sagemathgh-38614: some pep8 fixes in combinat/designs

    
fixing a few pycodestyle suggestions in `combinat/designs`

### 📝 Checklist

- [x] The title is concise and informative.
- [x] 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 and checked the documentation
preview.
    
URL: sagemath#38614
Reported by: Frédéric Chapoton
Reviewer(s): David Coudert

src/sage/combinat/designs/bibd.py

@@ -1355,10 +1355,10 @@ def BIBD_from_arc_in_desarguesian_projective_plane(n,k,existence=False):
        :doi:`10.1016/S0021-9800(69)80095-5`
     """
     q = (n-1)//(k-1)-1
-    if (k % 2                 or
-        q % 2                 or
-        q <= k                or
-        n != (k-1)*(q+1)+1    or
+    if (k % 2 or
+        q % 2 or
+        q <= k or
+        n != (k-1)*(q+1)+1 or
         not is_prime_power(k) or
         not is_prime_power(q)):
         if existence:
@@ -1391,12 +1391,10 @@ def BIBD_from_arc_in_desarguesian_projective_plane(n,k,existence=False):
     # [Denniston69] is the set of all elements of K of degree < log_n
     # (seeing elements of K as polynomials in 'a')
 
-    K_iter = list(K) # faster iterations
-    log_n = is_prime_power(n,get_data=True)[1]
-    C = [(x,y,one)
-         for x in K_iter
-         for y in K_iter
-         if Q(x,y).polynomial().degree() < log_n]
+    K_iter = list(K)  # faster iterations
+    log_n = is_prime_power(n, get_data=True)[1]
+    C = [(x, y, one) for x in K_iter for y in K_iter
+         if Q(x, y).polynomial().degree() < log_n]
 
     from sage.combinat.designs.block_design import DesarguesianProjectivePlaneDesign
     return DesarguesianProjectivePlaneDesign(q).trace(C)._blocks

src/sage/combinat/designs/block_design.py

@@ -42,7 +42,7 @@
 ---------------------
 """
 
-#*****************************************************************************
+# ****************************************************************************
 #       Copyright (C) 2007 Peter Dobcsanyi <peter@designtheory.org>
 #       Copyright (C) 2007 David Joyner <wdjoyner@gmail.com>
 #
@@ -51,7 +51,7 @@
 # the Free Software Foundation, either version 2 of the License, or
 # (at your option) any later version.
 #                  https://www.gnu.org/licenses/
-#*****************************************************************************
+# ****************************************************************************
 from sage.arith.misc import binomial, integer_floor, is_prime_power
 from sage.categories.sets_cat import EmptySetError
 from sage.misc.lazy_import import lazy_import
@@ -69,7 +69,7 @@
 
 BlockDesign = IncidenceStructure
 
-###  utility functions  -------------------------------------------------------
+#  utility functions  -----------------------------------------------------
 
 
 def tdesign_params(t, v, k, L):
@@ -338,9 +338,10 @@ def DesarguesianProjectivePlaneDesign(n, point_coordinates=True, check=True):
     """
     K = FiniteField(n, 'a')
     n2 = n**2
-    relabel = {x:i for i,x in enumerate(K)}
-    Kiter = relabel  # it is much faster to iterate through a dict than through
-                     # the finite field K
+    relabel = {x: i for i, x in enumerate(K)}
+    Kiter = relabel
+    # it is much faster to iterate through a dict than through
+    # the finite field K
 
     # we decompose the (equivalence class) of points [x:y:z] of the projective
     # plane into an affine plane, an affine line and a point. At the same time,
@@ -996,14 +997,14 @@ def HadamardDesign(n):
     """
     from sage.combinat.matrices.hadamard_matrix import hadamard_matrix
     from sage.matrix.constructor import matrix
-    H = hadamard_matrix(n+1) #assumed to be normalised.
+    H = hadamard_matrix(n + 1)  # assumed to be normalised.
     H1 = H.matrix_from_columns(range(1,n+1))
     H2 = H1.matrix_from_rows(range(1,n+1))
     J = matrix(ZZ,n,n,[1]*n*n)
     MS = J.parent()
-    A = MS((H2+J)/2) # convert -1's to 0's; coerce entries to ZZ
+    A = MS((H2+J)/2)  # convert -1's to 0's; coerce entries to ZZ
     # A is the incidence matrix of the block design
-    return IncidenceStructure(incidence_matrix=A,name='HadamardDesign')
+    return IncidenceStructure(incidence_matrix=A, name='HadamardDesign')
 
