I chose the weighting (1 : g + 1 : 1) following Galbraith's
textbook https://www.math.auckland.ac.nz/~sgal018/crypto-book/ch10.pdf when
implementing the arithmetic on the Jacobian. This is not a "good" answer
though.
I would love to hear from more people about what they use / would want to
use.
As for deprecations, I won't know exactly how much will change before I
start working on this but if anyone's code fundamentally uses the fact it's
a projective variety and the functions coming from this then I suppose
everything will simply have to exist as a second class with deprecation
warnings. I don't know what's best here.
Ultimately (even if I wait 2 years) I think it would be good for sage to
have more functioning arithmetic on Jacobians but this is obviously a very
small slice of pie in the whole meal of hyperellptic curves.
As one data point, the following magma code
```
R<x> := PolynomialRing(Rationals());
f := x^6 + x + 1;
H := HyperellipticCurve(f);
Ambient(H)
```
Outputs
Projective Space of dimension 2 over Rational Field
Variables: $.1, $.2, $.3
The grading is:
1, 3, 1
Matching my proposed grading.
On Monday, March 11, 2024 at 9:52:09 PM UTC Nils Bruin wrote:
> The change makes sense, but you should investigate if it is at all
> possible to do this going through normal deprecation procedures, which
> would probably involve having both functionalities for some time (likely
> via differently named methods or via a flag implemented in a
> backward-compatime way), then having a deprecation period on the "old"
> functionality. After that the deprecated functionality can be removed.
> After a suitable wait period, the vacated space in the namespace can now be
> used for the new method. You'll be taking a couple of years before you're
> there.
>
> If it's not possible, you'd better have very good reasons to probably
> break people's code out there with very little warning.
>
> Once you find a way to do this, there's another choice in convention to
> consider: do you go with (1:1:g+1) weights or with (1:g+1:1) ? I.e., with
> [X:Z:Y] or [X:Y:Z]. Both have precedent and people who are used to the
> other convention will find it really annoying to adjust.
>
>
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