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fix cardinality for PartitionDiagrams, BrauerDiagrams, TemperleyLiebD…
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…iagrams and PlanarDiagrams, improve doctests
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@mantepse
mantepse committed Jun 23, 2018
1 parent 010ba97 commit 9630c5a
Showing 1 changed file with 142 additions and 22 deletions.
164 changes: 142 additions & 22 deletions src/sage/combinat/diagram_algebras.py
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Expand Up @@ -43,7 +43,7 @@
from sage.misc.lazy_attribute import lazy_attribute
from sage.misc.flatten import flatten
from sage.misc.misc_c import prod
from sage.rings.all import ZZ
from sage.rings.all import ZZ, QQ
from sage.functions.other import ceil

import itertools
Expand Down Expand Up @@ -112,6 +112,7 @@ def brauer_diagrams(k):
[{{-3, 3}, {-2, 1}, {-1, 2}}, {{-3, 3}, {-2, 2}, {-1, 1}}, {{-3, 3}, {-2, -1}, {1, 2}}]
"""
if k in ZZ:
k = ZZ(k)
S = SetPartitions(list(range(1,k+1)) + list(range(-k,0)), [2]*k)
for i in S._iterator_part(S.parts):
yield list(i)
Expand Down Expand Up @@ -1073,11 +1074,12 @@ def __init__(self, order, category=None):
if category is None:
category = FiniteEnumeratedSets()
Parent.__init__(self, category=category)
self.order = order
if order in ZZ:
self.order = ZZ(order)
base_set = frozenset(list(range(1,order+1)) + list(range(-order,0)))
else:
#order is a half-integer.
self.order = QQ(order)
base_set = frozenset(list(range(1,ZZ(ZZ(1)/ZZ(2) + order)+1))
+ list(range(ZZ(-ZZ(1)/ZZ(2) - order),0)))
self._set = base_set
Expand Down Expand Up @@ -1216,20 +1218,43 @@ class PartitionDiagrams(AbstractPartitionDiagrams):
EXAMPLES::
sage: import sage.combinat.diagram_algebras as da
sage: pd = da.PartitionDiagrams(1); pd
Partition diagrams of order 1
sage: pd.list()
[{{-1, 1}}, {{-1}, {1}}]
sage: pd = da.PartitionDiagrams(3/2); pd
Partition diagrams of order 3/2
sage: pd.list()
[{{-2, -1, 1, 2}},
{{-2, 1, 2}, {-1}},
{{-2, 2}, {-1, 1}},
{{-2, -1, 2}, {1}},
{{-2, 2}, {-1}, {1}}]
TESTS::
sage: import sage.combinat.diagram_algebras as da
sage: pd = da.PartitionDiagrams(3)
sage: pd.an_element() in pd
True
sage: pd.cardinality() == len(pd.list())
True
sage: pd = da.PartitionDiagrams(5/2)
sage: pd.an_element() in pd
True
sage: pd.cardinality() == len(pd.list())
True
"""
Element = PartitionDiagram
_name = "Partition"
_diagram_func = partition_diagrams

def cardinality(self):
r"""
The cardinality of partition diagrams of integer order `n` is
The cardinality of partition diagrams of half-integer order `n` is
the `2n`-th Bell number.
EXAMPLES::
Expand All @@ -1238,10 +1263,12 @@ def cardinality(self):
sage: pd = da.PartitionDiagrams(3)
sage: pd.cardinality()
203
sage: pd = da.PartitionDiagrams(7/2)
sage: pd.cardinality()
877
"""
if self.order in ZZ:
return bell_number(2*self.order)
return bell_number(2*(self.order-1/2))
return bell_number(ZZ(2*self.order))

