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
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:

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Description (last modified by mstreng)

Implement the algorithm of John Cremona and Mark van Hoeij for finding conics over fraction fields of polynomial rings.

The article 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 AlexGhitza

  • Component changed from algebra to algebraic geometry

comment:2 Changed 11 years ago by mstreng

  • Report Upstream set to N/A

See #727 A patch defining a conic class and using Simon's algorithms for finding points over Q is in progress.

comment:3 Changed 11 years ago by mstreng

  • Cc mstreng added

comment:4 Changed 11 years ago by mstreng

  • 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.

  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.

  1. Getting primes of bad reduction of conics.

This is as good as in #727: make a Conic C. Then do C.determinant().factor()

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