def my_hyperbolic_triangle(a, b, c, **options):
"""
Return a hyperbolic triangle in the complex hyperbolic plane with points
(a, b, c). Type ``?hyperbolic_triangle`` to see all options.
INPUT:
- ``a, b, c`` - complex numbers in the upper half complex plane
OPTIONS:
- ``alpha`` - default: 1
- ``fill`` - default: False
- ``thickness`` - default: 1
- ``rgbcolor`` - default: 'blue'
- ``linestyle`` - default: 'solid'
EXAMPLES:
Show a hyperbolic triangle with coordinates 0, `1/2+i\sqrt{3}/2` and
`-1/2+i\sqrt{3}/2`::
sage: hyperbolic_triangle(0, -1/2+I*sqrt(3)/2, 1/2+I*sqrt(3)/2)
A hyperbolic triangle with coordinates 0, 1 and 2+i::
sage: hyperbolic_triangle(0, 1, 2+i, fill=true, rgbcolor='red')
"""
from sage.plot.all import Graphics
g = Graphics()
g._set_extra_kwds(g._extract_kwds_for_show(options))
model = options['model']
npts = options.get('npts',10)
sides = options.pop('sides',[1,2,3]) ## Which of the sides we will draw.
verbose = options.get('verbose',0)
options.pop('model',None); options.pop('method',None)
if model=="D":
#g.add_primitive(HyperbolicTriangleDisc(a, b, c, **options))
#print "options=",options
options['sides']=sides
H = HyperbolicTriangleDisc(a, b, c, **options)
g += H()
else:
options.pop('npts',None)
if sides == [1,2,3]:
if verbose>0:
print "adding HyperbolicTriangle({0}, {1}, {2},options={3})".format(a,b,c,options)
options.pop('verbose',0)
g.add_primitive(HyperbolicTriangle(a, b, c, options))
else:
options['sides']=sides
if verbose>0:
print "adding MyHyperbolicTriangle({0}, {1}, {2},options={3})".format(a,b,c,options)
g.add_primitive(MyHyperbolicTriangle(a, b, c, options))
g.set_aspect_ratio(1)
return g
def draw_funddom_d(coset_reps,format="MP",z0=I):
r""" Draw a fundamental domain for self in the circle model
INPUT:
- ''format'' -- (default 'Disp') How to present the f.d.
= 'S' -- Display directly on the screen
- z0 -- (default I) the upper-half plane is mapped to the disk by z-->(z-z0)/(z-z0.conjugate())
EXAMPLES::
sage: G=MySubgroup(Gamma0(3))
sage: G._draw_funddom_d()
"""
# The fundamental domain consists of copies of the standard fundamental domain
pi=RR.pi()
from sage.plot.plot import (Graphics,line)
g=Graphics()
bdcirc=_circ_arc(0 ,2 *pi,0 ,1 ,1000 )
g=g+bdcirc
# Corners
x1=-RR(0.5) ; y1=RR(sqrt(3 )/2)
x2=RR(0.5) ; y2=RR(sqrt(3 )/2)
z_inf=1
l1 = _geodesic_between_two_points_d(x1,y1,x1,infinity)
l2 = _geodesic_between_two_points_d(x2,y2,x2,infinity)
c0 = _geodesic_between_two_points_d(x1,y1,x2,y2)
tri=c0+l1+l2
g=g+tri
for A in coset_reps:
[a,b,c,d]=A
if(a==1 and b==0 and c==0 and d==1 ):
continue
if(a<0 ):
a=-a; b=-b; c=-c; d=-1
if(c==0 ): # then this is easier
l1 = _geodesic_between_two_points_d(x1+b,y1,x1+b,infinity)
l2 = _geodesic_between_two_points_d(x2+b,y2,x2+b,infinity)
c0 = _geodesic_between_two_points_d(x1+b,y1,x2+b,y2)
# c0=line(L0); l1=line(L1); l2=line(L2); l3=line(L3)
tri=c0+l1+l2
g=g+tri
else:
den=(c*x1+d)**2 +c**2 *y1**2
x1_t=(a*c*(x1**2 +y1**2 )+(a*d+b*c)*x1+b*d)/den
y1_t=y1/den
den=(c*x2+d)**2 +c**2 *y2**2
x2_t=(a*c*(x2**2 +y2**2 )+(a*d+b*c)*x2+b*d)/den
y2_t=y2/den
inf_t=a/c
c0=_geodesic_between_two_points_d(x1_t,y1_t,x2_t,y2_t)
c1=_geodesic_between_two_points_d(x1_t,y1_t,inf_t,0.0 )
c2=_geodesic_between_two_points_d(x2_t,y2_t,inf_t,0.0 )
tri=c0+c1+c2
g=g+tri
g.xmax(1 )
g.ymax(1 )
g.xmin(-1 )
g.ymin(-1 )
g.set_aspect_ratio(1 )
return g
def newton_plot(self):
S = [QQ(s) for s in self.slopes]
C = Counter(S)
pts = [(0,0)]
x = y = 0
for s in sorted(C):
c = C[s]
x += c
y += c*s
pts.append((x,y))
L = Graphics()
L += line([(0,0),(0,y+0.2)],color="grey")
for i in range(1,y+1):
L += line([(0,i),(0.06,i)],color="grey")
for i in range(1,C[0]):
L += line([(i,0),(i,0.06)],color="grey")
for i in range(len(pts)-1):
P = pts[i]
Q = pts[i+1]
for x in range(P[0],Q[0]+1):
L += line([(x,P[1]),(x,P[1] + (x-P[0])*(Q[1]-P[1])/(Q[0]-P[0]))],color="grey")
for y in range(P[1],Q[1]):
L += line([(P[0] + (y-P[1])*(Q[0]-P[0])/(Q[1]-P[1]),y),(Q[0],y)],color="grey")
L += line(pts, thickness = 2)
L.axes(False)
L.set_aspect_ratio(1)
return encode_plot(L, pad=0, pad_inches=0, bbox_inches='tight')
def newton_plot(self):
S = [QQ(s) for s in self.polygon_slopes]
C = Counter(S)
pts = [(0, 0)]
x = y = 0
for s in sorted(C):
c = C[s]
x += c
y += c * s
pts.append((x, y))
L = Graphics()
L += line([(0, 0), (0, y + 0.2)], color="grey")
for i in range(1, y + 1):
L += line([(0, i), (0.06, i)], color="grey")
for i in range(1, C[0]):
L += line([(i, 0), (i, 0.06)], color="grey")
for i in range(len(pts) - 1):
P = pts[i]
Q = pts[i + 1]
for x in range(P[0], Q[0] + 1):
L += line(
[(x, P[1]),
(x, P[1] + (x - P[0]) * (Q[1] - P[1]) / (Q[0] - P[0]))],
color="grey",
)
for y in range(P[1], Q[1]):
L += line(
[(P[0] + (y - P[1]) * (Q[0] - P[0]) / (Q[1] - P[1]), y),
(Q[0], y)],
color="grey",
)
L += line(pts, thickness=2)
L.axes(False)
L.set_aspect_ratio(1)
return encode_plot(L, pad=0, pad_inches=0, bbox_inches="tight")
def hyperbolic_polygon(pts, **options):
r"""
Return a hyperbolic polygon in the hyperbolic plane with vertices ``pts``.
Type ``?hyperbolic_polygon`` to see all options.
INPUT:
- ``pts`` -- a list or tuple of complex numbers
OPTIONS:
- ``alpha`` -- default: 1
- ``fill`` -- default: ``False``
- ``thickness`` -- default: 1
- ``rgbcolor`` -- default: ``'blue'``
- ``linestyle`` -- (default: ``'solid'``) The style of the line, which is
one of ``'dashed'``, ``'dotted'``, ``'solid'``, ``'dashdot'``, or ``'--'``,
``':'``, ``'-'``, ``'-.'``, respectively.
EXAMPLES:
Show a hyperbolic polygon with coordinates `-1`, `3i`, `2+2i`, `1+i`::
sage: hyperbolic_polygon([-1,3*I,2+2*I,1+I])
Graphics object consisting of 1 graphics primitive
.. PLOT::
P = hyperbolic_polygon([-1,3*I,2+2*I,1+I])
sphinx_plot(P)
With more options::
sage: hyperbolic_polygon([-1,3*I,2+2*I,1+I], fill=True, color='red')
Graphics object consisting of 1 graphics primitive
.. PLOT::
P = hyperbolic_polygon([-1,3*I,2+2*I,1+I], fill=True, color='red')
sphinx_plot(P)
"""
from sage.plot.all import Graphics
g = Graphics()
g._set_extra_kwds(g._extract_kwds_for_show(options))
g.add_primitive(HyperbolicPolygon(pts, options))
g.set_aspect_ratio(1)
return g
def hyperbolic_arc(a, b, **options):
"""
Plot an arc from a to b in hyperbolic geometry in the complex upper
half plane.
INPUT:
- ``a, b`` - complex numbers in the upper half complex plane
connected bye the arc
OPTIONS:
- ``alpha`` - default: 1
- ``thickness`` - default: 1
- ``rgbcolor`` - default: 'blue'
- ``linestyle`` - (default: ``'solid'``) The style of the line, which is one
of ``'dashed'``, ``'dotted'``, ``'solid'``, ``'dashdot'``, or ``'--'``,
``':'``, ``'-'``, ``'-.'``, respectively.
Examples:
Show a hyperbolic arc from 0 to 1::
sage: hyperbolic_arc(0, 1)
Graphics object consisting of 1 graphics primitive
Show a hyperbolic arc from 1/2 to `i` with a red thick line::
sage: hyperbolic_arc(1/2, I, color='red', thickness=2)
Graphics object consisting of 1 graphics primitive
Show a hyperbolic arc form `i` to `2 i` with dashed line::
sage: hyperbolic_arc(I, 2*I, linestyle='dashed')
Graphics object consisting of 1 graphics primitive
sage: hyperbolic_arc(I, 2*I, linestyle='--')
Graphics object consisting of 1 graphics primitive
"""
from sage.plot.all import Graphics
g = Graphics()
g._set_extra_kwds(g._extract_kwds_for_show(options))
g.add_primitive(HyperbolicArc(a, b, options))
g.set_aspect_ratio(1)
return g
def hyperbolic_arc(a, b, **options):
"""
Plot an arc from a to b in hyperbolic geometry in the complex upper
half plane.
INPUT:
- ``a, b`` - complex numbers in the upper half complex plane
connected bye the arc
OPTIONS:
- ``alpha`` - default: 1
- ``thickness`` - default: 1
- ``rgbcolor`` - default: 'blue'
- ``linestyle`` - (default: ``'solid'``) The style of the line, which is one
of ``'dashed'``, ``'dotted'``, ``'solid'``, ``'dashdot'``, or ``'--'``,
``':'``, ``'-'``, ``'-.'``, respectively.
