def test_div_by_zero():
IntMod.modulus = 5
a = IntMod(4)
b = IntMod(0)
with pytest.raises(ZeroDivisionError):
a // b # pylint: disable=pointless-statement
def test_create_with_coefs():
IntMod.modulus = 5
p = PolyMod([IntMod(2)])
assert p.coef_list == [IntMod(2)]
assert p.degree == 0
def test_div_no_inverse():
IntMod.modulus = 8
a = IntMod(6)
b = IntMod(4)
with pytest.raises(ArithmeticError,
match='No inverse for 6 with modulus 8'):
a // b # pylint: disable=pointless-statement
def test_create_no_quotient():
IntMod.modulus = 0
rp = RemainderPoly(coef_list=[
IntMod(1), IntMod(4),
IntMod(6), IntMod(4),
IntMod(1)
])
x = str(rp)
assert x == 'x^4 + 4x^3 + 6x^2 + 4x + 1'
def test_plus_no_quotient():
IntMod.modulus = 2
rp1 = RemainderPoly(coef_list=[IntMod(0), IntMod(1)])
rp2 = RemainderPoly(coef_list=[IntMod(1), IntMod(1)])
rp = rp1 + rp2
rp_expected = RemainderPoly(coef_list=[IntMod(1)])
assert rp == rp_expected
def __call__(self, const_term: Union[IntMod, int]) -> IntMod:
value = const_term if isinstance(const_term,
IntMod) else IntMod(const_term)
result = IntMod(0)
term = IntMod(1)
for coef in self:
result = result + coef * term
term = term * value
return result
def test_create_with_quotient():
IntMod.modulus = 7
qp = PolyMod([IntMod(1), IntMod(2), IntMod(1)])
RemainderPoly.quotient = qp
rp = RemainderPoly([IntMod(1), IntMod(4), IntMod(6), IntMod(4), IntMod(1)])
rp._residue() # pylint: disable=protected-access
x = str(rp)
assert x == '0'
def __str__(self) -> str:
if self.degree == 0 or all(c.value == 0 for c in self):
return str(self.coef_list[0])
zero = IntMod(0)
one = IntMod(1)
content = []
for index, coef in reversed(list(enumerate(self))):
if coef != zero:
content.append("{}{}{}".format(
str(coef) if coef != one or index == 0 else '',
'x' if index >= 1 else '',
f'^{index}' if index >= 2 else ''))
return ' + '.join(content)
def test_times():
IntMod.modulus = 3
qp = PolyMod([IntMod(1), IntMod(1), IntMod(1)])
RemainderPoly.quotient = qp
rp1 = RemainderPoly(coef_list=[IntMod(1), IntMod(1)])
rp2 = RemainderPoly(coef_list=[IntMod(1), IntMod(1)])
rp = rp1 * rp2
rp_expected = RemainderPoly(coef_list=[IntMod(0), IntMod(1)])
assert rp == rp_expected
def is_reducible(self) -> bool:
zero = IntMod(0)
value = IntMod(0)
if self(value) == zero:
return True
value += 1
while value != zero:
# Check if p(value) = 0.
if self(value) == zero:
# If p( value )=0, then ( x - value ) factors p
return True
value += 1
return False
def test_plus_different_degrees():
IntMod.modulus = 2
rp1 = RemainderPoly(coef_list=[IntMod(0), IntMod(1)])
rp2 = RemainderPoly(coef_list=[IntMod(1), IntMod(1), IntMod(1)])
rp = rp1 + rp2
rp_expected = RemainderPoly(coef_list=[IntMod(1), IntMod(0), IntMod(1)])
assert rp == rp_expected
def __mul__(self, operand: 'RemainderPoly') -> 'RemainderPoly':
result_degree = self.degree + operand.degree
result = RemainderPoly(coef_list=[IntMod(0)] * (result_degree + 1))
for k in range(result_degree + 1):
min_index = k - operand.degree if k - operand.degree > 0 else 0
max_index = k if k < self.degree else self.degree
for m in range(min_index, max_index + 1): # pylint: disable=invalid-name
result[k] = result[k] + self[m] * operand[k - m]
result._residue()
return result
def test_collapse_to_one_poly():
IntMod.modulus = 5
p = PolyMod([
IntMod(1),
IntMod(0),
IntMod(0),
IntMod(0),
IntMod(0),
IntMod(0),
IntMod(0)
])
p.collapse_degree()
expected_p = PolyMod([IntMod(1)])
assert p == expected_p
def test_collapse_degree_all_zeros():
IntMod.modulus = 5
p = PolyMod([
IntMod(0),
IntMod(0),
IntMod(0),
IntMod(0),
IntMod(0),
IntMod(0),
IntMod(0)
])
p.collapse_degree()
expected_p = PolyMod([IntMod(0)])
assert p == expected_p
def test_field_4():
f = Field(4)
assert [str(e) for e in f.elements] == ['0', '1', 'x', 'x + 1']
assert f.elements == [
RemainderPoly(coef_list=[IntMod(0)]),
RemainderPoly(coef_list=[IntMod(1)]),
RemainderPoly(coef_list=[IntMod(0), IntMod(1)]),
RemainderPoly(coef_list=[IntMod(1), IntMod(1)])
]
def test_times():
IntMod.modulus = 5
a = IntMod(3)
b = IntMod(3)
assert a * b == IntMod(4)
def test_div_no_modulus():
IntMod.modulus = 0
a = IntMod(8)
b = IntMod(4)
assert a // b == IntMod(2)
def test_increment():
IntMod.modulus = 5
a = IntMod(4)
a += 1
assert a == IntMod(0)
def test_create_default():
IntMod.modulus = 0
a = IntMod()
assert a.value == 0
def test_str():
IntMod.modulus = 5
a = IntMod(4)
assert str(a) == "4"
def test_increment_no_modulus():
IntMod.modulus = 0
a = IntMod(4)
a += 1
assert a == IntMod(5)
def test_mod_create_with_value():
IntMod.modulus = 5
a = IntMod(7)
assert a.value == 2
def constant(cls, value: int) -> 'RemainderPoly':
return cls([IntMod(value)])
def test_not_equal_true():
IntMod.modulus = 5
a = IntMod(9)
b = IntMod(3)
assert a != b
def __add__(self, operand: 'RemainderPoly') -> 'RemainderPoly':
coef_tuples = itertools.zip_longest(self, operand, fillvalue=IntMod(0))
result_coefs = [a + b for a, b in coef_tuples]
result = RemainderPoly(result_coefs)
result.collapse_degree()
return result
def test_equal_false():
IntMod.modulus = 5
a = IntMod(9)
b = IntMod(3)
assert not a == b # pylint: disable=unneeded-not
def test_equal_true():
IntMod.modulus = 5
a = IntMod(8)
b = IntMod(3)
assert a == b
def test_mod_create_with_value_becomes_zero():
IntMod.modulus = 5
a = IntMod(10)
assert a.value == 0
def test_mod_create_with_negative_value():
IntMod.modulus = 5
a = IntMod(-2)
assert a.value == 3
def test_div():
IntMod.modulus = 5
a = IntMod(4)
b = IntMod(3)
assert a // b == IntMod(3)