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Sort, sort and sort(sort).
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@jm58660
jm58660 committed Feb 25, 2019
1 parent 217cb83 commit 0e3ba99
Showing 1 changed file with 46 additions and 34 deletions.
80 changes: 46 additions & 34 deletions src/sage/categories/finite_posets.py
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Original file line number Diff line number Diff line change
Expand Up @@ -296,21 +296,25 @@ def order_ideal_generators(self, ideal, direction='down'):
ordered by inclusion, and compute an order ideal there::
sage: P = Poset((Subsets([1,2,3]), attrcall("issubset")))
sage: I = P.order_ideal([Set([1,2]), Set([2,3]), Set([1])]); I
[{}, {3}, {2}, {2, 3}, {1}, {1, 2}]
sage: I = P.order_ideal([Set([1,2]), Set([2,3]), Set([1])])
sage: sorted(sorted(p) for p in I)
[[], [1], [1, 2], [2], [2, 3], [3]]
Then, we retrieve the generators of this ideal::
sage: P.order_ideal_generators(I)
{{1, 2}, {2, 3}}
sage: gen = P.order_ideal_generators(I)
sage: sorted(sorted(p) for p in gen)
[[1, 2], [2, 3]]
If ``direction`` is 'up', then this instead computes
the minimal generators for an order filter::
sage: I = P.order_filter([Set([1,2]), Set([2,3]), Set([1])]); I
[{2, 3}, {1}, {1, 2}, {1, 3}, {1, 2, 3}]
sage: P.order_ideal_generators(I, direction='up')
{{2, 3}, {1}}
sage: I = P.order_filter([Set([1,2]), Set([2,3]), Set([1])])
sage: sorted(sorted(p) for p in I)
[[1], [1, 2], [1, 2, 3], [1, 3], [2, 3]]
sage: gen = P.order_ideal_generators(I, direction='up')
sage: sorted(sorted(p) for p in gen)
[[1], [2, 3]]
Complexity: `O(n+m)` where `n` is the cardinality of `I`,
and `m` the number of upper covers of elements of `I`.
Expand All @@ -335,10 +339,12 @@ def order_filter_generators(self, filter):
EXAMPLES::
sage: P = Poset((Subsets([1,2,3]), attrcall("issubset")))
sage: I = P.order_filter([Set([1,2]), Set([2,3]), Set([1])]); I
[{2, 3}, {1}, {1, 2}, {1, 3}, {1, 2, 3}]
sage: P.order_filter_generators(I)
{{2, 3}, {1}}
sage: I = P.order_filter([Set([1,2]), Set([2,3]), Set([1])])
sage: sorted(sorted(p) for p in I)
[[1], [1, 2], [1, 2, 3], [1, 3], [2, 3]]
sage: gen = P.order_filter_generators(I)
sage: sorted(sorted(p) for p in gen)
[[1], [2, 3]]
.. SEEALSO:: :meth:`order_ideal_generators`
"""
Expand Down Expand Up @@ -1338,15 +1344,19 @@ def panyushev_orbits(self, element_constructor = set):
EXAMPLES::
sage: P = Poset( ( [1,2,3], [ [1,3], [2,3] ] ) )
sage: P.panyushev_orbits()
[[{2}, {1}], [set(), {1, 2}, {3}]]
sage: P.panyushev_orbits(element_constructor=list)
[[[2], [1]], [[], [1, 2], [3]]]
sage: P.panyushev_orbits(element_constructor=frozenset)
[[frozenset({2}), frozenset({1})],
[frozenset(), frozenset({1, 2}), frozenset({3})]]
sage: P.panyushev_orbits(element_constructor=tuple)
[[(2,), (1,)], [(), (1, 2), (3,)]]
sage: orb = P.panyushev_orbits()
sage: sorted(sorted(o) for o in orb)
[[set(), {1, 2}, {3}], [{2}, {1}]]
