Graphics objects#

This file contains the definition of the class Graphics. Usually, you don’t call the constructor of this class directly (although you can do it), you would use plot() instead.

AUTHORS:

class sage.plot.graphics.Graphics[source]#

Bases: WithEqualityById, SageObject

The Graphics object is an empty list of graphics objects. It is useful to use this object when initializing a for loop where different graphics object will be added to the empty object.

EXAMPLES:

sage: G = Graphics(); print(G)
Graphics object consisting of 0 graphics primitives
sage: c = circle((1,1), 1)
sage: G += c; print(G)
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> G = Graphics(); print(G)
Graphics object consisting of 0 graphics primitives
>>> c = circle((Integer(1),Integer(1)), Integer(1))
>>> G += c; print(G)
Graphics object consisting of 1 graphics primitive

Here we make a graphic of embedded isosceles triangles, coloring each one with a different color as we go:

sage: h = 10; c = 0.4; p = 0.5
sage: G = Graphics()
sage: for x in srange(1, h+1):                                                  # needs sage.symbolic
....:     l = [[0,x*sqrt(3)],[-x/2,-x*sqrt(3)/2],[x/2,-x*sqrt(3)/2],[0,x*sqrt(3)]]
....:     G += line(l, color=hue(c + p*(x/h)))
sage: G.show(figsize=[5,5])                                                     # needs sage.symbolic

>>> from sage.all import *
>>> h = Integer(10); c = RealNumber('0.4'); p = RealNumber('0.5')
>>> G = Graphics()
>>> for x in srange(Integer(1), h+Integer(1)):                                                  # needs sage.symbolic
...     l = [[Integer(0),x*sqrt(Integer(3))],[-x/Integer(2),-x*sqrt(Integer(3))/Integer(2)],[x/Integer(2),-x*sqrt(Integer(3))/Integer(2)],[Integer(0),x*sqrt(Integer(3))]]
...     G += line(l, color=hue(c + p*(x/h)))
>>> G.show(figsize=[Integer(5),Integer(5)])                                                     # needs sage.symbolic

We can change the scale of the axes in the graphics before displaying.:

sage: G = plot(exp, 1, 10)              # long time                             # needs sage.symbolic
sage: G.show(scale='semilogy')          # long time                             # needs sage.symbolic

>>> from sage.all import *
>>> G = plot(exp, Integer(1), Integer(10))              # long time                             # needs sage.symbolic
>>> G.show(scale='semilogy')          # long time                             # needs sage.symbolic
_rich_repr_(display_manager, **kwds)[source]#

Rich Output Magic Method

See sage.repl.rich_output for details.

EXAMPLES:

sage: from sage.repl.rich_output import get_display_manager
sage: dm = get_display_manager()
sage: g = Graphics()
sage: g._rich_repr_(dm)
OutputImagePng container

>>> from sage.all import *
>>> from sage.repl.rich_output import get_display_manager
>>> dm = get_display_manager()
>>> g = Graphics()
>>> g._rich_repr_(dm)
OutputImagePng container
LEGEND_OPTIONS = {'back_color': 'white', 'borderaxespad': None, 'borderpad': 0.6, 'columnspacing': None, 'fancybox': False, 'font_family': 'sans-serif', 'font_size': 'medium', 'font_style': 'normal', 'font_variant': 'normal', 'font_weight': 'medium', 'handlelength': 0.05, 'handletextpad': 0.5, 'labelspacing': 0.02, 'loc': 'best', 'markerscale': 0.6, 'ncol': 1, 'numpoints': 2, 'shadow': True, 'title': None}#
SHOW_OPTIONS = {'aspect_ratio': None, 'axes': None, 'axes_labels': None, 'axes_labels_size': None, 'axes_pad': None, 'base': None, 'dpi': 100, 'fig_tight': True, 'figsize': None, 'flip_x': False, 'flip_y': False, 'fontsize': None, 'frame': False, 'gridlines': None, 'gridlinesstyle': None, 'hgridlinesstyle': None, 'legend_options': {}, 'scale': None, 'show_legend': None, 'tick_formatter': None, 'ticks': None, 'ticks_integer': False, 'title': None, 'title_pos': None, 'transparent': False, 'typeset': 'default', 'vgridlinesstyle': None, 'xmax': None, 'xmin': None, 'ymax': None, 'ymin': None}#
add_primitive(primitive)[source]#

Adds a primitive to this graphics object.

EXAMPLES:

We give a very explicit example:

sage: G = Graphics()
sage: from math import e
sage: from sage.plot.line import Line
sage: from sage.plot.arrow import Arrow
sage: L = Line([3,4,2,7,-2], [1,2,e,4,5.],
....:          {'alpha': 1, 'thickness': 2, 'rgbcolor': (0,1,1),
....:           'legend_label': ''})
sage: A = Arrow(2, -5, .1, .2,
....:           {'width': 3, 'head': 0, 'rgbcolor': (1,0,0),
....:            'linestyle': 'dashed', 'zorder': 8, 'legend_label': ''})
sage: G.add_primitive(L)
sage: G.add_primitive(A)
sage: G
Graphics object consisting of 2 graphics primitives

>>> from sage.all import *
>>> G = Graphics()
>>> from math import e
>>> from sage.plot.line import Line
>>> from sage.plot.arrow import Arrow
>>> L = Line([Integer(3),Integer(4),Integer(2),Integer(7),-Integer(2)], [Integer(1),Integer(2),e,Integer(4),RealNumber('5.')],
...          {'alpha': Integer(1), 'thickness': Integer(2), 'rgbcolor': (Integer(0),Integer(1),Integer(1)),
...           'legend_label': ''})
>>> A = Arrow(Integer(2), -Integer(5), RealNumber('.1'), RealNumber('.2'),
...           {'width': Integer(3), 'head': Integer(0), 'rgbcolor': (Integer(1),Integer(0),Integer(0)),
...            'linestyle': 'dashed', 'zorder': Integer(8), 'legend_label': ''})
>>> G.add_primitive(L)
>>> G.add_primitive(A)
>>> G
Graphics object consisting of 2 graphics primitives
aspect_ratio()[source]#

Get the current aspect ratio, which is the ratio of height to width of a unit square, or 'automatic'.

OUTPUT: a positive float (height/width of a unit square), or 'automatic' (expand to fill the figure).

EXAMPLES:

The default aspect ratio for a new blank Graphics object is 'automatic':

sage: P = Graphics()
sage: P.aspect_ratio()
'automatic'

>>> from sage.all import *
>>> P = Graphics()
>>> P.aspect_ratio()
'automatic'

The aspect ratio can be explicitly set different from the object’s default:

sage: P = circle((1,1), 1)
sage: P.aspect_ratio()
1.0
sage: P.set_aspect_ratio(2)
sage: P.aspect_ratio()
2.0
sage: P.set_aspect_ratio('automatic')
sage: P.aspect_ratio()
'automatic'

>>> from sage.all import *
>>> P = circle((Integer(1),Integer(1)), Integer(1))
>>> P.aspect_ratio()
1.0
>>> P.set_aspect_ratio(Integer(2))
>>> P.aspect_ratio()
2.0
>>> P.set_aspect_ratio('automatic')
>>> P.aspect_ratio()
'automatic'
axes(show=None)[source]#

Set whether or not the \(x\) and \(y\) axes are shown by default.

INPUT:

  • show – bool

If called with no input, return the current axes setting.

EXAMPLES:

sage: L = line([(1,2), (3,-4), (2, 5), (1,2)])

>>> from sage.all import *
>>> L = line([(Integer(1),Integer(2)), (Integer(3),-Integer(4)), (Integer(2), Integer(5)), (Integer(1),Integer(2))])

By default the axes are displayed.

sage: L.axes()
True

>>> from sage.all import *
>>> L.axes()
True

But we turn them off, and verify that they are off

sage: L.axes(False)
sage: L.axes()
False

>>> from sage.all import *
>>> L.axes(False)
>>> L.axes()
False

Displaying L now shows a triangle but no axes.

sage: L
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> L
Graphics object consisting of 1 graphics primitive
axes_color(c=None)[source]#

Set the axes color.

If called with no input, return the current axes_color setting.

INPUT:

  • c – an RGB color 3-tuple, where each tuple entry is a float between 0 and 1

EXAMPLES: We create a line, which has like everything a default axes color of black.

sage: L = line([(1,2), (3,-4), (2, 5), (1,2)])
sage: L.axes_color()
(0, 0, 0)

>>> from sage.all import *
>>> L = line([(Integer(1),Integer(2)), (Integer(3),-Integer(4)), (Integer(2), Integer(5)), (Integer(1),Integer(2))])
>>> L.axes_color()
(0, 0, 0)

We change the axes color to red and verify the change.

sage: L.axes_color((1,0,0))
sage: L.axes_color()
(1.0, 0.0, 0.0)

>>> from sage.all import *
>>> L.axes_color((Integer(1),Integer(0),Integer(0)))
>>> L.axes_color()
(1.0, 0.0, 0.0)

When we display the plot, we’ll see a blue triangle and bright red axes.

sage: L
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> L
Graphics object consisting of 1 graphics primitive
axes_label_color(c=None)[source]#

Set the color of the axes labels.

The axes labels are placed at the edge of the x and y axes, and are not on by default (use the axes_labels() command to set them; see the example below). This function just changes their color.

INPUT:

  • c – an RGB 3-tuple of numbers between 0 and 1

If called with no input, return the current axes_label_color setting.

EXAMPLES: We create a plot, which by default has axes label color black.

sage: p = plot(sin, (-1,1))                                                 # needs sage.symbolic
sage: p.axes_label_color()                                                  # needs sage.symbolic
(0, 0, 0)

>>> from sage.all import *
>>> p = plot(sin, (-Integer(1),Integer(1)))                                                 # needs sage.symbolic
>>> p.axes_label_color()                                                  # needs sage.symbolic
(0, 0, 0)

We change the labels to be red, and confirm this:

sage: p.axes_label_color((1,0,0))                                           # needs sage.symbolic
sage: p.axes_label_color()                                                  # needs sage.symbolic
(1.0, 0.0, 0.0)

>>> from sage.all import *
>>> p.axes_label_color((Integer(1),Integer(0),Integer(0)))                                           # needs sage.symbolic
>>> p.axes_label_color()                                                  # needs sage.symbolic
(1.0, 0.0, 0.0)

We set labels, since otherwise we won’t see anything.

sage: p.axes_labels(['$x$ axis', '$y$ axis'])                               # needs sage.symbolic

>>> from sage.all import *
>>> p.axes_labels(['$x$ axis', '$y$ axis'])                               # needs sage.symbolic

In the plot below, notice that the labels are red:

sage: p                                                                     # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> p                                                                     # needs sage.symbolic
Graphics object consisting of 1 graphics primitive
axes_labels(l=None)[source]#

Set the axes labels.

