gh-37245: a few details in combinat folder
    
namely

- use ruff to fix some containement tests

- add links to some error codes in the doc

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
    
URL: #37245
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert, Frédéric Chapoton

Author: Release Manager

src/sage/combinat/cluster_algebra_quiver/mutation_type.py

@@ -1045,7 +1045,7 @@ def _connected_mutation_type_AAtildeD(dg, ret_conn_vert=False):
         # if one edge appearing in exactly two oriented triangles, test that it is not a double-edge and then
         # test that either the third or fourth vertices (from the oriented triangles) is of degree 2.
         # Then initializes the long_cycle as this triangle including the degree 2 vertex, as long as no other long_cycles.
-        elif count == 1 and not dg.has_multiple_edges() and not multiple_trian_edges[0] in dg.multiple_edges():
+        elif count == 1 and not dg.has_multiple_edges() and multiple_trian_edges[0] not in dg.multiple_edges():
             multiple_trian_edge = multiple_trian_edges[0]
             neighbors = list(set(dg.neighbors( multiple_trian_edge[0] )).intersection(dg.neighbors( multiple_trian_edge[1] )))
             if dg.degree( neighbors[0] ) == 2:

src/sage/combinat/designs/bibd.py

@@ -879,7 +879,7 @@ def BIBD_from_PBD(PBD, v, k, check=True, base_cases=None):
     for X in PBD:
         n = len(X)
         N = (k-1)*n+1
-        if not (n,k) in base_cases:
+        if (n,k) not in base_cases:
             base_cases[n,k] = _relabel_bibd(balanced_incomplete_block_design(N,k), N)
 
         for XX in base_cases[n,k]:

src/sage/combinat/designs/database.py

@@ -2469,7 +2469,7 @@ def QDM_57_9_1_1_8():
                              ((45,7,1,1,9), QDM_45_7_1_1_9),
                              ((54,7,1,1,8), QDM_54_7_1_1_8),
                              ((57,9,1,1,8), QDM_57_9_1_1_8)]:
-    if not (n+u,lmbda) in QDM:
+    if (n+u,lmbda) not in QDM:
         QDM[n+u,lmbda] = {}
     QDM[n+u,lmbda][n,lmbda,mu,u] = (k,f)
 
@@ -2701,7 +2701,7 @@ def QDM_57_9_1_1_8():
 # Translate all V(m,t) into (mt+1,m+2;1,0;t)-QDM constructors
 for (m,t),(vec,source) in Vmt_vectors.items():
     n,k,lmbda,mu,u = (m*t+1,m+2,1,0,t)
-    if not (n+u,lmbda) in QDM:
+    if (n+u,lmbda) not in QDM:
         QDM[n+u,lmbda] = {}
     QDM[n+u,lmbda][n,lmbda,mu,u] = (k,lambda m=m,t=t,vec=vec:QDM_from_Vmt(m,t,vec))
 

src/sage/combinat/designs/difference_family.py

@@ -3138,8 +3138,9 @@ def difference_family(v, k, l=1, existence=False, explain_construction=False, ch
 
     See also :wikipedia:`Difference_set`.
 
-    If there is no such difference family, an ``EmptySetError`` is raised and if
-    there is no construction at the moment ``NotImplementedError`` is raised.
+    If there is no such difference family, an ``EmptySetError`` is raised and
+    if there is no construction at the moment :class:`NotImplementedError`
+    is raised.
 
     INPUT:
 

src/sage/combinat/designs/latin_squares.py

@@ -299,7 +299,7 @@ def mutually_orthogonal_latin_squares(k, n, partitions=False, check=True):
         Unknown
 
     If you ask for such a MOLS then you will respectively get an informative
-    ``EmptySetError`` or ``NotImplementedError``::
+    ``EmptySetError`` or :class:`NotImplementedError`::
 
         sage: designs.mutually_orthogonal_latin_squares(5, 5)
         Traceback (most recent call last):

src/sage/combinat/designs/orthogonal_arrays.py

@@ -190,7 +190,7 @@ def transversal_design(k, n, resolvable=False, check=True, existence=False):
         Unknown
 
     If you ask for a transversal design that Sage is not able to build then an
-    ``EmptySetError`` or a ``NotImplementedError`` is raised::
+    ``EmptySetError`` or a :class:`NotImplementedError` is raised::
 
         sage: designs.transversal_design(47, 100)
         Traceback (most recent call last):
@@ -1359,7 +1359,7 @@ def incomplete_orthogonal_array(k,n,holes,resolvable=False, existence=False):
             return True
         independent_set = OA_find_disjoint_blocks(OA,k,n,number_of_holes)
 
-    elif max_hole == 1 and not orthogonal_array(k,n,existence=True) is True:
+    elif max_hole == 1 and orthogonal_array(k,n,existence=True) is not True:
         return orthogonal_array(k,n,existence=existence)
 
