def is_a(x, n=None):
r"""
Check whether a list is a parking function.
If a size `n` is specified, checks if a list is a parking function
of size `n`.
TESTS::
sage: from sage.combinat.parking_functions import is_a
sage: is_a([1,1,2])
True
sage: is_a([1,2,1])
True
sage: is_a([1,1,4])
False
sage: is_a([3,1,1], 3)
True
"""
if not isinstance(
x, list): # from Florent Hivert non_decreasing_parking_function
return False
A = sorted(x)
from sage.combinat.non_decreasing_parking_function import is_a
return is_a(A, n)
def __init__(self, lst):
"""
TESTS::
sage: ParkingFunction([1, 1, 2, 2, 5, 6])
[1, 1, 2, 2, 5, 6]
"""
if not is_a(lst):
raise ValueError("%s is not a parking function." % lst)
CombinatorialObject.__init__(self, lst)
def __init__(self, lst):
"""
TESTS::
sage: ParkingFunction([1, 1, 2, 2, 5, 6])
[1, 1, 2, 2, 5, 6]
"""
if not is_a(lst):
raise ValueError("%s is not a parking function." % lst)
CombinatorialObject.__init__(self, lst)
def __contains__(self, x):
"""
TESTS::
sage: [] in ParkingFunctions()
True
sage: [1] in ParkingFunctions()
True
sage: [2] in ParkingFunctions()
False
sage: [1,3,1] in ParkingFunctions()
True
sage: [1,4,1] in ParkingFunctions()
False
"""
if isinstance(x, ParkingFunction_class):
return True
return is_a(x)
def __contains__(self, x):
"""
TESTS::
sage: [] in ParkingFunctions()
True
sage: [1] in ParkingFunctions()
True
sage: [2] in ParkingFunctions()
False
sage: [1,3,1] in ParkingFunctions()
True
sage: [1,4,1] in ParkingFunctions()
False
"""
if isinstance(x, ParkingFunction_class):
return True
return is_a(x)
def __contains__(self, x):
"""
TESTS::
sage: PF3 = ParkingFunctions(3); PF3
Parking functions of size 3
sage: [] in PF3
False
sage: [1] in PF3
False
sage: [1,3,1] in PF3
True
sage: [1,1,1] in PF3
True
sage: [1,4,1] in PF3
False
sage: all([p in PF3 for p in PF3])
True
"""
if isinstance(x, ParkingFunction_class):
return True
return is_a(x, self.n)
def __contains__(self, x):
"""
TESTS::
sage: PF3 = ParkingFunctions(3); PF3
Parking functions of size 3
sage: [] in PF3
False
sage: [1] in PF3
False
sage: [1,3,1] in PF3
True
sage: [1,1,1] in PF3
True
sage: [1,4,1] in PF3
False
sage: all([p in PF3 for p in PF3])
True
"""
if isinstance(x, ParkingFunction_class):
return True
return is_a(x, self.n)
def is_a(x, n=None):
"""
Checks whether a list is a parking function. If a size `n` is specified, checks if a
list is a parking function of size `n`.
TESTS::
sage: from sage.combinat.parking_functions import is_a
sage: is_a([1,1,2])
True
sage: is_a([1,2,1])
True
sage: is_a([1,1,4])
False
sage: is_a([3,1,1], 3)
True
"""
if not isinstance(x, list): # from Florent Hivert non_decreasing_parking_function
return False
A = sorted(x)
from sage.combinat.non_decreasing_parking_function import is_a
return is_a(A, n)