INPUT:

  • l – (default: None) a list of two strings or None

OUTPUT: a 2-tuple of strings

If l is None, returns the current axes_labels, which is itself by default None. The default labels are both empty.

EXAMPLES: We create a plot and put x and y axes labels on it.

sage: p = plot(sin(x), (x, 0, 10))                                          # needs sage.symbolic
sage: p.axes_labels(['$x$','$y$'])                                          # needs sage.symbolic
sage: p.axes_labels()                                                       # needs sage.symbolic
('$x$', '$y$')

>>> from sage.all import *
>>> p = plot(sin(x), (x, Integer(0), Integer(10)))                                          # needs sage.symbolic
>>> p.axes_labels(['$x$','$y$'])                                          # needs sage.symbolic
>>> p.axes_labels()                                                       # needs sage.symbolic
('$x$', '$y$')

Now when you plot p, you see x and y axes labels:

sage: p                                                                     # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> p                                                                     # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

Notice that some may prefer axes labels which are not typeset:

sage: plot(sin(x), (x, 0, 10), axes_labels=['x','y'])                       # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(sin(x), (x, Integer(0), Integer(10)), axes_labels=['x','y'])                       # needs sage.symbolic
Graphics object consisting of 1 graphics primitive
axes_labels_size(s=None)[source]#

Set the relative size of axes labels w.r.t. the axes tick marks.

INPUT:

  • s – float, relative size of axes labels w.r.t. to the tick marks, the size of the tick marks being set by fontsize().

If called with no input, return the current relative size.

EXAMPLES:

sage: # needs sage.symbolic
sage: p = plot(sin(x^2), (x, -3, 3), axes_labels=['$x$','$y$'])
sage: p.axes_labels_size()  # default value
1.6
sage: p.axes_labels_size(2.5)
sage: p.axes_labels_size()
2.5

>>> from sage.all import *
>>> # needs sage.symbolic
>>> p = plot(sin(x**Integer(2)), (x, -Integer(3), Integer(3)), axes_labels=['$x$','$y$'])
>>> p.axes_labels_size()  # default value
1.6
>>> p.axes_labels_size(RealNumber('2.5'))
>>> p.axes_labels_size()
2.5

Now the axes labels are large w.r.t. the tick marks:

sage: p                                                                     # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> p                                                                     # needs sage.symbolic
Graphics object consisting of 1 graphics primitive
axes_range(xmin=None, xmax=None, ymin=None, ymax=None)[source]#

Set the ranges of the \(x\) and \(y\) axes.

INPUT:

  • xmin, xmax, ymin, ymax – floats

EXAMPLES:

sage: L = line([(1,2), (3,-4), (2, 5), (1,2)])
sage: L.set_axes_range(-1, 20, 0, 2)
sage: d = L.get_axes_range()
sage: d['xmin'], d['xmax'], d['ymin'], d['ymax']
(-1.0, 20.0, 0.0, 2.0)

>>> from sage.all import *
>>> L = line([(Integer(1),Integer(2)), (Integer(3),-Integer(4)), (Integer(2), Integer(5)), (Integer(1),Integer(2))])
>>> L.set_axes_range(-Integer(1), Integer(20), Integer(0), Integer(2))
>>> d = L.get_axes_range()
>>> d['xmin'], d['xmax'], d['ymin'], d['ymax']
(-1.0, 20.0, 0.0, 2.0)
axes_width(w=None)[source]#

Set the axes width. Use this to draw a plot with really fat or really thin axes.

INPUT:

  • w – a float

If called with no input, return the current axes_width setting.

EXAMPLES: We create a plot, see the default axes width (with funny Python float rounding), then reset the width to 10 (very fat).

sage: # needs sage.symbolic
sage: p = plot(cos, (-3,3))
sage: p.axes_width()
0.8
sage: p.axes_width(10)
sage: p.axes_width()
10.0

>>> from sage.all import *
>>> # needs sage.symbolic
>>> p = plot(cos, (-Integer(3),Integer(3)))
>>> p.axes_width()
0.8
>>> p.axes_width(Integer(10))
>>> p.axes_width()
10.0

Finally we plot the result, which is a graph with very fat axes.

sage: p                                                                     # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> p                                                                     # needs sage.symbolic
Graphics object consisting of 1 graphics primitive
description()[source]#

Print a textual description to stdout.

This method is mostly used for doctests.

EXAMPLES:

sage: print(polytopes.hypercube(2).plot().description())                    # needs sage.geometry.polyhedron
Polygon defined by 4 points: [(-1.0, -1.0), (1.0, -1.0), (1.0, 1.0), (-1.0, 1.0)]
Line defined by 2 points: [(-1.0, 1.0), (-1.0, -1.0)]
Line defined by 2 points: [(1.0, -1.0), (-1.0, -1.0)]
Line defined by 2 points: [(1.0, -1.0), (1.0, 1.0)]
Line defined by 2 points: [(1.0, 1.0), (-1.0, 1.0)]
Point set defined by 4 point(s): [(1.0, -1.0), (1.0, 1.0), (-1.0, 1.0), (-1.0, -1.0)]

>>> from sage.all import *
>>> print(polytopes.hypercube(Integer(2)).plot().description())                    # needs sage.geometry.polyhedron
Polygon defined by 4 points: [(-1.0, -1.0), (1.0, -1.0), (1.0, 1.0), (-1.0, 1.0)]
Line defined by 2 points: [(-1.0, 1.0), (-1.0, -1.0)]
Line defined by 2 points: [(1.0, -1.0), (-1.0, -1.0)]
Line defined by 2 points: [(1.0, -1.0), (1.0, 1.0)]
Line defined by 2 points: [(1.0, 1.0), (-1.0, 1.0)]
Point set defined by 4 point(s): [(1.0, -1.0), (1.0, 1.0), (-1.0, 1.0), (-1.0, -1.0)]
flip(flip_x=False, flip_y=False)[source]#

Get the flip options and optionally mirror this graphics object.

INPUT:

  • flip_x – boolean (default: False); if True, replace the current flip_x option by its opposite

  • flip_y – boolean (default: False); if True, replace the current flip_y option by its opposite

OUTPUT: a tuple containing the new flip options

EXAMPLES:

When called without arguments, this just returns the current flip options:

sage: L = line([(1, 0), (2, 3)])
sage: L.flip()
(False, False)

>>> from sage.all import *
>>> L = line([(Integer(1), Integer(0)), (Integer(2), Integer(3))])
>>> L.flip()
(False, False)

Otherwise, the specified options are changed and the new options are returned:

sage: L.flip(flip_y=True)
(False, True)
sage: L.flip(True, True)
(True, False)

>>> from sage.all import *
>>> L.flip(flip_y=True)
(False, True)
>>> L.flip(True, True)
(True, False)
fontsize(s=None)[source]#

Set the font size of axes labels and tick marks.

Note that the relative size of the axes labels font w.r.t. the tick marks font can be adjusted via axes_labels_size().

INPUT:

  • s – integer, a font size in points.

If called with no input, return the current fontsize.

EXAMPLES:

sage: L = line([(1,2), (3,-4), (2, 5), (1,2)])
sage: L.fontsize()
10
sage: L.fontsize(20)
sage: L.fontsize()
20

>>> from sage.all import *
>>> L = line([(Integer(1),Integer(2)), (Integer(3),-Integer(4)), (Integer(2), Integer(5)), (Integer(1),Integer(2))])
>>> L.fontsize()
10
>>> L.fontsize(Integer(20))
>>> L.fontsize()
20

All the numbers on the axes will be very large in this plot:

sage: L
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> L
Graphics object consisting of 1 graphics primitive
get_axes_range()[source]#

Returns a dictionary of the range of the axes for this graphics object. This is fall back to the ranges in get_minmax_data() for any value which the user has not explicitly set.

Warning

Changing the dictionary returned by this function does not change the axes range for this object. To do that, use the set_axes_range() method.

EXAMPLES:

sage: L = line([(1,2), (3,-4), (2, 5), (1,2)])
sage: list(sorted(L.get_axes_range().items()))
[('xmax', 3.0), ('xmin', 1.0), ('ymax', 5.0), ('ymin', -4.0)]
sage: L.set_axes_range(xmin=-1)
sage: list(sorted(L.get_axes_range().items()))
[('xmax', 3.0), ('xmin', -1.0), ('ymax', 5.0), ('ymin', -4.0)]

>>> from sage.all import *
>>> L = line([(Integer(1),Integer(2)), (Integer(3),-Integer(4)), (Integer(2), Integer(5)), (Integer(1),Integer(2))])
>>> list(sorted(L.get_axes_range().items()))
[('xmax', 3.0), ('xmin', 1.0), ('ymax', 5.0), ('ymin', -4.0)]
>>> L.set_axes_range(xmin=-Integer(1))
>>> list(sorted(L.get_axes_range().items()))
[('xmax', 3.0), ('xmin', -1.0), ('ymax', 5.0), ('ymin', -4.0)]
get_minmax_data()[source]#

Return the x and y coordinate minimum and maximum

Warning

The returned dictionary is mutable, but changing it does not change the xmin/xmax/ymin/ymax data. The minmax data is a function of the primitives which make up this Graphics object. To change the range of the axes, call methods xmin(), xmax(), ymin(), ymax(), or set_axes_range().

OUTPUT:

A dictionary whose keys give the xmin, xmax, ymin, and ymax data for this graphic.

