def plot_fan_stereographically(rays, walls, northsign=1, north=vector((-1,-1,-1)), right=vector((1,0,0)), colors=None, thickness=None):
    from sage.plot.graphics import Graphics
    from sage.plot.point import point
    from sage.misc.flatten import flatten
    from sage.plot.line import line
    from sage.misc.functional import norm
    
    if colors == None:
        colors = dict([('walls','black'),('rays','red')])

    if thickness == None:
        thickness = dict([('walls',0.5),('rays',20)])


    G = Graphics()
    
    for (u,v) in walls:
        G += _stereo_arc(vector(u),vector(v),vector(u+v),north=northsign*north,right=right,color=colors['walls'],thickness=thickness['walls'],zorder=len(G))
   
    for v in rays: 
        G += point(_stereo_coordinates(vector(v),north=northsign*north,right=right),color=colors['rays'],zorder=len(G),size=thickness['rays'])
    
    G.set_aspect_ratio(1)
    G._show_axes = False
    return G

def legend_3d(hyperplane_arrangement, hyperplane_colors, length):
    r"""
    Create plot of a 3d legend for an arrangement of planes in 3-space.  The
    ``length`` parameter determines whether short or long labels are used in
    the legend.

    INPUT:

    - ``hyperplane_arrangement`` -- a hyperplane arrangement
    
    - ``hyperplane_colors`` -- list of colors

    - ``length`` -- either ``'short'`` or ``'long'``

    OUTPUT:

    - A graphics object.

    EXAMPLES::

        sage: a = hyperplane_arrangements.semiorder(3)
        sage: from sage.geometry.hyperplane_arrangement.plot import legend_3d
        sage: legend_3d(a, list(colors.values())[:6],length='long')
        Graphics object consisting of 6 graphics primitives

        sage: b = hyperplane_arrangements.semiorder(4)
        sage: c = b.essentialization()
        sage: legend_3d(c, list(colors.values())[:12], length='long')
        Graphics object consisting of 12 graphics primitives

        sage: legend_3d(c, list(colors.values())[:12], length='short')
        Graphics object consisting of 12 graphics primitives

        sage: p = legend_3d(c, list(colors.values())[:12], length='short')
        sage: p.set_legend_options(ncol=4)
        sage: type(p)
        <class 'sage.plot.graphics.Graphics'>
    """
    if hyperplane_arrangement.dimension() != 3:
        raise ValueError('arrangements must be in 3-space')
    hyps = hyperplane_arrangement.hyperplanes()
    N = len(hyperplane_arrangement)
    if length == 'short':
        labels = ['  ' + str(i) for i in range(N)]
    else:
        labels = ['  ' + hyps[i]._repr_linear(include_zero=False) for i in
                  range(N)]
    p = Graphics()
    for i in range(N):
        p += line([(0,0),(0,0)], color=hyperplane_colors[i], thickness=8,
                legend_label=labels[i], axes=False)
    p.set_legend_options(title='Hyperplanes', loc='center', labelspacing=0.4, 
            fancybox=True, font_size='x-large', ncol=2)
    p.legend(True)
    return p

    def bezier_path(self):
        """
        Return ``self`` as a Bezier path.

        This is needed to concatenate arcs, in order to
        create hyperbolic polygons.

        EXAMPLES::

            sage: from sage.plot.arc import Arc
            sage: op = {'alpha':1,'thickness':1,'rgbcolor':'blue','zorder':0,
            ....:     'linestyle':'--'}
            sage: Arc(2,3,2.2,2.2,0,2,3,op).bezier_path()
            Graphics object consisting of 1 graphics primitive

            sage: a = arc((0,0),2,1,0,(pi/5,pi/2+pi/12), linestyle="--", color="red")
            sage: b = a[0].bezier_path()
            sage: b[0]
            Bezier path from (1.133..., 0.8237...) to (-0.2655..., 0.9911...)
        """
        from sage.plot.bezier_path import BezierPath
        from sage.plot.graphics import Graphics
        from matplotlib.path import Path
        import numpy as np
        ma = self._matplotlib_arc()
        def theta_stretch(theta, scale):
            theta = np.deg2rad(theta)
            x = np.cos(theta)
            y = np.sin(theta)
            return np.rad2deg(np.arctan2(scale * y, x))
        theta1 = theta_stretch(ma.theta1, ma.width / ma.height)
        theta2 = theta_stretch(ma.theta2, ma.width / ma.height)

        pa = ma
        pa._path = Path.arc(theta1, theta2)
        transform = pa.get_transform().get_matrix()
        cA, cC, cE = transform[0]
        cB, cD, cF = transform[1]
        points = []
        for u in pa._path.vertices:
            x, y = list(u)
            points += [(cA * x + cC * y + cE, cB * x + cD * y + cF)]
        cutlist = [points[0: 4]]
        N = 4
        while N < len(points):
            cutlist += [points[N: N + 3]]
            N += 3
        g = Graphics()
        opt = self.options()
        opt['fill'] = False
        g.add_primitive(BezierPath(cutlist, opt))
        return g

def bar_chart(datalist, **options):
    """
    A bar chart of (currently) one list of numerical data.
    Support for more data lists in progress.

