path: root/sagemath-gap-4.10.patch

diff --git a/src/doc/en/constructions/groups.rst b/src/doc/en/constructions/groups.rst
index e769171..c771783 100644
--- a/src/doc/en/constructions/groups.rst
+++ b/src/doc/en/constructions/groups.rst
@@ -163,7 +163,7 @@ If you want to find all the normal subgroups of a permutation group
 
     sage: G = AlternatingGroup( 5 )
     sage: gap(G).NormalSubgroups()
-    [ Group( () ), AlternatingGroup( [ 1 .. 5 ] ) ]
+    [ AlternatingGroup( [ 1 .. 5 ] ), Group( () ) ]
 
 or
 
@@ -171,22 +171,22 @@ or
 
     sage: G = gap("AlternatingGroup( 5 )")
     sage: G.NormalSubgroups()
-    [ Group( () ), AlternatingGroup( [ 1 .. 5 ] ) ]
+    [ AlternatingGroup( [ 1 .. 5 ] ), Group( () ) ]
 
 Here's another way, working more directly with GAP::
 
     sage: print(gap.eval("G := AlternatingGroup( 5 )"))
     Alt( [ 1 .. 5 ] )
     sage: print(gap.eval("normal := NormalSubgroups( G )"))
-    [ Group(()), Alt( [ 1 .. 5 ] ) ]
+    [ Alt( [ 1 .. 5 ] ), Group(()) ]
     sage: G = gap.new("DihedralGroup( 10 )")
     sage: G.NormalSubgroups()
-    [ Group( <identity> of ... ), Group( [ f2 ] ), Group( [ f1, f2 ] ) ]
+    [ Group( [ f1, f2 ] ), Group( [ f2 ] ), Group( <identity> of ... ) ]
     sage: print(gap.eval("G := SymmetricGroup( 4 )"))
     Sym( [ 1 .. 4 ] )
     sage: print(gap.eval("normal := NormalSubgroups( G );"))
-    [ Group(()), Group([ (1,4)(2,3), (1,3)(2,4) ]), Group([ (2,4,3), (1,4)
-      (2,3), (1,3)(2,4) ]), Sym( [ 1 .. 4 ] ) ]
+    [ Sym( [ 1 .. 4 ] ), Alt( [ 1 .. 4 ] ), Group([ (1,4)(2,3), (1,3)(2,4) ]),
+      Group(()) ]
 
 .. index::
    pair: groups; center
diff --git a/src/doc/en/prep/Quickstarts/Abstract-Algebra.rst b/src/doc/en/prep/Quickstarts/Abstract-Algebra.rst
index 042b786..041d6f9 100644
--- a/src/doc/en/prep/Quickstarts/Abstract-Algebra.rst
+++ b/src/doc/en/prep/Quickstarts/Abstract-Algebra.rst
@@ -85,13 +85,13 @@ rather than just a list of numbers.  This can be very powerful.
 
     sage: for K in D.normal_subgroups():
     ....:     print(K)
-    Subgroup of (Dihedral group of order 16 as a permutation group) generated by [()]
-    Subgroup of (Dihedral group of order 16 as a permutation group) generated by [(1,5)(2,6)(3,7)(4,8)]
-    Subgroup of (Dihedral group of order 16 as a permutation group) generated by [(1,3,5,7)(2,4,6,8), (1,5)(2,6)(3,7)(4,8)]
-    Subgroup of (Dihedral group of order 16 as a permutation group) generated by [(1,2)(3,8)(4,7)(5,6), (1,3,5,7)(2,4,6,8), (1,5)(2,6)(3,7)(4,8)]
-    Subgroup of (Dihedral group of order 16 as a permutation group) generated by [(2,8)(3,7)(4,6), (1,3,5,7)(2,4,6,8), (1,5)(2,6)(3,7)(4,8)]
-    Subgroup of (Dihedral group of order 16 as a permutation group) generated by [(1,2,3,4,5,6,7,8), (1,3,5,7)(2,4,6,8), (1,5)(2,6)(3,7)(4,8)]
     Subgroup of (Dihedral group of order 16 as a permutation group) generated by [(1,2,3,4,5,6,7,8), (1,8)(2,7)(3,6)(4,5)]
+    Subgroup of (Dihedral group of order 16 as a permutation group) generated by [(1,2,3,4,5,6,7,8), (1,3,5,7)(2,4,6,8), (1,5)(2,6)(3,7)(4,8)]
+    Subgroup of (Dihedral group of order 16 as a permutation group) generated by [(1,3,5,7)(2,4,6,8), (1,5)(2,6)(3,7)(4,8), (1,8)(2,7)(3,6)(4,5)]
+    Subgroup of (Dihedral group of order 16 as a permutation group) generated by [(2,8)(3,7)(4,6), (1,3,5,7)(2,4,6,8), (1,5)(2,6)(3,7)(4,8)]
+    Subgroup of (Dihedral group of order 16 as a permutation group) generated by [(1,3,5,7)(2,4,6,8), (1,5)(2,6)(3,7)(4,8)]
+    Subgroup of (Dihedral group of order 16 as a permutation group) generated by [(1,5)(2,6)(3,7)(4,8)]
+    Subgroup of (Dihedral group of order 16 as a permutation group) generated by [()]
 
 We can access specific subgroups if we know the generators as a
 permutation group.
diff --git a/src/doc/en/thematic_tutorials/group_theory.rst b/src/doc/en/thematic_tutorials/group_theory.rst
index 5d2fba0..868aefa 100644
--- a/src/doc/en/thematic_tutorials/group_theory.rst
+++ b/src/doc/en/thematic_tutorials/group_theory.rst
@@ -586,7 +586,12 @@ subgroups. ::
 
     sage: C20 = CyclicPermutationGroup(20)
     sage: C20.conjugacy_classes_subgroups()
-    [Subgroup of (Cyclic group of order 20 as a permutation group) generated by [()], Subgroup of (Cyclic group of order 20 as a permutation group) generated by [(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)], Subgroup of (Cyclic group of order 20 as a permutation group) generated by [(1,6,11,16)(2,7,12,17)(3,8,13,18)(4,9,14,19)(5,10,15,20)], Subgroup of (Cyclic group of order 20 as a permutation group) generated by [(1,5,9,13,17)(2,6,10,14,18)(3,7,11,15,19)(4,8,12,16,20)], Subgroup of (Cyclic group of order 20 as a permutation group) generated by [(1,3,5,7,9,11,13,15,17,19)(2,4,6,8,10,12,14,16,18,20)], Subgroup of (Cyclic group of order 20 as a permutation group) generated by [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)]]
+    [Subgroup of (Cyclic group of order 20 as a permutation group) generated by [()],
+     Subgroup of (Cyclic group of order 20 as a permutation group) generated by [(1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)],
+     Subgroup of (Cyclic group of order 20 as a permutation group) generated by [(1,6,11,16)(2,7,12,17)(3,8,13,18)(4,9,14,19)(5,10,15,20), (1,11)(2,12)(3,13)(4,14)(5,15)(6,16)(7,17)(8,18)(9,19)(10,20)],
+     Subgroup of (Cyclic group of order 20 as a permutation group) generated by [(1,5,9,13,17)(2,6,10,14,18)(3,7,11,15,19)(4,8,12,16,20)],
+     Subgroup of (Cyclic group of order 20 as a permutation group) generated by [(1,3,5,7,9,11,13,15,17,19)(2,4,6,8,10,12,14,16,18,20), (1,5,9,13,17)(2,6,10,14,18)(3,7,11,15,19)(4,8,12,16,20)],
+     Subgroup of (Cyclic group of order 20 as a permutation group) generated by [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20), (1,3,5,7,9,11,13,15,17,19)(2,4,6,8,10,12,14,16,18,20), (1,5,9,13,17)(2,6,10,14,18)(3,7,11,15,19)(4,8,12,16,20)]]
 
 Be careful, this command uses some more advanced ideas and will not
 usually list *all* of the subgroups of a group. Here we are relying on
@@ -639,10 +644,26 @@ suitable `g`. As an illustration, the code below:
     sage: K = DihedralGroup(12)
     sage: sg = K.conjugacy_classes_subgroups()
     sage: sg
-    [Subgroup of (Dihedral group of order 24 as a permutation group) generated by [()], Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,2)(3,12)(4,11)(5,10)(6,9)(7,8)], Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)], Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(2,12)(3,11)(4,10)(5,9)(6,8)], Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,5,9)(2,6,10)(3,7,11)(4,8,12)], Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(2,12)(3,11)(4,10)(5,9)(6,8), (1,7)(2,8)(3,9)(4,10)(5,11)(6,12)], Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,2)(3,12)(4,11)(5,10)(6,9)(7,8), (1,7)(2,8)(3,9)(4,10)(5,11)(6,12)], Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,7)(2,8)(3,9)(4,10)(5,11)(6,12), (1,10,7,4)(2,11,8,5)(3,12,9,6)], Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,3,5,7,9,11)(2,4,6,8,10,12), (1,5,9)(2,6,10)(3,7,11)(4,8,12)], Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,2)(3,12)(4,11)(5,10)(6,9)(7,8), (1,5,9)(2,6,10)(3,7,11)(4,8,12)], Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(2,12)(3,11)(4,10)(5,9)(6,8), (1,5,9)(2,6,10)(3,7,11)(4,8,12)], Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(2,12)(3,11)(4,10)(5,9)(6,8), (1,7)(2,8)(3,9)(4,10)(5,11)(6,12), (1,10,7,4)(2,11,8,5)(3,12,9,6)], Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(2,12)(3,11)(4,10)(5,9)(6,8), (1,3,5,7,9,11)(2,4,6,8,10,12), (1,5,9)(2,6,10)(3,7,11)(4,8,12)], Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,2)(3,12)(4,11)(5,10)(6,9)(7,8), (1,3,5,7,9,11)(2,4,6,8,10,12), (1,5,9)(2,6,10)(3,7,11)(4,8,12)], Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,2,3,4,5,6,7,8,9,10,11,12), (1,3,5,7,9,11)(2,4,6,8,10,12), (1,5,9)(2,6,10)(3,7,11)(4,8,12)], Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(2,12)(3,11)(4,10)(5,9)(6,8), (1,2,3,4,5,6,7,8,9,10,11,12), (1,3,5,7,9,11)(2,4,6,8,10,12), (1,5,9)(2,6,10)(3,7,11)(4,8,12)]]
+    [Subgroup of (Dihedral group of order 24 as a permutation group) generated by [()],
+     Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,7)(2,8)(3,9)(4,10)(5,11)(6,12)],
+     Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(2,12)(3,11)(4,10)(5,9)(6,8)],
+     Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,2)(3,12)(4,11)(5,10)(6,9)(7,8)],
+     Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,5,9)(2,6,10)(3,7,11)(4,8,12)],
+     Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(2,12)(3,11)(4,10)(5,9)(6,8), (1,7)(2,8)(3,9)(4,10)(5,11)(6,12)],
+     Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,7)(2,8)(3,9)(4,10)(5,11)(6,12), (1,10,7,4)(2,11,8,5)(3,12,9,6)],
+     Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,2)(3,12)(4,11)(5,10)(6,9)(7,8), (1,7)(2,8)(3,9)(4,10)(5,11)(6,12)],
+     Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,3,5,7,9,11)(2,4,6,8,10,12), (1,5,9)(2,6,10)(3,7,11)(4,8,12)],
+     Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(2,12)(3,11)(4,10)(5,9)(6,8), (1,5,9)(2,6,10)(3,7,11)(4,8,12)],
+     Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,2)(3,12)(4,11)(5,10)(6,9)(7,8), (1,5,9)(2,6,10)(3,7,11)(4,8,12)],
+     Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(2,12)(3,11)(4,10)(5,9)(6,8), (1,7)(2,8)(3,9)(4,10)(5,11)(6,12), (1,10,7,4)(2,11,8,5)(3,12,9,6)],
+     Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(2,12)(3,11)(4,10)(5,9)(6,8), (1,3,5,7,9,11)(2,4,6,8,10,12), (1,5,9)(2,6,10)(3,7,11)(4,8,12)],
+     Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,2,3,4,5,6,7,8,9,10,11,12), (1,3,5,7,9,11)(2,4,6,8,10,12), (1,5,9)(2,6,10)(3,7,11)(4,8,12)],
+     Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(1,2)(3,12)(4,11)(5,10)(6,9)(7,8), (1,3,5,7,9,11)(2,4,6,8,10,12), (1,5,9)(2,6,10)(3,7,11)(4,8,12)],
+     Subgroup of (Dihedral group of order 24 as a permutation group) generated by [(2,12)(3,11)(4,10)(5,9)(6,8), (1,2,3,4,5,6,7,8,9,10,11,12), (1,3,5,7,9,11)(2,4,6,8,10,12), (1,5,9)(2,6,10)(3,7,11)(4,8,12)]]
+
     sage: print("An order two subgroup:\n{}".format(sg[1].list()))
     An order two subgroup:
-    [(), (1,2)(3,12)(4,11)(5,10)(6,9)(7,8)]
+    [(), (1,7)(2,8)(3,9)(4,10)(5,11)(6,12)]
 
 It is important to note that this is a nice long list of subgroups,
 but will rarely create *every* such subgroup.  For example, the
diff --git a/src/doc/en/thematic_tutorials/lie/weyl_groups.rst b/src/doc/en/thematic_tutorials/lie/weyl_groups.rst
index c32cd12..64f5436 100644
--- a/src/doc/en/thematic_tutorials/lie/weyl_groups.rst
+++ b/src/doc/en/thematic_tutorials/lie/weyl_groups.rst
@@ -219,7 +219,7 @@ this as follows::
     sage: def bi(u,v) : return [t for t in W if u.bruhat_le(t) and t.bruhat_le(v)]
     ...
     sage: bi(s1,s1*s2*s1)
-    [s1*s2*s1, s1*s2, s1, s2*s1]
+    [s1*s2, s2*s1, s1, s1*s2*s1]
 
 This would not be a good definition since it would fail if `W` is
 affine and be inefficient of `W` is large. Sage has a Bruhat interval
diff --git a/src/doc/ja/tutorial/tour_groups.rst b/src/doc/ja/tutorial/tour_groups.rst
index d62d8ed..059313a 100644
--- a/src/doc/ja/tutorial/tour_groups.rst
+++ b/src/doc/ja/tutorial/tour_groups.rst
@@ -21,7 +21,7 @@ Sageでは，置換群，有限古典群(例えば :math:`SU(n,q)`)，有限行�
     False
     sage: G.derived_series()           # 結果は変化しがち
     [Subgroup of (Permutation Group with generators [(3,4), (1,2,3)(4,5)]) generated by [(3,4), (1,2,3)(4,5)],
-     Subgroup of (Permutation Group with generators [(3,4), (1,2,3)(4,5)]) generated by [(1,5,3), (1,5)(3,4), (1,5)(2,4)]]
+     Subgroup of (Permutation Group with generators [(3,4), (1,2,3)(4,5)]) generated by [(1,3,5), (1,5)(3,4), (1,5)(2,4)]]
     sage: G.center()
     Subgroup of (Permutation Group with generators [(3,4), (1,2,3)(4,5)]) generated by [()]
     sage: G.random_element()           # random 出力は変化する
diff --git a/src/ext/gap/sage.g b/src/ext/gap/sage.g
index 54fa74f..12402a7 100644
--- a/src/ext/gap/sage.g
+++ b/src/ext/gap/sage.g
@@ -1,7 +1,22 @@
-
 #
 # SAGE support utilities to read into the GAP session.
 #
+
+# Prevent loading the xgap package; we use the -p flag to GAP in order to
+# communicate with it via the pexpect interface; this is normally used by
+# for an xgap window to communicate with GAP, so unfortunatelly setting this
+# flag also allows the xgap package to be loaded and for some packages to
+# attempt to communicate with a "window handler" that doesn't exist.
+# Therefore we must explicitly disable loading of the xgap package.
+#
+# Don't use SetUserPreference since that leads to reloading the workspace,
+# which is confusing to the pexpect interface
+if IsBound(GAPInfo.ExcludeFromAutoload) then
+    Append(GAPInfo.ExcludeFromAutoload, "xgap");
+else
+    GAPInfo.ExcludeFromAutoload := [ "xgap" ];
+fi;
+
 \$SAGE := rec();
 
 \$SAGE.OldPager := Pager;
@@ -62,19 +77,15 @@ end;
 SetAllInfoLevels(0);
 
 \$SAGE.OperationsAdmittingFirstArgument := function(obj)
-    local   hits,  myflags,  i,  flagss,  flags;
-    hits := [];
-    myflags := FlagsType(TypeObj(obj));
-    for i in [1,3..Length(OPERATIONS)-1] do
-        flagss := OPERATIONS[i+1];
-        for flags in flagss do
-            if Length(flags) >= 1 and IS_SUBSET_FLAGS(myflags, flags[1]) then
-                Add(hits, OPERATIONS[i]);
-                break;
-            fi;
-        od;
-    od;
-    return hits;
+    local   myflags, mfi;
+    myflags := FlagsObj(obj);
+    mfi := function(o)
+        local f;
+        f := GET_OPER_FLAGS(o);
+        return f<>[] and f[1]<>[] and
+          IS_SUBSET_FLAGS(myflags, f[1][1]);
+    end;
+    return Filtered(OPERATIONS, mfi);
 end;
 
 
diff --git a/src/sage/categories/modules_with_basis.py b/src/sage/categories/modules_with_basis.py
index 3619868..0e56128 100644
--- a/src/sage/categories/modules_with_basis.py
+++ b/src/sage/categories/modules_with_basis.py
@@ -1201,8 +1201,8 @@ class ModulesWithBasis(CategoryWithAxiom_over_base_ring):
                 sage: DihedralGroup(6).algebra(QQ).random_element()
                 -1/95*() - 1/2*(1,4)(2,5)(3,6)
                 sage: SU(2, 13).algebra(QQ).random_element(1)
-                1/2*[       3        0]
-                [11*a + 1        9]
+                1/2*[       5 2*a + 12]
+                [   a + 6        6]
                 sage: CombinatorialFreeModule(ZZ, Partitions(4)).random_element() # random
                 2*B[[2, 1, 1]] + B[[2, 2]]
             """
diff --git a/src/sage/coding/codecan/autgroup_can_label.pyx b/src/sage/coding/codecan/autgroup_can_label.pyx
index 569ce32..fa0eb65 100644
--- a/src/sage/coding/codecan/autgroup_can_label.pyx
+++ b/src/sage/coding/codecan/autgroup_can_label.pyx
@@ -76,7 +76,7 @@ columns do share the same coloring::
     [[1],
      [2],
      [3, 5, 4],
-     [6, 16, 8, 21, 12, 9, 13, 18, 11, 19, 15, 7, 20, 14, 17, 10]]
+     [6, 19, 9, 21, 16, 14, 11, 20, 15, 8, 10, 12, 7, 13, 18, 17]]
 
 We can also restrict the group action to linear isometries::
 
diff --git a/src/sage/coding/linear_code.py b/src/sage/coding/linear_code.py
index 18f53b4..b31b869 100644
--- a/src/sage/coding/linear_code.py
+++ b/src/sage/coding/linear_code.py
@@ -801,27 +801,31 @@ class AbstractLinearCode(Module):
 
             sage: C = codes.HammingCode(GF(4, 'z'), 3)
             sage: C.automorphism_group_gens()
-            ([((z, 1, z, z, z, z + 1, 1, z + 1, 1, 1, 1, z + 1, 1, z + 1, z + 1, z + 1, 1, z, 1, z + 1, z); (1,9,5,15,20,13,4)(2,8,12,7,10,14,16,3,21,18,19,6,11,17), Ring endomorphism of Finite Field in z of size 2^2
+            ([((z, 1, z + 1, z + 1, 1, 1, z + 1, z, z, 1, z + 1, z + 1, z + 1, 1, z, z + 1, 1, z, z + 1, z + 1, z); (1,5,4,2)(6,17,10,20,19,18,12,8)(7,14,15,21,16,9,11,13), Ring endomorphism of Finite Field in z of size 2^2
                 Defn: z |--> z + 1),
-            ((z, z, z, z, z, 1, z + 1, 1, z + 1, z + 1, z + 1, 1, z, z + 1, z, z, 1, z + 1, 1, 1, 1); (1,10,20,16,6,3,11,19,15,8,5,9,17,12,13)(4,7,21,14,18), Ring endomorphism of Finite Field in z of size 2^2
+              ((z + 1, 1, z + 1, z + 1, z + 1, z, 1, z, 1, 1, 1, z + 1, z + 1, z, 1, z, z, 1, z, z, z); (1,5,20,19,16,6,4,12,2,18,21,10,11,15,8,14,13,7,3,9,17), Ring endomorphism of Finite Field in z of size 2^2
                 Defn: z |--> z),
-            ((z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z); (), Ring endomorphism of Finite Field in z of size 2^2
+              ((z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z); (), Ring endomorphism of Finite Field in z of size 2^2
                 Defn: z |--> z)],
             362880)
             sage: C.automorphism_group_gens(equivalence="linear")
-            ([((z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, 1, z + 1, z + 1, z + 1, z + 1, z, z + 1, z + 1, z + 1, z + 1, 1, z + 1, z + 1, z + 1); (1,3,17,20,12,16)(2,18)(4,11,21,9,14,10)(5,15,19)(6,8), Ring endomorphism of Finite Field in z of size 2^2
+            ([((1, 1, 1, z, z + 1, z, z + 1, 1, 1, z, z + 1, z, 1, 1, z, z + 1, z, 1, 1, z, z + 1); (1,8,3,4,12,13,17,6,18,15,20,5,19,21,16)(2,11,10,9,7), Ring endomorphism of Finite Field in z of size 2^2
                 Defn: z |--> z),
-            ((z + 1, z, 1, z + 1, z, z + 1, z + 1, z, 1, z + 1, z, z + 1, z, 1, z, z, z + 1, z, 1, 1, z); (1,15,18,20,13,7,21,17,9,11,5,14,19,4,2,16,10,6,8,3,12), Ring endomorphism of Finite Field in z of size 2^2
+              ((1, z + 1, z, z + 1, z + 1, 1, 1, z + 1, z, z, z + 1, 1, z + 1, z, 1, z + 1, 1, z + 1, z, 1, z + 1); (1,21,12,14,11,5,9,3,15,13,16,20,6,18,19,17,7,4,8,10,2), Ring endomorphism of Finite Field in z of size 2^2
                 Defn: z |--> z),
-            ((z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1); (), Ring endomorphism of Finite Field in z of size 2^2
+              ((z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1, z + 1); (), Ring endomorphism of Finite Field in z of size 2^2
                 Defn: z |--> z)],
             181440)
             sage: C.automorphism_group_gens(equivalence="permutational")
-            ([((1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1); (1,11)(3,10)(4,9)(5,7)(12,21)(14,20)(15,19)(16,17), Ring endomorphism of Finite Field in z of size 2^2
-                  Defn: z |--> z), ((1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1); (2,18)(3,19)(4,10)(5,16)(8,13)(9,14)(11,21)(15,20), Ring endomorphism of Finite Field in z of size 2^2
-                  Defn: z |--> z), ((1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1); (1,19)(3,17)(4,21)(5,20)(7,14)(9,12)(10,16)(11,15), Ring endomorphism of Finite Field in z of size 2^2
-                  Defn: z |--> z), ((1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1); (2,13)(3,14)(4,20)(5,11)(8,18)(9,19)(10,15)(16,21), Ring endomorphism of Finite Field in z of size 2^2
-                  Defn: z |--> z)], 64)
+            ([((1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1); (1,19)(3,17)(4,21)(5,20)(7,14)(9,12)(10,16)(11,15), Ring endomorphism of Finite Field in z of size 2^2
+                Defn: z |--> z),
+              ((1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1); (1,11)(3,10)(4,9)(5,7)(12,21)(14,20)(15,19)(16,17), Ring endomorphism of Finite Field in z of size 2^2
+                Defn: z |--> z),
+              ((1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1); (1,17)(2,8)(3,14)(4,10)(7,12)(9,19)(13,18)(15,20), Ring endomorphism of Finite Field in z of size 2^2
+                Defn: z |--> z),
+              ((1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1); (2,13)(3,14)(4,20)(5,11)(8,18)(9,19)(10,15)(16,21), Ring endomorphism of Finite Field in z of size 2^2
+                Defn: z |--> z)],
+            64)
         """
         aut_group_can_label = self._canonize(equivalence)
         return aut_group_can_label.get_autom_gens(), \
@@ -1069,12 +1073,12 @@ class AbstractLinearCode(Module):
             sage: C_iso == aut_group_can_label.get_canonical_form()
             True
             sage: aut_group_can_label.get_autom_gens()
-            [((z, 1, z + 1, z, 1, 1, z, 1, z + 1, 1, 1, z, 1, z + 1, z, 1, z, 1, z + 1, z + 1, 1); (1,10,8,21,3,20,2,4,6,18,14,9,12,16,17)(5,15,13,7,19), Ring endomorphism of Finite Field in z of size 2^2
-            Defn: z |--> z),
-            ((z + 1, z, z, z + 1, 1, 1, 1, z + 1, z + 1, z, 1, z, z + 1, 1, 1, z + 1, z + 1, 1, 1, z, z); (1,18,17,5,16,3,10,11,8,21,7,12,9,4)(2,19,15,14,6,20,13), Ring endomorphism of Finite Field in z of size 2^2
-            Defn: z |--> z + 1),
-            ((z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z); (), Ring endomorphism of Finite Field in z of size 2^2
-            Defn: z |--> z)]
+            [((z + 1, z + 1, z, z, 1, z, z, z, z, z, z, z + 1, z + 1, z + 1, z + 1, z + 1, 1, 1, 1, 1, 1); (1,2,13,11,7,19,4,18)(3,6,20,9,15,12,21,16)(5,8,14,10), Ring endomorphism of Finite Field in z of size 2^2
+               Defn: z |--> z + 1),
+             ((z, 1, z + 1, 1, 1, 1, z + 1, z + 1, z, 1, 1, 1, z + 1, 1, z, z + 1, 1, z, 1, z + 1, z); (1,17,5,21,12,8,6,10,11,13,4,2,20,9)(3,19,18,15,7,14,16), Ring endomorphism of Finite Field in z of size 2^2
+               Defn: z |--> z + 1),
+             ((z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z, z); (), Ring endomorphism of Finite Field in z of size 2^2
+               Defn: z |--> z)]
         """
         from sage.coding.codecan.autgroup_can_label import LinearCodeAutGroupCanLabel
         return LinearCodeAutGroupCanLabel(self, algorithm_type=equivalence)
diff --git a/src/sage/combinat/root_system/hecke_algebra_representation.py b/src/sage/combinat/root_system/hecke_algebra_representation.py
index 32112c3..6498afb 100644
--- a/src/sage/combinat/root_system/hecke_algebra_representation.py
+++ b/src/sage/combinat/root_system/hecke_algebra_representation.py
@@ -358,7 +358,7 @@ class HeckeAlgebraRepresentation(WithEqualityById, SageObject):
             sage: q1, q2 = K.gens()
             sage: KW = W.algebra(K)
             sage: x = KW.an_element(); x
-            2*12321 + 3*1231 + 123 + e
+            123 + 3*32 + 2*3 + e
 
             sage: T = KW.demazure_lusztig_operators(q1,q2)
             sage: T12 = T.Tw( (1,2) )
diff --git a/src/sage/combinat/root_system/root_system.py b/src/sage/combinat/root_system/root_system.py
index efddfa05..6fb83f1 100644
--- a/src/sage/combinat/root_system/root_system.py
+++ b/src/sage/combinat/root_system/root_system.py
@@ -207,13 +207,13 @@ class RootSystem(UniqueRepresentation, SageObject):
         sage: W = L.weyl_group()
         sage: S3 = [ w.action(id) for w in W.classical() ]
         sage: [L.classical()(x) for x in S3]
-        [(1, 2, 3), (3, 2, 1), (3, 1, 2), (2, 1, 3), (2, 3, 1), (1, 3, 2)]
+        [(1, 2, 3), (3, 1, 2), (2, 3, 1), (2, 1, 3), (1, 3, 2), (3, 2, 1)]
 
