gh-37610: src/sage/combinat: Doctest cosmetics
    
<!-- ^ Please provide a concise and informative title. -->
<!-- ^ Don't put issue numbers in the title, do this in the PR
description below. -->
<!-- ^ For example, instead of "Fixes #12345" use "Introduce new method
to calculate 1 + 2". -->
<!-- v Describe your changes below in detail. -->
<!-- v Why is this change required? What problem does it solve? -->
<!-- v If this PR resolves an open issue, please link to it here. For
example, "Fixes #12345". -->

Standard reformatting of doctests and their outputs

Split out from #35095

### 📝 Checklist

<!-- Put an `x` in all the boxes that apply. -->

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

### ⌛ Dependencies

<!-- List all open PRs that this PR logically depends on. For example,
-->
<!-- - #12345: short description why this is a dependency -->
<!-- - #34567: ... -->
    
URL: #37610
Reported by: Matthias Köppe
Reviewer(s): David Coudert, Matthias Köppe

Author: Release Manager

src/sage/combinat/binary_tree.py

@@ -1617,7 +1617,7 @@ def to_tilting(self):
             sage: t = from_hexacode('2020222002000', BinaryTrees())
             sage: print(t.to_tilting())
             [(0, 1), (2, 3), (4, 5), (6, 7), (4, 7), (8, 9), (10, 11),
-            (8, 11), (4, 11), (12, 13), (4, 13), (2, 13), (0, 13)]
+             (8, 11), (4, 11), (12, 13), (4, 13), (2, 13), (0, 13)]
 
             sage: w = DyckWord([1,1,1,1,0,1,1,0,0,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0,0])   # needs sage.combinat
             sage: t2 = w.to_binary_tree()                                               # needs sage.combinat

src/sage/combinat/designs/difference_family.py

@@ -3186,11 +3186,12 @@ def difference_family(v, k, l=1, existence=False, explain_construction=False, ch
         sage: print(designs.difference_family(15,7,3,explain_construction=True))
         Singer difference set
 
-        sage: print(designs.difference_family(91,10,1,explain_construction=True))       # needs sage.libs.pari
+        sage: # needs sage.libs.pari
+        sage: print(designs.difference_family(91,10,1,explain_construction=True))
         Singer difference set
-        sage: print(designs.difference_family(64,28,12, explain_construction=True))     # needs sage.libs.pari
+        sage: print(designs.difference_family(64,28,12, explain_construction=True))
         McFarland 1973 construction
-        sage: print(designs.difference_family(576, 276, 132, explain_construction=True))            # needs sage.libs.pari
+        sage: print(designs.difference_family(576, 276, 132, explain_construction=True))
         Hadamard difference set product from N1=2 and N2=3
 
     For `k=6,7` we look at the set of small prime powers for which a
@@ -3203,9 +3204,10 @@ def difference_family(v, k, l=1, existence=False, explain_construction=False, ch
         ....:             yield k
         ....:         k += m
 
+        sage: # needs sage.libs.pari
         sage: from itertools import islice
-        sage: l6 = {True:[], False: [], Unknown: []}
-        sage: for q in islice(prime_power_mod(1,30), int(60)):                          # needs sage.libs.pari
+        sage: l6 = {True: [], False: [], Unknown: []}
+        sage: for q in islice(prime_power_mod(1,30), int(60)):
         ....:     l6[designs.difference_family(q,6,existence=True)].append(q)
         sage: l6[True]
         [31, 121, 151, 181, 211, ...,  3061, 3121, 3181]
@@ -3214,8 +3216,9 @@ def difference_family(v, k, l=1, existence=False, explain_construction=False, ch
         sage: l6[False]
         []
 
+        sage: # needs sage.libs.pari
         sage: l7 = {True: [], False: [], Unknown: []}
-        sage: for q in islice(prime_power_mod(1,42), int(60)):                          # needs sage.libs.pari
+        sage: for q in islice(prime_power_mod(1,42), int(60)):
         ....:     l7[designs.difference_family(q,7,existence=True)].append(q)
         sage: l7[True]
         [169, 337, 379, 421, 463, 547, 631, 673, 757, 841, 883, 967, ...,  4621, 4957, 5167]

src/sage/combinat/free_dendriform_algebra.py

@@ -87,7 +87,8 @@ class FreeDendriformAlgebra(CombinatorialFreeModule):
         sage: F = algebras.FreeDendriform(ZZ, 'xyz')
         sage: x,y,z = F.gens()
         sage: (x * y) * z
-        B[x[., y[., z[., .]]]] + B[x[., z[y[., .], .]]] + B[y[x[., .], z[., .]]] + B[z[x[., y[., .]], .]] + B[z[y[x[., .], .], .]]
+        B[x[., y[., z[., .]]]] + B[x[., z[y[., .], .]]] + B[y[x[., .], z[., .]]]
+         + B[z[x[., y[., .]], .]] + B[z[y[x[., .], .], .]]
 
