Trac #24345: Disallow boolean operations with Unknown

The `Unknown` from `misc/unknown.py` incorrectly behaves like `False` in
the context of boolean operations. It is mostly useless as long as
Python has no tristate conditionals and logic operators. This ticket
raises an error instead.

As a consequence of this modification, Sage code is adapted as follows
for a given tristate `troolean`
{{{
if troolean is True:
    ...
elif troolean is False:
    ...
else:
    ...
}}}

URL: https://trac.sagemath.org/24345
Reported by: rws
Ticket author(s): Ralf Stephan
Reviewer(s): Vincent Delecroix

Author: Release Manager

src/sage/combinat/designs/bibd.py

@@ -232,7 +232,7 @@ def balanced_incomplete_block_design(v, k, existence=False, use_LJCR=False):
             return True
         B = BIBD_from_arc_in_desarguesian_projective_plane(v,k)
         return BalancedIncompleteBlockDesign(v, B, copy=False)
-    if BIBD_from_TD(v,k,existence=True):
+    if BIBD_from_TD(v,k,existence=True) is True:
         if existence:
             return True
         return BalancedIncompleteBlockDesign(v, BIBD_from_TD(v,k), copy=False)
@@ -241,7 +241,7 @@ def balanced_incomplete_block_design(v, k, existence=False, use_LJCR=False):
             return True
         from .block_design import projective_plane
         return BalancedIncompleteBlockDesign(v, projective_plane(k-1),copy=False)
-    if difference_family(v,k,existence=True):
+    if difference_family(v,k,existence=True) is True:
         if existence:
             return True
         G,D = difference_family(v,k)
@@ -434,8 +434,8 @@ def BIBD_from_TD(v,k,existence=False):
     """
     # First construction
     if (v%k == 0 and
-        balanced_incomplete_block_design(v//k,k,existence=True) and
-        transversal_design(k,v//k,existence=True)):
+        balanced_incomplete_block_design(v//k,k,existence=True) is True and
+        transversal_design(k,v//k,existence=True) is True):
 
         if existence:
             return True
@@ -467,9 +467,8 @@ def BIBD_from_TD(v,k,existence=False):
 
     # Third construction
     elif ((v-k)%k == 0 and
-        balanced_incomplete_block_design((v-k)//k+k,k,existence=True) and
-        transversal_design(k,(v-k)//k,existence=True)):
-
+        balanced_incomplete_block_design((v-k)//k+k,k,existence=True) is True
+        and transversal_design(k,(v-k)//k,existence=True) is True):
         if existence:
             return True
 

src/sage/combinat/designs/difference_family.py

@@ -219,8 +219,6 @@ def is_difference_family(G, D, v=None, k=None, l=None, verbose=False):
         sage: _
         False
     """
-    import operator
-
     identity, mul, inv = group_law(G)
 
     Glist = list(G)
@@ -426,7 +424,7 @@ def df_q_6_1(K, existence=False, check=True):
 
         sage: from sage.combinat.designs.difference_family import is_difference_family, df_q_6_1
         sage: prime_powers = [v for v in range(31,500,30) if is_prime_power(v)]
-        sage: parameters = [v for v in prime_powers if df_q_6_1(GF(v,'a'), existence=True)]
+        sage: parameters = [v for v in prime_powers if df_q_6_1(GF(v,'a'), existence=True) is True]
         sage: parameters
         [31, 151, 181, 211, 241, 271, 331, 361, 421]
         sage: for v in parameters:
@@ -507,7 +505,7 @@ def radical_difference_set(K, k, l=1, existence=False, check=True):
         sage: for k in range(2,50):
         ....:     for l in reversed(divisors(k*(k-1))):
         ....:         v = k*(k-1)//l + 1
-        ....:         if is_prime_power(v) and radical_difference_set(GF(v,'a'),k,l,existence=True):
+        ....:         if is_prime_power(v) and radical_difference_set(GF(v,'a'),k,l,existence=True) is True:
         ....:             _ = radical_difference_set(GF(v,'a'),k,l)
         ....:             print("{:3} {:3} {:3}".format(v,k,l))
           3   2   1
@@ -878,7 +876,7 @@ def radical_difference_family(K, k, l=1, existence=False, check=True):
         ....:     for q in range(k*(k-1)+1, 2000, k*(k-1)):
         ....:          if is_prime_power(q):
         ....:              K = GF(q,'a')
-        ....:              if radical_difference_family(K, k, existence=True):
+        ....:              if radical_difference_family(K, k, existence=True) is True:
         ....:                  list_q.append(q)
         ....:                  _ = radical_difference_family(K,k)
         ....:     print(" ".join(str(p) for p in list_q))
@@ -896,7 +894,6 @@ def radical_difference_family(K, k, l=1, existence=False, check=True):
     """
     v = K.cardinality()
     x = K.multiplicative_generator()
-    one = K.one()
     e = k*(k-1)
     if (l*(v-1)) % e:
         raise ValueError("k (k-1) = {} should be a multiple of l (v-1) ={}".format(
@@ -1209,11 +1206,11 @@ def hadamard_difference_set_product(G1, D1, G2, D2):
 