    EXAMPLES:

    A bar_chart with blue bars::

        sage: bar_chart([1,2,3,4])
        Graphics object consisting of 1 graphics primitive

    A bar_chart with thinner bars::

        sage: bar_chart([x^2 for x in range(1,20)], width=0.2)
        Graphics object consisting of 1 graphics primitive

    A bar_chart with negative values and red bars::

        sage: bar_chart([-3,5,-6,11], rgbcolor=(1,0,0))
        Graphics object consisting of 1 graphics primitive

    A bar chart with a legend (it's possible, not necessarily useful)::

        sage: bar_chart([-1,1,-1,1], legend_label='wave')
        Graphics object consisting of 1 graphics primitive

    Extra options will get passed on to show(), as long as they are valid::

        sage: bar_chart([-2,8,-7,3], rgbcolor=(1,0,0), axes=False)
        Graphics object consisting of 1 graphics primitive
        sage: bar_chart([-2,8,-7,3], rgbcolor=(1,0,0)).show(axes=False) # These are equivalent
    """
    dl = len(datalist)
    #if dl > 1:
    #    print "WARNING, currently only 1 data set allowed"
    #    datalist = datalist[0]
    if dl == 3:
        datalist = datalist+[0]
    #bardata = []
    #cnt = 1
    #for pnts in datalist:
        #ind = [i+cnt/dl for i in range(len(pnts))]
        #bardata.append([ind, pnts, xrange, yrange])
        #cnt += 1

    g = Graphics()
    g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
    #TODO: improve below for multiple data sets!
    #cnt = 1
    #for ind, pnts, xrange, yrange in bardata:
        #options={'rgbcolor':hue(cnt/dl),'width':0.5/dl}
    #    g._bar_chart(ind, pnts, xrange, yrange, options=options)
    #    cnt += 1
    #else:
    ind = list(range(len(datalist)))
    g.add_primitive(BarChart(ind, datalist, options=options))
    if options['legend_label']:
        g.legend(True)
    return g

    def plot_n_matrices_eigenvectors(self, n, side='right', color_index=0, draw_line=False):
        r"""
        INPUT:

        - ``n`` -- integer, length
        - ``side`` -- ``'left'`` or ``'right'``, drawing left or right
          eigenvectors
        - ``color_index`` -- 0 for first letter, -1 for last letter
        - ``draw_line`` -- boolean

        EXAMPLES::

            sage: from slabbe.matrix_cocycle import cocycles
            sage: ARP = cocycles.ARP()
            sage: G = ARP.plot_n_matrices_eigenvectors(2)
        """
        from sage.plot.graphics import Graphics
        from sage.plot.point import point
        from sage.plot.line import line
        from sage.plot.text import text
        from sage.plot.colors import hue
        from sage.modules.free_module_element import vector
        from .matrices import M3to2
        R = self.n_matrices_eigenvectors(n)
        L = [(w, M3to2*(a/sum(a)), M3to2*(b/sum(b))) for (w,a,b) in R]
        G = Graphics()
        alphabet = self._language._alphabet
        color_ = dict( (letter, hue(i/float(len(alphabet)))) for i,letter in
                enumerate(alphabet))
        for letter in alphabet:
            L_filtered = [(w,p1,p2) for (w,p1,p2) in L if w[color_index] == letter]
            words,rights,lefts = zip(*L_filtered)
            if side == 'right':
                G += point(rights, color=color_[letter], legend_label=letter)
            elif side == 'left':
                G += point(lefts,  color=color_[letter], legend_label=letter)
            else:
                raise ValueError("side(=%s) should be left or right" % side)

        if draw_line:
            for (a,b) in L:
                G += line([a,b], color='black', linestyle=":")
        G += line([M3to2*vector(a) for a in [(1,0,0), (0,1,0), (0,0,1), (1,0,0)]]) 
        title = "%s eigenvectors, colored by letter w[%s] of cylinder w" % (side, color_index)
        G += text(title, (0.5, 1.05), axis_coords=True)
        G.axes(False)
        return G

    def plot3d(self,depth=None):
        # FIXME: refactor this before publishing
        from sage.plot.graphics import Graphics
        from sage.plot.point import point
        from sage.misc.flatten import flatten
        from sage.plot.plot3d.shapes2 import sphere
        if self._n !=3:
            raise ValueError("Can only 3d plot fans.")
        if depth == None:
            depth = self._depth
        if not self.is_finite() and depth==infinity:
            raise ValueError("For infinite algebras you must specify the depth.")