     The free dendriform algebra is associative::
 
@@ -114,7 +115,8 @@ class FreeDendriformAlgebra(CombinatorialFreeModule):
         sage: w = F1.gen(0); w
         B[[., .]]
         sage: w * w * w
-        B[[., [., [., .]]]] + B[[., [[., .], .]]] + B[[[., .], [., .]]] + B[[[., [., .]], .]] + B[[[[., .], .], .]]
+        B[[., [., [., .]]]] + B[[., [[., .], .]]] + B[[[., .], [., .]]]
+         + B[[[., [., .]], .]] + B[[[[., .], .], .]]
 
     The set `E` can be infinite::
 

src/sage/combinat/interval_posets.py

@@ -1129,7 +1129,8 @@ def rise_contact_involution(self) -> TIP:
 
         EXAMPLES::
 
-            sage: tip = TamariIntervalPoset(8, [(1,2), (2,4), (3,4), (6,7), (3,2), (5,4), (6,4), (8,7)])
+            sage: tip = TamariIntervalPoset(8, [(1,2), (2,4), (3,4), (6,7),
+            ....:                               (3,2), (5,4), (6,4), (8,7)])
             sage: t = tip.rise_contact_involution(); t
             The Tamari interval of size 8 induced by relations [(2, 8), (3, 8),
             (4, 5), (5, 7), (6, 7), (7, 8), (8, 1), (7, 2), (6, 2), (5, 3),
@@ -1840,13 +1841,16 @@ def lower_binary_tree(self):
 
         EXAMPLES::
 
-            sage: ip = TamariIntervalPoset(6,[(3,2),(4,3),(5,2),(6,5),(1,2),(4,5)]); ip
-            The Tamari interval of size 6 induced by relations [(1, 2), (4, 5), (6, 5), (5, 2), (4, 3), (3, 2)]
+            sage: ip = TamariIntervalPoset(6, [(3,2),(4,3),(5,2),(6,5),(1,2),(4,5)]); ip
+            The Tamari interval of size 6 induced by relations
+             [(1, 2), (4, 5), (6, 5), (5, 2), (4, 3), (3, 2)]
             sage: ip.lower_binary_tree()
             [[., .], [[., [., .]], [., .]]]
-            sage: TamariIntervalPosets.final_forest(ip.lower_binary_tree()) == ip.final_forest()
+            sage: ff = TamariIntervalPosets.final_forest(ip.lower_binary_tree())
+            sage: ff == ip.final_forest()
             True
-            sage: ip == TamariIntervalPosets.from_binary_trees(ip.lower_binary_tree(),ip.upper_binary_tree())
+            sage: ip == TamariIntervalPosets.from_binary_trees(ip.lower_binary_tree(),
+            ....:                                              ip.upper_binary_tree())
             True
         """
         return self.min_linear_extension().binary_search_tree_shape(left_to_right=False)
@@ -1891,9 +1895,11 @@ def upper_binary_tree(self):
         EXAMPLES::
 
             sage: ip = TamariIntervalPoset(6,[(3,2),(4,3),(5,2),(6,5),(1,2),(4,5)]); ip
-            The Tamari interval of size 6 induced by relations [(1, 2), (4, 5), (6, 5), (5, 2), (4, 3), (3, 2)]
+            The Tamari interval of size 6 induced by relations
+             [(1, 2), (4, 5), (6, 5), (5, 2), (4, 3), (3, 2)]
             sage: ip.upper_binary_tree()
             [[., .], [., [[., .], [., .]]]]
+
             sage: TamariIntervalPosets.initial_forest(ip.upper_binary_tree()) == ip.initial_forest()
             True
             sage: ip == TamariIntervalPosets.from_binary_trees(ip.lower_binary_tree(),ip.upper_binary_tree())
@@ -1941,8 +1947,9 @@ def subposet(self, start, end) -> TIP:
 
         EXAMPLES::
 
