gh-36478: some details in pyx files in combinat
    
This is fixing some of the messages of `cython-lint` on pyx files in the
`combinat` folder.

### 📝 Checklist

- [x] The title is concise, informative, and self-explanatory.
- [x] The description explains in detail what this PR is about.
    
URL: #36478
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert

Author: Release Manager

src/sage/combinat/combinat_cython.pyx

@@ -134,6 +134,7 @@ cdef mpz_stirling_s2(mpz_t s, unsigned long n, unsigned long k):
         mpz_clear(t)
         mpz_clear(u)
 
+
 def _stirling_number2(n, k):
     """
     Python wrapper of mpz_stirling_s2.
@@ -148,8 +149,9 @@ def _stirling_number2(n, k):
     mpz_stirling_s2(s.value, n, k)
     return s
 
+
 #####################################################################
-## Lyndon word iterator
+#  Lyndon word iterator
 
 def lyndon_word_iterator(Py_ssize_t n, Py_ssize_t k):
     r"""
@@ -204,7 +206,8 @@ def lyndon_word_iterator(Py_ssize_t n, Py_ssize_t k):
         while a[i] == n - 1:
             i -= 1
 
-## Perfect matchings iterator
+
+#  Perfect matchings iterator
 
 def perfect_matchings_iterator(Py_ssize_t n):
     r"""
@@ -276,6 +279,7 @@ def perfect_matchings_iterator(Py_ssize_t n):
     sig_free(e)
     sig_free(f)
 
+
 cdef list convert(Py_ssize_t* f, Py_ssize_t n):
     """
     Convert a list ``f`` representing a fixed-point free involution
@@ -288,8 +292,9 @@ cdef list convert(Py_ssize_t* f, Py_ssize_t n):
             ret.append((i, f[i]))
     return ret
 
+
 #####################################################################
-## Set partition composition
+#  Set partition composition
 
 def set_partition_composition(tuple sp1, tuple sp2):
     r"""

src/sage/combinat/debruijn_sequence.pyx

@@ -57,15 +57,16 @@ AUTHOR:
 
 """
 
-#*******************************************************************************
+# ******************************************************************************
 #         Copyright (C) 2011 Eviatar Bach <[email protected]>
 #
 # Distributed  under  the  terms  of  the  GNU  General  Public  License (GPL)
-#                         http://www.gnu.org/licenses/
-#*******************************************************************************
+#                         https://www.gnu.org/licenses/
+# ******************************************************************************
 
 from sage.data_structures.bitset_base cimport *
 
+
 def debruijn_sequence(int k, int n):
     """
     The generating function for De Bruijn sequences. This avoids the object
@@ -93,6 +94,7 @@ def debruijn_sequence(int k, int n):
     gen(1, 1, k, n)
     return sequence
 
+
 cdef gen(int t, int p, k, n):
     """
     The internal generation function. This should not be accessed by the
@@ -183,13 +185,15 @@ def is_debruijn_sequence(seq, k, n):
 
     return answer
 
+
 from sage.categories.finite_sets import FiniteSets
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.structure.parent import Parent
 
 from sage.rings.integer cimport Integer
 from sage.rings.integer_ring import ZZ
 
+
 class DeBruijnSequences(UniqueRepresentation, Parent):
     """
     Represents the De Bruijn sequences of given parameters `k` and `n`.
@@ -256,35 +260,32 @@ class DeBruijnSequences(UniqueRepresentation, Parent):
         """
         Constructor.
 
-        Checks the consistency of the given arguments.
+        This checks the consistency of the given arguments.
 
         TESTS:
 
-        Setting ``n`` orr ``k`` to anything under 1 will return a ValueError:
-
-        ::
+        Setting ``n`` or ``k`` to anything under 1 will return
+        a :class:`ValueError`::
 
             sage: DeBruijnSequences(3, 0).an_element()
             Traceback (most recent call last):
             ...
-            ValueError: k and n cannot be under 1.
+            ValueError: k and n cannot be under 1
 
         Setting ``n`` or ``k`` to any type except an integer will return a
-        TypeError:
-
-        ::
+        :class:`TypeError`::
 
             sage: DeBruijnSequences(2.5, 3).an_element()
             Traceback (most recent call last):
             ...
-            TypeError: k and n must be integers.
+            TypeError: k and n must be integers
         """
         Parent.__init__(self, category=FiniteSets())
         if n < 1 or k < 1:
-            raise ValueError('k and n cannot be under 1.')
+            raise ValueError('k and n cannot be under 1')
         if (not isinstance(n, (Integer, int)) or
-            not isinstance(k, (Integer,int))):
-            raise TypeError('k and n must be integers.')
+                not isinstance(k, (Integer, int))):
+            raise TypeError('k and n must be integers')
 
         self.k = k
         self.n = n

src/sage/combinat/degree_sequences.pyx

@@ -57,9 +57,9 @@ An integer sequence need not necessarily be a degree sequence. Indeed, in a
 degree sequence of length `n` no integer can be larger than `n-1` -- the degree
 of a vertex is at most `n-1` -- and the sum of them is at most `n(n-1)`.
 