 
 def Hadamard3Design(n):
@@ -1060,10 +1061,10 @@ def Hadamard3Design(n):
         raise ValueError("The Hadamard design with n = %s does not extend to a three design." % n)
     from sage.combinat.matrices.hadamard_matrix import hadamard_matrix
     from sage.matrix.constructor import matrix, block_matrix
-    H = hadamard_matrix(n) #assumed to be normalised.
+    H = hadamard_matrix(n)  # assumed to be normalised.
     H1 = H.matrix_from_columns(range(1, n))
     J = matrix(ZZ, n, n-1, [1]*(n-1)*n)
-    A1 = (H1+J)/2
-    A2 = (J-H1)/2
-    A = block_matrix(1, 2, [A1, A2]) #the incidence matrix of the design.
+    A1 = (H1 + J) / 2
+    A2 = (J - H1) / 2
+    A = block_matrix(1, 2, [A1, A2])  # the incidence matrix of the design.
     return IncidenceStructure(incidence_matrix=A, name='HadamardThreeDesign')

src/sage/combinat/designs/database.py

@@ -1109,7 +1109,7 @@ def OA_10_205():
     baer_subplane_size = 4**2+4+1
 
     B = [0, 1, 22, 33, 83, 122, 135, 141, 145, 159, 175, 200, 226, 229, 231, 238, 246]
-    pplane = [[(xx+i) % pplane_size for xx in B]  for i in range(pplane_size)]
+    pplane = [[(xx+i) % pplane_size for xx in B] for i in range(pplane_size)]
     baer_subplane = set([i*pplane_size/baer_subplane_size for i in range(baer_subplane_size)])
 
     p = list(baer_subplane)[0]
@@ -1284,7 +1284,7 @@ def OA_11_254():
 
     # Base block of a PG(2,19)
     B = (0,1,19,28,96,118,151,153,176,202,240,254,290,296,300,307,337,361,366,369)
-    BIBD = [[(x+i) % 381 for x in B]  for i in range(381)]
+    BIBD = [[(x+i) % 381 for x in B] for i in range(381)]
 
     # We only keep points congruent to 0,1 mod 3 and relabel the PBD. The result is
     # a (254,{11,13,16})-PBD
@@ -1708,7 +1708,7 @@ def OA_10_469():
          731,824,837,848,932,1002,1051,1055,1089,1105,1145,1165,1196,1217,1226,
          1274,1281,1309,1405)
 
-    BIBD = [[(x+i) % 1407 for x in B]  for i in range(1407)]
+    BIBD = [[(x+i) % 1407 for x in B] for i in range(1407)]
 
     # Only keep points v congruent to 0 mod 3 and relabel
     PBD = [[x//3 for x in B if x % 3 == 0] for B in BIBD]
@@ -4171,7 +4171,7 @@ def RBIBD_120_8_1():
 
     # A (precomputed) set that every block of the BIBD intersects on 0 or 2 points
     hyperoval = [128, 192, 194, 4, 262, 140, 175, 48, 81, 180, 245, 271, 119, 212, 249, 189, 62, 255]
-    #for B in BIBD:
+    # for B in BIBD:
     #    len_trace = sum(x in hyperoval for x in B)
     #    assert len_trace == 0 or len_trace == 2
 
@@ -4577,13 +4577,9 @@ def HigmanSimsDesign():
     from sage.combinat.designs.block_design import WittDesign
     from .incidence_structures import IncidenceStructure
     W = WittDesign(24)
-    a,b = 0,1
-    Wa = [set(B) for B in W
-          if (a     in B and
-              b not in B)]
-    Wb = [set(B) for B in W
-          if (b     in B and
-              a not in B)]
+    a, b = 0, 1
+    Wa = [set(B) for B in W if a in B and b not in B]
+    Wb = [set(B) for B in W if b in B and a not in B]
 
     H = [[i for i, A in enumerate(Wa) if len(A & B) != 2]
          for B in Wb]

src/sage/combinat/designs/difference_family.py

@@ -123,8 +123,8 @@ def block_stabilizer(G, B):
     S = []
     for b in B:
         # fun: if we replace +(-b) with -b it completely fails!!
-        bb0 = op(b,b0) # bb0 = b-B[0]
-        if all(op(bb0,c) in B for c in B):
+        bb0 = op(b, b0)  # bb0 = b-B[0]
+        if all(op(bb0, c) in B for c in B):
             S.append(bb0)
     return S
 
