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annotate Lib/numbers.py @ 79691:05c8928362ee

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Merge __next__ method link fixes with 3.3.
author Ezio Melotti <ezio.melotti@gmail.com>
date Fri, 12 Oct 2012 13:46:37 +0300
parents e979b26a9172
children
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1 # Copyright 2007 Google, Inc. All Rights Reserved.
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2 # Licensed to PSF under a Contributor Agreement.
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3
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4 """Abstract Base Classes (ABCs) for numbers, according to PEP 3141.
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5
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6 TODO: Fill out more detailed documentation on the operators."""
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7
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8 from abc import ABCMeta, abstractmethod
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10 __all__ = ["Number", "Complex", "Real", "Rational", "Integral"]
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11
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12 class Number(metaclass=ABCMeta):
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13 """All numbers inherit from this class.
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14
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15 If you just want to check if an argument x is a number, without
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16 caring what kind, use isinstance(x, Number).
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17 """
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18 __slots__ = ()
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19
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20 # Concrete numeric types must provide their own hash implementation
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21 __hash__ = None
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24 ## Notes on Decimal
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25 ## ----------------
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26 ## Decimal has all of the methods specified by the Real abc, but it should
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27 ## not be registered as a Real because decimals do not interoperate with
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28 ## binary floats (i.e. Decimal('3.14') + 2.71828 is undefined). But,
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29 ## abstract reals are expected to interoperate (i.e. R1 + R2 should be
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30 ## expected to work if R1 and R2 are both Reals).
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32 class Complex(Number):
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33 """Complex defines the operations that work on the builtin complex type.
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34
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35 In short, those are: a conversion to complex, .real, .imag, +, -,
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36 *, /, abs(), .conjugate, ==, and !=.
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37
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38 If it is given heterogenous arguments, and doesn't have special
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39 knowledge about them, it should fall back to the builtin complex
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40 type as described below.
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41 """
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42
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43 __slots__ = ()
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44
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45 @abstractmethod
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46 def __complex__(self):
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47 """Return a builtin complex instance. Called for complex(self)."""
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48
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49 def __bool__(self):
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50 """True if self != 0. Called for bool(self)."""
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51 return self != 0
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52
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53 @property
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54 @abstractmethod
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55 def real(self):
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56 """Retrieve the real component of this number.
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57
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58 This should subclass Real.
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59 """
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60 raise NotImplementedError
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61
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62 @property
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63 @abstractmethod
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64 def imag(self):
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65 """Retrieve the imaginary component of this number.
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66
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67 This should subclass Real.
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68 """
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69 raise NotImplementedError
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70
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71 @abstractmethod
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72 def __add__(self, other):
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73 """self + other"""
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74 raise NotImplementedError
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75
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76 @abstractmethod
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77 def __radd__(self, other):
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78 """other + self"""
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79 raise NotImplementedError
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80
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81 @abstractmethod
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82 def __neg__(self):
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83 """-self"""
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84 raise NotImplementedError
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85
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86 @abstractmethod
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87 def __pos__(self):
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88 """+self"""
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89 raise NotImplementedError
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90
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91 def __sub__(self, other):
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92 """self - other"""
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93 return self + -other
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94
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95 def __rsub__(self, other):
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96 """other - self"""
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97 return -self + other
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98
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99 @abstractmethod
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100 def __mul__(self, other):
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101 """self * other"""
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102 raise NotImplementedError
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103
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104 @abstractmethod
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105 def __rmul__(self, other):
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106 """other * self"""
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107 raise NotImplementedError
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108
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109 @abstractmethod
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110 def __truediv__(self, other):
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111 """self / other: Should promote to float when necessary."""
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112 raise NotImplementedError
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113
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114 @abstractmethod
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115 def __rtruediv__(self, other):
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116 """other / self"""
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117 raise NotImplementedError
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118
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119 @abstractmethod
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120 def __pow__(self, exponent):
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121 """self**exponent; should promote to float or complex when necessary."""