     And the action of `s_0` on these yields::
 
         sage: s = W.simple_reflections()
         sage: [L.classical()(s[0].action(x)) for x in S3]
-        [(0, 2, 4), (-2, 2, 6), (-1, 1, 6), (0, 1, 5), (-2, 3, 5), (-1, 3, 4)]
+        [(0, 2, 4), (-1, 1, 6), (-2, 3, 5), (0, 1, 5), (-1, 3, 4), (-2, 2, 6)]
 
     We can also plot various components of the ambient spaces::
 
diff --git a/src/sage/combinat/symmetric_group_algebra.py b/src/sage/combinat/symmetric_group_algebra.py
index d5f8637..d89cfca 100644
--- a/src/sage/combinat/symmetric_group_algebra.py
+++ b/src/sage/combinat/symmetric_group_algebra.py
@@ -103,7 +103,7 @@ def SymmetricGroupAlgebra(R, W, category=None):
         sage: SGA.group()
         Weyl Group of type ['A', 3] (as a matrix group acting on the ambient space)
         sage: SGA.an_element()
-        2*s1*s2*s3*s2*s1 + 3*s1*s2*s3*s1 + s1*s2*s3 + 1
+        s1*s2*s3 + 3*s3*s2 + 2*s3 + 1
 
     The preferred way to construct the symmetric group algebra is to
     go through the usual ``algebra`` method::
diff --git a/src/sage/combinat/tiling.py b/src/sage/combinat/tiling.py
index 580e01a..2f8713a 100644
--- a/src/sage/combinat/tiling.py
+++ b/src/sage/combinat/tiling.py
@@ -325,21 +325,21 @@ def ncube_isometry_group(n, orientation_preserving=True):
 
         sage: ncube_isometry_group(3)
         [
-        [1 0 0]  [ 1  0  0]  [-1  0  0]  [-1  0  0]  [0 0 1]  [ 0  0 -1]
-        [0 1 0]  [ 0 -1  0]  [ 0  1  0]  [ 0 -1  0]  [1 0 0]  [ 1  0  0]
-        [0 0 1], [ 0  0 -1], [ 0  0 -1], [ 0  0  1], [0 1 0], [ 0 -1  0],
+        [1 0 0]  [ 1  0  0]  [ 0  1  0]  [ 0  0 -1]  [ 1  0  0]  [ 0  1  0]
+        [0 1 0]  [ 0  0  1]  [ 0  0 -1]  [ 0 -1  0]  [ 0  0 -1]  [-1  0  0]
+        [0 0 1], [ 0 -1  0], [-1  0  0], [-1  0  0], [ 0  1  0], [ 0  0  1],
         <BLANKLINE>
-        [ 0  0 -1]  [ 0  0  1]  [0 1 0]  [ 0 -1  0]  [ 0  1  0]  [ 0 -1  0]
-        [-1  0  0]  [-1  0  0]  [0 0 1]  [ 0  0 -1]  [ 0  0 -1]  [ 0  0  1]
-        [ 0  1  0], [ 0 -1  0], [1 0 0], [ 1  0  0], [-1  0  0], [-1  0  0],
+        [ 1  0  0]  [ 0  0  1]  [0 1 0]  [ 0  0  1]  [ 0  0 -1]  [ 0 -1  0]
+        [ 0 -1  0]  [-1  0  0]  [0 0 1]  [ 0 -1  0]  [-1  0  0]  [-1  0  0]
+        [ 0  0 -1], [ 0 -1  0], [1 0 0], [ 1  0  0], [ 0  1  0], [ 0  0 -1],
         <BLANKLINE>
-        [ 0  1  0]  [ 0 -1  0]  [ 0  1  0]  [ 0 -1  0]  [ 1  0  0]  [ 1  0  0]
-        [ 1  0  0]  [ 1  0  0]  [-1  0  0]  [-1  0  0]  [ 0  0 -1]  [ 0  0  1]
-        [ 0  0 -1], [ 0  0  1], [ 0  0  1], [ 0  0 -1], [ 0  1  0], [ 0 -1  0],
+        [ 0  1  0]  [ 0  0  1]  [ 0  0 -1]  [ 0 -1  0]  [0 0 1]  [ 0 -1  0]
+        [ 1  0  0]  [ 0  1  0]  [ 1  0  0]  [ 0  0  1]  [1 0 0]  [ 1  0  0]
+        [ 0  0 -1], [-1  0  0], [ 0 -1  0], [-1  0  0], [0 1 0], [ 0  0  1],
         <BLANKLINE>
-        [-1  0  0]  [-1  0  0]  [ 0  0 -1]  [ 0  0  1]  [ 0  0  1]  [ 0  0 -1]
-        [ 0  0  1]  [ 0  0 -1]  [ 0  1  0]  [ 0 -1  0]  [ 0  1  0]  [ 0 -1  0]
-        [ 0  1  0], [ 0 -1  0], [ 1  0  0], [ 1  0  0], [-1  0  0], [-1  0  0]
+        [-1  0  0]  [-1  0  0]  [ 0  0 -1]  [-1  0  0]  [ 0 -1  0]  [-1  0  0]
+        [ 0  1  0]  [ 0  0 -1]  [ 0  1  0]  [ 0  0  1]  [ 0  0 -1]  [ 0 -1  0]
+        [ 0  0 -1], [ 0 -1  0], [ 1  0  0], [ 0  1  0], [ 1  0  0], [ 0  0  1]
         ]
 
     TESTS::
diff --git a/src/sage/env.py b/src/sage/env.py
index 77e0596..3a64c2d 100644
--- a/src/sage/env.py
+++ b/src/sage/env.py
@@ -164,7 +164,7 @@ _add_variable_or_fallback('CONWAY_POLYNOMIALS_DATA_DIR',  opj('$SAGE_SHARE','con
 _add_variable_or_fallback('GRAPHS_DATA_DIR',  opj('$SAGE_SHARE','graphs'))
 _add_variable_or_fallback('ELLCURVE_DATA_DIR',opj('$SAGE_SHARE','ellcurves'))
 _add_variable_or_fallback('POLYTOPE_DATA_DIR',opj('$SAGE_SHARE','reflexive_polytopes'))
-_add_variable_or_fallback('GAP_ROOT_DIR',     opj('$SAGE_LOCAL','gap','latest'))
+_add_variable_or_fallback('GAP_ROOT_DIR',     opj('$SAGE_SHARE','gap'))
 _add_variable_or_fallback('THEBE_DIR',        opj('$SAGE_SHARE','thebe'))
 _add_variable_or_fallback('COMBINATORIAL_DESIGN_DATA_DIR', opj('$SAGE_SHARE', 'combinatorial_designs'))
 _add_variable_or_fallback('CREMONA_MINI_DATA_DIR', opj('$SAGE_SHARE', 'cremona'))
diff --git a/src/sage/graphs/generators/families.py b/src/sage/graphs/generators/families.py
index 8e24817..ac7ea93 100644
--- a/src/sage/graphs/generators/families.py
+++ b/src/sage/graphs/generators/families.py
@@ -3177,15 +3177,16 @@ def MathonPseudocyclicStronglyRegularGraph(t, G=None, L=None):
         sage: ff = list(map(lambda y: (y[0]-1,y[1]-1),
         ....:          Permutation(map(lambda x: 1+r.index(x^-1), r)).cycle_tuples()[1:]))
         sage: L = sum(i*(r[a]-r[b]) for i,(a,b) in zip(range(1,len(ff)+1), ff)); L
-        [ 0 -1  1 -2 -3 -4  2  4  3]
-        [ 1  0 -1 -4 -2 -3  3  2  4]
-        [-1  1  0 -3 -4 -2  4  3  2]
-        [ 2  4  3  0 -1  1 -2 -3 -4]
-        [ 3  2  4  1  0 -1 -4 -2 -3]
-        [ 4  3  2 -1  1  0 -3 -4 -2]
-        [-2 -3 -4  2  4  3  0 -1  1]
-        [-4 -2 -3  3  2  4  1  0 -1]
-        [-3 -4 -2  4  3  2 -1  1  0]
+        [ 0  1 -1 -3 -2 -4  3  4  2]
+        [-1  0  1 -4 -3 -2  2  3  4]
+        [ 1 -1  0 -2 -4 -3  4  2  3]
+        [ 3  4  2  0  1 -1 -3 -2 -4]
+        [ 2  3  4 -1  0  1 -4 -3 -2]
+        [ 4  2  3  1 -1  0 -2 -4 -3]
+        [-3 -2 -4  3  4  2  0  1 -1]
+        [-4 -3 -2  2  3  4 -1  0  1]
+        [-2 -4 -3  4  2  3  1 -1  0]
+
         sage: G.relabel()
         sage: G3x3=graphs.MathonPseudocyclicStronglyRegularGraph(2,G=G,L=L)
         sage: G3x3.is_strongly_regular(parameters=True)
diff --git a/src/sage/groups/abelian_gps/abelian_group_gap.py b/src/sage/groups/abelian_gps/abelian_group_gap.py
index cebcd39..55a20ed 100644
--- a/src/sage/groups/abelian_gps/abelian_group_gap.py
+++ b/src/sage/groups/abelian_gps/abelian_group_gap.py
@@ -363,10 +363,10 @@ class AbelianGroup_gap(UniqueRepresentation, GroupMixinLibGAP, ParentLibGAP, Abe
             sage: from sage.groups.abelian_gps.abelian_group_gap import AbelianGroupGap
             sage: G = AbelianGroupGap([2, 3])
             sage: G.all_subgroups()
-            [Subgroup of Abelian group with gap, generator orders (2, 3) generated by (1,),
+            [Subgroup of Abelian group with gap, generator orders (2, 3) generated by (),
              Subgroup of Abelian group with gap, generator orders (2, 3) generated by (f1,),
              Subgroup of Abelian group with gap, generator orders (2, 3) generated by (f2,),
-             Subgroup of Abelian group with gap, generator orders (2, 3) generated by (f1, f2)]
+             Subgroup of Abelian group with gap, generator orders (2, 3) generated by (f2, f1)]
         """
         subgroups_gap = self.gap().AllSubgroups()
         subgroups_sage = []
diff --git a/src/sage/groups/braid.py b/src/sage/groups/braid.py
index 4eda6e8..07a765c 100644
--- a/src/sage/groups/braid.py
+++ b/src/sage/groups/braid.py
@@ -2163,7 +2163,8 @@ class BraidGroup_class(FiniteTypeArtinGroup):
 
             sage: B = BraidGroup(5)
             sage: B._element_from_libbraiding([[-2], [2, 1], [1, 2], [2, 1]])
-            (s0^-1*s1^-1*s2^-1*s3^-1*s0^-1*s1^-1*s2^-1*s0^-1*s1^-1*s0^-1)^2*s1*s0^2*s1^2*s0
+            (s0^-1*s1^-1*s2^-1*s3^-1*s0^-1*s1^-1*s2^-1*s0^-1*s1^-1*s0^-1)^2*s1*s0^2*s1^2*s\
+            0
             sage: B._element_from_libbraiding([[0]])
             1
         """
diff --git a/src/sage/groups/finitely_presented.py b/src/sage/groups/finitely_presented.py
index 8f9c192..f27f334 100644
--- a/src/sage/groups/finitely_presented.py
+++ b/src/sage/groups/finitely_presented.py
@@ -231,7 +231,6 @@ class FinitelyPresentedGroupElement(FreeGroupElement):
 
             sage: TestSuite(G).run()
             sage: TestSuite(H).run()
-
             sage: G.<a,b> = FreeGroup()
             sage: H = G / (G([1]), G([2, 2, 2]))
             sage: x = H([1, 2, -1, -2])
@@ -1096,6 +1095,7 @@ class FinitelyPresentedGroup(GroupMixinLibGAP, UniqueRepresentation,
             sage: C7 = G / [G.0**7]; C6 =  G / [G.0**6]
             sage: C14 = G / [G.0**14]; C3 =  G / [G.0**3]
             sage: C7.direct_product(C6).is_isomorphic(C14.direct_product(C3))
+            #I  Forcing finiteness test
             True
             sage: F = FreeGroup(2); D = F / [F([1,1,1,1,1]),F([2,2]),F([1,2])**2]
             sage: D.direct_product(D).as_permutation_group().is_isomorphic(
@@ -1189,6 +1189,7 @@ class FinitelyPresentedGroup(GroupMixinLibGAP, UniqueRepresentation,
             sage: alpha = (Q.gens(), [a,b])
             sage: S2 = C2.semidirect_product(Q, ([C2.0],[alpha]))
             sage: S1.is_isomorphic(S2)
+            #I  Forcing finiteness test
             True
 
         Dihedral groups can be constructed as semidirect products
@@ -1247,6 +1248,8 @@ class FinitelyPresentedGroup(GroupMixinLibGAP, UniqueRepresentation,
             sage: Se2 =  D.semidirect_product(C ,id2)
             sage: Dp1 = C.direct_product(D)
             sage: Dp1.is_isomorphic(Se1), Dp1.is_isomorphic(Se2)
+            #I  Forcing finiteness test
+            #I  Forcing finiteness test
             (True, True)
 
         Most checks for validity of input are left to GAP to handle::
@@ -1445,27 +1448,27 @@ class FinitelyPresentedGroup(GroupMixinLibGAP, UniqueRepresentation,
             sage: H = AlternatingGroup(3)
             sage: G.epimorphisms(H)
             [Generic morphism:
-            From: Finitely presented group < x0, x1, x2 | (x0*x1*x2)^2, x0^3 >
-            To:   Alternating group of order 3!/2 as a permutation group
-            Defn: x0 |--> ()
-                  x1 |--> (1,2,3)
-                  x2 |--> (1,3,2), Generic morphism:
-            From: Finitely presented group < x0, x1, x2 | (x0*x1*x2)^2, x0^3 >
-            To:   Alternating group of order 3!/2 as a permutation group
-            Defn: x0 |--> (1,2,3)
-                  x1 |--> ()
-                  x2 |--> (1,3,2), Generic morphism:
-            From: Finitely presented group < x0, x1, x2 | (x0*x1*x2)^2, x0^3 >
-            To:   Alternating group of order 3!/2 as a permutation group
-            Defn: x0 |--> (1,2,3)
-                  x1 |--> (1,2,3)
-                  x2 |--> (1,2,3), Generic morphism:
-            From: Finitely presented group < x0, x1, x2 | (x0*x1*x2)^2, x0^3 >
-            To:   Alternating group of order 3!/2 as a permutation group
-            Defn: x0 |--> (1,2,3)
-                  x1 |--> (1,3,2)
-                  x2 |--> ()]
-        
+               From: Finitely presented group < x0, x1, x2 | (x0*x1*x2)^2, x0^3 >
+               To:   Alternating group of order 3!/2 as a permutation group
+               Defn: x0 |--> ()
+                     x1 |--> (1,3,2)
+                     x2 |--> (1,2,3), Generic morphism:
+               From: Finitely presented group < x0, x1, x2 | (x0*x1*x2)^2, x0^3 >
+               To:   Alternating group of order 3!/2 as a permutation group
+               Defn: x0 |--> (1,3,2)
+                     x1 |--> ()
+                     x2 |--> (1,2,3), Generic morphism:
+               From: Finitely presented group < x0, x1, x2 | (x0*x1*x2)^2, x0^3 >
+               To:   Alternating group of order 3!/2 as a permutation group
+               Defn: x0 |--> (1,3,2)
+                     x1 |--> (1,2,3)
+                     x2 |--> (), Generic morphism:
+               From: Finitely presented group < x0, x1, x2 | (x0*x1*x2)^2, x0^3 >
+               To:   Alternating group of order 3!/2 as a permutation group
+               Defn: x0 |--> (1,2,3)
+                     x1 |--> (1,2,3)
+                     x2 |--> (1,2,3)]
+
         ALGORITHM:
         
         Uses libgap's GQuotients function.
diff --git a/src/sage/groups/finitely_presented_named.py b/src/sage/groups/finitely_presented_named.py
index cfd8953..c8075f9 100644
--- a/src/sage/groups/finitely_presented_named.py
+++ b/src/sage/groups/finitely_presented_named.py
@@ -447,6 +447,7 @@ def QuaternionPresentation():
         sage: Q.order(), Q.is_abelian()
         (8, False)
         sage: Q.is_isomorphic(groups.presentation.DiCyclic(2))
+        #I  Forcing finiteness test
         True
     """
     F = FreeGroup(['a','b'])
@@ -546,6 +547,12 @@ def BinaryDihedralPresentation(n):
         ....:     P = groups.presentation.BinaryDihedral(n)
         ....:     M = groups.matrix.BinaryDihedral(n)
         ....:     assert P.is_isomorphic(M)
+        #I  Forcing finiteness test
+        #I  Forcing finiteness test
+        #I  Forcing finiteness test
+        #I  Forcing finiteness test
+        #I  Forcing finiteness test
+        #I  Forcing finiteness test
     """
     F = FreeGroup('x,y,z')
     x,y,z = F.gens()
diff --git a/src/sage/groups/matrix_gps/finitely_generated.py b/src/sage/groups/matrix_gps/finitely_generated.py
index 78391d5..1946000 100644
--- a/src/sage/groups/matrix_gps/finitely_generated.py
+++ b/src/sage/groups/matrix_gps/finitely_generated.py
@@ -543,7 +543,7 @@ class FinitelyGeneratedMatrixGroup_gap(MatrixGroup_gap):
         smallest one.
 
         EXAMPLES::
-        
+
             sage: MS = MatrixSpace(GF(2), 5, 5)
             sage: A = MS([[0,0,0,0,1],[0,0,0,1,0],[0,0,1,0,0],[0,1,0,0,0],[1,0,0,0,0]])
             sage: G = MatrixGroup([A])
@@ -711,8 +711,8 @@ class FinitelyGeneratedMatrixGroup_gap(MatrixGroup_gap):
             sage: gens = [MS([[0,1],[-1,0]]),MS([[1,1],[2,3]])]
             sage: G = MatrixGroup(gens)
             sage: G.invariant_generators()
-            [x1^7*x2 - x1*x2^7, 
-             x1^12 - 2*x1^9*x2^3 - x1^6*x2^6 + 2*x1^3*x2^9 + x2^12, 
+            [x1^7*x2 - x1*x2^7,
+             x1^12 - 2*x1^9*x2^3 - x1^6*x2^6 + 2*x1^3*x2^9 + x2^12,
              x1^18 + 2*x1^15*x2^3 + 3*x1^12*x2^6 + 3*x1^6*x2^12 - 2*x1^3*x2^15 + x2^18]
 
             sage: q = 4; a = 2
@@ -1069,10 +1069,10 @@ class FinitelyGeneratedMatrixGroup_gap(MatrixGroup_gap):
             sage: chi = G.character(G.character_table()[1])
             sage: R.<x,y,z> = K[]
             sage: G.reynolds_operator(x*y^5, chi)
-            1/3*x*y^5 + (-2/3*izeta3^3 - izeta3^2 - 8/3*izeta3 - 4/3)*x^5*z + (2/3*izeta3^3 + izeta3^2 + 8/3*izeta3 + 1)*y*z^5
+            1/3*x*y^5 + (2/3*izeta3^3 + izeta3^2 + 8/3*izeta3 + 1)*x^5*z + (-2/3*izeta3^3 - izeta3^2 - 8/3*izeta3 - 4/3)*y*z^5
             sage: R.<x,y,z> = QQbar[]
             sage: G.reynolds_operator(x*y^5, chi)
-            1/3*x*y^5 + (-0.1666666666666667? + 0.2886751345948129?*I)*x^5*z + (-0.1666666666666667? - 0.2886751345948129?*I)*y*z^5
+             1/3*x*y^5 + (-0.1666666666666667? - 0.2886751345948129?*I)*x^5*z + (-0.1666666666666667? + 0.2886751345948129?*I)*y*z^5
 
         ::
 
@@ -1288,8 +1288,8 @@ class FinitelyGeneratedMatrixGroup_gap(MatrixGroup_gap):
             sage: chi = G.character(G.character_table()[1])
             sage: R.<x,y,z> = K[]
             sage: sorted(G.invariants_of_degree(2, R=R, chi=chi))
-            [x*y + (-2*izeta3^3 - 3*izeta3^2 - 8*izeta3 - 4)*x*z + (2*izeta3^3 + 3*izeta3^2 + 8*izeta3 + 3)*y*z,
-             x^2 + (2*izeta3^3 + 3*izeta3^2 + 8*izeta3 + 3)*y^2 + (-2*izeta3^3 - 3*izeta3^2 - 8*izeta3 - 4)*z^2]
+            [x*y + (2*izeta3^3 + 3*izeta3^2 + 8*izeta3 + 3)*x*z + (-2*izeta3^3 - 3*izeta3^2 - 8*izeta3 - 4)*y*z,
+             x^2 + (-2*izeta3^3 - 3*izeta3^2 - 8*izeta3 - 4)*y^2 + (2*izeta3^3 + 3*izeta3^2 + 8*izeta3 + 3)*z^2]
 
         ::
 
diff --git a/src/sage/groups/perm_gps/permgroup.py b/src/sage/groups/perm_gps/permgroup.py
index 2ae3a51..8b24ee6 100644
--- a/src/sage/groups/perm_gps/permgroup.py
+++ b/src/sage/groups/perm_gps/permgroup.py
@@ -325,7 +325,7 @@ def PermutationGroup(gens=None, gap_group=None, domain=None, canonicalize=True,
         sage: G = PermutationGroup([[(1,2,3),(4,5)],[(3,4)]])
         sage: current_randstate().set_seed_gap()
         sage: G._gap_().DerivedSeries()
-        [ Group( [ (3,4), (1,2,3)(4,5) ] ), Group( [ (1,5)(3,4), (1,5)(2,4), (1,5,3) ] ) ]
+        [ Group( [ (3,4), (1,2,3)(4,5) ] ), Group( [ (1,5)(3,4), (1,5)(2,4), (1,3,5) ] ) ]
 
     TESTS::
 
