Removing this -- complex numbers are now builtin,
and there is already a similar demo in Demo/classes/Complex.py.
diff --git a/Lib/Complex.py b/Lib/Complex.py
deleted file mode 100644
index f4892f3..0000000
--- a/Lib/Complex.py
+++ /dev/null
@@ -1,275 +0,0 @@
-# Complex numbers
-# ---------------
-
-# This module represents complex numbers as instances of the class Complex.
-# A Complex instance z has two data attribues, z.re (the real part) and z.im
-# (the imaginary part). In fact, z.re and z.im can have any value -- all
-# arithmetic operators work regardless of the type of z.re and z.im (as long
-# as they support numerical operations).
-#
-# The following functions exist (Complex is actually a class):
-# Complex([re [,im]) -> creates a complex number from a real and an imaginary part
-# IsComplex(z) -> true iff z is a complex number (== has .re and .im attributes)
-# Polar([r [,phi [,fullcircle]]]) ->
-# the complex number z for which r == z.radius() and phi == z.angle(fullcircle)
-# (r and phi default to 0)
-#
-# Complex numbers have the following methods:
-# z.abs() -> absolute value of z
-# z.radius() == z.abs()
-# z.angle([fullcircle]) -> angle from positive X axis; fullcircle gives units
-# z.phi([fullcircle]) == z.angle(fullcircle)
-#
-# These standard functions and unary operators accept complex arguments:
-# abs(z)
-# -z
-# +z
-# not z
-# repr(z) == `z`
-# str(z)
-# hash(z) -> a combination of hash(z.re) and hash(z.im) such that if z.im is zero
-# the result equals hash(z.re)
-# Note that hex(z) and oct(z) are not defined.
-#
-# These conversions accept complex arguments only if their imaginary part is zero:
-# int(z)
-# long(z)
-# float(z)
-#
-# The following operators accept two complex numbers, or one complex number
-# and one real number (int, long or float):
-# z1 + z2
-# z1 - z2
-# z1 * z2
-# z1 / z2
-# pow(z1, z2)
-# cmp(z1, z2)
-# Note that z1 % z2 and divmod(z1, z2) are not defined,
-# nor are shift and mask operations.
-#
-# The standard module math does not support complex numbers.
-# (I suppose it would be easy to implement a cmath module.)
-#
-# Idea:
-# add a class Polar(r, phi) and mixed-mode arithmetic which
-# chooses the most appropriate type for the result:
-# Complex for +,-,cmp
-# Polar for *,/,pow
-
-
-import types, math
-
-if not hasattr(math, 'hypot'):
- def hypot(x, y):
- # XXX I know there's a way to compute this without possibly causing
- # overflow, but I can't remember what it is right now...
- return math.sqrt(x*x + y*y)
- math.hypot = hypot
-
-twopi = math.pi*2.0
-halfpi = math.pi/2.0
-
-def IsComplex(obj):
- return hasattr(obj, 're') and hasattr(obj, 'im')
-
-def Polar(r = 0, phi = 0, fullcircle = twopi):
- phi = phi * (twopi / fullcircle)
- return Complex(math.cos(phi)*r, math.sin(phi)*r)
-
-class Complex:
-
- def __init__(self, re=0, im=0):
- if IsComplex(re):
- im = im + re.im
- re = re.re
- if IsComplex(im):
- re = re - im.im
- im = im.re
- self.re = re
- self.im = im
-
- def __setattr__(self, name, value):
- if hasattr(self, name):
- raise TypeError, "Complex numbers have set-once attributes"
- self.__dict__[name] = value
-
- def __repr__(self):
- if not self.im:
- return 'Complex(%s)' % `self.re`
- else:
- return 'Complex(%s, %s)' % (`self.re`, `self.im`)
-
- def __str__(self):
- if not self.im:
- return `self.re`
- else:
- return 'Complex(%s, %s)' % (`self.re`, `self.im`)
-
- def __coerce__(self, other):
- if IsComplex(other):
- return self, other
- return self, Complex(other) # May fail
-
- def __cmp__(self, other):
- return cmp(self.re, other.re) or cmp(self.im, other.im)
-
- def __hash__(self):
- if not self.im: return hash(self.re)
- mod = sys.maxint + 1L
- return int((hash(self.re) + 2L*hash(self.im) + mod) % (2L*mod) - mod)
-
- def __neg__(self):
- return Complex(-self.re, -self.im)
-
- def __pos__(self):
- return self
-
- def __abs__(self):
