def _render_on_subplot(self, subplot):
        """
        Render this arrow in a subplot.  This is the key function that
        defines how this arrow graphics primitive is rendered in
        matplotlib's library.

        EXAMPLES:

        This function implicitly ends up rendering this arrow on 
        a matplotlib subplot::

            sage: arrow((0,1), (2,-1))
        """
        options = self.options()
        head = options.pop('head')
        if head == 0: style = '<|-'
        elif head == 1: style = '-|>'
        elif head == 2: style = '<|-|>'
        else: raise KeyError('head parameter must be one of 0 (start), 1 (end) or 2 (both).')
        width = float(options['width'])
        arrowshorten_end = float(options.get('arrowshorten',0))/2.0+width*2
        arrowsize = float(options.get('arrowsize',5))
        head_width=arrowsize
        head_length=arrowsize*2.0
        color = to_mpl_color(options['rgbcolor'])
        from matplotlib.patches import FancyArrowPatch
        p = FancyArrowPatch((self.xtail, self.ytail), (self.xhead, self.yhead),
                            lw=width, arrowstyle='%s,head_width=%s,head_length=%s'%(style,head_width, head_length), 
                            shrinkA=arrowshorten_end, shrinkB=arrowshorten_end,
                            fc=color, ec=color, linestyle=options['linestyle'])
        p.set_zorder(options['zorder'])
        p.set_label(options['legend_label'])
        subplot.add_patch(p)
        return p

    def _render_on_subplot(self, subplot):
        """
        Render this arrow in a subplot.  This is the key function that
        defines how this arrow graphics primitive is rendered in
        matplotlib's library.

        EXAMPLES:

        This function implicitly ends up rendering this arrow on 
        a matplotlib subplot::

            sage: arrow((0,1), (2,-1))

        TESTS:

        The length of the ends (shrinkA and shrinkB) should not depend
        on the width of the arrow, because Matplotlib already takes
        this into account. See :trac:`12836`::

            sage: fig = Graphics().matplotlib()
            sage: sp = fig.add_subplot(1,1,1)
            sage: a = arrow((0,0), (1,1))
            sage: b = arrow((0,0), (1,1), width=20)
            sage: p1 = a[0]._render_on_subplot(sp)
            sage: p2 = b[0]._render_on_subplot(sp)
            sage: p1.shrinkA == p2.shrinkA
            True
            sage: p1.shrinkB == p2.shrinkB
            True

        """
        options = self.options()
        head = options.pop('head')
        if head == 0: style = '<|-'
        elif head == 1: style = '-|>'
        elif head == 2: style = '<|-|>'
        else: raise KeyError('head parameter must be one of 0 (start), 1 (end) or 2 (both).')
        width = float(options['width'])
        arrowshorten_end = float(options.get('arrowshorten',0))/2.0
        arrowsize = float(options.get('arrowsize',5))
        head_width=arrowsize
        head_length=arrowsize*2.0
        color = to_mpl_color(options['rgbcolor'])
        from matplotlib.patches import FancyArrowPatch
        p = FancyArrowPatch((self.xtail, self.ytail), (self.xhead, self.yhead),
                            lw=width, arrowstyle='%s,head_width=%s,head_length=%s'%(style,head_width, head_length), 
                            shrinkA=arrowshorten_end, shrinkB=arrowshorten_end,
                            fc=color, ec=color, linestyle=options['linestyle'])
        p.set_zorder(options['zorder'])
        p.set_label(options['legend_label'])
        subplot.add_patch(p)
        return p

    def _render_on_subplot(self, subplot):
        """
        Render this arrow in a subplot.  This is the key function that
        defines how this arrow graphics primitive is rendered in
        matplotlib's library.

        EXAMPLES::

        This function implicitly ends up rendering this arrow on a matplotlib subplot:
            sage: arrow(path=[[(0,1), (2,-1), (4,5)]])
        """
        from sage.plot.misc import get_matplotlib_linestyle

        options = self.options()
        width = float(options['width'])
        head = options.pop('head')
        if head == 0: style = '<|-'
        elif head == 1: style = '-|>'
        elif head == 2: style = '<|-|>'
        else: raise KeyError('head parameter must be one of 0 (start), 1 (end) or 2 (both).')
        arrowsize = float(options.get('arrowsize',5))
        head_width=arrowsize
        head_length=arrowsize*2.0
        color = to_mpl_color(options['rgbcolor'])
        from matplotlib.patches import FancyArrowPatch
        from matplotlib.path import Path
        bpath = Path(self.vertices, self.codes)
        p = FancyArrowPatch(path=bpath,
                            lw=width, arrowstyle='%s,head_width=%s,head_length=%s'%(style,head_width, head_length),
                            fc=color, ec=color)
        p.set_linestyle(get_matplotlib_linestyle(options['linestyle'],return_type='long'))
        p.set_zorder(options['zorder'])
        p.set_label(options['legend_label'])
        subplot.add_patch(p)
        return p

    def _render_on_subplot(self, subplot):
        """
        Render this arrow in a subplot.  This is the key function that
        defines how this arrow graphics primitive is rendered in
        matplotlib's library.

