def __classcall_private__(cls, p):
r"""
This function tries to recognize the input (it can be either a list or
a tuple of pairs, or a fix-point free involution given as a list or as
a permutation), constructs the parent (enumerated set of
PerfectMatchings of the ground set) and calls the __init__ function to
construct our object.
EXAMPLES::
sage: m = PerfectMatching([('a','e'),('b','c'),('d','f')]);m
[('a', 'e'), ('b', 'c'), ('d', 'f')]
sage: isinstance(m,PerfectMatching)
True
sage: n = PerfectMatching([3, 8, 1, 7, 6, 5, 4, 2]);n
[(1, 3), (2, 8), (4, 7), (5, 6)]
sage: n.parent()
Set of perfect matchings of {1, 2, 3, 4, 5, 6, 7, 8}
sage: PerfectMatching([(1, 4), (2, 3), (5, 6)]).is_non_crossing()
True
The function checks that the given list or permutation is a valid perfect
matching (i.e. a list of pairs with pairwise disjoint elements or a
fixpoint-free involution) and raises a ValueError otherwise:
sage: PerfectMatching([(1, 2, 3), (4, 5)])
Traceback (most recent call last):
...
ValueError: [(1, 2, 3), (4, 5)] is not a valid perfect matching: all elements of the list must be pairs
If you know your datas are in a good format, use directly
``PerfectMatchings(objects)(data)``.
TESTS::
sage: m = PerfectMatching([('a','e'),('b','c'),('d','f')])
sage: TestSuite(m).run()
sage: m = PerfectMatching([])
sage: TestSuite(m).run()
sage: PerfectMatching(6)
Traceback (most recent call last):
...
ValueError: cannot convert p (= 6) to a PerfectMatching
sage: PerfectMatching([(1,2,3)])
Traceback (most recent call last):
...
ValueError: [(1, 2, 3)] is not a valid perfect matching:
all elements of the list must be pairs
sage: PerfectMatching([(1,1)])
Traceback (most recent call last):
...
ValueError: [(1, 1)] is not a valid perfect matching:
there are some repetitions
sage: PerfectMatching(Permutation([4,2,1,3]))
Traceback (most recent call last):
...
ValueError: The permutation p (= [4, 2, 1, 3]) is not a fixed point free involution
"""
# we have to extract from the argument p the set of objects of the
# matching and the list of pairs.
# First case: p is a list (resp tuple) of lists (resp tuple).
if (isinstance(p, list) or isinstance(p, tuple)) and (
all([isinstance(x, list) or isinstance(x, tuple) for x in p])):
objects = Set(flatten(p))
data = (map(tuple, p))
#check if the data are correct
if not all([len(t) == 2 for t in data]):
raise ValueError("%s is not a valid perfect matching:\n"
"all elements of the list must be pairs" % p)
if len(objects) < 2*len(data):
raise ValueError("%s is not a valid perfect matching:\n"
"there are some repetitions" % p)
# Second case: p is a permutation or a list of integers, we have to
# check if it is a fix-point-free involution.
elif ((isinstance(p, list) and
all(map(lambda x: (isinstance(x, Integer) or isinstance(x, int)), p)))
or isinstance(p, Permutation)):
p = Permutation(p)
n = len(p)
if not(p.cycle_type() == [2 for i in range(n//2)]):
raise ValueError("The permutation p (= %s) is not a "
"fixed point free involution" % p)
objects = Set(range(1, n+1))
data = p.to_cycles()
# Third case: p is already a perfect matching, we return p directly
elif isinstance(p, PerfectMatching):
return p
else:
raise ValueError("cannot convert p (= %s) to a PerfectMatching" % p)
# Finally, we create the parent and the element using the element
# class of the parent. Note: as this function is private, when we
# create an object via parent.element_class(...), __init__ is directly
# executed and we do not have an infinite loop.
return PerfectMatchings(objects)(data)
def __classcall_private__(cls, p):
r"""
This function tries to recognize the input (it can be either a list or
a tuple of pairs, or a fix-point free involution given as a list or as
a permutation), constructs the parent (enumerated set of
PerfectMatchings of the ground set) and calls the __init__ function to
construct our object.