        colors = dict([(0,'red'),(1,'green'),(2,'blue'),(3,'cyan')])
        G = Graphics()

        roots = self.d_vectors(depth=depth)
        compatible = []
        while roots:
            x = roots.pop()
            for y in roots:
                if self.compatibility_degree(x,y) == 0:
                    compatible.append((x,y))
        for (u,v) in compatible:
            G += _arc3d((_normalize(vector(u)),_normalize(vector(v))),thickness=0.5,color='black')

        for i in range(3):
            orbit = self.ith_orbit(i,depth=depth)
            for j in orbit:
                G += point(_normalize(vector(orbit[j])),color=colors[i],size=10,zorder=len(G.all))

        if self.is_affine():
            tube_vectors=map(vector,flatten(self.affine_tubes()))
            tube_vectors=map(_normalize,tube_vectors)
            for v in tube_vectors:
                G += point(v,color=colors[3],size=10,zorder=len(G.all))
            G += _arc3d((tube_vectors[0],tube_vectors[1]),thickness=5,color='gray',zorder=0)
        
        G += sphere((0,0,0),opacity=0.1,zorder=0)
        G._extra_kwds['frame']=False
        G._extra_kwds['aspect_ratio']=1 
        return G

    def plot2d(self,depth=None):
        # FIXME: refactor this before publishing
        from sage.plot.line import line
        from sage.plot.graphics import Graphics
        if self._n !=2:
            raise ValueError("Can only 2d plot fans.")
        if depth == None:
            depth = self._depth
        if not self.is_finite() and depth==infinity:
            raise ValueError("For infinite algebras you must specify the depth.")

        colors = dict([(0,'red'),(1,'green')])
        G = Graphics()
        for i in range(2):
            orbit = self.ith_orbit(i,depth=depth)
            for j in orbit:
                G += line([(0,0),vector(orbit[j])],color=colors[i],thickness=0.5, zorder=2*j+1)
    
        G.set_aspect_ratio(1)
        G._show_axes = False
        return G

    def bezier_path(self):
        """
        Return ``self`` as a Bezier path.

        This is needed to concatenate arcs, in order to
        create hyperbolic polygons.

        EXAMPLES::

            sage: from sage.plot.arc import Arc
            sage: op = {'alpha':1,'thickness':1,'rgbcolor':'blue','zorder':0,
            ....:     'linestyle':'--'}
            sage: Arc(2,3,2.2,2.2,0,2,3,op).bezier_path()
            Graphics object consisting of 1 graphics primitive

            sage: a = arc((0,0),2,1,0,(pi/5,pi/2+pi/12), linestyle="--", color="red")
            sage: b = a[0].bezier_path()
            sage: b[0]
            Bezier path from (1.618..., 0.5877...) to (-0.5176..., 0.9659...)
        """
        from sage.plot.bezier_path import BezierPath
        from sage.plot.graphics import Graphics
        ma = self._matplotlib_arc()
        transform = ma.get_transform().get_matrix()
        cA, cC, cE = transform[0]
        cB, cD, cF = transform[1]
        points = []
        for u in ma._path.vertices:
            x, y = list(u)
            points += [(cA * x + cC * y + cE, cB * x + cD * y + cF)]
        cutlist = [points[0: 4]]
        N = 4
        while N < len(points):
            cutlist += [points[N: N + 3]]
            N += 3
        g = Graphics()
        opt = self.options()
        opt['fill'] = False
        g.add_primitive(BezierPath(cutlist, opt))
        return g

    def plot(self, m, pointsize=100, thickness=3, axes=False):
        r"""
        Return 2d graphics object contained in the primal box [-m,m]^d.

        INPUT:

        - ``pointsize``, integer (default:``100``),
        - ``thickness``, integer (default:``3``),
        - ``axes``, bool (default:``False``),

        EXAMPLES::

            sage: from slabbe import BondPercolationSample
            sage: S = BondPercolationSample(0.5,2)
            sage: S.plot(2)           # optional long

        It works in 3d!!::

            sage: S = BondPercolationSample(0.5,3)
            sage: S.plot(3, pointsize=10, thickness=1)     # optional long
            Graphics3d Object

        """
        s = ""
        s += "\\begin{tikzpicture}\n"
        s += "[inner sep=0pt,thick,\n"
        s += "reddot/.style={fill=red,draw=red,circle,minimum size=5pt}]\n"
        s += "\\clip %s rectangle %s;\n" % ((-m-.4,-m-.4), (m+.4,m+.4))
        G = Graphics()
        for u in self.cluster_in_box(m+1):
            G += point(u, color='blue', size=pointsize)
        for (u,v) in self.edges_in_box(m+1):
            G += line((u,v), thickness=thickness, alpha=0.8)
        G += text("p=%.3f" % self._p, (0.5,1.03), axis_coords=True, color='black')
        G += circle((0,0), 0.5, color='red', thickness=thickness)
        if self._dimension == 2:
            G.axes(axes)
        return G

    def plot_cluster_fan_stereographically(self, northsign=1, north=None, right=None, colors=None):
        from sage.plot.graphics import Graphics
        from sage.plot.point import point
        from sage.misc.flatten import flatten
        from sage.plot.line import line
        from sage.misc.functional import norm

        if self.rk !=3:
            raise ValueError("Can only stereographically project fans in 3d.")
        if not self.is_finite() and self._depth == infinity:
            raise ValueError("For infinite algebras you must specify the depth.")

