def elliptic_eu_f(u, m):
r"""
Internal function for numeric evaluation of ``elliptic_eu``, defined as
`E\left(\operatorname{am}(u, m)|m\right)`, where `E` is the incomplete
elliptic integral of the second kind and `\operatorname{am}` is the Jacobi
amplitude function.
EXAMPLES::
sage: from sage.functions.special import elliptic_eu_f
sage: elliptic_eu_f(0.5, 0.1)
mpf('0.49605455128659691')
"""
from mpmath import mp
from sage.functions.jacobi import jacobi_am_f
ctx = mp
prec = ctx.prec
try:
u = ctx.convert(u)
m = ctx.convert(m)
ctx.prec += 10
return ctx.ellipe(jacobi_am_f(u, m), m)
finally:
ctx.prec = prec
def elliptic_eu_f(u, m):
r"""
Internal function for numeric evaluation of ``elliptic_eu``, defined as
`E\left(\operatorname{am}(u, m)|m\right)`, where `E` is the incomplete
elliptic integral of the second kind and `\operatorname{am}` is the Jacobi
amplitude function.
EXAMPLES::
sage: from sage.functions.special import elliptic_eu_f
sage: elliptic_eu_f(0.5, 0.1)
mpf('0.49605455128659691')
"""
from mpmath import mp
from sage.functions.jacobi import jacobi_am_f
ctx = mp
prec = ctx.prec
try:
u = ctx.convert(u)
m = ctx.convert(m)
ctx.prec += 10
return ctx.ellipe(jacobi_am_f(u, m), m)
finally:
ctx.prec = prec