EXAMPLES::
sage: m=PerfectMatching([('a','e'),('b','c'),('d','f')]);m
[('a', 'e'), ('b', 'c'), ('d', 'f')]
sage: isinstance(m,PerfectMatching)
True
sage: n=PerfectMatching([3, 8, 1, 7, 6, 5, 4, 2]);n
[(1, 3), (2, 8), (4, 7), (5, 6)]
sage: n.parent()
Set of perfect matchings of {1, 2, 3, 4, 5, 6, 7, 8}
sage: PerfectMatching([(1, 4), (2, 3), (5, 6)]).is_non_crossing()
True
The function checks that the given list or permutation is a valid perfect
matching (i.e. a list of pairs with pairwise disjoint elements or a
fixpoint-free involution) and raises a ValueError otherwise:
sage: PerfectMatching([(1, 2, 3), (4, 5)])
Traceback (most recent call last):
...
ValueError: [(1, 2, 3), (4, 5)] is not a valid perfect matching: all elements of the list must be pairs
If you know your datas are in a good format, use directly
``PerfectMatchings(objects)(data)``.
TESTS::
sage: m=PerfectMatching([('a','e'),('b','c'),('d','f')])
sage: TestSuite(m).run()
sage: m=PerfectMatching([])
sage: TestSuite(m).run()
sage: PerfectMatching(6)
Traceback (most recent call last):
...
ValueError: cannot convert p (= 6) to a PerfectMatching
sage: PerfectMatching([(1,2,3)])
Traceback (most recent call last):
...
ValueError: [(1, 2, 3)] is not a valid perfect matching:
all elements of the list must be pairs
sage: PerfectMatching([(1,1)])
Traceback (most recent call last):
...
ValueError: [(1, 1)] is not a valid perfect matching:
there are some repetitions
sage: PerfectMatching(Permutation([4,2,1,3]))
Traceback (most recent call last):
...
ValueError: The permutation p (= [4, 2, 1, 3]) is not a fixed point free involution
"""
# we have to extract from the argument p the set of objects of the
# matching and the list of pairs.
# First case: p is a list (resp tuple) of lists (resp tuple).
if (isinstance(p, list) or isinstance(p, tuple)) and (all(
[isinstance(x, list) or isinstance(x, tuple) for x in p])):
objects = Set(flatten(p))
data = (map(tuple, p))
#check if the data are correct
if not all([len(t) == 2 for t in data]):
raise ValueError, ("%s is not a valid perfect matching:\n"
"all elements of the list must be pairs" %
p)
if len(objects) < 2 * len(data):
raise ValueError, ("%s is not a valid perfect matching:\n"
"there are some repetitions" % p)
# Second case: p is a permutation or a list of integers, we have to
# check if it is a fix-point-free involution.
elif ((isinstance(p, list) and all(
map(lambda x:
(isinstance(x, Integer) or isinstance(x, int)), p)))
or isinstance(p, Permutation_class)):
p = Permutation(p)
n = len(p)
if not (p.cycle_type() == [2 for i in range(n // 2)]):
raise ValueError, ("The permutation p (= %s) is not a "
"fixed point free involution" % p)
objects = Set(range(1, n + 1))
data = p.to_cycles()
# Third case: p is already a perfect matching, we return p directly
elif isinstance(p, PerfectMatching):
return p
else:
raise ValueError, "cannot convert p (= %s) to a PerfectMatching" % p
# Finally, we create the parent and the element using the element
# class of the parent. Note: as this function is private, when we
# create an object via parent.element_class(...), __init__ is directly
# executed and we do not have an infinite loop.
return PerfectMatchings(objects)(data)
def __classcall_private__(cls, parts):
"""
Create a perfect matching from ``parts`` with the appropriate parent.
This function tries to recognize the input (it can be either a list or
a tuple of pairs, or a fix-point free involution given as a list or as
a permutation), constructs the parent (enumerated set of
PerfectMatchings of the ground set) and calls the __init__ function to
construct our object.
EXAMPLES::
sage: m = PerfectMatching([('a','e'),('b','c'),('d','f')]);m
[('a', 'e'), ('b', 'c'), ('d', 'f')]
sage: isinstance(m, PerfectMatching)
True
sage: n = PerfectMatching([3, 8, 1, 7, 6, 5, 4, 2]);n
[(1, 3), (2, 8), (4, 7), (5, 6)]
sage: n.parent()
Perfect matchings of {1, 2, 3, 4, 5, 6, 7, 8}
sage: PerfectMatching([(1, 4), (2, 3), (5, 6)]).is_noncrossing()
True
The function checks that the given list or permutation is
a valid perfect matching (i.e. a list of pairs with pairwise
disjoint elements or a fix point free involution) and raises
a ``ValueError`` otherwise::
sage: PerfectMatching([(1, 2, 3), (4, 5)])
Traceback (most recent call last):
...
