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graphs: make init_short_digraph always sort neighbors but without the extra log complexity #38427

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graphs: make init_short_digraph always sort neighbors but without the extra log complexity #38427

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b4556fa
graphs: init_short_digraph always sort neighbors without extra log co…
cyrilbouvier Jul 26, 2024
bd63dd7
Remove sorting in StaticSparseBackend
cyrilbouvier Aug 21, 2024
71113cd
Fix some tests whose output depend on the inner representation of sta…
cyrilbouvier Aug 22, 2024
07fc3e3
Fix more tests whose output depend on the inner representation of sta…
cyrilbouvier Aug 22, 2024
e22d5f1
Improve doctests syntax + respect linter + remove empty line
cyrilbouvier Sep 4, 2024
7d085d9
Merge branch 'develop' into linear-sorted-init-short-digraph
cyrilbouvier Sep 4, 2024
d82009e
Merge branch 'develop' into linear-sorted-init-short-digraph
cyrilbouvier Sep 4, 2024
23494ba
Fix doctest by adding a sort
cyrilbouvier Sep 11, 2024
f742133
Maybe sorting will fix this doctests...
cyrilbouvier Sep 11, 2024
6f4b168
doctests in bgg_dual_module.py should passed now
cyrilbouvier Sep 11, 2024
8627957
doctests: more sort and disabling
cyrilbouvier Sep 11, 2024
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60 changes: 33 additions & 27 deletions src/sage/algebras/lie_algebras/bgg_dual_module.py
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Expand Up @@ -202,15 +202,18 @@ def degree_on_basis(self, m):
sage: M = g.verma_module(La[1] + La[4] - 1/3*La[5])
sage: Mc = M.dual()
sage: elt = Mc.an_element(); elt
f[-alpha[5]]^2*f[-alpha[4]]^2*f[-alpha[3]]^3*v[Lambda[1] + Lambda[4] - 1/3*Lambda[5]]^*
+ 2*f[-alpha[5]]*v[Lambda[1] + Lambda[4] - 1/3*Lambda[5]]^*
+ 3*f[-alpha[4]]*v[Lambda[1] + Lambda[4] - 1/3*Lambda[5]]^*
+ v[Lambda[1] + Lambda[4] - 1/3*Lambda[5]]^*
f[-alpha[2]]^2*f[-alpha[5]]^2*f[-alpha[3]]^3*v[Lambda[1] # 64-bit
+ Lambda[4] - 1/3*Lambda[5]]^* + 2*f[-alpha[2]]*v[Lambda[1] # 64-bit
+ Lambda[4] - 1/3*Lambda[5]]^* + 3*f[-alpha[5]]*v[Lambda[1] # 64-bit
+ Lambda[4] - 1/3*Lambda[5]]^* + v[Lambda[1] + Lambda[4] # 64-bit
- 1/3*Lambda[5]]^* # 64-bit
... # 32-bit
sage: [M.degree_on_basis(m) for m in elt.support()]
[Lambda[1] + 3*Lambda[2] - 2*Lambda[3] - 4/3*Lambda[5],
Lambda[1] + Lambda[4] - 1/3*Lambda[5],
Lambda[1] + Lambda[3] + Lambda[4] - 7/3*Lambda[5],
Lambda[1] + Lambda[3] - Lambda[4] - 1/3*Lambda[5]]
[3*Lambda[1] - Lambda[2] - 2*Lambda[3] + 4*Lambda[4] - 4/3*Lambda[5], # 64-bit
Lambda[1] + Lambda[4] - 1/3*Lambda[5], # 64-bit
2*Lambda[1] - 2*Lambda[2] + Lambda[3] + Lambda[4] - 1/3*Lambda[5], # 64-bit
Lambda[1] + Lambda[3] + Lambda[4] - 7/3*Lambda[5]] # 64-bit
... # 32-bit
"""
return self._module.degree_on_basis(m)

