Recover polynomial from 1 root

[Valentin Albillo]

(10-12-2018 07:34 AM)Tim Wessman Wrote:  

(10-09-2018 12:37 PM)Albert Chan Wrote:  Using XCas simplify on root r, I were expecting little or no effect, but I get this:

r := sqrt(6) / (5^(1/3) + sqrt(3))
simplify(r)

=> rootof( [3018245, 37511698, ... (Total 12 numbers) ], [1, 0, -54, -20 ... (Total 13 numbers)]])

Does above have any relation to the polynomial that have r as a root ?

And hence you've discovered why we, after much persuasion, convinced Dr Parisse to turn "rootof" off in Prime. Nobody can understand WTH it is supposed to be describing or is useful for. Despite having heard the explanation many times it still is a mystery...

Indeed. I do understand what it does but, frankly, it's next to useless in most cases and the result is highly unfathomable as Albert Chan has experienced first hand.

I would suggest renaming this existing functionality to something that best describes what it does (if at all possible) and using instead the name "rootof" to return the minimum polynomial which has the input as a root (i.e.: the well-known minpol functionality).

That would be much more generally useful, IMHO.

V.
.