def rank(self, sub):
"""
Returns the rank of sub as a subset of s of size k.
EXAMPLES::
sage: Subsets(3,2).rank([1,2])
0
sage: Subsets([2,3,4],2).rank([3,4])
2
sage: Subsets([2,3,4],2).rank([2])
Traceback (most recent call last):
...
ValueError: {2} is not a subset of length 2 of {2, 3, 4}
sage: Subsets([2,3,4],4).rank([2,3,4,5])
Traceback (most recent call last):
...
ValueError: {2, 3, 4, 5} is not a subset of length 4 of {2, 3, 4}
"""
sub = Set(sub)
n = self._s.cardinality()
if self._k != sub.cardinality() or self._k > n:
raise ValueError("{} is not a subset of length {} of {}".format(
sub, self._k, self._s))
try:
index_list = sorted(self._s.rank(x) for x in sub)
except ValueError:
raise ValueError("{} is not a subset of length {} of {}".format(
sub, self._k, self._s))
return choose_nk.rank(index_list, n)
def rank(self, sub):
"""
Returns the rank of sub as a subset of s of size k.
EXAMPLES::
sage: Subsets(3,2).rank([1,2])
0
sage: Subsets([2,3,4],2).rank([3,4])
2
sage: Subsets([2,3,4],2).rank([2])
Traceback (most recent call last):
...
ValueError: {2} is not a subset of length 2 of {2, 3, 4}
sage: Subsets([2,3,4],4).rank([2,3,4,5])
Traceback (most recent call last):
...
ValueError: {2, 3, 4, 5} is not a subset of length 4 of {2, 3, 4}
"""
sub = Set(sub)
n = self._s.cardinality()
if self._k != sub.cardinality() or self._k > n:
raise ValueError("{} is not a subset of length {} of {}".format(
sub, self._k, self._s))
try:
index_list = sorted(self._s.rank(x) for x in sub)
except ValueError:
raise ValueError("{} is not a subset of length {} of {}".format(
sub, self._k, self._s))
return choose_nk.rank(index_list, n)
def rank(self, sub):
"""
Returns the rank of sub as a subset of s.
EXAMPLES::
sage: Subsets(3).rank([])
0
sage: Subsets(3).rank([1,2])
4
sage: Subsets(3).rank([1,2,3])
7
sage: Subsets(3).rank([2,3,4])
Traceback (most recent call last):
...
ValueError: {2, 3, 4} is not a subset of {1, 2, 3}
"""
if sub not in Sets():
ssub = Set(sub)
if len(sub) != len(ssub):
raise ValueError("repeated elements in {}".format(sub))
sub = ssub
try:
index_list = sorted(self._s.rank(x) for x in sub)
except (ValueError, IndexError):
raise ValueError("{} is not a subset of {}".format(
Set(sub), self._s))
n = self._s.cardinality()
r = sum(binomial(n, i) for i in xrange(len(index_list)))
return r + choose_nk.rank(index_list, n)
def rank(self, sub):
"""
Returns the rank of sub as a subset of s.
EXAMPLES::
sage: Subsets(3).rank([])
0
sage: Subsets(3).rank([1,2])
4
sage: Subsets(3).rank([1,2,3])
7
sage: Subsets(3).rank([2,3,4])
Traceback (most recent call last):
...
ValueError: {2, 3, 4} is not a subset of {1, 2, 3}
"""
if sub not in Sets():
ssub = Set(sub)
if len(sub) != len(ssub):
raise ValueError("repeated elements in {}".format(sub))
sub = ssub
try:
index_list = sorted(self._s.rank(x) for x in sub)
except (ValueError,IndexError):
raise ValueError("{} is not a subset of {}".format(
Set(sub), self._s))
n = self._s.cardinality()
r = sum(binomial(n,i) for i in xrange(len(index_list)))
return r + choose_nk.rank(index_list,n)
def rank(self, x):
"""
EXAMPLES::
sage: c = Combinations([1,2,3], 2)
sage: range(c.cardinality()) == map(c.rank, c.list())
True
"""
x = map(self.mset.index, x)
return rank(x, len(self.mset))
def rank(self, x):
"""
EXAMPLES::
sage: c = Combinations([1,2,3], 2)
sage: range(c.cardinality()) == map(c.rank, c.list())
True
"""
x = [self.mset.index(_) for _ in x]
return rank(x, len(self.mset))
def rank(self, x):
"""
EXAMPLES::
sage: c = Combinations([1,2,3])
sage: range(c.cardinality()) == map(c.rank, c)
True
"""
x = map(self.mset.index, x)
r = 0
n = len(self.mset)
for i in range(len(x)):
r += binomial(n, i)
r += rank(x, n)
return r
def rank(self, x):
"""
EXAMPLES::
sage: c = Combinations([1,2,3])
sage: range(c.cardinality()) == map(c.rank, c)
True
"""
x = [self.mset.index(_) for _ in x]
r = 0
n = len(self.mset)
for i in range(len(x)):
r += binomial(n, i)
r += rank(x, n)
return r