-            sage: ip = TamariIntervalPoset(6,[(3,2),(4,3),(5,2),(6,5),(1,2),(3,5),(4,5)]); ip
-            The Tamari interval of size 6 induced by relations [(1, 2), (3, 5), (4, 5), (6, 5), (5, 2), (4, 3), (3, 2)]
+            sage: ip = TamariIntervalPoset(6, [(3,2),(4,3),(5,2),(6,5),(1,2),(3,5),(4,5)]); ip
+            The Tamari interval of size 6 induced by relations
+             [(1, 2), (3, 5), (4, 5), (6, 5), (5, 2), (4, 3), (3, 2)]
             sage: ip.subposet(1,3)
             The Tamari interval of size 2 induced by relations [(1, 2)]
             sage: ip.subposet(1,4)
@@ -2109,12 +2116,16 @@ def lower_contained_intervals(self) -> Iterator[TIP]:
 
         EXAMPLES::
 
-            sage: ip = TamariIntervalPoset(4,[(2,4),(3,4),(2,1),(3,1)])
+            sage: ip = TamariIntervalPoset(4, [(2,4),(3,4),(2,1),(3,1)])
             sage: list(ip.lower_contained_intervals())
-            [The Tamari interval of size 4 induced by relations [(2, 4), (3, 4), (3, 1), (2, 1)],
-             The Tamari interval of size 4 induced by relations [(1, 4), (2, 4), (3, 4), (3, 1), (2, 1)],
-             The Tamari interval of size 4 induced by relations [(2, 3), (3, 4), (3, 1), (2, 1)],
-             The Tamari interval of size 4 induced by relations [(1, 4), (2, 3), (3, 4), (3, 1), (2, 1)]]
+            [The Tamari interval of size 4 induced by relations
+              [(2, 4), (3, 4), (3, 1), (2, 1)],
+             The Tamari interval of size 4 induced by relations
+              [(1, 4), (2, 4), (3, 4), (3, 1), (2, 1)],
+             The Tamari interval of size 4 induced by relations
+              [(2, 3), (3, 4), (3, 1), (2, 1)],
+             The Tamari interval of size 4 induced by relations
+              [(1, 4), (2, 3), (3, 4), (3, 1), (2, 1)]]
             sage: ip = TamariIntervalPoset(4,[])
             sage: len(list(ip.lower_contained_intervals()))
             14
@@ -2256,12 +2267,15 @@ def maximal_chain_tamari_intervals(self) -> Iterator[TIP]:
 
         EXAMPLES::
 
-            sage: ip = TamariIntervalPoset(4,[(2,4),(3,4),(2,1),(3,1)])
+            sage: ip = TamariIntervalPoset(4, [(2,4),(3,4),(2,1),(3,1)])
             sage: list(ip.maximal_chain_tamari_intervals())
-            [The Tamari interval of size 4 induced by relations [(2, 4), (3, 4), (3, 1), (2, 1)],
-             The Tamari interval of size 4 induced by relations [(2, 4), (3, 4), (4, 1), (3, 1), (2, 1)],
-             The Tamari interval of size 4 induced by relations [(2, 4), (3, 4), (4, 1), (3, 2), (2, 1)]]
-            sage: ip = TamariIntervalPoset(4,[])
+            [The Tamari interval of size 4 induced by relations
+              [(2, 4), (3, 4), (3, 1), (2, 1)],
+             The Tamari interval of size 4 induced by relations
+              [(2, 4), (3, 4), (4, 1), (3, 1), (2, 1)],
+             The Tamari interval of size 4 induced by relations
+              [(2, 4), (3, 4), (4, 1), (3, 2), (2, 1)]]
+            sage: ip = TamariIntervalPoset(4, [])
             sage: list(ip.maximal_chain_tamari_intervals())
             [The Tamari interval of size 4 induced by relations [],
              The Tamari interval of size 4 induced by relations [(2, 1)],
@@ -2405,7 +2419,8 @@ def tamari_inversions_iter(self) -> Iterator[tuple[int, int]]:
             sage: list(T.tamari_inversions_iter())
             [(4, 5)]
 
-            sage: T = TamariIntervalPoset(8, [(2, 7), (3, 7), (4, 7), (5, 7), (6, 7), (8, 7), (6, 4), (5, 4), (4, 3), (3, 2)])
+            sage: T = TamariIntervalPoset(8, [(2, 7), (3, 7), (4, 7), (5, 7), (6, 7),
+            ....:                             (8, 7), (6, 4), (5, 4), (4, 3), (3, 2)])
             sage: list(T.tamari_inversions_iter())
             [(1, 2), (1, 7), (5, 6)]
 
@@ -2565,12 +2580,14 @@ def decomposition_to_triple(self) -> None | tuple[TIP, TIP, int]:
 
