Trac #21319: recognizable series: hash, comparison, TestSuite

- Implement hashing and comparison.
- Make TestSuite pass all tests.

See also meta ticket #21202.

URL: https://trac.sagemath.org/21319
Reported by: dkrenn
Ticket author(s): Daniel Krenn
Reviewer(s): Clemens Heuberger

src/sage/combinat/k_regular_sequence.py

@@ -208,7 +208,7 @@ def __getitem__(self, n, **kwds):
             sage: W = Seq2.indices()
             sage: M0 = Matrix([[1, 0], [0, 1]])
             sage: M1 = Matrix([[0, -1], [1, 2]])
-            sage: S = Seq2((M0, M1), [0, 1], [1, 1])
+            sage: S = Seq2((M0, M1), vector([0, 1]), vector([1, 1]))
             sage: S._mu_of_word_(W(0.digits(2))) == M0
             True
             sage: S._mu_of_word_(W(1.digits(2))) == M1
@@ -540,7 +540,8 @@ def shift_left(self, b=1, **kwds):
 
         TESTS::
 
-            sage: C.shift_left(0) == C  # not tested, #21319
+            sage: C.shift_left(0) == C
+            True
             sage: C.shift_left(2).shift_right(2)
             2-regular sequence 0, 0, 2, 3, 4, 5, 6, 7, 8, 9, ...
         """
@@ -585,11 +586,14 @@ def shift_right(self, b=1, **kwds):
 
         TESTS::
 
-            sage: C.shift_right(0) == C  # not tested, #21319
+            sage: C.shift_right(0) == C
+            True
             sage: C.shift_right().shift_left()
             2-regular sequence 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...
             sage: C.shift_right(2).shift_left(2)
             2-regular sequence 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...
+            sage: _ == C
+            True
         """
         return self.subsequence(1, -b, **kwds)
 
@@ -765,6 +769,21 @@ def partial_sums(self, include_n=False):
         return result
 
 
+def _pickle_kRegularSequenceSpace(k, coefficients, category):
+    r"""
+    Pickle helper.
+
+    TESTS::
+
+        sage: Seq2 = kRegularSequenceSpace(2, ZZ)
+        sage: from sage.combinat.k_regular_sequence import _pickle_kRegularSequenceSpace
+        sage: _pickle_kRegularSequenceSpace(
+        ....:     Seq2.k, Seq2.coefficient_ring(), Seq2.category())
+        Space of 2-regular sequences over Integer Ring
+    """
+    return kRegularSequenceSpace(k, coefficients, category=category)
+
+
 class kRegularSequenceSpace(RecognizableSeriesSpace):
     r"""
     The space of `k`-regular Sequences over the given ``coefficient_ring``.
@@ -831,6 +850,13 @@ def __init__(self, k, *args, **kwds):
             sage: kRegularSequenceSpace(3, ZZ)
             Space of 3-regular sequences over Integer Ring
 
+        ::
+
+            sage: from itertools import islice
+            sage: Seq2 = kRegularSequenceSpace(2, ZZ)
+            sage: TestSuite(Seq2).run(  # long time
+            ....:    elements=tuple(islice(Seq2.some_elements(), 4)))
+
         .. SEEALSO::
 
             :doc:`k-regular sequence <k_regular_sequence>`,
@@ -839,6 +865,19 @@ def __init__(self, k, *args, **kwds):
         self.k = k
         super(kRegularSequenceSpace, self).__init__(*args, **kwds)
 
+    def __reduce__(self):
+        r"""
+        Pickling support.
+
+        TESTS::
+
+            sage: Seq2 = kRegularSequenceSpace(2, ZZ)
+            sage: loads(dumps(Seq2))  # indirect doctest
+            Space of 2-regular sequences over Integer Ring
+        """
+        return _pickle_kRegularSequenceSpace, \
+            (self.k, self.coefficient_ring(), self.category())
+
     def _repr_(self):
         r"""
         Return a representation string of this `k`-regular sequence space.