def _eval_(self, n, z):
"""
EXAMPLES::
sage: lambert_w(6.0)
1.43240477589830
sage: lambert_w(1)
lambert_w(1)
sage: lambert_w(x+1)
lambert_w(x + 1)
There are three special values which are automatically simplified::
sage: lambert_w(0)
0
sage: lambert_w(e)
1
sage: lambert_w(-1/e)
-1
sage: lambert_w(SR(0))
0
The special values only hold on the principal branch::
sage: lambert_w(1,e)
lambert_w(1, e)
sage: lambert_w(1, e.n())
-0.532092121986380 + 4.59715801330257*I
TESTS:
When automatic simplication occurs, the parent of the output value should be
either the same as the parent of the input, or a Sage type::
sage: parent(lambert_w(int(0)))
<type 'int'>
sage: parent(lambert_w(Integer(0)))
Integer Ring
sage: parent(lambert_w(e))
Integer Ring
"""
if not isinstance(z, Expression):
if is_inexact(z):
return self._evalf_(n,
z,
parent=sage_structure_coerce_parent(z))
elif n == 0 and z == 0:
return sage_structure_coerce_parent(z)(Integer(0))
elif n == 0:
if z.is_trivial_zero():
return sage_structure_coerce_parent(z)(Integer(0))
elif (z - const_e).is_trivial_zero():
return sage_structure_coerce_parent(z)(Integer(1))
elif (z + 1 / const_e).is_trivial_zero():
return sage_structure_coerce_parent(z)(Integer(-1))
return None
def _eval_(self, n, z):
"""
EXAMPLES::
sage: lambert_w(6.0)
1.43240477589830
sage: lambert_w(1)
lambert_w(1)
sage: lambert_w(x+1)
lambert_w(x + 1)
There are three special values which are automatically simplified::
sage: lambert_w(0)
0
sage: lambert_w(e)
1
sage: lambert_w(-1/e)
-1
sage: lambert_w(SR(0))
0
The special values only hold on the principal branch::
sage: lambert_w(1,e)
lambert_w(1, e)
sage: lambert_w(1, e.n())
-0.532092121986380 + 4.59715801330257*I
TESTS:
When automatic simplication occurs, the parent of the output value should be
either the same as the parent of the input, or a Sage type::
sage: parent(lambert_w(int(0)))
<type 'int'>
sage: parent(lambert_w(Integer(0)))
Integer Ring
sage: parent(lambert_w(e))
Integer Ring
"""
if not isinstance(z, Expression):
if is_inexact(z):
return self._evalf_(n, z, parent=sage_structure_coerce_parent(z))
elif n == 0 and z == 0:
return sage_structure_coerce_parent(z)(Integer(0))
elif n == 0:
if z.is_trivial_zero():
return sage_structure_coerce_parent(z)(Integer(0))
elif (z-const_e).is_trivial_zero():
return sage_structure_coerce_parent(z)(Integer(1))
elif (z+1/const_e).is_trivial_zero():
return sage_structure_coerce_parent(z)(Integer(-1))
return None
def _evalf_(self, n, z, parent=None, algorithm=None):
"""
EXAMPLES::
sage: N(lambert_w(1))
0.567143290409784
sage: lambert_w(RealField(100)(1))
0.56714329040978387299996866221
SciPy is used to evaluate for float, RDF, and CDF inputs::
sage: lambert_w(RDF(1))
0.5671432904097838
"""
R = parent or sage_structure_coerce_parent(z)
if R is float or R is complex or R is RDF or R is CDF:
import scipy.special
return scipy.special.lambertw(z, n)
else:
import mpmath
return mpmath_utils.call(mpmath.lambertw, z, n, parent=R)
def _evalf_(self, n, z, parent=None, algorithm=None):
"""
EXAMPLES::
sage: N(lambert_w(1))
0.567143290409784
sage: lambert_w(RealField(100)(1))
0.56714329040978387299996866221
SciPy is used to evaluate for float, RDF, and CDF inputs::
sage: lambert_w(RDF(1))
0.56714329041
"""
R = parent or sage_structure_coerce_parent(z)
if R is float or R is complex or R is RDF or R is CDF:
import scipy.special
return scipy.special.lambertw(z, n)
else:
import mpmath
return mpmath_utils.call(mpmath.lambertw, z, n, parent=R)