Absolute value: sometimes CAS is very clever, sometimes not!

[parisse]

I'm sorry, but I don't understand what's wrong with the current comparison commands. I can clarify if you give me oneliners (but please not a collection of 10 or more commands with comments that are difficult to understand).
But let's be clear: even if I can understand some requests, I will not change the behavior of ==, != or < >, because it is too much intricated in the CAS. Modifying something there would have side-effects in many other parts and that would mean lot of bugs.
A CAS will not magically do maths for you, and it will not replace a math teacher for students. It's a tool that is primarily meant to replace hard computations by hand.