Implement some trivial bounds as well as the interesting ones.

diff --git a/bounds.py b/bounds.py
index a26bb5e8f3c605b8910cac32364feb0600aca24b..742a78c118f8788939658c84f3d375bffca12f51 100644 (file)
--- a/bounds.py
+++ b/bounds.py
@@ -115,20 +115,35 @@ than our presumed minimum fragment. Contradiction."""
         return m/3
     return None
 
+def most_trivial(n, m):
+    """The most trivial possible bound."""
+    return m
+
+def trivial(n, m):
+    """Trivial upper bound of m/2.
+
+If m does not divide n, then at least one m-stick must be cut into
+more than one piece, reducing the best option to at most m/2."""
+    if n % m == 0:
+        return None
+    return Fraction(m, 2)
+
 bounds = [
     (writinghawk, "writinghawk's piece-counting bound"),
     (fivemack, "fivemack's conditional m/3 bound"),
+    (trivial, "trivial bound of m/2"),
+    (most_trivial, "trivial bound of m"),
 ]
 
 def upper_bound(n, m):
     assert n > m
-    best = m, "trivial bound of m"
+    best = m+1, None
     for boundtype in bounds:
         b = boundtype[0](n, m)
         if b is not None:
-            if b < m:
+            if b < best[0]:
                 best = b, boundtype[1]
-            elif b == m:
+            elif b == best[0]:
                 best = b, best[1] + ", " + boundtype[1]
     return best