def RiemannSurfacePath_from_complex_path(self,
complex_path,
x0=None,
y0=None):
r"""Constructs a :class:`RiemannSurfacePath` object from x-path data.
Parameters
----------
complex_path : ComplexPath
A complex path.
x0 : complex (default `self.base_point`)
The starting x-point of the path.
y0 : complex list (default `self.base_sheets`)
The starting ordering of the y-sheets.
Returns
-------
RiemannSurfacePath
A path on the Riemann surface with the prescribed x-path.
"""
if x0 is None:
x0 = self.base_point
if y0 is None:
y0 = self.base_sheets
# coerce and assert that x0,y0 lies on the path and curve
x0 = complex(x0)
y0 = array(y0, dtype=complex)
if abs(x0 - complex_path(0)) > 1e-7:
raise ValueError('The point %s is not at the start of the '
'ComplexPath %s' % (x0, complex_path))
f = self.riemann_surface.f
curve_error = [abs(complex(f(x0, y0k))) for y0k in y0]
if max(curve_error) > 1e-7:
raise ValueError('The fibre %s above %s does not lie on the '
'curve %s' % (y0.tolist(), x0, f))
# build a list of path segments from each tuple of xdata. build a line
# segment or arc depending on xdata input
x0_segment = x0
y0_segment = y0
segments = []
for segment_x in complex_path.segments:
# for each segment determine if we're far enough away to use Smale
# alpha theory paths or if we have to use Puiseux. we add a
# relazation factor to the radius to account for monodromy paths
xend = segment_x(1.0)
b = self.complex_path_factory.closest_discriminant_point(xend)
R = self.complex_path_factory.radius(b)
if abs(xend - b) > 0.9 * R:
segment = RiemannSurfacePathSmale(self.riemann_surface,
segment_x, y0_segment)
else:
segment = RiemannSurfacePathPuiseux(self.riemann_surface,
segment_x, y0_segment)
# determine the starting place of the next segment
x0_segment = segment.get_x(1.0)
y0_segment = segment.get_y(1.0)
segments.append(segment)
# build the entire path from the path segments
gamma = RiemannSurfacePath(self.riemann_surface, complex_path, y0,
segments)
return gamma
def RiemannSurfacePath_from_complex_path(self, complex_path, x0=None, y0=None):
r"""Constructs a :class:`RiemannSurfacePath` object from x-path data.
Parameters
----------
complex_path : ComplexPath
A complex path.
x0 : complex (default `self.base_point`)
The starting x-point of the path.
y0 : complex list (default `self.base_sheets`)
The starting ordering of the y-sheets.
Returns
-------
RiemannSurfacePath
A path on the Riemann surface with the prescribed x-path.
"""
if x0 is None:
x0 = self.base_point
if y0 is None:
y0 = self.base_sheets
# coerce and assert that x0,y0 lies on the path and curve
x0 = complex(x0)
y0 = array(y0, dtype=complex)
if abs(x0 - complex_path(0)) > 1e-7:
raise ValueError('The point %s is not at the start of the '
'ComplexPath %s'%(x0, complex_path))
f = self.riemann_surface.f
curve_error = [abs(complex(f(x0,y0k))) for y0k in y0]
if max(curve_error) > 1e-7:
raise ValueError('The fibre %s above %s does not lie on the '
'curve %s'%(y0.tolist(), x0, f))
# build a list of path segments from each tuple of xdata. build a line
# segment or arc depending on xdata input
x0_segment = x0
y0_segment = y0
segments = []
for segment_x in complex_path.segments:
# for each segment determine if we're far enough away to use Smale
# alpha theory paths or if we have to use Puiseux. we add a
# relazation factor to the radius to account for monodromy paths
xend = segment_x(1.0)
b = self.complex_path_factory.closest_discriminant_point(xend)
R = self.complex_path_factory.radius(b)
if abs(xend - b) > 0.9*R:
segment = RiemannSurfacePathSmale(
self.riemann_surface, segment_x, y0_segment)
else:
segment = RiemannSurfacePathPuiseux(
self.riemann_surface, segment_x, y0_segment)
# determine the starting place of the next segment
x0_segment = segment.get_x(1.0)
y0_segment = segment.get_y(1.0)
segments.append(segment)
# build the entire path from the path segments
gamma = RiemannSurfacePath(self.riemann_surface, complex_path, y0,
segments)
return gamma
