In some previous incarnation, where Sage used Maxima for things like
this, your simplification happened.
(%i1) 1/sqrt(5);
1
(%o1) -------
sqrt(5)
(%i2) sqrt(5)/5;
1
(%o2) -------
sqrt(5)
Now we use Ginac for basic symbolic stuff. Once in a while we (i.e.,
Burcin) changes some internal representation, or Ginac does. But in
general I think it just goes for positive powers - you may want to
read its documentation. In particular, "sqrt" is not a builtin
function ("square root (not a GiNaC function, rather an alias for
pow(x, numeric(1, 2)))"), so the behavior is analogous to
sage: 1/5^(1/3)
1/5*5^(2/3)
Naturally, GiNaC is Not a CAS, so perhaps that is one reason for the
distinction. You are also right about black arts! So I don't pretend
to judge Maxima *or* Ginac on this one.
I'm sorry if that doesn't help, but it might give you some background,
at least.
- kcrisman
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