EXAMPLES:

sage: g = line([(-1,1), (3,2)])
sage: list(sorted(g.get_minmax_data().items()))
[('xmax', 3.0), ('xmin', -1.0), ('ymax', 2.0), ('ymin', 1.0)]

>>> from sage.all import *
>>> g = line([(-Integer(1),Integer(1)), (Integer(3),Integer(2))])
>>> list(sorted(g.get_minmax_data().items()))
[('xmax', 3.0), ('xmin', -1.0), ('ymax', 2.0), ('ymin', 1.0)]

Note that changing ymax doesn’t change the output of get_minmax_data:

sage: g.ymax(10)
sage: list(sorted(g.get_minmax_data().items()))
[('xmax', 3.0), ('xmin', -1.0), ('ymax', 2.0), ('ymin', 1.0)]

>>> from sage.all import *
>>> g.ymax(Integer(10))
>>> list(sorted(g.get_minmax_data().items()))
[('xmax', 3.0), ('xmin', -1.0), ('ymax', 2.0), ('ymin', 1.0)]

The width/height ratio (in output units, after factoring in the chosen aspect ratio) of the plot is limited to \(10^{-15}\dots 10^{15}\), otherwise floating point errors cause problems in matplotlib:

sage: l = line([(1e-19,-1), (-1e-19,+1)], aspect_ratio=1.0)
sage: l.get_minmax_data()
{'xmax': 1.00010000000000e-15,
 'xmin': -9.99900000000000e-16,
 'ymax': 1.0,
 'ymin': -1.0}
sage: l = line([(0,0), (1,1)], aspect_ratio=1e19)
sage: l.get_minmax_data()
{'xmax': 5000.50000000000, 'xmin': -4999.50000000000,
 'ymax': 1.0, 'ymin': 0.0}

>>> from sage.all import *
>>> l = line([(RealNumber('1e-19'),-Integer(1)), (-RealNumber('1e-19'),+Integer(1))], aspect_ratio=RealNumber('1.0'))
>>> l.get_minmax_data()
{'xmax': 1.00010000000000e-15,
 'xmin': -9.99900000000000e-16,
 'ymax': 1.0,
 'ymin': -1.0}
>>> l = line([(Integer(0),Integer(0)), (Integer(1),Integer(1))], aspect_ratio=RealNumber('1e19'))
>>> l.get_minmax_data()
{'xmax': 5000.50000000000, 'xmin': -4999.50000000000,
 'ymax': 1.0, 'ymin': 0.0}
inset(graphics, pos=None, fontsize=None)[source]#

Add a graphics object as an inset.

INPUT:

  • graphics – the graphics object (instance of Graphics) to be added as an inset to the current graphics

  • pos – (default: None) 4-tuple (left, bottom, width, height) specifying the location and size of the inset on the final figure, all quantities being in fractions of the figure width and height; if None, the value (0.7, 0.7, 0.2, 0.2) is used

  • fontsize – (default: None) integer, font size (in points) for the inset; if None, the value of 6 points is used, unless fontsize has been explicitly set in the construction of graphics (in this case, it is not overwritten here)

OUTPUT:

EXAMPLES:

sage: # needs sage.symbolic
sage: f(x) = x^2*sin(1/x)
sage: g1 = plot(f(x), (x, -2, 2), axes_labels=['$x$', '$y$'])
sage: g2 = plot(f(x), (x, -0.3, 0.3), axes_labels=['$x$', '$y$'],
....:           frame=True)
sage: g1.inset(g2)
Multigraphics with 2 elements

>>> from sage.all import *
>>> # needs sage.symbolic
>>> __tmp__=var("x"); f = symbolic_expression(x**Integer(2)*sin(Integer(1)/x)).function(x)
>>> g1 = plot(f(x), (x, -Integer(2), Integer(2)), axes_labels=['$x$', '$y$'])
>>> g2 = plot(f(x), (x, -RealNumber('0.3'), RealNumber('0.3')), axes_labels=['$x$', '$y$'],
...           frame=True)
>>> g1.inset(g2)
Multigraphics with 2 elements
../../_images/graphics-1.svg

Using non-default values for the position/size and the font size:

sage: g1.inset(g2, pos=(0.15, 0.7, 0.25, 0.25), fontsize=8)                 # needs sage.symbolic
Multigraphics with 2 elements

>>> from sage.all import *
>>> g1.inset(g2, pos=(RealNumber('0.15'), RealNumber('0.7'), RealNumber('0.25'), RealNumber('0.25')), fontsize=Integer(8))                 # needs sage.symbolic
Multigraphics with 2 elements
../../_images/graphics-2.svg

We can add another inset by invoking inset on the last output:

sage: g1g2 = _                                                              # needs sage.symbolic
sage: g3 = plot(f(x), (x, -0.05, 0.05), axes_labels=['$x$', '$y$'],         # needs sage.symbolic
....:           frame=True)
sage: g1g2.inset(g3, pos=(0.65, 0.12, 0.25, 0.25))                          # needs sage.symbolic
Multigraphics with 3 elements

>>> from sage.all import *
>>> g1g2 = _                                                              # needs sage.symbolic
>>> g3 = plot(f(x), (x, -RealNumber('0.05'), RealNumber('0.05')), axes_labels=['$x$', '$y$'],         # needs sage.symbolic
...           frame=True)
>>> g1g2.inset(g3, pos=(RealNumber('0.65'), RealNumber('0.12'), RealNumber('0.25'), RealNumber('0.25')))                          # needs sage.symbolic
Multigraphics with 3 elements
../../_images/graphics-3.svg
legend(show=None)[source]#

Set whether or not the legend is shown by default.

INPUT:

  • show – (default: None) a boolean

If called with no input, return the current legend setting.

EXAMPLES:

By default no legend is displayed:

sage: P = plot(sin)                                                         # needs sage.symbolic
sage: P.legend()                                                            # needs sage.symbolic
False

>>> from sage.all import *
>>> P = plot(sin)                                                         # needs sage.symbolic
>>> P.legend()                                                            # needs sage.symbolic
False

But if we put a label then the legend is shown:

sage: P = plot(sin, legend_label='sin')                                     # needs sage.symbolic
sage: P.legend()                                                            # needs sage.symbolic
True

>>> from sage.all import *
>>> P = plot(sin, legend_label='sin')                                     # needs sage.symbolic
>>> P.legend()                                                            # needs sage.symbolic
True

We can turn it on or off:

sage: # needs sage.symbolic
sage: P.legend(False)
sage: P.legend()
False
sage: P.legend(True)
sage: P  #  show with the legend
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> # needs sage.symbolic
>>> P.legend(False)
>>> P.legend()
False
>>> P.legend(True)
>>> P  #  show with the legend
Graphics object consisting of 1 graphics primitive
matplotlib(filename=None, xmin=None, xmax=None, ymin=None, ymax=None, figsize=None, figure=None, sub=None, axes=None, axes_labels=None, axes_labels_size=None, flip_x=False, flip_y=False, fontsize=None, frame=False, verify=True, aspect_ratio=None, gridlines=None, gridlinesstyle=None, vgridlinesstyle=None, hgridlinesstyle=None, show_legend=None, legend_options=None, axes_pad=None, ticks_integer=None, tick_formatter=None, ticks=None, title=None, title_pos=None, base=None, scale=None, stylesheet=None, typeset='default')[source]#

Construct or modify a Matplotlib figure by drawing self on it.

INPUT (partial description, involving only Matplotlib objects; see show() for the other arguments):

  • figure – (default: None) Matplotlib figure (class matplotlib.figure.Figure) on which self is to be displayed; if None, the figure will be created from the parameter figsize

  • figsize – (default: None) width or [width, height] in inches of the Matplotlib figure in case figure is None; if figsize is None, Matplotlib’s default (6.4 x 4.8 inches) is used

  • sub – (default: None) subpart of the figure, as an instance of Matplotlib “axes” (class matplotlib.axes.Axes) on which self is to be drawn; if None, the subpart will be created so as to cover the whole figure

OUTPUT:

  • a matplotlib.figure.Figure object; if the argument figure is provided, this is the same object as figure.

EXAMPLES:

sage: c = circle((1,1),1)
sage: print(c.matplotlib())
Figure(640x480)

>>> from sage.all import *
>>> c = circle((Integer(1),Integer(1)),Integer(1))
>>> print(c.matplotlib())
Figure(640x480)

To obtain the first Matplotlib Axes object inside of the figure, you can do something like the following.

sage: p = plot(sin(x), (x, -2*pi, 2*pi))                                    # needs sage.symbolic
sage: figure = p.matplotlib()                                               # needs sage.symbolic
sage: axes = figure.axes[0]                                                 # needs sage.symbolic

>>> from sage.all import *
>>> p = plot(sin(x), (x, -Integer(2)*pi, Integer(2)*pi))                                    # needs sage.symbolic
>>> figure = p.matplotlib()                                               # needs sage.symbolic
>>> axes = figure.axes[Integer(0)]                                                 # needs sage.symbolic
plot()[source]#

Draw a 2D plot of this graphics object, which just returns this object since this is already a 2D graphics object.

EXAMPLES:

sage: S = circle((0,0), 2)
sage: S.plot() is S
True

>>> from sage.all import *
>>> S = circle((Integer(0),Integer(0)), Integer(2))
>>> S.plot() is S
True

It does not accept any argument (Issue #19539):

sage: S.plot(1)
Traceback (most recent call last):
...
TypeError: ...plot() takes 1 positional argument but 2 were given

sage: S.plot(hey="hou")
Traceback (most recent call last):
...
TypeError: ...plot() got an unexpected keyword argument 'hey'

>>> from sage.all import *
>>> S.plot(Integer(1))
Traceback (most recent call last):
...
TypeError: ...plot() takes 1 positional argument but 2 were given

>>> S.plot(hey="hou")
Traceback (most recent call last):
...
TypeError: ...plot() got an unexpected keyword argument 'hey'
plot3d(z=0, **kwds)[source]#

Return an embedding of this 2D plot into the xy-plane of 3D space, as a 3D plot object. An optional parameter z can be given to specify the z-coordinate.

EXAMPLES:

sage: sum(plot(z*sin(x), 0, 10).plot3d(z)   # long time                     # needs sage.symbolic
....:     for z in range(6))
Graphics3d Object

>>> from sage.all import *
>>> sum(plot(z*sin(x), Integer(0), Integer(10)).plot3d(z)   # long time                     # needs sage.symbolic
...     for z in range(Integer(6)))
Graphics3d Object
save(filename, legend_back_color='white', legend_borderpad=0.6, legend_borderaxespad=None, legend_columnspacing=None, legend_fancybox=False, legend_font_family='sans-serif', legend_font_size='medium', legend_font_style='normal', legend_font_variant='normal', legend_font_weight='medium', legend_handlelength=0.05, legend_handletextpad=0.5, legend_labelspacing=0.02, legend_loc='best', legend_markerscale=0.6, legend_ncol=1, legend_numpoints=2, legend_shadow=True, legend_title=None, **kwds)[source]#

Save the graphics to an image file.

INPUT:

  • filename – string. The filename and the image format given by the extension, which can be one of the following:

    • .eps,

    • .pdf,

    • .pgf,

    • .png,

    • .ps,

    • .sobj (for a Sage object you can load later),

    • .svg,

    • empty extension will be treated as .sobj.

