From 9ba3ea3e0fb495c2a8deea509ffc3e965bbdf265 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Tue, 9 Apr 2024 09:36:45 +0200
Subject: [PATCH 1/3] some C4 fixes in combinat folder

---
 .../algebras/quatalg/quaternion_algebra.py    |  9 +++--
 src/sage/combinat/sloane_functions.py         |  2 +-
 .../combinat/species/partition_species.py     |  2 +-
 src/sage/combinat/subset.py                   |  3 +-
 src/sage/combinat/subword_complex.py          | 12 +++----
 src/sage/combinat/superpartition.py           |  2 +-
 src/sage/combinat/tableau_residues.py         |  4 +--
 src/sage/combinat/tableau_tuple.py            |  9 +++--
 src/sage/combinat/tamari_lattices.py          |  8 ++---
 src/sage/combinat/tiling.py                   | 33 +++++++++----------
 src/sage/combinat/tuple.py                    |  4 +--
 src/sage/combinat/words/finite_word.py        |  6 ++--
 src/sage/combinat/words/morphism.py           | 24 +++++++-------
 src/sage/combinat/yang_baxter_graph.py        |  4 +--
 14 files changed, 63 insertions(+), 59 deletions(-)

diff --git a/src/sage/algebras/quatalg/quaternion_algebra.py b/src/sage/algebras/quatalg/quaternion_algebra.py
index 02d0ccf0326..c5860eec5a1 100644
--- a/src/sage/algebras/quatalg/quaternion_algebra.py
+++ b/src/sage/algebras/quatalg/quaternion_algebra.py
@@ -1190,9 +1190,12 @@ def ramified_primes(self):
         if not is_RationalField(self.base_ring()):
             raise ValueError("base field must be the rational numbers")
 
-        return sorted([p for p in set([2]).union(prime_divisors(self._a.numerator()),
-                prime_divisors(self._a.denominator()), prime_divisors(self._b.numerator()),
-                prime_divisors(self._b.denominator())) if hilbert_symbol(self._a, self._b, p) == -1])
+        a, b = self._a, self._b
+        return sorted(p for p in {2}.union(prime_divisors(a.numerator()),
+                                           prime_divisors(a.denominator()),
+                                           prime_divisors(b.numerator()),
+                                           prime_divisors(b.denominator()))
+                      if hilbert_symbol(self._a, self._b, p) == -1)
 
     def is_isomorphic(self, A) -> bool:
         """
diff --git a/src/sage/combinat/sloane_functions.py b/src/sage/combinat/sloane_functions.py
index e9911d47506..808bcfd849d 100644
--- a/src/sage/combinat/sloane_functions.py
+++ b/src/sage/combinat/sloane_functions.py
@@ -859,7 +859,7 @@ def _eval(self, n):
             sage: [sloane.A003418._eval(n) for n in range(1,11)]
             [1, 2, 6, 12, 60, 60, 420, 840, 2520, 2520]
         """
-        return arith.lcm([i for i in range(1, n+1)])
+        return arith.lcm(list(range(1, n + 1)))
 
 
 class A007318(SloaneSequence):
diff --git a/src/sage/combinat/species/partition_species.py b/src/sage/combinat/species/partition_species.py
index dea38378a7a..8d9a83d1e00 100644
--- a/src/sage/combinat/species/partition_species.py
+++ b/src/sage/combinat/species/partition_species.py
@@ -182,7 +182,7 @@ def _structures(self, structure_class, labels):
             yield structure_class(self, labels, [])
             return
 
-        u = [i for i in reversed(range(1, n + 1))]
+        u = list(range(n, 0, -1))
         s0 = u.pop()
 
         # Reconstruct the set partitions from
diff --git a/src/sage/combinat/subset.py b/src/sage/combinat/subset.py
index 822420d6514..4d036ad6c93 100644
--- a/src/sage/combinat/subset.py
+++ b/src/sage/combinat/subset.py
@@ -741,7 +741,8 @@ def last(self):
         if self._k > self._s.cardinality():
             raise EmptySetError
 
