def plot_fan_stereographically(rays, walls, northsign=1, north=vector((-1,-1,-1)), right=vector((1,0,0)), colors=None, thickness=None):
from sage.plot.graphics import Graphics
from sage.plot.point import point
from sage.misc.flatten import flatten
from sage.plot.line import line
from sage.misc.functional import norm
if colors == None:
colors = dict([('walls','black'),('rays','red')])
if thickness == None:
thickness = dict([('walls',0.5),('rays',20)])
G = Graphics()
for (u,v) in walls:
G += _stereo_arc(vector(u),vector(v),vector(u+v),north=northsign*north,right=right,color=colors['walls'],thickness=thickness['walls'],zorder=len(G))
for v in rays:
G += point(_stereo_coordinates(vector(v),north=northsign*north,right=right),color=colors['rays'],zorder=len(G),size=thickness['rays'])
G.set_aspect_ratio(1)
G._show_axes = False
return G
def plot2d(self, depth=None):
# FIXME: refactor this before publishing
from sage.plot.line import line
from sage.plot.graphics import Graphics
if self._n != 2:
raise ValueError("Can only 2d plot fans.")
if depth == None:
depth = self._depth
if not self.is_finite() and depth == infinity:
raise ValueError(
"For infinite algebras you must specify the depth.")
colors = dict([(0, 'red'), (1, 'green')])
G = Graphics()
for i in range(2):
orbit = self.ith_orbit(i, depth=depth)
for j in orbit:
G += line([(0, 0), vector(orbit[j])],
color=colors[i],
thickness=0.5,
zorder=2 * j + 1)
G.set_aspect_ratio(1)
G._show_axes = False
return G
def plot_cluster_fan_stereographically(self, northsign=1, north=None, right=None, colors=None):
from sage.plot.graphics import Graphics
from sage.plot.point import point
from sage.misc.flatten import flatten
from sage.plot.line import line
from sage.misc.functional import norm
if self.rk !=3:
raise ValueError("Can only stereographically project fans in 3d.")
if not self.is_finite() and self._depth == infinity:
raise ValueError("For infinite algebras you must specify the depth.")
if north == None:
if self.is_affine():
north = vector(self.delta())
else:
north = vector( (-1,-1,-1) )
if right == None:
if self.is_affine():
right = vector(self.gamma())
else:
right = vector( (1,0,0) )
if colors == None:
colors = dict([(0,'red'),(1,'green'),(2,'blue'),(3,'cyan'),(4,'yellow')])
G = Graphics()
roots = list(self.g_vectors())
compatible = []
while roots:
x = roots.pop()
for y in roots:
if self.compatibility_degree(x,y) == 0:
compatible.append((x,y))
for (u,v) in compatible:
G += _stereo_arc(vector(u),vector(v),vector(u+v),north=northsign*north,right=right,thickness=0.5,color='black')
for i in range(3):
orbit = self.ith_orbit(i)
for j in orbit:
G += point(_stereo_coordinates(vector(orbit[j]),north=northsign*north,right=right),color=colors[i],zorder=len(G))
if self.is_affine():
tube_vectors = map(vector,flatten(self.affine_tubes()))
for v in tube_vectors:
G += point(_stereo_coordinates(v,north=northsign*north,right=right),color=colors[3],zorder=len(G))
if north != vector(self.delta()):
G += _stereo_arc(tube_vectors[0],tube_vectors[1],vector(self.delta()),north=northsign*north,right=right,thickness=2,color=colors[4],zorder=0)
else:
# FIXME: refactor this before publishing
tube_projections = [
_stereo_coordinates(v,north=northsign*north,right=right)
for v in tube_vectors ]
t=min((G.get_minmax_data()['xmax'],G.get_minmax_data()['ymax']))
G += line([tube_projections[0],tube_projections[0]+t*(_normalize(tube_projections[0]-tube_projections[1]))],thickness=2,color=colors[4],zorder=0)
G += line([tube_projections[1],tube_projections[1]+t*(_normalize(tube_projections[1]-tube_projections[0]))],thickness=2,color=colors[4],zorder=0)
G.set_aspect_ratio(1)
G._show_axes = False
return G
def plot2d(self,depth=None):
# FIXME: refactor this before publishing
from sage.plot.line import line
from sage.plot.graphics import Graphics
if self._n !=2:
raise ValueError("Can only 2d plot fans.")
