Opened 13 years ago
Closed 7 years ago
#8801 closed enhancement (fixed)
implement the projective dual of a plane curve
Reported by: | Alex Ghitza | Owned by: | Alex Ghitza |
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Priority: | minor | Milestone: | sage-7.1 |
Component: | algebraic geometry | Keywords: | projective duality |
Cc: | Merged in: | ||
Authors: | David Eklund | Reviewers: | Volker Braun |
Report Upstream: | N/A | Work issues: | |
Branch: | 5a4b960 (Commits, GitHub, GitLab) | Commit: | 5a4b960e08005915ff86afb9f8207d33a0f76dee |
Dependencies: | Stopgaps: |
Description
This was requested by Ursula Whitcher on sage-support. She adds:
I'm playing with a family of plane curves with rational coefficients in the complex projective plane. So rational or complex numbers would be enough for me to test examples. In a perfect world I'd be able to specify a family using rational functions of arbitrary constants (something like a x^2 + b/(a-1) y^2), and compute the projective dual in terms of those constants.
A good place to start in implementing this could be http://www.emilvolcheck.com/dual.ps
Attachments (1)
Change History (19)
comment:1 Changed 11 years ago by
comment:2 Changed 11 years ago by
Authors: | → David Eklund |
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Priority: | major → minor |
Changed 10 years ago by
Attachment: | trac_8801_projective_duals.patch added |
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The patch implements duals of projective hypersurfaces. Patch rebased on top of Sage 5.2.
comment:4 Changed 9 years ago by
Branch: | → u/chapoton/8801 |
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Commit: | → 04c7bd0eed549d404bdd72d2ef1faf6ac73c7c67 |
comment:5 Changed 9 years ago by
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:7 Changed 8 years ago by
Commit: | 04c7bd0eed549d404bdd72d2ef1faf6ac73c7c67 → d8cb633d95220f171a9bb257ca6b620629134378 |
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Branch pushed to git repo; I updated commit sha1. New commits:
d8cb633 | Merge branch 'u/chapoton/8801' into 6.5.b6
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comment:8 Changed 8 years ago by
Status: | new → needs_review |
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turning that into needs review
to require feedback:
what is the class of rings over which this can currently work ?
comment:9 Changed 8 years ago by
Commit: | d8cb633d95220f171a9bb257ca6b620629134378 → ba23a276ff64a8708a4a581d61a0e60f30a33d6e |
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comment:10 Changed 8 years ago by
Milestone: | sage-wishlist → sage-6.7 |
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comment:11 Changed 8 years ago by
Keywords: | projective duality added |
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Milestone: | sage-6.7 → sage-6.8 |
comment:12 Changed 7 years ago by
Milestone: | sage-6.8 → sage-6.9 |
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comment:13 Changed 7 years ago by
Milestone: | sage-6.9 → sage-6.10 |
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nobody interested by this ticket ?
comment:14 Changed 7 years ago by
Milestone: | sage-6.10 → sage-7.0 |
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comment:15 Changed 7 years ago by
Commit: | ba23a276ff64a8708a4a581d61a0e60f30a33d6e → 5a4b960e08005915ff86afb9f8207d33a0f76dee |
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Branch pushed to git repo; I updated commit sha1. New commits:
5a4b960 | Merge branch 'u/chapoton/8801' into 7.0.rc1
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comment:16 Changed 7 years ago by
Milestone: | sage-7.0 → sage-7.1 |
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comment:17 Changed 7 years ago by
Reviewers: | → Volker Braun |
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Status: | needs_review → positive_review |
comment:18 Changed 7 years ago by
Branch: | u/chapoton/8801 → 5a4b960e08005915ff86afb9f8207d33a0f76dee |
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Resolution: | → fixed |
Status: | positive_review → closed |
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.