CAS and exponents issues

[sasa]

(09-28-2018 11:13 AM)parisse Wrote:  Why do you say it fails? The CAS is not using your prefered representation but there is nothing wrong.
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.

Elementary simplification fail, in this case. As well, in this case, rootofs is not needed...
However yes, I understand that approach and methodology is quite different.

For instance, let take mentioned high order derivative, as example:
diff(acos(x),x,6)

On online Xcas/Giac it returns quite long expression without simplification which may indicate that there is no simplification between steps. With simplification and factoring it gives shorter expression, which is still bit more complex than wolfram alpha offer at once, even both appears to be essentially correct.

All in all, I believe all is clear - different methodology made quite a difference in simplicity of the final result, while it essentially remain correct.