Opened 12 years ago
Last modified 6 years ago
#6881 closed enhancement
Solving conics over polynomial rings. — at Version 4
Reported by: | victor | Owned by: | tbd |
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Priority: | major | Milestone: | sage-6.10 |
Component: | algebraic geometry | Keywords: | conic, curve, function field |
Cc: | mstreng | Merged in: | |
Authors: | Victor Miller | Reviewers: | |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
Implement the algorithm of John Cremona and Mark van Hoeij for finding conics over fraction fields of polynomial rings.
The article http://www.warwick.ac.uk/~masgaj/papers/conicFT.pdf contains references to implementations in Maple (van Hoeij) and Magma (Cremona-Roberts). All one needs to do is ask the authors if it can be GPL'ed and to translate the code into sage.
#727 provides classes for conic curves that this code should build upon
Change History (4)
comment:1 Changed 12 years ago by
- Component changed from algebra to algebraic geometry
comment:2 Changed 11 years ago by
- Report Upstream set to N/A
comment:3 Changed 11 years ago by
- Cc mstreng added
comment:4 Changed 11 years ago by
- Description modified (diff)
- Summary changed from Conics to Solving conics over polynomial rings.
I changed the description to better fit what is already in #727. Besides things that are already in #727, all that I removed from the original description were the following two requests.
- Use John Cremona's algorithms for finding points on conics over QQ.
It seems that Simon's algorithms (in #727) are better, but that doesn't have to stop us from giving Cremona's code as an option. It is inside mwrank, which is part of Sage. If someone wants to do it, then it can be made into a separate ticket.
- Getting primes of bad reduction of conics.
This is as good as in #727: make a Conic C. Then do C.determinant().factor()
See #727 A patch defining a conic class and using Simon's algorithms for finding points over Q is in progress.