def test_conway_poly():
assert galois.conway_poly(2, 8) == galois.Poly.Degrees([8, 4, 3, 2, 0])
GF3 = galois.GF(3)
assert galois.conway_poly(3, 8) == galois.Poly.Degrees(
[8, 5, 4, 2, 1, 0], coeffs=[1, 2, 1, 2, 2, 2], field=GF3)
GF5 = galois.GF(5)
assert galois.conway_poly(5,
8) == galois.Poly.Degrees([8, 4, 2, 1, 0],
coeffs=[1, 1, 3, 4, 2],
field=GF5)
def test_conway_poly_exceptions():
with pytest.raises(TypeError):
galois.conway_poly(2.0, 3)
with pytest.raises(TypeError):
galois.conway_poly(2, 3.0)
with pytest.raises(ValueError):
galois.conway_poly(4, 3)
with pytest.raises(ValueError):
galois.conway_poly(2, 0)
with pytest.raises(LookupError):
# GF(2^409) is the largest characteristic-2 field in Frank Luebeck's database
galois.conway_poly(2, 410)
def test_is_primitive_poly():
"""
Verify the `is_primitive_poly` boolean is calculated correctly for fields constructed with explicitly-specified
irreducible polynomials.
"""
# GF(2^m) with integer dtype
poly = galois.conway_poly(2, 32)
GF = galois.GF(2**32, irreducible_poly=poly, primitive_element="x", verify=False)
assert GF.is_primitive_poly == True
# GF(2^m) with object dtype
poly = galois.conway_poly(2, 100)
GF = galois.GF(2**100, irreducible_poly=poly, primitive_element="x", verify=False)
assert GF.is_primitive_poly == True
# GF(p^m) with integer dtype
poly = galois.conway_poly(3, 20)
GF = galois.GF(3**20, irreducible_poly=poly, primitive_element="x", verify=False)
assert GF.is_primitive_poly == True
# GF(p^m) with object dtype
poly = galois.conway_poly(3, 101)
GF = galois.GF(3**101, irreducible_poly=poly, primitive_element="x", verify=False)
assert GF.is_primitive_poly == True
def test_gf2_output_2():
"""
The states of the Galois LFSR generate the binary extension field with the connection polynomial as its
irreducible polynomial.
"""
GF = galois.GF2
poly = galois.conway_poly(2, 8)
state = GF([0,0,0,0,0,0,0,1])
lfsr = galois.LFSR(poly, state=state, config="galois")
GFE = galois.GF(2**8, irreducible_poly=poly)
alpha = GFE.primitive_element
for i in range(GFE.order - 1):
np.array_equal(lfsr.state, (alpha**i).vector())
lfsr.step()
def test_primitive_elements_exceptions():
p = galois.conway_poly(2, 8)
with pytest.raises(TypeError):
galois.primitive_elements(p.coeffs)
with pytest.raises(TypeError):
galois.primitive_elements(p, start=2.0)
with pytest.raises(TypeError):
galois.primitive_elements(p, stop=256.0)
with pytest.raises(TypeError):
galois.primitive_elements(p, reverse=1)
with pytest.raises(ValueError):
galois.primitive_elements(galois.Poly.Random(0))
with pytest.raises(ValueError):
galois.primitive_elements(galois.Poly.Random(2)*galois.Poly.Random(2))
with pytest.raises(ValueError):
galois.primitive_elements(p, start=200, stop=100)