@@ -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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+
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+ TESTS::
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+
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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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"""
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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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"""
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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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-
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"""
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return self .universal_cover_map ().domain ()
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-
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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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