All other keyword arguments will be passed to the plotter.

OUTPUT:

  • none.

EXAMPLES:

sage: c = circle((1,1), 1, color='red')
sage: from tempfile import NamedTemporaryFile
sage: with NamedTemporaryFile(suffix=".png") as f:
....:     c.save(f.name, xmin=-1, xmax=3, ymin=-1, ymax=3)

>>> from sage.all import *
>>> c = circle((Integer(1),Integer(1)), Integer(1), color='red')
>>> from tempfile import NamedTemporaryFile
>>> with NamedTemporaryFile(suffix=".png") as f:
...     c.save(f.name, xmin=-Integer(1), xmax=Integer(3), ymin=-Integer(1), ymax=Integer(3))

To make a figure bigger or smaller, use figsize:

sage: c.save(f.name, figsize=5, xmin=-1, xmax=3, ymin=-1, ymax=3)

>>> from sage.all import *
>>> c.save(f.name, figsize=Integer(5), xmin=-Integer(1), xmax=Integer(3), ymin=-Integer(1), ymax=Integer(3))

By default, the figure grows to include all of the graphics and text, so the final image may not be exactly the figure size you specified. If you want a figure to be exactly a certain size, specify the keyword fig_tight=False:

sage: c.save(f.name, figsize=[8,4], fig_tight=False,
....:        xmin=-1, xmax=3, ymin=-1, ymax=3)

>>> from sage.all import *
>>> c.save(f.name, figsize=[Integer(8),Integer(4)], fig_tight=False,
...        xmin=-Integer(1), xmax=Integer(3), ymin=-Integer(1), ymax=Integer(3))

You can also pass extra options to the plot command instead of this method, e.g.

sage: plot(x^2 - 5, (x, 0, 5), ymin=0).save(tmp_filename(ext='.png'))       # needs sage.symbolic

>>> from sage.all import *
>>> plot(x**Integer(2) - Integer(5), (x, Integer(0), Integer(5)), ymin=Integer(0)).save(tmp_filename(ext='.png'))       # needs sage.symbolic

will save the same plot as the one shown by this command:

sage: plot(x^2 - 5, (x, 0, 5), ymin=0)                                      # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(x**Integer(2) - Integer(5), (x, Integer(0), Integer(5)), ymin=Integer(0))                                      # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

(This test verifies that Issue #8632 is fixed.)

save_image(filename=None, *args, **kwds)[source]#

Save an image representation of self.

The image type is determined by the extension of the filename. For example, this could be .png, .jpg, .gif, .pdf, .svg. Currently this is implemented by calling the save() method of self, passing along all arguments and keywords.

Note

Not all image types are necessarily implemented for all graphics types. See save() for more details.

EXAMPLES:

sage: import tempfile
sage: c = circle((1,1), 1, color='red')
sage: with tempfile.NamedTemporaryFile(suffix=".png") as f:
....:     c.save_image(f.name, xmin=-1, xmax=3,
....:                  ymin=-1, ymax=3)

>>> from sage.all import *
>>> import tempfile
>>> c = circle((Integer(1),Integer(1)), Integer(1), color='red')
>>> with tempfile.NamedTemporaryFile(suffix=".png") as f:
...     c.save_image(f.name, xmin=-Integer(1), xmax=Integer(3),
...                  ymin=-Integer(1), ymax=Integer(3))
set_aspect_ratio(ratio)[source]#

Set the aspect ratio, which is the ratio of height and width of a unit square (i.e., height/width of a unit square), or ‘automatic’ (expand to fill the figure).

INPUT:

  • ratio – a positive real number or ‘automatic’

EXAMPLES: We create a plot of the upper half of a circle, but it doesn’t look round because the aspect ratio is off:

sage: P = plot(sqrt(1-x^2),(x,-1,1)); P                                     # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> P = plot(sqrt(Integer(1)-x**Integer(2)),(x,-Integer(1),Integer(1))); P                                     # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

So we set the aspect ratio and now it is round:

sage: P.set_aspect_ratio(1)                                                 # needs sage.symbolic
sage: P.aspect_ratio()                                                      # needs sage.symbolic
1.0
sage: P                                                                     # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> P.set_aspect_ratio(Integer(1))                                                 # needs sage.symbolic
>>> P.aspect_ratio()                                                      # needs sage.symbolic
1.0
>>> P                                                                     # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

Note that the aspect ratio is inherited upon addition (which takes the max of aspect ratios of objects whose aspect ratio has been set):

sage: P + plot(sqrt(4-x^2),(x,-2,2))                                        # needs sage.symbolic
Graphics object consisting of 2 graphics primitives

>>> from sage.all import *
>>> P + plot(sqrt(Integer(4)-x**Integer(2)),(x,-Integer(2),Integer(2)))                                        # needs sage.symbolic
Graphics object consisting of 2 graphics primitives

In the following example, both plots produce a circle that looks twice as tall as wide:

sage: Q = circle((0,0), 0.5); Q.set_aspect_ratio(2)
sage: (P + Q).aspect_ratio(); P + Q                                         # needs sage.symbolic
2.0
Graphics object consisting of 2 graphics primitives
sage: (Q + P).aspect_ratio(); Q + P                                         # needs sage.symbolic
2.0
Graphics object consisting of 2 graphics primitives

>>> from sage.all import *
>>> Q = circle((Integer(0),Integer(0)), RealNumber('0.5')); Q.set_aspect_ratio(Integer(2))
>>> (P + Q).aspect_ratio(); P + Q                                         # needs sage.symbolic
2.0
Graphics object consisting of 2 graphics primitives
>>> (Q + P).aspect_ratio(); Q + P                                         # needs sage.symbolic
2.0
Graphics object consisting of 2 graphics primitives
set_axes_range(xmin=None, xmax=None, ymin=None, ymax=None)[source]#

Set the ranges of the \(x\) and \(y\) axes.

INPUT:

  • xmin, xmax, ymin, ymax – floats

EXAMPLES:

sage: L = line([(1,2), (3,-4), (2, 5), (1,2)])
sage: L.set_axes_range(-1, 20, 0, 2)
sage: d = L.get_axes_range()
sage: d['xmin'], d['xmax'], d['ymin'], d['ymax']
(-1.0, 20.0, 0.0, 2.0)

>>> from sage.all import *
>>> L = line([(Integer(1),Integer(2)), (Integer(3),-Integer(4)), (Integer(2), Integer(5)), (Integer(1),Integer(2))])
>>> L.set_axes_range(-Integer(1), Integer(20), Integer(0), Integer(2))
>>> d = L.get_axes_range()
>>> d['xmin'], d['xmax'], d['ymin'], d['ymax']
(-1.0, 20.0, 0.0, 2.0)
set_flip(flip_x=None, flip_y=None)[source]#

Set the flip options for this graphics object.

INPUT:

  • flip_x – boolean (default: None); if not None, set the flip_x option to this value

  • flip_y – boolean (default: None); if not None, set the flip_y option to this value

EXAMPLES:

sage: L = line([(1, 0), (2, 3)])
sage: L.set_flip(flip_y=True)
sage: L.flip()
(False, True)
sage: L.set_flip(True, False)
sage: L.flip()
(True, False)

>>> from sage.all import *
>>> L = line([(Integer(1), Integer(0)), (Integer(2), Integer(3))])
>>> L.set_flip(flip_y=True)
>>> L.flip()
(False, True)
>>> L.set_flip(True, False)
>>> L.flip()
(True, False)
set_legend_options(**kwds)[source]#

Set various legend options.

INPUT:

  • title – (default: None) string, the legend title

  • ncol – (default: 1) positive integer, the number of columns

  • columnspacing – (default: None) the spacing between columns

  • borderaxespad – (default: None) float, length between the axes and the legend

  • back_color – (default: ‘white’) This parameter can be a string denoting a color or an RGB tuple. The string can be a color name as in (‘red’, ‘green’, ‘yellow’, …) or a floating point number like ‘0.8’ which gets expanded to (0.8, 0.8, 0.8). The tuple form is just a floating point RGB tuple with all values ranging from 0 to 1.

  • handlelength – (default: 0.05) float, the length of the legend handles

  • handletextpad – (default: 0.5) float, the pad between the legend handle and text

  • labelspacing – (default: 0.02) float, vertical space between legend entries

  • loc – (default: ‘best’) May be a string, an integer or a tuple. String or

    integer inputs must be one of the following:

    • 0, ‘best’

    • 1, ‘upper right’

    • 2, ‘upper left’

    • 3, ‘lower left’

    • 4, ‘lower right’

    • 5, ‘right’

    • 6, ‘center left’

    • 7, ‘center right’

    • 8, ‘lower center’

    • 9, ‘upper center’

    • 10, ‘center’

    • Tuple arguments represent an absolute (x, y) position on the plot in axes coordinates (meaning from 0 to 1 in each direction).

  • markerscale – (default: 0.6) float, how much to scale the markers in the legend.

  • numpoints – (default: 2) integer, the number of points in the legend for line

  • borderpad – (default: 0.6) float, the fractional whitespace inside the legend border (between 0 and 1)

  • font_family – (default: ‘sans-serif’) string, one of ‘serif’, ‘sans-serif’, ‘cursive’, ‘fantasy’, ‘monospace’

  • font_style – (default: ‘normal’) string, one of ‘normal’, ‘italic’, ‘oblique’

  • font_variant – (default: ‘normal’) string, one of ‘normal’, ‘small-caps’

  • font_weight – (default: ‘medium’) string, one of ‘black’, ‘extra bold’, ‘bold’, ‘semibold’, ‘medium’, ‘normal’, ‘light’

  • font_size – (default: ‘medium’) string, one of ‘xx-small’, ‘x-small’, ‘small’, ‘medium’, ‘large’, ‘x-large’, ‘xx-large’ or an absolute font size (e.g. 12)

  • shadow – (default: True) boolean – draw a shadow behind the legend

  • fancybox – (default: False) a boolean. If True, draws a frame with a round fancybox.

These are all keyword arguments.

