def extract_leading_order(self, symbols, point=None):
"""
Returns the leading term and it's order.
Examples
========
>>> from sympy.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)),)
"""
lst = []
symbols = list(symbols if is_sequence(symbols) else [symbols])
if not point:
point = [0] * len(symbols)
seq = [(f, C.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 __new__(cls, *args, **options):
args = list(map(_sympify, args))
args = [a for a in args if a is not cls.identity]
if not options.pop('evaluate', True):
return cls._from_args(args)
if len(args) == 0:
return cls.identity
if len(args) == 1:
return args[0]
c_part, nc_part, order_symbols = cls.flatten(args)
is_commutative = not nc_part
obj = cls._from_args(c_part + nc_part, is_commutative)
if order_symbols is not None:
return C.Order(obj, *order_symbols)
return obj