On Mon, Feb 29, 2016 at 9:19 AM, Ben Hutz <bn4...@gmail.com> wrote:
> I was exploring some quotient ring operations and came across the
> following:
>
> {{{
> R.<y>=QQ[]
> K.<w>=NumberField(y^3 + 2*y - 2401)
> k.<v>=K.quo(K.prime_factors(7)[1])
> R.<x,y>=PolynomialRing(k)
> R.monomial_divides(y,x^3*y)
> Error
> }}}
>
> {{{
> R.<y>=QQ[]
> K.<w>=NumberField(y^3 + 2*y - 2401)
> k.<v>=K.residue_field(K.prime_factors(7)[1])
> R.<x,y>=PolynomialRing(k)
> R.monomial_divides(y,x^3*y)
> True
> }}}
>
> The second works, the first does not. I came across this since
> .monomial_divides is used is a groebner basis computation. So played around
> a little more and the following seems weirder
>
> {{{
> A.<x,y,z> = PolynomialRing(Zmod(42))
> A.monomial_divides(y,x^2*y)
> True
> }}}
>
> {{{
> A.<x,y,z> = PolynomialRing(Zmod(2521515232)) #but one less digit works
> A.monomial_divides(y,x^2*y)
> Error
> }}
>
> The first works, but the 2nd does not, even though neither is prime. It
> seems to have to do with what type of polynomial ring they are initialized
> as, but I had a hard time tracking down where that code lived and how it
> decided. Is there someone familiar with polynomial rings in Sage who could
> shed some light on whether this is expected behavior?
>
The difference is that we use singular over Z/n for small enough n. You
can detect this in the types of the polynomial rings:
sage: A.<x,y,z> = PolynomialRing(Zmod(42))
sage: type(A)
<type
'sage.rings.polynomial.multi_polynomial_libsingular.MPolynomialRing_libsingular'>
sage: A.<x,y,z> = PolynomialRing(Zmod(2521515232))
sage: type(A)
<class
'sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_polydict_with_category'>
The monomial_divides method just isn't implemented
for MPolynomialRing_polydict.
David
>
> Thanks,
> Ben
>
> --
> You received this message because you are subscribed to the Google Groups
> "sage-devel" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to sage-devel+unsubscr...@googlegroups.com.
> To post to this group, send email to sage-devel@googlegroups.com.
> Visit this group at https://groups.google.com/group/sage-devel.
> For more options, visit https://groups.google.com/d/optout.
>
--
You received this message because you are subscribed to the Google Groups
"sage-devel" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-devel+unsubscr...@googlegroups.com.
To post to this group, send email to sage-devel@googlegroups.com.
Visit this group at https://groups.google.com/group/sage-devel.
For more options, visit https://groups.google.com/d/optout.