-        return self.element_class([i for i in itertools.islice(reversed(self._s), int(self._k))])
+        return self.element_class(list(itertools.islice(reversed(self._s),
+                                                        int(self._k))))
 
     def _fast_iterator(self):
         r"""
diff --git a/src/sage/combinat/subword_complex.py b/src/sage/combinat/subword_complex.py
index 0439d7f72f0..f280a5901f3 100644
--- a/src/sage/combinat/subword_complex.py
+++ b/src/sage/combinat/subword_complex.py
@@ -1854,8 +1854,8 @@ def cover_relations(self, label=False):
         """
         N = len(self.group().long_element(as_word=True))
         F = self.greedy_facet(side="positive")
-        Fs = set([F])
-        seen = set([F])
+        Fs = {F}
+        seen = {F}
         covers = []
         while Fs:
             F = Fs.pop()
@@ -1895,7 +1895,7 @@ def increasing_flip_graph(self, label=True):
         from sage.graphs.digraph import DiGraph
         return DiGraph(self.cover_relations(label=label))
 
-    def interval(self, I, J):
+    def interval(self, I, J) -> set:
         """
         Return the interval [I,J] in the increasing flip graph subword complex.
 
@@ -1924,7 +1924,7 @@ def interval(self, I, J):
         """
         G = self.increasing_flip_graph()
         paths = G.all_paths(I, J)
-        return set(K for path in paths for K in path)
+        return {K for path in paths for K in path}
 
     def increasing_flip_poset(self):
         """
@@ -2125,8 +2125,8 @@ def _greedy_flip_algorithm(Q, w):
                     flip_to_ancestors.append(j)
                     next_index = i + 1
                     has_new_child = True
-                    facet_list.append([x for x in F])
-                    extended_root_conf_indices_list.append([x for x in R])
+                    facet_list.append(list(F))
+                    extended_root_conf_indices_list.append(list(R))
         if not has_new_child:
             i = flip_to_ancestors.pop()
             if i != -1:
diff --git a/src/sage/combinat/superpartition.py b/src/sage/combinat/superpartition.py
index a2e77f8a5b1..e16e87fa9f0 100644
--- a/src/sage/combinat/superpartition.py
+++ b/src/sage/combinat/superpartition.py
@@ -691,7 +691,7 @@ def add_horizontal_border_strip_star(self, h) -> list:
                       # TODO: Check that this is not supposed to be
                       #   a tuple of size 1
                       + [(i) for i in circ_list if row_changed[i[0]] == 0]]
-            if len(set([k for (j, k) in new_sp[1]])) == len(new_sp[1]):
+            if len({k for j, k in new_sp[1]}) == len(new_sp[1]):
                 out += [SuperPartition.from_circled_diagram(*new_sp)]
         return out
 
diff --git a/src/sage/combinat/tableau_residues.py b/src/sage/combinat/tableau_residues.py
index ae3f65e7196..db94461f6ef 100644
--- a/src/sage/combinat/tableau_residues.py
+++ b/src/sage/combinat/tableau_residues.py
@@ -340,7 +340,7 @@ def __getitem__(self, k):
         except (IndexError, KeyError):
             raise IndexError('k must be in the range 1, 2, ..., {}'.format(len(self)))
 
-    def residues(self):
+    def residues(self) -> list:
         r"""
         Return a list of the residue sequence.
 
@@ -350,7 +350,7 @@ def residues(self):
             sage: ResidueSequence(3,(0,0,1),[0,0,1,1,2,2,3,3]).residues()
             [0, 0, 1, 1, 2, 2, 0, 0]
         """
-        return [r for r in self]
+        return list(self)
 
     def restrict(self, m):
         r"""
diff --git a/src/sage/combinat/tableau_tuple.py b/src/sage/combinat/tableau_tuple.py
index 1568175325e..511b98d3e1b 100644
--- a/src/sage/combinat/tableau_tuple.py
+++ b/src/sage/combinat/tableau_tuple.py
@@ -597,7 +597,7 @@ def components(self):
               6  7
               8  9
         """
-        return [t for t in self]
+        return list(self)
 
     def to_list(self):
         """
@@ -2371,9 +2371,8 @@ def list(self):
              ([[3, 5], [4]], [[1, 2]])]
         """
         if self.is_finite():
-            return [y for y in self]
-        else:
-            raise NotImplementedError('this is an infinite set of tableaux')
+            return list(self)
+        raise NotImplementedError('this is an infinite set of tableaux')
 
 
 class TableauTuples_all(TableauTuples):
@@ -2666,7 +2665,7 @@ def an_element(self):
         if self.size() == 0:
             return self.element_class(self, [[] for _ in range(self.level())])
 