Examples:
Show a hyperbolic arc from 0 to 1::
sage: hyperbolic_arc(0, 1)
Graphics object consisting of 1 graphics primitive
Show a hyperbolic arc from 1/2 to `i` with a red thick line::
sage: hyperbolic_arc(1/2, I, color='red', thickness=2)
Graphics object consisting of 1 graphics primitive
Show a hyperbolic arc form `i` to `2 i` with dashed line::
sage: hyperbolic_arc(I, 2*I, linestyle='dashed')
Graphics object consisting of 1 graphics primitive
sage: hyperbolic_arc(I, 2*I, linestyle='--')
Graphics object consisting of 1 graphics primitive
"""
from sage.plot.all import Graphics
g = Graphics()
g._set_extra_kwds(g._extract_kwds_for_show(options))
g.add_primitive(HyperbolicArc(a, b, options))
g.set_aspect_ratio(1)
return g
def my_hyperbolic_triangle(a, b, c, **options):
"""
Return a hyperbolic triangle in the complex hyperbolic plane with points
(a, b, c). Type ``?hyperbolic_triangle`` to see all options.
INPUT:
- ``a, b, c`` - complex numbers in the upper half complex plane
OPTIONS:
- ``alpha`` - default: 1
- ``fill`` - default: False
- ``thickness`` - default: 1
- ``rgbcolor`` - default: 'blue'
- ``linestyle`` - default: 'solid'
EXAMPLES:
Show a hyperbolic triangle with coordinates 0, `1/2+i\sqrt{3}/2` and
`-1/2+i\sqrt{3}/2`::
sage: hyperbolic_triangle(0, -1/2+I*sqrt(3)/2, 1/2+I*sqrt(3)/2)
A hyperbolic triangle with coordinates 0, 1 and 2+i::
sage: hyperbolic_triangle(0, 1, 2+i, fill=true, rgbcolor='red')
"""
from sage.plot.all import Graphics
g = Graphics()
g._set_extra_kwds(g._extract_kwds_for_show(options))
model = options['model']
options.pop('model',None); options.pop('method',None)
if model=="D":
#g.add_primitive(HyperbolicTriangleDisc(a, b, c, **options))
H = HyperbolicTriangleDisc(a, b, c, **options)
g += H()
else:
g.add_primitive(HyperbolicTriangle(a, b, c, options))
g.set_aspect_ratio(1)
return g
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
def hyperbolic_triangle(a, b, c, **options):
"""
Return a hyperbolic triangle in the complex hyperbolic plane with points
(a, b, c). Type ``?hyperbolic_triangle`` to see all options.
INPUT:
- ``a, b, c`` - complex numbers in the upper half complex plane
OPTIONS:
- ``alpha`` - default: 1
- ``fill`` - default: False
- ``thickness`` - default: 1
- ``rgbcolor`` - default: 'blue'
- ``linestyle`` - (default: ``'solid'``) The style of the line, which is
one of ``'dashed'``, ``'dotted'``, ``'solid'``, ``'dashdot'``, or ``'--'``,
``':'``, ``'-'``, ``'-.'``, respectively.
EXAMPLES:
Show a hyperbolic triangle with coordinates 0, `1/2+i\sqrt{3}/2` and
`-1/2+i\sqrt{3}/2`::
sage: hyperbolic_triangle(0, -1/2+I*sqrt(3)/2, 1/2+I*sqrt(3)/2)
Graphics object consisting of 1 graphics primitive
A hyperbolic triangle with coordinates 0, 1 and 2+i and a dashed line::
sage: hyperbolic_triangle(0, 1, 2+i, fill=true, rgbcolor='red', linestyle='--')
Graphics object consisting of 1 graphics primitive
"""
from sage.plot.all import Graphics
g = Graphics()
g._set_extra_kwds(g._extract_kwds_for_show(options))
g.add_primitive(HyperbolicTriangle(a, b, c, options))
g.set_aspect_ratio(1)
return g
def hyperbolic_arc(a, b, **options):
"""
Plot an arc from a to b in hyperbolic geometry in the complex upper
half plane.
INPUT:
- ``a, b`` - complex numbers in the upper half complex plane
connected bye the arc
OPTIONS:
- ``alpha`` - default: 1
- ``thickness`` - default: 1
- ``rgbcolor`` - default: 'blue'
- ``linestyle`` - default: 'solid'
Examples:
Show a hyperbolic arc from 0 to 1::
sage: hyperbolic_arc(0, 1)
Show a hyperbolic arc from 1/2 to `i` with a red thick line::
sage: hyperbolic_arc(1/2, I, color='red', thickness=2)
Show a hyperbolic arc form `i` to `2 i` with dashed line::
sage: hyperbolic_arc(I, 2*I, linestyle='dashed')
"""
from sage.plot.all import Graphics
g = Graphics()
g._set_extra_kwds(g._extract_kwds_for_show(options))
g.add_primitive(HyperbolicArc(a, b, options))
g.set_aspect_ratio(1)
return g
def hyperbolic_arc(a, b, **options):
"""
Plot an arc from a to b in hyperbolic geometry in the complex upper
half plane.
INPUT:
- ``a, b`` - complex numbers in the upper half complex plane
connected bye the arc
OPTIONS:
- ``alpha`` - default: 1
- ``thickness`` - default: 1
- ``rgbcolor`` - default: 'blue'
- ``linestyle`` - default: 'solid'
Examples:
Show a hyperbolic arc from 0 to 1::
sage: hyperbolic_arc(0, 1)
Show a hyperbolic arc from 1/2 to `i` with a red thick line::
sage: hyperbolic_arc(1/2, I, color='red', thickness=2)
Show a hyperbolic arc form `i` to `2 i` with dashed line::
sage: hyperbolic_arc(I, 2*I, linestyle='dashed')
"""
from sage.plot.all import Graphics
g = Graphics()
g._set_extra_kwds(g._extract_kwds_for_show(options))
g.add_primitive(HyperbolicArc(a, b, options))
g.set_aspect_ratio(1)
return g
def hyperbolic_triangle(a, b, c, **options):
"""
Return a hyperbolic triangle in the complex hyperbolic plane with points
(a, b, c). Type ``?hyperbolic_triangle`` to see all options.
INPUT:
- ``a, b, c`` - complex numbers in the upper half complex plane
OPTIONS:
- ``alpha`` - default: 1
- ``fill`` - default: False
- ``thickness`` - default: 1
- ``rgbcolor`` - default: 'blue'
- ``linestyle`` - (default: ``'solid'``) The style of the line, which is
one of ``'dashed'``, ``'dotted'``, ``'solid'``, ``'dashdot'``, or ``'--'``,
``':'``, ``'-'``, ``'-.'``, respectively.
EXAMPLES:
Show a hyperbolic triangle with coordinates 0, `1/2+i\sqrt{3}/2` and
`-1/2+i\sqrt{3}/2`::
sage: hyperbolic_triangle(0, -1/2+I*sqrt(3)/2, 1/2+I*sqrt(3)/2)
A hyperbolic triangle with coordinates 0, 1 and 2+i and a dashed line::
sage: hyperbolic_triangle(0, 1, 2+i, fill=true, rgbcolor='red', linestyle='--')
"""
from sage.plot.all import Graphics
g = Graphics()
g._set_extra_kwds(g._extract_kwds_for_show(options))
g.add_primitive(HyperbolicTriangle(a, b, c, options))
g.set_aspect_ratio(1)
return g
def hyperbolic_triangle(a, b, c, **options):
"""
Return a hyperbolic triangle in the complex hyperbolic plane with points
(a, b, c). Type ``?hyperbolic_triangle`` to see all options.
INPUT:
- ``a, b, c`` - complex numbers in the upper half complex plane
OPTIONS:
- ``alpha`` - default: 1
- ``fill`` - default: False
- ``thickness`` - default: 1
- ``rgbcolor`` - default: 'blue'
- ``linestyle`` - default: 'solid'
EXAMPLES:
Show a hyperbolic triangle with coordinates 0, `1/2+i\sqrt{3}/2` and
`-1/2+i\sqrt{3}/2`::
sage: hyperbolic_triangle(0, -1/2+I*sqrt(3)/2, 1/2+I*sqrt(3)/2)
A hyperbolic triangle with coordinates 0, 1 and 2+i::
sage: hyperbolic_triangle(0, 1, 2+i, fill=true, rgbcolor='red')
"""
from sage.plot.all import Graphics
g = Graphics()
g._set_extra_kwds(g._extract_kwds_for_show(options))
g.add_primitive(HyperbolicTriangle(a, b, c, options))
g.set_aspect_ratio(1)
return g
def my_hyperbolic_triangle(a, b, c, **options):
"""
Return a hyperbolic triangle in the complex hyperbolic plane with points
(a, b, c). Type ``?hyperbolic_triangle`` to see all options.
INPUT:
- ``a, b, c`` - complex numbers in the upper half complex plane
OPTIONS:
- ``alpha`` - default: 1
- ``fill`` - default: False
- ``thickness`` - default: 1
- ``rgbcolor`` - default: 'blue'
- ``linestyle`` - default: 'solid'
EXAMPLES:
Show a hyperbolic triangle with coordinates 0, `1/2+i\sqrt{3}/2` and
`-1/2+i\sqrt{3}/2`::
sage: hyperbolic_triangle(0, -1/2+I*sqrt(3)/2, 1/2+I*sqrt(3)/2)
A hyperbolic triangle with coordinates 0, 1 and 2+i::
sage: hyperbolic_triangle(0, 1, 2+i, fill=true, rgbcolor='red')
"""
from sage.plot.all import Graphics
g = Graphics()
g._set_extra_kwds(g._extract_kwds_for_show(options))
model = options['model']
npts = options.get('npts', 10)
sides = options.pop('sides',
[1, 2, 3]) ## Which of the sides we will draw.
verbose = options.get('verbose', 0)
options.pop('model', None)
options.pop('method', None)
if model == "D":
#g.add_primitive(HyperbolicTriangleDisc(a, b, c, **options))
#print "options=",options
options['sides'] = sides
H = HyperbolicTriangleDisc(a, b, c, **options)
g += H()
else:
options.pop('npts', None)
if sides == [1, 2, 3]:
if verbose > 0:
print "adding HyperbolicTriangle({0}, {1}, {2},options={3})".format(
a, b, c, options)
options.pop('verbose', 0)
## check if We need my class or the original class
g.add_primitive(HyperbolicTriangle(a, b, c, options))
else:
options['sides'] = sides
if verbose > 0:
print "adding HyperbolicTriangle({0}, {1}, {2},options={3})".format(
a, b, c, options)
g.add_primitive(HyperbolicTriangle(a, b, c, options))
g.set_aspect_ratio(1)
return g
def plot(self, **kwds):
"""
Returns a graphics object representing the (di)graph.
INPUT:
- pos -- an optional positioning dictionary
- layout -- what kind of layout to use, takes precedence over pos
- 'circular' -- plots the graph with vertices evenly distributed
on a circle
- 'spring' -- uses the traditional spring layout, using the
graph's current positions as initial positions
- 'tree' -- the (di)graph must be a tree. One can specify the root
of the tree using the keyword tree_root, otherwise a root
will be selected at random. Then the tree will be plotted in
levels, depending on minimum distance for the root.
- vertex_labels -- whether to print vertex labels
edge_labels -- whether to print edge labels. By default, False,
but if True, the result of str(l) is printed on the edge for
each label l. Labels equal to None are not printed (to set edge
labels, see set_edge_label).
- vertex_size -- size of vertices displayed
- vertex_shape -- the shape to draw the vertices (Not available for
multiedge digraphs.
- graph_border -- whether to include a box around the graph
- vertex_colors -- optional dictionary to specify vertex colors: each
key is a color recognizable by matplotlib, and each corresponding
entry is a list of vertices. If a vertex is not listed, it looks
invisible on the resulting plot (it doesn't get drawn).
