93 lines
2.6 KiB
Python
93 lines
2.6 KiB
Python
|
"""Ensure all `Field`s fulfill the axioms from math.
|
||
|
|
|
||
|
|
Source: https://en.wikipedia.org/wiki/Field_(mathematics)#Classic_definition
|
||
|
|
"""
|
||
|
|
|
||
|
|
import contextlib
|
||
|
|
import operator
|
||
|
|
|
||
|
|
import pytest
|
||
|
|
|
||
|
|
from tests.fields import utils
|
||
|
|
|
||
|
|
|
||
|
|
@pytest.mark.repeat(utils.N_RANDOM_DRAWS)
|
||
|
|
@pytest.mark.parametrize("field", utils.ALL_FIELDS)
|
||
|
|
class TestAllFieldsManyTimes:
|
||
|
|
"""Run the tests many times for all `field`s."""
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("opr", [operator.add, operator.mul])
|
||
|
|
def test_associativity(self, field, opr):
|
||
|
|
"""`a + (b + c) == (a + b) + c` ...
|
||
|
|
|
||
|
|
... and `a * (b * c) == (a * b) * c`.
|
||
|
|
"""
|
||
|
|
a, b, c = field.random(), field.random(), field.random()
|
||
|
|
|
||
|
|
left = opr(a, opr(b, c))
|
||
|
|
right = opr(opr(a, b), c)
|
||
|
|
|
||
|
|
assert left == pytest.approx(right, abs=utils.DEFAULT_THRESHOLD)
|
||
|
|
|
||
|
|
@pytest.mark.parametrize("opr", [operator.add, operator.mul])
|
||
|
|
def test_commutativity(self, field, opr):
|
||
|
|
"""`a + b == b + a` ...
|
||
|
|
|
||
|
|
... and `a * b == b * a`.
|
||
|
|
"""
|
||
|
|
a, b = field.random(), field.random()
|
||
|
|
|
||
|
|
left = opr(a, b)
|
||
|
|
right = opr(b, a)
|
||
|
|
|
||
|
|
assert left == pytest.approx(right, abs=utils.DEFAULT_THRESHOLD)
|
||
|
|
|
||
|
|
def test_additive_identity(self, field):
|
||
|
|
"""`a + 0 == a`."""
|
||
|
|
a = field.random()
|
||
|
|
|
||
|
|
left = a + field.zero
|
||
|
|
right = a
|
||
|
|
|
||
|
|
assert left == pytest.approx(right, abs=utils.DEFAULT_THRESHOLD)
|
||
|
|
|
||
|
|
def test_multiplicative_identity(self, field):
|
||
|
|
"""`a * 1 == a`."""
|
||
|
|
a = field.random()
|
||
|
|
|
||
|
|
left = a * field.one
|
||
|
|
right = a
|
||
|
|
|
||
|
|
assert left == pytest.approx(right, abs=utils.DEFAULT_THRESHOLD)
|
||
|
|
|
||
|
|
def test_additive_inverse(self, field):
|
||
|
|
"""`a + (-a) == 0`."""
|
||
|
|
a = field.random()
|
||
|
|
|
||
|
|
left = a + (-a)
|
||
|
|
right = field.zero
|
||
|
|
|
||
|
|
assert left == pytest.approx(right, abs=utils.DEFAULT_THRESHOLD)
|
||
|
|
|
||
|
|
def test_multiplicative_inverse(self, field):
|
||
|
|
"""`a * (1 / a) == 1`."""
|
||
|
|
a = field.random()
|
||
|
|
|
||
|
|
# Realistically, `ZeroDivisionError` only occurs for `GF2`
|
||
|
|
# => With a high enough `utils.N_RANDOM_DRAWS`
|
||
|
|
# this test case is also `assert`ed for `GF2`
|
||
|
|
with contextlib.suppress(ZeroDivisionError):
|
||
|
|
left = a * (field.one / a)
|
||
|
|
right = field.one
|
||
|
|
|
||
|
|
assert left == pytest.approx(right, abs=utils.DEFAULT_THRESHOLD)
|
||
|
|
|
||
|
|
def test_distributivity(self, field):
|
||
|
|
"""`a * (b + c) == (a * b) + (a * c)`."""
|
||
|
|
a, b, c = field.random(), field.random(), field.random()
|
||
|
|
|
||
|
|
left = a * (b + c)
|
||
|
|
right = (a * b) + (a * c)
|
||
|
|
|
||
|
|
assert left == pytest.approx(right, abs=utils.DEFAULT_THRESHOLD)
|