Help on function plot in module sage.plot.plot:
plot(*args, **kwds)
Use plot by writing
``plot(X, ...)``
where `X` is a Sage object (or list of Sage objects) that
either is callable and returns numbers that can be coerced to
floats, or has a plot method that returns a
``GraphicPrimitive`` object.
There are many other specialized 2D plot commands available
in Sage, such as ``plot_slope_field``, as well as various
graphics primitives like :class:`~sage.plot.arrow.Arrow`;
type ``sage.plot.plot?`` for a current list.
Type ``plot.options`` for a dictionary of the default
options for plots. You can change this to change the defaults for
all future plots. Use ``plot.reset()`` to reset to the
default options.
PLOT OPTIONS:
- ``plot_points`` - (default: 200) the minimal number of plot points.
- ``adaptive_recursion`` - (default: 5) how many levels of recursion to go
before giving up when doing adaptive refinement. Setting this to 0
disables adaptive refinement.
- ``adaptive_tolerance`` - (default: 0.01) how large a difference should be
before the adaptive refinement code considers it significant. See the
documentation further below for more information, starting at "the
algorithm used to insert".
- ``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.
- ``xmin`` - starting x value in the rendered figure. This parameter is
passed directly to the ``show`` procedure and it could be overwritten.
- ``xmax`` - ending x value in the rendered figure. This parameter is passed
directly to the ``show`` procedure and it could be overwritten.
- ``ymin`` - starting y value in the rendered figure. This parameter is
passed directly to the ``show`` procedure and it could be overwritten.
- ``ymax`` - ending y value in the rendered figure. This parameter is passed
directly to the ``show`` procedure and it could be overwritten.
- ``color`` - an RGB tuple (r,g,b) with each of r,g,b between 0 and 1,
or a color name as a string (e.g., 'purple'), or an HTML color
such as '#aaff0b'.
- ``detect_poles`` - (Default: False) If set to True poles are detected.
If set to "show" vertical asymptotes are drawn.
- ``legend_color`` - the color of the text for this item in the legend
- ``legend_label`` - the label for this item in the legend
.. note::
- If the ``scale`` is ``"linear"``, then irrespective of what
``base`` is set to, it will default to 10 and will remain unused.
- If you want to limit the plot along the horizontal axis in the
final rendered figure, then pass the ``xmin`` and ``xmax``
keywords to the :meth:`~sage.plot.graphics.Graphics.show` method.
To limit the plot along the vertical axis, ``ymin`` and ``ymax``
keywords can be provided to either this ``plot`` command or to
the ``show`` command.
- For the other keyword options that the ``plot`` function can
take, refer to the method :meth:`~sage.plot.graphics.Graphics.show`.
APPEARANCE OPTIONS:
The following options affect the appearance of
the line through the points on the graph of `X` (these are
the same as for the line function):
INPUT:
- ``alpha`` - How transparent the line is
- ``thickness`` - How thick the line is
- ``rgbcolor`` - The color as an RGB tuple
- ``hue`` - The color given as a hue
Any MATPLOTLIB line option may also be passed in. E.g.,
- ``linestyle`` - (default: "-") The style of the line, which is one of
- ``"-"`` or ``"solid"``
- ``"--"`` or ``"dashed"``
- ``"-."`` or ``"dash dot"``
- ``":"`` or ``"dotted"``
- ``"None"`` or ``" "`` or ``""`` (nothing)
The linestyle can also be prefixed with a drawing style (e.g., ``"steps--"``)
- ``"default"`` (connect the points with straight lines)
- ``"steps"`` or ``"steps-pre"`` (step function; horizontal
line is to the left of point)
- ``"steps-mid"`` (step function; points are in the middle of
horizontal lines)
- ``"steps-post"`` (step function; horizontal line is to the
right of point)
- ``marker`` - The style of the markers, which is one of
- ``"None"`` or ``" "`` or ``""`` (nothing) -- default
- ``","`` (pixel), ``"."`` (point)
- ``"_"`` (horizontal line), ``"|"`` (vertical line)
- ``"o"`` (circle), ``"p"`` (pentagon), ``"s"`` (square), ``"x"`` (x), ``"+"`` (plus), ``"*"`` (star)
- ``"D"`` (diamond), ``"d"`` (thin diamond)
