def plot_known(self):
r"""
TESTS::
sage: from ore_algebra import *
sage: from ore_algebra.analytic.function import DFiniteFunction
sage: DiffOps, x, Dx = DifferentialOperators()
sage: f = DFiniteFunction((x^2 + 1)*Dx^2 + 2*x*Dx, [0, 1])
sage: f(-10, 100) # long time
[-1.4711276743037345918528755717...]
sage: f.approx(5, post_transform=Dx) # long time
[0.038461538461538...]
sage: f.plot_known() # long time
Graphics object consisting of ... graphics primitives
"""
g = plot.Graphics()
for center, polys in self._polys.iteritems():
center, rad = self._disk(Point(center, self.dop))
xrange = (center - rad).mid(), (center + rad).mid()
for i, a in enumerate(polys):
# color palette copied from sage.plot.plot.plot
color = plot.Color((0.66666 + i * 0.61803) % 1,
1,
0.4,
space='hsl')
Balls = a.pol.base_ring()
g += plot.plot(lambda x: a.pol(Balls(x)).mid(),
xrange,
color=color)
g += plot.text(str(a.prec), (center, a.pol(center).mid()),
color=color)
for point, ini in self._inivecs.iteritems():
g += plot.point2d((point, 0), size=50)
return g
def triangulation_render_2d(triangulation, **kwds):
r"""
Return a graphical representation of a 2-d triangulation.
INPUT:
- ``triangulation`` -- a :class:`Triangulation`.
- ``**kwds`` -- keywords that are passed on to the graphics primitives.
OUTPUT:
A 2-d graphics object.
EXAMPLES::
sage: points = PointConfiguration([[0,0],[0,1],[1,0],[1,1],[-1,-1]])
sage: triang = points.triangulate()
sage: triang.plot(axes=False, aspect_ratio=1) # indirect doctest
Graphics object consisting of 12 graphics primitives
"""
from sage.plot.all import point2d, line2d, arrow, polygon2d
points = [point.reduced_affine() for point in triangulation.point_configuration()]
coord = [[p[0], p[1]] for p in points]
plot_points = sum([point2d(p, zorder=2, pointsize=10, **kwds) for p in coord])
tmp_lines = []
for t in triangulation:
if len(t) >= 2:
tmp_lines.append([t[0], t[1]])
if len(t) >= 3:
tmp_lines.append([t[0], t[2]])
tmp_lines.append([t[1], t[2]])
all_lines = []
interior_lines = []
for l in tmp_lines:
if l not in all_lines:
all_lines.append(l)
else:
interior_lines.append(l)
exterior_lines = [l for l in all_lines if not l in interior_lines]
plot_interior_lines = sum(
[line2d([coord[l[0]], coord[l[1]]], zorder=1, rgbcolor=(0, 1, 0), **kwds) for l in interior_lines]
)
plot_exterior_lines = sum(
[line2d([coord[l[0]], coord[l[1]]], zorder=1, rgbcolor=(0, 0, 1), **kwds) for l in exterior_lines]
)
plot_triangs = sum(
[
polygon2d([coord[t[0]], coord[t[1]], coord[t[2]]], zorder=0, rgbcolor=(0.8, 1, 0.8), **kwds)
for t in triangulation
if len(t) >= 3
]
)
return plot_points + plot_interior_lines + plot_exterior_lines + plot_triangs
def triangulation_render_2d(triangulation, **kwds):
r"""
Return a graphical representation of a 2-d triangulation.
INPUT:
- ``triangulation`` -- a :class:`Triangulation`.
- ``**kwds`` -- keywords that are passed on to the graphics primitives.
OUTPUT:
A 2-d graphics object.
