def _eval_as_leading_term(self, x, cdir=0):
from sympy import expand_mul, Order
old = self
expr = expand_mul(self)
if not expr.is_Add:
return expr.as_leading_term(x, cdir=cdir)
infinite = [t for t in expr.args if t.is_infinite]
leading_terms = [t.as_leading_term(x, cdir=cdir) for t in expr.args]
min, new_expr = Order(0), 0
try:
for term in leading_terms:
order = Order(term, x)
if not min or order not in min:
min = order
new_expr = term
elif min in order:
new_expr += term
except TypeError:
return expr
new_expr = new_expr.together()
if new_expr.is_Add:
new_expr = new_expr.simplify()
if not new_expr:
# simple leading term analysis gave us cancelled terms but we have to send
# back a term, so compute the leading term (via series)
n0 = min.getn()
res = Order(1)
incr = S.One
while res.is_Order:
res = old._eval_nseries(
x, n=n0 + incr, logx=None,
cdir=cdir).cancel().powsimp().trigsimp()
incr *= 2
return res.as_leading_term(x, cdir=cdir)
elif new_expr is S.NaN:
return old.func._from_args(infinite)
else:
return new_expr
def _eval_as_leading_term(self, x, logx=None, cdir=0):
from sympy import expand_mul, Order, Piecewise, piecewise_fold, log
old = self
if old.has(Piecewise):
old = piecewise_fold(old)
# This expansion is the last part of expand_log. expand_log also calls
# expand_mul with factor=True, which would be more expensive
if any(isinstance(a, log) for a in self.args):
logflags = dict(deep=True,
log=True,
mul=False,
power_exp=False,
power_base=False,
multinomial=False,
basic=False,
force=False,
factor=False)
old = old.expand(**logflags)
expr = expand_mul(old)
if not expr.is_Add:
return expr.as_leading_term(x, logx=logx, cdir=cdir)
infinite = [t for t in expr.args if t.is_infinite]
leading_terms = [
t.as_leading_term(x, logx=logx, cdir=cdir) for t in expr.args
]
min, new_expr = Order(0), 0
try:
for term in leading_terms:
order = Order(term, x)
if not min or order not in min:
min = order
new_expr = term
elif min in order:
new_expr += term
except TypeError:
return expr
is_zero = new_expr.is_zero
if is_zero is None:
new_expr = new_expr.trigsimp().cancel()
is_zero = new_expr.is_zero
if is_zero is True:
# simple leading term analysis gave us cancelled terms but we have to send
# back a term, so compute the leading term (via series)
n0 = min.getn()
res = Order(1)
incr = S.One
while res.is_Order:
res = old._eval_nseries(
x, n=n0 + incr, logx=None,
cdir=cdir).cancel().powsimp().trigsimp()
incr *= 2
return res.as_leading_term(x, logx=logx, cdir=cdir)
elif new_expr is S.NaN:
return old.func._from_args(infinite)
else:
return new_expr
