Question about polynomial rings with symbolic coefficients

[Matteo Ruffini]

Hi all,
I have a basic question about the definition of polynomial rings;

In general I work with polinomials on QQ[a..h], so the coefficients are just numbers.

Now, I would like to add a symbolic variable to the coefficients, so to manage polynomials like

a^2+y

where y is not an unknown of the polynomial but just a general nonzero real variable (so, we can divide for it and so on).

My final objective, is, given a set of polynomials whose coefficients are known real numbers, to get the Groebner basis and express the coefficient of the Groebner basis polynomials
as a function of the original polynomials coefficients.

Is that possible?

Thanks
Matteo

[Thomas Kahle]

Hi,

yes, you can make a fraction field and use it as a coefficient ring like
this:

K = frac (QQ[a])
R = K[x,y]

The arithmetics in K is of course much more expansive now, so your
Gröbner bases in R will take longer than with rational coefficients.

Cheers,
Thomas

> --
> You received this message because you are subscribed to the Google
> Groups "Macaulay2" group.
> To unsubscribe from this group and stop receiving emails from it, send
> an email to macaulay2+...@googlegroups.com
> <mailto:macaulay2+...@googlegroups.com>.
> To post to this group, send email to maca...@googlegroups.com
> <mailto:maca...@googlegroups.com>.
> Visit this group at https://groups.google.com/group/macaulay2.
> For more options, visit https://groups.google.com/d/optout.

--
Thomas Kahle

[Matteo Ruffini]

Thanks! If the parameters are more than one (say a and b) the right syntax is

K = frac (QQ[a,b])?

Thanks
Matteo

[Thomas Kahle]

On 18/03/16 10:01, Matteo Ruffini wrote:
> Thanks! If the parameters are more than one (say a and b) the right
> syntax is
>
> K = frac (QQ[a,b])?

Yes, 'frac' returns a fraction field of the domain in its argument. You
could even build frac of the domain ZZ[a,b].

You can use the command

help frac

to learn more.

Cheers,
Thomas

> > an email to macaulay2+...@googlegroups.com <javascript:>
> > <mailto:macaulay2+...@googlegroups.com <javascript:>>.

> > To post to this group, send email to maca...@googlegroups.com

> <javascript:>
> > <mailto:maca...@googlegroups.com <javascript:>>.

> > Visit this group at https://groups.google.com/group/macaulay2

> <https://groups.google.com/group/macaulay2>.

> > For more options, visit https://groups.google.com/d/optout

> <https://groups.google.com/d/optout>.
>
> --
> Thomas Kahle