The lack of handling root functions in hp prime

[parisse]

It's certainly possible to implement simple algorithms to simplify expressions like that, but they will just be able to handle some kind of expressions, and that's precisely expressions that a human can easily detect and simplify mentally. What I have implemented is a normal form, a little bit like when you expand a polynomial expression, if it does not return 0 then you are sure the polynomial is not 0. An analogy could be integration by table lookup and integration using the Risch algorithm.
The algorithm is computationnally expensive, because you must handle several algebraic extensions of Q[x,y]. I agree that this is not really adapted to the Prime, because the normal form is expressed as a rootof, an object that HP found mathematically to complicated to be in a command result.