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122 raise NotImplementedError
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123
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124 @abstractmethod
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125 def __rpow__(self, base):
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126 """base ** self"""
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127 raise NotImplementedError
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128
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129 @abstractmethod
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130 def __abs__(self):
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131 """Returns the Real distance from 0. Called for abs(self)."""
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132 raise NotImplementedError
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133
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134 @abstractmethod
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135 def conjugate(self):
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136 """(x+y*i).conjugate() returns (x-y*i)."""
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137 raise NotImplementedError
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138
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139 @abstractmethod
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140 def __eq__(self, other):
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141 """self == other"""
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142 raise NotImplementedError
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143
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144 def __ne__(self, other):
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145 """self != other"""
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146 # The default __ne__ doesn't negate __eq__ until 3.0.
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147 return not (self == other)
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148
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149 Complex.register(complex)
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150
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151
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152 class Real(Complex):
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153 """To Complex, Real adds the operations that work on real numbers.
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154
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155 In short, those are: a conversion to float, trunc(), divmod,
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156 %, <, <=, >, and >=.
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157
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158 Real also provides defaults for the derived operations.
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159 """
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160
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161 __slots__ = ()
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162
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163 @abstractmethod
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164 def __float__(self):
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165 """Any Real can be converted to a native float object.
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166
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167 Called for float(self)."""
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168 raise NotImplementedError
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169
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170 @abstractmethod
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171 def __trunc__(self):
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172 """trunc(self): Truncates self to an Integral.
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173
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174 Returns an Integral i such that:
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175 * i>0 iff self>0;
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176 * abs(i) <= abs(self);
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177 * for any Integral j satisfying the first two conditions,
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178 abs(i) >= abs(j) [i.e. i has "maximal" abs among those].
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179 i.e. "truncate towards 0".
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180 """
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181 raise NotImplementedError
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182
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183 @abstractmethod
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184 def __floor__(self):
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185 """Finds the greatest Integral <= self."""
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186 raise NotImplementedError
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187
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188 @abstractmethod
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189 def __ceil__(self):
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190 """Finds the least Integral >= self."""
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191 raise NotImplementedError
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192
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193 @abstractmethod
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194 def __round__(self, ndigits=None):
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195 """Rounds self to ndigits decimal places, defaulting to 0.
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196
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197 If ndigits is omitted or None, returns an Integral, otherwise
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198 returns a Real. Rounds half toward even.
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199 """
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200 raise NotImplementedError
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201
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202 def __divmod__(self, other):
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203 """divmod(self, other): The pair (self // other, self % other).
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204
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205 Sometimes this can be computed faster than the pair of
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206 operations.
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207 """
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208 return (self // other, self % other)
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209
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210 def __rdivmod__(self, other):
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211 """divmod(other, self): The pair (self // other, self % other).
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212
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213 Sometimes this can be computed faster than the pair of
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214 operations.
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215 """
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216 return (other // self, other % self)
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217
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218 @abstractmethod
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219 def __floordiv__(self, other):
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220 """self // other: The floor() of self/other."""
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221 raise NotImplementedError
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222
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223 @abstractmethod
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224 def __rfloordiv__(self, other):
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225 """other // self: The floor() of other/self."""
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226 raise NotImplementedError
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227
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228 @abstractmethod
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229 def __mod__(self, other):
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230 """self % other"""
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231 raise NotImplementedError
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232
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233 @abstractmethod
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234 def __rmod__(self, other):
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235 """other % self"""
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236 raise NotImplementedError
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237
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238 @abstractmethod
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239 def __lt__(self, other):
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240 """self < other
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241
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242 < on Reals defines a total ordering, except perhaps for NaN."""
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243 raise NotImplementedError
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244
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245 @abstractmethod
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246 def __le__(self, other):
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247 """self <= other"""
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248 raise NotImplementedError
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249
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250 # Concrete implementations of Complex abstract methods.