- return math.hypot(self.re, self.im)
- ##return math.sqrt(self.re*self.re + self.im*self.im)
-
-
- def __int__(self):
- if self.im:
- raise ValueError, "can't convert Complex with nonzero im to int"
- return int(self.re)
-
- def __long__(self):
- if self.im:
- raise ValueError, "can't convert Complex with nonzero im to long"
- return long(self.re)
-
- def __float__(self):
- if self.im:
- raise ValueError, "can't convert Complex with nonzero im to float"
- return float(self.re)
-
- def __nonzero__(self):
- return not (self.re == self.im == 0)
-
- abs = radius = __abs__
-
- def angle(self, fullcircle = twopi):
- return (fullcircle/twopi) * ((halfpi - math.atan2(self.re, self.im)) % twopi)
-
- phi = angle
-
- def __add__(self, other):
- return Complex(self.re + other.re, self.im + other.im)
-
- __radd__ = __add__
-
- def __sub__(self, other):
- return Complex(self.re - other.re, self.im - other.im)
-
- def __rsub__(self, other):
- return Complex(other.re - self.re, other.im - self.im)
-
- def __mul__(self, other):
- return Complex(self.re*other.re - self.im*other.im,
- self.re*other.im + self.im*other.re)
-
- __rmul__ = __mul__
-
- def __div__(self, other):
- # Deviating from the general principle of not forcing re or im
- # to be floats, we cast to float here, otherwise division
- # of Complex numbers with integer re and im parts would use
- # the (truncating) integer division
- d = float(other.re*other.re + other.im*other.im)
- if not d: raise ZeroDivisionError, 'Complex division'
- return Complex((self.re*other.re + self.im*other.im) / d,
- (self.im*other.re - self.re*other.im) / d)
-
- def __rdiv__(self, other):
- return other / self
-
- def __pow__(self, n, z=None):
- if z is not None:
- raise TypeError, 'Complex does not support ternary pow()'
- if IsComplex(n):
- if n.im: raise TypeError, 'Complex to the Complex power'
- n = n.re
- r = pow(self.abs(), n)
- phi = n*self.angle()
- return Complex(math.cos(phi)*r, math.sin(phi)*r)
-
- def __rpow__(self, base):
- return pow(base, self)
-
-
-# Everything below this point is part of the test suite
-
-def checkop(expr, a, b, value, fuzz = 1e-6):
- import sys
- print ' ', a, 'and', b,
- try:
- result = eval(expr)
- except:
- result = sys.exc_type
- print '->', result
- if (type(result) == type('') or type(value) == type('')):
- ok = result == value
- else:
- ok = abs(result - value) <= fuzz
- if not ok:
- print '!!\t!!\t!! should be', value, 'diff', abs(result - value)
-
-
-def test():
- testsuite = {
- 'a+b': [
- (1, 10, 11),
- (1, Complex(0,10), Complex(1,10)),
- (Complex(0,10), 1, Complex(1,10)),
- (Complex(0,10), Complex(1), Complex(1,10)),
- (Complex(1), Complex(0,10), Complex(1,10)),
- ],
- 'a-b': [
- (1, 10, -9),
- (1, Complex(0,10), Complex(1,-10)),
- (Complex(0,10), 1, Complex(-1,10)),
- (Complex(0,10), Complex(1), Complex(-1,10)),
- (Complex(1), Complex(0,10), Complex(1,-10)),
- ],
- 'a*b': [
- (1, 10, 10),
- (1, Complex(0,10), Complex(0, 10)),
- (Complex(0,10), 1, Complex(0,10)),
- (Complex(0,10), Complex(1), Complex(0,10)),
- (Complex(1), Complex(0,10), Complex(0,10)),
- ],
- 'a/b': [
- (1., 10, 0.1),
- (1, Complex(0,10), Complex(0, -0.1)),
- (Complex(0, 10), 1, Complex(0, 10)),
- (Complex(0, 10), Complex(1), Complex(0, 10)),
- (Complex(1), Complex(0,10), Complex(0, -0.1)),
- ],
- 'pow(a,b)': [
- (1, 10, 1),
- (1, Complex(0,10), 'TypeError'),
- (Complex(0,10), 1, Complex(0,10)),
- (Complex(0,10), Complex(1), Complex(0,10)),
- (Complex(1), Complex(0,10), 'TypeError'),
- (2, Complex(4,0), 16),
- ],
- 'cmp(a,b)': [
- (1, 10, -1),
- (1, Complex(0,10), 1),
- (Complex(0,10), 1, -1),
- (Complex(0,10), Complex(1), -1),
- (Complex(1), Complex(0,10), 1),
- ],
- }
- exprs = testsuite.keys()
- exprs.sort()
- for expr in exprs:
- print expr + ':'
- t = (expr,)
- for item in testsuite[expr]:
- apply(checkop, t+item)
-
-
-if __name__ == '__main__':
- test()