,n):\n",
+      "        self.num += self.den\n",
+      "        return self\n",
+      "    def reduce(self):\n",
+      "        # enforce invariant(den > 0):\n",
+      "        if (self.num == 0 or self.den == 0):\n",
+      "            self.num = 0\n",
+      "            self.den = 1\n",
+      "            return\n",
+      "        if (self.den < 0):\n",
+      "            self.den *= -1\n",
+      "            self.num *= -1\n",
+      "        # enforce invariant(gcd(num,den) == 1):\n",
+      "        if (self.den == 1):\n",
+      "            return\n",
+      "        # it's already reduced\n",
+      "        sgn = 0\n",
+      "        if self.num < 0:\n",
+      "            sgn = -1\n",
+      "        else:\n",
+      "            sgn = 1\n",
+      "        g = gcd(sgn*self.num,self.den)\n",
+      "        self.num /= g\n",
+      "        self.den /= g\n",
+      "\n",
+      "x = Ratio(22,7)\n",
+      "y = Ratio(x.num,x.den)\n",
+      "x += 1\n",
+      "print \"y = \" ,\n",
+      "y.print_()\n",
+      "print \", x = \",\n",
+      "x.print_()\n",
+      "\n"
+     ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "output_type": "stream",
        "stream": "stdout",
-       "text": "y =  22 / 7\n, x =  29 / 7\n"
+       "text": [
+        "y =  22 / 7\n",
+        ", x =  29 / 7\n"
+       ]
       }
      ],
      "prompt_number": 9
@@ -184,14 +603,70 @@
     {
      "cell_type": "code",
      "collapsed": false,
-     "input": "'''\nEXAMPLE 11.13\nAdding a Subscript Operator to the Ratio Class\n'''\ndef gcd(m,n):\n    # returns the greatest common divisor of m and n:\n    if (m<n):\n        m,n = n,m\n    while (n>0):\n        r = m % n\n        m = n\n        n = r\n    return m\nclass Ratio:\n    def __init__(self,n=0,d=1):\n        self.num = n\n        self.den = d\n        self.reduce()\n    def __mul__(self,y):\n        z = Ratio(self.num * y.num, self.den * y.den)\n        return z\n    def print_(self):\n        print self.num , '/', self.den\n        \n    def __getitem__(self,k):\n        if k == 1:\n            return  self.num\n        else:\n            return self.den\n    def reduce(self):\n        # enforce invariant(den > 0):\n        if (self.num == 0 or self.den == 0):\n            self.num = 0\n            self.den = 1\n            return\n        if (self.den < 0):\n            self.den *= -1\n            self.num *= -1\n        # enforce invariant(gcd(num,den) == 1):\n        if (self.den == 1):\n            return\n        # it's already reduced\n        sgn = 0\n        if self.num < 0:\n            sgn = -1\n        else:\n            sgn = 1\n        g = gcd(sgn*self.num,self.den)\n        self.num /= g\n        self.den /= g\n\nx = Ratio(22,7)\nprint \"x = \" ,\nx.print_()\nprint \"x[1] = \" , x[1] , \", x[2] = \" , x[2]\n",
+     "input": [
+      "\n",
+      "def gcd(m,n):\n",
+      "    # returns the greatest common divisor of m and n:\n",
+      "    if (m<n):\n",
+      "        m,n = n,m\n",
+      "    while (n>0):\n",
+      "        r = m % n\n",
+      "        m = n\n",
+      "        n = r\n",
+      "    return m\n",
+      "class Ratio:\n",
+      "    def __init__(self,n=0,d=1):\n",
+      "        self.num = n\n",
+      "        self.den = d\n",
+      "        self.reduce()\n",
+      "    def __mul__(self,y):\n",
+      "        z = Ratio(self.num * y.num, self.den * y.den)\n",
+      "        return z\n",
+      "    def print_(self):\n",
+      "        print self.num , '/', self.den\n",
+      "        \n",
+      "    def __getitem__(self,k):\n",
+      "        if k == 1:\n",
+      "            return  self.num\n",
+      "        else:\n",
+      "            return self.den\n",
+      "    def reduce(self):\n",
+      "        # enforce invariant(den > 0):\n",
+      "        if (self.num == 0 or self.den == 0):\n",
+      "            self.num = 0\n",
+      "            self.den = 1\n",
+      "            return\n",
+      "        if (self.den < 0):\n",
+      "            self.den *= -1\n",
+      "            self.num *= -1\n",
+      "        # enforce invariant(gcd(num,den) == 1):\n",
+      "        if (self.den == 1):\n",
+      "            return\n",
+      "        # it's already reduced\n",
+      "        sgn = 0\n",
+      "        if self.num < 0:\n",
+      "            sgn = -1\n",
+      "        else:\n",
+      "            sgn = 1\n",
+      "        g = gcd(sgn*self.num,self.den)\n",
+      "        self.num /= g\n",
+      "        self.den /= g\n",
+      "\n",
+      "x = Ratio(22,7)\n",
+      "print \"x = \" ,\n",
+      "x.print_()\n",
+      "print \"x[1] = \" , x[1] , \", x[2] = \" , x[2]\n"
+     ],
      "language": "python",
      "metadata": {},
      "outputs": [
       {
        "output_type": "stream",
        "stream": "stdout",
-       "text": "x =  22 / 7\nx[1] =  22 , x[2] =  7\n"
+       "text": [
+        "x =  22 / 7\n",
+        "x[1] =  22 , x[2] =  7\n"
+       ]
       }
      ],
      "prompt_number": 7
@@ -199,7 +674,7 @@
     {
      "cell_type": "code",
      "collapsed": false,
-     "input": "",
+     "input": [],
      "language": "python",
      "metadata": {},
      "outputs": []