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251 def __complex__(self):
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252 """complex(self) == complex(float(self), 0)"""
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253 return complex(float(self))
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254
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255 @property
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256 def real(self):
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257 """Real numbers are their real component."""
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258 return +self
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259
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260 @property
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261 def imag(self):
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262 """Real numbers have no imaginary component."""
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263 return 0
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264
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265 def conjugate(self):
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266 """Conjugate is a no-op for Reals."""
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267 return +self
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268
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269 Real.register(float)
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270
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271
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272 class Rational(Real):
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273 """.numerator and .denominator should be in lowest terms."""
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274
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275 __slots__ = ()
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276
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277 @property
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278 @abstractmethod
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279 def numerator(self):
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280 raise NotImplementedError
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281
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282 @property
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283 @abstractmethod
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284 def denominator(self):
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285 raise NotImplementedError
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286
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287 # Concrete implementation of Real's conversion to float.
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288 def __float__(self):
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289 """float(self) = self.numerator / self.denominator
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290
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291 It's important that this conversion use the integer's "true"
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292 division rather than casting one side to float before dividing
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293 so that ratios of huge integers convert without overflowing.
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294
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295 """
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296 return self.numerator / self.denominator
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297
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298
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299 class Integral(Rational):
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300 """Integral adds a conversion to int and the bit-string operations."""
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301
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302 __slots__ = ()
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303
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304 @abstractmethod
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305 def __int__(self):
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306 """int(self)"""
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307 raise NotImplementedError
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308
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309 def __index__(self):
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310 """Called whenever an index is needed, such as in slicing"""
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311 return int(self)
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312
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313 @abstractmethod
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314 def __pow__(self, exponent, modulus=None):
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315 """self ** exponent % modulus, but maybe faster.
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316
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317 Accept the modulus argument if you want to support the
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318 3-argument version of pow(). Raise a TypeError if exponent < 0
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319 or any argument isn't Integral. Otherwise, just implement the
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320 2-argument version described in Complex.
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321 """
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322 raise NotImplementedError
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323
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324 @abstractmethod
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325 def __lshift__(self, other):
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326 """self << other"""
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327 raise NotImplementedError
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328
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329 @abstractmethod
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330 def __rlshift__(self, other):
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331 """other << self"""
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332 raise NotImplementedError
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333
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334 @abstractmethod
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335 def __rshift__(self, other):
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336 """self >> other"""
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337 raise NotImplementedError
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338
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339 @abstractmethod
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340 def __rrshift__(self, other):
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341 """other >> self"""
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342 raise NotImplementedError
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343
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344 @abstractmethod
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345 def __and__(self, other):
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346 """self & other"""
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347 raise NotImplementedError
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348
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349 @abstractmethod
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350 def __rand__(self, other):
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351 """other & self"""
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352 raise NotImplementedError
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353
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354 @abstractmethod
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355 def __xor__(self, other):
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356 """self ^ other"""
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357 raise NotImplementedError
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358
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359 @abstractmethod
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360 def __rxor__(self, other):
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361 """other ^ self"""
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362 raise NotImplementedError
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363
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364 @abstractmethod
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365 def __or__(self, other):
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366 """self | other"""
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367 raise NotImplementedError
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368
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369 @abstractmethod
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370 def __ror__(self, other):
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371 """other | self"""
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372 raise NotImplementedError
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373
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374 @abstractmethod
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375 def __invert__(self):
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376 """~self"""
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377 raise NotImplementedError
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378
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379 # Concrete implementations of Rational and Real abstract methods.
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380 def __float__(self):
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381 """float(self) == float(int(self))"""
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382 return float(int(self))
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383
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384 @property
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385 def numerator(self):
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386 """Integers are their own numerators."""
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387 return +self
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388
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389 @property
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390 def denominator(self):
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391 """Integers have a denominator of 1."""
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392 return 1
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393
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394 Integral.register(int)