- ``"H"`` (hexagon), ``"h"`` (alternative hexagon)
- ``"<"`` (triangle left), ``">"`` (triangle right), ``"^"`` (triangle up), ``"v"`` (triangle down)
- ``"1"`` (tri down), ``"2"`` (tri up), ``"3"`` (tri left), ``"4"`` (tri right)
- ``0`` (tick left), ``1`` (tick right), ``2`` (tick up), ``3`` (tick down)
- ``4`` (caret left), ``5`` (caret right), ``6`` (caret up), ``7`` (caret down), ``8`` (octagon)
- ``"$...$"`` (math TeX string)
- ``(numsides, style, angle)`` to create a custom, regular symbol
- ``numsides`` -- the number of sides
- ``style`` -- ``0`` (regular polygon), ``1`` (star shape), ``2`` (asterisk), ``3`` (circle)
- ``angle`` -- the angular rotation in degrees
- ``markersize`` - the size of the marker in points
- ``markeredgecolor`` -- the color of the marker edge
- ``markerfacecolor`` -- the color of the marker face
- ``markeredgewidth`` - the size of the marker edge in points
- ``exclude`` - (Default: None) values which are excluded from the plot range.
Either a list of real numbers, or an equation in one variable.
FILLING OPTIONS:
- ``fill`` - (Default: False) One of:
- "axis" or True: Fill the area between the function and the x-axis.
- "min": Fill the area between the function and its minimal value.
- "max": Fill the area between the function and its maximal value.
- a number c: Fill the area between the function and the horizontal line y = c.
- a function g: Fill the area between the function that is plotted and g.
- a dictionary ``d`` (only if a list of functions are plotted):
The keys of the dictionary should be integers.
The value of ``d[i]`` specifies the fill options for the i-th function
in the list. If ``d[i] == [j]``: Fill the area between the i-th and
the j-th function in the list. (But if ``d[i] == j``: Fill the area
between the i-th function in the list and the horizontal line y = j.)
- ``fillcolor`` - (default: 'automatic') The color of the fill.
Either 'automatic' or a color.
- ``fillalpha`` - (default: 0.5) How transparent the fill is.
A number between 0 and 1.
.. note::
- this function does NOT simply sample equally spaced points
between xmin and xmax. Instead it computes equally spaced points
and adds small perturbations to them. This reduces the possibility
of, e.g., sampling `\sin` only at multiples of `2\pi`, which would
yield a very misleading graph.
- if there is a range of consecutive points where the function has
no value, then those points will be excluded from the plot. See
the example below on automatic exclusion of points.
EXAMPLES:
We plot the `\sin` function::
sage: P = plot(sin, (0,10)); print P
Graphics object consisting of 1 graphics primitive
sage: len(P) # number of graphics primitives
1
sage: len(P[0]) # how many points were computed (random)
225
sage: P # render
Graphics object consisting of 1 graphics primitive
::
sage: P = plot(sin, (0,10), plot_points=10); print P
Graphics object consisting of 1 graphics primitive
sage: len(P[0]) # random output
32
sage: P # render
Graphics object consisting of 1 graphics primitive
We plot with ``randomize=False``, which makes the initial sample points
evenly spaced (hence always the same). Adaptive plotting might
insert other points, however, unless ``adaptive_recursion=0``.
::
sage: p=plot(1, (x,0,3), plot_points=4, randomize=False, adaptive_recursion=0)
sage: list(p[0])
[(0.0, 1.0), (1.0, 1.0), (2.0, 1.0), (3.0, 1.0)]
Some colored functions::
sage: plot(sin, 0, 10, color='purple')
Graphics object consisting of 1 graphics primitive
sage: plot(sin, 0, 10, color='#ff00ff')
Graphics object consisting of 1 graphics primitive
We plot several functions together by passing a list of functions
as input::
sage: plot([sin(n*x) for n in [1..4]], (0, pi))
Graphics object consisting of 4 graphics primitives
We can also build a plot step by step from an empty plot::
sage: a = plot([]); a # passing an empty list returns an empty plot (Graphics() object)
Graphics object consisting of 0 graphics primitives
sage: a += plot(x**2); a # append another plot
Graphics object consisting of 1 graphics primitive
sage: a += plot(x**3); a # append yet another plot
Graphics object consisting of 2 graphics primitives
The function `\sin(1/x)` wiggles wildly near `0`.