        if north == None:
            if self.is_affine():
                north = vector(self.delta())
            else:
                north = vector( (-1,-1,-1) )
        if right == None:
            if self.is_affine():
                right = vector(self.gamma())
            else:
                right = vector( (1,0,0) )
        if colors == None:
            colors = dict([(0,'red'),(1,'green'),(2,'blue'),(3,'cyan'),(4,'yellow')])
        G = Graphics()

        roots = list(self.g_vectors())
        compatible = []
        while roots:
            x = roots.pop()
            for y in roots:
                if self.compatibility_degree(x,y) == 0:
                    compatible.append((x,y))
        for (u,v) in compatible:
            G += _stereo_arc(vector(u),vector(v),vector(u+v),north=northsign*north,right=right,thickness=0.5,color='black')

        for i in range(3):
            orbit = self.ith_orbit(i)
            for j in orbit:
                G += point(_stereo_coordinates(vector(orbit[j]),north=northsign*north,right=right),color=colors[i],zorder=len(G))

        if self.is_affine():
            tube_vectors = map(vector,flatten(self.affine_tubes()))
            for v in tube_vectors:
                G += point(_stereo_coordinates(v,north=northsign*north,right=right),color=colors[3],zorder=len(G))
            if north != vector(self.delta()):
                G += _stereo_arc(tube_vectors[0],tube_vectors[1],vector(self.delta()),north=northsign*north,right=right,thickness=2,color=colors[4],zorder=0)
            else:
                # FIXME: refactor this before publishing
                tube_projections = [
                        _stereo_coordinates(v,north=northsign*north,right=right)
                        for v in tube_vectors ]
                t=min((G.get_minmax_data()['xmax'],G.get_minmax_data()['ymax']))
                G += line([tube_projections[0],tube_projections[0]+t*(_normalize(tube_projections[0]-tube_projections[1]))],thickness=2,color=colors[4],zorder=0)
                G += line([tube_projections[1],tube_projections[1]+t*(_normalize(tube_projections[1]-tube_projections[0]))],thickness=2,color=colors[4],zorder=0)
        G.set_aspect_ratio(1)
        G._show_axes = False
        return G

    def finalize(self, G):
        r"""
        Finalize a root system plot.

        INPUT:

        - ``G`` -- a root system plot or ``0``

        This sets the aspect ratio to 1 and remove the axes. This
        should be called by all the user-level plotting methods of
        root systems. This will become mostly obsolete when
        customization options won't be lost anymore upon addition of
        graphics objects and there will be a proper empty object for
        2D and 3D plots.

        EXAMPLES::

            sage: L = RootSystem(["B",2,1]).ambient_space()
            sage: options = L.plot_parse_options()
            sage: p = L.plot_roots(plot_options=options)
            sage: p += L.plot_coroots(plot_options=options)
            sage: p.axes()
            True
            sage: p = options.finalize(p)
            sage: p.axes()
            False
            sage: p.aspect_ratio()
            1.0

            sage: options = L.plot_parse_options(affine=False)
            sage: p = L.plot_roots(plot_options=options)
            sage: p += point([[1,1,0]])
            sage: p = options.finalize(p)
            sage: p.aspect_ratio()
            [1.0, 1.0, 1.0]

        If the input is ``0``, this returns an empty graphics object::

            sage: type(options.finalize(0))
            <class 'sage.plot.plot3d.base.Graphics3dGroup'>

            sage: options = L.plot_parse_options()
            sage: type(options.finalize(0))
            <class 'sage.plot.graphics.Graphics'>
            sage: list(options.finalize(0))
            []
        """
        from sage.plot.graphics import Graphics
        if self.dimension == 2:
            if G == 0:
                G = Graphics()
            G.set_aspect_ratio(1)
            # TODO: make this customizable
            G.axes(False)
        elif self.dimension == 3:
            if G == 0:
                from sage.plot.plot3d.base import Graphics3dGroup
                G = Graphics3dGroup()
            G.aspect_ratio(1)
            # TODO: Configuration axes
        return G

    def plot(self, chart=None, ambient_coords=None, mapping=None,
             chart_domain=None, fixed_coords=None, ranges=None, max_value=8,
             nb_values=None, steps=None,scale=1, color='blue', parameters=None,
             label_axes=True, **extra_options):
        r"""
        Plot the vector field in a Cartesian graph based on the coordinates
        of some ambient chart.

