def test_alphabet(self):
with self.assertRaises(ValueError):
FpMonoid("", [["a", "aa"]])
with self.assertRaises(ValueError):
FpMonoid("a", [["b", "aa"]])
with self.assertRaises(ValueError):
FpMonoid("aa", [["b", "aa"]])
def test_rels(self):
with self.assertRaises(TypeError):
FpMonoid("ab", "[\"a\", \"aa\"]")
with self.assertRaises(TypeError):
FpMonoid("ab", ["\"b\", \"aa\""])
with self.assertRaises(TypeError):
FpMonoid("ab", [["a", "aa", "b"]])
with self.assertRaises(TypeError):
FpMonoid("ab", [["b", ["a", "a"]]])
with self.assertRaises(ValueError):
FpMonoid("ab", [["b", "ca"]])
def test_normal_form(self):
S = FpSemigroup("a", [["a", "aa"]])
self.assertEqual(S.normal_form("a^1000"), "a")
S = FpMonoid("a", [["a", "aa"]])
self.assertEqual(S.normal_form("a^0"), "1")
S = FpSemigroup("ab", [["a", "aaa"], ["b", "bb"], ["ab", "ba"]])
self.assertEqual(S.normal_form("(ba)^10"), "aab")
def test_identity(self):
FpS = FpSemigroup("ab", [["a^10", "a"], ["bbb", "b"], ["ba", "ab"]])
a = FpS[0].get_value()
self.assertEqual(a.identity().word, "")
FpS = FpMonoid("ab", [["a^10", "a"], ["bbb", "b"], ["ba", "ab"]])
a = FpS[1].get_value()
self.assertEqual(a.identity().word, "1")
def test_nridempotents(self):
S = FpSemigroup("ab", [["a", "a^5"], ["b", "bb"], ["ab", "ba"]])
self.assertEqual(S.nridempotents(), 3)
S = FpMonoid("ab", [["a", "a^5"], ["b", "bb"], ["ab", "ba"]])
self.assertEqual(S.nridempotents(), 4)
S = FpSemigroup("ab", [])
with self.assertRaises(ValueError):
S.nridempotents()
def test_valid_init(self):
FpMonoid("", [])
FpMonoid("a", [])
with self.assertRaises(ValueError):
FpMonoid("1", [])
FpMonoid("a", [["a", "aa"]])
FpMonoid("ab", [["b", "aa"]])
FpMonoid("ab", [["1", "aa"]])
FpMonoid("ab", [["b", "a^2"]])
FpMonoid("ab", [["1", "(a)^6"]])
def test_word_to_class_index(self):
M = FpMonoid("ab", [["a", "aa"], ["b", "bb"], ["ab", "ba"]])
self.assertEqual(M.word_to_class_index('a'),
M.word_to_class_index('aa'))
self.assertNotEqual(M.word_to_class_index('a'),
M.word_to_class_index('bb'))
self.assertIsInstance(M.word_to_class_index('aba'), int)
def test_repr(self):
M = FpMonoid("ab", [["aa", "a"], ["bbb", "ab"], ["ab", "ba"]])
self.assertEqual(M.__repr__(),
"<fp monoid with 2 generators and 3 relations>")
def test_size(self):
self.assertEqual(FpMonoid("a", [["a", "aa"]]).size(), 2)
self.assertEqual(
FpMonoid("ab", [["a", "aa"], ["b", "bb"], ["ab", "ba"]]).size(), 4)
def test_set_report(self):
M = FpMonoid("a", [["a", "aa"]])
M.set_report(True)
M.set_report(False)
with self.assertRaises(TypeError):
M.set_report("False")
def test_contains(self):
FpM = FpMonoid("ab", [["aa", "a"], ["bbb", "b"], ["ba", "ab"]])
self.assertFalse(1 in FpM)
self.assertTrue("abb" in FpM)
self.assertTrue("" in FpM)
def test_contains(self):
FpM = FpMonoid("ab", [["aa", "a"], ["bbb", "b"], ["ba", "ab"]])
with self.assertRaises(ValueError):
1 in FpM
self.assertTrue("abb" in FpM)
self.assertTrue("" in FpM)
def test_valid_init(self):
FpMonoid([], [])
FpMonoid(["a"], [])
FpMonoid(["a"], [["a", "aa"]])
FpMonoid(["a", "b"], [["b", "aa"]])
FpMonoid(["a", "b"], [["1", "aa"]])