@@ -3256,7 +3256,7 @@ class PermutationGroup_generic(FiniteGroup):
             [Subgroup of (Cyclic group of order 14 as a permutation group) generated by [()],
              Subgroup of (Cyclic group of order 14 as a permutation group) generated by [(1,8)(2,9)(3,10)(4,11)(5,12)(6,13)(7,14)],
              Subgroup of (Cyclic group of order 14 as a permutation group) generated by [(1,3,5,7,9,11,13)(2,4,6,8,10,12,14)],
-             Subgroup of (Cyclic group of order 14 as a permutation group) generated by [(1,2,3,4,5,6,7,8,9,10,11,12,13,14)]]
+             Subgroup of (Cyclic group of order 14 as a permutation group) generated by [(1,2,3,4,5,6,7,8,9,10,11,12,13,14), (1,3,5,7,9,11,13)(2,4,6,8,10,12,14)]]
 
         AUTHOR:
 
@@ -3658,7 +3658,8 @@ class PermutationGroup_generic(FiniteGroup):
             rec(
               name := "Z(5)",
               parameter := 5,
-              series := "Z" )
+              series := "Z",
+              shortname := "C5" )
 
         TESTS:
 
diff --git a/src/sage/groups/perm_gps/permgroup_element.pyx b/src/sage/groups/perm_gps/permgroup_element.pyx
index 03944d9..d459c0e 100644
--- a/src/sage/groups/perm_gps/permgroup_element.pyx
+++ b/src/sage/groups/perm_gps/permgroup_element.pyx
@@ -116,7 +116,7 @@ import sage.structure.coerce as coerce
 from sage.structure.richcmp cimport richcmp_not_equal, rich_to_bool
 
 from sage.libs.gap.element cimport GapElement_List
-from sage.libs.gap.gap_includes cimport libGAP_Obj, libGAP_INT_INTOBJ, libGAP_ELM_LIST
+from sage.libs.gap.gap_includes cimport Obj, INT_INTOBJ, ELM_LIST
 
 import operator
 
@@ -951,7 +951,7 @@ cdef class PermutationGroupElement(MultiplicativeGroupElement):
             (1,4)(2,3)
         """
         cdef GapElement_List lst = <GapElement_List?> lst_in
-        cdef libGAP_Obj obj = lst.value
+        cdef Obj obj = lst.value
 
         cdef PermutationGroupElement new = self._new_c()
         cdef Py_ssize_t i, j, vn = len(lst)
@@ -959,7 +959,7 @@ cdef class PermutationGroupElement(MultiplicativeGroupElement):
         assert vn <= self.n
 
         for i in range(vn):
-            j = libGAP_INT_INTOBJ(libGAP_ELM_LIST(obj, i+1))
+            j = INT_INTOBJ(ELM_LIST(obj, i+1))
             new.perm[i] = j - 1
         for i in range(vn, self.n):
             new.perm[i] = i
diff --git a/src/sage/interfaces/gap.py b/src/sage/interfaces/gap.py
index 55d41aa..8db06a9 100644
--- a/src/sage/interfaces/gap.py
+++ b/src/sage/interfaces/gap.py
@@ -1,3 +1,4 @@
+# -*- coding: UTF-8 -*-
 r"""
 Interface to GAP
 
@@ -187,6 +188,7 @@ from sage.misc.cachefunc import cached_method
 from sage.docs.instancedoc import instancedoc
 from sage.interfaces.tab_completion import ExtraTabCompletion
 from sage.structure.element import ModuleElement
+
 import re
 import os
 import io
@@ -194,12 +196,10 @@ import pexpect
 import time
 import platform
 import string
+import warnings
 
 WORKSPACE = gap_workspace_file()
 
-from sage.env import GAP_ROOT_DIR
-GAP_BINARY = os.path.join(GAP_ROOT_DIR, 'bin', 'gap.sh')
-
 first_try = True
 
 gap_cmd = "gap -r"
@@ -514,7 +514,7 @@ class Gap_generic(ExtraTabCompletion, Expect):
             RuntimeError: Error loading Gap package chevie. You may want to install the gap_packages and/or database_gap SPKGs.
         """
         if verbose:
-            print("Loading GAP package %s" % pkg)
+            print("Loading GAP package {}" % pkg)
         x = self.eval('LoadPackage("%s")'%pkg)
         if x == 'fail':
             raise RuntimeError("Error loading Gap package "+str(pkg)+". "+
@@ -610,8 +610,9 @@ class Gap_generic(ExtraTabCompletion, Expect):
                 current_outputs.append(E.before)
                 if x == 0:   # @p
                     if E.after != b'@p1.':
-                        print("Warning: possibly wrong version of GAP package interface\n")
-                        print("Crossing fingers and continuing\n")
+                        warnings.warn(
+                            "possibly wrong version of GAP package "
+                            "interface. Crossing fingers and continuing.")
                 elif x == 1: #@@
                     current_outputs.append(b'@')
                 elif x == 2: #special char
@@ -626,11 +627,11 @@ class Gap_generic(ExtraTabCompletion, Expect):
                 elif x == 4: # @e -- break loop
                     E.sendline("quit;")
                 elif x == 5: # @c completion, doesn't seem to happen when -p is in use
-                    print("I didn't think GAP could do this\n")
+                    warnings.warn("I didn't think GAP could do this")
                 elif x == 6: # @f GAP error message
                     current_outputs = error_outputs;
                 elif x == 7: # @h help text, but this stopped happening with new help
-                    print("I didn't think GAP could do this")
+                    warnings.warn("I didn't think GAP could do this")
                 elif x == 8: # @i awaiting normal input
                     break;
                 elif x == 9: # @m finished running a child
@@ -640,9 +641,9 @@ class Gap_generic(ExtraTabCompletion, Expect):
                 elif x==11: #@r echoing input
                     current_outputs = terminal_echo
                 elif x==12: #@sN shouldn't happen
-                    print("Warning: this should never happen")
+                    warnings.warn("this should never happen")
                 elif x==13: #@w GAP is trying to send a Window command
-                    print("Warning: this should never happen")
+                    warnings.warn("this should never happen")
                 elif x ==14: #@x seems to be safely ignorable
                     pass
                 elif x == 15:#@z GAP starting a subprocess
@@ -908,17 +909,16 @@ class Gap_generic(ExtraTabCompletion, Expect):
 
             sage: g = Gap()
             sage: g.function_call("ConjugacyClassesSubgroups", sage.interfaces.gap.GapElement(g, 'SymmetricGroup(2)', name = 'a_variable_with_a_very_very_very_long_name'))
-            [ ConjugacyClassSubgroups(SymmetricGroup( [ 1 .. 2 ] ),Group( [ () ] )),
-              ConjugacyClassSubgroups(SymmetricGroup( [ 1 .. 2 ] ),SymmetricGroup( [ 1 .. 2 ] )) ]
+            [ ConjugacyClassSubgroups(SymmetricGroup( [ 1 .. 2 ] ),Group( () )),
+              ConjugacyClassSubgroups(SymmetricGroup( [ 1 .. 2 ] ),Group( [ (1,2) ] )) ]
 
         When the command itself is so long that it warrants use of a temporary
         file to be communicated to GAP, this does not cause problems since
         the file will contain a single command::
 
             sage: g.function_call("ConjugacyClassesSubgroups", sage.interfaces.gap.GapElement(g, 'SymmetricGroup(2)', name = 'a_variable_with_a_name_so_very_very_very_long_that_even_by_itself_will_make_expect_use_a_file'))
-            [ ConjugacyClassSubgroups(SymmetricGroup( [ 1 .. 2 ] ),Group( [ () ] )),
-              ConjugacyClassSubgroups(SymmetricGroup( [ 1 .. 2 ] ),SymmetricGroup( [ 1 .. 2 ] )) ]
-
+            [ ConjugacyClassSubgroups(SymmetricGroup( [ 1 .. 2 ] ),Group( () )),
+              ConjugacyClassSubgroups(SymmetricGroup( [ 1 .. 2 ] ),Group( [ (1,2) ] )) ]
         """
         args, kwds = self._convert_args_kwds(args, kwds)
         self._check_valid_function_name(function)
@@ -1129,13 +1129,20 @@ class Gap(Gap_generic):
         """
         self.__use_workspace_cache = use_workspace_cache
         cmd, self.__make_workspace = gap_command(use_workspace_cache, server is None)
-        cmd += " -b -p -T"
+        # -b: suppress banner
+        # -p: enable "package output mode"; this confusingly named option
+        #     causes GAP to output special control characters that are normally
+        #     intended for communication with a window manager (i.e. for xgap)
+        #     but that we also use to control GAP with pexepect
+        # -T: disable interactive break loop when encountering errors
+        # -E: disable readline support
+        cmd += " -b -p -T -E"
         if max_workspace_size is None:
             max_workspace_size = _get_gap_memory_pool_size_MB()
         cmd += ' -o ' + str(max_workspace_size)
         cmd += ' -s ' + str(max_workspace_size)
         cmd += ' -m 64m '   # attempt at a workaround for http://tracker.gap-system.org/issues/224
-        cmd += ' ' + os.path.join(SAGE_EXTCODE,'gap','sage.g')
+        cmd += ' ' + os.path.join(SAGE_EXTCODE, 'gap', 'sage.g')
         Expect.__init__(self,
                         name='gap',
                         prompt='gap> ',
@@ -1343,11 +1350,11 @@ class Gap(Gap_generic):
 
             sage: print(gap.help('SymmetricGroup', pager=False))
             <BLANKLINE>
-            50 Group Libraries
+              50.1-... SymmetricGroup
             <BLANKLINE>
-            When you start GAP, it already knows several groups. Currently GAP initially
-            knows the following groups:
+              ‣ SymmetricGroup( [filt, ]deg ) ─────────────────────────────────── function
             ...
+            <BLANKLINE>
         """
         tmp_to_use = self._local_tmpfile()
         if self.is_remote():
@@ -1364,6 +1371,7 @@ class Gap(Gap_generic):
             print(line)
         else:
             (sline,) = match.groups()
+            sline = int(sline) - 1
             if self.is_remote():
                 self._get_tmpfile()
             with io.open(self._local_tmpfile(), "r",
@@ -1371,9 +1379,20 @@ class Gap(Gap_generic):
                 help = fobj.read()
                 if pager:
                     from IPython.core.page import page
-                    page(help, start=int(sline) - 1)
+                    page(help, start=sline)
                 else:
-                    return help
+                    # Find the n-th line and return from there
+                    idx = -1
+                    while sline:
+                        try:
+                            idx = help.find('\n', idx + 1)
+                            sline -= 1
+                        except ValueError:
+                            # We ran out of lines early somehow; this shouldn't
+                            # happen though
+                            break
+
+                    return help[idx:]
 
     def set(self, var, value):
         """
@@ -1552,8 +1571,8 @@ def gap_reset_workspace(max_workspace_size=None, verbose=False):
     # Create new workspace with filename WORKSPACE
     g = Gap(use_workspace_cache=False, max_workspace_size=None)
     g.eval('SetUserPreference("HistoryMaxLines", 30)')
-    for pkg in ['GAPDoc', 'ctbllib', 'sonata', 'guava', 'factint', \
-                'gapdoc', 'grape', 'design', \
+    for pkg in ['GAPDoc', 'ctbllib', 'sonata', 'guava', 'factint',
+                'gapdoc', 'grape', 'design',
                 'toric', 'laguna', 'braid', 'polycyclic', 'nq']:
         # NOTE: Do *not* autoload hap - it screws up PolynomialRing(Rationals,2)
         try:
@@ -1647,10 +1666,9 @@ class GapFunctionElement(FunctionElement):
 
             sage: print(gap(4).SymmetricGroup.__doc__)
             <BLANKLINE>
-            50 Group Libraries
+              50.1-... SymmetricGroup
             <BLANKLINE>
-            When you start GAP, it already knows several groups. Currently GAP initially
-            knows the following groups:
+              ‣ SymmetricGroup( [filt, ]deg ) ─────────────────────────────────── function
             ...
         """
         M = self._obj.parent()
@@ -1660,16 +1678,15 @@ class GapFunctionElement(FunctionElement):
 
 @instancedoc
 class GapFunction(ExpectFunction):
-    def _instancedoc(self):
+    def _instancedoc_(self):
         """
         EXAMPLES::
 
             sage: print(gap.SymmetricGroup.__doc__)
             <BLANKLINE>
-            50 Group Libraries
+              50.1-... SymmetricGroup
             <BLANKLINE>
-            When you start GAP, it already knows several groups. Currently GAP initially
-            knows the following groups:
+              ‣ SymmetricGroup( [filt, ]deg ) ─────────────────────────────────── function
             ...
         """
         M = self._parent
diff --git a/src/sage/knots/link.py b/src/sage/knots/link.py
index fe11d9c..7e305c4 100644
--- a/src/sage/knots/link.py
+++ b/src/sage/knots/link.py
@@ -479,9 +479,8 @@ class Link(object):
              x1*x3^-1*x2^-1*x3, x3*x1^-1*x0^-1*x1 >
             sage: GB = K8.fundamental_group(presentation='braid')
             sage: GB
-            Finitely presented group < x0, x1, x2 |
-             x1*x2^-1*x1^-1*x0*x1*x2*x1*x2^-1*x1^-1*x0^-1*x1*x2*x1^-1*x0^-1,
-             x1*x2^-1*x1^-1*x0*x1*x2*x1^-1*x2^-1*x1^-1*x0^-1*x1*x2*x1^-1*x0*x1*x2*x1*x2^-1*x1^-1*x0^-1*x1*x2*x1^-2, x1*x2^-1*x1^-1*x0*x1*x2*x1^-1*x2^-1 >
+            Finitely presented group < x0, x1, x2 | x1*x2^-1*x1^-1*x0*x1*x2*x1*x2^-1*x1^-1*x0^-1*x1*x2*x1^-1*x0^-1, x1*x2^-1*x1^-1*x0*x1*x2*x1^-1*x2^-1*x1^-1*x0^-1*x1*x2*x1^-1*x0*x1*x2*x1*x2^-1*\
+            x1^-1*x0^-1*x1*x2*x1^-2, x1*x2^-1*x1^-1*x0*x1*x2*x1^-1*x2^-1 >
             sage: GA.simplified()
             Finitely presented group < x0, x1 |
              x1^-1*x0*x1*x0^-1*x1*x0*x1^-1*x0^-1*x1*x0^-1 >
diff --git a/src/sage/libs/gap/assigned_names.py b/src/sage/libs/gap/assigned_names.py
index a3633a4..ab5d973 100644
--- a/src/sage/libs/gap/assigned_names.py
+++ b/src/sage/libs/gap/assigned_names.py
@@ -27,7 +27,7 @@ from sage.libs.gap.saved_workspace import workspace
 
 
 NamesGVars = libgap.function_factory('NamesGVars')
-Filtered =libgap.function_factory('Filtered')
+Filtered = libgap.function_factory('Filtered')
 ValueGlobal = libgap.function_factory('ValueGlobal')
 IsBoundGlobal = libgap.function_factory('IsBoundGlobal')
 IsFunction = libgap.function_factory('IsFunction')
diff --git a/src/sage/libs/gap/element.pxd b/src/sage/libs/gap/element.pxd
index c803ade..74e7d6c 100644
--- a/src/sage/libs/gap/element.pxd
+++ b/src/sage/libs/gap/element.pxd
@@ -8,31 +8,31 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from .types cimport libGAP_Obj, libGAP_UInt
+from .gap_includes cimport Obj, UInt
 from sage.structure.sage_object cimport SageObject
 from sage.structure.element cimport Element, ModuleElement, RingElement
 
-cdef libGAP_Obj make_gap_list(sage_list) except NULL
-cdef libGAP_Obj make_gap_record(sage_dict) except NULL
-cdef libGAP_Obj make_gap_integer(sage_dict) except NULL
-cdef libGAP_Obj make_gap_string(sage_string) except NULL
-
-cdef GapElement make_any_gap_element(parent, libGAP_Obj obj)
-cdef GapElement make_GapElement(parent, libGAP_Obj obj)
-cdef GapElement_List make_GapElement_List(parent, libGAP_Obj obj)
-cdef GapElement_Record make_GapElement_Record(parent, libGAP_Obj obj)
-cdef GapElement_Integer make_GapElement_Integer(parent, libGAP_Obj obj)
-cdef GapElement_Rational make_GapElement_Rational(parent, libGAP_Obj obj)
-cdef GapElement_String make_GapElement_String(parent, libGAP_Obj obj)
-cdef GapElement_Boolean make_GapElement_Boolean(parent, libGAP_Obj obj)
-cdef GapElement_Function make_GapElement_Function(parent, libGAP_Obj obj)
+cdef Obj make_gap_list(sage_list) except NULL
+cdef Obj make_gap_record(sage_dict) except NULL
+cdef Obj make_gap_integer(sage_dict) except NULL
+cdef Obj make_gap_string(sage_string) except NULL
 
+cdef GapElement make_any_gap_element(parent, Obj obj)
+cdef GapElement make_GapElement(parent, Obj obj)
+cdef GapElement_List make_GapElement_List(parent, Obj obj)
+cdef GapElement_Record make_GapElement_Record(parent, Obj obj)
+cdef GapElement_Integer make_GapElement_Integer(parent, Obj obj)
+cdef GapElement_Rational make_GapElement_Rational(parent, Obj obj)
+cdef GapElement_String make_GapElement_String(parent, Obj obj)
+cdef GapElement_Boolean make_GapElement_Boolean(parent, Obj obj)
+cdef GapElement_Function make_GapElement_Function(parent, Obj obj)
+cdef char *crepr(Obj)
 
 
 cdef class GapElement(RingElement):
 
     # the pointer to the GAP object (memory managed by GASMAN)
-    cdef libGAP_Obj value
+    cdef Obj value
 
     # comparison
     cdef bint _compare_by_id
@@ -41,7 +41,7 @@ cdef class GapElement(RingElement):
     cpdef _set_compare_by_id(self)
     cpdef _assert_compare_by_id(self)
 
-    cdef _initialize(self, parent, libGAP_Obj obj)
+    cdef _initialize(self, parent, Obj obj)
     cpdef _type_number(self)
     cpdef is_bool(self)
     cpdef _add_(self, other)
@@ -81,11 +81,11 @@ cdef class GapElement_MethodProxy(GapElement_Function):
     cdef GapElement first_argument
 
 cdef class GapElement_Record(GapElement):
-    cpdef libGAP_UInt record_name_to_index(self, name)
+    cpdef UInt record_name_to_index(self, name)
 
 cdef class GapElement_RecordIterator(object):
     cdef GapElement_Record rec
-    cdef libGAP_UInt i
+    cdef UInt i
 
 cdef class GapElement_List(GapElement):
     pass
diff --git a/src/sage/libs/gap/element.pyx b/src/sage/libs/gap/element.pyx
index 446c393..0aa9c32 100644
--- a/src/sage/libs/gap/element.pyx
+++ b/src/sage/libs/gap/element.pyx
@@ -23,7 +23,7 @@ from cysignals.signals cimport sig_on, sig_off
 
 from .gap_includes cimport *
 from .util cimport *
-from sage.cpython.string cimport char_to_str, str_to_bytes
+from sage.cpython.string cimport str_to_bytes, char_to_str
 from sage.misc.cachefunc import cached_method
 from sage.structure.sage_object cimport SageObject
 from sage.structure.parent import Parent
@@ -33,33 +33,33 @@ from sage.groups.perm_gps.permgroup_element cimport PermutationGroupElement
 from sage.combinat.permutation import Permutation
 
 decode_type_number = {
-    libGAP_T_INT: 'T_INT (integer)',
-    libGAP_T_INTPOS: 'T_INTPOS (positive integer)',
-    libGAP_T_INTNEG: 'T_INTNEG (negative integer)',
-    libGAP_T_RAT: 'T_RAT (rational number)',
-    libGAP_T_CYC: 'T_CYC (universal cylotomic)',
-    libGAP_T_FFE: 'T_FFE (finite field element)',
-    libGAP_T_PERM2: 'T_PERM2',
-    libGAP_T_PERM4: 'T_PERM4',
-    libGAP_T_BOOL: 'T_BOOL',
-    libGAP_T_CHAR: 'T_CHAR',
-    libGAP_T_FUNCTION: 'T_FUNCTION',
-    libGAP_T_PLIST: 'T_PLIST',
-    libGAP_T_PLIST_CYC: 'T_PLIST_CYC',
-    libGAP_T_BLIST: 'T_BLIST',
-    libGAP_T_STRING: 'T_STRING',
-    libGAP_T_MACFLOAT: 'T_MACFLOAT (hardware floating point number)',
-    libGAP_T_COMOBJ: 'T_COMOBJ (component object)',
-    libGAP_T_POSOBJ: 'T_POSOBJ (positional object)',
-    libGAP_T_DATOBJ: 'T_DATOBJ (data object)',
-    libGAP_T_WPOBJ:  'T_WPOBJ (weak pointer object)',
+    0: 'T_INT (integer)',
+    T_INTPOS: 'T_INTPOS (positive integer)',
+    T_INTNEG: 'T_INTNEG (negative integer)',
+    T_RAT: 'T_RAT (rational number)',
+    T_CYC: 'T_CYC (universal cylotomic)',
+    T_FFE: 'T_FFE (finite field element)',
+    T_PERM2: 'T_PERM2',
+    T_PERM4: 'T_PERM4',
+    T_BOOL: 'T_BOOL',
+    T_CHAR: 'T_CHAR',
+    T_FUNCTION: 'T_FUNCTION',
+    T_PLIST: 'T_PLIST',
+    T_PLIST_CYC: 'T_PLIST_CYC',
+    T_BLIST: 'T_BLIST',
+    T_STRING: 'T_STRING',
+    T_MACFLOAT: 'T_MACFLOAT (hardware floating point number)',
+    T_COMOBJ: 'T_COMOBJ (component object)',
+    T_POSOBJ: 'T_POSOBJ (positional object)',
+    T_DATOBJ: 'T_DATOBJ (data object)',
+    T_WPOBJ:  'T_WPOBJ (weak pointer object)',
     }
 
 ############################################################################
 ### helper functions to construct lists and records ########################
 ############################################################################
 
-cdef libGAP_Obj make_gap_list(sage_list) except NULL:
+cdef Obj make_gap_list(sage_list) except NULL:
     """
     Convert Sage lists into Gap lists
 
@@ -71,15 +71,50 @@ cdef libGAP_Obj make_gap_list(sage_list) except NULL:
 
     The list of the elements in ``a`` as a Gap ``Obj``.
     """
-    # FIXME slow -- to make fast directly use ADD_LIST in Gap's C code.
     from sage.libs.gap.libgap import libgap
     cdef GapElement l = libgap.eval('[]')
+    cdef GapElement elem
     for x in sage_list:
-        l.Add(x)
+        if not isinstance(x, GapElement):
+            elem = <GapElement>libgap(x)
+        else:
+            elem = <GapElement>x
+
+        AddList(l.value, elem.value)
     return l.value
 
 
-cdef libGAP_Obj make_gap_record(sage_dict) except NULL:
+cdef char *crepr(Obj obj):
+    cdef Obj s, stream, output_text_string, view_obj
+    cdef UInt res
+    # The only way to get a string representation of an object that is truly
+    # consistent with how it would be represented at the GAP REPL is to call
+    # ViewObj on it.  Unfortunately, ViewObj *prints* to the output stream,
+    # and there is no equivalent that simply returns the string that would be
+    # printed.  The closest approximation would be DisplayString, but this
+    # bypasses any type-specific overrides for ViewObj so for many objects
+    # that does not give consistent results.
+    # TODO: This is probably needlessly slow, but we might need better
+    # support from GAP to improve this...
+    try:
+        GAP_Enter()
+        s = NEW_STRING(0)
+        output_text_string = GAP_ValueGlobalVariable("OutputTextString")
+        stream = CALL_2ARGS(output_text_string, s, GAP_True)
+
+        if not OpenOutputStream(stream):
+            raise RuntimeError("failed to open output capture stream for "
+                               "representing GAP object")
+
+        viewobj = GAP_ValueGlobalVariable("ViewObj")
+        CALL_1ARGS(viewobj, obj)
+        CloseOutput()
+        return CSTR_STRING(s)
+    finally:
+        GAP_Leave()
+
+
+cdef Obj make_gap_record(sage_dict) except NULL:
     """
     Convert Sage lists into Gap lists
 
@@ -99,19 +134,23 @@ cdef libGAP_Obj make_gap_record(sage_dict) except NULL:
     from sage.libs.gap.libgap import libgap
     data = [ (str(key), libgap(value)) for key, value in sage_dict.iteritems() ]
 
-    libgap_enter()
-    cdef libGAP_Obj rec = libGAP_NEW_PREC(len(data))
+    cdef Obj rec
     cdef GapElement val
-    cdef libGAP_UInt rnam
-    for d in data:
-        key, val = d
-        rnam = libGAP_RNamName(str_to_bytes(key))
-        libGAP_AssPRec(rec, rnam, val.value)
-    libgap_exit()
-    return rec
+    cdef UInt rnam
 
+    try:
+        GAP_Enter()
+        rec = NEW_PREC(len(data))
+        for d in data:
+            key, val = d
+            rnam = RNamName(str_to_bytes(key))
+            AssPRec(rec, rnam, val.value)
+        return rec
+    finally:
+        GAP_Leave()
 
-cdef libGAP_Obj make_gap_integer(sage_int) except NULL:
+
+cdef Obj make_gap_integer(sage_int) except NULL:
     """
     Convert Sage integer into Gap integer
 
@@ -128,19 +167,22 @@ cdef libGAP_Obj make_gap_integer(sage_int) except NULL:
         sage: libgap(1)   # indirect doctest
         1
     """
-    libgap_enter()
-    cdef libGAP_Obj result = libGAP_INTOBJ_INT(<int>sage_int)
-    libgap_exit()
-    return result
+    cdef Obj result
+    try:
+        GAP_Enter()
+        result = INTOBJ_INT(<int>sage_int)
+        return result
+    finally:
+        GAP_Leave()
 
 
-cdef libGAP_Obj make_gap_string(sage_string) except NULL:
+cdef Obj make_gap_string(sage_string) except NULL:
     """
-    Convert a Sage string to a Gap string
+    Convert a Python string to a Gap string
 
     INPUT:
 
-    - ``sage_string`` -- a Sage integer.
+    - ``sage_string`` -- a Python str.
 
