def mu_portrait(n):
""" returns an encoded scatter plot of the nth roots of unity in the complex plane """
if n <= 120:
plot = list_plot([(cos(2*pi*m/n),sin(2*pi*m/n)) for m in range(n)],pointsize=30+60/n, axes=False)
else:
plot = circle((0,0),1,thickness=3)
plot.xmin(-1); plot.xmax(1); plot.ymin(-1); plot.ymax(1)
plot.set_aspect_ratio(4.0/3.0)
return encode_plot(plot)
def mu_portrait(n):
""" returns an encoded scatter plot of the nth roots of unity in the complex plane """
if n <= 120:
plot = list_plot([(cos(2*pi*m/n),sin(2*pi*m/n)) for m in range(n)],pointsize=30+60/n, axes=False)
else:
plot = circle((0,0),1,thickness=3)
plot.xmin(-1); plot.xmax(1); plot.ymin(-1); plot.ymax(1)
plot.set_aspect_ratio(4.0/3.0)
return encode_plot(plot)
def nu1_mu_portrait(n):
""" returns an encoded scatter plot of the nth roots of unity in the complex plane """
if n == 1:
return db.gps_sato_tate.lookup('1.2.1.2.1a').get('trace_histogram')
if n <= 120:
plot = sum([
line2d([(-2 * cos(2 * pi * m / n), -2 * sin(2 * pi * m / n)),
(2 * cos(2 * pi * m / n), 2 * sin(2 * pi * m / n))],
thickness=3) for m in range(n)
]) + circle((0, 0), 0.1, rgbcolor=(0, 0, 0), fill=True)
else:
plot = circle((0, 0), 2, fill=True)
plot.xmin(-2)
plot.xmax(2)
plot.ymin(-2)
plot.ymax(2)
plot.set_aspect_ratio(4.0 / 3.0)
plot.axes(False)
return encode_plot(plot)
def show(self, unit=10, labels=True):
from sage.all import circle, text, line, Graphics
pos = self.basic_grid_embedding()
for v, (a, b) in pos.items():
pos[v] = (unit * a, unit * b)
if not labels:
verts = [circle(p, 1, fill=True) for p in pos.values()]
else:
verts = [
text(repr(v), p, fontsize=20, color='black')
for v, p in pos.items()
]
verts += [circle(p, 1.5, fill=False) for p in pos.values()]
edges = [
line([pos[e.tail], pos[e.head]]) for e in self.edges
if e not in self.dummy
]
G = sum(verts + edges, Graphics())
G.axes(False)
return G
def nu1_mu_portrait(n):
""" returns an encoded scatter plot of the nth roots of unity in the complex plane """
if n == 1:
return db.gps_sato_tate.lookup('1.2.1.2.1a').get('trace_histogram')
if n <= 120:
plot = sum([line2d([(-2*cos(2*pi*m/n),-2*sin(2*pi*m/n)),(2*cos(2*pi*m/n),2*sin(2*pi*m/n))],thickness=3) for m in range(n)]) + circle((0,0),0.1,rgbcolor=(0,0,0),fill=True)
else:
plot = circle((0,0),2,fill=True)
plot.xmin(-2); plot.xmax(2); plot.ymin(-2); plot.ymax(2)
plot.set_aspect_ratio(4.0/3.0)
plot.axes(False)
return encode_plot(plot)
def su2_mu_portrait(n):
""" returns an encoded line plot of SU(2) x mu(n) in the complex plane """
if n == 1:
return db.gps_sato_tate.lookup('1.2.3.1.1a').get('trace_histogram')
if n <= 120:
plot = sum([line2d([(-2*cos(2*pi*m/n),-2*sin(2*pi*m/n)),(2*cos(2*pi*m/n),2*sin(2*pi*m/n))],thickness=3) for m in range(n)])
else:
plot = circle((0,0),2,fill=True)
plot.xmin(-2); plot.xmax(2); plot.ymin(-2); plot.ymax(2)
plot.set_aspect_ratio(4.0/3.0)
plot.axes(False)
return encode_plot(plot)
def su2_mu_portrait(n):
""" returns an encoded line plot of SU(2) x mu(n) in the complex plane """
if n == 1:
return db.gps_st.lookup('1.2.A.1.1a').get('trace_histogram')
if n <= 120:
plot = sum([line2d([(-2*cos(2*pi*m/n),-2*sin(2*pi*m/n)),(2*cos(2*pi*m/n),2*sin(2*pi*m/n))],thickness=3) for m in range(n)])
else:
plot = circle((0,0),2,fill=True)
plot.xmin(-2); plot.xmax(2); plot.ymin(-2); plot.ymax(2)
plot.set_aspect_ratio(4.0/3.0)
plot.axes(False)
return encode_plot(plot)
