def _eval_expand_complex(self, *args):
if self[0].is_real:
return self
re, im = self[0].as_real_imag()
denom = sinh(re)**2 + Basic.cos(im)**2
return (sinh(re)*cosh(re) + \
S.ImaginaryUnit*Basic.sin(im)*Basic.cos(im))/denom
def apothem(self):
"""
Returns the apothem/inradius of the regular polygon (i.e., the
radius of the inscribed circle).
"""
n = self.__getitem__(2)
return self.radius * Basic.cos(S.Pi/n)
def vertices(self):
Polygon.vertices.__doc__
points = []
c, r, n = self[:]
v = 2*S.Pi/n
for k in xrange(0, n):
points.append( Point(c[0] + r*Basic.cos(k*v), c[1] + r*Basic.sin(k*v)) )
return points
def _eval_apply(self, arg):
arg = Basic.sympify(arg)
if isinstance(arg, Basic.Number):
if isinstance(arg, Basic.NaN):
return S.NaN
elif isinstance(arg, Basic.Infinity):
return S.Infinity
elif isinstance(arg, Basic.NegativeInfinity):
return S.Infinity
elif isinstance(arg, Basic.Zero):
return S.One
elif arg.is_negative:
return self(-arg)
else:
i_coeff = arg.as_coefficient(S.ImaginaryUnit)
if i_coeff is not None:
return Basic.cos(i_coeff)
else:
coeff, terms = arg.as_coeff_terms()
if coeff.is_negative:
return self(-arg)
def _eval_apply(cls, n, k):
if not 0 <= k < n:
raise ValueError, "must have 0 <= k < n"
return Basic.cos(S.Pi*(k+1)/(n+1))
def _eval_expand_complex(self, *args):
if self[0].is_real:
return self
re, im = self[0].as_real_imag()
return sinh(re)*Basic.cos(im) + cosh(re)*Basic.sin(im)*S.ImaginaryUnit
def _eval_expand_complex(self, *args):
re, im = self[0].as_real_imag()
cos, sin = Basic.cos(im), Basic.sin(im)
return exp(re) * cos + S.ImaginaryUnit * exp(re) * sin
def arbitrary_point(self, parameter_name='t'):
"""Returns a symbolic point that is on the ellipse."""
t = Basic.Symbol(parameter_name, real=True)
return Point(
self.center[0] + self.hradius*Basic.cos(t),
self.center[1] + self.vradius*Basic.sin(t))