     OUTPUT:
 
@@ -151,19 +193,21 @@ cdef libGAP_Obj make_gap_string(sage_string) except NULL:
         sage: libgap('string')   # indirect doctest
         "string"
     """
-    libgap_enter()
-    cdef libGAP_Obj result
-    sage_string = str_to_bytes(sage_string)
-    libGAP_C_NEW_STRING(result, len(sage_string), sage_string)
-    libgap_exit()
-    return result
+    cdef Obj result
+    try:
+        GAP_Enter()
+        b = str_to_bytes(sage_string)
+        C_NEW_STRING(result, len(b), b)
+        return result
+    finally:
+        GAP_Leave()
 
 
 ############################################################################
 ### generic construction of GapElements ####################################
 ############################################################################
 
-cdef GapElement make_any_gap_element(parent, libGAP_Obj obj):
+cdef GapElement make_any_gap_element(parent, Obj obj):
     """
     Return the libGAP element wrapper of ``obj``
 
@@ -199,55 +243,59 @@ cdef GapElement make_any_gap_element(parent, libGAP_Obj obj):
         sage: irr[1]
         0
     """
-    if obj is NULL:
-        return make_GapElement(parent, obj)
-    cdef int num = libGAP_TNUM_OBJ(obj)
-    if num == libGAP_T_INT or num == libGAP_T_INTPOS or num == libGAP_T_INTNEG:
-        return make_GapElement_Integer(parent, obj)
-    elif num == libGAP_T_MACFLOAT:
-        return make_GapElement_Float(parent, obj)
-    elif num == libGAP_T_CYC:
-        return make_GapElement_Cyclotomic(parent, obj)
-    elif num == libGAP_T_FFE:
-        return make_GapElement_FiniteField(parent, obj)
-    elif num == libGAP_T_RAT:
-        return make_GapElement_Rational(parent, obj)
-    elif num == libGAP_T_BOOL:
-        return make_GapElement_Boolean(parent, obj)
-    elif num == libGAP_T_FUNCTION:
-        return make_GapElement_Function(parent, obj)
-    elif num == libGAP_T_PERM2 or num == libGAP_T_PERM4:
-        return make_GapElement_Permutation(parent, obj)
-    elif libGAP_FIRST_RECORD_TNUM <= num <= libGAP_LAST_RECORD_TNUM:
-        return make_GapElement_Record(parent, obj)
-    elif libGAP_FIRST_LIST_TNUM <= num <= libGAP_LAST_LIST_TNUM and libGAP_LEN_PLIST(obj) == 0:
-        # Empty lists are lists and not strings in Python
-        return make_GapElement_List(parent, obj)
-    elif libGAP_IsStringConv(obj):
-        # GAP strings are lists, too. Make sure this comes before non-empty make_GapElement_List
-        return make_GapElement_String(parent, obj)
-    elif libGAP_IS_LIST(obj):
-        return make_GapElement_List(parent, obj)
-    elif num == libGAP_T_CHAR:
-        ch = make_GapElement(parent, obj).IntChar().sage()
-        return make_GapElement_String(parent, make_gap_string(chr(ch)))
-    result = make_GapElement(parent, obj)
-    if num == libGAP_T_POSOBJ:
-        if result.IsZmodnZObj():
-            return make_GapElement_IntegerMod(parent, obj)
-    if num == libGAP_T_COMOBJ:
-        if result.IsRing():
-            return make_GapElement_Ring(parent, obj)
-    return result
-
+    cdef int num
 
+    try:
+        GAP_Enter()
+        if obj is NULL:
+            return make_GapElement(parent, obj)
+        num = TNUM_OBJ(obj)
+        if IS_INT(obj):
+            return make_GapElement_Integer(parent, obj)
+        elif num == T_MACFLOAT:
+            return make_GapElement_Float(parent, obj)
+        elif num == T_CYC:
+            return make_GapElement_Cyclotomic(parent, obj)
+        elif num == T_FFE:
+            return make_GapElement_FiniteField(parent, obj)
+        elif num == T_RAT:
+            return make_GapElement_Rational(parent, obj)
+        elif num == T_BOOL:
+            return make_GapElement_Boolean(parent, obj)
+        elif num == T_FUNCTION:
+            return make_GapElement_Function(parent, obj)
+        elif num == T_PERM2 or num == T_PERM4:
+            return make_GapElement_Permutation(parent, obj)
+        elif IS_REC(obj):
+            return make_GapElement_Record(parent, obj)
+        elif IS_LIST(obj) and LEN_LIST(obj) == 0:
+            # Empty lists are lists and not strings in Python
+            return make_GapElement_List(parent, obj)
+        elif IsStringConv(obj):
+            # GAP strings are lists, too. Make sure this comes before non-empty make_GapElement_List
+            return make_GapElement_String(parent, obj)
+        elif IS_LIST(obj):
+            return make_GapElement_List(parent, obj)
+        elif num == T_CHAR:
+            ch = make_GapElement(parent, obj).IntChar().sage()
+            return make_GapElement_String(parent, make_gap_string(chr(ch)))
+        result = make_GapElement(parent, obj)
+        if num == T_POSOBJ:
+            if result.IsZmodnZObj():
+                return make_GapElement_IntegerMod(parent, obj)
+        if num == T_COMOBJ:
+            if result.IsRing():
+                return make_GapElement_Ring(parent, obj)
+        return result
+    finally:
+        GAP_Leave()
 
 
 ############################################################################
 ### GapElement #############################################################
 ############################################################################
 
-cdef GapElement make_GapElement(parent, libGAP_Obj obj):
+cdef GapElement make_GapElement(parent, Obj obj):
     r"""
     Turn a Gap C object (of type ``Obj``) into a Cython ``GapElement``.
 
@@ -270,8 +318,6 @@ cdef GapElement make_GapElement(parent, libGAP_Obj obj):
         <type 'sage.libs.gap.element.GapElement_Integer'>
 
         sage: libgap.eval('')
-        NULL
-
         sage: libgap(None)
         Traceback (most recent call last):
         ...
@@ -344,7 +390,7 @@ cdef class GapElement(RingElement):
         """
         raise TypeError('this class cannot be instantiated from Python')
 
-    cdef _initialize(self, parent, libGAP_Obj obj):
+    cdef _initialize(self, parent, Obj obj):
         r"""
         Initialize the GapElement.
 
@@ -424,8 +470,8 @@ cdef class GapElement(RingElement):
             sage: a
             [ [ 0, -2 ], [ 2, 3, 4 ] ]
         """
-        if libGAP_IS_MUTABLE_OBJ(self.value):
-            return make_any_gap_element(self.parent(), libGAP_SHALLOW_COPY_OBJ(self.value))
+        if IS_MUTABLE_OBJ(self.value):
+            return make_any_gap_element(self.parent(), SHALLOW_COPY_OBJ(self.value))
         else:
             return self
 
@@ -456,8 +502,8 @@ cdef class GapElement(RingElement):
             sage: l.deepcopy(1).IsMutable()
             true
         """
-        if libGAP_IS_MUTABLE_OBJ(self.value):
-            return make_any_gap_element(self.parent(), libGAP_CopyObj(self.value, mut))
+        if IS_MUTABLE_OBJ(self.value):
+            return make_any_gap_element(self.parent(), CopyObj(self.value, mut))
         else:
             return self
 
@@ -514,7 +560,7 @@ cdef class GapElement(RingElement):
             sage: x._type_number()
             (0L, 'T_INT (integer)')
         """
-        n = libGAP_TNUM_OBJ(self.value)
+        n = TNUM_OBJ(self.value)
         global decode_type_number
         name = decode_type_number.get(n, 'unknown')
         return (n, name)
@@ -592,7 +638,6 @@ cdef class GapElement(RingElement):
             sage: libgap(0)
             0
             sage: libgap.eval('')
-            NULL
             sage: libgap(0)
             0
             sage: libgap(0)._repr_()
@@ -600,15 +645,9 @@ cdef class GapElement(RingElement):
         """
         if  self.value == NULL:
             return 'NULL'
-        try:
-            libgap_enter()
-            libgap_start_interaction('')
-            libGAP_ViewObjHandler(self.value)
-            s = char_to_str(libgap_get_output())
-            return s.strip()
-        finally:
-            libgap_finish_interaction()
-            libgap_exit()
+
+        s = char_to_str(crepr(self.value))
+        return s.strip()
 
     cpdef _set_compare_by_id(self):
         """
@@ -777,17 +816,15 @@ cdef class GapElement(RingElement):
         if self._compare_by_id:
             return id(self) == id(other)
         cdef GapElement c_other = <GapElement>other
-        cdef bint result
-        libgap_enter()
+        sig_on()
         try:
-            sig_on()
-            result = libGAP_EQ(self.value, c_other.value)
-            sig_off()
+            GAP_Enter()
+            return EQ(self.value, c_other.value)
         except RuntimeError as msg:
             raise ValueError('libGAP: cannot compare equality: '+str(msg))
         finally:
-            libgap_exit()
-        return result
+            GAP_Leave()
+            sig_off()
 
     cdef bint _compare_less(self, Element other) except -2:
         """
@@ -802,18 +839,16 @@ cdef class GapElement(RingElement):
         """
         if self._compare_by_id:
             return id(self) < id(other)
-        cdef bint result
         cdef GapElement c_other = <GapElement>other
-        libgap_enter()
+        sig_on()
         try:
-            sig_on()
-            result = libGAP_LT(self.value, c_other.value)
-            sig_off()
+            GAP_Enter()
+            return LT(self.value, c_other.value)
         except RuntimeError as msg:
             raise ValueError('libGAP: cannot compare less than: '+str(msg))
         finally:
-            libgap_exit()
-        return result
+            GAP_Leave()
+            sig_off()
 
     cpdef _add_(self, right):
         r"""
@@ -834,18 +869,17 @@ cdef class GapElement(RingElement):
             ValueError: libGAP: Error, no method found!
             Error, no 1st choice method found for `+' on 2 arguments
         """
-        cdef libGAP_Obj result
+        cdef Obj result
+        sig_on()
         try:
-            libgap_enter()
-            sig_on()
-            result = libGAP_SUM(self.value, (<GapElement>right).value)
-            sig_off()
+            GAP_Enter()
+            result = SUM(self.value, (<GapElement>right).value)
+            return make_any_gap_element(self.parent(), result)
         except RuntimeError as msg:
-            libGAP_ClearError()
             raise ValueError('libGAP: '+str(msg))
         finally:
-            libgap_exit()
-        return make_any_gap_element(self.parent(), result)
+            GAP_Leave()
+            sig_off()
 
 
     cpdef _sub_(self, right):
@@ -867,18 +901,17 @@ cdef class GapElement(RingElement):
             ValueError: libGAP: Error, no method found!
             Error, no 1st choice method found for `-' on 2 arguments
         """
-        cdef libGAP_Obj result
+        cdef Obj result
+        sig_on()
         try:
-            libgap_enter()
-            sig_on()
-            result = libGAP_DIFF(self.value, (<GapElement>right).value)
-            sig_off()
+            GAP_Enter()
+            result = DIFF(self.value, (<GapElement>right).value)
+            return make_any_gap_element(self.parent(), result)
         except RuntimeError as msg:
-            libGAP_ClearError()
             raise ValueError('libGAP: {}'.format(msg))
         finally:
-            libgap_exit()
-        return make_any_gap_element(self.parent(), result)
+            GAP_Leave()
+            sig_off()
 
 
     cpdef _mul_(self, right):
@@ -900,18 +933,17 @@ cdef class GapElement(RingElement):
             ValueError: libGAP: Error, no method found!
             Error, no 1st choice method found for `*' on 2 arguments
         """
-        cdef libGAP_Obj result
+        cdef Obj result
+        sig_on()
         try:
-            libgap_enter()
-            sig_on()
-            result = libGAP_PROD(self.value, (<GapElement>right).value)
-            sig_off()
+            GAP_Enter()
+            result = PROD(self.value, (<GapElement>right).value)
+            return make_any_gap_element(self.parent(), result)
         except RuntimeError as msg:
-            libGAP_ClearError()
             raise ValueError('libGAP: {}'.format(msg))
         finally:
-            libgap_exit()
-        return make_any_gap_element(self.parent(), result)
+            GAP_Leave()
+            sig_off()
 
 
     cpdef _div_(self, right):
@@ -938,18 +970,17 @@ cdef class GapElement(RingElement):
             ...
             ValueError: libGAP: Error, Rational operations: <divisor> must not be zero
         """
-        cdef libGAP_Obj result
+        cdef Obj result
+        sig_on()
         try:
-            libgap_enter()
-            sig_on()
-            result = libGAP_QUO(self.value, (<GapElement>right).value)
-            sig_off()
+            GAP_Enter()
+            result = QUO(self.value, (<GapElement>right).value)
+            return make_any_gap_element(self.parent(), result)
         except RuntimeError as msg:
-            libGAP_ClearError()
             raise ValueError('libGAP: '+str(msg))
         finally:
-            libgap_exit()
-        return make_any_gap_element(self.parent(), result)
+            GAP_Leave()
+            sig_off()
 
     cpdef _mod_(self, right):
         r"""
@@ -968,18 +999,17 @@ cdef class GapElement(RingElement):
             ValueError: libGAP: Error, no method found!
             Error, no 1st choice method found for `mod' on 2 arguments
         """
-        cdef libGAP_Obj result
+        cdef Obj result
+        sig_on()
         try:
-            libgap_enter()
-            sig_on()
-            result = libGAP_MOD(self.value, (<GapElement>right).value)
-            sig_off()
+            GAP_Enter()
+            result = MOD(self.value, (<GapElement>right).value)
+            return make_any_gap_element(self.parent(), result)
         except RuntimeError as msg:
-            libGAP_ClearError()
             raise ValueError('libGAP: '+str(msg))
         finally:
-            libgap_exit()
-        return make_any_gap_element(self.parent(), result)
+            GAP_Leave()
+            sig_off()
 
 
     def __pow__(GapElement self, right, dummy):
@@ -1008,18 +1038,17 @@ cdef class GapElement(RingElement):
         if not isinstance(right, GapElement):
             libgap = self.parent()
             right = libgap(right)
-        cdef libGAP_Obj result
+        cdef Obj result
+        sig_on()
         try:
-            libgap_enter()
-            sig_on()
-            result = libGAP_POW(self.value, (<GapElement>right).value)
-            sig_off()
+            GAP_Enter()
+            result = POW(self.value, (<GapElement>right).value)
+            return make_any_gap_element(self.parent(), result)
         except RuntimeError as msg:
-            libGAP_ClearError()
             raise ValueError('libGAP: ' + str(msg))
         finally:
-            libgap_exit()
-        return make_any_gap_element(self.parent(), result)
+            GAP_Leave()
+            sig_off()
 
 
     def is_function(self):
@@ -1039,7 +1068,7 @@ cdef class GapElement(RingElement):
             sage: a.is_function()
             False
         """
-        return libGAP_IS_FUNC(self.value)
+        return IS_FUNC(self.value)
 
 
     def is_list(self):
@@ -1057,7 +1086,7 @@ cdef class GapElement(RingElement):
             sage: libgap.eval('3/2').is_list()
             False
         """
-        return libGAP_IS_LIST(self.value)
+        return IS_LIST(self.value)
 
 
     def is_record(self):
@@ -1075,7 +1104,7 @@ cdef class GapElement(RingElement):
             sage: libgap.eval('rec(a:=1, b:=3)').is_record()
             True
         """
-        return libGAP_IS_REC(self.value)
+        return IS_REC(self.value)
 
 
     cpdef is_bool(self):
@@ -1093,9 +1122,8 @@ cdef class GapElement(RingElement):
         """
         libgap = self.parent()
         cdef GapElement r_sage = libgap.IsBool(self)
-        cdef libGAP_Obj r_gap = r_sage.value
-        return r_gap == libGAP_True
-
+        cdef Obj r_gap = r_sage.value
+        return r_gap == GAP_True
 
     def is_string(self):
         r"""
@@ -1110,7 +1138,7 @@ cdef class GapElement(RingElement):
             sage: libgap('this is a string').is_string()
             True
         """
-        return libGAP_IS_STRING(self.value)
+        return IS_STRING(self.value)
 
 
     def is_permutation(self):
@@ -1130,8 +1158,8 @@ cdef class GapElement(RingElement):
             sage: libgap('this is a string').is_permutation()
             False
         """
-        return (libGAP_TNUM_OBJ(self.value) == libGAP_T_PERM2 or
-                libGAP_TNUM_OBJ(self.value) == libGAP_T_PERM4)
+        return (TNUM_OBJ(self.value) == T_PERM2 or
+                TNUM_OBJ(self.value) == T_PERM4)
 
 
     def sage(self):
@@ -1191,7 +1219,7 @@ cdef class GapElement(RingElement):
 ### GapElement_Integer #####################################################
 ############################################################################
 
-cdef GapElement_Integer make_GapElement_Integer(parent, libGAP_Obj obj):
+cdef GapElement_Integer make_GapElement_Integer(parent, Obj obj):
     r"""
     Turn a Gap integer object into a GapElement_Integer Sage object
 
@@ -1250,7 +1278,7 @@ cdef class GapElement_Integer(GapElement):
             sage: N.IsInt()
             true
         """
-        return libGAP_IS_INTOBJ(self.value)
+        return IS_INTOBJ(self.value)
 
     def _rational_(self):
         r"""
@@ -1301,7 +1329,7 @@ cdef class GapElement_Integer(GapElement):
         if ring is None:
             ring = ZZ
         if self.is_C_int():
-            return ring(libGAP_INT_INTOBJ(self.value))
+            return ring(INT_INTOBJ(self.value))
         else:
             # TODO: waste of time!
             # gap integers are stored as a mp_limb_t and we have a much more direct
@@ -1318,13 +1346,13 @@ cdef class GapElement_Integer(GapElement):
 
             sage: int(libgap(3))
             3
-            sage: type(_) is int
-            True
+            sage: type(_)
+            <... 'int'>
 
             sage: int(libgap(2)**128)
             340282366920938463463374607431768211456L
-            sage: type(_) is long
-            True
+            sage: type(_)
+            <type 'long'>
         """
         return self.sage(ring=int)
 
@@ -1345,7 +1373,7 @@ cdef class GapElement_Integer(GapElement):
 ### GapElement_Float #####################################################
 ##########################################################################
 
-cdef GapElement_Float make_GapElement_Float(parent, libGAP_Obj obj):
+cdef GapElement_Float make_GapElement_Float(parent, Obj obj):
     r"""
     Turn a Gap macfloat object into a GapElement_Float Sage object
 
@@ -1401,7 +1429,7 @@ cdef class GapElement_Float(GapElement):
         """
         if ring is None:
             ring = RDF
-        return ring(libGAP_VAL_MACFLOAT(self.value))
+        return ring(VAL_MACFLOAT(self.value))
 
     def __float__(self):
         r"""
@@ -1410,7 +1438,7 @@ cdef class GapElement_Float(GapElement):
             sage: float(libgap.eval("Float(3.5)"))
             3.5
         """
-        return libGAP_VAL_MACFLOAT(self.value)
+        return VAL_MACFLOAT(self.value)
 
 
 
@@ -1418,7 +1446,7 @@ cdef class GapElement_Float(GapElement):
 ### GapElement_IntegerMod #####################################################
 ############################################################################
 
-cdef GapElement_IntegerMod make_GapElement_IntegerMod(parent, libGAP_Obj obj):
+cdef GapElement_IntegerMod make_GapElement_IntegerMod(parent, Obj obj):
     r"""
     Turn a Gap integer object into a :class:`GapElement_IntegerMod` Sage object
 
@@ -1499,7 +1527,7 @@ cdef class GapElement_IntegerMod(GapElement):
 ### GapElement_FiniteField #####################################################
 ############################################################################
 
-cdef GapElement_FiniteField make_GapElement_FiniteField(parent, libGAP_Obj obj):
+cdef GapElement_FiniteField make_GapElement_FiniteField(parent, Obj obj):
     r"""
     Turn a GAP finite field object into a :class:`GapElement_FiniteField` Sage object
 
@@ -1666,7 +1694,7 @@ cdef class GapElement_FiniteField(GapElement):
 ### GapElement_Cyclotomic #####################################################
 ############################################################################
 
-cdef GapElement_Cyclotomic make_GapElement_Cyclotomic(parent, libGAP_Obj obj):
+cdef GapElement_Cyclotomic make_GapElement_Cyclotomic(parent, Obj obj):
     r"""
     Turn a Gap cyclotomic object into a :class:`GapElement_Cyclotomic` Sage
     object.
@@ -1754,7 +1782,7 @@ cdef class GapElement_Cyclotomic(GapElement):
 ### GapElement_Rational ####################################################
 ############################################################################
 
-cdef GapElement_Rational make_GapElement_Rational(parent, libGAP_Obj obj):
+cdef GapElement_Rational make_GapElement_Rational(parent, Obj obj):
     r"""
     Turn a Gap Rational number (of type ``Obj``) into a Cython ``GapElement_Rational``.
 
@@ -1826,7 +1854,7 @@ cdef class GapElement_Rational(GapElement):
 ### GapElement_Ring #####################################################
 ############################################################################
 
-cdef GapElement_Ring make_GapElement_Ring(parent, libGAP_Obj obj):
+cdef GapElement_Ring make_GapElement_Ring(parent, Obj obj):
     r"""
     Turn a Gap integer object into a :class:`GapElement_Ring` Sage
     object.
@@ -1968,7 +1996,7 @@ cdef class GapElement_Ring(GapElement):
 ### GapElement_Boolean #####################################################
 ############################################################################
 
-cdef GapElement_Boolean make_GapElement_Boolean(parent, libGAP_Obj obj):
+cdef GapElement_Boolean make_GapElement_Boolean(parent, Obj obj):
     r"""
     Turn a Gap Boolean number (of type ``Obj``) into a Cython ``GapElement_Boolean``.
 
@@ -2023,11 +2051,12 @@ cdef class GapElement_Boolean(GapElement):
             ...
             ValueError: the GAP boolean value "fail" cannot be represented in Sage
         """
-        if self.value == libGAP_True:   return True
-        if self.value == libGAP_False:  return False
+        if self.value == GAP_True:
+            return True
+        if self.value == GAP_False:
+            return False
         raise ValueError('the GAP boolean value "fail" cannot be represented in Sage')
 
-
     def __nonzero__(self):
         """
         Check that the boolean is "true".
@@ -2051,15 +2080,15 @@ cdef class GapElement_Boolean(GapElement):
             ....:         print("{} {}".format( x, type(x)))
             false <type 'sage.libs.gap.element.GapElement_Boolean'>
             fail <type 'sage.libs.gap.element.GapElement_Boolean'>
-       """
-        return self.value == libGAP_True
+        """
+        return self.value == GAP_True
 
 
 ############################################################################
 ### GapElement_String ####################################################
 ############################################################################
 
-cdef GapElement_String make_GapElement_String(parent, libGAP_Obj obj):
+cdef GapElement_String make_GapElement_String(parent, Obj obj):
     r"""
     Turn a Gap String (of type ``Obj``) into a Cython ``GapElement_String``.
 
@@ -2108,11 +2137,9 @@ cdef class GapElement_String(GapElement):
             sage: s.sage()
             'string'
             sage: type(_)
-            <... 'str'>
+            <type 'str'>
         """
-        libgap_enter()
-        s = char_to_str(libGAP_CSTR_STRING(self.value))
-        libgap_exit()
+        s = char_to_str(CSTR_STRING(self.value))
         return s
 
     sage = __str__
@@ -2121,7 +2148,7 @@ cdef class GapElement_String(GapElement):
 ### GapElement_Function ####################################################
 ############################################################################
 
-cdef GapElement_Function make_GapElement_Function(parent, libGAP_Obj obj):
+cdef GapElement_Function make_GapElement_Function(parent, Obj obj):
     r"""
     Turn a Gap C function object (of type ``Obj``) into a Cython ``GapElement_Function``.
 
