Added tests/docstrings for the new functions in testutil.py

sympy/combinatorics/tests/test_testutil.py

@@ -1,5 +1,24 @@
-from sympy.combinatorics.named_groups import SymmetricGroup
-from sympy.combinatorics.testutil import _verify_bsgs
+from sympy.combinatorics.named_groups import SymmetricGroup, AlternatingGroup, CyclicGroup
+from sympy.combinatorics.testutil import _verify_bsgs, _cmp_perm_lists, _naive_list_centralizer, _verify_centralizer,\
+_verify_normal_closure
+from sympy.combinatorics.permutations import Permutation
+from sympy.combinatorics.perm_groups import PermutationGroup
+from random import shuffle
+
+
+def test_cmp_perm_lists():
+    S = SymmetricGroup(4)
+    els = list(S.generate_dimino())
+    other = els[:]
+    shuffle(other)
+    assert _cmp_perm_lists(els, other) == True
+
+def test_naive_list_centralizer():
+    # verified by GAP
+    S = SymmetricGroup(3)
+    A = AlternatingGroup(3)
+    assert _naive_list_centralizer(S, S) == [Permutation([0, 1, 2])]
+    assert PermutationGroup(_naive_list_centralizer(S, A)) == A
 
 def test_verify_bsgs():
     S = SymmetricGroup(5)
@@ -11,3 +30,21 @@ def test_verify_bsgs():
     assert _verify_bsgs(S, base[:-1], strong_gens) == False
     assert _verify_bsgs(S, base, S.generators) == False
 
+def test_verify_centralizer():
+    # verified by GAP
+    S = SymmetricGroup(3)
+    A = AlternatingGroup(3)
+    triv = PermutationGroup([Permutation([0, 1, 2])])
+    assert _verify_centralizer(S, S, centr=triv)
+    assert _verify_centralizer(S, A, centr=A)
+
+def test_verify_normal_closure():
+    # verified by GAP
+    S = SymmetricGroup(3)
+    A = AlternatingGroup(3)
+    assert _verify_normal_closure(S, A, closure=A)
+    S = SymmetricGroup(5)
+    A = AlternatingGroup(5)
+    C = CyclicGroup(5)
+    assert _verify_normal_closure(S, A, closure=A)
+    assert _verify_normal_closure(S, C, closure=A)

sympy/combinatorics/testutil.py

@@ -137,6 +137,27 @@ def _verify_centralizer(group, arg, centr=None):
 
 def _verify_normal_closure(group, arg, closure=None):
     from sympy.combinatorics.perm_groups import PermutationGroup
+    """
+    Verify the normal closure of a subgroup/subset/element in a group.
+
+    This is used to test sympy.combinatorics.perm_groups.PermutationGroup.normal_closure
+
+    Examples
+    ========
+
+    >>> from sympy.combinatorics.named_groups import SymmetricGroup, AlternatingGroup
+    >>> from sympy.combinatorics.testutil import _verify_normal_closure
+    >>> S = SymmetricGroup(3)
+    >>> A = AlternatingGroup(3)
+    >>> _verify_normal_closure(S, A, closure=A)
+    True
+
+    See Also
+    ========
+
+    sympy.combinatorics.perm_groups.PermutationGroup.normal_closure
+
+    """
     if closure is None:
         closure = group.normal_closure(arg)
     conjugates = []