        The vector field is drawn in terms of two (2D graphics) or three
        (3D graphics) coordinates of a given chart, called hereafter the
        *ambient chart*.
        The vector field's base points `p` (or their images `\Phi(p)` by some
        differentiable mapping `\Phi`) must lie in the ambient chart's domain.

        INPUT:

        - ``chart`` -- (default: ``None``) the ambient chart (see above); if
          ``None``, the default chart of the vector field's domain is used
        - ``ambient_coords`` -- (default: ``None``) tuple containing the 2 or 3
          coordinates of the ambient chart in terms of which the plot is
          performed; if ``None``, all the coordinates of the ambient chart are
          considered
        - ``mapping`` -- (default: ``None``) differentiable mapping `\Phi`
          (instance of
          :class:`~sage.geometry.manifolds.diffmapping.DiffMapping`)
          providing the link between the vector field's domain and
          the ambient chart ``chart``; if ``None``, the identity mapping is
          assumed
        - ``chart_domain`` -- (default: ``None``) chart on the vector
          field's domain to define the points at which vector arrows are to be
          plotted; if ``None``, the default chart of the vector field's domain
          is used
        - ``fixed_coords`` -- (default: ``None``) dictionary with keys the
          coordinates of ``chart_domain`` that are kept fixed and with values
          the value of these coordinates; if ``None``, all the coordinates of
          ``chart_domain`` are used
        - ``ranges`` -- (default: ``None``) dictionary with keys the
          coordinates of ``chart_domain`` to be used and values
          tuples ``(x_min,x_max)`` specifying the
          coordinate range for the plot; if ``None``, the entire coordinate
          range declared during the construction of ``chart_domain`` is
          considered (with ``-Infinity`` replaced by ``-max_value`` and
          ``+Infinity`` by ``max_value``)
        - ``max_value`` -- (default: 8) numerical value substituted to
          ``+Infinity`` if the latter is the upper bound of the range of a
          coordinate for which the plot is performed over the entire coordinate
          range (i.e. for which no specific plot range has been set in
          ``ranges``); similarly ``-max_value`` is the numerical valued
          substituted for ``-Infinity``
        - ``nb_values`` -- (default: ``None``) either an integer or a dictionary
          with keys the coordinates of ``chart_domain`` to be used and values
          the number of values of the coordinate for sampling
          the part of the vector field's domain involved in the plot ; if
          ``nb_values`` is a single integer, it represents the number of
          values for all coordinates; if ``nb_values`` is ``None``, it is set
          to 9 for a 2D plot and to 5 for a 3D plot
        - ``steps`` -- (default: ``None``) dictionary with keys the coordinates
          of ``chart_domain`` to be used and values the step between each
          constant value of the coordinate; if ``None``, the step is computed
          from the coordinate range (specified in ``ranges``) and ``nb_values``.
          On the contrary, if the step is provided for some coordinate, the
          corresponding number of values is deduced from it and the coordinate
          range.
        - ``scale`` -- (default: 1) value by which the lengths of the arrows
          representing the vectors is multiplied
        - ``color`` -- (default: 'blue') color of the arrows representing the
          vectors
        - ``parameters`` -- (default: ``None``) dictionary giving the numerical
          values of the parameters that may appear in the coordinate expression
          of the vector field (see example below)
        - ``label_axes`` -- (default: ``True``) boolean determining whether the
          labels of the coordinate axes of ``chart`` shall be added to the
          graph; can be set to ``False`` if the graph is 3D and must be
          superposed with another graph.
        - ``**extra_options`` -- extra options for the arrow plot, like
          ``linestyle``, ``width`` or ``arrowsize`` (see
          :func:`~sage.plot.arrow.arrow2d` and
          :func:`~sage.plot.plot3d.shapes.arrow3d` for details)

        OUTPUT:

        - a graphic object, either an instance of
          :class:`~sage.plot.graphics.Graphics` for a 2D plot (i.e. based on
          2 coordinates of ``chart``) or an instance of
          :class:`~sage.plot.plot3d.base.Graphics3d` for a 3D plot (i.e.
          based on 3 coordinates of ``chart``)

        EXAMPLES:

        Plot of a vector field on a 2-dimensional manifold::

            sage: Manifold._clear_cache_() # for doctests only
            sage: M = Manifold(2, 'M')
            sage: X.<x,y> = M.chart()
            sage: v = M.vector_field(name='v')
            sage: v[:] = -y, x ; v.display()
            v = -y d/dx + x d/dy
            sage: v.plot()
            Graphics object consisting of 80 graphics primitives

#.........这里部分代码省略.........

    def _graphics(self, plot_curve, ambient_coords, thickness=1,
                  aspect_ratio='automatic', color='red', style='-',
                  label_axes=True):
        r"""
        Plot a 2D or 3D curve in a Cartesian graph with axes labeled by
        the ambient coordinates; it is invoked by the methods
        :meth:`plot` of
        :class:`~sage.manifolds.differentiable.curve.DifferentiableCurve`,
        and its subclasses
        (:class:`~sage.manifolds.differentiable.integrated_curve.IntegratedCurve`,
        :class:`~sage.manifolds.differentiable.integrated_curve.IntegratedAutoparallelCurve`,
        and
        :class:`~sage.manifolds.differentiable.integrated_curve.IntegratedGeodesic`).

