Mercurial > cpython-lru_cache-weakref
annotate Demo/classes/Rat.py @ 5817:48b94de85bf3 legacy-trunk
Extensive changes by AMK.
| author | Guido van Rossum <guido@python.org> |
|---|---|
| date | Thu, 17 Jul 1997 16:29:42 +0000 |
| parents | ba005e4db4c5 |
| children | c447d1ad7851 |
| rev | line source |
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1 '''\ |
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2 This module implements rational numbers. |
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3 |
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4 The entry point of this module is the function |
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5 rat(numerator, denominator) |
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6 If either numerator or denominator is of an integral or rational type, |
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7 the result is a rational number, else, the result is the simplest of |
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8 the types float and complex which can hold numerator/denominator. |
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9 If denominator is omitted, it defaults to 1. |
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10 Rational numbers can be used in calculations with any other numeric |
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11 type. The result of the calculation will be rational if possible. |
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12 |
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13 There is also a test function with calling sequence |
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14 test() |
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15 The documentation string of the test function contains the expected |
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16 output. |
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17 ''' |
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18 |
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19 # Contributed by Sjoerd Mullender |
| 945 | 20 |
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21 from types import * |
| 945 | 22 |
| 23 def gcd(a, b): | |
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24 '''Calculate the Greatest Common Divisor.''' |
| 945 | 25 while b: |
| 26 a, b = b, a%b | |
| 27 return a | |
| 28 | |
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29 def rat(num, den = 1): |
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30 # must check complex before float |
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31 if type(num) is ComplexType or type(den) is ComplexType: |
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32 # numerator or denominator is complex: return a complex |
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33 return complex(num) / complex(den) |
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34 if type(num) is FloatType or type(den) is FloatType: |
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35 # numerator or denominator is float: return a float |
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36 return float(num) / float(den) |
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37 # otherwise return a rational |
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38 return Rat(num, den) |
| 945 | 39 |
| 40 class Rat: | |
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41 '''This class implements rational numbers.''' |
| 945 | 42 |
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43 def __init__(self, num, den = 1): |
| 945 | 44 if den == 0: |
| 45 raise ZeroDivisionError, 'rat(x, 0)' | |
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46 |
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47 # normalize |
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48 |
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49 # must check complex before float |
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50 if type(num) is ComplexType or type(den) is ComplexType: |
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51 # numerator or denominator is complex: |
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52 # normalized form has denominator == 1+0j |
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53 self.__num = complex(num) / complex(den) |
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54 self.__den = complex(1) |
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55 return |
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56 if type(num) is FloatType or type(den) is FloatType: |
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57 # numerator or denominator is float: |
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58 # normalized form has denominator == 1.0 |
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59 self.__num = float(num) / float(den) |
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60 self.__den = 1.0 |
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61 return |
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62 if (type(num) is InstanceType and |
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63 num.__class__ is self.__class__) or \ |
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64 (type(den) is InstanceType and |
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65 den.__class__ is self.__class__): |
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66 # numerator or denominator is rational |
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67 new = num / den |
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68 if type(new) is not InstanceType or \ |
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69 new.__class__ is not self.__class__: |
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70 self.__num = new |
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71 if type(new) is ComplexType: |
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72 self.__den = complex(1) |
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73 else: |
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74 self.__den = 1.0 |
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75 else: |
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76 self.__num = new.__num |
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77 self.__den = new.__den |
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78 else: |
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79 # make sure numerator and denominator don't |
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80 # have common factors |
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81 # this also makes sure that denominator > 0 |
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82 g = gcd(num, den) |
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83 self.__num = num / g |
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84 self.__den = den / g |
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85 # try making numerator and denominator of IntType if they fit |
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86 try: |
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87 numi = int(self.__num) |
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88 deni = int(self.__den) |
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89 except (OverflowError, TypeError): |
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90 pass |
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91 else: |
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92 if self.__num == numi and self.__den == deni: |
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93 self.__num = numi |
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94 self.__den = deni |
| 945 | 95 |