-        tab = [[[m for m in range(1, self.size() + 1)]]]
+        tab = [[list(range(1, self.size() + 1))]]
         for _ in range(self.level() - 1):
             tab.append([])
         return self.element_class(self, tab)
diff --git a/src/sage/combinat/tamari_lattices.py b/src/sage/combinat/tamari_lattices.py
index b84b587e1b3..f3e4de13a28 100644
--- a/src/sage/combinat/tamari_lattices.py
+++ b/src/sage/combinat/tamari_lattices.py
@@ -92,11 +92,11 @@ def paths_in_triangle(i, j, a, b) -> list[tuple[int, ...]]:
         return [tuple([1] * j)]
 
     if (j - 1) * a >= (i) * b:
-        result = [u + tuple([1]) for u in paths_in_triangle(i, j - 1, a, b)]
-        result += [u + tuple([0]) for u in paths_in_triangle(i - 1, j, a, b)]
+        result = [u + (1,) for u in paths_in_triangle(i, j - 1, a, b)]
+        result += [u + (0,) for u in paths_in_triangle(i - 1, j, a, b)]
         return result
 
-    return [u + tuple([0]) for u in paths_in_triangle(i - 1, j, a, b)]
+    return [u + (0,) for u in paths_in_triangle(i - 1, j, a, b)]
 
 
 def swap(p, i, m=1) -> tuple[int, ...]:
@@ -156,7 +156,7 @@ def swap(p, i, m=1) -> tuple[int, ...]:
             height -= 1
         if height <= 0:
             found = True
-    q = [k for k in p]
+    q = list(p)
     for k in range(i, j):
         q[k] = p[k + 1]
     q[j] = 0
diff --git a/src/sage/combinat/tiling.py b/src/sage/combinat/tiling.py
index a6284b83e1b..2190c5b2119 100644
--- a/src/sage/combinat/tiling.py
+++ b/src/sage/combinat/tiling.py
@@ -991,12 +991,13 @@ def canonical_isometric_copies(self, orientation_preserving=True,
         """
         if mod_box_isometries:
             L = ncube_isometry_group_cosets(self._dimension, orientation_preserving)
-            P_cosets = set(frozenset((m * self).canonical() for m in coset) for coset in L)
+            P_cosets = {frozenset((m * self).canonical() for m in coset)
+                        for coset in L}
             P_cosets_representents = [min(s, key=lambda a: a.sorted_list()) for s in P_cosets]
-            return sorted(P_cosets_representents, key=lambda a:a.sorted_list())
+            return sorted(P_cosets_representents, key=lambda a: a.sorted_list())
         else:
             L = ncube_isometry_group(self._dimension, orientation_preserving)
-            P_images = set((m * self).canonical() for m in L)
+            P_images = {(m * self).canonical() for m in L}
             return sorted(P_images, key=lambda a: a.sorted_list())
 
     def translated_copies(self, box):
@@ -1222,8 +1223,8 @@ def isometric_copies(self, box, orientation_preserving=True,
             raise ValueError("Dimension of input box must match the "
                              "dimension of the polyomino")
         box_min_coords, box_max_coords = box.bounding_box()
-        if mod_box_isometries and len(set(b-a for (a,b) in zip(box_min_coords,
-                                      box_max_coords))) < box._dimension:
+        if mod_box_isometries and len({b - a for a, b in zip(box_min_coords,
+                                                             box_max_coords)}) < box._dimension:
             raise NotImplementedError("The code below assumes that the"
                     " sizes of the box (={}) are all distinct when"
                     " argument `mod_box_isometries` is True.".format(box))
@@ -1267,8 +1268,8 @@ def isometric_copies_intersection(self, box, orientation_preserving=True):
         """
         all_distinct_cano = self.canonical_isometric_copies(orientation_preserving,
                                                             mod_box_isometries=False)
-        return set([t for cano in all_distinct_cano
-                    for t in cano.translated_copies_intersection(box=box)])
+        return {t for cano in all_distinct_cano
+                for t in cano.translated_copies_intersection(box=box)}
 
     def neighbor_edges(self):
         r"""
@@ -1766,11 +1767,10 @@ def coord_to_int_dict(self):
              ((2, 0), 4), ((2, 1), 5)]
         """
         if self._reusable:
-            return dict((c, i) for i, c in enumerate(self.space()))
-        else:
-            number_of_pieces = len(self._pieces)
-            return dict((c, i+number_of_pieces)
-                        for i, c in enumerate(self.space()))
+            return {c: i for i, c in enumerate(self.space())}
+
+        number_of_pieces = len(self._pieces)
+        return {c: i + number_of_pieces for i, c in enumerate(self.space())}
 