        TESTS::

            sage: M = Manifold(2, 'R^2')
            sage: X.<x,y> = M.chart()
            sage: R.<t> = RealLine()
            sage: c = M.curve([cos(t), sin(t)], (t, 0, 2*pi), name='c')
            sage: graph = c._graphics([[1,2], [3,4]], [x,y])
            sage: graph._objects[0].xdata == [1,3]
            True
            sage: graph._objects[0].ydata == [2,4]
            True
            sage: graph._objects[0]._options['thickness'] == 1
            True
            sage: graph._extra_kwds['aspect_ratio'] == 'automatic'
            True
            sage: graph._objects[0]._options['rgbcolor'] == 'red'
            True
            sage: graph._objects[0]._options['linestyle'] == '-'
            True
            sage: l = [r'$'+latex(x)+r'$', r'$'+latex(y)+r'$']
            sage: graph._extra_kwds['axes_labels'] == l
            True

        """

        from sage.plot.graphics import Graphics
        from sage.plot.line import line
        from sage.manifolds.utilities import set_axes_labels


        #
        # The plot
        #
        n_pc = len(ambient_coords)
        resu = Graphics()
        resu += line(plot_curve, color=color, linestyle=style,
                     thickness=thickness)
        if n_pc == 2:  # 2D graphic
            resu.set_aspect_ratio(aspect_ratio)
            if label_axes:
                # We update the dictionary _extra_kwds (options to be passed
                # to show()), instead of using the method
                # Graphics.axes_labels() since the latter is not robust w.r.t.
                # graph addition
                resu._extra_kwds['axes_labels'] = [r'$'+latex(pc)+r'$'
                                                   for pc in ambient_coords]
        else: # 3D graphic
            if aspect_ratio == 'automatic':
                aspect_ratio = 1
            resu.aspect_ratio(aspect_ratio)
            if label_axes:
                labels = [str(pc) for pc in ambient_coords]
                resu = set_axes_labels(resu, *labels)
        return resu

def plot(hyperplane_arrangement, **kwds):
    r"""
    Return a plot of the hyperplane arrangement.  

    If the arrangement is in 4 dimensions but inessential, a plot of
    the essentialization is returned.

    .. NOTE::

        This function is available as the
        :meth:`~sage.geometry.hyperplane_arrangement.arrangement.HyperplaneArrangementElement.plot`
        method of hyperplane arrangements. You should not call this
        function directly, only through the method.

    INPUT:

    - ``hyperplane_arrangement`` -- the hyperplane arrangement to plot

    - ``**kwds`` -- plot options: see
      :mod:`sage.geometry.hyperplane_arrangement.plot`.

    OUTPUT:
    
    A graphics object of the plot.

    EXAMPLES::

        sage: B = hyperplane_arrangements.semiorder(4)
        sage: B.plot()
        Displaying the essentialization.
        Graphics3d Object
    """
    N = len(hyperplane_arrangement)
    dim = hyperplane_arrangement.dimension()
    if hyperplane_arrangement.base_ring().characteristic() != 0:
        raise NotImplementedError('must be a field of characteristic 0')
    elif dim == 4:
        if not hyperplane_arrangement.is_essential():
            print('Displaying the essentialization.')
            hyperplane_arrangement = hyperplane_arrangement.essentialization()
    elif dim not in [1,2,3]: # revise to handle 4d
        return # silently
    # handle extra keywords
    if 'hyperplane_colors' in kwds:
        hyp_colors = kwds.pop('hyperplane_colors')
        if not isinstance(hyp_colors, list): # we assume its a single color then
            hyp_colors = [hyp_colors] * N
    else:
        HSV_tuples = [(i*1.0/N, 0.8, 0.9) for i in range(N)]
        hyp_colors = [hsv_to_rgb(*x) for x in HSV_tuples]
    if 'hyperplane_labels' in kwds:
        hyp_labels = kwds.pop('hyperplane_labels')
        has_hyp_label = True
        if not isinstance(hyp_labels, list): # we assume its a boolean then
            hyp_labels = [hyp_labels] * N
        relabeled = []
        for i in range(N):
            if hyp_labels[i] in [True,'long']:
                relabeled.append(True)
            else:
                relabeled.append(str(i))
        hyp_labels = relabeled
    else:
        has_hyp_label = False
    if 'label_colors' in kwds:
        label_colors = kwds.pop('label_colors')
        has_label_color = True
        if not isinstance(label_colors, list): # we assume its a single color then
            label_colors = [label_colors] * N
    else:
        has_label_color = False
    if 'label_fontsize' in kwds:
        label_fontsize = kwds.pop('label_fontsize')
        has_label_fontsize = True
        if not isinstance(label_fontsize, list): # we assume its a single size then
            label_fontsize = [label_fontsize] * N
    else:
        has_label_fontsize = False
    if 'label_offsets' in kwds:
        has_offsets = True
        offsets = kwds.pop('label_offsets')
    else:
        has_offsets = False # give default values below
    hyperplane_legend = kwds.pop('hyperplane_legend', 'long' if dim < 3 else False)
    if 'hyperplane_opacities' in kwds:
        hyperplane_opacities = kwds.pop('hyperplane_opacities')
        has_opacity = True
        if not isinstance(hyperplane_opacities, list): # we assume a single number then
            hyperplane_opacities = [hyperplane_opacities] * N
    else:
        has_opacity = False
    point_sizes = kwds.pop('point_sizes', 50)
    if not isinstance(point_sizes, list):
        point_sizes = [point_sizes] * N
    if 'ranges' in kwds:
        ranges_set = True
        ranges = kwds.pop('ranges')
        if not type(ranges) in [list,tuple]: # ranges is a single number
            ranges = [ranges] * N
        # So ranges is some type of list.
#.........这里部分代码省略.........