@@ -2201,30 +2228,31 @@ cdef class GapElement_Function(GapElement):
             <Gap function "NormalSubgroups">
             sage: b
             Sym( [ 1 .. 4 ] )
-            sage: a(b)
-            [ Group(()),
-              Group([ (1,4)(2,3), (1,3)(2,4) ]),
-              Group([ (2,4,3), (1,4)(2,3), (1,3)(2,4) ]),
-              Sym( [ 1 .. 4 ] ) ]
+            sage: sorted(a(b))
+            [Group(()),
+             Sym( [ 1 .. 4 ] ),
+             Alt( [ 1 .. 4 ] ),
+             Group([ (1,4)(2,3), (1,2)(3,4) ])]
 
             sage: libgap.eval("a := NormalSubgroups")
             <Gap function "NormalSubgroups">
             sage: libgap.eval("b := SymmetricGroup(4)")
             Sym( [ 1 .. 4 ] )
             sage: libgap.collect()
-            sage: libgap.eval('a') (libgap.eval('b'))
-            [ Group(()),
-              Group([ (1,4)(2,3), (1,3)(2,4) ]),
-              Group([ (2,4,3), (1,4)(2,3), (1,3)(2,4) ]),
-              Sym( [ 1 .. 4 ] ) ]
+            sage: sorted(libgap.eval('a') (libgap.eval('b')))
+            [Group(()),
+             Sym( [ 1 .. 4 ] ),
+             Alt( [ 1 .. 4 ] ),
+             Group([ (1,4)(2,3), (1,2)(3,4) ])]
+
             sage: a = libgap.eval('a')
             sage: b = libgap.eval('b')
             sage: libgap.collect()
-            sage: a(b)
-            [ Group(()),
-              Group([ (1,4)(2,3), (1,3)(2,4) ]),
-              Group([ (2,4,3), (1,4)(2,3), (1,3)(2,4) ]),
-              Sym( [ 1 .. 4 ] ) ]
+            sage: sorted(a(b))
+            [Group(()),
+             Sym( [ 1 .. 4 ] ),
+             Alt( [ 1 .. 4 ] ),
+             Group([ (1,4)(2,3), (1,2)(3,4) ])]
 
         Not every ``GapElement`` is callable::
 
@@ -2269,46 +2297,46 @@ cdef class GapElement_Function(GapElement):
             sage: libgap_exec('echo hello from the shell')
             hello from the shell
         """
-        cdef libGAP_Obj result = NULL
-        cdef libGAP_Obj arg_list
+        cdef Obj result = NULL
+        cdef Obj arg_list
         cdef int i, n = len(args)
 
         if n > 0:
             libgap = self.parent()
-            a = [x if isinstance(x,GapElement) else libgap(x) for x in args]
+            a = [x if isinstance(x, GapElement) else libgap(x) for x in args]
 
+        sig_on()
         try:
-            libgap_enter()
-            sig_on()
+            GAP_Enter()
             if n == 0:
-                result = libGAP_CALL_0ARGS(self.value)
+                result = CALL_0ARGS(self.value)
             elif n == 1:
-                result = libGAP_CALL_1ARGS(self.value,
+                result = CALL_1ARGS(self.value,
                                            (<GapElement>a[0]).value)
             elif n == 2:
-                result = libGAP_CALL_2ARGS(self.value,
+                result = CALL_2ARGS(self.value,
                                            (<GapElement>a[0]).value,
                                            (<GapElement>a[1]).value)
             elif n == 3:
-                result = libGAP_CALL_3ARGS(self.value,
+                result = CALL_3ARGS(self.value,
                                            (<GapElement>a[0]).value,
                                            (<GapElement>a[1]).value,
                                            (<GapElement>a[2]).value)
             elif n == 4:
-                result = libGAP_CALL_4ARGS(self.value,
+                result = CALL_4ARGS(self.value,
                                            (<GapElement>a[0]).value,
                                            (<GapElement>a[1]).value,
                                            (<GapElement>a[2]).value,
                                            (<GapElement>a[3]).value)
             elif n == 5:
-                result = libGAP_CALL_5ARGS(self.value,
+                result = CALL_5ARGS(self.value,
                                            (<GapElement>a[0]).value,
                                            (<GapElement>a[1]).value,
                                            (<GapElement>a[2]).value,
                                            (<GapElement>a[3]).value,
                                            (<GapElement>a[4]).value)
             elif n == 6:
-                result = libGAP_CALL_6ARGS(self.value,
+                result = CALL_6ARGS(self.value,
                                            (<GapElement>a[0]).value,
                                            (<GapElement>a[1]).value,
                                            (<GapElement>a[2]).value,
@@ -2316,21 +2344,20 @@ cdef class GapElement_Function(GapElement):
                                            (<GapElement>a[4]).value,
                                            (<GapElement>a[5]).value)
             elif n >= 7:
-                libgap_exit()
                 arg_list = make_gap_list(args)
-                libgap_enter()
-                result = libGAP_CALL_XARGS(self.value, arg_list)
-            sig_off()
+                result = CALL_XARGS(self.value, arg_list)
+
+            if result == NULL:
+                # We called a procedure that does not return anything
+                return None
+
+            return make_any_gap_element(self.parent(), result)
         except RuntimeError as msg:
             raise ValueError('libGAP: ' + str(msg))
         finally:
-            libgap_exit()
-
-        if result == NULL:
-            # We called a procedure that does not return anything
-            return None
+            GAP_Leave()
+            sig_off()
 
-        return make_any_gap_element(self.parent(), result)
 
 
     def _instancedoc_(self):
@@ -2356,7 +2383,7 @@ cdef class GapElement_Function(GapElement):
 ### GapElement_MethodProxy #################################################
 ############################################################################
 
-cdef GapElement_MethodProxy make_GapElement_MethodProxy(parent, libGAP_Obj function, GapElement base_object):
+cdef GapElement_MethodProxy make_GapElement_MethodProxy(parent, Obj function, GapElement base_object):
     r"""
     Turn a Gap C rec object (of type ``Obj``) into a Cython ``GapElement_Record``.
 
@@ -2435,7 +2462,7 @@ cdef class GapElement_MethodProxy(GapElement_Function):
             sage: lst
             [ 1,, 3, 4, 5 ]
         """
-        if args:
+        if len(args) > 0:
             return GapElement_Function.__call__(self, * ([self.first_argument] + list(args)))
         else:
             return GapElement_Function.__call__(self, self.first_argument)
@@ -2446,7 +2473,7 @@ cdef class GapElement_MethodProxy(GapElement_Function):
 ### GapElement_List ########################################################
 ############################################################################
 
-cdef GapElement_List make_GapElement_List(parent, libGAP_Obj obj):
+cdef GapElement_List make_GapElement_List(parent, Obj obj):
     r"""
     Turn a Gap C List object (of type ``Obj``) into a Cython ``GapElement_List``.
 
@@ -2498,6 +2525,21 @@ cdef class GapElement_List(GapElement):
         IndexError: index out of range.
     """
 
+    def __bool__(self):
+        r"""
+        Return True if the list is non-empty, as with Python ``list``s.
+
+        EXAMPLES::
+
+            sage: lst = libgap.eval('[1,,,4]')
+            sage: bool(lst)
+            True
+            sage: lst = libgap.eval('[]')
+            sage: bool(lst)
+            False
+        """
+        return bool(len(self))
+
     def __len__(self):
         r"""
         Return the length of the list.
@@ -2512,7 +2554,7 @@ cdef class GapElement_List(GapElement):
             sage: len(lst)
             4
         """
-        return libGAP_LEN_LIST(self.value)
+        return LEN_LIST(self.value)
 
     def __getitem__(self, i):
         r"""
@@ -2556,21 +2598,21 @@ cdef class GapElement_List(GapElement):
             ValueError: too many indices
         """
         cdef int j
-        cdef libGAP_Obj obj = self.value
+        cdef Obj obj = self.value
 
         if isinstance(i, tuple):
             for j in i:
-                if not libGAP_IS_LIST(obj):
+                if not IS_LIST(obj):
                     raise ValueError('too many indices')
-                if j < 0 or j >= libGAP_LEN_LIST(obj):
+                if j < 0 or j >= LEN_LIST(obj):
                     raise IndexError('index out of range')
-                obj = libGAP_ELM_LIST(obj, j+1)
+                obj = ELM_LIST(obj, j+1)
 
         else:
             j = i
-            if j < 0 or j >= libGAP_LEN_LIST(obj):
+            if j < 0 or j >= LEN_LIST(obj):
                 raise IndexError('index out of range.')
-            obj = libGAP_ELM_LIST(obj, j+1)
+            obj = ELM_LIST(obj, j+1)
 
         return make_any_gap_element(self.parent(), obj)
 
@@ -2623,20 +2665,20 @@ cdef class GapElement_List(GapElement):
             sage: m
             [ [ 1, 2 ], [ 3, 4 ] ]
         """
-        if not libGAP_IS_MUTABLE_OBJ(self.value):
+        if not IS_MUTABLE_OBJ(self.value):
             raise TypeError('immutable Gap object does not support item assignment')
 
         cdef int j
-        cdef libGAP_Obj obj = self.value
+        cdef Obj obj = self.value
 
         if isinstance(i, tuple):
             for j in i[:-1]:
-                if not libGAP_IS_LIST(obj):
+                if not IS_LIST(obj):
                     raise ValueError('too many indices')
-                if j < 0 or j >= libGAP_LEN_LIST(obj):
+                if j < 0 or j >= LEN_LIST(obj):
                     raise IndexError('index out of range')
-                obj = libGAP_ELM_LIST(obj, j+1)
-            if not libGAP_IS_LIST(obj):
+                obj = ELM_LIST(obj, j+1)
+            if not IS_LIST(obj):
                 raise ValueError('too many indices')
             j = i[-1]
         else:
@@ -2651,7 +2693,7 @@ cdef class GapElement_List(GapElement):
         else:
             celt= self.parent()(elt)
 
-        libGAP_ASS_LIST(obj, j+1, celt.value)
+        ASS_LIST(obj, j+1, celt.value)
 
     def sage(self, **kwds):
         r"""
@@ -2769,7 +2811,7 @@ cdef class GapElement_List(GapElement):
 ############################################################################
 
 
-cdef GapElement_Permutation make_GapElement_Permutation(parent, libGAP_Obj obj):
+cdef GapElement_Permutation make_GapElement_Permutation(parent, Obj obj):
     r"""
     Turn a Gap C permutation object (of type ``Obj``) into a Cython ``GapElement_Permutation``.
 
@@ -2834,7 +2876,7 @@ cdef class GapElement_Permutation(GapElement):
 ### GapElement_Record ######################################################
 ############################################################################
 
-cdef GapElement_Record make_GapElement_Record(parent, libGAP_Obj obj):
+cdef GapElement_Record make_GapElement_Record(parent, Obj obj):
     r"""
     Turn a Gap C rec object (of type ``Obj``) into a Cython ``GapElement_Record``.
 
@@ -2876,7 +2918,8 @@ cdef class GapElement_Record(GapElement):
         sage: rec['no_such_element']
         Traceback (most recent call last):
         ...
-        IndexError: libGAP: Error, Record: '<rec>.no_such_element' must have an assigned value
+        IndexError: libGAP: Error, Record Element: '<rec>.no_such_element' must
+        have an assigned value
     """
 
     def __len__(self):
@@ -2893,7 +2936,7 @@ cdef class GapElement_Record(GapElement):
             sage: len(rec)
             3
         """
-        return libGAP_LEN_PREC(self.value)
+        return LEN_PREC(self.value)
 
 
     def __iter__(self):
@@ -2910,19 +2953,19 @@ cdef class GapElement_Record(GapElement):
             sage: iter = rec.__iter__()
             sage: type(iter)
             <type 'sage.libs.gap.element.GapElement_RecordIterator'>
-            sage: list(rec)
+            sage: sorted(rec)
             [('a', 123), ('b', 456)]
         """
         return GapElement_RecordIterator(self)
 
 
-    cpdef libGAP_UInt record_name_to_index(self, name):
+    cpdef UInt record_name_to_index(self, name):
         r"""
         Convert string to GAP record index.
 
         INPUT:
 
-        - ``name`` -- a python string.
+        - ``py_name`` -- a python string.
 
         OUTPUT:
 
@@ -2939,12 +2982,7 @@ cdef class GapElement_Record(GapElement):
             3776L
         """
         name = str_to_bytes(name)
-
-        try:
-            libgap_enter()
-            return libGAP_RNamName(name)
-        finally:
-            libgap_exit()
+        return RNamName(name)
 
     def __getitem__(self, name):
         r"""
@@ -2964,15 +3002,18 @@ cdef class GapElement_Record(GapElement):
             sage: rec['first']
             123
         """
-        cdef libGAP_UInt i = self.record_name_to_index(name)
-        cdef libGAP_Obj result
+        cdef UInt i = self.record_name_to_index(name)
+        cdef Obj result
+        sig_on()
         try:
-            sig_on()
-            result = libGAP_ELM_REC(self.value, i)
-            sig_off()
+            GAP_Enter()
+            result = ELM_REC(self.value, i)
+            return make_any_gap_element(self.parent(), result)
         except RuntimeError as msg:
             raise IndexError('libGAP: ' + str(msg))
-        return make_any_gap_element(self.parent(), result)
+        finally:
+            GAP_Leave()
+            sig_off()
 
 
     def sage(self):
@@ -3016,7 +3057,7 @@ cdef class GapElement_RecordIterator(object):
     EXAMPLES::
 
         sage: rec = libgap.eval('rec(a:=123, b:=456)')
-        sage: list(rec)
+        sage: sorted(rec)
         [('a', 123), ('b', 456)]
         sage: dict(rec)
         {'a': 123, 'b': 456}
@@ -3052,20 +3093,18 @@ cdef class GapElement_RecordIterator(object):
 
             sage: rec = libgap.eval('rec(a:=123, b:=456)')
             sage: iter = rec.__iter__()
-            sage: iter.__next__()
-            ('a', 123)
-            sage: next(iter)
-            ('b', 456)
+            sage: a = iter.__next__()
+            sage: b = next(iter)
+            sage: sorted([a, b])
+            [('a', 123), ('b', 456)]
         """
-        cdef libGAP_UInt i = self.i
+        cdef UInt i = self.i
         if i>len(self.rec):
             raise StopIteration
         # note the abs: negative values mean the rec keys are not sorted
-        libgap_enter()
-        key_index = abs(libGAP_GET_RNAM_PREC(self.rec.value, i))
-        key = char_to_str(libGAP_NAME_RNAM(key_index))
-        cdef libGAP_Obj result = libGAP_GET_ELM_PREC(self.rec.value,i)
-        libgap_exit()
+        key_index = abs(GET_RNAM_PREC(self.rec.value, i))
+        key = char_to_str(CSTR_STRING(NAME_RNAM(key_index)))
+        cdef Obj result = GET_ELM_PREC(self.rec.value,i)
         val = make_any_gap_element(self.rec.parent(), result)
         self.i += 1
         return (key, val)
diff --git a/src/sage/libs/gap/gap_functions.py b/src/sage/libs/gap/gap_functions.py
index 271a8aa..f7dac14 100644
--- a/src/sage/libs/gap/gap_functions.py
+++ b/src/sage/libs/gap/gap_functions.py
@@ -1,4 +1,4 @@
-"Gap functions"
+"""Common global functions defined by GAP."""
 
 ###############################################################################
 #       Copyright (C) 2009, William Stein <wstein@gmail.com>
@@ -11,8 +11,9 @@
 ###############################################################################
 
 
+
 # selected gap functions to use in tab completion
-common_gap_functions = [
+common_gap_functions = set([
   'AbelianGroup',
   'AbelianInvariants',
   'AbelianInvariantsMultiplier',
@@ -37,13 +38,11 @@ common_gap_functions = [
   'AppendTo',
   'Apply',
   'AsGroup',
-  'Assert',
-  'AtlasGroup',
   'AutomorphismGroup',
   'BaseOfGroup',
   'Basis',
   'BasisVectors',
-  'Bell', 
+  'Bell',
   'Binomial',
   'BlockMatrix',
   'Blocks',
@@ -125,7 +124,6 @@ common_gap_functions = [
   'CyclicGroup',
   'CyclotomicField',
   'CyclotomicPolynomial',
-  'Cyclotomics',
   'DefiningPolynomial',
   'Degree',
   'DegreeFFE',
@@ -210,8 +208,6 @@ common_gap_functions = [
   'GaloisGroup',
   'GaloisMat',
   'GaloisStabilizer',
-  'GaussianIntegers',
-  'GaussianRationals',
   'Gcd',
   'GcdInt',
   'GcdOp',
@@ -225,7 +221,6 @@ common_gap_functions = [
   'GeneratorsOfField',
   'GeneratorsOfGroup',
   'GeneratorsOfIdeal',
-  'GlobalMersenneTwister',
   'GroebnerBasis',
   'Group',
   'GroupHomomorphismByFunction',
@@ -243,23 +238,7 @@ common_gap_functions = [
   'Image',
   'Images',
   'Index',
-  'InfoAlgebra',
-  'InfoAttributes',
-  'InfoBckt',
-  'InfoCharacterTable',
-  'InfoCoh',
-  'InfoComplement',
-  'InfoCoset',
-  'InfoFpGroup',
-  'InfoGroebner',
-  'InfoGroup',
-  'InfoLattice',
   'InfoLevel',
-  'InfoMatrix',
-  'InfoMonomial',
-  'InfoNumtheor',
-  'InfoOptions',
-  'InfoPcSubgroup',
   'InfoText',
   'InnerAutomorphism',
   'InnerAutomorphismsAutomorphismGroup',
@@ -269,7 +248,6 @@ common_gap_functions = [
   'IntHexString',
   'IntScalarProducts',
   'IntVecFFE',
-  'Integers',
   'IntersectSet',
   'Intersection',
   'InvariantBilinearForm',
@@ -319,7 +297,6 @@ common_gap_functions = [
   'IsBinaryRelation',
   'IsBlockMatrixRep',
   'IsBool',
-  'IsBound',
   'IsBoundGlobal',
   'IsBrauerTable',
   'IsBravaisGroup',
@@ -528,7 +505,6 @@ common_gap_functions = [
   'IsTransitive',
   'IsTransitiveBinaryRelation',
   'IsTrivial',
-  'IsTuple',
   'IsUniqueFactorizationRing',
   'IsUnit',
   'IsUnivariatePolynomial',
@@ -718,7 +694,6 @@ common_gap_functions = [
   'MonomialGrevlexOrdering',
   'MonomialGrlexOrdering',
   'MonomialLexOrdering',
-  'MonomialTotalDegreeLess',
   'MostFrequentGeneratorFpGroup',
   'MovedPoints',
   'MultRowVector',
@@ -742,7 +717,6 @@ common_gap_functions = [
   'NextIterator',
   'NextPrimeInt',
   'NiceBasis',
-  'NiceBasisFiltersInfo',
   'NiceFreeLeftModule',
   'NiceFreeLeftModuleInfo',
   'NiceMonomorphism',
@@ -933,7 +907,6 @@ common_gap_functions = [
   'Position',
   'PositionBound',
   'PositionCanonical',
-  'PositionFirstComponent',
   'PositionNonZero',
   'PositionNot',
   'PositionNthOccurrence',
@@ -976,7 +949,6 @@ common_gap_functions = [
   'PrimePGroup',
   'PrimePowersInt',
   'PrimeResidues',
-  'Primes',
   'PrimitiveElement',
   'PrimitiveGroup',
   'PrimitiveIdentification',
@@ -1047,7 +1019,6 @@ common_gap_functions = [
   'RationalClass',
   'RationalClasses',
   'RationalizedMat',
-  'Rationals',
   'Read',
   'ReadAll',
   'ReadAllLine',
@@ -1094,7 +1065,6 @@ common_gap_functions = [
   'ReesMatrixSemigroupElement',
   'ReesZeroMatrixSemigroup',
   'ReesZeroMatrixSemigroupElement',
-  'ReesZeroMatrixSemigroupElementIsZero',
   'RefinedPcGroup',
   'RegularActionHomomorphism',
   'RegularModule',
@@ -1124,7 +1094,6 @@ common_gap_functions = [
   'Reread',
   'RereadPackage',
   'Reset',
-  'RestoreStateRandom',
   'RestrictOutputsOfSLP',
   'Restricted',
   'RestrictedClassFunction',
@@ -1157,8 +1126,6 @@ common_gap_functions = [
   'SSortedList',
   'SU',
   'SameBlock',
-  'SandwichMatrixOfReesMatrixSemigroup',
-  'SandwichMatrixOfReesZeroMatrixSemigroup',
   'SaveWorkspace',
   'ScalarProduct',
   'SchurCover',
@@ -1249,7 +1216,6 @@ common_gap_functions = [
   'StabilizerOfExternalSet',
   'StabilizerPcgs',
   'StandardAssociate',
-  'StandardGeneratorsInfo',
   'StandardizeTable',
   'StarCyc',
   'Stirling1',
@@ -1296,7 +1262,6 @@ common_gap_functions = [
   'SumIntersectionMat',
   'SumX',
   'SupersolvableResiduum',
-  'SupportedCharacterTableInfo',
   'SurjectiveActionHomomorphismAttr',
   'SuzukiGroup',
   'SylowComplement',
@@ -1314,7 +1279,6 @@ common_gap_functions = [
   'TableAutomorphisms',
   'TableOfMarks',
   'TableOfMarksByLattice',
-  'TableOfMarksComponents',
   'TableOfMarksCyclic',
   'TableOfMarksDihedral',
   'TableOfMarksFrobenius',
@@ -1332,9 +1296,6 @@ common_gap_functions = [
   'TracedCosetFpGroup',
   'TransferDiagram',
   'Transformation',
-  'TransformationData',
-  'TransformationRelation',
-  'TransformationType',
   'TransformingPermutations',
   'TransformingPermutationsCharacterTables',
   'TransitiveClosureBinaryRelation',
@@ -1365,7 +1326,6 @@ common_gap_functions = [
   'TrivialSubspace',
   'Tuple',
   'Tuples',
-  'Unbind',
   'UnbindElmWPObj',
   'UnbindGlobal',
   'UnderlyingCharacterTable',
@@ -1441,4 +1401,6 @@ common_gap_functions = [
   'ZeroOp',
   'ZeroSM',
   'ZeroSameMutability',
- ]
+  'GASMAN_STATS',
+  'GASMAN',
+ ])
diff --git a/src/sage/libs/gap/gap_globals.py b/src/sage/libs/gap/gap_globals.py
new file mode 100644
index 00000000..99b3921
--- /dev/null
+++ b/src/sage/libs/gap/gap_globals.py
@@ -0,0 +1,46 @@
+"""Common globals defined by GAP."""
+
+###############################################################################
+#       Copyright (C) 2009, William Stein <wstein@gmail.com>
+#       Copyright (C) 2012, Volker Braun <vbraun.name@gmail.com>
+#
+#   Distributed under the terms of the GNU General Public License (GPL)
+#   as published by the Free Software Foundation; either version 2 of
+#   the License, or (at your option) any later version.
+#                   http://www.gnu.org/licenses/
+###############################################################################
+
+
+from .gap_functions import common_gap_functions
+
+
+# selected gap globals to use in tab completion
+common_gap_globals = set([
+  'Assert',
+  'Cyclotomics',
+  'GaussianIntegers',
+  'GaussianRationals',
+  'GlobalMersenneTwister',
+  'GlobalRandomSource',
+  'InfoAlgebra',
+  'InfoAttributes',
+  'InfoBckt',
+  'InfoCharacterTable',
+  'InfoCoh',
+  'InfoComplement',
+  'InfoCoset',
+  'InfoFpGroup',
+  'InfoGroebner',
+  'InfoGroup',
+  'InfoLattice',
+  'InfoMatrix',
+  'InfoMonomial',
+  'InfoNumtheor',
+  'InfoOptions',
+  'InfoPcSubgroup',
+  'Integers',
+  'NiceBasisFiltersInfo',
+  'Primes',
+  'Rationals',
+  'TableOfMarksComponents'
+]) | common_gap_functions
diff --git a/src/sage/libs/gap/gap_includes.pxd b/src/sage/libs/gap/gap_includes.pxd
index c3f4dcb..f62b24e 100644
--- a/src/sage/libs/gap/gap_includes.pxd
+++ b/src/sage/libs/gap/gap_includes.pxd
@@ -10,318 +10,152 @@
 ###############################################################################
 
 
-from .types cimport *
-
-cdef extern from "<gap/libgap.h>":
-    void libgap_initialize(int argc, char** argv)
-    ctypedef void(*libgap_gasman_callback_ptr)()
-    void libgap_set_gasman_callback(libgap_gasman_callback_ptr callback)
-    ctypedef void(*libgap_error_func_ptr)(char* msg)
-    void libgap_set_error_handler(libgap_error_func_ptr error_handler)
-    void libgap_call_error_handler()
-    void libgap_finalize()
-    void libgap_start_interaction(char* inputline)
-    char* libgap_get_output()
-    char* libgap_get_error()
-    void libgap_finish_interaction()
-    void libgap_mark_stack_bottom()
-    void libgap_enter()
-    void libgap_exit()
-
-cdef extern from "<gap/gap.h>":
-    void libGAP_ViewObjHandler(void*)
-    void libGAP_InitializeGap(int*, char** argv)
-    void libGAP_set_system_variables(char**, char**)
-    cdef libGAP_UInt libGAP_Last
-    cdef libGAP_UInt libGAP_Last2
-    cdef libGAP_UInt libGAP_Last3
-    cdef libGAP_ExecStatus libGAP_STATUS_END
-    cdef libGAP_ExecStatus libGAP_STATUS_RETURN_VAL
-    cdef libGAP_ExecStatus libGAP_STATUS_RETURN_VOID
-    cdef libGAP_ExecStatus libGAP_STATUS_TNM
-    cdef libGAP_ExecStatus libGAP_STATUS_QUIT
-    cdef libGAP_ExecStatus libGAP_STATUS_EOF
-    cdef libGAP_ExecStatus libGAP_STATUS_ERROR
-    cdef libGAP_ExecStatus libGAP_STATUS_QQUIT
+cdef extern from "<gap/system.h>":
+    ctypedef char Char
+    ctypedef int Int
+    ctypedef unsigned int UInt
+    ctypedef void* Obj
 