        EXAMPLES::

        This function implicitly ends up rendering this arrow on a matplotlib subplot:
            sage: arrow(path=[[(0,1), (2,-1), (4,5)]])
            Graphics object consisting of 1 graphics primitive
        """
        from sage.plot.misc import get_matplotlib_linestyle

        options = self.options()
        width = float(options["width"])
        head = options.pop("head")
        if head == 0:
            style = "<|-"
        elif head == 1:
            style = "-|>"
        elif head == 2:
            style = "<|-|>"
        else:
            raise KeyError("head parameter must be one of 0 (start), 1 (end) or 2 (both).")
        arrowsize = float(options.get("arrowsize", 5))
        head_width = arrowsize
        head_length = arrowsize * 2.0
        color = to_mpl_color(options["rgbcolor"])
        from matplotlib.patches import FancyArrowPatch
        from matplotlib.path import Path

        bpath = Path(self.vertices, self.codes)
        p = FancyArrowPatch(
            path=bpath,
            lw=width,
            arrowstyle="%s,head_width=%s,head_length=%s" % (style, head_width, head_length),
            fc=color,
            ec=color,
        )
        p.set_linestyle(get_matplotlib_linestyle(options["linestyle"], return_type="long"))
        p.set_zorder(options["zorder"])
        p.set_label(options["legend_label"])
        subplot.add_patch(p)
        return p

    def _render_on_subplot(self, subplot):
        """
        TESTS:

        A somewhat random plot, but fun to look at::

            sage: x,y = var('x,y')
            sage: contour_plot(x^2-y^3+10*sin(x*y), (x, -4, 4), (y, -4, 4),plot_points=121,cmap='hsv')
        """
        from sage.rings.integer import Integer
        options = self.options()
        fill = options['fill']
        contours = options['contours']
        if options.has_key('cmap'):
            cmap = get_cmap(options['cmap'])
        elif fill or contours is None:
            cmap = get_cmap('gray')
        else:
            if isinstance(contours, (int, Integer)):
                cmap = get_cmap([(i,i,i) for i in xsrange(0,1,1/contours)])
            else:
                l = Integer(len(contours))
                cmap = get_cmap([(i,i,i) for i in xsrange(0,1,1/l)])

        x0,x1 = float(self.xrange[0]), float(self.xrange[1])
        y0,y1 = float(self.yrange[0]), float(self.yrange[1])

        if isinstance(contours, (int, Integer)):
            contours = int(contours)

        CSF=None
        if fill:
            if contours is None:
                CSF=subplot.contourf(self.xy_data_array, cmap=cmap, extent=(x0,x1,y0,y1), label=options['legend_label'])
            else:
                CSF=subplot.contourf(self.xy_data_array, contours, cmap=cmap, extent=(x0,x1,y0,y1),extend='both', label=options['legend_label'])

        linewidths = options.get('linewidths',None)
        if isinstance(linewidths, (int, Integer)):
            linewidths = int(linewidths)
        elif isinstance(linewidths, (list, tuple)):
            linewidths = tuple(int(x) for x in linewidths)
        linestyles = options.get('linestyles',None)
        if contours is None:
            CS = subplot.contour(self.xy_data_array, cmap=cmap, extent=(x0,x1,y0,y1),
                                 linewidths=linewidths, linestyles=linestyles, label=options['legend_label'])
        else:
            CS = subplot.contour(self.xy_data_array, contours, cmap=cmap, extent=(x0,x1,y0,y1),
                            linewidths=linewidths, linestyles=linestyles, label=options['legend_label'])
        if options.get('labels', False):
            label_options = options['label_options']
            label_options['fontsize'] = int(label_options['fontsize'])
            if fill and label_options is None:
                label_options['inline']=False
            subplot.clabel(CS, **label_options)
        if options.get('colorbar', False):
            colorbar_options = options['colorbar_options']
            from matplotlib import colorbar
            cax,kwds=colorbar.make_axes_gridspec(subplot,**colorbar_options)
            if CSF is None:
                cb=colorbar.Colorbar(cax,CS, **kwds)
            else:
                cb=colorbar.Colorbar(cax,CSF, **kwds)
                cb.add_lines(CS)

    def _render_on_subplot(self, subplot):
        r"""
        Render this arrow in a subplot.  This is the key function that
        defines how this arrow graphics primitive is rendered in
        matplotlib's library.