-Degree sequences are completely characterized by a result from Erdos and Gallai:
+Degree sequences are completely characterized by a result from Erdős and Gallai:
 
-**Erdos and Gallai:** *The sequence of integers* `d_1 \geq \cdots \geq d_n`
+**Erdős and Gallai:** *The sequence of integers* `d_1 \geq \cdots \geq d_n`
 *is a degree sequence if and only if* `\sum_i d_i` is even and `\forall i`
 
 .. MATH::
@@ -281,6 +281,7 @@ from cysignals.signals cimport sig_on, sig_off
 cdef unsigned char * seq
 cdef list sequences
 
+
 class DegreeSequences:
 
     def __init__(self, n):
@@ -307,16 +308,16 @@ class DegreeSequences:
             sage: DegreeSequences(-1)
             Traceback (most recent call last):
             ...
-            ValueError: The input parameter must be >= 0.
+            ValueError: the input parameter must be >= 0
         """
         if n < 0:
-            raise ValueError("The input parameter must be >= 0.")
+            raise ValueError("the input parameter must be >= 0")
         self._n = n
 
     def __contains__(self, seq):
         """
-        Checks whether a given integer sequence is the degree sequence
-        of a graph on `n` elements
+        Check whether a given integer sequence is the degree sequence
+        of a graph on `n` elements.
 
         EXAMPLES::
 
@@ -342,7 +343,7 @@ class DegreeSequences:
             [[0]]
         """
         cdef int n = self._n
-        if len(seq)!=n:
+        if len(seq) != n:
             return False
 
         # Is the sum even ?
@@ -352,13 +353,13 @@ class DegreeSequences:
         # Partial represents the left side of Erdos and Gallai's inequality,
         # i.e. the sum of the i first integers.
         cdef int partial = 0
-        cdef int i,d,dd, right
+        cdef int i, d, dd, right
 
         # Temporary variable to ensure that the sequence is indeed
         # non-increasing
-        cdef int prev = n-1
+        cdef int prev = n - 1
 
-        for i,d in enumerate(seq):
+        for i, d in enumerate(seq):
 
             # Non-increasing ?
             if d > prev:
@@ -370,9 +371,9 @@ class DegreeSequences:
             partial += d
 
             # Evaluating the right hand side
-            right = i*(i+1)
-            for dd in seq[i+1:]:
-                right += min(dd,i+1)
+            right = i * (i + 1)
+            for dd in seq[i + 1:]:
+                right += min(dd, i + 1)
 
             # Comparing the two
             if partial > right:
@@ -404,14 +405,15 @@ class DegreeSequences:
             sage: all(seq in DS for seq in DS)
             True
         """
-        return iter( init(self._n) )
+        yield from init(self._n)
 
     def __dealloc__():
         """
         Freeing the memory
         """
         sig_free(seq)
 
+
 cdef init(int n):
     """
     Initializes the memory and starts the enumeration algorithm.
@@ -432,7 +434,7 @@ cdef init(int n):
 
     N = n
     sequences = []
-    enum(1,0)
+    enum(1, 0)
     sig_free(seq)
     return sequences
 
@@ -467,7 +469,7 @@ cdef void enum(int k, int M):
     - ``k`` -- depth of the partial degree sequence
     - ``M`` -- value of a maximum element in the partial degree sequence
     """
-    cdef int i,j
+    cdef int i, j
     global seq
     cdef int taken = 0
     cdef int current_box
@@ -491,21 +493,21 @@ cdef void enum(int k, int M):
     if M == 0:
 
         seq[0] += 1
-        enum(k+1, M)
+        enum(k + 1, M)
         seq[0] -= 1
 
     # We need not automatically increase the degree at each step. In this case,
     # we have no other choice but to link the new vertex of degree M to vertices
     # of degree M-1, which will become vertices of degree M too.
-    elif seq[M-1] >= M:
+    elif seq[M - 1] >= M:
 
-        seq[M]   += M+1
-        seq[M-1] -= M
+        seq[M] += M + 1
+        seq[M - 1] -= M
 
-        enum(k+1, M)
+        enum(k + 1, M)
 
-        seq[M]   -= M+1
-        seq[M-1] += M
+        seq[M] -= M + 1
+        seq[M - 1] += M
 
     ###############################################
     # Creating vertices of Vertices of degree > M #
@@ -542,13 +544,13 @@ cdef void enum(int k, int M):
             seq[current_box] -= i
             seq[current_box+1] += i
 