-cdef extern from "<gap/objects.h>":
-    bint libGAP_IS_MUTABLE_OBJ(libGAP_Obj obj)
-    bint libGAP_IS_COPYABLE_OBJ(libGAP_Obj obj)
-    libGAP_Obj libGAP_SHALLOW_COPY_OBJ(libGAP_Obj obj)
-    libGAP_Obj libGAP_CopyObj(libGAP_Obj obj, int mut)
-
-    bint libGAP_IS_INTOBJ(libGAP_Obj obj)
-    libGAP_Obj libGAP_INTOBJ_INT(libGAP_Int)
-    libGAP_Int libGAP_INT_INTOBJ(libGAP_Obj)
-    libGAP_UInt libGAP_TNUM_OBJ(libGAP_Obj obj)
-    char* libGAP_TNAM_OBJ(libGAP_Obj obj)
-    cdef int libGAP_FIRST_REAL_TNUM
-    cdef int libGAP_FIRST_CONSTANT_TNUM
-    cdef int libGAP_T_INT
-    cdef int libGAP_T_INTPOS
-    cdef int libGAP_T_INTNEG
-    cdef int libGAP_T_RAT
-    cdef int libGAP_T_CYC
-    cdef int libGAP_T_FFE
-    cdef int libGAP_T_PERM2
-    cdef int libGAP_T_PERM4
-    cdef int libGAP_T_BOOL
-    cdef int libGAP_T_CHAR
-    cdef int libGAP_T_FUNCTION
-    cdef int libGAP_T_FLAGS
-    cdef int libGAP_T_MACFLOAT
-    cdef int libGAP_T_RESERVED_BY_GAP
-    cdef int libGAP_LAST_CONSTANT_TNUM
-    cdef int libGAP_IMMUTABLE
-    cdef int libGAP_FIRST_IMM_MUT_TNUM
-    cdef int libGAP_FIRST_RECORD_TNUM
-    cdef int libGAP_T_PREC
-    cdef int libGAP_LAST_RECORD_TNUM
-    cdef int libGAP_FIRST_LIST_TNUM
-    cdef int libGAP_FIRST_PLIST_TNUM
-    cdef int libGAP_T_PLIST
-    cdef int libGAP_T_PLIST_NDENSE
-    cdef int libGAP_T_PLIST_DENSE
-    cdef int libGAP_T_PLIST_DENSE_NHOM
-    cdef int libGAP_T_PLIST_DENSE_NHOM_SSORT
-    cdef int libGAP_T_PLIST_DENSE_NHOM_NSORT
-    cdef int libGAP_T_PLIST_EMPTY
-    cdef int libGAP_T_PLIST_HOM
-    cdef int libGAP_T_PLIST_HOM_NSORT
-    cdef int libGAP_T_PLIST_HOM_SSORT
-    cdef int libGAP_T_PLIST_TAB
-    cdef int libGAP_T_PLIST_TAB_NSORT
-    cdef int libGAP_T_PLIST_TAB_SSORT
-    cdef int libGAP_T_PLIST_TAB_RECT
-    cdef int libGAP_T_PLIST_TAB_RECT_NSORT
-    cdef int libGAP_T_PLIST_TAB_RECT_SSORT
-    cdef int libGAP_T_PLIST_CYC
-    cdef int libGAP_T_PLIST_CYC_NSORT
-    cdef int libGAP_T_PLIST_CYC_SSORT
-    cdef int libGAP_T_PLIST_FFE
-    cdef int libGAP_LAST_PLIST_TNUM
-    cdef int libGAP_T_RANGE_NSORT
-    cdef int libGAP_T_RANGE_SSORT
-    cdef int libGAP_T_BLIST
-    cdef int libGAP_T_BLIST_NSORT
-    cdef int libGAP_T_BLIST_SSORT
-    cdef int libGAP_T_STRING
-    cdef int libGAP_T_STRING_NSORT
-    cdef int libGAP_T_STRING_SSORT
-    cdef int libGAP_LAST_LIST_TNUM
-    cdef int libGAP_LAST_IMM_MUT_TNUM
-    cdef int libGAP_FIRST_EXTERNAL_TNUM
-    cdef int libGAP_T_COMOBJ
-    cdef int libGAP_T_POSOBJ
-    cdef int libGAP_T_DATOBJ
-    cdef int libGAP_T_WPOBJ
-    cdef int libGAP_LAST_EXTERNAL_TNUM
-    cdef int libGAP_LAST_REAL_TNUM
-    cdef int libGAP_LAST_VIRTUAL_TNUM
-    cdef int libGAP_FIRST_COPYING_TNUM
-    cdef int libGAP_COPYING
-    cdef int libGAP_LAST_COPYING_TNUM
-    cdef int libGAP_FIRST_TESTING_TNUM
-    cdef int libGAP_TESTING
-    cdef int libGAP_LAST_TESTING_TNUM
-
-cdef extern from "<gap/read.h>":
-    void* libGAP_ReadEvalCommand(libGAP_Obj context, libGAP_UInt *dualSemicolon)
-    void* libGAP_ReadEvalFile()
-    void* libGAP_ReadEvalResult
-    bint libGAP_READ_ERROR()
-
-cdef extern from "<gap/scanner.h>":
-    void libGAP_ClearError()
-    libGAP_UInt libGAP_NrError
-    libGAP_UInt libGAP_Symbol
-    void libGAP_GetSymbol()
-    void libGAP_Match (libGAP_UInt symbol, char* msg, libGAP_UInt skipto)
-    int libGAP_S_ILLEGAL
-    int libGAP_S_IDENT
-    int libGAP_S_UNBIND
-    int libGAP_S_ISBOUND
-    int libGAP_S_TRYNEXT
-    int libGAP_S_INFO
-    int libGAP_S_ASSERT
-    int libGAP_S_SAVEWS
-    int libGAP_S_LOADWS
-    int libGAP_S_LBRACK
-    int libGAP_S_LBRACE
-    int libGAP_S_BLBRACK
-    int libGAP_S_BLBRACE
-    int libGAP_S_RBRACK
-    int libGAP_S_RBRACE
-    int libGAP_S_DOT
-    int libGAP_S_BDOT
-    int libGAP_S_LPAREN
-    int libGAP_S_RPAREN
-    int libGAP_S_COMMA
-    int libGAP_S_DOTDOT
-    int libGAP_S_COLON
-    int libGAP_S_PARTIALINT
-    int libGAP_S_INT
-    int libGAP_S_TRUE
-    int libGAP_S_FALSE
-    int libGAP_S_CHAR
-    int libGAP_S_STRING
-    int libGAP_S_PARTIALSTRING
-    int libGAP_S_REC
-    int libGAP_S_FUNCTION
-    int libGAP_S_LOCAL
-    int libGAP_S_END
-    int libGAP_S_MAPTO
-    int libGAP_S_MULT
-    int libGAP_S_DIV
-    int libGAP_S_MOD
-    int libGAP_S_POW
-    int libGAP_S_PLUS
-    int libGAP_S_MINUS
-    int libGAP_S_EQ
-    int libGAP_S_LT
-    int libGAP_S_GT
-    int libGAP_S_NE
-    int libGAP_S_LE
-    int libGAP_S_GE
-    int libGAP_S_IN
-    int libGAP_S_NOT
-    int libGAP_S_AND
-    int libGAP_S_OR
-    int libGAP_S_ASSIGN
-    int libGAP_S_IF
-    int libGAP_S_FOR
-    int libGAP_S_WHILE
-    int libGAP_S_REPEAT
-    int libGAP_S_THEN
-    int libGAP_S_ELIF
-    int libGAP_S_ELSE
-    int libGAP_S_FI
-    int libGAP_S_DO
-    int libGAP_S_OD
-    int libGAP_S_UNTIL
-    int libGAP_S_BREAK
-    int libGAP_S_RETURN
-    int libGAP_S_QUIT
-    int libGAP_S_QQUIT
-    int libGAP_S_CONTINUE
-    int libGAP_S_SEMICOLON
-    int libGAP_S_EOF
 
-cdef extern from "<gap/gvars.h>":
-    libGAP_UInt libGAP_GVarName(char* name)
-    void libGAP_AssGVar(libGAP_UInt gvar, libGAP_Obj val)
-    libGAP_Obj libGAP_VAL_GVAR(libGAP_UInt gvar)
-
-cdef extern from "<gap/string.h>":
-    char* libGAP_CSTR_STRING(libGAP_Obj list)
-    int libGAP_GET_LEN_STRING(libGAP_Obj list)
-    bint libGAP_IS_STRING(libGAP_Obj obj)
-    bint libGAP_IsStringConv(libGAP_Obj obj)
-    bint libGAP_ConvString(libGAP_Obj obj)
-    void libGAP_C_NEW_STRING(libGAP_Obj new_gap_string, int length, char* c_string)
+cdef extern from "<gap/ariths.h>":
+    Obj SUM(Obj, Obj)
+    Obj DIFF(Obj, Obj)
+    Obj PROD(Obj, Obj)
+    Obj QUO(Obj, Obj)
+    Obj POW(Obj, Obj)
+    Obj MOD(Obj, Obj)
+    bint EQ(Obj opL, Obj opR)
+    bint LT(Obj opL, Obj opR)
 
-cdef extern from "<gap/gasman.h>":
-    void libGAP_InitGlobalBag(libGAP_Obj* addr, char* cookie)
-    libGAP_Obj libGAP_NewBag(libGAP_UInt type, libGAP_UInt size)
-    void libGAP_CHANGED_BAG(libGAP_Obj bag)
-    void libGAP_MARK_BAG(libGAP_Obj bag)
-    bint libGAP_IS_MARKED_ALIVE(libGAP_Obj bag)
-    bint libGAP_IS_MARKED_DEAD(libGAP_Obj bag)
-    bint libGAP_IS_MARKED_HALFDEAD(libGAP_Obj bag)
-    cdef libGAP_UInt libGAP_NrAllBags
-    cdef libGAP_UInt libGAP_SizeAllBags
-    cdef libGAP_UInt libGAP_NrLiveBags
-    cdef libGAP_UInt libGAP_SizeLiveBags
-    cdef libGAP_UInt libGAP_NrDeadBags
-    cdef libGAP_UInt libGAP_SizeDeadBags
-    cdef libGAP_UInt libGAP_NrHalfDeadBags
-    libGAP_UInt libGAP_CollectBags(libGAP_UInt size, libGAP_UInt full)
-    void libGAP_CallbackForAllBags(void (*func)(libGAP_Obj))
-    char* libGAP_TNAM_BAG(libGAP_Obj obj)
-    libGAP_UInt libGAP_TNUM_BAG(libGAP_Obj)
-    libGAP_UInt libGAP_SIZE_BAG(libGAP_Obj)
-    void libGAP_CheckMasterPointers()
-    libGAP_Obj* libGAP_MptrBags
-    libGAP_Obj* libGAP_YoungBags
-    libGAP_Obj* libGAP_OldBags
-    libGAP_Obj* libGAP_AllocBags
-    libGAP_Obj* libGAP_MarkedBags
-    libGAP_Obj* libGAP_ChangedBags
-
-# in gasman.c but not declared in gasman.h
-cdef extern:
-    libGAP_Obj* libGAP_StopBags
-    libGAP_Obj* libGAP_EndBags
 
-cdef extern from "<gap/ariths.h>":
-    libGAP_Obj libGAP_SUM (libGAP_Obj, libGAP_Obj)
-    libGAP_Obj libGAP_DIFF(libGAP_Obj, libGAP_Obj)
-    libGAP_Obj libGAP_PROD(libGAP_Obj, libGAP_Obj)
-    libGAP_Obj libGAP_QUO(libGAP_Obj, libGAP_Obj)
-    libGAP_Obj libGAP_POW(libGAP_Obj, libGAP_Obj)
-    libGAP_Obj libGAP_MOD(libGAP_Obj, libGAP_Obj)
-    libGAP_Obj libGAP_CALL_0ARGS(libGAP_Obj f)              # 0 arguments
-    libGAP_Obj libGAP_CALL_1ARGS(libGAP_Obj f, libGAP_Obj a1)      # 1 argument
-    libGAP_Obj libGAP_CALL_2ARGS(libGAP_Obj f, libGAP_Obj a1, libGAP_Obj a2)
-    libGAP_Obj libGAP_CALL_3ARGS(libGAP_Obj f, libGAP_Obj a1, libGAP_Obj a2, libGAP_Obj a3)
-    libGAP_Obj libGAP_CALL_4ARGS(libGAP_Obj f, libGAP_Obj a1, libGAP_Obj a2, libGAP_Obj a3,
-                                 libGAP_Obj a4)
-    libGAP_Obj libGAP_CALL_5ARGS(libGAP_Obj f, libGAP_Obj a1, libGAP_Obj a2, libGAP_Obj a3,
-                                 libGAP_Obj a4, libGAP_Obj a5)
-    libGAP_Obj libGAP_CALL_6ARGS(libGAP_Obj f, libGAP_Obj a1, libGAP_Obj a2, libGAP_Obj a3,
-                                 libGAP_Obj a4, libGAP_Obj a5, libGAP_Obj a6)
-    libGAP_Obj libGAP_CALL_XARGS(libGAP_Obj f, libGAP_Obj args)   # more than 6 arguments
-    bint libGAP_EQ(libGAP_Obj opL, libGAP_Obj opR)
-    bint libGAP_LT(libGAP_Obj opL, libGAP_Obj opR)
+cdef extern from "<gap/bool.h>":
+    cdef Obj GAP_True "True"
+    cdef Obj GAP_False "False"
+
 
 cdef extern from "<gap/calls.h>":
-    bint libGAP_IS_FUNC(libGAP_Obj)
+    bint IS_FUNC(Obj)
+    Obj CALL_0ARGS(Obj f)              # 0 arguments
+    Obj CALL_1ARGS(Obj f, Obj a1)      # 1 argument
+    Obj CALL_2ARGS(Obj f, Obj a1, Obj a2)
+    Obj CALL_3ARGS(Obj f, Obj a1, Obj a2, Obj a3)
+    Obj CALL_4ARGS(Obj f, Obj a1, Obj a2, Obj a3, Obj a4)
+    Obj CALL_5ARGS(Obj f, Obj a1, Obj a2, Obj a3, Obj a4, Obj a5)
+    Obj CALL_6ARGS(Obj f, Obj a1, Obj a2, Obj a3, Obj a4, Obj a5, Obj a6)
+    Obj CALL_XARGS(Obj f, Obj args)   # more than 6 arguments
+
+
+cdef extern from "<gap/gasman.h>":
+    Obj NewBag "NewBag"(UInt type, UInt size)
+    void MarkBag(Obj bag)
+    UInt CollectBags(UInt size, UInt full)
+
+
+cdef extern from "<gap/gasman_intern.h>":
+    void CallbackForAllBags(void (*func)(Obj))
+
+
+cdef extern from "<gap/gvars.h>":
+    UInt GVarName "GVarName"(char* name)
+    void AssGVar "AssGVar"(UInt gvar, Obj val)
+
+
+cdef extern from "<gap/integer.h>":
+    Int IS_INT(Obj)
+
+
+cdef extern from "<gap/intobj.h>":
+    bint IS_INTOBJ(Obj obj)
+    Obj INTOBJ_INT(Int)
+    Int INT_INTOBJ(Obj)
+
+
+cdef extern from "<gap/io.h>":
+    UInt OpenOutputStream(Obj stream)
+    UInt CloseOutput()
+
+
+cdef extern from "<gap/libgap-api.h>":
+    ctypedef void (*CallbackFunc)()
+    void GAP_Initialize(int argc, char ** argv, char ** env,
+        CallbackFunc, CallbackFunc)
+    Obj GAP_EvalString(const char *) except *
+    Obj GAP_EvalStringNoExcept "GAP_EvalString"(const char *)
+    Obj GAP_ValueGlobalVariable(const char *)
+
+
+cdef extern from "<gap/libgap-api.h>" nogil:
+    cdef void GAP_EnterStack()
+    cdef void GAP_LeaveStack()
+    cdef int GAP_Enter() except 0
+    cdef void GAP_Leave()
+    cdef int GAP_Error_Setjmp() except 0
 
-cdef extern from "<gap/plist.h>":
-    libGAP_Obj libGAP_NEW_PLIST(int type, int len)
-    bint libGAP_IS_PLIST(libGAP_Obj lst)
-    int libGAP_LEN_PLIST(libGAP_Obj lst)
-    libGAP_Obj libGAP_ELM_PLIST(libGAP_Obj lst, int pos)
 
 cdef extern from "<gap/lists.h>":
-    void libGAP_UNB_LIST(libGAP_Obj lst, int pos)
-    bint libGAP_IS_LIST(libGAP_Obj lst)
-    int libGAP_LEN_LIST(libGAP_Obj lst)
-    libGAP_Obj libGAP_ELM_LIST(libGAP_Obj lst, int pos)
-    void libGAP_ASS_LIST(libGAP_Obj lst, int pos, libGAP_Obj elt)
+    bint IS_LIST(Obj lst)
+    int LEN_LIST(Obj lst)
+    Obj ELM_LIST(Obj lst, int pos)
+    Obj ELM0_LIST(Obj lst, int pos)
+    void ASS_LIST(Obj lst, int pos, Obj elt)
+
 
 cdef extern from "<gap/listfunc.h>":
-    void libGAP_AddList(libGAP_Obj list, libGAP_Obj obj)
-    void libGAP_AddPlist(libGAP_Obj list, libGAP_Obj obj)
+    void AddList(Obj list, Obj obj)
+
 
 cdef extern from "<gap/macfloat.h>":
-    bint libGAP_IS_MACFLOAT(libGAP_Obj obj)
-    double libGAP_VAL_MACFLOAT(libGAP_Obj obj)
+    double VAL_MACFLOAT(Obj obj)
+
+
+cdef extern from "<gap/objects.h>":
+    bint IS_MUTABLE_OBJ(Obj obj)
+    Obj SHALLOW_COPY_OBJ(Obj obj)
+    Obj CopyObj(Obj obj, int mut)
+
+    UInt SIZE_OBJ(Obj obj)
+    UInt TNUM_OBJ(Obj obj)
+    char* TNAM_OBJ(Obj obj)
+
+    cdef int T_INTPOS
+    cdef int T_INTNEG
+    cdef int T_RAT
+    cdef int T_CYC
+    cdef int T_FFE
+    cdef int T_PERM2
+    cdef int T_PERM4
+    cdef int T_BOOL
+    cdef int T_CHAR
+    cdef int T_FUNCTION
+    cdef int T_MACFLOAT
+    cdef int T_PLIST
+    cdef int T_PLIST_CYC
+    cdef int T_BLIST
+    cdef int T_STRING
+    cdef int T_COMOBJ
+    cdef int T_POSOBJ
+    cdef int T_DATOBJ
+    cdef int T_WPOBJ
 
-cdef extern from "<gap/records.h>":
-    char* libGAP_NAME_RNAM(libGAP_UInt rnam)
-    libGAP_UInt libGAP_RNamIntg(int i)
-    bint libGAP_IS_REC(libGAP_Obj obj)
-    libGAP_Obj libGAP_ELM_REC(libGAP_Obj rec, libGAP_UInt rnam)
-    libGAP_UInt libGAP_RNamName(libGAP_Char* name)
 
 cdef extern from "<gap/precord.h>":
-    libGAP_Obj libGAP_NEW_PREC(int len)
-    int libGAP_LEN_PREC(libGAP_Obj rec)
-    int libGAP_GET_RNAM_PREC(libGAP_Obj rec, int i)
-    libGAP_Obj libGAP_GET_ELM_PREC(libGAP_Obj rec, int i)
-    void libGAP_AssPRec(libGAP_Obj rec, libGAP_UInt rnam, libGAP_Obj val)
-    void libGAP_UnbPRec(libGAP_Obj rec, libGAP_UInt rnam)
-    bint libGAP_IsbPRec(libGAP_Obj rec, libGAP_UInt rnam)
-    libGAP_Obj libGAP_ElmPRec(libGAP_Obj rec, libGAP_UInt rnam)
-
-cdef extern from "<gap/cyclotom.h>":
-    pass
+    Obj NEW_PREC(int len)
+    int LEN_PREC(Obj rec)
+    int GET_RNAM_PREC(Obj rec, int i)
+    Obj GET_ELM_PREC(Obj rec, int i)
+    void AssPRec(Obj rec, UInt rnam, Obj val)
 
-cdef extern from "<gap/bool.h>":
-    cdef libGAP_Obj libGAP_True
-    cdef libGAP_Obj libGAP_False
 
-cdef extern from "<gap/vars.h>":
-     cdef int libGAP_T_LVARS
-     libGAP_Obj libGAP_BottomLVars
+cdef extern from "<gap/records.h>":
+    char* NAME_RNAM(UInt rnam)
+    bint IS_REC(Obj obj)
+    Obj ELM_REC(Obj rec, UInt rnam)
+    UInt RNamName(Char* name)
+
+
+cdef extern from "<gap/stringobj.h>":
+    char* CSTR_STRING(Obj list)
+    bint IS_STRING(Obj obj)
+    bint IsStringConv(Obj obj)
+    Obj NEW_STRING(Int)
+    void C_NEW_STRING(Obj new_gap_string, int length, char* c_string)
diff --git a/src/sage/libs/gap/libgap.pyx b/src/sage/libs/gap/libgap.pyx
index 8d2fc46..cb7b2cb 100644
--- a/src/sage/libs/gap/libgap.pyx
+++ b/src/sage/libs/gap/libgap.pyx
@@ -160,53 +160,10 @@ using the recursive expansion of the
 Using the libGAP C library from Cython
 ======================================
 
-The lower-case ``libgap_foobar`` functions are ones that we added to
-make the libGAP C shared library. The ``libGAP_foobar`` methods are
-the original GAP methods simply prefixed with the string
-``libGAP_``. The latter were originally not designed to be in a
-library, so some care needs to be taken to call them.
-
-In particular, you must call ``libgap_mark_stack_bottom()`` in every
-function that calls into the libGAP C functions. The reason is that
-the GAP memory manager will automatically keep objects alive that are
-referenced in local (stack-allocated) variables. While convenient,
-this requires to look through the stack to find anything that looks
-like an address to a memory bag. But this requires vigilance against
-the following pattern::
-
-    cdef f()
-      libgap_mark_stack_bottom()
-      libGAP_function()
-
-    cdef g()
-      libgap_mark_stack_bottom();
-      f()                #  f() changed the stack bottom marker
-      libGAP_function()  #  boom
-
-The solution is to re-order ``g()`` to first call ``f()``. In order to
-catch this error, it is recommended that you wrap calls into libGAP in
-``libgap_enter`` / ``libgap_exit`` blocks and not call
-``libgap_mark_stack_bottom`` manually. So instead, always write
-
-    cdef f()
-      libgap_enter()
-      libGAP_function()
-      libgap_exit()
-
-    cdef g()
-      f()
-      libgap_enter()
-      libGAP_function()
-      libgap_exit()
-
-If you accidentally call ``libgap_enter()`` twice then an error
-message is printed to help you debug this::
-
-    sage: from sage.libs.gap.util import error_enter_libgap_block_twice
-    sage: error_enter_libgap_block_twice()
-    Traceback (most recent call last):
-    ...
-    RuntimeError: Entered a critical block twice
+.. TODO:: Update the following text
+
+   We are using libgap API provided by the GAP project since
+   GAP 4.10.
 
