def _evalf_(self, n, x, **kwds):
"""
Evaluate :class:`chebyshev_U` numerically with mpmath.
EXAMPLES::
sage: chebyshev_U(5,-4+3.*I)
98280.0000000000 - 11310.0000000000*I
sage: chebyshev_U(10,3).n(75)
4.661117900000000000000e7
sage: chebyshev_U._evalf_(1.5, Mod(8,9))
Traceback (most recent call last):
...
TypeError: cannot evaluate chebyshev_U with parent Ring of integers modulo 9
"""
try:
real_parent = kwds['parent']
except KeyError:
real_parent = parent(x)
if not is_RealField(real_parent) and not is_ComplexField(
real_parent):
# parent is not a real or complex field: figure out a good parent
if x in RR:
x = RR(x)
real_parent = RR
elif x in CC:
x = CC(x)
real_parent = CC
if not is_RealField(real_parent) and not is_ComplexField(real_parent):
raise TypeError(
"cannot evaluate chebyshev_U with parent {}".format(
real_parent))
from sage.libs.mpmath.all import call as mpcall
from sage.libs.mpmath.all import chebyu as mpchebyu
return mpcall(mpchebyu, n, x, parent=real_parent)
def _evalf_(self, n, x, **kwds):
"""
Evaluate :class:`chebyshev_U` numerically with mpmath.
EXAMPLES::
sage: chebyshev_U(5,-4+3.*I)
98280.0000000000 - 11310.0000000000*I
sage: chebyshev_U(10,3).n(75)
4.661117900000000000000e7
sage: chebyshev_U._evalf_(1.5, Mod(8,9))
Traceback (most recent call last):
...
TypeError: cannot evaluate chebyshev_U with parent Ring of integers modulo 9
"""
try:
real_parent = kwds["parent"]
except KeyError:
real_parent = parent(x)
if not is_RealField(real_parent) and not is_ComplexField(real_parent):
# parent is not a real or complex field: figure out a good parent
if x in RR:
x = RR(x)
real_parent = RR
elif x in CC:
x = CC(x)
real_parent = CC
if not is_RealField(real_parent) and not is_ComplexField(real_parent):
raise TypeError("cannot evaluate chebyshev_U with parent {}".format(real_parent))
from sage.libs.mpmath.all import call as mpcall
from sage.libs.mpmath.all import chebyu as mpchebyu
return mpcall(mpchebyu, n, x, parent=real_parent)
def _evalf_(self, n, x, **kwds):
"""
Evaluates :class:`chebyshev_T` numerically with mpmath.
EXAMPLES::
sage: chebyshev_T._evalf_(10,3)
2.26195370000000e7
sage: chebyshev_T._evalf_(10,3,parent=RealField(75))
2.261953700000000000000e7
sage: chebyshev_T._evalf_(10,I)
-3363.00000000000
sage: chebyshev_T._evalf_(5,0.3)
0.998880000000000
sage: chebyshev_T(1/2, 0)
0.707106781186548
sage: chebyshev_T(1/2, 3/2)
1.11803398874989
sage: chebyshev_T._evalf_(1.5, Mod(8,9))
Traceback (most recent call last):
...
TypeError: cannot evaluate chebyshev_T with parent Ring of integers modulo 9
This simply evaluates using :class:`RealField` or :class:`ComplexField`::
sage: chebyshev_T(1234.5, RDF(2.1))
5.48174256255782e735
sage: chebyshev_T(1234.5, I)
-1.21629397684152e472 - 1.21629397684152e472*I
For large values of ``n``, mpmath fails (but the algebraic formula
still works)::
sage: chebyshev_T._evalf_(10^6, 0.1)
Traceback (most recent call last):
...
NoConvergence: Hypergeometric series converges too slowly. Try increasing maxterms.
sage: chebyshev_T(10^6, 0.1)
0.636384327171504
"""
try:
real_parent = kwds['parent']
except KeyError:
real_parent = parent(x)
if not is_RealField(real_parent) and not is_ComplexField(
real_parent):
# parent is not a real or complex field: figure out a good parent
if x in RR:
x = RR(x)
real_parent = RR
elif x in CC:
x = CC(x)
real_parent = CC
if not is_RealField(real_parent) and not is_ComplexField(real_parent):
raise TypeError(
"cannot evaluate chebyshev_T with parent {}".format(
real_parent))
from sage.libs.mpmath.all import call as mpcall
from sage.libs.mpmath.all import chebyt as mpchebyt
return mpcall(mpchebyt, n, x, parent=real_parent)
def _evalf_(self, n, x, **kwds):
"""
Evaluates :class:`chebyshev_T` numerically with mpmath.
EXAMPLES::
sage: chebyshev_T._evalf_(10,3)
2.26195370000000e7
sage: chebyshev_T._evalf_(10,3,parent=RealField(75))
2.261953700000000000000e7
sage: chebyshev_T._evalf_(10,I)
-3363.00000000000
sage: chebyshev_T._evalf_(5,0.3)
0.998880000000000
sage: chebyshev_T(1/2, 0)
0.707106781186548
sage: chebyshev_T(1/2, 3/2)
1.11803398874989
sage: chebyshev_T._evalf_(1.5, Mod(8,9))
Traceback (most recent call last):
...
TypeError: cannot evaluate chebyshev_T with parent Ring of integers modulo 9
This simply evaluates using :class:`RealField` or :class:`ComplexField`::
sage: chebyshev_T(1234.5, RDF(2.1))
5.48174256255782e735
sage: chebyshev_T(1234.5, I)
-1.21629397684152e472 - 1.21629397684152e472*I
For large values of ``n``, mpmath fails (but the algebraic formula
still works)::
sage: chebyshev_T._evalf_(10^6, 0.1)
Traceback (most recent call last):
...
NoConvergence: Hypergeometric series converges too slowly. Try increasing maxterms.
sage: chebyshev_T(10^6, 0.1)
0.636384327171504
"""
try:
real_parent = kwds["parent"]
except KeyError:
real_parent = parent(x)
if not is_RealField(real_parent) and not is_ComplexField(real_parent):
# parent is not a real or complex field: figure out a good parent
if x in RR:
x = RR(x)
real_parent = RR
elif x in CC:
x = CC(x)
real_parent = CC
if not is_RealField(real_parent) and not is_ComplexField(real_parent):
raise TypeError("cannot evaluate chebyshev_T with parent {}".format(real_parent))
from sage.libs.mpmath.all import call as mpcall
from sage.libs.mpmath.all import chebyt as mpchebyt
return mpcall(mpchebyt, n, x, parent=real_parent)