OUTPUT: a dictionary of all current legend options

EXAMPLES:

By default, no options are set:

sage: p = plot(tan, legend_label='tan')                                     # needs sage.symbolic
sage: p.set_legend_options()                                                # needs sage.symbolic
{}

>>> from sage.all import *
>>> p = plot(tan, legend_label='tan')                                     # needs sage.symbolic
>>> p.set_legend_options()                                                # needs sage.symbolic
{}

We build a legend without a shadow:

sage: p.set_legend_options(shadow=False)                                    # needs sage.symbolic
sage: p.set_legend_options()['shadow']                                      # needs sage.symbolic
False

>>> from sage.all import *
>>> p.set_legend_options(shadow=False)                                    # needs sage.symbolic
>>> p.set_legend_options()['shadow']                                      # needs sage.symbolic
False

To set the legend position to the center of the plot, all these methods are roughly equivalent:

sage: p.set_legend_options(loc='center'); p                                 # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> p.set_legend_options(loc='center'); p                                 # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

sage: p.set_legend_options(loc=10); p                                       # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> p.set_legend_options(loc=Integer(10)); p                                       # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

sage: p.set_legend_options(loc=(0.5,0.5)); p  # aligns the bottom of the box to the center                  # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> p.set_legend_options(loc=(RealNumber('0.5'),RealNumber('0.5'))); p  # aligns the bottom of the box to the center                  # needs sage.symbolic
Graphics object consisting of 1 graphics primitive
show(legend_back_color='white', legend_borderpad=0.6, legend_borderaxespad=None, legend_columnspacing=None, legend_fancybox=False, legend_font_family='sans-serif', legend_font_size='medium', legend_font_style='normal', legend_font_variant='normal', legend_font_weight='medium', legend_handlelength=0.05, legend_handletextpad=0.5, legend_labelspacing=0.02, legend_loc='best', legend_markerscale=0.6, legend_ncol=1, legend_numpoints=2, legend_shadow=True, legend_title=None, **kwds)[source]#

Show this graphics image immediately.

This method attempts to display the graphics immediately, without waiting for the currently running code (if any) to return to the command line. Be careful, calling it from within a loop will potentially launch a large number of external viewer programs.

OPTIONAL INPUT:

  • dpi – (default: 100) dots per inch

  • figsize – (default: [6.4, 4.8]) [width, height] inches. The maximum value of each of the width and the height can be 327 inches, at the default dpi of 100 dpi, which is just shy of the maximum allowed value of 32768 dots (pixels).

  • fig_tight – (default: True) whether to clip the drawing tightly around drawn objects. If True, then the resulting image will usually not have dimensions corresponding to figsize. If False, the resulting image will have dimensions corresponding to figsize.

  • aspect_ratio – the perceived height divided by the perceived width. For example, if the aspect ratio is set to 1, circles will look round and a unit square will appear to have sides of equal length, and if the aspect ratio is set 2, vertical units will be twice as long as horizontal units, so a unit square will be twice as high as it is wide. If set to 'automatic', the aspect ratio is determined by figsize and the picture fills the figure.

  • axes – (default: True)

  • axes_labels – (default: None) list (or tuple) of two strings; the first is used as the label for the horizontal axis, and the second for the vertical axis.

  • axes_labels_size – (default: current setting – 1.6) scale factor relating the size of the axes labels with respect to the size of the tick marks.

  • fontsize – (default: current setting – 10) positive integer; used for axes labels; if you make this very large, you may have to increase figsize to see all labels.

  • frame – (default: False) draw a frame around the image

  • gridlines – (default: None) can be any of the following:

    • None, False: do not add grid lines.

    • True, “automatic”, “major”: add grid lines at major ticks of the axes.

    • “minor”: add grid at major and minor ticks.

    • [xlist,ylist]: a tuple or list containing two elements, where xlist (or ylist) can be any of the following.

      • None, False: don’t add horizontal (or vertical) lines.

      • True, “automatic”, “major”: add horizontal (or vertical) grid lines at the major ticks of the axes.

      • “minor”: add horizontal (or vertical) grid lines at major and minor ticks of axes.

      • an iterable yielding numbers n or pairs (n,opts), where n is the coordinate of the line and opt is a dictionary of MATPLOTLIB options for rendering the line.

  • gridlinesstyle, hgridlinesstyle, vgridlinesstyle - (default: None) a dictionary of MATPLOTLIB options for the rendering of the grid lines, the horizontal grid lines or the vertical grid lines, respectively.

  • transparent – (default: False) If True, make the background transparent.

  • axes_pad – (default: 0.02 on "linear" scale, 1 on "log" scale).

    • In the "linear" scale, it determines the percentage of the axis range that is added to each end of each axis. This helps avoid problems like clipping lines because of line-width, etc. To get axes that are exactly the specified limits, set axes_pad to zero.

    • On the "log" scale, it determines the exponent of the fraction of the minimum (resp. maximum) that is subtracted from the minimum (resp. added to the maximum) value of the axis. For instance if the minimum is \(m\) and the base of the axis is \(b\) then the new minimum after padding the axis will be \(m - m/b^{\mathrm{axes\_pad}}\).

  • ticks_integer – (default: False) guarantee that the ticks are integers (the ticks option, if specified, will override this)

  • ticks – A matplotlib locator for the major ticks, or a number. There are several options. For more information about locators, type from matplotlib import ticker and then ticker?.

    • If this is a locator object, then it is the locator for the horizontal axis. A value of None means use the default locator.

    • If it is a list of two locators, then the first is for the horizontal axis and one for the vertical axis. A value of None means use the default locator (so a value of [None, my_locator] uses my_locator for the vertical axis and the default for the horizontal axis).

    • If in either case above one of the entries is a number \(m\) (something which can be coerced to a float), it will be replaced by a MultipleLocator which places major ticks at integer multiples of \(m\). See examples.

    • If in either case above one of the entries is a list of numbers, it will be replaced by a FixedLocator which places ticks at the locations specified. This includes the case of of the empty list, which will give no ticks. See examples.

  • tick_formatter – A matplotlib formatter for the major ticks. There are several options. For more information about formatters, type from matplotlib import ticker and then ticker?.

    If the value of this keyword is a single item, then this will give the formatting for the horizontal axis only (except for the "latex" option). If it is a list or tuple, the first is for the horizontal axis, the second for the vertical axis. The options are below:

    • If one of the entries is a formatter object, then it used. A value of None means to use the default locator (so using tick_formatter=[None, my_formatter] uses my_formatter for the vertical axis and the default for the horizontal axis).

    • If one of the entries is a symbolic constant such as \(\pi\), \(e\), or \(sqrt(2)\), ticks will be formatted nicely at rational multiples of this constant.

    Warning

    This should only be used with the ticks option using nice rational multiples of that constant!

    • If one of the entries is the string "latex", then the formatting will be nice typesetting of the ticks. This is intended to be used when the tick locator for at least one of the axes is a list including some symbolic elements. This uses matplotlib’s internal LaTeX rendering engine. If you want to use an external LaTeX compiler, then set the keyword option typeset. See examples.

  • title – (default: None) The title for the plot

  • title_pos – (default: None) The position of the title for the

    plot. It must be a tuple or a list of two real numbers (x_pos, y_pos) which indicate the relative position of the title within the plot. The plot itself can be considered to occupy, in relative terms, the region within a unit square \([0, 1] \times [0, 1]\). The title text is centered around the horizontal factor x_pos of the plot. The baseline of the title text is present at the vertical factor y_pos of the plot. Hence, title_pos=(0.5, 0.5) will center the title in the plot, whereas title_pos=(0.5, 1.1) will center the title along the horizontal direction, but will place the title a fraction \(0.1\) times above the plot.

    • If the first entry is a list of strings (or numbers), then the formatting for the horizontal axis will be typeset with the strings present in the list. Each entry of the list of strings must be provided with a corresponding number in the first entry of ticks to indicate its position on the axis. To typeset the strings with "latex" enclose them within "$" symbols. To have similar custom formatting of the labels along the vertical axis, the second entry must be a list of strings and the second entry of ticks must also be a list of numbers which give the positions of the labels. See the examples below.

  • show_legend – (default: None) If True, show the legend

  • legend_* – all the options valid for set_legend_options()

    prefixed with 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" – linear scaling of both the axes

    • "loglog" – sets both the horizontal and vertical axes to logarithmic scale

    • "semilogx" – sets only the horizontal axis to logarithmic scale.

    • "semilogy" – sets only the vertical axis to logarithmic scale.

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

    Note

    • If the scale is "linear", then irrespective of what base is set to, it will default to 10 and will remain unused.

  • xmin – starting x value in the rendered figure.

  • xmax – ending x value in the rendered figure.

  • ymin – starting y value in the rendered figure.

  • ymax – ending y value in the rendered figure.

  • flip_x – (default: False) boolean. If True, flip the horizontal axis.

  • flip_y – (default: False) boolean. If True, flip the vertical axis.

  • typeset – (default: "default") string. The type of font rendering that should be used for the text. The possible values are

    • "default" – Uses matplotlib’s internal text rendering engine called Mathtext ( see https://matplotlib.org/users/mathtext.html ). If you have modified the default matplotlib settings, for instance via a matplotlibrc file, then this option will not change any of those settings.

    • "latex" – LaTeX is used for rendering the fonts. This requires LaTeX, dvipng and Ghostscript to be installed.

    • "type1" – Type 1 fonts are used by matplotlib in the text in the figure. This requires LaTeX, dvipng and Ghostscript to be installed.

OUTPUT:

This method does not return anything. Use save() if you want to save the figure as an image.

