20
111
(x, y, z)
x^4 + 4*x^3*y + 6*x^2*y^2 + 4*x*y^3 + y^4 + 4*x^3*z + 12*x^2*y*z + 12*x*y^2*z + 4*y^3*z + 6*x^2*z^2 + 12*x*y*z^2 + 6*y^2*z^2 + 4*x*z^3 + 4*y*z^3 + z^4
0
3
1
4
4
6
6
4
4
1
4
4
1
12
1
12
4
4
6
6
1
12
6
6
4
4
4
4
1
65
166
'478'
1729
216
True
(x, a)
1/2*sqrt(5) + 1/2
(1/2*sqrt(5) + 1/2)^(2*a/pi)
Help on function polar_plot in module sage.plot.plot:
polar_plot(*args, **kwds)
``polar_plot`` takes a single function or a list or
tuple of functions and plots them with polar coordinates in the given
domain.
This function is equivalent to the :func:`plot` command with the options
``polar=True`` and ``aspect_ratio=1``. For more help on options,
see the documentation for :func:`plot`.
INPUT:
- ``funcs`` - a function
- other options are passed to plot
EXAMPLES:
Here is a blue 8-leaved petal::
sage: polar_plot(sin(5*x)^2, (x, 0, 2*pi), color='blue')
Graphics object consisting of 1 graphics primitive
.. PLOT::
g = polar_plot(sin(5*x)**2, (x, 0, 2*pi), color='blue')
sphinx_plot(g)
A red figure-8::
sage: polar_plot(abs(sqrt(1 - sin(x)^2)), (x, 0, 2*pi), color='red')
Graphics object consisting of 1 graphics primitive
.. PLOT::
g = polar_plot(abs(sqrt(1 - sin(x)**2)), (x, 0, 2*pi), color='red')
sphinx_plot(g)
A green limacon of Pascal::
sage: polar_plot(2 + 2*cos(x), (x, 0, 2*pi), color=hue(0.3))
Graphics object consisting of 1 graphics primitive
.. PLOT::
g = polar_plot(2 + 2*cos(x), (x, 0, 2*pi), color=hue(0.3))
sphinx_plot(g)
Several polar plots::
sage: polar_plot([2*sin(x), 2*cos(x)], (x, 0, 2*pi))
Graphics object consisting of 2 graphics primitives
.. PLOT::
g = polar_plot([2*sin(x), 2*cos(x)], (x, 0, 2*pi))
sphinx_plot(g)
A filled spiral::
sage: polar_plot(sqrt, 0, 2 * pi, fill=True)
Graphics object consisting of 2 graphics primitives
.. PLOT::
g = polar_plot(sqrt, 0, 2 * pi, fill=True)
sphinx_plot(g)
Fill the area between two functions::
sage: polar_plot(cos(4*x) + 1.5, 0, 2*pi, fill=0.5 * cos(4*x) + 2.5, fillcolor='orange')
Graphics object consisting of 2 graphics primitives
.. PLOT::
g = polar_plot(cos(4*x) + 1.5, 0, 2*pi, fill=0.5 * cos(4*x) + 2.5, fillcolor='orange')
sphinx_plot(g)
Fill the area between several spirals::
sage: polar_plot([(1.2+k*0.2)*log(x) for k in range(6)], 1, 3 * pi, fill={0: [1], 2: [3], 4: [5]})
Graphics object consisting of 9 graphics primitives
.. PLOT::
g = polar_plot([(1.2+k*0.2)*log(x) for k in range(6)], 1, 3 * pi, fill={0: [1], 2: [3], 4: [5]})
sphinx_plot(g)
Exclude points at discontinuities::
sage: polar_plot(log(floor(x)), (x, 1, 4*pi), exclude=[1..12])
Graphics object consisting of 12 graphics primitives
.. PLOT::
g = polar_plot(log(floor(x)), (x, 1, 4*pi), exclude=list(range(1,13)))
sphinx_plot(g)