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Added doctest for _universal_cover_dict
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src/sage/categories/simplicial_sets.py

Lines changed: 8 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -343,6 +343,14 @@ def _universal_cover_dict(self):
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r"""
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Return the fundamental group and dictionary sending each edge to
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the corresponding group element
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TESTS::
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sage: RP2 = simplicial_sets.RealProjectiveSpace(2)
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sage: RP2._universal_cover_dict()
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(Finitely presented group < e | e^2 >, {f: e})
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sage: RP2.nondegenerate_simplices()
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[1, f, f * f]
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"""
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from sage.groups.free_group import FreeGroup
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skel = self.n_skeleton(2)
@@ -445,7 +453,6 @@ def covering_map(self, character):
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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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"""
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from sage.topology.simplicial_set import AbstractSimplex, SimplicialSet
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from sage.topology.simplicial_set_morphism import SimplicialSetMorphism
@@ -528,7 +535,6 @@ def cover(self, character):
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Z x Z x Z x Z
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sage: C.fundamental_group()
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Finitely presented group < e0, e1, e2, e3 | >
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"""
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return self.covering_map(character).domain()
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@@ -555,12 +561,9 @@ def universal_cover(self):
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(f * f * f, e): ((f * f, 1), s_0 (f, e), s_1 (f, e), (f * f, e))}
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sage: C.fundamental_group()
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Finitely presented group < | >
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"""
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return self.universal_cover_map().domain()
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def is_simply_connected(self):
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"""
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Return ``True`` if this pointed simplicial set is simply connected.

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