        EXAMPLES:

        This function implicitly ends up rendering this arrow on
        a matplotlib subplot::

            sage: arrow((0,1), (2,-1))

        TESTS:

        The length of the ends (shrinkA and shrinkB) should not depend
        on the width of the arrow, because Matplotlib already takes
        this into account. See :trac:`12836`::

            sage: fig = Graphics().matplotlib()
            sage: sp = fig.add_subplot(1,1,1)
            sage: a = arrow((0,0), (1,1))
            sage: b = arrow((0,0), (1,1), width=20)
            sage: p1 = a[0]._render_on_subplot(sp)
            sage: p2 = b[0]._render_on_subplot(sp)
            sage: p1.shrinkA == p2.shrinkA
            True
            sage: p1.shrinkB == p2.shrinkB
            True

        Dashed arrows should have solid arrowheads,
        :trac:`12852`. This test saves the plot of a dashed arrow to
        an EPS file. Within the EPS file, ``stroke`` will be called
        twice: once to draw the line, and again to draw the
        arrowhead. We check that both calls do not occur while the
        dashed line style is enabled::

            sage: a = arrow((0,0), (1,1), linestyle='dashed')
            sage: filename = tmp_filename(ext='.eps')
            sage: a.save(filename=filename)
            sage: with open(filename, 'r') as f:
            ....:     contents = f.read().replace('\n', ' ')
            sage: two_stroke_pattern = r'setdash.*stroke.*stroke.*setdash'
            sage: import re
            sage: two_stroke_re = re.compile(two_stroke_pattern)
            sage: two_stroke_re.search(contents) is None
            True
        """
        options = self.options()
        head = options.pop('head')
        if head == 0: style = '<|-'
        elif head == 1: style = '-|>'
        elif head == 2: style = '<|-|>'
        else: raise KeyError('head parameter must be one of 0 (start), 1 (end) or 2 (both).')
        width = float(options['width'])
        arrowshorten_end = float(options.get('arrowshorten',0))/2.0
        arrowsize = float(options.get('arrowsize',5))
        head_width=arrowsize
        head_length=arrowsize*2.0
        color = to_mpl_color(options['rgbcolor'])
        from matplotlib.patches import FancyArrowPatch
        p = FancyArrowPatch((self.xtail, self.ytail), (self.xhead, self.yhead),
                            lw=width, arrowstyle='%s,head_width=%s,head_length=%s'%(style,head_width, head_length),
                            shrinkA=arrowshorten_end, shrinkB=arrowshorten_end,
                            fc=color, ec=color, linestyle=options['linestyle'])
        p.set_zorder(options['zorder'])
        p.set_label(options['legend_label'])

        if options['linestyle']!='solid':
            # The next few lines work around a design issue in matplotlib. Currently, the specified
            # linestyle is used to draw both the path and the arrowhead.  If linestyle is 'dashed', this
            # looks really odd.  This code is from Jae-Joon Lee in response to a post to the matplotlib mailing
            # list.  See http://sourceforge.net/mailarchive/forum.php?thread_name=CAG%3DuJ%2Bnw2dE05P9TOXTz_zp-mGP3cY801vMH7yt6vgP9_WzU8w%40mail.gmail.com&forum_name=matplotlib-users

            import matplotlib.patheffects as pe
            class CheckNthSubPath(object):
                def __init__(self, patch, n):
                    """
                    creates an callable object that returns True if the provided
                    path is the n-th path from the patch.
                    """
                    self._patch = patch
                    self._n = n

                def get_paths(self, renderer):
                    self._patch.set_dpi_cor(renderer.points_to_pixels(1.))
                    paths, fillables = self._patch.get_path_in_displaycoord()
                    return paths

                def __call__(self, renderer, gc, tpath, affine, rgbFace):
                    path = self.get_paths(renderer)[self._n]
                    vert1, code1 = path.vertices, path.codes
                    import numpy as np

                    if np.all(vert1 == tpath.vertices) and np.all(code1 == tpath.codes):
                        return True
                    else:
                        return False


#.........这里部分代码省略.........

def disk(point, radius, angle, **options):
    r"""
    A disk (that is, a sector or wedge of a circle) with center
    at a point = `(x,y)` (or `(x,y,z)` and parallel to the
    `xy`-plane) with radius = `r` spanning (in radians)
    angle=`(rad1, rad2)`.

    Type ``disk.options`` to see all options.

    EXAMPLES:

    Make some dangerous disks::

        sage: bl = disk((0.0,0.0), 1, (pi, 3*pi/2), color='yellow')
        sage: tr = disk((0.0,0.0), 1, (0, pi/2), color='yellow')
        sage: tl = disk((0.0,0.0), 1, (pi/2, pi), color='black')
        sage: br = disk((0.0,0.0), 1, (3*pi/2, 2*pi), color='black')
        sage: P  = tl+tr+bl+br
        sage: P.show(xmin=-2,xmax=2,ymin=-2,ymax=2)

    The default aspect ratio is 1.0::

        sage: disk((0.0,0.0), 1, (pi, 3*pi/2)).aspect_ratio()
        1.0

    Another example of a disk::

        sage: bl = disk((0.0,0.0), 1, (pi, 3*pi/2), rgbcolor=(1,1,0))
        sage: bl.show(figsize=[5,5])

    Note that since ``thickness`` defaults to zero, it is best to change
    that option when using ``fill=False``::

        sage: disk((2,3), 1, (pi/4,pi/3), hue=.8, alpha=.3, fill=False, thickness=2)

    The previous two examples also illustrate using ``hue`` and ``rgbcolor``
    as ways of specifying the color of the graphic.

