Hello Qian,

Le sam. 4 mai 2024 à 09:58, Qian Yun <oldk1...@gmail.com> a écrit :
>
>
>
> On 5/4/24 15:30, Grégory Vanuxem wrote:
> > As a matter of fact, use of FLINT in FriCAS:
> >
>
> My experience with FLINT is that is uses dense representation
> for univariate polynomial.
>
> That representation makes it fast for multiplication (when polynomials
> are dense).
>
> But I think very spare polynomial will choke it, for example
>
> (x^10000000+1)^n  (for n is some small integer).

Wow, very specific here. In the real world, is it of use?
Cryptography? Theoretical mathematics?
I looked at SAGE and they also use FLINT for generic cases like the
one I mentioned.

I will likely take a look at PARI/GP, NTL and Singular, just to inform
me, I don't really know some libraries/softwares that handle
specifically well sparse representations of polynomials, For now I
will have a look at SAGE with the keyword :sparse when instantiating a
polynomial ring. Thanks for this example.

- Greg


>
> ====
>
> So for FriCAS, lacking a dense representation makes it
> performs very bad at certain tasks (for example, multiplication).
>
> The karatsuba method implemented in
> UnivariatePolynomialMultiplicationPackage is not working
> at all because of the spare representation we have.
>
> - Qian
>
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