Maximal ideal in FriCAS

[Grégory Vanuxem]

Hello,

There are tons of conditions in FriCAS/Mathematics, I agree, but are
there some conditions on ideals (I am not a mathematician), I just
see that as _special_ subset. No condition? Maximal ideal is my
concern.

So, any conditions to use for conditional exports?

Greg

PS: Not too a lot of mathematics I have also tons of books, _just in FriCAS_

[Waldek Hebisch]

It is not clear to me what you want. We have domain 'PolynomialIdeal'
which represents ideals in a polynomial ring. Do you want a
function to determine if an ideal (that is element of PolynomialIdeal)
is a maximal ideal? ATM I do not see any. In ring of polynomials
over algebraically closed field checking if an ideal is maximal is
quite easy. In general it is more tricky, but probably we could add
such a function.

--
Waldek Hebisch

[Grégory Vanuxem]

Hello Waldek,

Le ven. 26 juin 2026 à 16:58, Waldek Hebisch <de...@fricas.org> a écrit :
>
> On Fri, Jun 26, 2026 at 03:57:35PM +0200, Grégory Vanuxem wrote:
> > Hello,
> >
> > There are tons of conditions in FriCAS/Mathematics, I agree, but are
> > there some conditions on ideals (I am not a mathematician), I just
> > see that as _special_ subset. No condition? Maximal ideal is my
> > concern.
> >
> > So, any conditions to use for conditional exports?
> >
> > Greg
> >
> > PS: Not too a lot of mathematics I have also tons of books, _just in FriCAS_
>
> It is not clear to me what you want. We have domain 'PolynomialIdeal'
> which represents ideals in a polynomial ring. Do you want a
> function to determine if an ideal (that is element of PolynomialIdeal)
> is a maximal ideal?

Yes this is exactly what I would want. Thanks for pointing me to
PolynomialIdeal. I am looking at it.

To respond to your question, I am
working on adding an interface to generic residue rings
(https://nemocas.github.io/Nemo.jl/stable/residue/ ,
https://nemocas.github.io/AbstractAlgebra.jl/latest/residue/ and
https://nemocas.github.io/AbstractAlgebra.jl/latest/residue_interface/).

And, so, I would like to know if the ideal generated by the polynomial
given (not a list) is maximal (to have ring or field interface).

> ATM I do not see any. In ring of polynomials
> over algebraically closed field checking if an ideal is maximal is
> quite easy. In general it is more tricky, but probably we could add
> such a function.

I have a preliminary implementation of maximal? in ideal.spad (more a
proof of concept right now). I will put it here for comments later.

Greg