         EXAMPLES::
 
-            sage: tip = TamariIntervalPoset(8, [(1,2), (2,4), (3,4), (6,7), (3,2), (5,4), (6,4), (8,7)])
+            sage: tip = TamariIntervalPoset(8, [(1,2), (2,4), (3,4), (6,7),
+            ....:                               (3,2), (5,4), (6,4), (8,7)])
             sage: tip.decomposition_to_triple()
             (The Tamari interval of size 3 induced by relations [(1, 2), (3, 2)],
-            The Tamari interval of size 4 induced by relations [(2, 3), (4, 3)],
-            2)
-            sage: tip == TamariIntervalPosets.recomposition_from_triple(*tip.decomposition_to_triple())
+             The Tamari interval of size 4 induced by relations [(2, 3), (4, 3)],
+             2)
+            sage: tip == TamariIntervalPosets.recomposition_from_triple(
+            ....:            *tip.decomposition_to_triple())
             True
 
         TESTS::
@@ -2600,7 +2617,8 @@ def grafting_tree(self) -> LabelledBinaryTree:
 
         EXAMPLES::
 
-            sage: tip = TamariIntervalPoset(8, [(1,2), (2,4), (3,4), (6,7), (3,2), (5,4), (6,4), (8,7)])
+            sage: tip = TamariIntervalPoset(8, [(1,2), (2,4), (3,4), (6,7),
+            ....:                               (3,2), (5,4), (6,4), (8,7)])
             sage: tip.grafting_tree()
             2[1[0[., .], 0[., .]], 0[., 1[0[., .], 0[., .]]]]
             sage: tip == TamariIntervalPosets.from_grafting_tree(tip.grafting_tree())
@@ -2906,7 +2924,7 @@ class options(GlobalOptions):
             sage: TIP = TamariIntervalPosets
             sage: TIP.options.latex_color_decreasing
             red
-            sage: TIP.options.latex_color_decreasing='green'
+            sage: TIP.options.latex_color_decreasing = 'green'
             sage: TIP.options.latex_color_decreasing
             green
             sage: TIP.options._reset()
@@ -3243,7 +3261,8 @@ def from_binary_trees(tree1, tree2) -> TIP:
             sage: tree1 = BinaryTree([[],[[None,[]],[]]])
             sage: tree2 = BinaryTree([None,[None,[None,[[],[]]]]])
             sage: TamariIntervalPosets.from_binary_trees(tree1,tree2)
-            The Tamari interval of size 6 induced by relations [(4, 5), (6, 5), (5, 2), (4, 3), (3, 2)]
+            The Tamari interval of size 6 induced by relations
+             [(4, 5), (6, 5), (5, 2), (4, 3), (3, 2)]
 
             sage: tree3 = BinaryTree([None,[None,[[],[None,[]]]]])
             sage: TamariIntervalPosets.from_binary_trees(tree1,tree3)

src/sage/combinat/matrices/latin.py

@@ -41,8 +41,8 @@
 #. some named latin squares (back circulant, forward circulant, abelian
    `2`-group);
 
-#. functions is\_partial\_latin\_square and is\_latin\_square to test
-   if a LatinSquare object satisfies the definition of a latin square
+#. methods :meth:`is_partial_latin_square` and :meth:`is_latin_square` to test
+   if a :class:`LatinSquare` object satisfies the definition of a latin square
    or partial latin square, respectively;
 
 #. tests for completion and unique completion (these use the C++
@@ -57,7 +57,7 @@
 
 #. a few examples of `\tau_i` representations of bitrades constructed
    from the action of a group on itself by right multiplication,
-   functions for converting to a pair of LatinSquare objects.
+   functions for converting to a pair of :class:`LatinSquare` objects.
 
 EXAMPLES::
 

src/sage/combinat/necklace.py

@@ -210,7 +210,7 @@ def cardinality(self) -> Integer:
 
         ::
 
-            sage: comps = [[],[2,2],[3,2,7],[4,2],[0,4,2],[2,0,4]]+Compositions(4).list()
+            sage: comps = [[],[2,2],[3,2,7],[4,2],[0,4,2],[2,0,4]] + Compositions(4).list()
             sage: ns = [Necklaces(comp) for comp in comps]
             sage: all(n.cardinality() == len(n.list()) for n in ns)                     # needs sage.libs.pari
             True

src/sage/combinat/partition.py

@@ -5197,7 +5197,8 @@ def dimension(self, smaller=None, k=1):
         Checks that the sum of squares of dimensions of characters of the
         symmetric group is the order of the group::
 
