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_fill_2d(self, **kwds):
"""
Return the filled interior (a polygon) of a polyhedron in 2d.
EXAMPLES::
sage: cps = [i^3 for i in srange(-2,2,1/5)]
sage: p = Polyhedron(vertices = [[(t^2-1)/(t^2+1),2*t/(t^2+1)] for t in cps])
sage: proj = p.projection()
sage: filled_poly = proj.render_fill_2d()
sage: filled_poly.axes_width()
0.8
"""
poly = [polygon2d(self.coordinates_of(p), **kwds)
for p in self.polygons]
return sum(poly)
def render_fill_2d(self, **kwds):
"""
Return the filled interior (a polygon) of a polyhedron in 2d.
EXAMPLES::
sage: cps = [i^3 for i in srange(-2,2,1/5)]
sage: p = Polyhedron(vertices = [[(t^2-1)/(t^2+1),2*t/(t^2+1)] for t in cps])
sage: proj = p.projection()
sage: filled_poly = proj.render_fill_2d()
sage: filled_poly.axes_width()
0.8
"""
poly = [polygon2d(self.coordinates_of(p), **kwds)
for p in self.polygons]
return sum(poly)
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 geomrep(M1, B1=None, lineorders1=None, pd=None, sp=False):
"""
Return a sage graphics object containing geometric representation of
matroid M1.
INPUT:
- ``M1`` -- A matroid.
- ``B1`` -- (optional) A list of elements in ``M1.groundset()`` that
correspond to a basis of ``M1`` and will be placed as vertices of the
triangle in the geometric representation of ``M1``.
- ``lineorders1`` -- (optional) A list of ordered lists of elements of
``M1.grondset()`` such that if a line in geometric representation is
setwise same as any of these then points contained will be traversed in
that order thus overriding internal order deciding heuristic.
- ``pd`` - (optional) A dictionary mapping ground set elements to their
(x,y) positions.
- ``sp`` -- (optional) If True, a positioning dictionary and line orders
will be placed in ``M._cached_info``.
OUTPUT:
A sage graphics object of type <class 'sage.plot.graphics.Graphics'> that
corresponds to the geometric representation of the matroid.
EXAMPLES::
sage: from sage.matroids import matroids_plot_helpers
sage: M=matroids.named_matroids.P7()
sage: G=matroids_plot_helpers.geomrep(M)
sage: G.show(xmin=-2, xmax=3, ymin=-2, ymax=3)
sage: M=matroids.named_matroids.P7()
sage: G=matroids_plot_helpers.geomrep(M,lineorders1=[['f','e','d']])
sage: G.show(xmin=-2, xmax=3, ymin=-2, ymax=3)
.. NOTE::
This method does NOT do any checks.
"""
G = Graphics()
# create lists of loops and parallel elements and simplify given matroid
[M, L, P] = slp(M1, pos_dict=pd, B=B1)
if B1 is None:
B1 = list(M.basis())
M._cached_info = M1._cached_info
if M.rank() == 0:
limits = None
loops = L
looptext = ", ".join([str(l) for l in loops])
rectx = -1
recty = -1
rectw = 0.5 + 0.4*len(loops) + 0.5 # controlled based on len(loops)
recth = 0.6
G += polygon2d([[rectx, recty], [rectx, recty+recth],
[rectx+rectw, recty+recth], [rectx+rectw, recty]],
color='black', fill=False, thickness=4)
G += text(looptext, (rectx+0.5, recty+0.3), color='black',
fontsize=13)
G += point((rectx+0.2, recty+0.3), color=Color('#BDBDBD'), size=300,
zorder=2)
G += text('Loop(s)', (rectx+0.5+0.4*len(loops)+0.1, recty+0.3),
fontsize=13, color='black')
limits = tracklims(limits, [rectx, rectx+rectw], [recty, recty+recth])
G.axes(False)
G.axes_range(xmin=limits[0]-0.5, xmax=limits[1]+0.5,
ymin=limits[2]-0.5, ymax=limits[3]+0.5)
return G
elif M.rank() == 1:
if M._cached_info is not None and \
'plot_positions' in M._cached_info.keys() and \
M._cached_info['plot_positions'] is not None:
