def _eval_power(self, other, terms=False):
# n n n
# (-3 + y) -> (-1) * (3 - y)
#
# If terms=True then return the arguments that should be
# multiplied together rather than multiplying them.
#
# At present, as_coeff_terms return +/-1 but the
# following should work even if that changes.
if Basic.keep_sign:
return None
rv = None
c, t = self.as_coeff_mul()
if c.is_negative and not other.is_integer:
if c is not S.NegativeOne and self.is_positive:
coeff = C.Pow(-c, other)
assert len(t) == 1, 't'
b = -t[0]
rv = (coeff, C.Pow(b, other))
elif c is not S.One:
coeff = C.Pow(c, other)
assert len(t) == 1, 't'
b = t[0]
rv = (coeff, C.Pow(b, other))
if not rv or terms:
return rv
else:
return C.Mul(*rv)
def _eval_is_real(self):
real_b = self.base.is_real
if real_b is None:
return
real_e = self.exp.is_real
if real_e is None:
return
if real_b and real_e:
if self.base.is_positive:
return True
else: # negative or zero (or positive)
if self.exp.is_integer:
return True
elif self.base.is_negative:
if self.exp.is_Rational:
return False
im_b = self.base.is_imaginary
im_e = self.exp.is_imaginary
if im_b:
if self.exp.is_integer:
if self.exp.is_even:
return True
elif self.exp.is_odd:
return False
elif (self.exp in [S.ImaginaryUnit, -S.ImaginaryUnit] and
self.base in [S.ImaginaryUnit, -S.ImaginaryUnit]):
return True
elif self.exp.is_Add:
c, a = self.exp.as_coeff_Add()
if c and c.is_Integer:
return C.Mul(
self.base**c, self.base**a, evaluate=False).is_real
if real_b and im_e:
if self.base is S.NegativeOne:
return True
c = self.exp.coeff(S.ImaginaryUnit)
if c:
ok = (c*C.log(self.base)/S.Pi).is_Integer
if ok is not None:
return ok