EXAMPLES:

sage: c = circle((1,1), 1, color='red')
sage: c.show(xmin=-1, xmax=3, ymin=-1, ymax=3)

>>> from sage.all import *
>>> c = circle((Integer(1),Integer(1)), Integer(1), color='red')
>>> c.show(xmin=-Integer(1), xmax=Integer(3), ymin=-Integer(1), ymax=Integer(3))

You can make the picture larger by changing figsize with width, height each having a maximum value of 327 inches at default dpi:

sage: p = ellipse((0,0),4,1)
sage: p.show(figsize=[327,10], dpi=100)
sage: p.show(figsize=[328,10], dpi=80)

>>> from sage.all import *
>>> p = ellipse((Integer(0),Integer(0)),Integer(4),Integer(1))
>>> p.show(figsize=[Integer(327),Integer(10)], dpi=Integer(100))
>>> p.show(figsize=[Integer(328),Integer(10)], dpi=Integer(80))

You can turn off the drawing of the axes:

sage: show(plot(sin,-4,4), axes=False)                                      # needs sage.symbolic

>>> from sage.all import *
>>> show(plot(sin,-Integer(4),Integer(4)), axes=False)                                      # needs sage.symbolic

You can also label the axes. Putting something in dollar signs formats it as a mathematical expression:

sage: show(plot(sin,-4,4), axes_labels=('$x$','$y$'))                       # needs sage.symbolic

>>> from sage.all import *
>>> show(plot(sin,-Integer(4),Integer(4)), axes_labels=('$x$','$y$'))                       # needs sage.symbolic

You can add a title to a plot:

sage: show(plot(sin,-4,4), title=r'A plot of $\sin(x)$')                    # needs sage.symbolic

>>> from sage.all import *
>>> show(plot(sin,-Integer(4),Integer(4)), title=r'A plot of $\sin(x)$')                    # needs sage.symbolic

You can also provide the position for the title to the plot. In the plot below the title is placed on the bottom left of the figure.:

sage: plot(sin, -4, 4, title='Plot sin(x)', title_pos=(0.05,-0.05))         # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(sin, -Integer(4), Integer(4), title='Plot sin(x)', title_pos=(RealNumber('0.05'),-RealNumber('0.05')))         # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

If you want all the text to be rendered by using an external LaTeX installation then set the typeset to "latex". This requires that LaTeX, dvipng and Ghostscript be installed:

sage: plot(x, typeset='latex')                                      # optional - latex, needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(x, typeset='latex')                                      # optional - latex, needs sage.symbolic
Graphics object consisting of 1 graphics primitive

If you want all the text in your plot to use Type 1 fonts, then set the typeset option to "type1". This requires that LaTeX, dvipng and Ghostscript be installed:

sage: plot(x, typeset='type1')                                      # optional - latex, needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(x, typeset='type1')                                      # optional - latex, needs sage.symbolic
Graphics object consisting of 1 graphics primitive

You can turn on the drawing of a frame around the plots:

sage: show(plot(sin,-4,4), frame=True)                                      # needs sage.symbolic

>>> from sage.all import *
>>> show(plot(sin,-Integer(4),Integer(4)), frame=True)                                      # needs sage.symbolic

You can make the background transparent:

sage: plot(sin(x), (x, -4, 4), transparent=True)                            # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(sin(x), (x, -Integer(4), Integer(4)), transparent=True)                            # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

Prior to Issue #19485, legends by default had a shadowless gray background. This behavior can be recovered by passing in certain legend_options:

sage: p = plot(sin(x), legend_label=r'$\sin(x)$')                           # needs sage.symbolic
sage: p.show(legend_options={'back_color': (0.9,0.9,0.9),                   # needs sage.symbolic
....:                        'shadow': False})

>>> from sage.all import *
>>> p = plot(sin(x), legend_label=r'$\sin(x)$')                           # needs sage.symbolic
>>> p.show(legend_options={'back_color': (RealNumber('0.9'),RealNumber('0.9'),RealNumber('0.9')),                   # needs sage.symbolic
...                        'shadow': False})

We can change the scale of the axes in the graphics before displaying:

sage: G = plot(exp, 1, 10)                                                  # needs sage.symbolic
sage: G.show(scale='semilogy')                                              # needs sage.symbolic

>>> from sage.all import *
>>> G = plot(exp, Integer(1), Integer(10))                                                  # needs sage.symbolic
>>> G.show(scale='semilogy')                                              # needs sage.symbolic

We can change the base of the logarithm too. The following changes the vertical axis to be on log scale, and with base 2. Note that the base argument will ignore any changes to the axis which is in linear scale.:

sage: G.show(scale='semilogy', base=2)  # y axis as powers of 2         # long time, needs sage.symbolic

>>> from sage.all import *
>>> G.show(scale='semilogy', base=Integer(2))  # y axis as powers of 2         # long time, needs sage.symbolic

sage: G.show(scale='semilogy', base=(3,2))  # base ignored for x-axis       # needs sage.symbolic

>>> from sage.all import *
>>> G.show(scale='semilogy', base=(Integer(3),Integer(2)))  # base ignored for x-axis       # needs sage.symbolic

The scale can be also given as a 2-tuple or a 3-tuple.:

sage: G.show(scale=('loglog', 2.1))   # both x and y axes in base 2.1   # long time, needs sage.symbolic

>>> from sage.all import *
>>> G.show(scale=('loglog', RealNumber('2.1')))   # both x and y axes in base 2.1   # long time, needs sage.symbolic

sage: G.show(scale=('loglog', 2, 3))  # x in base 2, y in base 3        # long time, needs sage.symbolic

>>> from sage.all import *
>>> G.show(scale=('loglog', Integer(2), Integer(3)))  # x in base 2, y in base 3        # long time, needs sage.symbolic

The base need not be an integer, though it does have to be made a float.:

sage: G.show(scale='semilogx', base=float(e))  # base is e                  # needs sage.symbolic

>>> from sage.all import *
>>> G.show(scale='semilogx', base=float(e))  # base is e                  # needs sage.symbolic

Logarithmic scale can be used for various kinds of plots. Here are some examples.:

sage: G = list_plot([10**i for i in range(10)])                         # long time, needs sage.symbolic
sage: G.show(scale='semilogy')                                          # long time, needs sage.symbolic

>>> from sage.all import *
>>> G = list_plot([Integer(10)**i for i in range(Integer(10))])                         # long time, needs sage.symbolic
>>> G.show(scale='semilogy')                                          # long time, needs sage.symbolic

sage: G = parametric_plot((x, x**2), (x, 1, 10))                            # needs sage.symbolic
sage: G.show(scale='loglog')                                                # needs sage.symbolic

>>> from sage.all import *
>>> G = parametric_plot((x, x**Integer(2)), (x, Integer(1), Integer(10)))                            # needs sage.symbolic
>>> G.show(scale='loglog')                                                # needs sage.symbolic

sage: disk((5,5), 4, (0, 3*pi/2)).show(scale='loglog',base=2)               # needs sage.symbolic

>>> from sage.all import *
>>> disk((Integer(5),Integer(5)), Integer(4), (Integer(0), Integer(3)*pi/Integer(2))).show(scale='loglog',base=Integer(2))               # needs sage.symbolic

sage: x, y = var('x, y')                                                    # needs sage.symbolic
sage: G = plot_vector_field((2^x,y^2), (x,1,10), (y,1,100))                 # needs sage.symbolic
sage: G.show(scale='semilogx',base=2)                                       # needs sage.symbolic

>>> from sage.all import *
>>> x, y = var('x, y')                                                    # needs sage.symbolic
>>> G = plot_vector_field((Integer(2)**x,y**Integer(2)), (x,Integer(1),Integer(10)), (y,Integer(1),Integer(100)))                 # needs sage.symbolic
>>> G.show(scale='semilogx',base=Integer(2))                                       # needs sage.symbolic

Flip the horizontal or vertical axis.

sage: G = plot(x^3, -2, 3)                                                  # needs sage.symbolic
sage: G.show(flip_x=True)                                                   # needs sage.symbolic
sage: G.show(flip_y=True)                                                   # needs sage.symbolic

>>> from sage.all import *
>>> G = plot(x**Integer(3), -Integer(2), Integer(3))                                                  # needs sage.symbolic
>>> G.show(flip_x=True)                                                   # needs sage.symbolic
>>> G.show(flip_y=True)                                                   # needs sage.symbolic

Add grid lines at the major ticks of the axes.

sage: c = circle((0,0), 1)
sage: c.show(gridlines=True)
sage: c.show(gridlines="automatic")
sage: c.show(gridlines="major")

>>> from sage.all import *
>>> c = circle((Integer(0),Integer(0)), Integer(1))
>>> c.show(gridlines=True)
>>> c.show(gridlines="automatic")
>>> c.show(gridlines="major")

Add grid lines at the major and minor ticks of the axes.

sage: # needs sage.symbolic
sage: u,v = var('u v')
sage: f = exp(-(u^2+v^2))
sage: p = plot_vector_field(f.gradient(), (u,-2,2), (v,-2,2))
sage: p.show(gridlines="minor")

>>> from sage.all import *
>>> # needs sage.symbolic
>>> u,v = var('u v')
>>> f = exp(-(u**Integer(2)+v**Integer(2)))
>>> p = plot_vector_field(f.gradient(), (u,-Integer(2),Integer(2)), (v,-Integer(2),Integer(2)))
>>> p.show(gridlines="minor")

Add only horizontal or vertical grid lines.

sage: p = plot(sin, -10, 20)                                                # needs sage.symbolic
sage: p.show(gridlines=[None, "automatic"])                                 # needs sage.symbolic
sage: p.show(gridlines=["minor", False])                                    # needs sage.symbolic

>>> from sage.all import *
>>> p = plot(sin, -Integer(10), Integer(20))                                                # needs sage.symbolic
>>> p.show(gridlines=[None, "automatic"])                                 # needs sage.symbolic
>>> p.show(gridlines=["minor", False])                                    # needs sage.symbolic

Add grid lines at specific positions (using lists/tuples).

sage: x, y = var('x, y')                                                    # needs sage.symbolic
sage: p = implicit_plot((y^2-x^2)*(x-1)*(2*x-3) - 4*(x^2+y^2-2*x)^2,        # needs sage.symbolic
....:                   (x,-2,2), (y,-2,2), plot_points=1000)
sage: p.show(gridlines=[[1,0],[-1,0,1]])                                    # needs sage.symbolic

>>> from sage.all import *
>>> x, y = var('x, y')                                                    # needs sage.symbolic
>>> p = implicit_plot((y**Integer(2)-x**Integer(2))*(x-Integer(1))*(Integer(2)*x-Integer(3)) - Integer(4)*(x**Integer(2)+y**Integer(2)-Integer(2)*x)**Integer(2),        # needs sage.symbolic
...                   (x,-Integer(2),Integer(2)), (y,-Integer(2),Integer(2)), plot_points=Integer(1000))
>>> p.show(gridlines=[[Integer(1),Integer(0)],[-Integer(1),Integer(0),Integer(1)]])                                    # needs sage.symbolic

Add grid lines at specific positions (using iterators).

sage: def maple_leaf(t):
....:     return (100/(100+(t-pi/2)^8))*(2-sin(7*t)-cos(30*t)/2)
sage: p = polar_plot(maple_leaf, -pi/4, 3*pi/2,                         # long time, needs sage.symbolic
....:                color="red",plot_points=1000)
sage: p.show(gridlines=([-3,-2.75,..,3], range(-1,5,2)))                # long time, needs sage.symbolic

