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# Complex numbers
from math import sqrt
def complex(re, im):
return Complex().init(re, im)
class Complex:
def init(self, re, im):
self.re = float(re)
self.im = float(im)
return self
def __repr__(self):
return 'complex' + `self.re, self.im`
def __cmp__(a, b):
a = a.__abs__()
b = b.__abs__()
return (a > b) - (a < b)
def __float__(self):
if self.im:
raise ValueError, 'cannot convert complex to float'
return float(self.re)
def __long__(self):
return long(float(self))
def __int__(self):
return int(float(self))
def __abs__(self):
# XXX overflow?
return sqrt(self.re*self.re + self.im*self.im)
def __add__(a, b):
return complex(a.re + b.re, a.im + b.im)
def __sub__(a, b):
return complex(a.re - b.re, a.im - b.im)
def __mul__(a, b):
return complex(a.re*b.re - a.im*b.im, a.re*b.im + a.im*b.re)
def __div__(a, b):
q = (b.re*b.re + b.im*b.im)
re = (a.re*b.re + a.im*b.im) / q
im = (a.im*b.re - b.im*a.re) / q
return complex(re, im)
def __neg__(self):
return complex(-self.re, -self.im)
def test():
a = complex(2, 0)
b = complex(3, 4)
print a, b
print a+b, a-b, a*b, a/b
print b+a, b-a, b*a, b/a
i = complex(0, 1)
print i, i*i, i*i*i, i*i*i*i
j = complex(1, 1)
print j, j*j, j*j*j, j*j*j*j
print abs(j), abs(j*j), abs(j*j*j), abs(j*j*j*j)
print i/-i
test()
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