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_create_with_coefs():
IntMod.modulus = 5
p = PolyMod([IntMod(2)])
assert p.coef_list == [IntMod(2)]
assert p.degree == 0
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_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 test_create():
IntMod.modulus = 5
p = PolyMod()
assert p.coef_list == []
with pytest.raises(ValueError,
match='Degree of null polynomial undefined.'):
# noinspection PyStatementEffect
p.degree # pylint: disable=pointless-statement
def test_times_no_residue_needed():
IntMod.modulus = 3
qp = PolyMod([IntMod(1), 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(1), IntMod(2), IntMod(1)])
assert rp == rp_expected
class RemainderPoly(PolyMod):
quotient = PolyMod()
def __repr__(self) -> str:
return f"RemainderPoly(coef_list={self.coef_list})"
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 __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 _residue(self):
qdegree = len(RemainderPoly.quotient) - \
1 if RemainderPoly.quotient.coef_list else -1
if qdegree > 0:
while self.degree >= qdegree:
factor = self[self.degree] // RemainderPoly.quotient[qdegree]
for qindex in range(0, qdegree + 1):
cindex = self.degree - qdegree + qindex
self[cindex] = self[cindex] - factor * \
RemainderPoly.quotient[qindex]
self.collapse_degree()
@classmethod
def constant(cls, value: int) -> 'RemainderPoly':
return cls([IntMod(value)])
def test_degree():
IntMod.modulus = 5
p = PolyMod([IntMod(2), IntMod(3), IntMod(0), IntMod(1), IntMod(4)])
assert p.degree == 4
def test_enumerate():
IntMod.modulus = 5
p = PolyMod([IntMod(2), IntMod(3), IntMod(4)])
assert p.enumerate() == 117
def test_str_one_handling():
IntMod.modulus = 5
p = PolyMod([IntMod(1), IntMod(1), IntMod(1)])
assert str(p) == "x^2 + x + 1"
def test_str_zero_handling():
IntMod.modulus = 5
p = PolyMod([IntMod(0), IntMod(0), IntMod(0), IntMod(4)])
assert str(p) == "4x^3"
def test_str_one_poly():
IntMod.modulus = 5
p = PolyMod([IntMod(1)])
assert str(p) == "1"
def test_str_degree_zero():
IntMod.modulus = 5
p = PolyMod([IntMod(2)])
assert str(p) == "2"
def test_str_zero_poly():
IntMod.modulus = 5
p = PolyMod([IntMod(0)])
assert str(p) == "0"
def test_str():
IntMod.modulus = 5
p = PolyMod([IntMod(2), IntMod(3), IntMod(0), IntMod(1), IntMod(4)])
assert str(p) == "4x^4 + x^3 + 3x + 2"
def test_evaluate():
IntMod.modulus = 5
p = PolyMod([IntMod(2), IntMod(3), IntMod(4)])
assert p(IntMod(3)) == IntMod(2)
def test_reducible_false():
IntMod.modulus = 5
p = PolyMod([IntMod(2), IntMod(3), IntMod(4)])
assert not p.is_reducible()
def test_reducible_factors():
IntMod.modulus = 5
p = PolyMod([IntMod(1), IntMod(2), IntMod(1)])
assert p.is_reducible()
def test_reducible_true():
IntMod.modulus = 5
p = PolyMod([IntMod(0), IntMod(1)])
assert p.is_reducible()
