class _MPMathFunction(SageFunction):
attributes = ('Listable', 'NumericFunction')
def eval(self, z):
return None
def apply_exact(self, z, evaluation):
'%(name)s[z_?ExactNumberQ]'
expr = Expression(self.get_name(), z).to_sympy()
result = from_sympy(expr)
# evaluate leaves to convert e.g. Plus[2, I] -> Complex[2, 1]
result = result.evaluate_leaves(evaluation)
return result
def apply_inexact(self, z, evaluation):
'%(name)s[z_Real|z_Complex?InexactNumberQ]'
with workprec(z.get_precision()):
z = gmpy2mpmath(z.value)
try:
result = self.eval(z)
except ValueError, exc:
text = str(exc)
if text == 'gamma function pole':
return Symbol('ComplexInfinity')
else:
raise
except ZeroDivisionError:
return
try:
result = mpmath2gmpy(result)
except SpecialValueError, exc:
return Symbol(exc.name)
def apply_N(self, prec, evaluation):
'N[E, prec_]'
prec = get_precision(prec, evaluation)
if prec is not None:
with workprec(prec):
return Real(mpmath2gmpy(mpmath.e))
def apply_inexact(self, n, k, evaluation):
'Binomial[n_?InexactNumberQ, k_?NumberQ]'
with workprec(min_prec(n, k)):
n = gmpy2mpmath(n.value)
k = gmpy2mpmath(k.value)
result = mpmath.binomial(n, k)
try:
result = mpmath2gmpy(result)
except SpecialValueError, exc:
return Symbol(exc.name)
number = Number.from_mp(result)
return number
def apply_inexact(self, n, k, evaluation):
'Binomial[n_?InexactNumberQ, k_?NumberQ]'
with workprec(min_prec(n, k)):
n = gmpy2mpmath(n.value)
k = gmpy2mpmath(k.value)
result = mpmath.binomial(n, k)
try:
result = mpmath2gmpy(result)
except SpecialValueError, exc:
return Symbol(exc.name)
number = Number.from_mp(result)
return number
def apply(self, n, b, evaluation):
'IntegerLength[n_, b_]'
# Use interval arithmetic to account for "right" rounding
n, b = n.get_int_value(), b.get_int_value()
if n is None or b is None:
evaluation.message('IntegerLength', 'int')
return
if b <= 1:
evaluation.message('IntegerLength', 'base', b)
return
result = mp.mpf(iv.log(iv.mpf(mpz2mpmath(abs(n))), mpz2mpmath(b)).b)
result = mpz(mpmath2gmpy(result)) + 1
return Integer(result)