pts = M._cached_info['plot_positions']
else:
pts = {}
gnd = sorted(M.groundset())
pts[gnd[0]] = (1, float(2)/3)
G += point((1, float(2)/3), size=300, color=Color('#BDBDBD'), zorder=2)
pt = [1, float(2)/3]
if len(P) == 0:
G += text(gnd[0], (float(pt[0]), float(pt[1])), color='black',
fontsize=13)
pts2 = pts
# track limits [xmin,xmax,ymin,ymax]
pl = [list(x) for x in pts2.values()]
lims = tracklims([None, None, None, None], [pt[0] for pt in pl],
[pt[1] for pt in pl])
elif M.rank() == 2:
nB1 = list(set(list(M.groundset())) - set(B1))
bline = []
for j in nB1:
if M.is_dependent([j, B1[0], B1[1]]):
bline.append(j)
interval = len(bline)+1
if M._cached_info is not None and \
'plot_positions' in M._cached_info.keys() and \
M._cached_info['plot_positions'] is not None:
pts2 = M._cached_info['plot_positions']
else:
pts2 = {}
pts2[B1[0]] = (0, 0)
pts2[B1[1]] = (2, 0)
lpt = list(pts2[B1[0]])
rpt = list(pts2[B1[1]])
for k in range(len(bline)):
cc = (float(1)/interval)*(k+1)
pts2[bline[k]] = (cc*lpt[0]+(1-cc)*rpt[0],
cc*lpt[1]+(1-cc)*rpt[1])
if sp is True:
M._cached_info['plot_positions'] = pts2
# track limits [xmin,xmax,ymin,ymax]
pl = [list(x) for x in pts2.values()]
lims = tracklims([None, None, None, None], [pt[0] for pt in pl],
[pt[1] for pt in pl])
bline.extend(B1)
ptsx, ptsy, x_i, y_i = createline(pts2, bline, lineorders1)
lims = tracklims(lims, x_i, y_i)
G += line(zip(x_i, y_i), color='black', thickness=3, zorder=1)
pels = [p for p in pts2.keys() if any([M1.rank([p, q]) == 1
for q in P])]
allpts = [list(pts2[i]) for i in M.groundset()]
xpts = [float(k[0]) for k in allpts]
ypts = [float(k[1]) for k in allpts]
G += points(zip(xpts, ypts), color=Color('#BDBDBD'), size=300,
zorder=2)
for i in pts2:
if i not in pels:
pt = list(pts2[i])
G += text(i, (float(pt[0]), float(pt[1])), color='black',
fontsize=13)
else:
if M._cached_info is None or \
'plot_positions' not in M._cached_info.keys() or \
M._cached_info['plot_positions'] is None:
(pts, trilines,
nontripts, curvedlines) = it(M1, B1,
list(set(M.groundset())-set(B1)),
list(set(L) | set(P)))
pts2 = addnontripts([B1[0], B1[1], B1[2]], nontripts, pts)
trilines.extend(curvedlines)
else:
pts2 = M._cached_info['plot_positions']
trilines = [list(set(list(x)).difference(L | P))
for x in M1.flats(2)
if len(list(x)) >= 3]
pl = [list(x) for x in pts2.values()]
lims = tracklims([None, None, None, None], [pt[0] for pt in pl],
[pt[1] for pt in pl])
j = 0
for ll in trilines:
if len(ll) >= 3:
ptsx, ptsy, x_i, y_i = createline(pts2, ll, lineorders1)
lims = tracklims(lims, x_i, y_i)
G += line(zip(x_i, y_i), color='black', thickness=3, zorder=1)
pels = [p for p in pts2.keys() if any([M1.rank([p, q]) == 1
for q in P])]
allpts = [list(pts2[i]) for i in M.groundset()]
xpts = [float(k[0]) for k in allpts]
ypts = [float(k[1]) for k in allpts]
G += points(zip(xpts, ypts), color=Color('#BDBDBD'), size=300,
zorder=2)
for i in pts2:
if i not in pels:
pt = list(pts2[i])
G += text(i, (float(pt[0]), float(pt[1])), color='black',
fontsize=13)
if sp is True:
M1._cached_info['plot_positions'] = pts2
M1._cached_info['plot_lineorders'] = lineorders1
# deal with loops and parallel elements
G, lims = addlp(M1, M, L, P, pts2, G, lims)
G.axes(False)
G.axes_range(xmin=lims[0]-0.5, xmax=lims[1]+0.5, ymin=lims[2]-0.5,
ymax=lims[3]+0.5)
return G
def addlp(M, M1, L, P, ptsdict, G=None, limits=None):
"""
Return a graphics object containing loops (in inset) and parallel elements
of matroid.