- edge_colors -- a dictionary specifying edge colors: each key is a
color recognized by matplotlib, and each entry is a list of edges.
- partition -- a partition of the vertex set. if specified, plot will
show each cell in a different color. vertex_colors takes precedence.
- talk -- if true, prints large vertices with white backgrounds so that
labels are legible on slides
- iterations -- how many iterations of the spring layout algorithm to
go through, if applicable
- color_by_label -- if True, color edges by their labels
- heights -- if specified, this is a dictionary from a set of
floating point heights to a set of vertices
- edge_style -- keyword arguments passed into the
edge-drawing routine. This currently only works for
directed graphs, since we pass off the undirected graph to
networkx
- tree_root -- a vertex of the tree to be used as the root for
the layout="tree" option. If no root is specified, then one
is chosen at random. Ignored unless layout='tree'.
- tree_orientation -- "up" or "down" (default is "down").
If "up" (resp., "down"), then the root of the tree will
appear on the bottom (resp., top) and the tree will grow
upwards (resp. downwards). Ignored unless layout='tree'.
- save_pos -- save position computed during plotting
EXAMPLES::
sage: from sage.graphs.graph_plot import graphplot_options
sage: list(sorted(graphplot_options.iteritems()))
[('by_component', 'Whether to do the spring layout by connected component -- a boolean.'),
('color_by_label', 'Whether or not to color the edges by their label values.'),
('dim', 'The dimension of the layout -- 2 or 3.'),
('dist', 'The distance between multiedges.'),
('edge_color', 'The default color for edges.'),
('edge_colors', 'Dictionary of edge coloring.'),
('edge_labels', 'Whether or not to draw edge labels.'),
('edge_style', 'The linestyle of the edges-- one of "solid", "dashed", "dotted", dashdot".'),
('graph_border', 'Whether or not to draw a frame around the graph.'),
('heights', 'A dictionary mapping heights to the list of vertices at this height.'),
('iterations', 'The number of times to execute the spring layout algorithm.'),
('layout', 'A layout algorithm -- one of "acyclic", "circular", "ranked", "graphviz", "planar", "spring", or "tree".'),
('loop_size', 'The radius of the smallest loop.'),
('max_dist', 'The max distance range to allow multiedges.'),
('partition', 'A partition of the vertex set. (Draws each cell of vertices in a different color).'),
('pos', 'The position dictionary of vertices'),
('prog', 'Which graphviz layout program to use -- one of "circo", "dot", "fdp", "neato", or "twopi".'),
('save_pos', 'Whether or not to save the computed position for the graph.'),
('spring', 'Use spring layout to finalize the current layout.'),
('talk', 'Whether to display the vertices in talk mode (larger and white)'),
('tree_orientation', 'The direction of tree branches -- "up" or "down".'),
('tree_root', 'A vertex designation for drawing trees.'),
('vertex_colors', 'Dictionary of vertex coloring.'),
('vertex_labels', 'Whether or not to draw vertex labels.'),
('vertex_shape', 'The shape to draw the vertices, Currently unavailable for Multi-edged DiGraphs.'),
('vertex_size', 'The size to draw the vertices.')]
sage: from math import sin, cos, pi
sage: P = graphs.PetersenGraph()
sage: d = {'#FF0000':[0,5], '#FF9900':[1,6], '#FFFF00':[2,7], '#00FF00':[3,8], '#0000FF':[4,9]}
sage: pos_dict = {}
sage: for i in range(5):
... x = float(cos(pi/2 + ((2*pi)/5)*i))
... y = float(sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: for i in range(10)[5:]:
... x = float(0.5*cos(pi/2 + ((2*pi)/5)*i))
... y = float(0.5*sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: pl = P.graphplot(pos=pos_dict, vertex_colors=d)
sage: pl.show()
sage: C = graphs.CubeGraph(8)
sage: P = C.graphplot(vertex_labels=False, vertex_size=0, graph_border=True)
sage: P.show()
sage: G = graphs.HeawoodGraph().copy(sparse=True)
sage: for u,v,l in G.edges():
... G.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: G.graphplot(edge_labels=True).show()
sage: D = DiGraph( { 0: [1, 10, 19], 1: [8, 2], 2: [3, 6], 3: [19, 4], 4: [17, 5], 5: [6, 15], 6: [7], 7: [8, 14], 8: [9], 9: [10, 13], 10: [11], 11: [12, 18], 12: [16, 13], 13: [14], 14: [15], 15: [16], 16: [17], 17: [18], 18: [19], 19: []}, implementation='networkx' )
sage: for u,v,l in D.edges():
... D.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: D.graphplot(edge_labels=True, layout='circular').show()
sage: from sage.plot.colors import rainbow
sage: C = graphs.CubeGraph(5)
sage: R = rainbow(5)
sage: edge_colors = {}
sage: for i in range(5):
... edge_colors[R[i]] = []
sage: for u,v,l in C.edges():
... for i in range(5):
... if u[i] != v[i]:
... edge_colors[R[i]].append((u,v,l))
sage: C.graphplot(vertex_labels=False, vertex_size=0, edge_colors=edge_colors).show()
sage: D = graphs.DodecahedralGraph()
sage: Pi = [[6,5,15,14,7],[16,13,8,2,4],[12,17,9,3,1],[0,19,18,10,11]]
sage: D.show(partition=Pi)
sage: G = graphs.PetersenGraph()
sage: G.allow_loops(True)
sage: G.add_edge(0,0)
sage: G.show()
sage: D = DiGraph({0:[0,1], 1:[2], 2:[3]}, loops=True)
sage: D.show()
sage: D.show(edge_colors={(0,1,0):[(0,1,None),(1,2,None)],(0,0,0):[(2,3,None)]})
sage: pos = {0:[0.0, 1.5], 1:[-0.8, 0.3], 2:[-0.6, -0.8], 3:[0.6, -0.8], 4:[0.8, 0.3]}
sage: g = Graph({0:[1], 1:[2], 2:[3], 3:[4], 4:[0]})
sage: g.graphplot(pos=pos, layout='spring', iterations=0).plot()
sage: G = Graph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
sage: G = DiGraph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
sage: t.set_edge_label(0,1,-7)
sage: t.set_edge_label(0,5,3)
sage: t.set_edge_label(0,5,99)
sage: t.set_edge_label(1,2,1000)
sage: t.set_edge_label(3,2,'spam')
sage: t.set_edge_label(2,6,3/2)
sage: t.set_edge_label(0,4,66)
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}, edge_labels=True).plot()
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(layout='tree').show()
sage: t = DiGraph('JCC???@A??GO??CO??GO??')
sage: t.graphplot(layout='tree', tree_root=0, tree_orientation="up").show()
sage: D = DiGraph({0:[1,2,3], 2:[1,4], 3:[0]})
sage: D.graphplot().show()
sage: D = DiGraph(multiedges=True, sparse=True)
sage: for i in range(5):
... D.add_edge((i,i+1,'a'))
... D.add_edge((i,i-1,'b'))
sage: D.graphplot(edge_labels=True,edge_colors=D._color_by_label()).plot()
sage: g = Graph({}, loops=True, multiedges=True, sparse=True)
sage: g.add_edges([(0,0,'a'),(0,0,'b'),(0,1,'c'),(0,1,'d'),
... (0,1,'e'),(0,1,'f'),(0,1,'f'),(2,1,'g'),(2,2,'h')])
sage: g.graphplot(edge_labels=True, color_by_label=True, edge_style='dashed').plot()
"""
G = Graphics()
for comp in self._plot_components.values():
if not isinstance(comp, list):
G += comp
else:
for item in comp:
G += item
G.set_axes_range(*(self._graph._layout_bounding_box(self._pos)))
if self._options['graph_border']:
xmin = G.xmin()
xmax = G.xmax()
ymin = G.ymin()
ymax = G.ymax()
dx = (xmax-xmin)/10.0
dy = (ymax-ymin)/10.0
border = (line([( xmin - dx, ymin - dy), ( xmin - dx, ymax + dy ), ( xmax + dx, ymax + dy ), ( xmax + dx, ymin - dy ), ( xmin - dx, ymin - dy )], thickness=1.3))
border.axes_range(xmin = (xmin - dx), xmax = (xmax + dx), ymin = (ymin - dy), ymax = (ymax + dy))
G += border
G.set_aspect_ratio(1)
G.axes(False)
G._extra_kwds['axes_pad']=.05
return G
def plot(self, **kwds):
"""
Returns a graphics object representing the (di)graph.
INPUT:
The options accepted by this method are to be found in the documentation
of module :mod:`sage.graphs.graph_plot`.
.. NOTE::
See :mod:`the module's documentation <sage.graphs.graph_plot>` for
information on default values of this method.
We can specify some pretty precise plotting of familiar graphs::
sage: from math import sin, cos, pi
sage: P = graphs.PetersenGraph()
sage: d = {'#FF0000':[0,5], '#FF9900':[1,6], '#FFFF00':[2,7], '#00FF00':[3,8], '#0000FF':[4,9]}
sage: pos_dict = {}
sage: for i in range(5):
... x = float(cos(pi/2 + ((2*pi)/5)*i))
... y = float(sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: for i in range(10)[5:]:
... x = float(0.5*cos(pi/2 + ((2*pi)/5)*i))
... y = float(0.5*sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: pl = P.graphplot(pos=pos_dict, vertex_colors=d)
sage: pl.show()
Here are some more common graphs with typical options::
sage: C = graphs.CubeGraph(8)
sage: P = C.graphplot(vertex_labels=False, vertex_size=0, graph_border=True)
sage: P.show()
sage: G = graphs.HeawoodGraph().copy(sparse=True)
sage: for u,v,l in G.edges():
... G.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: G.graphplot(edge_labels=True).show()
The options for plotting also work with directed graphs::
sage: D = DiGraph( { 0: [1, 10, 19], 1: [8, 2], 2: [3, 6], 3: [19, 4], 4: [17, 5], 5: [6, 15], 6: [7], 7: [8, 14], 8: [9], 9: [10, 13], 10: [11], 11: [12, 18], 12: [16, 13], 13: [14], 14: [15], 15: [16], 16: [17], 17: [18], 18: [19], 19: []}, implementation='networkx' )
sage: for u,v,l in D.edges():
... D.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: D.graphplot(edge_labels=True, layout='circular').show()
This example shows off the coloring of edges::
sage: from sage.plot.colors import rainbow
sage: C = graphs.CubeGraph(5)
sage: R = rainbow(5)
sage: edge_colors = {}
sage: for i in range(5):
... edge_colors[R[i]] = []
sage: for u,v,l in C.edges():
... for i in range(5):
... if u[i] != v[i]:
... edge_colors[R[i]].append((u,v,l))
sage: C.graphplot(vertex_labels=False, vertex_size=0, edge_colors=edge_colors).show()
With the ``partition`` option, we can separate out same-color groups
of vertices::
sage: D = graphs.DodecahedralGraph()
sage: Pi = [[6,5,15,14,7],[16,13,8,2,4],[12,17,9,3,1],[0,19,18,10,11]]
sage: D.show(partition=Pi)
Loops are also plotted correctly::
sage: G = graphs.PetersenGraph()
sage: G.allow_loops(True)
sage: G.add_edge(0,0)
sage: G.show()
::
sage: D = DiGraph({0:[0,1], 1:[2], 2:[3]}, loops=True)
sage: D.show()
sage: D.show(edge_colors={(0,1,0):[(0,1,None),(1,2,None)],(0,0,0):[(2,3,None)]})
More options::
sage: pos = {0:[0.0, 1.5], 1:[-0.8, 0.3], 2:[-0.6, -0.8], 3:[0.6, -0.8], 4:[0.8, 0.3]}
sage: g = Graph({0:[1], 1:[2], 2:[3], 3:[4], 4:[0]})
sage: g.graphplot(pos=pos, layout='spring', iterations=0).plot()
sage: G = Graph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
sage: G = DiGraph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
We can plot multiple graphs::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
sage: t.set_edge_label(0,1,-7)
sage: t.set_edge_label(0,5,3)
sage: t.set_edge_label(0,5,99)
sage: t.set_edge_label(1,2,1000)
sage: t.set_edge_label(3,2,'spam')
sage: t.set_edge_label(2,6,3/2)
sage: t.set_edge_label(0,4,66)
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}, edge_labels=True).plot()
::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(layout='tree').show()
The tree layout is also useful::
sage: t = DiGraph('JCC???@A??GO??CO??GO??')
