def test_log_expand():
w = Symbol('w', positive=True)
e = log(w**(log(5)/log(3)))
assert e.expand() == log(5)/log(3) * log(w)
x, y, z = symbols('x,y,z', positive=True)
assert log(x*(y + z)).expand(mul=False) == log(x) + log(y + z)
assert log(log(x**2)*log(y*z)).expand() in [log(2*log(x)*log(y) +
2*log(x)*log(z)), log(log(x)*log(z) + log(y)*log(x)) + log(2),
log((log(y) + log(z))*log(x)) + log(2)]
assert log(x**log(x**2)).expand(deep=False) == log(x)*log(x**2)
assert log(x**log(x**2)).expand() == 2*log(x)**2
assert ((log(x*(y + z))*(x + y)).expand(mul=True, log=True) ==
y*log(x) + y*log(y + z) + x*log(x) + x*log(y + z))
x, y = symbols('x,y')
assert log(x*y).expand(force=True) == log(x) + log(y)
assert log(x**y).expand(force=True) == y*log(x)
assert log(exp(x)).expand(force=True) == x
# there's generally no need to expand out logs since this requires
# factoring and if simplification is sought, it's cheaper to put
# logs together than it is to take them apart.
assert log(2*3**2).expand() != 2*log(3) + log(2)
# issue sympy/sympy#8866
assert simplify(log(x, 10, evaluate=False)) == simplify(log(x, 10))
assert expand_log(log(x, 10, evaluate=False)) == expand_log(log(x, 10))
y = Symbol('y', positive=True)
l1 = log(exp(y), exp(10))
b1 = log(exp(y), exp(5))
l2 = log(exp(y), exp(10), evaluate=False)
b2 = log(exp(y), exp(5), evaluate=False)
assert simplify(log(l1, b1)) == simplify(log(l2, b2))
assert expand_log(log(l1, b1)) == expand_log(log(l2, b2))
def test_sympyissue_8866():
assert simplify(log(x, 10, evaluate=False)) == simplify(log(x, 10))
assert expand_log(log(x, 10, evaluate=False)) == expand_log(log(x, 10))
y = Symbol('y', positive=True)
l1 = log(exp(y), exp(10))
b1 = log(exp(y), exp(5))
l2 = log(exp(y), exp(10), evaluate=False)
b2 = log(exp(y), exp(5), evaluate=False)
assert simplify(log(l1, b1)) == simplify(log(l2, b2))
assert expand_log(log(l1, b1)) == expand_log(log(l2, b2))
def test_sympyissue_8866():
assert simplify(log(x, 10, evaluate=False)) == simplify(log(x, 10))
assert expand_log(log(x, 10, evaluate=False)) == expand_log(log(x, 10))
y = Symbol('y', positive=True)
l1 = log(exp(y), exp(10))
b1 = log(exp(y), exp(5))
l2 = log(exp(y), exp(10), evaluate=False)
b2 = log(exp(y), exp(5), evaluate=False)
assert simplify(log(l1, b1)) == simplify(log(l2, b2))
assert expand_log(log(l1, b1)) == expand_log(log(l2, b2))
def _eval_simplify(self, ratio, measure):
from diofant.simplify.simplify import expand_log, simplify
if (len(self.args) == 2):
return simplify(self.func(*self.args), ratio=ratio, measure=measure)
expr = self.func(simplify(self.args[0], ratio=ratio, measure=measure))
expr = expand_log(expr, deep=True)
return min([expr, self], key=measure)
def _eval_expand_log(self, deep=True, **hints):
from diofant import unpolarify, expand_log
from diofant.concrete import Sum, Product
force = hints.get('force', False)
if (len(self.args) == 2):
return expand_log(self.func(*self.args), deep=deep, force=force)
arg = self.args[0]
if arg.is_Integer:
# remove perfect powers
p = perfect_power(int(arg))
if p is not False:
return p[1]*self.func(p[0])
elif arg.is_Mul:
expr = []
nonpos = []
for x in arg.args:
if force or x.is_positive or x.is_polar:
a = self.func(x)
if isinstance(a, log):
expr.append(self.func(x)._eval_expand_log(**hints))
else:
expr.append(a)
elif x.is_negative:
a = self.func(-x)
expr.append(a)
nonpos.append(S.NegativeOne)
else:
nonpos.append(x)
return Add(*expr) + log(Mul(*nonpos))
elif arg.is_Pow:
if force or (arg.exp.is_extended_real and arg.base.is_positive) or \
arg.base.is_polar:
b = arg.base
e = arg.exp
a = self.func(b)
if isinstance(a, log):
return unpolarify(e) * a._eval_expand_log(**hints)
else:
return unpolarify(e) * a
elif isinstance(arg, Product):
if arg.function.is_positive:
return Sum(log(arg.function), *arg.limits)
return self.func(arg)
def test_log_simplify():
x = Symbol("x", positive=True)
assert log(x**2).expand() == 2 * log(x)
assert expand_log(log(x**(2 + log(2)))) == (2 + log(2)) * log(x)
def test_log_simplify():
x = Symbol("x", positive=True)
assert log(x**2).expand() == 2*log(x)
assert expand_log(log(x**(2 + log(2)))) == (2 + log(2))*log(x)