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sage.combinat: Update # needs #36916

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Dec 26, 2023
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sage.combinat: Update # needs #36916

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daeae86
sage.{coding,combinat}: Update # needs
mkoeppe Sep 5, 2023
cf0357d
sage.combinat.root_system: Update # needs
mkoeppe Sep 9, 2023
1a9086c
sage.combinat: Update # needs
mkoeppe Sep 9, 2023
e6ac103
sage.combinat: Update # needs
mkoeppe Sep 23, 2023
8ee19f2
sage -fixdoctests src/sage/combinat
mkoeppe Dec 12, 2023
403e60b
pkgs/sagemath-gap: Move reflection_group, weyl_group here from sagema…
mkoeppe Sep 1, 2023
801e5c9
src/sage/combinat/permutation.py: Fix # needs
mkoeppe Dec 24, 2023
182d81f
src/sage/combinat/root_system/non_symmetric_macdonald_polynomials.py:…
mkoeppe Dec 24, 2023
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sage.combinat: Update # needs
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Matthias Koeppe committed Dec 19, 2023
commit e6ac10361c4ef494be88ffa49fa8cee9f70ab536
76 changes: 45 additions & 31 deletions src/sage/combinat/posets/lattices.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2298,8 +2298,8 @@ def is_orthocomplemented(self, unique=False):
sage: D6.is_orthocomplemented(unique=True) # needs sage.groups
False

sage: hexagon = LatticePoset({0:[1, 2], 1:[3], 2:[4], 3:[5], 4:[5]})
sage: hexagon.is_orthocomplemented(unique=True)
sage: hexagon = LatticePoset({0: [1, 2], 1: [3], 2: [4], 3:[5], 4: [5]})
sage: hexagon.is_orthocomplemented(unique=True) # needs sage.groups
True

.. SEEALSO::
Expand Down Expand Up @@ -4046,7 +4046,7 @@ def is_subdirectly_reducible(self, certificate=False):

TESTS::

sage: [posets.ChainPoset(i).is_subdirectly_reducible() for i in range(5)]
sage: [posets.ChainPoset(i).is_subdirectly_reducible() for i in range(5)] # needs sage.combinat
[False, False, False, True, True]
"""
H = self._hasse_diagram
Expand Down Expand Up @@ -4256,7 +4256,7 @@ def is_constructible_by_doublings(self, type) -> bool:
sage: L = L.day_doubling([(3,0), (1,1), (2,1)]) # An upper pseudo-interval
sage: L.is_constructible_by_doublings('upper')
False
sage: L.is_constructible_by_doublings('convex')
sage: L.is_constructible_by_doublings('convex') # needs sage.combinat
True

An example of a lattice that can be constructed by doublings
Expand Down Expand Up @@ -4378,18 +4378,20 @@ def is_isoform(self, certificate=False):

EXAMPLES::

sage: L = LatticePoset({1:[2, 3, 4], 2: [5, 6], 3: [6, 7], 4: [7], 5: [8], 6: [8], 7: [8]})
sage: L.is_isoform()
sage: L = LatticePoset({1: [2, 3, 4], 2: [5, 6], 3: [6, 7],
....: 4: [7], 5: [8], 6: [8], 7: [8]})
sage: L.is_isoform() # needs sage.combinat
True

Every isoform lattice is (trivially) uniform, but the converse is
not true::

sage: L = LatticePoset({1: [2, 3, 6], 2: [4, 5], 3: [5], 4: [9, 8], 5: [7, 8], 6: [9], 7: [10], 8: [10], 9: [10]})
sage: L.is_isoform(), L.is_uniform()
sage: L = LatticePoset({1: [2, 3, 6], 2: [4, 5], 3: [5], 4: [9, 8],
....: 5: [7, 8], 6: [9], 7: [10], 8: [10], 9: [10]})
sage: L.is_isoform(), L.is_uniform() # needs sage.combinat
(False, True)

sage: L.is_isoform(certificate=True)
sage: L.is_isoform(certificate=True) # needs sage.combinat
(False, {{1, 2, 4, 6, 9}, {3, 5, 7, 8, 10}})