sage: t.graphplot(layout='tree', tree_root=0, tree_orientation="up").show()
More examples::
sage: D = DiGraph({0:[1,2,3], 2:[1,4], 3:[0]})
sage: D.graphplot().show()
sage: D = DiGraph(multiedges=True, sparse=True)
sage: for i in range(5):
... D.add_edge((i,i+1,'a'))
... D.add_edge((i,i-1,'b'))
sage: D.graphplot(edge_labels=True,edge_colors=D._color_by_label()).plot()
sage: g = Graph({}, loops=True, multiedges=True, sparse=True)
sage: g.add_edges([(0,0,'a'),(0,0,'b'),(0,1,'c'),(0,1,'d'),
... (0,1,'e'),(0,1,'f'),(0,1,'f'),(2,1,'g'),(2,2,'h')])
sage: g.graphplot(edge_labels=True, color_by_label=True, edge_style='dashed').plot()
Wrong input (any input) :trac:`13891`::
sage: graphs.PetersenGraph().graphplot().plot(aertataert=346345345)
doctest:...: DeprecationWarning: This method takes no argument ! You may want to give it as an argument to graphplot instead.
See http://trac.sagemath.org/13891 for details.
<BLANKLINE>
"""
# This method takes NO input
# This has been added in early 2013. Remove it before my death, please.
if kwds:
from sage.misc.superseded import deprecation
deprecation(13891, "This method takes no argument ! You may want "
"to give it as an argument to graphplot instead.")
G = Graphics()
for comp in self._plot_components.values():
if not isinstance(comp, list):
G += comp
else:
for item in comp:
G += item
G.set_axes_range(*(self._graph._layout_bounding_box(self._pos)))
if self._options['graph_border']:
xmin = G.xmin()
xmax = G.xmax()
ymin = G.ymin()
ymax = G.ymax()
dx = (xmax-xmin)/10.0
dy = (ymax-ymin)/10.0
border = (line([( xmin - dx, ymin - dy), ( xmin - dx, ymax + dy ), ( xmax + dx, ymax + dy ), ( xmax + dx, ymin - dy ), ( xmin - dx, ymin - dy )], thickness=1.3))
border.axes_range(xmin = (xmin - dx), xmax = (xmax + dx), ymin = (ymin - dy), ymax = (ymax + dy))
G += border
G.set_aspect_ratio(1)
G.axes(False)
G._extra_kwds['axes_pad']=.05
return G
def plot(self, **kwds):
"""
Returns a graphics object representing the (di)graph.
INPUT:
The options accepted by this method are to be found in the documentation
of the :mod:`sage.graphs.graph_plot` module, and the
:meth:`~sage.plot.graphics.Graphics.show` method.
.. NOTE::
See :mod:`the module's documentation <sage.graphs.graph_plot>` for
information on default values of this method.
We can specify some pretty precise plotting of familiar graphs::
sage: from math import sin, cos, pi
sage: P = graphs.PetersenGraph()
sage: d = {'#FF0000':[0,5], '#FF9900':[1,6], '#FFFF00':[2,7], '#00FF00':[3,8], '#0000FF':[4,9]}
sage: pos_dict = {}
sage: for i in range(5):
... x = float(cos(pi/2 + ((2*pi)/5)*i))
... y = float(sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: for i in range(10)[5:]:
... x = float(0.5*cos(pi/2 + ((2*pi)/5)*i))
... y = float(0.5*sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: pl = P.graphplot(pos=pos_dict, vertex_colors=d)
sage: pl.show()
Here are some more common graphs with typical options::
sage: C = graphs.CubeGraph(8)
sage: P = C.graphplot(vertex_labels=False, vertex_size=0, graph_border=True)
sage: P.show()
sage: G = graphs.HeawoodGraph().copy(sparse=True)
sage: for u,v,l in G.edges():
... G.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: G.graphplot(edge_labels=True).show()
The options for plotting also work with directed graphs::
sage: D = DiGraph( { 0: [1, 10, 19], 1: [8, 2], 2: [3, 6], 3: [19, 4], 4: [17, 5], 5: [6, 15], 6: [7], 7: [8, 14], 8: [9], 9: [10, 13], 10: [11], 11: [12, 18], 12: [16, 13], 13: [14], 14: [15], 15: [16], 16: [17], 17: [18], 18: [19], 19: []})
sage: for u,v,l in D.edges():
... D.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: D.graphplot(edge_labels=True, layout='circular').show()
This example shows off the coloring of edges::
sage: from sage.plot.colors import rainbow
sage: C = graphs.CubeGraph(5)
sage: R = rainbow(5)
sage: edge_colors = {}
sage: for i in range(5):
... edge_colors[R[i]] = []
sage: for u,v,l in C.edges():
... for i in range(5):
... if u[i] != v[i]:
... edge_colors[R[i]].append((u,v,l))
sage: C.graphplot(vertex_labels=False, vertex_size=0, edge_colors=edge_colors).show()
With the ``partition`` option, we can separate out same-color groups
of vertices::
sage: D = graphs.DodecahedralGraph()
sage: Pi = [[6,5,15,14,7],[16,13,8,2,4],[12,17,9,3,1],[0,19,18,10,11]]
sage: D.show(partition=Pi)
Loops are also plotted correctly::
sage: G = graphs.PetersenGraph()
sage: G.allow_loops(True)
sage: G.add_edge(0,0)
sage: G.show()
::
sage: D = DiGraph({0:[0,1], 1:[2], 2:[3]}, loops=True)
sage: D.show()
sage: D.show(edge_colors={(0,1,0):[(0,1,None),(1,2,None)],(0,0,0):[(2,3,None)]})
More options::
sage: pos = {0:[0.0, 1.5], 1:[-0.8, 0.3], 2:[-0.6, -0.8], 3:[0.6, -0.8], 4:[0.8, 0.3]}
sage: g = Graph({0:[1], 1:[2], 2:[3], 3:[4], 4:[0]})
sage: g.graphplot(pos=pos, layout='spring', iterations=0).plot()
Graphics object consisting of 11 graphics primitives
sage: G = Graph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
sage: G = DiGraph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
We can plot multiple graphs::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
Graphics object consisting of 14 graphics primitives
::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
Graphics object consisting of 14 graphics primitives
sage: t.set_edge_label(0,1,-7)
sage: t.set_edge_label(0,5,3)
sage: t.set_edge_label(0,5,99)
sage: t.set_edge_label(1,2,1000)
sage: t.set_edge_label(3,2,'spam')
sage: t.set_edge_label(2,6,3/2)
sage: t.set_edge_label(0,4,66)
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}, edge_labels=True).plot()
Graphics object consisting of 20 graphics primitives
::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(layout='tree').show()
The tree layout is also useful::
sage: t = DiGraph('JCC???@A??GO??CO??GO??')
sage: t.graphplot(layout='tree', tree_root=0, tree_orientation="up").show()
More examples::
sage: D = DiGraph({0:[1,2,3], 2:[1,4], 3:[0]})
sage: D.graphplot().show()
sage: D = DiGraph(multiedges=True, sparse=True)
sage: for i in range(5):
... D.add_edge((i,i+1,'a'))
... D.add_edge((i,i-1,'b'))
sage: D.graphplot(edge_labels=True,edge_colors=D._color_by_label()).plot()
Graphics object consisting of 34 graphics primitives
sage: g = Graph({}, loops=True, multiedges=True, sparse=True)
sage: g.add_edges([(0,0,'a'),(0,0,'b'),(0,1,'c'),(0,1,'d'),
... (0,1,'e'),(0,1,'f'),(0,1,'f'),(2,1,'g'),(2,2,'h')])
sage: g.graphplot(edge_labels=True, color_by_label=True, edge_style='dashed').plot()
Graphics object consisting of 22 graphics primitives
The ``edge_style`` option may be provided in the short format too::
sage: g.graphplot(edge_labels=True, color_by_label=True, edge_style='--').plot()
Graphics object consisting of 22 graphics primitives
TESTS:
Make sure that show options work with plot also::
sage: g = Graph({})
sage: g.plot(title='empty graph', axes=True)
Graphics object consisting of 0 graphics primitives
Check for invalid inputs::
sage: p = graphs.PetersenGraph().plot(egabrag='garbage')
Traceback (most recent call last):
...
ValueError: Invalid input 'egabrag=garbage'
Make sure that no graphics primitive is clipped::
sage: tadpole = Graph({0:[0,1]}).plot()
sage: bbox = tadpole.get_minmax_data()
sage: for part in tadpole:
....: part_bbox = part.get_minmax_data()
....: assert bbox['xmin'] <= part_bbox['xmin'] <= part_bbox['xmax'] <= bbox['xmax']
....: assert bbox['ymin'] <= part_bbox['ymin'] <= part_bbox['ymax'] <= bbox['ymax']
"""
G = Graphics()
options = self._options.copy()
options.update(kwds)
G._set_extra_kwds(Graphics._extract_kwds_for_show(options))
# Check the arguments
for o in options:
if o not in graphplot_options and o not in G._extra_kwds:
raise ValueError("Invalid input '{}={}'".format(o, options[o]))
for comp in self._plot_components.values():
if not isinstance(comp, list):
G += comp
else:
for item in comp:
G += item
if self._options['graph_border']:
xmin = G.xmin()
xmax = G.xmax()
ymin = G.ymin()
ymax = G.ymax()
dx = (xmax-xmin)/10.0
dy = (ymax-ymin)/10.0
border = (line([( xmin - dx, ymin - dy), ( xmin - dx, ymax + dy ), ( xmax + dx, ymax + dy ), ( xmax + dx, ymin - dy ), ( xmin - dx, ymin - dy )], thickness=1.3))
border.axes_range(xmin = (xmin - dx), xmax = (xmax + dx), ymin = (ymin - dy), ymax = (ymax + dy))
G += border
G.set_aspect_ratio(1)
G.axes(False)
return G
def plot(self, **kwds):
"""
Returns a graphics object representing the (di)graph.
