[Axiom-developer] Denesting radicals?

[daly]

Denesting radicals is a deep problem. There are subtle issues
when you are using symbols and solving equations. If I remember
correctly, one of the issues is that you can't decide if something
is square-free if it contains certain kinds of radicals (don't 
depend on my memory though). 

Simplification of radicals usually involves algebraic field extensions
but (again, if I remember correctly) the issue is independence. Doing
a field extension with sqrt(2) and sqrt(6) causes problems.

Plus the question arises whether you're working over real or complex.

We had these discussions in the last century (around 1980) and I don't
remember all the details except to say that it is MUCH harder and
more subtle than it looks.

The person I'd ask is either Barry Trager or James Davenport.

Tim