Expand Down Expand Up @@ -608,13 +611,13 @@ def __contains__(self, m):
1 True
f[-alpha[1]] True
f[-alpha[1] - alpha[2]] True
sage: gens = list(I.gens()); gens
[f[-alpha[2]],
sage: gens = list(sorted(I.gens())); gens
[f[-3*alpha[1] - 2*alpha[2]],
f[-3*alpha[1] - alpha[2]],
f[-2*alpha[1] - alpha[2]],
f[-alpha[1]],
f[-alpha[1] - alpha[2]],
f[-2*alpha[1] - alpha[2]],
f[-3*alpha[1] - alpha[2]],
f[-3*alpha[1] - 2*alpha[2]]]
f[-alpha[2]]]
sage: gens[1] in I
True
sage: gens[0] * gens[1] in I
Expand Down Expand Up @@ -896,24 +899,27 @@ def lift(self):
sage: g = LieAlgebra(QQ, cartan_type=['G', 2])
sage: La = g.cartan_type().root_system().weight_lattice().fundamental_weights()
sage: L = g.simple_module(La[1])
sage: [L.lift(b) for b in L.basis()] # long time
sage: sorted([L.lift(b) for b in L.basis()]) # long time
[v[Lambda[1]]^*,
f[-alpha[1]]*v[Lambda[1]]^*,
f[-alpha[2]]*f[-alpha[1]]*v[Lambda[1]]^* - f[-alpha[1] - alpha[2]]*v[Lambda[1]]^*,
f[-alpha[1]]*f[-alpha[1] - alpha[2]]*v[Lambda[1]]^*
+ f[-2*alpha[1] - alpha[2]]*v[Lambda[1]]^*,
f[-alpha[2]]*f[-alpha[1]]^2*f[-alpha[1] - alpha[2]]*v[Lambda[1]]^*
+ f[-alpha[2]]*f[-alpha[1]]*f[-2*alpha[1]
- alpha[2]]*v[Lambda[1]]^* + 1/2*f[-alpha[2]]*f[-3*alpha[1]
- alpha[2]]*v[Lambda[1]]^* - f[-alpha[1]
- alpha[2]]*f[-2*alpha[1] - alpha[2]]*v[Lambda[1]]^*
+ 1/2*f[-3*alpha[1] - 2*alpha[2]]*v[Lambda[1]]^*,
f[-alpha[1]]^2*f[-alpha[1] - alpha[2]]*v[Lambda[1]]^*
+ f[-alpha[1]]*f[-2*alpha[1] - alpha[2]]*v[Lambda[1]]^*
+ 1/2*f[-3*alpha[1] - alpha[2]]*v[Lambda[1]]^*,
f[-alpha[2]]*f[-alpha[1]]^2*f[-alpha[1] - alpha[2]]*v[Lambda[1]]^*
+ f[-alpha[2]]*f[-alpha[1]]*f[-2*alpha[1] - alpha[2]]*v[Lambda[1]]^*
+ 1/2*f[-alpha[2]]*f[-3*alpha[1] - alpha[2]]*v[Lambda[1]]^*
- f[-alpha[1] - alpha[2]]*f[-2*alpha[1] - alpha[2]]*v[Lambda[1]]^*
+ 1/2*f[-3*alpha[1] - 2*alpha[2]]*v[Lambda[1]]^*,
f[-alpha[1]]*f[-alpha[1] - alpha[2]]*f[-2*alpha[1] - alpha[2]]*v[Lambda[1]]^*
- 1/2*f[-alpha[1]]*f[-3*alpha[1] - 2*alpha[2]]*v[Lambda[1]]^*
- 1/2*f[-alpha[1] - alpha[2]]*f[-3*alpha[1] - alpha[2]]*v[Lambda[1]]^*
+ f[-2*alpha[1] - alpha[2]]^2*v[Lambda[1]]^*]
f[-alpha[1]]*f[-alpha[1] - alpha[2]]*v[Lambda[1]]^*
+ f[-2*alpha[1] - alpha[2]]*v[Lambda[1]]^*,
f[-alpha[1]]*f[-alpha[1] - alpha[2]]*f[-2*alpha[1]
- alpha[2]]*v[Lambda[1]]^* - 1/2*f[-alpha[1]]*f[-3*alpha[1]
- 2*alpha[2]]*v[Lambda[1]]^* - 1/2*f[-alpha[1]
- alpha[2]]*f[-3*alpha[1] - alpha[2]]*v[Lambda[1]]^*
+ f[-2*alpha[1] - alpha[2]]^2*v[Lambda[1]]^*,
f[-alpha[1]]*v[Lambda[1]]^*,
f[-alpha[2]]*f[-alpha[1]]*v[Lambda[1]]^*
- f[-alpha[1] - alpha[2]]*v[Lambda[1]]^*]
"""
return self.module_morphism(self._lift_on_basis, codomain=self._ambient, unitriangular="upper")