.. SEEALSO::
Expand All @@ -4404,7 +4406,7 @@ def is_isoform(self, certificate=False):
sage: [posets.ChainPoset(i).is_isoform() for i in range(5)]
[True, True, True, False, False]

sage: posets.DiamondPoset(5).is_isoform() # Simple, so trivially isoform
sage: posets.DiamondPoset(5).is_isoform() # Simple, so trivially isoform # needs sage.combinat
True
"""
ok = (True, None) if certificate else True
Expand Down Expand Up @@ -4451,8 +4453,9 @@ def is_uniform(self, certificate=False):

EXAMPLES::

sage: L = LatticePoset({1: [2, 3, 4], 2: [6, 7], 3: [5], 4: [5], 5: [9, 8], 6: [9], 7: [10], 8: [10], 9: [10]})
sage: L.is_uniform()
sage: L = LatticePoset({1: [2, 3, 4], 2: [6, 7], 3: [5], 4: [5],
....: 5: [9, 8], 6: [9], 7: [10], 8: [10], 9: [10]})
sage: L.is_uniform() # needs sage.combinat
True

Every uniform lattice is regular, but the converse is not true::
Expand All @@ -4461,7 +4464,7 @@ def is_uniform(self, certificate=False):
sage: N6.is_uniform(), N6.is_regular()
(False, True)

sage: N6.is_uniform(certificate=True)
sage: N6.is_uniform(certificate=True) # needs sage.combinat
(False, {{1, 2, 3, 4}, {5, 6}})

.. SEEALSO::
Expand All @@ -4475,7 +4478,7 @@ def is_uniform(self, certificate=False):
sage: [posets.ChainPoset(i).is_uniform() for i in range(5)]
[True, True, True, False, False]

sage: posets.DiamondPoset(5).is_uniform() # Simple, so trivially uniform
sage: posets.DiamondPoset(5).is_uniform() # Simple, so trivially uniform # needs sage.combinat
True
"""
ok = (True, None) if certificate else True
Expand Down Expand Up @@ -4532,14 +4535,15 @@ def is_regular(self, certificate=False):

EXAMPLES::

sage: L = LatticePoset({1: [2, 3, 4], 2: [5, 6], 3: [8, 7], 4: [6, 7], 5: [8], 6: [9], 7: [9], 8: [9]})
sage: L.is_regular()
sage: L = LatticePoset({1: [2, 3, 4], 2: [5, 6], 3: [8, 7], 4: [6, 7],
....: 5: [8], 6: [9], 7: [9], 8: [9]})
sage: L.is_regular() # needs sage.combinat
True

sage: N5 = posets.PentagonPoset()
sage: N5.is_regular()
sage: N5.is_regular() # needs sage.combinat
False
sage: N5.is_regular(certificate=True)
sage: N5.is_regular(certificate=True) # needs sage.combinat
(False, ({{0}, {1}, {2, 3}, {4}}, [0]))

.. SEEALSO::
Expand All @@ -4552,7 +4556,7 @@ def is_regular(self, certificate=False):

TESTS::

sage: [posets.ChainPoset(i).is_regular() for i in range(5)]
sage: [posets.ChainPoset(i).is_regular() for i in range(5)] # needs sage.combinat
[True, True, True, False, False]
"""
ok = (True, None) if certificate else True
Expand Down Expand Up @@ -4598,6 +4602,7 @@ def is_simple(self, certificate=False):

EXAMPLES::

sage: # needs sage.combinat
sage: posets.DiamondPoset(5).is_simple() # Smallest nontrivial example
True
sage: L = LatticePoset({1: [2, 3], 2: [4, 5], 3: [6], 4: [6], 5: [6]})
Expand All @@ -4611,11 +4616,11 @@ def is_simple(self, certificate=False):

sage: L = LatticePoset({1: [2, 3, 4], 2: [5], 3: [5], 4: [6, 7],
....: 5: [8], 6: [8], 7: [8]})
sage: L.is_simple()
sage: L.is_simple() # needs sage.combinat
False
sage: L = LatticePoset({1: [2, 3], 2: [4, 5], 3: [6, 7], 4: [8],
....: 5: [8], 6: [8], 7: [8]})
sage: L.is_simple()
sage: L.is_simple() # needs sage.combinat
True