     @cached_method
     def int_to_coord_dict(self):
@@ -1814,11 +1814,10 @@ def int_to_coord_dict(self):
 
         """
         if self._reusable:
-            return dict((i, c) for i, c in enumerate(self.space()))
-        else:
-            number_of_pieces = len(self._pieces)
-            return dict((i+number_of_pieces, c)
-                        for i, c in enumerate(self.space()))
+            return dict(enumerate(self.space()))
+
+        number_of_pieces = len(self._pieces)
+        return {i + number_of_pieces: c for i, c in enumerate(self.space())}
 
     @cached_method
     def rows_for_piece(self, i, mod_box_isometries=False):
diff --git a/src/sage/combinat/tuple.py b/src/sage/combinat/tuple.py
index 54d1caf9181..196d869769d 100644
--- a/src/sage/combinat/tuple.py
+++ b/src/sage/combinat/tuple.py
@@ -77,7 +77,7 @@ def __init__(self, S, k):
         """
         self.S = S
         self.k = k
-        self._index_list = list(set(S.index(s) for s in S))
+        self._index_list = list({S.index(s) for s in S})
         category = FiniteEnumeratedSets()
         Parent.__init__(self, category=category)
 
@@ -168,7 +168,7 @@ def __init__(self, S, k):
         """
         self.S = S
         self.k = k
-        self._index_list = list(set(S.index(s) for s in S))
+        self._index_list = list({S.index(s) for s in S})
         category = FiniteEnumeratedSets()
         Parent.__init__(self, category=category)
 
diff --git a/src/sage/combinat/words/finite_word.py b/src/sage/combinat/words/finite_word.py
index b596f87e56d..1bdd38e92c7 100644
--- a/src/sage/combinat/words/finite_word.py
+++ b/src/sage/combinat/words/finite_word.py
@@ -1426,7 +1426,7 @@ def factor_set(self, n=None, algorithm='suffix tree'):
             return Set(self.factor_iterator(n))
         elif algorithm == 'naive':
             if n is None:
-                S = set([self[0:0]])
+                S = {self[0:0]}
                 for n in range(1, self.length()+1):
                     for i in range(self.length()-n+1):
                         S.add(self[i:i+n])
@@ -3006,7 +3006,7 @@ def palindromes(self, f=None):
             [word: , word: ab, word: abbabaab, word: ba, word: baba, word: bbabaa]
         """
         LPS = self.lps_lengths(f)
-        return set(self[i - LPS[i]: i] for i in range(len(self) + 1))
+        return {self[i - LPS[i]: i] for i in range(len(self) + 1)}
 
     def palindromic_complexity(self, n):
         r"""
@@ -6415,7 +6415,7 @@ def delta(self):
             return Words()([])
         ss = self[0]
         c = 0
-        v = list()
+        v = []
         max_c = 0
         for s in self:
             if s == ss:
diff --git a/src/sage/combinat/words/morphism.py b/src/sage/combinat/words/morphism.py
index f490ac96cd0..abd66da0650 100644
--- a/src/sage/combinat/words/morphism.py
+++ b/src/sage/combinat/words/morphism.py
@@ -401,7 +401,7 @@ def __init__(self, data, domain=None, codomain=None):
 
             self._morph = {}
 
-            dom_alph = list()
+            dom_alph = []
             for key, val in data.items():
                 dom_alph.append(key)
                 if val in codomain.alphabet():
@@ -950,7 +950,8 @@ def __mul__(self, other):
             sage: m * WordMorphism('')
             WordMorphism:
         """
-        return WordMorphism(dict((key, self(w)) for key, w in other._morph.items()), codomain=self.codomain())
+        return WordMorphism({key: self(w) for key, w in other._morph.items()},
+                            codomain=self.codomain())
 
     def __pow__(self, exp):
         r"""
@@ -1090,7 +1091,8 @@ def restrict_domain(self, alphabet):
             ...
             TypeError: 'sage.rings.integer.Integer' object is not iterable
         """
-        return WordMorphism(dict((a, self(a)) for a in alphabet if a in self.domain().alphabet()))
+        return WordMorphism({a: self(a) for a in alphabet
+                             if a in self.domain().alphabet()})
 
     def _matrix_(self, R=None):
         r"""
@@ -1276,7 +1278,7 @@ def image(self, letter):
         """
         return self._morph[letter]
 
