On 18 September 2015 at 19:02, Nils Bruin <nbr...@sfu.ca> wrote:
> I wondered about this one:
>
> sage: k=GF(2)
> sage: kx.<x>=GF(2)[]
> sage: kxy.<y>=kx[]
> sage: kx.extension(y^3+y+1)
> Univariate Quotient Polynomial Ring in y over Univariate Polynomial Ring in
> x over Finite Field of size 2 (using NTL) with modulus y^3 + y + 1
> sage: exit
> Exiting Sage (CPU time 0m0.11s, Wall time 0m21.50s).
> Exiting Singular with PID 19781 running
> /usr/local/sage/sage-git/local/bin/Singular -t --ticks-per-sec 1000
> --cntrlc=a
>
> Observations:
>
>  - this extension does not need a name specified, whereas in another case a
> name is required:
>
> sage: kx.<x>=GF(2)[]
> sage: k.extension(x^3+x+1)
> ValueError: parameter 'conway' is required if no name given

I never used to like Magma's convention of using names like $.1, $.2
for variables when the user did not supply one, but at the moment I am
inclined to allow all such constructions to be valid without the user
creating a name: deep in some library code a number field was
constructed, and needed a name, so used 'a', which was usually OK but
not when that name was in use already for a related field. (See
http://trac.sagemath.org/ticket/19229 if interested).  In that
situation no element of the field was ever going to be displayed, so
the name is useless.

John
>
>  - Polynomial quotient rings seem to trigger starting a separate Singular
> process. Shouldn't we be doing this with LibSingular?
>
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