def _eval_power(b, e):
if isinstance(e, Number):
if isinstance(e, NaN): return S.NaN
if isinstance(e, Real):
return Real(decimal_math.pow(b._as_decimal(), e.num))
if e.is_negative:
# (3/4)**-2 -> (4/3)**2
ne = -e
if isinstance(ne, One):
return Rational(1, b.p)
return Rational(1, b.p) ** ne
if isinstance(e, Infinity):
if b.p > 1:
# (3)**oo -> oo
return S.Infinity
if b.p < -1:
# (-3)**oo -> oo + I*oo
return S.Infinity + S.Infinity * S.ImaginaryUnit
return S.Zero
if isinstance(e, Integer):
# (4/3)**2 -> 4**2 / 3**2
return Integer(b.p ** e.p)
if isinstance(e, Rational):
if b == -1: # any one has tested this ???
# calculate the roots of -1
if e.q.is_odd:
return -1
r = cos(pi/e.q) + S.ImaginaryUnit*sin(pi/e.q)
return r**e.p
if b >= 0:
x, xexact = integer_nthroot(b.p, e.q)
if xexact:
res = Integer(x ** abs(e.p))
if e >= 0:
return res
else:
return 1/res
# Now check also devisors of the exponents denominator
# TODO: Check if this slows down to much.
for i in xrange(2, e.q/2 + 1):
if e.q % i == 0:
x, xexact = integer_nthroot(b.p, i)
if xexact:
return Integer(x)**(e * i)
# Try to get some part of the base out, if exponent > 1
if e.p > e.q:
i = e.p / e.q
r = e.p % e.q
return b**i * b**Rational(r, e.q)
else:
return (-1)**e * (-b)**e
c,t = b.as_coeff_terms()
if e.is_even and isinstance(c, Basic.Number) and c < 0:
return (-c * Basic.Mul(*t)) ** e
return
def _eval_power(b, e):
if isinstance(e, Number):
if isinstance(e, NaN): return S.NaN
if isinstance(e, Real):
return Real(decimal_math.pow(b._as_decimal(), e.num))
if e.is_negative:
# (3/4)**-2 -> (4/3)**2
ne = -e
if isinstance(ne, One):
return Rational(b.q, b.p)
return Rational(b.q, b.p) ** ne
if isinstance(e, Infinity):
if b.p > b.q:
# (3/2)**oo -> oo
return S.Infinity
if b.p < -b.q:
# (-3/2)**oo -> oo + I*oo
return S.Infinity + S.Infinity * S.ImaginaryUnit
return S.Zero
if isinstance(e, Integer):
# (4/3)**2 -> 4**2 / 3**2
return Rational(b.p ** e.p, b.q ** e.p)
if isinstance(e, Rational):
if b.p != 1:
# (4/3)**(5/6) -> 4**(5/6) * 3**(-5/6)
return Integer(b.p) ** e * Integer(b.q) ** (-e)
if b >= 0:
x, xexact = integer_nthroot(b.p, e.q)
y, yexact = integer_nthroot(b.q, e.q)
if xexact and yexact:
res = Rational(x ** abs(e.p), y ** abs(e.p))
if e >= 0:
return res
else:
return 1/res
# Now check also devisors of the exponents denominator
# TODO: Check if this slows down to much.
for i in xrange(2, e.q/2 + 1):
if e.q % i == 0:
x, xexact = integer_nthroot(b.p, i)
y, yexact = integer_nthroot(b.q, i)
if xexact and yexact:
return Rational(x, y)**Rational(e.p, e.q/i)
else:
# Try to get some part of the base out, if exp > 1
if e.p > e.q:
i = e.p / e.q
r = e.p % e.q
return b**i * b**Rational(r, e.q)
else:
return (-1)**e * (-b)**e
c,t = b.as_coeff_terms()
if e.is_even and isinstance(c, Basic.Number) and c < 0:
return (-c * Basic.Mul(*t)) ** e
return
def _eval_power(b, e):
"""
b is Real but not equal to rationals, integers, 0.5, oo, -oo, nan
e is symbolic object but not equal to 0, 1
(-p) ** r -> exp(r * log(-p)) -> exp(r * (log(p) + I*Pi)) ->
-> p ** r * (sin(Pi*r) + cos(Pi*r) * I)
"""
if isinstance(e, Number):
if isinstance(e, Integer):
e = e.p
return Real(decimal_math.pow(b.num, e))
e2 = e._as_decimal()
if b.is_negative and not e.is_integer:
m = decimal_math.pow(-b.num, e2)
a = decimal_math.pi() * e2
s = m * decimal_math.sin(a)
c = m * decimal_math.cos(a)
return Real(s) + Real(c) * S.ImaginaryUnit
return Real(decimal_math.pow(b.num, e2))
return
