The absolute value function in Maxima is called "abs". Like all
mathematical functions in Maxima, it operates both on specific numeric
values and on symbolic expressions.
For example:
abs(-23) => 23
abs(5.4e23) => 5.4e23
abs(-5/3) => 5/3
abs(x^2) => x^2
Maxima assumes variables are real, so x^2 is always >= 0)
abs(atan(x^2)) => atan(x^2)
atan is an odd function, so since x^2>=0, it can conclude that
atan(x^2)>=0
abs(x) => abs(x)
if not given additional information, Maxima returns the symbolic
expression
assume(qq>1)
tell Maxima about qq
abs(qq) => qq
takes advantage of assumption
abs(qq-qq^2) => qq^2-qq
takes advantage of assumption
Of course, Maxima cannot *always* find the simplest form:
abs(x^2-atan(x)^2) => abs(x^2-atan(x)^2)
Hope this helps.
-s