ValueError: [(1, 2, 3), (4, 5)] is not an element of
Perfect matchings of {1, 2, 3, 4, 5}
TESTS::
sage: m = PerfectMatching([('a','e'),('b','c'),('d','f')])
sage: TestSuite(m).run()
sage: m = PerfectMatching([])
sage: TestSuite(m).run()
sage: PerfectMatching(6)
Traceback (most recent call last):
...
TypeError: 'sage.rings.integer.Integer' object is not iterable
sage: PerfectMatching([(1,2,3)])
Traceback (most recent call last):
...
ValueError: [(1, 2, 3)] is not an element of
Perfect matchings of {1, 2, 3}
sage: PerfectMatching([(1,1)])
Traceback (most recent call last):
...
ValueError: [(1)] is not an element of Perfect matchings of {1}
sage: PerfectMatching(Permutation([4,2,1,3]))
Traceback (most recent call last):
...
ValueError: permutation p (= [4, 2, 1, 3]) is not a
fixed point free involution
"""
if ((isinstance(parts, list) and all(
(isinstance(x, (int, Integer)) for x in parts)))
or isinstance(parts, Permutation)):
s = Permutation(parts)
if not all(e == 2 for e in s.cycle_type()):
raise ValueError("permutation p (= {}) is not a "
"fixed point free involution".format(s))
parts = s.to_cycles()
base_set = frozenset(e for p in parts for e in p)
P = PerfectMatchings(base_set)
return P(parts)
def __classcall_private__(cls, parts):
"""
Create a perfect matching from ``parts`` with the appropriate parent.
This function tries to recognize the input (it can be either a list or
a tuple of pairs, or a fix-point free involution given as a list or as
a permutation), constructs the parent (enumerated set of
PerfectMatchings of the ground set) and calls the __init__ function to
construct our object.
EXAMPLES::
sage: m = PerfectMatching([('a','e'),('b','c'),('d','f')]);m
[('a', 'e'), ('b', 'c'), ('d', 'f')]
sage: isinstance(m, PerfectMatching)
True
sage: n = PerfectMatching([3, 8, 1, 7, 6, 5, 4, 2]);n
[(1, 3), (2, 8), (4, 7), (5, 6)]
sage: n.parent()
Perfect matchings of {1, 2, 3, 4, 5, 6, 7, 8}
sage: PerfectMatching([(1, 4), (2, 3), (5, 6)]).is_noncrossing()
True
The function checks that the given list or permutation is
a valid perfect matching (i.e. a list of pairs with pairwise
disjoint elements or a fix point free involution) and raises
a ``ValueError`` otherwise::
sage: PerfectMatching([(1, 2, 3), (4, 5)])
Traceback (most recent call last):
...
ValueError: [(1, 2, 3), (4, 5)] is not an element of
Perfect matchings of {1, 2, 3, 4, 5}
TESTS::
sage: m = PerfectMatching([('a','e'),('b','c'),('d','f')])
sage: TestSuite(m).run()
sage: m = PerfectMatching([])
sage: TestSuite(m).run()
sage: PerfectMatching(6)
Traceback (most recent call last):
...
TypeError: 'sage.rings.integer.Integer' object is not iterable
sage: PerfectMatching([(1,2,3)])
Traceback (most recent call last):
...
ValueError: [(1, 2, 3)] is not an element of
Perfect matchings of {1, 2, 3}
sage: PerfectMatching([(1,1)])
Traceback (most recent call last):
...
ValueError: [(1)] is not an element of Perfect matchings of {1}
sage: PerfectMatching(Permutation([4,2,1,3]))
Traceback (most recent call last):
...
ValueError: permutation p (= [4, 2, 1, 3]) is not a
fixed point free involution
"""
if ((isinstance(parts, list) and
all((isinstance(x, (int, Integer)) for x in parts)))
or isinstance(parts, Permutation)):
s = Permutation(parts)
if not all(e == 2 for e in s.cycle_type()):
raise ValueError("permutation p (= {}) is not a "
"fixed point free involution".format(s))
parts = s.to_cycles()
base_set = frozenset(e for p in parts for e in p)
P = PerfectMatchings(base_set)
return P(parts)