| 96 def __repr__(self): | |
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97 return 'Rat(%s,%s)' % (self.__num, self.__den) |
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98 |
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99 def __str__(self): |
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100 if self.__den == 1: |
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101 return str(self.__num) |
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102 else: |
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103 return '%s/%s' % (str(self.__num), str(self.__den)) |
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104 |
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105 # a + b |
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106 def __add__(a, b): |
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107 try: |
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108 return rat(a.__num * b.__den + b.__num * a.__den, |
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109 a.__den * b.__den) |
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110 except OverflowError: |
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111 return rat(long(a.__num) * long(b.__den) + |
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112 long(b.__num) * long(a.__den), |
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113 long(a.__den) * long(b.__den)) |
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114 |
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115 def __radd__(b, a): |
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116 return Rat(a) + b |
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117 |
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118 # a - b |
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119 def __sub__(a, b): |
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120 try: |
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121 return rat(a.__num * b.__den - b.__num * a.__den, |
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122 a.__den * b.__den) |
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123 except OverflowError: |
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124 return rat(long(a.__num) * long(b.__den) - |
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125 long(b.__num) * long(a.__den), |
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126 long(a.__den) * long(b.__den)) |
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127 |
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128 def __rsub__(b, a): |
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129 return Rat(a) - b |
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130 |
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131 # a * b |
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132 def __mul__(a, b): |
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133 try: |
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134 return rat(a.__num * b.__num, a.__den * b.__den) |
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135 except OverflowError: |
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136 return rat(long(a.__num) * long(b.__num), |
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137 long(a.__den) * long(b.__den)) |
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138 |
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139 def __rmul__(b, a): |
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140 return Rat(a) * b |
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141 |
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142 # a / b |
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143 def __div__(a, b): |
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144 try: |
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145 return rat(a.__num * b.__den, a.__den * b.__num) |
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146 except OverflowError: |
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147 return rat(long(a.__num) * long(b.__den), |
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148 long(a.__den) * long(b.__num)) |
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149 |
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150 def __rdiv__(b, a): |
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151 return Rat(a) / b |
| 945 | 152 |
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153 # a % b |
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154 def __mod__(a, b): |
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155 div = a / b |
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156 try: |
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157 div = int(div) |
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158 except OverflowError: |
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159 div = long(div) |
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160 return a - b * div |
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161 |
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162 def __rmod__(b, a): |
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163 return Rat(a) % b |
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164 |
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165 # a ** b |
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166 def __pow__(a, b): |
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167 if b.__den != 1: |
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168 if type(a.__num) is ComplexType: |
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169 a = complex(a) |
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170 else: |
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171 a = float(a) |
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172 if type(b.__num) is ComplexType: |
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173 b = complex(b) |
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174 else: |
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175 b = float(b) |
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176 return a ** b |
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177 try: |
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178 return rat(a.__num ** b.__num, a.__den ** b.__num) |
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179 except OverflowError: |
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180 return rat(long(a.__num) ** b.__num, |
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181 long(a.__den) ** b.__num) |
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182 |
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183 def __rpow__(b, a): |
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184 return Rat(a) ** b |
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185 |
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186 # -a |
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187 def __neg__(a): |
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188 try: |
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189 return rat(-a.__num, a.__den) |
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190 except OverflowError: |
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191 # a.__num == sys.maxint |
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192 return rat(-long(a.__num), a.__den) |
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193 |
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194 # abs(a) |
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195 def __abs__(a): |
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196 return rat(abs(a.__num), a.__den) |
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197 |
