Re: charpoly via Newton

[Pascal Molin <molinp@math.jussieu.fr>]

> However flag 1 and 2 are even faster.
indeed ! I agree with Karim that charpoly deserves better input detection.

>> Dans tous les cas, je souhaiterais proposer pour Pari un certain
>> nombre d'opérations sur les polynômes (reconstruction à partir
>> des sommes de Newton, produits composés, puissances symétriques --
>> c'est initialement ça que je voulais --...), modalités et
>> syntaxe à voir par exemple durant l'atelier de janvier.
>
> A lot of them arealready available. Maybe it is missing a GP interface.
> At least:
> polsym(x,n): column vector of symmetric powers of the roots of x up to n.

I think translation from and to newton sums should be available in gp with
easy names (personnaly I do not like polsym), and in any characteristic.
This is very useful.

pol2newton and newton2pol, for example, or poltonewton and polfromnewton
(I think it is nice that all function primarily related to pols start with pol)

The others I mention are

polcomposed(P,Q) = prod_{P(a)=Q(b)=0} (x-ab)

and if P(x) = prod_{i<=d} (x-xi)

polsympow(P,r) = prod_{i1<=i2<=... ir<=d} (x- xi1xi2...xir)

which appears in symmetric powers of representations.
I have formulas based on Newton sums for the latter.

Pascal