def test_pow_gentle_simplify():
# these simplify to 0 and 1
weird0 = Add([x, -x])
weird1 = Mul([x, 1 / x])
assert weird0 != mathify(0)
assert weird1 != mathify(1)
assert weird0.gentle_simplify() == mathify(0)
assert weird1.gentle_simplify() == mathify(1)
assert Pow(x, Thing()).gentle_simplify() == Pow(x, Thing(True))
assert Pow(Thing(), y).gentle_simplify() == Pow(Thing(True), y)
assert Pow(Pow(x, y), z).gentle_simplify() == Pow(x, y * z)
assert Pow(x * y, z).gentle_simplify() == Mul([Pow(x, z), Pow(y, z)])
assert Pow(weird0, x).gentle_simplify() == mathify(0)
assert Pow(weird1, x).gentle_simplify() == mathify(1)
assert Pow(weird0, weird0).gentle_simplify() == mathify(0**0)
assert Pow(x, weird0).gentle_simplify() == mathify(1)
assert Pow(x, weird1).gentle_simplify() == x
assert Pow(2, 3).gentle_simplify() == mathify(8)
assert isinstance(Pow(2, -3).gentle_simplify(), Pow)
for base in range(-10, 10):
for exponent in range(-10, 10):
try:
value = base**exponent
except ZeroDivisionError:
continue # TODO: derivater should also raise an error :(
simplified = Pow(base, exponent).gentle_simplify()
if abs(value - int(value)) > 1e-12:
# not an integer
assert isinstance(simplified, Pow)
else:
assert simplified == mathify(int(value))
def test_add_repr():
assert repr(x + y) == 'x + y'
assert repr(x - y) == 'x - y'
assert repr(-x - y) == '-x - y'
assert repr(Add([])) == '0'
assert repr(Add([-x])) == '-x'
assert repr(Add([x])) == 'x'
def test_with_fraction_coeff():
assert Pow(3, 4).with_fraction_coeff() == (Pow(3, 4), mathify(1))
assert Pow(3, -4).with_fraction_coeff() == (Pow(3, -4), mathify(1))
assert Mul([2, Pow(3, -4)]).with_fraction_coeff() == (mathify(2) / 81,
mathify(1))
assert Mul([half, x, 3]).with_fraction_coeff() == (half * 3, x)
assert Add([2 * x / 3, 4 * y / 5
]).with_fraction_coeff() == (mathify(2) / 15, 5 * x + 6 * y)
assert Add([]).with_fraction_coeff() == (mathify(1), Add([]))
def test_mathify_pythonify():
math2python = {
Integer(1): 1,
Integer(1) / 2: fractions.Fraction(1, 2),
Integer(3) / (-5): fractions.Fraction(-3, 5),
Pow(4, 2): fractions.Fraction(4)**2,
Pow(5, 3): 5**3,
}
# keys() and values() are guaranteed to be in the same order, although a
# different order shouldn't matter
math_sum = Add(math2python.keys()) # not gentle_simplify()ied
python_sum = sum(math2python.values())
math2python[math_sum] = python_sum
math_product = Mul(math2python.keys())
python_product = functools.reduce(operator.mul, math2python.values())
math2python[math_product] = python_product
for math, python in math2python.items():
assert mathify(math) == math # returned as is
assert mathify(python) == math.gentle_simplify()
assert pythonify(math) == python
assert pythonify(python) == python
# make sure that fractions aren't returned when not needed
assert type(mathify(fractions.Fraction(2, 1))) is Integer
assert type(pythonify(Mul([4, half]))) is int
with pytest.raises(TypeError, match="don't know how to pythonify <Toot>$"):
pythonify(Toot())
with pytest.raises(TypeError, match="don't know how to mathify 'lol'$"):
mathify('lol')
def test_automagic_gentle_simplify():
assert (Thing() + x).objects[0].gentle
assert (Thing() * x).objects[0].gentle
assert (Thing()**x).base.gentle
assert (x**Thing()).exponent.gentle
