def test_abs(self):
r0 = RationalNumber(-1, 2)
r1 = RationalNumber(3, 6)
r2 = RationalNumber(1, 2)
self.assertEqual(abs(r0), r1)
self.assertEqual(abs(r2), r1)
def test_pow(self):
r0 = RationalNumber(1, 2)
r1 = RationalNumber(0, 1)
self.assertEqual(r0**3, RationalNumber(1, 8))
self.assertEqual(r1**4, 0)
self.assertEqual(r0**0, 1)
self.assertEqual(r0**(-2), 4)
def test__init__(self):
m = Matrix([[3, 2], [RationalNumber(1, 2), 3]])
self.assertEqual(m[[0, 0]], RationalNumber(3))
self.assertEqual(m[[0, 1]], RationalNumber(2))
self.assertEqual(m[[1, 0]], RationalNumber(1, 2))
self.assertEqual(m[[1, 1]], RationalNumber(3))
self.assertEqual(str(m), '( 3, 2) \n( 1/2, 3) \n')
def test_neg(self):
values = (
(RationalNumber(1, 2), RationalNumber(-1, 2)),
(RationalNumber(0, 1), 0),
(RationalNumber(-4, 8), RationalNumber(1, 2))
)
for v in values:
r = -v[0]
self.assertEqual(r, v[1])
def test_init(self):
values = (
(1, 2, 1, 2),
(1, 1, 1, 1),
(1, -3, -1, 3),
(RationalNumber(3, 1), RationalNumber(2, 9), 27, 2),
(0.005, 5, 1, 1000),
(0.00000005, 1, 0, 1)
)
for v in values:
r = RationalNumber(v[0], v[1])
self.assertEqual(r.num, v[2])
self.assertEqual(r.den, v[3])
def __init__(self, terms):
# term['1'] is a coefficient of integer term.
dict_ = {'1': 0}
for key in terms.keys():
# We check this kwargs.
if isinstance(terms[key], (int, RationalNumber, float)):
terms[key] = RationalNumber(terms[key])
else:
raise TypeError('you should input int after =, for example x_2=7')
if terms[key] == 0:
continue
t_key = Polynomial.normalize_representation_of(key)
# input coefficient into terms.
try:
dict_[t_key] = terms[key] + dict_[t_key]
except KeyError:
dict_[t_key] = terms[key]
self.terms = {}
# we change the order of terms
for key in Polynomial.sort_order_of(list(dict_.keys())):
self.terms[key] = dict_[key]
def __init__(self, args):
if not isinstance(args, (list, tuple)):
raise TypeError('args is not list')
self.args = []
for i, row in enumerate(args):
if not isinstance(row, (list, tuple)):
raise TypeError('Row' + str(i) + 'is not list.')
if len(row) != len(args[0]):
raise TypeError('Row' + str(i) + 'is failed.')
s_row = []
for comp in row:
if isinstance(comp, type(args[0][0])):
s_row.append(comp)
elif isinstance(comp, (int, RationalNumber, float)):
s_row.append(RationalNumber(comp))
else:
raise TypeError('component in row ' + str(i) +
'is failed.')
self.args.append(tuple(s_row))
self.args = tuple(self.args)
def __init__(self, a, b=0, c=0):
if 'internal_access' in dir(EllipticCurve):
if EllipticCurve.internal_access:
EllipticCurve.internal_access = False
else:
raise TypeError('you are wrong')
else:
raise TypeError('you are wrong')
a = RationalNumber(a)
b = RationalNumber(b)
c = RationalNumber(c)
if -4 * (a**3) * (c**3) + (a**2) * (b**2) + 18 * a * b * c - 4 * (
b**3) - 27 * (c**2) == 0:
raise TypeError('this poly has multiple root. ')
else:
super().__init__({'y^2': -1, 'x^3': 1, 'x^2': a, 'x^1': b, '1': c})
def __init__(self, x0=0, x1=None):
ec = None
if EllipticCurve.has_instance():
ec = EllipticCurve.get_instance()
self.ec = ec
else:
raise TypeError('EC does not exist')
if x0 is None or x1 is None:
