>> But of course the idea is not how to make it happen, but rather what
>> the default behavior is.
>
> Two issues actually:
> 1) default value of radexpand
> 2) how hard general simplification should work in analyzing expressions.
> Maxima general simplification does not do major reorganizations of
> expressions, such as factoring. ?This was a ?design decision (a long time
> ago) with two major parts: 1) let the user control the *form* of expression
> as well as its meaning; 2) don't spend potentially large amounts of time on
> general simplification.
> See Joel Moses' Algebraic Simplification: a guide for the perplexed (1971)
> Having sqrt(x^2-2*x+1) simplify to abs(x-1) requires finding the square
> factors of the inner expression, which is more a bigger transformation than
> general simplification normally does.
Absolutely, and I'm not suggesting it should all the time. I think
that the real question was why the answer was -1, when the function
(considered as a *function*) is clearly not -1. Which rjf responded
to more than adequately. I knew radcan was trouble for Sage at times,
but I hadn't seen this one before.
Readers of this might also want to see rjf's post [1] on
ask.sagemath.org responding to the original post, which among other
things discusses why Derive is not a good comparison to Maxima - you
can even give him Sage karma by upvoting his answer ;-)
[1] http://ask.sagemath.org/question/767/simplification-errors-in-simple-expressions