-    def images(self):
+    def images(self) -> list:
         r"""
         Return the list of all the images of the letters of the alphabet
         under ``self``.
@@ -1727,9 +1729,8 @@ def is_uniform(self, k=None):
             True
         """
         if k is None:
-            return len(set(w.length() for w in self.images())) == 1
-        else:
-            return all(w.length() == k for w in self.images())
+            k = self.images()[0].length()
+        return all(w.length() == k for w in self.images())
 
     def fixed_point(self, letter):
         r"""
@@ -1980,7 +1981,7 @@ def periodic_points(self):
             raise NotImplementedError("f should be non erasing")
 
         A = self.domain().alphabet()
-        d = dict((letter, self(letter)[0]) for letter in A)
+        d = {letter: self(letter)[0] for letter in A}
         G = set(self.growing_letters())
 
         res = []
@@ -2173,7 +2174,8 @@ def conjugate(self, pos):
             sage: m.conjugate(2)
             WordMorphism: a->cdeab, b->zxy
         """
-        return WordMorphism(dict((key, w.conjugate(pos)) for (key, w) in self._morph.items()))
+        return WordMorphism({key: w.conjugate(pos)
+                             for (key, w) in self._morph.items()})
 
     def has_left_conjugate(self):
         r"""
@@ -3785,7 +3787,7 @@ def try_create_h(f, k):
             h = {letter: [letter] if image else [] for letter, image in f.items()}
         elif len(Y) < len(X):  # Trivial case #2.
             k = {x: [y] for x, y in zip(X, Y)}
-            k_inverse = {y: x for y, x in zip(Y, X)}
+            k_inverse = dict(zip(Y, X))
             h = {x: [k_inverse[y] for y in image] for x, image in f.items()}
         elif not self.is_injective():  # Non-trivial but a fast case.
             k = dict(f)
@@ -3822,7 +3824,7 @@ def try_create_h(f, k):
             for comb in combinations(factors, len(X) - 1):
                 if any(x.is_proper_prefix(y) for x in comb for y in comb):
                     continue
-                k = {x: image for x, image in zip(X, comb)}
+                k = dict(zip(X, comb))
                 h = try_create_h(f, k)
                 if h:
                     break
diff --git a/src/sage/combinat/yang_baxter_graph.py b/src/sage/combinat/yang_baxter_graph.py
index bcfac20fdb3..f2fdb7a5a47 100644
--- a/src/sage/combinat/yang_baxter_graph.py
+++ b/src/sage/combinat/yang_baxter_graph.py
@@ -335,7 +335,7 @@ def _edges_in_bfs(self):
         seen[self._root] = True
         while queue:
             u = queue.pop()
-            l = sorted(list(digraph.neighbor_out_iterator(u)))
+            l = sorted(digraph.neighbor_out_iterator(u))
             for w in l:
                 if w not in seen:
                     seen[w] = True
@@ -585,7 +585,7 @@ def __init__(self, partition):
         """
         self._partition = partition
         beta = sorted(self._partition, reverse=True)
-        root = sum([tuple(range(b)) for b in beta], tuple())[::-1]
+        root = sum((tuple(range(b)) for b in beta), ())[::-1]
         operators = [SwapIncreasingOperator(i)
                      for i in range(sum(partition) - 1)]
         super().__init__(root, operators)

From 6e73c11e5f6e4de90b141d7d01dc6f143e2ce088 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Wed, 10 Apr 2024 09:30:10 +0200
Subject: [PATCH 2/3] fix suggestions

---
 src/sage/arith/functions.pyx          |  4 ++--
 src/sage/combinat/sloane_functions.py |  2 +-
 src/sage/combinat/tiling.py           |  5 +----
 src/sage/combinat/words/morphism.py   | 11 ++++++++++-
 4 files changed, 14 insertions(+), 8 deletions(-)

diff --git a/src/sage/arith/functions.pyx b/src/sage/arith/functions.pyx
index f0c7c03220e..a3a9c4ae216 100644
--- a/src/sage/arith/functions.pyx
+++ b/src/sage/arith/functions.pyx
@@ -30,7 +30,7 @@ def lcm(a, b=None):
 
     - ``a,b`` -- two elements of a ring with lcm or
 
-    - ``a`` -- a list or tuple of elements of a ring with lcm
+    - ``a`` -- a list, tuple or iterable of elements of a ring with lcm
 
     OUTPUT:
 
@@ -135,7 +135,7 @@ cpdef LCM_list(v):
 
     INPUT:
 