INPUT:
- pos -- an optional positioning dictionary
- layout -- what kind of layout to use, takes precedence over pos
- 'circular' -- plots the graph with vertices evenly distributed
on a circle
- 'spring' -- uses the traditional spring layout, using the
graph's current positions as initial positions
- 'tree' -- the (di)graph must be a tree. One can specify the root
of the tree using the keyword tree_root, otherwise a root
will be selected at random. Then the tree will be plotted in
levels, depending on minimum distance for the root.
- vertex_labels -- whether to print vertex labels
edge_labels -- whether to print edge labels. By default, False,
but if True, the result of str(l) is printed on the edge for
each label l. Labels equal to None are not printed (to set edge
labels, see set_edge_label).
- vertex_size -- size of vertices displayed
- vertex_shape -- the shape to draw the vertices (Not available for
multiedge digraphs.
- graph_border -- whether to include a box around the graph
- vertex_colors -- optional dictionary to specify vertex colors: each
key is a color recognizable by matplotlib, and each corresponding
entry is a list of vertices. If a vertex is not listed, it looks
invisible on the resulting plot (it doesn't get drawn).
- edge_colors -- a dictionary specifying edge colors: each key is a
color recognized by matplotlib, and each entry is a list of edges.
- partition -- a partition of the vertex set. if specified, plot will
show each cell in a different color. vertex_colors takes precedence.
- talk -- if true, prints large vertices with white backgrounds so that
labels are legible on slides
- iterations -- how many iterations of the spring layout algorithm to
go through, if applicable
- color_by_label -- if True, color edges by their labels
- heights -- if specified, this is a dictionary from a set of
floating point heights to a set of vertices
- edge_style -- keyword arguments passed into the
edge-drawing routine. This currently only works for
directed graphs, since we pass off the undirected graph to
networkx
- tree_root -- a vertex of the tree to be used as the root for
the layout="tree" option. If no root is specified, then one
is chosen at random. Ignored unless layout='tree'.
- tree_orientation -- "up" or "down" (default is "down").
If "up" (resp., "down"), then the root of the tree will
appear on the bottom (resp., top) and the tree will grow
upwards (resp. downwards). Ignored unless layout='tree'.
- save_pos -- save position computed during plotting
EXAMPLES::
sage: from sage.graphs.graph_plot import graphplot_options
sage: list(sorted(graphplot_options.iteritems()))
[('by_component', 'Whether to do the spring layout by connected component -- a boolean.'),
('color_by_label', 'Whether or not to color the edges by their label values.'),
('dim', 'The dimension of the layout -- 2 or 3.'),
('dist', 'The distance between multiedges.'),
('edge_color', 'The default color for edges.'),
('edge_colors', 'Dictionary of edge coloring.'),
('edge_labels', 'Whether or not to draw edge labels.'),
('edge_style', 'The linestyle of the edges-- one of "solid", "dashed", "dotted", dashdot".'),
('graph_border', 'Whether or not to draw a frame around the graph.'),
('heights', 'A dictionary mapping heights to the list of vertices at this height.'),
('iterations', 'The number of times to execute the spring layout algorithm.'),
('layout', 'A layout algorithm -- one of "acyclic", "circular", "ranked", "graphviz", "planar", "spring", or "tree".'),
('loop_size', 'The radius of the smallest loop.'),
('max_dist', 'The max distance range to allow multiedges.'),
('partition', 'A partition of the vertex set. (Draws each cell of vertices in a different color).'),
('pos', 'The position dictionary of vertices'),
('prog', 'Which graphviz layout program to use -- one of "circo", "dot", "fdp", "neato", or "twopi".'),
('save_pos', 'Whether or not to save the computed position for the graph.'),
('spring', 'Use spring layout to finalize the current layout.'),
('talk', 'Whether to display the vertices in talk mode (larger and white)'),
('tree_orientation', 'The direction of tree branches -- "up" or "down".'),
('tree_root', 'A vertex designation for drawing trees.'),
('vertex_colors', 'Dictionary of vertex coloring.'),
('vertex_labels', 'Whether or not to draw vertex labels.'),
('vertex_shape', 'The shape to draw the vertices, Currently unavailable for Multi-edged DiGraphs.'),
('vertex_size', 'The size to draw the vertices.')]
sage: from math import sin, cos, pi
sage: P = graphs.PetersenGraph()
sage: d = {'#FF0000':[0,5], '#FF9900':[1,6], '#FFFF00':[2,7], '#00FF00':[3,8], '#0000FF':[4,9]}
sage: pos_dict = {}
sage: for i in range(5):
... x = float(cos(pi/2 + ((2*pi)/5)*i))
... y = float(sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: for i in range(10)[5:]:
... x = float(0.5*cos(pi/2 + ((2*pi)/5)*i))
... y = float(0.5*sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: pl = P.graphplot(pos=pos_dict, vertex_colors=d)
sage: pl.show()
sage: C = graphs.CubeGraph(8)
sage: P = C.graphplot(vertex_labels=False, vertex_size=0, graph_border=True)
sage: P.show()
sage: G = graphs.HeawoodGraph().copy(sparse=True)
sage: for u,v,l in G.edges():
... G.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: G.graphplot(edge_labels=True).show()
sage: D = DiGraph( { 0: [1, 10, 19], 1: [8, 2], 2: [3, 6], 3: [19, 4], 4: [17, 5], 5: [6, 15], 6: [7], 7: [8, 14], 8: [9], 9: [10, 13], 10: [11], 11: [12, 18], 12: [16, 13], 13: [14], 14: [15], 15: [16], 16: [17], 17: [18], 18: [19], 19: []}, implementation='networkx' )
sage: for u,v,l in D.edges():
... D.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: D.graphplot(edge_labels=True, layout='circular').show()
sage: from sage.plot.colors import rainbow
sage: C = graphs.CubeGraph(5)
sage: R = rainbow(5)
sage: edge_colors = {}
sage: for i in range(5):
... edge_colors[R[i]] = []
sage: for u,v,l in C.edges():
... for i in range(5):
... if u[i] != v[i]:
... edge_colors[R[i]].append((u,v,l))
sage: C.graphplot(vertex_labels=False, vertex_size=0, edge_colors=edge_colors).show()
sage: D = graphs.DodecahedralGraph()
sage: Pi = [[6,5,15,14,7],[16,13,8,2,4],[12,17,9,3,1],[0,19,18,10,11]]
sage: D.show(partition=Pi)
sage: G = graphs.PetersenGraph()
sage: G.allow_loops(True)
sage: G.add_edge(0,0)
sage: G.show()
sage: D = DiGraph({0:[0,1], 1:[2], 2:[3]}, loops=True)
sage: D.show()
sage: D.show(edge_colors={(0,1,0):[(0,1,None),(1,2,None)],(0,0,0):[(2,3,None)]})
sage: pos = {0:[0.0, 1.5], 1:[-0.8, 0.3], 2:[-0.6, -0.8], 3:[0.6, -0.8], 4:[0.8, 0.3]}
sage: g = Graph({0:[1], 1:[2], 2:[3], 3:[4], 4:[0]})
sage: g.graphplot(pos=pos, layout='spring', iterations=0).plot()
sage: G = Graph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
sage: G = DiGraph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
sage: t.set_edge_label(0,1,-7)
sage: t.set_edge_label(0,5,3)
sage: t.set_edge_label(0,5,99)
sage: t.set_edge_label(1,2,1000)
sage: t.set_edge_label(3,2,'spam')
sage: t.set_edge_label(2,6,3/2)
sage: t.set_edge_label(0,4,66)
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}, edge_labels=True).plot()
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(layout='tree').show()
sage: t = DiGraph('JCC???@A??GO??CO??GO??')
sage: t.graphplot(layout='tree', tree_root=0, tree_orientation="up").show()
sage: D = DiGraph({0:[1,2,3], 2:[1,4], 3:[0]})
sage: D.graphplot().show()
sage: D = DiGraph(multiedges=True, sparse=True)
sage: for i in range(5):
... D.add_edge((i,i+1,'a'))
... D.add_edge((i,i-1,'b'))
sage: D.graphplot(edge_labels=True,edge_colors=D._color_by_label()).plot()
sage: g = Graph({}, loops=True, multiedges=True, sparse=True)
sage: g.add_edges([(0,0,'a'),(0,0,'b'),(0,1,'c'),(0,1,'d'),
... (0,1,'e'),(0,1,'f'),(0,1,'f'),(2,1,'g'),(2,2,'h')])
sage: g.graphplot(edge_labels=True, color_by_label=True, edge_style='dashed').plot()
"""
G = Graphics()
for comp in self._plot_components.values():
if not isinstance(comp, list):
G += comp
else:
for item in comp:
G += item
G.set_axes_range(*(self._graph._layout_bounding_box(self._pos)))
if self._options['graph_border']:
xmin = G.xmin()
xmax = G.xmax()
ymin = G.ymin()
ymax = G.ymax()
dx = (xmax - xmin) / 10.0
dy = (ymax - ymin) / 10.0
border = (line([(xmin - dx, ymin - dy), (xmin - dx, ymax + dy),
(xmax + dx, ymax + dy), (xmax + dx, ymin - dy),
(xmin - dx, ymin - dy)],
thickness=1.3))
border.axes_range(xmin=(xmin - dx),
xmax=(xmax + dx),
ymin=(ymin - dy),
ymax=(ymax + dy))
G += border
G.set_aspect_ratio(1)
G.axes(False)
G._extra_kwds['axes_pad'] = .05
return G
def plot(self, **kwds):
"""
Returns a graphics object representing the (di)graph.
INPUT:
The options accepted by this method are to be found in the documentation
of the :mod:`sage.graphs.graph_plot` module, and the
:meth:`~sage.plot.graphics.Graphics.show` method.
.. NOTE::
See :mod:`the module's documentation <sage.graphs.graph_plot>` for
information on default values of this method.
