I would like to plot the "effects" of an 2 by 2 matrix over the reals on the
unit sphere in the p-norm. By effects I mean I would like to plot the unit
sphere and it's image under a given matrix. In clearest case when p=2 I found
the following code from trac #9728 which does exactly what I want.
@interact
def linear_transformation(
theta = slider(0, 2*pi, .1),
r = slider(0.1, 2, .1, default=1),
A = input_grid(2, 2, default = [[1,2],[0,2]],
to_value=matrix)):
"""An interact which illustrates ...
"""
v=vector([r*cos(theta), r*sin(theta)])
w = A*v
unit_sphere = circle((0,0), radius = 1, rgbcolor = (1,0,0))
var('t')
image_of_sphere = parametric_plot(A*vector([sin(t),cos(t)]),
(t, 0, 2*pi), rgbcolor=(0,0,1))
html("$v = %s,; %s w=%s$"%(v.n(4),latex(A),w.n(4)))
show(v.plot(rgbcolor=(1,0,0)) +
w.plot(rgbcolor=(0,0,1)) +
unit_sphere + image_of_sphere,
aspect_ratio=1)
I'm a total newb when it comes to plotting in sage, so I would very much
appreciate the help.
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