    def plot(self, chart=None, ambient_coords=None, mapping=None,
             chart_domain=None, fixed_coords=None, ranges=None,
             number_values=None, steps=None,
             parameters=None, label_axes=True, **extra_options):
        r"""
        Plot the vector field in a Cartesian graph based on the coordinates
        of some ambient chart.

        The vector field is drawn in terms of two (2D graphics) or three
        (3D graphics) coordinates of a given chart, called hereafter the
        *ambient chart*.
        The vector field's base points `p` (or their images `\Phi(p)` by some
        differentiable mapping `\Phi`) must lie in the ambient chart's domain.

        INPUT:

        - ``chart`` -- (default: ``None``) the ambient chart (see above); if
          ``None``, the default chart of the vector field's domain is used

        - ``ambient_coords`` -- (default: ``None``) tuple containing the 2
          or 3 coordinates of the ambient chart in terms of which the plot
          is performed; if ``None``, all the coordinates of the ambient
          chart are considered

        - ``mapping`` -- :class:`~sage.manifolds.differentiable.diff_map.DiffMap`
          (default: ``None``); differentiable map `\Phi` providing the link
          between the vector field's domain and the ambient chart ``chart``;
          if ``None``, the identity map is assumed

        - ``chart_domain`` -- (default: ``None``) chart on the vector field's
          domain to define the points at which vector arrows are to be plotted;
          if ``None``, the default chart of the vector field's domain is used

        - ``fixed_coords`` -- (default: ``None``) dictionary with keys the
          coordinates of ``chart_domain`` that are kept fixed and with values
          the value of these coordinates; if ``None``, all the coordinates of
          ``chart_domain`` are used

        - ``ranges`` -- (default: ``None``) dictionary with keys the
          coordinates of ``chart_domain`` to be used and values tuples
          ``(x_min, x_max)`` specifying the coordinate range for the plot;
          if ``None``, the entire coordinate range declared during the
          construction of ``chart_domain`` is considered (with ``-Infinity``
          replaced by ``-max_range`` and ``+Infinity`` by ``max_range``)

        - ``number_values`` -- (default: ``None``) either an integer or a
          dictionary with keys the coordinates of ``chart_domain`` to be
          used and values the number of values of the coordinate for sampling
          the part of the vector field's domain involved in the plot ; if
          ``number_values`` is a single integer, it represents the number of
          values for all coordinates; if ``number_values`` is ``None``, it is
          set to 9 for a 2D plot and to 5 for a 3D plot

        - ``steps`` -- (default: ``None``) dictionary with keys the
          coordinates of ``chart_domain`` to be used and values the step
          between each constant value of the coordinate; if ``None``, the
          step is computed from the coordinate range (specified in ``ranges``)
          and ``number_values``; on the contrary, if the step is provided
          for some coordinate, the corresponding number of values is deduced
          from it and the coordinate range

        - ``parameters`` -- (default: ``None``) dictionary giving the numerical
          values of the parameters that may appear in the coordinate expression
          of the vector field (see example below)

        - ``label_axes`` -- (default: ``True``) boolean determining whether
          the labels of the coordinate axes of ``chart`` shall be added to
          the graph; can be set to ``False`` if the graph is 3D and must be
          superposed with another graph

        - ``color`` -- (default: 'blue') color of the arrows representing
          the vectors