 AUTHORS:
 
@@ -215,6 +172,8 @@ AUTHORS:
     almost complete rewrite; first usable version.
   - Volker Braun (2012-08-28, GAP/Singular workshop): update to
     gap-4.5.5, make it ready for public consumption.
+  - Dima Pasechnik (2018-09-18, GAP Days): started the port to native
+    libgap API
 """
 
 ###############################################################################
@@ -254,6 +213,8 @@ AUTHORS:
 
 from __future__ import print_function, absolute_import
 
+from pprint import pprint
+
 from .gap_includes cimport *
 from .util cimport *
 from .element cimport *
@@ -263,23 +224,20 @@ from sage.structure.parent cimport Parent
 from sage.structure.element cimport ModuleElement, RingElement, Vector
 from sage.rings.all import ZZ
 from sage.misc.cachefunc import cached_method
-from sage.misc.superseded import deprecated_function_alias
+from sage.misc.superseded import deprecated_function_alias, deprecation
 
 
 ############################################################################
 ### Debugging ##############################################################
 ############################################################################
 
-cdef void report(libGAP_Obj bag):
-    print(libGAP_TNAM_OBJ(bag), <int>libGAP_TNUM_BAG(bag), <int>libGAP_SIZE_BAG(bag))
 
-
-cdef void print_gasman_objects():
-    libgap_enter()
-    libGAP_CallbackForAllBags(report)
-    libgap_exit()
+cdef void report(Obj bag):
+    print(TNAM_OBJ(bag),  <int>SIZE_OBJ(bag))
 
 
+cdef void print_gasman_objects():
+    CallbackForAllBags(report)
 
 
 from sage.misc.lazy_import import is_during_startup
@@ -370,7 +328,7 @@ class Gap(Parent):
             return make_GapElement_Record(self, make_gap_record(x))
         elif isinstance(x, bool):
             # attention: must come before int
-            return make_GapElement_Boolean(self, libGAP_True if x else libGAP_False)
+            return make_GapElement_Boolean(self, GAP_True if x else GAP_False)
         elif isinstance(x, int):
             return make_GapElement_Integer(self, make_gap_integer(x))
         elif isinstance(x, basestring):
@@ -443,9 +401,18 @@ class Gap(Parent):
             sage: libgap.eval('"string"')
             "string"
         """
+        cdef GapElement elem
+
         if not isinstance(gap_command, basestring):
             gap_command = str(gap_command._gap_init_())
-        return make_any_gap_element(self, gap_eval(gap_command))
+
+        elem = make_any_gap_element(self, gap_eval(gap_command))
+
+        # If the element is NULL just return None instead
+        if elem.value == NULL:
+            return None
+
+        return elem
 
     @cached_method
     def function_factory(self, function_name):
@@ -520,9 +487,11 @@ class Gap(Parent):
             ...
             ValueError: libGAP: Error, VAL_GVAR: No value bound to FooBar
         """
+        is_readonlyglobal = self.function_factory('IsReadOnlyGlobal')
         make_readwrite = self.function_factory('MakeReadWriteGlobal')
         unbind_global = self.function_factory('UnbindGlobal')
-        make_readwrite(variable)
+        if is_readonlyglobal(variable):
+            make_readwrite(variable)
         unbind_global(variable)
 
     def get_global(self, variable):
@@ -634,7 +603,6 @@ class Gap(Parent):
             <class 'sage.libs.gap.libgap.Gap'>
         """
         initialize()
-        libgap_set_gasman_callback(gasman_callback)
         from sage.rings.integer_ring import ZZ
         Parent.__init__(self, base=ZZ)
 
@@ -663,12 +631,13 @@ class Gap(Parent):
            sage: 'OctaveAlgebra' in dir(libgap)
            True
         """
-        from sage.libs.gap.gap_functions import common_gap_functions
-        return dir(self.__class__) + list(common_gap_functions)
+        from sage.libs.gap.gap_globals import common_gap_globals
+        return dir(self.__class__) + sorted(common_gap_globals)
 
     def __getattr__(self, name):
         r"""
-        The attributes of the Gap object are the Gap functions.
+        The attributes of the Gap object are the Gap functions, and in some
+        cases other global variables from GAP.
 
         INPUT:
 
@@ -677,32 +646,52 @@ class Gap(Parent):
 
         OUTPUT:
 
-        A :class:`GapElement_Function`. A ``AttributeError`` is raised
-        if there is no such function.
+        A :class:`GapElement`. A ``AttributeError`` is raised
+        if there is no such function or global variable.
 
         EXAMPLES::
 
             sage: libgap.List
             <Gap function "List">
+            sage: libgap.GlobalRandomSource
+            <RandomSource in IsGlobalRandomSource>
         """
         if name in dir(self.__class__):
             return getattr(self.__class__, name)
+
         from sage.libs.gap.gap_functions import common_gap_functions
+        from sage.libs.gap.gap_globals import common_gap_globals
         if name in common_gap_functions:
-            f = make_GapElement_Function(self, gap_eval(str(name)))
-            assert f.is_function()
-            self.__dict__[name] = f
-            return f
+            g = make_GapElement_Function(self, gap_eval(name))
+            assert g.is_function()
+        elif name in common_gap_globals:
+            g = make_any_gap_element(self, gap_eval(name))
         else:
-            raise AttributeError('No such attribute: '+name+'.')
+            raise AttributeError(f'No such attribute: {name}.')
+
+        self.__dict__[name] = g
+        return g
 
     def show(self):
         """
-        Print statistics about the GAP owned object list
+        Return statistics about the GAP owned object list
+
+        This includes the total memory allocated by GAP as returned by
+        ``libgap.eval('TotalMemoryAllocated()'), as well as garbage collection
+        / object count statistitics as returned by
+        ``libgap.eval('GasmanStatistics')``, and finally the total number of
+        GAP objects held by Sage as :class:`~sage.libs.gap.element.GapElement`
+        instances.
 
-        Slight complication is that we want to do it without accessing
-        libgap objects, so we don't create new GapElements as a side
-        effect.
+        The value ``livekb + deadkb`` will roughly equal the total memory
+        allocated for GAP objects (see
+        ``libgap.eval('TotalMemoryAllocated()')``).
+
+        .. note::
+
+            Slight complication is that we want to do it without accessing
+            libgap objects, so we don't create new GapElements as a side
+            effect.
 
         EXAMPLES::
 
@@ -710,15 +699,25 @@ class Gap(Parent):
             sage: b = libgap(456)
             sage: c = libgap(789)
             sage: del b
-            sage: libgap.show() # random output
-            11 LibGAP elements currently alive
-            rec( full := rec( cumulative := 122, deadbags := 9,
-            deadkb := 0, freekb := 7785, livebags := 304915,
-            livekb := 47367, time := 33, totalkb := 68608 ),
-            nfull := 3, npartial := 14 )
-        """
-        print('{} LibGAP elements currently alive'.format(self.count_GAP_objects()))
-        print(self.eval('GasmanStatistics()'))
+            sage: libgap.collect()
+            sage: libgap.show()  # random output
+            {'gasman_stats': {'full': {'cumulative': 110,
+               'deadbags': 321400,
+               'deadkb': 12967,
+               'freekb': 15492,
+               'livebags': 396645,
+               'livekb': 37730,
+               'time': 110,
+               'totalkb': 65536},
+              'nfull': 1,
+              'npartial': 1},
+             'nelements': 23123,
+             'total_alloc': 3234234}
+        """
+        d = {'nelements': self.count_GAP_objects()}
+        d['total_alloc'] = self.eval('TotalMemoryAllocated()').sage()
+        d['gasman_stats'] = self.eval('GasmanStatistics()').sage()
+        return d
 
     def count_GAP_objects(self):
         """
@@ -734,57 +733,19 @@ class Gap(Parent):
             sage: libgap.count_GAP_objects()   # random output
             5
         """
-        return sum([1 for obj in get_owned_objects()])
+        return len(get_owned_objects())
 
     def mem(self):
         """
-        Return information about libGAP memory usage
+        Return information about GAP memory usage
 
-        The GAP workspace is partitioned into 5 pieces (see gasman.c
-        in the GAP sources for more details):
-
-        * The **masterpointer area**  contains  all the masterpointers  of  the bags.
-
-        * The **old bags area** contains the bodies of all the  bags that survived at
-          least one  garbage collection.  This area is  only  scanned for dead bags
-          during a full garbage collection.
-
-        * The **young bags area** contains the bodies of all  the bags that have been
-          allocated since the  last garbage collection.  This  area is scanned  for
-          dead  bags during  each garbage  collection.
-
-        * The **allocation area** is the storage  that is available for allocation of
-          new bags.  When a new bag is allocated the storage for  the body is taken
-          from  the beginning of   this area,  and  this  area  is  correspondingly
-          reduced.   If  the body does not   fit in the  allocation  area a garbage
-          collection is  performed.
-
-        * The **unavailable  area** is  the free  storage that  is not  available for
-          allocation.
-
-        OUTPUT:
-
-        This function returns a tuple containing 5 integers. Each is
-        the size (in bytes) of the five partitions of the
-        workspace. This will potentially change after each GAP garbage
-        collection.
-
-        EXAMPLES::
-
-            sage: libgap.collect()
-            sage: libgap.mem()   # random output
-            (1048576, 6706782, 0, 960930, 0)
-
-            sage: libgap.FreeGroup(3)
-            <free group on the generators [ f1, f2, f3 ]>
-            sage: libgap.mem()   # random output
-            (1048576, 6706782, 47571, 913359, 0)
-
-            sage: libgap.collect()
-            sage: libgap.mem()   # random output
-            (1048576, 6734785, 0, 998463, 0)
+        This method is deprecated and is a no-op.  Use :meth:`Gap.show` to
+        display memory-usage and bag count statistics from GASMAN.
         """
-        return memory_usage()
+
+        deprecation(22626, 'this functionality is not supported by GAP; use '
+                           'libgap.show() for GAP memory usage statistics')
+        return (0, 0, 0, 0, 0)
 
     def collect(self):
         """
@@ -796,9 +757,7 @@ class Gap(Parent):
             sage: del a
             sage: libgap.collect()
         """
-        libgap_enter()
-        rc = libGAP_CollectBags(0, 1)
-        libgap_exit()
+        rc = CollectBags(0, 1)
         if rc != 1:
             raise RuntimeError('Garbage collection failed.')
 
diff --git a/src/sage/libs/gap/operations.py b/src/sage/libs/gap/operations.py
index 92ffc3d..f28b4ab 100644
--- a/src/sage/libs/gap/operations.py
+++ b/src/sage/libs/gap/operations.py
@@ -11,6 +11,7 @@ lists all GAP operations for which ``Operation(x, ...)`` is defined.
 
 import re
 import string
+
 from sage.structure.sage_object import SageObject
 from sage.libs.gap.libgap import libgap
 
@@ -18,6 +19,7 @@ Length = libgap.function_factory('Length')
 FlagsType = libgap.function_factory('FlagsType')
 TypeObj = libgap.function_factory('TypeObj')
 IS_SUBSET_FLAGS = libgap.function_factory('IS_SUBSET_FLAGS')
+GET_OPER_FLAGS = libgap.function_factory('GET_OPER_FLAGS')
 OPERATIONS = libgap.get_global('OPERATIONS')
 NameFunction = libgap.function_factory('NameFunction')
 
@@ -74,7 +76,7 @@ class OperationInspector(SageObject):
 
             sage: from sage.libs.gap.operations import OperationInspector
             sage: x = OperationInspector(libgap(123))
-            sage: x.obj
+            sage: print(x.obj)
             123
         """
         return self._obj
@@ -95,20 +97,12 @@ class OperationInspector(SageObject):
             sage: Unknown in x.operations()
             True
         """
-        result = []
-        for i in range(len(OPERATIONS) // 2):
-            match = False
-            for flag_list in OPERATIONS[2*i + 1]:
-                if Length(flag_list) == 0:
-                    continue
-                first_flag = flag_list[0]
-                if IS_SUBSET_FLAGS(self.flags, first_flag):
-                    match = True
-                    break
-            if match:
-                op = OPERATIONS[2*i]
-                result.append(op)
-        return result
+        def mfi(o):
+            filts = GET_OPER_FLAGS(o)
+            return any(all(IS_SUBSET_FLAGS(self.flags, fl) for fl in fls)
+                       for fls in filts)
+
+        return filter(mfi, OPERATIONS)
 
     def op_names(self):
         """
diff --git a/src/sage/libs/gap/sage.gaprc b/src/sage/libs/gap/sage.gaprc
new file mode 100644
index 00000000..17613fa
--- /dev/null
+++ b/src/sage/libs/gap/sage.gaprc
@@ -0,0 +1,12 @@
+# This file is run by Sage when initializing libgap via GAP_Initialize, and may
+# contain bug fixes/workarounds and/or any Sage-specific patches necessary for
+# Sage's libgap interface.
+
+if GAPInfo.CommandLineOptions.norepl then
+    # GAP 4.10.0 has a bug that an interactive session will be started
+    # even if --norepl was set; see https://github.com/gap-system/gap/pull/2840
+    # To work around this we redefine the SESSION function to a no-op
+    MAKE_READ_WRITE_GLOBAL("SESSION");
+    UNBIND_GLOBAL("SESSION");
+    BIND_GLOBAL("SESSION", function() end);
+fi;
diff --git a/src/sage/libs/gap/saved_workspace.py b/src/sage/libs/gap/saved_workspace.py
index 3cb8fd3..ad5adec 100644
--- a/src/sage/libs/gap/saved_workspace.py
+++ b/src/sage/libs/gap/saved_workspace.py
@@ -9,7 +9,6 @@ workspaces.
 import os
 import glob
 from sage.env import GAP_ROOT_DIR
-from sage.interfaces.gap import GAP_BINARY
 from sage.interfaces.gap_workspace import gap_workspace_file
 
 
@@ -33,7 +32,7 @@ def timestamp():
     libgap_dir = os.path.dirname(__file__)
     libgap_files = glob.glob(os.path.join(libgap_dir, '*'))
     gap_packages = glob.glob(os.path.join(GAP_ROOT_DIR, 'pkg', '*'))
-    files = libgap_files + [GAP_BINARY] + gap_packages
+    files = libgap_files + gap_packages
     if len(files) == 0:
         print('Unable to find LibGAP files.')
         return float('inf')
diff --git a/src/sage/libs/gap/types.pxd b/src/sage/libs/gap/types.pxd
deleted file mode 100644
index dcf5003..00000000
--- a/src/sage/libs/gap/types.pxd
+++ /dev/null
@@ -1,26 +0,0 @@
-###############################################################################
-#       Copyright (C) 2009, William Stein <wstein@gmail.com>
-#       Copyright (C) 2012, Volker Braun <vbraun.name@gmail.com>
-#
-#   Distributed under the terms of the GNU General Public License (GPL)
-#   as published by the Free Software Foundation; either version 2 of
-#   the License, or (at your option) any later version.
-#                   http://www.gnu.org/licenses/
-###############################################################################
-
-
-cdef extern from "<gap/system.h>":
-    ctypedef char libGAP_Char
-    ctypedef int libGAP_Int
-    ctypedef unsigned char libGAP_UChar
-
-cdef extern from "<gap/code.h>":
-    ctypedef unsigned int libGAP_Stat
-    ctypedef libGAP_Stat* libGAP_PtrBody
-
-cdef extern from "<gap/gap.h>":
-    ctypedef unsigned int libGAP_UInt
-    ctypedef void* libGAP_ExecStatus
-
-cdef extern from "<gap/objects.h>":
-    ctypedef void* libGAP_Obj
diff --git a/src/sage/libs/gap/util.pxd b/src/sage/libs/gap/util.pxd
index 2a82834..d2ce2d0 100644
--- a/src/sage/libs/gap/util.pxd
+++ b/src/sage/libs/gap/util.pxd
@@ -8,25 +8,24 @@
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from .types cimport libGAP_Obj
-
+from .gap_includes cimport Obj
 
 ############################################################################
 ### Hooking into the GAP memory management #################################
 ############################################################################
 
 cdef class ObjWrapper(object):
-    cdef libGAP_Obj value
+    cdef Obj value
 
-cdef ObjWrapper wrap_obj(libGAP_Obj obj)
+cdef ObjWrapper wrap_obj(Obj obj)
 
 # returns the refcount dictionary for debugging purposes
 cpdef get_owned_objects()
 
 # Reference count GAP objects that you want to prevent from being
 # garbage collected
-cdef void reference_obj(libGAP_Obj obj)
-cdef void dereference_obj(libGAP_Obj obj)
+cdef void reference_obj(Obj obj)
+cdef void dereference_obj(Obj obj)
 
 # callback from the GAP memory manager so we can mark all_gap_elements.values()
 cdef void gasman_callback()
@@ -44,12 +43,4 @@ cdef initialize()
 ############################################################################
 
 # Evaluate a string
-cdef libGAP_Obj gap_eval(str gap_string) except? NULL
-
-
-############################################################################
-### Debug functions ########################################################
-############################################################################
-
-# Return details of the GAP memory pool
-cpdef memory_usage()
+cdef Obj gap_eval(str gap_string) except? NULL
diff --git a/src/sage/libs/gap/util.pyx b/src/sage/libs/gap/util.pyx
index 5ff6710..5e2805d 100644
--- a/src/sage/libs/gap/util.pyx
+++ b/src/sage/libs/gap/util.pyx
@@ -14,24 +14,33 @@ Utility functions for libGAP
 
 from __future__ import print_function, absolute_import
 
-import os.path
+import os
+import signal
+import warnings
 
-from cpython.exc cimport PyErr_SetObject
+from libc.string cimport strcpy, strlen
+
+from cpython.exc cimport PyErr_SetObject, PyErr_Occurred, PyErr_Fetch
 from cpython.object cimport Py_LT, Py_LE, Py_EQ, Py_NE, Py_GT, Py_GE
+from cpython.ref cimport PyObject
+from cysignals.memory cimport sig_malloc
+from cysignals.pysignals import changesignal
 from cysignals.signals cimport sig_on, sig_off, sig_error
 
+import sage.env
+
 from .gap_includes cimport *
 from .element cimport *
 from sage.cpython.string import FS_ENCODING
 from sage.cpython.string cimport str_to_bytes, char_to_str
 from sage.interfaces.gap_workspace import prepare_workspace_dir
-from sage.env import SAGE_LOCAL, GAP_ROOT_DIR
 
 
 ############################################################################
 ### Hooking into the GAP memory management #################################
 ############################################################################
 
+
 cdef class ObjWrapper(object):
     """
     Wrapper for GAP master pointers
@@ -47,7 +56,7 @@ cdef class ObjWrapper(object):
 
     def __richcmp__(ObjWrapper self, ObjWrapper other, int op):
         r"""
-        Comparison wrapped libGAP_Obj.
+        Comparison wrapped Obj.
 
         INPUT:
 
@@ -68,8 +77,8 @@ cdef class ObjWrapper(object):
             True
         """
         cdef result
-        cdef libGAP_Obj self_value = self.value
-        cdef libGAP_Obj other_value = other.value
+        cdef Obj self_value = self.value
+        cdef Obj other_value = other.value
         if op == Py_LT:
             return self_value < other_value
         elif op == Py_LE:
@@ -99,7 +108,7 @@ cdef class ObjWrapper(object):
         return <int>(self.value)
 
 
-cdef ObjWrapper wrap_obj(libGAP_Obj obj):
+cdef ObjWrapper wrap_obj(Obj obj):
     """
     Constructor function for :class:`ObjWrapper`
     """
@@ -109,8 +118,13 @@ cdef ObjWrapper wrap_obj(libGAP_Obj obj):
 
 
 # a dictionary to keep all GAP elements
+# needed for GASMAN callbacks
+#
 cdef dict owned_objects_refcount = dict()
 
+#
+# used in Sage's libgap.Gap.count_GAP_objects
+#
 cpdef get_owned_objects():
     """
     Helper to access the refcount dictionary from Python code
@@ -118,19 +132,20 @@ cpdef get_owned_objects():
     return owned_objects_refcount
 
 
-cdef void reference_obj(libGAP_Obj obj):
+cdef void reference_obj(Obj obj):
     """
     Reference ``obj``
     """
     cdef ObjWrapper wrapped = wrap_obj(obj)
     global owned_objects_refcount
+#    print("reference_obj called "+ crepr(obj) +"\n")
     if wrapped in owned_objects_refcount:
         owned_objects_refcount[wrapped] += 1
     else:
         owned_objects_refcount[wrapped] = 1
 
 
-cdef void dereference_obj(libGAP_Obj obj):
+cdef void dereference_obj(Obj obj):
     """
     Reference ``obj``
     """
@@ -147,7 +162,7 @@ cdef void gasman_callback():
     """
     global owned_objects_refcount
     for obj in owned_objects_refcount:
-        libGAP_MARK_BAG((<ObjWrapper>obj).value)
+        MarkBag((<ObjWrapper>obj).value)
 
 
 
@@ -157,25 +172,6 @@ cdef void gasman_callback():
 ### Initialization of libGAP ###############################################
 ############################################################################
 
-def _guess_gap_root():
-    """
-    Used as a fallback to determine gapdir if if GAP_ROOT_DIR is undefined or
-    pointing to the wrong location.
-
-    EXAMPLES::
-
-        sage: from sage.libs.gap.util import _guess_gap_root
-        sage: _guess_gap_root()
-        The gap-4.5.5.spkg (or later) seems to be not installed!
-        ...
-    """
-    print('The gap-4.5.5.spkg (or later) seems to be not installed!')
-    gap_sh = open(os.path.join(SAGE_LOCAL, 'bin', 'gap')).read().splitlines()
-    gapdir = next(dir for dir in gap_sh if dir.strip().startswith('GAP_DIR'))
-    gapdir = gapdir.split('"')[1]
-    gapdir = gapdir.replace('$SAGE_LOCAL', SAGE_LOCAL)
-    return gapdir
-
 def gap_root():
     """
     Find the location of the GAP root install which is stored in the gap
@@ -187,17 +183,68 @@ def gap_root():
         sage: gap_root()   # random output
         '/home/vbraun/opt/sage-5.3.rc0/local/gap/latest'
     """
-    try:
-        if os.path.exists(GAP_ROOT_DIR):
-            return GAP_ROOT_DIR
-    except TypeError:
-        raise RuntimeError('The GAP_ROOT_DIR environment variable is set to an invalid path: "{}"'.format(GAP_ROOT_DIR))
+    if os.path.exists(sage.env.GAP_ROOT_DIR):
+        return sage.env.GAP_ROOT_DIR
 
-    return _guess_gap_root()
+    # Attempt to figure out the appropriate GAP_ROOT by reading the
+    # local/bin/gap shell script; this is an ugly hack that exists for
+    # historical reasons; the best approach to setting where Sage looks for
+    # the appropriate GAP_ROOT is to set the GAP_ROOT_DIR variable
+    SAGE_LOCAL = sage.env.SAGE_LOCAL
+    gap_sh = open(os.path.join(SAGE_LOCAL, 'bin', 'gap')).read().splitlines()
+    gapdir = filter(lambda dir:dir.strip().startswith('GAP_ROOT'), gap_sh)[0]
+    gapdir = gapdir.split('"')[1]
+    gapdir = gapdir.replace('$SAGE_LOCAL', SAGE_LOCAL)
+    return gapdir
 
 
 # To ensure that we call initialize_libgap only once.
 cdef bint _gap_is_initialized = False
+cdef extern char **environ
+
+
+cdef char* _reset_error_output_cmd = """\
+libgap_errout := "";
+MakeReadWriteGlobal("ERROR_OUTPUT");
+ERROR_OUTPUT := OutputTextString(libgap_errout, false);
+MakeReadOnlyGlobal("ERROR_OUTPUT");
+"""
+
+cdef char* _close_error_output_cmd = """\
+CloseStream(ERROR_OUTPUT);
+MakeReadWriteGlobal("ERROR_OUTPUT");
+ERROR_OUTPUT := "*errout*";
+MakeReadOnlyGlobal("ERROR_OUTPUT");
+MakeImmutable(libgap_errout);
+"""
+
+
+cdef char** copy_environ(char** env):
+    """
+    Make a copy of the environment block given by ``env``.
+
+    Returns a pointer to the copy, which is the caller's responsibility to
+    free.
+    """
+
+    cdef char** env_copy
+    cdef int envc = 0;
+    cdef int idx
+    cdef size_t size
+
+    while env[envc]:
+        envc += 1
+
+    env_copy = <char**>sig_malloc((envc + 1) * sizeof(char*))
+
+    for idx in range(envc):
+        size = strlen(env[idx]) + 1
+        env_copy[idx] = <char*>sig_malloc(size)
+        strcpy(env_copy[idx], env[idx])
+
+    env_copy[envc] = NULL
+    return env_copy
+
 
 cdef initialize():
     """
@@ -209,13 +256,14 @@ cdef initialize():
         sage: libgap(123)   # indirect doctest
         123
     """
-    global _gap_is_initialized
+    global _gap_is_initialized, environ
     if _gap_is_initialized: return
 
     # Define argv and environ variables, which we will pass in to
     # initialize GAP. Note that we must pass define the memory pool
     # size!
-    cdef char* argv[14]
+    cdef char** env
+    cdef char* argv[16]
     argv[0] = "sage"
     argv[1] = "-l"
     s = str_to_bytes(gap_root(), FS_ENCODING, "surrogateescape")
@@ -232,36 +280,56 @@ cdef initialize():
     argv[8] = "64m"
 
     argv[9] = "-q"    # no prompt!
-    argv[10] = "-T"    # no debug loop
-    argv[11] = NULL
-    cdef int argc = 11   # argv[argc] must be NULL
+    argv[10] = "-E"   # don't use readline as this will interfere with Python
+    argv[11] = "--nointeract"  # Implies -T
+
+    cdef int argc = 12   # argv[argc] must be NULL
 
     from .saved_workspace import workspace
     workspace, workspace_is_up_to_date = workspace()
     ws = str_to_bytes(workspace, FS_ENCODING, "surrogateescape")
     if workspace_is_up_to_date:
-        argv[11] = "-L"
-        argv[12] = ws
-        argv[13] = NULL
-        argc = 13
+        argv[argc] = "-L"
+        argv[argc + 1] = ws
+        argc += 2
+
+    # Get the path to the sage.gaprc file and check that it exists
+    sage_gaprc = os.path.join(os.path.dirname(__file__), 'sage.gaprc')
+    if not os.path.exists(sage_gaprc):
+        warnings.warn(f"Sage's GAP initialization file {sage_gaprc} is "
+                       "is missing; some functionality may be limited")
+    else:
+        sage_gaprc = str_to_bytes(sage_gaprc, FS_ENCODING, "surrogateescape")
+        argv[argc] = sage_gaprc
+        argc += 1
+
+    argv[argc] = NULL
+
+    env = copy_environ(environ)
 
     # Initialize GAP and capture any error messages
     # The initialization just prints error and does not use the error handler
-    libgap_start_interaction('')
-    libgap_initialize(argc, argv)
-    gap_error_msg = char_to_str(libgap_get_output())
-    libgap_finish_interaction()
-    if gap_error_msg:
-        raise RuntimeError('libGAP initialization failed\n' + gap_error_msg)
+    sig_on()
+    try:
+        with changesignal(signal.SIGCHLD, signal.SIG_DFL), \
+                changesignal(signal.SIGINT, signal.SIG_DFL):
+            # Need to save/restore current SIGINT handling since GAP_Initialize
+            # currently clobbers it; it doesn't matter what we set SIGINT to
+            # temporarily.
+            GAP_Initialize(argc, argv, env, &gasman_callback,
+                           &error_handler)
+    except RuntimeError as msg:
+        raise RuntimeError('libGAP initialization failed\n' + msg)
+    finally:
+        sig_off()
 
-    # The error handler is called if a GAP evaluation fails, e.g. 1/0
-    libgap_set_error_handler(&error_handler)
+    # Set the ERROR_OUTPUT global in GAP to an output stream in which to
+    # receive error output
+    GAP_EvalString(_reset_error_output_cmd)
 
     # Prepare global GAP variable to hold temporary GAP objects
     global reference_holder
-    libgap_enter()
-    reference_holder = libGAP_GVarName("$SAGE_libgap_reference_holder")
-    libgap_exit()
+    reference_holder = GVarName("$SAGE_libgap_reference_holder")
 
     # Finished!
     _gap_is_initialized = True
@@ -279,7 +347,7 @@ cdef initialize():
 ### Evaluate string in GAP #################################################
 ############################################################################
 
-cdef libGAP_Obj gap_eval(str gap_string) except? NULL:
+cdef Obj gap_eval(str gap_string) except? NULL:
     r"""
     Evaluate a string in GAP.
 