assert not Add([Thing(), x]).objects[0].gentle
assert not Mul([Thing(), x]).objects[0].gentle
assert not Pow(Thing(), x).base.gentle
assert not Pow(x, Thing()).exponent.gentle
def test_operators():
pairs = [
(2 * x, y),
(2 * ln(4), y),
(x, x),
(x, 2 * x),
(y, -2 * x),
# not all things are MathObjects, they must be mathified
(1, -2 * x),
(-10, -x),
]
pairs.extend([(b, a) for (a, b) in pairs])
for a, b in pairs:
if not isinstance(b, int):
assert 0 - b == -b
assert 1 / b == pow(b, -1)
assert a + b == Add([a, b]).gentle_simplify()
assert a - b == Add([a, -b]).gentle_simplify()
assert a * b == Mul([a, b]).gentle_simplify()
assert a / b == Mul([a, Pow(b, -1)]).gentle_simplify()
assert a**b == Pow(a, b).gentle_simplify()
def test_add_partial_replaces():
# this checks .objects to make sure the order is correct
assert Add([x, y, z]).replace(Add([x, y]), a).objects == [a, z]
assert Add([x, y, z]).replace(Add([y, x]), a).objects == [a, z]
assert Add([x, y, z]).replace(Add([y, z]), a).objects == [x, a]
assert Add([x, y, z]).replace(Add([z, y]), a).objects == [x, a]
assert Add([x, y, z]).replace(Add([x, z]), a).objects == [y, a]
assert Add([x, y, z]).replace(Add([z, x]), a).objects == [a, y]
assert Mul([x, y, z]).replace(Mul([x, y]), a).objects == [a, z]
assert Mul([x, y, z]).replace(Mul([y, x]), a).objects == [a, z]
assert Mul([x, y, z]).replace(Mul([y, z]), a).objects == [x, a]
assert Mul([x, y, z]).replace(Mul([z, y]), a).objects == [x, a]
assert Mul([x, y, z]).replace(Mul([x, z]), a).objects == [y, a]
assert Mul([x, y, z]).replace(Mul([z, x]), a).objects == [a, y]
for klass, name, instead in [(Add, 'Add', 'zeros'), (Mul, 'Mul', 'ones')]:
with pytest.raises(ValueError,
match=((r"cannot replace %s\(\[\]\) by something, "
r"maybe use gentle_simplify\(\) to turn "
r"%s\(\[\]\)'s into %s\?$") %
(name, name, instead))):
klass([x, y]).replace(klass([]), z)
# make sure that gentle_simplify() is not called
assert not Add([x, y, z]).replace(x + y, Thing()).objects[0].gentle
assert not Mul([x, y, z]).replace(x * y, Thing()).objects[0].gentle
# even -x which is Mul([-1, x]) doesn't turn into Integer(-1), instead it
# turns into Mul([-1, 1]) which looks a lot like Integer(-1) ... (lol)
assert Add([x, -x]).replace(x, 1) == Add([1, Mul([-1, 1])])
assert Mul([x, -x]).replace(x, 1) == Mul([1, Mul([-1, 1])])
def test_add_gentle_simplify():
assert Add([x, y, Thing()]).gentle_simplify() == Add([x, y, Thing(True)])
assert (Add([x, y, Add([z, Thing()])
]).gentle_simplify() == Add([x, y, z, Thing(True)]))
assert Add([1, x, 2, y, 3]).gentle_simplify() == Add([x, y, 6])
assert Add([1, x, 2, y, 3]).gentle_simplify().objects[-1] == mathify(6)
assert Add([x, x, y]).gentle_simplify() == Add([2 * x, y])
assert Add([2 * x, 3 * y, 4 * x]).gentle_simplify() == Add([6 * x, 3 * y])
assert Add([x, x]).gentle_simplify() == 2 * x
assert Add([y]).gentle_simplify() == y
assert Add([2 * x, -2 * x]).gentle_simplify() == mathify(0)
assert Add([]).gentle_simplify() == mathify(0)
assert Add([2, x, half]).gentle_simplify().objects == [x, half * 5]
assert Add([3 * x, half * x]).gentle_simplify() == half * 7 * x
# these were broken in old derivater versions
assert Add([x, y, -x]).gentle_simplify() == y
assert Add([x, -x]).gentle_simplify() == mathify(0)