CAS and exponents issues

[Komanguy]

(09-28-2018 11:13 AM)parisse Wrote:  Please note that simplify(2^(1/3)*3^(1/3)-6^(1/3)) returns 0, i.e. you will not accidentally divide by an expression that does not look like 0 but is 0, and that is what really matters when you run computations. If you simplify(2^(1/3)*3^(1/3)), it remains as is on the Prime because HP does not want to see rootofs, but in Xcas it will be rewritten as a rootof, i.e. as an element of an algebraic extension of Q that contains 2^(1/3) and 3^(1/3), that's the best way I know to make sure you don't miss 0 simplifications.

(09-28-2018 11:13 AM)parisse Wrote:  Xcas was primarily implemented to run big computations that a human would never make by hand (i.e. mostly big integers and polynomials computations).

Totally agree with that.

I can also add, we can't demand a CAS to give a representation of a calculation exactly we'd like. Sometimes, we have to do manually some steps.
That's why we have several functions to simplify, factor an expression or solve an equation.