    We can also use this command to plot three-dimensional disks parallel
    to the `xy`-plane::

        sage: d = disk((1,1,3), 1, (pi,3*pi/2), rgbcolor=(1,0,0))
        sage: d
        sage: type(d)
        <type 'sage.plot.plot3d.index_face_set.IndexFaceSet'>

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

        sage: disk((0, 0), 5, (0, pi/2), xmin=0, xmax=5, ymin=0, ymax=5, figsize=(2,2), rgbcolor=(1, 0, 1))
        sage: disk((0, 0), 5, (0, pi/2), rgbcolor=(1, 0, 1)).show(xmin=0, xmax=5, ymin=0, ymax=5, figsize=(2,2)) # These are equivalent

    TESTS:

    Testing that legend labels work right::

        sage: disk((2,4), 3, (pi/8, pi/4), hue=1, legend_label='disk', legend_color='blue')

    We cannot currently plot disks in more than three dimensions::

        sage: d = disk((1,1,1,1), 1, (0,pi))
        Traceback (most recent call last):
        ...
        ValueError: The center point of a plotted disk should have two or three coordinates.
    """
    from sage.plot.all import Graphics
    g = Graphics()

    # Reset aspect_ratio to 'automatic' in case scale is 'semilog[xy]'.
    # Otherwise matplotlib complains.
    scale = options.get('scale', None)
    if isinstance(scale, (list, tuple)):
        scale = scale[0]
    if scale == 'semilogy' or scale == 'semilogx':
        options['aspect_ratio'] = 'automatic'

    g._set_extra_kwds(Graphics._extract_kwds_for_show(options))
    g.add_primitive(Disk(point, radius, angle, options))
    if options['legend_label']:
        g.legend(True)
        g._legend_colors = [options['legend_color']]
    if len(point)==2:
        return g
    elif len(point)==3:
        return g[0].plot3d(z=point[2])
    else:
        raise ValueError, 'The center point of a plotted disk should have two or three coordinates.'

def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options):
    r"""
    ``region_plot`` takes a boolean function of two variables, `f(x,y)`
    and plots the region where f is True over the specified
    ``xrange`` and ``yrange`` as demonstrated below.

    ``region_plot(f, (xmin, xmax), (ymin, ymax), ...)``

    INPUT:

    - ``f`` -- a boolean function of two variables

    - ``(xmin, xmax)`` -- 2-tuple, the range of ``x`` values OR 3-tuple
      ``(x,xmin,xmax)``

    - ``(ymin, ymax)`` -- 2-tuple, the range of ``y`` values OR 3-tuple
      ``(y,ymin,ymax)``

    - ``plot_points``  -- integer (default: 100); number of points to plot
      in each direction of the grid

    - ``incol`` -- a color (default: ``'blue'``), the color inside the region

    - ``outcol`` -- a color (default: ``'white'``), the color of the outside
      of the region

    If any of these options are specified, the border will be shown as indicated,
    otherwise it is only implicit (with color ``incol``) as the border of the
    inside of the region.

     - ``bordercol`` -- a color (default: ``None``), the color of the border
       (``'black'`` if ``borderwidth`` or ``borderstyle`` is specified but not ``bordercol``)

    - ``borderstyle``  -- string (default: 'solid'), one of ``'solid'``,
      ``'dashed'``, ``'dotted'``, ``'dashdot'``, respectively ``'-'``,
      ``'--'``, ``':'``, ``'-.'``.

    - ``borderwidth``  -- integer (default: None), the width of the border in pixels

    - ``legend_label`` -- the label for this item in the legend

    - ``base`` - (default: 10) the base of the logarithm if
      a logarithmic scale is set. This must be greater than 1. The base
      can be also given as a list or tuple ``(basex, basey)``.
      ``basex`` sets the base of the logarithm along the horizontal
      axis and ``basey`` sets the base along the vertical axis.

    - ``scale`` -- (default: ``"linear"``) string. The scale of the axes.
      Possible values are ``"linear"``, ``"loglog"``, ``"semilogx"``,
      ``"semilogy"``.

      The scale can be also be given as single argument that is a list
      or tuple ``(scale, base)`` or ``(scale, basex, basey)``.

