def test_fuzz_sqrt():
for field in list(random_finite_fields(3)) + [Rational]:
for _ in range(100):
x = field.random()
if x.is_square():
y = x.sqrt()
assert y*y == x
else:
assert_raises(ValueError, x.sqrt)
def test_fuzz_sqrt():
for field in list(random_finite_fields(3)) + [Rational]:
for _ in range(100):
x = field.random()
if x.is_square():
y = x.sqrt()
assert y * y == x
else:
assert_raises(ValueError, x.sqrt)
def test_fuzz_reduce():
for field in list(random_finite_fields(3)) + [Rational]:
for _ in range(100):
x, y, z = field.random(), field.random(), field.random()
x1, y1, z1 = x.reduce([y, z])
assert x*y1 == y*x1
assert y*z1 == z*y1
assert z*x1 == x*z1
x1.reduce([])[0] == x1
y1.reduce([])[0] == y1
z1.reduce([])[0] == z1
def test_fuzz_reduce():
for field in list(random_finite_fields(3)) + [Rational]:
for _ in range(100):
x, y, z = field.random(), field.random(), field.random()
x1, y1, z1 = x.reduce([y, z])
assert x * y1 == y * x1
assert y * z1 == z * y1
assert z * x1 == x * z1
x1.reduce([])[0] == x1
y1.reduce([])[0] == y1
z1.reduce([])[0] == z1
def test_fuzz_axioms():
for field in list(random_finite_fields(3)) + [Rational]:
for _ in range(100):
x, y, z = field.random(), field.random(), field.random()
zero = field(0)
one = field(1)
# 1. Closure under addition
assert type(x + y) == field
# 2. Associative law of addition
assert (x + y) + z == x + (y + z)
# 3. Commutative law of addition
assert x + y == y + x
# 4. Existance of a zero
assert x + zero == zero + x == x
# 5. Existance of a negative
w = -x
assert x + w == 0
# 6. Closure under multiplication
assert type(x*y) == field
# 7. Associative law of multiplication
assert x*(y*z) == (x*y)*z
# 8. Commutative law of multiplication
assert x*y == y*x
# 9. Existance of a one
assert x*one == one*x == x
# 10. Existance of an inverse for multiplication
if x != 0:
print "X =", x, x == 0, x != 0
w = one/x
assert x*w == x*w == one
else:
assert_raises(ZeroDivisionError, x.__rdiv__, one)
assert_raises(ZeroDivisionError, one.__div__, x)
# 11. Distributive law
assert x*(y + z) == x*y + x*z
# 12. Distributive law
assert (x + y)*z == x*z + y*z
def test_fuzz_axioms():
for field in list(random_finite_fields(3)) + [Rational]:
for _ in range(100):
x, y, z = field.random(), field.random(), field.random()
zero = field(0)
one = field(1)
# 1. Closure under addition
assert type(x + y) == field
# 2. Associative law of addition
assert (x + y) + z == x + (y + z)
# 3. Commutative law of addition
assert x + y == y + x
# 4. Existance of a zero
assert x + zero == zero + x == x
# 5. Existance of a negative
w = -x
assert x + w == 0
# 6. Closure under multiplication
assert type(x * y) == field
# 7. Associative law of multiplication
assert x * (y * z) == (x * y) * z
# 8. Commutative law of multiplication
assert x * y == y * x
# 9. Existance of a one
assert x * one == one * x == x
# 10. Existance of an inverse for multiplication
if x != 0:
print "X =", x, x == 0, x != 0
w = one / x
assert x * w == x * w == one
else:
assert_raises(ZeroDivisionError, x.__rdiv__, one)
assert_raises(ZeroDivisionError, one.__div__, x)
# 11. Distributive law
assert x * (y + z) == x * y + x * z
# 12. Distributive law
assert (x + y) * z == x * z + y * z