-    -  ``v`` -- an iterable
+    - ``v`` -- an iterable
 
     OUTPUT: integer
 
diff --git a/src/sage/combinat/sloane_functions.py b/src/sage/combinat/sloane_functions.py
index 808bcfd849d..76a05d6dc18 100644
--- a/src/sage/combinat/sloane_functions.py
+++ b/src/sage/combinat/sloane_functions.py
@@ -859,7 +859,7 @@ def _eval(self, n):
             sage: [sloane.A003418._eval(n) for n in range(1,11)]
             [1, 2, 6, 12, 60, 60, 420, 840, 2520, 2520]
         """
-        return arith.lcm(list(range(1, n + 1)))
+        return arith.lcm(range(1, n + 1))
 
 
 class A007318(SloaneSequence):
diff --git a/src/sage/combinat/tiling.py b/src/sage/combinat/tiling.py
index 2190c5b2119..43c7817f13a 100644
--- a/src/sage/combinat/tiling.py
+++ b/src/sage/combinat/tiling.py
@@ -1811,13 +1811,10 @@ def int_to_coord_dict(self):
             True
             sage: all(B[A[i]] == i for i in A)
             True
-
         """
         if self._reusable:
             return dict(enumerate(self.space()))
-
-        number_of_pieces = len(self._pieces)
-        return {i + number_of_pieces: c for i, c in enumerate(self.space())}
+        return dict(enumerate(self.space(), start=len(self._pieces)))
 
     @cached_method
     def rows_for_piece(self, i, mod_box_isometries=False):
diff --git a/src/sage/combinat/words/morphism.py b/src/sage/combinat/words/morphism.py
index abd66da0650..24f22dad7e4 100644
--- a/src/sage/combinat/words/morphism.py
+++ b/src/sage/combinat/words/morphism.py
@@ -1727,9 +1727,18 @@ def is_uniform(self, k=None):
             False
             sage: tau.is_uniform(k=2)
             True
+
+        TESTS:
+
+            sage: phi = WordMorphism('')
+            sage: phi.is_uniform()
+            False
         """
         if k is None:
-            k = self.images()[0].length()
+            try:
+                k = self.images()[0].length()
+            except IndexError:
+                return False
         return all(w.length() == k for w in self.images())
 
     def fixed_point(self, letter):

From b9ae35b104c07b046ab1a4b12f2a1f1a9b797ea1 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Fr=C3=A9d=C3=A9ric=20Chapoton?= <chapoton@unistra.fr>
Date: Wed, 10 Apr 2024 20:10:18 +0200
Subject: [PATCH 3/3] fix suggested details

---
 src/sage/combinat/words/morphism.py | 15 ++++++++-------
 1 file changed, 8 insertions(+), 7 deletions(-)

diff --git a/src/sage/combinat/words/morphism.py b/src/sage/combinat/words/morphism.py
index 24f22dad7e4..9424a3370b7 100644
--- a/src/sage/combinat/words/morphism.py
+++ b/src/sage/combinat/words/morphism.py
@@ -1700,7 +1700,7 @@ def is_prolongable(self, letter):
 
     def is_uniform(self, k=None):
         r"""
-        Return True if self is a `k`-uniform morphism.
+        Return ``True`` if ``self`` is a `k`-uniform morphism.
 
         Let `k` be a positive integer. A morphism `\phi` is called `k`-uniform
         if for every letter `\alpha`, we have `|\phi(\alpha)| = k`. In other
@@ -1709,9 +1709,10 @@ def is_uniform(self, k=None):
 
         INPUT:
 
-        - ``k`` - a positive integer or None. If set to a positive integer,
-          then the function return True if self is `k`-uniform. If set to
-          None, then the function return True if self is uniform.
+        - ``k`` - a positive integer or ``None``. If set to a positive integer,
+          then the function return ``True`` if ``self`` is `k`-uniform.
+          If set to ``None``, then the function return ``True`` if ``self``
+          is uniform.
 
         EXAMPLES::
 
@@ -1728,17 +1729,17 @@ def is_uniform(self, k=None):
             sage: tau.is_uniform(k=2)
             True
 
-        TESTS:
+        TESTS::
 
             sage: phi = WordMorphism('')
             sage: phi.is_uniform()
-            False
+            True
         """
         if k is None:
             try:
                 k = self.images()[0].length()
             except IndexError:
-                return False
+                return True
         return all(w.length() == k for w in self.images())
 
     def fixed_point(self, letter):