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198 # int(a) |
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199 def __int__(a): |
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200 return int(a.__num / a.__den) |
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201 |
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202 # long(a) |
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203 def __long__(a): |
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204 return long(a.__num) / long(a.__den) |
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205 |
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206 # float(a) |
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207 def __float__(a): |
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208 return float(a.__num) / float(a.__den) |
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209 |
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210 # complex(a) |
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211 def __complex__(a): |
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212 return complex(a.__num) / complex(a.__den) |
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213 |
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214 # cmp(a,b) |
| 945 | 215 def __cmp__(a, b): |
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216 diff = a - b |
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217 if diff.__num < 0: |
| 945 | 218 return -1 |
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219 elif diff.__num > 0: |
| 945 | 220 return 1 |
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221 else: |
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222 return 0 |
| 945 | 223 |
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224 def __rcmp__(b, a): |
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225 return cmp(Rat(a), b) |
| 945 | 226 |
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227 # a != 0 |
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228 def __nonzero__(a): |
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229 return a.__num != 0 |
| 945 | 230 |
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231 # coercion |
| 945 | 232 def __coerce__(a, b): |
|
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233 return a, Rat(b) |
| 945 | 234 |
| 235 def test(): | |
|
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236 '''\ |
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237 Test function for rat module. |
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238 |
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239 The expected output is (module some differences in floating |
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240 precission): |
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241 -1 |
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242 -1 |
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|
243 0 0L 0.1 (0.1+0j) |
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244 [Rat(1,2), Rat(-3,10), Rat(1,25), Rat(1,4)] |
|
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245 [Rat(-3,10), Rat(1,25), Rat(1,4), Rat(1,2)] |
|
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246 0 |
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|
247 11/10 |
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248 11/10 |
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249 1.1 |
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|
250 OK |
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|
251 2 1.5 3/2 (1.5+1.5j) 15707963/5000000 |
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252 2 2 2.0 (2+0j) |
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|
253 |
|
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254 4 0 4 1 4 0 |
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255 3.5 0.5 3.0 1.33333333333 2.82842712475 1 |
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256 7/2 1/2 3 4/3 2.82842712475 1 |
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257 (3.5+1.5j) (0.5-1.5j) (3+3j) (0.666666666667-0.666666666667j) (1.43248815986+2.43884761145j) 1 |
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258 1.5 1 1.5 (1.5+0j) |
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259 |
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260 3.5 -0.5 3.0 0.75 2.25 -1 |
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261 3.0 0.0 2.25 1.0 1.83711730709 0 |
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262 3.0 0.0 2.25 1.0 1.83711730709 1 |
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263 (3+1.5j) -1.5j (2.25+2.25j) (0.5-0.5j) (1.50768393746+1.04970907623j) -1 |
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264 3/2 1 1.5 (1.5+0j) |
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265 |
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266 7/2 -1/2 3 3/4 9/4 -1 |
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267 3.0 0.0 2.25 1.0 1.83711730709 -1 |
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268 3 0 9/4 1 1.83711730709 0 |
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269 (3+1.5j) -1.5j (2.25+2.25j) (0.5-0.5j) (1.50768393746+1.04970907623j) -1 |
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270 (1.5+1.5j) (1.5+1.5j) |
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271 |
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272 (3.5+1.5j) (-0.5+1.5j) (3+3j) (0.75+0.75j) 4.5j -1 |
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273 (3+1.5j) 1.5j (2.25+2.25j) (1+1j) (1.18235814075+2.85446505899j) 1 |
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274 (3+1.5j) 1.5j (2.25+2.25j) (1+1j) (1.18235814075+2.85446505899j) 1 |
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275 (3+3j) 0j 4.5j (1+0j) (-0.638110484918+0.705394566962j) 0 |
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276 ''' |
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277 print rat(-1L, 1) |
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278 print rat(1, -1) |
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279 a = rat(1, 10) |
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280 print int(a), long(a), float(a), complex(a) |
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281 b = rat(2, 5) |
| 945 | 282 l = [a+b, a-b, a*b, a/b] |
| 283 print l | |
| 284 l.sort() | |
| 285 print l | |
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286 print rat(0, 1) |
| 945 | 287 print a+1 |
| 288 print a+1L | |
| 289 print a+1.0 | |
| 1371 | 290 try: |
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291 print rat(1, 0) |
| 1371 | 292 raise SystemError, 'should have been ZeroDivisionError' |
| 293 except ZeroDivisionError: | |
| 294 print 'OK' | |
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295 print rat(2), rat(1.5), rat(3, 2), rat(1.5+1.5j), rat(31415926,10000000) |
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296 list = [2, 1.5, rat(3,2), 1.5+1.5j] |
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297 for i in list: |
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298 print i, |
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299 if type(i) is not ComplexType: |
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300 print int(i), float(i), |
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301 print complex(i) |
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302 print |
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303 for j in list: |
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304 print i + j, i - j, i * j, i / j, i ** j, cmp(i, j) |
| 945 | 305 |
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306 if __name__ == '__main__': |
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307 test() |
