Add cardinality set methods, conformance tests

setclass/setclass.py

@@ -168,3 +168,35 @@ class SetClass(list):
             pitches += f"{pitch}{sub}"
         sup = superscript(self.brightness)
         return f"[{pitches}]{sup}"
+
+    # Class methods -----------------------------------------------------------
+
+    def all_of_cardinality(cardinality: int, tonality: int = 12) -> set:
+        """
+        Returns all set classes of a given cardinality. Tonality can be specified, default is 12.
+        Warning: high values of tonality can take a long time to calculate (T=24 takes about a
+        minute on an Intel i7-13700H CPU).
+        """
+        def _powerset(seq):
+            """Set of all possible unique subsets."""
+            from itertools import chain, combinations
+            return chain.from_iterable(combinations(seq, r) for r in range(len(seq) + 1))
+
+        if tonality < cardinality:
+            return ValueError("Set classes of cardinality {cardinality} are not possible in a {tonality}-tone octave.")
+
+        a = set(SetClass(*i) for i in _powerset(range(tonality)) if len(i) == cardinality and 0 in i)
+        return a
+
+    def darkest_of_cardinality(cardinality: int, tonality: int = 12, prime: bool = False) -> set:
+        """
+        Returns all set classes of a given cardinality, in their darkest forms (ignore rotations).
+        Tonality can be specified, default is 12.
+        Warning: high values of tonality can take a long time to calculate (T=24 takes about a
+        minute on an Intel i7-13700H CPU).
+        """
+        if tonality < cardinality:
+            return ValueError("Set classes of cardinality {cardinality} are not possible in a {tonality}-tone octave.")
+
+        a = set(i.darkest_form for i in SetClass.all_of_cardinality(cardinality, tonality))
+        return a

setclass/tests/test_setclass.py

@@ -248,3 +248,51 @@ def test_empty_complement_dozenal_notation():
 
 def test_empty_complement_leonard_notation():
     assert f121.leonard_notation == '[0₁1₁2₁3₁4₁5₁6₁7₁8₁9₁10₁11₁]⁶⁶'
+
+
+# ----------------------------------------------------------------------------
+
+def test_all_of_cardinality_set_lengths():
+    "Confirm expected lengths of the sets of set classes, for cardinality 1 through 12"
+    sets = [SetClass.all_of_cardinality(i + 1) for i in range(12)]
+    assert [len(s) for s in sets] == [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1]
+
+
+def test_darkest_of_cardinality_set_lengths():
+    "Confirm expected lengths of the sets of set classes, for cardinality 1 through 12"
+    sets = [SetClass.darkest_of_cardinality(i + 1) for i in range(12)]
+    assert [len(s) for s in sets] == [1, 6, 22, 55, 66, 127, 66, 55, 22, 6, 1, 1]
+
+
+def test_all_of_cardinality():
+    s3 = SetClass.all_of_cardinality(3)
+    s6 = SetClass.all_of_cardinality(6)
+    assert len(s3) == 55
+    assert len(s6) == 462
+
+    # all versions (rotations) of each set class are present
+    assert SetClass(0, 1, 2) in s3
+    assert SetClass(0, 10, 11) in s3
+
+    assert SetClass(0, 4, 6) in s3
+    assert SetClass(0, 6, 10) in s3
+
+    assert SetClass(0, 1, 3, 4, 8, 10) in s6
+    assert SetClass(0, 4, 6, 8, 9, 11) in s6
+
+
+def test_darkest_of_cardinality():
+    s3 = SetClass.darkest_of_cardinality(3)
+    s6 = SetClass.darkest_of_cardinality(6)
+    assert len(s3) == 22
+    assert len(s6) == 127
+
+    # only one version (rotation) of each set class is present
+    assert SetClass(0, 1, 2) in s3
+    assert SetClass(0, 10, 11) not in s3
+
+    assert SetClass(0, 4, 6) in s3
+    assert SetClass(0, 6, 10) not in s3
+
+    assert SetClass(0, 1, 3, 4, 8, 10) in s6
+    assert SetClass(0, 4, 6, 8, 9, 11) not in s6