         sage: G11,D11 = hadamard_difference_set_product(G1,D1,G1,D1)
         sage: assert is_difference_family(G11, D11, 256, 120, 56)
-        sage: assert designs.difference_family(256, 120, 56, existence=True)
+        sage: assert designs.difference_family(256, 120, 56, existence=True) is True
 
         sage: G12,D12 = hadamard_difference_set_product(G1,D1,G2,D2)
         sage: assert is_difference_family(G12, D12, 576, 276, 132)
-        sage: assert designs.difference_family(576, 276, 132, existence=True)
+        sage: assert designs.difference_family(576, 276, 132, existence=True) is True
     """
     from sage.categories.cartesian_product import cartesian_product
 
@@ -1379,7 +1376,8 @@ def difference_family(v, k, l=1, existence=False, explain_construction=False, ch
         ....:     constructions = []
         ....:     for k in range(2,10):
         ....:         for l in range(1,10):
-        ....:             if designs.difference_family(v,k,l,existence=True):
+        ....:             ret = designs.difference_family(v,k,l,existence=True)
+        ....:             if ret is True:
         ....:                 constructions.append((k,l))
         ....:                 _ = designs.difference_family(v,k,l)
         ....:     if constructions:
@@ -1490,7 +1488,7 @@ def difference_family(v, k, l=1, existence=False, explain_construction=False, ch
         sage: for N in range(2,21):
         ....:     v = 4*N^2; k = 2*N^2-N; l = N^2-N
         ....:     status = designs.difference_family(v,k,l,existence=True)
-        ....:     print("{:2} {}".format(N,designs.difference_family(v,k,l,explain_construction=True) if status else status))
+        ....:     print("{:2} {}".format(N,designs.difference_family(v,k,l,explain_construction=True) if status is True else status))
         2 McFarland 1973 construction
         3 Turyn 1965 construction
         4 McFarland 1973 construction
@@ -1602,7 +1600,6 @@ def difference_family(v, k, l=1, existence=False, explain_construction=False, ch
         if existence:
             return Unknown
         raise NotImplementedError("No construction available for ({},{},{})-difference family".format(v,k,l))
-    t = l*(v-1) // e  # number of blocks
 
     # trivial construction
     if k == (v-1) and l == (v-2):
@@ -1666,7 +1663,7 @@ def difference_family(v, k, l=1, existence=False, explain_construction=False, ch
         else:
             raise EmptySetError("by McFarland 1989 such difference family does not exist")
 
-    elif len(factorization) == 1 and radical_difference_family(K, k, l, existence=True):
+    elif len(factorization) == 1 and radical_difference_family(K, k, l, existence=True) is True:
         if existence:
             return True
         elif explain_construction:
@@ -1675,7 +1672,10 @@ def difference_family(v, k, l=1, existence=False, explain_construction=False, ch
             D = radical_difference_family(K,k,l)
             G = K
 
-    elif len(factorization) == 1 and l == 1 and k == 6 and df_q_6_1(K, existence=True):
+    elif (len(factorization) == 1
+        and l == 1
+        and k == 6
+        and df_q_6_1(K, existence=True) is True):
         if existence:
             return True
         elif explain_construction:

src/sage/combinat/designs/difference_matrices.py

@@ -66,8 +66,8 @@ def find_product_decomposition(g, k, lmbda=1):
             g2 = g//g1
             if g1 > g2:
                 break
-            if (difference_matrix(g1,k,lmbda1,existence=True) and
-                difference_matrix(g2,k,lmbda2,existence=True)):
+            if (difference_matrix(g1,k,lmbda1,existence=True) is True and
+                difference_matrix(g2,k,lmbda2,existence=True) is True):
                 return (g1,lmbda1),(g2,lmbda2)
 
     return False
@@ -245,7 +245,7 @@ def difference_matrix(g,k,lmbda=1,existence=False,check=True):
     # (find the max k such that there exists a DM)
     elif k is None:
         i = 2
-        while difference_matrix(g=g,k=i,lmbda=lmbda,existence=True):
+        while difference_matrix(g=g,k=i,lmbda=lmbda,existence=True) is True:
             i += 1
         return i-1
 

src/sage/combinat/designs/orthogonal_arrays.py

@@ -45,7 +45,7 @@
 
 REFERENCES:
 