      The ``"loglog"`` scale sets both the horizontal and vertical axes to
      logarithmic scale. The ``"semilogx"`` scale sets the horizontal axis
      to logarithmic scale. The ``"semilogy"`` scale sets the vertical axis
      to logarithmic scale. The ``"linear"`` scale is the default value
      when :class:`~sage.plot.graphics.Graphics` is initialized.


    EXAMPLES:

    Here we plot a simple function of two variables::

        sage: x,y = var('x,y')
        sage: region_plot(cos(x^2+y^2) <= 0, (x, -3, 3), (y, -3, 3))

    Here we play with the colors::

        sage: region_plot(x^2+y^3 < 2, (x, -2, 2), (y, -2, 2), incol='lightblue', bordercol='gray')

    An even more complicated plot, with dashed borders::

        sage: region_plot(sin(x)*sin(y) >= 1/4, (x,-10,10), (y,-10,10), incol='yellow', bordercol='black', borderstyle='dashed', plot_points=250)

    A disk centered at the origin::

        sage: region_plot(x^2+y^2<1, (x,-1,1), (y,-1,1))

    A plot with more than one condition (all conditions must be true for the statement to be true)::

        sage: region_plot([x^2+y^2<1, x<y], (x,-2,2), (y,-2,2))

    Since it doesn't look very good, let's increase ``plot_points``::

        sage: region_plot([x^2+y^2<1, x<y], (x,-2,2), (y,-2,2), plot_points=400)

    To get plots where only one condition needs to be true, use a function.
    Using lambda functions, we definitely need the extra ``plot_points``::

        sage: region_plot(lambda x,y: x^2+y^2<1 or x<y, (x,-2,2), (y,-2,2), plot_points=400)

    The first quadrant of the unit circle::

        sage: region_plot([y>0, x>0, x^2+y^2<1], (x,-1.1, 1.1), (y,-1.1, 1.1), plot_points = 400)

    Here is another plot, with a huge border::

        sage: region_plot(x*(x-1)*(x+1)+y^2<0, (x, -3, 2), (y, -3, 3), incol='lightblue', bordercol='gray', borderwidth=10, plot_points=50)
#.........这里部分代码省略.........

def contour_plot(f, xrange, yrange, **options):
    r"""
    ``contour_plot`` takes a function of two variables, `f(x,y)`
    and plots contour lines of the function over the specified
    ``xrange`` and ``yrange`` as demonstrated below.

    ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)``

    INPUT:

    - ``f`` -- a function of two variables

    - ``(xmin, xmax)`` -- 2-tuple, the range of ``x`` values OR 3-tuple
      ``(x,xmin,xmax)``

    - ``(ymin, ymax)`` -- 2-tuple, the range of ``y`` values OR 3-tuple
      ``(y,ymin,ymax)``

    The following inputs must all be passed in as named parameters:

    - ``plot_points``  -- integer (default: 100); number of points to plot
      in each direction of the grid.  For old computers, 25 is fine, but
      should not be used to verify specific intersection points.

    - ``fill`` -- bool (default: ``True``), whether to color in the area
      between contour lines

    - ``cmap`` -- a colormap (default: ``'gray'``), the name of
      a predefined colormap, a list of colors or an instance of a matplotlib
      Colormap. Type: ``import matplotlib.cm; matplotlib.cm.datad.keys()``
      for available colormap names.

    - ``contours`` -- integer or list of numbers (default: ``None``):
      If a list of numbers is given, then this specifies the contour levels
      to use.  If an integer is given, then this many contour lines are
      used, but the exact levels are determined automatically. If ``None``
      is passed (or the option is not given), then the number of contour
      lines is determined automatically, and is usually about 5.

    - ``linewidths`` -- integer or list of integer (default: None), if
      a single integer all levels will be of the width given,
      otherwise the levels will be plotted with the width in the order
      given.  If the list is shorter than the number of contours, then
      the widths will be repeated cyclically.

    - ``linestyles`` -- string or list of strings (default: None), the
      style of the lines to be plotted, one of: ``"solid"``, ``"dashed"``,
      ``"dashdot"``, ``"dotted"``, respectively ``"-"``, ``"--"``,
      ``"-."``, ``":"``.  If the list is shorter than the number of
      contours, then the styles will be repeated cyclically.

    - ``labels`` -- boolean (default: False) Show level labels or not.

      The following options are to adjust the style and placement of
      labels, they have no effect if no labels are shown.

      - ``label_fontsize`` -- integer (default: 9), the font size of the labels.

      - ``label_colors`` -- string or sequence of colors (default:
        None) If a string, gives the name of a single color with which
        to draw all labels.  If a sequence, gives the colors of the
        labels.  A color is a string giving the name of one or a
        3-tuple of floats.

      - ``label_inline`` -- boolean (default: False if fill is True,
        otherwise True), controls whether the underlying contour is
        removed or not.

      - ``label_inline_spacing`` -- integer (default: 3), When inline,
        this is the amount of contour that is removed from each side,
        in pixels.