# pair = (0, None) is a point at infinity.
# because the point at infinity in elliptic curve is x = 0. (x^3=0)
x0 = 0
x1 = None
else:
x0 = RationalNumber(x0, 1)
x1 = RationalNumber(x1, 1)
if ec.includes(x0, x1) or x1 is None:
self.pair = (x0, x1)
else:
raise TypeError('EC does not have this point')
def test__operator__(self):
m1 = Matrix([[3, 2], [RationalNumber(1, 2), 3]])
m2 = Matrix([[1, 2], [RationalNumber(1, 5), 2]])
m3 = Matrix([[3, 2], [RationalNumber(1, 2), 3]])
self.assertEqual(m1+m2, Matrix([[4, 4], [RationalNumber(7, 10), 5]]))
self.assertEqual(m2*m3, Matrix([
[4, 8], [RationalNumber(8, 5), RationalNumber(32, 5)]
]))
self.assertEqual(m2*3, Matrix(
[[3, 6], [RationalNumber(3, 5), 6]]))
def __mul__(self, other):
if isinstance(other, Matrix):
if self.clm_size != other.row_size:
raise TypeError('we can not do multication')
args = []
for i in range(self.row_size):
args.append([])
for j in range(other.clm_size):
args[i].append(0)
for k in range(self.clm_size):
args[i][j] += (self[i][k]) * (other[k][j])
return Matrix(args)
elif isinstance(other, type(self.args[0][0])):
return Matrix([[comp * other for comp in row] for row in self])
elif isinstance(other, (int, RationalNumber, float)):
return Matrix([[comp * RationalNumber(other) for comp in row]
for row in self])
else:
return NotImplemented
def test_order(self):
r0 = RationalNumber(1, 2)
r1 = RationalNumber(3, 6)
r2 = RationalNumber(3, 1)
r3 = RationalNumber(-12, -4)
self.assertEqual(r0, r1)
self.assertEqual(r2, r3)
self.assertEqual(r2, 3)
self.assertTrue(r0.__ge__(r1))
self.assertTrue(r1.__gt__(0))
self.assertTrue(r3.__gt__(-0.1))
self.assertFalse(r1 < r0)
self.assertFalse(r1.__rgt__(0))
self.assertFalse(r3.__rgt__(-0.1))
def test_add(self):
values = (
(RationalNumber(1, 2), RationalNumber(1, 3), RationalNumber(5, 6)),
(RationalNumber(1, 2), 1, RationalNumber(3, 2)),
(1, RationalNumber(1, 3), RationalNumber(4, 3)),
(RationalNumber(1, 2), 0.5, 1),
(1.5, RationalNumber(1, 3), RationalNumber(11, 6)),
(RationalNumber(1, 6), RationalNumber(5, 6), 1),
(RationalNumber(1, 6), RationalNumber(-1, 6), 0)
)
for v in values:
r = v[0] + v[1]
self.assertEqual(r, v[2])
def test_mul(self):
values = (
(RationalNumber(1, 2), RationalNumber(1, 3), RationalNumber(1, 6)),
(RationalNumber(1, 2), 2, 1),
(-6, RationalNumber(1, 3), -2),
(RationalNumber(1, 2), 0.5, RationalNumber(1, 4)),
(-0.3, RationalNumber(1, 3), RationalNumber(1, -10)),
(RationalNumber(1, 6), RationalNumber(-6, 1), -1),
(RationalNumber(1, 6), RationalNumber(0, 1), 0)
)
for v in values:
r = v[0] * v[1]
self.assertEqual(r, v[2])
def test_str_(self):
self.assertEqual(str(RationalNumber(-2, 3)), '-2/3')
def test_is_integer(self):
r0 = RationalNumber(1, 2)
r1 = RationalNumber(3, 3)
self.assertFalse(r0.is_integer())
self.assertTrue(r1.is_integer())
def test_div(self):
values = (
(RationalNumber(1, 2), RationalNumber(1, 3), RationalNumber(3, 2)),
(RationalNumber(1, 2), 2, RationalNumber(1, 4)),
(6, RationalNumber(1, 3), 18),
(RationalNumber(1, 2), 2.5, RationalNumber(1, 5)),
(0.4, RationalNumber(1, 3), RationalNumber(12, 10)),
(RationalNumber(1, 6), RationalNumber(-1, 3), RationalNumber(-1, 2)),
(RationalNumber(0, 6), RationalNumber(1, 1), 0)
)
for v in values:
r = v[0] / v[1]
self.assertEqual(r, v[2])
def test_init_error(self):
with self.assertRaises(TypeError):
RationalNumber(1, 0.000005)
with self.assertRaises(TypeError):
RationalNumber(1, 0)
def test_convertion(self):
r0 = RationalNumber(3, 1)
r1 = RationalNumber(1, 2)
self.assertEqual(int(r0), 3)
self.assertEqual(float(r1), 0.5)
def test(self):
EllipticCurve.get_instance(0, -2)
o = RationalPointInEC()
p0 = RationalPointInEC(2, 2)
p1 = RationalPointInEC(2, -2)
p2 = RationalPointInEC(RationalNumber(9, 4), RationalNumber(-21, 8))
p3 = RationalPointInEC(RationalNumber(12769, 7056), RationalNumber(900271, 592704))
self.assertEqual(p0.pair, (2, 2))
self.assertEqual(p1.pair, (2, -2))
self.assertEqual((-p1).pair, (2, 2))
self.assertEqual(p2.pair, (RationalNumber(9, 4), RationalNumber(-21, 8)))
self.assertEqual(p3.pair, (RationalNumber(12769, 7056), RationalNumber(900271, 592704)))
self.assertEqual(2 * p0, p2)
self.assertEqual(3 * p0 + p1, p2)
self.assertEqual(4 * p0, p3)
self.assertEqual(2 * p0 + 2 * p0, p3)
self.assertEqual(p0 + p1, o)
self.assertEqual(p0 - p1, p2)
EllipticCurve.remove_instance()
EllipticCurve.get_instance(0, -2)
r0 = RationalPointInEC(0, 0)
r1 = RationalPointInEC(-1, 1)
r2 = RationalPointInEC(2, 2)
r3 = RationalPointInEC(RationalNumber(-8, 9), RationalNumber(-28, 27))
r4 = RationalPointInEC(RationalNumber(-1, 169), RationalNumber(239, 2197))
self.assertEqual(r0.pair, (0, 0))
self.assertEqual(r1.pair, (-1, 1))
self.assertEqual(r2.pair, (2, 2))
self.assertEqual(r3.pair, (RationalNumber(-8, 9), RationalNumber(-28, 27)))
self.assertEqual(r4.pair, (RationalNumber(-1, 169), RationalNumber(239, 2197)))
self.assertEqual(r1 + r2, r3)
self.assertEqual(r1 + 2 * r2, r4)
with self.assertRaises(TypeError):
RationalPointInEC(0, -1)