class BrauerDiagrams(AbstractPartitionDiagrams):
r"""
Expand All @@ -1251,13 +1278,34 @@ class BrauerDiagrams(AbstractPartitionDiagrams):
EXAMPLES::
sage: import sage.combinat.diagram_algebras as da
sage: bd = da.BrauerDiagrams(2); bd
Brauer diagrams of order 2
sage: bd.list()
[{{-2, 1}, {-1, 2}}, {{-2, 2}, {-1, 1}}, {{-2, -1}, {1, 2}}]
sage: bd = da.BrauerDiagrams(5/2); bd
Brauer diagrams of order 5/2
sage: bd.list()
[{{-3, 3}, {-2, 1}, {-1, 2}},
{{-3, 3}, {-2, 2}, {-1, 1}},
{{-3, 3}, {-2, -1}, {1, 2}}]
TESTS::
sage: import sage.combinat.diagram_algebras as da
sage: bd = da.BrauerDiagrams(3)
sage: bd.an_element() in bd
True
sage: bd.cardinality() == len(bd.list())
True
sage: bd = da.BrauerDiagrams(5/2)
sage: bd.an_element() in bd
True
sage: bd.cardinality() == len(bd.list())
True
These diagrams also come equipped with a compact representation based
on their bipartition triple representation. See the
:meth:`from_involution_permutation_triple` method for more information.
Expand Down Expand Up @@ -1301,8 +1349,16 @@ def __contains__(self, obj):
True
sage: [[1,2,-1,-2]] in bd
False
sage: bd = da.BrauerDiagrams(3/2)
sage: bd.an_element() in bd
True
"""
return super(BrauerDiagrams, self).__contains__(obj) and [len(i) for i in obj] == [2]*self.order
if self.order in ZZ:
r = ZZ(self.order)
else:
r = ZZ(self.order + ZZ(1)/ZZ(2))
return super(BrauerDiagrams, self).__contains__(obj) and [len(i) for i in obj] == [2]*r

def cardinality(self):
r"""
Expand All @@ -1316,11 +1372,15 @@ def cardinality(self):
sage: bd = da.BrauerDiagrams(3)
sage: bd.cardinality()
15
sage: bd = da.BrauerDiagrams(7/2)
sage: bd.cardinality()
15
"""
if self.order in ZZ:
return (2*self.order-1).multifactorial(2)
return (2*ZZ(self.order)-1).multifactorial(2)
else:
return (2*(self.order-1/2)-1).multifactorial(2)
return (2*ZZ(self.order-1/2)-1).multifactorial(2)