-- [CD1996]_
+-- [CD1996]_
 
 Functions
 ---------
@@ -917,7 +917,7 @@ def orthogonal_array(k,n,t=2,resolvable=False, check=True,existence=False,explai
         return [[i,j,(i+j)%n] for i in range(n) for j in range(n)]
 
     # projective spaces are equivalent to OA(n+1,n,2)
-    elif (projective_plane(n, existence=True) or
+    elif (projective_plane(n, existence=True) is True or
            (k == n+1 and projective_plane(n, existence=True) is False)):
         _OA_cache_set(n+1,n,projective_plane(n, existence=True))
         if k == n+1:
@@ -983,7 +983,7 @@ def orthogonal_array(k,n,t=2,resolvable=False, check=True,existence=False,explai
                 break
 
     # From Difference Matrices
-    elif may_be_available and difference_matrix(n,k-1,existence=True):
+    elif may_be_available and difference_matrix(n,k-1,existence=True) is True:
         _OA_cache_set(k,n,True)
         if existence:
             return True
@@ -1050,7 +1050,7 @@ def largest_available_k(n,t=2):
         from sage.rings.infinity import Infinity
         return Infinity
     elif t == 2:
-        if projective_plane(n,existence=True):
+        if projective_plane(n,existence=True) is True:
             return n+1
         else:
             k=1
@@ -1337,15 +1337,15 @@ def incomplete_orthogonal_array(k,n,holes,resolvable=False, existence=False):
                              "intersect in a projective plane.").format(number_of_holes))
 
     # Holes of size 1 from OA(k+1,n)
-    elif max_hole==1 and orthogonal_array(k+1,n,existence=True):
+    elif max_hole==1 and orthogonal_array(k+1,n,existence=True) is True:
         if existence:
             return True
         OA = orthogonal_array(k+1,n)
         independent_set = [B[:-1] for B in OA if B[-1] == 0][:number_of_holes]
         OA = [B[:-1] for B in OA]
 
-    elif max_hole==1 and orthogonal_array(k,n,existence=True):
-        OA = orthogonal_array(k, n)
+    elif max_hole==1 and orthogonal_array(k,n,existence=True) is True:
+        OA = orthogonal_array(k,n)
         try:
             independent_set = OA_find_disjoint_blocks(OA,k,n,number_of_holes)
         except ValueError:
@@ -1356,7 +1356,7 @@ 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):
+    elif max_hole==1 and not orthogonal_array(k,n,existence=True) is True:
         return orthogonal_array(k,n,existence=existence)
 
     # From a quasi-difference matrix

src/sage/combinat/designs/resolvable_bibd.py

@@ -92,7 +92,7 @@ def resolvable_balanced_incomplete_block_design(v,k,existence=False):
 
         sage: for v in range(40):
         ....:     for k in range(v):
-        ....:         if designs.resolvable_balanced_incomplete_block_design(v,k,existence=True):
+        ....:         if designs.resolvable_balanced_incomplete_block_design(v,k,existence=True) is True:
         ....:             _ = designs.resolvable_balanced_incomplete_block_design(v,k)
     """
     # Trivial cases
@@ -448,7 +448,7 @@ def PBD_4_7(v,check=True, existence=False):
 
         sage: for i in range(1,300,3):
         ....:     if i not in [10,19,31]:
-        ....:         assert PBD_4_7(i,existence=True)
+        ....:         assert PBD_4_7(i,existence=True) is True
         ....:         _ = PBD_4_7(i,check=True)
     """
     if v%3 != 1 or v in [10,19,31]:
@@ -623,7 +623,7 @@ def PBD_4_7(v,check=True, existence=False):
 
         return PBD_4_7_from_Y(GDD,check=check)
 
-    elif v % 6 == 1 and GDD_4_2((v - 1) // 6, existence=True):
+    elif v % 6 == 1 and GDD_4_2((v - 1) // 6, existence=True) is True:
         # VII.5.17 from [BJL99]
         gdd = GDD_4_2((v - 1) // 6)
         return PBD_4_7_from_Y(gdd, check=check)
@@ -634,9 +634,9 @@ def PBD_4_7(v,check=True, existence=False):
         PBD = PBD_4_7_from_Y(PBD,check=False)
         return PBD_4_7_from_Y(PBD,check=check)
 