INPUT:
- ``M`` -- A matroid.
- ``M1`` -- A simple matroid corresponding to ``M``.
- ``L`` -- List of elements in ``M.groundset()`` that are loops of matroid
``M``.
- ``P`` -- List of elements in ``M.groundset()`` not in
``M.simplify.groundset()`` or ``L``.
- ``ptsdict`` -- A dictionary containing elements in ``M.groundset()`` not
necessarily containing elements of ``L``.
- ``G`` -- (optional) A sage graphics object to which loops and parallel
elements of matroid `M` added .
- ``limits``-- (optional) Current axes limits [xmin,xmax,ymin,ymax].
OUTPUT:
A 2-tuple containing:
1. A sage graphics object containing loops and parallel elements of
matroid ``M``
2. axes limits array
EXAMPLES::
sage: from sage.matroids import matroids_plot_helpers
sage: M=Matroid(ring=GF(2), matrix=[[1, 0, 0, 0, 1, 1, 1,0,1],
....: [0, 1, 0, 1, 0, 1, 1,0,0],[0, 0, 1, 1, 1, 0, 1,0,0]])
sage: [M1,L,P]=matroids_plot_helpers.slp(M)
sage: G,lims=matroids_plot_helpers.addlp(M,M1,L,P,{0:(0,0)})
sage: G.show(axes=False)
.. NOTE::
This method does NOT do any checks.
"""
if G is None:
G = Graphics()
# deal with loops
if len(L) > 0:
loops = L
looptext = ", ".join([str(l) for l in loops])
if(limits is None):
rectx = -1
recty = -1
else:
rectx = limits[0]
recty = limits[2]-1
rectw = 0.5 + 0.4*len(loops) + 0.5 # controlled based on len(loops)
recth = 0.6
G += polygon2d([[rectx, recty], [rectx, recty+recth],
[rectx+rectw, recty+recth], [rectx+rectw, recty]],
color='black', fill=False, thickness=4)
G += text(looptext, (rectx+0.5, recty+0.3), color='black',
fontsize=13)
G += point((rectx+0.2, recty+0.3), color=Color('#BDBDBD'), size=300,
zorder=2)
G += text('Loop(s)', (rectx+0.5+0.4*len(loops)+0.1, recty+0.3),
fontsize=13, color='black')
limits = tracklims(limits, [rectx, rectx+rectw], [recty, recty+recth])
# deal with parallel elements
if len(P) > 0:
# create list of lists where inner lists are parallel classes
pcls = []
gnd = sorted(list(M1.groundset()))
for g in gnd:
pcl = [g]
for p in P:
if M.rank([g, p]) == 1:
pcl.extend([p])
pcls.append(pcl)
ext_gnd = list(M.groundset())
for pcl in pcls:
if len(pcl) > 1:
basept = list(ptsdict[pcl[0]])
if len(pcl) <= 2:
# add side by side
ptsdict[pcl[1]] = (basept[0], basept[1]-0.13)
G += points(zip([basept[0]], [basept[1]-0.13]),
color=Color('#BDBDBD'), size=300, zorder=2)
G += text(pcl[0], (float(basept[0]),
float(basept[1])), color='black',
fontsize=13)
G += text(pcl[1], (float(basept[0]),
float(basept[1])-0.13), color='black',
fontsize=13)
limits = tracklims(limits, [basept[0]], [basept[1]-0.13])
else:
# add in a bracket
pce = sorted([str(kk) for kk in pcl])
l = newlabel(set(ext_gnd))
ext_gnd.append(l)
G += text(l+'={ '+", ".join(pce)+' }', (float(basept[0]),
float(basept[1]-0.2)-0.034), color='black',
fontsize=13)
G += text(l, (float(basept[0]),
float(basept[1])), color='black',
fontsize=13)
limits = tracklims(limits, [basept[0]],
[(basept[1]-0.2)-0.034])
return G, limits
def geomrep(M1, B1=None, lineorders1=None, pd=None, sp=False):
"""
Return a sage graphics object containing geometric representation of
matroid M1.