.. SEEALSO::
Expand Down Expand Up @@ -4652,9 +4657,10 @@ def subdirect_decomposition(self):

EXAMPLES::

sage: posets.ChainPoset(3).subdirect_decomposition()
sage: posets.ChainPoset(3).subdirect_decomposition() # needs sage.combinat
[Finite lattice containing 2 elements, Finite lattice containing 2 elements]

sage: # needs sage.combinat
sage: L = LatticePoset({1: [2, 4], 2: [3], 3: [6, 7], 4: [5, 7],
....: 5: [9, 8], 6: [9], 7: [9], 8: [10], 9: [10]})
sage: Ldecomp = L.subdirect_decomposition()
Expand All @@ -4665,6 +4671,7 @@ def subdirect_decomposition(self):

TESTS::

sage: # needs sage.combinat
sage: posets.ChainPoset(0).subdirect_decomposition()
[Finite lattice containing 0 elements]
sage: posets.ChainPoset(1).subdirect_decomposition()
Expand All @@ -4676,7 +4683,7 @@ def subdirect_decomposition(self):
has only one element::

sage: N5 = posets.PentagonPoset()
sage: N5.subdirect_decomposition()
sage: N5.subdirect_decomposition() # needs sage.combinat
[Finite lattice containing 5 elements]
"""
H = self._hasse_diagram
Expand Down Expand Up @@ -4737,6 +4744,7 @@ def congruence(self, S):

EXAMPLES::

sage: # needs sage.combinat
sage: L = posets.DivisorLattice(12)
sage: cong = L.congruence([[1, 3]])
sage: sorted(sorted(c) for c in cong)
Expand All @@ -4745,19 +4753,20 @@ def congruence(self, S):
{{1, 2, 4}, {3, 6, 12}}

sage: L = LatticePoset({1: [2, 3], 2: [4], 3: [4], 4: [5]})
sage: L.congruence([[1, 2]])
sage: L.congruence([[1, 2]]) # needs sage.combinat
{{1, 2}, {3, 4}, {5}}

sage: L = LatticePoset({1: [2, 3], 2: [4, 5, 6], 4: [5], 5: [7, 8],
....: 6: [8], 3: [9], 7: [10], 8: [10], 9:[10]})
sage: cong = L.congruence([[1, 2]])
sage: cong[0]
sage: cong = L.congruence([[1, 2]]) # needs sage.combinat
sage: cong[0] # needs sage.combinat
frozenset({1, 2, 3, 4, 5, 6, 7, 8, 9, 10})

.. SEEALSO:: :meth:`quotient`

TESTS::

sage: # needs sage.combinat
sage: P = posets.PentagonPoset()
sage: P.congruence([])
{{0}, {1}, {2}, {3}, {4}}
Expand All @@ -4774,13 +4783,13 @@ def congruence(self, S):
works::

sage: L = LatticePoset(DiGraph('P^??@_?@??B_?@??B??@_?@??B_?@??B??@??A??C??G??O???'))
sage: sorted(sorted(p) for p in L.congruence([[1,6]]))
sage: sorted(sorted(p) for p in L.congruence([[1,6]])) # needs sage.combinat
[[0], [1, 6], [2], [3, 8], [4], [5, 10], [7, 12], [9, 14], [11], [13], [15], [16]]

Simple lattice, i.e. a lattice without any nontrivial congruence::

sage: L = LatticePoset(DiGraph('GPb_@?OC@?O?'))
sage: L.congruence([[1,2]])
sage: L.congruence([[1,2]]) # needs sage.combinat
{{0, 1, 2, 3, 4, 5, 6, 7}}
"""
from sage.combinat.set_partition import SetPartition
Expand Down Expand Up @@ -4821,6 +4830,7 @@ def quotient(self, congruence, labels='tuple'):