-    elif balanced_incomplete_block_design(v,4,existence=True):
+    elif balanced_incomplete_block_design(v,4,existence=True) is True:
         return balanced_incomplete_block_design(v,4)
-    elif balanced_incomplete_block_design(v,7,existence=True):
+    elif balanced_incomplete_block_design(v,7,existence=True) is True:
         return balanced_incomplete_block_design(v,7)
     else:
         from sage.combinat.designs.orthogonal_arrays import orthogonal_array
@@ -651,9 +651,9 @@ def PBD_4_7(v,check=True, existence=False):
         vv = (v - 1) // 3
         for g in range((vv + 5 - 1) // 5, vv // 4 + 1):
             u = vv-4*g
-            if (orthogonal_array(5,g,existence=True) and
-                PBD_4_7(3*g+1,existence=True)        and
-                PBD_4_7(3*u+1,existence=True)):
+            if (orthogonal_array(5,g,existence=True) is True and
+                PBD_4_7(3*g+1,existence=True) is True and
+                PBD_4_7(3*u+1,existence=True) is True):
                 from .orthogonal_arrays import transversal_design
                 domain = set(range(vv))
                 GDD = transversal_design(5,g)
@@ -723,7 +723,7 @@ 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):
+        if not PBD_4_7(3*gs+1,existence=True) is 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/matrices/hadamard_matrix.py

@@ -653,8 +653,8 @@ def true():
     elif (  e  == 1                 and
           not sqn is None           and
           sqn%4 == 2            and
-          True == strongly_regular_graph(sqn-1,(sqn-2)//2,(sqn-6)//4,
-                    existence=True) and
+          strongly_regular_graph(sqn-1,(sqn-2)//2,(sqn-6)//4,
+            existence=True) is True and
           is_prime_power(ZZ(sqn+1))):
         if existence:
             return true()
@@ -666,8 +666,8 @@ def true():
         for n1,e1 in product(divisors(n)[1:-1],[-1,1]):
             e2 = e1*e
             n2 = n//n1
-            if (regular_symmetric_hadamard_matrix_with_constant_diagonal(n1,e1,existence=True) and
-                regular_symmetric_hadamard_matrix_with_constant_diagonal(n2,e2,existence=True)):
+            if (regular_symmetric_hadamard_matrix_with_constant_diagonal(n1,e1,existence=True) is True and
+                regular_symmetric_hadamard_matrix_with_constant_diagonal(n2,e2,existence=True)) is True:
                 if existence:
                     return true()
                 M1 = regular_symmetric_hadamard_matrix_with_constant_diagonal(n1,e1)
@@ -1122,7 +1122,7 @@ def true():
         M = hadamard_matrix_paleyI(n, normalize=False)
 
     elif n % 8 == 0:
-        if skew_hadamard_matrix(n//2,existence=True): # (Lemma 14.1.6 in [Ha83]_)
+        if skew_hadamard_matrix(n//2,existence=True) is True: # (Lemma 14.1.6 in [Ha83]_)
             if existence:
                 return true()
             H = skew_hadamard_matrix(n//2,check=False)
@@ -1132,7 +1132,7 @@ def true():
             for d in divisors(n)[2:-2]: # skip 1, 2, n/2, and n
                 n1 = n//d
                 if is_prime_power(d - 1) and (d % 4 == 0) and (n1 % 4 == 0)\
-                    and skew_hadamard_matrix(n1,existence=True):
+                    and skew_hadamard_matrix(n1,existence=True) is True:
                     if existence:
                         return true()
                     H = skew_hadamard_matrix(n1, check=False)-I(n1)
@@ -1145,7 +1145,7 @@ def true():
                     M = A.tensor_product(I(n1))+(U*A).tensor_product(H)
                     break
     if M is None: # try Williamson-Goethals-Seidel construction
-        if GS_skew_hadamard_smallcases(n, existence=True):
+        if GS_skew_hadamard_smallcases(n, existence=True) is True:
             if existence:
                 return true()
             M = GS_skew_hadamard_smallcases(n)

src/sage/databases/oeis.py

@@ -1470,7 +1470,7 @@ def __iter__(self):
         """
         for x in self.first_terms():
             yield x
-        if not self.is_full():
+        if not self.is_full() is True:
             raise LookupError("Future values not provided by OEIS.")
 
     def references(self):