We can specify some pretty precise plotting of familiar graphs::
sage: from math import sin, cos, pi
sage: P = graphs.PetersenGraph()
sage: d = {'#FF0000':[0,5], '#FF9900':[1,6], '#FFFF00':[2,7], '#00FF00':[3,8], '#0000FF':[4,9]}
sage: pos_dict = {}
sage: for i in range(5):
... x = float(cos(pi/2 + ((2*pi)/5)*i))
... y = float(sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: for i in range(10)[5:]:
... x = float(0.5*cos(pi/2 + ((2*pi)/5)*i))
... y = float(0.5*sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: pl = P.graphplot(pos=pos_dict, vertex_colors=d)
sage: pl.show()
Here are some more common graphs with typical options::
sage: C = graphs.CubeGraph(8)
sage: P = C.graphplot(vertex_labels=False, vertex_size=0, graph_border=True)
sage: P.show()
sage: G = graphs.HeawoodGraph().copy(sparse=True)
sage: for u,v,l in G.edges():
... G.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: G.graphplot(edge_labels=True).show()
The options for plotting also work with directed graphs::
sage: D = DiGraph( { 0: [1, 10, 19], 1: [8, 2], 2: [3, 6], 3: [19, 4], 4: [17, 5], 5: [6, 15], 6: [7], 7: [8, 14], 8: [9], 9: [10, 13], 10: [11], 11: [12, 18], 12: [16, 13], 13: [14], 14: [15], 15: [16], 16: [17], 17: [18], 18: [19], 19: []})
sage: for u,v,l in D.edges():
... D.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: D.graphplot(edge_labels=True, layout='circular').show()
This example shows off the coloring of edges::
sage: from sage.plot.colors import rainbow
sage: C = graphs.CubeGraph(5)
sage: R = rainbow(5)
sage: edge_colors = {}
sage: for i in range(5):
... edge_colors[R[i]] = []
sage: for u,v,l in C.edges():
... for i in range(5):
... if u[i] != v[i]:
... edge_colors[R[i]].append((u,v,l))
sage: C.graphplot(vertex_labels=False, vertex_size=0, edge_colors=edge_colors).show()
With the ``partition`` option, we can separate out same-color groups
of vertices::
sage: D = graphs.DodecahedralGraph()
sage: Pi = [[6,5,15,14,7],[16,13,8,2,4],[12,17,9,3,1],[0,19,18,10,11]]
sage: D.show(partition=Pi)
Loops are also plotted correctly::
sage: G = graphs.PetersenGraph()
sage: G.allow_loops(True)
sage: G.add_edge(0,0)
sage: G.show()
::
sage: D = DiGraph({0:[0,1], 1:[2], 2:[3]}, loops=True)
sage: D.show()
sage: D.show(edge_colors={(0,1,0):[(0,1,None),(1,2,None)],(0,0,0):[(2,3,None)]})
More options::
sage: pos = {0:[0.0, 1.5], 1:[-0.8, 0.3], 2:[-0.6, -0.8], 3:[0.6, -0.8], 4:[0.8, 0.3]}
sage: g = Graph({0:[1], 1:[2], 2:[3], 3:[4], 4:[0]})
sage: g.graphplot(pos=pos, layout='spring', iterations=0).plot()
Graphics object consisting of 11 graphics primitives
sage: G = Graph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
sage: G = DiGraph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
We can plot multiple graphs::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
Graphics object consisting of 14 graphics primitives
::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
Graphics object consisting of 14 graphics primitives
sage: t.set_edge_label(0,1,-7)
sage: t.set_edge_label(0,5,3)
sage: t.set_edge_label(0,5,99)
sage: t.set_edge_label(1,2,1000)
sage: t.set_edge_label(3,2,'spam')
sage: t.set_edge_label(2,6,3/2)
sage: t.set_edge_label(0,4,66)
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}, edge_labels=True).plot()
Graphics object consisting of 20 graphics primitives
::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(layout='tree').show()
The tree layout is also useful::
sage: t = DiGraph('JCC???@A??GO??CO??GO??')
sage: t.graphplot(layout='tree', tree_root=0, tree_orientation="up").show()
More examples::
sage: D = DiGraph({0:[1,2,3], 2:[1,4], 3:[0]})
sage: D.graphplot().show()
sage: D = DiGraph(multiedges=True, sparse=True)
sage: for i in range(5):
... D.add_edge((i,i+1,'a'))
... D.add_edge((i,i-1,'b'))
sage: D.graphplot(edge_labels=True,edge_colors=D._color_by_label()).plot()
Graphics object consisting of 34 graphics primitives
sage: g = Graph({}, loops=True, multiedges=True, sparse=True)
sage: g.add_edges([(0,0,'a'),(0,0,'b'),(0,1,'c'),(0,1,'d'),
... (0,1,'e'),(0,1,'f'),(0,1,'f'),(2,1,'g'),(2,2,'h')])
sage: g.graphplot(edge_labels=True, color_by_label=True, edge_style='dashed').plot()
Graphics object consisting of 22 graphics primitives
The ``edge_style`` option may be provided in the short format too::
sage: g.graphplot(edge_labels=True, color_by_label=True, edge_style='--').plot()
Graphics object consisting of 22 graphics primitives
TESTS:
Make sure that show options work with plot also::
sage: g = Graph({})
sage: g.plot(title='empty graph', axes=True)
Graphics object consisting of 0 graphics primitives
Check for invalid inputs::
sage: p = graphs.PetersenGraph().plot(egabrag='garbage')
Traceback (most recent call last):
...
ValueError: Invalid input 'egabrag=garbage'
Make sure that no graphics primitive is clipped::
sage: tadpole = Graph({0:[0,1]}).plot()
sage: bbox = tadpole.get_minmax_data()
sage: for part in tadpole:
....: part_bbox = part.get_minmax_data()
....: assert bbox['xmin'] <= part_bbox['xmin'] <= part_bbox['xmax'] <= bbox['xmax']
....: assert bbox['ymin'] <= part_bbox['ymin'] <= part_bbox['ymax'] <= bbox['ymax']
"""
G = Graphics()
options = self._options.copy()
options.update(kwds)
G._set_extra_kwds(Graphics._extract_kwds_for_show(options))
# Check the arguments
for o in options:
if o not in graphplot_options and o not in G._extra_kwds:
raise ValueError("Invalid input '{}={}'".format(o, options[o]))
for comp in self._plot_components.values():
if not isinstance(comp, list):
G += comp
else:
for item in comp:
G += item
if self._options['graph_border']:
xmin = G.xmin()
xmax = G.xmax()
ymin = G.ymin()
ymax = G.ymax()
dx = (xmax - xmin) / 10.0
dy = (ymax - ymin) / 10.0
border = (line([(xmin - dx, ymin - dy), (xmin - dx, ymax + dy),
(xmax + dx, ymax + dy), (xmax + dx, ymin - dy),
(xmin - dx, ymin - dy)],
thickness=1.3))
border.axes_range(xmin=(xmin - dx),
xmax=(xmax + dx),
ymin=(ymin - dy),
ymax=(ymax + dy))
G += border
G.set_aspect_ratio(1)
G.axes(False)
return G
def draw_funddom_d(coset_reps, format="MP", z0=I, verbose=0):
r""" Draw a fundamental domain for self in the circle model
INPUT:
- ''format'' -- (default 'Disp') How to present the f.d.
= 'S' -- Display directly on the screen
- z0 -- (default I) the upper-half plane is mapped to the disk by z-->(z-z0)/(z-z0.conjugate())
EXAMPLES::
sage: G=MySubgroup(Gamma0(3))
sage: G._draw_funddom_d()
"""
# The fundamental domain consists of copies of the standard fundamental domain
pi = RR.pi()
from sage.plot.plot import (Graphics, line)
g = Graphics()
bdcirc = _circ_arc(0, 2 * pi, 0, 1, 1000)
g = g + bdcirc
# Corners
x1 = -RR(0.5)
y1 = RR(sqrt(3) / 2)
x2 = RR(0.5)
y2 = RR(sqrt(3) / 2)
z_inf = 1
l1 = _geodesic_between_two_points_d(x1, y1, x1, infinity)
l2 = _geodesic_between_two_points_d(x2, y2, x2, infinity)
c0 = _geodesic_between_two_points_d(x1, y1, x2, y2)
tri = c0 + l1 + l2
g = g + tri
for A in coset_reps:
a, b, c, d = A
if a == 1 and b == 0 and c == 0 and d == 1:
continue
if a < 0:
a = -a
b = -b
c = -c
d = -d
if verbose > 0:
print "a,b,c,d=", a, b, c, d
if c == 0: # then this is easier
l1 = _geodesic_between_two_points_d(x1 + b, y1, x1 + b, infinity)
l2 = _geodesic_between_two_points_d(x2 + b, y2, x2 + b, infinity)
c0 = _geodesic_between_two_points_d(x1 + b, y1, x2 + b, y2)
# c0=line(L0); l1=line(L1); l2=line(L2); l3=line(L3)
tri = c0 + l1 + l2
g = g + tri
else:
den = (c * x1 + d)**2 + c**2 * y1**2
x1_t = (a * c * (x1**2 + y1**2) +
(a * d + b * c) * x1 + b * d) / den
y1_t = y1 / den
den = (c * x2 + d)**2 + c**2 * y2**2
x2_t = (a * c * (x2**2 + y2**2) +
(a * d + b * c) * x2 + b * d) / den
y2_t = y2 / den
inf_t = a / c
if verbose > 0:
print "x1_t=", x1_t
print "y1_t=", y1_t
print "x2_t=", x2_t
print "y2_t=", y2_t
print "inf_t=", inf_t
c0 = _geodesic_between_two_points_d(x1_t, y1_t, x2_t, y2_t)
c1 = _geodesic_between_two_points_d(x1_t, y1_t, inf_t, 1.0)
c2 = _geodesic_between_two_points_d(x2_t, y2_t, inf_t, 1.0)
tri = c0 + c1 + c2
g = g + tri
g.xmax(1)
g.ymax(1)
g.xmin(-1)
g.ymin(-1)
g.set_aspect_ratio(1)
return g
def hyperbolic_regular_polygon(sides, i_angle, center=CC(0,1), **options):
r"""
Return a hyperbolic regular polygon in the upper half model of
Hyperbolic plane given the number of sides, interior angle and
possibly a center.
Type ``?hyperbolic_regular_polygon`` to see all options.
INPUT:
- ``sides`` -- number of sides of the polygon
- ``i_angle`` -- interior angle of the polygon
- ``center`` -- (default: `i`) hyperbolic center point
(complex number) of the polygon
OPTIONS:
- ``alpha`` -- default: 1
- ``fill`` -- default: ``False``
- ``thickness`` -- default: 1
- ``rgbcolor`` -- default: ``'blue'``
- ``linestyle`` -- (default: ``'solid'``) the style of the line,
which can be one of the following:
* ``'dashed'`` or ``'--'``
* ``'dotted'`` or ``':'``
* ``'solid'`` or ``'-'``
* ``'dashdot'`` or ``'-.'``
EXAMPLES:
Show a hyperbolic regular polygon with 6 sides and square angles::
sage: g = hyperbolic_regular_polygon(6, pi/2)
sage: g.plot()
Graphics object consisting of 1 graphics primitive
.. PLOT::
g = hyperbolic_regular_polygon(6, pi/2)
sphinx_plot(g.plot())
With more options::
sage: g = hyperbolic_regular_polygon(6, pi/2, center=3+2*I, fill=True, color='red')
sage: g.plot()
Graphics object consisting of 1 graphics primitive
.. PLOT::
g = hyperbolic_regular_polygon(6, pi/2, center=3+2*I, fill=True, color='red')
sphinx_plot(g.plot())
The code verifies is there exists a hyperbolic regular polygon
with the given data, checking
.. MATH::
A(\mathcal{P}) = \pi(s-2) - s \cdot \alpha > 0,
where `s` is ``sides`` and `\alpha` is ``i_angle`. This raises an error if
the ``i_angle`` is less than the minimum to generate a compact polygon::
sage: hyperbolic_regular_polygon(4, pi/2)
Traceback (most recent call last):
...
ValueError: there exists no hyperbolic regular compact polygon,
for sides=4 the interior angle must be less than 1/2*pi
It is an error to give a center outside the upper half plane in
this model::
sage: from sage.plot.hyperbolic_regular_polygon import hyperbolic_regular_polygon
sage: hyperbolic_regular_polygon(4, pi/4, 1-I)
Traceback (most recent call last):
...
ValueError: center: 1.00000000000000 - 1.00000000000000*I is not
a valid point in the upper half plane model of the hyperbolic plane
"""
g = Graphics()
g._set_extra_kwds(g._extract_kwds_for_show(options))
g.add_primitive(HyperbolicRegularPolygon(sides, i_angle, center, options))
g.set_aspect_ratio(1)
return g
def plot(self, size=[[0],[0]], projection='usual', simple_roots=True, fundamental_weights=True, alcovewalks=[]):
r"""
Return a graphics object built from a space of weight(space/lattice).