      - ``label_fmt`` -- a format string (default: "%1.2f"), this is
        used to get the label text from the level.  This can also be a
        dictionary with the contour levels as keys and corresponding
        text string labels as values.  It can also be any callable which
        returns a string when called with a numeric contour level.

    - ``colorbar`` -- boolean (default: False) Show a colorbar or not.

      The following options are to adjust the style and placement of
      colorbars.  They have no effect if a colorbar is not shown.

      - ``colorbar_orientation`` -- string (default: 'vertical'),
        controls placement of the colorbar, can be either 'vertical'
        or 'horizontal'

      - ``colorbar_format`` -- a format string, this is used to format
        the colorbar labels.

      - ``colorbar_spacing`` -- string (default: 'proportional').  If
        'proportional', make the contour divisions proportional to
        values.  If 'uniform', space the colorbar divisions uniformly,
        without regard for numeric values.

    - ``legend_label`` -- the label for this item in the legend

    -  ``region`` - (default: None) If region is given, it must be a function
        of two variables. Only segments of the surface where region(x,y) returns a
        number >0 will be included in the plot.
#.........这里部分代码省略.........

def circle(center, radius, **options):
    """
    Return a circle at a point center = `(x,y)` (or `(x,y,z)` and 
    parallel to the `xy`-plane) with radius = `r`.  Type 
    ``circle.options`` to see all options.
    
    OPTIONS:

    - ``alpha`` - default: 1

    - ``fill`` - default: False

    - ``thickness`` - default: 1

    - ``linestyle`` - default: 'solid' (2D plotting only)

    - ``edgecolor`` - default: 'blue' (2D plotting only)

    - ``facecolor`` - default: 'blue' (2D plotting only, useful only
      if ``fill=True``)

    - ``rgbcolor`` - 2D or 3D plotting.  This option overrides
      ``edgecolor`` and ``facecolor`` for 2D plotting.

    - ``legend_label`` - the label for this item in the legend

    EXAMPLES:

    The default color is blue, but this is easy to change::

        sage: c = circle((1,1), 1)
        sage: c

    ::

        sage: c = circle((1,1), 1, rgbcolor=(1,0,0))
        sage: c

    We can also use this command to plot three-dimensional circles parallel
    to the `xy`-plane::

        sage: c = circle((1,1,3), 1, rgbcolor=(1,0,0))
        sage: c
        sage: type(c)
        <class 'sage.plot.plot3d.base.TransformGroup'>

    To correct the aspect ratio of certain graphics, it is necessary
    to show with a ``figsize`` of square dimensions::

        sage: c.show(figsize=[5,5],xmin=-1,xmax=3,ymin=-1,ymax=3)

    Here we make a more complicated plot, with many circles of different colors::

        sage: g = Graphics()
        sage: step=6; ocur=1/5; paths=16;
        sage: PI = math.pi    # numerical for speed -- fine for graphics
        sage: for r in range(1,paths+1):
        ...       for x,y in [((r+ocur)*math.cos(n), (r+ocur)*math.sin(n)) for n in srange(0, 2*PI+PI/step, PI/step)]:
        ...           g += circle((x,y), ocur, rgbcolor=hue(r/paths))
        ...       rnext = (r+1)^2
        ...       ocur = (rnext-r)-ocur
        ...
        sage: g.show(xmin=-(paths+1)^2, xmax=(paths+1)^2, ymin=-(paths+1)^2, ymax=(paths+1)^2, figsize=[6,6])

    Note that the ``rgbcolor`` option overrides the other coloring options.
    This produces red fill in a blue circle::

        sage: circle((2,3), 1, fill=True, edgecolor='blue')

    This produces an all-green filled circle::

        sage: circle((2,3), 1, fill=True, edgecolor='blue', rgbcolor='green')

    The option ``hue`` overrides *all* other options, so be careful with its use.
    This produces a purplish filled circle::

        sage: circle((2,3), 1, fill=True, edgecolor='blue', rgbcolor='green', hue=.8)

    And a circle with a legend::

        sage: circle((4,5), 1, rgbcolor='yellow', fill=True, legend_label='the sun').show(xmin=0, ymin=0)

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

        sage: circle((0, 0), 2, figsize=[10,10]) # That circle is huge!

    ::

        sage: circle((0, 0), 2).show(figsize=[10,10]) # These are equivalent

    TESTS:

    We cannot currently plot circles in more than three dimensions::

        sage: circle((1,1,1,1), 1, rgbcolor=(1,0,0))
        Traceback (most recent call last):
        ...
        ValueError: The center of a plotted circle should have two or three coordinates.

