[IPOL discuss] Question sur les librairies ipol.

[eml]

Dear Jonathan and Thibaud,

I reply in english because the subject is of general interest to IPOL authors.

> Nous aimerions savoir quelles librairies en C nous
> pouvions utiliser pour calculer les racines réelles d'équations polynomiales
> allant jusqu'à l'ordre 8.

There are currently no libraries natively supported by IPOL to compute
roots of polynomials.  Thus, the code to compute these roots must be
embedded in your submission.  So you have three options:

1. write the code yourself
2. copy a whole mathematics library into your program, and call its
root-finding function from your code
3. copy some code for root-finding into your program

The decision is entirely personal, and you should pick what is more
confortable to you.  My suggestion is to copy some root-finding code
from elsewhere, but this is admittedly less generalizable to other
situations.  If your polynomials have repeated roots, the functions to
factorize them will necessarily be more complicated.  As an example,
see the attached file.

>
> Nous avons également besoin d'une librairie pour le calcul matriciel simple
> et pour la diagonalisation de matrices allant jusqu'à l'ordre 8 donnant la
> matrice diagonalisée et la matrice de passage.

There is a library natively supported by IPOL for doing linear
algebra, which is clapack.  It is fairly standard and easy to use, but
its interface may seem a bit outdated to some people.  Other
non-supported standard and modern libraries are GSL (in C) and Eigen
(in C++).  Being non-supported means that you have to include them in
your submission if you want to use them.  Or, at least, copy the
relevant parts into your program.  In this case, my suggestion is the
same as before: find some simple code that performs the desired
computation, and copy it into your program.  Using a general linear
algebra library seems a bit of overkill if you only want to solve
8-dimensional systems, where most naive algorithms will work well
enough.

regards,
Enric
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