Sage adapts to this and plots extra points near the origin.
::
sage: plot(sin(1/x), (x, -1, 1))
Graphics object consisting of 1 graphics primitive
Via the matplotlib library, Sage makes it easy to tell whether
a graph is on both sides of both axes, as the axes only cross
if the origin is actually part of the viewing area::
sage: plot(x^3,(x,0,2)) # this one has the origin
Graphics object consisting of 1 graphics primitive
sage: plot(x^3,(x,1,2)) # this one does not
Graphics object consisting of 1 graphics primitive
Another thing to be aware of with axis labeling is that when
the labels have quite different orders of magnitude or are very
large, scientific notation (the `e` notation for powers of ten) is used::
sage: plot(x^2,(x,480,500)) # this one has no scientific notation
Graphics object consisting of 1 graphics primitive
sage: plot(x^2,(x,300,500)) # this one has scientific notation on y-axis
Graphics object consisting of 1 graphics primitive
You can put a legend with ``legend_label`` (the legend is only put
once in the case of multiple functions)::
sage: plot(exp(x), 0, 2, legend_label='$e^x$')
Graphics object consisting of 1 graphics primitive
Sage understands TeX, so these all are slightly different, and you can choose
one based on your needs::
sage: plot(sin, legend_label='sin')
Graphics object consisting of 1 graphics primitive
sage: plot(sin, legend_label='$sin$')
Graphics object consisting of 1 graphics primitive
sage: plot(sin, legend_label='$\sin$')
Graphics object consisting of 1 graphics primitive
It is possible to use a different color for the text of each label::
sage: p1 = plot(sin, legend_label='sin', legend_color='red')
sage: p2 = plot(cos, legend_label='cos', legend_color='green')
sage: p1 + p2
Graphics object consisting of 2 graphics primitives
Prior to :trac:`19485`, legends by default had a shadowless gray
background. This behavior can be recovered by setting the legend
options on your plot object::
sage: p = plot(sin(x), legend_label='$\sin(x)$')
sage: p.set_legend_options(back_color=(0.9,0.9,0.9), shadow=False)
Note that the independent variable may be omitted if there is no
ambiguity::
sage: plot(sin(1/x), (-1, 1))
Graphics object consisting of 1 graphics primitive
Plotting in logarithmic scale is possible for 2D plots. There
are two different syntaxes supported::
sage: plot(exp, (1, 10), scale='semilogy') # log axis on vertical
Graphics object consisting of 1 graphics primitive
::
sage: plot_semilogy(exp, (1, 10)) # same thing
Graphics object consisting of 1 graphics primitive
::
sage: plot_loglog(exp, (1, 10)) # both axes are log
Graphics object consisting of 1 graphics primitive
::
sage: plot(exp, (1, 10), scale='loglog', base=2) # long time # base of log is 2
Graphics object consisting of 1 graphics primitive
We can also change the scale of the axes in the graphics just before
displaying::
sage: G = plot(exp, 1, 10) # long time
sage: G.show(scale=('semilogy', 2)) # long time
The algorithm used to insert extra points is actually pretty
simple. On the picture drawn by the lines below::
sage: p = plot(x^2, (-0.5, 1.4)) + line([(0,0), (1,1)], color='green')
sage: p += line([(0.5, 0.5), (0.5, 0.5^2)], color='purple')
sage: p += point(((0, 0), (0.5, 0.5), (0.5, 0.5^2), (1, 1)), color='red', pointsize=20)
sage: p += text('A', (-0.05, 0.1), color='red')
sage: p += text('B', (1.01, 1.1), color='red')
sage: p += text('C', (0.48, 0.57), color='red')
sage: p += text('D', (0.53, 0.18), color='red')
sage: p.show(axes=False, xmin=-0.5, xmax=1.4, ymin=0, ymax=2)
You have the function (in blue) and its approximation (in green)
passing through the points A and B. The algorithm finds the
midpoint C of AB and computes the distance between C and D. If that
distance exceeds the ``adaptive_tolerance`` threshold (*relative* to
the size of the initial plot subintervals), the point D is
added to the curve. If D is added to the curve, then the
algorithm is applied recursively to the points A and D, and D and
B. It is repeated ``adaptive_recursion`` times (5, by default).
The actual sample points are slightly randomized, so the above
plots may look slightly different each time you draw them.