@@ -290,79 +358,109 @@ cdef libGAP_Obj gap_eval(str gap_string) except? NULL:
     OUTPUT:
 
     The resulting GAP object or NULL+Python Exception in case of error.
+    The result object may also be NULL without a Python exception set for
+    statements that do not return a value.
 
     EXAMPLES::
 
         sage: libgap.eval('if 4>3 then\nPrint("hi");\nfi')
-        NULL
         sage: libgap.eval('1+1')   # testing that we have successfully recovered
         2
 
         sage: libgap.eval('if 4>3 thenPrint("hi");\nfi')
         Traceback (most recent call last):
         ...
-        ValueError: libGAP: Syntax error: then expected
+        ValueError: libGAP: Syntax error: then expected in stream:1
         if 4>3 thenPrint("hi");
-        fi;
-                       ^
+               ^^^^^^^^^
         sage: libgap.eval('1+1')   # testing that we have successfully recovered
         2
 
     TESTS:
 
-    Check that we fail gracefully if this is called within
-    ``libgap_enter()``::
+    A bad eval string that results in multiple statement evaluations by GAP
+    and hence multiple errors should still result in a single exception
+    with a message capturing all errors that occurrer::
 
-        sage: cython('''
-        ....: # distutils: libraries = gap
-        ....: from sage.libs.gap.gap_includes cimport libgap_enter
-        ....: libgap_enter()
-        ....: ''')
-        sage: libgap.eval('1+1')
+        sage: libgap.eval('Complex Field with 53 bits of precision;')
         Traceback (most recent call last):
         ...
-        ValueError: libGAP: Entered a critical block twice
+        ValueError: libGAP: Error, Variable: 'Complex' must have a value
+        Syntax error: ; expected in stream:1
+        Complex Field with 53 bits of precision;;
+         ^^^^^^^^^^^^
+        Error, Variable: 'with' must have a value
+        Syntax error: ; expected in stream:1
+        Complex Field with 53 bits of precision;;
+         ^^^^^^^^^^^^^^^^^^^^
+        Error, Variable: 'bits' must have a value
+        Syntax error: ; expected in stream:1
+        Complex Field with 53 bits of precision;;
+         ^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+        Error, Variable: 'precision' must have a value
+
+
+    Test that on a subsequent attemt we get the same message (no garbage was
+    left in the error stream)::
+
+        sage: libgap.eval('Complex Field with 53 bits of precision;')
+        Traceback (most recent call last):
+        ...
+        ValueError: libGAP: Error, Variable: 'Complex' must have a value
+        ...
+        Error, Variable: 'precision' must have a value
+
+        sage: libgap.eval('1+1')  # test that we successfully recover
+        2
     """
     initialize()
-    cdef libGAP_ExecStatus status
+    cdef Obj result
+    cdef int i, j, nresults
 
     # Careful: We need to keep a reference to the bytes object here
     # so that Cython doesn't dereference it before libGAP is done with
     # its contents.
     cmd = str_to_bytes(gap_string + ';\n')
+    sig_on()
     try:
-        try:
-            sig_on()
-            libgap_enter()
-            libgap_start_interaction(cmd)
-            status = libGAP_ReadEvalCommand(libGAP_BottomLVars, NULL)
-            if status != libGAP_STATUS_END:
-                libgap_call_error_handler()
-            sig_off()
-        except RuntimeError as msg:
-            raise ValueError('libGAP: '+str(msg).strip())
-
-        if libGAP_Symbol != libGAP_S_SEMICOLON:
-            raise ValueError('did not end with semicolon')
-        libGAP_GetSymbol()
-        if libGAP_Symbol != libGAP_S_EOF:
+        GAP_Enter()
+        result = GAP_EvalString(cmd)
+        # We can assume that the result object is a GAP PList (plain list)
+        # and we should use functions for PLists directly for now; see
+        # https://github.com/gap-system/gap/pull/2988/files#r233021437
+
+        # If an error occurred in GAP_EvalString we won't even get
+        # here if the error handler was set; but in case it wasn't
+        # let's still check the result...
+        nresults = LEN_LIST(result)
+        if nresults > 1:  # to mimick the old libGAP
+            # TODO: Get rid of this restriction eventually?
             raise ValueError('can only evaluate a single statement')
 
-    finally:
-        libgap_finish_interaction()
-        libgap_exit()
+        # Get the result of the first statement
+        result = ELM0_LIST(result, 1) # 1-indexed!
 
-    if libGAP_ReadEvalResult != NULL:
-        libgap_enter()
-        libGAP_AssGVar(libGAP_Last3, libGAP_VAL_GVAR(libGAP_Last2))
-        libGAP_AssGVar(libGAP_Last2, libGAP_VAL_GVAR(libGAP_Last))
-        libGAP_AssGVar(libGAP_Last, libGAP_ReadEvalResult)
-        libgap_exit()
+        if ELM0_LIST(result, 1) != GAP_True:
+            # An otherwise unhandled error occurred in GAP (such as a
+            # syntax error).  Try running the error handler manually
+            # to capture the error output, if any.
+            # This should result in a RuntimeError being set.
+            error_handler_check_exception()
 
-    return libGAP_ReadEvalResult   # may be NULL, thats ok
+        # The actual resultant object, if any, is in the second entry
+        # (which may be unassigned--see previous github comment; in this case
+        # 0 is returned without setting a a Python exception, so we should treat
+        # this like returning None)
 
+        return ELM0_LIST(result, 2)
+    except RuntimeError as msg:
+        raise ValueError(f'libGAP: {msg}')
+    finally:
+        GAP_Leave()
+        sig_off()
 
-############################################################################
+
+###########################################################################
 ### Helper to protect temporary objects from deletion ######################
 ############################################################################
 
@@ -370,9 +468,9 @@ cdef libGAP_Obj gap_eval(str gap_string) except? NULL:
 # get deleted this works by assigning it to a global variable. This is
 # very simple, but you can't use it to keep two objects alive. Be
 # careful.
-cdef libGAP_UInt reference_holder
+cdef UInt reference_holder
 
-cdef void hold_reference(libGAP_Obj obj):
+cdef void hold_reference(Obj obj):
     """
     Hold a reference (inside the GAP kernel) to obj
 
@@ -381,177 +479,79 @@ cdef void hold_reference(libGAP_Obj obj):
     very simple, but you can't use it to keep two objects alive. Be
     careful.
     """
-    libgap_enter()
     global reference_holder
-    libGAP_AssGVar(reference_holder, obj)
-    libgap_exit()
+    AssGVar(reference_holder, obj)
 
 
 ############################################################################
 ### Error handler ##########################################################
 ############################################################################
 
-cdef void error_handler(char* msg):
-    """
-    The libgap error handler
-
-    We call ``sig_error()`` which causes us to jump back to the Sage
-    signal handler. Since we wrap libGAP C calls in ``sig_on`` /
-    ``sig_off`` blocks, this then jumps back to the ``sig_on`` where
-    the ``RuntimeError`` we raise here will be seen.
-    """
-    msg_py = char_to_str(msg)
-    msg_py = msg_py.replace('For debugging hints type ?Recovery from NoMethodFound\n', '')
-    PyErr_SetObject(RuntimeError, msg_py)
-    sig_error()
-
-
-############################################################################
-### Debug functions ########################################################
-############################################################################
 
-cdef inline void DEBUG_CHECK(libGAP_Obj obj):
+cdef object extract_libgap_errout():
     """
-    Check that ``obj`` is valid.
-
-    This function is only useful for debugging.
+    Reads the global variable libgap_errout and returns a Python string
+    containing the error message (with some boilerplate removed).
     """
-    libgap_enter()
-    libGAP_CheckMasterPointers()
-    libgap_exit()
-    if obj == NULL:
-        print('DEBUG_CHECK: Null pointer!')
-
-
+    cdef Obj r
+    cdef char *msg
 
+    r = GAP_ValueGlobalVariable("libgap_errout")
 
-cpdef memory_usage():
-    """
-    Return information about the memory usage.
-
-    See :meth:`~sage.libs.gap.libgap.Gap.mem` for details.
-    """
-    cdef size_t SizeMptrsArea = libGAP_OldBags - libGAP_MptrBags
-    cdef size_t SizeOldBagsArea = libGAP_YoungBags - libGAP_OldBags
-    cdef size_t SizeYoungBagsArea = libGAP_AllocBags - libGAP_YoungBags
-    cdef size_t SizeAllocationArea = libGAP_StopBags - libGAP_AllocBags
-    cdef size_t SizeUnavailableArea = libGAP_EndBags - libGAP_StopBags
-    return (SizeMptrsArea, SizeOldBagsArea, SizeYoungBagsArea, SizeAllocationArea, SizeUnavailableArea)
-
-
-cpdef error_enter_libgap_block_twice():
-    """
-    Demonstrate that we catch errors from entering a block twice.
-
-    EXAMPLES::
-
-        sage: from sage.libs.gap.util import error_enter_libgap_block_twice
-        sage: error_enter_libgap_block_twice()
-        Traceback (most recent call last):
-        ...
-        RuntimeError: Entered a critical block twice
-    """
-    from sage.libs.gap.libgap import libgap
-    try:
-        # The exception will be seen by this sig_on() after being
-        # raised by the second libgap_enter().
-        sig_on()
-        libgap_enter()
-        libgap_enter()
-        sig_off()
-    finally:
-        libgap_exit()
-
-
-cpdef error_exit_libgap_block_without_enter():
-    """
-    Demonstrate that we catch errors from omitting libgap_enter.
-
-    EXAMPLES::
-
-        sage: from sage.libs.gap.util import error_exit_libgap_block_without_enter
-        sage: error_exit_libgap_block_without_enter()
-        Traceback (most recent call last):
-        ...
-        RuntimeError: Called libgap_exit without previous libgap_enter
-    """
-    from sage.libs.gap.libgap import libgap
-    sig_on()
-    libgap_exit()
-    sig_off()
+    # Grab a pointer to the C string underlying the GAP string libgap_errout
+    # then copy it to a Python str (char_to_str contains an implicit strcpy)
+    msg = CSTR_STRING(r)
+    if msg != NULL:
+        msg_py = char_to_str(msg)
+        msg_py = msg_py.replace('For debugging hints type ?Recovery from '
+                                'NoMethodFound\n', '').strip()
+    else:
+        # Shouldn't happen but just in case...
+        msg_py = ""
 
-############################################################################
-### Auxilliary functions ###################################################
-############################################################################
+    return msg_py
 
 
-def command(command_string):
+cdef void error_handler():
     """
-    Playground for accessing Gap via libGap.
+    The libgap error handler.
 
-    You should not use this function in your own programs. This is
-    just here for convenience if you want to play with the libgap
-    libray code.
-
-    EXAMPLES::
+    If an error occurred we set a RuntimeError; when the original
+    GAP_EvalString returns this exception will be raised.
 
-        sage: from sage.libs.gap.util import command
-        sage: command('1')
-        Output follows...
-        1
-
-        sage: command('1/0')
-        Traceback (most recent call last):
-        ...
-        ValueError: libGAP: Error, Rational operations: <divisor> must not be zero
-
-        sage: command('NormalSubgroups')
-        Output follows...
-        <Attribute "NormalSubgroups">
-
-        sage: command('rec(a:=1, b:=2)')
-        Output follows...
-        rec( a := 1, b := 2 )
+    TODO: We should probably prevent re-entering this function if we
+    are already handling an error; if there is an error in our stream
+    handling code below it could result in a stack overflow.
     """
-    initialize()
-    cdef libGAP_ExecStatus status
+    cdef PyObject* exc_type
+    cdef PyObject* exc_val
+    cdef PyObject* exc_tb
 
-    cmd = str_to_bytes(command_string + ';\n')
+    # Close the error stream: This flushes any remaining output and closes
+    # the stream for further writing; reset ERROR_OUTPUT to something sane
+    # just in case (trying to print to a closed stream segfaults GAP)
     try:
-        libgap_enter()
-        libgap_start_interaction(cmd)
-        try:
-            sig_on()
-            status = libGAP_ReadEvalCommand(libGAP_BottomLVars, NULL)
-            if status != libGAP_STATUS_END:
-                libgap_call_error_handler()
-            sig_off()
-        except RuntimeError as msg:
-            raise ValueError('libGAP: '+str(msg).strip())
-
-        assert libGAP_Symbol == libGAP_S_SEMICOLON, 'Did not end with semicolon?'
-        libGAP_GetSymbol()
-        if libGAP_Symbol != libGAP_S_EOF:
-            raise ValueError('command() expects a single statement.')
-
-        if libGAP_ReadEvalResult:
-            libGAP_ViewObjHandler(libGAP_ReadEvalResult)
-            s = char_to_str(libgap_get_output())
-            print('Output follows...')
-            print(s.strip())
-        else:
-            print('No output.')
-
+        GAP_EnterStack()
+        GAP_EvalStringNoExcept(_close_error_output_cmd)
+        msg = extract_libgap_errout()
+
+        if PyErr_Occurred() != NULL and msg:
+            # Sometimes error_handler() can be called multiple times from a
+            # single GAP_EvalString call before it returns; in this case we
+            # just update the exception by appending to the existing exception
+            # message
+            PyErr_Fetch(&exc_type, &exc_val, &exc_tb)
+            if exc_val != NULL:
+                msg = str(<object>exc_val) + '\n' + msg
+        elif not msg:
+            msg = "An unknown error occurred in libGAP"
+
+        PyErr_SetObject(RuntimeError, msg)
     finally:
-        libgap_exit()
-        libgap_finish_interaction()
-
-    DEBUG_CHECK(libGAP_ReadEvalResult)
+        # Reset ERROR_OUTPUT with a new text string stream
+        GAP_EvalStringNoExcept(_reset_error_output_cmd)
+        GAP_LeaveStack()
 
-    if libGAP_ReadEvalResult != NULL:
-        libgap_enter()
-        libGAP_AssGVar(libGAP_Last3, libGAP_VAL_GVAR(libGAP_Last2))
-        libGAP_AssGVar(libGAP_Last2, libGAP_VAL_GVAR(libGAP_Last))
-        libGAP_AssGVar(libGAP_Last, libGAP_ReadEvalResult)
-        libgap_exit()
 
+cdef void error_handler_check_exception() except *:
+    error_handler()
diff --git a/src/sage/misc/randstate.pyx b/src/sage/misc/randstate.pyx
index d2f173c..0e13d60 100644
--- a/src/sage/misc/randstate.pyx
+++ b/src/sage/misc/randstate.pyx
@@ -54,23 +54,23 @@ Here we see that setting the random number seed really does make the
 results of these random number generators reproducible. ::
 
     sage: set_random_seed(0)
-    sage: rtest()
-    (303, -0.266166246380421, 1/6, (1,2), [ 1, 1, 1, 1, 0 ], 265625921, 79302, 0.2450652680687958)
+    sage: print(rtest())
+    (303, -0.266166246380421, 1/6, (1,2), [ 0, 1, 1, 0, 0 ], 265625921, 79302, 0.2450652680687958)
     sage: set_random_seed(1)
-    sage: rtest()
+    sage: print(rtest())
     (978, 0.0557699430711638, -1/8*x^2 - 1/2*x + 1/2, (1,2,3), [ 1, 0, 0, 0, 1 ], 807447831, 23865, 0.6170498912488264)
     sage: set_random_seed(2)
-    sage: rtest()
-    (207, -0.0141049486533456, 0, (1,3)(4,5), [ 1, 1, 1, 1, 1 ], 1642898426, 16190, 0.9343331114872127)
+    sage: print(rtest())
+    (207, -0.0141049486533456, 0, (1,3)(4,5), [ 1, 0, 1, 1, 1 ], 1642898426, 16190, 0.9343331114872127)
     sage: set_random_seed(0)
-    sage: rtest()
-    (303, -0.266166246380421, 1/6, (1,2), [ 1, 1, 1, 1, 0 ], 265625921, 79302, 0.2450652680687958)
+    sage: print(rtest())
+    (303, -0.266166246380421, 1/6, (1,2), [ 0, 1, 1, 0, 0 ], 265625921, 79302, 0.2450652680687958)
     sage: set_random_seed(1)
-    sage: rtest()
+    sage: print(rtest())
     (978, 0.0557699430711638, -1/8*x^2 - 1/2*x + 1/2, (1,2,3), [ 1, 0, 0, 0, 1 ], 807447831, 23865, 0.6170498912488264)
     sage: set_random_seed(2)
-    sage: rtest()
-    (207, -0.0141049486533456, 0, (1,3)(4,5), [ 1, 1, 1, 1, 1 ], 1642898426, 16190, 0.9343331114872127)
+    sage: print(rtest())
+    (207, -0.0141049486533456, 0, (1,3)(4,5), [ 1, 0, 1, 1, 1 ], 1642898426, 16190, 0.9343331114872127)
 
 Once we've set the random number seed, we can check what seed was used.
 (This is not the current random number state; it does not change when
@@ -79,8 +79,8 @@ random numbers are generated.)  ::
     sage: set_random_seed(12345)
     sage: initial_seed()
     12345L
-    sage: rtest()
-    (720, -0.612180244315804, 0, (1,3), [ 1, 0, 1, 1, 1 ], 1911581957, 65175, 0.8043027951758298)
+    sage: print(rtest())
+    (720, -0.612180244315804, 0, (1,3), [ 1, 0, 1, 1, 0 ], 1911581957, 65175, 0.8043027951758298)
     sage: initial_seed()
     12345L
 
@@ -214,9 +214,9 @@ We'll demonstrate isolation.  First, we show the sequence of random numbers
 that you get without intervening ``with seed``. ::
 
     sage: set_random_seed(0)
-    sage: r1 = rtest(); r1
-    (303, -0.266166246380421, 1/6, (1,2), [ 1, 1, 1, 1, 0 ], 265625921, 79302, 0.2450652680687958)
-    sage: r2 = rtest(); r2
+    sage: r1 = rtest(); print(r1)
+    (303, -0.266166246380421, 1/6, (1,2), [ 0, 1, 1, 0, 0 ], 265625921, 79302, 0.2450652680687958)
+    sage: r2 = rtest(); print(r2)
     (443, 0.185001351421963, -2, (1,3), [ 0, 0, 1, 1, 0 ], 53231108, 8171, 0.28363811590618193)
 
 We get slightly different results with an intervening ``with seed``. ::
@@ -242,10 +242,10 @@ case, as we see in this example::
     sage: r1 == rtest()
     True
     sage: with seed(1):
-    ....:     rtest()
-    ....:     rtest()
+    ....:     print(rtest())
+    ....:     print(rtest())
     (978, 0.0557699430711638, -1/8*x^2 - 1/2*x + 1/2, (1,2,3), [ 1, 0, 0, 0, 1 ], 807447831, 23865, 0.6170498912488264)
-    (181, 0.607995392046754, -x + 1/2, (2,3)(4,5), [ 0, 1, 1, 0, 0 ], 1010791326, 9693, 0.5691716786307407)
+    (181, 0.607995392046754, -x + 1/2, (2,3)(4,5), [ 1, 0, 0, 1, 1 ], 1010791326, 9693, 0.5691716786307407)
     sage: r2m == rtest()
     True
 
@@ -702,8 +702,8 @@ cdef class randstate:
             sage: gap.Random(1, 10^50)
             1496738263332555434474532297768680634540939580077
             sage: gap(35).SCRRandomString()
-            [ 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0,
-              0, 0, 1, 0, 0, 1, 1, 0, 0, 1 ]
+            [ 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1,
+              1, 0, 0, 1, 1, 1, 1, 1, 0, 1 ]
         """
         global _gap_seed_randstate
         if _gap_seed_randstate is not self:
diff --git a/src/sage/tests/books/judson-abstract-algebra/homomorph-sage-exercises.py b/src/sage/tests/books/judson-abstract-algebra/homomorph-sage-exercises.py
index d5ebaa6..84ed100 100644
--- a/src/sage/tests/books/judson-abstract-algebra/homomorph-sage-exercises.py
+++ b/src/sage/tests/books/judson-abstract-algebra/homomorph-sage-exercises.py
@@ -60,7 +60,6 @@ r"""
 ~~~~~~~~~~~~~~~~~~~~~~ ::
 
     sage: G = DihedralGroup(20)
-    sage: [H.order() for H in G.normal_subgroups()]
+    sage: l=[H.order() for H in G.normal_subgroups()]; l.sort(); l
     [1, 2, 4, 5, 10, 20, 20, 20, 40]
-
 """
diff --git a/src/sage/tests/books/judson-abstract-algebra/normal-sage.py b/src/sage/tests/books/judson-abstract-algebra/normal-sage.py
index 16119fd..3db475d 100644
--- a/src/sage/tests/books/judson-abstract-algebra/normal-sage.py
+++ b/src/sage/tests/books/judson-abstract-algebra/normal-sage.py
@@ -128,7 +128,7 @@ r"""
 
     sage: G = DihedralGroup(8)
     sage: N = G.normal_subgroups()
-    sage: [H.order() for H in N]
+    sage: l=[H.order() for H in N]; l.sort(); l
     [1, 2, 4, 8, 8, 8, 16]
 
 """
diff --git a/src/sage/tests/books/judson-abstract-algebra/sylow-sage.py b/src/sage/tests/books/judson-abstract-algebra/sylow-sage.py
index d6cf39c..8b32726 100644
--- a/src/sage/tests/books/judson-abstract-algebra/sylow-sage.py
+++ b/src/sage/tests/books/judson-abstract-algebra/sylow-sage.py
@@ -226,7 +226,7 @@ r"""
 ~~~~~~~~~~~~~~~~~~~~~~ ::
 
     sage: gap.version()
-    '4.8.6'
+    '4.10.0'
 
 ~~~~~~~~~~~~~~~~~~~~~~ ::
 
diff --git a/src/sage/tests/gap_packages.py b/src/sage/tests/gap_packages.py
index ca961ed..4a3479b 100644
--- a/src/sage/tests/gap_packages.py
+++ b/src/sage/tests/gap_packages.py
@@ -124,7 +124,7 @@ def all_installed_packages(ignore_dot_gap=False):
         (...'GAPDoc'...)
     """
     packages = []
-    for path in libgap.eval('GAP_ROOT_PATHS').sage():
+    for path in libgap.eval('GAPInfo.RootPaths').sage():
         if ignore_dot_gap and path.endswith('/.gap/'):
             continue
         pkg_dir = os.path.join(path, 'pkg')
diff --git a/src/setup.py b/src/setup.py
index bc8fe12..9d31c9d 100755
--- a/src/setup.py
+++ b/src/setup.py
@@ -948,6 +948,9 @@ code = setup(name = 'sage',
       author_email= 'http://groups.google.com/group/sage-support',
       url         = 'http://www.sagemath.org',
       packages    = python_packages,
+      package_data = {
+          'sage.libs.gap': ['sage.gaprc'],
+      },
       cmdclass = dict(build=sage_build,
                       build_cython=sage_build_cython,
                       build_ext=sage_build_ext,