gh-36011: Regular sequence: closing experimental phase of regular sequence module
    
This PR closes the experimental-phase of the regular sequences module.
This module has been experimental für a very long time now. Lately
#35894 has been completed so this is now a fully-functional
ring/algebra. Except for the consequences of  #35894 (renaming; see
below), the interface is stable for very long time.

This PR does:
- Rename to `RegularSequenceRing` (as this structure now is a ring due
to #35894).
- Remove the experimental warning.

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [x] I have updated the documentation accordingly.

### ⌛ Dependencies

- #35894
    
URL: #36011
Reported by: Daniel Krenn
Reviewer(s): cheuberg, Daniel Krenn

Author: Release Manager

src/doc/en/reference/combinat/module_list.rst

@@ -143,7 +143,6 @@ Comprehensive Module List
     sage/combinat/integer_vector_weighted
     sage/combinat/integer_vectors_mod_permgroup
     sage/combinat/interval_posets
-    sage/combinat/k_regular_sequence
     sage/combinat/k_tableau
     sage/combinat/kazhdan_lusztig
     sage/combinat/key_polynomial
@@ -206,6 +205,7 @@ Comprehensive Module List
     sage/combinat/quickref
     sage/combinat/ranker
     sage/combinat/recognizable_series
+    sage/combinat/regular_sequence
     sage/combinat/restricted_growth
     sage/combinat/ribbon
     sage/combinat/ribbon_shaped_tableau

src/sage/combinat/all.py

@@ -277,7 +277,7 @@
 lazy_import('sage.combinat.binary_recurrence_sequences',
             'BinaryRecurrenceSequence')
 lazy_import('sage.combinat.recognizable_series', 'RecognizableSeriesSpace')
-lazy_import('sage.combinat.k_regular_sequence', 'kRegularSequenceSpace')
+lazy_import('sage.combinat.regular_sequence', 'RegularSequenceRing')
 
 # Six Vertex Model
 lazy_import('sage.combinat.six_vertex_model', 'SixVertexModel')

src/sage/combinat/recognizable_series.py

@@ -27,27 +27,13 @@
     In particular, minimization is called before checking if a series is
     nonzero.
 
-.. WARNING::
-
-    As this code is experimental, warnings are thrown when a
-    recognizable series space is created for the first time in a
-    session (see :class:`sage.misc.superseded.experimental`).
-
-    TESTS::
-
-        sage: Rec = RecognizableSeriesSpace(ZZ, [0, 1])
-        doctest:...: FutureWarning: This class/method/function is
-        marked as experimental. It, its functionality or its interface
-        might change without a formal deprecation.
-        See https://github.com/sagemath/sage/issues/21202 for details.
-
 
 Various
 =======
 
 .. SEEALSO::
 
-    :mod:`k-regular sequence <sage.combinat.k_regular_sequence>`,
+    :mod:`k-regular sequence <sage.combinat.regular_sequence>`,
     :mod:`sage.rings.cfinite_sequence`,
     :mod:`sage.combinat.binary_recurrence_sequences`.
 
@@ -79,7 +65,6 @@
 from functools import wraps
 
 from sage.misc.cachefunc import cached_method
-from sage.misc.superseded import experimental
 from sage.structure.element import ModuleElement
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
@@ -1297,7 +1282,7 @@ def _add_(self, other):
 
         EXAMPLES::
 
-            sage: Seq2 = kRegularSequenceSpace(2, ZZ)
+            sage: Seq2 = RegularSequenceRing(2, ZZ)
             sage: E = Seq2((Matrix([[0, 1], [0, 1]]), Matrix([[0, 0], [0, 1]])),
             ....:          vector([1, 0]), vector([1, 1]))
             sage: E
@@ -1336,7 +1321,7 @@ def _neg_(self):
 
         EXAMPLES::
 
-            sage: Seq2 = kRegularSequenceSpace(2, ZZ)
+            sage: Seq2 = RegularSequenceRing(2, ZZ)
             sage: E = Seq2((Matrix([[0, 1], [0, 1]]), Matrix([[0, 0], [0, 1]])),
             ....:          vector([1, 0]), vector([1, 1]))
             sage: -E
@@ -1363,7 +1348,7 @@ def _rmul_(self, other):
 
         EXAMPLES::
 
-            sage: Seq2 = kRegularSequenceSpace(2, ZZ)
+            sage: Seq2 = RegularSequenceRing(2, ZZ)
             sage: E = Seq2((Matrix([[0, 1], [0, 1]]), Matrix([[0, 0], [0, 1]])),
             ....:          vector([1, 0]), vector([1, 1]))
             sage: M = 2 * E  # indirect doctest
@@ -1427,7 +1412,7 @@ def _lmul_(self, other):
 
         EXAMPLES::
 
-            sage: Seq2 = kRegularSequenceSpace(2, ZZ)
+            sage: Seq2 = RegularSequenceRing(2, ZZ)
             sage: E = Seq2((Matrix([[0, 1], [0, 1]]), Matrix([[0, 0], [0, 1]])),
             ....:          vector([1, 0]), vector([1, 1]))
             sage: M = E * 2 # indirect doctest
@@ -1497,7 +1482,7 @@ def hadamard_product(self, other):
 
         EXAMPLES::
 
-            sage: Seq2 = kRegularSequenceSpace(2, ZZ)
+            sage: Seq2 = RegularSequenceRing(2, ZZ)
 
             sage: E = Seq2((Matrix([[0, 1], [0, 1]]), Matrix([[0, 0], [0, 1]])),
             ....:          vector([1, 0]), vector([1, 1]))
@@ -1741,7 +1726,6 @@ def __normalize__(cls,
 
         return (coefficient_ring, indices, category, minimize_results)
 
-    @experimental(issue_number=21202)
     def __init__(self, coefficient_ring, indices, category, minimize_results):
         r"""
         See :class:`RecognizableSeriesSpace` for details.