Fixing some doctests and details.

Author: tscrim

src/sage/combinat/permutation.py

@@ -6844,9 +6844,10 @@ def _from_cactus_group_element(self, x):
 
             sage: J3 = groups.misc.Cactus(3)
             sage: s12,s13,s23 = J3.gens()
-            sage: elt = s12*s23*s13
+            sage: elt = s12 * s23 * s13
             sage: P5 = Permutations(5)
             sage: P5._from_cactus_group_element(elt)
+            [1, 3, 2, 4, 5]
         """
         return self(x.to_permutation())
 

src/sage/groups/finitely_presented_catalog.py

@@ -23,3 +23,4 @@
 from .finitely_presented_named import QuaternionPresentation as Quaternion
 from .finitely_presented_named import AlternatingPresentation as Alternating
 from .finitely_presented_named import BinaryDihedralPresentation as BinaryDihedral
+from .finitely_presented_named import CactusPresentation as Cactus

src/sage/groups/finitely_presented_named.py

@@ -12,6 +12,9 @@
 - Alternating group, `A_n` of order `n!/2` --
   :func:`groups.presentation.Alternating <sage.groups.finitely_presented_named.AlternatingPresentation>`
 
+- Cactus group, `J_n` --
+  :func:`groups.presentation.Cactus <sage.groups.finitely_presented_named.CactusPresentation>`
+
 - Cyclic group, `C_n` of order `n` --
   :func:`groups.presentation.Cyclic <sage.groups.finitely_presented_named.CyclicPresentation>`
 
@@ -580,12 +583,13 @@ def CactusPresentation(n):
     F = FreeGroup(G.variable_names())
     gens = F.gens()
     rls = [g**2 for g in gens]
-    K = G.group_generators().keys()
+    Gg = G.group_generators()
+    K = Gg.keys()
     for i,key in enumerate(K):
         for j,key2 in enumerate(K):
             if i == j:
                 continue
-            x,y = G._product_on_gens(key, key2)
+            x,y = (Gg[key] * Gg[key2])._data
             if key == x and key2 == y:
                 continue
             elt = gens[i] * gens[j] * ~gens[K.index(y)] * ~gens[K.index(x)]

src/sage/groups/perm_gps/permgroup_named.py

@@ -339,11 +339,13 @@ def _coerce_map_from_(self, G):
 
             sage: J3 = groups.misc.Cactus(3)
             sage: S5 = SymmetricGroup(5)
-            sage: S5._coerce_map_from_(J3)
-            True
+            sage: S5.coerce_map_from(J3)
+            Conversion via _from_cactus_group_element map:
+              From: Cactus Group with 3 fruit
+              To:   Symmetric group of order 5! as a permutation group
             sage: S2 = SymmetricGroup(2)
-            sage: S2._coerce_map_from_(J3)
-            False
+            sage: S2._coerce_map_from_(J3) is None
+            True
         """
         from sage.groups.cactus_group import CactusGroup
         if isinstance(G, CactusGroup) and G._n <= self._deg:
@@ -361,6 +363,7 @@ def _from_cactus_group_element(self, x):
             sage: elt = s12*s23*s13
             sage: S5 = SymmetricGroup(5)
             sage: S5._from_cactus_group_element(elt)
+            (2,3)
         """
         return self(x.to_permutation())