        - ``max_range`` -- (default: 8) numerical value substituted to
          ``+Infinity`` if the latter is the upper bound of the range of a
          coordinate for which the plot is performed over the entire coordinate
          range (i.e. for which no specific plot range has been set in
          ``ranges``); similarly ``-max_range`` is the numerical valued
          substituted for ``-Infinity``

        - ``scale`` -- (default: 1) value by which the lengths of the arrows
          representing the vectors is multiplied

        - ``**extra_options`` -- extra options for the arrow plot, like
          ``linestyle``, ``width`` or ``arrowsize`` (see
          :func:`~sage.plot.arrow.arrow2d` and
          :func:`~sage.plot.plot3d.shapes.arrow3d` for details)

        OUTPUT:

        - a graphic object, either an instance of
          :class:`~sage.plot.graphics.Graphics` for a 2D plot (i.e. based on
          2 coordinates of ``chart``) or an instance of
          :class:`~sage.plot.plot3d.base.Graphics3d` for a 3D plot (i.e.
          based on 3 coordinates of ``chart``)

        EXAMPLES:

        Plot of a vector field on a 2-dimensional manifold::

#.........这里部分代码省略.........

    def plot(self,radius=1, orientation=1, cyclic_order_0=None, cyclic_order_1=None,verbose=False):

        """Plot the set of ideal curves on the surface S=S(g,1) of genus g with
        one puncture.

        The free group has rank N=2g, the trees T0 and T1 are roses
        transverse to a maximal set of ideal curves on S. The convex
        core is transverse to the two collections of curves: vertices
        are connected components of the complement of the union of the
        two sets of curves, edges are arcs separating two regions and
        squares are around intersections points of curves.

        For instance T0 can be set to be the rose with the trivial
        marking, while T1 is obtained from T0 by applying a mapping
        class (and not a general automorphism). The embedding of the
        mapping class group is that generated by the
        ``surface_dehn_twist()`` method of the ``FreeGroup`` class.

        The set of ideal curves of T0 is drawn as the boundary of a
        regular 2N-gone, and the set of ideal curves of T1 is drawn
        inside this 2N-gone.

        INPUT:

        - ``radius``: (default 1) the radius of the regular 2N-gone
          which is the fondamental domain of the surface.

        -``cyclic_order_0``: (default None) List of edges outgoing
         from the sole vertex of T0 ordered according to the embedding
         in the surface. A typical value in rank 4, compatible with
         the definition of ``FreeGroup.surface_dehn_twist()`` is :
         ['A','B','a','C','D','c','d','b']

        -``cyclic_order_1``: (default None) List of edges outgoing
         from the sole vertex of T1 ordered according to the embedding
         in the surface.

        EXAMPLES::
        
        sage: F=FreeGroup(4)
        sage: phi=mul([F.surface_dehn_twist(i) for i in [2,1,1,4]])
        sage: C=ConvexCore(phi)
        sage: C.plot_ideal_curve_diagram(cyclic_order_0=['A','B','a','C','D','c','d','b'])

        """

        from sage.plot.graphics import Graphics
        from sage.plot.line import Line
        from sage.plot.arrow import Arrow
        
        T0=self.tree(0)
        T1=self.tree(1)
        A0=T0.alphabet()
        N=len(A0)
        A1=T1.alphabet()

        # Let ``self`` be the convex core of trees T0 and T1. T0 and
        # T1 need to be roses. The trees T0 and T1 may be given as
        # embedded inside the surface. In this case the edges outgoing
        # from the sole vertex are cyclically ordered.

        if len(T0.vertices())!=1:
            raise ValueError('The tree on side 0 must be a rose')
        if len(T1.vertices())!=1:
            raise ValueError('The tree on side 1 must be a rose')
            
        
        if cyclic_order_0 is None:
            cyclic_order_0=getattr(T0,'cyclic_order',None)
        if cyclic_order_1 is None:
            cyclic_order_1=getattr(T1,'cyclic_order',None)

        if verbose:
            if cyclic_order_0 is not None:
                print "The tree on side 0 is embedded in the surface:",cyclic_order_0
            else:
                print "The tree on side 0 is not embedded in the surface, we will try to guess an embedding"
            if cyclic_order_1 is not None:
                print "The tree on side 1 is embedded in the surface:",cyclic_order_1
            else:
                print "The tree on side 1 is not embedded in the surface, we will try to guess an embedding"
            
        squares=self.squares()

        # Coherent orientation of the squares
            

        orientation=self.squares_orientation(orientation=orientation,verbose=verbose and verbose>1 and verbose-1)
            
        if verbose:
            print "Orientation of the squares:"
            if verbose>1:
                for i,sq in enumerate(squares):
                    print i,":",sq,":",orientation[i] 

        boundary=self.surface_boundary(orientation=orientation,verbose=verbose and verbose>1 and verbose-1)


        if verbose:
            print "Edges of the boundary:"
#.........这里部分代码省略.........