Expand Down
13 changes: 5 additions & 8 deletions src/sage/algebras/lie_algebras/classical_lie_algebra.py
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Expand Up @@ -1996,14 +1996,11 @@ def degree_on_basis(self, m):
EXAMPLES::

sage: L = LieAlgebra(QQ, cartan_type=['G', 2])
sage: [L.degree_on_basis(m) for m in L.basis().keys()]
[alpha[2], alpha[1], alpha[1] + alpha[2],
2*alpha[1] + alpha[2], 3*alpha[1] + alpha[2],
3*alpha[1] + 2*alpha[2],
0, 0,
-alpha[2], -alpha[1], -alpha[1] - alpha[2],
-2*alpha[1] - alpha[2], -3*alpha[1] - alpha[2],
-3*alpha[1] - 2*alpha[2]]
sage: sorted([L.degree_on_basis(m) for m in L.basis().keys()])
[0, 0, -3*alpha[1] - 2*alpha[2], -3*alpha[1] - alpha[2],
-2*alpha[1] - alpha[2], -alpha[1], -alpha[1] - alpha[2], alpha[1],
alpha[1] + alpha[2], 2*alpha[1] + alpha[2], 3*alpha[1] + alpha[2],
3*alpha[1] + 2*alpha[2], -alpha[2], alpha[2]]
"""
if m.parent() is self._Q:
return m
Expand Down
7 changes: 4 additions & 3 deletions src/sage/algebras/lie_algebras/lie_algebra_element.pyx
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Expand Up @@ -965,9 +965,10 @@ cdef class UntwistedAffineLieAlgebraElement(Element):
sage: L = lie_algebras.Affine(QQ, ['B', 3, 1])
sage: elt = L.an_element()
sage: elt._repr_generic(str, str, lambda t: "T^{}".format(t), '.', '(x)')
'(E[alpha[3]] + E[alpha[2]] + E[alpha[1]] + h1 + h2 + h3 + E[-alpha[3]]
+ E[-alpha[2]] + E[-alpha[1]])(x)T^0 + (E[-alpha[1] - 2*alpha[2]
- 2*alpha[3]])(x)T^1 + (E[alpha[1] + 2*alpha[2] + 2*alpha[3]])(x)T^-1 + c + d'
'(E[alpha[3]] + E[alpha[2]] + E[alpha[1]] + h1 + h2 + h3 + E[-alpha[3]] # 64-bit
+ E[-alpha[2]] + E[-alpha[1]])(x)T^0 + (E[-alpha[1] - 2*alpha[2] # 64-bit
- 2*alpha[3]])(x)T^1 + (E[alpha[1] + 2*alpha[2] + 2*alpha[3]])(x)T^-1 + c + d' # 64-bit
... # 32-bit
"""
ret = style('')
mult = style(mult)
Expand Down
17 changes: 9 additions & 8 deletions src/sage/algebras/lie_algebras/poincare_birkhoff_witt.py
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Expand Up @@ -543,12 +543,13 @@ def casimir_element(self, order=2, *args, **kwds):
sage: L = LieAlgebra(QQ, cartan_type=['G', 2])
sage: U = L.pbw_basis()
sage: C = U.casimir_element(); C
1/4*PBW[alpha[2]]*PBW[-alpha[2]] + 1/12*PBW[alpha[1]]*PBW[-alpha[1]]
+ 1/12*PBW[alpha[1] + alpha[2]]*PBW[-alpha[1] - alpha[2]] + 1/12*PBW[2*alpha[1] + alpha[2]]*PBW[-2*alpha[1] - alpha[2]]
+ 1/4*PBW[3*alpha[1] + alpha[2]]*PBW[-3*alpha[1] - alpha[2]]
+ 1/4*PBW[3*alpha[1] + 2*alpha[2]]*PBW[-3*alpha[1] - 2*alpha[2]]
+ 1/12*PBW[alphacheck[1]]^2 + 1/4*PBW[alphacheck[1]]*PBW[alphacheck[2]]
+ 1/4*PBW[alphacheck[2]]^2 - 5/12*PBW[alphacheck[1]] - 3/4*PBW[alphacheck[2]]
1/4*PBW[alpha[2]]*PBW[-alpha[2]] + 1/12*PBW[alpha[1]]*PBW[-alpha[1]] # 64-bit
+ 1/12*PBW[alpha[1] + alpha[2]]*PBW[-alpha[1] - alpha[2]] + 1/12*PBW[2*alpha[1] + alpha[2]]*PBW[-2*alpha[1] - alpha[2]] # 64-bit
+ 1/4*PBW[3*alpha[1] + alpha[2]]*PBW[-3*alpha[1] - alpha[2]] # 64-bit
+ 1/4*PBW[3*alpha[1] + 2*alpha[2]]*PBW[-3*alpha[1] - 2*alpha[2]] # 64-bit
+ 1/12*PBW[alphacheck[1]]^2 + 1/4*PBW[alphacheck[1]]*PBW[alphacheck[2]] # 64-bit
+ 1/4*PBW[alphacheck[2]]^2 - 5/12*PBW[alphacheck[1]] - 3/4*PBW[alphacheck[2]] # 64-bit
... # 32-bit
sage: all(g * C == C * g for g in U.algebra_generators())
True

