def _eval_as_leading_term(self, x, logx=None, cdir=0):
if len(self.args) == 1:
arg = self.args[0]
arg0 = arg.subs(x, 0).cancel()
if not arg0.is_zero:
return self.func(arg0)
return arg.as_leading_term(x)
def simp_heaviside(arg):
a = arg.subs(exp(-t), u)
if a.has(t):
return Heaviside(arg)
rel = _solve_inequality(a > 0, u)
if rel.lhs == u:
k = log(rel.rhs)
return Heaviside(t + k)
else:
k = log(rel.lhs)
return Heaviside(-(t + k))
def simp_heaviside(arg):
a = arg.subs(exp(-t), u)
if a.has(t):
return Heaviside(arg)
rel = _solve_inequality(a > 0, u)
if rel.lhs == u:
k = log(rel.rhs)
return Heaviside(t + k)
else:
k = log(rel.lhs)
return Heaviside(-(t + k))
def _eval_as_leading_term(self, x, cdir=0):
from sympy import I, im
arg = self.args[0].together()
x0 = arg.subs(x, 0)
if x0 == 1:
return (arg - S.One).as_leading_term(x)
if cdir != 0:
cdir = self.args[0].dir(x, cdir)
if x0.is_real and x0.is_negative and im(cdir) < 0:
return self.func(x0) - 2 * I * S.Pi
return self.func(arg.as_leading_term(x))