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implement the projective dual of a plane curve #8801
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comment:1
The attached patch implements this for (reduced and irreducible) hypersurfaces over the rationals. I intend to generalize this. I use Grobner bases and elimination. Resultants might be faster so I might switch to that approach. If you plug in a variety I think the dual should be reduced. I'm not sure exactly what the scheme structure of the output is at the moment. Something related to think about for the general case: given a subscheme X of projective space, what should the dual of X be? I will look at the approach described in the attached paper. When the dual is a hypersurface and has smaller degree than "expected", that approach seems to be better than the one used at the moment. |
Author: David Eklund |
Attachment: trac_8801_projective_duals.patch.gz The patch implements duals of projective hypersurfaces. Patch rebased on top of Sage 5.2. |
comment:3
Patch rebased on top of Sage 5.2. |
Commit: |
Branch: u/chapoton/8801 |
comment:5
I guess it could be reviewed. It could be useful as it is. I had some plans to do something better but someone stole all my time... There is no particular reason to stick to hypersurfaces, it was just meant as an initial simplification. |
comment:6
Nor is there any particular reason to stick to varieties over Q. |
Branch pushed to git repo; I updated commit sha1. New commits:
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comment:8
turning that into what is the class of rings over which this can currently work ? |
Changed keywords from none to projective duality |
comment:13
nobody interested by this ticket ? |
Branch pushed to git repo; I updated commit sha1. New commits:
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Reviewer: Volker Braun |
Changed branch from u/chapoton/8801 to |
This was requested by Ursula Whitcher on sage-support. She adds:
A good place to start in implementing this could be http://www.emilvolcheck.com/dual.ps
Component: algebraic geometry
Keywords: projective duality
Author: David Eklund
Branch/Commit:
5a4b960
Reviewer: Volker Braun
Issue created by migration from https://trac.sagemath.org/ticket/8801
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