#6881: Solving conics over polynomial rings.
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Reporter: victor | Owner: tbd
Type: enhancement | Status: new
Priority: minor | Milestone: sage-feature
Component: algebraic geometry | Keywords: conic, curve
Author: Victor Miller | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Old description:
> We should have a class (or classes) for conic curves, and, more specially
> diagonal conics. In particular, one of the methods should be John
> Cremona's algorithms for finding points on solvable conics, both over Q
> and over fraction fields of polynomial rings. Other methods might
> include getting discriminants, primes of bad reduction, producing
> parametrized solutions, etc.
New description:
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
--
Comment(by mstreng):
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.
1. 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.
2. Getting primes of bad reduction of conics.
This is as good as in #727: make a Conic C. Then do
C.determinant().factor()
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6881#comment:4>
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