sage: orb = P.panyushev_orbits(element_constructor=list)
sage: sorted(sorted(o) for o in orb)
[[[], [1, 2], [3]], [[1], [2]]]
sage: orb = P.panyushev_orbits(element_constructor=frozenset)
sage: sorted(sorted(o) for o in orb)
[[frozenset(), frozenset({1, 2}), frozenset({3})],
[frozenset({2}), frozenset({1})]]
sage: orb = P.panyushev_orbits(element_constructor=tuple)
sage: sorted(sorted(o) for o in orb)
[[(), (1, 2), (3,)], [(1,), (2,)]]
sage: P = Poset( {} )
sage: P.panyushev_orbits()
[[set()]]
Expand Down Expand Up @@ -1395,12 +1405,14 @@ def rowmotion_orbits(self, element_constructor = set):
sage: P = Poset( {1: [2, 3], 2: [], 3: [], 4: [2]} )
sage: sorted(len(o) for o in P.rowmotion_orbits())
[3, 5]
sage: sorted(P.rowmotion_orbits(element_constructor=list))
[[[1, 3], [4], [1], [4, 1, 3], [4, 1, 2]], [[4, 1], [4, 1, 2, 3], []]]
sage: sorted(P.rowmotion_orbits(element_constructor=tuple))
[[(1, 3), (4,), (1,), (4, 1, 3), (4, 1, 2)], [(4, 1), (4, 1, 2, 3), ()]]
sage: orb = P.rowmotion_orbits(element_constructor=list)
sage: sorted(sorted(e) for e in orb)
[[[], [4, 1], [4, 1, 2, 3]], [[1], [1, 3], [4], [4, 1, 2], [4, 1, 3]]]
sage: orb = P.rowmotion_orbits(element_constructor=tuple)
sage: sorted(sorted(e) for e in orb)
[[(), (4, 1), (4, 1, 2, 3)], [(1,), (1, 3), (4,), (4, 1, 2), (4, 1, 3)]]
sage: P = Poset({})
sage: sorted(P.rowmotion_orbits(element_constructor=tuple))
sage: P.rowmotion_orbits(element_constructor=tuple)
[[()]]
"""
pan_orbits = self.panyushev_orbits(element_constructor = list)
Expand Down Expand Up @@ -1848,24 +1860,24 @@ def order_ideals_lattice(self, as_ideals=True, facade=None):
[[0, 1], [0, 2], [1, 4], [2, 3], [3, 4]]
sage: J = P.order_ideals_lattice(); J
Finite lattice containing 8 elements
sage: list(J)
[{}, {0}, {0, 2}, {0, 2, 3}, {0, 1}, {0, 1, 2}, {0, 1, 2, 3}, {0, 1, 2, 3, 4}]
sage: sorted(sorted(e) for e in J)
[[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 2], [0, 2, 3]]
As a lattice on antichains::
sage: J2 = P.order_ideals_lattice(False); J2
Finite lattice containing 8 elements
sage: list(J2)
[(0,), (1, 2), (1, 3), (1,), (2,), (3,), (4,), ()]
sage: sorted(J2)
[(), (0,), (1,), (1, 2), (1, 3), (2,), (3,), (4,)]
TESTS::
sage: J = posets.DiamondPoset(4, facade = True).order_ideals_lattice(); J
Finite lattice containing 6 elements
sage: list(J)
[{}, {0}, {0, 2}, {0, 1}, {0, 1, 2}, {0, 1, 2, 3}]
sage: J.cover_relations()
[[{}, {0}], [{0}, {0, 2}], [{0}, {0, 1}], [{0, 2}, {0, 1, 2}], [{0, 1}, {0, 1, 2}], [{0, 1, 2}, {0, 1, 2, 3}]]
sage: sorted(sorted(e) for e in J)
[[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 2]]
sage: sorted(sorted(sorted(e) for e in c) for c in J.cover_relations())
[[[], [0]], [[0], [0, 1]], [[0], [0, 2]], [[0, 1], [0, 1, 2]], [[0, 1, 2], [0, 1, 2, 3]], [[0, 1, 2], [0, 2]]]
sage: P = Poset({1:[2]})
sage: J_facade = P.order_ideals_lattice()
Expand Down

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