    The default aspect ratio for a circle is 1.0::
#.........这里部分代码省略.........

    def _render_on_subplot(self, subplot):
        """
        TESTS::

            sage: matrix_plot(random_matrix(RDF, 50), cmap='jet')
            Graphics object consisting of 1 graphics primitive
        """
        options = self.options()
        cmap = get_cmap(options.pop('cmap',None))
        origin=options['origin']

        norm=options['norm']

        if norm=='value':
            import matplotlib
            norm=matplotlib.colors.NoNorm()

        if options['subdivisions']:
            subdiv_options=options['subdivision_options']
            if isinstance(subdiv_options['boundaries'], (list, tuple)):
                rowsub,colsub=subdiv_options['boundaries']
            else:
                rowsub=subdiv_options['boundaries']
                colsub=subdiv_options['boundaries']
            if isinstance(subdiv_options['style'], (list, tuple)):
                rowstyle,colstyle=subdiv_options['style']
            else:
                rowstyle=subdiv_options['style']
                colstyle=subdiv_options['style']
            if rowstyle is None:
                rowstyle=dict()
            if colstyle is None:
                colstyle=dict()

            # Make line objects for subdivisions
            from line import line2d
            lim=self.get_minmax_data()
            # First draw horizontal lines representing row subdivisions
            for y in rowsub:
                l=line2d([(lim['xmin'],y-0.5), (lim['xmax'],y-0.5)], **rowstyle)[0]
                l._render_on_subplot(subplot)
            for x in colsub:
                l=line2d([(x-0.5, lim['ymin']), (x-0.5, lim['ymax'])], **colstyle)[0]
                l._render_on_subplot(subplot)

        if hasattr(self.xy_data_array, 'tocoo'):
            # Sparse matrix -- use spy
            opts=options.copy()
            for opt in ['vmin', 'vmax', 'norm', 'origin','subdivisions','subdivision_options',
                        'colorbar','colorbar_options']:
                del opts[opt]
            if origin=='lower':
                subplot.spy(self.xy_data_array.tocsr()[::-1], **opts)
            else:
                subplot.spy(self.xy_data_array, **opts)
        else:
            opts = dict(cmap=cmap, interpolation='nearest', aspect='equal',
                      norm=norm, vmin=options['vmin'], vmax=options['vmax'],
                      origin=origin,zorder=options.get('zorder',None))
            image=subplot.imshow(self.xy_data_array, **opts)

            if options.get('colorbar', False):
                colorbar_options = options['colorbar_options']
                from matplotlib import colorbar
                cax,kwds=colorbar.make_axes_gridspec(subplot,**colorbar_options)
                cb=colorbar.Colorbar(cax,image, **kwds)

        if origin=='upper':
            subplot.xaxis.tick_top()
        elif origin=='lower':
            subplot.xaxis.tick_bottom()
        subplot.xaxis.set_ticks_position('both') #only tick marks, not tick labels

def polygon2d(points, **options):
    r"""
    Returns a 2-dimensional polygon defined by ``points``.

    Type ``polygon2d.options`` for a dictionary of the default
    options for polygons.  You can change this to change the
    defaults for all future polygons.  Use ``polygon2d.reset()``
    to reset to the default options.

    EXAMPLES:

    We create a purple-ish polygon::

        sage: polygon2d([[1,2], [5,6], [5,0]], rgbcolor=(1,0,1))

    By default, polygons are filled in, but we can make them
    without a fill as well::

        sage: polygon2d([[1,2], [5,6], [5,0]], fill=False)

    In either case, the thickness of the border can be controlled::

        sage: polygon2d([[1,2], [5,6], [5,0]], fill=False, thickness=4, color='orange')

    Some modern art -- a random polygon, with legend::

        sage: v = [(randrange(-5,5), randrange(-5,5)) for _ in range(10)]
        sage: polygon2d(v, legend_label='some form')

    A purple hexagon::

        sage: L = [[cos(pi*i/3),sin(pi*i/3)] for i in range(6)]
        sage: polygon2d(L, rgbcolor=(1,0,1))

    A green deltoid::

        sage: L = [[-1+cos(pi*i/100)*(1+cos(pi*i/100)),2*sin(pi*i/100)*(1-cos(pi*i/100))] for i in range(200)]
        sage: polygon2d(L, rgbcolor=(1/8,3/4,1/2))

    A blue hypotrochoid::

        sage: L = [[6*cos(pi*i/100)+5*cos((6/2)*pi*i/100),6*sin(pi*i/100)-5*sin((6/2)*pi*i/100)] for i in range(200)]
        sage: polygon2d(L, rgbcolor=(1/8,1/4,1/2))

    Another one::

        sage: n = 4; h = 5; b = 2
        sage: L = [[n*cos(pi*i/100)+h*cos((n/b)*pi*i/100),n*sin(pi*i/100)-h*sin((n/b)*pi*i/100)] for i in range(200)]
        sage: polygon2d(L, rgbcolor=(1/8,1/4,3/4))