>>> from sage.all import *
>>> def maple_leaf(t):
...     return (Integer(100)/(Integer(100)+(t-pi/Integer(2))**Integer(8)))*(Integer(2)-sin(Integer(7)*t)-cos(Integer(30)*t)/Integer(2))
>>> p = polar_plot(maple_leaf, -pi/Integer(4), Integer(3)*pi/Integer(2),                         # long time, needs sage.symbolic
...                color="red",plot_points=Integer(1000))
>>> p.show(gridlines=((ellipsis_range(-Integer(3),-RealNumber('2.75'),Ellipsis,Integer(3))), range(-Integer(1),Integer(5),Integer(2))))                # long time, needs sage.symbolic

Add grid lines at specific positions (using functions).

sage: # needs sage.symbolic
sage: y = x^5 + 4*x^4 - 10*x^3 - 40*x^2 + 9*x + 36
sage: p = plot(y, -4.1, 1.1)
sage: xlines = lambda a, b: [z for z, m in y.roots()]
sage: p.show(gridlines=[xlines, [0]], frame=True, axes=False)

>>> from sage.all import *
>>> # needs sage.symbolic
>>> y = x**Integer(5) + Integer(4)*x**Integer(4) - Integer(10)*x**Integer(3) - Integer(40)*x**Integer(2) + Integer(9)*x + Integer(36)
>>> p = plot(y, -RealNumber('4.1'), RealNumber('1.1'))
>>> xlines = lambda a, b: [z for z, m in y.roots()]
>>> p.show(gridlines=[xlines, [Integer(0)]], frame=True, axes=False)

Change the style of all the grid lines.

sage: b = bar_chart([-3,5,-6,11], color='red')
sage: b.show(gridlines=([-1,-0.5,..,4], True),
....:        gridlinesstyle=dict(color="blue", linestyle=":"))

>>> from sage.all import *
>>> b = bar_chart([-Integer(3),Integer(5),-Integer(6),Integer(11)], color='red')
>>> b.show(gridlines=((ellipsis_range(-Integer(1),-RealNumber('0.5'),Ellipsis,Integer(4))), True),
...        gridlinesstyle=dict(color="blue", linestyle=":"))

Change the style of the horizontal or vertical grid lines separately.

sage: p = polar_plot(2 + 2*cos(x), 0, 2*pi, color=hue(0.3))                 # needs sage.symbolic
sage: p.show(gridlines=True,                                                # needs sage.symbolic
....:        hgridlinesstyle=dict(color="orange", linewidth=1.0),
....:        vgridlinesstyle=dict(color="blue", linestyle=":"))

>>> from sage.all import *
>>> p = polar_plot(Integer(2) + Integer(2)*cos(x), Integer(0), Integer(2)*pi, color=hue(RealNumber('0.3')))                 # needs sage.symbolic
>>> p.show(gridlines=True,                                                # needs sage.symbolic
...        hgridlinesstyle=dict(color="orange", linewidth=RealNumber('1.0')),
...        vgridlinesstyle=dict(color="blue", linestyle=":"))

Change the style of each grid line individually.

sage: x, y = var('x, y')                                                    # needs sage.symbolic
sage: p = implicit_plot((y^2-x^2)*(x-1)*(2*x-3) - 4*(x^2+y^2-2*x)^2,        # needs sage.symbolic
....:                   (x,-2,2), (y,-2,2), plot_points=1000)
sage: p.show(gridlines=(                                                    # needs sage.symbolic
....:    [
....:     (1,{"color":"red","linestyle":":"}),
....:     (0,{"color":"blue","linestyle":"--"})
....:    ],
....:    [
....:     (-1,{"color":"red","linestyle":":"}),
....:     (0,{"color":"blue","linestyle":"--"}),
....:     (1,{"color":"red","linestyle":":"}),
....:    ]
....:    ),
....:    gridlinesstyle=dict(marker='x',color="black"))

>>> from sage.all import *
>>> x, y = var('x, y')                                                    # needs sage.symbolic
>>> p = implicit_plot((y**Integer(2)-x**Integer(2))*(x-Integer(1))*(Integer(2)*x-Integer(3)) - Integer(4)*(x**Integer(2)+y**Integer(2)-Integer(2)*x)**Integer(2),        # needs sage.symbolic
...                   (x,-Integer(2),Integer(2)), (y,-Integer(2),Integer(2)), plot_points=Integer(1000))
>>> p.show(gridlines=(                                                    # needs sage.symbolic
...    [
...     (Integer(1),{"color":"red","linestyle":":"}),
...     (Integer(0),{"color":"blue","linestyle":"--"})
...    ],
...    [
...     (-Integer(1),{"color":"red","linestyle":":"}),
...     (Integer(0),{"color":"blue","linestyle":"--"}),
...     (Integer(1),{"color":"red","linestyle":":"}),
...    ]
...    ),
...    gridlinesstyle=dict(marker='x',color="black"))

Grid lines can be added to contour plots.

sage: f = sin(x^2 + y^2)*cos(x)*sin(y)                                      # needs sage.symbolic
sage: c = contour_plot(f, (x, -4, 4), (y, -4, 4), plot_points=100)          # needs sage.symbolic
sage: c.show(gridlines=True,                                                # needs sage.symbolic
....:        gridlinesstyle={'linestyle': ':', 'linewidth': 1, 'color': 'red'})

>>> from sage.all import *
>>> f = sin(x**Integer(2) + y**Integer(2))*cos(x)*sin(y)                                      # needs sage.symbolic
>>> c = contour_plot(f, (x, -Integer(4), Integer(4)), (y, -Integer(4), Integer(4)), plot_points=Integer(100))          # needs sage.symbolic
>>> c.show(gridlines=True,                                                # needs sage.symbolic
...        gridlinesstyle={'linestyle': ':', 'linewidth': Integer(1), 'color': 'red'})

Grid lines can be added to matrix plots.

sage: M = MatrixSpace(QQ,10).random_element()
sage: matrix_plot(M).show(gridlines=True)

>>> from sage.all import *
>>> M = MatrixSpace(QQ,Integer(10)).random_element()
>>> matrix_plot(M).show(gridlines=True)

By default, Sage increases the horizontal and vertical axes limits by a certain percentage in all directions. This is controlled by the axes_pad parameter. Increasing the range of the axes helps avoid problems with lines and dots being clipped because the linewidth extends beyond the axes. To get axes limits that are exactly what is specified, set axes_pad to zero. Compare the following two examples

sage: (plot(sin(x), (x, -pi, pi), thickness=2)                              # needs sage.symbolic
....:   + point((pi, -1), pointsize=15))
Graphics object consisting of 2 graphics primitives
sage: (plot(sin(x), (x, -pi, pi), thickness=2, axes_pad=0)                  # needs sage.symbolic
....:   + point((pi, -1), pointsize=15))
Graphics object consisting of 2 graphics primitives

>>> from sage.all import *
>>> (plot(sin(x), (x, -pi, pi), thickness=Integer(2))                              # needs sage.symbolic
...   + point((pi, -Integer(1)), pointsize=Integer(15)))
Graphics object consisting of 2 graphics primitives
>>> (plot(sin(x), (x, -pi, pi), thickness=Integer(2), axes_pad=Integer(0))                  # needs sage.symbolic
...   + point((pi, -Integer(1)), pointsize=Integer(15)))
Graphics object consisting of 2 graphics primitives

The behavior of the axes_pad parameter is different if the axis is in the "log" scale. If \(b\) is the base of the axis, the minimum value of the axis, is decreased by the factor \(1/b^{\mathrm{axes\_pad}}\) of the minimum and the maximum value of the axis is increased by the same factor of the maximum value. Compare the axes in the following two plots to see the difference.

sage: plot_loglog(x, (1.1*10**-2, 9990))                                    # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

sage: plot_loglog(x, (1.1*10**-2, 9990), axes_pad=0)                        # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot_loglog(x, (RealNumber('1.1')*Integer(10)**-Integer(2), Integer(9990)))                                    # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> plot_loglog(x, (RealNumber('1.1')*Integer(10)**-Integer(2), Integer(9990)), axes_pad=Integer(0))                        # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

Via matplotlib, Sage allows setting of custom ticks. See above for more details.

Here the labels are not so useful:

sage: plot(sin(pi*x), (x, -8, 8))                                           # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(sin(pi*x), (x, -Integer(8), Integer(8)))                                           # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

Now put ticks at multiples of 2:

sage: plot(sin(pi*x), (x, -8, 8), ticks=2)                                  # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(sin(pi*x), (x, -Integer(8), Integer(8)), ticks=Integer(2))                                  # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

Or just choose where you want the ticks:

sage: plot(sin(pi*x), (x, -8, 8), ticks=[[-7,-3,0,3,7], [-1/2,0,1/2]])      # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(sin(pi*x), (x, -Integer(8), Integer(8)), ticks=[[-Integer(7),-Integer(3),Integer(0),Integer(3),Integer(7)], [-Integer(1)/Integer(2),Integer(0),Integer(1)/Integer(2)]])      # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

Or no ticks at all:

sage: plot(sin(pi*x), (x, -8, 8), ticks=[[], []])                           # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(sin(pi*x), (x, -Integer(8), Integer(8)), ticks=[[], []])                           # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

This can be very helpful in showing certain features of plots.

sage: plot(1.5/(1+e^(-x)), (x, -10, 10))  # doesn't quite show value of inflection point                    # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(RealNumber('1.5')/(Integer(1)+e**(-x)), (x, -Integer(10), Integer(10)))  # doesn't quite show value of inflection point                    # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

sage: plot(1.5/(1+e^(-x)), (x, -10, 10),  # It's right at f(x)=0.75!        # needs sage.symbolic
....:      ticks=[None, 1.5/4])
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(RealNumber('1.5')/(Integer(1)+e**(-x)), (x, -Integer(10), Integer(10)),  # It's right at f(x)=0.75!        # needs sage.symbolic
...      ticks=[None, RealNumber('1.5')/Integer(4)])
Graphics object consisting of 1 graphics primitive

But be careful to leave enough room for at least two major ticks, so that the user can tell what the scale is:

sage: plot(x^2, (x,1,8), ticks=6).show()                                    # needs sage.symbolic
Traceback (most recent call last):
...
ValueError: Expand the range of the independent variable to
allow two multiples of your tick locator (option `ticks`).

>>> from sage.all import *
>>> plot(x**Integer(2), (x,Integer(1),Integer(8)), ticks=Integer(6)).show()                                    # needs sage.symbolic
Traceback (most recent call last):
...
ValueError: Expand the range of the independent variable to
allow two multiples of your tick locator (option `ticks`).

