We know that $|x| + |y| - 1 = 0$ is the equation of a square having its vertices on the axes.
I asked to represent the equation $|x| + |y| + |z| - 1 - 0$, believing to obtain a cube in space.
But I obtain an octahedron. Why? And how do you get a cube?
# with SageMath 7.3
var('x, y, z')
f = abs(x) + abs(y) + abs(z) - 1
implicit_plot3d(f, (x, -1, 1), (y, -1, 1), (z, -1, 1), color='aquamarine ')
This is not really a Sage question, rather a mathematical question. What you are drawing is the unit ball of the L1 norm, which is an ocatahedron. If you want to obtain a cube, you should rather draw the unit ball of the L-infinity norm. This norm does not sum the absolute values of the coordinates, but it takes their maximum.
Note that the maximum for symbolic expression, is max_symbolic.
Asked: 2020-12-15 11:00:00 +0100
Seen: 303 times
Last updated: Dec 15 '20
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