We draw the graph of an elliptic curve as the union of graphs of 2
functions.
::
sage: def h1(x): return abs(sqrt(x^3 - 1))
sage: def h2(x): return -abs(sqrt(x^3 - 1))
sage: P = plot([h1, h2], 1,4)
sage: P # show the result
Graphics object consisting of 2 graphics primitives
It is important to mention that when we draw several graphs at the same time,
parameters ``xmin``, ``xmax``, ``ymin`` and ``ymax`` are just passed directly
to the ``show`` procedure. In fact, these parameters would be overwritten::
sage: p=plot(x^3, x, xmin=-1, xmax=1,ymin=-1, ymax=1)
sage: q=plot(exp(x), x, xmin=-2, xmax=2, ymin=0, ymax=4)
sage: (p+q).show()
As a workaround, we can perform the trick::
sage: p1 = line([(a,b) for a,b in zip(p[0].xdata,p[0].ydata) if (b>=-1 and b<=1)])
sage: q1 = line([(a,b) for a,b in zip(q[0].xdata,q[0].ydata) if (b>=0 and b<=4)])
sage: (p1+q1).show()
We can also directly plot the elliptic curve::
sage: E = EllipticCurve([0,-1])
sage: plot(E, (1, 4), color=hue(0.6))
Graphics object consisting of 1 graphics primitive
We can change the line style as well::
sage: plot(sin(x), (x, 0, 10), linestyle='-.')
Graphics object consisting of 1 graphics primitive
If we have an empty linestyle and specify a marker, we can see the
points that are actually being plotted::
sage: plot(sin(x), (x,0,10), plot_points=20, linestyle='', marker='.')
Graphics object consisting of 1 graphics primitive
The marker can be a TeX symbol as well::
sage: plot(sin(x), (x,0,10), plot_points=20, linestyle='', marker=r'$\checkmark$')
Graphics object consisting of 1 graphics primitive
Sage currently ignores points that cannot be evaluated
::
sage: set_verbose(-1)
sage: plot(-x*log(x), (x,0,1)) # this works fine since the failed endpoint is just skipped.
Graphics object consisting of 1 graphics primitive
sage: set_verbose(0)
This prints out a warning and plots where it can (we turn off the
warning by setting the verbose mode temporarily to -1.)
::
sage: set_verbose(-1)
sage: plot(x^(1/3), (x,-1,1))
Graphics object consisting of 1 graphics primitive
sage: set_verbose(0)
Plotting the real cube root function for negative input
requires avoiding the complex numbers one would usually get.
