On Tue, Jan 23, 2024 at 6:29 PM Gareth Ma <[email protected]> wrote:
>
> Hi all,
>
> I am working with `ToricVariety` within Sage, and I have a question. Say I
> define a toric variety as follows:
>
> sage: PP = toric_varieties.WP([1, 3, 1]); PP
> 2-d toric variety covered by 3 affine patches
> sage: PP.linear_equivalence_ideal()
> Ideal (z0 - z2, z1 - 3*z2) of Multivariate Polynomial Ring in z0, z1, z2 over
> Rational Field
>
> (The repr output of toric varieties is too simplified, but that's another
> issue.) As seen in the second output, the "3" is definitely "somewhere within
> the object". Thus I would expect the polynomial ring / coordinate ring to
> also be a weighted one. However, that's not the case:
>
> sage: PP.coordinate_ring().term_order()
> Degree reverse lexicographic term order
> sage: [g.degree() for g in PP.coordinate_ring().gens()]
> [1, 1, 1]
>
> Is this intended or should it return a weighted polynomial ring, something
> like this?
>
> sage: to = TermOrder("wdegrevlex", [1, 3, 1])
> sage: R = PolynomialRing(QQ, 3, names="z", order=to)
> sage: [g.degree() for g in R.gens()]
> [1, 3, 1]
Yes, this seems to be a bug. The Cox ring of a weighted projective
space must be weighted.
Here is what Macaulay2 says about your example:
$ M2
Macaulay2, version 1.22.0.1
with packages: ConwayPolynomials, Elimination, IntegralClosure,
InverseSystems, Isomorphism, LLLBases, MinimalPrimes, OnlineLookup,
PrimaryDecomposition, ReesAlgebra, Saturation, TangentCone
i1 : loadPackage("NormalToricVarieties");
i2 : PP = weightedProjectiveSpace {1,3,1}
o2 = PP
o2 : NormalToricVariety
i3 : S = ring PP
o3 = S
o3 : PolynomialRing
i4 : degrees S
o4 = {{1}, {3}, {1}}
I've opened https://github.com/sagemath/sage/issues/37167 to track this
>
> --
> You received this message because you are subscribed to the Google Groups
> "sage-support" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to [email protected].
> To view this discussion on the web visit
> https://groups.google.com/d/msgid/sage-support/53d1f2e8-f01d-4bae-8a1b-ae6dbb8d7a65n%40googlegroups.com.
--
You received this message because you are subscribed to the Google Groups
"sage-support" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To view this discussion on the web visit
https://groups.google.com/d/msgid/sage-support/CAAWYfq0d5Z8-qR2G94j1oq7vDOa_CZnfTna3HnLyLBUBdEtokA%40mail.gmail.com.
