@@ -444,29 +444,31 @@ def covering_map(self, character):
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sage: # needs sage.graphs sage.groups
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sage: S1 = simplicial_sets.Sphere(1)
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- sage: W = S1.wedge(S1)
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+ sage: S1_ = simplicial_sets.Sphere(1)
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+ sage: S1_.n_cells(1)[0].rename("sigma_1'")
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+ sage: W = S1.wedge(S1_)
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sage: G = CyclicPermutationGroup(3)
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sage: a, b = W.n_cells(1)
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sage: C = W.covering_map({a : G.gen(0), b : G.one()}); C
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Simplicial set morphism:
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From: Simplicial set with 9 non-degenerate simplices
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To: Wedge: (S^1 v S^1)
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- Defn: [(*, ()), (*, (1,2,3)), (*, (1,3,2)), (sigma_1, ()),
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- (sigma_1, ()), (sigma_1, (1,2,3 )), (sigma_1, (1,2,3 )),
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- (sigma_1, (1,3,2 )), (sigma_1, (1,3,2))]
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- --> [*, *, *, sigma_1, sigma_1, sigma_1, sigma_1, sigma_1, sigma_1]
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+ Defn: [(*, ()), (*, (1,2,3)), (*, (1,3,2)), (sigma_1' , ()),
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+ (sigma_1' , (1,2,3 )), (sigma_1' , (1,3,2 )), (sigma_1, ()),
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+ (sigma_1, (1,2,3 )), (sigma_1, (1,3,2))]
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+ --> [*, *, *, sigma_1' , sigma_1' , sigma_1' , sigma_1, sigma_1, sigma_1]
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sage: C.domain()
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Simplicial set with 9 non-degenerate simplices
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sage: C.domain().face_data()
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{(*, ()): None,
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(*, (1,2,3)): None,
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(*, (1,3,2)): None,
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+ (sigma_1', ()): ((*, ()), (*, ())),
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+ (sigma_1', (1,2,3)): ((*, (1,2,3)), (*, (1,2,3))),
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+ (sigma_1', (1,3,2)): ((*, (1,3,2)), (*, (1,3,2))),
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(sigma_1, ()): ((*, (1,2,3)), (*, ())),
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- (sigma_1, ()): ((*, ()), (*, ())),
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(sigma_1, (1,2,3)): ((*, (1,3,2)), (*, (1,2,3))),
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- (sigma_1, (1,2,3)): ((*, (1,2,3)), (*, (1,2,3))),
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- (sigma_1, (1,3,2)): ((*, ()), (*, (1,3,2))),
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- (sigma_1, (1,3,2)): ((*, (1,3,2)), (*, (1,3,2)))}
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+ (sigma_1, (1,3,2)): ((*, ()), (*, (1,3,2)))}
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"""
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from sage .topology .simplicial_set import AbstractSimplex , SimplicialSet
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from sage .topology .simplicial_set_morphism import SimplicialSetMorphism
@@ -531,20 +533,22 @@ def cover(self, character):
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sage: # needs sage.graphs sage.groups
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sage: S1 = simplicial_sets.Sphere(1)
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- sage: W = S1.wedge(S1)
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+ sage: S1_ = simplicial_sets.Sphere(1)
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+ sage: S1_.n_cells(1)[0].rename("sigma_1'")
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+ sage: W = S1.wedge(S1_)
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sage: G = CyclicPermutationGroup(3)
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sage: (a, b) = W.n_cells(1)
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sage: C = W.cover({a : G.gen(0), b : G.gen(0)^2})
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sage: C.face_data()
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{(*, ()): None,
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(*, (1,2,3)): None,
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(*, (1,3,2)): None,
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+ (sigma_1', ()): ((*, (1,3,2)), (*, ())),
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+ (sigma_1', (1,2,3)): ((*, ()), (*, (1,2,3))),
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+ (sigma_1', (1,3,2)): ((*, (1,2,3)), (*, (1,3,2))),
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(sigma_1, ()): ((*, (1,2,3)), (*, ())),
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- (sigma_1, ()): ((*, (1,3,2)), (*, ())),
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(sigma_1, (1,2,3)): ((*, (1,3,2)), (*, (1,2,3))),
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- (sigma_1, (1,2,3)): ((*, ()), (*, (1,2,3))),
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- (sigma_1, (1,3,2)): ((*, ()), (*, (1,3,2))),
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- (sigma_1, (1,3,2)): ((*, (1,2,3)), (*, (1,3,2)))}
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+ (sigma_1, (1,3,2)): ((*, ()), (*, (1,3,2)))}
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sage: C.homology(1) # needs sage.modules
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Z x Z x Z x Z
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sage: C.fundamental_group()
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