def test_mult_int(self):
group = c.generate_a2()
hecke = h.HeckeAlgebra(group)
element = hecke.element({
'e': l.Laurent({
-100: 20,
0: 10,
100: 20
}),
'rsr': l.Laurent({
-25: -12,
-2: -1,
2: 2
})
})
result = element * 3
expected_result = hecke.element({
'e':
l.Laurent({
-100: 60,
0: 30,
100: 60
}),
'rsr':
l.Laurent({
-25: -36,
-2: -3,
2: 6
})
})
self.assertEqual(result, expected_result)
def test_sub(self):
group = c.generate_a2()
hecke = h.HeckeAlgebra(group)
h1 = hecke.element({'s': l.Laurent({-1: 1, 1: 1})})
h2 = hecke.element({
'e': l.Laurent({-3: 5}),
's': l.Laurent({
0: 1,
1: 4
})
})
h3 = hecke.element(({
'e': l.Laurent({-3: -5}),
's': l.Laurent({
-1: 1,
0: -1,
1: -3
})
}))
self.assertEqual(h1 - h1, hecke.zero)
self.assertEqual(h2 - h2, hecke.zero)
self.assertEqual(h1 - h2, h3)
def test_shift(self):
p = l.Laurent({-4: 1, -1: 0, 2: 3})
self.assertEqual(p.shift(3), l.Laurent({-1: 1, 2: 0, 5: 3}))
p = l.Laurent({-1: 1, 0: 1, 2: 3})
self.assertEqual(p.shift(-10), l.Laurent({-11: 1, -10: 1, -8: 3}))
p = l.Laurent({0: 0})
self.assertEqual(p.shift(100), l.zero)
def test_evaluate(self):
p = l.Laurent({0: 1, 1: 2, 2: 1})
self.assertEqual(p(2), 3**2)
self.assertEqual(p(-1), 0)
p = l.Laurent({-1: 1, 0: 1})
self.assertEqual(p(1), 2)
def test_top_and_bottom(self):
p = l.Laurent({-4: 1, -1: 0, 2: 3})
self.assertEqual(p.bottom(), -4)
self.assertEqual(p.top(), 2)
p = l.Laurent({-1: 1, 0: 1, 2: 3})
self.assertEqual(p.bottom(), -1)
self.assertEqual(p.top(), 2)
p = l.Laurent({0: 0})
self.assertEqual(p.bottom(), None)
self.assertEqual(p.top(), None)
def test_mult_laurent(self):
group = c.generate_a2()
hecke = h.HeckeAlgebra(group)
l1 = l.Laurent({0: 1, 1: -1})
l2 = l.Laurent({-2: 10, 3: 5})
element = hecke.element({'e': l1})
result = element * l2
expected_result = hecke.element({'e': l1 * l2})
self.assertEqual(result, expected_result)
def testSub(self):
result = (l.Laurent({
-1: 1,
0: 2,
1: 3
}) - l.Laurent({
-2: 10,
-1: -1,
1: 2
}))
self.assertEqual(result, l.Laurent({-2: -10, -1: 2, 0: 2, 1: 1}))
def testAdd(self):
result = (l.Laurent({
0: 10,
1: 2
}) + l.Laurent({
-1: 1,
0: 2,
1: 3,
2: 3
}))
self.assertEqual(result, l.Laurent({-1: 1, 0: 12, 1: 5, 2: 3}))
def test_w0_central(self):
group = c.generate_a2()
hecke = h.HeckeAlgebra(group)
w0 = hecke.element({'rsr': l.Laurent({0: 1})})
w02 = w0 * w0
h1 = hecke.element({
'e': l.Laurent({1: 2}),
'sr': l.Laurent({
-10: 20,
2: 1
})
})
h2 = hecke.element({'e': l.Laurent({0: 1})})
self.assertEqual(w02 * h1, h1 * w02)
self.assertEqual(w02 * h2, h2 * w02)
def testMult(self):
result = (l.Laurent({
-1: 1,
0: 2,
1: 3
}) * l.Laurent({
0: 2,
1: 4,
2: -1
}))
self.assertEqual(
result,
l.Laurent({
-1: 1 * 2,
0: 2 * 2 + 1 * 4,
1: 1 * (-1) + 2 * 4 + 3 * 2,
2: 2 * (-1) + 3 * 4,
3: 3 * (-1)
}))
def test_add(self):
group = c.generate_a2()
hecke = h.HeckeAlgebra(group)
h1 = hecke.element({'s': l.Laurent({-1: 1, 1: 1})})
h2 = hecke.element({
'e': l.Laurent({-3: 5}),
's': l.Laurent({
0: 1,
1: 4
})
})
expected_sum = hecke.element({
'e': l.Laurent({-3: 5}),
's': l.Laurent({
-1: 1,
0: 1,
1: 5
})
})
self.assertEqual(h1 + h2, expected_sum)
def test_mul_identity(self):
group = c.generate_a2()
hecke = h.HeckeAlgebra(group)