     # From a quasi-difference matrix
@@ -2117,8 +2117,8 @@ class OAMainFunctions:
         6
 
     If you ask for an orthogonal array that does not exist, then you will
-    either obtain an ``EmptySetError`` (if it knows that such an orthogonal array
-    does not exist) or a ``NotImplementedError``::
+    either obtain an ``EmptySetError`` (if it knows that such an orthogonal
+    array does not exist) or a :class:`NotImplementedError`::
 
         sage: designs.orthogonal_arrays.build(4,2)
         Traceback (most recent call last):

src/sage/combinat/designs/resolvable_bibd.py

@@ -738,7 +738,7 @@ def PBD_4_7_from_Y(gdd,check=True):
                          "but there are other: {}".format(txt))
 
     for gs in group_sizes:
-        if not PBD_4_7(3*gs+1,existence=True) is True:
+        if PBD_4_7(3*gs+1,existence=True) is not True:
             raise RuntimeError("A group has size {} but I do not know how to "
                                "build a ({},[4,7])-PBD".format(gs,3*gs+1))
 

src/sage/combinat/designs/steiner_quadruple_systems.py

@@ -709,7 +709,7 @@ def steiner_quadruple_system(n, check=False):
         ....:         sqs = designs.steiner_quadruple_system(n, check=True)
     """
     n = int(n)
-    if not ((n % 6) in [2, 4]):
+    if (n % 6) not in [2, 4]:
         raise ValueError("n mod 6 must be equal to 2 or 4")
     elif n == 4:
         sqs = IncidenceStructure(4, [[0,1,2,3]], copy=False, check=False)

src/sage/combinat/finite_state_machine.py

@@ -591,8 +591,7 @@
     ...
     ValueError: Invalid input sequence.
 
-The raised ``ValueError``
-means `13` is not divisible by `3`.
+The raised :class:`ValueError` means `13` is not divisible by `3`.
 
 .. _finite_state_machine_gray_code_example:
 
@@ -2120,7 +2119,7 @@ def _epsilon_cycle_output_empty_(self, fsm=None):
 
         ``True`` or ``False``
 
-        A ``ValueError`` is raised when ``self`` is not in an epsilon
+        A :class:`ValueError` is raised when ``self`` is not in an epsilon
         cycle.
 
         TESTS::
@@ -2537,7 +2536,9 @@ def duplicate_transition_ignore(old_transition, new_transition):
 def duplicate_transition_raise_error(old_transition, new_transition):
     """
     Alternative function for handling duplicate transitions in finite
-    state machines. This implementation raises a ``ValueError``.
+    state machines.
+
+    This implementation raises a :class:`ValueError`.
 
     See the documentation of the ``on_duplicate_transition`` parameter
     of :class:`FiniteStateMachine`.
@@ -2551,7 +2552,7 @@ def duplicate_transition_raise_error(old_transition, new_transition):
 
     OUTPUT:
 
-    Nothing. A ``ValueError`` is raised.
+    Nothing. A :class:`ValueError` is raised.
 
     EXAMPLES::
 
@@ -2812,7 +2813,7 @@ class FiniteStateMachine(SageObject):
         non-deterministic).
 
         If the transition does not exist, the function should raise a
-        ``LookupError`` or return an empty list.
+        :class:`LookupError` or return an empty list.
 
         When constructing a finite state machine in this way, some
         initial states and an input alphabet have to be specified.
@@ -5507,7 +5508,7 @@ def state(self, state):
 
         The state of the finite state machine corresponding to ``state``.
 
-        If no state is found, then a ``LookupError`` is thrown.
+        If no state is found, then a :class:`LookupError` is thrown.
 
         EXAMPLES::
 
@@ -5553,7 +5554,7 @@ def transition(self, transition):
         The transition of the finite state machine corresponding
         to ``transition``.
 
-        If no transition is found, then a ``LookupError`` is thrown.
+        If no transition is found, then a :class:`LookupError` is thrown.
 
         EXAMPLES::
 
@@ -7622,7 +7623,7 @@ def product_FiniteStateMachine(self, other, function,
           for `j\in\{1, \ldots, d\}` and returns a pair ``(word_in, word_out)``
           which is the label of the transition `A=(A_1, \ldots, A_d)` to `B=(B_1,
           \ldots, B_d)`. If there is no transition from `A` to `B`,
-          then ``function`` should raise a ``LookupError``.
+          then ``function`` should raise a :class:`LookupError`.
 
         - ``new_input_alphabet`` (optional) -- the new input alphabet
           as a list.
@@ -7637,7 +7638,7 @@ def product_FiniteStateMachine(self, other, function,
           the corresponding state in the new finite state machine. By
           default, the final output is the empty word if both final
           outputs of the constituent states are empty; otherwise, a
-          ``ValueError`` is raised.
+          :class:`ValueError` is raised.
 
         - ``new_class`` -- Class of the new finite state machine. By
           default (``None``), the class of ``self`` is used.
@@ -12685,7 +12686,7 @@ def process(self, *args, **kwargs):
         - ``full_output`` -- (default: ``True``) a boolean. If set,
           then the full output is given, otherwise only the generated
           output (the third entry below only). If the input is not
-          accepted, a ``ValueError`` is raised.
+          accepted, a :class:`ValueError` is raised.
 
         - ``always_include_output`` -- if set (not by default), always
           include the output. This is inconsequential for a

src/sage/combinat/partition.py

@@ -3017,7 +3017,7 @@ def arm_length(self, i, j):
 
         OUTPUT:
 
-        An integer or a ``ValueError``
+        An integer or a :class:`ValueError`
 
         EXAMPLES::
 
@@ -3111,7 +3111,7 @@ def leg_length(self, i, j):
 
         OUTPUT:
 
-        An integer or a ``ValueError``
+        An integer or a :class:`ValueError`
 
         EXAMPLES::
 
@@ -6201,8 +6201,9 @@ def __contains__(self, x):
 
     def subset(self, *args, **kwargs):
         r"""
-        Return ``self`` if no arguments are given, otherwise raises a
-        ``ValueError``.
+        Return ``self`` if no arguments are given.
+
+        Otherwise, it raises a :class:`ValueError`.
 
         EXAMPLES::
 
@@ -9017,7 +9018,7 @@ def number_of_partitions(n, algorithm='default'):
         sage: len(v)
         7
 
-    The input must be a nonnegative integer or a ``ValueError`` is raised.
+    The input must be a nonnegative integer or a :class:`ValueError` is raised.
 
     ::