-            for max(0,((M+1)-taken-i)) <= j <= n_previous_box:
+            for max(0, ((M+1)-taken-i)) <= j <= n_previous_box:
                 seq[current_box-1] -= j
                 seq[current_box] += j
 
                 new_vertex = taken + i + j
                 seq[new_vertex] += 1
-                enum(k+1,new_vertex)
+                enum(k+1, new_vertex)
                 seq[new_vertex] -= 1
 
                 seq[current_box-1] += j
@@ -566,7 +568,7 @@ cdef void enum(int k, int M):
     # Now current_box = 0. All the vertices of nonzero degree are taken, we just
     # want to know how many vertices of degree 0 will be neighbors of the new
     # vertex.
-    for max(0,((M+1)-taken)) <= i <= seq[0]:
+    for max(0, ((M+1)-taken)) <= i <= seq[0]:
 
         seq[1] += i
         seq[0] -= i

src/sage/combinat/designs/designs_pyx.pyx

@@ -15,6 +15,7 @@ from cysignals.memory cimport sig_malloc, sig_calloc, sig_realloc, sig_free
 
 from sage.misc.unknown import Unknown
 
+
 def is_covering_array(array, strength=None, levels=None, verbose=False, parameters=False):
     r"""
     Check if the input is a covering array with given strength.
@@ -349,6 +350,7 @@ def is_orthogonal_array(OA, int k, int n, int t=2, verbose=False, terminology="O
     bitset_free(seen)
     return True
 
+
 def is_group_divisible_design(groups,blocks,v,G=None,K=None,lambd=1,verbose=False):
     r"""
     Checks that input is a Group Divisible Design on `\{0,...,v-1\}`
@@ -588,6 +590,7 @@ def is_pairwise_balanced_design(blocks,v,K=None,lambd=1,verbose=False):
                                      lambd=lambd,
                                      verbose=verbose)
 
+
 def is_projective_plane(blocks, verbose=False):
     r"""
     Test whether the blocks form a projective plane on `\{0,...,v-1\}`
@@ -661,6 +664,7 @@ def is_projective_plane(blocks, verbose=False):
                                      lambd=1,
                                      verbose=verbose)
 
+
 def is_difference_matrix(M,G,k,lmbda=1,verbose=False):
     r"""
     Test if `M` is a `(G,k,\lambda)`-difference matrix.
@@ -725,6 +729,7 @@ def is_difference_matrix(M,G,k,lmbda=1,verbose=False):
     """
     return is_quasi_difference_matrix(M,G,k,lmbda=lmbda,mu=lmbda,u=0,verbose=verbose)
 
+
 def is_quasi_difference_matrix(M,G,int k,int lmbda,int mu,int u,verbose=False):
     r"""
     Test if the matrix is a `(G,k;\lambda,\mu;u)`-quasi-difference matrix
@@ -938,6 +943,7 @@ def is_quasi_difference_matrix(M,G,int k,int lmbda,int mu,int u,verbose=False):
     sig_free(M_c)
     return True
 
+
 # Cached information for OA constructions (see .pxd file for more info)
 
 _OA_cache = <cache_entry *> sig_malloc(2*sizeof(cache_entry))

src/sage/combinat/designs/gen_quadrangles_with_spread.pyx

@@ -123,6 +123,7 @@ def generalised_quadrangle_with_spread(const int s, const int t,
     raise RuntimeError(
         f"Sage can't build a GQ of order ({s}, {t}) with a spread")
 
+
 def is_GQ_with_spread(GQ, S, s=None, t=None):
     r"""
     Check if GQ is a generalised quadrangle of order `(s,t)` and
@@ -233,6 +234,7 @@ def dual_GQ_ovoid(GQ, O):
     D = IncidenceStructure(newBlocks)
     return (D, S)
 
+
 def generalised_quadrangle_hermitian_with_ovoid(const int q):
     r"""
     Construct the generalised quadrangle `H(3,q^2)` with an ovoid.

src/sage/combinat/designs/orthogonal_arrays_find_recursive.pyx

@@ -51,6 +51,7 @@ from .orthogonal_arrays import orthogonal_array
 from sage.rings.integer cimport smallInteger
 from sage.arith.misc import prime_powers
 
+
 @cached_function
 def find_recursive_construction(k, n):
     r"""
@@ -114,6 +115,7 @@ def find_recursive_construction(k, n):
             return res
     return False
 
+
 cpdef find_product_decomposition(int k,int n):
     r"""
     Find `n_1n_2=n` to obtain an `OA(k,n)` by the product construction.
@@ -880,6 +882,7 @@ def int_as_sum(int value, list S, int k_max):
 
     return None
 
+
 cpdef find_brouwer_van_rees_with_one_truncated_column(int k,int n):
     r"""
     Find `rm+x_1+...+x_c=n` such that the Brouwer-van Rees constructions yields a `OA(k,n)`.