INPUT:
- ``M1`` -- A matroid.
- ``B1`` -- (optional) A list of elements in ``M1.groundset()`` that
correspond to a basis of ``M1`` and will be placed as vertices of the
triangle in the geometric representation of ``M1``.
- ``lineorders1`` -- (optional) A list of ordered lists of elements of
``M1.grondset()`` such that if a line in geometric representation is
setwise same as any of these then points contained will be traversed in
that order thus overriding internal order deciding heuristic.
- ``pd`` - (optional) A dictionary mapping ground set elements to their
(x,y) positions.
- ``sp`` -- (optional) If True, a positioning dictionary and line orders
will be placed in ``M._cached_info``.
OUTPUT:
A sage graphics object of type <class 'sage.plot.graphics.Graphics'> that
corresponds to the geometric representation of the matroid.
EXAMPLES::
sage: from sage.matroids import matroids_plot_helpers
sage: M=matroids.named_matroids.P7()
sage: G=matroids_plot_helpers.geomrep(M)
sage: G.show(xmin=-2, xmax=3, ymin=-2, ymax=3)
sage: M=matroids.named_matroids.P7()
sage: G=matroids_plot_helpers.geomrep(M,lineorders1=[['f','e','d']])
sage: G.show(xmin=-2, xmax=3, ymin=-2, ymax=3)
.. NOTE::
This method does NOT do any checks.
"""
G = Graphics()
# create lists of loops and parallel elements and simplify given matroid
[M, L, P] = slp(M1, pos_dict=pd, B=B1)
if B1 is None:
B1 = list(M.basis())
M._cached_info = M1._cached_info
if M.rank() == 0:
limits = None
loops = L
looptext = ", ".join([str(l) for l in loops])
rectx = -1
recty = -1
rectw = 0.5 + 0.4 * len(loops) + 0.5 # controlled based on len(loops)
recth = 0.6
G += polygon2d(
[[rectx, recty], [rectx, recty + recth],
[rectx + rectw, recty + recth], [rectx + rectw, recty]],
color='black',
fill=False,
thickness=4)
G += text(looptext, (rectx + 0.5, recty + 0.3),
color='black',
fontsize=13)
G += point((rectx + 0.2, recty + 0.3),
color=Color('#BDBDBD'),
size=300,
zorder=2)
G += text('Loop(s)',
(rectx + 0.5 + 0.4 * len(loops) + 0.1, recty + 0.3),
fontsize=13,
color='black')
limits = tracklims(limits, [rectx, rectx + rectw],
[recty, recty + recth])
G.axes(False)
G.axes_range(xmin=limits[0] - 0.5,
xmax=limits[1] + 0.5,
ymin=limits[2] - 0.5,
ymax=limits[3] + 0.5)
return G
elif M.rank() == 1:
if M._cached_info is not None and \
'plot_positions' in M._cached_info.keys() and \
M._cached_info['plot_positions'] is not None:
pts = M._cached_info['plot_positions']
else:
pts = {}
gnd = sorted(M.groundset())
pts[gnd[0]] = (1, float(2) / 3)
G += point((1, float(2) / 3),
size=300,
color=Color('#BDBDBD'),
zorder=2)
pt = [1, float(2) / 3]
if len(P) == 0:
G += text(gnd[0], (float(pt[0]), float(pt[1])),
color='black',
fontsize=13)
pts2 = pts
# track limits [xmin,xmax,ymin,ymax]
pl = [list(x) for x in pts2.values()]
lims = tracklims([None, None, None, None], [pt[0] for pt in pl],
[pt[1] for pt in pl])
elif M.rank() == 2:
nB1 = list(set(list(M.groundset())) - set(B1))
bline = []
