def __call__(self, x, im=None):
"""
Construct an element.
EXAMPLES::
sage: CIF(2) # indirect doctest
2
sage: CIF(CIF.0)
1*I
sage: CIF('1+I')
1 + 1*I
sage: CIF(2,3)
2 + 3*I
sage: CIF(pi, e)
3.141592653589794? + 2.718281828459046?*I
sage: ComplexIntervalField(100)(CIF(RIF(2,3)))
3.?
"""
if im is None:
if isinstance(x, complex_interval.ComplexIntervalFieldElement):
if x.parent() is self:
return x
else:
return complex_interval.ComplexIntervalFieldElement(
self, x)
elif isinstance(x, complex_double.ComplexDoubleElement):
return complex_interval.ComplexIntervalFieldElement(
self, x.real(), x.imag())
elif isinstance(x, str):
# TODO: this is probably not the best and most
# efficient way to do this. -- Martin Albrecht
return complex_interval.ComplexIntervalFieldElement(
self,
sage_eval(x.replace(' ', ''),
locals={
"I": self.gen(),
"i": self.gen()
}))
late_import()
if isinstance(x, NumberFieldElement_quadratic) and list(
x.parent().polynomial()) == [1, 0, 1]:
(re, im) = list(x)
return complex_interval.ComplexIntervalFieldElement(
self, re, im)
try:
return x._complex_mpfi_(self)
except AttributeError:
pass
try:
return x._complex_mpfr_field_(self)
except AttributeError:
pass
return complex_interval.ComplexIntervalFieldElement(self, x, im)
def zeta(self, n=2):
"""
Return a primitive $n$-th root of unity.
INPUT:
n -- an integer (default: 2)
OUTPUT:
a complex n-th root of unity.
"""
from integer import Integer
n = Integer(n)
if n == 1:
x = self(1)
elif n == 2:
x = self(-1)
elif n >= 3:
# Use De Moivre
# e^(2*pi*i/n) = cos(2pi/n) + i *sin(2pi/n)
RR = self._real_field()
pi = RR.pi()
z = 2 * pi / n
x = complex_interval.ComplexIntervalFieldElement(
self, z.cos(), z.sin())
x._set_multiplicative_order(n)
return x
def gen(self, n=0):
"""
Return the generator of the complex (interval) field.
EXAMPLES::
sage: CIF.0
1*I
sage: CIF.gen(0)
1*I
"""
if n != 0:
raise IndexError("n must be 0")
return complex_interval.ComplexIntervalFieldElement(self, 0, 1)
def zeta(self, n=2):
r"""
Return a primitive `n`-th root of unity.
.. TODO::
Implement :class:`ComplexIntervalFieldElement` multiplicative order
and set this output to have multiplicative order ``n``.
INPUT:
- ``n`` -- an integer (default: 2)
OUTPUT:
A complex `n`-th root of unity.
EXAMPLES::
sage: CIF.zeta(2)
-1
sage: CIF.zeta(5)
0.309016994374948? + 0.9510565162951536?*I
"""
from integer import Integer
n = Integer(n)
if n == 1:
x = self(1)
elif n == 2:
x = self(-1)
elif n >= 3:
# Use De Moivre
# e^(2*pi*i/n) = cos(2pi/n) + i *sin(2pi/n)
RR = self._real_field()
pi = RR.pi()
z = 2 * pi / n
x = complex_interval.ComplexIntervalFieldElement(
self, z.cos(), z.sin())
# Uncomment after implemented
#x._set_multiplicative_order( n )
return x
def gen(self, n=0):
if n != 0:
raise IndexError, "n must be 0"
return complex_interval.ComplexIntervalFieldElement(self, 0, 1)