    A purple epicycloid::

        sage: m = 9; b = 1
        sage: L = [[m*cos(pi*i/100)+b*cos((m/b)*pi*i/100),m*sin(pi*i/100)-b*sin((m/b)*pi*i/100)] for i in range(200)]
        sage: polygon2d(L, rgbcolor=(7/8,1/4,3/4))

    A brown astroid::

        sage: L = [[cos(pi*i/100)^3,sin(pi*i/100)^3] for i in range(200)]
        sage: polygon2d(L, rgbcolor=(3/4,1/4,1/4))

    And, my favorite, a greenish blob::

        sage: L = [[cos(pi*i/100)*(1+cos(pi*i/50)), sin(pi*i/100)*(1+sin(pi*i/50))] for i in range(200)]
        sage: polygon2d(L, rgbcolor=(1/8, 3/4, 1/2))

    This one is for my wife::

        sage: L = [[sin(pi*i/100)+sin(pi*i/50),-(1+cos(pi*i/100)+cos(pi*i/50))] for i in range(-100,100)]
        sage: polygon2d(L, rgbcolor=(1,1/4,1/2))

    One can do the same one with a colored legend label::

        sage: polygon2d(L, color='red', legend_label='For you!', legend_color='red')

    Polygons have a default aspect ratio of 1.0::

        sage: polygon2d([[1,2], [5,6], [5,0]]).aspect_ratio()
        1.0

    AUTHORS:

    - David Joyner (2006-04-14): the long list of examples above.

    """
    from sage.plot.plot import xydata_from_point_list
    from sage.plot.all import Graphics
    if options["thickness"] is None:    # If the user did not specify thickness
        if options["fill"]:                 # If the user chose fill
            options["thickness"] = 0
        else:
            options["thickness"] = 1
    xdata, ydata = xydata_from_point_list(points)
    g = Graphics()

    # Reset aspect_ratio to 'automatic' in case scale is 'semilog[xy]'.
    # Otherwise matplotlib complains.
    scale = options.get('scale', None)
    if isinstance(scale, (list, tuple)):
        scale = scale[0]
#.........这里部分代码省略.........

    def _render_on_subplot(self, subplot):
        """
        TESTS::

            sage: matrix_plot(random_matrix(RDF, 50), cmap='jet')
        """
        options = self.options()
        cmap = get_cmap(options.pop("cmap", None))
        origin = options["origin"]

        norm = options["norm"]

        if norm == "value":
            import matplotlib

            norm = matplotlib.colors.NoNorm()

        if options["subdivisions"]:
            subdiv_options = options["subdivision_options"]
            if isinstance(subdiv_options["boundaries"], (list, tuple)):
                rowsub, colsub = subdiv_options["boundaries"]
            else:
                rowsub = subdiv_options["boundaries"]
                colsub = subdiv_options["boundaries"]
            if isinstance(subdiv_options["style"], (list, tuple)):
                rowstyle, colstyle = subdiv_options["style"]
            else:
                rowstyle = subdiv_options["style"]
                colstyle = subdiv_options["style"]
            if rowstyle is None:
                rowstyle = dict()
            if colstyle is None:
                colstyle = dict()

            # Make line objects for subdivisions
            from line import line2d

            lim = self.get_minmax_data()
            # First draw horizontal lines representing row subdivisions
            for y in rowsub:
                l = line2d([(lim["xmin"], y - 0.5), (lim["xmax"], y - 0.5)], **rowstyle)[0]
                l._render_on_subplot(subplot)
            for x in colsub:
                l = line2d([(x - 0.5, lim["ymin"]), (x - 0.5, lim["ymax"])], **colstyle)[0]
                l._render_on_subplot(subplot)

        if hasattr(self.xy_data_array, "tocoo"):
            # Sparse matrix -- use spy
            opts = options.copy()
            for opt in [
                "vmin",
                "vmax",
                "norm",
                "origin",
                "subdivisions",
                "subdivision_options",
                "colorbar",
                "colorbar_options",
            ]:
                del opts[opt]
            if origin == "lower":
                subplot.spy(self.xy_data_array.tocsr()[::-1], **opts)
            else:
                subplot.spy(self.xy_data_array, **opts)
        else:
            opts = dict(
                cmap=cmap,
                interpolation="nearest",
                aspect="equal",
                norm=norm,
                vmin=options["vmin"],
                vmax=options["vmax"],
                origin=origin,
                zorder=options.get("zorder", None),
            )
            image = subplot.imshow(self.xy_data_array, **opts)

            if options.get("colorbar", False):
                colorbar_options = options["colorbar_options"]
                from matplotlib import colorbar

                cax, kwds = colorbar.make_axes_gridspec(subplot, **colorbar_options)
                cb = colorbar.Colorbar(cax, image, **kwds)

        if origin == "upper":
            subplot.xaxis.tick_top()
        elif origin == "lower":
            subplot.xaxis.tick_bottom()
        subplot.xaxis.set_ticks_position("both")  # only tick marks, not tick labels