@@ -279,7 +279,7 @@ def is_difference_family(G, D, v=None, k=None, l=None, verbose=False):
             for c in d:
                 if b == c:
                     continue
-                gg = mul(b,inv(c)) # = b-c or bc^{-1}
+                gg = mul(b, inv(c))  # = b-c or bc^{-1}
                 if gg not in tmp_counter:
                     tmp_counter[gg] = 0
                 where[gg].add(i)
@@ -319,7 +319,7 @@ def is_difference_family(G, D, v=None, k=None, l=None, verbose=False):
                         g, counter[g], sorted(where[g])))
     if too_much:
         print("Too much:")
-        for g  in too_much:
+        for g in too_much:
             print("  {} is obtained {} times in blocks {}".format(
                         g, counter[g], sorted(where[g])))
     if too_few or too_much:
@@ -388,9 +388,10 @@ def singer_difference_set(q,d):
     # build a polynomial c over GF(q) such that GF(q)[x] / (c(x)) is a
     # GF(q**(d+1)) and such that x is a multiplicative generator.
     p,e = q.factor()[0]
-    c = conway_polynomial(p,e*(d+1))
-    if e != 1:  # i.e. q is not a prime, so we factorize c over GF(q) and pick
-                # one of its factor
+    c = conway_polynomial(p, e*(d+1))
+    if e != 1:
+        # i.e. q is not a prime, so we factorize c over GF(q) and pick
+        # one of its factor
         K = GF(q,'z')
         c = c.change_ring(K).factor()[0][0]
     else:
@@ -454,7 +455,7 @@ def df_q_6_1(K, existence=False, check=True):
     xx = x**5
     to_coset = {x**i * xx**j: i for i in range(5) for j in range((v-1)/5)}
 
-    for c in to_coset: # the loop runs through all nonzero elements of K
+    for c in to_coset:  # the loop runs through all nonzero elements of K
         if c == one or c == r or c == r2:
             continue
         if len(set(to_coset[elt] for elt in (r-one, c*(r-one), c-one, c-r, c-r**2))) == 5:
@@ -796,13 +797,13 @@ def one_radical_difference_family(K, k):
         A = [r**i - 1 for i in range(1,m+1)]
     else:
         m = k // 2
-        r = x ** ((q-1) // (k-1)) # (k-1)-th root of unity
+        r = x ** ((q-1) // (k-1))  # (k-1)-th root of unity
         A = [r**i - 1 for i in range(1,m)]
         A.append(K.one())
 
     # instead of the complicated multiplicative group K^*/(±C) we use the
     # discrete logarithm to convert everything into the additive group Z/cZ
-    c = m * (q-1) // e # cardinal of ±C
+    c = m * (q-1) // e  # cardinal of ±C
     from sage.groups.generic import discrete_log
     logA = [discrete_log(a,x) % c for a in A]
 
@@ -1036,18 +1037,18 @@ def are_mcfarland_1973_parameters(v, k, lmbda, return_parameters=False):
         96 20 4 4 1
     """
     if v <= k or k <= lmbda:
-        return (False,None) if return_parameters else False
+        return (False, None) if return_parameters else False
     k = ZZ(k)
     lmbda = ZZ(lmbda)
-    qs,r = (k - lmbda).sqrtrem() # sqrt(k-l) should be q^s
+    qs, r = (k - lmbda).sqrtrem()  # sqrt(k-l) should be q^s
     if r or (qs*(qs-1)) % lmbda:
-        return (False,None) if return_parameters else False
+        return (False, None) if return_parameters else False
 
     q = qs*(qs-1) // lmbda + 1
     if (q <= 1 or
-        v * (q-1) != qs*q * (qs*q+q-2)  or
+        v * (q-1) != qs*q * (qs*q+q-2) or
         k * (q-1) != qs * (qs*q-1)):
-        return (False,None) if return_parameters else False
+        return (False, None) if return_parameters else False
 
