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TODO: Fill out more detailed documentation on the operators. )ABCMetaabstractmethod)NumberComplexRealRationalIntegralc \ rS rSrSrSrSrSrg)r % zAll numbers inherit from this class.
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r\S 5 r\S 5 r\S 5 r\S 5 r\S 5 r\S 5 r\S 5 r\S 5 r\S 5 rSrg)r 9 aN Complex defines the operations that work on the builtin complex type.
In short, those are: a conversion to complex, .real, .imag, +, -,
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knowledge about them, it should fall back to the builtin complex
type as described below.
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5 r\S 5 r\S 5 r\S 5 r\S 5 rS r\S 5 r\S 5 rS rSrg)r zTo Complex, Real adds the operations that work on real numbers.
In short, those are: a conversion to float, trunc(), divmod,
%, <, <=, >, and >=.
Real also provides defaults for the derived operations.
r c [ e)zLAny Real can be converted to a native float object.
Called for float(self).r# r s r __float__Real.__float__
"!r c [ e)a trunc(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".
r# r s r __trunc__Real.__trunc__ s
"!r c [ e)z$Finds the greatest Integral <= self.r# r s r __floor__Real.__floor__ r0 r c [ e)z!Finds the least Integral >= self.r# r s r __ceil__
Real.__ceil__ r0 r Nc [ e)zRounds self to ndigits decimal places, defaulting to 0.
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returns a Real. Rounds half toward even.
r# )r ndigitss r __round__Real.__round__ r' r c X- X- 4$ )zdivmod(self, other): The pair (self // other, self % other).
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t|,,r c X- X- 4$ )zdivmod(other, self): The pair (other // self, other % self).
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r r, s r __rdivmod__Real.__rdivmod__ s
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__rfloordiv__Real.__rfloordiv__ r0 r c [ e)z self % otherr# r, s r __mod__ Real.__mod__ r0 r c [ e)z other % selfr# r, s r __rmod__
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self <= otherr# r, s r __le__ Real.__le__ r0 r c * [ [ U 5 5 $ )z(complex(self) == complex(float(self), 0))complexfloatr s r r Real.__complex__ s uT{##r c U 7$ )z&Real numbers are their real component.r r s r r% Real.real u r c g)z)Real numbers have no imaginary component.r r r s r r) Real.imag r c U 7$ )z Conjugate is a no-op for Reals.r r s r rX Real.conjugate s u r N)r
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Sr g)r i$ zTo Real, Rational adds numerator and denominator properties.
The numerator and denominator values should be in lowest terms,
with a positive denominator.
r c [ e)z3The numerator of a rational number in lowest terms.r# r s r numeratorRational.numerator- s
"!r c [ e)z\The denominator of a rational number in lowest terms.
This denominator should be positive.
r# r s r denominatorRational.denominator3 r' r c X [ U R 5 [ U R 5 - $ )zfloat(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.
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5 r\S 5 r\S 5 r\S 5 r\S 5 r\S 5 rS r\S 5 r\S 5 rSrg)r iH zIntegral adds methods that work on integral numbers.
In short, these are conversion to int, pow with modulus, and the
bit-string operations.
r c [ e)z int(self)r# r s r __int__Integral.__int__Q r0 r c [ U 5 $ )z6Called whenever an index is needed, such as in slicing)r r s r __index__Integral.__index__V s 4yr Nc [ e)a self ** exponent % modulus, but maybe faster.
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or any argument isn't Integral. Otherwise, just implement the
2-argument version described in Complex.
r# )r rM moduluss r rN Integral.__pow__Z s
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self << otherr# r, s r
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other << selfr# r, s r __rlshift__Integral.__rlshift__j r0 r c [ e)z
self >> otherr# r, s r
__rshift__Integral.__rshift__o r0 r c [ e)z
other >> selfr# r, s r __rrshift__Integral.__rrshift__t r0 r c [ e)z self & otherr# r, s r __and__Integral.__and__y r0 r c [ e)z other & selfr# r, s r __rand__Integral.__rand__~ r0 r c [ e)z self ^ otherr# r, s r __xor__Integral.__xor__ r0 r c [ e)z other ^ selfr# r, s r __rxor__Integral.__rxor__ r0 r c [ e)z self | otherr# r, s r __or__Integral.__or__ r0 r c [ e)z other | selfr# r, s r __ror__Integral.__ror__ r0 r c [ e)z~selfr# r s r
__invert__Integral.__invert__ r0 r c * [ [ U 5 5 $ )z float(self) == float(int(self)))r r r s r ra Integral.__float__ s SY r c U 7$ )z"Integers are their own numerators.r r s r r Integral.numerator r r c g)z!Integers have a denominator of 1. r r s r r Integral.denominator r r r )r
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