for j in nB1:
if M.is_dependent([j, B1[0], B1[1]]):
bline.append(j)
interval = len(bline) + 1
if M._cached_info is not None and \
'plot_positions' in M._cached_info.keys() and \
M._cached_info['plot_positions'] is not None:
pts2 = M._cached_info['plot_positions']
else:
pts2 = {}
pts2[B1[0]] = (0, 0)
pts2[B1[1]] = (2, 0)
lpt = list(pts2[B1[0]])
rpt = list(pts2[B1[1]])
for k in range(len(bline)):
cc = (float(1) / interval) * (k + 1)
pts2[bline[k]] = (cc * lpt[0] + (1 - cc) * rpt[0],
cc * lpt[1] + (1 - cc) * rpt[1])
if sp is True:
M._cached_info['plot_positions'] = pts2
# track limits [xmin,xmax,ymin,ymax]
pl = [list(x) for x in pts2.values()]
lims = tracklims([None, None, None, None], [pt[0] for pt in pl],
[pt[1] for pt in pl])
bline.extend(B1)
ptsx, ptsy, x_i, y_i = createline(pts2, bline, lineorders1)
lims = tracklims(lims, x_i, y_i)
G += line(zip(x_i, y_i), color='black', thickness=3, zorder=1)
pels = [
p for p in pts2.keys() if any([M1.rank([p, q]) == 1 for q in P])
]
allpts = [list(pts2[i]) for i in M.groundset()]
xpts = [float(k[0]) for k in allpts]
ypts = [float(k[1]) for k in allpts]
G += points(zip(xpts, ypts),
color=Color('#BDBDBD'),
size=300,
zorder=2)
for i in pts2:
if i not in pels:
pt = list(pts2[i])
G += text(i, (float(pt[0]), float(pt[1])),
color='black',
fontsize=13)
else:
if M._cached_info is None or \
'plot_positions' not in M._cached_info.keys() or \
M._cached_info['plot_positions'] is None:
(pts, trilines, nontripts,
curvedlines) = it(M1, B1, list(set(M.groundset()) - set(B1)),
list(set(L) | set(P)))
pts2 = addnontripts([B1[0], B1[1], B1[2]], nontripts, pts)
trilines.extend(curvedlines)
else:
pts2 = M._cached_info['plot_positions']
trilines = [
list(set(list(x)).difference(L | P)) for x in M1.flats(2)
if len(list(x)) >= 3
]
pl = [list(x) for x in pts2.values()]
lims = tracklims([None, None, None, None], [pt[0] for pt in pl],
[pt[1] for pt in pl])
j = 0
for ll in trilines:
if len(ll) >= 3:
ptsx, ptsy, x_i, y_i = createline(pts2, ll, lineorders1)
lims = tracklims(lims, x_i, y_i)
G += line(zip(x_i, y_i), color='black', thickness=3, zorder=1)
pels = [
p for p in pts2.keys() if any([M1.rank([p, q]) == 1 for q in P])
]
allpts = [list(pts2[i]) for i in M.groundset()]
xpts = [float(k[0]) for k in allpts]
ypts = [float(k[1]) for k in allpts]
G += points(zip(xpts, ypts),
color=Color('#BDBDBD'),
size=300,
zorder=2)
for i in pts2:
if i not in pels:
pt = list(pts2[i])
G += text(i, (float(pt[0]), float(pt[1])),
color='black',
fontsize=13)
if sp is True:
M1._cached_info['plot_positions'] = pts2
M1._cached_info['plot_lineorders'] = lineorders1
# deal with loops and parallel elements
G, lims = addlp(M1, M, L, P, pts2, G, lims)
G.axes(False)
G.axes_range(xmin=lims[0] - 0.5,
xmax=lims[1] + 0.5,
ymin=lims[2] - 0.5,
ymax=lims[3] + 0.5)
return G
def addlp(M, M1, L, P, ptsdict, G=None, limits=None):
"""
Return a graphics object containing loops (in inset) and parallel elements
of matroid.