EXAMPLES::

sage: # needs sage.combinat
sage: L = posets.PentagonPoset()
sage: c = L.congruence([[0, 1]])
sage: I = L.quotient(c); I
Expand All @@ -4831,6 +4841,7 @@ def quotient(self, congruence, labels='tuple'):
sage: I.top()
Finite lattice containing 3 elements

sage: # needs sage.combinat
sage: B3 = posets.BooleanLattice(3)
sage: c = B3.congruence([[0,1]])
sage: B2 = B3.quotient(c, labels='integer')
Expand All @@ -4846,7 +4857,7 @@ def quotient(self, congruence, labels='tuple'):
Finite lattice containing 0 elements

sage: L = posets.PentagonPoset()
sage: L.quotient(L.congruence([[1]])).is_isomorphic(L)
sage: L.quotient(L.congruence([[1]])).is_isomorphic(L) # needs sage.combinat
True
"""
if labels not in ['lattice', 'tuple', 'integer']:
Expand Down Expand Up @@ -4894,6 +4905,7 @@ def congruences_lattice(self, labels='congruence'):

EXAMPLES::

sage: # needs sage.combinat
sage: N5 = posets.PentagonPoset()
sage: CL = N5.congruences_lattice(); CL
Finite lattice containing 5 elements
Expand All @@ -4903,12 +4915,13 @@ def congruences_lattice(self, labels='congruence'):
[{{0, 1}, {2, 3, 4}}, {{0, 2, 3}, {1, 4}}]

sage: C4 = posets.ChainPoset(4)
sage: CL = C4.congruences_lattice(labels='integer')
sage: CL.is_isomorphic(posets.BooleanLattice(3))
sage: CL = C4.congruences_lattice(labels='integer') # needs sage.combinat
sage: CL.is_isomorphic(posets.BooleanLattice(3)) # needs sage.combinat
True

TESTS::

sage: # needs sage.combinat
sage: posets.ChainPoset(0).congruences_lattice()
Finite lattice containing 1 elements
sage: posets.ChainPoset(1).congruences_lattice()
Expand Down Expand Up @@ -5002,6 +5015,7 @@ def feichtner_yuzvinsky_ring(self, G, use_defining=False, base_ring=None):

We reproduce the example from Section 5 of [Coron2023]_::

sage: # needs sage.geometry.polyhedron
sage: H.<a,b,c,d> = HyperplaneArrangements(QQ)
sage: Arr = H(a-b, b-c, c-d, d-a)
sage: P = LatticePoset(Arr.intersection_poset())
Expand Down
30 changes: 15 additions & 15 deletions src/sage/combinat/posets/posets.py
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Original file line number Diff line number Diff line change
Expand Up @@ -3745,9 +3745,9 @@ def magnitude(self) -> Integer:
sage: P.magnitude() == m1*m2
True

sage: Poset({}).magnitude()
sage: Poset({}).magnitude() # needs sage.libs.flint
0
sage: Poset({1:[]}).magnitude()
sage: Poset({1: []}).magnitude() # needs sage.libs.flint
1
"""
H = self._hasse_diagram
Expand Down Expand Up @@ -4314,7 +4314,7 @@ def coxeter_transformation(self):

EXAMPLES::

sage: posets.PentagonPoset().coxeter_transformation()
sage: posets.PentagonPoset().coxeter_transformation() # needs sage.libs.flint
[ 0 0 0 0 -1]
[ 0 0 0 1 -1]
[ 0 1 0 0 -1]
Expand All @@ -4327,8 +4327,8 @@ def coxeter_transformation(self):