EXAMPLES::
sage: points = PointConfiguration([[0,0],[0,1],[1,0],[1,1],[-1,-1]])
sage: triang = points.triangulate()
sage: triang.plot(axes=False, aspect_ratio=1) # indirect doctest
Graphics object consisting of 12 graphics primitives
"""
from sage.plot.all import point2d, line2d, arrow, polygon2d
points = [ point.reduced_affine() for point in triangulation.point_configuration() ]
coord = [ [p[0], p[1]] for p in points ]
plot_points = sum([ point2d(p,
zorder=2, pointsize=10, **kwds)
for p in coord ])
tmp_lines = []
for t in triangulation:
if len(t)>=2:
tmp_lines.append([t[0], t[1]])
if len(t)>=3:
tmp_lines.append([t[0], t[2]])
tmp_lines.append([t[1], t[2]])
all_lines = []
interior_lines = []
for l in tmp_lines:
if l not in all_lines:
all_lines.append(l)
else:
interior_lines.append(l)
exterior_lines = [ l for l in all_lines if not l in interior_lines ]
plot_interior_lines = sum([ line2d([ coord[l[0]], coord[l[1]] ],
zorder=1, rgbcolor=(0,1,0), **kwds)
for l in interior_lines ])
plot_exterior_lines = sum([ line2d([ coord[l[0]], coord[l[1]] ],
zorder=1, rgbcolor=(0,0,1), **kwds)
for l in exterior_lines ])
plot_triangs = sum([ polygon2d([coord[t[0]], coord[t[1]], coord[t[2]]],
zorder=0, rgbcolor=(0.8, 1, 0.8), **kwds)
for t in triangulation if len(t)>=3 ])
return \
plot_points + \
plot_interior_lines + plot_exterior_lines + \
plot_triangs
def render_points_2d(self, **kwds):
"""
Return the points of a polyhedron in 2d.
EXAMPLES::
sage: hex = polytopes.regular_polygon(6)
sage: proj = hex.projection()
sage: hex_points = proj.render_points_2d()
sage: hex_points._objects
[Point set defined by 6 point(s)]
"""
return point2d(self.coordinates_of(self.points), **kwds)
def render_points_2d(self, **kwds):
"""
Return the points of a polyhedron in 2d.
EXAMPLES::
sage: hex = polytopes.regular_polygon(6)
sage: proj = hex.projection()
sage: hex_points = proj.render_points_2d()
sage: hex_points._objects
[Point set defined by 6 point(s)]
"""
return point2d(self.coordinates_of(self.points), **kwds)
def plot(self, disks=False, **kwds):
gr = plot.point2d(self.dop._singularities(CC),
marker='*', color='red', **kwds)
gr += plot.line([z.iv().mid() for z in self.vert])
gr.set_aspect_ratio(1)
if disks:
for step in self:
z = step.start.iv().mid()
gr += plot.circle((z.real(), z.imag()),
step.start.dist_to_sing().lower(),
linestyle='dotted', color='red')
gr += plot.circle((z.real(), z.imag()),
step.length().lower(),
linestyle='dashed')
return gr
def plot(self, disks=False):
gr = plot.point2d(dop_singularities(self.dop, CC),
marker='*',
size=200,
color='red')
for step in self:
gr += step.plot()
gr.set_aspect_ratio(1)
if disks:
for step in self:
z = step.start.iv().mid()
gr += plot.circle((z.real(), z.imag()),
step.start.dist_to_sing().lower(),
linestyle='dotted',
color='red')
gr += plot.circle((z.real(), z.imag()),
step.length().lower(),
linestyle='dashed')
return gr
def plot_completely_periodic(self):
from sage.plot.all import polygon2d, Graphics, point2d, text
O = self.orbit
G = []
u = self.u # direction (that we put horizontal)
m = matrix(2, [u[1], -u[0], u[1], u[0]])
indices = {}
xmin = xmax = ymin = ymax = 0
for comp in self.decomposition.components():
H = Graphics()
x = O.V2._isomorphic_vector_space.zero()
pts = [x]
below = True
for p in comp.perimeter():
sc = p.saddleConnection()
y = x + m * O.V2._isomorphic_vector_space(
O.V2(p.saddleConnection().vector()))
if p.vertical():
if sc in indices:
i = indices[sc]
else:
i = len(indices) // 2
indices[sc] = i
indices[-sc] = i
if below:
H += text(str(i), (x + y) / 2, color='black')
x = y
xmin = min(xmin, x[0])
xmax = max(xmax, x[0])
ymin = min(ymin, x[1])
ymax = max(ymax, x[1])
pts.append(x)
H += polygon2d(pts, color='blue', alpha=0.3)
H += point2d(pts, color='red', pointsize=20)
G.append(H)
aspect_ratio = float(xmax - xmin) / float(ymax - ymin)
for H in G:
H.set_axes_range(xmin, xmax, ymin, ymax)
H.axes(False)
H.set_aspect_ratio(aspect_ratio)
return G