if depth == None:
depth = self._depth
if not self.is_finite() and depth==infinity:
raise ValueError("For infinite algebras you must specify the depth.")
colors = dict([(0,'red'),(1,'green')])
G = Graphics()
for i in range(2):
orbit = self.ith_orbit(i,depth=depth)
for j in orbit:
G += line([(0,0),vector(orbit[j])],color=colors[i],thickness=0.5, zorder=2*j+1)
G.set_aspect_ratio(1)
G._show_axes = False
return G
def plot_cluster_fan_stereographically(self,
northsign=1,
north=None,
right=None,
colors=None,
d_vectors=False):
from sage.plot.graphics import Graphics
from sage.plot.point import point
from sage.misc.flatten import flatten
from sage.plot.line import line
from sage.misc.functional import norm
if self.rk != 3:
raise ValueError("Can only stereographically project fans in 3d.")
if not self.is_finite() and self._depth == infinity:
raise ValueError(
"For infinite algebras you must specify the depth.")
if north == None:
if self.is_affine():
north = vector(self.delta())
else:
north = vector((-1, -1, -1))
if right == None:
if self.is_affine():
right = vector(self.gamma())
else:
right = vector((1, 0, 0))
if colors == None:
colors = dict([(0, 'red'), (1, 'green'), (2, 'blue'), (3, 'cyan'),
(4, 'yellow')])
G = Graphics()
roots = list(self.g_vectors())
compatible = []
while roots:
x = roots.pop()
if x in self.initial_cluster() and d_vectors:
x1 = -self.simple_roots()[list(
self.initial_cluster()).index(x)]
else:
x1 = x
for y in roots:
if self.compatibility_degree(x, y) == 0:
if y in self.initial_cluster() and d_vectors:
y1 = -self.simple_roots()[list(
self.initial_cluster()).index(y)]
else:
y1 = y
compatible.append((x1, y1))
for (u, v) in compatible:
G += _stereo_arc(vector(u),
vector(v),
vector(u + v),
north=northsign * north,
right=right,
thickness=0.5,
color='black')
for i in range(3):
orbit = self.ith_orbit(i)
if d_vectors:
orbit[0] = -self.simple_roots()[list(
self.initial_cluster()).index(orbit[0])]
for j in orbit:
G += point(_stereo_coordinates(vector(orbit[j]),
north=northsign * north,
right=right),
color=colors[i],
zorder=len(G))
if self.is_affine():
tube_vectors = map(vector, flatten(self.affine_tubes()))
for v in tube_vectors:
G += point(_stereo_coordinates(v,
north=northsign * north,
right=right),
color=colors[3],
zorder=len(G))
if north != vector(self.delta()):
G += _stereo_arc(tube_vectors[0],
tube_vectors[1],
vector(self.delta()),
north=northsign * north,
right=right,
thickness=2,
color=colors[4],
zorder=0)
else:
# FIXME: refactor this before publishing
tube_projections = [
_stereo_coordinates(v,
north=northsign * north,
right=right) for v in tube_vectors
]
t = min(
(G.get_minmax_data()['xmax'], G.get_minmax_data()['ymax']))
G += line([
tube_projections[0], tube_projections[0] + t *
(_normalize(tube_projections[0] - tube_projections[1]))
],
thickness=2,
color=colors[4],
zorder=0)
G += line([
tube_projections[1], tube_projections[1] + t *
(_normalize(tube_projections[1] - tube_projections[0]))
],
thickness=2,
color=colors[4],
zorder=0)
G.set_aspect_ratio(1)
G._show_axes = False
return G