There is a different technic to plot if the Cartan type is affine or not.
The graphics returned is a Graphics object.
This function is experimental, and is subject to short term evolutions.
EXAMPLES::
By default, the plot returned has no axes and the ratio between axes is 1.
sage: G = RootSystem(['C',2]).weight_lattice().plot()
sage: G.axes(True)
sage: G.set_aspect_ratio(2)
For a non affine Cartan type, the plot method work for type with 2 generators,
it will draw the hyperlane(line for this dimension) accrow the fundamentals weights.
sage: G = RootSystem(['A',2]).weight_lattice().plot()
sage: G = RootSystem(['B',2]).weight_lattice().plot()
sage: G = RootSystem(['G',2]).weight_lattice().plot()
The plot returned has a size of one fundamental polygon by default. We can
ask plot to give a bigger plot by using the argument size
sage: G = RootSystem(['G',2,1]).weight_space().plot(size = [[0..1],[-1..1]])
sage: G = RootSystem(['A',2,1]).weight_space().plot(size = [[-1..1],[-1..1]])
A very important argument is the projection which will draw the plot. There are
some usual projections is this method. If you want to draw in the plane a very
special Cartan type, Sage will ask you to specify the projection. The projection
is a matrix over a ring. In practice, calcul over float is a good way to draw.
sage: L = RootSystem(['A',2,1]).weight_space()
sage: G = L.plot(projection=matrix(RR, [[0,0.5,-0.5],[0,0.866,0.866]]))
sage: G = RootSystem(['C',2,1]).weight_space().plot()
By default, the plot method draw the simple roots, this can be disabled by setting
the argument simple_roots=False
sage: G = RootSystem(['A',2]).weight_space().plot(simple_roots=False)
By default, the plot method draw the fundamental weights,this can be disabled by
setting the argument fundamental_weights=False
sage: G = RootSystem(['A',2]).weight_space().plot(fundamental_weights=False, simple_roots=False)
There is in a plot an argument to draw alcoves walks. The good way to do this is
to use the crystals theory. the plot method contains only the drawing part...
sage: L = RootSystem(['A',2,1]).weight_space()
sage: G = L.plot(size=[[-1..1],[-1..1]],alcovewalks=[[0,2,0,1,2,1,2,0,2,1]])
"""
from sage.plot.all import Graphics
from sage.plot.line import line
from cartan_type import CartanType
from sage.matrix.constructor import matrix
from sage.rings.all import QQ, RR
from sage.plot.arrow import arrow
from sage.plot.point import point
# We begin with an empty plot G
G = Graphics()
ct = self.cartan_type()
n = ct.n
# Define a set of colors
# TODO : Colors in option ?
colors=[(0,1,0),(1,0,0),(0,0,1),(1,1,0),(0,1,1),(1,0,1)]
# plot the affine types:
if ct.is_affine():
# Check the projection
# TODO : try to have usual_projection for main plotable types
if projection == 'usual':
if ct == CartanType(['A',2,1]):
projection = matrix(RR, [[0,0.5,-0.5],[0,0.866,0.866]])
elif ct == CartanType(['C',2,1]):
projection = matrix(QQ, [[0,1,1],[0,0,1]])
elif ct == CartanType(['G',2,1]):
projection = matrix(RR, [[0,0.5,0],[0,0.866,1.732]])
else:
raise 'There is no usual projection for this Cartan type, you have to give one in argument'
assert(n + 1 == projection.ncols())
assert(2 == projection.nrows())
# Check the size is correct with the lattice
assert(len(size) == n)
# Select the center of the translated fundamental polygon to plot
translation_factors = ct.translation_factors()
simple_roots = self.simple_roots()
translation_vectors = [translation_factors[i]*simple_roots[i] for i in ct.classical().index_set()]
initial = [[]]
for i in range(n):
prod_list = []
for elem in size[i]:
for partial_list in initial:
prod_list.append( [elem]+partial_list );
initial = prod_list;
part_lattice = []
for combinaison in prod_list:
elem_lattice = self.zero()
for i in range(n):
elem_lattice = elem_lattice + combinaison[i]*translation_vectors[i]
part_lattice.append(elem_lattice)
# Get the vertices of the fundamental alcove
fundamental_weights = self.fundamental_weights()
vertices = map(lambda x: (1/x.level())*x, fundamental_weights.list())
# Recup the group which act on the fundamental polygon
classical = self.weyl_group().classical()
for center in part_lattice:
for w in classical:
# for each center of polygon and each element of classical
# parabolic subgroup, we have to draw an alcove.
#first, iterate over pairs of fundamental weights, drawing lines border of polygons:
for i in range(1,n+1):
for j in range(i+1,n+1):
p1=projection*((w.action(vertices[i])).to_vector() + center.to_vector())
p2=projection*((w.action(vertices[j])).to_vector() + center.to_vector())
G+=line([p1,p2],rgbcolor=(0,0,0),thickness=2)
#next, get all lines from point to a fundamental weight, that separe different
#chanber in a same polygon (important: associate a color with a fundamental weight)
pcenter = projection*(center.to_vector())
for i in range(1,n+1):
p3=projection*((w.action(vertices[i])).to_vector() + center.to_vector())
G+=line([p3,pcenter], rgbcolor=colors[n-i+1])
#Draw alcovewalks
#FIXME : The good way to draw this is to use the alcoves walks works made in Cristals
#The code here just draw like example and import the good things.
rho = (1/self.rho().level())*self.rho()
W = self.weyl_group()
for walk in alcovewalks:
target = W.from_reduced_word(walk).action(rho)
for i in range(len(walk)):
walk.pop()
origin = W.from_reduced_word(walk).action(rho)
G+=arrow(projection*(origin.to_vector()),projection*(target.to_vector()), rgbcolor=(0.6,0,0.6), width=1, arrowsize=5)
target = origin
else:
# non affine plot
# Check the projection
# TODO : try to have usual_projection for main plotable types
if projection == 'usual':
if ct == CartanType(['A',2]):
projection = matrix(RR, [[0.5,-0.5],[0.866,0.866]])
elif ct == CartanType(['B',2]):
projection = matrix(QQ, [[1,0],[1,1]])
elif ct == CartanType(['C',2]):
projection = matrix(QQ, [[1,1],[0,1]])
elif ct == CartanType(['G',2]):
projection = matrix(RR, [[0.5,0],[0.866,1.732]])
else:
raise 'There is no usual projection for this Cartan type, you have to give one in argument'
# Get the fundamental weights
fundamental_weights = self.fundamental_weights()
WeylGroup = self.weyl_group()
#Draw not the alcove but the cones delimited by the hyperplanes
#The size of the line depend of the fundamental weights.
pcenter = projection*(self.zero().to_vector())
for w in WeylGroup:
for i in range(1,n+1):
p3=3*projection*((w.action(fundamental_weights[i])).to_vector())
G+=line([p3,pcenter], rgbcolor=colors[n-i+1])
#Draw the simple roots
if simple_roots:
SimpleRoots = self.simple_roots()
if ct.is_affine():
G+=arrow((0,0), projection*(SimpleRoots[0].to_vector()), rgbcolor=(0,0,0))
for j in range(1,n+1):
G+=arrow((0,0),projection*(SimpleRoots[j].to_vector()), rgbcolor=colors[j])
#Draw the fundamental weights
if fundamental_weights:
FundWeight = self.fundamental_weights()
for j in range(1,n+1):
G+=point(projection*(FundWeight[j].to_vector()), rgbcolor=colors[j], pointsize=60)
G.set_aspect_ratio(1)
G.axes(False)
return G
def plot(self,
size=[[0], [0]],
projection='usual',
simple_roots=True,
fundamental_weights=True,
alcovewalks=[]):
r"""
Return a graphics object built from a space of weight(space/lattice).
There is a different technic to plot if the Cartan type is affine or not.
The graphics returned is a Graphics object.
This function is experimental, and is subject to short term evolutions.
EXAMPLES::
By default, the plot returned has no axes and the ratio between axes is 1.
sage: G = RootSystem(['C',2]).weight_lattice().plot()
sage: G.axes(True)
sage: G.set_aspect_ratio(2)
For a non affine Cartan type, the plot method work for type with 2 generators,
it will draw the hyperlane(line for this dimension) accrow the fundamentals weights.
sage: G = RootSystem(['A',2]).weight_lattice().plot()
sage: G = RootSystem(['B',2]).weight_lattice().plot()
sage: G = RootSystem(['G',2]).weight_lattice().plot()
The plot returned has a size of one fundamental polygon by default. We can
ask plot to give a bigger plot by using the argument size
sage: G = RootSystem(['G',2,1]).weight_space().plot(size = [[0..1],[-1..1]])
sage: G = RootSystem(['A',2,1]).weight_space().plot(size = [[-1..1],[-1..1]])
A very important argument is the projection which will draw the plot. There are
some usual projections is this method. If you want to draw in the plane a very
special Cartan type, Sage will ask you to specify the projection. The projection
is a matrix over a ring. In practice, calcul over float is a good way to draw.
sage: L = RootSystem(['A',2,1]).weight_space()
sage: G = L.plot(projection=matrix(RR, [[0,0.5,-0.5],[0,0.866,0.866]]))
sage: G = RootSystem(['C',2,1]).weight_space().plot()
By default, the plot method draw the simple roots, this can be disabled by setting
the argument simple_roots=False
sage: G = RootSystem(['A',2]).weight_space().plot(simple_roots=False)
By default, the plot method draw the fundamental weights,this can be disabled by
setting the argument fundamental_weights=False
sage: G = RootSystem(['A',2]).weight_space().plot(fundamental_weights=False, simple_roots=False)
There is in a plot an argument to draw alcoves walks. The good way to do this is
to use the crystals theory. the plot method contains only the drawing part...
