def values_along_line(self, s0, s1, number_samples):
"""
Return values of $L(E, s)$ at \code{number_samples}
equally-spaced sample points along the line from $s_0$ to
$s_1$ in the complex plane.
\note{The L-series is normalized so that the center of the
critical strip is 1.}
INPUT:
s0, s1 -- complex numbers
number_samples -- integer
OUTPUT:
list -- list of pairs (s, zeta(s)), where the s are
equally spaced sampled points on the line from
s0 to s1.
EXAMPLES::
sage: E = EllipticCurve('37a')
sage: E.lseries().values_along_line(1, 0.5 + 20*I, 5)
[(0.500000000, ...),
(0.400000000 + 4.00000000*I, 3.31920245 - 2.60028054*I),
(0.300000000 + 8.00000000*I, -0.886341185 - 0.422640337*I),
(0.200000000 + 12.0000000*I, -3.50558936 - 0.108531690*I),
(0.100000000 + 16.0000000*I, -3.87043288 - 1.88049411*I)]
"""
from sage.lfunctions.lcalc import lcalc
return lcalc.values_along_line(s0-RationalField()('1/2'),
s1-RationalField()('1/2'),
number_samples, L=self.__E)
def values_along_line(self, s0, s1, number_samples):
r"""
Return values of `L(E, s)` at ``number_samples``
equally-spaced sample points along the line from `s_0` to
`s_1` in the complex plane.
.. note::
The `L`-series is normalized so that the center of the
critical strip is 1.
INPUT:
- ``s0``, ``s1`` -- complex numbers
- ``number_samples`` -- integer
OUTPUT:
list -- list of pairs (`s`, `L(E,s)`), where the `s` are
equally spaced sampled points on the line from
``s0`` to ``s1``.
EXAMPLES::
sage: E = EllipticCurve('37a')
sage: E.lseries().values_along_line(1, 0.5 + 20*I, 5)
[(0.500000000, ...),
(0.400000000 + 4.00000000*I, 3.31920245 - 2.60028054*I),
(0.300000000 + 8.00000000*I, -0.886341185 - 0.422640337*I),
(0.200000000 + 12.0000000*I, -3.50558936 - 0.108531690*I),
(0.100000000 + 16.0000000*I, -3.87043288 - 1.88049411*I)]
"""
from sage.lfunctions.lcalc import lcalc
return lcalc.values_along_line(s0 - RationalField()('1/2'),
s1 - RationalField()('1/2'),
number_samples,
L=self.__E)
def values_along_line(self, s0, s1, number_samples):
r"""
Return values of `L(E, s)` at ``number_samples``
equally-spaced sample points along the line from `s_0` to
`s_1` in the complex plane.
.. note::
The `L`-series is normalized so that the center of the
critical strip is 1.
INPUT:
- ``s0``, ``s1`` -- complex numbers
- ``number_samples`` -- integer
OUTPUT:
list -- list of pairs (`s`, `L(E,s)`), where the `s` are
equally spaced sampled points on the line from
``s0`` to ``s1``.
EXAMPLES::
sage: E = EllipticCurve('37a')
sage: E.lseries().values_along_line(1, 0.5 + 20*I, 5)
[(0.500000000, ...),
(0.400000000 + 4.00000000*I, 3.31920245 - 2.60028054*I),
(0.300000000 + 8.00000000*I, -0.886341185 - 0.422640337*I),
(0.200000000 + 12.0000000*I, -3.50558936 - 0.108531690*I),
(0.100000000 + 16.0000000*I, -3.87043288 - 1.88049411*I)]
"""
from sage.lfunctions.lcalc import lcalc
return lcalc.values_along_line(
s0 - RationalField()("1/2"), s1 - RationalField()("1/2"), number_samples, L=self.__E
)
