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If it is given heterogeneous arguments, and doesn't have special knowledge about them, it should fall back to the builtin complex type as described below. r có—y)z, and >=. Real also provides defaults for the derived operations. r có—t‚)zTAny Real can be converted to a native float object. Called for float(self).rrs rÚ __float__zReal.__float__·ó €ô "Ð!rcó—t‚)aKtrunc(self): Truncates self to an Integral. Returns an Integral i such that: * i > 0 iff self > 0; * abs(i) <= abs(self); * for any Integral j satisfying the first two conditions, abs(i) >= abs(j) [i.e. i has "maximal" abs among those]. i.e. "truncate towards 0". rrs rÚ __trunc__zReal.__trunc__¾s €ô"Ð!rcó—t‚)z$Finds the greatest Integral <= self.rrs rÚ __floor__zReal.__floor__Ër'rcó—t‚)z!Finds the least Integral >= self.rrs rÚ__ceil__z Real.__ceil__Ðr'rNcó—t‚)z¸Rounds self to ndigits decimal places, defaulting to 0. If ndigits is omitted or None, returns an Integral, otherwise returns a Real. Rounds half toward even. r)rÚndigitss rÚ __round__zReal.__round__Õr rcó—||z||zfS)z™divmod(self, other): The pair (self // other, self % other). Sometimes this can be computed faster than the pair of operations. r r$s rÚ __divmod__zReal.__divmod__Þs€ð ˜‘ ˜t e™|Ð,Ð,rcó—||z||zfS)z™divmod(other, self): The pair (other // self, other % self). Sometimes this can be computed faster than the pair of operations. r r$s rÚ __rdivmod__zReal.__rdivmod__æs€ð ˜‘ ˜u t™|Ð,Ð,rcó—t‚)z)self // other: The floor() of self/other.rr$s rÚ __floordiv__zReal.__floordiv__îr'rcó—t‚)z)other // self: The floor() of other/self.rr$s rÚ __rfloordiv__zReal.__rfloordiv__ór'rcó—t‚)z self % otherrr$s rÚ__mod__z Real.__mod__ør'rcó—t‚)z other % selfrr$s rÚ__rmod__z Real.__rmod__ýr'rcó—t‚)zRself < other < on Reals defines a total ordering, except perhaps for NaN.rr$s rÚ__lt__z Real.__lt__rJrcó—t‚)z self <= otherrr$s rÚ__le__z Real.__le__ r'rcó*—tt|««S)z(complex(self) == complex(float(self), 0))ÚcomplexÚfloatrs rrzReal.__complex__s€ä”u˜T“{Ó#Ð#rcó—|­S)z&Real numbers are their real component.r rs rrz Real.realó €ðˆuˆ rcó—y)z)Real numbers have no imaginary component.rr rs rr"z Real.imagó€ðrcó—|­S)zConjugate is a no-op for Reals.r rs rrCzReal.conjugates €àˆuˆ r©N)r r rrrrrIrLrNrPrSrUrWrYr[r]r_rarcrrFrr"rCr rrrr¬s$„ñð€Iàñ"óð"ð ñ "óð "ðñ"óð"ðñ"óð"ðò"óð"ò-ò-ðñ"óð"ðñ"óð"ðñ"óð"ðñ"óð"ðñ"óð"ð ñ"óð"ò $ðñóððñóðórrcóN—eZdZdZdZeed„««Zeed„««Zd„Z y)rz6.numerator and .denominator should be in lowest terms.r có—t‚rlrrs rÚ numeratorzRational.numerator)r'rcó—t‚rlrrs rÚ denominatorzRational.denominator.r'rcóX—t|j«t|j«z S)a float(self) = self.numerator / self.denominator It's important that this conversion use the integer's "true" division rather than casting one side to float before dividing so that ratios of huge integers convert without overflowing. )Úintrorqrs rrIzRational.__float__4s#€ô�4—>‘>Ó"¤S¨×)9Ñ)9Ó%:Ñ:Ð:rN) r r rrrrFrrorqrIr rrrr$sE„Ù@à€Ià Øñ"óóð"ðØñ"óóð"ó;rrcó—eZdZdZdZed„«Zd„Zedd„«Zed„«Z ed„«Z ed „«Z ed „«Z ed „«Z ed „«Zed „«Zed„«Zed„«Zed„«Zed„«Zd„Zed„«Zed„«Zy)r zšIntegral adds methods that work on integral numbers. In short, these are conversion to int, pow with modulus, and the bit-string operations. r có—t‚)z int(self)rrs rÚ__int__zIntegral.__int__Hr'rcó—t|«S)z6Called whenever an index is needed, such as in slicing)rsrs rÚ __index__zIntegral.__index__Ms €ä�4‹yÐrNcó—t‚)a4self ** exponent % modulus, but maybe faster. Accept the modulus argument if you want to support the 3-argument version of pow(). Raise a TypeError if exponent < 0 or any argument isn't Integral. Otherwise, just implement the 2-argument version described in Complex. r)rr;Úmoduluss rr<zIntegral.__pow__Qs €ô"Ð!rcó—t‚)z self << otherrr$s rÚ __lshift__zIntegral.__lshift__\r'rcó—t‚)z other << selfrr$s rÚ __rlshift__zIntegral.__rlshift__ar'rcó—t‚)z self >> otherrr$s rÚ __rshift__zIntegral.__rshift__fr'rcó—t‚)z other >> selfrr$s rÚ __rrshift__zIntegral.__rrshift__kr'rcó—t‚)z self & otherrr$s rÚ__and__zIntegral.__and__pr'rcó—t‚)z other & selfrr$s rÚ__rand__zIntegral.__rand__ur'rcó—t‚)z self ^ otherrr$s rÚ__xor__zIntegral.__xor__zr'rcó—t‚)z other ^ selfrr$s rÚ__rxor__zIntegral.__rxor__r'rcó—t‚)z self | otherrr$s rÚ__or__zIntegral.__or__„r'rcó—t‚)z other | selfrr$s rÚ__ror__zIntegral.__ror__‰r'rcó—t‚)z~selfrrs rÚ __invert__zIntegral.__invert__Žr'rcó*—tt|««S)zfloat(self) == float(int(self)))rfrsrs rrIzIntegral.__float__”s€ä”S˜“YÓÐrcó—|­S)z"Integers are their own numerators.r rs rrozIntegral.numerator˜rhrcó—y)z!Integers have a denominator of 1.ér rs rrqzIntegral.denominator�rjrrl)r r rrrrrvrxr<r|r~r€r‚r„r†rˆrŠrŒrŽr�rIrFrorqr rrr r ?sB„ñð €Iàñ"óð"òðò"óð"ðñ"óð"ðñ"óð"ðñ"óð"ðñ"óð"ðñ"óð"ðñ"óð"ðñ"óð"ðñ"óð"ðñ"óð"ðñ"óð"ðñ"óð"ò  ðñóððñóñrr N)rÚabcrrÚ__all__rrÚregisterrerrfrr rsr rrÚr˜sˆðñ@÷:(â ?€ô �wõ ô(n"ˆfôn"ð`×Ñ�Ôôsˆ7ôsðj‡ � ˆeÔô;ˆtô;ô6aˆxôaðF ×Ñ�#Õr