Expand Down Expand Up @@ -767,8 +768,8 @@ def _transpose_on_basis(self, m):
sage: f1, f2, f3, f4, f5, f6 = U.f()
sage: e1, e2, e3, e4, e5, e6 = U.e()
sage: elt = e1 * e4^2 * f1 * f2^3
sage: U._transpose_on_basis(elt.support()[0])
PBW[alpha[2]]^3*PBW[alpha[1]]*PBW[-alpha[4]]^2*PBW[-alpha[1]]
sage: U._transpose_on_basis(elt.support()[0]) == e2^3*e1*f1*f4^2
True
"""
I = self._indices
basis_mapping = self._g._transpose_basis_mapping
Expand Down
5 changes: 3 additions & 2 deletions src/sage/algebras/lie_algebras/verma_module.py
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Expand Up @@ -1354,8 +1354,9 @@ def singular_vector(self):
sage: Mp = L.verma_module(mu)
sage: H = Hom(Mp, M)
sage: v = H.singular_vector(); v
f[-alpha[2]]*f[-alpha[1]]^3*v[Lambda[1] - Lambda[3]]
+ 3*f[-alpha[1]]^2*f[-alpha[1] - alpha[2]]*v[Lambda[1] - Lambda[3]]
f[-alpha[2]]*f[-alpha[1]]^3*v[Lambda[1] - Lambda[3]] # 64-bit
+ 3*f[-alpha[1]]^2*f[-alpha[1] - alpha[2]]*v[Lambda[1] - Lambda[3]] # 64-bit
... # 32-bit
sage: v.degree() == Mp.highest_weight()
True

Expand Down
3 changes: 2 additions & 1 deletion src/sage/algebras/lie_conformal_algebras/lie_conformal_algebra_element.py
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Expand Up @@ -168,7 +168,8 @@ def _repr_(self):

