Add a test for Leonard brightness conjecture

setclass/tests/test_exploration.py

@@ -0,0 +1,21 @@
+from setclass.setclass import SetClass
+
+
+def test_brightness_conjecture():
+    """
+    Test that the difference in brightness between the (darkest) Rahn normal forms of any set class
+    and its complement (inverted, if assymetrical) satisfy the following quadratic:
+
+    ΔB = (T-1)(T/2 - C)
+
+    where B is brightness, T is tonality (number of divisions of the octave) and C is set
+    cardinality.
+    Note: see the performance note in the documentation for `darkest_of_cardinality`. High values of
+    tonality can take a while to calculate (T=24 takes about a minute on an Intel i7-13700H CPU).
+    """
+    for T in range(1, 13):  # 1 to 12
+        for C in range(T + 1):  # 0 to T
+            for sc in SetClass.darkest_of_cardinality(C, tonality=T):
+                test = sc.complement.inversion.darkest_form.brightness - sc.brightness
+                ΔB = int((T - 1) * (T / 2 - C))
+                assert test == ΔB, f"T={T}, C={C}, ΔB={ΔB}, diff={test}: {sc.darkest_form}, {sc.complement.inversion.darkest_form}"