The easiest way is to use absolute value::
sage: plot(sign(x)*abs(x)^(1/3), (x,-1,1))
Graphics object consisting of 1 graphics primitive
We can also use the following::
sage: plot(sign(x)*(x*sign(x))^(1/3), (x,-4,4))
Graphics object consisting of 1 graphics primitive
A way that points to how to plot other functions without
symbolic variants is using lambda functions::
sage: plot(lambda x : RR(x).nth_root(3), (x,-1, 1))
Graphics object consisting of 1 graphics primitive
We can detect the poles of a function::
sage: plot(gamma, (-3, 4), detect_poles = True).show(ymin = -5, ymax = 5)
We draw the Gamma-Function with its poles highlighted::
sage: plot(gamma, (-3, 4), detect_poles = 'show').show(ymin = -5, ymax = 5)
The basic options for filling a plot::
sage: p1 = plot(sin(x), -pi, pi, fill = 'axis')
sage: p2 = plot(sin(x), -pi, pi, fill = 'min')
sage: p3 = plot(sin(x), -pi, pi, fill = 'max')
sage: p4 = plot(sin(x), -pi, pi, fill = 0.5)
sage: graphics_array([[p1, p2], [p3, p4]]).show(frame=True, axes=False) # long time
sage: plot([sin(x), cos(2*x)*sin(4*x)], -pi, pi, fill = {0: 1}, fillcolor = 'red', fillalpha = 1)
Graphics object consisting of 3 graphics primitives
A example about the growth of prime numbers::
sage: plot(1.13*log(x), 1, 100, fill = lambda x: nth_prime(x)/floor(x), fillcolor = 'red')
Graphics object consisting of 2 graphics primitives
Fill the area between a function and its asymptote::
sage: f = (2*x^3+2*x-1)/((x-2)*(x+1))
sage: plot([f, 2*x+2], -7,7, fill = {0: [1]}, fillcolor='#ccc').show(ymin=-20, ymax=20)
Fill the area between a list of functions and the x-axis::
sage: def b(n): return lambda x: bessel_J(n, x)
sage: plot([b(n) for n in [1..5]], 0, 20, fill = 'axis')
Graphics object consisting of 10 graphics primitives
Note that to fill between the ith and jth functions, you
must use dictionary key-value pairs ``i:[j]``; key-value pairs
like ``i:j`` will fill between the ith function and the line y=j::
sage: def b(n): return lambda x: bessel_J(n, x) + 0.5*(n-1)
sage: plot([b(c) for c in [1..5]], 0, 40, fill = dict([(i, [i+1]) for i in [0..3]]))
Graphics object consisting of 9 graphics primitives
sage: plot([b(c) for c in [1..5]], 0, 40, fill = dict([(i, i+1) for i in [0..3]])) # long time
Graphics object consisting of 9 graphics primitives
Extra options will get passed on to :meth:`~sage.plot.graphics.Graphics.show`,
as long as they are valid::
sage: plot(sin(x^2), (x, -3, 3), title='Plot of $\sin(x^2)$', axes_labels=['$x$','$y$']) # These labels will be nicely typeset
Graphics object consisting of 1 graphics primitive
sage: plot(sin(x^2), (x, -3, 3), title='Plot of sin(x^2)', axes_labels=['x','y']) # These will not
Graphics object consisting of 1 graphics primitive
sage: plot(sin(x^2), (x, -3, 3), axes_labels=['x','y'], axes_labels_size=2.5) # Large axes labels (w.r.t. the tick marks)
Graphics object consisting of 1 graphics primitive
::
sage: plot(sin(x^2), (x, -3, 3), figsize=[8,2])
Graphics object consisting of 1 graphics primitive
sage: plot(sin(x^2), (x, -3, 3)).show(figsize=[8,2]) # These are equivalent
This includes options for custom ticks and formatting. See documentation
for :meth:`show` for more details.
::
sage: plot(sin(pi*x), (x, -8, 8), ticks=[[-7,-3,0,3,7],[-1/2,0,1/2]])
Graphics object consisting of 1 graphics primitive
sage: plot(2*x+1,(x,0,5),ticks=[[0,1,e,pi,sqrt(20)],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)
Graphics object consisting of 1 graphics primitive
You can even have custom tick labels along with custom positioning. ::
sage: plot(x**2, (x,0,3), ticks=[[1,2.5],[0.5,1,2]], tick_formatter=[["$x_1$","$x_2$"],["$y_1$","$y_2$","$y_3$"]])
Graphics object consisting of 1 graphics primitive
You can force Type 1 fonts in your figures by providing the relevant
option as shown below. This also requires that LaTeX, dvipng and
Ghostscript be installed::
sage: plot(x, typeset='type1') # optional - latex
A example with excluded values::