sage: R = lie_conformal_algebras.Affine(QQ, 'B3')
sage: R.2.T()+3*R.3
TB[alpha[1]] + 3*B[alpha[2] + alpha[3]]
TB[alpha[1]] + 3*B[alpha[2] + alpha[3]] # 64-bit
... # 32-bit
"""
if self.is_zero():
return "0"
Expand Down
12 changes: 6 additions & 6 deletions src/sage/categories/regular_crystals.py
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Expand Up @@ -838,13 +838,13 @@ def dual_equivalence_class(self, index_set=None):
([[1, 3], [2, 4]], [[1, 2], [3, 4]], 3)]
sage: T = crystals.Tableaux(['A',4], shape=[3,2])
sage: G = T(2,1,4,3,5).dual_equivalence_class()
sage: G.edges(sort=True)
[([[1, 3, 5], [2, 4]], [[1, 3, 4], [2, 5]], 4),
([[1, 3, 5], [2, 4]], [[1, 2, 5], [3, 4]], 2),
([[1, 3, 5], [2, 4]], [[1, 2, 5], [3, 4]], 3),
sage: G.edges(sort=True,sort_vertices=True)
[([[1, 3, 4], [2, 5]], [[1, 3, 5], [2, 4]], 4),
([[1, 3, 4], [2, 5]], [[1, 2, 4], [3, 5]], 2),
([[1, 2, 4], [3, 5]], [[1, 2, 3], [4, 5]], 3),
([[1, 2, 4], [3, 5]], [[1, 2, 3], [4, 5]], 4)]
([[1, 2, 5], [3, 4]], [[1, 3, 5], [2, 4]], 2),
([[1, 2, 5], [3, 4]], [[1, 3, 5], [2, 4]], 3),
([[1, 2, 3], [4, 5]], [[1, 2, 4], [3, 5]], 3),
([[1, 2, 3], [4, 5]], [[1, 2, 4], [3, 5]], 4)]
"""
if index_set is None:
index_set = self.index_set()
Expand Down
6 changes: 3 additions & 3 deletions src/sage/combinat/growth.py
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Expand Up @@ -1775,7 +1775,7 @@ def _check_duality(self, n):
...
ValueError: D U - U D differs from 1 I for vertex [2]:
D U = [[2]]
U D + 1 I = [[1, 1], [2], [2]]
U D + 1 I = [[2], [1, 1], [2]]
"""
if self.has_multiple_edges:
def check_vertex(w, P, Q):
Expand Down Expand Up @@ -1841,8 +1841,8 @@ def Q_graph(self, n):
sage: Q = Domino.Q_graph(3); Q
Finite poset containing 8 elements

sage: Q.upper_covers(Partition([1,1]))
[[1, 1, 1, 1], [3, 1], [2, 2]]
sage: sorted(Q.upper_covers(Partition([1,1])))
[[1, 1, 1, 1], [2, 2], [3, 1]]
"""
if self.has_multiple_edges:
D = DiGraph([(x, y, e) for k in range(n - 1)
Expand Down
8 changes: 4 additions & 4 deletions src/sage/combinat/permutation.py
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Expand Up @@ -4785,12 +4785,12 @@ def permutation_poset(self):
EXAMPLES::

sage: # needs sage.combinat sage.graphs
sage: Permutation([3,1,5,4,2]).permutation_poset().cover_relations()
[[(2, 1), (5, 2)],
sage: sorted(Permutation([3,1,5,4,2]).permutation_poset().cover_relations())
[[(1, 3), (3, 5)],
[(1, 3), (4, 4)],
[(2, 1), (3, 5)],
[(2, 1), (4, 4)],
[(1, 3), (3, 5)],
[(1, 3), (4, 4)]]
[(2, 1), (5, 2)]]
sage: Permutation([]).permutation_poset().cover_relations()
[]
sage: Permutation([1,3,2]).permutation_poset().cover_relations()
Expand Down
6 changes: 3 additions & 3 deletions src/sage/combinat/posets/hasse_diagram.py
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Expand Up @@ -1074,9 +1074,9 @@ def moebius_function_matrix(self, algorithm='cython'):
True
sage: H = posets.TamariLattice(3)._hasse_diagram
sage: M = H.moebius_function_matrix('matrix'); M
[ 1 -1 -1 0 1]
[ 0 1 0 0 -1]
[ 0 0 1 -1 0]
[ 1 -1 0 -1 1]
[ 0 1 -1 0 0]
[ 0 0 1 0 -1]
[ 0 0 0 1 -1]
[ 0 0 0 0 1]
sage: _ = H.__dict__.pop('_moebius_function_matrix')
Expand Down
8 changes: 4 additions & 4 deletions src/sage/combinat/posets/lattices.py
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Expand Up @@ -349,8 +349,8 @@ def submeetsemilattice(self, elms):
sage: L = posets.DivisorLattice(1000)
sage: L_ = L.submeetsemilattice([200, 250, 125]); L_
Finite meet-semilattice containing 5 elements
sage: L_.list()
[25, 50, 200, 125, 250]
sage: sorted(L_.list())
[25, 50, 125, 200, 250]

.. SEEALSO::