INPUT:
- ``M`` -- A matroid.
- ``M1`` -- A simple matroid corresponding to ``M``.
- ``L`` -- List of elements in ``M.groundset()`` that are loops of matroid
``M``.
- ``P`` -- List of elements in ``M.groundset()`` not in
``M.simplify.groundset()`` or ``L``.
- ``ptsdict`` -- A dictionary containing elements in ``M.groundset()`` not
necessarily containing elements of ``L``.
- ``G`` -- (optional) A sage graphics object to which loops and parallel
elements of matroid `M` added .
- ``limits``-- (optional) Current axes limits [xmin,xmax,ymin,ymax].
OUTPUT:
A 2-tuple containing:
1. A sage graphics object containing loops and parallel elements of
matroid ``M``
2. axes limits array
EXAMPLES::
sage: from sage.matroids import matroids_plot_helpers
sage: M=Matroid(ring=GF(2), matrix=[[1, 0, 0, 0, 1, 1, 1,0,1],
....: [0, 1, 0, 1, 0, 1, 1,0,0],[0, 0, 1, 1, 1, 0, 1,0,0]])
sage: [M1,L,P]=matroids_plot_helpers.slp(M)
sage: G,lims=matroids_plot_helpers.addlp(M,M1,L,P,{0:(0,0)})
sage: G.show(axes=False)
.. NOTE::
This method does NOT do any checks.
"""
if G is None:
G = Graphics()
# deal with loops
if len(L) > 0:
loops = L
looptext = ", ".join([str(l) for l in loops])
if (limits is None):
rectx = -1
recty = -1
else:
rectx = limits[0]
recty = limits[2] - 1
rectw = 0.5 + 0.4 * len(loops) + 0.5 # controlled based on len(loops)
recth = 0.6
G += polygon2d(
[[rectx, recty], [rectx, recty + recth],
[rectx + rectw, recty + recth], [rectx + rectw, recty]],
color='black',
fill=False,
thickness=4)
G += text(looptext, (rectx + 0.5, recty + 0.3),
color='black',
fontsize=13)
G += point((rectx + 0.2, recty + 0.3),
color=Color('#BDBDBD'),
size=300,
zorder=2)
G += text('Loop(s)',
(rectx + 0.5 + 0.4 * len(loops) + 0.1, recty + 0.3),
fontsize=13,
color='black')
limits = tracklims(limits, [rectx, rectx + rectw],
[recty, recty + recth])
# deal with parallel elements
if len(P) > 0:
# create list of lists where inner lists are parallel classes
pcls = []
gnd = sorted(list(M1.groundset()))
for g in gnd:
pcl = [g]
for p in P:
if M.rank([g, p]) == 1:
pcl.extend([p])
pcls.append(pcl)
ext_gnd = list(M.groundset())
for pcl in pcls:
if len(pcl) > 1:
basept = list(ptsdict[pcl[0]])
if len(pcl) <= 2:
# add side by side
ptsdict[pcl[1]] = (basept[0], basept[1] - 0.13)
G += points(zip([basept[0]], [basept[1] - 0.13]),
color=Color('#BDBDBD'),
size=300,
zorder=2)
G += text(pcl[0], (float(basept[0]), float(basept[1])),
color='black',
fontsize=13)
G += text(pcl[1],
(float(basept[0]), float(basept[1]) - 0.13),
color='black',
fontsize=13)
limits = tracklims(limits, [basept[0]], [basept[1] - 0.13])
else:
# add in a bracket
pce = sorted([str(kk) for kk in pcl])
l = newlabel(set(ext_gnd))
ext_gnd.append(l)
G += text(
l + '={ ' + ", ".join(pce) + ' }',
(float(basept[0]), float(basept[1] - 0.2) - 0.034),
color='black',
fontsize=13)
G += text(l, (float(basept[0]), float(basept[1])),
color='black',
fontsize=13)
limits = tracklims(limits, [basept[0]],
[(basept[1] - 0.2) - 0.034])
return G, limits