sage: plot(floor(x), (x, 1, 10), exclude = [1..10])
Graphics object consisting of 11 graphics primitives
We exclude all points where :class:`~sage.functions.prime_pi.PrimePi`
makes a jump::
sage: jumps = [n for n in [1..100] if prime_pi(n) != prime_pi(n-1)]
sage: plot(lambda x: prime_pi(x), (x, 1, 100), exclude = jumps)
Graphics object consisting of 26 graphics primitives
Excluded points can also be given by an equation::
sage: g(x) = x^2-2*x-2
sage: plot(1/g(x), (x, -3, 4), exclude = g(x) == 0, ymin = -5, ymax = 5) # long time
Graphics object consisting of 3 graphics primitives
``exclude`` and ``detect_poles`` can be used together::
sage: f(x) = (floor(x)+0.5) / (1-(x-0.5)^2)
sage: plot(f, (x, -3.5, 3.5), detect_poles = 'show', exclude = [-3..3], ymin = -5, ymax = 5)
Graphics object consisting of 12 graphics primitives
Regions in which the plot has no values are automatically excluded. The
regions thus excluded are in addition to the exclusion points present
in the ``exclude`` keyword argument.::
sage: set_verbose(-1)
sage: plot(arcsec, (x, -2, 2)) # [-1, 1] is excluded automatically
Graphics object consisting of 2 graphics primitives
sage: plot(arcsec, (x, -2, 2), exclude=[1.5]) # x=1.5 is also excluded
Graphics object consisting of 3 graphics primitives
sage: plot(arcsec(x/2), -2, 2) # plot should be empty; no valid points
Graphics object consisting of 0 graphics primitives
sage: plot(sqrt(x^2-1), -2, 2) # [-1, 1] is excluded automatically
Graphics object consisting of 2 graphics primitives
sage: plot(arccsc, -2, 2) # [-1, 1] is excluded automatically
Graphics object consisting of 2 graphics primitives
sage: set_verbose(0)
TESTS:
We do not randomize the endpoints::
sage: p = plot(x, (x,-1,1))
sage: p[0].xdata[0] == -1
True
sage: p[0].xdata[-1] == 1
True
We check to make sure that the x/y min/max data get set correctly
when there are multiple functions.
::
sage: d = plot([sin(x), cos(x)], 100, 120).get_minmax_data()
sage: d['xmin']
100.0
sage: d['xmax']
120.0
We check various combinations of tuples and functions, ending with
tests that lambda functions work properly with explicit variable
declaration, without a tuple.
::
sage: p = plot(lambda x: x,(x,-1,1))
sage: p = plot(lambda x: x,-1,1)
sage: p = plot(x,x,-1,1)
sage: p = plot(x,-1,1)
sage: p = plot(x^2,x,-1,1)
sage: p = plot(x^2,xmin=-1,xmax=2)
sage: p = plot(lambda x: x,x,-1,1)
sage: p = plot(lambda x: x^2,x,-1,1)
sage: p = plot(lambda x: 1/x,x,-1,1)
sage: f(x) = sin(x+3)-.1*x^3
sage: p = plot(lambda x: f(x),x,-1,1)
We check to handle cases where the function gets evaluated at a
point which causes an 'inf' or '-inf' result to be produced.
::
sage: p = plot(1/x, 0, 1)
sage: p = plot(-1/x, 0, 1)
Bad options now give better errors::
sage: P = plot(sin(1/x), (x,-1,3), foo=10)
Traceback (most recent call last):
...
RuntimeError: Error in line(): option 'foo' not valid.
sage: P = plot(x, (x,1,1)) # trac ticket #11753
Traceback (most recent call last):
...
ValueError: plot start point and end point must be different
We test that we can plot `f(x)=x` (see :trac:`10246`)::
sage: f(x)=x; f
x |--> x
sage: plot(f,(x,-1,1))
Graphics object consisting of 1 graphics primitive
Check that :trac:`15030` is fixed::
sage: plot(abs(log(x)), x)
Graphics object consisting of 1 graphics primitive
Check that if excluded points are less than xmin then the exclusion
still works for polar and parametric plots. The following should
show two excluded points::
sage: set_verbose(-1)
sage: polar_plot(sin(sqrt(x^2-1)), (x,0,2*pi), exclude=[1/2,2,3])
Graphics object consisting of 3 graphics primitives
sage: parametric_plot((sqrt(x^2-1),sqrt(x^2-1/2)), (x,0,5), exclude=[1,2,3])
Graphics object consisting of 3 graphics primitives
sage: set_verbose(0)
Legends can contain variables with long names, :trac:`13543`::
sage: hello = var('hello')
sage: label = '$' + latex(hello) + '$'
sage: plot(x, x, 0, 1, legend_label=label)
Graphics object consisting of 1 graphics primitive