Maxima Function
unit_step (x)
The left-continuous unit step function; thus unit_step (x) vanishes for x <= 0 and equals 1 for x > 0.
x <= 0
x > 0
If you want a unit step function that takes on the value 1/2 at zero, use (1 + signum (x))/2.
(1 + signum (x))/2