Cosmetics

src/sage/groups/abelian_gps/abelian_aut.py

@@ -14,32 +14,32 @@
     sage: g = G.an_element()
     sage: f = autG.an_element()
     sage: f
-    [ g2^2, g1, g2^3 ] -> [ g2^4, g1*g2^3, g2^3 ]
+    Pcgs([ f1, f2, f3 ]) -> [ f1, f1*f2*f3^2, f3^2 ]
     sage: (g, f(g))
-    (g1*g2, g1*g2^2)
+    (f1*f2, f2*f3^2)
 
 Or anything coercible into its domain::
 
     sage: A = AbelianGroup([2,6])
     sage: a = A.an_element()
     sage: (a, f(a))
-    (f0*f1, g1*g2^2)
+    (f0*f1, f2*f3^2)
     sage: A = AdditiveAbelianGroup([2,6])
     sage: a = A.an_element()
     sage: (a, f(a))
-    ((1, 0), g1*g2^3)
+    ((1, 0), f1)
     sage: f((1,1))
-    g1*g2^2
+    f2*f3^2
 
 We can compute conjugacy classes::
 
     sage: autG.conjugacy_classes_representatives()
     (1,
-     [ g2^2, g1, g2^3 ] -> [ g2^2, g2^3, g1 ],
-     [ g2^2, g1, g2^3 ] -> [ g2^4, g1*g2^3, g2^3 ],
-     [ g2^2, g1, g2^3 ] -> [ g2^4, g2^3, g1*g2^3 ],
-     [ g2^2, g1, g2^3 ] -> [ g2^2, g2^3, g1*g2^3 ],
-     [ g1, g2^3, g2^2 ] -> [ g1, g2^3, g2^4 ])
+     Pcgs([ f1, f2, f3 ]) -> [ f2*f3, f1*f2, f3 ],
+     Pcgs([ f1, f2, f3 ]) -> [ f1*f2*f3, f2*f3^2, f3^2 ],
+     [ f3^2, f1*f2*f3, f1 ] -> [ f3^2, f1, f1*f2*f3 ],
+     Pcgs([ f1, f2, f3 ]) -> [ f2*f3, f1*f2*f3^2, f3^2 ],
+     [ f1*f2*f3, f1, f3^2 ] -> [ f1*f2*f3, f1, f3 ])
 
 the group order::
 
@@ -145,7 +145,7 @@ def __reduce__(self):
         """
         return (self.parent(), (self.matrix(),))
 
-    def __call__(self,a):
+    def __call__(self, a):
         r"""
         Return the image of ``a`` under this automorphism.
 
@@ -159,7 +159,7 @@ def __call__(self,a):
             sage: G = AbelianGroupGap([2,3,4])
             sage: f = G.aut().an_element()
             sage: f
-            [ g2^2, g1*g3^3, g1 ] -> [ g2, g3, g1*g3^2 ]
+            Pcgs([ f1, f2, f3, f4 ]) -> [ f1*f4, f2^2, f1*f3, f4 ]
         """
         g = self.gap().ImageElm
         dom = self.parent()._domain
@@ -184,7 +184,7 @@ def matrix(self):
             sage: G = AbelianGroupGap([2,3,4])
             sage: f = G.aut().an_element()
             sage: f
-            [ g2^2, g1*g3^3, g1 ] -> [ g2, g3, g1*g3^2 ]
+            Pcgs([ f1, f2, f3, f4 ]) -> [ f1*f4, f2^2, f1*f3, f4 ]
             sage: f.matrix()
             [1 0 2]
             [0 2 0]
@@ -287,7 +287,7 @@ def _element_constructor_(self, x, check=True):
             sage: f
             Morphism from module over Integer Ring with invariants (2, 10) to module with invariants (2, 10) that sends the generators to [(1, 5), (0, 3)]
             sage: aut(f)
-            [ g1, g2 ] -> [ g1*g2^5, g2^3 ]
+            [ f1, f2 ] -> [ f1*f2*f3^2, f2*f3 ]
         """
         if x in self._covering_matrix_ring:
             dom = self._domain
@@ -470,7 +470,7 @@ def __repr__(self):
             sage: G = AbelianGroupGap([2,3,4,5])
             sage: aut = G.automorphism_group()
         """
-        s = "Full group of automorphisms of %s"%self.domain()
+        s = "Full group of automorphisms of %s" %self.domain()
         return s
 
 class AbelianGroupAutomorphismGroup_subgroup(AbelianGroupAutomorphismGroup_gap):
@@ -482,7 +482,7 @@ class AbelianGroupAutomorphismGroup_subgroup(AbelianGroupAutomorphismGroup_gap):
     .. Note::
 
         Do not use this class directly instead use.
-        meth:`subgroup`.
+        meth:`sage.groups.abelian_gps.abelian_group_gap.AbelianGroup_gap.subgroup`.
 
     INPUT:
 
@@ -541,5 +541,5 @@ def _repr_(self):
             sage: sub = aut.subgroup([f])
         """
         s = "Subgroup of automorphisms of %s \n generated by %s automorphisms"%(
-            self.domain(),len(self.gens()))
+            self.domain(), len(self.gens()))
         return s

src/sage/groups/abelian_gps/abelian_group_gap.py

@@ -385,6 +385,7 @@ def automorphism_group(self):
             sage: from sage.groups.abelian_gps.abelian_group_gap import AbelianGroupGap
             sage: G = AbelianGroupGap([2, 3])
             sage: G.aut()
+            Full group of automorphisms of Abelian group with gap, generator orders (2, 3)
         """
         from sage.groups.abelian_gps.abelian_aut import AbelianGroupAutomorphismGroup
         return AbelianGroupAutomorphismGroup(self)