Expand Down Expand Up @@ -3159,8 +3159,8 @@ def sublattice(self, elms):
EXAMPLES::

sage: L = LatticePoset(([], [[1,2],[1,17],[1,8],[2,3],[2,22],[2,5],[2,7],[17,22],[17,13],[8,7],[8,13],[3,16],[3,9],[22,16],[22,18],[22,10],[5,18],[5,14],[7,9],[7,14],[7,10],[13,10],[16,6],[16,19],[9,19],[18,6],[18,33],[14,33],[10,19],[10,33],[6,4],[19,4],[33,4]]))
sage: L.sublattice([14, 13, 22]).list()
[1, 2, 8, 7, 14, 17, 13, 22, 10, 33]
sage: sorted(L.sublattice([14, 13, 22]).list())
[1, 2, 7, 8, 10, 13, 14, 17, 22, 33]

sage: L = posets.BooleanLattice(3)
sage: L.sublattice([3,5,6,7])
Expand Down
4 changes: 2 additions & 2 deletions src/sage/combinat/posets/poset_examples.py
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Expand Up @@ -1459,7 +1459,7 @@ def YoungsLattice(n):

sage: P = posets.YoungsLattice(3); P
Finite meet-semilattice containing 7 elements
sage: P.cover_relations()
sage: sorted(P.cover_relations())
[[[], [1]],
[[1], [1, 1]],
[[1], [2]],
Expand Down Expand Up @@ -1488,7 +1488,7 @@ def YoungsLatticePrincipalOrderIdeal(lam):
sage: P = posets.YoungsLatticePrincipalOrderIdeal(Partition([2,2]))
sage: P
Finite lattice containing 6 elements
sage: P.cover_relations()
sage: sorted(P.cover_relations())
[[[], [1]],
[[1], [1, 1]],
[[1], [2]],
Expand Down
18 changes: 9 additions & 9 deletions src/sage/combinat/posets/posets.py
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Expand Up @@ -6335,8 +6335,8 @@ def graphviz_string(self, graph_string='graph', edge_string='--'):
sage: P = Poset({'a':['b'],'b':['d'],'c':['d'],'d':['f'],'e':['f'],'f':[]})
sage: print(P.graphviz_string())
graph {
"f";"d";"b";"a";"c";"e";
"f"--"e";"d"--"c";"b"--"a";"d"--"b";"f"--"d";
"f";"e";"d";"c";"b";"a";
"b"--"a";"d"--"b";"d"--"c";"f"--"d";"f"--"e";
}
"""
s = '%s {\n' % graph_string
Expand All @@ -6359,8 +6359,8 @@ def subposet(self, elements):
....: 'd': ['f'], 'e': ['f']})
sage: Q = P.subposet(['a', 'b', 'f']); Q
Finite poset containing 3 elements
sage: Q.cover_relations()
[['b', 'f'], ['a', 'f']]
sage: sorted(Q.cover_relations())
[['a', 'f'], ['b', 'f']]

A subposet of a non-facade poset is again a non-facade poset::

Expand Down Expand Up @@ -6640,8 +6640,8 @@ def order_filter(self, elements):
EXAMPLES::

sage: P = Poset((divisors(1000), attrcall("divides")))
sage: P.order_filter([20, 25])
[20, 40, 25, 50, 100, 200, 125, 250, 500, 1000]
sage: sorted(P.order_filter([20, 25]))
[20, 25, 40, 50, 100, 125, 200, 250, 500, 1000]

.. SEEALSO::

Expand Down Expand Up @@ -6672,7 +6672,7 @@ def order_ideal(self, elements):
EXAMPLES::

sage: P = Poset((divisors(1000), attrcall("divides")))
sage: P.order_ideal([20, 25])
sage: sorted(P.order_ideal([20, 25]))
[1, 2, 4, 5, 10, 20, 25]

.. SEEALSO::
Expand Down Expand Up @@ -6778,7 +6778,7 @@ def closed_interval(self, x, y):
EXAMPLES::

sage: P = Poset((divisors(1000), attrcall("divides")))
sage: P.closed_interval(2, 100)
sage: sorted(P.closed_interval(2, 100))
[2, 4, 10, 20, 50, 100]

.. SEEALSO::
Expand Down Expand Up @@ -6806,7 +6806,7 @@ def open_interval(self, x, y):
EXAMPLES::

sage: P = Poset((divisors(1000), attrcall("divides")))
sage: P.open_interval(2, 100)
sage: sorted(P.open_interval(2, 100))
[4, 10, 20, 50]

.. SEEALSO::
Expand Down
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