TESTS::

sage: M = posets.PentagonPoset().coxeter_transformation()
sage: M ** 8 == 1
sage: M = posets.PentagonPoset().coxeter_transformation() # needs sage.libs.flint
sage: M ** 8 == 1 # needs sage.libs.flint
True
"""
return self._hasse_diagram.coxeter_transformation()
Expand All @@ -4348,11 +4348,11 @@ def coxeter_polynomial(self):
EXAMPLES::

sage: P = posets.PentagonPoset()
sage: P.coxeter_polynomial()
sage: P.coxeter_polynomial() # needs sage.libs.flint
x^5 + x^4 + x + 1

sage: p = posets.SymmetricGroupWeakOrderPoset(3) # needs sage.groups
sage: p.coxeter_polynomial() # needs sage.groups
sage: p.coxeter_polynomial() # needs sage.groups sage.libs.flint
x^6 + x^5 - x^3 + x + 1

.. SEEALSO::
Expand Down Expand Up @@ -4398,7 +4398,7 @@ def coxeter_smith_form(self, algorithm='singular'):
TESTS::

sage: P = posets.PentagonPoset()
sage: P.coxeter_smith_form(algorithm='sage')
sage: P.coxeter_smith_form(algorithm='sage') # needs sage.libs.flint
[1, 1, 1, 1, x^5 + x^4 + x + 1]
sage: P.coxeter_smith_form(algorithm='gap') # needs sage.libs.gap
[1, 1, 1, 1, x^5 + x^4 + x + 1]
Expand Down Expand Up @@ -8099,33 +8099,33 @@ def is_eulerian(self, k=None, certificate=False):

sage: P = Poset({0: [1, 2, 3], 1: [4, 5], 2: [4, 6], 3: [5, 6],
....: 4: [7, 8], 5: [7, 8], 6: [7, 8], 7: [9], 8: [9]})
sage: P.is_eulerian()
sage: P.is_eulerian() # needs sage.libs.flint
True
sage: P = Poset({0: [1, 2, 3], 1: [4, 5, 6], 2: [4, 6], 3: [5,6],
....: 4: [7], 5:[7], 6:[7]})
sage: P.is_eulerian()
sage: P.is_eulerian() # needs sage.libs.flint
False

Canonical examples of Eulerian posets are the face lattices of
convex polytopes::

sage: P = polytopes.cube().face_lattice() # needs sage.geometry.polyhedron
sage: P.is_eulerian() # needs sage.geometry.polyhedron
sage: P.is_eulerian() # needs sage.geometry.polyhedron sage.libs.flint
True

A poset that is 3- but not 4-eulerian::

sage: P = Poset(DiGraph('MWW@_?W?@_?W??@??O@_?W?@_?W?@??O??')); P
Finite poset containing 14 elements
sage: P.is_eulerian(k=3)
sage: P.is_eulerian(k=3) # needs sage.libs.flint
True
sage: P.is_eulerian(k=4)
sage: P.is_eulerian(k=4) # needs sage.libs.flint
False

Getting an interval that is not Eulerian::

sage: P = posets.DivisorLattice(12)
sage: P.is_eulerian(certificate=True)
sage: P.is_eulerian(certificate=True) # needs sage.libs.flint
(False, (1, 4))

TESTS::
Expand All @@ -8143,7 +8143,7 @@ def is_eulerian(self, k=None, certificate=False):
...
ValueError: the poset is not graded

sage: posets.BooleanLattice(3).is_eulerian(k=123, certificate=True)
sage: posets.BooleanLattice(3).is_eulerian(k=123, certificate=True) # needs sage.libs.flint
(True, None)
"""
if k is not None:
Expand Down
2 changes: 1 addition & 1 deletion src/sage/combinat/root_system/coxeter_group.py
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Original file line number Diff line number Diff line change
Expand Up @@ -116,7 +116,7 @@ def CoxeterGroup(data, implementation="reflection", base_ring=None, index_set=No

TESTS::

sage: W = groups.misc.CoxeterGroup(["H",3]) # needs sage.groups
sage: W = groups.misc.CoxeterGroup(["H",3]) # needs sage.graphs sage.groups
"""
if implementation not in ["permutation", "matrix", "coxeter3", "reflection", "chevie", None]:
raise ValueError("invalid type implementation")
Expand Down
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