     # NOTE: below we compute the value of s so that qs = q^s. If the method
     # is_power_of of integers would be able to return the exponent, we could use
@@ -1057,7 +1058,7 @@ def are_mcfarland_1973_parameters(v, k, lmbda, return_parameters=False):
     p2,a2 = q.is_prime_power(get_data=True)
 
     if a1 == 0 or a2 == 0 or p1 != p2 or a1 % a2:
-        return (False,None) if return_parameters else False
+        return (False, None) if return_parameters else False
 
     return (True, (q, a1//a2)) if return_parameters else True
 
@@ -1265,10 +1266,10 @@ def turyn_1965_3x3xK(k=4):
     else:
         raise ValueError("k must be 2 or 4")
 
-    L = [[(0,1),(1,1),(2,1),(0,2),(1,2),(2,2)], # complement of y=0
-         [(0,0),(1,1),(2,2)],                   # x-y=0
-         [(0,0),(1,2),(2,1)],                   # x+y=0
-         [(0,0),(0,1),(0,2)]]                   # x=0
+    L = [[(0,1),(1,1),(2,1),(0,2),(1,2),(2,2)],  # complement of y=0
+         [(0,0),(1,1),(2,2)],                    # x-y=0
+         [(0,0),(1,2),(2,1)],                    # x+y=0
+         [(0,0),(0,1),(0,2)]]                    # x=0
 
     return G, [[G(v + k) for l, k in zip(L, K) for v in l]]
 
@@ -1835,7 +1836,7 @@ def supplementary_difference_set_from_rel_diff_set(q, existence=False, check=Tru
     from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
     P = PolynomialRing(ZZ, 'x')
 
-    #Compute psi3, psi4
+    # Compute psi3, psi4
     hall = 0
     for d in set1:
         hall += P.monomial(d[0])

src/sage/combinat/designs/ext_rep.py

@@ -869,11 +869,11 @@ def _start_element(self, name, attrs):
             check_dtrs_protocols('source', attrs['dtrs_protocol'])
             if self.list_of_designs_start_proc:
                 self.list_of_designs_start_proc(attrs)
-            #self.outf.write('<%s' % name)
-            #pp_attributes(self.outf, attrs, indent='', precision_stack=[])
-            #self.outf.write('>\n')
+            # self.outf.write('<%s' % name)
+            # pp_attributes(self.outf, attrs, indent='', precision_stack=[])
+            # self.outf.write('>\n')
         elif name == 'designs':
-            pass # self.outf.write(' <%s>\n' % name)
+            pass  # self.outf.write(' <%s>\n' % name)
         if self.in_item:
             for k, v in attrs.items():
                 attrs[k] = _encode_attribute(v)
@@ -916,7 +916,7 @@ def _end_element(self, name):
                     if name == 'block' or name == 'permutation' \
                        or name == 'preimage' or name == 'ksubset' \
                        or name == 'cycle_type' or name == 'row':
-                       # these enclose lists of numbers
+                        # these enclose lists of numbers
                         children.append(ps)
                     else:
                         # the rest is a single number
@@ -929,19 +929,19 @@ def _end_element(self, name):
                 if self.save_designs:
                     init_bd = XTree(self.current_node[2][0])
                     self.list_of_designs.append((init_bd.v, list(init_bd.blocks)))
-                #print_subxt(self.current_node[2][0], level=2, outf=self.outf)
+                # print_subxt(self.current_node[2][0], level=2, outf=self.outf)
                 self._init()
             elif name == 'info':
                 if self.info_proc:
                     self.info_proc(self.current_node[2][0])
-                #print_subxt(self.current_node[2][0], level=1, outf=self.outf)
+                # print_subxt(self.current_node[2][0], level=1, outf=self.outf)
                 self._init()
         else:
             if name == 'designs':
                 if self.designs_end_proc:
                     self.designs_end_proc()
-                #self.outf.write(' ')
-            #self.outf.write('</%s>\n' % name)
+                # self.outf.write(' ')
+            # self.outf.write('</%s>\n' % name)
 
     def _char_data(self, data):
         """
@@ -962,9 +962,8 @@ def _char_data(self, data):
              {'b': 26, 'id': 't2-v13-b26-r6-k3-L1-0', 'v': 13},
              ['[ DESIGN-1.1, GRAPE-4.2, GAPDoc-0.9999, GAP-4.4.3]'])
         """
-
         if self.in_item:
-            #@ this stripping may distort char data in the <info> subtree
+            # @ this stripping may distort char data in the <info> subtree
             # if they are not bracketed in some way.
             data = data.strip()
             if data: