def mysimp(expr):
from diofant import expand, logcombine, powsimp
return expand(powsimp(logcombine(expr, force=True),
force=True,
deep=True),
force=True).replace(exp_polar, exp)
def mysimp(expr):
return expand(powsimp(logcombine(expr, force=True),
force=True,
deep=True),
force=True).replace(exp_polar, exp)
def test_logcombine_1():
z, w = symbols("z,w", positive=True)
b = Symbol("b", extended_real=True)
assert logcombine(log(x) + 2 * log(y)) == log(x) + 2 * log(y)
assert logcombine(log(x) + 2 * log(y), force=True) == log(x * y**2)
assert logcombine(a * log(w) + log(z)) == a * log(w) + log(z)
assert logcombine(b * log(z) + b * log(x)) == log(z**b) + b * log(x)
assert logcombine(b * log(z) - log(w)) == log(z**b / w)
assert logcombine(log(x) * log(z)) == log(x) * log(z)
assert logcombine(log(w) * log(x)) == log(w) * log(x)
assert logcombine(cos(-2 * log(z) + b * log(w))) in [
cos(log(w**b / z**2)), cos(log(z**2 / w**b))
]
assert logcombine(log(log(x) - log(y)) - log(z), force=True) == \
log(log(x/y)/z)
assert logcombine((2 + I) * log(x), force=True) == (2 + I) * log(x)
assert logcombine((x**2 + log(x) - log(y))/(x*y), force=True) == \
(x**2 + log(x/y))/(x*y)
# the following could also give log(z*x**log(y**2)), what we
# are testing is that a canonical result is obtained
assert logcombine(log(x)*2*log(y) + log(z), force=True) == \
log(z*y**log(x**2))
assert logcombine(
(x * y + sqrt(x**4 + y**4) + log(x) - log(y)) /
(pi * x**Rational(2, 3) * sqrt(y)**3),
force=True) == (x * y + sqrt(x**4 + y**4) + log(x / y)) / (
pi * x**Rational(2, 3) * y**Rational(3, 2))
assert logcombine(gamma(-log(x/y))*acos(-log(x/y)), force=True) == \
acos(-log(x/y))*gamma(-log(x/y))
assert logcombine(2*log(z)*log(w)*log(x) + log(z) + log(w)) == \
log(z**log(w**2))*log(x) + log(w*z)
assert logcombine(3 * log(w) + 3 * log(z)) == log(w**3 * z**3)
assert logcombine(x * (y + 1) + log(2) + log(3)) == x * (y + 1) + log(6)
assert logcombine((x + y) * log(w) +
(-x - y) * log(3)) == (x + y) * log(w / 3)
def test_logcombine_complex_coeff():
i = Integral((sin(x**2) + cos(x**3)) / x, x)
assert logcombine(i, force=True) == i
assert logcombine(i + 2 * log(x), force=True) == i + log(x**2)
def mysimp(expr):
return expand(
powsimp(logcombine(expr, force=True), force=True, deep=True),
force=True).replace(exp_polar, exp)