sage: L = RootSystem(['A',2,1]).weight_space()
sage: G = L.plot(size=[[-1..1],[-1..1]],alcovewalks=[[0,2,0,1,2,1,2,0,2,1]])
"""
from sage.plot.all import Graphics
from sage.plot.line import line
from cartan_type import CartanType
from sage.matrix.constructor import matrix
from sage.rings.all import QQ, RR
from sage.plot.arrow import arrow
from sage.plot.point import point
# We begin with an empty plot G
G = Graphics()
ct = self.cartan_type()
n = ct.n
# Define a set of colors
# TODO : Colors in option ?
colors = [(0, 1, 0), (1, 0, 0), (0, 0, 1), (1, 1, 0), (0, 1, 1),
(1, 0, 1)]
# plot the affine types:
if ct.is_affine():
# Check the projection
# TODO : try to have usual_projection for main plotable types
if projection == 'usual':
if ct == CartanType(['A', 2, 1]):
projection = matrix(
RR, [[0, 0.5, -0.5], [0, 0.866, 0.866]])
elif ct == CartanType(['C', 2, 1]):
projection = matrix(QQ, [[0, 1, 1], [0, 0, 1]])
elif ct == CartanType(['G', 2, 1]):
projection = matrix(RR,
[[0, 0.5, 0], [0, 0.866, 1.732]])
else:
raise 'There is no usual projection for this Cartan type, you have to give one in argument'
assert (n + 1 == projection.ncols())
assert (2 == projection.nrows())
# Check the size is correct with the lattice
assert (len(size) == n)
# Select the center of the translated fundamental polygon to plot
translation_factors = ct.translation_factors()
simple_roots = self.simple_roots()
translation_vectors = [
translation_factors[i] * simple_roots[i]
for i in ct.classical().index_set()
]
initial = [[]]
for i in range(n):
prod_list = []
for elem in size[i]:
for partial_list in initial:
prod_list.append([elem] + partial_list)
initial = prod_list
part_lattice = []
for combinaison in prod_list:
elem_lattice = self.zero()
for i in range(n):
elem_lattice = elem_lattice + combinaison[
i] * translation_vectors[i]
part_lattice.append(elem_lattice)
# Get the vertices of the fundamental alcove
fundamental_weights = self.fundamental_weights()
vertices = map(lambda x: (1 / x.level()) * x,
fundamental_weights.list())
# Recup the group which act on the fundamental polygon
classical = self.weyl_group().classical()
for center in part_lattice:
for w in classical:
# for each center of polygon and each element of classical
# parabolic subgroup, we have to draw an alcove.
#first, iterate over pairs of fundamental weights, drawing lines border of polygons:
for i in range(1, n + 1):
for j in range(i + 1, n + 1):
p1 = projection * (
(w.action(vertices[i])).to_vector() +
center.to_vector())
p2 = projection * (
(w.action(vertices[j])).to_vector() +
center.to_vector())
G += line([p1, p2],
rgbcolor=(0, 0, 0),
thickness=2)
#next, get all lines from point to a fundamental weight, that separe different
#chanber in a same polygon (important: associate a color with a fundamental weight)
pcenter = projection * (center.to_vector())
for i in range(1, n + 1):
p3 = projection * (
(w.action(vertices[i])).to_vector() +
center.to_vector())
G += line([p3, pcenter],
rgbcolor=colors[n - i + 1])
#Draw alcovewalks
#FIXME : The good way to draw this is to use the alcoves walks works made in Cristals
#The code here just draw like example and import the good things.
rho = (1 / self.rho().level()) * self.rho()
W = self.weyl_group()
for walk in alcovewalks:
target = W.from_reduced_word(walk).action(rho)
for i in range(len(walk)):
walk.pop()
origin = W.from_reduced_word(walk).action(rho)
G += arrow(projection * (origin.to_vector()),
projection * (target.to_vector()),
rgbcolor=(0.6, 0, 0.6),
width=1,
arrowsize=5)
target = origin
else:
# non affine plot
# Check the projection
# TODO : try to have usual_projection for main plotable types
if projection == 'usual':
if ct == CartanType(['A', 2]):
projection = matrix(RR, [[0.5, -0.5], [0.866, 0.866]])
elif ct == CartanType(['B', 2]):
projection = matrix(QQ, [[1, 0], [1, 1]])
elif ct == CartanType(['C', 2]):
projection = matrix(QQ, [[1, 1], [0, 1]])
elif ct == CartanType(['G', 2]):
projection = matrix(RR, [[0.5, 0], [0.866, 1.732]])
else:
raise 'There is no usual projection for this Cartan type, you have to give one in argument'
# Get the fundamental weights
fundamental_weights = self.fundamental_weights()
WeylGroup = self.weyl_group()
#Draw not the alcove but the cones delimited by the hyperplanes
#The size of the line depend of the fundamental weights.
pcenter = projection * (self.zero().to_vector())
for w in WeylGroup:
for i in range(1, n + 1):
p3 = 3 * projection * (
(w.action(fundamental_weights[i])).to_vector())
G += line([p3, pcenter], rgbcolor=colors[n - i + 1])
#Draw the simple roots
if simple_roots:
SimpleRoots = self.simple_roots()
if ct.is_affine():
G += arrow((0, 0),
projection * (SimpleRoots[0].to_vector()),
rgbcolor=(0, 0, 0))
for j in range(1, n + 1):
G += arrow((0, 0),
projection * (SimpleRoots[j].to_vector()),
rgbcolor=colors[j])
#Draw the fundamental weights
if fundamental_weights:
FundWeight = self.fundamental_weights()
for j in range(1, n + 1):
G += point(projection * (FundWeight[j].to_vector()),
rgbcolor=colors[j],
pointsize=60)
G.set_aspect_ratio(1)
G.axes(False)
return G
def plot(self, **kwds):
"""
Returns a graphics object representing the (di)graph.
INPUT:
The options accepted by this method are to be found in the documentation
of module :mod:`sage.graphs.graph_plot`.
.. NOTE::
See :mod:`the module's documentation <sage.graphs.graph_plot>` for
information on default values of this method.
We can specify some pretty precise plotting of familiar graphs::
sage: from math import sin, cos, pi
sage: P = graphs.PetersenGraph()
sage: d = {'#FF0000':[0,5], '#FF9900':[1,6], '#FFFF00':[2,7], '#00FF00':[3,8], '#0000FF':[4,9]}
sage: pos_dict = {}
sage: for i in range(5):
... x = float(cos(pi/2 + ((2*pi)/5)*i))
... y = float(sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: for i in range(10)[5:]:
... x = float(0.5*cos(pi/2 + ((2*pi)/5)*i))
... y = float(0.5*sin(pi/2 + ((2*pi)/5)*i))
... pos_dict[i] = [x,y]
...
sage: pl = P.graphplot(pos=pos_dict, vertex_colors=d)
sage: pl.show()
Here are some more common graphs with typical options::
sage: C = graphs.CubeGraph(8)
sage: P = C.graphplot(vertex_labels=False, vertex_size=0, graph_border=True)
sage: P.show()
sage: G = graphs.HeawoodGraph().copy(sparse=True)
sage: for u,v,l in G.edges():
... G.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: G.graphplot(edge_labels=True).show()
The options for plotting also work with directed graphs::
sage: D = DiGraph( { 0: [1, 10, 19], 1: [8, 2], 2: [3, 6], 3: [19, 4], 4: [17, 5], 5: [6, 15], 6: [7], 7: [8, 14], 8: [9], 9: [10, 13], 10: [11], 11: [12, 18], 12: [16, 13], 13: [14], 14: [15], 15: [16], 16: [17], 17: [18], 18: [19], 19: []}, implementation='networkx' )
sage: for u,v,l in D.edges():
... D.set_edge_label(u,v,'(' + str(u) + ',' + str(v) + ')')
sage: D.graphplot(edge_labels=True, layout='circular').show()
This example shows off the coloring of edges::
sage: from sage.plot.colors import rainbow
sage: C = graphs.CubeGraph(5)
sage: R = rainbow(5)
sage: edge_colors = {}
sage: for i in range(5):
... edge_colors[R[i]] = []
sage: for u,v,l in C.edges():
... for i in range(5):
... if u[i] != v[i]:
... edge_colors[R[i]].append((u,v,l))
sage: C.graphplot(vertex_labels=False, vertex_size=0, edge_colors=edge_colors).show()
With the ``partition`` option, we can separate out same-color groups
of vertices::
sage: D = graphs.DodecahedralGraph()
sage: Pi = [[6,5,15,14,7],[16,13,8,2,4],[12,17,9,3,1],[0,19,18,10,11]]
sage: D.show(partition=Pi)
Loops are also plotted correctly::
sage: G = graphs.PetersenGraph()
sage: G.allow_loops(True)
sage: G.add_edge(0,0)
sage: G.show()
::
sage: D = DiGraph({0:[0,1], 1:[2], 2:[3]}, loops=True)
sage: D.show()
sage: D.show(edge_colors={(0,1,0):[(0,1,None),(1,2,None)],(0,0,0):[(2,3,None)]})
More options::
sage: pos = {0:[0.0, 1.5], 1:[-0.8, 0.3], 2:[-0.6, -0.8], 3:[0.6, -0.8], 4:[0.8, 0.3]}
sage: g = Graph({0:[1], 1:[2], 2:[3], 3:[4], 4:[0]})
sage: g.graphplot(pos=pos, layout='spring', iterations=0).plot()
sage: G = Graph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
sage: G = DiGraph()
sage: P = G.graphplot().plot()
sage: P.axes()
False
We can plot multiple graphs::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}).plot()
sage: t.set_edge_label(0,1,-7)
sage: t.set_edge_label(0,5,3)
sage: t.set_edge_label(0,5,99)
sage: t.set_edge_label(1,2,1000)
sage: t.set_edge_label(3,2,'spam')
sage: t.set_edge_label(2,6,3/2)
sage: t.set_edge_label(0,4,66)
sage: t.graphplot(heights={0:[0], 1:[4,5,1], 2:[2], 3:[3,6]}, edge_labels=True).plot()
::
sage: T = list(graphs.trees(7))
sage: t = T[3]
sage: t.graphplot(layout='tree').show()
The tree layout is also useful::
sage: t = DiGraph('JCC???@A??GO??CO??GO??')
sage: t.graphplot(layout='tree', tree_root=0, tree_orientation="up").show()
More examples::
sage: D = DiGraph({0:[1,2,3], 2:[1,4], 3:[0]})
sage: D.graphplot().show()
sage: D = DiGraph(multiedges=True, sparse=True)
sage: for i in range(5):
... D.add_edge((i,i+1,'a'))
... D.add_edge((i,i-1,'b'))
sage: D.graphplot(edge_labels=True,edge_colors=D._color_by_label()).plot()
sage: g = Graph({}, loops=True, multiedges=True, sparse=True)
sage: g.add_edges([(0,0,'a'),(0,0,'b'),(0,1,'c'),(0,1,'d'),
... (0,1,'e'),(0,1,'f'),(0,1,'f'),(2,1,'g'),(2,2,'h')])
sage: g.graphplot(edge_labels=True, color_by_label=True, edge_style='dashed').plot()
Wrong input (any input) :trac:`13891`::
sage: graphs.PetersenGraph().graphplot().plot(aertataert=346345345)
doctest:...: DeprecationWarning: This method takes no argument ! You may want to give it as an argument to graphplot instead.
See http://trac.sagemath.org/13891 for details.
<BLANKLINE>
"""
# This method takes NO input
# This has been added in early 2013. Remove it before my death, please.
if kwds:
from sage.misc.superseded import deprecation
deprecation(
13891, "This method takes no argument ! You may want "
"to give it as an argument to graphplot instead.")
G = Graphics()
for comp in self._plot_components.values():
if not isinstance(comp, list):
G += comp
else:
for item in comp:
G += item
G.set_axes_range(*(self._graph._layout_bounding_box(self._pos)))
if self._options['graph_border']:
xmin = G.xmin()
xmax = G.xmax()
ymin = G.ymin()
ymax = G.ymax()
dx = (xmax - xmin) / 10.0
dy = (ymax - ymin) / 10.0
border = (line([(xmin - dx, ymin - dy), (xmin - dx, ymax + dy),
(xmax + dx, ymax + dy), (xmax + dx, ymin - dy),
(xmin - dx, ymin - dy)],
thickness=1.3))
border.axes_range(xmin=(xmin - dx),
xmax=(xmax + dx),
ymin=(ymin - dy),
ymax=(ymax + dy))
G += border
G.set_aspect_ratio(1)
G.axes(False)
G._extra_kwds['axes_pad'] = .05
return G