We can also do custom formatting if you need it. See above for full details:

sage: plot(2*x + 1, (x,0,5),        # not tested (broken with matplotlib 3.6), needs sage.symbolic
....:      ticks=[[0,1,e,pi,sqrt(20)], 2],
....:      tick_formatter="latex")
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(Integer(2)*x + Integer(1), (x,Integer(0),Integer(5)),        # not tested (broken with matplotlib 3.6), needs sage.symbolic
...      ticks=[[Integer(0),Integer(1),e,pi,sqrt(Integer(20))], Integer(2)],
...      tick_formatter="latex")
Graphics object consisting of 1 graphics primitive

This is particularly useful when setting custom ticks in multiples of \(\pi\).

sage: plot(sin(x), (x,0,2*pi), ticks=pi/3, tick_formatter=pi)               # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(sin(x), (x,Integer(0),Integer(2)*pi), ticks=pi/Integer(3), tick_formatter=pi)               # needs sage.symbolic
Graphics object consisting of 1 graphics primitive

But keep in mind that you will get exactly the formatting you asked for if you specify both formatters. The first syntax is recommended for best style in that case.

sage: plot(arcsin(x), (x,-1,1), ticks=[None, pi/6],  # Nice-looking!        # needs sage.symbolic
....:      tick_formatter=["latex", pi])
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(arcsin(x), (x,-Integer(1),Integer(1)), ticks=[None, pi/Integer(6)],  # Nice-looking!        # needs sage.symbolic
...      tick_formatter=["latex", pi])
Graphics object consisting of 1 graphics primitive

sage: plot(arcsin(x), (x,-1,1), ticks=[None, pi/6],  # Not so nice-looking  # needs sage.symbolic
....:      tick_formatter=[None, pi])
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(arcsin(x), (x,-Integer(1),Integer(1)), ticks=[None, pi/Integer(6)],  # Not so nice-looking  # needs sage.symbolic
...      tick_formatter=[None, pi])
Graphics object consisting of 1 graphics primitive

Custom tick labels can be provided by providing the keyword tick_formatter with the list of labels, and simultaneously providing the keyword ticks with the positions of the labels.

sage: plot(x, (x,0,3), ticks=[[1,2.5], [0.5,1,2]],                          # needs sage.symbolic
....:      tick_formatter=[["$x_1$","$x_2$"], ["$y_1$","$y_2$","$y_3$"]])
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(x, (x,Integer(0),Integer(3)), ticks=[[Integer(1),RealNumber('2.5')], [RealNumber('0.5'),Integer(1),Integer(2)]],                          # needs sage.symbolic
...      tick_formatter=[["$x_1$","$x_2$"], ["$y_1$","$y_2$","$y_3$"]])
Graphics object consisting of 1 graphics primitive

The following sets the custom tick labels only along the horizontal axis.

sage: plot(x**2, (x,0,2), ticks=[[1,2], None],                              # needs sage.symbolic
....:      tick_formatter=[["$x_1$","$x_2$"], None])
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(x**Integer(2), (x,Integer(0),Integer(2)), ticks=[[Integer(1),Integer(2)], None],                              # needs sage.symbolic
...      tick_formatter=[["$x_1$","$x_2$"], None])
Graphics object consisting of 1 graphics primitive

If the number of tick labels do not match the number of positions of tick labels, then it results in an error.:

sage: plot(x**2, (x,0,2), ticks=[[2], None],                                # needs sage.symbolic
....:      tick_formatter=[["$x_1$","$x_2$"], None]).show()
Traceback (most recent call last):
...
ValueError: If the first component of the list `tick_formatter` is a list
then the first component of `ticks` must also be a list of equal length.

>>> from sage.all import *
>>> plot(x**Integer(2), (x,Integer(0),Integer(2)), ticks=[[Integer(2)], None],                                # needs sage.symbolic
...      tick_formatter=[["$x_1$","$x_2$"], None]).show()
Traceback (most recent call last):
...
ValueError: If the first component of the list `tick_formatter` is a list
then the first component of `ticks` must also be a list of equal length.

When using logarithmic scale along the axis, make sure to have enough room for two ticks so that the user can tell what the scale is. This can be effected by increasing the range of the independent variable, or by changing the base, or by providing enough tick locations by using the ticks parameter.

By default, Sage will expand the variable range so that at least two ticks are included along the logarithmic axis. However, if you specify ticks manually, this safety measure can be defeated:

sage: list_plot_loglog([(1,2),(2,3)], plotjoined=True, ticks=[[1],[1]])
doctest:...: UserWarning: The x-axis contains fewer than 2 ticks;
the logarithmic scale of the plot may not be apparent to the reader.
doctest:...: UserWarning: The y-axis contains fewer than 2 ticks;
the logarithmic scale of the plot may not be apparent to the reader.
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> list_plot_loglog([(Integer(1),Integer(2)),(Integer(2),Integer(3))], plotjoined=True, ticks=[[Integer(1)],[Integer(1)]])
doctest:...: UserWarning: The x-axis contains fewer than 2 ticks;
the logarithmic scale of the plot may not be apparent to the reader.
doctest:...: UserWarning: The y-axis contains fewer than 2 ticks;
the logarithmic scale of the plot may not be apparent to the reader.
Graphics object consisting of 1 graphics primitive

This one works, since the horizontal axis is automatically expanded to contain two ticks and the vertical axis is provided with two ticks:

sage: list_plot_loglog([(1,2),(2,3)], plotjoined=True, ticks=[None,[1,10]])
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> list_plot_loglog([(Integer(1),Integer(2)),(Integer(2),Integer(3))], plotjoined=True, ticks=[None,[Integer(1),Integer(10)]])
Graphics object consisting of 1 graphics primitive

Another example in the log scale where both the axes are automatically expanded to show two major ticks:

sage: list_plot_loglog([(2,0.5), (3, 4)], plotjoined=True)
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> list_plot_loglog([(Integer(2),RealNumber('0.5')), (Integer(3), Integer(4))], plotjoined=True)
Graphics object consisting of 1 graphics primitive

When using title_pos, it must be ensured that a list or a tuple of length two is used. Otherwise, a warning is raised:

sage: plot(x, -4, 4, title='Plot x', title_pos=0.05)                        # needs sage.symbolic
doctest:...: ...RichReprWarning: Exception in _rich_repr_ while displaying
object: 'title_pos' must be a list or tuple of two real numbers.
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> plot(x, -Integer(4), Integer(4), title='Plot x', title_pos=RealNumber('0.05'))                        # needs sage.symbolic
doctest:...: ...RichReprWarning: Exception in _rich_repr_ while displaying
object: 'title_pos' must be a list or tuple of two real numbers.
Graphics object consisting of 1 graphics primitive
tick_label_color(c=None)[source]#

Set the color of the axes tick labels.

INPUT:

  • c – an RGB 3-tuple of numbers between 0 and 1

If called with no input, return the current tick_label_color setting.

EXAMPLES:

sage: # needs sage.symbolic
sage: p = plot(cos, (-3,3))
sage: p.tick_label_color()
(0, 0, 0)
sage: p.tick_label_color((1,0,0))
sage: p.tick_label_color()
(1.0, 0.0, 0.0)
sage: p
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> # needs sage.symbolic
>>> p = plot(cos, (-Integer(3),Integer(3)))
>>> p.tick_label_color()
(0, 0, 0)
>>> p.tick_label_color((Integer(1),Integer(0),Integer(0)))
>>> p.tick_label_color()
(1.0, 0.0, 0.0)
>>> p
Graphics object consisting of 1 graphics primitive
xmax(xmax=None)[source]#

EXAMPLES:

sage: g = line([(-1,1), (3,2)])
sage: g.xmax()
3.0
sage: g.xmax(10)
sage: g.xmax()
10.0

>>> from sage.all import *
>>> g = line([(-Integer(1),Integer(1)), (Integer(3),Integer(2))])
>>> g.xmax()
3.0
>>> g.xmax(Integer(10))
>>> g.xmax()
10.0
xmin(xmin=None)[source]#

EXAMPLES:

sage: g = line([(-1,1), (3,2)])
sage: g.xmin()
-1.0
sage: g.xmin(-3)
sage: g.xmin()
-3.0

>>> from sage.all import *
>>> g = line([(-Integer(1),Integer(1)), (Integer(3),Integer(2))])
>>> g.xmin()
-1.0
>>> g.xmin(-Integer(3))
>>> g.xmin()
-3.0
ymax(ymax=None)[source]#

EXAMPLES:

sage: g = line([(-1,1), (3,2)])
sage: g.ymax()
2.0
sage: g.ymax(10)
sage: g.ymax()
10.0

>>> from sage.all import *
>>> g = line([(-Integer(1),Integer(1)), (Integer(3),Integer(2))])
>>> g.ymax()
2.0
>>> g.ymax(Integer(10))
>>> g.ymax()
10.0
ymin(ymin=None)[source]#

EXAMPLES:

sage: g = line([(-1,1), (3,2)])
sage: g.ymin()
1.0
sage: g.ymin(-3)
sage: g.ymin()
-3.0

>>> from sage.all import *
>>> g = line([(-Integer(1),Integer(1)), (Integer(3),Integer(2))])
>>> g.ymin()
1.0
>>> g.ymin(-Integer(3))
>>> g.ymin()
-3.0
sage.plot.graphics.GraphicsArray(*args, **kwargs)[source]#

This is deprecated (see Issue #28675). Use sage.plot.multigraphics.GraphicsArray instead.

sage.plot.graphics.is_Graphics(x)[source]#

Return True if \(x\) is a Graphics object.

EXAMPLES:

sage: from sage.plot.graphics import is_Graphics
sage: is_Graphics(1)
doctest:warning...
DeprecationWarning: The function is_Graphics is deprecated;
use 'isinstance(..., Graphics)' instead.
See https://github.com/sagemath/sage/issues/38184 for details.
False
sage: is_Graphics(disk((0.0, 0.0), 1, (0, pi/2)))                               # needs sage.symbolic
True

>>> from sage.all import *
>>> from sage.plot.graphics import is_Graphics
>>> is_Graphics(Integer(1))
doctest:warning...
DeprecationWarning: The function is_Graphics is deprecated;
use 'isinstance(..., Graphics)' instead.
See https://github.com/sagemath/sage/issues/38184 for details.
False
>>> is_Graphics(disk((RealNumber('0.0'), RealNumber('0.0')), Integer(1), (Integer(0), pi/Integer(2))))                               # needs sage.symbolic
True