We have a question at
http://ask.sagemath.org/question/767/simplification-errors-in-simple-expressions
which seems to find a bug in radcan. Here is the relevant Maxima
session.
(%i3) b:((1-x)/sqrt(1-2*x+x^2));
1 - x
(%o3) ------------------
2
sqrt(x - 2 x + 1)
(%i4) radcan(b);
(%o4) - 1
which seems a little aggressive. But
(%i7) d:((1-x)/sqrt((1-x)^2));
1 - x
(%o7) ----------
abs(x - 1)
Radcan's documentation is a little confusing.
radicals, by converting it into a form which is canonical over a
large class of expressions and a given ordering of variables; that
is, all functionally equivalent forms are mapped into a unique
form. For a somewhat larger class of expressions, `radcan'
doesn't give very many details. But I'm certainly not an expert in
making expressions canonical :)
Thanks for any help!