more libgap in permutation groups ; get rid of _libgap_init_

Author: fchapoton

src/sage/groups/perm_gps/permgroup_element.pyx

@@ -410,7 +410,7 @@ cdef class PermutationGroupElement(MultiplicativeGroupElement):
             sage: k._gap_()
             (1,2)(3,5,6)
             sage: k._gap_().parent()
-            Gap
+            C library interface to GAP
 
         List notation::
 
@@ -835,13 +835,11 @@ cdef class PermutationGroupElement(MultiplicativeGroupElement):
             sage: g._gap_()
             (1,2,3)(4,5)
         """
-        if gap is None:
-            from sage.interfaces.gap import gap
-        return gap(self._gap_init_())
+        return self._libgap_()
 
     def _libgap_(self):
         r"""
-        Returns self as a libgap element
+        Return ``self`` as a libgap element.
 
         EXAMPLES::
 
@@ -867,7 +865,7 @@ cdef class PermutationGroupElement(MultiplicativeGroupElement):
             sage: p_libgap == p_pexpect
             True
             sage: type(p_libgap) == type(p_pexpect)
-            False
+            True
 
         If the permutation element is built from a libgap element, it is cached
         and returned by this function::

src/sage/groups/perm_gps/permgroup_morphism.py

@@ -84,7 +84,7 @@ def kernel(self):
             sage: G.is_isomorphic(pr1.kernel())
             True
         """
-        return self.domain().subgroup(gap_group=self._gap_().Kernel())
+        return self.domain().subgroup(gap_group=self._libgap_().Kernel())
 
     def image(self, J):
         r"""
@@ -133,10 +133,10 @@ def image(self, J):
         H = self.codomain()
         if J in self.domain():
             J = PermutationGroup([J])
-            G = self._gap_().Image(J)
+            G = self._libgap_().Image(J)
             return H.subgroup(gap_group=G).gens()[0]
         else:
-            G = self._gap_().Image(J)
+            G = self._libgap_().Image(J)
             return H.subgroup(gap_group=G)
 
     def __call__(self, g):
@@ -210,7 +210,7 @@ def _repr_defn(self):
         """
         return str(self._gap_hom).replace('\n', '')
 
-    def _gap_(self, gap=None):
+    def _libgap_(self):
         r"""
         Return a GAP version of this morphism.
 
@@ -220,7 +220,7 @@ def _gap_(self, gap=None):
             sage: G = PermutationGroup([[(1,2),(3,4)], [(1,2,3,4)]])
             sage: H = G.subgroup([G([(1,2,3,4)])])
             sage: phi = PermutationGroupMorphism_from_gap(H, G, gap.Identity)
-            sage: phi._gap_()
+            sage: phi._libgap_()
             Identity
         """
         return self._gap_hom
@@ -239,7 +239,7 @@ def __call__(self, g):
             sage: [pr1(g) for g in G.gens()]
             [(3,7,5)(4,8,6), (1,2,6)(3,4,8)]
         """
-        return self.codomain()(self._gap_().Image(g))
+        return self.codomain()(self._libgap_().Image(g))
 
 
 class PermutationGroupMorphism_im_gens(PermutationGroupMorphism):
@@ -295,7 +295,7 @@ def _repr_defn(self):
         """
         return "%s -> %s" % (list(self.domain().gens()), self._images)
 
-    def _gap_(self):
+    def _libgap_(self):
         r"""
         Return a GAP representation of this morphism.
 
@@ -304,11 +304,10 @@ def _gap_(self):
             sage: G = CyclicPermutationGroup(4)
             sage: H = DihedralGroup(4)
             sage: phi = PermutationGroupMorphism_im_gens(G, H, map(H, G.gens()))
-            sage: phi._gap_()
-            GroupHomomorphismByImages( Group( [ (1,2,3,4) ] ), Group(
-            [ (1,2,3,4), (1,4)(2,3) ] ), [ (1,2,3,4) ], [ (1,2,3,4) ] )
+            sage: phi._libgap_()
+            [ (1,2,3,4) ] -> [ (1,2,3,4) ]
         """
-        return self.domain()._gap_().GroupHomomorphismByImages(self.codomain(), self.domain().gens(), self._images)
+        return self.domain()._libgap_().GroupHomomorphismByImages(self.codomain(), self.domain().gens(), self._images)
 
 
 def is_PermutationGroupMorphism(f) -> bool:

src/sage/libs/gap/element.pyx

@@ -380,7 +380,7 @@ cdef GapElement make_GapElement(parent, Obj obj) noexcept:
         sage: libgap(None)
         Traceback (most recent call last):
         ...
-        AttributeError: 'NoneType' object has no attribute '_libgap_init_'...
+        AttributeError: 'NoneType' object has no attribute '_gap_init_'...
     """
     cdef GapElement r = GapElement.__new__(GapElement)
     r._initialize(parent, obj)

src/sage/libs/gap/libgap.pyx

@@ -319,7 +319,7 @@ class Gap(Parent):
                 return x._libgap_()
             except AttributeError:
                 pass
-            x = str(x._libgap_init_())
+            x = str(x._gap_init_())
             return make_any_gap_element(self, gap_eval(x))
 
     def _construct_matrix(self, M):
@@ -400,7 +400,7 @@ class Gap(Parent):
         cdef GapElement elem
 
         if not isinstance(gap_command, str):
-            gap_command = str(gap_command._libgap_init_())
+            gap_command = str(gap_command._gap_init_())
 
         initialize()
         elem = make_any_gap_element(self, gap_eval(gap_command))

src/sage/structure/sage_object.pyx

@@ -755,14 +755,7 @@ cdef class SageObject:
 
     def _libgap_(self):
         from sage.libs.gap.libgap import libgap
-        return libgap.eval(self._libgap_init_())
-
-    def _libgap_init_(self):
-        """
-        For consistency's sake we provide a ``_libgap_init_`` but in most cases
-        we can use the same as ``_gap_init_`` here.
-        """
-        return self._gap_init_()
+        return libgap.eval(self._gap_init_())
 
     def _gp_(self, G=None):
         if G is None: