trac #15310: Merged into 6.2.rc1

src/sage/combinat/designs/bibd.py

@@ -64,8 +64,8 @@ def BalancedIncompleteBlockDesign(v,k,use_LJCR=False):
 
     .. SEEALSO::
 
-        * :meth:`steiner_triple_system`
-        * :meth:`v_4_1_bibd`
+        * :func:`steiner_triple_system`
+        * :func:`v_4_1_BIBD`
 
     TODO:
 
@@ -452,7 +452,7 @@ def _relabel_bibd(B,n):
 
 def PBD_4_5_8_9_12(v, check=True):
     """
-    Returns a `(v,\{4,5,8,9,12\})-PBD` on `v` elements.
+    Returns a `(v,\{4,5,8,9,12\})`-PBD on `v` elements.
 
     A `(v,\{4,5,8,9,12\})`-PBD exists if and only if `v\equiv 0,1 \pmod 4`. The
     construction implemented here appears page 168 in [Stinson2004]_.

src/sage/combinat/designs/latin_squares.py

@@ -92,7 +92,7 @@ def are_mutually_orthogonal_latin_squares(l, verbose=False):
     return True
 
 
-def mutually_orthogonal_latin_squares(n,k=None, partitions = False):
+def mutually_orthogonal_latin_squares(n,k=None, partitions = False, availability=False):
     r"""
     Returns `k` Mutually Orthogonal `n\times n` Latin Squares (MOLS).
 
@@ -128,6 +128,11 @@ def mutually_orthogonal_latin_squares(n,k=None, partitions = False):
       partitions satisfying this intersection property instead of the `k+2` MOLS
       (though the data is exactly the same in both cases).
 
+    - ``availability`` (boolean) -- if ``availability`` is set to ``True``, the
+      function only returns boolean answers according to whether Sage knows how
+      to build such a collection. This should be much faster than actually
+      building it.
+
     EXAMPLES::
 
         sage: designs.mutually_orthogonal_latin_squares(5)
@@ -176,6 +181,8 @@ def mutually_orthogonal_latin_squares(n,k=None, partitions = False):
         Traceback (most recent call last):
         ...
         ValueError: There exist at most n-1 MOLS of size n.
+        sage: designs.mutually_orthogonal_latin_squares(6,3,availability=True)
+        Unknown
     """
     from sage.rings.finite_rings.constructor import FiniteField
     from sage.combinat.designs.block_design import AffineGeometryDesign
@@ -184,9 +191,15 @@ def mutually_orthogonal_latin_squares(n,k=None, partitions = False):
     from sage.rings.arith import factor
 
     if k is not None and k >= n:
-        raise ValueError("There exist at most n-1 MOLS of size n.")
+        if availability:
+            return False
+        else:
+            raise ValueError("There exist at most n-1 MOLS of size n.")
 
     if is_prime_power(n):
+        if availability:
+            return n-1 if k is None else True
+
         if k is None:
             k = n-1
         # Section 6.4.1 of [Stinson2004]
@@ -217,8 +230,17 @@ def mutually_orthogonal_latin_squares(n,k=None, partitions = False):
         s = min(subcases)-1
         if k is None:
             k = s
+            if availability:
+                return k
         elif k > s:
-            raise NotImplementedError("I don't know how to build these MOLS.")
+            if availability:
+                from sage.misc.unknown import Unknown
+                return Unknown
+            else:
+                raise NotImplementedError("I don't know how to build these MOLS.")
+        elif availability:
+            return True
+
         subcalls = [mutually_orthogonal_latin_squares(p,k) for p in subcases]
         matrices = [latin_square_product(*[sc[i] for sc in subcalls])
                     for i in range(k)]