-            sage: all(sum(mu.dimension()^2 for mu in Partitions(i))==factorial(i) for i in range(10))
+            sage: all(sum(mu.dimension()^2 for mu in Partitions(i)) == factorial(i)
+            ....:     for i in range(10))
             True
 
         A check coming from the theory of `k`-differentiable posets::
@@ -5716,14 +5717,14 @@ class Partitions(UniqueRepresentation, Parent):
     Here are some more examples illustrating ``min_part``, ``max_part``,
     and ``length``::
 
-        sage: Partitions(5,min_part=2)
+        sage: Partitions(5, min_part=2)
         Partitions of the integer 5 satisfying constraints min_part=2
-        sage: Partitions(5,min_part=2).list()
+        sage: Partitions(5, min_part=2).list()
         [[5], [3, 2]]
 
     ::
 
-        sage: Partitions(3,max_length=2).list()
+        sage: Partitions(3, max_length=2).list()
         [[3], [2, 1]]
 
     ::
@@ -5836,7 +5837,7 @@ class Partitions(UniqueRepresentation, Parent):
         ...
         ValueError: the size must be specified with any keyword argument
 
-        sage: Partitions(max_part = 3)
+        sage: Partitions(max_part=3)
         3-Bounded Partitions
 
     Check that :issue:`14145` has been fixed::

src/sage/combinat/partition_tuple.py

@@ -155,7 +155,7 @@ class of modules for the algebras, which are generalisations of the Specht
        *   **        *
        *             *
                      *
-    sage: lam=PartitionTuples(3)([[3,2],[],[1,1,1,1]]); lam
+    sage: lam = PartitionTuples(3)([[3,2],[],[1,1,1,1]]); lam
     ([3, 2], [], [1, 1, 1, 1])
     sage: lam.level()
     3
@@ -200,7 +200,7 @@ class of modules for the algebras, which are generalisations of the Specht
 
 Every partition tuple behaves every much like a tuple of partitions::
 
-    sage: mu=PartitionTuple([[4,1],[],[2,2,1],[3]])
+    sage: mu = PartitionTuple([[4,1],[],[2,2,1],[3]])
     sage: [ nu for nu in mu ]
     [[4, 1], [], [2, 2, 1], [3]]
     sage: Set([ type(nu) for nu in mu ])
@@ -228,9 +228,11 @@ class of modules for the algebras, which are generalisations of the Specht
     sage: len(mu)
     4
     sage: mu.cells()
-    [(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3), (0, 1, 0), (2, 0, 0), (2, 0, 1), (2, 1, 0), (2, 1, 1), (2, 2, 0), (3, 0, 0), (3, 0, 1), (3, 0, 2)]
+    [(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3), (0, 1, 0), (2, 0, 0), (2, 0, 1),
+     (2, 1, 0), (2, 1, 1), (2, 2, 0), (3, 0, 0), (3, 0, 1), (3, 0, 2)]
     sage: mu.addable_cells()
-    [(0, 0, 4), (0, 1, 1), (0, 2, 0), (1, 0, 0), (2, 0, 2), (2, 2, 1), (2, 3, 0), (3, 0, 3), (3, 1, 0)]
+    [(0, 0, 4), (0, 1, 1), (0, 2, 0), (1, 0, 0), (2, 0, 2), (2, 2, 1),
+     (2, 3, 0), (3, 0, 3), (3, 1, 0)]
     sage: mu.removable_cells()
     [(0, 0, 3), (0, 1, 0), (2, 1, 1), (2, 2, 0), (3, 0, 2)]
 
@@ -2376,7 +2378,7 @@ def _repr_(self):
 
             sage: PartitionTuples(4,2)
             Partition tuples of level 4 and size 2
-            sage: PartitionTuples(size=2,level=4)
+            sage: PartitionTuples(size=2, level=4)
             Partition tuples of level 4 and size 2
         """
         return 'Partition tuples of level {} and size {}'.format(self._level, self._size)
@@ -3037,7 +3039,7 @@ def _repr_(self):
             (2, 1, 4)-Regular partition tuples of level 3 and size 7
             sage: PartitionTuples(4,2,3)
             3-Regular partition tuples of level 4 and size 2
-            sage: PartitionTuples(size=2,level=4,regular=3)
+            sage: PartitionTuples(size=2, level=4, regular=3)
             3-Regular partition tuples of level 4 and size 2
         """
         if self._ell[1:] == self._ell[:-1]: