def testMultiplicationOfElements(self):
a = Element.word("a");
b = Element.word("b");
actual = a * b
self.assertEquals(Element.word("ab"), actual)
def testCommutate(self):
a = Element.word("a")
b = Element.word("b")
actual = a.commutate(b)
self.assertEquals(Element.word("aba^-1b^-1"), actual)
def testSolution(self):
for n in range(1,2):
word = Solver().solve(n)
letterCount = 0
for letter in word.letters():
letterCount += 1
self.assertEquals(Element.word(""), word.remove(letter))
self.assertEquals(n, letterCount)
def solve(self, n):
if (n == 1):
self.index += 1
return Element.word(string.letters[self.index])
else:
floor = n / 2
ceil = n - floor
a = self.solve(ceil)
b = self.solve(floor)
return a * b.inverse() * a.inverse() * b
def testCreationOfElement(self):
self.assertNotEqual(None, Element.word("a"))
def testRemoval(self):
element = Element.word("aba^-1b^-1");
actual = element.remove('a')
self.assertEquals(Element.word(""), actual)
def testNormalisation(self):
element = Element.word("ab^2b^-2a^-1");
actual = element * element.inverse()
self.assertEquals(Element.word(""), actual)
def testInverseOfElements(self):
element = Element.word("a^2b^-1");
actual = element.inverse()
self.assertEquals(Element.word("ba^-2"), actual)
def over(*generators):
return FreeGroup([Element.word(g) for g in generators])
def testGeneratorAccess(self):
self.assertEquals(Element.word("a"), self.group[0])
self.assertEquals(Element.word("b"), self.group[1])
