def extract_leading_order(self, symbols):
"""Returns the leading term and its order.
Examples
========
>>> from diofant.abc import x
>>> (x + 1 + 1/x**5).extract_leading_order(x)
((x**(-5), O(x**(-5))),)
>>> (1 + x).extract_leading_order(x)
((1, O(1)),)
>>> (x + x**2).extract_leading_order(x)
((x, O(x)),)
"""
from diofant import Order
lst = []
symbols = list(symbols if is_sequence(symbols) else [symbols])
point = [0] * len(symbols)
seq = [(f, Order(f, *zip(symbols, point))) for f in self.args]
for ef, of in seq:
for e, o in lst:
if o.contains(of) and o != of:
of = None
break
if of is None:
continue
new_lst = [(ef, of)]
for e, o in lst:
if of.contains(o) and o != of:
continue
new_lst.append((e, o))
lst = new_lst
return tuple(lst)
def test_Order():
assert precedence(Order(x)) == PRECEDENCE["Atom"]
def test_series():
for c in (Limit, Limit(y, x, 1), Order, Order(y)):
check(c)