def symmetric_diagrams(self, l=None, perm=None):
r"""
Expand All @@ -1331,17 +1391,28 @@ def symmetric_diagrams(self, l=None, perm=None):
sage: import sage.combinat.diagram_algebras as da
sage: bd = da.BrauerDiagrams(4)
sage: bd.symmetric_diagrams(l=1,perm=[2,1])
sage: bd.symmetric_diagrams(l=1, perm=[2,1])
[{{-4, -3}, {-2, 1}, {-1, 2}, {3, 4}},
{{-4, -2}, {-3, 1}, {-1, 3}, {2, 4}},
{{-4, 1}, {-3, -2}, {-1, 4}, {2, 3}},
{{-4, -1}, {-3, 2}, {-2, 3}, {1, 4}},
{{-4, 2}, {-3, -1}, {-2, 4}, {1, 3}},
{{-4, 3}, {-3, 4}, {-2, -1}, {1, 2}}]
TESTS::
sage: import sage.combinat.diagram_algebras as da
sage: bd = da.BrauerDiagrams(3/2)
sage: bd.symmetric_diagrams(l=1, perm=[2,1])
Traceback (most recent call last):
...
NotImplementedError: symmetric_diagrams is only implemented for Brauer diagrams of integer order, not for order 3/2
"""
# perm = permutation on free nodes
# l = number of arcs
n = self.order
if self.order not in ZZ:
raise NotImplementedError("symmetric_diagrams is only implemented for Brauer diagrams of integer order, not for order %s" %(self.order))
n = ZZ(self.order)
if l is None:
l = 0
if perm is None:
Expand Down Expand Up @@ -1384,7 +1455,18 @@ def from_involution_permutation_triple(self, D1_D2_pi):
sage: bd = da.BrauerDiagrams(4)
sage: bd.from_involution_permutation_triple([[[1,2]],[[3,4]],[2,1]])
{{-4, -3}, {-2, 3}, {-1, 4}, {1, 2}}
TESTS::
sage: import sage.combinat.diagram_algebras as da
sage: bd = da.BrauerDiagrams(5/2)
sage: bd.from_involution_permutation_triple([[[1,2]],[[3,4]],[2,1]])
Traceback (most recent call last):
...
NotImplementedError: from_involution_permutation_triple is only implemented for Brauer diagrams of integer order, not for order 5/2
"""
if self.order not in ZZ:
raise NotImplementedError("from_involution_permutation_triple is only implemented for Brauer diagrams of integer order, not for order %s" %(self.order))
try:
(D1,D2,pi) = tuple(D1_D2_pi)
except ValueError:
Expand Down Expand Up @@ -1413,12 +1495,35 @@ class TemperleyLiebDiagrams(AbstractPartitionDiagrams):
EXAMPLES::
sage: import sage.combinat.diagram_algebras as da
sage: td = da.TemperleyLiebDiagrams(3); td
Temperley Lieb diagrams of order 3
sage: td.list()
[{{-3, 1}, {-2, -1}, {2, 3}},
{{-3, 3}, {-2, 2}, {-1, 1}},
{{-3, 3}, {-2, -1}, {1, 2}},
{{-3, -2}, {-1, 1}, {2, 3}},
{{-3, -2}, {-1, 3}, {1, 2}}]
sage: td = da.TemperleyLiebDiagrams(5/2); td
Temperley Lieb diagrams of order 5/2
sage: td.list()
[{{-3, 3}, {-2, 2}, {-1, 1}}, {{-3, 3}, {-2, -1}, {1, 2}}]
TESTS::
sage: import sage.combinat.diagram_algebras as da
sage: td = da.TemperleyLiebDiagrams(3)
sage: td.an_element() in td
True
sage: td.cardinality() == len(td.list())
True
sage: td = da.TemperleyLiebDiagrams(7/2)
sage: td.an_element() in td
True
sage: td.cardinality() == len(td.list())
True
"""
Element = TemperleyLiebDiagram
_name = "Temperley Lieb"
Expand All @@ -1439,9 +1544,9 @@ def cardinality(self):
5
"""
if self.order in ZZ:
return catalan_number(self.order)
return catalan_number(ZZ(self.order))
else:
return catalan_number(self.order-1/2)
return catalan_number(ZZ(self.order-1/2))

def __contains__(self, obj):
r"""
Expand All @@ -1463,24 +1568,42 @@ def __contains__(self, obj):
obj = self._element_constructor_(obj)
except (ValueError, TypeError):
return False
if obj not in BrauerDiagrams(self.order):
return False
if not obj.is_planar():
return False
return True
return obj in BrauerDiagrams(self.order) and obj.is_planar()

class PlanarDiagrams(AbstractPartitionDiagrams):
r"""
All planar diagrams of integer or integer `+1/2` order.
EXAMPLES::
sage: import sage.combinat.diagram_algebras as da
sage: pld = da.PlanarDiagrams(1); pld
Planar diagrams of order 1
sage: pld.list()
[{{-1, 1}}, {{-1}, {1}}]
sage: pld = da.PlanarDiagrams(3/2); pld
Planar diagrams of order 3/2
sage: pld.list()
[{{-2, -1, 1, 2}},
{{-2, 1, 2}, {-1}},
{{-2, 2}, {-1, 1}},
{{-2, -1, 2}, {1}},
{{-2, 2}, {-1}, {1}}]
TESTS::
sage: import sage.combinat.diagram_algebras as da
sage: pld = da.PlanarDiagrams(3)
sage: pld.an_element() in pld
True
sage: pld.cardinality() == len(pld.list())
True
sage: pld = da.PlanarDiagrams(5/2)
sage: pld.an_element() in pld
True
sage: pld.cardinality() == len(pld.list())
True
"""
Element = PlanarDiagram
_name = "Planar"
Expand All @@ -1500,10 +1623,7 @@ def cardinality(self):
sage: pld.cardinality()
132
"""
if self.order in ZZ:
return catalan_number(2*self.order)
else:
return catalan_number(2*self.order-1)
return catalan_number(2*self.order)

def __contains__(self, obj):
r"""
Expand Down

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