e = hecke.element({'e': l.Laurent({0: 1})})
self.assertEqual(e * e, e)
h1 = hecke.element({
's': l.Laurent({
10: 1,
20: 2
}),
'rs': l.Laurent({
-1: 2,
0: 1
})
})
self.assertEqual(h1 * e, h1)
h2 = hecke.element({
'e': l.Laurent({
-100: 20,
0: 10,
100: 20
}),
'rsr': l.Laurent({
-25: -12,
-2: -1,
2: 2
})
})
self.assertEqual(h2 * e, h2)
self.assertEqual(e * h2, h2)
def test_dual(self):
group = c.generate_a2()
hecke = h.HeckeAlgebra(group)
self.assertEqual(
hecke.get_standard_basis_element('e').dual().dual(),
hecke.get_standard_basis_element('e'))
self.assertEqual(
hecke.get_standard_basis_element('r').dual().dual(),
hecke.get_standard_basis_element('r'))
self.assertEqual(
hecke.get_standard_basis_element('s').dual().dual(),
hecke.get_standard_basis_element('s'))
self.assertEqual(
hecke.get_standard_basis_element('rs').dual().dual(),
hecke.get_standard_basis_element('rs'))
self.assertEqual(
hecke.get_standard_basis_element('sr').dual().dual(),
hecke.get_standard_basis_element('sr'))
self.assertEqual(
hecke.get_standard_basis_element('rsr').dual().dual(),
hecke.get_standard_basis_element('rsr'))
h1 = hecke.element({
'e': l.Laurent({
-1: 10,
2: 3
}),
's': l.Laurent({
0: 1,
1: 3
}),
'rsr': l.Laurent({20: -12})
})
self.assertEqual(h1.dual().dual(), h1)
hs = hecke.element({'e': l.Laurent({1: 1}), 's': l.Laurent({0: 1})})
self.assertEqual(hs.dual(), hs)
print(hs * hs)
self.assertEqual(hs * hs, hs * l.Laurent({-1: 1, 1: 1}))
def test_mul_generator(self):
group = c.generate_a2()
hecke = h.HeckeAlgebra(group)
e = hecke.element({'e': l.Laurent({0: 1})})
r = hecke.element({'r': l.Laurent({0: 1})})
s = hecke.element({'s': l.Laurent({0: 1})})
rs = hecke.element({'rs': l.Laurent({0: 1})})
sr = hecke.element({'sr': l.Laurent({0: 1})})
rsr = hecke.element({'rsr': l.Laurent({0: 1})})
self.assertEqual(e * s, s)
self.assertEqual(e * r, r)
self.assertEqual(r * s, rs)
self.assertEqual(s * r, sr)
self.assertEqual(r * s * r, rsr)
self.assertEqual(rs * r, rsr)
self.assertEqual(r * sr, rsr)
self.assertEqual(sr * s, rsr)
self.assertEqual(
s * s,
hecke.element({
's': l.Laurent({
-1: 1,
1: -1
}),
'e': l.Laurent({0: 1})
}))
self.assertEqual(
sr * r,
hecke.element({
'sr': l.Laurent({
-1: 1,
1: -1
}),
's': l.Laurent({0: 1})
}))
self.assertEqual(
hecke.element({'r': l.Laurent({0: 2})}) *
hecke.element({'sr': l.Laurent({0: 2})}),
hecke.element({'rsr': l.Laurent({0: 4})}))
def testEquals(self):
self.assertEqual(l.Laurent({0: 1, 1: 2}), l.Laurent({0: 1, 1: 2}))
self.assertNotEqual(l.Laurent({0: 1, 1: 2}), l.Laurent({0: 1, 1: 3}))
def testMultInt(self):
result = l.Laurent({-4: 2, -1: 0, 2: 3}) * 3
self.assertEqual(result, l.Laurent({-4: 6, -1: 0, 2: 9}))
def testInvolution(self):
p = l.Laurent({-4: 2, -1: 0, 2: 3})
result = p.involute()
self.assertEqual(result, l.Laurent({-2: 3, 1: 0, 4: 2}))
self.assertEqual(p.involute().involute(), p)
def testNeg(self):
result = -l.Laurent({-1: 1, 0: -10, 2: 15})
self.assertEqual(result, l.Laurent({-1: -1, 0: 10, 2: -15}))
def test_shift(self):
p = l.Laurent({-4: 2, -1: 0, 2: 3})
self.assertEqual(p.shift(1), l.Laurent({-3: 2, 0: 0, 3: 3}))
self.assertEqual(p.shift(-5), l.Laurent({-9: 2, -6: 0, -3: 3}))